Compound Units
PROCEDURALUse compound units such as speed (distance ÷ time), unit pricing (cost ÷ quantity), and density (mass ÷ volume); solve problems involving compound units
Mastery Evidence
- Calculate average speed given distance and time, converting between km/h and m/s if needed
- Compare unit prices of two products sold in different quantities to find the better deal
- Use the density formula to find mass, volume, or density given the other two values
Assessment Prompt
“If a car travels 150 miles in 2.5 hours, can [child] work out its average speed — and use the same idea to solve problems about price per kilogram or density of a material?”
Curriculum Standards3 alignments
6.RP.3bCommon Core State Standards for MathematicsSolve unit rate problems including those involving unit pricing and constant speed. For example, if it took 7 hours to mow 4 lawns, then at that rate, how many lawns could be mowed in 35 hours? At what rate were lawns being mowed?
7.RP.1Common Core State Standards for MathematicsCompute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units. For example, if a person walks 1/2 mile in each 1/4 hour, compute the unit rate as the complex fraction 1/2/1/4 miles per hour, equivalently 2 miles per hour.
KS3.Maths.Ratio.10The national curriculum in Englanduse compound units such as speed, unit pricing and density to solve problems
Prerequisites5
- Simple formulaesoftAges 12—14
- ProportionhardAges 12—14
- Proportional Reasoning VocabularyhardAges 11—14
- Proportion GraphssoftAges 11—14
- Unit ConversionshardAges 11—12
Show full prerequisite tree
- Simple formulae soft
Rearranging compound unit formulae (speed = distance/time) uses formula rearrangement skills
- Solving Linear Equations hard
Rearranging formulae uses the same inverse-operation techniques as solving equations
- Expressions & Equations Vocabulary hard
Collecting like terms requires knowing what terms, coefficients, and like terms mean
- Writing Algebraic Equations hard
Algebraic notation builds on KS2 expressing missing-number problems algebraically
- Writing Number Sentences hard
Writing algebraic expressions extends writing/interpreting numerical expressions
- Brackets in Expressions hard
Writing/interpreting expressions requires understanding grouping symbols
- Division with remainders hard
Evaluating grouped expressions formalises multi-step calculation skills from Y5
- Multiply & Add Problems hard
Y4 M×D problem-solving is prerequisite to multi-step four-operation problems
- Arrays for multiplication (age 9+) hard
Must have formal division method before solving multi-step problems
- Brackets in Expressions hard
The full BODMAS/PEMDAS convention extends understanding of grouping symbols to all operations
- Division with remainders hard
Evaluating grouped expressions formalises multi-step calculation skills from Y5
- Multiply & Add Problems hard
Y4 M×D problem-solving is prerequisite to multi-step four-operation problems
- Arrays for multiplication (age 9+) hard
Must have formal division method before solving multi-step problems
- Brackets in Expressions hard
Writing/interpreting expressions requires understanding grouping symbols
- Division with remainders hard
Evaluating grouped expressions formalises multi-step calculation skills from Y5
- Multiply & Add Problems hard
Y4 M×D problem-solving is prerequisite to multi-step four-operation problems
- Arrays for multiplication (age 9+) hard
Must have formal division method before solving multi-step problems
- Brackets in Expressions hard
The full BODMAS/PEMDAS convention extends understanding of grouping symbols to all operations
- Division with remainders hard
Evaluating grouped expressions formalises multi-step calculation skills from Y5
- Multiply & Add Problems hard
Y4 M×D problem-solving is prerequisite to multi-step four-operation problems
- Arrays for multiplication (age 9+) hard
Must have formal division method before solving multi-step problems
- Writing Number Sentences hard
Writing algebraic expressions extends writing/interpreting numerical expressions
- Brackets in Expressions hard
Writing/interpreting expressions requires understanding grouping symbols
- Division with remainders hard
Evaluating grouped expressions formalises multi-step calculation skills from Y5
- Multiply & Add Problems hard
Y4 M×D problem-solving is prerequisite to multi-step four-operation problems
- Written Multiplication & Division hard
Formal short multiplication extends Y3 written multiplication
- The three digits of a three-digit number soft
Two-digit × one-digit uses place-value partitioning (e.g. 23 × 4 = 20 × 4 + 3 × 4)
- Reading ×, ÷, and = Symbols hard
Writing multiplication/division statements requires fluency with symbols
- Skip Counting (4s, 8s, 50s, 100s) hard
Counting in 6s/7s/9s/25s/1000s extends counting in 4s/8s/50s/100s
- The three digits of a three-digit number soft
Two-digit × one-digit uses place-value partitioning (e.g. 23 × 4 = 20 × 4 + 3 × 4)
- Reading ×, ÷, and = Symbols hard
Writing multiplication/division statements requires fluency with symbols
- Multiplication as repeated addition (age 6+) hard
Scaling and correspondence problems extend Y2 problem-solving with mult/div
- Arrays for multiplication soft
Arrays are a key representation for solving multiplication/division problems
- Division as equal sharing hard
Using arrays for division requires understanding division as grouping
- Multiplication as repeated addition hard
Using arrays requires understanding what multiplication means
- Multiplication as repeated addition hard
Recalling times table facts requires understanding multiplication as repeated addition/grouping
- Commutative Multiplication hard
Applying all three properties extends Y2 commutativity understanding
- Division as equal sharing hard
Using arrays for division requires understanding division as grouping
- Multiplication as repeated addition hard
Using arrays requires understanding what multiplication means
- Multiplication as repeated addition hard
Commutativity of multiplication requires understanding multiplication
- Addition as combining or putting together two hard
Multiplication as repeated addition requires understanding addition as combining groups
- Arrays for multiplication (age 7+) hard
Extends array-based repeated addition to formal multiplication interpretation
- Arrays for multiplication hard
Rectangular arrays with repeated addition extends array representation from Y2
- Multiplication as repeated addition hard
Expressing array totals as sums of equal addends requires understanding multiplication as repeated addition
- Multiplication as repeated addition hard
Interpreting products formalises repeated addition/equal groups from Y1
- Addition as combining or putting together two hard
Multiplication as repeated addition requires understanding addition as combining groups
- Arrays for multiplication (age 9+) hard
Must have formal division method before solving multi-step problems
- Division as Unknown Factor hard
Understanding division as unknown-factor supports short division strategy
- What Multiplication Means hard
Connecting division to multiplication requires understanding products
- Arrays for multiplication (age 7+) hard
Extends array-based repeated addition to formal multiplication interpretation
- Arrays for multiplication hard
Rectangular arrays with repeated addition extends array representation from Y2
- Multiplication as repeated addition hard
Expressing array totals as sums of equal addends requires understanding multiplication as repeated addition
- Multiplication as repeated addition hard
Interpreting products formalises repeated addition/equal groups from Y1
- Addition as combining or putting together two hard
Multiplication as repeated addition requires understanding addition as combining groups
- Subtraction as taking away or separating hard
Division as equal sharing/grouping requires understanding subtraction as taking away/separating
- Fluent multiplication and division facts hard
Fluent ×÷ within 100 is prerequisite to short division of larger numbers
- What Multiplication Means hard
Connecting division to multiplication requires understanding products
- Arrays for multiplication (age 7+) hard
Extends array-based repeated addition to formal multiplication interpretation
- Multiplication as repeated addition hard
Interpreting products formalises repeated addition/equal groups from Y1
- Multiplication as repeated addition hard
Recalling times table facts requires understanding multiplication as repeated addition/grouping
- Addition as combining or putting together two hard
Multiplication as repeated addition requires understanding addition as combining groups
- Multiplication as repeated addition hard
Recalling times table facts requires understanding multiplication as repeated addition/grouping
- Written Multiplication hard
2/3-digit × 1-digit written method is prerequisite to 4-digit × 1-digit and 2-digit × 2-digit
- Written Multiplication & Division hard
Formal short multiplication extends Y3 written multiplication
- The three digits of a three-digit number soft
Two-digit × one-digit uses place-value partitioning (e.g. 23 × 4 = 20 × 4 + 3 × 4)
- Reading ×, ÷, and = Symbols hard
Writing multiplication/division statements requires fluency with symbols
- Skip Counting (4s, 8s, 50s, 100s) hard
Counting in 6s/7s/9s/25s/1000s extends counting in 4s/8s/50s/100s
- Area and the distributive property soft
Area models for distributive property support understanding long multiplication layout
- Understanding angles (age 8+) hard
Must multiply side lengths for area before using area models for distributive property
- Area by Tiling hard
Must see tiling→multiplication connection before computing area via side lengths
- Written Multiplication hard
2/3-digit × 1-digit written method is prerequisite to 4-digit × 1-digit and 2-digit × 2-digit
- Written Multiplication & Division hard
Formal short multiplication extends Y3 written multiplication
- The three digits of a three-digit number soft
Two-digit × one-digit uses place-value partitioning (e.g. 23 × 4 = 20 × 4 + 3 × 4)
- Reading ×, ÷, and = Symbols hard
Writing multiplication/division statements requires fluency with symbols
- Skip Counting (4s, 8s, 50s, 100s) hard
Counting in 6s/7s/9s/25s/1000s extends counting in 4s/8s/50s/100s
- Area and the distributive property soft
Area models for distributive property support understanding long multiplication layout
- Understanding angles (age 8+) hard
Must multiply side lengths for area before using area models for distributive property
- Area by Tiling hard
Must see tiling→multiplication connection before computing area via side lengths
- Brackets in Expressions hard
The full BODMAS/PEMDAS convention extends understanding of grouping symbols to all operations
- Division with remainders hard
Evaluating grouped expressions formalises multi-step calculation skills from Y5
- Multiply & Add Problems hard
Y4 M×D problem-solving is prerequisite to multi-step four-operation problems
- Written Multiplication & Division hard
Formal short multiplication extends Y3 written multiplication
- The three digits of a three-digit number soft
Two-digit × one-digit uses place-value partitioning (e.g. 23 × 4 = 20 × 4 + 3 × 4)
- Reading ×, ÷, and = Symbols hard
Writing multiplication/division statements requires fluency with symbols
- Skip Counting (4s, 8s, 50s, 100s) hard
Counting in 6s/7s/9s/25s/1000s extends counting in 4s/8s/50s/100s
- The three digits of a three-digit number soft
Two-digit × one-digit uses place-value partitioning (e.g. 23 × 4 = 20 × 4 + 3 × 4)
- Reading ×, ÷, and = Symbols hard
Writing multiplication/division statements requires fluency with symbols
- Multiplication as repeated addition (age 6+) hard
Scaling and correspondence problems extend Y2 problem-solving with mult/div
- Arrays for multiplication soft
Arrays are a key representation for solving multiplication/division problems
- Division as equal sharing hard
Using arrays for division requires understanding division as grouping
- Multiplication as repeated addition hard
Using arrays requires understanding what multiplication means
- Multiplication as repeated addition hard
Recalling times table facts requires understanding multiplication as repeated addition/grouping
- Commutative Multiplication hard
Applying all three properties extends Y2 commutativity understanding
- Division as equal sharing hard
Using arrays for division requires understanding division as grouping
- Multiplication as repeated addition hard
Using arrays requires understanding what multiplication means
- Multiplication as repeated addition hard
Commutativity of multiplication requires understanding multiplication
- Addition as combining or putting together two hard
Multiplication as repeated addition requires understanding addition as combining groups
- Arrays for multiplication (age 7+) hard
Extends array-based repeated addition to formal multiplication interpretation
- Arrays for multiplication hard
Rectangular arrays with repeated addition extends array representation from Y2
- Multiplication as repeated addition hard
Expressing array totals as sums of equal addends requires understanding multiplication as repeated addition
- Multiplication as repeated addition hard
Interpreting products formalises repeated addition/equal groups from Y1
- Addition as combining or putting together two hard
Multiplication as repeated addition requires understanding addition as combining groups
- Arrays for multiplication (age 9+) hard
Must have formal division method before solving multi-step problems
- Division as Unknown Factor hard
Understanding division as unknown-factor supports short division strategy
- What Multiplication Means hard
Connecting division to multiplication requires understanding products
- Arrays for multiplication (age 7+) hard
Extends array-based repeated addition to formal multiplication interpretation
- Arrays for multiplication hard
Rectangular arrays with repeated addition extends array representation from Y2
- Multiplication as repeated addition hard
Expressing array totals as sums of equal addends requires understanding multiplication as repeated addition
- Multiplication as repeated addition hard
Interpreting products formalises repeated addition/equal groups from Y1
- Addition as combining or putting together two hard
Multiplication as repeated addition requires understanding addition as combining groups
- Subtraction as taking away or separating hard
Division as equal sharing/grouping requires understanding subtraction as taking away/separating
- Fluent multiplication and division facts hard
Fluent ×÷ within 100 is prerequisite to short division of larger numbers
- What Multiplication Means hard
Connecting division to multiplication requires understanding products
- Arrays for multiplication (age 7+) hard
Extends array-based repeated addition to formal multiplication interpretation
- Multiplication as repeated addition hard
Interpreting products formalises repeated addition/equal groups from Y1
- Multiplication as repeated addition hard
Recalling times table facts requires understanding multiplication as repeated addition/grouping
- Addition as combining or putting together two hard
Multiplication as repeated addition requires understanding addition as combining groups
- Multiplication as repeated addition hard
Recalling times table facts requires understanding multiplication as repeated addition/grouping
- Written Multiplication hard
2/3-digit × 1-digit written method is prerequisite to 4-digit × 1-digit and 2-digit × 2-digit
- Written Multiplication & Division hard
Formal short multiplication extends Y3 written multiplication
- The three digits of a three-digit number soft
Two-digit × one-digit uses place-value partitioning (e.g. 23 × 4 = 20 × 4 + 3 × 4)
- Reading ×, ÷, and = Symbols hard
Writing multiplication/division statements requires fluency with symbols
- Skip Counting (4s, 8s, 50s, 100s) hard
Counting in 6s/7s/9s/25s/1000s extends counting in 4s/8s/50s/100s
- Area and the distributive property soft
Area models for distributive property support understanding long multiplication layout
- Understanding angles (age 8+) hard
Must multiply side lengths for area before using area models for distributive property
- Area by Tiling hard
Must see tiling→multiplication connection before computing area via side lengths
- Written Multiplication hard
2/3-digit × 1-digit written method is prerequisite to 4-digit × 1-digit and 2-digit × 2-digit
- Written Multiplication & Division hard
Formal short multiplication extends Y3 written multiplication
- The three digits of a three-digit number soft
Two-digit × one-digit uses place-value partitioning (e.g. 23 × 4 = 20 × 4 + 3 × 4)
- Reading ×, ÷, and = Symbols hard
Writing multiplication/division statements requires fluency with symbols
- Skip Counting (4s, 8s, 50s, 100s) hard
Counting in 6s/7s/9s/25s/1000s extends counting in 4s/8s/50s/100s
- Area and the distributive property soft
Area models for distributive property support understanding long multiplication layout
- Understanding angles (age 8+) hard
Must multiply side lengths for area before using area models for distributive property
- Area by Tiling hard
Must see tiling→multiplication connection before computing area via side lengths
- Writing Algebraic Equations hard
Algebraic notation builds on KS2 expressing missing-number problems algebraically
- Writing Number Sentences hard
Writing algebraic expressions extends writing/interpreting numerical expressions
- Brackets in Expressions hard
Writing/interpreting expressions requires understanding grouping symbols
- Division with remainders hard
Evaluating grouped expressions formalises multi-step calculation skills from Y5
- Multiply & Add Problems hard
Y4 M×D problem-solving is prerequisite to multi-step four-operation problems
- Written Multiplication & Division hard
Formal short multiplication extends Y3 written multiplication
- Multiplication as repeated addition (age 6+) hard
Scaling and correspondence problems extend Y2 problem-solving with mult/div
- Commutative Multiplication hard
Applying all three properties extends Y2 commutativity understanding
- Arrays for multiplication (age 9+) hard
Must have formal division method before solving multi-step problems
- Division as Unknown Factor hard
Understanding division as unknown-factor supports short division strategy
- What Multiplication Means hard
Connecting division to multiplication requires understanding products
- Fluent multiplication and division facts hard
Fluent ×÷ within 100 is prerequisite to short division of larger numbers
- Written Multiplication hard
2/3-digit × 1-digit written method is prerequisite to 4-digit × 1-digit and 2-digit × 2-digit
- Written Multiplication & Division hard
Formal short multiplication extends Y3 written multiplication
- Area and the distributive property soft
Area models for distributive property support understanding long multiplication layout
- Understanding angles (age 8+) hard
Must multiply side lengths for area before using area models for distributive property
- Written Multiplication hard
2/3-digit × 1-digit written method is prerequisite to 4-digit × 1-digit and 2-digit × 2-digit
- Written Multiplication & Division hard
Formal short multiplication extends Y3 written multiplication
- Area and the distributive property soft
Area models for distributive property support understanding long multiplication layout
- Understanding angles (age 8+) hard
Must multiply side lengths for area before using area models for distributive property
- Brackets in Expressions hard
The full BODMAS/PEMDAS convention extends understanding of grouping symbols to all operations
- Division with remainders hard
Evaluating grouped expressions formalises multi-step calculation skills from Y5
- Multiply & Add Problems hard
Y4 M×D problem-solving is prerequisite to multi-step four-operation problems
- Written Multiplication & Division hard
Formal short multiplication extends Y3 written multiplication
- Multiplication as repeated addition (age 6+) hard
Scaling and correspondence problems extend Y2 problem-solving with mult/div
- Commutative Multiplication hard
Applying all three properties extends Y2 commutativity understanding
- Arrays for multiplication (age 9+) hard
Must have formal division method before solving multi-step problems
- Division as Unknown Factor hard
Understanding division as unknown-factor supports short division strategy
- What Multiplication Means hard
Connecting division to multiplication requires understanding products
- Fluent multiplication and division facts hard
Fluent ×÷ within 100 is prerequisite to short division of larger numbers
- Written Multiplication hard
2/3-digit × 1-digit written method is prerequisite to 4-digit × 1-digit and 2-digit × 2-digit
- Written Multiplication & Division hard
Formal short multiplication extends Y3 written multiplication
- Area and the distributive property soft
Area models for distributive property support understanding long multiplication layout
- Understanding angles (age 8+) hard
Must multiply side lengths for area before using area models for distributive property
- Written Multiplication hard
2/3-digit × 1-digit written method is prerequisite to 4-digit × 1-digit and 2-digit × 2-digit
- Written Multiplication & Division hard
Formal short multiplication extends Y3 written multiplication
- Area and the distributive property soft
Area models for distributive property support understanding long multiplication layout
- Understanding angles (age 8+) hard
Must multiply side lengths for area before using area models for distributive property
- Brackets in Expressions hard
Writing/interpreting expressions requires understanding grouping symbols
- Division with remainders hard
Evaluating grouped expressions formalises multi-step calculation skills from Y5
- Multiply & Add Problems hard
Y4 M×D problem-solving is prerequisite to multi-step four-operation problems
- Written Multiplication & Division hard
Formal short multiplication extends Y3 written multiplication
- Multiplication as repeated addition (age 6+) hard
Scaling and correspondence problems extend Y2 problem-solving with mult/div
- Commutative Multiplication hard
Applying all three properties extends Y2 commutativity understanding
- Arrays for multiplication (age 9+) hard
Must have formal division method before solving multi-step problems
- Division as Unknown Factor hard
Understanding division as unknown-factor supports short division strategy
- What Multiplication Means hard
Connecting division to multiplication requires understanding products
- Fluent multiplication and division facts hard
Fluent ×÷ within 100 is prerequisite to short division of larger numbers
- Written Multiplication hard
2/3-digit × 1-digit written method is prerequisite to 4-digit × 1-digit and 2-digit × 2-digit
- Written Multiplication & Division hard
Formal short multiplication extends Y3 written multiplication
- Area and the distributive property soft
Area models for distributive property support understanding long multiplication layout
- Understanding angles (age 8+) hard
Must multiply side lengths for area before using area models for distributive property
- Written Multiplication hard
2/3-digit × 1-digit written method is prerequisite to 4-digit × 1-digit and 2-digit × 2-digit
- Written Multiplication & Division hard
Formal short multiplication extends Y3 written multiplication
- Area and the distributive property soft
Area models for distributive property support understanding long multiplication layout
- Understanding angles (age 8+) hard
Must multiply side lengths for area before using area models for distributive property
- Brackets in Expressions hard
The full BODMAS/PEMDAS convention extends understanding of grouping symbols to all operations
- Division with remainders hard
Evaluating grouped expressions formalises multi-step calculation skills from Y5
- Multiply & Add Problems hard
Y4 M×D problem-solving is prerequisite to multi-step four-operation problems
- Written Multiplication & Division hard
Formal short multiplication extends Y3 written multiplication
- Multiplication as repeated addition (age 6+) hard
Scaling and correspondence problems extend Y2 problem-solving with mult/div
- Commutative Multiplication hard
Applying all three properties extends Y2 commutativity understanding
- Arrays for multiplication (age 9+) hard
Must have formal division method before solving multi-step problems
- Division as Unknown Factor hard
Understanding division as unknown-factor supports short division strategy
- What Multiplication Means hard
Connecting division to multiplication requires understanding products
- Fluent multiplication and division facts hard
Fluent ×÷ within 100 is prerequisite to short division of larger numbers
- Written Multiplication hard
2/3-digit × 1-digit written method is prerequisite to 4-digit × 1-digit and 2-digit × 2-digit
- Written Multiplication & Division hard
Formal short multiplication extends Y3 written multiplication
- Area and the distributive property soft
Area models for distributive property support understanding long multiplication layout
- Understanding angles (age 8+) hard
Must multiply side lengths for area before using area models for distributive property
- Written Multiplication hard
2/3-digit × 1-digit written method is prerequisite to 4-digit × 1-digit and 2-digit × 2-digit
- Written Multiplication & Division hard
Formal short multiplication extends Y3 written multiplication
- Area and the distributive property soft
Area models for distributive property support understanding long multiplication layout
- Understanding angles (age 8+) hard
Must multiply side lengths for area before using area models for distributive property
- Using inverse operations hard
Solving linear equations by rearrangement requires applying inverse operations to isolate an unknown
- Order of operations hard
Understanding order of operations (BODMAS) is required before studying how operations undo each other via inverse relationships
- Brackets in Expressions hard
The full BODMAS/PEMDAS convention extends understanding of grouping symbols to all operations
- Division with remainders hard
Evaluating grouped expressions formalises multi-step calculation skills from Y5
- Multiply & Add Problems hard
Y4 M×D problem-solving is prerequisite to multi-step four-operation problems
- Written Multiplication & Division hard
Formal short multiplication extends Y3 written multiplication
- The three digits of a three-digit number soft
Two-digit × one-digit uses place-value partitioning (e.g. 23 × 4 = 20 × 4 + 3 × 4)
- Reading ×, ÷, and = Symbols hard
Writing multiplication/division statements requires fluency with symbols
- Skip Counting (4s, 8s, 50s, 100s) hard
Counting in 6s/7s/9s/25s/1000s extends counting in 4s/8s/50s/100s
- The three digits of a three-digit number soft
Two-digit × one-digit uses place-value partitioning (e.g. 23 × 4 = 20 × 4 + 3 × 4)
- Reading ×, ÷, and = Symbols hard
Writing multiplication/division statements requires fluency with symbols
- Multiplication as repeated addition (age 6+) hard
Scaling and correspondence problems extend Y2 problem-solving with mult/div
- Arrays for multiplication soft
Arrays are a key representation for solving multiplication/division problems
- Division as equal sharing hard
Using arrays for division requires understanding division as grouping
- Multiplication as repeated addition hard
Using arrays requires understanding what multiplication means
- Multiplication as repeated addition hard
Recalling times table facts requires understanding multiplication as repeated addition/grouping
- Commutative Multiplication hard
Applying all three properties extends Y2 commutativity understanding
- Division as equal sharing hard
Using arrays for division requires understanding division as grouping
- Multiplication as repeated addition hard
Using arrays requires understanding what multiplication means
- Multiplication as repeated addition hard
Commutativity of multiplication requires understanding multiplication
- Addition as combining or putting together two hard
Multiplication as repeated addition requires understanding addition as combining groups
- Arrays for multiplication (age 7+) hard
Extends array-based repeated addition to formal multiplication interpretation
- Arrays for multiplication hard
Rectangular arrays with repeated addition extends array representation from Y2
- Multiplication as repeated addition hard
Expressing array totals as sums of equal addends requires understanding multiplication as repeated addition
- Multiplication as repeated addition hard
Interpreting products formalises repeated addition/equal groups from Y1
- Addition as combining or putting together two hard
Multiplication as repeated addition requires understanding addition as combining groups
- Arrays for multiplication (age 9+) hard
Must have formal division method before solving multi-step problems
- Division as Unknown Factor hard
Understanding division as unknown-factor supports short division strategy
- What Multiplication Means hard
Connecting division to multiplication requires understanding products
- Arrays for multiplication (age 7+) hard
Extends array-based repeated addition to formal multiplication interpretation
- Arrays for multiplication hard
Rectangular arrays with repeated addition extends array representation from Y2
- Multiplication as repeated addition hard
Expressing array totals as sums of equal addends requires understanding multiplication as repeated addition
- Multiplication as repeated addition hard
Interpreting products formalises repeated addition/equal groups from Y1
- Addition as combining or putting together two hard
Multiplication as repeated addition requires understanding addition as combining groups
- Subtraction as taking away or separating hard
Division as equal sharing/grouping requires understanding subtraction as taking away/separating
- Fluent multiplication and division facts hard
Fluent ×÷ within 100 is prerequisite to short division of larger numbers
- What Multiplication Means hard
Connecting division to multiplication requires understanding products
- Arrays for multiplication (age 7+) hard
Extends array-based repeated addition to formal multiplication interpretation
- Multiplication as repeated addition hard
Interpreting products formalises repeated addition/equal groups from Y1
- Multiplication as repeated addition hard
Recalling times table facts requires understanding multiplication as repeated addition/grouping
- Addition as combining or putting together two hard
Multiplication as repeated addition requires understanding addition as combining groups
- Multiplication as repeated addition hard
Recalling times table facts requires understanding multiplication as repeated addition/grouping
- Written Multiplication hard
2/3-digit × 1-digit written method is prerequisite to 4-digit × 1-digit and 2-digit × 2-digit
- Written Multiplication & Division hard
Formal short multiplication extends Y3 written multiplication
- The three digits of a three-digit number soft
Two-digit × one-digit uses place-value partitioning (e.g. 23 × 4 = 20 × 4 + 3 × 4)
- Reading ×, ÷, and = Symbols hard
Writing multiplication/division statements requires fluency with symbols
- Skip Counting (4s, 8s, 50s, 100s) hard
Counting in 6s/7s/9s/25s/1000s extends counting in 4s/8s/50s/100s
- Area and the distributive property soft
Area models for distributive property support understanding long multiplication layout
- Understanding angles (age 8+) hard
Must multiply side lengths for area before using area models for distributive property
- Area by Tiling hard
Must see tiling→multiplication connection before computing area via side lengths
- Written Multiplication hard
2/3-digit × 1-digit written method is prerequisite to 4-digit × 1-digit and 2-digit × 2-digit
- Written Multiplication & Division hard
Formal short multiplication extends Y3 written multiplication
- The three digits of a three-digit number soft
Two-digit × one-digit uses place-value partitioning (e.g. 23 × 4 = 20 × 4 + 3 × 4)
- Reading ×, ÷, and = Symbols hard
Writing multiplication/division statements requires fluency with symbols
- Skip Counting (4s, 8s, 50s, 100s) hard
Counting in 6s/7s/9s/25s/1000s extends counting in 4s/8s/50s/100s
- Area and the distributive property soft
Area models for distributive property support understanding long multiplication layout
- Understanding angles (age 8+) hard
Must multiply side lengths for area before using area models for distributive property
- Area by Tiling hard
Must see tiling→multiplication connection before computing area via side lengths
- Multi-step problems: choosing operations hard
Fluency with all four operations in context is required before formalising inverse relationships between them
- Brackets in Expressions hard
The full BODMAS/PEMDAS convention extends understanding of grouping symbols to all operations
- Division with remainders hard
Evaluating grouped expressions formalises multi-step calculation skills from Y5
- Multiply & Add Problems hard
Y4 M×D problem-solving is prerequisite to multi-step four-operation problems
- Written Multiplication & Division hard
Formal short multiplication extends Y3 written multiplication
- The three digits of a three-digit number soft
Two-digit × one-digit uses place-value partitioning (e.g. 23 × 4 = 20 × 4 + 3 × 4)
- Reading ×, ÷, and = Symbols hard
Writing multiplication/division statements requires fluency with symbols
- The three digits of a three-digit number soft
Two-digit × one-digit uses place-value partitioning (e.g. 23 × 4 = 20 × 4 + 3 × 4)
- Reading ×, ÷, and = Symbols hard
Writing multiplication/division statements requires fluency with symbols
- Multiplication as repeated addition (age 6+) hard
Scaling and correspondence problems extend Y2 problem-solving with mult/div
- Arrays for multiplication soft
Arrays are a key representation for solving multiplication/division problems
- Commutative Multiplication hard
Applying all three properties extends Y2 commutativity understanding
- Multiplication as repeated addition hard
Commutativity of multiplication requires understanding multiplication
- Arrays for multiplication (age 7+) hard
Extends array-based repeated addition to formal multiplication interpretation
- Multiplication as repeated addition hard
Interpreting products formalises repeated addition/equal groups from Y1
- Arrays for multiplication (age 9+) hard
Must have formal division method before solving multi-step problems
- Division as Unknown Factor hard
Understanding division as unknown-factor supports short division strategy
- What Multiplication Means hard
Connecting division to multiplication requires understanding products
- Arrays for multiplication (age 7+) hard
Extends array-based repeated addition to formal multiplication interpretation
- Multiplication as repeated addition hard
Interpreting products formalises repeated addition/equal groups from Y1
- Fluent multiplication and division facts hard
Fluent ×÷ within 100 is prerequisite to short division of larger numbers
- What Multiplication Means hard
Connecting division to multiplication requires understanding products
- Multiplication as repeated addition hard
Recalling times table facts requires understanding multiplication as repeated addition/grouping
- Written Multiplication hard
2/3-digit × 1-digit written method is prerequisite to 4-digit × 1-digit and 2-digit × 2-digit
- Written Multiplication & Division hard
Formal short multiplication extends Y3 written multiplication
- The three digits of a three-digit number soft
Two-digit × one-digit uses place-value partitioning (e.g. 23 × 4 = 20 × 4 + 3 × 4)
- Reading ×, ÷, and = Symbols hard
Writing multiplication/division statements requires fluency with symbols
- Area and the distributive property soft
Area models for distributive property support understanding long multiplication layout
- Understanding angles (age 8+) hard
Must multiply side lengths for area before using area models for distributive property
- Area by Tiling hard
Must see tiling→multiplication connection before computing area via side lengths
- Written Multiplication hard
2/3-digit × 1-digit written method is prerequisite to 4-digit × 1-digit and 2-digit × 2-digit
- Written Multiplication & Division hard
Formal short multiplication extends Y3 written multiplication
- The three digits of a three-digit number soft
Two-digit × one-digit uses place-value partitioning (e.g. 23 × 4 = 20 × 4 + 3 × 4)
- Reading ×, ÷, and = Symbols hard
Writing multiplication/division statements requires fluency with symbols
- Area and the distributive property soft
Area models for distributive property support understanding long multiplication layout
- Understanding angles (age 8+) hard
Must multiply side lengths for area before using area models for distributive property
- Area by Tiling hard
Must see tiling→multiplication connection before computing area via side lengths
- Multiply & Add Problems hard
Y4 M×D problem-solving is prerequisite to multi-step four-operation problems
- Written Multiplication & Division hard
Formal short multiplication extends Y3 written multiplication
- The three digits of a three-digit number soft
Two-digit × one-digit uses place-value partitioning (e.g. 23 × 4 = 20 × 4 + 3 × 4)
- The two digits of a two-digit number hard
Must understand two-digit place value before extending to hundreds
- A Ten Is Ten Ones hard
Understanding tens and ones place value requires the concept of 10 as a bundle
- The teen numbers hard
General two-digit place value extends from understanding teen number composition
- Multiplication as repeated addition hard
Recalling times table facts requires understanding multiplication as repeated addition/grouping
- Reading ×, ÷, and = Symbols hard
Writing multiplication/division statements requires fluency with symbols
- Reading and writing numbers to 20 hard
Writing number sentences requires reading and writing numerals
- Addition as combining or putting together two hard
Reading/writing the + symbol requires understanding what addition means
- Subtraction as taking away or separating hard
Reading/writing the − symbol requires understanding what subtraction means
- Subtraction as taking away or separating hard
Division as equal sharing/grouping requires understanding subtraction as taking away/separating
- Addition as combining or putting together two hard
Multiplication as repeated addition requires understanding addition as combining groups
- Skip Counting (4s, 8s, 50s, 100s) hard
Counting in 6s/7s/9s/25s/1000s extends counting in 4s/8s/50s/100s
- Multiplication as repeated addition hard
Recalling times table facts requires understanding multiplication as repeated addition/grouping
- The three digits of a three-digit number soft
Two-digit × one-digit uses place-value partitioning (e.g. 23 × 4 = 20 × 4 + 3 × 4)
- The two digits of a two-digit number hard
Must understand two-digit place value before extending to hundreds
- A Ten Is Ten Ones hard
Understanding tens and ones place value requires the concept of 10 as a bundle
- The teen numbers hard
General two-digit place value extends from understanding teen number composition
- Multiplication as repeated addition hard
Recalling times table facts requires understanding multiplication as repeated addition/grouping
- Reading ×, ÷, and = Symbols hard
Writing multiplication/division statements requires fluency with symbols
- Reading and writing numbers to 20 hard
Writing number sentences requires reading and writing numerals
- Addition as combining or putting together two hard
Reading/writing the + symbol requires understanding what addition means
- Subtraction as taking away or separating hard
Reading/writing the − symbol requires understanding what subtraction means
- Subtraction as taking away or separating hard
Division as equal sharing/grouping requires understanding subtraction as taking away/separating
- Addition as combining or putting together two hard
Multiplication as repeated addition requires understanding addition as combining groups
- Multiplication as repeated addition (age 6+) hard
Scaling and correspondence problems extend Y2 problem-solving with mult/div
- Arrays for multiplication soft
Arrays are a key representation for solving multiplication/division problems
- Division as equal sharing hard
Using arrays for division requires understanding division as grouping
- Subtraction as taking away or separating hard
Division as equal sharing/grouping requires understanding subtraction as taking away/separating
- Multiplication as repeated addition hard
Using arrays requires understanding what multiplication means
- Addition as combining or putting together two hard
Multiplication as repeated addition requires understanding addition as combining groups
- Multiplication as repeated addition hard
Recalling times table facts requires understanding multiplication as repeated addition/grouping
- Addition as combining or putting together two hard
Multiplication as repeated addition requires understanding addition as combining groups
- Commutative Multiplication hard
Applying all three properties extends Y2 commutativity understanding
- Division as equal sharing hard
Using arrays for division requires understanding division as grouping
- Subtraction as taking away or separating hard
Division as equal sharing/grouping requires understanding subtraction as taking away/separating
- Multiplication as repeated addition hard
Using arrays requires understanding what multiplication means
- Addition as combining or putting together two hard
Multiplication as repeated addition requires understanding addition as combining groups
- Multiplication as repeated addition hard
Commutativity of multiplication requires understanding multiplication
- Addition as combining or putting together two hard
Multiplication as repeated addition requires understanding addition as combining groups
- How Many in Total? hard
Understanding addition as combining groups requires knowing numbers represent quantities (cardinality)
- Arrays for multiplication (age 7+) hard
Extends array-based repeated addition to formal multiplication interpretation
- Arrays for multiplication hard
Rectangular arrays with repeated addition extends array representation from Y2
- Division as equal sharing hard
Using arrays for division requires understanding division as grouping
- Multiplication as repeated addition hard
Using arrays requires understanding what multiplication means
- Multiplication as repeated addition hard
Expressing array totals as sums of equal addends requires understanding multiplication as repeated addition
- Addition as combining or putting together two hard
Multiplication as repeated addition requires understanding addition as combining groups
- Multiplication as repeated addition hard
Interpreting products formalises repeated addition/equal groups from Y1
- Addition as combining or putting together two hard
Multiplication as repeated addition requires understanding addition as combining groups
- How Many in Total? hard
Understanding addition as combining groups requires knowing numbers represent quantities (cardinality)
- Arrays for multiplication (age 9+) hard
Must have formal division method before solving multi-step problems
- Division as Unknown Factor hard
Understanding division as unknown-factor supports short division strategy
- What Multiplication Means hard
Connecting division to multiplication requires understanding products
- Arrays for multiplication (age 7+) hard
Extends array-based repeated addition to formal multiplication interpretation
- Arrays for multiplication hard
Rectangular arrays with repeated addition extends array representation from Y2
- Division as equal sharing hard
Using arrays for division requires understanding division as grouping
- Multiplication as repeated addition hard
Using arrays requires understanding what multiplication means
- Multiplication as repeated addition hard
Expressing array totals as sums of equal addends requires understanding multiplication as repeated addition
- Addition as combining or putting together two hard
Multiplication as repeated addition requires understanding addition as combining groups
- Multiplication as repeated addition hard
Interpreting products formalises repeated addition/equal groups from Y1
- Addition as combining or putting together two hard
Multiplication as repeated addition requires understanding addition as combining groups
- How Many in Total? hard
Understanding addition as combining groups requires knowing numbers represent quantities (cardinality)
- Subtraction as taking away or separating hard
Division as equal sharing/grouping requires understanding subtraction as taking away/separating
- How Many in Total? hard
Understanding subtraction as taking away requires knowing numbers represent quantities (cardinality)
- Fluent multiplication and division facts hard
Fluent ×÷ within 100 is prerequisite to short division of larger numbers
- What Multiplication Means hard
Connecting division to multiplication requires understanding products
- Arrays for multiplication (age 7+) hard
Extends array-based repeated addition to formal multiplication interpretation
- Arrays for multiplication hard
Rectangular arrays with repeated addition extends array representation from Y2
- Multiplication as repeated addition hard
Expressing array totals as sums of equal addends requires understanding multiplication as repeated addition
- Multiplication as repeated addition hard
Interpreting products formalises repeated addition/equal groups from Y1
- Addition as combining or putting together two hard
Multiplication as repeated addition requires understanding addition as combining groups
- Subtraction as taking away or separating hard
Division as equal sharing/grouping requires understanding subtraction as taking away/separating
- Multiplication as repeated addition hard
Recalling times table facts requires understanding multiplication as repeated addition/grouping
- Addition as combining or putting together two hard
Multiplication as repeated addition requires understanding addition as combining groups
- How Many in Total? hard
Understanding addition as combining groups requires knowing numbers represent quantities (cardinality)
- Multiplication as repeated addition hard
Recalling times table facts requires understanding multiplication as repeated addition/grouping
- Addition as combining or putting together two hard
Multiplication as repeated addition requires understanding addition as combining groups
- Written Multiplication hard
2/3-digit × 1-digit written method is prerequisite to 4-digit × 1-digit and 2-digit × 2-digit
- Written Multiplication & Division hard
Formal short multiplication extends Y3 written multiplication
- The three digits of a three-digit number soft
Two-digit × one-digit uses place-value partitioning (e.g. 23 × 4 = 20 × 4 + 3 × 4)
- The two digits of a two-digit number hard
Must understand two-digit place value before extending to hundreds
- A Ten Is Ten Ones hard
Understanding tens and ones place value requires the concept of 10 as a bundle
- The teen numbers hard
General two-digit place value extends from understanding teen number composition
- Multiplication as repeated addition hard
Recalling times table facts requires understanding multiplication as repeated addition/grouping
- Reading ×, ÷, and = Symbols hard
Writing multiplication/division statements requires fluency with symbols
- Reading and writing numbers to 20 hard
Writing number sentences requires reading and writing numerals
- Addition as combining or putting together two hard
Reading/writing the + symbol requires understanding what addition means
- Subtraction as taking away or separating hard
Reading/writing the − symbol requires understanding what subtraction means
- Subtraction as taking away or separating hard
Division as equal sharing/grouping requires understanding subtraction as taking away/separating
- Addition as combining or putting together two hard
Multiplication as repeated addition requires understanding addition as combining groups
- Skip Counting (4s, 8s, 50s, 100s) hard
Counting in 6s/7s/9s/25s/1000s extends counting in 4s/8s/50s/100s
- Multiplication as repeated addition hard
Recalling times table facts requires understanding multiplication as repeated addition/grouping
- Area and the distributive property soft
Area models for distributive property support understanding long multiplication layout
- Understanding angles (age 8+) hard
Must multiply side lengths for area before using area models for distributive property
- Area by Tiling hard
Must see tiling→multiplication connection before computing area via side lengths
- Arrays for multiplication (age 9+) hard
Long division by 2-digit extends Y5 short division by 1-digit
- Division as Unknown Factor hard
Understanding division as unknown-factor supports short division strategy
- What Multiplication Means hard
Connecting division to multiplication requires understanding products
- Arrays for multiplication (age 7+) hard
Extends array-based repeated addition to formal multiplication interpretation
- Arrays for multiplication hard
Rectangular arrays with repeated addition extends array representation from Y2
- Division as equal sharing hard
Using arrays for division requires understanding division as grouping
- Multiplication as repeated addition hard
Using arrays requires understanding what multiplication means
- Multiplication as repeated addition hard
Expressing array totals as sums of equal addends requires understanding multiplication as repeated addition
- Addition as combining or putting together two hard
Multiplication as repeated addition requires understanding addition as combining groups
- Multiplication as repeated addition hard
Interpreting products formalises repeated addition/equal groups from Y1
- Addition as combining or putting together two hard
Multiplication as repeated addition requires understanding addition as combining groups
- How Many in Total? hard
Understanding addition as combining groups requires knowing numbers represent quantities (cardinality)
- Subtraction as taking away or separating hard
Division as equal sharing/grouping requires understanding subtraction as taking away/separating
- How Many in Total? hard
Understanding subtraction as taking away requires knowing numbers represent quantities (cardinality)
- Fluent multiplication and division facts hard
Fluent ×÷ within 100 is prerequisite to short division of larger numbers
- What Multiplication Means hard
Connecting division to multiplication requires understanding products
- Arrays for multiplication (age 7+) hard
Extends array-based repeated addition to formal multiplication interpretation
- Arrays for multiplication hard
Rectangular arrays with repeated addition extends array representation from Y2
- Multiplication as repeated addition hard
Expressing array totals as sums of equal addends requires understanding multiplication as repeated addition
- Multiplication as repeated addition hard
Interpreting products formalises repeated addition/equal groups from Y1
- Addition as combining or putting together two hard
Multiplication as repeated addition requires understanding addition as combining groups
- Subtraction as taking away or separating hard
Division as equal sharing/grouping requires understanding subtraction as taking away/separating
- Multiplication as repeated addition hard
Recalling times table facts requires understanding multiplication as repeated addition/grouping
- Addition as combining or putting together two hard
Multiplication as repeated addition requires understanding addition as combining groups
- How Many in Total? hard
Understanding addition as combining groups requires knowing numbers represent quantities (cardinality)
- Multiplication as repeated addition hard
Recalling times table facts requires understanding multiplication as repeated addition/grouping
- Addition as combining or putting together two hard
Multiplication as repeated addition requires understanding addition as combining groups
- Long multiplication (age 10+) soft
Checking division with multiplication requires fluent multiplication
- Written Multiplication hard
2/3-digit × 1-digit written method is prerequisite to 4-digit × 1-digit and 2-digit × 2-digit
- Written Multiplication & Division hard
Formal short multiplication extends Y3 written multiplication
- The three digits of a three-digit number soft
Two-digit × one-digit uses place-value partitioning (e.g. 23 × 4 = 20 × 4 + 3 × 4)
- Reading ×, ÷, and = Symbols hard
Writing multiplication/division statements requires fluency with symbols
- Skip Counting (4s, 8s, 50s, 100s) hard
Counting in 6s/7s/9s/25s/1000s extends counting in 4s/8s/50s/100s
- Area and the distributive property soft
Area models for distributive property support understanding long multiplication layout
- Understanding angles (age 8+) hard
Must multiply side lengths for area before using area models for distributive property
- Area by Tiling hard
Must see tiling→multiplication connection before computing area via side lengths
- Writing Algebraic Equations hard
Algebraic notation builds on KS2 expressing missing-number problems algebraically
- Writing Number Sentences hard
Writing algebraic expressions extends writing/interpreting numerical expressions
- Brackets in Expressions hard
Writing/interpreting expressions requires understanding grouping symbols
- Division with remainders hard
Evaluating grouped expressions formalises multi-step calculation skills from Y5
- Multiply & Add Problems hard
Y4 M×D problem-solving is prerequisite to multi-step four-operation problems
- Written Multiplication & Division hard
Formal short multiplication extends Y3 written multiplication
- The three digits of a three-digit number soft
Two-digit × one-digit uses place-value partitioning (e.g. 23 × 4 = 20 × 4 + 3 × 4)
- Reading ×, ÷, and = Symbols hard
Writing multiplication/division statements requires fluency with symbols
- The three digits of a three-digit number soft
Two-digit × one-digit uses place-value partitioning (e.g. 23 × 4 = 20 × 4 + 3 × 4)
- Reading ×, ÷, and = Symbols hard
Writing multiplication/division statements requires fluency with symbols
- Multiplication as repeated addition (age 6+) hard
Scaling and correspondence problems extend Y2 problem-solving with mult/div
- Arrays for multiplication soft
Arrays are a key representation for solving multiplication/division problems
- Commutative Multiplication hard
Applying all three properties extends Y2 commutativity understanding
- Multiplication as repeated addition hard
Commutativity of multiplication requires understanding multiplication
- Arrays for multiplication (age 7+) hard
Extends array-based repeated addition to formal multiplication interpretation
- Multiplication as repeated addition hard
Interpreting products formalises repeated addition/equal groups from Y1
- Arrays for multiplication (age 9+) hard
Must have formal division method before solving multi-step problems
- Division as Unknown Factor hard
Understanding division as unknown-factor supports short division strategy
- What Multiplication Means hard
Connecting division to multiplication requires understanding products
- Arrays for multiplication (age 7+) hard
Extends array-based repeated addition to formal multiplication interpretation
- Multiplication as repeated addition hard
Interpreting products formalises repeated addition/equal groups from Y1
- Fluent multiplication and division facts hard
Fluent ×÷ within 100 is prerequisite to short division of larger numbers
- What Multiplication Means hard
Connecting division to multiplication requires understanding products
- Multiplication as repeated addition hard
Recalling times table facts requires understanding multiplication as repeated addition/grouping
- Written Multiplication hard
2/3-digit × 1-digit written method is prerequisite to 4-digit × 1-digit and 2-digit × 2-digit
- Written Multiplication & Division hard
Formal short multiplication extends Y3 written multiplication
- The three digits of a three-digit number soft
Two-digit × one-digit uses place-value partitioning (e.g. 23 × 4 = 20 × 4 + 3 × 4)
- Reading ×, ÷, and = Symbols hard
Writing multiplication/division statements requires fluency with symbols
- Area and the distributive property soft
Area models for distributive property support understanding long multiplication layout
- Understanding angles (age 8+) hard
Must multiply side lengths for area before using area models for distributive property
- Area by Tiling hard
Must see tiling→multiplication connection before computing area via side lengths
- Written Multiplication hard
2/3-digit × 1-digit written method is prerequisite to 4-digit × 1-digit and 2-digit × 2-digit
- Written Multiplication & Division hard
Formal short multiplication extends Y3 written multiplication
- The three digits of a three-digit number soft
Two-digit × one-digit uses place-value partitioning (e.g. 23 × 4 = 20 × 4 + 3 × 4)
- Reading ×, ÷, and = Symbols hard
Writing multiplication/division statements requires fluency with symbols
- Area and the distributive property soft
Area models for distributive property support understanding long multiplication layout
- Understanding angles (age 8+) hard
Must multiply side lengths for area before using area models for distributive property
- Area by Tiling hard
Must see tiling→multiplication connection before computing area via side lengths
- Brackets in Expressions hard
The full BODMAS/PEMDAS convention extends understanding of grouping symbols to all operations
- Division with remainders hard
Evaluating grouped expressions formalises multi-step calculation skills from Y5
- Multiply & Add Problems hard
Y4 M×D problem-solving is prerequisite to multi-step four-operation problems
- Written Multiplication & Division hard
Formal short multiplication extends Y3 written multiplication
- The three digits of a three-digit number soft
Two-digit × one-digit uses place-value partitioning (e.g. 23 × 4 = 20 × 4 + 3 × 4)
- Reading ×, ÷, and = Symbols hard
Writing multiplication/division statements requires fluency with symbols
- The three digits of a three-digit number soft
Two-digit × one-digit uses place-value partitioning (e.g. 23 × 4 = 20 × 4 + 3 × 4)
- Reading ×, ÷, and = Symbols hard
Writing multiplication/division statements requires fluency with symbols
- Multiplication as repeated addition (age 6+) hard
Scaling and correspondence problems extend Y2 problem-solving with mult/div
- Arrays for multiplication soft
Arrays are a key representation for solving multiplication/division problems
- Commutative Multiplication hard
Applying all three properties extends Y2 commutativity understanding
- Multiplication as repeated addition hard
Commutativity of multiplication requires understanding multiplication
- Arrays for multiplication (age 7+) hard
Extends array-based repeated addition to formal multiplication interpretation
- Multiplication as repeated addition hard
Interpreting products formalises repeated addition/equal groups from Y1
- Arrays for multiplication (age 9+) hard
Must have formal division method before solving multi-step problems
- Division as Unknown Factor hard
Understanding division as unknown-factor supports short division strategy
- What Multiplication Means hard
Connecting division to multiplication requires understanding products
- Arrays for multiplication (age 7+) hard
Extends array-based repeated addition to formal multiplication interpretation
- Multiplication as repeated addition hard
Interpreting products formalises repeated addition/equal groups from Y1
- Fluent multiplication and division facts hard
Fluent ×÷ within 100 is prerequisite to short division of larger numbers
- What Multiplication Means hard
Connecting division to multiplication requires understanding products
- Multiplication as repeated addition hard
Recalling times table facts requires understanding multiplication as repeated addition/grouping
- Written Multiplication hard
2/3-digit × 1-digit written method is prerequisite to 4-digit × 1-digit and 2-digit × 2-digit
- Written Multiplication & Division hard
Formal short multiplication extends Y3 written multiplication
- The three digits of a three-digit number soft
Two-digit × one-digit uses place-value partitioning (e.g. 23 × 4 = 20 × 4 + 3 × 4)
- Reading ×, ÷, and = Symbols hard
Writing multiplication/division statements requires fluency with symbols
- Area and the distributive property soft
Area models for distributive property support understanding long multiplication layout
- Understanding angles (age 8+) hard
Must multiply side lengths for area before using area models for distributive property
- Area by Tiling hard
Must see tiling→multiplication connection before computing area via side lengths
- Written Multiplication hard
2/3-digit × 1-digit written method is prerequisite to 4-digit × 1-digit and 2-digit × 2-digit
- Written Multiplication & Division hard
Formal short multiplication extends Y3 written multiplication
- The three digits of a three-digit number soft
Two-digit × one-digit uses place-value partitioning (e.g. 23 × 4 = 20 × 4 + 3 × 4)
- Reading ×, ÷, and = Symbols hard
Writing multiplication/division statements requires fluency with symbols
- Area and the distributive property soft
Area models for distributive property support understanding long multiplication layout
- Understanding angles (age 8+) hard
Must multiply side lengths for area before using area models for distributive property
- Area by Tiling hard
Must see tiling→multiplication connection before computing area via side lengths
- Brackets in Expressions hard
Writing/interpreting expressions requires understanding grouping symbols
- Division with remainders hard
Evaluating grouped expressions formalises multi-step calculation skills from Y5
- Multiply & Add Problems hard
Y4 M×D problem-solving is prerequisite to multi-step four-operation problems
- Written Multiplication & Division hard
Formal short multiplication extends Y3 written multiplication
- The three digits of a three-digit number soft
Two-digit × one-digit uses place-value partitioning (e.g. 23 × 4 = 20 × 4 + 3 × 4)
- Reading ×, ÷, and = Symbols hard
Writing multiplication/division statements requires fluency with symbols
- The three digits of a three-digit number soft
Two-digit × one-digit uses place-value partitioning (e.g. 23 × 4 = 20 × 4 + 3 × 4)
- Reading ×, ÷, and = Symbols hard
Writing multiplication/division statements requires fluency with symbols
- Multiplication as repeated addition (age 6+) hard
Scaling and correspondence problems extend Y2 problem-solving with mult/div
- Arrays for multiplication soft
Arrays are a key representation for solving multiplication/division problems
- Commutative Multiplication hard
Applying all three properties extends Y2 commutativity understanding
- Multiplication as repeated addition hard
Commutativity of multiplication requires understanding multiplication
- Arrays for multiplication (age 7+) hard
Extends array-based repeated addition to formal multiplication interpretation
- Multiplication as repeated addition hard
Interpreting products formalises repeated addition/equal groups from Y1
- Arrays for multiplication (age 9+) hard
Must have formal division method before solving multi-step problems
- Division as Unknown Factor hard
Understanding division as unknown-factor supports short division strategy
- What Multiplication Means hard
Connecting division to multiplication requires understanding products
- Arrays for multiplication (age 7+) hard
Extends array-based repeated addition to formal multiplication interpretation
- Multiplication as repeated addition hard
Interpreting products formalises repeated addition/equal groups from Y1
- Fluent multiplication and division facts hard
Fluent ×÷ within 100 is prerequisite to short division of larger numbers
- What Multiplication Means hard
Connecting division to multiplication requires understanding products
- Multiplication as repeated addition hard
Recalling times table facts requires understanding multiplication as repeated addition/grouping
- Written Multiplication hard
2/3-digit × 1-digit written method is prerequisite to 4-digit × 1-digit and 2-digit × 2-digit
- Written Multiplication & Division hard
Formal short multiplication extends Y3 written multiplication
- The three digits of a three-digit number soft
Two-digit × one-digit uses place-value partitioning (e.g. 23 × 4 = 20 × 4 + 3 × 4)
- Reading ×, ÷, and = Symbols hard
Writing multiplication/division statements requires fluency with symbols
- Area and the distributive property soft
Area models for distributive property support understanding long multiplication layout
- Understanding angles (age 8+) hard
Must multiply side lengths for area before using area models for distributive property
- Area by Tiling hard
Must see tiling→multiplication connection before computing area via side lengths
- Written Multiplication hard
2/3-digit × 1-digit written method is prerequisite to 4-digit × 1-digit and 2-digit × 2-digit
- Written Multiplication & Division hard
Formal short multiplication extends Y3 written multiplication
- The three digits of a three-digit number soft
Two-digit × one-digit uses place-value partitioning (e.g. 23 × 4 = 20 × 4 + 3 × 4)
- Reading ×, ÷, and = Symbols hard
Writing multiplication/division statements requires fluency with symbols
- Area and the distributive property soft
Area models for distributive property support understanding long multiplication layout
- Understanding angles (age 8+) hard
Must multiply side lengths for area before using area models for distributive property
- Area by Tiling hard
Must see tiling→multiplication connection before computing area via side lengths
- Brackets in Expressions hard
The full BODMAS/PEMDAS convention extends understanding of grouping symbols to all operations
- Division with remainders hard
Evaluating grouped expressions formalises multi-step calculation skills from Y5
- Multiply & Add Problems hard
Y4 M×D problem-solving is prerequisite to multi-step four-operation problems
- Written Multiplication & Division hard
Formal short multiplication extends Y3 written multiplication
- The three digits of a three-digit number soft
Two-digit × one-digit uses place-value partitioning (e.g. 23 × 4 = 20 × 4 + 3 × 4)
- Reading ×, ÷, and = Symbols hard
Writing multiplication/division statements requires fluency with symbols
- The three digits of a three-digit number soft
Two-digit × one-digit uses place-value partitioning (e.g. 23 × 4 = 20 × 4 + 3 × 4)
- Reading ×, ÷, and = Symbols hard
Writing multiplication/division statements requires fluency with symbols
- Multiplication as repeated addition (age 6+) hard
Scaling and correspondence problems extend Y2 problem-solving with mult/div
- Arrays for multiplication soft
Arrays are a key representation for solving multiplication/division problems
- Commutative Multiplication hard
Applying all three properties extends Y2 commutativity understanding
- Multiplication as repeated addition hard
Commutativity of multiplication requires understanding multiplication
- Arrays for multiplication (age 7+) hard
Extends array-based repeated addition to formal multiplication interpretation
- Multiplication as repeated addition hard
Interpreting products formalises repeated addition/equal groups from Y1
- Arrays for multiplication (age 9+) hard
Must have formal division method before solving multi-step problems
- Division as Unknown Factor hard
Understanding division as unknown-factor supports short division strategy
- What Multiplication Means hard
Connecting division to multiplication requires understanding products
- Arrays for multiplication (age 7+) hard
Extends array-based repeated addition to formal multiplication interpretation
- Multiplication as repeated addition hard
Interpreting products formalises repeated addition/equal groups from Y1
- Fluent multiplication and division facts hard
Fluent ×÷ within 100 is prerequisite to short division of larger numbers
- What Multiplication Means hard
Connecting division to multiplication requires understanding products
- Multiplication as repeated addition hard
Recalling times table facts requires understanding multiplication as repeated addition/grouping
- Written Multiplication hard
2/3-digit × 1-digit written method is prerequisite to 4-digit × 1-digit and 2-digit × 2-digit
- Written Multiplication & Division hard
Formal short multiplication extends Y3 written multiplication
- The three digits of a three-digit number soft
Two-digit × one-digit uses place-value partitioning (e.g. 23 × 4 = 20 × 4 + 3 × 4)
- Reading ×, ÷, and = Symbols hard
Writing multiplication/division statements requires fluency with symbols
- Area and the distributive property soft
Area models for distributive property support understanding long multiplication layout
- Understanding angles (age 8+) hard
Must multiply side lengths for area before using area models for distributive property
- Area by Tiling hard
Must see tiling→multiplication connection before computing area via side lengths
- Written Multiplication hard
2/3-digit × 1-digit written method is prerequisite to 4-digit × 1-digit and 2-digit × 2-digit
- Written Multiplication & Division hard
Formal short multiplication extends Y3 written multiplication
- The three digits of a three-digit number soft
Two-digit × one-digit uses place-value partitioning (e.g. 23 × 4 = 20 × 4 + 3 × 4)
- Reading ×, ÷, and = Symbols hard
Writing multiplication/division statements requires fluency with symbols
- Area and the distributive property soft
Area models for distributive property support understanding long multiplication layout
- Understanding angles (age 8+) hard
Must multiply side lengths for area before using area models for distributive property
- Area by Tiling hard
Must see tiling→multiplication connection before computing area via side lengths
- Using inverse operations hard
Rearranging formulae to change the subject is an application of inverse operations to algebraic expressions
- Order of operations hard
Understanding order of operations (BODMAS) is required before studying how operations undo each other via inverse relationships
- Brackets in Expressions hard
The full BODMAS/PEMDAS convention extends understanding of grouping symbols to all operations
- Division with remainders hard
Evaluating grouped expressions formalises multi-step calculation skills from Y5
- Multiply & Add Problems hard
Y4 M×D problem-solving is prerequisite to multi-step four-operation problems
- Written Multiplication & Division hard
Formal short multiplication extends Y3 written multiplication
- The three digits of a three-digit number soft
Two-digit × one-digit uses place-value partitioning (e.g. 23 × 4 = 20 × 4 + 3 × 4)
- The two digits of a two-digit number hard
Must understand two-digit place value before extending to hundreds
- A Ten Is Ten Ones hard
Understanding tens and ones place value requires the concept of 10 as a bundle
- The teen numbers hard
General two-digit place value extends from understanding teen number composition
- Multiplication as repeated addition hard
Recalling times table facts requires understanding multiplication as repeated addition/grouping
- Reading ×, ÷, and = Symbols hard
Writing multiplication/division statements requires fluency with symbols
- Reading and writing numbers to 20 hard
Writing number sentences requires reading and writing numerals
- Addition as combining or putting together two hard
Reading/writing the + symbol requires understanding what addition means
- Subtraction as taking away or separating hard
Reading/writing the − symbol requires understanding what subtraction means
- Subtraction as taking away or separating hard
Division as equal sharing/grouping requires understanding subtraction as taking away/separating
- Addition as combining or putting together two hard
Multiplication as repeated addition requires understanding addition as combining groups
- Skip Counting (4s, 8s, 50s, 100s) hard
Counting in 6s/7s/9s/25s/1000s extends counting in 4s/8s/50s/100s
- Multiplication as repeated addition hard
Recalling times table facts requires understanding multiplication as repeated addition/grouping
- The three digits of a three-digit number soft
Two-digit × one-digit uses place-value partitioning (e.g. 23 × 4 = 20 × 4 + 3 × 4)
- The two digits of a two-digit number hard
Must understand two-digit place value before extending to hundreds
- A Ten Is Ten Ones hard
Understanding tens and ones place value requires the concept of 10 as a bundle
- The teen numbers hard
General two-digit place value extends from understanding teen number composition
- Multiplication as repeated addition hard
Recalling times table facts requires understanding multiplication as repeated addition/grouping
- Reading ×, ÷, and = Symbols hard
Writing multiplication/division statements requires fluency with symbols
- Reading and writing numbers to 20 hard
Writing number sentences requires reading and writing numerals
- Addition as combining or putting together two hard
Reading/writing the + symbol requires understanding what addition means
- Subtraction as taking away or separating hard
Reading/writing the − symbol requires understanding what subtraction means
- Subtraction as taking away or separating hard
Division as equal sharing/grouping requires understanding subtraction as taking away/separating
- Addition as combining or putting together two hard
Multiplication as repeated addition requires understanding addition as combining groups
- Multiplication as repeated addition (age 6+) hard
Scaling and correspondence problems extend Y2 problem-solving with mult/div
- Arrays for multiplication soft
Arrays are a key representation for solving multiplication/division problems
- Division as equal sharing hard
Using arrays for division requires understanding division as grouping
- Subtraction as taking away or separating hard
Division as equal sharing/grouping requires understanding subtraction as taking away/separating
- Multiplication as repeated addition hard
Using arrays requires understanding what multiplication means
- Addition as combining or putting together two hard
Multiplication as repeated addition requires understanding addition as combining groups
- Multiplication as repeated addition hard
Recalling times table facts requires understanding multiplication as repeated addition/grouping
- Addition as combining or putting together two hard
Multiplication as repeated addition requires understanding addition as combining groups
- Commutative Multiplication hard
Applying all three properties extends Y2 commutativity understanding
- Division as equal sharing hard
Using arrays for division requires understanding division as grouping
- Subtraction as taking away or separating hard
Division as equal sharing/grouping requires understanding subtraction as taking away/separating
- Multiplication as repeated addition hard
Using arrays requires understanding what multiplication means
- Addition as combining or putting together two hard
Multiplication as repeated addition requires understanding addition as combining groups
- Multiplication as repeated addition hard
Commutativity of multiplication requires understanding multiplication
- Addition as combining or putting together two hard
Multiplication as repeated addition requires understanding addition as combining groups
- How Many in Total? hard
Understanding addition as combining groups requires knowing numbers represent quantities (cardinality)
- Arrays for multiplication (age 7+) hard
Extends array-based repeated addition to formal multiplication interpretation
- Arrays for multiplication hard
Rectangular arrays with repeated addition extends array representation from Y2
- Division as equal sharing hard
Using arrays for division requires understanding division as grouping
- Multiplication as repeated addition hard
Using arrays requires understanding what multiplication means
- Multiplication as repeated addition hard
Expressing array totals as sums of equal addends requires understanding multiplication as repeated addition
- Addition as combining or putting together two hard
Multiplication as repeated addition requires understanding addition as combining groups
- Multiplication as repeated addition hard
Interpreting products formalises repeated addition/equal groups from Y1
- Addition as combining or putting together two hard
Multiplication as repeated addition requires understanding addition as combining groups
- How Many in Total? hard
Understanding addition as combining groups requires knowing numbers represent quantities (cardinality)
- Arrays for multiplication (age 9+) hard
Must have formal division method before solving multi-step problems
- Division as Unknown Factor hard
Understanding division as unknown-factor supports short division strategy
- What Multiplication Means hard
Connecting division to multiplication requires understanding products
- Arrays for multiplication (age 7+) hard
Extends array-based repeated addition to formal multiplication interpretation
- Arrays for multiplication hard
Rectangular arrays with repeated addition extends array representation from Y2
- Division as equal sharing hard
Using arrays for division requires understanding division as grouping
- Multiplication as repeated addition hard
Using arrays requires understanding what multiplication means
- Multiplication as repeated addition hard
Expressing array totals as sums of equal addends requires understanding multiplication as repeated addition
- Addition as combining or putting together two hard
Multiplication as repeated addition requires understanding addition as combining groups
- Multiplication as repeated addition hard
Interpreting products formalises repeated addition/equal groups from Y1
- Addition as combining or putting together two hard
Multiplication as repeated addition requires understanding addition as combining groups
- How Many in Total? hard
Understanding addition as combining groups requires knowing numbers represent quantities (cardinality)
- Subtraction as taking away or separating hard
Division as equal sharing/grouping requires understanding subtraction as taking away/separating
- How Many in Total? hard
Understanding subtraction as taking away requires knowing numbers represent quantities (cardinality)
- Fluent multiplication and division facts hard
Fluent ×÷ within 100 is prerequisite to short division of larger numbers
- What Multiplication Means hard
Connecting division to multiplication requires understanding products
- Arrays for multiplication (age 7+) hard
Extends array-based repeated addition to formal multiplication interpretation
- Arrays for multiplication hard
Rectangular arrays with repeated addition extends array representation from Y2
- Multiplication as repeated addition hard
Expressing array totals as sums of equal addends requires understanding multiplication as repeated addition
- Multiplication as repeated addition hard
Interpreting products formalises repeated addition/equal groups from Y1
- Addition as combining or putting together two hard
Multiplication as repeated addition requires understanding addition as combining groups
- Subtraction as taking away or separating hard
Division as equal sharing/grouping requires understanding subtraction as taking away/separating
- Multiplication as repeated addition hard
Recalling times table facts requires understanding multiplication as repeated addition/grouping
- Addition as combining or putting together two hard
Multiplication as repeated addition requires understanding addition as combining groups
- How Many in Total? hard
Understanding addition as combining groups requires knowing numbers represent quantities (cardinality)
- Multiplication as repeated addition hard
Recalling times table facts requires understanding multiplication as repeated addition/grouping
- Addition as combining or putting together two hard
Multiplication as repeated addition requires understanding addition as combining groups
- Written Multiplication hard
2/3-digit × 1-digit written method is prerequisite to 4-digit × 1-digit and 2-digit × 2-digit
- Written Multiplication & Division hard
Formal short multiplication extends Y3 written multiplication
- The three digits of a three-digit number soft
Two-digit × one-digit uses place-value partitioning (e.g. 23 × 4 = 20 × 4 + 3 × 4)
- The two digits of a two-digit number hard
Must understand two-digit place value before extending to hundreds
- A Ten Is Ten Ones hard
Understanding tens and ones place value requires the concept of 10 as a bundle
- The teen numbers hard
General two-digit place value extends from understanding teen number composition
- Multiplication as repeated addition hard
Recalling times table facts requires understanding multiplication as repeated addition/grouping
- Reading ×, ÷, and = Symbols hard
Writing multiplication/division statements requires fluency with symbols
- Reading and writing numbers to 20 hard
Writing number sentences requires reading and writing numerals
- Addition as combining or putting together two hard
Reading/writing the + symbol requires understanding what addition means
- Subtraction as taking away or separating hard
Reading/writing the − symbol requires understanding what subtraction means
- Subtraction as taking away or separating hard
Division as equal sharing/grouping requires understanding subtraction as taking away/separating
- Addition as combining or putting together two hard
Multiplication as repeated addition requires understanding addition as combining groups
- Skip Counting (4s, 8s, 50s, 100s) hard
Counting in 6s/7s/9s/25s/1000s extends counting in 4s/8s/50s/100s
- Multiplication as repeated addition hard
Recalling times table facts requires understanding multiplication as repeated addition/grouping
- Area and the distributive property soft
Area models for distributive property support understanding long multiplication layout
- Understanding angles (age 8+) hard
Must multiply side lengths for area before using area models for distributive property
- Area by Tiling hard
Must see tiling→multiplication connection before computing area via side lengths
- Written Multiplication hard
2/3-digit × 1-digit written method is prerequisite to 4-digit × 1-digit and 2-digit × 2-digit
- Written Multiplication & Division hard
Formal short multiplication extends Y3 written multiplication
- The three digits of a three-digit number soft
Two-digit × one-digit uses place-value partitioning (e.g. 23 × 4 = 20 × 4 + 3 × 4)
- The two digits of a two-digit number hard
Must understand two-digit place value before extending to hundreds
- A Ten Is Ten Ones hard
Understanding tens and ones place value requires the concept of 10 as a bundle
- The teen numbers hard
General two-digit place value extends from understanding teen number composition
- Multiplication as repeated addition hard
Recalling times table facts requires understanding multiplication as repeated addition/grouping
- Reading ×, ÷, and = Symbols hard
Writing multiplication/division statements requires fluency with symbols
- Reading and writing numbers to 20 hard
Writing number sentences requires reading and writing numerals
- Addition as combining or putting together two hard
Reading/writing the + symbol requires understanding what addition means
- Subtraction as taking away or separating hard
Reading/writing the − symbol requires understanding what subtraction means
- Subtraction as taking away or separating hard
Division as equal sharing/grouping requires understanding subtraction as taking away/separating
- Addition as combining or putting together two hard
Multiplication as repeated addition requires understanding addition as combining groups
- Skip Counting (4s, 8s, 50s, 100s) hard
Counting in 6s/7s/9s/25s/1000s extends counting in 4s/8s/50s/100s
- Multiplication as repeated addition hard
Recalling times table facts requires understanding multiplication as repeated addition/grouping
- Area and the distributive property soft
Area models for distributive property support understanding long multiplication layout
- Understanding angles (age 8+) hard
Must multiply side lengths for area before using area models for distributive property
- Area by Tiling hard
Must see tiling→multiplication connection before computing area via side lengths
- Multi-step problems: choosing operations hard
Fluency with all four operations in context is required before formalising inverse relationships between them
- Brackets in Expressions hard
The full BODMAS/PEMDAS convention extends understanding of grouping symbols to all operations
- Division with remainders hard
Evaluating grouped expressions formalises multi-step calculation skills from Y5
- Multiply & Add Problems hard
Y4 M×D problem-solving is prerequisite to multi-step four-operation problems
- Written Multiplication & Division hard
Formal short multiplication extends Y3 written multiplication
- The three digits of a three-digit number soft
Two-digit × one-digit uses place-value partitioning (e.g. 23 × 4 = 20 × 4 + 3 × 4)
- Reading ×, ÷, and = Symbols hard
Writing multiplication/division statements requires fluency with symbols
- Skip Counting (4s, 8s, 50s, 100s) hard
Counting in 6s/7s/9s/25s/1000s extends counting in 4s/8s/50s/100s
- The three digits of a three-digit number soft
Two-digit × one-digit uses place-value partitioning (e.g. 23 × 4 = 20 × 4 + 3 × 4)
- Reading ×, ÷, and = Symbols hard
Writing multiplication/division statements requires fluency with symbols
- Multiplication as repeated addition (age 6+) hard
Scaling and correspondence problems extend Y2 problem-solving with mult/div
- Arrays for multiplication soft
Arrays are a key representation for solving multiplication/division problems
- Division as equal sharing hard
Using arrays for division requires understanding division as grouping
- Multiplication as repeated addition hard
Using arrays requires understanding what multiplication means
- Multiplication as repeated addition hard
Recalling times table facts requires understanding multiplication as repeated addition/grouping
- Commutative Multiplication hard
Applying all three properties extends Y2 commutativity understanding
- Division as equal sharing hard
Using arrays for division requires understanding division as grouping
- Multiplication as repeated addition hard
Using arrays requires understanding what multiplication means
- Multiplication as repeated addition hard
Commutativity of multiplication requires understanding multiplication
- Addition as combining or putting together two hard
Multiplication as repeated addition requires understanding addition as combining groups
- Arrays for multiplication (age 7+) hard
Extends array-based repeated addition to formal multiplication interpretation
- Arrays for multiplication hard
Rectangular arrays with repeated addition extends array representation from Y2
- Multiplication as repeated addition hard
Expressing array totals as sums of equal addends requires understanding multiplication as repeated addition
- Multiplication as repeated addition hard
Interpreting products formalises repeated addition/equal groups from Y1
- Addition as combining or putting together two hard
Multiplication as repeated addition requires understanding addition as combining groups
- Arrays for multiplication (age 9+) hard
Must have formal division method before solving multi-step problems
- Division as Unknown Factor hard
Understanding division as unknown-factor supports short division strategy
- What Multiplication Means hard
Connecting division to multiplication requires understanding products
- Arrays for multiplication (age 7+) hard
Extends array-based repeated addition to formal multiplication interpretation
- Arrays for multiplication hard
Rectangular arrays with repeated addition extends array representation from Y2
- Multiplication as repeated addition hard
Expressing array totals as sums of equal addends requires understanding multiplication as repeated addition
- Multiplication as repeated addition hard
Interpreting products formalises repeated addition/equal groups from Y1
- Addition as combining or putting together two hard
Multiplication as repeated addition requires understanding addition as combining groups
- Subtraction as taking away or separating hard
Division as equal sharing/grouping requires understanding subtraction as taking away/separating
- Fluent multiplication and division facts hard
Fluent ×÷ within 100 is prerequisite to short division of larger numbers
- What Multiplication Means hard
Connecting division to multiplication requires understanding products
- Arrays for multiplication (age 7+) hard
Extends array-based repeated addition to formal multiplication interpretation
- Multiplication as repeated addition hard
Interpreting products formalises repeated addition/equal groups from Y1
- Multiplication as repeated addition hard
Recalling times table facts requires understanding multiplication as repeated addition/grouping
- Addition as combining or putting together two hard
Multiplication as repeated addition requires understanding addition as combining groups
- Multiplication as repeated addition hard
Recalling times table facts requires understanding multiplication as repeated addition/grouping
- Written Multiplication hard
2/3-digit × 1-digit written method is prerequisite to 4-digit × 1-digit and 2-digit × 2-digit
- Written Multiplication & Division hard
Formal short multiplication extends Y3 written multiplication
- The three digits of a three-digit number soft
Two-digit × one-digit uses place-value partitioning (e.g. 23 × 4 = 20 × 4 + 3 × 4)
- Reading ×, ÷, and = Symbols hard
Writing multiplication/division statements requires fluency with symbols
- Skip Counting (4s, 8s, 50s, 100s) hard
Counting in 6s/7s/9s/25s/1000s extends counting in 4s/8s/50s/100s
- Area and the distributive property soft
Area models for distributive property support understanding long multiplication layout
- Understanding angles (age 8+) hard
Must multiply side lengths for area before using area models for distributive property
- Area by Tiling hard
Must see tiling→multiplication connection before computing area via side lengths
- Written Multiplication hard
2/3-digit × 1-digit written method is prerequisite to 4-digit × 1-digit and 2-digit × 2-digit
- Written Multiplication & Division hard
Formal short multiplication extends Y3 written multiplication
- The three digits of a three-digit number soft
Two-digit × one-digit uses place-value partitioning (e.g. 23 × 4 = 20 × 4 + 3 × 4)
- Reading ×, ÷, and = Symbols hard
Writing multiplication/division statements requires fluency with symbols
- Skip Counting (4s, 8s, 50s, 100s) hard
Counting in 6s/7s/9s/25s/1000s extends counting in 4s/8s/50s/100s
- Area and the distributive property soft
Area models for distributive property support understanding long multiplication layout
- Understanding angles (age 8+) hard
Must multiply side lengths for area before using area models for distributive property
- Area by Tiling hard
Must see tiling→multiplication connection before computing area via side lengths
- Multiply & Add Problems hard
Y4 M×D problem-solving is prerequisite to multi-step four-operation problems
- Written Multiplication & Division hard
Formal short multiplication extends Y3 written multiplication
- The three digits of a three-digit number soft
Two-digit × one-digit uses place-value partitioning (e.g. 23 × 4 = 20 × 4 + 3 × 4)
- The teen numbers hard
Understanding 10 as a bundle builds on understanding teen numbers as 'a ten and some ones'
- The two digits of a two-digit number hard
Must understand two-digit place value before extending to hundreds
- A Ten Is Ten Ones hard
Understanding tens and ones place value requires the concept of 10 as a bundle
- The teen numbers hard
General two-digit place value extends from understanding teen number composition
- A Ten Is Ten Ones hard
Understanding tens and ones place value requires the concept of 10 as a bundle
- The teen numbers hard
Understanding 10 as a bundle builds on understanding teen numbers as 'a ten and some ones'
- The teen numbers hard
General two-digit place value extends from understanding teen number composition
- How Many in Total? hard
Understanding tens-and-ones composition requires cardinality — knowing numbers represent quantities
- Reading and writing numbers to 20 hard
Composing/decomposing teen numbers requires reading and writing those numerals
- Multiplication as repeated addition hard
Recalling times table facts requires understanding multiplication as repeated addition/grouping
- Addition as combining or putting together two hard
Multiplication as repeated addition requires understanding addition as combining groups
- Reading ×, ÷, and = Symbols hard
Writing multiplication/division statements requires fluency with symbols
- Reading and writing numbers to 20 hard
Writing number sentences requires reading and writing numerals
- How Many in Total? hard
Reading/writing numerals 0–20 requires understanding that numerals represent quantities (cardinality)
- Writing digits 0-9 hard
Writing numerals requires the motor skill of forming digits 0-9 (taught in English handwriting)
- Addition as combining or putting together two hard
Reading/writing the + symbol requires understanding what addition means
- How Many in Total? hard
Understanding addition as combining groups requires knowing numbers represent quantities (cardinality)
- Subtraction as taking away or separating hard
Reading/writing the − symbol requires understanding what subtraction means
- How Many in Total? hard
Understanding subtraction as taking away requires knowing numbers represent quantities (cardinality)
- Subtraction as taking away or separating hard
Division as equal sharing/grouping requires understanding subtraction as taking away/separating
- How Many in Total? hard
Understanding subtraction as taking away requires knowing numbers represent quantities (cardinality)
- Addition as combining or putting together two hard
Multiplication as repeated addition requires understanding addition as combining groups
- How Many in Total? hard
Understanding addition as combining groups requires knowing numbers represent quantities (cardinality)
- Skip Counting (4s, 8s, 50s, 100s) hard
Counting in 6s/7s/9s/25s/1000s extends counting in 4s/8s/50s/100s
- Multiplication as repeated addition hard
Recalling times table facts requires understanding multiplication as repeated addition/grouping
- Addition as combining or putting together two hard
Multiplication as repeated addition requires understanding addition as combining groups
- The three digits of a three-digit number soft
Two-digit × one-digit uses place-value partitioning (e.g. 23 × 4 = 20 × 4 + 3 × 4)
- The teen numbers hard
Understanding 10 as a bundle builds on understanding teen numbers as 'a ten and some ones'
- The two digits of a two-digit number hard
Must understand two-digit place value before extending to hundreds
- A Ten Is Ten Ones hard
Understanding tens and ones place value requires the concept of 10 as a bundle
- The teen numbers hard
General two-digit place value extends from understanding teen number composition
- A Ten Is Ten Ones hard
Understanding tens and ones place value requires the concept of 10 as a bundle
- The teen numbers hard
Understanding 10 as a bundle builds on understanding teen numbers as 'a ten and some ones'
- The teen numbers hard
General two-digit place value extends from understanding teen number composition
- How Many in Total? hard
Understanding tens-and-ones composition requires cardinality — knowing numbers represent quantities
- Reading and writing numbers to 20 hard
Composing/decomposing teen numbers requires reading and writing those numerals
- Multiplication as repeated addition hard
Recalling times table facts requires understanding multiplication as repeated addition/grouping
- Addition as combining or putting together two hard
Multiplication as repeated addition requires understanding addition as combining groups
- Reading ×, ÷, and = Symbols hard
Writing multiplication/division statements requires fluency with symbols
- Reading and writing numbers to 20 hard
Writing number sentences requires reading and writing numerals
- How Many in Total? hard
Reading/writing numerals 0–20 requires understanding that numerals represent quantities (cardinality)
- Writing digits 0-9 hard
Writing numerals requires the motor skill of forming digits 0-9 (taught in English handwriting)
- Addition as combining or putting together two hard
Reading/writing the + symbol requires understanding what addition means
- How Many in Total? hard
Understanding addition as combining groups requires knowing numbers represent quantities (cardinality)
- Subtraction as taking away or separating hard
Reading/writing the − symbol requires understanding what subtraction means
- How Many in Total? hard
Understanding subtraction as taking away requires knowing numbers represent quantities (cardinality)
- Subtraction as taking away or separating hard
Division as equal sharing/grouping requires understanding subtraction as taking away/separating
- How Many in Total? hard
Understanding subtraction as taking away requires knowing numbers represent quantities (cardinality)
- Addition as combining or putting together two hard
Multiplication as repeated addition requires understanding addition as combining groups
- How Many in Total? hard
Understanding addition as combining groups requires knowing numbers represent quantities (cardinality)
- Multiplication as repeated addition (age 6+) hard
Scaling and correspondence problems extend Y2 problem-solving with mult/div
- Arrays for multiplication soft
Arrays are a key representation for solving multiplication/division problems
- Division as equal sharing hard
Using arrays for division requires understanding division as grouping
- Subtraction as taking away or separating hard
Division as equal sharing/grouping requires understanding subtraction as taking away/separating
- How Many in Total? hard
Understanding subtraction as taking away requires knowing numbers represent quantities (cardinality)
- Multiplication as repeated addition hard
Using arrays requires understanding what multiplication means
- Addition as combining or putting together two hard
Multiplication as repeated addition requires understanding addition as combining groups
- How Many in Total? hard
Understanding addition as combining groups requires knowing numbers represent quantities (cardinality)
- Multiplication as repeated addition hard
Recalling times table facts requires understanding multiplication as repeated addition/grouping
- Addition as combining or putting together two hard
Multiplication as repeated addition requires understanding addition as combining groups
- How Many in Total? hard
Understanding addition as combining groups requires knowing numbers represent quantities (cardinality)
- Commutative Multiplication hard
Applying all three properties extends Y2 commutativity understanding
- Division as equal sharing hard
Using arrays for division requires understanding division as grouping
- Subtraction as taking away or separating hard
Division as equal sharing/grouping requires understanding subtraction as taking away/separating
- How Many in Total? hard
Understanding subtraction as taking away requires knowing numbers represent quantities (cardinality)
- Multiplication as repeated addition hard
Using arrays requires understanding what multiplication means
- Addition as combining or putting together two hard
Multiplication as repeated addition requires understanding addition as combining groups
- How Many in Total? hard
Understanding addition as combining groups requires knowing numbers represent quantities (cardinality)
- Multiplication as repeated addition hard
Commutativity of multiplication requires understanding multiplication
- Addition as combining or putting together two hard
Multiplication as repeated addition requires understanding addition as combining groups
- How Many in Total? hard
Understanding addition as combining groups requires knowing numbers represent quantities (cardinality)
- One-to-one counting hard
Cardinality principle builds on one-to-one correspondence — you must count correctly to know the last number tells 'how many'
- Arrays for multiplication (age 7+) hard
Extends array-based repeated addition to formal multiplication interpretation
- Arrays for multiplication hard
Rectangular arrays with repeated addition extends array representation from Y2
- Division as equal sharing hard
Using arrays for division requires understanding division as grouping
- Subtraction as taking away or separating hard
Division as equal sharing/grouping requires understanding subtraction as taking away/separating
- Multiplication as repeated addition hard
Using arrays requires understanding what multiplication means
- Addition as combining or putting together two hard
Multiplication as repeated addition requires understanding addition as combining groups
- Multiplication as repeated addition hard
Expressing array totals as sums of equal addends requires understanding multiplication as repeated addition
- Addition as combining or putting together two hard
Multiplication as repeated addition requires understanding addition as combining groups
- How Many in Total? hard
Understanding addition as combining groups requires knowing numbers represent quantities (cardinality)
- Multiplication as repeated addition hard
Interpreting products formalises repeated addition/equal groups from Y1
- Addition as combining or putting together two hard
Multiplication as repeated addition requires understanding addition as combining groups
- How Many in Total? hard
Understanding addition as combining groups requires knowing numbers represent quantities (cardinality)
- One-to-one counting hard
Cardinality principle builds on one-to-one correspondence — you must count correctly to know the last number tells 'how many'
- Arrays for multiplication (age 9+) hard
Must have formal division method before solving multi-step problems
- Division as Unknown Factor hard
Understanding division as unknown-factor supports short division strategy
- What Multiplication Means hard
Connecting division to multiplication requires understanding products
- Arrays for multiplication (age 7+) hard
Extends array-based repeated addition to formal multiplication interpretation
- Arrays for multiplication hard
Rectangular arrays with repeated addition extends array representation from Y2
- Division as equal sharing hard
Using arrays for division requires understanding division as grouping
- Subtraction as taking away or separating hard
Division as equal sharing/grouping requires understanding subtraction as taking away/separating
- Multiplication as repeated addition hard
Using arrays requires understanding what multiplication means
- Addition as combining or putting together two hard
Multiplication as repeated addition requires understanding addition as combining groups
- Multiplication as repeated addition hard
Expressing array totals as sums of equal addends requires understanding multiplication as repeated addition
- Addition as combining or putting together two hard
Multiplication as repeated addition requires understanding addition as combining groups
- How Many in Total? hard
Understanding addition as combining groups requires knowing numbers represent quantities (cardinality)
- Multiplication as repeated addition hard
Interpreting products formalises repeated addition/equal groups from Y1
- Addition as combining or putting together two hard
Multiplication as repeated addition requires understanding addition as combining groups
- How Many in Total? hard
Understanding addition as combining groups requires knowing numbers represent quantities (cardinality)
- One-to-one counting hard
Cardinality principle builds on one-to-one correspondence — you must count correctly to know the last number tells 'how many'
- Subtraction as taking away or separating hard
Division as equal sharing/grouping requires understanding subtraction as taking away/separating
- How Many in Total? hard
Understanding subtraction as taking away requires knowing numbers represent quantities (cardinality)
- One-to-one counting hard
Cardinality principle builds on one-to-one correspondence — you must count correctly to know the last number tells 'how many'
- Fluent multiplication and division facts hard
Fluent ×÷ within 100 is prerequisite to short division of larger numbers
- What Multiplication Means hard
Connecting division to multiplication requires understanding products
- Arrays for multiplication (age 7+) hard
Extends array-based repeated addition to formal multiplication interpretation
- Arrays for multiplication hard
Rectangular arrays with repeated addition extends array representation from Y2
- Division as equal sharing hard
Using arrays for division requires understanding division as grouping
- Multiplication as repeated addition hard
Using arrays requires understanding what multiplication means
- Multiplication as repeated addition hard
Expressing array totals as sums of equal addends requires understanding multiplication as repeated addition
- Addition as combining or putting together two hard
Multiplication as repeated addition requires understanding addition as combining groups
- Multiplication as repeated addition hard
Interpreting products formalises repeated addition/equal groups from Y1
- Addition as combining or putting together two hard
Multiplication as repeated addition requires understanding addition as combining groups
- How Many in Total? hard
Understanding addition as combining groups requires knowing numbers represent quantities (cardinality)
- Subtraction as taking away or separating hard
Division as equal sharing/grouping requires understanding subtraction as taking away/separating
- How Many in Total? hard
Understanding subtraction as taking away requires knowing numbers represent quantities (cardinality)
- Multiplication as repeated addition hard
Recalling times table facts requires understanding multiplication as repeated addition/grouping
- Addition as combining or putting together two hard
Multiplication as repeated addition requires understanding addition as combining groups
- How Many in Total? hard
Understanding addition as combining groups requires knowing numbers represent quantities (cardinality)
- One-to-one counting hard
Cardinality principle builds on one-to-one correspondence — you must count correctly to know the last number tells 'how many'
- Multiplication as repeated addition hard
Recalling times table facts requires understanding multiplication as repeated addition/grouping
- Addition as combining or putting together two hard
Multiplication as repeated addition requires understanding addition as combining groups
- How Many in Total? hard
Understanding addition as combining groups requires knowing numbers represent quantities (cardinality)
- Written Multiplication hard
2/3-digit × 1-digit written method is prerequisite to 4-digit × 1-digit and 2-digit × 2-digit
- Written Multiplication & Division hard
Formal short multiplication extends Y3 written multiplication
- The three digits of a three-digit number soft
Two-digit × one-digit uses place-value partitioning (e.g. 23 × 4 = 20 × 4 + 3 × 4)
- The teen numbers hard
Understanding 10 as a bundle builds on understanding teen numbers as 'a ten and some ones'
- The two digits of a two-digit number hard
Must understand two-digit place value before extending to hundreds
- A Ten Is Ten Ones hard
Understanding tens and ones place value requires the concept of 10 as a bundle
- The teen numbers hard
General two-digit place value extends from understanding teen number composition
- A Ten Is Ten Ones hard
Understanding tens and ones place value requires the concept of 10 as a bundle
- The teen numbers hard
Understanding 10 as a bundle builds on understanding teen numbers as 'a ten and some ones'
- The teen numbers hard
General two-digit place value extends from understanding teen number composition
- How Many in Total? hard
Understanding tens-and-ones composition requires cardinality — knowing numbers represent quantities
- Reading and writing numbers to 20 hard
Composing/decomposing teen numbers requires reading and writing those numerals
- Multiplication as repeated addition hard
Recalling times table facts requires understanding multiplication as repeated addition/grouping
- Addition as combining or putting together two hard
Multiplication as repeated addition requires understanding addition as combining groups
- Reading ×, ÷, and = Symbols hard
Writing multiplication/division statements requires fluency with symbols
- Reading and writing numbers to 20 hard
Writing number sentences requires reading and writing numerals
- How Many in Total? hard
Reading/writing numerals 0–20 requires understanding that numerals represent quantities (cardinality)
- Writing digits 0-9 hard
Writing numerals requires the motor skill of forming digits 0-9 (taught in English handwriting)
- Addition as combining or putting together two hard
Reading/writing the + symbol requires understanding what addition means
- How Many in Total? hard
Understanding addition as combining groups requires knowing numbers represent quantities (cardinality)
- Subtraction as taking away or separating hard
Reading/writing the − symbol requires understanding what subtraction means
- How Many in Total? hard
Understanding subtraction as taking away requires knowing numbers represent quantities (cardinality)
- Subtraction as taking away or separating hard
Division as equal sharing/grouping requires understanding subtraction as taking away/separating
- How Many in Total? hard
Understanding subtraction as taking away requires knowing numbers represent quantities (cardinality)
- Addition as combining or putting together two hard
Multiplication as repeated addition requires understanding addition as combining groups
- How Many in Total? hard
Understanding addition as combining groups requires knowing numbers represent quantities (cardinality)
- Skip Counting (4s, 8s, 50s, 100s) hard
Counting in 6s/7s/9s/25s/1000s extends counting in 4s/8s/50s/100s
- Multiplication as repeated addition hard
Recalling times table facts requires understanding multiplication as repeated addition/grouping
- Addition as combining or putting together two hard
Multiplication as repeated addition requires understanding addition as combining groups
- Area and the distributive property soft
Area models for distributive property support understanding long multiplication layout
- Understanding angles (age 8+) hard
Must multiply side lengths for area before using area models for distributive property
- Area by Tiling hard
Must see tiling→multiplication connection before computing area via side lengths
- Measuring length (age 7+) soft
Length measurement experience supports understanding area as a 2D measurement
- Arrays for multiplication (age 9+) hard
Long division by 2-digit extends Y5 short division by 1-digit
- Division as Unknown Factor hard
Understanding division as unknown-factor supports short division strategy
- What Multiplication Means hard
Connecting division to multiplication requires understanding products
- Arrays for multiplication (age 7+) hard
Extends array-based repeated addition to formal multiplication interpretation
- Arrays for multiplication hard
Rectangular arrays with repeated addition extends array representation from Y2
- Division as equal sharing hard
Using arrays for division requires understanding division as grouping
- Subtraction as taking away or separating hard
Division as equal sharing/grouping requires understanding subtraction as taking away/separating
- Multiplication as repeated addition hard
Using arrays requires understanding what multiplication means
- Addition as combining or putting together two hard
Multiplication as repeated addition requires understanding addition as combining groups
- Multiplication as repeated addition hard
Expressing array totals as sums of equal addends requires understanding multiplication as repeated addition
- Addition as combining or putting together two hard
Multiplication as repeated addition requires understanding addition as combining groups
- How Many in Total? hard
Understanding addition as combining groups requires knowing numbers represent quantities (cardinality)
- Multiplication as repeated addition hard
Interpreting products formalises repeated addition/equal groups from Y1
- Addition as combining or putting together two hard
Multiplication as repeated addition requires understanding addition as combining groups
- How Many in Total? hard
Understanding addition as combining groups requires knowing numbers represent quantities (cardinality)
- One-to-one counting hard
Cardinality principle builds on one-to-one correspondence — you must count correctly to know the last number tells 'how many'
- Subtraction as taking away or separating hard
Division as equal sharing/grouping requires understanding subtraction as taking away/separating
- How Many in Total? hard
Understanding subtraction as taking away requires knowing numbers represent quantities (cardinality)
- One-to-one counting hard
Cardinality principle builds on one-to-one correspondence — you must count correctly to know the last number tells 'how many'
- Fluent multiplication and division facts hard
Fluent ×÷ within 100 is prerequisite to short division of larger numbers
- What Multiplication Means hard
Connecting division to multiplication requires understanding products
- Arrays for multiplication (age 7+) hard
Extends array-based repeated addition to formal multiplication interpretation
- Arrays for multiplication hard
Rectangular arrays with repeated addition extends array representation from Y2
- Division as equal sharing hard
Using arrays for division requires understanding division as grouping
- Multiplication as repeated addition hard
Using arrays requires understanding what multiplication means
- Multiplication as repeated addition hard
Expressing array totals as sums of equal addends requires understanding multiplication as repeated addition
- Addition as combining or putting together two hard
Multiplication as repeated addition requires understanding addition as combining groups
- Multiplication as repeated addition hard
Interpreting products formalises repeated addition/equal groups from Y1
- Addition as combining or putting together two hard
Multiplication as repeated addition requires understanding addition as combining groups
- How Many in Total? hard
Understanding addition as combining groups requires knowing numbers represent quantities (cardinality)
- Subtraction as taking away or separating hard
Division as equal sharing/grouping requires understanding subtraction as taking away/separating
- How Many in Total? hard
Understanding subtraction as taking away requires knowing numbers represent quantities (cardinality)
- Multiplication as repeated addition hard
Recalling times table facts requires understanding multiplication as repeated addition/grouping
- Addition as combining or putting together two hard
Multiplication as repeated addition requires understanding addition as combining groups
- How Many in Total? hard
Understanding addition as combining groups requires knowing numbers represent quantities (cardinality)
- One-to-one counting hard
Cardinality principle builds on one-to-one correspondence — you must count correctly to know the last number tells 'how many'
- Multiplication as repeated addition hard
Recalling times table facts requires understanding multiplication as repeated addition/grouping
- Addition as combining or putting together two hard
Multiplication as repeated addition requires understanding addition as combining groups
- How Many in Total? hard
Understanding addition as combining groups requires knowing numbers represent quantities (cardinality)
- Long multiplication (age 10+) soft
Checking division with multiplication requires fluent multiplication
- Written Multiplication hard
2/3-digit × 1-digit written method is prerequisite to 4-digit × 1-digit and 2-digit × 2-digit
- Written Multiplication & Division hard
Formal short multiplication extends Y3 written multiplication
- The three digits of a three-digit number soft
Two-digit × one-digit uses place-value partitioning (e.g. 23 × 4 = 20 × 4 + 3 × 4)
- The two digits of a two-digit number hard
Must understand two-digit place value before extending to hundreds
- A Ten Is Ten Ones hard
Understanding tens and ones place value requires the concept of 10 as a bundle
- The teen numbers hard
General two-digit place value extends from understanding teen number composition
- Multiplication as repeated addition hard
Recalling times table facts requires understanding multiplication as repeated addition/grouping
- Reading ×, ÷, and = Symbols hard
Writing multiplication/division statements requires fluency with symbols
- Reading and writing numbers to 20 hard
Writing number sentences requires reading and writing numerals
- Addition as combining or putting together two hard
Reading/writing the + symbol requires understanding what addition means
- Subtraction as taking away or separating hard
Reading/writing the − symbol requires understanding what subtraction means
- Subtraction as taking away or separating hard
Division as equal sharing/grouping requires understanding subtraction as taking away/separating
- Addition as combining or putting together two hard
Multiplication as repeated addition requires understanding addition as combining groups
- Skip Counting (4s, 8s, 50s, 100s) hard
Counting in 6s/7s/9s/25s/1000s extends counting in 4s/8s/50s/100s
- Multiplication as repeated addition hard
Recalling times table facts requires understanding multiplication as repeated addition/grouping
- Area and the distributive property soft
Area models for distributive property support understanding long multiplication layout
- Understanding angles (age 8+) hard
Must multiply side lengths for area before using area models for distributive property
- Area by Tiling hard
Must see tiling→multiplication connection before computing area via side lengths
- Proportional Reasoning Vocabulary hard
Direct and inverse proportion require 'direct proportion' and 'inverse proportion' as precisely understood contrasting terms
- Proportion Graphs hard
Direct and inverse proportion with graphical representations requires reading and plotting proportion graphs (y = kx through origin)
- Proportional Reasoning Vocabulary hard
Dividing in a given ratio requires 'ratio', 'part-to-part', and 'part-to-whole' vocabulary
- Bar Models for Ratios hard
Dividing a quantity in a given ratio is the natural next step from the bar model representation
- Simplifying Fractions hard
Understanding fraction of total requires simplification/common denominator skills
- Equivalent fractions on a number line hard
Understanding equivalence conceptually is prerequisite to explaining algebraically
- Equivalent fractions hard
Diagram-based equivalent fractions is prerequisite to formal equivalence understanding
- Finding halves and quarters (age 5+) hard
Working with 1/4, 2/4, 3/4 extends from Y1 understanding of quarters
- What Is a Half? hard
Understanding quarters extends from understanding halves — both are equal parts but quarters requires dividing into 4
- Division as equal sharing hard
Finding a half requires equal sharing into 2 groups — a division concept
- Subtraction as taking away or separating hard
Division as equal sharing/grouping requires understanding subtraction as taking away/separating
- Fraction Notation hard
Writing fractions like 1/3 and 3/4 requires knowing numerator and denominator
- Finding halves and quarters (age 5+) hard
Working with 1/4, 2/4, 3/4 extends from Y1 understanding of quarters
- Fraction Notation hard
Writing fractions like 1/3 and 3/4 requires knowing numerator and denominator
- Reading +, −, and = symbols soft
Writing fraction sentences (1/2 of 6 = 3) requires understanding the = sign
- Reading and writing numbers to 20 hard
Writing number sentences requires reading and writing numerals
- How Many in Total? hard
Reading/writing numerals 0–20 requires understanding that numerals represent quantities (cardinality)
- Writing digits 0-9 hard
Writing numerals requires the motor skill of forming digits 0-9 (taught in English handwriting)
- Addition as combining or putting together two hard
Reading/writing the + symbol requires understanding what addition means
- How Many in Total? hard
Understanding addition as combining groups requires knowing numbers represent quantities (cardinality)
- Subtraction as taking away or separating hard
Reading/writing the − symbol requires understanding what subtraction means
- How Many in Total? hard
Understanding subtraction as taking away requires knowing numbers represent quantities (cardinality)
- Fractions of amounts hard
Writing fractions and recognising equivalence requires knowing what the fractions mean
- Finding halves and quarters (age 5+) hard
Working with 1/4, 2/4, 3/4 extends from Y1 understanding of quarters
- What Is a Half? hard
Understanding quarters extends from understanding halves — both are equal parts but quarters requires dividing into 4
- Division as equal sharing hard
Finding a half requires equal sharing into 2 groups — a division concept
- Subtraction as taking away or separating hard
Division as equal sharing/grouping requires understanding subtraction as taking away/separating
- Fraction Notation hard
Writing fractions like 1/3 and 3/4 requires knowing numerator and denominator
- Fraction Notation hard
Writing fractions and recognising equivalence requires 'equivalent fraction' vocabulary
- Fractions of amounts hard
Recognising fractions of shapes/quantities is prerequisite to formal unit fraction understanding
- Finding halves and quarters (age 5+) hard
Working with 1/4, 2/4, 3/4 extends from Y1 understanding of quarters
- What Is a Half? hard
Understanding quarters extends from understanding halves — both are equal parts but quarters requires dividing into 4
- Division as equal sharing hard
Finding a half requires equal sharing into 2 groups — a division concept
- Division as equal sharing hard
Finding a half requires equal sharing into 2 groups — a division concept
- Subtraction as taking away or separating hard
Division as equal sharing/grouping requires understanding subtraction as taking away/separating
- Subtraction as taking away or separating hard
Division as equal sharing/grouping requires understanding subtraction as taking away/separating
- How Many in Total? hard
Understanding subtraction as taking away requires knowing numbers represent quantities (cardinality)
- Fraction Notation hard
Writing fractions like 1/3 and 3/4 requires knowing numerator and denominator
- Fraction Notation hard
Understanding a/b as a parts of 1/b requires numerator, denominator, and unit fraction vocabulary
- Splitting shapes into equal parts (age 7+) hard
Partition into equal shares is prerequisite to understanding unit fractions
- Decomposing a shape into more equal shares hard
Understanding equal shares of different shapes requires concept of more shares = smaller
- Halves & Quarters of Shapes hard
Comparing share sizes requires experience partitioning into halves and quarters
- Finding halves and quarters (age 5+) hard
Partitioning into fourths/quarters extends from Y1 understanding of quarters
- Finding halves and quarters (age 5+) hard
Partitioning into fourths/quarters extends from Y1 understanding of quarters
- What Is a Half? hard
Understanding quarters extends from understanding halves — both are equal parts but quarters requires dividing into 4
- Division as equal sharing hard
Finding a half requires equal sharing into 2 groups — a division concept
- Fractions on a number line (age 8+) hard
Equivalent fractions as the same point on a number line directly uses the fraction number-line representation
- Fractions on a number line hard
Prior number-line fraction experience feeds into formal unit-fraction placement
- Finding halves and quarters (age 5+) hard
Working with 1/4, 2/4, 3/4 extends from Y1 understanding of quarters
- What Is a Half? hard
Understanding quarters extends from understanding halves — both are equal parts but quarters requires dividing into 4
- Division as equal sharing hard
Finding a half requires equal sharing into 2 groups — a division concept
- Subtraction as taking away or separating hard
Division as equal sharing/grouping requires understanding subtraction as taking away/separating
- Fraction Notation hard
Writing fractions like 1/3 and 3/4 requires knowing numerator and denominator
- Finding halves and quarters (age 5+) hard
Working with 1/4, 2/4, 3/4 extends from Y1 understanding of quarters
- Fraction Notation hard
Writing fractions like 1/3 and 3/4 requires knowing numerator and denominator
- Fractions of amounts hard
Recognising fractions of shapes/quantities is prerequisite to formal unit fraction understanding
- Finding halves and quarters (age 5+) hard
Working with 1/4, 2/4, 3/4 extends from Y1 understanding of quarters
- What Is a Half? hard
Understanding quarters extends from understanding halves — both are equal parts but quarters requires dividing into 4
- Division as equal sharing hard
Finding a half requires equal sharing into 2 groups — a division concept
- Subtraction as taking away or separating hard
Division as equal sharing/grouping requires understanding subtraction as taking away/separating
- Fraction Notation hard
Writing fractions like 1/3 and 3/4 requires knowing numerator and denominator
- Fraction Notation hard
Understanding a/b as a parts of 1/b requires numerator, denominator, and unit fraction vocabulary
- Splitting shapes into equal parts (age 7+) hard
Partition into equal shares is prerequisite to understanding unit fractions
- Decomposing a shape into more equal shares hard
Understanding equal shares of different shapes requires concept of more shares = smaller
- Halves & Quarters of Shapes hard
Comparing share sizes requires experience partitioning into halves and quarters
- Finding halves and quarters (age 5+) hard
Partitioning into fourths/quarters extends from Y1 understanding of quarters
- Equivalent fractions (age 8+) hard
Generating equivalent fractions with visual models is prerequisite to algebraic explanation of equivalence
- Equivalent fractions on a number line hard
Must understand equivalence before generating equivalent fractions
- Equivalent fractions hard
Diagram-based equivalent fractions is prerequisite to formal equivalence understanding
- Finding halves and quarters (age 5+) hard
Working with 1/4, 2/4, 3/4 extends from Y1 understanding of quarters
- Fraction Notation hard
Writing fractions like 1/3 and 3/4 requires knowing numerator and denominator
- Reading +, −, and = symbols soft
Writing fraction sentences (1/2 of 6 = 3) requires understanding the = sign
- Reading and writing numbers to 20 hard
Writing number sentences requires reading and writing numerals
- Addition as combining or putting together two hard
Reading/writing the + symbol requires understanding what addition means
- Subtraction as taking away or separating hard
Reading/writing the − symbol requires understanding what subtraction means
- Fractions of amounts hard
Writing fractions and recognising equivalence requires knowing what the fractions mean
- Finding halves and quarters (age 5+) hard
Working with 1/4, 2/4, 3/4 extends from Y1 understanding of quarters
- Fraction Notation hard
Writing fractions like 1/3 and 3/4 requires knowing numerator and denominator
- Fraction Notation hard
Writing fractions and recognising equivalence requires 'equivalent fraction' vocabulary
- Fractions of amounts hard
Recognising fractions of shapes/quantities is prerequisite to formal unit fraction understanding
- Finding halves and quarters (age 5+) hard
Working with 1/4, 2/4, 3/4 extends from Y1 understanding of quarters
- What Is a Half? hard
Understanding quarters extends from understanding halves — both are equal parts but quarters requires dividing into 4
- Division as equal sharing hard
Finding a half requires equal sharing into 2 groups — a division concept
- Subtraction as taking away or separating hard
Division as equal sharing/grouping requires understanding subtraction as taking away/separating
- Fraction Notation hard
Writing fractions like 1/3 and 3/4 requires knowing numerator and denominator
- Fraction Notation hard
Understanding a/b as a parts of 1/b requires numerator, denominator, and unit fraction vocabulary
- Splitting shapes into equal parts (age 7+) hard
Partition into equal shares is prerequisite to understanding unit fractions
- Decomposing a shape into more equal shares hard
Understanding equal shares of different shapes requires concept of more shares = smaller
- Halves & Quarters of Shapes hard
Comparing share sizes requires experience partitioning into halves and quarters
- Finding halves and quarters (age 5+) hard
Partitioning into fourths/quarters extends from Y1 understanding of quarters
- Fractions on a number line (age 8+) hard
Equivalent fractions as the same point on a number line directly uses the fraction number-line representation
- Fractions on a number line hard
Prior number-line fraction experience feeds into formal unit-fraction placement
- Finding halves and quarters (age 5+) hard
Working with 1/4, 2/4, 3/4 extends from Y1 understanding of quarters
- Fraction Notation hard
Writing fractions like 1/3 and 3/4 requires knowing numerator and denominator
- Fractions of amounts hard
Recognising fractions of shapes/quantities is prerequisite to formal unit fraction understanding
- Finding halves and quarters (age 5+) hard
Working with 1/4, 2/4, 3/4 extends from Y1 understanding of quarters
- Fraction Notation hard
Writing fractions like 1/3 and 3/4 requires knowing numerator and denominator
- Fraction Notation hard
Understanding a/b as a parts of 1/b requires numerator, denominator, and unit fraction vocabulary
- Splitting shapes into equal parts (age 7+) hard
Partition into equal shares is prerequisite to understanding unit fractions
- Decomposing a shape into more equal shares hard
Understanding equal shares of different shapes requires concept of more shares = smaller
- Factors, multiples, and primes hard
Using common factors/multiples requires knowledge of common factors and multiples
- All times tables to 12×12 hard
Tables to 12×12 fluency is prerequisite to finding factor pairs up to 100
- Skip Counting (4s, 8s, 50s, 100s) hard
Counting in 6s/7s/9s/25s/1000s extends counting in 4s/8s/50s/100s
- Multiplication as repeated addition hard
Recalling times table facts requires understanding multiplication as repeated addition/grouping
- Addition as combining or putting together two hard
Multiplication as repeated addition requires understanding addition as combining groups
- How Many in Total? hard
Understanding addition as combining groups requires knowing numbers represent quantities (cardinality)
- Factor Pairs & Commutativity hard
Recognising factor pairs at Y4 is prerequisite to systematically finding all factor pairs
- Skip Counting (4s, 8s, 50s, 100s) hard
Counting in 6s/7s/9s/25s/1000s extends counting in 4s/8s/50s/100s
- Multiplication as repeated addition hard
Recalling times table facts requires understanding multiplication as repeated addition/grouping
- Addition as combining or putting together two hard
Multiplication as repeated addition requires understanding addition as combining groups
- Commutative Multiplication hard
Applying all three properties extends Y2 commutativity understanding
- Division as equal sharing hard
Using arrays for division requires understanding division as grouping
- Subtraction as taking away or separating hard
Division as equal sharing/grouping requires understanding subtraction as taking away/separating
- Multiplication as repeated addition hard
Using arrays requires understanding what multiplication means
- Addition as combining or putting together two hard
Multiplication as repeated addition requires understanding addition as combining groups
- Multiplication as repeated addition hard
Commutativity of multiplication requires understanding multiplication
- Addition as combining or putting together two hard
Multiplication as repeated addition requires understanding addition as combining groups
- How Many in Total? hard
Understanding addition as combining groups requires knowing numbers represent quantities (cardinality)
- Arrays for multiplication (age 7+) hard
Extends array-based repeated addition to formal multiplication interpretation
- Arrays for multiplication hard
Rectangular arrays with repeated addition extends array representation from Y2
- Division as equal sharing hard
Using arrays for division requires understanding division as grouping
- Multiplication as repeated addition hard
Using arrays requires understanding what multiplication means
- Multiplication as repeated addition hard
Expressing array totals as sums of equal addends requires understanding multiplication as repeated addition
- Addition as combining or putting together two hard
Multiplication as repeated addition requires understanding addition as combining groups
- Multiplication as repeated addition hard
Interpreting products formalises repeated addition/equal groups from Y1
- Addition as combining or putting together two hard
Multiplication as repeated addition requires understanding addition as combining groups
- How Many in Total? hard
Understanding addition as combining groups requires knowing numbers represent quantities (cardinality)
- Fraction Notation hard
Simplifying fractions to simplest form requires 'simplest form' and 'common factor' vocabulary
- Bar Models for Ratios hard
Unequal sharing problems are the canonical use case for tape diagrams — the visual model makes the structure of the problem transparent
- Percentages (age 9+) hard
Unequal sharing problems require 'ratio', 'unequal', 'part-to-part', and 'proportion' vocabulary
- Equivalent fractions on a number line hard
Understanding equivalence conceptually is prerequisite to explaining algebraically
- Equivalent fractions hard
Diagram-based equivalent fractions is prerequisite to formal equivalence understanding
- Reading +, −, and = symbols soft
Writing fraction sentences (1/2 of 6 = 3) requires understanding the = sign
- Fractions of amounts hard
Writing fractions and recognising equivalence requires knowing what the fractions mean
- Fraction Notation hard
Writing fractions and recognising equivalence requires 'equivalent fraction' vocabulary
- Fractions of amounts hard
Recognising fractions of shapes/quantities is prerequisite to formal unit fraction understanding
- Finding halves and quarters (age 5+) hard
Working with 1/4, 2/4, 3/4 extends from Y1 understanding of quarters
- Fraction Notation hard
Writing fractions like 1/3 and 3/4 requires knowing numerator and denominator
- Fraction Notation hard
Understanding a/b as a parts of 1/b requires numerator, denominator, and unit fraction vocabulary
- Splitting shapes into equal parts (age 7+) hard
Partition into equal shares is prerequisite to understanding unit fractions
- Decomposing a shape into more equal shares hard
Understanding equal shares of different shapes requires concept of more shares = smaller
- Fractions on a number line (age 8+) hard
Equivalent fractions as the same point on a number line directly uses the fraction number-line representation
- Fractions on a number line hard
Prior number-line fraction experience feeds into formal unit-fraction placement
- Fractions of amounts hard
Recognising fractions of shapes/quantities is prerequisite to formal unit fraction understanding
- Fraction Notation hard
Understanding a/b as a parts of 1/b requires numerator, denominator, and unit fraction vocabulary
- Splitting shapes into equal parts (age 7+) hard
Partition into equal shares is prerequisite to understanding unit fractions
- Equivalent fractions (age 8+) hard
Generating equivalent fractions with visual models is prerequisite to algebraic explanation of equivalence
- Equivalent fractions on a number line hard
Must understand equivalence before generating equivalent fractions
- Equivalent fractions hard
Diagram-based equivalent fractions is prerequisite to formal equivalence understanding
- Fractions of amounts hard
Recognising fractions of shapes/quantities is prerequisite to formal unit fraction understanding
- Fraction Notation hard
Understanding a/b as a parts of 1/b requires numerator, denominator, and unit fraction vocabulary
- Splitting shapes into equal parts (age 7+) hard
Partition into equal shares is prerequisite to understanding unit fractions
- Fractions on a number line (age 8+) hard
Equivalent fractions as the same point on a number line directly uses the fraction number-line representation
- Fractions on a number line hard
Prior number-line fraction experience feeds into formal unit-fraction placement
- Factors, multiples, and primes hard
Using common factors/multiples requires knowledge of common factors and multiples
- All times tables to 12×12 hard
Tables to 12×12 fluency is prerequisite to finding factor pairs up to 100
- Skip Counting (4s, 8s, 50s, 100s) hard
Counting in 6s/7s/9s/25s/1000s extends counting in 4s/8s/50s/100s
- Multiplication as repeated addition hard
Recalling times table facts requires understanding multiplication as repeated addition/grouping
- Factor Pairs & Commutativity hard
Recognising factor pairs at Y4 is prerequisite to systematically finding all factor pairs
- Skip Counting (4s, 8s, 50s, 100s) hard
Counting in 6s/7s/9s/25s/1000s extends counting in 4s/8s/50s/100s
- Commutative Multiplication hard
Applying all three properties extends Y2 commutativity understanding
- Multiplication as repeated addition hard
Commutativity of multiplication requires understanding multiplication
- Arrays for multiplication (age 7+) hard
Extends array-based repeated addition to formal multiplication interpretation
- Multiplication as repeated addition hard
Interpreting products formalises repeated addition/equal groups from Y1
- Fraction Notation hard
Simplifying fractions to simplest form requires 'simplest form' and 'common factor' vocabulary
- Understanding fractions (age 9+) hard
a/b as sum of 1/b is prerequisite to understanding a/b as multiple of 1/b
- Fractions of a whole hard
Understanding a/b as a parts of size 1/b is prerequisite to understanding a/b as sum of 1/b
- Fractions of amounts hard
Recognising fractions of shapes/quantities is prerequisite to formal unit fraction understanding
- Finding halves and quarters (age 5+) hard
Working with 1/4, 2/4, 3/4 extends from Y1 understanding of quarters
- What Is a Half? hard
Understanding quarters extends from understanding halves — both are equal parts but quarters requires dividing into 4
- Division as equal sharing hard
Finding a half requires equal sharing into 2 groups — a division concept
- Subtraction as taking away or separating hard
Division as equal sharing/grouping requires understanding subtraction as taking away/separating
- Fraction Notation hard
Writing fractions like 1/3 and 3/4 requires knowing numerator and denominator
- Fraction Notation hard
Understanding a/b as a parts of 1/b requires numerator, denominator, and unit fraction vocabulary
- Splitting shapes into equal parts (age 7+) hard
Partition into equal shares is prerequisite to understanding unit fractions
- Decomposing a shape into more equal shares hard
Understanding equal shares of different shapes requires concept of more shares = smaller
- Halves & Quarters of Shapes hard
Comparing share sizes requires experience partitioning into halves and quarters
- Finding halves and quarters (age 5+) hard
Partitioning into fourths/quarters extends from Y1 understanding of quarters
- Bar Models for Ratios hard
Solving relative-sizes problems is most reliably scaffolded by drawing a bar model to set up the relationship
- Percentages (age 9+) hard
Solving relative sizes problems requires 'ratio', 'proportion', and 'relative size' as understood terms
- What Multiplication Means hard
Interpreting products is prerequisite to interpreting multiplication as comparison
- Arrays for multiplication (age 7+) hard
Extends array-based repeated addition to formal multiplication interpretation
- Arrays for multiplication hard
Rectangular arrays with repeated addition extends array representation from Y2
- Division as equal sharing hard
Using arrays for division requires understanding division as grouping
- Subtraction as taking away or separating hard
Division as equal sharing/grouping requires understanding subtraction as taking away/separating
- How Many in Total? hard
Understanding subtraction as taking away requires knowing numbers represent quantities (cardinality)
- Multiplication as repeated addition hard
Using arrays requires understanding what multiplication means
- Addition as combining or putting together two hard
Multiplication as repeated addition requires understanding addition as combining groups
- How Many in Total? hard
Understanding addition as combining groups requires knowing numbers represent quantities (cardinality)
- Multiplication as repeated addition hard
Expressing array totals as sums of equal addends requires understanding multiplication as repeated addition
- Addition as combining or putting together two hard
Multiplication as repeated addition requires understanding addition as combining groups
- How Many in Total? hard
Understanding addition as combining groups requires knowing numbers represent quantities (cardinality)
- One-to-one counting hard
Cardinality principle builds on one-to-one correspondence — you must count correctly to know the last number tells 'how many'
- Multiplication as repeated addition hard
Interpreting products formalises repeated addition/equal groups from Y1
- Addition as combining or putting together two hard
Multiplication as repeated addition requires understanding addition as combining groups
- How Many in Total? hard
Understanding addition as combining groups requires knowing numbers represent quantities (cardinality)
- One-to-one counting hard
Cardinality principle builds on one-to-one correspondence — you must count correctly to know the last number tells 'how many'
- Ratio Notation hard
Dividing in a ratio requires understanding ratio notation and simplification first
- Proportional Reasoning Vocabulary hard
Ratio notation (a:b) requires 'ratio', 'simplify', and 'equivalent' as defined terms
- Factors, multiples, and primes hard
Simplifying ratios requires finding common factors — extends KS2 factor pairs and common factors
- All times tables to 12×12 hard
Tables to 12×12 fluency is prerequisite to finding factor pairs up to 100
- Skip Counting (4s, 8s, 50s, 100s) hard
Counting in 6s/7s/9s/25s/1000s extends counting in 4s/8s/50s/100s
- Multiplication as repeated addition hard
Recalling times table facts requires understanding multiplication as repeated addition/grouping
- Addition as combining or putting together two hard
Multiplication as repeated addition requires understanding addition as combining groups
- How Many in Total? hard
Understanding addition as combining groups requires knowing numbers represent quantities (cardinality)
- One-to-one counting hard
Cardinality principle builds on one-to-one correspondence — you must count correctly to know the last number tells 'how many'
- Factor Pairs & Commutativity hard
Recognising factor pairs at Y4 is prerequisite to systematically finding all factor pairs
- Skip Counting (4s, 8s, 50s, 100s) hard
Counting in 6s/7s/9s/25s/1000s extends counting in 4s/8s/50s/100s
- Multiplication as repeated addition hard
Recalling times table facts requires understanding multiplication as repeated addition/grouping
- Addition as combining or putting together two hard
Multiplication as repeated addition requires understanding addition as combining groups
- How Many in Total? hard
Understanding addition as combining groups requires knowing numbers represent quantities (cardinality)
- Commutative Multiplication hard
Applying all three properties extends Y2 commutativity understanding
- Division as equal sharing hard
Using arrays for division requires understanding division as grouping
- Subtraction as taking away or separating hard
Division as equal sharing/grouping requires understanding subtraction as taking away/separating
- How Many in Total? hard
Understanding subtraction as taking away requires knowing numbers represent quantities (cardinality)
- Multiplication as repeated addition hard
Using arrays requires understanding what multiplication means
- Addition as combining or putting together two hard
Multiplication as repeated addition requires understanding addition as combining groups
- How Many in Total? hard
Understanding addition as combining groups requires knowing numbers represent quantities (cardinality)
- Multiplication as repeated addition hard
Commutativity of multiplication requires understanding multiplication
- Addition as combining or putting together two hard
Multiplication as repeated addition requires understanding addition as combining groups
- How Many in Total? hard
Understanding addition as combining groups requires knowing numbers represent quantities (cardinality)
- One-to-one counting hard
Cardinality principle builds on one-to-one correspondence — you must count correctly to know the last number tells 'how many'
- Arrays for multiplication (age 7+) hard
Extends array-based repeated addition to formal multiplication interpretation
- Arrays for multiplication hard
Rectangular arrays with repeated addition extends array representation from Y2
- Division as equal sharing hard
Using arrays for division requires understanding division as grouping
- Subtraction as taking away or separating hard
Division as equal sharing/grouping requires understanding subtraction as taking away/separating
- Multiplication as repeated addition hard
Using arrays requires understanding what multiplication means
- Addition as combining or putting together two hard
Multiplication as repeated addition requires understanding addition as combining groups
- Multiplication as repeated addition hard
Expressing array totals as sums of equal addends requires understanding multiplication as repeated addition
- Addition as combining or putting together two hard
Multiplication as repeated addition requires understanding addition as combining groups
- How Many in Total? hard
Understanding addition as combining groups requires knowing numbers represent quantities (cardinality)
- Multiplication as repeated addition hard
Interpreting products formalises repeated addition/equal groups from Y1
- Addition as combining or putting together two hard
Multiplication as repeated addition requires understanding addition as combining groups
- How Many in Total? hard
Understanding addition as combining groups requires knowing numbers represent quantities (cardinality)
- One-to-one counting hard
Cardinality principle builds on one-to-one correspondence — you must count correctly to know the last number tells 'how many'
- Understanding fractions hard
Ratio notation and simplification extends KS2 unequal sharing and grouping with ratios
- Simplifying Fractions hard
Understanding fraction of total requires simplification/common denominator skills
- Equivalent fractions on a number line hard
Understanding equivalence conceptually is prerequisite to explaining algebraically
- Equivalent fractions hard
Diagram-based equivalent fractions is prerequisite to formal equivalence understanding
- Finding halves and quarters (age 5+) hard
Working with 1/4, 2/4, 3/4 extends from Y1 understanding of quarters
- Fraction Notation hard
Writing fractions like 1/3 and 3/4 requires knowing numerator and denominator
- Reading +, −, and = symbols soft
Writing fraction sentences (1/2 of 6 = 3) requires understanding the = sign
- Reading and writing numbers to 20 hard
Writing number sentences requires reading and writing numerals
- Addition as combining or putting together two hard
Reading/writing the + symbol requires understanding what addition means
- Subtraction as taking away or separating hard
Reading/writing the − symbol requires understanding what subtraction means
- Fractions of amounts hard
Writing fractions and recognising equivalence requires knowing what the fractions mean
- Finding halves and quarters (age 5+) hard
Working with 1/4, 2/4, 3/4 extends from Y1 understanding of quarters
- Fraction Notation hard
Writing fractions like 1/3 and 3/4 requires knowing numerator and denominator
- Fraction Notation hard
Writing fractions and recognising equivalence requires 'equivalent fraction' vocabulary
- Fractions of amounts hard
Recognising fractions of shapes/quantities is prerequisite to formal unit fraction understanding
- Finding halves and quarters (age 5+) hard
Working with 1/4, 2/4, 3/4 extends from Y1 understanding of quarters
- What Is a Half? hard
Understanding quarters extends from understanding halves — both are equal parts but quarters requires dividing into 4
- Division as equal sharing hard
Finding a half requires equal sharing into 2 groups — a division concept
- Subtraction as taking away or separating hard
Division as equal sharing/grouping requires understanding subtraction as taking away/separating
- Fraction Notation hard
Writing fractions like 1/3 and 3/4 requires knowing numerator and denominator
- Fraction Notation hard
Understanding a/b as a parts of 1/b requires numerator, denominator, and unit fraction vocabulary
- Splitting shapes into equal parts (age 7+) hard
Partition into equal shares is prerequisite to understanding unit fractions
- Decomposing a shape into more equal shares hard
Understanding equal shares of different shapes requires concept of more shares = smaller
- Halves & Quarters of Shapes hard
Comparing share sizes requires experience partitioning into halves and quarters
- Finding halves and quarters (age 5+) hard
Partitioning into fourths/quarters extends from Y1 understanding of quarters
- Fractions on a number line (age 8+) hard
Equivalent fractions as the same point on a number line directly uses the fraction number-line representation
- Fractions on a number line hard
Prior number-line fraction experience feeds into formal unit-fraction placement
- Finding halves and quarters (age 5+) hard
Working with 1/4, 2/4, 3/4 extends from Y1 understanding of quarters
- Fraction Notation hard
Writing fractions like 1/3 and 3/4 requires knowing numerator and denominator
- Fractions of amounts hard
Recognising fractions of shapes/quantities is prerequisite to formal unit fraction understanding
- Finding halves and quarters (age 5+) hard
Working with 1/4, 2/4, 3/4 extends from Y1 understanding of quarters
- Fraction Notation hard
Writing fractions like 1/3 and 3/4 requires knowing numerator and denominator
- Fraction Notation hard
Understanding a/b as a parts of 1/b requires numerator, denominator, and unit fraction vocabulary
- Splitting shapes into equal parts (age 7+) hard
Partition into equal shares is prerequisite to understanding unit fractions
- Decomposing a shape into more equal shares hard
Understanding equal shares of different shapes requires concept of more shares = smaller
- Equivalent fractions (age 8+) hard
Generating equivalent fractions with visual models is prerequisite to algebraic explanation of equivalence
- Equivalent fractions on a number line hard
Must understand equivalence before generating equivalent fractions
- Equivalent fractions hard
Diagram-based equivalent fractions is prerequisite to formal equivalence understanding
- Reading +, −, and = symbols soft
Writing fraction sentences (1/2 of 6 = 3) requires understanding the = sign
- Fractions of amounts hard
Writing fractions and recognising equivalence requires knowing what the fractions mean
- Fraction Notation hard
Writing fractions and recognising equivalence requires 'equivalent fraction' vocabulary
- Fractions of amounts hard
Recognising fractions of shapes/quantities is prerequisite to formal unit fraction understanding
- Finding halves and quarters (age 5+) hard
Working with 1/4, 2/4, 3/4 extends from Y1 understanding of quarters
- Fraction Notation hard
Writing fractions like 1/3 and 3/4 requires knowing numerator and denominator
- Fraction Notation hard
Understanding a/b as a parts of 1/b requires numerator, denominator, and unit fraction vocabulary
- Splitting shapes into equal parts (age 7+) hard
Partition into equal shares is prerequisite to understanding unit fractions
- Decomposing a shape into more equal shares hard
Understanding equal shares of different shapes requires concept of more shares = smaller
- Fractions on a number line (age 8+) hard
Equivalent fractions as the same point on a number line directly uses the fraction number-line representation
- Fractions on a number line hard
Prior number-line fraction experience feeds into formal unit-fraction placement
- Fractions of amounts hard
Recognising fractions of shapes/quantities is prerequisite to formal unit fraction understanding
- Fraction Notation hard
Understanding a/b as a parts of 1/b requires numerator, denominator, and unit fraction vocabulary
- Splitting shapes into equal parts (age 7+) hard
Partition into equal shares is prerequisite to understanding unit fractions
- Factors, multiples, and primes hard
Using common factors/multiples requires knowledge of common factors and multiples
- All times tables to 12×12 hard
Tables to 12×12 fluency is prerequisite to finding factor pairs up to 100
- Skip Counting (4s, 8s, 50s, 100s) hard
Counting in 6s/7s/9s/25s/1000s extends counting in 4s/8s/50s/100s
- Multiplication as repeated addition hard
Recalling times table facts requires understanding multiplication as repeated addition/grouping
- Addition as combining or putting together two hard
Multiplication as repeated addition requires understanding addition as combining groups
- Factor Pairs & Commutativity hard
Recognising factor pairs at Y4 is prerequisite to systematically finding all factor pairs
- Skip Counting (4s, 8s, 50s, 100s) hard
Counting in 6s/7s/9s/25s/1000s extends counting in 4s/8s/50s/100s
- Multiplication as repeated addition hard
Recalling times table facts requires understanding multiplication as repeated addition/grouping
- Commutative Multiplication hard
Applying all three properties extends Y2 commutativity understanding
- Division as equal sharing hard
Using arrays for division requires understanding division as grouping
- Multiplication as repeated addition hard
Using arrays requires understanding what multiplication means
- Multiplication as repeated addition hard
Commutativity of multiplication requires understanding multiplication
- Addition as combining or putting together two hard
Multiplication as repeated addition requires understanding addition as combining groups
- Arrays for multiplication (age 7+) hard
Extends array-based repeated addition to formal multiplication interpretation
- Arrays for multiplication hard
Rectangular arrays with repeated addition extends array representation from Y2
- Multiplication as repeated addition hard
Expressing array totals as sums of equal addends requires understanding multiplication as repeated addition
- Multiplication as repeated addition hard
Interpreting products formalises repeated addition/equal groups from Y1
- Addition as combining or putting together two hard
Multiplication as repeated addition requires understanding addition as combining groups
- Fraction Notation hard
Simplifying fractions to simplest form requires 'simplest form' and 'common factor' vocabulary
- Bar Models for Ratios hard
Unequal sharing problems are the canonical use case for tape diagrams — the visual model makes the structure of the problem transparent
- Percentages (age 9+) hard
Unequal sharing problems require 'ratio', 'unequal', 'part-to-part', and 'proportion' vocabulary
- Equivalent fractions on a number line hard
Understanding equivalence conceptually is prerequisite to explaining algebraically
- Equivalent fractions hard
Diagram-based equivalent fractions is prerequisite to formal equivalence understanding
- Fractions of amounts hard
Recognising fractions of shapes/quantities is prerequisite to formal unit fraction understanding
- Fraction Notation hard
Understanding a/b as a parts of 1/b requires numerator, denominator, and unit fraction vocabulary
- Splitting shapes into equal parts (age 7+) hard
Partition into equal shares is prerequisite to understanding unit fractions
- Fractions on a number line (age 8+) hard
Equivalent fractions as the same point on a number line directly uses the fraction number-line representation
- Fractions on a number line hard
Prior number-line fraction experience feeds into formal unit-fraction placement
- Equivalent fractions (age 8+) hard
Generating equivalent fractions with visual models is prerequisite to algebraic explanation of equivalence
- Equivalent fractions on a number line hard
Must understand equivalence before generating equivalent fractions
- Equivalent fractions hard
Diagram-based equivalent fractions is prerequisite to formal equivalence understanding
- Fractions on a number line (age 8+) hard
Equivalent fractions as the same point on a number line directly uses the fraction number-line representation
- Factors, multiples, and primes hard
Using common factors/multiples requires knowledge of common factors and multiples
- All times tables to 12×12 hard
Tables to 12×12 fluency is prerequisite to finding factor pairs up to 100
- Skip Counting (4s, 8s, 50s, 100s) hard
Counting in 6s/7s/9s/25s/1000s extends counting in 4s/8s/50s/100s
- Factor Pairs & Commutativity hard
Recognising factor pairs at Y4 is prerequisite to systematically finding all factor pairs
- Commutative Multiplication hard
Applying all three properties extends Y2 commutativity understanding
- Fraction Notation hard
Simplifying fractions to simplest form requires 'simplest form' and 'common factor' vocabulary
- Understanding fractions (age 9+) hard
a/b as sum of 1/b is prerequisite to understanding a/b as multiple of 1/b
- Fractions of a whole hard
Understanding a/b as a parts of size 1/b is prerequisite to understanding a/b as sum of 1/b
- Fractions of amounts hard
Recognising fractions of shapes/quantities is prerequisite to formal unit fraction understanding
- Finding halves and quarters (age 5+) hard
Working with 1/4, 2/4, 3/4 extends from Y1 understanding of quarters
- Fraction Notation hard
Writing fractions like 1/3 and 3/4 requires knowing numerator and denominator
- Fraction Notation hard
Understanding a/b as a parts of 1/b requires numerator, denominator, and unit fraction vocabulary
- Splitting shapes into equal parts (age 7+) hard
Partition into equal shares is prerequisite to understanding unit fractions
- Decomposing a shape into more equal shares hard
Understanding equal shares of different shapes requires concept of more shares = smaller
- Bar Models for Ratios hard
Solving relative-sizes problems is most reliably scaffolded by drawing a bar model to set up the relationship
- Percentages (age 9+) hard
Solving relative sizes problems requires 'ratio', 'proportion', and 'relative size' as understood terms
- What Multiplication Means hard
Interpreting products is prerequisite to interpreting multiplication as comparison
- Arrays for multiplication (age 7+) hard
Extends array-based repeated addition to formal multiplication interpretation
- Arrays for multiplication hard
Rectangular arrays with repeated addition extends array representation from Y2
- Division as equal sharing hard
Using arrays for division requires understanding division as grouping
- Subtraction as taking away or separating hard
Division as equal sharing/grouping requires understanding subtraction as taking away/separating
- Multiplication as repeated addition hard
Using arrays requires understanding what multiplication means
- Addition as combining or putting together two hard
Multiplication as repeated addition requires understanding addition as combining groups
- Multiplication as repeated addition hard
Expressing array totals as sums of equal addends requires understanding multiplication as repeated addition
- Addition as combining or putting together two hard
Multiplication as repeated addition requires understanding addition as combining groups
- How Many in Total? hard
Understanding addition as combining groups requires knowing numbers represent quantities (cardinality)
- Multiplication as repeated addition hard
Interpreting products formalises repeated addition/equal groups from Y1
- Addition as combining or putting together two hard
Multiplication as repeated addition requires understanding addition as combining groups
- How Many in Total? hard
Understanding addition as combining groups requires knowing numbers represent quantities (cardinality)
- One-to-one counting hard
Cardinality principle builds on one-to-one correspondence — you must count correctly to know the last number tells 'how many'
- Proportion Graphs soft
Ratio notation and simplification is complemented by double number line representations
- Linear Function Graphs soft
Graphical representations of proportion connect to linear graphs (y = kx through origin)
- Coordinates (age 8+) hard
Plotting in all four quadrants extends first-quadrant coordinate grid plotting skills
- Position, direction, and movement soft
Position/direction vocabulary supports understanding coordinate grid
- Positional Language hard
Position/direction vocabulary with right angles extends basic positional language
- Turns & Directions hard
Right-angle turns (clockwise/anti-clockwise) build directly on whole/half/quarter turns from Year 1
- What Is a Half? soft
Understanding half and quarter turns benefits from the concept of halves and quarters
- Division as equal sharing hard
Finding a half requires equal sharing into 2 groups — a division concept
- Subtraction as taking away or separating hard
Division as equal sharing/grouping requires understanding subtraction as taking away/separating
- How Many in Total? hard
Understanding subtraction as taking away requires knowing numbers represent quantities (cardinality)
- 2-D shapes (age 6+) hard
Identifying 2D shape properties is prerequisite to classifying by shared attributes
- Angles in triangles (age 6+) soft
Understanding defining attributes supports describing shape properties formally
- 2-D shapes hard
Distinguishing defining vs non-defining attributes requires knowing common 2-D shape names first
- 3-D shapes (age 5+) hard
Identifying defining attributes builds on informal analysis and comparison of shapes
- 2-D shapes hard
Describing properties of 2-D shapes (sides, symmetry) requires knowing the shapes first
- 3-D shapes (age 5+) hard
Formal property description extends informal analysis of sides and vertices
- Angles in triangles (age 7+) hard
Recognising shapes by attributes is prerequisite to quadrilateral hierarchy classification
- Angles in triangles (age 6+) hard
Drawing shapes by attributes extends understanding defining vs non-defining attributes
- 2-D shapes hard
Distinguishing defining vs non-defining attributes requires knowing common 2-D shape names first
- 3-D shapes (age 5+) hard
Identifying defining attributes builds on informal analysis and comparison of shapes
- 2-D shapes (age 6+) hard
Identifying pentagons, hexagons, quadrilaterals extends knowing 2-D shape properties
- Angles in triangles (age 6+) soft
Understanding defining attributes supports describing shape properties formally
- 2-D shapes hard
Distinguishing defining vs non-defining attributes requires knowing common 2-D shape names first
- 3-D shapes (age 5+) hard
Identifying defining attributes builds on informal analysis and comparison of shapes
- 2-D shapes hard
Describing properties of 2-D shapes (sides, symmetry) requires knowing the shapes first
- 3-D shapes (age 5+) hard
Formal property description extends informal analysis of sides and vertices
- Coordinates (age 8+) hard
Working across the full coordinate grid requires first-quadrant plotting as a foundation
- Position, direction, and movement soft
Position/direction vocabulary supports understanding coordinate grid
- Positional Language hard
Position/direction vocabulary with right angles extends basic positional language
- Turns & Directions hard
Right-angle turns (clockwise/anti-clockwise) build directly on whole/half/quarter turns from Year 1
- What Is a Half? soft
Understanding half and quarter turns benefits from the concept of halves and quarters
- Division as equal sharing hard
Finding a half requires equal sharing into 2 groups — a division concept
- Subtraction as taking away or separating hard
Division as equal sharing/grouping requires understanding subtraction as taking away/separating
- 2-D shapes (age 6+) hard
Identifying 2D shape properties is prerequisite to classifying by shared attributes
- Angles in triangles (age 6+) soft
Understanding defining attributes supports describing shape properties formally
- 2-D shapes hard
Distinguishing defining vs non-defining attributes requires knowing common 2-D shape names first
- 3-D shapes (age 5+) hard
Identifying defining attributes builds on informal analysis and comparison of shapes
- 2-D shapes hard
Describing properties of 2-D shapes (sides, symmetry) requires knowing the shapes first
- 3-D shapes (age 5+) hard
Formal property description extends informal analysis of sides and vertices
- Angles in triangles (age 7+) hard
Recognising shapes by attributes is prerequisite to quadrilateral hierarchy classification
- Angles in triangles (age 6+) hard
Drawing shapes by attributes extends understanding defining vs non-defining attributes
- 2-D shapes hard
Distinguishing defining vs non-defining attributes requires knowing common 2-D shape names first
- 3-D shapes (age 5+) hard
Identifying defining attributes builds on informal analysis and comparison of shapes
- 2-D shapes (age 6+) hard
Identifying pentagons, hexagons, quadrilaterals extends knowing 2-D shape properties
- Angles in triangles (age 6+) soft
Understanding defining attributes supports describing shape properties formally
- 2-D shapes hard
Distinguishing defining vs non-defining attributes requires knowing common 2-D shape names first
- 3-D shapes (age 5+) hard
Identifying defining attributes builds on informal analysis and comparison of shapes
- 2-D shapes hard
Describing properties of 2-D shapes (sides, symmetry) requires knowing the shapes first
- 3-D shapes (age 5+) hard
Formal property description extends informal analysis of sides and vertices
- Negative numbers in context hard
Calculating intervals across zero extends Y5 negative number context
- Negative Numbers hard
Counting through zero is prerequisite to interpreting negative numbers in context
- The two digits of a two-digit number hard
Must understand two-digit place value before extending to hundreds
- Transformations on a grid soft
Working with the full coordinate grid (all four quadrants) extends the transformation diagram to negative coordinates
- Types of angles hard
Y4 acute/obtuse angle identification is prerequisite to drawing and labelling angle types
- Right Angles & Turns hard
Identifying right angles and greater/less than right angle is prerequisite to naming acute/obtuse
- 2-D shapes (age 6+) soft
Understanding angles as shape properties requires knowing basic shape properties
- Position, direction, and movement hard
Recognising angles as turns extends Y2 work on quarter/half/three-quarter turns
- Types of angles (age 8+) soft
Identifying right angles and turns is supported by the convention of marking right angles with a small square
- Positional Language hard
Position/direction vocabulary with right angles extends basic positional language
- Turns & Directions hard
Right-angle turns (clockwise/anti-clockwise) build directly on whole/half/quarter turns from Year 1
- Parallel and perpendicular lines hard
Y3 horizontal/vertical/perpendicular/parallel lines is prerequisite to drawing and identifying them formally
- 2-D shapes (age 6+) soft
Understanding angles as shape properties requires knowing basic shape properties
- Position, direction, and movement hard
Recognising angles as turns extends Y2 work on quarter/half/three-quarter turns
- Types of angles (age 8+) soft
Identifying right angles and turns is supported by the convention of marking right angles with a small square
- Positional Language hard
Position/direction vocabulary with right angles extends basic positional language
- Turns & Directions hard
Right-angle turns (clockwise/anti-clockwise) build directly on whole/half/quarter turns from Year 1
- Fractions on a number line (age 11+) hard
Plotting coordinates in all four quadrants requires understanding positive and negative values on both axes
- Positive and Negative Numbers hard
Ordering all number types (integers, decimals, fractions) on a number line extends the negative-number number-line representation
- Negative numbers in context hard
Calculating intervals across zero extends Y5 negative number context
- Negative Numbers hard
Counting through zero is prerequisite to interpreting negative numbers in context
- Fractions on a number line hard
Ordering all number types requires understanding place value across the full system
- Reading and writing numbers to 10,000,000 hard
Extending place value to any size builds directly on Y6 reading/writing/ordering numbers to 10,000,000
- Decimals for Tenths & Hundredths hard
Decimal notation for 10ths/100ths is prerequisite to extending to thousandths
- Tenths (age 8+) hard
Understanding hundredths is prerequisite to working with 10ths and 100ths together
- Equivalent fractions (age 9+) hard
Generating equivalent fractions supports converting 10ths to 100ths
- Decimal equivalents of tenths and hundredths hard
Y4 decimal equivalents of 10ths/100ths is prerequisite to formal decimal notation for fractions
- Decimal & Percent Notation hard
Writing decimal equivalents of tenths and hundredths requires decimal point and place-value vocabulary
- Decimal & Percent Notation hard
Using decimal notation for fractions requires decimal, tenths, and hundredths vocabulary
- Place value of each digit hard
Four-digit place value is prerequisite to understanding ×10 relationship between places
- The three digits of a three-digit number hard
Four-digit place value extends three-digit place value
- The three digits of a three-digit number hard
Comparing three-digit numbers requires three-digit place value
- The two digits of a two-digit number hard
Comparing two-digit numbers using PV requires understanding tens and ones
- Two written numerals between 1 and 10 soft
Comparing two-digit numbers extends from comparing single-digit written numerals
- The three digits of a three-digit number hard
Four-digit place value extends three-digit place value
- Numbers to 10,000 hard
Ordering and comparing numbers over 1000 requires the full 10,000 representations toolkit
- The three digits of a three-digit number hard
Representing numbers requires place-value understanding
- Representing numbers with objects hard
Representing and estimating numbers on a number line builds on Y1 number representations
- The two digits of a two-digit number soft
Estimating placement on a 0-100 number line benefits from place value understanding
- The three digits of a three-digit number hard
Four-digit place value extends three-digit place value
- Place Value × 10 Pattern hard
Understanding ×10 place-value relationship supports reading/writing larger numbers
- Place value of each digit hard
Four-digit place value is prerequisite to understanding ×10 relationship between places
- The three digits of a three-digit number hard
Four-digit place value extends three-digit place value
- Measuring temperature hard
Ordering with inequality symbols extends Y6 work with negative numbers in context
- Negative numbers in context hard
Calculating intervals across zero extends Y5 negative number context
- Negative Numbers hard
Counting through zero is prerequisite to interpreting negative numbers in context
- The two digits of a two-digit number hard
Must understand two-digit place value before extending to hundreds
- Substituting into Formulae hard
Interpreting y = mx + c requires substitution to generate coordinate pairs
- Writing Algebraic Equations hard
Algebraic notation builds on KS2 expressing missing-number problems algebraically
- Writing Number Sentences hard
Writing algebraic expressions extends writing/interpreting numerical expressions
- Brackets in Expressions hard
Writing/interpreting expressions requires understanding grouping symbols
- Division with remainders hard
Evaluating grouped expressions formalises multi-step calculation skills from Y5
- Multiply & Add Problems hard
Y4 M×D problem-solving is prerequisite to multi-step four-operation problems
- Written Multiplication & Division hard
Formal short multiplication extends Y3 written multiplication
- Multiplication as repeated addition (age 6+) hard
Scaling and correspondence problems extend Y2 problem-solving with mult/div
- Commutative Multiplication hard
Applying all three properties extends Y2 commutativity understanding
- Arrays for multiplication (age 9+) hard
Must have formal division method before solving multi-step problems
- Division as Unknown Factor hard
Understanding division as unknown-factor supports short division strategy
- What Multiplication Means hard
Connecting division to multiplication requires understanding products
- Fluent multiplication and division facts hard
Fluent ×÷ within 100 is prerequisite to short division of larger numbers
- Written Multiplication hard
2/3-digit × 1-digit written method is prerequisite to 4-digit × 1-digit and 2-digit × 2-digit
- Written Multiplication & Division hard
Formal short multiplication extends Y3 written multiplication
- Area and the distributive property soft
Area models for distributive property support understanding long multiplication layout
- Understanding angles (age 8+) hard
Must multiply side lengths for area before using area models for distributive property
- Written Multiplication hard
2/3-digit × 1-digit written method is prerequisite to 4-digit × 1-digit and 2-digit × 2-digit
- Written Multiplication & Division hard
Formal short multiplication extends Y3 written multiplication
- Area and the distributive property soft
Area models for distributive property support understanding long multiplication layout
- Understanding angles (age 8+) hard
Must multiply side lengths for area before using area models for distributive property
- Brackets in Expressions hard
The full BODMAS/PEMDAS convention extends understanding of grouping symbols to all operations
- Division with remainders hard
Evaluating grouped expressions formalises multi-step calculation skills from Y5
- Multiply & Add Problems hard
Y4 M×D problem-solving is prerequisite to multi-step four-operation problems
- Written Multiplication & Division hard
Formal short multiplication extends Y3 written multiplication
- Multiplication as repeated addition (age 6+) hard
Scaling and correspondence problems extend Y2 problem-solving with mult/div
- Commutative Multiplication hard
Applying all three properties extends Y2 commutativity understanding
- Arrays for multiplication (age 9+) hard
Must have formal division method before solving multi-step problems
- Division as Unknown Factor hard
Understanding division as unknown-factor supports short division strategy
- What Multiplication Means hard
Connecting division to multiplication requires understanding products
- Fluent multiplication and division facts hard
Fluent ×÷ within 100 is prerequisite to short division of larger numbers
- Written Multiplication hard
2/3-digit × 1-digit written method is prerequisite to 4-digit × 1-digit and 2-digit × 2-digit
- Written Multiplication & Division hard
Formal short multiplication extends Y3 written multiplication
- Area and the distributive property soft
Area models for distributive property support understanding long multiplication layout
- Understanding angles (age 8+) hard
Must multiply side lengths for area before using area models for distributive property
- Written Multiplication hard
2/3-digit × 1-digit written method is prerequisite to 4-digit × 1-digit and 2-digit × 2-digit
- Written Multiplication & Division hard
Formal short multiplication extends Y3 written multiplication
- Area and the distributive property soft
Area models for distributive property support understanding long multiplication layout
- Understanding angles (age 8+) hard
Must multiply side lengths for area before using area models for distributive property
- Brackets in Expressions hard
Writing/interpreting expressions requires understanding grouping symbols
- Division with remainders hard
Evaluating grouped expressions formalises multi-step calculation skills from Y5
- Multiply & Add Problems hard
Y4 M×D problem-solving is prerequisite to multi-step four-operation problems
- Written Multiplication & Division hard
Formal short multiplication extends Y3 written multiplication
- Multiplication as repeated addition (age 6+) hard
Scaling and correspondence problems extend Y2 problem-solving with mult/div
- Commutative Multiplication hard
Applying all three properties extends Y2 commutativity understanding
- Arrays for multiplication (age 9+) hard
Must have formal division method before solving multi-step problems
- Division as Unknown Factor hard
Understanding division as unknown-factor supports short division strategy
- What Multiplication Means hard
Connecting division to multiplication requires understanding products
- Fluent multiplication and division facts hard
Fluent ×÷ within 100 is prerequisite to short division of larger numbers
- Written Multiplication hard
2/3-digit × 1-digit written method is prerequisite to 4-digit × 1-digit and 2-digit × 2-digit
- Written Multiplication & Division hard
Formal short multiplication extends Y3 written multiplication
- Area and the distributive property soft
Area models for distributive property support understanding long multiplication layout
- Understanding angles (age 8+) hard
Must multiply side lengths for area before using area models for distributive property
- Written Multiplication hard
2/3-digit × 1-digit written method is prerequisite to 4-digit × 1-digit and 2-digit × 2-digit
- Written Multiplication & Division hard
Formal short multiplication extends Y3 written multiplication
- Area and the distributive property soft
Area models for distributive property support understanding long multiplication layout
- Understanding angles (age 8+) hard
Must multiply side lengths for area before using area models for distributive property
- Brackets in Expressions hard
The full BODMAS/PEMDAS convention extends understanding of grouping symbols to all operations
- Division with remainders hard
Evaluating grouped expressions formalises multi-step calculation skills from Y5
- Multiply & Add Problems hard
Y4 M×D problem-solving is prerequisite to multi-step four-operation problems
- Written Multiplication & Division hard
Formal short multiplication extends Y3 written multiplication
- Multiplication as repeated addition (age 6+) hard
Scaling and correspondence problems extend Y2 problem-solving with mult/div
- Commutative Multiplication hard
Applying all three properties extends Y2 commutativity understanding
- Arrays for multiplication (age 9+) hard
Must have formal division method before solving multi-step problems
- Division as Unknown Factor hard
Understanding division as unknown-factor supports short division strategy
- What Multiplication Means hard
Connecting division to multiplication requires understanding products
- Fluent multiplication and division facts hard
Fluent ×÷ within 100 is prerequisite to short division of larger numbers
- Written Multiplication hard
2/3-digit × 1-digit written method is prerequisite to 4-digit × 1-digit and 2-digit × 2-digit
- Written Multiplication & Division hard
Formal short multiplication extends Y3 written multiplication
- Area and the distributive property soft
Area models for distributive property support understanding long multiplication layout
- Understanding angles (age 8+) hard
Must multiply side lengths for area before using area models for distributive property
- Written Multiplication hard
2/3-digit × 1-digit written method is prerequisite to 4-digit × 1-digit and 2-digit × 2-digit
- Written Multiplication & Division hard
Formal short multiplication extends Y3 written multiplication
- Area and the distributive property soft
Area models for distributive property support understanding long multiplication layout
- Understanding angles (age 8+) hard
Must multiply side lengths for area before using area models for distributive property
- Algebraic Transformations hard
Recognising the relationship between y=mx+c and its graph requires moving fluently between algebraic and graphical representations
- Writing Algebraic Equations hard
Algebraic notation builds on KS2 expressing missing-number problems algebraically
- Writing Number Sentences hard
Writing algebraic expressions extends writing/interpreting numerical expressions
- Brackets in Expressions hard
Writing/interpreting expressions requires understanding grouping symbols
- Division with remainders hard
Evaluating grouped expressions formalises multi-step calculation skills from Y5
- Multiply & Add Problems hard
Y4 M×D problem-solving is prerequisite to multi-step four-operation problems
- Written Multiplication & Division hard
Formal short multiplication extends Y3 written multiplication
- Multiplication as repeated addition (age 6+) hard
Scaling and correspondence problems extend Y2 problem-solving with mult/div
- Commutative Multiplication hard
Applying all three properties extends Y2 commutativity understanding
- Arrays for multiplication (age 9+) hard
Must have formal division method before solving multi-step problems
- Division as Unknown Factor hard
Understanding division as unknown-factor supports short division strategy
- What Multiplication Means hard
Connecting division to multiplication requires understanding products
- Fluent multiplication and division facts hard
Fluent ×÷ within 100 is prerequisite to short division of larger numbers
- Written Multiplication hard
2/3-digit × 1-digit written method is prerequisite to 4-digit × 1-digit and 2-digit × 2-digit
- Written Multiplication & Division hard
Formal short multiplication extends Y3 written multiplication
- Area and the distributive property soft
Area models for distributive property support understanding long multiplication layout
- Understanding angles (age 8+) hard
Must multiply side lengths for area before using area models for distributive property
- Written Multiplication hard
2/3-digit × 1-digit written method is prerequisite to 4-digit × 1-digit and 2-digit × 2-digit
- Written Multiplication & Division hard
Formal short multiplication extends Y3 written multiplication
- Area and the distributive property soft
Area models for distributive property support understanding long multiplication layout
- Understanding angles (age 8+) hard
Must multiply side lengths for area before using area models for distributive property
- Brackets in Expressions hard
The full BODMAS/PEMDAS convention extends understanding of grouping symbols to all operations
- Division with remainders hard
Evaluating grouped expressions formalises multi-step calculation skills from Y5
- Multiply & Add Problems hard
Y4 M×D problem-solving is prerequisite to multi-step four-operation problems
- Written Multiplication & Division hard
Formal short multiplication extends Y3 written multiplication
- Multiplication as repeated addition (age 6+) hard
Scaling and correspondence problems extend Y2 problem-solving with mult/div
- Commutative Multiplication hard
Applying all three properties extends Y2 commutativity understanding
- Arrays for multiplication (age 9+) hard
Must have formal division method before solving multi-step problems
- Division as Unknown Factor hard
Understanding division as unknown-factor supports short division strategy
- What Multiplication Means hard
Connecting division to multiplication requires understanding products
- Fluent multiplication and division facts hard
Fluent ×÷ within 100 is prerequisite to short division of larger numbers
- Written Multiplication hard
2/3-digit × 1-digit written method is prerequisite to 4-digit × 1-digit and 2-digit × 2-digit
- Written Multiplication & Division hard
Formal short multiplication extends Y3 written multiplication
- Area and the distributive property soft
Area models for distributive property support understanding long multiplication layout
- Understanding angles (age 8+) hard
Must multiply side lengths for area before using area models for distributive property
- Written Multiplication hard
2/3-digit × 1-digit written method is prerequisite to 4-digit × 1-digit and 2-digit × 2-digit
- Written Multiplication & Division hard
Formal short multiplication extends Y3 written multiplication
- Area and the distributive property soft
Area models for distributive property support understanding long multiplication layout
- Understanding angles (age 8+) hard
Must multiply side lengths for area before using area models for distributive property
- Brackets in Expressions hard
Writing/interpreting expressions requires understanding grouping symbols
- Division with remainders hard
Evaluating grouped expressions formalises multi-step calculation skills from Y5
- Multiply & Add Problems hard
Y4 M×D problem-solving is prerequisite to multi-step four-operation problems
- Written Multiplication & Division hard
Formal short multiplication extends Y3 written multiplication
- Multiplication as repeated addition (age 6+) hard
Scaling and correspondence problems extend Y2 problem-solving with mult/div
- Commutative Multiplication hard
Applying all three properties extends Y2 commutativity understanding
- Arrays for multiplication (age 9+) hard
Must have formal division method before solving multi-step problems
- Division as Unknown Factor hard
Understanding division as unknown-factor supports short division strategy
- What Multiplication Means hard
Connecting division to multiplication requires understanding products
- Fluent multiplication and division facts hard
Fluent ×÷ within 100 is prerequisite to short division of larger numbers
- Written Multiplication hard
2/3-digit × 1-digit written method is prerequisite to 4-digit × 1-digit and 2-digit × 2-digit
- Written Multiplication & Division hard
Formal short multiplication extends Y3 written multiplication
- Area and the distributive property soft
Area models for distributive property support understanding long multiplication layout
- Understanding angles (age 8+) hard
Must multiply side lengths for area before using area models for distributive property
- Written Multiplication hard
2/3-digit × 1-digit written method is prerequisite to 4-digit × 1-digit and 2-digit × 2-digit
- Written Multiplication & Division hard
Formal short multiplication extends Y3 written multiplication
- Area and the distributive property soft
Area models for distributive property support understanding long multiplication layout
- Understanding angles (age 8+) hard
Must multiply side lengths for area before using area models for distributive property
- Brackets in Expressions hard
The full BODMAS/PEMDAS convention extends understanding of grouping symbols to all operations
- Division with remainders hard
Evaluating grouped expressions formalises multi-step calculation skills from Y5
- Multiply & Add Problems hard
Y4 M×D problem-solving is prerequisite to multi-step four-operation problems
- Written Multiplication & Division hard
Formal short multiplication extends Y3 written multiplication
- Multiplication as repeated addition (age 6+) hard
Scaling and correspondence problems extend Y2 problem-solving with mult/div
- Commutative Multiplication hard
Applying all three properties extends Y2 commutativity understanding
- Arrays for multiplication (age 9+) hard
Must have formal division method before solving multi-step problems
- Division as Unknown Factor hard
Understanding division as unknown-factor supports short division strategy
- What Multiplication Means hard
Connecting division to multiplication requires understanding products
- Fluent multiplication and division facts hard
Fluent ×÷ within 100 is prerequisite to short division of larger numbers
- Written Multiplication hard
2/3-digit × 1-digit written method is prerequisite to 4-digit × 1-digit and 2-digit × 2-digit
- Written Multiplication & Division hard
Formal short multiplication extends Y3 written multiplication
- Area and the distributive property soft
Area models for distributive property support understanding long multiplication layout
- Understanding angles (age 8+) hard
Must multiply side lengths for area before using area models for distributive property
- Written Multiplication hard
2/3-digit × 1-digit written method is prerequisite to 4-digit × 1-digit and 2-digit × 2-digit
- Written Multiplication & Division hard
Formal short multiplication extends Y3 written multiplication
- Area and the distributive property soft
Area models for distributive property support understanding long multiplication layout
- Understanding angles (age 8+) hard
Must multiply side lengths for area before using area models for distributive property
- Expressions & Equations Vocabulary hard
Collecting like terms requires knowing what terms, coefficients, and like terms mean
- Writing Algebraic Equations hard
Algebraic notation builds on KS2 expressing missing-number problems algebraically
- Writing Number Sentences hard
Writing algebraic expressions extends writing/interpreting numerical expressions
- Brackets in Expressions hard
Writing/interpreting expressions requires understanding grouping symbols
- Brackets in Expressions hard
The full BODMAS/PEMDAS convention extends understanding of grouping symbols to all operations
- Brackets in Expressions hard
Writing/interpreting expressions requires understanding grouping symbols
- Brackets in Expressions hard
The full BODMAS/PEMDAS convention extends understanding of grouping symbols to all operations
- Writing Number Sentences hard
Writing algebraic expressions extends writing/interpreting numerical expressions
- Brackets in Expressions hard
Writing/interpreting expressions requires understanding grouping symbols
- Division with remainders hard
Evaluating grouped expressions formalises multi-step calculation skills from Y5
- Multiply & Add Problems hard
Y4 M×D problem-solving is prerequisite to multi-step four-operation problems
- Written Multiplication & Division hard
Formal short multiplication extends Y3 written multiplication
- Multiplication as repeated addition (age 6+) hard
Scaling and correspondence problems extend Y2 problem-solving with mult/div
- Commutative Multiplication hard
Applying all three properties extends Y2 commutativity understanding
- Arrays for multiplication (age 9+) hard
Must have formal division method before solving multi-step problems
- Division as Unknown Factor hard
Understanding division as unknown-factor supports short division strategy
- What Multiplication Means hard
Connecting division to multiplication requires understanding products
- Fluent multiplication and division facts hard
Fluent ×÷ within 100 is prerequisite to short division of larger numbers
- Written Multiplication hard
2/3-digit × 1-digit written method is prerequisite to 4-digit × 1-digit and 2-digit × 2-digit
- Written Multiplication & Division hard
Formal short multiplication extends Y3 written multiplication
- Area and the distributive property soft
Area models for distributive property support understanding long multiplication layout
- Understanding angles (age 8+) hard
Must multiply side lengths for area before using area models for distributive property
- Written Multiplication hard
2/3-digit × 1-digit written method is prerequisite to 4-digit × 1-digit and 2-digit × 2-digit
- Written Multiplication & Division hard
Formal short multiplication extends Y3 written multiplication
- Area and the distributive property soft
Area models for distributive property support understanding long multiplication layout
- Understanding angles (age 8+) hard
Must multiply side lengths for area before using area models for distributive property
- Brackets in Expressions hard
The full BODMAS/PEMDAS convention extends understanding of grouping symbols to all operations
- Division with remainders hard
Evaluating grouped expressions formalises multi-step calculation skills from Y5
- Multiply & Add Problems hard
Y4 M×D problem-solving is prerequisite to multi-step four-operation problems
- Written Multiplication & Division hard
Formal short multiplication extends Y3 written multiplication
- Multiplication as repeated addition (age 6+) hard
Scaling and correspondence problems extend Y2 problem-solving with mult/div
- Commutative Multiplication hard
Applying all three properties extends Y2 commutativity understanding
- Arrays for multiplication (age 9+) hard
Must have formal division method before solving multi-step problems
- Division as Unknown Factor hard
Understanding division as unknown-factor supports short division strategy
- What Multiplication Means hard
Connecting division to multiplication requires understanding products
- Fluent multiplication and division facts hard
Fluent ×÷ within 100 is prerequisite to short division of larger numbers
- Written Multiplication hard
2/3-digit × 1-digit written method is prerequisite to 4-digit × 1-digit and 2-digit × 2-digit
- Written Multiplication & Division hard
Formal short multiplication extends Y3 written multiplication
- Area and the distributive property soft
Area models for distributive property support understanding long multiplication layout
- Understanding angles (age 8+) hard
Must multiply side lengths for area before using area models for distributive property
- Written Multiplication hard
2/3-digit × 1-digit written method is prerequisite to 4-digit × 1-digit and 2-digit × 2-digit
- Written Multiplication & Division hard
Formal short multiplication extends Y3 written multiplication
- Area and the distributive property soft
Area models for distributive property support understanding long multiplication layout
- Understanding angles (age 8+) hard
Must multiply side lengths for area before using area models for distributive property
- Writing Algebraic Equations hard
Algebraic notation builds on KS2 expressing missing-number problems algebraically
- Writing Number Sentences hard
Writing algebraic expressions extends writing/interpreting numerical expressions
- Brackets in Expressions hard
Writing/interpreting expressions requires understanding grouping symbols
- Division with remainders hard
Evaluating grouped expressions formalises multi-step calculation skills from Y5
- Multiply & Add Problems hard
Y4 M×D problem-solving is prerequisite to multi-step four-operation problems
- Arrays for multiplication (age 9+) hard
Must have formal division method before solving multi-step problems
- Brackets in Expressions hard
The full BODMAS/PEMDAS convention extends understanding of grouping symbols to all operations
- Division with remainders hard
Evaluating grouped expressions formalises multi-step calculation skills from Y5
- Multiply & Add Problems hard
Y4 M×D problem-solving is prerequisite to multi-step four-operation problems
- Arrays for multiplication (age 9+) hard
Must have formal division method before solving multi-step problems
- Brackets in Expressions hard
Writing/interpreting expressions requires understanding grouping symbols
- Division with remainders hard
Evaluating grouped expressions formalises multi-step calculation skills from Y5
- Multiply & Add Problems hard
Y4 M×D problem-solving is prerequisite to multi-step four-operation problems
- Arrays for multiplication (age 9+) hard
Must have formal division method before solving multi-step problems
- Brackets in Expressions hard
The full BODMAS/PEMDAS convention extends understanding of grouping symbols to all operations
- Division with remainders hard
Evaluating grouped expressions formalises multi-step calculation skills from Y5
- Multiply & Add Problems hard
Y4 M×D problem-solving is prerequisite to multi-step four-operation problems
- Arrays for multiplication (age 9+) hard
Must have formal division method before solving multi-step problems
- Using inverse operations hard
Solving linear equations by rearrangement requires applying inverse operations to isolate an unknown
- Order of operations hard
Understanding order of operations (BODMAS) is required before studying how operations undo each other via inverse relationships
- Brackets in Expressions hard
The full BODMAS/PEMDAS convention extends understanding of grouping symbols to all operations
- Division with remainders hard
Evaluating grouped expressions formalises multi-step calculation skills from Y5
- Multiply & Add Problems hard
Y4 M×D problem-solving is prerequisite to multi-step four-operation problems
- Written Multiplication & Division hard
Formal short multiplication extends Y3 written multiplication
- Multiplication as repeated addition (age 6+) hard
Scaling and correspondence problems extend Y2 problem-solving with mult/div
- Commutative Multiplication hard
Applying all three properties extends Y2 commutativity understanding
- Arrays for multiplication (age 9+) hard
Must have formal division method before solving multi-step problems
- Division as Unknown Factor hard
Understanding division as unknown-factor supports short division strategy
- What Multiplication Means hard
Connecting division to multiplication requires understanding products
- Fluent multiplication and division facts hard
Fluent ×÷ within 100 is prerequisite to short division of larger numbers
- Written Multiplication hard
2/3-digit × 1-digit written method is prerequisite to 4-digit × 1-digit and 2-digit × 2-digit
- Written Multiplication & Division hard
Formal short multiplication extends Y3 written multiplication
- Area and the distributive property soft
Area models for distributive property support understanding long multiplication layout
- Understanding angles (age 8+) hard
Must multiply side lengths for area before using area models for distributive property
- Written Multiplication hard
2/3-digit × 1-digit written method is prerequisite to 4-digit × 1-digit and 2-digit × 2-digit
- Written Multiplication & Division hard
Formal short multiplication extends Y3 written multiplication
- Area and the distributive property soft
Area models for distributive property support understanding long multiplication layout
- Understanding angles (age 8+) hard
Must multiply side lengths for area before using area models for distributive property
- Multi-step problems: choosing operations hard
Fluency with all four operations in context is required before formalising inverse relationships between them
- Brackets in Expressions hard
The full BODMAS/PEMDAS convention extends understanding of grouping symbols to all operations
- Division with remainders hard
Evaluating grouped expressions formalises multi-step calculation skills from Y5
- Multiply & Add Problems hard
Y4 M×D problem-solving is prerequisite to multi-step four-operation problems
- Arrays for multiplication (age 9+) hard
Must have formal division method before solving multi-step problems
- Division as Unknown Factor hard
Understanding division as unknown-factor supports short division strategy
- Fluent multiplication and division facts hard
Fluent ×÷ within 100 is prerequisite to short division of larger numbers
- Written Multiplication hard
2/3-digit × 1-digit written method is prerequisite to 4-digit × 1-digit and 2-digit × 2-digit
- Area and the distributive property soft
Area models for distributive property support understanding long multiplication layout
- Written Multiplication hard
2/3-digit × 1-digit written method is prerequisite to 4-digit × 1-digit and 2-digit × 2-digit
- Area and the distributive property soft
Area models for distributive property support understanding long multiplication layout
- Multiply & Add Problems hard
Y4 M×D problem-solving is prerequisite to multi-step four-operation problems
- Written Multiplication & Division hard
Formal short multiplication extends Y3 written multiplication
- The three digits of a three-digit number soft
Two-digit × one-digit uses place-value partitioning (e.g. 23 × 4 = 20 × 4 + 3 × 4)
- Reading ×, ÷, and = Symbols hard
Writing multiplication/division statements requires fluency with symbols
- The three digits of a three-digit number soft
Two-digit × one-digit uses place-value partitioning (e.g. 23 × 4 = 20 × 4 + 3 × 4)
- Reading ×, ÷, and = Symbols hard
Writing multiplication/division statements requires fluency with symbols
- Multiplication as repeated addition (age 6+) hard
Scaling and correspondence problems extend Y2 problem-solving with mult/div
- Arrays for multiplication soft
Arrays are a key representation for solving multiplication/division problems
- Commutative Multiplication hard
Applying all three properties extends Y2 commutativity understanding
- Multiplication as repeated addition hard
Commutativity of multiplication requires understanding multiplication
- Arrays for multiplication (age 7+) hard
Extends array-based repeated addition to formal multiplication interpretation
- Multiplication as repeated addition hard
Interpreting products formalises repeated addition/equal groups from Y1
- Arrays for multiplication (age 9+) hard
Must have formal division method before solving multi-step problems
- Division as Unknown Factor hard
Understanding division as unknown-factor supports short division strategy
- What Multiplication Means hard
Connecting division to multiplication requires understanding products
- Arrays for multiplication (age 7+) hard
Extends array-based repeated addition to formal multiplication interpretation
- Multiplication as repeated addition hard
Interpreting products formalises repeated addition/equal groups from Y1
- Fluent multiplication and division facts hard
Fluent ×÷ within 100 is prerequisite to short division of larger numbers
- What Multiplication Means hard
Connecting division to multiplication requires understanding products
- Multiplication as repeated addition hard
Recalling times table facts requires understanding multiplication as repeated addition/grouping
- Written Multiplication hard
2/3-digit × 1-digit written method is prerequisite to 4-digit × 1-digit and 2-digit × 2-digit
- Written Multiplication & Division hard
Formal short multiplication extends Y3 written multiplication
- The three digits of a three-digit number soft
Two-digit × one-digit uses place-value partitioning (e.g. 23 × 4 = 20 × 4 + 3 × 4)
- Reading ×, ÷, and = Symbols hard
Writing multiplication/division statements requires fluency with symbols
- Area and the distributive property soft
Area models for distributive property support understanding long multiplication layout
- Understanding angles (age 8+) hard
Must multiply side lengths for area before using area models for distributive property
- Area by Tiling hard
Must see tiling→multiplication connection before computing area via side lengths
- Arrays for multiplication (age 9+) hard
Long division by 2-digit extends Y5 short division by 1-digit
- Division as Unknown Factor hard
Understanding division as unknown-factor supports short division strategy
- What Multiplication Means hard
Connecting division to multiplication requires understanding products
- Arrays for multiplication (age 7+) hard
Extends array-based repeated addition to formal multiplication interpretation
- Multiplication as repeated addition hard
Interpreting products formalises repeated addition/equal groups from Y1
- Fluent multiplication and division facts hard
Fluent ×÷ within 100 is prerequisite to short division of larger numbers
- What Multiplication Means hard
Connecting division to multiplication requires understanding products
- Multiplication as repeated addition hard
Recalling times table facts requires understanding multiplication as repeated addition/grouping
- Long multiplication (age 10+) soft
Checking division with multiplication requires fluent multiplication
- Written Multiplication hard
2/3-digit × 1-digit written method is prerequisite to 4-digit × 1-digit and 2-digit × 2-digit
- Written Multiplication & Division hard
Formal short multiplication extends Y3 written multiplication
- Area and the distributive property soft
Area models for distributive property support understanding long multiplication layout
- Understanding angles (age 8+) hard
Must multiply side lengths for area before using area models for distributive property
- Ratio Notation and Relationships hard
Direct/inverse proportion requires understanding multiplicative relationships
- Proportional Reasoning Vocabulary hard
Multiplicative relationships require 'multiplicative relationship', 'direct proportion', and 'rate' vocabulary
- Proportion Graphs hard
Understanding multiplicative relationships as ratios or fractions is reinforced by the double number line and proportion graph
- Linear Function Graphs soft
Connecting ratios to linear functions links to understanding y = mx + c from algebra
- Coordinates (age 8+) hard
Plotting in all four quadrants extends first-quadrant coordinate grid plotting skills
- Position, direction, and movement soft
Position/direction vocabulary supports understanding coordinate grid
- Positional Language hard
Position/direction vocabulary with right angles extends basic positional language
- Turns & Directions hard
Right-angle turns (clockwise/anti-clockwise) build directly on whole/half/quarter turns from Year 1
- What Is a Half? soft
Understanding half and quarter turns benefits from the concept of halves and quarters
- Division as equal sharing hard
Finding a half requires equal sharing into 2 groups — a division concept
- Subtraction as taking away or separating hard
Division as equal sharing/grouping requires understanding subtraction as taking away/separating
- 2-D shapes (age 6+) hard
Identifying 2D shape properties is prerequisite to classifying by shared attributes
- Angles in triangles (age 6+) soft
Understanding defining attributes supports describing shape properties formally
- 2-D shapes hard
Distinguishing defining vs non-defining attributes requires knowing common 2-D shape names first
- 3-D shapes (age 5+) hard
Identifying defining attributes builds on informal analysis and comparison of shapes
- 2-D shapes hard
Describing properties of 2-D shapes (sides, symmetry) requires knowing the shapes first
- 3-D shapes (age 5+) hard
Formal property description extends informal analysis of sides and vertices
- Angles in triangles (age 7+) hard
Recognising shapes by attributes is prerequisite to quadrilateral hierarchy classification
- Angles in triangles (age 6+) hard
Drawing shapes by attributes extends understanding defining vs non-defining attributes
- 2-D shapes hard
Distinguishing defining vs non-defining attributes requires knowing common 2-D shape names first
- 3-D shapes (age 5+) hard
Identifying defining attributes builds on informal analysis and comparison of shapes
- 2-D shapes (age 6+) hard
Identifying pentagons, hexagons, quadrilaterals extends knowing 2-D shape properties
- Angles in triangles (age 6+) soft
Understanding defining attributes supports describing shape properties formally
- 2-D shapes hard
Distinguishing defining vs non-defining attributes requires knowing common 2-D shape names first
- 3-D shapes (age 5+) hard
Identifying defining attributes builds on informal analysis and comparison of shapes
- 2-D shapes hard
Describing properties of 2-D shapes (sides, symmetry) requires knowing the shapes first
- 3-D shapes (age 5+) hard
Formal property description extends informal analysis of sides and vertices
- Coordinates (age 8+) hard
Working across the full coordinate grid requires first-quadrant plotting as a foundation
- Position, direction, and movement soft
Position/direction vocabulary supports understanding coordinate grid
- Positional Language hard
Position/direction vocabulary with right angles extends basic positional language
- Turns & Directions hard
Right-angle turns (clockwise/anti-clockwise) build directly on whole/half/quarter turns from Year 1
- What Is a Half? soft
Understanding half and quarter turns benefits from the concept of halves and quarters
- Division as equal sharing hard
Finding a half requires equal sharing into 2 groups — a division concept
- 2-D shapes (age 6+) hard
Identifying 2D shape properties is prerequisite to classifying by shared attributes
- Angles in triangles (age 6+) soft
Understanding defining attributes supports describing shape properties formally
- 2-D shapes hard
Distinguishing defining vs non-defining attributes requires knowing common 2-D shape names first
- 3-D shapes (age 5+) hard
Identifying defining attributes builds on informal analysis and comparison of shapes
- 2-D shapes hard
Describing properties of 2-D shapes (sides, symmetry) requires knowing the shapes first
- 3-D shapes (age 5+) hard
Formal property description extends informal analysis of sides and vertices
- Angles in triangles (age 7+) hard
Recognising shapes by attributes is prerequisite to quadrilateral hierarchy classification
- Angles in triangles (age 6+) hard
Drawing shapes by attributes extends understanding defining vs non-defining attributes
- 2-D shapes hard
Distinguishing defining vs non-defining attributes requires knowing common 2-D shape names first
- 3-D shapes (age 5+) hard
Identifying defining attributes builds on informal analysis and comparison of shapes
- 2-D shapes (age 6+) hard
Identifying pentagons, hexagons, quadrilaterals extends knowing 2-D shape properties
- Angles in triangles (age 6+) soft
Understanding defining attributes supports describing shape properties formally
- 2-D shapes hard
Distinguishing defining vs non-defining attributes requires knowing common 2-D shape names first
- 3-D shapes (age 5+) hard
Identifying defining attributes builds on informal analysis and comparison of shapes
- 2-D shapes hard
Describing properties of 2-D shapes (sides, symmetry) requires knowing the shapes first
- 3-D shapes (age 5+) hard
Formal property description extends informal analysis of sides and vertices
- Negative numbers in context hard
Calculating intervals across zero extends Y5 negative number context
- Negative Numbers hard
Counting through zero is prerequisite to interpreting negative numbers in context
- Transformations on a grid soft
Working with the full coordinate grid (all four quadrants) extends the transformation diagram to negative coordinates
- Types of angles hard
Y4 acute/obtuse angle identification is prerequisite to drawing and labelling angle types
- Right Angles & Turns hard
Identifying right angles and greater/less than right angle is prerequisite to naming acute/obtuse
- Types of angles (age 8+) soft
Identifying right angles and turns is supported by the convention of marking right angles with a small square
- Parallel and perpendicular lines hard
Y3 horizontal/vertical/perpendicular/parallel lines is prerequisite to drawing and identifying them formally
- Types of angles (age 8+) soft
Identifying right angles and turns is supported by the convention of marking right angles with a small square
- Fractions on a number line (age 11+) hard
Plotting coordinates in all four quadrants requires understanding positive and negative values on both axes
- Positive and Negative Numbers hard
Ordering all number types (integers, decimals, fractions) on a number line extends the negative-number number-line representation
- Negative numbers in context hard
Calculating intervals across zero extends Y5 negative number context
- Negative Numbers hard
Counting through zero is prerequisite to interpreting negative numbers in context
- Fractions on a number line hard
Ordering all number types requires understanding place value across the full system
- Reading and writing numbers to 10,000,000 hard
Extending place value to any size builds directly on Y6 reading/writing/ordering numbers to 10,000,000
- Decimals for Tenths & Hundredths hard
Decimal notation for 10ths/100ths is prerequisite to extending to thousandths
- Decimal equivalents of tenths and hundredths hard
Y4 decimal equivalents of 10ths/100ths is prerequisite to formal decimal notation for fractions
- Decimal & Percent Notation hard
Using decimal notation for fractions requires decimal, tenths, and hundredths vocabulary
- Place value of each digit hard
Four-digit place value is prerequisite to understanding ×10 relationship between places
- The three digits of a three-digit number hard
Four-digit place value extends three-digit place value
- The three digits of a three-digit number hard
Comparing three-digit numbers requires three-digit place value
- The three digits of a three-digit number hard
Four-digit place value extends three-digit place value
- Numbers to 10,000 hard
Ordering and comparing numbers over 1000 requires the full 10,000 representations toolkit
- Place Value × 10 Pattern hard
Understanding ×10 place-value relationship supports reading/writing larger numbers
- Place value of each digit hard
Four-digit place value is prerequisite to understanding ×10 relationship between places
- The three digits of a three-digit number hard
Four-digit place value extends three-digit place value
- Measuring temperature hard
Ordering with inequality symbols extends Y6 work with negative numbers in context
- Negative numbers in context hard
Calculating intervals across zero extends Y5 negative number context
- Negative Numbers hard
Counting through zero is prerequisite to interpreting negative numbers in context
- Substituting into Formulae hard
Interpreting y = mx + c requires substitution to generate coordinate pairs
- Writing Algebraic Equations hard
Algebraic notation builds on KS2 expressing missing-number problems algebraically
- Writing Number Sentences hard
Writing algebraic expressions extends writing/interpreting numerical expressions
- Brackets in Expressions hard
Writing/interpreting expressions requires understanding grouping symbols
- Division with remainders hard
Evaluating grouped expressions formalises multi-step calculation skills from Y5
- Multiply & Add Problems hard
Y4 M×D problem-solving is prerequisite to multi-step four-operation problems
- Arrays for multiplication (age 9+) hard
Must have formal division method before solving multi-step problems
- Division as Unknown Factor hard
Understanding division as unknown-factor supports short division strategy
- Fluent multiplication and division facts hard
Fluent ×÷ within 100 is prerequisite to short division of larger numbers
- Written Multiplication hard
2/3-digit × 1-digit written method is prerequisite to 4-digit × 1-digit and 2-digit × 2-digit
- Area and the distributive property soft
Area models for distributive property support understanding long multiplication layout
- Written Multiplication hard
2/3-digit × 1-digit written method is prerequisite to 4-digit × 1-digit and 2-digit × 2-digit
- Area and the distributive property soft
Area models for distributive property support understanding long multiplication layout
- Brackets in Expressions hard
The full BODMAS/PEMDAS convention extends understanding of grouping symbols to all operations
- Division with remainders hard
Evaluating grouped expressions formalises multi-step calculation skills from Y5
- Multiply & Add Problems hard
Y4 M×D problem-solving is prerequisite to multi-step four-operation problems
- Arrays for multiplication (age 9+) hard
Must have formal division method before solving multi-step problems
- Division as Unknown Factor hard
Understanding division as unknown-factor supports short division strategy
- Fluent multiplication and division facts hard
Fluent ×÷ within 100 is prerequisite to short division of larger numbers
- Written Multiplication hard
2/3-digit × 1-digit written method is prerequisite to 4-digit × 1-digit and 2-digit × 2-digit
- Area and the distributive property soft
Area models for distributive property support understanding long multiplication layout
- Written Multiplication hard
2/3-digit × 1-digit written method is prerequisite to 4-digit × 1-digit and 2-digit × 2-digit
- Area and the distributive property soft
Area models for distributive property support understanding long multiplication layout
- Brackets in Expressions hard
Writing/interpreting expressions requires understanding grouping symbols
- Division with remainders hard
Evaluating grouped expressions formalises multi-step calculation skills from Y5
- Multiply & Add Problems hard
Y4 M×D problem-solving is prerequisite to multi-step four-operation problems
- Arrays for multiplication (age 9+) hard
Must have formal division method before solving multi-step problems
- Division as Unknown Factor hard
Understanding division as unknown-factor supports short division strategy
- Fluent multiplication and division facts hard
Fluent ×÷ within 100 is prerequisite to short division of larger numbers
- Written Multiplication hard
2/3-digit × 1-digit written method is prerequisite to 4-digit × 1-digit and 2-digit × 2-digit
- Area and the distributive property soft
Area models for distributive property support understanding long multiplication layout
- Written Multiplication hard
2/3-digit × 1-digit written method is prerequisite to 4-digit × 1-digit and 2-digit × 2-digit
- Area and the distributive property soft
Area models for distributive property support understanding long multiplication layout
- Brackets in Expressions hard
The full BODMAS/PEMDAS convention extends understanding of grouping symbols to all operations
- Division with remainders hard
Evaluating grouped expressions formalises multi-step calculation skills from Y5
- Multiply & Add Problems hard
Y4 M×D problem-solving is prerequisite to multi-step four-operation problems
- Arrays for multiplication (age 9+) hard
Must have formal division method before solving multi-step problems
- Division as Unknown Factor hard
Understanding division as unknown-factor supports short division strategy
- Fluent multiplication and division facts hard
Fluent ×÷ within 100 is prerequisite to short division of larger numbers
- Written Multiplication hard
2/3-digit × 1-digit written method is prerequisite to 4-digit × 1-digit and 2-digit × 2-digit
- Area and the distributive property soft
Area models for distributive property support understanding long multiplication layout
- Written Multiplication hard
2/3-digit × 1-digit written method is prerequisite to 4-digit × 1-digit and 2-digit × 2-digit
- Area and the distributive property soft
Area models for distributive property support understanding long multiplication layout
- Algebraic Transformations hard
Recognising the relationship between y=mx+c and its graph requires moving fluently between algebraic and graphical representations
- Writing Algebraic Equations hard
Algebraic notation builds on KS2 expressing missing-number problems algebraically
- Writing Number Sentences hard
Writing algebraic expressions extends writing/interpreting numerical expressions
- Brackets in Expressions hard
Writing/interpreting expressions requires understanding grouping symbols
- Division with remainders hard
Evaluating grouped expressions formalises multi-step calculation skills from Y5
- Multiply & Add Problems hard
Y4 M×D problem-solving is prerequisite to multi-step four-operation problems
- Arrays for multiplication (age 9+) hard
Must have formal division method before solving multi-step problems
- Division as Unknown Factor hard
Understanding division as unknown-factor supports short division strategy
- Fluent multiplication and division facts hard
Fluent ×÷ within 100 is prerequisite to short division of larger numbers
- Written Multiplication hard
2/3-digit × 1-digit written method is prerequisite to 4-digit × 1-digit and 2-digit × 2-digit
- Area and the distributive property soft
Area models for distributive property support understanding long multiplication layout
- Written Multiplication hard
2/3-digit × 1-digit written method is prerequisite to 4-digit × 1-digit and 2-digit × 2-digit
- Area and the distributive property soft
Area models for distributive property support understanding long multiplication layout
- Brackets in Expressions hard
The full BODMAS/PEMDAS convention extends understanding of grouping symbols to all operations
- Division with remainders hard
Evaluating grouped expressions formalises multi-step calculation skills from Y5
- Multiply & Add Problems hard
Y4 M×D problem-solving is prerequisite to multi-step four-operation problems
- Arrays for multiplication (age 9+) hard
Must have formal division method before solving multi-step problems
- Division as Unknown Factor hard
Understanding division as unknown-factor supports short division strategy
- Fluent multiplication and division facts hard
Fluent ×÷ within 100 is prerequisite to short division of larger numbers
- Written Multiplication hard
2/3-digit × 1-digit written method is prerequisite to 4-digit × 1-digit and 2-digit × 2-digit
- Area and the distributive property soft
Area models for distributive property support understanding long multiplication layout
- Written Multiplication hard
2/3-digit × 1-digit written method is prerequisite to 4-digit × 1-digit and 2-digit × 2-digit
- Area and the distributive property soft
Area models for distributive property support understanding long multiplication layout
- Brackets in Expressions hard
Writing/interpreting expressions requires understanding grouping symbols
- Division with remainders hard
Evaluating grouped expressions formalises multi-step calculation skills from Y5
- Multiply & Add Problems hard
Y4 M×D problem-solving is prerequisite to multi-step four-operation problems
- Arrays for multiplication (age 9+) hard
Must have formal division method before solving multi-step problems
- Division as Unknown Factor hard
Understanding division as unknown-factor supports short division strategy
- Fluent multiplication and division facts hard
Fluent ×÷ within 100 is prerequisite to short division of larger numbers
- Written Multiplication hard
2/3-digit × 1-digit written method is prerequisite to 4-digit × 1-digit and 2-digit × 2-digit
- Area and the distributive property soft
Area models for distributive property support understanding long multiplication layout
- Written Multiplication hard
2/3-digit × 1-digit written method is prerequisite to 4-digit × 1-digit and 2-digit × 2-digit
- Area and the distributive property soft
Area models for distributive property support understanding long multiplication layout
- Brackets in Expressions hard
The full BODMAS/PEMDAS convention extends understanding of grouping symbols to all operations
- Division with remainders hard
Evaluating grouped expressions formalises multi-step calculation skills from Y5
- Multiply & Add Problems hard
Y4 M×D problem-solving is prerequisite to multi-step four-operation problems
- Arrays for multiplication (age 9+) hard
Must have formal division method before solving multi-step problems
- Division as Unknown Factor hard
Understanding division as unknown-factor supports short division strategy
- Fluent multiplication and division facts hard
Fluent ×÷ within 100 is prerequisite to short division of larger numbers
- Written Multiplication hard
2/3-digit × 1-digit written method is prerequisite to 4-digit × 1-digit and 2-digit × 2-digit
- Area and the distributive property soft
Area models for distributive property support understanding long multiplication layout
- Written Multiplication hard
2/3-digit × 1-digit written method is prerequisite to 4-digit × 1-digit and 2-digit × 2-digit
- Area and the distributive property soft
Area models for distributive property support understanding long multiplication layout
- Expressions & Equations Vocabulary hard
Collecting like terms requires knowing what terms, coefficients, and like terms mean
- Writing Algebraic Equations hard
Algebraic notation builds on KS2 expressing missing-number problems algebraically
- Writing Number Sentences hard
Writing algebraic expressions extends writing/interpreting numerical expressions
- Writing Number Sentences hard
Writing algebraic expressions extends writing/interpreting numerical expressions
- Brackets in Expressions hard
Writing/interpreting expressions requires understanding grouping symbols
- Division with remainders hard
Evaluating grouped expressions formalises multi-step calculation skills from Y5
- Multiply & Add Problems hard
Y4 M×D problem-solving is prerequisite to multi-step four-operation problems
- Arrays for multiplication (age 9+) hard
Must have formal division method before solving multi-step problems
- Division as Unknown Factor hard
Understanding division as unknown-factor supports short division strategy
- Fluent multiplication and division facts hard
Fluent ×÷ within 100 is prerequisite to short division of larger numbers
- Written Multiplication hard
2/3-digit × 1-digit written method is prerequisite to 4-digit × 1-digit and 2-digit × 2-digit
- Area and the distributive property soft
Area models for distributive property support understanding long multiplication layout
- Written Multiplication hard
2/3-digit × 1-digit written method is prerequisite to 4-digit × 1-digit and 2-digit × 2-digit
- Area and the distributive property soft
Area models for distributive property support understanding long multiplication layout
- Brackets in Expressions hard
The full BODMAS/PEMDAS convention extends understanding of grouping symbols to all operations
- Division with remainders hard
Evaluating grouped expressions formalises multi-step calculation skills from Y5
- Multiply & Add Problems hard
Y4 M×D problem-solving is prerequisite to multi-step four-operation problems
- Arrays for multiplication (age 9+) hard
Must have formal division method before solving multi-step problems
- Division as Unknown Factor hard
Understanding division as unknown-factor supports short division strategy
- Fluent multiplication and division facts hard
Fluent ×÷ within 100 is prerequisite to short division of larger numbers
- Written Multiplication hard
2/3-digit × 1-digit written method is prerequisite to 4-digit × 1-digit and 2-digit × 2-digit
- Area and the distributive property soft
Area models for distributive property support understanding long multiplication layout
- Written Multiplication hard
2/3-digit × 1-digit written method is prerequisite to 4-digit × 1-digit and 2-digit × 2-digit
- Area and the distributive property soft
Area models for distributive property support understanding long multiplication layout
- Writing Algebraic Equations hard
Algebraic notation builds on KS2 expressing missing-number problems algebraically
- Writing Number Sentences hard
Writing algebraic expressions extends writing/interpreting numerical expressions
- Brackets in Expressions hard
Writing/interpreting expressions requires understanding grouping symbols
- Division with remainders hard
Evaluating grouped expressions formalises multi-step calculation skills from Y5
- Brackets in Expressions hard
The full BODMAS/PEMDAS convention extends understanding of grouping symbols to all operations
- Division with remainders hard
Evaluating grouped expressions formalises multi-step calculation skills from Y5
- Brackets in Expressions hard
Writing/interpreting expressions requires understanding grouping symbols
- Division with remainders hard
Evaluating grouped expressions formalises multi-step calculation skills from Y5
- Brackets in Expressions hard
The full BODMAS/PEMDAS convention extends understanding of grouping symbols to all operations
- Division with remainders hard
Evaluating grouped expressions formalises multi-step calculation skills from Y5
- Using inverse operations hard
Solving linear equations by rearrangement requires applying inverse operations to isolate an unknown
- Order of operations hard
Understanding order of operations (BODMAS) is required before studying how operations undo each other via inverse relationships
- Brackets in Expressions hard
The full BODMAS/PEMDAS convention extends understanding of grouping symbols to all operations
- Division with remainders hard
Evaluating grouped expressions formalises multi-step calculation skills from Y5
- Multiply & Add Problems hard
Y4 M×D problem-solving is prerequisite to multi-step four-operation problems
- Arrays for multiplication (age 9+) hard
Must have formal division method before solving multi-step problems
- Division as Unknown Factor hard
Understanding division as unknown-factor supports short division strategy
- Fluent multiplication and division facts hard
Fluent ×÷ within 100 is prerequisite to short division of larger numbers
- Written Multiplication hard
2/3-digit × 1-digit written method is prerequisite to 4-digit × 1-digit and 2-digit × 2-digit
- Area and the distributive property soft
Area models for distributive property support understanding long multiplication layout
- Written Multiplication hard
2/3-digit × 1-digit written method is prerequisite to 4-digit × 1-digit and 2-digit × 2-digit
- Area and the distributive property soft
Area models for distributive property support understanding long multiplication layout
- Multi-step problems: choosing operations hard
Fluency with all four operations in context is required before formalising inverse relationships between them
- Brackets in Expressions hard
The full BODMAS/PEMDAS convention extends understanding of grouping symbols to all operations
- Division with remainders hard
Evaluating grouped expressions formalises multi-step calculation skills from Y5
- Multiply & Add Problems hard
Y4 M×D problem-solving is prerequisite to multi-step four-operation problems
- Arrays for multiplication (age 9+) hard
Must have formal division method before solving multi-step problems
- Multiply & Add Problems hard
Y4 M×D problem-solving is prerequisite to multi-step four-operation problems
- Written Multiplication & Division hard
Formal short multiplication extends Y3 written multiplication
- Multiplication as repeated addition (age 6+) hard
Scaling and correspondence problems extend Y2 problem-solving with mult/div
- Commutative Multiplication hard
Applying all three properties extends Y2 commutativity understanding
- Arrays for multiplication (age 9+) hard
Must have formal division method before solving multi-step problems
- Division as Unknown Factor hard
Understanding division as unknown-factor supports short division strategy
- What Multiplication Means hard
Connecting division to multiplication requires understanding products
- Fluent multiplication and division facts hard
Fluent ×÷ within 100 is prerequisite to short division of larger numbers
- Written Multiplication hard
2/3-digit × 1-digit written method is prerequisite to 4-digit × 1-digit and 2-digit × 2-digit
- Written Multiplication & Division hard
Formal short multiplication extends Y3 written multiplication
- Area and the distributive property soft
Area models for distributive property support understanding long multiplication layout
- Understanding angles (age 8+) hard
Must multiply side lengths for area before using area models for distributive property
- Arrays for multiplication (age 9+) hard
Long division by 2-digit extends Y5 short division by 1-digit
- Division as Unknown Factor hard
Understanding division as unknown-factor supports short division strategy
- What Multiplication Means hard
Connecting division to multiplication requires understanding products
- Fluent multiplication and division facts hard
Fluent ×÷ within 100 is prerequisite to short division of larger numbers
- Long multiplication (age 10+) soft
Checking division with multiplication requires fluent multiplication
- Written Multiplication hard
2/3-digit × 1-digit written method is prerequisite to 4-digit × 1-digit and 2-digit × 2-digit
- Area and the distributive property soft
Area models for distributive property support understanding long multiplication layout
- One Quantity as a Fraction hard
Connecting ratios to fractions requires expressing quantities as fractions of each other
- Adding Fractions (Unlike Denominators) hard
Adding/subtracting fractions with unlike denominators is needed when comparing fractional parts
- Simplifying Fractions hard
Finding common denominators requires simplification/common multiples skills
- Equivalent fractions on a number line hard
Understanding equivalence conceptually is prerequisite to explaining algebraically
- Equivalent fractions hard
Diagram-based equivalent fractions is prerequisite to formal equivalence understanding
- Finding halves and quarters (age 5+) hard
Working with 1/4, 2/4, 3/4 extends from Y1 understanding of quarters
- Fraction Notation hard
Writing fractions like 1/3 and 3/4 requires knowing numerator and denominator
- Reading +, −, and = symbols soft
Writing fraction sentences (1/2 of 6 = 3) requires understanding the = sign
- Reading and writing numbers to 20 hard
Writing number sentences requires reading and writing numerals
- Addition as combining or putting together two hard
Reading/writing the + symbol requires understanding what addition means
- Subtraction as taking away or separating hard
Reading/writing the − symbol requires understanding what subtraction means
- Fractions of amounts hard
Writing fractions and recognising equivalence requires knowing what the fractions mean
- Finding halves and quarters (age 5+) hard
Working with 1/4, 2/4, 3/4 extends from Y1 understanding of quarters
- Fraction Notation hard
Writing fractions like 1/3 and 3/4 requires knowing numerator and denominator
- Fraction Notation hard
Writing fractions and recognising equivalence requires 'equivalent fraction' vocabulary
- Fractions of amounts hard
Recognising fractions of shapes/quantities is prerequisite to formal unit fraction understanding
- Finding halves and quarters (age 5+) hard
Working with 1/4, 2/4, 3/4 extends from Y1 understanding of quarters
- What Is a Half? hard
Understanding quarters extends from understanding halves — both are equal parts but quarters requires dividing into 4
- Division as equal sharing hard
Finding a half requires equal sharing into 2 groups — a division concept
- Subtraction as taking away or separating hard
Division as equal sharing/grouping requires understanding subtraction as taking away/separating
- Fraction Notation hard
Writing fractions like 1/3 and 3/4 requires knowing numerator and denominator
- Fraction Notation hard
Understanding a/b as a parts of 1/b requires numerator, denominator, and unit fraction vocabulary
- Splitting shapes into equal parts (age 7+) hard
Partition into equal shares is prerequisite to understanding unit fractions
- Decomposing a shape into more equal shares hard
Understanding equal shares of different shapes requires concept of more shares = smaller
- Halves & Quarters of Shapes hard
Comparing share sizes requires experience partitioning into halves and quarters
- Finding halves and quarters (age 5+) hard
Partitioning into fourths/quarters extends from Y1 understanding of quarters
- Fractions on a number line (age 8+) hard
Equivalent fractions as the same point on a number line directly uses the fraction number-line representation
- Fractions on a number line hard
Prior number-line fraction experience feeds into formal unit-fraction placement
- Finding halves and quarters (age 5+) hard
Working with 1/4, 2/4, 3/4 extends from Y1 understanding of quarters
- Fraction Notation hard
Writing fractions like 1/3 and 3/4 requires knowing numerator and denominator
- Fractions of amounts hard
Recognising fractions of shapes/quantities is prerequisite to formal unit fraction understanding
- Finding halves and quarters (age 5+) hard
Working with 1/4, 2/4, 3/4 extends from Y1 understanding of quarters
- Fraction Notation hard
Writing fractions like 1/3 and 3/4 requires knowing numerator and denominator
- Fraction Notation hard
Understanding a/b as a parts of 1/b requires numerator, denominator, and unit fraction vocabulary
- Splitting shapes into equal parts (age 7+) hard
Partition into equal shares is prerequisite to understanding unit fractions
- Decomposing a shape into more equal shares hard
Understanding equal shares of different shapes requires concept of more shares = smaller
- Equivalent fractions (age 8+) hard
Generating equivalent fractions with visual models is prerequisite to algebraic explanation of equivalence
- Equivalent fractions on a number line hard
Must understand equivalence before generating equivalent fractions
- Equivalent fractions hard
Diagram-based equivalent fractions is prerequisite to formal equivalence understanding
- Reading +, −, and = symbols soft
Writing fraction sentences (1/2 of 6 = 3) requires understanding the = sign
- Fractions of amounts hard
Writing fractions and recognising equivalence requires knowing what the fractions mean
- Fraction Notation hard
Writing fractions and recognising equivalence requires 'equivalent fraction' vocabulary
- Fractions of amounts hard
Recognising fractions of shapes/quantities is prerequisite to formal unit fraction understanding
- Finding halves and quarters (age 5+) hard
Working with 1/4, 2/4, 3/4 extends from Y1 understanding of quarters
- Fraction Notation hard
Writing fractions like 1/3 and 3/4 requires knowing numerator and denominator
- Fraction Notation hard
Understanding a/b as a parts of 1/b requires numerator, denominator, and unit fraction vocabulary
- Splitting shapes into equal parts (age 7+) hard
Partition into equal shares is prerequisite to understanding unit fractions
- Decomposing a shape into more equal shares hard
Understanding equal shares of different shapes requires concept of more shares = smaller
- Fractions on a number line (age 8+) hard
Equivalent fractions as the same point on a number line directly uses the fraction number-line representation
- Fractions on a number line hard
Prior number-line fraction experience feeds into formal unit-fraction placement
- Fractions of amounts hard
Recognising fractions of shapes/quantities is prerequisite to formal unit fraction understanding
- Fraction Notation hard
Understanding a/b as a parts of 1/b requires numerator, denominator, and unit fraction vocabulary
- Splitting shapes into equal parts (age 7+) hard
Partition into equal shares is prerequisite to understanding unit fractions
- Factors, multiples, and primes hard
Using common factors/multiples requires knowledge of common factors and multiples
- All times tables to 12×12 hard
Tables to 12×12 fluency is prerequisite to finding factor pairs up to 100
- Skip Counting (4s, 8s, 50s, 100s) hard
Counting in 6s/7s/9s/25s/1000s extends counting in 4s/8s/50s/100s
- Multiplication as repeated addition hard
Recalling times table facts requires understanding multiplication as repeated addition/grouping
- Addition as combining or putting together two hard
Multiplication as repeated addition requires understanding addition as combining groups
- Factor Pairs & Commutativity hard
Recognising factor pairs at Y4 is prerequisite to systematically finding all factor pairs
- Skip Counting (4s, 8s, 50s, 100s) hard
Counting in 6s/7s/9s/25s/1000s extends counting in 4s/8s/50s/100s
- Multiplication as repeated addition hard
Recalling times table facts requires understanding multiplication as repeated addition/grouping
- Commutative Multiplication hard
Applying all three properties extends Y2 commutativity understanding
- Division as equal sharing hard
Using arrays for division requires understanding division as grouping
- Multiplication as repeated addition hard
Using arrays requires understanding what multiplication means
- Multiplication as repeated addition hard
Commutativity of multiplication requires understanding multiplication
- Addition as combining or putting together two hard
Multiplication as repeated addition requires understanding addition as combining groups
- Arrays for multiplication (age 7+) hard
Extends array-based repeated addition to formal multiplication interpretation
- Arrays for multiplication hard
Rectangular arrays with repeated addition extends array representation from Y2
- Multiplication as repeated addition hard
Expressing array totals as sums of equal addends requires understanding multiplication as repeated addition
- Multiplication as repeated addition hard
Interpreting products formalises repeated addition/equal groups from Y1
- Addition as combining or putting together two hard
Multiplication as repeated addition requires understanding addition as combining groups
- Fraction Notation hard
Simplifying fractions to simplest form requires 'simplest form' and 'common factor' vocabulary
- Mixed numbers and improper fractions soft
Mixed number operations benefit from mixed/improper conversion
- Understanding fractions (age 9+) hard
Fraction as sum of unit fractions supports understanding improper fractions
- Fractions of a whole hard
Understanding a/b as a parts of size 1/b is prerequisite to understanding a/b as sum of 1/b
- Fractions of amounts hard
Recognising fractions of shapes/quantities is prerequisite to formal unit fraction understanding
- Finding halves and quarters (age 5+) hard
Working with 1/4, 2/4, 3/4 extends from Y1 understanding of quarters
- What Is a Half? hard
Understanding quarters extends from understanding halves — both are equal parts but quarters requires dividing into 4
- Division as equal sharing hard
Finding a half requires equal sharing into 2 groups — a division concept
- Division as equal sharing hard
Finding a half requires equal sharing into 2 groups — a division concept
- Subtraction as taking away or separating hard
Division as equal sharing/grouping requires understanding subtraction as taking away/separating
- Subtraction as taking away or separating hard
Division as equal sharing/grouping requires understanding subtraction as taking away/separating
- How Many in Total? hard
Understanding subtraction as taking away requires knowing numbers represent quantities (cardinality)
- Fraction Notation hard
Writing fractions like 1/3 and 3/4 requires knowing numerator and denominator
- Fraction Notation hard
Understanding a/b as a parts of 1/b requires numerator, denominator, and unit fraction vocabulary
- Splitting shapes into equal parts (age 7+) hard
Partition into equal shares is prerequisite to understanding unit fractions
- Decomposing a shape into more equal shares hard
Understanding equal shares of different shapes requires concept of more shares = smaller
- Halves & Quarters of Shapes hard
Comparing share sizes requires experience partitioning into halves and quarters
- Finding halves and quarters (age 5+) hard
Partitioning into fourths/quarters extends from Y1 understanding of quarters
- Finding halves and quarters (age 5+) hard
Partitioning into fourths/quarters extends from Y1 understanding of quarters
- What Is a Half? hard
Understanding quarters extends from understanding halves — both are equal parts but quarters requires dividing into 4
- Division as equal sharing hard
Finding a half requires equal sharing into 2 groups — a division concept
- Fractions of a whole (age 8+) hard
Understanding whole numbers as fractions supports mixed↔improper conversion
- Fractions of amounts hard
Recognising fractions of shapes/quantities is prerequisite to formal unit fraction understanding
- Finding halves and quarters (age 5+) hard
Working with 1/4, 2/4, 3/4 extends from Y1 understanding of quarters
- What Is a Half? hard
Understanding quarters extends from understanding halves — both are equal parts but quarters requires dividing into 4
- Division as equal sharing hard
Finding a half requires equal sharing into 2 groups — a division concept
- Division as equal sharing hard
Finding a half requires equal sharing into 2 groups — a division concept
- Subtraction as taking away or separating hard
Division as equal sharing/grouping requires understanding subtraction as taking away/separating
- Subtraction as taking away or separating hard
Division as equal sharing/grouping requires understanding subtraction as taking away/separating
- How Many in Total? hard
Understanding subtraction as taking away requires knowing numbers represent quantities (cardinality)
- Fraction Notation hard
Writing fractions like 1/3 and 3/4 requires knowing numerator and denominator
- Fraction Notation hard
Understanding a/b as a parts of 1/b requires numerator, denominator, and unit fraction vocabulary
- Splitting shapes into equal parts (age 7+) hard
Partition into equal shares is prerequisite to understanding unit fractions
- Decomposing a shape into more equal shares hard
Understanding equal shares of different shapes requires concept of more shares = smaller
- Halves & Quarters of Shapes hard
Comparing share sizes requires experience partitioning into halves and quarters
- Finding halves and quarters (age 5+) hard
Partitioning into fourths/quarters extends from Y1 understanding of quarters
- Finding halves and quarters (age 5+) hard
Partitioning into fourths/quarters extends from Y1 understanding of quarters
- What Is a Half? hard
Understanding quarters extends from understanding halves — both are equal parts but quarters requires dividing into 4
- Division as equal sharing hard
Finding a half requires equal sharing into 2 groups — a division concept
- Adding fractions (different denominators) hard
Unlike-denominator add/sub extends Y5 add/sub with related denominators
- Equivalent fractions on a number line hard
Understanding equivalence conceptually is prerequisite to explaining algebraically
- Equivalent fractions hard
Diagram-based equivalent fractions is prerequisite to formal equivalence understanding
- Finding halves and quarters (age 5+) hard
Working with 1/4, 2/4, 3/4 extends from Y1 understanding of quarters
- Fraction Notation hard
Writing fractions like 1/3 and 3/4 requires knowing numerator and denominator
- Reading +, −, and = symbols soft
Writing fraction sentences (1/2 of 6 = 3) requires understanding the = sign
- Reading and writing numbers to 20 hard
Writing number sentences requires reading and writing numerals
- Addition as combining or putting together two hard
Reading/writing the + symbol requires understanding what addition means
- Subtraction as taking away or separating hard
Reading/writing the − symbol requires understanding what subtraction means
- Fractions of amounts hard
Writing fractions and recognising equivalence requires knowing what the fractions mean
- Finding halves and quarters (age 5+) hard
Working with 1/4, 2/4, 3/4 extends from Y1 understanding of quarters
- Fraction Notation hard
Writing fractions like 1/3 and 3/4 requires knowing numerator and denominator
- Fraction Notation hard
Writing fractions and recognising equivalence requires 'equivalent fraction' vocabulary
- Fractions of amounts hard
Recognising fractions of shapes/quantities is prerequisite to formal unit fraction understanding
- Finding halves and quarters (age 5+) hard
Working with 1/4, 2/4, 3/4 extends from Y1 understanding of quarters
- What Is a Half? hard
Understanding quarters extends from understanding halves — both are equal parts but quarters requires dividing into 4
- Division as equal sharing hard
Finding a half requires equal sharing into 2 groups — a division concept
- Subtraction as taking away or separating hard
Division as equal sharing/grouping requires understanding subtraction as taking away/separating
- Fraction Notation hard
Writing fractions like 1/3 and 3/4 requires knowing numerator and denominator
- Fraction Notation hard
Understanding a/b as a parts of 1/b requires numerator, denominator, and unit fraction vocabulary
- Splitting shapes into equal parts (age 7+) hard
Partition into equal shares is prerequisite to understanding unit fractions
- Decomposing a shape into more equal shares hard
Understanding equal shares of different shapes requires concept of more shares = smaller
- Halves & Quarters of Shapes hard
Comparing share sizes requires experience partitioning into halves and quarters
- Finding halves and quarters (age 5+) hard
Partitioning into fourths/quarters extends from Y1 understanding of quarters
- Fractions on a number line (age 8+) hard
Equivalent fractions as the same point on a number line directly uses the fraction number-line representation
- Fractions on a number line hard
Prior number-line fraction experience feeds into formal unit-fraction placement
- Finding halves and quarters (age 5+) hard
Working with 1/4, 2/4, 3/4 extends from Y1 understanding of quarters
- Fraction Notation hard
Writing fractions like 1/3 and 3/4 requires knowing numerator and denominator
- Fractions of amounts hard
Recognising fractions of shapes/quantities is prerequisite to formal unit fraction understanding
- Finding halves and quarters (age 5+) hard
Working with 1/4, 2/4, 3/4 extends from Y1 understanding of quarters
- Fraction Notation hard
Writing fractions like 1/3 and 3/4 requires knowing numerator and denominator
- Fraction Notation hard
Understanding a/b as a parts of 1/b requires numerator, denominator, and unit fraction vocabulary
- Splitting shapes into equal parts (age 7+) hard
Partition into equal shares is prerequisite to understanding unit fractions
- Decomposing a shape into more equal shares hard
Understanding equal shares of different shapes requires concept of more shares = smaller
- Equivalent fractions (age 8+) hard
Generating equivalent fractions with visual models is prerequisite to algebraic explanation of equivalence
- Equivalent fractions on a number line hard
Must understand equivalence before generating equivalent fractions
- Equivalent fractions hard
Diagram-based equivalent fractions is prerequisite to formal equivalence understanding
- Reading +, −, and = symbols soft
Writing fraction sentences (1/2 of 6 = 3) requires understanding the = sign
- Fractions of amounts hard
Writing fractions and recognising equivalence requires knowing what the fractions mean
- Fraction Notation hard
Writing fractions and recognising equivalence requires 'equivalent fraction' vocabulary
- Fractions of amounts hard
Recognising fractions of shapes/quantities is prerequisite to formal unit fraction understanding
- Finding halves and quarters (age 5+) hard
Working with 1/4, 2/4, 3/4 extends from Y1 understanding of quarters
- Fraction Notation hard
Writing fractions like 1/3 and 3/4 requires knowing numerator and denominator
- Fraction Notation hard
Understanding a/b as a parts of 1/b requires numerator, denominator, and unit fraction vocabulary
- Splitting shapes into equal parts (age 7+) hard
Partition into equal shares is prerequisite to understanding unit fractions
- Decomposing a shape into more equal shares hard
Understanding equal shares of different shapes requires concept of more shares = smaller
- Fractions on a number line (age 8+) hard
Equivalent fractions as the same point on a number line directly uses the fraction number-line representation
- Fractions on a number line hard
Prior number-line fraction experience feeds into formal unit-fraction placement
- Fractions of amounts hard
Recognising fractions of shapes/quantities is prerequisite to formal unit fraction understanding
- Fraction Notation hard
Understanding a/b as a parts of 1/b requires numerator, denominator, and unit fraction vocabulary
- Splitting shapes into equal parts (age 7+) hard
Partition into equal shares is prerequisite to understanding unit fractions
- Understanding fractions (age 9+) hard
Fraction as sum of unit fractions is prerequisite to decomposing and adding/subtracting
- Fractions of a whole hard
Understanding a/b as a parts of size 1/b is prerequisite to understanding a/b as sum of 1/b
- Fractions of amounts hard
Recognising fractions of shapes/quantities is prerequisite to formal unit fraction understanding
- Finding halves and quarters (age 5+) hard
Working with 1/4, 2/4, 3/4 extends from Y1 understanding of quarters
- What Is a Half? hard
Understanding quarters extends from understanding halves — both are equal parts but quarters requires dividing into 4
- Division as equal sharing hard
Finding a half requires equal sharing into 2 groups — a division concept
- Subtraction as taking away or separating hard
Division as equal sharing/grouping requires understanding subtraction as taking away/separating
- Fraction Notation hard
Writing fractions like 1/3 and 3/4 requires knowing numerator and denominator
- Fraction Notation hard
Understanding a/b as a parts of 1/b requires numerator, denominator, and unit fraction vocabulary
- Splitting shapes into equal parts (age 7+) hard
Partition into equal shares is prerequisite to understanding unit fractions
- Decomposing a shape into more equal shares hard
Understanding equal shares of different shapes requires concept of more shares = smaller
- Halves & Quarters of Shapes hard
Comparing share sizes requires experience partitioning into halves and quarters
- Finding halves and quarters (age 5+) hard
Partitioning into fourths/quarters extends from Y1 understanding of quarters
- Adding Fractions (Same Denominator) hard
Y4 add/sub fractions same denom is prerequisite to decomposition and joining/separating
- Finding halves and quarters (age 5+) hard
Working with 1/4, 2/4, 3/4 extends from Y1 understanding of quarters
- Fraction Notation hard
Writing fractions like 1/3 and 3/4 requires knowing numerator and denominator
- Addition as combining or putting together two soft
Adding fractions extends the concept of addition as combining
- How Many in Total? hard
Understanding addition as combining groups requires knowing numbers represent quantities (cardinality)
- One-to-one counting hard
Cardinality principle builds on one-to-one correspondence — you must count correctly to know the last number tells 'how many'
- Decimals and fractions (age 10+) hard
Expressing one quantity as a fraction of another requires fluent fraction-decimal equivalence
- Fractions of a whole (age 10+) hard
Calculating decimal equivalents requires understanding fraction as division
- Multiplying fractions hard
Understanding fraction as division builds on fraction × whole number (inverse reasoning)
- Understanding fractions (age 9+) hard
a/b as sum of 1/b is prerequisite to understanding a/b as multiple of 1/b
- Fractions of a whole hard
Understanding a/b as a parts of size 1/b is prerequisite to understanding a/b as sum of 1/b
- Fractions of amounts hard
Recognising fractions of shapes/quantities is prerequisite to formal unit fraction understanding
- Finding halves and quarters (age 5+) hard
Working with 1/4, 2/4, 3/4 extends from Y1 understanding of quarters
- What Is a Half? hard
Understanding quarters extends from understanding halves — both are equal parts but quarters requires dividing into 4
- Division as equal sharing hard
Finding a half requires equal sharing into 2 groups — a division concept
- Subtraction as taking away or separating hard
Division as equal sharing/grouping requires understanding subtraction as taking away/separating
- Fraction Notation hard
Writing fractions like 1/3 and 3/4 requires knowing numerator and denominator
- Fraction Notation hard
Understanding a/b as a parts of 1/b requires numerator, denominator, and unit fraction vocabulary
- Splitting shapes into equal parts (age 7+) hard
Partition into equal shares is prerequisite to understanding unit fractions
- Decomposing a shape into more equal shares hard
Understanding equal shares of different shapes requires concept of more shares = smaller
- Halves & Quarters of Shapes hard
Comparing share sizes requires experience partitioning into halves and quarters
- Finding halves and quarters (age 5+) hard
Partitioning into fourths/quarters extends from Y1 understanding of quarters
- Division with remainders (age 10+) soft
Division leading to fractions connects to long division skills
- Arrays for multiplication (age 9+) hard
Long division by 2-digit extends Y5 short division by 1-digit
- Division as Unknown Factor hard
Understanding division as unknown-factor supports short division strategy
- What Multiplication Means hard
Connecting division to multiplication requires understanding products
- Arrays for multiplication (age 7+) hard
Extends array-based repeated addition to formal multiplication interpretation
- Arrays for multiplication hard
Rectangular arrays with repeated addition extends array representation from Y2
- Multiplication as repeated addition hard
Expressing array totals as sums of equal addends requires understanding multiplication as repeated addition
- Multiplication as repeated addition hard
Interpreting products formalises repeated addition/equal groups from Y1
- Addition as combining or putting together two hard
Multiplication as repeated addition requires understanding addition as combining groups
- Subtraction as taking away or separating hard
Division as equal sharing/grouping requires understanding subtraction as taking away/separating
- Fluent multiplication and division facts hard
Fluent ×÷ within 100 is prerequisite to short division of larger numbers
- What Multiplication Means hard
Connecting division to multiplication requires understanding products
- Arrays for multiplication (age 7+) hard
Extends array-based repeated addition to formal multiplication interpretation
- Multiplication as repeated addition hard
Interpreting products formalises repeated addition/equal groups from Y1
- Multiplication as repeated addition hard
Recalling times table facts requires understanding multiplication as repeated addition/grouping
- Addition as combining or putting together two hard
Multiplication as repeated addition requires understanding addition as combining groups
- Multiplication as repeated addition hard
Recalling times table facts requires understanding multiplication as repeated addition/grouping
- Long multiplication (age 10+) soft
Checking division with multiplication requires fluent multiplication
- Written Multiplication hard
2/3-digit × 1-digit written method is prerequisite to 4-digit × 1-digit and 2-digit × 2-digit
- Written Multiplication & Division hard
Formal short multiplication extends Y3 written multiplication
- The three digits of a three-digit number soft
Two-digit × one-digit uses place-value partitioning (e.g. 23 × 4 = 20 × 4 + 3 × 4)
- Reading ×, ÷, and = Symbols hard
Writing multiplication/division statements requires fluency with symbols
- Area and the distributive property soft
Area models for distributive property support understanding long multiplication layout
- Understanding angles (age 8+) hard
Must multiply side lengths for area before using area models for distributive property
- Area by Tiling hard
Must see tiling→multiplication connection before computing area via side lengths
- Percentage and decimal equivalents hard
Extends Y5 percentage/decimal equivalents to broader range of fractions
- Fraction-Decimal Equivalents soft
Decimal equivalents of 1/4, 1/2, 3/4 support percentage equivalence problems
- Equivalent fractions on a number line soft
Equivalent fractions understanding supports recognising decimal equivalents of common fractions
- Equivalent fractions hard
Diagram-based equivalent fractions is prerequisite to formal equivalence understanding
- Finding halves and quarters (age 5+) hard
Working with 1/4, 2/4, 3/4 extends from Y1 understanding of quarters
- Fraction Notation hard
Writing fractions like 1/3 and 3/4 requires knowing numerator and denominator
- Reading +, −, and = symbols soft
Writing fraction sentences (1/2 of 6 = 3) requires understanding the = sign
- Reading and writing numbers to 20 hard
Writing number sentences requires reading and writing numerals
- Addition as combining or putting together two hard
Reading/writing the + symbol requires understanding what addition means
- Subtraction as taking away or separating hard
Reading/writing the − symbol requires understanding what subtraction means
- Fractions of amounts hard
Writing fractions and recognising equivalence requires knowing what the fractions mean
- Finding halves and quarters (age 5+) hard
Working with 1/4, 2/4, 3/4 extends from Y1 understanding of quarters
- Fraction Notation hard
Writing fractions like 1/3 and 3/4 requires knowing numerator and denominator
- Fraction Notation hard
Writing fractions and recognising equivalence requires 'equivalent fraction' vocabulary
- Fractions of amounts hard
Recognising fractions of shapes/quantities is prerequisite to formal unit fraction understanding
- Finding halves and quarters (age 5+) hard
Working with 1/4, 2/4, 3/4 extends from Y1 understanding of quarters
- What Is a Half? hard
Understanding quarters extends from understanding halves — both are equal parts but quarters requires dividing into 4
- Division as equal sharing hard
Finding a half requires equal sharing into 2 groups — a division concept
- Subtraction as taking away or separating hard
Division as equal sharing/grouping requires understanding subtraction as taking away/separating
- Fraction Notation hard
Writing fractions like 1/3 and 3/4 requires knowing numerator and denominator
- Fraction Notation hard
Understanding a/b as a parts of 1/b requires numerator, denominator, and unit fraction vocabulary
- Splitting shapes into equal parts (age 7+) hard
Partition into equal shares is prerequisite to understanding unit fractions
- Decomposing a shape into more equal shares hard
Understanding equal shares of different shapes requires concept of more shares = smaller
- Halves & Quarters of Shapes hard
Comparing share sizes requires experience partitioning into halves and quarters
- Finding halves and quarters (age 5+) hard
Partitioning into fourths/quarters extends from Y1 understanding of quarters
- Fractions on a number line (age 8+) hard
Equivalent fractions as the same point on a number line directly uses the fraction number-line representation
- Fractions on a number line hard
Prior number-line fraction experience feeds into formal unit-fraction placement
- Finding halves and quarters (age 5+) hard
Working with 1/4, 2/4, 3/4 extends from Y1 understanding of quarters
- Fraction Notation hard
Writing fractions like 1/3 and 3/4 requires knowing numerator and denominator
- Fractions of amounts hard
Recognising fractions of shapes/quantities is prerequisite to formal unit fraction understanding
- Finding halves and quarters (age 5+) hard
Working with 1/4, 2/4, 3/4 extends from Y1 understanding of quarters
- Fraction Notation hard
Writing fractions like 1/3 and 3/4 requires knowing numerator and denominator
- Fraction Notation hard
Understanding a/b as a parts of 1/b requires numerator, denominator, and unit fraction vocabulary
- Splitting shapes into equal parts (age 7+) hard
Partition into equal shares is prerequisite to understanding unit fractions
- Decomposing a shape into more equal shares hard
Understanding equal shares of different shapes requires concept of more shares = smaller
- Decimal equivalents of tenths and hundredths hard
General decimal equivalents prerequisite to specific 1/4, 1/2, 3/4 equivalents
- Finding halves and quarters (age 5+) hard
Working with 1/4, 2/4, 3/4 extends from Y1 understanding of quarters
- Fraction Notation hard
Writing fractions like 1/3 and 3/4 requires knowing numerator and denominator
- Decimal & Percent Notation hard
Writing decimal equivalents of tenths and hundredths requires decimal point and place-value vocabulary
- Decimals for Tenths & Hundredths hard
Decimal notation for fractions is prerequisite to understanding % as parts per 100
- Tenths (age 8+) hard
Understanding hundredths is prerequisite to working with 10ths and 100ths together
- Equivalent fractions (age 9+) hard
Generating equivalent fractions supports converting 10ths to 100ths
- Equivalent fractions on a number line hard
Understanding equivalence conceptually is prerequisite to explaining algebraically
- Equivalent fractions hard
Diagram-based equivalent fractions is prerequisite to formal equivalence understanding
- Fractions on a number line (age 8+) hard
Equivalent fractions as the same point on a number line directly uses the fraction number-line representation
- Equivalent fractions (age 8+) hard
Generating equivalent fractions with visual models is prerequisite to algebraic explanation of equivalence
- Equivalent fractions on a number line hard
Must understand equivalence before generating equivalent fractions
- Decimal equivalents of tenths and hundredths hard
Y4 decimal equivalents of 10ths/100ths is prerequisite to formal decimal notation for fractions
- Decimal & Percent Notation hard
Writing decimal equivalents of tenths and hundredths requires decimal point and place-value vocabulary
- Decimal & Percent Notation hard
Using decimal notation for fractions requires decimal, tenths, and hundredths vocabulary
- Decimal & Percent Notation hard
Understanding the % symbol and 'per cent means parts per hundred' is the LANGUAGE node content
- Decimal & Percent Notation hard
Recalling equivalences between fractions, decimals, and percentages requires all three sets of vocabulary
- Decimals for Tenths & Hundredths hard
Decimal notation for fractions is prerequisite to understanding % as parts per 100
- Tenths (age 8+) hard
Understanding hundredths is prerequisite to working with 10ths and 100ths together
- Finding halves and quarters (age 5+) hard
Working with 1/4, 2/4, 3/4 extends from Y1 understanding of quarters
- Fraction Notation hard
Writing fractions like 1/3 and 3/4 requires knowing numerator and denominator
- Equivalent fractions (age 9+) hard
Generating equivalent fractions supports converting 10ths to 100ths
- Equivalent fractions on a number line hard
Understanding equivalence conceptually is prerequisite to explaining algebraically
- Equivalent fractions hard
Diagram-based equivalent fractions is prerequisite to formal equivalence understanding
- Fractions of amounts hard
Recognising fractions of shapes/quantities is prerequisite to formal unit fraction understanding
- Fraction Notation hard
Understanding a/b as a parts of 1/b requires numerator, denominator, and unit fraction vocabulary
- Splitting shapes into equal parts (age 7+) hard
Partition into equal shares is prerequisite to understanding unit fractions
- Fractions on a number line (age 8+) hard
Equivalent fractions as the same point on a number line directly uses the fraction number-line representation
- Fractions on a number line hard
Prior number-line fraction experience feeds into formal unit-fraction placement
- Equivalent fractions (age 8+) hard
Generating equivalent fractions with visual models is prerequisite to algebraic explanation of equivalence
- Equivalent fractions on a number line hard
Must understand equivalence before generating equivalent fractions
- Equivalent fractions hard
Diagram-based equivalent fractions is prerequisite to formal equivalence understanding
- Fractions on a number line (age 8+) hard
Equivalent fractions as the same point on a number line directly uses the fraction number-line representation
- Decimal equivalents of tenths and hundredths hard
Y4 decimal equivalents of 10ths/100ths is prerequisite to formal decimal notation for fractions
- Finding halves and quarters (age 5+) hard
Working with 1/4, 2/4, 3/4 extends from Y1 understanding of quarters
- Fraction Notation hard
Writing fractions like 1/3 and 3/4 requires knowing numerator and denominator
- Decimal & Percent Notation hard
Writing decimal equivalents of tenths and hundredths requires decimal point and place-value vocabulary
- Decimal & Percent Notation hard
Using decimal notation for fractions requires decimal, tenths, and hundredths vocabulary
- Decimal & Percent Notation hard
Understanding the % symbol and 'per cent means parts per hundred' is the LANGUAGE node content
- Proportional Reasoning Vocabulary soft
Expressing one quantity as a fraction of another uses 'proportion' and 'multiplicative relationship' vocabulary
- Proportional Reasoning Vocabulary hard
Ratio notation (a:b) requires 'ratio', 'simplify', and 'equivalent' as defined terms
- Factors, multiples, and primes hard
Simplifying ratios requires finding common factors — extends KS2 factor pairs and common factors
- All times tables to 12×12 hard
Tables to 12×12 fluency is prerequisite to finding factor pairs up to 100
- Skip Counting (4s, 8s, 50s, 100s) hard
Counting in 6s/7s/9s/25s/1000s extends counting in 4s/8s/50s/100s
- Multiplication as repeated addition hard
Recalling times table facts requires understanding multiplication as repeated addition/grouping
- Addition as combining or putting together two hard
Multiplication as repeated addition requires understanding addition as combining groups
- How Many in Total? hard
Understanding addition as combining groups requires knowing numbers represent quantities (cardinality)
- One-to-one counting hard
Cardinality principle builds on one-to-one correspondence — you must count correctly to know the last number tells 'how many'
- Factor Pairs & Commutativity hard
Recognising factor pairs at Y4 is prerequisite to systematically finding all factor pairs
- Skip Counting (4s, 8s, 50s, 100s) hard
Counting in 6s/7s/9s/25s/1000s extends counting in 4s/8s/50s/100s
- Multiplication as repeated addition hard
Recalling times table facts requires understanding multiplication as repeated addition/grouping
- Addition as combining or putting together two hard
Multiplication as repeated addition requires understanding addition as combining groups
- How Many in Total? hard
Understanding addition as combining groups requires knowing numbers represent quantities (cardinality)
- Commutative Multiplication hard
Applying all three properties extends Y2 commutativity understanding
- Division as equal sharing hard
Using arrays for division requires understanding division as grouping
- Subtraction as taking away or separating hard
Division as equal sharing/grouping requires understanding subtraction as taking away/separating
- How Many in Total? hard
Understanding subtraction as taking away requires knowing numbers represent quantities (cardinality)
- Multiplication as repeated addition hard
Using arrays requires understanding what multiplication means
- Addition as combining or putting together two hard
Multiplication as repeated addition requires understanding addition as combining groups
- How Many in Total? hard
Understanding addition as combining groups requires knowing numbers represent quantities (cardinality)
- Multiplication as repeated addition hard
Commutativity of multiplication requires understanding multiplication
- Addition as combining or putting together two hard
Multiplication as repeated addition requires understanding addition as combining groups
- How Many in Total? hard
Understanding addition as combining groups requires knowing numbers represent quantities (cardinality)
- One-to-one counting hard
Cardinality principle builds on one-to-one correspondence — you must count correctly to know the last number tells 'how many'
- Arrays for multiplication (age 7+) hard
Extends array-based repeated addition to formal multiplication interpretation
- Arrays for multiplication hard
Rectangular arrays with repeated addition extends array representation from Y2
- Division as equal sharing hard
Using arrays for division requires understanding division as grouping
- Subtraction as taking away or separating hard
Division as equal sharing/grouping requires understanding subtraction as taking away/separating
- Multiplication as repeated addition hard
Using arrays requires understanding what multiplication means
- Addition as combining or putting together two hard
Multiplication as repeated addition requires understanding addition as combining groups
- Multiplication as repeated addition hard
Expressing array totals as sums of equal addends requires understanding multiplication as repeated addition
- Addition as combining or putting together two hard
Multiplication as repeated addition requires understanding addition as combining groups
- How Many in Total? hard
Understanding addition as combining groups requires knowing numbers represent quantities (cardinality)
- Multiplication as repeated addition hard
Interpreting products formalises repeated addition/equal groups from Y1
- Addition as combining or putting together two hard
Multiplication as repeated addition requires understanding addition as combining groups
- How Many in Total? hard
Understanding addition as combining groups requires knowing numbers represent quantities (cardinality)
- One-to-one counting hard
Cardinality principle builds on one-to-one correspondence — you must count correctly to know the last number tells 'how many'
- Understanding fractions hard
Ratio notation and simplification extends KS2 unequal sharing and grouping with ratios
- Simplifying Fractions hard
Understanding fraction of total requires simplification/common denominator skills
- Equivalent fractions on a number line hard
Understanding equivalence conceptually is prerequisite to explaining algebraically
- Equivalent fractions hard
Diagram-based equivalent fractions is prerequisite to formal equivalence understanding
- Finding halves and quarters (age 5+) hard
Working with 1/4, 2/4, 3/4 extends from Y1 understanding of quarters
- Fraction Notation hard
Writing fractions like 1/3 and 3/4 requires knowing numerator and denominator
- Reading +, −, and = symbols soft
Writing fraction sentences (1/2 of 6 = 3) requires understanding the = sign
- Reading and writing numbers to 20 hard
Writing number sentences requires reading and writing numerals
- Addition as combining or putting together two hard
Reading/writing the + symbol requires understanding what addition means
- Subtraction as taking away or separating hard
Reading/writing the − symbol requires understanding what subtraction means
- Fractions of amounts hard
Writing fractions and recognising equivalence requires knowing what the fractions mean
- Finding halves and quarters (age 5+) hard
Working with 1/4, 2/4, 3/4 extends from Y1 understanding of quarters
- Fraction Notation hard
Writing fractions like 1/3 and 3/4 requires knowing numerator and denominator
- Fraction Notation hard
Writing fractions and recognising equivalence requires 'equivalent fraction' vocabulary
- Fractions of amounts hard
Recognising fractions of shapes/quantities is prerequisite to formal unit fraction understanding
- Finding halves and quarters (age 5+) hard
Working with 1/4, 2/4, 3/4 extends from Y1 understanding of quarters
- What Is a Half? hard
Understanding quarters extends from understanding halves — both are equal parts but quarters requires dividing into 4
- Division as equal sharing hard
Finding a half requires equal sharing into 2 groups — a division concept
- Subtraction as taking away or separating hard
Division as equal sharing/grouping requires understanding subtraction as taking away/separating
- Fraction Notation hard
Writing fractions like 1/3 and 3/4 requires knowing numerator and denominator
- Fraction Notation hard
Understanding a/b as a parts of 1/b requires numerator, denominator, and unit fraction vocabulary
- Splitting shapes into equal parts (age 7+) hard
Partition into equal shares is prerequisite to understanding unit fractions
- Decomposing a shape into more equal shares hard
Understanding equal shares of different shapes requires concept of more shares = smaller
- Halves & Quarters of Shapes hard
Comparing share sizes requires experience partitioning into halves and quarters
- Finding halves and quarters (age 5+) hard
Partitioning into fourths/quarters extends from Y1 understanding of quarters
- Fractions on a number line (age 8+) hard
Equivalent fractions as the same point on a number line directly uses the fraction number-line representation
- Fractions on a number line hard
Prior number-line fraction experience feeds into formal unit-fraction placement
- Finding halves and quarters (age 5+) hard
Working with 1/4, 2/4, 3/4 extends from Y1 understanding of quarters
- Fraction Notation hard
Writing fractions like 1/3 and 3/4 requires knowing numerator and denominator
- Fractions of amounts hard
Recognising fractions of shapes/quantities is prerequisite to formal unit fraction understanding
- Finding halves and quarters (age 5+) hard
Working with 1/4, 2/4, 3/4 extends from Y1 understanding of quarters
- Fraction Notation hard
Writing fractions like 1/3 and 3/4 requires knowing numerator and denominator
- Fraction Notation hard
Understanding a/b as a parts of 1/b requires numerator, denominator, and unit fraction vocabulary
- Splitting shapes into equal parts (age 7+) hard
Partition into equal shares is prerequisite to understanding unit fractions
- Decomposing a shape into more equal shares hard
Understanding equal shares of different shapes requires concept of more shares = smaller
- Equivalent fractions (age 8+) hard
Generating equivalent fractions with visual models is prerequisite to algebraic explanation of equivalence
- Equivalent fractions on a number line hard
Must understand equivalence before generating equivalent fractions
- Equivalent fractions hard
Diagram-based equivalent fractions is prerequisite to formal equivalence understanding
- Reading +, −, and = symbols soft
Writing fraction sentences (1/2 of 6 = 3) requires understanding the = sign
- Fractions of amounts hard
Writing fractions and recognising equivalence requires knowing what the fractions mean
- Fraction Notation hard
Writing fractions and recognising equivalence requires 'equivalent fraction' vocabulary
- Fractions of amounts hard
Recognising fractions of shapes/quantities is prerequisite to formal unit fraction understanding
- Finding halves and quarters (age 5+) hard
Working with 1/4, 2/4, 3/4 extends from Y1 understanding of quarters
- Fraction Notation hard
Writing fractions like 1/3 and 3/4 requires knowing numerator and denominator
- Fraction Notation hard
Understanding a/b as a parts of 1/b requires numerator, denominator, and unit fraction vocabulary
- Splitting shapes into equal parts (age 7+) hard
Partition into equal shares is prerequisite to understanding unit fractions
- Decomposing a shape into more equal shares hard
Understanding equal shares of different shapes requires concept of more shares = smaller
- Fractions on a number line (age 8+) hard
Equivalent fractions as the same point on a number line directly uses the fraction number-line representation
- Fractions on a number line hard
Prior number-line fraction experience feeds into formal unit-fraction placement
- Fractions of amounts hard
Recognising fractions of shapes/quantities is prerequisite to formal unit fraction understanding
- Fraction Notation hard
Understanding a/b as a parts of 1/b requires numerator, denominator, and unit fraction vocabulary
- Splitting shapes into equal parts (age 7+) hard
Partition into equal shares is prerequisite to understanding unit fractions
- Factors, multiples, and primes hard
Using common factors/multiples requires knowledge of common factors and multiples
- All times tables to 12×12 hard
Tables to 12×12 fluency is prerequisite to finding factor pairs up to 100
- Skip Counting (4s, 8s, 50s, 100s) hard
Counting in 6s/7s/9s/25s/1000s extends counting in 4s/8s/50s/100s
- Multiplication as repeated addition hard
Recalling times table facts requires understanding multiplication as repeated addition/grouping
- Addition as combining or putting together two hard
Multiplication as repeated addition requires understanding addition as combining groups
- Factor Pairs & Commutativity hard
Recognising factor pairs at Y4 is prerequisite to systematically finding all factor pairs
- Skip Counting (4s, 8s, 50s, 100s) hard
Counting in 6s/7s/9s/25s/1000s extends counting in 4s/8s/50s/100s
- Multiplication as repeated addition hard
Recalling times table facts requires understanding multiplication as repeated addition/grouping
- Commutative Multiplication hard
Applying all three properties extends Y2 commutativity understanding
- Division as equal sharing hard
Using arrays for division requires understanding division as grouping
- Multiplication as repeated addition hard
Using arrays requires understanding what multiplication means
- Multiplication as repeated addition hard
Commutativity of multiplication requires understanding multiplication
- Addition as combining or putting together two hard
Multiplication as repeated addition requires understanding addition as combining groups
- Arrays for multiplication (age 7+) hard
Extends array-based repeated addition to formal multiplication interpretation
- Arrays for multiplication hard
Rectangular arrays with repeated addition extends array representation from Y2
- Multiplication as repeated addition hard
Expressing array totals as sums of equal addends requires understanding multiplication as repeated addition
- Multiplication as repeated addition hard
Interpreting products formalises repeated addition/equal groups from Y1
- Addition as combining or putting together two hard
Multiplication as repeated addition requires understanding addition as combining groups
- Fraction Notation hard
Simplifying fractions to simplest form requires 'simplest form' and 'common factor' vocabulary
- Bar Models for Ratios hard
Unequal sharing problems are the canonical use case for tape diagrams — the visual model makes the structure of the problem transparent
- Percentages (age 9+) hard
Unequal sharing problems require 'ratio', 'unequal', 'part-to-part', and 'proportion' vocabulary
- Equivalent fractions on a number line hard
Understanding equivalence conceptually is prerequisite to explaining algebraically
- Equivalent fractions hard
Diagram-based equivalent fractions is prerequisite to formal equivalence understanding
- Fractions of amounts hard
Recognising fractions of shapes/quantities is prerequisite to formal unit fraction understanding
- Fraction Notation hard
Understanding a/b as a parts of 1/b requires numerator, denominator, and unit fraction vocabulary
- Splitting shapes into equal parts (age 7+) hard
Partition into equal shares is prerequisite to understanding unit fractions
- Fractions on a number line (age 8+) hard
Equivalent fractions as the same point on a number line directly uses the fraction number-line representation
- Fractions on a number line hard
Prior number-line fraction experience feeds into formal unit-fraction placement
- Equivalent fractions (age 8+) hard
Generating equivalent fractions with visual models is prerequisite to algebraic explanation of equivalence
- Equivalent fractions on a number line hard
Must understand equivalence before generating equivalent fractions
- Equivalent fractions hard
Diagram-based equivalent fractions is prerequisite to formal equivalence understanding
- Fractions on a number line (age 8+) hard
Equivalent fractions as the same point on a number line directly uses the fraction number-line representation
- Factors, multiples, and primes hard
Using common factors/multiples requires knowledge of common factors and multiples
- All times tables to 12×12 hard
Tables to 12×12 fluency is prerequisite to finding factor pairs up to 100
- Skip Counting (4s, 8s, 50s, 100s) hard
Counting in 6s/7s/9s/25s/1000s extends counting in 4s/8s/50s/100s
- Factor Pairs & Commutativity hard
Recognising factor pairs at Y4 is prerequisite to systematically finding all factor pairs
- Commutative Multiplication hard
Applying all three properties extends Y2 commutativity understanding
- Fraction Notation hard
Simplifying fractions to simplest form requires 'simplest form' and 'common factor' vocabulary
- Understanding fractions (age 9+) hard
a/b as sum of 1/b is prerequisite to understanding a/b as multiple of 1/b
- Fractions of a whole hard
Understanding a/b as a parts of size 1/b is prerequisite to understanding a/b as sum of 1/b
- Fractions of amounts hard
Recognising fractions of shapes/quantities is prerequisite to formal unit fraction understanding
- Finding halves and quarters (age 5+) hard
Working with 1/4, 2/4, 3/4 extends from Y1 understanding of quarters
- Fraction Notation hard
Writing fractions like 1/3 and 3/4 requires knowing numerator and denominator
- Fraction Notation hard
Understanding a/b as a parts of 1/b requires numerator, denominator, and unit fraction vocabulary
- Splitting shapes into equal parts (age 7+) hard
Partition into equal shares is prerequisite to understanding unit fractions
- Decomposing a shape into more equal shares hard
Understanding equal shares of different shapes requires concept of more shares = smaller
- Bar Models for Ratios hard
Solving relative-sizes problems is most reliably scaffolded by drawing a bar model to set up the relationship
- Percentages (age 9+) hard
Solving relative sizes problems requires 'ratio', 'proportion', and 'relative size' as understood terms
- What Multiplication Means hard
Interpreting products is prerequisite to interpreting multiplication as comparison
- Arrays for multiplication (age 7+) hard
Extends array-based repeated addition to formal multiplication interpretation
- Arrays for multiplication hard
Rectangular arrays with repeated addition extends array representation from Y2
- Division as equal sharing hard
Using arrays for division requires understanding division as grouping
- Subtraction as taking away or separating hard
Division as equal sharing/grouping requires understanding subtraction as taking away/separating
- Multiplication as repeated addition hard
Using arrays requires understanding what multiplication means
- Addition as combining or putting together two hard
Multiplication as repeated addition requires understanding addition as combining groups
- Multiplication as repeated addition hard
Expressing array totals as sums of equal addends requires understanding multiplication as repeated addition
- Addition as combining or putting together two hard
Multiplication as repeated addition requires understanding addition as combining groups
- How Many in Total? hard
Understanding addition as combining groups requires knowing numbers represent quantities (cardinality)
- Multiplication as repeated addition hard
Interpreting products formalises repeated addition/equal groups from Y1
- Addition as combining or putting together two hard
Multiplication as repeated addition requires understanding addition as combining groups
- How Many in Total? hard
Understanding addition as combining groups requires knowing numbers represent quantities (cardinality)
- One-to-one counting hard
Cardinality principle builds on one-to-one correspondence — you must count correctly to know the last number tells 'how many'
- Proportion Graphs soft
Ratio notation and simplification is complemented by double number line representations
- Proportional Reasoning Vocabulary hard
Compound units (speed, density) require 'compound unit', 'rate', 'speed', and 'density' as named and defined vocabulary
- Proportion Graphs soft
Compound units like speed and density involve proportional relationships visible on proportion graphs
- Decimal place value hard
KS3 unit conversion extends KS2 (Y6) metric conversion with decimals to area/volume units
- Dividing by 10 and 100 hard
Dividing by 10/100 (Y4 fractions context) is prerequisite to ×÷ by 10/100/1000 with decimals
- Finding halves and quarters (age 5+) hard
Working with 1/4, 2/4, 3/4 extends from Y1 understanding of quarters
- What Is a Half? hard
Understanding quarters extends from understanding halves — both are equal parts but quarters requires dividing into 4
- Division as equal sharing hard
Finding a half requires equal sharing into 2 groups — a division concept
- Division as equal sharing hard
Finding a half requires equal sharing into 2 groups — a division concept
- Subtraction as taking away or separating hard
Division as equal sharing/grouping requires understanding subtraction as taking away/separating
- Subtraction as taking away or separating hard
Division as equal sharing/grouping requires understanding subtraction as taking away/separating
- How Many in Total? hard
Understanding subtraction as taking away requires knowing numbers represent quantities (cardinality)
- Fraction Notation hard
Writing fractions like 1/3 and 3/4 requires knowing numerator and denominator
- Decimal equivalents of tenths and hundredths hard
Must know decimal notation to express results of dividing by 10/100
- Finding halves and quarters (age 5+) hard
Working with 1/4, 2/4, 3/4 extends from Y1 understanding of quarters
- What Is a Half? hard
Understanding quarters extends from understanding halves — both are equal parts but quarters requires dividing into 4
- Division as equal sharing hard
Finding a half requires equal sharing into 2 groups — a division concept
- Subtraction as taking away or separating hard
Division as equal sharing/grouping requires understanding subtraction as taking away/separating
- Fraction Notation hard
Writing fractions like 1/3 and 3/4 requires knowing numerator and denominator
- Decimal & Percent Notation hard
Writing decimal equivalents of tenths and hundredths requires decimal point and place-value vocabulary
- Place value of each digit hard
Four-digit place value is prerequisite to understanding ×10 relationship between places
- The three digits of a three-digit number hard
Four-digit place value extends three-digit place value
- The teen numbers hard
Understanding 10 as a bundle builds on understanding teen numbers as 'a ten and some ones'
- How Many in Total? hard
Understanding tens-and-ones composition requires cardinality — knowing numbers represent quantities
- Reading and writing numbers to 20 hard
Composing/decomposing teen numbers requires reading and writing those numerals
- The two digits of a two-digit number hard
Must understand two-digit place value before extending to hundreds
- A Ten Is Ten Ones hard
Understanding tens and ones place value requires the concept of 10 as a bundle
- The teen numbers hard
Understanding 10 as a bundle builds on understanding teen numbers as 'a ten and some ones'
- The teen numbers hard
General two-digit place value extends from understanding teen number composition
- How Many in Total? hard
Understanding tens-and-ones composition requires cardinality — knowing numbers represent quantities
- Reading and writing numbers to 20 hard
Composing/decomposing teen numbers requires reading and writing those numerals
- A Ten Is Ten Ones hard
Understanding tens and ones place value requires the concept of 10 as a bundle
- The teen numbers hard
Understanding 10 as a bundle builds on understanding teen numbers as 'a ten and some ones'
- How Many in Total? hard
Understanding tens-and-ones composition requires cardinality — knowing numbers represent quantities
- Reading and writing numbers to 20 hard
Composing/decomposing teen numbers requires reading and writing those numerals
- The teen numbers hard
General two-digit place value extends from understanding teen number composition
- How Many in Total? hard
Understanding tens-and-ones composition requires cardinality — knowing numbers represent quantities
- One-to-one counting hard
Cardinality principle builds on one-to-one correspondence — you must count correctly to know the last number tells 'how many'
- Reading and writing numbers to 20 hard
Composing/decomposing teen numbers requires reading and writing those numerals
- How Many in Total? hard
Reading/writing numerals 0–20 requires understanding that numerals represent quantities (cardinality)
- Writing digits 0-9 hard
Writing numerals requires the motor skill of forming digits 0-9 (taught in English handwriting)
- Reading Decimal Places hard
Understanding digit shifting requires knowing what each decimal place represents
- Reading and writing numbers (age 10+) hard
Identifying digit value in 3dp numbers requires reading decimals to thousandths
- Decimal place value (age 8+) hard
Comparing decimals to 2dp (Y4) is prerequisite to comparing to 3dp
- Decimal equivalents of tenths and hundredths hard
Must understand decimal notation to compare decimals
- Decimal & Percent Notation hard
Writing decimal equivalents of tenths and hundredths requires decimal point and place-value vocabulary
- Decimals for Tenths & Hundredths hard
Decimal notation for 10ths/100ths is prerequisite to extending to thousandths
- Tenths (age 8+) hard
Understanding hundredths is prerequisite to working with 10ths and 100ths together
- Equivalent fractions (age 9+) hard
Generating equivalent fractions supports converting 10ths to 100ths
- Equivalent fractions on a number line hard
Understanding equivalence conceptually is prerequisite to explaining algebraically
- Equivalent fractions (age 8+) hard
Generating equivalent fractions with visual models is prerequisite to algebraic explanation of equivalence
- Decimal equivalents of tenths and hundredths hard
Y4 decimal equivalents of 10ths/100ths is prerequisite to formal decimal notation for fractions
- Decimal & Percent Notation hard
Writing decimal equivalents of tenths and hundredths requires decimal point and place-value vocabulary
- Decimal & Percent Notation hard
Using decimal notation for fractions requires decimal, tenths, and hundredths vocabulary
- Decimals for Tenths & Hundredths hard
Decimal notation for 10ths/100ths is prerequisite to extending to thousandths
- Tenths (age 8+) hard
Understanding hundredths is prerequisite to working with 10ths and 100ths together
- Equivalent fractions (age 9+) hard
Generating equivalent fractions supports converting 10ths to 100ths
- Equivalent fractions on a number line hard
Understanding equivalence conceptually is prerequisite to explaining algebraically
- Equivalent fractions (age 8+) hard
Generating equivalent fractions with visual models is prerequisite to algebraic explanation of equivalence
- Decimal equivalents of tenths and hundredths hard
Y4 decimal equivalents of 10ths/100ths is prerequisite to formal decimal notation for fractions
- Decimal & Percent Notation hard
Writing decimal equivalents of tenths and hundredths requires decimal point and place-value vocabulary
- Decimal & Percent Notation hard
Using decimal notation for fractions requires decimal, tenths, and hundredths vocabulary
- Place value of each digit hard
Four-digit place value is prerequisite to understanding ×10 relationship between places
- The three digits of a three-digit number hard
Four-digit place value extends three-digit place value
- The two digits of a two-digit number hard
Must understand two-digit place value before extending to hundreds
- A Ten Is Ten Ones hard
Understanding tens and ones place value requires the concept of 10 as a bundle
- The teen numbers hard
General two-digit place value extends from understanding teen number composition
- Tenths (age 9+) hard
Reading/writing decimals to thousandths requires understanding thousandths place
- Decimals for Tenths & Hundredths hard
Decimal notation for 10ths/100ths is prerequisite to extending to thousandths
- Tenths (age 8+) hard
Understanding hundredths is prerequisite to working with 10ths and 100ths together
- Equivalent fractions (age 9+) hard
Generating equivalent fractions supports converting 10ths to 100ths
- Equivalent fractions on a number line hard
Understanding equivalence conceptually is prerequisite to explaining algebraically
- Equivalent fractions hard
Diagram-based equivalent fractions is prerequisite to formal equivalence understanding
- Fractions on a number line (age 8+) hard
Equivalent fractions as the same point on a number line directly uses the fraction number-line representation
- Equivalent fractions (age 8+) hard
Generating equivalent fractions with visual models is prerequisite to algebraic explanation of equivalence
- Equivalent fractions on a number line hard
Must understand equivalence before generating equivalent fractions
- Decimal equivalents of tenths and hundredths hard
Y4 decimal equivalents of 10ths/100ths is prerequisite to formal decimal notation for fractions
- Decimal & Percent Notation hard
Writing decimal equivalents of tenths and hundredths requires decimal point and place-value vocabulary
- Decimal & Percent Notation hard
Using decimal notation for fractions requires decimal, tenths, and hundredths vocabulary
- Converting measurement units (age 9+) hard
Y6 unit conversion with decimals extends Y5 metric conversion
- Converting measurement units hard
Y4 unit conversion is prerequisite to systematic metric conversions with tables
- Calculating with measurements hard
Measuring in standard units is prerequisite to converting between units
- Comparing and ordering measurements hard
Extends comparing/ordering measures to adding/subtracting them
- Choosing measurement units hard
Comparing and ordering measurements with symbols requires being able to measure in standard units
- Capacity and volume hard
Using standard units for capacity extends from beginning to measure capacity
- Comparing Capacity hard
Measuring capacity with units requires first being able to compare capacities
- Measurable Attributes of Objects hard
Comparing capacity requires understanding capacity as a measurable attribute
- Measuring length and height (age 5+) hard
Using standard units for length extends from beginning to measure length
- Comparing Lengths & Heights hard
Measuring length with units requires first being able to compare lengths directly
- Measurable Attributes of Objects hard
Comparing lengths/heights requires first identifying length as a measurable attribute
- Measuring mass and weight (age 4+) hard
Measuring mass with units requires first being able to compare masses directly
- Measurable Attributes of Objects hard
Comparing mass/weight requires first identifying mass as a measurable attribute
- The two digits of a two-digit number hard
Comparing two-digit numbers using PV requires understanding tens and ones
- A Ten Is Ten Ones hard
Understanding tens and ones place value requires the concept of 10 as a bundle
- The teen numbers hard
Understanding 10 as a bundle builds on understanding teen numbers as 'a ten and some ones'
- How Many in Total? hard
Understanding tens-and-ones composition requires cardinality — knowing numbers represent quantities
- Reading and writing numbers to 20 hard
Composing/decomposing teen numbers requires reading and writing those numerals
- The teen numbers hard
General two-digit place value extends from understanding teen number composition
- How Many in Total? hard
Understanding tens-and-ones composition requires cardinality — knowing numbers represent quantities
- One-to-one counting hard
Cardinality principle builds on one-to-one correspondence — you must count correctly to know the last number tells 'how many'
- Reading and writing numbers to 20 hard
Composing/decomposing teen numbers requires reading and writing those numerals
- How Many in Total? hard
Reading/writing numerals 0–20 requires understanding that numerals represent quantities (cardinality)
- Writing digits 0-9 hard
Writing numerals requires the motor skill of forming digits 0-9 (taught in English handwriting)
- Two written numerals between 1 and 10 soft
Comparing two-digit numbers extends from comparing single-digit written numerals
- Comparing groups: more or fewer soft
Comparing written numerals is the symbolic form of comparing quantities — conceptual comparison helps but isn't strictly required
- Counting objects to 20 soft
Counting a set helps when comparing groups, but younger children (GB age 4) can compare using matching without formal counting to 20
- Choosing measurement units hard
Extends Y2 standard unit measurement to include mm and to add/subtract measures
- Capacity and volume hard
Using standard units for capacity extends from beginning to measure capacity
- Comparing Capacity hard
Measuring capacity with units requires first being able to compare capacities
- Measurable Attributes of Objects hard
Comparing capacity requires understanding capacity as a measurable attribute
- Measuring length and height (age 5+) hard
Using standard units for length extends from beginning to measure length
- Comparing Lengths & Heights hard
Measuring length with units requires first being able to compare lengths directly
- Measurable Attributes of Objects hard
Comparing lengths/heights requires first identifying length as a measurable attribute
- Measuring mass and weight (age 4+) hard
Measuring mass with units requires first being able to compare masses directly
- Measurable Attributes of Objects hard
Comparing mass/weight requires first identifying mass as a measurable attribute
- Time Units and Calendar Facts hard
Knowing seconds/minute, days/month etc. is prerequisite to unit conversion problems
- Number of minutes in an hour hard
Extends knowing minutes in an hour to seconds in a minute and days in months
- Telling time to the minute hard
Knowing 60 min = 1 hour and 24 hours = 1 day extends from measuring time in hours/minutes/seconds
- Comparing durations hard
Measuring time in units requires understanding time comparison language first
- Dividing by 10 and 100 hard
Dividing by 10/100 (Y4 fractions context) is prerequisite to ×÷ by 10/100/1000 with decimals
- Finding halves and quarters (age 5+) hard
Working with 1/4, 2/4, 3/4 extends from Y1 understanding of quarters
- What Is a Half? hard
Understanding quarters extends from understanding halves — both are equal parts but quarters requires dividing into 4
- Division as equal sharing hard
Finding a half requires equal sharing into 2 groups — a division concept
- Division as equal sharing hard
Finding a half requires equal sharing into 2 groups — a division concept
- Subtraction as taking away or separating hard
Division as equal sharing/grouping requires understanding subtraction as taking away/separating
- Subtraction as taking away or separating hard
Division as equal sharing/grouping requires understanding subtraction as taking away/separating
- How Many in Total? hard
Understanding subtraction as taking away requires knowing numbers represent quantities (cardinality)
- Fraction Notation hard
Writing fractions like 1/3 and 3/4 requires knowing numerator and denominator
- Decimal equivalents of tenths and hundredths hard
Must know decimal notation to express results of dividing by 10/100
- Finding halves and quarters (age 5+) hard
Working with 1/4, 2/4, 3/4 extends from Y1 understanding of quarters
- What Is a Half? hard
Understanding quarters extends from understanding halves — both are equal parts but quarters requires dividing into 4
- Division as equal sharing hard
Finding a half requires equal sharing into 2 groups — a division concept
- Subtraction as taking away or separating hard
Division as equal sharing/grouping requires understanding subtraction as taking away/separating
- Fraction Notation hard
Writing fractions like 1/3 and 3/4 requires knowing numerator and denominator
- Decimal & Percent Notation hard
Writing decimal equivalents of tenths and hundredths requires decimal point and place-value vocabulary
- Place value of each digit hard
Four-digit place value is prerequisite to understanding ×10 relationship between places
- The three digits of a three-digit number hard
Four-digit place value extends three-digit place value
- The teen numbers hard
Understanding 10 as a bundle builds on understanding teen numbers as 'a ten and some ones'
- How Many in Total? hard
Understanding tens-and-ones composition requires cardinality — knowing numbers represent quantities
- Reading and writing numbers to 20 hard
Composing/decomposing teen numbers requires reading and writing those numerals
- The two digits of a two-digit number hard
Must understand two-digit place value before extending to hundreds
- A Ten Is Ten Ones hard
Understanding tens and ones place value requires the concept of 10 as a bundle
- The teen numbers hard
Understanding 10 as a bundle builds on understanding teen numbers as 'a ten and some ones'
- The teen numbers hard
General two-digit place value extends from understanding teen number composition
- How Many in Total? hard
Understanding tens-and-ones composition requires cardinality — knowing numbers represent quantities
- Reading and writing numbers to 20 hard
Composing/decomposing teen numbers requires reading and writing those numerals
- A Ten Is Ten Ones hard
Understanding tens and ones place value requires the concept of 10 as a bundle
- The teen numbers hard
Understanding 10 as a bundle builds on understanding teen numbers as 'a ten and some ones'
- How Many in Total? hard
Understanding tens-and-ones composition requires cardinality — knowing numbers represent quantities
- Reading and writing numbers to 20 hard
Composing/decomposing teen numbers requires reading and writing those numerals
- The teen numbers hard
General two-digit place value extends from understanding teen number composition
- How Many in Total? hard
Understanding tens-and-ones composition requires cardinality — knowing numbers represent quantities
- One-to-one counting hard
Cardinality principle builds on one-to-one correspondence — you must count correctly to know the last number tells 'how many'
- Reading and writing numbers to 20 hard
Composing/decomposing teen numbers requires reading and writing those numerals
- How Many in Total? hard
Reading/writing numerals 0–20 requires understanding that numerals represent quantities (cardinality)
- Writing digits 0-9 hard
Writing numerals requires the motor skill of forming digits 0-9 (taught in English handwriting)
- Proportional Reasoning Vocabulary soft
Unit conversion draws on 'rate', 'unit rate', and 'scale factor' vocabulary
Unlocks2
- Reading Distance-Time GraphssoftAges 10—13
- Speed & Distance-Time GraphssoftAges 11—12