Types of angles (age 13+)
PROCEDURALApply Pythagoras’ Theorem (a² + b² = c²) to calculate unknown side lengths in right-angled triangles, including in real-world and coordinate-geometry contexts
Mastery Evidence
- Calculate the hypotenuse of a right-angled triangle given the two shorter sides
- Find a shorter side given the hypotenuse and the other short side
- Use Pythagoras’ Theorem to find the distance between two points on a coordinate grid
Assessment Prompt
“If [child] wants to check whether a shelf bracket makes a perfect right angle and the sides measure 30 cm, 40 cm, and 50 cm, can they use Pythagoras to verify?”
Curriculum Standards5 alignments
8.G.6Common Core State Standards for MathematicsExplain a proof of the Pythagorean Theorem and its converse.
8.G.7Common Core State Standards for MathematicsApply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions.
8.G.8Common Core State Standards for MathematicsApply the Pythagorean Theorem to find the distance between two points in a coordinate system.
KS3.Maths.Geo.13The national curriculum in Englandapply angle facts, triangle congruence, similarity and properties of quadrilaterals to derive results about angles and sides, including Pythagoras' Theorem, and use known results to obtain simple proofs
KS3.Maths.Geo.14The national curriculum in Englanduse Pythagoras' Theorem and trigonometric ratios in similar triangles to solve problems involving right-angled triangles
Prerequisites2
- Simple formulaesoftAges 12—14
- Angle sums in triangles and polygonshardAges 11—14
Show full prerequisite tree
- 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
- Angle sums in triangles and polygons hard
Pythagoras requires understanding triangle angle sums and properties
- Angles in triangles (age 10+) hard
Extends KS2 angle sums in triangles and quadrilaterals to general polygons
- Types of angles (age 8+) hard
Finding unknown angles in polygons requires reading diagrams where known angles are marked with arcs and tick marks
- Understanding angles (age 8+) hard
Shape classification supports distinguishing regular from irregular
- 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
- 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
- 2-D shapes (age 6+) soft
Understanding angles as shape properties requires knowing basic shape properties
- Angles in triangles (age 6+) soft
Understanding defining attributes supports describing shape properties formally
- 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
- Position, direction, and movement hard
Recognising angles as turns extends Y2 work on quarter/half/three-quarter turns
- 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
- 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
- What Is a Half? soft
Understanding half and quarter turns benefits from the concept of halves and quarters
- Classifying shapes by line properties hard
Property-based hierarchy extends Y5 classification by parallel/perpendicular lines
- 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
- 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
- Position, direction, and movement hard
Recognising angles as turns extends Y2 work on quarter/half/three-quarter turns
- 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
- 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
- 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
- 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
- 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
- Position, direction, and movement hard
Recognising angles as turns extends Y2 work on quarter/half/three-quarter turns
- 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
- 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
- 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
- Understanding angles (age 8+) hard
Y4 quadrilateral classification supports classifying by lines/angles
- 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
- Types of angles (age 8+) hard
Angle sum rules (360° at a point, 180° on a line) are applied through reading angle diagrams with correct notation
- 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
- 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
- Position, direction, and movement hard
Recognising angles as turns extends Y2 work on quarter/half/three-quarter turns
- 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
- 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
- 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+) soft
Understanding angles as shape properties requires knowing basic 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
- Position, direction, and movement hard
Recognising angles as turns extends Y2 work on quarter/half/three-quarter turns
- 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
- 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
- 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
- Algebraic Notation soft
Expressing angle sum as (n-2)×180 requires algebraic notation for the general formula
- 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
- 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
- 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
- Angle Sum Rules hard
Builds on KS2 knowledge that angles at a point sum to 360° and on a line to 180°
- Types of angles (age 8+) hard
Angle sum rules (360° at a point, 180° on a line) are applied through reading angle diagrams with correct notation
- 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
- 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
- Position, direction, and movement hard
Recognising angles as turns extends Y2 work on quarter/half/three-quarter turns
- 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
- 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
- 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+) soft
Understanding angles as shape properties requires knowing basic 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
- Position, direction, and movement hard
Recognising angles as turns extends Y2 work on quarter/half/three-quarter turns
- 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
- 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
- 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
- Understanding angles (age 10+) hard
KS3 angle facts extend KS2 angles at a point, on a line, and vertically opposite
- Types of angles (age 8+) hard
Measuring and drawing angles with a protractor requires knowing how to mark and label angles using standard notation
- 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
- 2-D shapes (age 6+) soft
Understanding angles as shape properties requires knowing basic shape properties
- Angles in triangles (age 6+) soft
Understanding defining attributes supports describing shape properties formally
- 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
- Position, direction, and movement hard
Recognising angles as turns extends Y2 work on quarter/half/three-quarter turns
- 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
- 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
- What Is a Half? soft
Understanding half and quarter turns benefits from the concept of halves and quarters
- Types of angles (age 8+) hard
Finding unknown angles using equations requires reading angle diagrams and interpreting arc marks and notation
- Types of angles (age 8+) hard
Angle sum rules (360° at a point, 180° on a line) are applied through reading angle diagrams with correct notation
- 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
- 2-D shapes (age 6+) soft
Understanding angles as shape properties requires knowing basic shape properties
- Angles in triangles (age 6+) soft
Understanding defining attributes supports describing shape properties formally
- 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
- Position, direction, and movement hard
Recognising angles as turns extends Y2 work on quarter/half/three-quarter turns
- 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
- 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
- What Is a Half? soft
Understanding half and quarter turns benefits from the concept of halves and quarters
- Types of angles (age 8+) hard
Angles at a point, on a straight line, and vertically opposite are identified through reading standard diagram notation
- Angle Sum Rules hard
Point/straight-line/vertically-opposite angle rules build on Y5 angle-sum knowledge
- Types of angles (age 8+) hard
Angle sum rules (360° at a point, 180° on a line) are applied through reading angle diagrams with correct notation
- 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
- Angles in triangles (age 6+) soft
Understanding defining attributes supports describing shape properties formally
- 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
- Position, direction, and movement hard
Recognising angles as turns extends Y2 work on quarter/half/three-quarter turns
- 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
- 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
- What Is a Half? soft
Understanding half and quarter turns benefits from the concept of halves and quarters
- 2-D shapes (age 6+) soft
Understanding angles as shape properties requires knowing basic 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
- Position, direction, and movement hard
Recognising angles as turns extends Y2 work on quarter/half/three-quarter turns
- 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
- 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
- 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
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- Trigonometry basicshardAges 13—15