Plotting Linear Graphs
REPRESENTATIONALPlot linear graphs by generating a table of values, reduce a two-variable linear equation to the form y = mx + c, and calculate gradients from two points on a line
Mastery Evidence
- Generate a table of (x, y) values for a linear equation and plot the points accurately
- Rearrange an equation such as 2x + 3y = 12 into the form y = mx + c
- Calculate the gradient between two coordinate points using rise over run
Assessment Prompt
“Can [child] draw the graph of a straight line by making a table of values and plotting the points — and work out the gradient from two points on the line?”
Curriculum Standards5 alignments
8.F.1Common Core State Standards for MathematicsUnderstand that a function is a rule that assigns to each input exactly one output. The graph of a function is the set of ordered pairs consisting of an input and the corresponding output.
8.F.4Common Core State Standards for MathematicsConstruct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (x, y) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values.
KS3.Maths.Alg.10The national curriculum in Englandinterpret mathematical relationships both algebraically and graphically
KS3.Maths.Alg.11The national curriculum in Englandreduce a given linear equation in 2 variables to the standard form y = mx + c; calculate and interpret gradients and intercepts of graphs of such linear equations numerically, graphically and algebraically
KS3.Maths.Alg.9The national curriculum in Englandrecognise, sketch and produce graphs of linear and quadratic functions of 1 variable with appropriate scaling, using equations in x and y and the Cartesian plane
Prerequisites2
- Simple formulaesoftAges 12—14
- Linear Function GraphshardAges 12—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
- Linear Function Graphs hard
Plotting linear graphs requires understanding what y = mx + c represents
- Coordinates (age 8+) hard
Plotting in all four quadrants extends first-quadrant coordinate grid plotting skills
- Position, direction, and movement soft
Position/direction vocabulary supports understanding coordinate grid
- Positional Language hard
Position/direction vocabulary with right angles extends basic positional language
- Turns & Directions hard
Right-angle turns (clockwise/anti-clockwise) build directly on whole/half/quarter turns from Year 1
- What Is a Half? soft
Understanding half and quarter turns benefits from the concept of halves and quarters
- Division as equal sharing hard
Finding a half requires equal sharing into 2 groups — a division concept
- Subtraction as taking away or separating hard
Division as equal sharing/grouping requires understanding subtraction as taking away/separating
- How Many in Total? hard
Understanding subtraction as taking away requires knowing numbers represent quantities (cardinality)
- 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'
- 2-D shapes (age 6+) hard
Identifying 2D shape properties is prerequisite to classifying by shared attributes
- Angles in triangles (age 6+) soft
Understanding defining attributes supports describing shape properties formally
- 2-D shapes hard
Distinguishing defining vs non-defining attributes requires knowing common 2-D shape names first
- 3-D shapes (age 5+) hard
Identifying defining attributes builds on informal analysis and comparison of shapes
- 2-D shapes hard
Describing properties of 2-D shapes (sides, symmetry) requires knowing the shapes first
- 3-D shapes (age 5+) hard
Formal property description extends informal analysis of sides and vertices
- Angles in triangles (age 7+) hard
Recognising shapes by attributes is prerequisite to quadrilateral hierarchy classification
- Angles in triangles (age 6+) hard
Drawing shapes by attributes extends understanding defining vs non-defining attributes
- 2-D shapes hard
Distinguishing defining vs non-defining attributes requires knowing common 2-D shape names first
- 3-D shapes (age 5+) hard
Identifying defining attributes builds on informal analysis and comparison of shapes
- 2-D shapes (age 6+) hard
Identifying pentagons, hexagons, quadrilaterals extends knowing 2-D shape properties
- Angles in triangles (age 6+) soft
Understanding defining attributes supports describing shape properties formally
- 2-D shapes hard
Distinguishing defining vs non-defining attributes requires knowing common 2-D shape names first
- 3-D shapes (age 5+) hard
Identifying defining attributes builds on informal analysis and comparison of shapes
- 2-D shapes hard
Describing properties of 2-D shapes (sides, symmetry) requires knowing the shapes first
- 3-D shapes (age 5+) hard
Formal property description extends informal analysis of sides and vertices
- Coordinates (age 8+) hard
Working across the full coordinate grid requires first-quadrant plotting as a foundation
- Position, direction, and movement soft
Position/direction vocabulary supports understanding coordinate grid
- Positional Language hard
Position/direction vocabulary with right angles extends basic positional language
- Turns & Directions hard
Right-angle turns (clockwise/anti-clockwise) build directly on whole/half/quarter turns from Year 1
- What Is a Half? soft
Understanding half and quarter turns benefits from the concept of halves and quarters
- Division as equal sharing hard
Finding a half requires equal sharing into 2 groups — a division concept
- Subtraction as taking away or separating hard
Division as equal sharing/grouping requires understanding subtraction as taking away/separating
- How Many in Total? hard
Understanding subtraction as taking away requires knowing numbers represent quantities (cardinality)
- 2-D shapes (age 6+) hard
Identifying 2D shape properties is prerequisite to classifying by shared attributes
- Angles in triangles (age 6+) soft
Understanding defining attributes supports describing shape properties formally
- 2-D shapes hard
Distinguishing defining vs non-defining attributes requires knowing common 2-D shape names first
- 3-D shapes (age 5+) hard
Identifying defining attributes builds on informal analysis and comparison of shapes
- 2-D shapes hard
Describing properties of 2-D shapes (sides, symmetry) requires knowing the shapes first
- 3-D shapes (age 5+) hard
Formal property description extends informal analysis of sides and vertices
- Angles in triangles (age 7+) hard
Recognising shapes by attributes is prerequisite to quadrilateral hierarchy classification
- Angles in triangles (age 6+) hard
Drawing shapes by attributes extends understanding defining vs non-defining attributes
- 2-D shapes hard
Distinguishing defining vs non-defining attributes requires knowing common 2-D shape names first
- 3-D shapes (age 5+) hard
Identifying defining attributes builds on informal analysis and comparison of shapes
- 2-D shapes (age 6+) hard
Identifying pentagons, hexagons, quadrilaterals extends knowing 2-D shape properties
- Angles in triangles (age 6+) soft
Understanding defining attributes supports describing shape properties formally
- 2-D shapes hard
Distinguishing defining vs non-defining attributes requires knowing common 2-D shape names first
- 3-D shapes (age 5+) hard
Identifying defining attributes builds on informal analysis and comparison of shapes
- 2-D shapes hard
Describing properties of 2-D shapes (sides, symmetry) requires knowing the shapes first
- 3-D shapes (age 5+) hard
Formal property description extends informal analysis of sides and vertices
- Negative numbers in context hard
Calculating intervals across zero extends Y5 negative number context
- Negative Numbers hard
Counting through zero is prerequisite to interpreting negative numbers in context
- The 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
- Transformations on a grid soft
Working with the full coordinate grid (all four quadrants) extends the transformation diagram to negative coordinates
- Types of angles hard
Y4 acute/obtuse angle identification is prerequisite to drawing and labelling angle types
- Right Angles & Turns hard
Identifying right angles and greater/less than right angle is prerequisite to naming acute/obtuse
- 2-D shapes (age 6+) soft
Understanding angles as shape properties requires knowing basic shape properties
- 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
- 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
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
- Fractions on a number line (age 11+) hard
Plotting coordinates in all four quadrants requires understanding positive and negative values on both axes
- Positive and Negative Numbers hard
Ordering all number types (integers, decimals, fractions) on a number line extends the negative-number number-line representation
- Negative numbers in context hard
Calculating intervals across zero extends Y5 negative number context
- Negative Numbers hard
Counting through zero is prerequisite to interpreting negative numbers in context
- The two digits of a two-digit number hard
Must understand two-digit place value before extending to hundreds
- Fractions on a number line hard
Ordering all number types requires understanding place value across the full system
- Reading and writing numbers to 10,000,000 hard
Extending place value to any size builds directly on Y6 reading/writing/ordering numbers to 10,000,000
- Decimals for Tenths & Hundredths hard
Decimal notation for 10ths/100ths is prerequisite to extending to thousandths
- Tenths (age 8+) hard
Understanding hundredths is prerequisite to working with 10ths and 100ths together
- Equivalent fractions (age 9+) hard
Generating equivalent fractions supports converting 10ths to 100ths
- Equivalent fractions on a number line hard
Understanding equivalence conceptually is prerequisite to explaining algebraically
- Equivalent fractions (age 8+) hard
Generating equivalent fractions with visual models is prerequisite to algebraic explanation of equivalence
- Decimal equivalents of tenths and hundredths hard
Y4 decimal equivalents of 10ths/100ths is prerequisite to formal decimal notation for fractions
- Decimal & Percent Notation hard
Writing decimal equivalents of tenths and hundredths requires decimal point and place-value vocabulary
- Decimal & Percent Notation hard
Using decimal notation for fractions requires decimal, tenths, and hundredths vocabulary
- Place value of each digit hard
Four-digit place value is prerequisite to understanding ×10 relationship between places
- The three digits of a three-digit number hard
Four-digit place value extends three-digit place value
- The two digits of a two-digit number hard
Must understand two-digit place value before extending to hundreds
- A Ten Is Ten Ones hard
Understanding tens and ones place value requires the concept of 10 as a bundle
- The teen numbers hard
General two-digit place value extends from understanding teen number composition
- The three digits of a three-digit number hard
Comparing three-digit numbers requires three-digit place value
- The two digits of a two-digit number hard
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
- The two digits of a two-digit number hard
Comparing two-digit numbers using PV requires understanding tens and ones
- A Ten Is Ten Ones hard
Understanding tens and ones place value requires the concept of 10 as a bundle
- The teen numbers hard
General two-digit place value extends from understanding teen number composition
- Two written numerals between 1 and 10 soft
Comparing two-digit numbers extends from comparing single-digit written numerals
- Comparing groups: more or fewer soft
Comparing written numerals is the symbolic form of comparing quantities — conceptual comparison helps but isn't strictly required
- The three digits of a three-digit number hard
Four-digit place value extends three-digit place value
- The two digits of a two-digit number hard
Must understand two-digit place value before extending to hundreds
- A Ten Is Ten Ones hard
Understanding tens and ones place value requires the concept of 10 as a bundle
- The teen numbers hard
General two-digit place value extends from understanding teen number composition
- Numbers to 10,000 hard
Ordering and comparing numbers over 1000 requires the full 10,000 representations toolkit
- The three digits of a three-digit number hard
Representing numbers requires place-value understanding
- Representing numbers with objects hard
Representing and estimating numbers on a number line builds on Y1 number representations
- How Many in Total? hard
Representing numbers with objects/pictures/number line requires understanding that numbers represent quantities
- The two digits of a two-digit number soft
Estimating placement on a 0-100 number line benefits from place value understanding
- 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
- The three digits of a three-digit number hard
Four-digit place value extends three-digit place value
- Place Value × 10 Pattern hard
Understanding ×10 place-value relationship supports reading/writing larger numbers
- Place value of each digit hard
Four-digit place value is prerequisite to understanding ×10 relationship between places
- The three digits of a three-digit number hard
Four-digit place value extends three-digit place value
- 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
- Measuring temperature hard
Ordering with inequality symbols extends Y6 work with negative numbers in context
- Negative numbers in context hard
Calculating intervals across zero extends Y5 negative number context
- Negative Numbers hard
Counting through zero is prerequisite to interpreting negative numbers in context
- The 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
- Substituting into Formulae hard
Interpreting y = mx + c requires substitution to generate coordinate pairs
- Writing Algebraic Equations hard
Algebraic notation builds on KS2 expressing missing-number problems algebraically
- Writing Number Sentences hard
Writing algebraic expressions extends writing/interpreting numerical expressions
- Brackets in Expressions hard
Writing/interpreting expressions requires understanding grouping symbols
- Division with remainders hard
Evaluating grouped expressions formalises multi-step calculation skills from Y5
- Multiply & Add Problems hard
Y4 M×D problem-solving is prerequisite to multi-step four-operation problems
- Written Multiplication & Division hard
Formal short multiplication extends Y3 written multiplication
- 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
- Algebraic Transformations hard
Recognising the relationship between y=mx+c and its graph requires moving fluently between algebraic and graphical representations
- Writing Algebraic Equations hard
Algebraic notation builds on KS2 expressing missing-number problems algebraically
- Writing Number Sentences hard
Writing algebraic expressions extends writing/interpreting numerical expressions
- Brackets in Expressions hard
Writing/interpreting expressions requires understanding grouping symbols
- Division with remainders hard
Evaluating grouped expressions formalises multi-step calculation skills from Y5
- Multiply & Add Problems hard
Y4 M×D problem-solving is prerequisite to multi-step four-operation problems
- Written Multiplication & Division hard
Formal short multiplication extends Y3 written multiplication
- 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
- 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
- Brackets in Expressions hard
The full BODMAS/PEMDAS convention extends understanding of grouping symbols to all operations
- Division with remainders hard
Evaluating grouped expressions formalises multi-step calculation skills from Y5
- Brackets in Expressions hard
Writing/interpreting expressions requires understanding grouping symbols
- Division with remainders hard
Evaluating grouped expressions formalises multi-step calculation skills from Y5
- Brackets in Expressions hard
The full BODMAS/PEMDAS convention extends understanding of grouping symbols to all operations
- Division with remainders hard
Evaluating grouped expressions formalises multi-step calculation skills from Y5
- 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
- Writing Algebraic Equations hard
Algebraic notation builds on KS2 expressing missing-number problems algebraically
- Writing Number Sentences hard
Writing algebraic expressions extends writing/interpreting numerical expressions
- Brackets in Expressions hard
Writing/interpreting expressions requires understanding grouping symbols
- Division with remainders hard
Evaluating grouped expressions formalises multi-step calculation skills from Y5
- Multiply & Add Problems hard
Y4 M×D problem-solving is prerequisite to multi-step four-operation problems
- Arrays for multiplication (age 9+) hard
Must have formal division method before solving multi-step problems
- Division as Unknown Factor hard
Understanding division as unknown-factor supports short division strategy
- Fluent multiplication and division facts hard
Fluent ×÷ within 100 is prerequisite to short division of larger numbers
- Written Multiplication hard
2/3-digit × 1-digit written method is prerequisite to 4-digit × 1-digit and 2-digit × 2-digit
- Area and the distributive property soft
Area models for distributive property support understanding long multiplication layout
- Written Multiplication hard
2/3-digit × 1-digit written method is prerequisite to 4-digit × 1-digit and 2-digit × 2-digit
- Area and the distributive property soft
Area models for distributive property support understanding long multiplication layout
- Brackets in Expressions hard
The full BODMAS/PEMDAS convention extends understanding of grouping symbols to all operations
- Division with remainders hard
Evaluating grouped expressions formalises multi-step calculation skills from Y5
- Multiply & Add Problems hard
Y4 M×D problem-solving is prerequisite to multi-step four-operation problems
- Arrays for multiplication (age 9+) hard
Must have formal division method before solving multi-step problems
- Division as Unknown Factor hard
Understanding division as unknown-factor supports short division strategy
- Fluent multiplication and division facts hard
Fluent ×÷ within 100 is prerequisite to short division of larger numbers
- Written Multiplication hard
2/3-digit × 1-digit written method is prerequisite to 4-digit × 1-digit and 2-digit × 2-digit
- Area and the distributive property soft
Area models for distributive property support understanding long multiplication layout
- Written Multiplication hard
2/3-digit × 1-digit written method is prerequisite to 4-digit × 1-digit and 2-digit × 2-digit
- Area and the distributive property soft
Area models for distributive property support understanding long multiplication layout
- Brackets in Expressions hard
Writing/interpreting expressions requires understanding grouping symbols
- Division with remainders hard
Evaluating grouped expressions formalises multi-step calculation skills from Y5
- Multiply & Add Problems hard
Y4 M×D problem-solving is prerequisite to multi-step four-operation problems
- Arrays for multiplication (age 9+) hard
Must have formal division method before solving multi-step problems
- Division as Unknown Factor hard
Understanding division as unknown-factor supports short division strategy
- Fluent multiplication and division facts hard
Fluent ×÷ within 100 is prerequisite to short division of larger numbers
- Written Multiplication hard
2/3-digit × 1-digit written method is prerequisite to 4-digit × 1-digit and 2-digit × 2-digit
- Area and the distributive property soft
Area models for distributive property support understanding long multiplication layout
- Written Multiplication hard
2/3-digit × 1-digit written method is prerequisite to 4-digit × 1-digit and 2-digit × 2-digit
- Area and the distributive property soft
Area models for distributive property support understanding long multiplication layout
- Brackets in Expressions hard
The full BODMAS/PEMDAS convention extends understanding of grouping symbols to all operations
- Division with remainders hard
Evaluating grouped expressions formalises multi-step calculation skills from Y5
- Multiply & Add Problems hard
Y4 M×D problem-solving is prerequisite to multi-step four-operation problems
- Arrays for multiplication (age 9+) hard
Must have formal division method before solving multi-step problems
- Division as Unknown Factor hard
Understanding division as unknown-factor supports short division strategy
- Fluent multiplication and division facts hard
Fluent ×÷ within 100 is prerequisite to short division of larger numbers
- Written Multiplication hard
2/3-digit × 1-digit written method is prerequisite to 4-digit × 1-digit and 2-digit × 2-digit
- Area and the distributive property soft
Area models for distributive property support understanding long multiplication layout
- Written Multiplication hard
2/3-digit × 1-digit written method is prerequisite to 4-digit × 1-digit and 2-digit × 2-digit
- Area and the distributive property soft
Area models for distributive property support understanding long multiplication layout
- 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
- 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
- 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
- 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
- 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
- Arrays for multiplication (age 9+) hard
Long division by 2-digit extends Y5 short division by 1-digit
- Division as Unknown Factor hard
Understanding division as unknown-factor supports short division strategy
- What Multiplication Means hard
Connecting division to multiplication requires understanding products
- Arrays for multiplication (age 7+) hard
Extends array-based repeated addition to formal multiplication interpretation
- Arrays for multiplication hard
Rectangular arrays with repeated addition extends array representation from Y2
- Multiplication as repeated addition hard
Expressing array totals as sums of equal addends requires understanding multiplication as repeated addition
- Multiplication as repeated addition hard
Interpreting products formalises repeated addition/equal groups from Y1
- Addition as combining or putting together two hard
Multiplication as repeated addition requires understanding addition as combining groups
- Subtraction as taking away or separating hard
Division as equal sharing/grouping requires understanding subtraction as taking away/separating
- Fluent multiplication and division facts hard
Fluent ×÷ within 100 is prerequisite to short division of larger numbers
- What Multiplication Means hard
Connecting division to multiplication requires understanding products
- Arrays for multiplication (age 7+) hard
Extends array-based repeated addition to formal multiplication interpretation
- Multiplication as repeated addition hard
Interpreting products formalises repeated addition/equal groups from Y1
- Multiplication as repeated addition hard
Recalling times table facts requires understanding multiplication as repeated addition/grouping
- Addition as combining or putting together two hard
Multiplication as repeated addition requires understanding addition as combining groups
- Multiplication as repeated addition hard
Recalling times table facts requires understanding multiplication as repeated addition/grouping
- Long multiplication (age 10+) soft
Checking division with multiplication requires fluent multiplication
- Written Multiplication hard
2/3-digit × 1-digit written method is prerequisite to 4-digit × 1-digit and 2-digit × 2-digit
- Written Multiplication & Division hard
Formal short multiplication extends Y3 written multiplication
- The three digits of a three-digit number soft
Two-digit × one-digit uses place-value partitioning (e.g. 23 × 4 = 20 × 4 + 3 × 4)
- Reading ×, ÷, and = Symbols hard
Writing multiplication/division statements requires fluency with symbols
- Area and the distributive property soft
Area models for distributive property support understanding long multiplication layout
- Understanding angles (age 8+) hard
Must multiply side lengths for area before using area models for distributive property
- Area by Tiling hard
Must see tiling→multiplication connection before computing area via side lengths
Unlocks3
- Quadratic GraphshardAges 13—14
- Simultaneous EquationshardAges 13—14
- Estimating answers (age 13+)hardAges 13—14