Number - Multiplication and Division
KS2MA-Y4-D003
All multiplication tables to 12 × 12, using place value and multiplication facts to derive related calculations, mental methods including commutativity and associativity, and formal written methods for multiplication and division.
National Curriculum context
Year 4 is the statutory point by which pupils must know all multiplication tables to 12 × 12, making it a landmark year for multiplicative fluency. The non-statutory guidance states that pupils should practise mental methods and should be able to derive quickly all multiplication and division facts from the tables they know, and should understand the distributive and commutative laws. Pupils are introduced to short multiplication (long multiplication is in Year 5) and short division, building on the mental and partial methods from Year 3. This thorough foundation in all multiplication facts is essential for fraction calculations, long division, ratio, and algebra throughout upper KS2 and into secondary school.
3
Concepts
2
Clusters
2
Prerequisites
3
With difficulty levels
Lesson Clusters
Recall all multiplication tables to 12 × 12 and use short multiplication
introduction CuratedComplete times table recall is the major Year 4 milestone; short multiplication applies it to 2- and 3-digit numbers. C007 co-teaches with C008.
Investigate factor pairs and use commutativity in mental calculation
practice CuratedFactor pairs and commutativity are the conceptual tools that underpin flexible mental multiplication strategies — a distinct cluster from the recall/procedural focus.
Teaching Suggestions (1)
Study units and activities that deliver concepts in this domain.
Multiplication and Division: Formal Methods and Factor Pairs
Mathematics Pattern SeekingPedagogical rationale
Y4 is the year of the Multiplication Tables Check (MTC) and complete table fluency to 12 x 12 is the statutory expectation. However, fluency alone is insufficient — children must understand the multiplicative structure that allows them to derive unknown facts from known ones. Factor pairs and commutativity are introduced as reasoning tools, not just pattern-spotting exercises. The ability to decompose calculations (e.g., 6 x 8 = 6 x 4 x 2) is the foundation for the formal written methods that follow in Y5.
Access and Inclusion
1 of 3 concepts have identified access barriers.
Barrier types in this domain
Recommended support strategies
Prerequisites
Concepts from other domains that pupils should know before this domain.
Concepts (3)
All multiplication tables to 12 × 12
Keystone knowledge AI DirectMA-Y4-C007
By end of Year 4, pupils must know all multiplication facts to 12 × 12 and the corresponding division facts to immediate recall. This is a statutory requirement and represents a major milestone in mathematical fluency. Mastery means automatic, accurate recall of any multiplication or division fact within the 12 × 12 grid without counting or deriving, enabling rapid computation and problem-solving.
Teaching guidance
By Year 4, pupils should know the 2, 3, 4, 5, 8 and 10 times tables from Year 3. New tables are 6, 7, 9, 11 and 12. Use commutativity to reduce the learning load: knowing 6 × 7 = 42 gives 7 × 6 = 42 for free. Highlight patterns: 9 times table (digit sum always 9; ones digits decrease by 1 as tens digits increase by 1). 11 times table (to 9 × 11 = 99, the digits repeat: 11, 22, 33...). 12 times table (connect to 10× and 2×: 12 × n = 10 × n + 2 × n). Use a range of practice methods: games, cards, rapid-fire oral tests, written grids.
Common misconceptions
The 6 × 7 = 42 and 7 × 8 = 56 facts are the most commonly misremembered in the 12 × 12 grid. Pupils who have memorised facts by rote without connections confuse similar-sounding facts (6 × 8 = 48 vs 6 × 7 = 42). Division facts are frequently less secure than multiplication facts, even when the multiplication is known — pupils must practise division recall explicitly.
Difficulty levels
Recalling multiplication facts for the 6 and 9 times tables using known facts (e.g. 6 = 2 × 3, 9 = 10 – 1 strategy).
Example task
What is 6 × 4? Use a fact you already know to help.
Model response: 6 × 4 = 24. I know 3 × 4 = 12, so 6 × 4 = double 12 = 24.
Recalling multiplication facts to 12 × 12 with increasing speed, including the hardest facts (6 × 7, 7 × 8, 8 × 9).
Example task
Answer as quickly as you can: 7 × 8 = ? 9 × 6 = ? 12 × 7 = ?
Model response: 7 × 8 = 56. 9 × 6 = 54. 12 × 7 = 84.
Instant recall of all multiplication and related division facts to 12 × 12, applied in calculation and problem-solving.
Example task
72 ÷ 8 = ? If 7 × 11 = 77, what is 770 ÷ 7?
Model response: 72 ÷ 8 = 9. 770 ÷ 7 = 110.
CPA Stages
concrete
Using arrays built from counters, Cuisenaire rods for skip-counting, and multiplication grid cards to practise all times tables to 12 × 12 with physical manipulation
Transition: Child recalls all multiplication facts to 12 × 12 and corresponding division facts without building arrays or using the grid
pictorial
Completing multiplication grids on paper, drawing arrays to verify tricky facts, and using pattern-spotting (digit sums for 9s, patterns for 11s) to consolidate recall
Transition: Child completes the full 12 × 12 grid from memory within 5 minutes and states division facts without the grid
abstract
Instant recall of all multiplication and division facts to 12 × 12, using known facts to derive related facts mentally
Transition: Child answers any times table fact within 2 seconds and derives related facts (×10, ×100, with decimals) without hesitation
Delivery rationale
Upper primary maths (Y4) — most pupils at pictorial/abstract stage. AI can deliver with virtual representations.
Short multiplication (2- and 3-digit × 1-digit)
skill AI DirectMA-Y4-C008
Short multiplication is the compact formal written method for multiplying a multi-digit number by a single-digit number, working right to left and carrying any value of 10 or more into the next column. In Year 4, this is used for two-digit and three-digit numbers multiplied by one-digit numbers. Mastery means pupils can reliably set out and complete any such calculation using the formal compact method.
Teaching guidance
Build from the grid method (used in Year 3) to the compact method. Show how the grid method's partial products combine into carries in the compact layout. The CPA sequence: Dienes blocks for physical regrouping → grid as pictorial → compact method. Emphasise: multiply the ones digit first, carry to the tens; multiply the tens digit, add the carry, carry to the hundreds; and so on. Carry digits written small above the relevant column. Example: 247 × 3 — ones: 7×3=21 (write 1, carry 2); tens: 4×3=12+2=14 (write 4, carry 1); hundreds: 2×3=6+1=7; answer 741.
Common misconceptions
The most common error is forgetting to add the carried digit. Some pupils multiply from left to right, which works but produces the wrong carry sequence. Others carry the complete partial product rather than just the tens digit (e.g. 7 × 3 = 21, carrying the '21' rather than writing 1 and carrying 2).
Difficulty levels
Multiplying a two-digit number by a one-digit number using the grid method as pictorial support.
Example task
Use the grid method: 34 × 6.
Model response: Grid: 30 × 6 = 180, 4 × 6 = 24. Total: 180 + 24 = 204.
Multiplying two-digit and three-digit numbers by one digit using the compact (short multiplication) method with carrying.
Example task
Use short multiplication: 247 × 3.
Model response: 7 × 3 = 21, write 1 carry 2. 4 × 3 = 12, + 2 = 14, write 4 carry 1. 2 × 3 = 6, + 1 = 7. Answer: 741.
Reliably completing short multiplication for any 2- or 3-digit × 1-digit calculation, checking with estimation.
Example task
Work out 368 × 7. Estimate first.
Model response: Estimate: 400 × 7 = 2,800. Calculation: 368 × 7 = 2,576. This is close to the estimate, so it looks correct.
Solving multi-step word problems that require short multiplication and explaining why the method works using place value.
Example task
A box holds 256 crayons. A school orders 8 boxes. How many crayons in total? Explain how the short multiplication method uses place value.
Model response: 256 × 8 = 2,048. The method works column by column from right: 6 ones × 8 = 48 ones (write 8, carry 4 tens), 5 tens × 8 = 40 tens + 4 = 44 tens (write 4, carry 4 hundreds), 2 hundreds × 8 = 16 hundreds + 4 = 20 hundreds = 2 thousands.
CPA Stages
concrete
Using Dienes blocks to model multi-digit × single-digit multiplication, physically partitioning the multi-digit number and combining partial products with exchanges
Transition: Child explains the partition and exchange process verbally and begins recording the compact method on paper alongside the blocks
pictorial
Using the grid method to partition and multiply, showing partial products visually, then connecting to the compact short multiplication layout
Transition: Child completes short multiplication using the compact method, explaining each carry, without needing the grid method alongside
abstract
Performing short multiplication of 2- and 3-digit numbers by 1-digit numbers fluently using the compact method, with estimation to check
Transition: Child sets up and completes any short multiplication independently with correct carrying, estimating before calculating
Delivery rationale
Upper primary maths (Y4) — most pupils at pictorial/abstract stage. AI can deliver with virtual representations.
Access barriers (2)
Year 4 is the statutory Multiplication Tables Check year. All times tables to 12x12 must be recalled within 6 seconds per question. This is the highest-stakes timed fluency assessment in primary school.
Recalling 144 multiplication facts (12x12) and their related division facts requires massive long-term memory storage. Children with working memory difficulties struggle to consolidate these facts from short-term practice into long-term recall.
Factor pairs and commutativity in mental calculation
knowledge AI DirectMA-Y4-C009
A factor pair of a number is a pair of integers that multiply to give that number (e.g. factor pairs of 24 include 1 × 24, 2 × 12, 3 × 8, 4 × 6). Commutativity means a × b = b × a. Together, these allow pupils to reorder and regroup calculations for efficiency: 4 × 17 × 5 = 4 × 5 × 17 = 20 × 17 = 340 (reordering to create a convenient factor pair). Mastery means pupils can identify factor pairs of numbers up to 100, apply commutativity to reorder calculations, and explain why these strategies work.
Teaching guidance
Use arrays to demonstrate commutativity: a 4 × 6 array is identical to a 6 × 4 array, just rotated. For factor pairs, systematic listing from 1 upwards helps ensure completeness: factors of 24: 1 and 24, 2 and 12, 3 and 8, 4 and 6 — stop when the smaller factor reaches the square root. Connect factor pairs to the multiplication table grid: every entry in the grid corresponds to a factor pair of that number.
Common misconceptions
Pupils often confuse factors and multiples (a factor of 24 divides 24 exactly; a multiple of 24 is 24 times a whole number). When listing factor pairs, pupils frequently miss pairs or stop before reaching all pairs. Some pupils do not spontaneously apply commutativity in mental calculation, missing opportunities to create simpler calculations.
Difficulty levels
Finding all factor pairs of a number up to 20 by systematic trial with concrete arrays.
Example task
Find all the ways to arrange 12 counters in equal rows. List the factor pairs of 12.
Model response: 1 × 12, 2 × 6, 3 × 4. Factor pairs: (1,12), (2,6), (3,4).
Finding factor pairs of numbers up to 50 systematically and using commutativity to reorder calculations.
Example task
List all factor pairs of 36. Use commutativity to work out 4 × 13 × 25 efficiently.
Model response: Factor pairs of 36: (1,36), (2,18), (3,12), (4,9), (6,6). For 4 × 13 × 25: rearrange to 4 × 25 × 13 = 100 × 13 = 1,300.
Finding all factor pairs of numbers up to 100, distinguishing factors from multiples, and using factor pairs in mental calculation.
Example task
Is 7 a factor of 42? Is 42 a multiple of 7? Explain the difference between factors and multiples.
Model response: Yes, 7 is a factor of 42 because 42 ÷ 7 = 6 exactly. Yes, 42 is a multiple of 7 because 7 × 6 = 42. Factors divide the number exactly; multiples are the products of multiplying.
CPA Stages
concrete
Finding factor pairs by building rectangular arrays from counters: for a given number of counters, how many different rectangles can you make?
Transition: Child lists factor pairs systematically from 1 upward and explains that a × b = b × a means each pair gives two multiplication facts
pictorial
Recording factor pairs in systematic lists and factor trees, drawing arrays on squared paper to verify, and showing how reordering factors simplifies calculations
Transition: Child finds all factor pairs of any number to 100 systematically and uses commutativity to simplify multi-factor calculations on paper
abstract
Identifying factor pairs mentally, applying commutativity and associativity to simplify mental calculations, and explaining why these strategies work
Transition: Child identifies factor pairs mentally, spontaneously reorders calculations for efficiency, and explains the commutative and associative laws
Delivery rationale
Upper primary maths (Y4) — most pupils at pictorial/abstract stage. AI can deliver with virtual representations.