Multiplication and Division
KS1MA-Y2-D003
Pupils recall and use multiplication and division facts for the 2, 5 and 10 times tables, write formal multiplication and division statements, and understand commutativity of multiplication.
National Curriculum context
Year 2 marks the formal introduction of multiplication tables, with pupils required to recall and use facts for the 2, 5 and 10 multiplication tables. Pupils are introduced to the multiplication tables and practise to become fluent, connecting the 2, 5 and 10 tables to each other — particularly the 10 multiplication table to place value, and the 5 multiplication table to the divisions on the clock face. They begin to use other multiplication tables and recall multiplication facts, including using related division facts to perform written and mental calculations. Pupils work with a range of materials and contexts in which multiplication and division relate to grouping and sharing discrete and continuous quantities, to arrays and to repeated addition. They begin to relate these to fractions and measures (for example, 40 ÷ 2 = 20, 20 is a half of 40) and use commutativity and inverse relations to develop multiplicative reasoning (for example, 4 × 5 = 20 and 20 ÷ 5 = 4). A key conceptual development is that pupils show that multiplication of two numbers can be done in any order (commutative) and division of one number by another cannot.
3
Concepts
2
Clusters
2
Prerequisites
3
With difficulty levels
Lesson Clusters
Recall the 2, 5 and 10 times tables and write multiplication and division statements
introduction CuratedTable recall and writing formal multiplication/division statements (using × and ÷) are taught together as the formal entry into multiplicative arithmetic. C008 and C009 mutually co-teach.
Understand commutativity of multiplication and non-commutativity of division
practice CuratedCommutativity is a distinct conceptual cluster that deepens understanding of the operation structure, building on table knowledge. Standalone as the domain has three well-separated concepts.
Teaching Suggestions (1)
Study units and activities that deliver concepts in this domain.
Multiplication and Division Facts for 2, 5, and 10
Mathematics Pattern SeekingPedagogical rationale
The 2, 5, and 10 times tables are the first multiplication facts pupils learn because they connect to skip-counting (already familiar from Y1), coin values (2p, 5p, 10p), and the structure of the number system (even numbers, numbers ending in 0 or 5). Arrays are the key representation: they make commutativity visible (rotate the array and the total stays the same) and bridge to the area model used in later years. Division is taught as both sharing (12 shared between 3 gives 4 each) and grouping (how many groups of 3 in 12?).
Access and Inclusion
2 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)
2, 5 and 10 times tables (recall and use)
Keystone knowledge AI FacilitatedMA-Y2-C008
The 2, 5 and 10 multiplication tables are the first formal multiplication tables introduced in the national curriculum. Pupils must recall multiplication facts (e.g. 5 × 4 = 20) and related division facts (e.g. 20 ÷ 5 = 4) fluently, connect the tables to each other and to place value, and apply them in calculation contexts. Mastery means instant recall of all facts in the 2, 5 and 10 times tables, both in multiplication and division form.
Teaching guidance
Introduce each table through skip counting (which pupils already practise), then build to recall of individual facts. Connect tables to each other: 10 × table is double the 5 × table, so if 3 × 5 = 15, then 3 × 10 = 30. Connect the 5 × table to the clock face (5-minute intervals) — this is explicitly mentioned in the non-statutory guidance. Connect the 10 × table to place value (multiplying by 10 shifts all digits one place to the left). Use arrays, number lines with jumps, and real-world contexts (2p coins, 5p coins, counting in 10s). Flash cards and games for rapid recall practice are essential. Ensure division facts are taught alongside: 20 ÷ 5 = 4 is part of the same fact family as 4 × 5 = 20.
Common misconceptions
Pupils often confuse multiplication and addition in early table work (e.g. 3 × 5 = 8 instead of 15, as if computing 3 + 5). They may know facts forward but not backward: knowing 5 × 4 = 20 but not 4 × 5 = 20. The connection between multiplication and division facts is not automatic: pupils may recall 5 × 4 = 20 but not know 20 ÷ 5 = 4. Recognising odd and even numbers from the 2 times table — even numbers are multiples of 2, odd numbers are not — is a conceptual milestone that some pupils learn procedurally (ends in 0, 2, 4, 6, 8) without understanding.
Difficulty levels
Counting in 2s, 5s and 10s using concrete groups and connecting to the matching times table fact.
Example task
Make 4 groups of 5 cubes. Count in 5s to find the total. What times table fact does this show?
Model response: 5, 10, 15, 20. There are 20 cubes. 4 × 5 = 20.
Recalling multiplication facts for the 2, 5 and 10 times tables and connecting to division facts.
Example task
What is 7 × 2? What is 14 ÷ 2?
Model response: 7 × 2 = 14. 14 ÷ 2 = 7.
Instant recall of all multiplication and division facts for 2, 5 and 10 times tables, applied in context.
Example task
Stickers come in packs of 5. I need 35 stickers. How many packs do I need?
Model response: 35 ÷ 5 = 7. I need 7 packs.
Explaining connections between the 2, 5 and 10 times tables and using known facts to derive unknown ones.
Example task
If you know 6 × 5 = 30, how can you work out 6 × 10?
Model response: 6 × 10 = 60. I know this because 10 is double 5, so 6 × 10 is double 6 × 5. Double 30 is 60.
CPA Stages
concrete
Children make groups of 2, 5 and 10 using cubes or counters and count the total using skip counting. They build arrays with physical objects, connecting each row/column to a times table fact. 2p, 5p and 10p coins provide real-world concrete resources for the corresponding tables.
Transition: Child builds arrays and states the corresponding multiplication and division facts, connecting skip counting to the times table: '4 groups of 5 is 20, so 4 × 5 = 20 and 20 ÷ 5 = 4.'
pictorial
Children use drawn arrays, number lines with equal jumps, and clock face diagrams (for the 5 times table) to practise and record times table facts. Fact family triangles show the multiplication and division relationship between three numbers.
Transition: Child draws arrays and number line jumps to represent any fact in the 2, 5 and 10 times tables, and writes both the multiplication and the related division fact from the picture.
abstract
Children recall all multiplication and division facts for the 2, 5 and 10 times tables instantly without any visual support. They apply these facts in word problems and explain connections between the tables (the 10 times table is double the 5 times table).
Transition: Child recalls any multiplication or division fact from the 2, 5 and 10 tables within 3 seconds, and explains connections between tables: 'The 10 table is double the 5 table.'
Delivery rationale
Primary maths (Y2) with concrete stage requiring physical manipulatives (Interlocking cubes for arrays, Counters for grouping). AI delivers instruction; facilitator sets up materials.
Access barriers (2)
Learning times tables requires extended repetitive practice. Children with ADHD find sustained drill practice particularly difficult to maintain, even when they understand the concept of multiplication.
Times table recall (2, 5, 10) is a fluency target often assessed through timed tests. The Multiplication Tables Check in Y4 intensifies this pressure retrospectively. Children with dyscalculia may need significantly more practice time.
Writing multiplication and division statements using × and ÷ symbols
skill AI FacilitatedMA-Y2-C009
In Year 2, pupils begin to write formal multiplication and division statements using the symbols × and ÷, alongside = signs. This formalises the informal grouping and sharing of Year 1 into mathematical notation. Mastery means pupils can write a complete mathematical statement from a context (e.g. 3 groups of 5 is 15, written as 3 × 5 = 15) and interpret a written statement in a real-world context.
Teaching guidance
Begin with concrete contexts — 3 groups of 5 objects — and model writing the multiplication statement alongside the physical action. Connect multiplication notation to repeated addition: 3 × 5 = 5 + 5 + 5. Connect arrays to both multiplication and division: a 3-row, 5-column array shows both 3 × 5 = 15 and 5 × 3 = 15 (commutativity). Show division as both sharing (15 ÷ 3 = 5, sharing 15 among 3) and grouping (15 ÷ 5 = 3, how many groups of 5 in 15). The curriculum requires pupils to use all three symbols (×, ÷, =) correctly in formal statements.
Common misconceptions
Pupils often write multiplication statements in the wrong order, confusing the multiplicand and multiplier (writing 5 × 3 when meaning '3 groups of 5'). Division notation is harder: pupils may write 3 ÷ 15 instead of 15 ÷ 3. The ÷ symbol itself may be confused with + or – at first. Pupils sometimes omit the = sign or place it incorrectly.
Difficulty levels
Writing a multiplication statement from a concrete arrangement of equal groups.
Example task
There are 3 plates with 2 biscuits on each. Write a multiplication to show this.
Model response: 3 × 2 = 6
Writing both multiplication and division statements from arrays and equal group contexts.
Example task
Look at this array: 4 rows of 5 dots. Write a multiplication and a division for it.
Model response: 4 × 5 = 20. 20 ÷ 5 = 4 (or 20 ÷ 4 = 5).
Writing multiplication and division statements from word problems and interpreting statements in context.
Example task
Write a number sentence: 'There are 30 children sitting at 5 tables with the same number at each table. How many at each table?'
Model response: 30 ÷ 5 = 6. There are 6 children at each table.
CPA Stages
concrete
Children write multiplication statements from concrete arrangements of equal groups. They lay out 3 plates with 5 cubes on each and write 3 × 5 = 15. They lay out arrays and write the corresponding statements for both orientations.
Transition: Child writes a correct multiplication or division statement for any physical arrangement of equal groups, using ×, ÷ and = symbols in the right order.
pictorial
Children write multiplication and division statements from drawn arrays and equal-group pictures. They practise writing all four facts in a fact family from a single array diagram, and begin to interpret word problems as multiplication or division.
Transition: Child writes complete fact families from drawn arrays and translates picture-based word problems into correct multiplication or division statements.
abstract
Children write multiplication and division statements from word problems without pictures or objects, selecting the correct operation. They use × and ÷ symbols confidently and interpret statements in context.
Transition: Child reads a word problem and writes the correct multiplication or division statement without needing to draw it first, placing the numbers and symbols in the right order.
Delivery rationale
Primary maths (Y2) with concrete stage requiring physical manipulatives (Plates and cubes for equal groups, Array trays with counters). AI delivers instruction; facilitator sets up materials.
Access barriers (1)
Writing multiplication and division statements requires accurate formation of the x and ÷ symbols, which are novel to Year 2. The ÷ symbol is particularly difficult for children with fine motor difficulties.
Commutativity of multiplication and non-commutativity of division
knowledge AI FacilitatedMA-Y2-C010
Multiplication is commutative: 4 × 5 = 5 × 4. This mirrors the commutativity of addition and can be shown using arrays (a 4-row, 5-column array is the same total as a 5-row, 4-column array). Division is not commutative: 20 ÷ 5 = 4 but 5 ÷ 20 does not equal 4. This parallel between the commutativity structures of addition/multiplication and the non-commutativity of subtraction/division is an important algebraic insight. Mastery means pupils can demonstrate commutativity with arrays, explain why it works, and correctly state that division cannot be reordered.
Teaching guidance
Use arrays as the primary concrete/pictorial demonstration: physically turn a 4 × 5 array and show it becomes a 5 × 4 array without changing the number of objects. Contrast with division using sharing contexts: you can share 20 between 5 (getting 4 each) but cannot 'share' 5 between 20 in the same way. The curriculum specifies that pupils should show commutativity — not just be told — so require them to construct and rotate their own arrays. Connect to the 'fact family' concept: 4 × 5 = 20 and 5 × 4 = 20 are both valid; 20 ÷ 5 = 4 and 20 ÷ 4 = 5 are also both valid, but these are different divisions from different factorings.
Common misconceptions
Pupils apply commutativity to division as they do to multiplication, stating that 20 ÷ 5 = 5 ÷ 20. Some pupils understand that × is commutative but confuse this with thinking all operations are commutative. When using arrays to demonstrate commutativity, pupils sometimes recount the array rather than reasoning about its rotational symmetry.
Difficulty levels
Using an array to show that multiplication gives the same answer when the groups are swapped.
Example task
Make a 3 × 4 array with counters. Now turn it sideways to make a 4 × 3 array. Is the total the same?
Model response: Yes. 3 × 4 = 12 and 4 × 3 = 12. Turning the array does not change the number of counters.
Applying commutativity to choose the easier order for a multiplication and recognising division is not commutative.
Example task
Which is easier to work out: 2 × 9 or 9 × 2? Does the same thing work for division: is 12 ÷ 3 the same as 3 ÷ 12?
Model response: 2 × 9 and 9 × 2 both equal 18 — I can do whichever is easier. But 12 ÷ 3 = 4 and 3 ÷ 12 does not give 4, so division is not the same both ways.
Explaining why multiplication is commutative using the language of groups, and explaining why division is not.
Example task
Explain why 5 × 3 = 3 × 5 but 15 ÷ 3 does not equal 3 ÷ 15.
Model response: 5 groups of 3 and 3 groups of 5 both give 15 objects — the array is the same, just turned. But sharing 15 among 3 gives 5 each, while sharing 3 among 15 gives less than 1 each. The answers are different.
CPA Stages
concrete
Children make a rectangular array with counters (e.g. 3 rows × 4 columns = 12), then physically rotate the array 90 degrees to see 4 rows × 3 columns = 12. The same total without recounting demonstrates commutativity. For division, they show that sharing 12 between 3 and sharing 12 between 4 give different results.
Transition: Child rotates arrays to demonstrate commutativity of multiplication and explains: 'Turning the array does not change the total.' They show with objects that sharing changes when you swap the number of groups.
pictorial
Children draw arrays in both orientations and write both multiplication facts. They use these drawn arrays to choose the easier order for calculation. For division, they draw sharing diagrams to show that reversing gives a different answer.
Transition: Child draws arrays in both orientations showing the same total, and explains why division diagrams give different answers when the numbers are swapped.
abstract
Children apply commutativity to choose the more efficient multiplication order, and state as a rule that multiplication can be done in any order but division cannot. They use commutativity to halve the number of facts they need to memorise.
Transition: Child states the commutativity rule for multiplication and non-commutativity of division in their own words, and uses commutativity to choose the easier calculation order without being told.
Delivery rationale
Primary maths (Y2) with concrete stage requiring physical manipulatives (Counters for arrays, Array frames or trays). AI delivers instruction; facilitator sets up materials.