Multiplication and Division
KS1MA-Y1-D003
Pupils begin to understand multiplication and division through grouping, sharing and arrays, connecting these to counting in twos, fives and tens.
National Curriculum context
In Year 1, multiplication and division are introduced informally through grouping and sharing small quantities, with the full support of the teacher and through the use of concrete objects, pictorial representations and arrays. Pupils begin to understand doubling numbers and quantities, and finding simple fractions of objects, numbers and quantities, which naturally connects to multiplicative thinking. The non-statutory guidance makes explicit that pupils should make connections between arrays, number patterns, and their counting in twos, fives and tens — creating a coherent thread from counting through to multiplication. At this stage there is no expectation that pupils record formal multiplication or division statements; the focus is on building intuitive understanding of equal groups and sharing through exploration and discussion. This exploratory approach prepares pupils for the more formal work with multiplication tables and written methods that begins in Year 2.
2
Concepts
1
Clusters
3
Prerequisites
2
With difficulty levels
Lesson Clusters
Explore grouping, sharing, doubling and halving
practice CuratedGrouping/sharing and doubling/halving are the two foundational lenses on multiplicative structure. C013 co_teaches with C012 directly. Only two concepts, so no introduction/practice split is warranted.
Teaching Suggestions (1)
Study units and activities that deliver concepts in this domain.
Doubling, Halving and Early Multiplication
Mathematics Worked Example SetPedagogical rationale
Y1 multiplication focuses on counting in 2s, 5s, and 10s and understanding that multiplication means repeated equal groups. Doubling is the entry point: children already understand 'two of the same'. Arrays (rows and columns of objects) make the multiplicative structure visible and lay the groundwork for times tables. Division at this stage means sharing equally into groups. The concrete experience of grouping and sharing must precede any symbolic notation.
Access and Inclusion
1 of 2 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 (2)
Grouping and sharing (early multiplication and division)
knowledge AI FacilitatedMA-Y1-C012
Grouping (how many groups of 3 in 12?) and sharing (share 12 equally among 4) are the two fundamental structures of division, and repeated grouping underpins multiplication. In Year 1, pupils explore these concepts informally using concrete objects and with teacher support. Mastery at this stage means pupils can physically group objects into equal groups and explain what they have done, connecting their actions to the vocabulary of multiplication and division.
Teaching guidance
Use concrete manipulatives exclusively at this stage — cubes, counters, toys — to model grouping and sharing. Present 'grouping' problems (put these 12 cubes into groups of 3, how many groups?) and 'sharing' problems (share these 12 cubes equally between 4 people) as practical activities before any numerical recording. Connect to arrays — a 3 by 4 arrangement shows both 3 groups of 4 and 4 groups of 3. Link to counting in twos, fives and tens as skip counting being 'repeated addition'. Connect doubling to multiplying by 2 and halving to dividing by 2.
Common misconceptions
Pupils often confuse grouping and sharing: in grouping you know the size of each group (and count the groups); in sharing you know the number of groups (and count the size of each). Pupils may share unequally (giving more to some recipients) and not recognise this as incorrect. They may not connect their concrete grouping activity to the word 'multiplication' or see it as connected to counting in multiples.
Difficulty levels
Sharing objects equally between 2 people by dealing one at a time ('one for you, one for me').
Example task
Share 10 cubes equally between 2 teddies. How many does each teddy get?
Model response: Each teddy gets 5 cubes.
Making equal groups of a given size from a collection (grouping) and counting the number of groups.
Example task
Put these 12 counters into groups of 3. How many groups did you make?
Model response: 4 groups. There are 4 groups of 3 in 12.
Solving simple grouping and sharing problems and connecting them to multiplication and division language.
Example task
There are 15 pencils. Put them in groups of 5. How many groups? Can you write this as a number sentence?
Model response: 3 groups. 15 ÷ 5 = 3 or 3 × 5 = 15.
CPA Stages
concrete
Children share objects equally between teddies, plates or people by dealing one at a time ('one for you, one for me'). They also make equal groups from a collection by counting out a fixed number of objects repeatedly. Toy sharing with real objects makes division tangible.
Transition: Child shares objects equally between 2, 3, 4 or 5 recipients by one-at-a-time dealing without making errors, and groups objects into specified equal groups, stating the number of groups made.
pictorial
Children draw arrays of dots to represent equal groups and use ring diagrams to show grouping. They begin to connect their pictures to the language of multiplication and division: '3 groups of 4' and '12 shared between 3'.
Transition: Child draws arrays and ring diagrams to represent grouping and sharing problems, and uses the language 'groups of' and 'shared between' to describe what the picture shows.
abstract
Children connect their grouping and sharing experience to multiplication and division vocabulary, beginning to describe situations using 'multiply', 'divide', 'groups of' and 'shared equally'. They may write informal multiplicative statements with teacher support.
Transition: Child uses multiplication and division vocabulary unprompted when describing grouping and sharing situations, connecting the language to their concrete and pictorial experience.
Delivery rationale
Primary maths (Y1) with concrete stage requiring physical manipulatives (Teddies or toy figures for sharing between, Plates or sorting hoops). AI delivers instruction; facilitator sets up materials.
Access barriers (1)
Grouping and sharing require following multi-step physical procedures: count out the total, decide on group size, distribute equally, count the groups. Children with working memory needs may lose track of the procedure mid-task.
Doubling and halving
skill AI FacilitatedMA-Y1-C013
Doubling (adding a quantity to itself) and halving (splitting a quantity into two equal parts) are the first multiplicative concepts pupils encounter and are deeply connected to the 2 times table, fractions (one half) and the relationship between multiplication and division. Mastery means pupils can quickly double and halve any number up to at least 10, recognise halving as the inverse of doubling, and connect these operations to their emerging knowledge of fractions and grouping.
Teaching guidance
Use mirrors to show doubling visually: place a row of cubes in front of a mirror and the image doubles the collection. Use two matching groups placed side by side. Connect doubling to addition: double 4 is 4 + 4 = 8. Connect halving to sharing equally between 2. Practise with small numbers (double 1 through 10) using concrete resources first, then pictorial representations, then as mental arithmetic. Explicitly connect 'half of' to the fraction one half introduced in the fractions domain.
Common misconceptions
Pupils may double by counting all rather than using addition (double 6: count 6 objects then count 6 more, then count all 12 from the beginning). They may confuse halving with 'cutting in half' in an informal sense that doesn't require equality. Some pupils do not recognise that halving is the inverse of doubling — knowing double 6 is 12 but not using this to halve 12.
Difficulty levels
Doubling numbers to 5 by making two identical groups of objects.
Example task
Make a group of 4 cubes. Now make another group the same size. How many altogether?
Model response: 8. Double 4 is 8 because 4 + 4 = 8.
Doubling numbers to 10 and halving even numbers to 20 using pictorial support.
Example task
What is double 7? What is half of 16?
Model response: Double 7 is 14. Half of 16 is 8.
Rapidly recalling doubles to 10 and corresponding halves, and recognising halving as the inverse of doubling.
Example task
Double 8 is 16. What is half of 16? How do you know without working it out?
Model response: Half of 16 is 8. I know because halving undoes doubling — if double 8 is 16, then half of 16 must be 8.
CPA Stages
concrete
Children make two identical groups of objects to double: build a tower of 4 cubes, then build an identical tower and count the total. For halving, they split a group into two equal piles. Mirrors placed behind a row of objects visually demonstrate the doubling effect.
Transition: Child makes two identical groups for any double up to double 10 without counting the second group one-by-one — they count out the same number as the first group confidently.
pictorial
Children draw butterfly-wing diagrams (mirrored patterns) showing doubles, and use simple drawings of matched groups. For halving, they draw a line down the middle of a group of pictures and count each side.
Transition: Child draws doubles and halves diagrams accurately, and begins to state the double or half before drawing, using the picture to confirm rather than to discover the answer.
abstract
Children rapidly recall doubles to 10 and the corresponding halves as known facts, and recognise that halving is the inverse of doubling. They connect doubling to addition (double 7 = 7 + 7 = 14) and halving to the fraction one half.
Transition: Child states any double up to double 10 and the corresponding half instantly, and explains the inverse relationship: 'I know half of 16 is 8 because double 8 is 16.'
Delivery rationale
Primary maths (Y1) with concrete stage requiring physical manipulatives (Interlocking cubes, Counters). AI delivers instruction; facilitator sets up materials.