How to teach multiplication with arrays
Use counters in equal rows to teach multiplication, connect it with division and help your child explain times tables with a simple array.
Your child can count objects and recognise equal groups.
Teach multiplication with arrays by arranging objects into equal rows. Your child can see the number of groups and how many objects belong to each group. Turning the arrangement then shows why two multiplication facts can have the same answer.
Use counters, buttons or drawn dots. Choose objects that are easy to move, and start with an amount your child can count comfortably.
Understand the idea
An array is an arrangement in equal rows and columns. Every row has the same number of objects, and the objects line up to form columns.
Multiplication can describe the total in equal groups. Four rows with six counters in each row contain four groups of six. We can write that as 4 × 6.
Say: "We could count every counter. Can we use the rows to find the total without starting from one each time?"
Your child might add six four times or count 6, 12, 18, 24. Both approaches help connect the arrangement with multiplication. If they count individually first, accept it and then demonstrate how knowing one row helps with the others.
See it worked through
Four equal rows
Arrange 24 counters into four rows of six. Point along one row and count its six counters. Then point to each of the four rows.
Write 4 × 6 = 24. Explain: "Our picture shows four groups of six, making 24 altogether."
Turn the paper or tray a quarter turn. The same counters now form six rows of four. Write 6 × 4 = 24.
The arrangement changed direction, but no counters were added or removed. That is why the total stayed 24.
Use the original picture to ask: "If we share the 24 counters equally among four rows, how many are in each row?" The answer is six, so 24 ÷ 4 = 6.
A story about four bags with six marbles each and a story about six bags with four marbles each have different groups. They still have the same total. Ask your child to explain both the group structure and the total, rather than treating the stories as identical.
Try it together
Rearrange the counters
Give your child 15 counters. Ask them to make three equal rows and find how many counters belong in each row.
Ask for a multiplication sentence that matches their picture. Then turn the arrangement and ask for another sentence.
Finally, ask: "If we split all 15 counters into groups of five, how many groups would we make?" Let them point to the groups in the array.
Check the answer
Three equal rows contain five counters each, so 3 × 5 = 15. Turning the array gives five rows of three, so 5 × 3 = 15. Splitting 15 counters into groups of five makes three groups: 15 ÷ 5 = 3.
Check their understanding
Build three rows containing four, four and five counters. Ask whether that picture shows 3 × 4. It does not, because the groups are unequal. Remove the extra counter and ask what changed.
Then show three rows of four again and ask your child to explain what the three, four and 12 mean in 3 × 4 = 12. Naming the quantities tells you more than hearing the answer alone.
Make it easier or harder
Make it easier with two rows of three counters. Keep the counters visible while your child adds 3 + 3 and connects that sum to 2 × 3.
Make it harder by splitting four rows of six into two groups of two rows. Each smaller array contains 12 counters, so doubling 12 gives 24. Another challenge is to find every rectangular array using 12 counters: 1 × 12, 2 × 6 and 3 × 4, plus their turned versions.
Teaching notes
NSW Education's parent numeracy guidance explains equal groups, arrays and the relationship between multiplication and division. The counter arrangements above are original examples for practising those ideas at home.
Numeracy practice
Help your child apply their maths understanding with practice questions and explanations.
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