Year 3 · Mathematics · Number
Equal groups and sharing
Exploring multiplication as equal groups and arrays, and division as sharing equally or making groups of a given size, using real objects.
Awaiting educator review. This material was drafted by our content team with AI assistance and is waiting for review by a qualified educator. Please check it suits your child before using it. Created 10 October 2026.
These lessons were written around Australian Curriculum strands and matched to New Zealand year levels by age (NZ Year 1 is the first year of school). They are not yet mapped to The New Zealand Curriculum, so check them against your own learning programme.
Learning goals
Learners will
- Make and describe equal groups and arrays.
- Use skip counting to find the total of equal groups.
- Share a collection equally and find how many groups can be made.
Success looks like
- I can make equal groups and say '3 groups of 4'.
- I can skip count by 2s, 5s and 10s to find a total.
- I can share objects fairly so everyone gets the same.
- I can arrange objects in rows and columns to make an array.
The big idea
Multiplication starts with equal groups. Put 4 grapes on each of 3 plates. We can say '3 groups of 4'. To find the total, skip count by 4: 4, 8, 12.
If the groups are not the same size, it is not multiplication. Make one plate with 2 grapes and ask whether this is still '3 groups of 4'. Talking about why it is not helps the idea stick.
An array is equal groups arranged in neat rows. A muffin tin with 2 rows of 6 is an array showing 12. Turning the tin shows 6 rows of 2 — still 12.
Division has two meanings. Sharing: 12 pegs shared between 3 children — deal them out one at a time like cards until all are gone. Each child gets 4.
Grouping: 15 strawberries put into groups of 5 — how many groups? Keep making groups of 5 until none are left. There are 3 groups.
Sometimes a collection cannot be shared equally. 7 biscuits shared between 2 people gives 3 each with 1 left over. Real life has leftovers, and that is okay to notice and talk about.
Worked examples
Counting equal groups
There are 4 bags with 5 apples in each bag. How many apples altogether?
- There are 4 equal groups of 5.
- Skip count by 5 for each bag: 5, 10, 15, 20.
Answer: There are 20 apples.
Sharing fairly
Share 12 pegs equally between 3 children.
- Set out 3 plates, one for each child.
- Deal the pegs one at a time onto each plate in turn.
- When all 12 are dealt, count one plate: 4 pegs.
- Check that every plate has 4: 4, 8, 12.
Answer: Each child gets 4 pegs.
Making groups
18 socks are put into pairs. How many pairs are there?
- A pair is a group of 2.
- Skip count by 2 until you reach 18: 2, 4, 6, 8, 10, 12, 14, 16, 18.
- Count how many numbers you said: 9.
Answer: There are 9 pairs of socks.
Practice check
Have a go, then check your answers. Each answer comes with an explanation.
Answer guide for parents
There are 3 plates with 4 strawberries on each plate. How many strawberries altogether?
12 — 3 groups of 4: skip count 4, 8, 12.
There are 5 packets with 2 biscuits in each packet. How many biscuits altogether?
10 — 5 groups of 2: skip count 2, 4, 6, 8, 10.
12 pegs are shared equally between 3 children. How many pegs does each child get?
4 — Deal the 12 pegs out one at a time to 3 children; each gets 4. Check: 4 + 4 + 4 = 12.
10 grapes are shared equally between 2 people. How many grapes does each person get?
5 — Half of 10 is 5, and 5 + 5 = 10.
A muffin tin has 2 rows with 6 cups in each row. How many cups are there?
12 — 2 rows of 6: 6, 12. There are 12 cups.
Each hand has 5 fingers. How many fingers are on 3 hands?
15 — Skip count by 5 three times: 5, 10, 15.
15 strawberries are put into groups of 5. How many groups are there?
3 — Skip count by 5 to 15: 5, 10, 15. That is 3 groups.
7 biscuits are shared equally between 2 people. How many biscuits are left over?
1 — Each person gets 3 biscuits (3 + 3 = 6), so 1 biscuit is left over.
Watch out for
- Counting groups instead of objects (answering 3 for '3 groups of 4'). Ask 'How many groups?' and 'How many in each group?' separately.
- Accepting unequal shares as fair. Always check that every group has the same number.
- Thinking 2 rows of 6 and 6 rows of 2 give different totals. Turn an egg carton around to show they are the same.
Tips for parents
- Use everyday sharing moments — splitting fruit, dealing cards, setting the table.
- Say the language aloud: 'four groups of three', 'shared between', 'each gets'.
- Skip counting songs and chants help children find totals quickly.
Go further
- Find arrays around the home or shops: egg cartons, window panes, drink bottle packs. Describe the rows and columns.
- Plan a teddy bears' picnic: share snacks equally among the toys and record what happens with leftovers.
- Arrange 12 buttons into as many different arrays as possible (1 by 12, 2 by 6, 3 by 4 and their turnarounds).