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Year 1 · Mathematics · Number

Making and breaking numbers to 10

Joining two small groups to find how many altogether, and splitting a group into two parts to see the numbers hiding inside it.

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

  • Join two small groups and find the total by counting.
  • Split a group of up to 10 objects into two parts in different ways.
  • Take some objects away from a group and count what is left.

Success looks like

  • I can put two groups together and count how many altogether.
  • I can split a number into two parts, like 5 is 3 and 2.
  • I can take some away and say how many are left.

The big idea

Every number can be made from smaller numbers. Five can be 4 and 1, 3 and 2, or 5 and 0. Seeing these 'parts' helps children add and subtract later on without counting every single object.

Start with joining. Put 2 red blocks in one bowl and 3 blue blocks in another. Ask how many in each bowl, then tip them together and count them all. Say the sentence together: '2 and 3 make 5.'

Next try splitting. Give your child 6 pieces of pasta and ask them to share them into two bowls any way they like. Count each bowl. Then try again a different way. Make a list together of all the ways to split 6.

Taking away is the opposite of joining. Put out 5 buttons, cover 2 of them with a tea towel and ask, 'How many can you still see?' Lift the towel to check.

Fingers are a wonderful tool. Ten fingers can show the pairs that make 10: hold up 7 fingers and see that 3 are folded down, so 7 and 3 make 10.

  • Joining: 2 and 3 make 5.
  • Splitting: 6 can be 4 and 2.
  • Taking away: 5 take away 2 leaves 3.

Worked examples

Joining two groups

There are 4 red blocks and 2 blue blocks. How many blocks altogether?

  1. Count the red blocks: 1, 2, 3, 4.
  2. Push the blue blocks next to them.
  3. Keep counting from 4: 5, 6.
  4. The last number said is 6.

Answer: 4 and 2 make 6 blocks altogether.

Hiding pasta under a cloth

There are 7 pieces of pasta. Some are hidden under a cloth and 3 can be seen. How many are hidden?

  1. We know the whole is 7.
  2. We can see 3, so count on from 3 up to 7 using fingers: 4, 5, 6, 7.
  3. Four fingers were used to count on.
  4. Lift the cloth and count to check.

Answer: 4 pieces are hidden, because 3 and 4 make 7.

Practice check

Have a go, then check your answers. Each answer comes with an explanation.

  1. 1.There are 2 red blocks and 3 blue blocks. How many blocks are there altogether?
  2. 2.Hold up 5 fingers on one hand and 1 finger on the other. How many fingers are up altogether?
  3. 3.Which pair of numbers makes 10?
  4. 4.You have 4 grapes. You eat 1 grape. How many grapes are left?
  5. 5.Seven pieces of pasta are split between your two hands. One hand has 3 pieces. How many are in the other hand?
  6. 6.8 is the same as 5 and how many more?
  7. 7.Which of these is a way to split 5 into two parts?
  8. 8.There are 10 ducks on a pond. 2 ducks swim away. How many ducks are still on the pond?
Answer guide for parents

  1. There are 2 red blocks and 3 blue blocks. How many blocks are there altogether?

    5 — Count 2, then keep going for 3 more: 3, 4, 5. So 2 and 3 make 5.

  2. Hold up 5 fingers on one hand and 1 finger on the other. How many fingers are up altogether?

    6 — 5 and 1 more make 6.

  3. Which pair of numbers makes 10?

    6 and 4 — 6 and 4 make 10. The others make 9.

  4. You have 4 grapes. You eat 1 grape. How many grapes are left?

    3 — 4 take away 1 leaves 3.

  5. Seven pieces of pasta are split between your two hands. One hand has 3 pieces. How many are in the other hand?

    4 — Count on from 3 to 7: 4, 5, 6, 7. That is 4 more, so 3 and 4 make 7.

  6. 8 is the same as 5 and how many more?

    3 — Count on from 5 to 8: 6, 7, 8. That is 3 more.

  7. Which of these is a way to split 5 into two parts?

    4 and 1 — 4 and 1 make 5. The others make 6, 6 and 4.

  8. There are 10 ducks on a pond. 2 ducks swim away. How many ducks are still on the pond?

    8 — 10 take away 2 leaves 8. Count back 2 from 10: 9, 8.

Watch out for

  • Counting the first group again when joining. Show how to start from the number in the first group and count on.
  • Thinking a number can only be split one way. Explore many splits of the same number to show there are lots of answers.
  • Believing the total changes when objects are moved around. Rearrange the same blocks and count again to show it stays the same.

Tips for parents

  • Use the same story language often: 'I had 5, I gave away 2, now I have 3.'
  • Let your child check answers by counting the real objects — checking is a good habit, not a sign of failure.
  • Snack time is perfect for take-away practice: count the crackers, eat some, count what is left.

Go further

  • Play 'Hide the teddies': hide some of 6 small toys under a cup and ask how many are hiding.
  • Make a 'ways to make 5' poster by gluing pasta in two colours onto paper in different splits.
  • Play a ten-finger game: one person holds up some fingers and the other says how many more are needed to make 10.