Composing and decomposing numbers

Numbers are made of parts

Every number can be broken into smaller numbers and put back together.

• To compose means to put parts together: 6 and 4 make 10.
• To decompose means to break apart: 10 is 6 and 4.

There are lots of ways to break a number. 10 can be 1 + 9, 2 + 8, 3 + 7, 4 + 6, 5 + 5 and more.

Number bonds

A number bond shows a whole and its two parts:

You may see it drawn as a circle on top (the whole) joined to two circles below (the parts). The parts always add back to the whole.

Ways to make 10

These pairs are worth knowing by heart. They make adding and subtracting much easier.

Breaking into tens and ones

Bigger numbers can be partitioned by place value:

• 46 = 40 + 6
• 46 = 30 + 16 (borrowing a ten as ones)
• 46 = 20 + 26

All are true! Flexible breaking helps with mental maths. For example, 46 + 7: break 7 into 4 + 3. 46 + 4 = 50, then 50 + 3 = 53.

Why this matters

Composing and decomposing is the secret behind:

• Make ten strategies in addition.
• Regrouping (carrying and borrowing).
• Mental maths with friendly numbers.

Worked examples

Example 1: 10 can be 6 + __.

What part goes with 6 to make 10? 4.

Example 2: Decompose 9 in three ways.

1 + 8, 4 + 5, 2 + 7 (also 3 + 6, 0 + 9).

Example 3: Use parts to work out 8 + 5.

Break 5 into 2 + 3. 8 + 2 = 10, then 10 + 3 = 13.

Common mistakes

• Forgetting that the parts must add back to the whole. Always check: part + part = whole.
• Only knowing one way to break a number. Try many!
• Mixing up whole and part in a number bond.

Try it yourself

1. 7 = 4 + __
2. Write two different number bonds for 12.
3. Partition 58 into tens and ones.
4. Use make ten to solve 9 + 6.

Answers: 1) 3 2) e.g. 10 + 2 and 6 + 6 3) 50 + 8 4) 9 + 1 = 10, 10 + 5 = 15

Quick recap

• Compose = put together; decompose = break apart.
• A number bond shows a whole and its parts.
• Partition numbers flexibly to make calculating easier.