Number bonds to 10 are the pairs of numbers that make 10: 7 and 3, 6 and 4, 5 and 5. Your child’s class might call them friends of 10 or rainbow facts, and the Victorian Curriculum calls the idea part-part-whole. Whatever the name, knowing these pairs well makes adding and taking away much easier. Here’s what number bonds are, when children learn them, and eight no-prep games for home.
What are number bonds to 10?
A number bond is a whole number split into two parts. Ten can be split into:
| Part | Part | Whole |
|---|---|---|
| 0 | 10 | 10 |
| 1 | 9 | 10 |
| 2 | 8 | 10 |
| 3 | 7 | 10 |
| 4 | 6 | 10 |
| 5 | 5 | 10 |
Turn each pair around (9 and 1, 8 and 2) and you have them all. Bonds work for every number, not just 10: 5 can be 4 and 1, or 3 and 2.
The Victorian Curriculum doesn’t use the words “number bonds”. It talks about partitioning and part-part-whole. Its glossary explains partitioning in the early years as thinking about “numbers as made up of 2 parts, for example, 10 is 8 and 2.” If your child’s teacher says “part-part-whole”, “friends of 10” or “rainbow facts”, they all mean the same thing. Use the words your child hears at school.
Why are number bonds important?
Ten is the heart of our number system, so knowing what makes 10 helps with almost everything that comes next.
- Adding past 10. To work out 8 + 5, a child who knows 8 and 2 make 10 can think “8 and 2 is 10, and 3 more is 13.” Teachers call this bridging through 10.
- Taking away. If 7 and 3 make 10, then 10 take away 3 is 7. One fact gives you several.
- Bigger numbers later. The same idea grows: if 3 and 7 make 10, then 30 and 70 make 100.
The Victorian Government’s maths-at-home guide says practising partitioning “will help your child understand that any number can be broken into different parts, which supports later learning in addition and subtraction.”
When should my child know their number bonds to 10?
Children build up to them over the first three years of school. Here’s the path in the Victorian Curriculum 2.0:
| Year | What children learn |
|---|---|
| Prep | “partition and combine collections up to 10 using part-part-whole relationships and subitising to recognise and name the parts” (VC2MFN04) |
| Year 1 | “add and subtract numbers within 20, using physical and virtual materials, part-part-whole knowledge to 10 and a variety of calculation strategies” (VC2M1N04) |
| Year 2 | “recall and demonstrate proficiency with addition facts to 20; extend and apply facts to develop related subtraction facts” (VC2M2A02) |
So in Prep (Foundation), children explore the different ways to make numbers up to 10 with real things. In Year 1 (Grade 1 at many schools), they use bonds to 10 to add and subtract within 20. By the end of Year 2, children are expected to recall the addition facts to 20, so they come quickly from memory. Other states and territories follow similar steps, though the exact years can differ a little.
Eight no-prep number bond games
All you need is a pack of cards, some pegs or pasta, and fingers. Pick one game and play for five minutes.
- Go Fish to make 10. Use the ace (as 1) to 9 from a pack of cards. Deal five cards each. On your turn, ask for the card that makes 10 with one of yours: “I have a 6. Do you have a 4?” If not, “Go fish!” and pick up. Lay down each pair that makes 10. Most pairs wins.
- Make 10 card flip. Lay 12 cards face up (ace to 9). Take turns finding two cards that make 10 and keeping them. Fill the gaps from the pack. When no pairs are left, shuffle and start again.
- Peg hanger. Clip 10 pegs on a coat hanger. Slide some to one end and cover them with your hand. “I can see 6. How many are hiding?” Then swap.
- How many more fingers? Hold up 7 fingers. “How many more to make 10?” Your child shows the missing fingers. Two hands make ten, which is why this one works so well.
- Draw a rainbow. Write 0 to 10 in a row. Draw a coloured arch joining 0 and 10, then 1 and 9, then 2 and 8, and so on. The arches make a rainbow, which is where the name rainbow facts comes from.
- Ten-frame flash. Draw two rows of five boxes. Put buttons in some boxes and show it for a second. “How many? How many empty?” The empty boxes are the other part of 10. Our post on subitising has more quick-look games.
- Skittles to 10. Line up 10 empty plastic bottles and roll a ball. “You knocked down 4. How many are still standing?” Then check by counting.
- Shake and spill. Colour one side of 10 dried beans or coins with a texta (or use two-coloured counters). Shake them in a cup and spill. “4 heads and 6 tails makes 10.” Keep a tally of which pairs come up.
From 10 to 20, and beyond
Once bonds to 10 feel easy, children use them for bigger sums. The Victorian Curriculum’s Year 2 examples list strategies like “doubles, near doubles, counting on, combinations to 10 and bridging to 10”. You can build these at home:
- Doubles. 6 and 6 is 12. Then near doubles: 6 and 7 is one more, 13.
- Teen numbers. 10 and 4 is 14. Ten and some more is always a teen number.
- Bridging. 9 + 5: take 1 from the 5 to make the 9 a 10. 10 and 4 is 14.
- Tens. 3 tens and 7 tens make 10 tens, which is 100. Bundles of 10 pop sticks with a hair tie show this nicely.
Money is great practice too: two 5c coins make 10c, and five 20c coins make $1. See our guide to Australian money for kids, and our ideas for everyday maths talk.
If it isn’t sticking yet
That’s normal. Bonds need lots of short, repeated practice over months. Go back to real objects, so your child can see and move the two parts. Ask “How did you work it out?” and praise good thinking, not just speed. If your child is anxious about maths, ask their teacher which words and models the class uses, so home and school match.
Questions parents ask
What are number bonds to 10?
They are the pairs of numbers that add to make 10: 0 and 10, 1 and 9, 2 and 8, 3 and 7, 4 and 6, and 5 and 5, plus their turnarounds.
Are number bonds the same as friends of 10 and rainbow facts?
Yes. Friends of 10, rainbow facts and number bonds all mean pairs that make 10. The Victorian Curriculum calls the idea partitioning, or part-part-whole.
When should my child know their number bonds to 10?
In Victoria, children explore making numbers up to 10 in Prep, use bonds to 10 to add and subtract within 20 in Year 1, and should recall addition facts to 20 by the end of Year 2.
Why are number bonds important?
They make adding and taking away easier. A child who knows 8 and 2 make 10 can work out 8 + 5 by going through 10, and one bond gives several subtraction facts too.
How do I teach number bonds at home?
Use real things your child can move: pegs on a coat hanger, fingers, buttons on a ten-frame, or a pack of cards. Play for a few minutes at a time, start with bonds to 5 if needed, and ask your child to explain their thinking.
How do you play Go Fish to make 10?
Use the ace to 9 cards and deal five each. On your turn, ask for the card that makes 10 with one of yours, like a 4 for your 6. If the other player doesn’t have it, pick up a card. Lay down pairs that make 10; most pairs wins.
Sources
- Victorian Curriculum F–10 Version 2.0: Mathematics, VCAA (VC2MFN04, VC2M1N04 and VC2M2A02)
- Mathematics glossary, VCAA
- Mathematics and numeracy at home, Victorian Government
