Number bonds, explained for parents
A number bond is a little picture of a number and two parts that make it: 10 at the top, 7 and 3 below. One picture gives four facts: 7 + 3 = 10, 3 + 7 = 10, 10 − 7 = 3, 10 − 3 = 7. It's how many classes teach addition and subtraction as one idea.
Checked October 29, 2026 against the sources listed at the end.
What a number bond is
A number bond shows a whole and its parts, usually as three circles joined by lines: the whole on top, the two parts below. It's sometimes called part-part-whole. If you know two of the circles, you can work out the third.
Why schools teach it
The Common Core asks kindergartners to break numbers up to 10 into pairs in more than one way (5 is 2 and 3, or 4 and 1), and to find the number that makes 10 with any number from 1 to 9. First graders use the link between adding and subtracting: knowing 8 + 4 = 12 means you know 12 − 8 = 4. A number bond is a picture of exactly that.
The term "number bond" isn't in the Common Core; it's a name many math programs use for this picture. Whatever it's called, the point is that subtraction stops being a separate list of facts to memorize. If a child knows the bond, the subtraction facts come with it.
The pairs that make 10
Bonds to 10 matter most, because so much later math leans on making a ten. These are the nine pairs (each one also works the other way round):
| Parts | Addition | Subtraction |
|---|---|---|
| 1 and 9 | 1 + 9 = 10 | 10 − 1 = 9 |
| 2 and 8 | 2 + 8 = 10 | 10 − 2 = 8 |
| 3 and 7 | 3 + 7 = 10 | 10 − 3 = 7 |
| 4 and 6 | 4 + 6 = 10 | 10 − 4 = 6 |
| 5 and 5 | 5 + 5 = 10 | 10 − 5 = 5 |
| 6 and 4 | 6 + 4 = 10 | 10 − 6 = 4 |
| 7 and 3 | 7 + 3 = 10 | 10 − 7 = 3 |
| 8 and 2 | 8 + 2 = 10 | 10 − 8 = 2 |
| 9 and 1 | 9 + 1 = 10 | 10 − 9 = 1 |
Helping with homework
- Use real things: 10 grapes, hide some under a cup, and ask how many are hiding. That's a missing part.
- Ask for every way to split a small number: "how many ways can you make 6?"
- When your child is stuck on a subtraction, draw the bond: "what goes with 8 to make 12?"
- Practice bonds to 10 until they are instant, a minute or two at a time. Speed comes from short, frequent practice.
- If your child's teacher uses different words or a different layout, use theirs. The point is that your child hears one way of explaining it, not two competing ones; a quick note to the teacher asking "how do you want this shown?" is always welcome.
Try it
Build bonds with the on-screen number bonds and ten frames, then print make 10 worksheets and addition within 10 worksheets. The next step is making ten to add bigger numbers.
Questions parents ask
What is a fact family?
The facts that share the same three numbers: for 7, 3 and 10, that's 7 + 3 = 10, 3 + 7 = 10, 10 − 7 = 3, 10 − 3 = 7. A number bond shows a whole fact family in one picture.
Can a number bond have more than two parts?
Yes, some classes split a whole into three parts later on. Two parts is where everyone starts.
Practice at your child's level
Peabody, our site for children, has free stories and learning games written at each reading level and math grade, with no sign-up. Start where your child is comfortable, not where the calendar says.
- Start reading on Peabody Peabody asks your child's grade, starts the stories a little under it, and moves the level as books run easy or hard.
- Reading levels and math by grade Where each grade starts, and a page for every level and math path.
- The free library Stories sorted by level, to read on screen.
- Decodable readers Stories built from the sounds a beginning reader has been taught.
Where this comes from
Written for parents, to use alongside your child's teacher, not instead of them. General information only, not professional, medical or legal advice. Checked on October 29, 2026. Something wrong or out of date? Write to hello@peabody.kids.