Number Bonds Explained: What They Are and How to Teach Them

Grab five small things, like buttons or raisins, and a cup. Hide some under the cup while your child looks away. Show what’s left and ask, “How many are hiding?” Five split into the ones you can see and the ones under the cup is a number bond.

The ideas below suit ages 5 to 7, roughly kindergarten to grade 1. Ages are a rough guide only. Children get to this point at different times, and that’s fine.

What is a number bond?

A number bond is a number split into two parts. The whole is the bigger number. The parts are the two smaller numbers that make it.

It’s often drawn as three circles. The whole sits in the top circle. Two lines run down to two smaller circles, one for each part.

For 10, you might write 10 at the top and 7 and 3 below. Read it as “7 and 3 make 10.”

You’ll see “number bond” in many UK and Singapore-style books, while US worksheets often say part-part-whole, and you may also see number partners or a number pair.

The Common Core kindergarten standard for operations (K.OA.A.3) asks children to split numbers up to 10 into pairs in more than one way, using objects or drawings, and to record each split as a drawing or an equation. Its own example is 5 = 2 + 3 and 5 = 4 + 1. That’s number bonds in all but name.

Why do number bonds matter?

A number bond holds addition and subtraction in one picture. If 7 and 3 make 10, then 10 take away 3 leaves 7. A child who sees that can treat subtraction as the same facts read the other way.

That link isn’t obvious to young children. In a study of 44 children aged 6 and 7, Ann Dowker found that using the link between adding and taking away (if 7 + 3 = 10, what is 10 - 3?) was among the hardest shortcuts for them. So it’s worth showing your child directly.

The same pairs help children go past 10. The grade 1 standard (1.OA.C.6) lists “making ten” as a strategy, with the example 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14. That move is easier when your child already knows 8 and 2 make 10.

Number bonds to 5 and to 10

Start with 5. It’s small enough to hold in one hand. Five has six splits: 0 and 5, 1 and 4, 2 and 3, 3 and 2, 4 and 1, and 5 and 0.

Then move to 10. Here are all the bonds to 10, written both ways:

That’s 11 rows, but only six different pairs, because 3 and 7 is the same pair as 7 and 3. Point this out early. 5 and 5 is the double in the list, the only pair with two equal parts. The pattern is easy to see too: as one part goes up by 1, the other goes down by 1.

The kindergarten standard (K.OA.A.4) asks children to find, for any number from 1 to 9, the number that makes 10 with it. Its next line (K.OA.A.5) asks for fluent adding and taking away within 5, which is one more reason to start with bonds to 5.

How do you teach number bonds step by step?

Go from things you can touch, to pictures, to numbers. Each step can take days or weeks. Stay on one until it feels easy.

1. Real objects (ages 5 and up). Take five or six counters. Split them into two piles and say what you see: “4 and 2 make 6.” Mix them up and split them a different way. Your child can find each total by counting the objects one by one, which is fine at this stage.
2. Fingers and ten frames (ages 5 to 6). Hold up 10 fingers and fold some down. “Seven up, so how many down?” A ten frame is a box of two rows of five. Fill some squares with counters and ask how many are empty.
3. Drawings (ages 5 to 6). Draw the three circles and dots inside them. Let your child draw the dots for the parts.
4. Numbers in the circles (ages 6 to 7). Write the whole and one part. Leave the other circle empty for your child to fill.
5. Quick recall (ages 6 to 7). Ask out loud: “7 and what make 10?” Count it as a win when the answer comes without counting from 1.

Leave one circle blank at random. Sometimes the whole is missing, and sometimes a part is. If your child only ever fills in a bottom circle, try hiding the whole now and then so the question doesn’t always look the same.

Five number bond games for home

These take a few minutes and use things most homes have. The kindergarten math games post has more ideas for ages 5 to 6.

• Two cups (ages 5 to 6). It’s a bigger version of the cup game at the top. Put 10 counters under two cups, lift one and ask how many are under the other. If 6 are under the first cup, 4 are under the second. Lift it to check.
• Shake and spill (ages 5 to 6). Paint one side of five beans, or use two-colored counters. Shake them in a cup and spill. Name the split: “3 red and 2 white make 5.” With 5 counters there are 6 different splits, if 3 red and 2 white counts as different from 2 red and 3 white.
• Bond snap (ages 5 to 7). Make a train of 10 building bricks. Snap it in two behind your back, show one piece and ask how long the hidden piece is.
• Make 10 with cards (ages 6 to 7). Use cards 1 to 9 and lay some face up. Take turns finding two that make 10, like 4 and 6. Our list of math games for kids has the full rules.
• Snack bonds (ages 5 to 7). “I have 8 grapes. If I eat 3, how many are left?” Then turn it around: “3 and what make 8?”

You can also play one right here. In the game below, one circle is empty and your child picks the missing number. A dots button shows the whole as dots, so a child can count the gap. After each answer, the game shows the number sentences that come from the bond.

Number bond buddies

A number bond shows how a whole splits into two parts. Find the missing number.

Which number is hiding behind the question mark?

Within 10Make 10Make 20

0 of 0

Show dots

0243

The fact family

•  
•  

Next

Start with “Within 10” and try “Make 20” once bonds to 10 feel easy.

From bonds to 10 to bonds to 20

Bonds to 20 usually come at ages 6 to 7 (grade 1), and they grow straight out of bonds to 10. If 6 and 4 make 10, then 16 and 4 make 20. 16 is one ten and 6 ones, and the 4 fills up the second ten. The same pattern runs through the whole list: 13 and 7, 18 and 2, 15 and 5.

Show it with two ten frames, or 20 bricks in two trains of 10. Fill one frame, then 6 squares of the next. The empty squares are the part that is still missing.

There are 11 different pairs that make 20, from 0 and 20 up to 10 and 10. Don’t drill them all at once. One new pair a week is plenty.

Knowing bonds to 10 pays off again when a sum crosses 10. Take 9 + 5. Nine needs 1 more to make 10, so split 5 into 1 and 4: 9 + 1 = 10, then 10 + 4 = 14. That’s the “making ten” strategy from the grade 1 standard, and it rests on knowing the bonds to 10.

How number bonds lead to subtraction

Each bond gives four number sentences, a set often called a fact family. This suits ages 6 to 7, once bonds to 10 feel familiar. The bond 10, 7 and 3 gives:

• 7 + 3 = 10
• 3 + 7 = 10
• 10 - 7 = 3
• 10 - 3 = 7

The grade 1 standard (1.OA.B.4) describes subtraction this way: to work out 10 - 8, find the number that makes 10 when added to 8. That number is 2. A child who knows the bond 8 and 2 already has the answer.

Ask about one bond in all four ways in the same chat. “7 and 3 make 10. So what’s 10 take away 3?” Pause, and let your child find it.

Dowker’s study suggests this link is hard at ages 6 and 7, so expect to come back to it often.

Common number bond mix-ups and quick fixes

• Counting from 1 every time. Your child counts all 10 dots to find the gap. It works, but it’s slow. Cover the known part with a hand and count only the gap, then try saying the answer before counting.
• Leaving out zero. “There’s no way to make 5 with 5.” There is: 5 and 0. Hide all the counters under the cup once in a while and ask how many are showing.
• Mixing up the whole and a part. Your child adds 10 and 7 when 10 is the whole. Point at the top circle and ask, “Is this the big number or a piece of it?” Use a bigger circle for the whole when you draw.
• Thinking 7 and 3 and 3 and 7 are different facts. Turn a train of bricks around. It’s the same train, so it’s the same bond.
• Guessing. If your child starts guessing, the task may have jumped ahead. Go back one step, to objects or the ten frame, for a few days. Keep it light and end on one your child gets right.

If you’d like extra practice with number sentences, Math Learner is a math practice app for children aged 3 to 10. Its Addition and Subtraction worlds use number sentences with four answer choices, and from the third difficulty step they include missing-number questions as well. Each level has eight questions, a wrong answer shows the right one, and the first 15 levels of each world are free, one lesson a day.

It has no ads, no account and no tracking tools. You can download it here and play one level with your child.

The short version

A number bond is two parts and a whole. Start with real objects and bonds to 5, move to 10 with fingers and ten frames, then to 20 with two frames side by side. Ask each bond in all four directions, and go back a step whenever guessing creeps in. For board-based practice that adds a little competition, see math board games for kids.