Number Bonds: What They Are and How to Practice Them

A number bond shows how two numbers (the parts) combine to make a bigger number (the whole). For example, 3 and 7 make 10, so 3, 7 and 10 form a number bond. Kids usually see it drawn as a circle for the whole joined by two lines to circles for the parts. Number bonds start in kindergarten: in the Common Core State Standards, kindergartners split numbers up to 10 into pairs in more than one way and find the number that makes 10 with any number from 1 to 9 (Common Core, K.OA.A.3 and K.OA.A.4).

How the number bond picture works

Draw one circle at the top and two below it, joined by lines:

      ( 10 )
      /    \
   ( 3 )  ( 7 )

• The top circle is the whole: 10.
• The two bottom circles are the parts: 3 and 7.
• Put the parts together and you get the whole. Take one part away from the whole and you get the other part.

That’s why the same picture holds an addition fact and a subtraction fact. One bond gives you four facts, often called a fact family:

• 3 + 7 = 10
• 7 + 3 = 10
• 10 − 3 = 7
• 10 − 7 = 3

The first-grade standard builds on exactly this. It asks kids to understand subtraction as finding a missing part, for example solving 10 − 8 by finding the number that makes 10 when added to 8 (Common Core, 1.OA.B.4).

All the number bonds to 10

Part	Part	Whole
0	10	10
1	9	10
2	8	10
3	7	10
4	6	10
5	5	10

Each pair also works the other way around (9 and 1, 8 and 2, and so on). A pattern kids like to spot: as one part goes up by 1, the other goes down by 1.

Number bonds for smaller numbers

Before 10, kids usually work through the smaller wholes. The kindergarten standard’s own example is 5 = 2 + 3 and 5 = 4 + 1 (Common Core, K.OA.A.3).

Whole	Pairs that make it
5	0 + 5, 1 + 4, 2 + 3
6	0 + 6, 1 + 5, 2 + 4, 3 + 3
7	0 + 7, 1 + 6, 2 + 5, 3 + 4
8	0 + 8, 1 + 7, 2 + 6, 3 + 5, 4 + 4
9	0 + 9, 1 + 8, 2 + 7, 3 + 6, 4 + 5

Number bonds to 20 and “making ten”

Once the bonds to 10 are easy, they unlock bigger sums. The first-grade standard lists “making ten” as a strategy for adding and subtracting within 20, with the example 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14 (Common Core, 1.OA.C.6).

Here’s how to talk a child through it:

1. “8 needs 2 more to make 10.” (That’s a bond to 10.)
2. “Take the 2 from the 6. That leaves 4.” (That’s a bond for 6: 2 and 4.)
3. “10 and 4 more is 14.”

It works for subtraction too. The same standard gives 13 − 4 = 13 − 3 − 1 = 10 − 1 = 9. By the end of second grade, kids are expected to know all sums of two one-digit numbers from memory (Common Core, 2.OA.B.2), and number bonds are one of the main roads there.

How to practice number bonds at home

Start with real objects, then pictures, then just numbers.

• Hide and find. Count out 10 small toys. Hide some under a cup while your child closes their eyes. They count what’s left and work out how many are hiding.
• Two-hand split. Put 7 crackers in front of your child and ask them to share them between two plates in as many ways as they can. Write each split as a bond.
• Ten-frame egg carton. Cut two cups off a 12-egg carton to make 10. Fill some cups with buttons: how many are full, and how many more make 10?
• Fingers. Hold up 6 fingers. How many are down? 6 and 4 make 10, and their own hands prove it.
• Make 10 card game. Remove the face cards from a deck (aces count as 1). Lay out 12 cards face up and take turns picking up pairs that make 10. Tens count on their own.
• Car questions. “I’m thinking of 10. One part is 3. What’s the other part?” No paper needed.

Keep sessions short. A few minutes on most days is easier for both of you to keep up than one long sit-down a week.

Signs your child is ready for the next step

• They answer “what goes with 7 to make 10?” without counting on fingers.
• They can split a number like 6 into pairs in more than one way.
• They start to use 10 on their own to solve something like 9 + 5.

When number bonds feel easy, skip counting is a good next step, and it leads straight into reading a clock to five minutes.