Introduction to Singapore Math: Number Bonds
Number bonds are one of the foundational ideas in Singapore-style math. They help children see part-part-whole relationships, which become the basis for addition, subtraction, and later algebraic thinking. If your child counts on their fingers for every sum, or treats addition and subtraction as two unrelated jobs, number bonds are often the missing link.
What Are Number Bonds?
A number bond is a simple diagram that shows how a number can be broken into parts. It has a "whole" and two "parts" that make up that whole. It is usually drawn as three circles: the whole on top, connected by short lines to the two parts below.
For example, the number 7 can be broken into 3 and 4, or 2 and 5, or 6 and 1. Each is a correct bond for 7.
The power of the diagram is that it holds one fact in a single picture. The bond 7, 3, 4 shows all of these at once:
When a child sees that these four facts are really one relationship, there is far less to memorize.
Why Number Bonds Matter
Making 10: The Strategy Bonds Unlock
The bonds of 10 deserve special attention, because so much later math leans on them. They are:
Once these are automatic, your child can add across 10 without counting. Take 8 + 5:
So 8 + 5 = 8 + 2 + 3 = 13.
The same idea works for subtraction. For 13 - 9, break 13 into 10 and 3. Take 9 from the 10 to get 1, then add the 3 back: 1 + 3 = 4. So 13 - 9 = 4.
Practicing bonds is not "baby math." It is the engine for fast, accurate work with numbers up to 20 and beyond.
Where Number Bonds Fit by Grade
In the usual Common Core sequence, kindergartners learn to break numbers up to 10 into pairs in more than one way and to find the number that makes 10 with a given number. They also build fluency with adding and subtracting within 5. First graders become fluent within 10 and use strategies like making 10 for sums within 20. By the end of second grade, children are expected to add and subtract within 20 fluently and to know all sums of two one-digit numbers from memory.
A child who is behind simply starts with smaller numbers and moves up when ready.
How to Teach Number Bonds
Start with small numbers (bonds within 5) and use real objects:
As your child masters small bonds, move to bonds within 10, then 20, and beyond.
A Five-Minute Routine
Here is a simple routine you can repeat a few times a week:
What to Say
Use the same words each time so the idea sticks. Try "6 is made of 4 and 2" or "4 and 2 make 6." When your child gets one right, name what they did: "You knew 4 needed 2 more to make 6." That kind of specific praise points them back to the strategy, not just the answer.
A Common Mistake and How to Respond
A frequent slip is writing parts that do not add up to the whole, such as a bond of 7 with parts 3 and 5. Rather than saying "wrong," hand back the objects: "Show me 3 and 5 with the blocks. Count them all together." When your child counts 8, they discover the mismatch themselves. Then ask, "We need 7. Which part should change?"
Another common pattern is a child who can do 3 + 4 = 7 but freezes at 7 - 3. Draw the bond and cover the 4 with your finger. "The whole is 7. One part is 3. What is hiding?" This shows that the subtraction question lives in the same picture.
Practice Activities
Moving Beyond 10
Once bonds within 10 are solid, the same diagram works for bigger numbers. A bond of 45 might split into 40 and 5, which supports place value. A bond of 100 might split into 70 and 30. Later, children use bonds to break numbers apart for mental multiplication, such as splitting 14 into 10 and 4 to find 14 × 3 = 30 + 12 = 42.
Short, regular practice matters more than long sessions. A few minutes of bonds most days will do more than an occasional hour, and it keeps math feeling manageable for a child who has been finding it hard.