Number Bonds

What is a number bond?

A number bond is a small diagram that shows how a number splits into two parts. The whole sits in the top circle, the two parts sit in the circles below it, and lines join them. 7 with the parts 3 and 4 is one number bond; 7 with 5 and 2 is another. Children learn it as part-part-whole: when both parts are known you add to find the whole, and when the whole and one part are known you find the missing part, which is subtraction in disguise. That is why number bonds sit between counting and the first addition and subtraction facts.

Here are the number bond examples children meet first. Each pair also works turned around, so 3 and 7 is the same bond as 7 and 3.

How to teach number bonds

1. Start with objects. Give a child 6 counters and ask for every way to split them into two groups. Record each split as a bond.
2. Move to a ten frame. Two colors of counters show both parts at once, and the empty boxes in a ten frame show what is missing to make 10. Set Picture help to Ten frame for this stage: the known part is filled in and the missing part is drawn as dashed circles to count.
3. Then the bond alone. Turn the help off so children work from the numbers.
4. Connect it to equations. One bond gives a fact family: 4 + 2 = 6, 2 + 4 = 6, 6 − 4 = 2 and 6 − 2 = 4. Equation boxes under each bond give space to write one.
5. Aim for recall. Number bonds to 10 are worth knowing by heart, because adding by making ten (8 + 5 = 8 + 2 + 3) depends on them.

Number bonds worksheets, templates and mats

Worksheets print 1 to 12 bonds per page with a name and date line. Bonds to 5, to 10 or to 20 keep the whole the same on every problem, the way number bonds for kindergarten usually start; within 10 and within 20 change the whole each time, which suits first grade. Missing a part gives subtraction number bonds, missing the whole gives addition, and Mixed blends the three positions. New worksheet draws a fresh set. Problems repeat on a page only when it has more bonds than there are facts: number bonds to 5 have just four splits without 0 (1 and 4, 2 and 3, 3 and 2, 4 and 1), so a page of 8 uses each twice. The generator leaves 0 out so every problem needs some thinking.

Answer key: set Answers to Show and print again. The missing numbers appear in red, or dark gray in black and white, on the same problems.

Blank number bond template: choose Blank template for empty bonds to fill with your own numbers. One per page makes a large number bond mat for counters or cubes; 4 to 12 per page suit writing. Picture help adds an empty ten frame, or a double ten frame when bonds go to 20. For more practice with the same ideas, use the ten frame maker, a number line for counting on, or the hundreds chart.

How we tested this tool

We checked the generator by script in Google Chrome on Windows across 1,680 sheets: both sheet types, all five bond ranges, the three missing options, 1 to 12 bonds per page, with and without picture help, equation boxes and answers, on Letter and A4. In the 7,920 worksheet problems every pair of parts adds up to the whole, bonds to 5, 10 or 20 always keep that whole, no part is 0, and a page never repeats a problem while unused facts remain. Each problem shows exactly two numbers (three on the answer key, all correct), the ten frame holds exactly as many counters as the whole with the missing part drawn dashed, and switching the answer key or picture help on and off keeps the same problems. We also measured that no bond, ten frame or equation box leaves its space on the page, that neighbouring bonds stay at least 14 mm apart, and that no two numbers or labels overlap. The first layout put bonds only a few millimetres apart at 4 per page, so the spacing was widened. We printed sheets to PDF with Microsoft Edge (one US Letter portrait page) and tested the page at a 375 px phone width.

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