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Number bonds

Part-whole diagrams for every bond to 10, 20 or 100, with gaps to fill and fresh sheets to print.

Printable chart
INTERACTIVE AND PRINTABLE

Number bonds

Type in a gap: the circle turns green when the number fits.

106
107
108
109
108
105
103
101
102
106
109
107

12 gaps to fill.

Number bondsstringmash.com/number-bonds

Using the sheets

Pick the whole the bonds make, from 5 up to 20, or 100 counted in tens. Mixed sheets change the whole on every diagram, from 2 up to 10 or 20. Every bond, complete lists them all in order with the sum under each one, which makes a good poster or a page to learn from.

The worksheets leave a circle empty. Type a number in it and the circle goes green when it fits, or red when it doesn't. The line under the sheet keeps score. A part or the whole missing also hides the top number on about a third of the diagrams, so the sum has to go the other way.

Print gives twelve diagrams to a page, with the gaps as empty circles even if something has been typed in them. New sheet deals another set. Tick Show answers and print again for the answer sheet.

What a number bond is

A number bond is a pair of numbers that make a whole. 3 and 7 make 10, so 3 + 7 = 10 and 7 + 3 = 10. The same three numbers give 10 − 3 = 7 and 10 − 7 = 3 as well. Learning the pair means knowing four facts at once.

The diagram is the whole in a circle with lines down to its two parts. England's Department for Education calls it a partitioning diagram. Its 2020 guidance asks year 1 pupils to describe one with the words whole and part. 6 is the whole, 4 is a part, 2 is a part.

Bonds to 10 matter most. Adding across ten leans on them. 7 + 5 is 7 + 3 to make 10, then 2 more, which is 12. The Common Core teaches the same move in grade 1 and calls it making ten (1.OA.C.6).

Which bonds, and when

In England the national curriculum asks year 1 pupils to represent and use number bonds and related subtraction facts within 20, and to know the number bonds to 20 by the end of year 2. Year 1 works with bonds to 10 and 20 in several forms. The guidance expects some bonds to 5 and to 10 to be memorised early, with the rest worked out.

Bonds to 100 come in year 3 as complements to 100. The tens version here, 30 and 70 or 60 and 40, comes straight from the bonds to 10. In the US, kindergarten children split numbers up to 10 into pairs in more than one way (K.OA.A.3) and find the partner that makes 10 for any number from 1 to 9 (K.OA.A.4).

Questions

How many number bonds to 10 are there?

Eleven, counting 0 and 10, from 0 + 10 and 1 + 9 up to 10 + 0. If 3 + 7 and 7 + 3 count as one bond, there are six.

Are zero bonds left out of the worksheets?

Mostly. For a whole of 7 or more the worksheets skip 0 and the whole itself, as the gap there is too easy. Bonds to 5 and 6 keep them, so there are enough bonds to go round.

Why does the whole go on top?

It reads like a family tree, with one number splitting into two. Nothing depends on the layout, though. Drawn sideways or upside down, the whole and its parts are the same numbers.

Can children use counters as well?

Yes. The Department for Education's guidance suggests having counters, tens frames or partitioning diagram templates to hand. Our [ten frame](/ten-frame) shows the same bonds with red and yellow counters.

Sources

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