Number Bonds Rainbow — to 10 — free printable diagram

All the number bonds to 10

A rainbow-facts diagram shows every pair of numbers that adds up to 10, each pair joined by a coloured arc. There are 6 arcs — 0 + 10, 1 + 9, 2 + 8 and so on up to 5 + 5 — and knowing them is what makes adding and subtracting within 10 quick rather than counted.

Total

10

Arcs in the rainbow

6

First pair

0 + 10

Last pair

5 + 5

The double in the middle

5 + 5 = 10

Written as number sentences

11 of them, counting 1 + 9 and 9 + 1 separately

• Each arc is one fact read two ways: 1 + 9 = 10 and 9 + 1 = 10, because adding can be done in either order. That is why there are 6 arcs but 11 number sentences.
• Every pair follows the same rule — pick any number a from 0 to 10, and its partner is 10 − a. The two always add back to 10.
• Because 10 is even, one number is its own partner: 5 + 5 = 10. That bond is the double, and it is the innermost of the 6 — there is no shorter pair left to make.
• Each bond carries two subtraction facts with it. From 1 + 9 = 10 you also get 10 − 1 = 9 and 10 − 9 = 1, which is why these are worth knowing by heart rather than working out.
• In a rainbow diagram the arcs are nested longest to shortest, and that shape IS the pattern: as the number on the left goes up by one, its partner on the right comes down by one, so every pair still totals 10.