Number Bonds Rainbow — to 20 — free printable diagram

All the number bonds to 20

A rainbow-facts diagram shows every pair of numbers that adds up to 20, each pair joined by a coloured arc. There are 11 arcs — 0 + 20, 1 + 19, 2 + 18 and so on up to 10 + 10 — and knowing them is what makes adding and subtracting within 20 quick rather than counted.

Total

20

Arcs in the rainbow

11

First pair

0 + 20

Last pair

10 + 10

The double in the middle

10 + 10 = 20

Written as number sentences

21 of them, counting 1 + 19 and 19 + 1 separately

• Each arc is one fact read two ways: 1 + 19 = 20 and 19 + 1 = 20, because adding can be done in either order. That is why there are 11 arcs but 21 number sentences.
• Every pair follows the same rule — pick any number a from 0 to 20, and its partner is 20 − a. The two always add back to 20.
• Because 20 is even, one number is its own partner: 10 + 10 = 20. That bond is the double, and it is the innermost of the 11 — there is no shorter pair left to make.
• Each bond carries two subtraction facts with it. From 1 + 19 = 20 you also get 20 − 1 = 19 and 20 − 19 = 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 20.