Number bonds to 20 are pairs of numbers that add up to 20, like 13 and 7 or 15 and 5. Counting both orders and including zero, there are 21 of them, from 0 + 20 to 20 + 0, made from 11 different pairs. Each one is a bond to 10 with an extra ten added.
This guide lists every pair, shows how they grow out of bonds to 10, explains the other meaning of "bonds within 20", and gives games you can play with cards, dice and household objects. Curriculum details come from England's national curriculum, the NCETM and the Education Endowment Foundation (EEF).
A number bond shows a whole split into two parts. With 20 as the whole, the parts are any two numbers that add to 20. Each bond also gives you subtraction facts for free: if 14 + 6 = 20, then 20 - 6 = 14 and 20 - 14 = 6.
You'll see the phrase used in two ways:
Bonds to 20: pairs that make exactly 20, like 12 + 8.
Bonds within 20: all the addition and subtraction facts with totals up to 20, like 9 + 7 = 16 and 16 - 7 = 9.
England's national curriculum covers both. In Year 1, pupils should represent and use number bonds and related subtraction facts within 20, and its guidance gives 9 + 7 = 16, 16 - 7 = 9 and 7 = 16 - 9 as examples of reasoning with bonds "in several forms". By the end of Year 2, pupils should know the number bonds to 20. If you're not sure which meaning your child's school uses, ask the teacher.
0 + 20 = 20 and 20 + 0 = 20
1 + 19 = 20 and 19 + 1 = 20
2 + 18 = 20 and 18 + 2 = 20
3 + 17 = 20 and 17 + 3 = 20
4 + 16 = 20 and 16 + 4 = 20
5 + 15 = 20 and 15 + 5 = 20
6 + 14 = 20 and 14 + 6 = 20
7 + 13 = 20 and 13 + 7 = 20
8 + 12 = 20 and 12 + 8 = 20
9 + 11 = 20 and 11 + 9 = 20
10 + 10 = 20
That's 11 different pairs, or 21 facts if you count both orders. 10 + 10 is the only one that can't be flipped. Notice the pattern: as one number goes up by 1, its partner goes down by 1.
If your child knows their bonds to 10, most of the work is done. Put a ten in front of one part and the total grows by ten:
3 + 7 = 10, so 13 + 7 = 20
6 + 4 = 10, so 16 + 4 = 20
8 + 2 = 10, so 8 + 12 = 20
The NCETM's Mastering Number overview for Year 2 builds the same bridge. Children first review bonds within 10 and the numbers 11 to 20. Then they use bonds of 10 to reason about bonds of 20 where the given number is greater than 10, such as 13 + ? = 20. Later they reason about bonds of 20 where the given number is less than 10, such as 6 + ? = 20.
Fingers make a good model. Two people hold up all 20 of their fingers. One person folds some down, and the other says how many are still up. Or draw two ten frames, each a grid of two rows of five boxes, and fill some with counters: the empty boxes are the partner number.
If bonds to 10 still feel shaky, start there. Our guide to number bonds to 10 lists all 11 and has games to practice them.
The wider meaning matters just as much. The NCETM overview has Year 2 children use known bonds within 10 to calculate within 20, including adding and subtracting across 10. The most common strategy is to make 10 first:
7 + 6: split 6 into 3 and 3. 7 + 3 = 10, then 10 + 3 = 13.
9 + 7: split 7 into 1 and 6. 9 + 1 = 10, then 10 + 6 = 16.
14 - 6: take away 4 to reach 10, then 2 more. 14 - 4 = 10, then 10 - 2 = 8.
Doubles and near doubles: if 6 + 6 = 12, then 6 + 7 = 13. The NCETM overview also includes using doubles to work out near doubles.
The EEF's guidance on early maths says board games such as Snakes and Ladders are particularly good for building understanding of numbers, and that maths can be woven into everyday moments like snack time. These games need little or no prep.
Pairs to 20. Write 0 to 20 on scraps of paper, with two 10s. Lay them face down. Take turns turning over two, and keep them if they make 20.
Partner ping-pong. Call out a number from 0 to 20. Your child answers with its partner to 20. Then swap roles.
Race to 20. Draw a track numbered 0 to 20. Roll a die and move. After each move, say how many more you need to reach 20. You must land on 20 exactly to win.
Snack-time bonds. Count out 20 raisins or crackers. Eat a few, then say how many are left and the bond: "6 eaten and 14 left make 20."
Missing number cards. Write cards like 13 + ? = 20, ? + 6 = 20 and 20 - ? = 9. Children check their answers with counters or fingers.
Coin change. If something costs 13 cents or pence, how much more makes 20? Use real coins to check.
Board game twist. Play Snakes and Ladders. While a counter is below square 20, ask how many squares it is from 20.
Short and often. England's curriculum notes that an emphasis on practice at this early stage will aid fluency. A few minutes most days beats one long session.
Objects, then pictures, then numbers. The curriculum mentions concrete objects and pictures for solving problems at this stage. Keep counters and fingers available as long as children need them.
Ask both ways. Mix "13 + ? = 20" with "20 - 13 = ?" so the subtraction facts come along too.
Praise the strategy. "You used 3 and 7 to work that out" is more useful feedback than "That was fast."
Look ahead to 100. England's Year 2 guidance uses 3 + 7 = 10 to work out 30 + 70 = 100. The same pattern scales up.
There are 21 if you count both orders and include zero, from 0 + 20 to 20 + 0. Ignoring order, there are 11 different pairs.
In England, Year 1 pupils work with number bonds within 20, and the curriculum expects children to know the number bonds to 20 by the end of Year 2, when most are 6 or 7. Other countries and schools order this differently, so check with your child's teacher.
Bonds to 20 are pairs that make exactly 20, like 11 + 9. Bonds within 20 are all the addition and subtraction facts with totals up to 20, like 8 + 5 = 13.
Get bonds to 10 solid first, then add a ten to one part. Short daily games, with objects at first, usually work better than long drills.
Number Beasts: Bond Lab is a free iPhone and iPad puzzle game about making 10, not 20, so it suits the bonds-to-10 groundwork this guide builds on. You launch a number at a beast and it pops when the total is exactly 10, and if you overshoot, the beast still pops and the leftover number keeps flying to the next one, across 45 handcrafted stages plus a Daily Lab puzzle each day. It has no ads, no accounts and no in-app purchases, and the whole game works offline.
Get Number Beasts free on the App Store
National curriculum in England: mathematics programmes of study (GOV.UK)
Improving Mathematics in the Early Years and Key Stage 1 (Education Endowment Foundation)