Number bonds to 10 are pairs of numbers that add up to 10, like 3 and 7 or 4 and 6. Counting both orders and including zero, there are 11 of them, from 0 + 10 to 10 + 0. They are a building block for adding and subtracting bigger numbers, so they are worth knowing by heart.
A number bond shows how a number splits into parts. With 10 as the whole, the two parts are any pair that adds to 10. Teachers often draw it as a circle with 10 inside, joined by lines to two smaller circles that hold the parts, such as 7 and 3.
Each bond also gives you subtraction facts for free. If 7 + 3 = 10, then 10 - 3 = 7 and 10 - 7 = 3. England's national curriculum asks Year 1 pupils to represent and use number bonds and related subtraction facts within 20, and its guidance suggests children memorize and reason with bonds to 10 and 20 in several forms.
0 + 10 = 10
1 + 9 = 10
2 + 8 = 10
3 + 7 = 10
4 + 6 = 10
5 + 5 = 10
6 + 4 = 10
7 + 3 = 10
8 + 2 = 10
9 + 1 = 10
10 + 0 = 10
Look closely and you will see only six different pairs: 0 and 10, 1 and 9, 2 and 8, 3 and 7, 4 and 6, and 5 and 5. The second half of the list is the first half flipped around. Point this out to children, because it halves what they need to remember.
A handy check: hold up 10 fingers and fold some down. The fingers still standing are the partner number.
Our number system is built on tens, so these facts come up everywhere:
Adding past 10. For 8 + 5, take 2 from the 5 to make 10, then add the 3 left over to get 13.
Subtracting. For 13 - 5, take away 3 to reach 10, then 2 more to get 8.
Bonds to 20 and 100. If 3 + 7 = 10, then 13 + 7 = 20 and 30 + 70 = 100.
Money. Working out change from a 10-dollar or 10-pound note uses the same pairs.
Adding three numbers. Spotting a pair that makes 10, as in 6 + 3 + 4, makes the sum quick: 10 + 3 = 13.
The NCETM's Mastering Number overview for Year 2 builds directly on this. Children use known bonds within 10 to calculate within 20, use bonds of 10 to reason about bonds of 20, and find three numbers that add to 10. The wider Mastering Number programme, which runs from Reception to Year 2, aims to give children good number sense along with confidence and flexibility with number.
Start with real objects. Use 10 buttons, pasta shapes or toy cars. Split them into two groups and say the bond out loud: "6 and 4 make 10." The Education Endowment Foundation's early maths guidance recommends everyday objects, such as buttons and pine cones, for building maths ideas.
Move to a ten frame. Draw a grid with two rows of five boxes. Fill some boxes with counters and ask how many are empty. The empty boxes are the partner number.
Use fingers. Show 7 fingers and ask how many are folded down.
Write it down. Record each bond both ways and as subtraction: 7 + 3 = 10, 3 + 7 = 10, 10 - 7 = 3 and 10 - 3 = 7.
Mix in missing numbers. Ask "4 + what = 10?" and "10 take away what leaves 2?" so children use the bonds flexibly.
Work toward instant recall. Once the idea is solid, play quick-fire games until children can answer without counting.
All of these work at the kitchen table or in a classroom, with little or no prep.
Make 10 card hunt. Take the ace (worth 1) to 9 cards from a deck. Lay 12 cards face up. Players take any two cards that make 10 and refill the gaps from the pile. Most pairs wins.
Tens Go Fish. Play Go Fish, but instead of asking for a match, ask for the card that makes 10 with one in your hand.
Shake and spill. Put 10 two-colored counters, or 10 coins, in a cup. Shake, spill and say the bond: "4 heads and 6 tails make 10."
Hide and guess. Show 10 small objects, hide some under a cup and ask how many are hiding.
Bottle bowling. Set up 10 plastic bottles as pins. After each roll, say how many fell and how many are still standing.
Bond partners. In class, give each child a card from 0 to 10, with two 5s. Each child finds the partner whose card makes 10 with theirs.
Snack-time maths. Count out 10 crackers, eat a few and ask how many are left. The EEF recommends weaving maths into daily routines such as snack time.
Board games with dice. The EEF notes that some board games, such as Snakes and Ladders, can support young children's understanding of numbers. Add a twist after each roll: "What would you need to make 10?"
Keep sessions short and frequent rather than long and rare.
Let children use fingers or objects for as long as they need them, then gently nudge toward recall.
Don't skip 0 + 10 and 10 + 0. They are easy to forget.
Praise the strategy, not just the speed: "You used 5 and 5 to work that out."
Once 10 feels easy, move on to bonds to 20, then to tens that make 100, such as 40 + 60.
There are 11 if you count both orders and include zero, from 0 + 10 to 10 + 0. Ignoring order, there are 6 different pairs.
It depends on the country and the school. In England, the national curriculum covers number bonds within 20 in Year 1, when most children are 5 or 6. Younger children can start exploring bonds to 10 through counting games and play.
A number bond shows a whole and its two parts. A fact family is the set of addition and subtraction sentences those three numbers make, such as 3 + 7, 7 + 3, 10 - 3 and 10 - 7.
Next come bonds to 20, adding and subtracting across 10, and then bonds to 100 using tens, such as 30 + 70.
Number Beasts: Bond Lab is a free puzzle game built on making 10: you launch a number at a beast, and if the total is exactly 10 the beast pops. A short shot makes the beast grow, and overshooting sends the leftover number flying on to the next beast, across 45 handcrafted stages plus a Daily Lab puzzle each day. It has no ads, no accounts and no in-app purchases, and it works offline, so it can sit alongside the hands-on games above.
Get Number Beasts free on the App Store
GOV.UK: National curriculum in England, mathematics programmes of study
Education Endowment Foundation: 5 recommendations to improve early maths