# Number bonds to 10: what they are and how to practise them at home Source: https://askthena.com/blog/number-bonds-to-10 Published 4 November 2026. For parents in the UK. Number bonds are pairs of numbers that add up to a total. The **[number bonds to 10](https://askthena.com/uk/number-bonds)** are 0 + 10, 1 + 9, 2 + 8, 3 + 7, 4 + 6 and 5 + 5, plus each one turned around, such as 9 + 1. Every bond also gives subtraction facts: 7 + 3 = 10, so 10 − 7 = 3 and 10 − 3 = 7. Children start on them in Reception, and schools aim for them to be known by heart during Year 1. ## All the number bonds to 10 Many teachers ask children to write them out in order, because the pattern helps them remember: ``` 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 ``` As the first number goes up by one, the second goes down by one, so the total stays at 10. That makes 11 facts, counting 0 + 10 and 10 + 0. A child who spots the pattern can rebuild a forgotten bond from its neighbour. ### The subtraction facts that go with them Each bond belongs to a group of four facts, which many schools call a **fact family**: ``` 7 + 3 = 10 3 + 7 = 10 10 − 7 = 3 10 − 3 = 7 ``` 5 + 5 is the odd one out, with only two facts: 5 + 5 = 10 and 10 − 5 = 5. Schools also write bonds with a gap to fill, such as 7 + ? = 10, or the other way round, such as 10 = 3 + 7. Mix these up at home too. ## When children learn number bonds ### Reception The statutory EYFS framework sets out the Early Learning Goals children work towards by the end of Reception. The goal for Number says children at the expected level will "automatically recall (without reference to rhymes, counting or other aids) number bonds up to 5 (including subtraction facts) and some number bonds to 10, including double facts." So the firm target in Reception is bonds up to 5, such as 2 + 3 = 5 and 5 − 2 = 3. Bonds to 10 are just beginning, and double facts are ones like 3 + 3 = 6 and 5 + 5 = 10. So if your Reception child is sure of 2 + 3 but still counts for 6 + 4, they are right where the framework expects them to be. ### Year 1 The National Curriculum for England says Year 1 children should "represent and use number bonds and related subtraction facts within 20". The guidance alongside it says they should memorise number bonds to 10 and 20 in several forms. ### Year 2 In Year 2, children should "recall and use addition and subtraction facts to 20 fluently, and derive and use related facts up to 100". The curriculum's own example is using 3 + 7 = 10 to work out 30 + 70 = 100. Many schools then teach bonds to 100 in Year 2 and Year 3. ## How schools teach number bonds Most primary schools start with real objects, then move to pictures, then to numbers on their own. ### Ten frames A ten frame is a grid of two rows of five boxes. Your child fills some boxes with counters and looks at the empty ones. Seven counters leave three gaps, so 7 + 3 = 10: ``` +---+---+---+---+---+ | O | O | O | O | O | +---+---+---+---+---+ | O | O | | | | +---+---+---+---+---+ ``` Because each row holds five, children start to see 7 as "a full row and 2 more" without counting every counter. ### Part-whole models A part-whole model shows the whole number in a circle, with the two parts in circles joined to it by lines. Some schools call it a cherry model, because it looks like two cherries on a stalk. ``` ( 10 ) / \ ( 7 ) ( 3 ) ``` Children put counters or numbers in the circles and read off the fact family. Teachers often draw it upside down or sideways too. ### Bar models A bar model does the same job with rectangles. The whole is one long bar, and the parts sit underneath it, together making the same length: ``` +-------------------------------+ | 10 | +---------------------+---------+ | 7 | 3 | +---------------------+---------+ ``` Children keep using bar models for years, especially for word problems. ### Numicon shapes Numicon is a set of plastic shapes with holes in them, one for each number from 1 to 10, each in its own colour. Children look for two shapes that fit together to match the 10 shape, such as the 7 and the 3. ### Rekenreks and bead strings A rekenrek is a small frame with two rows of ten beads, five of one colour and five of another on each row. A bead string works the same way on a single string. Your child slides 6 beads across and sees 4 left behind. The change of colour after five helps them see 6 without counting. ### Number bond rainbows Your child writes 0 to 10 in a line and draws an arc joining each pair: 0 to 10, 1 to 9, 2 to 8, 3 to 7 and 4 to 6. The arcs sit inside each other like a rainbow, and 5 in the middle pairs with itself. ### Find out what your child's school uses Ask your child to show you how they make 10 at school, or look through their maths book. Many schools put their calculation policy on the school website, and the class teacher can tell you which models the class uses. Then use the same pictures and words at home. ## Why number bonds to 10 matter so much Bonds to 10 turn up in almost every part of primary maths. ### Adding across 10 To work out 8 + 5, a child who knows 8 + 2 = 10 can split the 5 into 2 and 3. Then 8 + 2 = 10, and 10 + 3 = 13. Schools call this bridging through 10, and it's often drawn like this: ``` 8 + 5 = 13 / \ 2 3 ``` ### Subtraction Every bond gives a subtraction fact, so 10 − 3 = 7 needs no counting back. It works for bigger numbers too: for 13 − 5, take away 3 to get to 10, then 2 more to get to 8. Later, in [column subtraction](https://askthena.com/blog/column-subtraction-how-to-help-your-child), the ones column often needs exactly these facts, such as 13 − 8 = 5. ### Bonds to 100 and to 1 Because 3 + 7 = 10, 30 + 70 = 100. Later, 0.3 + 0.7 = 1 comes from the same bond, and in Year 5 the curriculum asks children to find pairs that make 1, such as 0.83 + 0.17. ### Money Change from 10p for something costing 6p is 4p. Change from £1 for something costing 70p is 30p. Both are number bonds. ### Moving on from fingers Counting on fingers is a perfectly good place to start, and ten fingers make a handy ten frame. The aim is for your child to know the bonds without counting. Then their attention is free for the harder part of a problem. ## Ten-minute games with things you already have Ten minutes a few times a week does more than an hour at the weekend. Stop while your child is still enjoying it. ### Egg box ten frame Cut the last two cups off a 12-egg box, or tape them shut, so you have two rows of five. Find small things in two colours, 10 of each, such as red and yellow pompoms. Fill the box with 7 of one colour and 3 of the other, and ask, "How many red? How many yellow? How many altogether?" Then ask your child to fill it a different way, and write each new bond down until you have all 11. ### Hide under a cup Count out 10 objects together. While your child closes their eyes, hide some under a cup. Then say, "There are 10 altogether. I can see 6. How many are hiding?" They answer, then lift the cup to check: 4. That's 10 − 6 = 4. Swap roles so they do the hiding. ### Bottle skittles Stand ten plastic bottles in a triangle (a little water in each keeps them up) and roll a ball at them. Before anyone counts, ask, "4 fell over. How many are still standing?" Then count to check: 6. Write each score as a bond, such as 4 + 6 = 10. ### Card pairs and snap Take the picture cards out of a pack. Use the aces to 9 from two suits, plus two 10s, and count an ace as 1. Lay them face down and take turns to turn over two. If they make 10, keep them. A 10 can be kept on its own, because 10 + 0 = 10. It's a handy reminder that 0 + 10 counts too. For snap, take turns to put a card face up on one pile. When the top two cards make 10, the first to shout "Snap" wins the pile. ### Fingers flash Hold up 7 fingers and ask how many more make 10. The fingers you're holding down are the answer, so your child can check by looking. Once that's easy, flash the fingers for just a second so they have to picture it. ### Make 10 with Lego Build towers 10 bricks tall from same-sized bricks in two colours, such as 6 red and 4 blue. Make each one different, then line them up from all blue to all red to see a staircase. ### Bonds in the bath or the car Say a number from 0 to 10 and your child says its partner: "6." "4." Then swap. In the bath, try 10 toys with some hidden under the bubbles. Songs help some children get started, but the Reception goal is recall without rhymes or counting, so treat a song as a first step. [Worksheets work best](https://askthena.com/uk/worksheets/number-bonds) after your child has made 10 with real objects. ## Four common mistakes and how to fix them These are normal, and each one has a simple fix. ### Counting all from one For 7 + 3, your child counts out 7 fingers, then 3 more, then counts all ten from one. They don't know the bond yet, so counting is their only way in. Go back to the egg box and ask, "How many empty spaces?" Show them that 7 is a full row of five and 2 more. Counting on from the bigger number ("7... 8, 9, 10") is a good step in between. ### Missing 0 + 10 and 5 + 5 Asked for all the ways to make 10, your child lists 1 + 9, 2 + 8, 3 + 7 and 4 + 6, and stops. Zero doesn't feel like a number you can add, and 5 + 5 uses the same number twice. Writing the list in order from 0 + 10 to 10 + 0 shows the gaps. An egg box filled with one colour is 10 + 0, and 5 + 5 sits in the middle of the rainbow. ### Knowing 7 + 3 but not 3 + 7 or 10 − 7 Your child says 7 + 3 = 10 straight away but counts for 3 + 7, or gets stuck on 10 − 7. They have learned the bond as a phrase that only goes one way. Draw a part-whole model and say all four facts together. Play hide under a cup, and ask in different ways: "7 and what make 10?" and "What's 10 take away 3?" ### Guessing You ask what goes with 7 to make 10, and your child says "4" straight away. Fast games can make speed feel like the point. Ask, "How do you know?" and let them check on their fingers or the egg box, where 7 and 4 make 11. Praise checking more than speed. Speed comes once the bonds are secure. ## The next step: bonds to 20 and 100 **Number bonds to 20** are pairs that make 20, such as 13 + 7 and 10 + 10. They grow straight out of bonds to 10: because 3 + 7 = 10, 13 + 7 = 20. Two egg boxes side by side make a twenty frame. When the curriculum says "within 20", it means all the facts with totals up to 20, such as 9 + 7 = 16. **Number bonds to 100** start with tens, such as 30 + 70 and 60 + 40. Then come pairs like 37 + 63, where the ones make 10 and the tens make 90: ``` 7 + 3 = 10 30 + 60 = 90 37 + 63 = 100 ``` A common slip is 37 + 73, where a child makes both the tens and the ones up to 10 and gets 110. Point out that the ones have already made a ten, so the tens only need to make 90. ## A simple plan for this week Ask your child to show you how they make 10 at school. Then try this: - **Day 1:** fill the egg box every way you can and write the bonds in order. - **Day 2:** play hide under a cup, five or six rounds. - **Day 3:** play card pairs. - **At the weekend:** set up bottle skittles and write each score as a bond. By the end of the week, ask a few quick questions in the car and notice which bonds your child still counts for. Those are the ones to play with next week. If they are still counting for every bond after a few weeks, have a quick word with the class teacher. ## How Thena teaches number bonds In Reception, Thena explores ways to make 10 with a ten frame and objects. In Year 1 she teaches number bonds to 10 and the subtraction facts that go with them, drawing each one on her board as she says it. Your child can tap and colour the ten frame themselves. Lessons for a 5-year-old are about 12 minutes. [Try 3 lessons free](https://askthena.com/register) ## Questions parents ask ### What year do children learn number bonds to 10? Children start in Reception, where the Early Learning Goal is to know number bonds up to 5 by heart and some bonds to 10, including doubles such as 5 + 5. In Year 1 the National Curriculum asks them to use number bonds and subtraction facts within 20, and by Year 2 they should recall facts to 20 fluently. ### What are number bonds to 20? Number bonds to 20 are pairs of numbers that add up to 20, from 0 + 20 and 1 + 19 through to 10 + 10. They grow out of bonds to 10: because 3 + 7 = 10, your child can work out that 13 + 7 = 20. ### Is it bad if my child counts on their fingers? No. Fingers make a natural ten frame and are a good place to start. Over time the aim is for your child to know each bond well enough that they no longer need to count, so encourage quick recall gently instead of banning fingers. ### How can I make learning number bonds fun? Keep it short and use real things: hide some of 10 objects under a cup, knock down 10 bottle skittles, or play pairs with playing cards where two cards that make 10 win. Ten minutes a few times a week is plenty. ### What is a part-whole model? A part-whole model is a diagram with the whole number in one circle and its two parts in circles joined to it, such as 10 above 7 and 3. Some schools call it a cherry model. It shows children that 7 + 3, 3 + 7, 10 − 7 and 10 − 3 all come from the same bond.