Number bonds to 10 are the pairs of numbers that add together to make 10: 0 and 10, 1 and 9, 2 and 8, 3 and 7, 4 and 6, and 5 and 5. Children who can recall these instantly, without counting on their fingers, have one of the most useful tools in early maths. The National Curriculum expects pupils to use number bonds within 20 by the end of Year 1 (gov.uk). This guide explains what bonds are, when children learn them, why they matter, and how to teach them at home or in class, with free games you can try right now.
What are number bonds?
Number bonds are pairs of numbers that combine to make a given total, and the bonds to 10 are the set every primary child needs by heart. The pairs are 0 and 10, 1 and 9, 2 and 8, 3 and 7, 4 and 6, and the double 5 and 5. Teachers often call this the "rainbow to 10" because each pair arcs across a number line like a coloured band.
The idea underneath number bonds is part-whole thinking. Ten is the whole. Any pair that makes it, like 6 and 4, are the two parts. Once a child grasps that a whole can be split into parts and rebuilt, addition and subtraction stop being separate skills. If you know 6 and 4 make 10, you also know 10 take away 6 leaves 4. That single fact does four jobs.
Why does this matter so early? Because it turns counting into knowing. A child counting on their fingers to work out 7 plus 3 is doing real cognitive work each time. A child who simply recalls that 7 and 3 are partners has freed up that mental effort for something harder.
The six pairs, written out
- 0 + 10 = 10
- 1 + 9 = 10
- 2 + 8 = 10
- 3 + 7 = 10
- 4 + 6 = 10
- 5 + 5 = 10
Read them backwards too: 10 and 0, 9 and 1, 8 and 2, and so on. A child does not truly "know" a bond until they can produce the partner from either side, fast.
Number bonds to 20: how do they build on bonds to 10?
Number bonds to 20 are the pairs that total 20, and they extend bonds to 10 rather than replacing them. If a child knows 4 and 6 make 10, they can reason that 14 and 6 make 20, or that 4 and 16 make 20. The National Curriculum groups both together: Year 1 pupils should "represent and use number bonds and related subtraction facts within 20" (gov.uk).
The most powerful technique that bonds to 10 unlock is bridging through 10. To work out 8 plus 5, a child splits the 5 into 2 and 3. The 2 fills the 8 up to a friendly 10, then the remaining 3 makes 13. This only works fluently if bonds to 10 are automatic, because the child has to see instantly that 8 needs 2.
Bridging works in reverse for subtraction. To take 7 from 13, a child can subtract 3 to reach 10, then take the remaining 4 to land on 6. Again, the 10 is the anchor. Strong bonds to 10 are the hinge that the whole of mental calculation swings on.
When do children learn number bonds?
Children begin number bonds in Reception and are expected to use bonds within 20 by the end of Year 1. The progression is gradual and the early expectation is smaller than many parents assume. The DfE's EYFS statutory framework sets out, in its Early Learning Goal for Number, that children at the end of Reception should recall bonds to 5 and some number bonds to 10, including doubles (DfE EYFS framework).
That word "some" matters. Reception is not the stage to expect every bond to 10 by heart. The full set comes in Key Stage 1.
EYFS, Year 1 and Year 2 compared
- EYFS (Reception): recall bonds to 5, and some bonds to 10, including doubles. This is an emerging skill, not a finished one.
- Year 1: represent and use number bonds and related subtraction facts within 20 (gov.uk). This is where the full set of bonds to 10, and bonds to 20, get embedded.
- Year 2: recall and use addition and subtraction facts to 20 fluently, and derive and use related facts up to 100 (gov.uk). Fluency is the word: the facts should be effortless and the child should extend them, for example knowing 60 and 40 make 100.
Why do number bonds matter for later maths?
Number bonds matter because they are the bedrock of mathematical fluency, the automatic recall that frees a child's working memory for harder thinking. The National Centre for Excellence in the Teaching of Mathematics describes fluency as resting on "the effortless recall of facts, such as number bonds within 10 and times tables facts" (NCETM). Without that effortless recall, every later calculation costs more.
Think about what happens in a child's head during a column addition. If they have to stop and count to find each small sum, the larger procedure falls apart before they reach the answer. Fluent bonds keep the working memory free for the structure of the problem. This is why fluency is treated as a foundation, not a finishing flourish.
The Education Endowment Foundation reaches the same conclusion through its evidence review. Its guidance report Improving Mathematics in the Early Years and Key Stage 1 (2020) recommends building number sense with manipulatives and visual representations, so that facts like bonds are understood and not just memorised by rote (EEF). Understanding and recall reinforce each other. A child who sees why 6 and 4 make 10 remembers it for longer than one who only chanted it.
There is a quieter benefit too. Confidence. A child who reliably knows their bonds walks into a maths lesson expecting to cope. A child still counting on fingers under the table is already half braced for failure. The emotional payoff of fluency is easy to overlook and hard to overstate.
How to teach number bonds: the CPA approach
The clearest way to teach number bonds is the CPA approach: concrete, then pictorial, then abstract. The EEF recommends using physical manipulatives and visual representations precisely because they let children see the structure of a fact before they handle the symbols (EEF). Move through the three stages in order, and do not rush the first one.
Concrete: objects you can hold
Start with things the child can touch and move. Ten counters, ten buttons, ten pasta shapes. Lay out 10, then physically separate them into two groups and name the parts: "six here, four there, still ten altogether." Tip them back together. Split them a different way. The child is feeling the part-whole idea before any number is written.
A ten frame is the single most useful piece of kit here. It is a two-by-five grid. Fill in 7 counters and the 3 empty boxes show, at a glance, that 7 needs 3 to make 10. The gap is the bond. Children stop counting and start seeing.
Pictorial: drawings and the part-whole model
Next, swap real objects for pictures and diagrams. The part-whole model is a circle for the whole with two circles branching off for the parts. Write 10 in the top circle, 6 in one part, and let the child work out the missing 4. Cherry diagrams, bar models and drawn ten frames all live in this stage.
Abstract: the numbers alone
Only when the picture is secure do you move to bare numbers: 6 + 4 = 10, or 10 - 6 = 4. By now the symbols carry meaning, because the child has built and drawn the fact dozens of times. Worksheets at this stage consolidate something already understood, rather than introducing something cold.
Number bonds activities and games
The best number bonds activities mix hands-on play with short, frequent practice. Oxford Owl puts the principle plainly: "For young children, practise is key to keeping their emerging understanding of how numbers work at their fingertips" (Oxford Owl). Little and often beats long and rare. A few minutes daily will outpace a single weekend cram every time.
At-home activities with no special kit
- Pairs that make 10 with a deck of cards. Remove the picture cards. Turn over two cards: do they make 10? If yes, keep the pair. A snappy game for two players.
- Egg-box ten frame. Cut an egg box down to ten cups. Drop in counters or coins and read off the bond from the empty cups.
- Hands up. Hold up some fingers; the child tells you how many more to make 10. The body is the manipulative.
- Skittles or stacking cups. Knock some down from ten and name how many fell and how many stand.
Free interactive games you can try now
Start with our two free games, no signup needed. Ten-Frame Fill turns the most useful classroom tool into a tap-and-see game, so children watch the bond appear as they fill the frame.
Quick Look builds subitising, the instant recognition of small quantities without counting. Subitising underpins bonds: a child who can see "that is 4" at a glance is halfway to knowing 4 needs 6.
When you are ready for focused bond practice, these games are free with no signup. Rainbow to 10 practises the rainbow pairs directly. Bond Pairs asks the child to tap the partner that makes 5, 10 or 20. Part-Whole Pop builds the part-whole model on screen. Tens Train extends bonds to 100 in tens, and Missing Number hides one part of a known fact for the child to find.
If you want a calm, no-pressure way to get a reluctant child talking before maths, our would you rather questions for kids make a gentle warm-up.
Number bonds for SEND learners
For SEND learners, number bonds are best taught through errorless, low-arousal practice that keeps cognitive load deliberately small. Many learners with additional needs can recall bonds well; the barrier is usually how the practice is delivered, not the maths itself. The EEF's emphasis on concrete and pictorial representations matters even more here, because it removes the load of holding an abstract idea in mind (EEF).
A few principles tend to make the difference in SEND tutoring and online therapy sessions. They are written from a QTS and SEND-tutor standpoint, and they apply equally to a parent at the kitchen table.
Reduce the cognitive load
Show one bond at a time. A full page of mixed sums is overwhelming for a learner who is also managing attention, anxiety or working-memory difficulty. Strip the screen or the page back to a single fact with a clear visual, like one ten frame. The maths is hard enough without visual noise competing for attention.
Use errorless learning
Errorless learning means setting the task up so the child succeeds first, then gently fading the support. Rather than asking "what makes 10 with 7?" and waiting for a possibly wrong answer, show the filled ten frame so the answer is visible, let the child say it, and praise it. Confidence comes first. The challenge is increased only once success is reliable.
Keep arousal low and pacing slow
Avoid timers, buzzers and loud "wrong" sounds for anxious or sensory-sensitive learners. These add arousal that crowds out thinking. Our learning games are built deliberately quiet: no harsh failure sounds, no countdown pressure, and the child sets the pace. Slow, calm repetition lets the fact settle without the nervous system getting in the way.
Overlearn, then revisit
A bond that seems secure on Monday can vanish by Friday for some learners. Plan to revisit. Short daily touches, then weekly checks, then occasional revisits across a term build durable recall far better than assuming one good session has fixed it for good.
Frequently asked questions
What are number bonds to 10?
Number bonds to 10 are the pairs of numbers that add together to make 10: 0 and 10, 1 and 9, 2 and 8, 3 and 7, 4 and 6, and 5 and 5. Knowing them by instant recall, rather than by counting, is a foundation skill the National Curriculum builds on from Year 1 onwards.
At what age do children learn number bonds?
Children start in Reception. The DfE's EYFS framework expects recall of bonds to 5 and some bonds to 10 by the end of Reception (DfE). The full, fluent set of bonds within 20 is a Year 1 and Year 2 expectation under the National Curriculum.
Why are number bonds important?
They are the basis of mathematical fluency. The NCETM describes fluency as resting on "the effortless recall of facts, such as number bonds within 10 and times tables facts" (NCETM). Fluent bonds free up working memory for harder calculations like column addition and bridging through 10.
How do I explain number bonds simply?
Use the idea of a whole made of two parts. Ten is the whole; 6 and 4 are two parts that build it. Show it with counters or a ten frame so the child sees the parts, then names them. The EEF recommends exactly this concrete-first approach (EEF).
What is the difference between number bonds to 10 and to 20?
Bonds to 10 are pairs that total 10; bonds to 20 are pairs that total 20. Bonds to 20 build directly on bonds to 10, so a child who knows 4 and 6 make 10 can reason that 14 and 6, or 4 and 16, make 20. Year 1 covers both under "within 20" (gov.uk).
Start with the free games today
Number bonds to 10 are the quiet engine of early maths. Get them automatic and bridging, bonds to 20, mental subtraction and column work all become easier. The route is simple: build understanding with concrete and pictorial models first, then practise little and often until recall is effortless. For SEND learners, keep the load light, the pace calm, and the success visible.
You can begin right now, for free, with Ten-Frame Fill and Quick Look, no signup needed. When your child is ready for targeted bond drills, Rainbow to 10 and Bond Pairs are there, also free.
Fearn Robinson is a UK SEND tutor with Qualified Teacher Status (QTS) who builds the calm, low-arousal learning games on Fun Games Now for children with special educational needs.