Numbers & Math
Number bonds explained for parents
Published · 10 minute read
Number bonds are the pairs that make a total, and schools teach them before column addition for a practical reason. Here is what they are, how bonds to 10 and 20 fit together, and how to build them with objects at the kitchen table.
Your child comes home with a worksheet full of little circles joined by lines, and no column addition anywhere in sight. You learnt to add by stacking numbers and carrying the one. Now the homework says number bonds, and you are not sure what you are meant to be helping with. Here is what number bonds are, why the maths comes in this order, and what to actually do at the kitchen table with a handful of pasta.
What a number bond actually is
A number bond is a pair of numbers that add up to a set total. Bonds to 10 are the pairs that make 10: 0 and 10, 1 and 9, 2 and 8, 3 and 7, 4 and 6, 5 and 5. That is the whole idea. The circles-and-lines diagram is just a picture of it: the total sits in one circle, the two parts sit in the circles below, and the lines show they belong together.
The aim is that a child eventually knows these pairs by heart rather than working them out each time. When a child sees 7 and thinks 3 without pausing, that is a number bond doing its job. Getting there takes a while, and working them out slowly is what most children do first.
Bonds work in both directions, and this matters more than it sounds. If 6 and 4 make 10, then 10 take away 4 leaves 6. Same fact, read the other way. Schools often call these fact families, and many teach the addition and the subtraction side by side rather than as separate topics.
Why schools teach bonds before column addition
Column addition is a procedure. It is fast and reliable, but it leans on the child already being able to add small numbers quickly. When a child writes 27 plus 15 in columns, the first thing they have to do is add 7 and 5. If that step takes ten seconds of finger counting, most of their attention goes on the small sum rather than on the method they are supposed to be learning.
There is a second reason, and it is the one most parents find genuinely useful. Bonds to 10 sit underneath a lot of the mental methods a child meets later. To work out 8 plus 5, a child who knows their bonds thinks: 8 needs 2 to make 10, so take 2 from the 5, that gives 10, and 3 left over, so 13. That is called bridging through ten, and it is much harder to do when the bonds themselves still have to be worked out.
So the order has a reason behind it. Bonds first, then bridging, then written methods once the mental facts are reasonably secure. Teachers tend to work in that direction, and when a child is finding column work heavy going, the usual move is to go back and firm up the small facts rather than to drill the layout again.
In England, number bonds within 20 sit in Year 1, roughly ages five to six. Recalling addition and subtraction facts to 20 fluently is a Year 2 expectation, around ages six to seven. Formal written column methods usually appear from Year 3, around ages seven to eight. Other countries order it differently, and schools vary in pace. If your child is in that range and still using fingers, that is very common. Fingers are a reasonable step on the way to knowing.
Bonds to 10, then bonds to 20
There are only six bonds to 10 if you treat 3 and 7 as the same fact as 7 and 3. Six facts. That is the entire set, and it is worth saying out loud to a child who feels swamped by the worksheet. Writing the six of them in a list on the back of an envelope makes the point better than saying it does.
Bonds to 20 come next, and most of them follow on once bonds to 10 are known. If 3 and 7 make 10, then 13 and 7 make 20. The child adds ten to one part and the total goes up by ten. It is worth showing that link out loud rather than letting them treat bonds to 20 as a second, unrelated list to memorise.
Alongside bonds to 20, schools usually teach bonds within 20, which means all the pairs making any total up to 20, not just 20 itself. Doubles are the useful shortcut here: 6 and 6 make 12, so 6 and 7 make 13. Near doubles are worth practising, and many children take to them quickly, because there is only one small step to remember on top of a fact they already have.
| Stage | Typical age | What the child should be able to do | A question to ask at home |
|---|---|---|---|
| Bonds to 10 | 5 to 6 | Say the missing part without a long pause, both ways round | I have 4, how many more to make 10? |
| Subtraction from 10 | 5 to 6 | Use the same pairs to take away | 10 biscuits, 6 eaten, how many left? |
| Bonds to 20 | 6 to 7 | Use bonds to 10 to work out bonds to 20 | 3 and 7 make 10, so what makes 20 with 13? |
| Bonds within 20 and doubles | 6 to 7 | Recall doubles, then adjust for near doubles | Double 7 is 14, so what is 7 add 8? |
| Bridging through ten | 6 to 7 | Split a number to make 10 first | 8 add 6: how much does 8 need to reach 10? |
The concrete-to-written progression, at the kitchen table
Most schools plan this work across three stages, usually called concrete, pictorial and abstract. Concrete means real objects the child can move. Pictorial means a drawing or a diagram of those objects. Abstract means the written numbers and symbols. Teachers generally start with the objects, move on when the child looks ready, and go back to objects whenever something new turns up. The easy mistake at home is to start at the written stage, because that is the stage the homework arrives in.
You do not need equipment. Pasta, buttons, pebbles, coins, small toys, cereal, socks, building bricks. Ten of anything, plus something to sort them into two groups: two saucers, an egg box, or a piece of paper with a line drawn down the middle. If you want the version the school uses, draw a grid of two rows of five boxes and put one object in each box. That is a ten frame, and it is worth the thirty seconds it takes to draw, because a full row of five is something a child can see at a glance without counting.
- Count out ten objects together and agree there are ten. Say it: we have ten. Push them all to one side.
- Move some across to the second saucer. Ask how many are in each. Say the sentence together: three and seven make ten. Let the child move them back and check.
- Do it again with a different split. Keep saying the full sentence each time. You are after the sound of it, not speed.
- Now hide some. Cover a handful with your hand and ask how many are hidden. Teachers lean on this step, because the child cannot count what they cannot see and has to reach for the fact instead.
- Draw it. Two circles side by side with a bigger one above, numbers written in. This is the diagram from the worksheet, and now the child knows what it is a picture of.
- Write it. 3 plus 7 equals 10. Then write the subtraction from the same picture: 10 take away 7 equals 3. Same objects, same story, different sentence.
- Once ten is easy, do the same with twenty, using two rows of ten so the ten stays visible as a whole rather than becoming twenty loose things.
Five or six minutes is plenty, and short sessions done often tend to suit this better than one long sitting at the weekend. Waiting for the kettle, laying the table, the bath: those are the good slots. It also helps to keep the same objects and the same wording for a few weeks, so the child is not working out what you mean before they can work out the answer.
A child who can move the objects but cannot yet say the answer is not stuck. That is a normal place to be on the way to knowing.
When it goes wrong
If the child counts every object from one each time, that is common early on and it usually gives way to something quicker. Nudge it along by asking them to start from the bigger number. Four, and then five, six, seven, is quicker than starting at one. This is called counting on, and it is a stepping stone rather than a bad habit.
If they can do bonds to 10 but freeze on bonds to 20, go back to objects arranged as two full tens. Often the child has lost sight of ten as one chunk and is trying to count twenty separate things. Leaving the first ten untouched on its own saucer, and only ever moving the second ten, tends to bring it back.
If they get the addition but not the subtraction, stop treating subtraction as a separate topic for a while. Set up the objects, cover some, and ask both questions about the same arrangement. Three and seven make ten. Ten take away seven leaves three. Point at the objects while you say both, so it is obvious the two sentences describe the same picture.
If it turns into tears, stop for the day and say so plainly: that is enough maths, let us do something else. Nothing much is lost by stopping, and it is worth keeping these few minutes something the child is willing to come back to tomorrow.
How to make practice stick without a worksheet
The practice that seems to help most is the kind where the child has to fetch the answer from memory rather than rebuild it by counting. Anything that asks a quick question and gets a quick answer will do. Say a number, they say the pair to 10. Take turns, and let them test you, including getting one wrong on purpose so they can catch you out.
Playing cards are useful. Take out the picture cards, deal two face up, and see whether they make 10; if they do, the child keeps the pair. Ten pairs of socks out of the wash, or ten pegs on the line, do the same job. Two dice cover bonds within 20 once doubles are in play. In the car it is just talking: you say six, they say four, and you swap over after ten goes each.
Written practice still has a place, particularly once the facts are mostly known and you want them quicker. A page of missing-number sentences takes a few minutes and gives you a clear read on which pairs are shaky. Children often have one or two that stay stubborn, and it helps to know which ones, so those can have a few extra turns instead of running the whole set again.
Expect this to take months rather than weeks. Bonds to 10 often settle over a school year of little-and-often practice, and there is usually a long stretch where a child knows some pairs instantly and still counts the rest. Going slowly with the objects at the start is rarely wasted time.