Number bonds to 10 and 20 with everyday objects

Ask a confident adult what 7 plus 8 is, and many will answer almost instantly. Ask how they did it and you will often hear something like "well, 7 and 3 make 10, and 5 more is 15". Without noticing, they used what teachers call number bonds: the pairs of numbers that make a given total. This article explains what number bonds are, why they matter so much in the early grades, and how to build them at home with objects like coins, buttons and egg cartons.

Written for children aged 5 to 7.

What a number bond is

A number bond is a way of seeing a number as made of two parts. Ten is made of 6 and 4. It is also made of 7 and 3, 5 and 5, 9 and 1, 10 and 0. The same total can be split in several ways, and the parts always go back together to make the whole.

Number bonds are often drawn as a small diagram, a circle on top for the whole and two circles beneath for the parts, but you do not need the picture. What matters is the idea: a whole can be split into parts, and the parts can be put back together. That one idea sits behind both addition and subtraction. If 6 and 4 make 10, then 10 take away 4 leaves 6, and 10 take away 6 leaves 4. One fact, four sentences.

Why they matter

Children who learn addition mainly by counting on their fingers can get the right answers, but slowly, and the method stops working as numbers get bigger. Children who know their bonds can handle numbers flexibly:

• Bridging through ten. To add 8 + 5, a child who knows that 8 and 2 make 10 can take 2 from the 5, make a 10, and then add the remaining 3: 13. This "make ten" strategy is one of the most useful in all of primary mathematics.
• Subtraction. Knowing that 10 is 3 and 7 makes 10 − 3 trivial.
• Place value. Seeing 10 as one complete unit prepares children for understanding that ten ones make one ten.
• Confidence. A child who sees that numbers have a structure no longer faces arithmetic as a pile of unrelated facts to memorise.

Teachers in many countries put real effort into bonds to 10 in kindergarten and first grade, followed by bonds to 20, because these facts are the most useful and the most reusable that a child will learn.

Starting small, with objects

Before any numbers are written down, children benefit from seeing and handling parts and wholes. Everyday objects are perfect.

Two-colour counters or coins. Take five coins and drop them on the table; some will land heads up and some tails up. Four heads and one tail makes five. Shake and drop again: three heads and two tails also makes five. Children quickly see that a total can be split in different ways, and that it is always five.

The egg carton. A carton of ten (or a muffin tin cut to ten) makes a natural container. Put some buttons in the cups, then ask: "How many cups are empty?" Six buttons in, four empty. Your child can see the bond to ten, because the whole is the carton.

Hiding game. Show your child ten buttons, then hide some under a cup while they watch. "There were ten. I can see six. How many are under the cup?" This is a gentle, visible form of subtraction and bonds at once.

Fingers. Hands are a built-in set of two fives. Seven fingers is "five and two". Showing ten fingers and folding down some to find the missing part is a perfectly respectable way to explore bonds, as long as the child gradually learns to see the patterns without needing the fingers.

Moving towards the facts

Once a child is comfortable with objects, you can talk about the number sentences without forcing memorisation.

Always connect the parts to the whole. When you find that 6 and 4 make 10, say it in different ways: "Six and four make ten. Ten is six and four. Ten, take away four, is six." The more ways a child hears the same relationship, the more securely it takes hold.

Use a systematic pattern. Write or build all the pairs that make 10 in order: 0 and 10, 1 and 9, 2 and 8, 3 and 7, 4 and 6, 5 and 5, then back again. Children notice that as one part grows, the other shrinks by the same amount, and that the list reads the same backwards. Spotting patterns is mathematical thinking.

Practise in short bursts. A minute or two while walking to school or waiting for dinner is much better than a long session. "I'm thinking of ten. I have seven. What do you have?" This kind of game is quick, needs nothing, and can be played anywhere.

Move on to 20. Once bonds to 10 feel automatic, extend them. A useful approach is to link bonds to 20 with what the child already knows: if 7 and 3 make 10, then 17 and 3 make 20, and 7 and 13 make 20. Ten-frames, or two egg cartons side by side, make the extension visible.

Doubles and near-doubles

Some facts are easier than others, and it helps to build on them. Doubles (4 and 4, 6 and 6) are easier to remember because there is a pattern and often a rhyme. Near-doubles follow naturally: 6 and 7 is "one more than 6 and 6", so 13. Encouraging children to notice such shortcuts gives them a toolkit of strategies rather than a list of facts.

What to avoid

Drilling without meaning. Flash cards can help once understanding is in place, but if a child does not yet see that 10 is made of parts, memorising "6 + 4 = 10" gives them a fact with nothing underneath it. Spend time with objects first.

Stopping the counting too early. Fingers and counters are not cheating. They are stepping stones. A child will let go of them when they no longer need them, usually sooner than their parents expect, if they have had enough time to see the patterns.

Worrying about speed. Fluency comes from understanding plus practice. Pushing for speed too soon can make a child anxious and lead to guessing. Accuracy and flexibility come first; speed follows.

A simple weekly rhythm

A manageable plan for a busy household might look like this. Early in the week, play a hiding game with ten objects. Midweek, do a "pairs to 10" pattern on paper, drawing circles in two colours. At the weekend, use a few quick questions in the car or on a walk: "What goes with 3 to make 10?" Five or ten minutes in total, and a child who is building a lasting understanding of how numbers fit together.

Number bonds may not look like much. But a child who knows them well sees numbers as friendly and flexible, and that confidence carries through every kind of arithmetic that comes after.

Try it in the app

Practise this at the screen too: Make-ten friends, Facts within five, Number bonds within 10. You may also like our articles on subitising: seeing small numbers at a glance and mental maths strategies.