How to teach number bonds to 10 and the make-ten strategy

What number bonds to 10 are, and why they matter

A number bond shows how a number splits into two parts. For 10 there are six different pairs if you ignore order, and eleven if you count 3 + 7 and 7 + 3 as separate facts. That sounds like a small list, and it is. The point is not the list itself but what a child can do once those pairs are automatic.

Ten is the hinge of our number system. A child who knows that 6 needs 4 more to make 10 can add 6 + 7 by thinking 6 + 4 + 3, can subtract 13 - 5 by going back to 10 first, and later uses the same idea with 60 + 40 and 0.6 + 0.4. Curricula reflect this. British Columbia's Grade 1 mathematics curriculum lists decomposing 10 into parts and using the benchmark of 10, and names counting on, making 10 and doubles as the mental strategies for addition and subtraction to 20. The United States Common Core asks kindergarteners to find the number that makes 10 with any number from 1 to 9, and gives making ten as a Grade 1 strategy.

Start with a ten frame and real objects

A ten frame is a 2 by 5 grid. Its power is that a child can see how many boxes are empty without counting them one at a time. Seven counters fill the top row and two of the bottom row, so three gaps are left. That picture of the gaps is exactly the bond 7 + 3.

Fill the top row first, left to right, every time. The fixed layout lets children see five as a chunk, then see numbers above five as five and some more. Use buttons, dried beans or small blocks in two colours so the two parts stand out.

1. Put 6 red counters in the frame. Ask: how many are there? How many more to fill it?
2. Let the child fill the gaps with yellow counters and say the whole sentence: 6 and 4 make 10.
3. Turn the frame round or swap colours and ask for the turnaround: 4 and 6 make 10.
4. Next, flash a frame for two seconds and cover it. Ask how many were missing. Covering it stops counting by ones and builds a mental picture.

Move to part-part-whole diagrams

The part-part-whole model is a big circle for the whole with two smaller circles for the parts, or a bar split into two pieces. It is the same idea as the ten frame, drawn more simply. Put 10 in the whole circle and 3 in one part. The child works out the other part. Over the next few weeks you can hide either part, so they meet 3 + □ = 10 and □ + 3 = 10 and 10 - 3 = □ as the same fact seen from different sides.

This is also where subtraction comes in for free. If a child knows 3 and 7 make 10, they already know 10 - 3 = 7 and 10 - 7 = 3. Say it out loud together: one fact, four sentences. Our make ten guide uses this missing-part layout, and the kindergarten number worksheets give practice with small amounts at a time.

Number bond games that work in five minutes

Children learn bonds through many short, varied encounters, not one long session. A few minutes a day for two or three weeks usually does more than an hour on Saturday. These games need almost nothing.

• Hide and seek counters. Put 10 counters under a cup, tip some out, and ask how many are still hidden. Swap roles so the child hides them.
• Make ten Go Fish. Use cards ace (1) to 10, with a picture card as 0. Instead of asking for a match, ask for the card that makes 10 with one in your hand.
• Ten frame flash. Show a ten frame card for two seconds. The child says the missing part. Keep a pile of the ones they get wrong and come back to those.
• Finger bonds. Hold up 4 fingers. The child holds up the rest. Ten fingers are a portable ten frame.
• Bond snap. Turn over two cards. Snap when they make 10. It moves quickly and is fun with siblings.

Keep the bar for success realistic. You are aiming for a quick answer from memory, not a race. If a child pauses but then knows, that bond is on its way. If they need to count up from the smaller number every time, stay with the ten frame for that bond a little longer.

How to teach the make-ten strategy for 8 + 5

Making ten is how children add across 10 without counting on by ones. It only works once the bonds to 10 are fast, because the first step is to ask what the bigger number needs to reach 10.

Show it first with two ten frames. Put 8 counters in one frame and 5 in the other. Slide 2 of the 5 across to fill the first frame. Now the child sees a full ten and 3 extra, which is 13. The written version (8 + 2 + 3) should come after they have moved the counters themselves several times.

The third example shows a useful habit: start from the bigger number, because it needs fewer to reach 10. The last one shows the same idea run backwards for subtraction, which is the strategy the Common Core describes as decomposing a number leading to a ten.

A teaching progression from Kindergarten to Grade 2

Every child moves at their own pace, so treat this as an order of steps rather than a calendar. The sign to move on is in the last column.

Most children work through the first three stages in kindergarten and early Grade 1, and the last three during Grades 1 and 2, but there is a wide normal range. Printable practice for each stage is in the Grade 1 arithmetic worksheets and the Grade 2 arithmetic worksheets. If you are not sure where a child is, the short Grade 1 maths check is a quick way to find out.

Common problems and quick fixes

Most stalls come from moving to symbols before the picture is secure. Going back a stage is not a failure; it is usually the fastest route forward.

• Counts every counter, every time. Use the flash-and-cover game and fill the top row first so five is seen as one chunk.
• Knows 3 + 7 but not 7 + 3. Turn the ten frame round in front of them. The counters do not change, only the order you say them in.
• Muddles bonds to 10 with doubles. Practise them on different days at first, then mix them once both are steady.
• Can make ten with counters but not in their head. Ask them to describe the counters they would move, without touching any. Talking through the picture is the bridge.
• Guesses quickly and is often wrong. Slow down and ask them to show it on fingers or a frame. Accuracy first, speed later.

A short, cheerful routine done most days works well. Ten minutes of games and a few written questions, checked together, helps most children move from counting dots to knowing the bonds, and from there to adding 8 + 5 in their head.