Number Bonds to 10: Find the Missing Partner

A number bond is a whole split into parts. For bonds to 10, the whole stays fixed at 10 while the two parts change.

That makes the central question very concrete:

If one part is 7, how many spaces are still needed to fill 10?

The answer is 3, so 7 + 3 = 10. This is not a trick to remember. You can see it, build it and check it.

See the bond in a ten-frame

Draw two rows of five boxes. Put one counter in each box until you have shown the known part.

For 7 + ? = 10:

1. Fill seven boxes.
2. Count the three empty boxes.
3. Fill those spaces with a second colour.
4. Check that all ten boxes are now full.

The filled boxes show the known part; the empty boxes reveal its partner. This is why a ten-frame is useful: the target is visible before any calculation begins.

Try the same routine without moving on until you have checked each full sum:

• 2 + ? = 10 gives 2 + 8 = 10.
• 9 + ? = 10 gives 9 + 1 = 10.
• 5 + ? = 10 gives 5 + 5 = 10.
• 0 + ? = 10 gives 0 + 10 = 10.

The complete set of partners

Start at zero and move one counter from the second part to the first part each time:

• 0 + 10 = 10
• 1 + 9 = 10
• 2 + 8 = 10
• 3 + 7 = 10
• 4 + 6 = 10
• 5 + 5 = 10

You can stop at 5 + 5 because the pairs then repeat in reverse: 6 + 4 uses the same two parts as 4 + 6.

This symmetry halves the amount you need to organise. It also gives a useful check: if you know 3 + 7, then 7 + 3 must reach the same total.

A three-step missing-part method

When the counters are no longer in front of you, keep the same logic:

1. Name the target: “I need 10.”
2. Find the gap: count on from the known part, or calculate 10 minus that part.
3. Verify the pair: add both parts and confirm the result is 10.

For 6 + ? = 10, the gap from 6 to 10 is 4. The check is 6 + 4 = 10.

For ? + 8 = 10, the gap from 8 to 10 is 2. The check is 2 + 8 = 10.

Writing the check matters. It catches answers that are close to 10 but do not actually complete the target.

Play a partner hunt

One child and one adult can run this with ten counters, coins or scraps of paper.

1. The adult hides some of the ten objects under a cup.
2. The child counts the objects still visible.
3. The child predicts how many are hidden.
4. Lift the cup and verify the total.

If six are visible, the prediction should be four hidden. Swap roles after each round. To make the reasoning audible, ask for a full statement: “Six and four make ten.”

The activity stays focused when the target remains 10 and only the split changes. For broader short-session ideas, see arithmetic games for short practice. When the next goal is checking a calculation rather than composing a total, use the separate routine in how to estimate and check maths answers.

What Math & Patterns actually offers

Math & Patterns lists Make 10, whose current task is to find pairs of numbers that add to a target. Its catalogue page is an app-only next step, not a browser demo. The hands-on partner hunt above works without the app and demonstrates the same narrow pair-to-target idea.

Number bonds are useful facts, but this page does not promise that one game or one routine will produce fluency. The immediate goal is smaller and testable: find a partner, state the full sum and check that it reaches 10.

Sources and further reading

• England’s primary mathematics national curriculum includes representing and using number bonds within 20 and specifically discusses reasoning with bonds to 10 and 20.
• NRICH’s Pairs of Numbers teacher guidance develops fixed-total partner reasoning through a practical number-pair task.