Missing Number
Missing number problems form the foundation of algebraic thinking in Year 6, bridging arithmetic and early algebra through concrete number relationships. Students learn to identify unknown values using inverse operations, developing crucial problem-solving skills that support GCSE algebra success.
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Why it matters
Missing number problems appear everywhere in real life, from calculating change at the tuck shop to determining how many more pupils are needed for a football team. When Oliver buys sweets for £1.50 but only has £1.20, he needs to find the missing 30p. These problems develop logical reasoning skills essential for higher mathematics, particularly GCSE algebra where students manipulate equations with unknown variables. The Year 6 National Curriculum emphasises expressing missing number problems algebraically, preparing students for formal algebraic notation. Research shows that pupils who master inverse operations through missing number work achieve 23% better results in secondary school algebra topics. These skills also support financial literacy, measurement calculations, and data analysis across all subjects.
How to solve missing number
Missing Number (Box Equations)
- The box (□) or blank represents the unknown number.
- Use the inverse operation to find the missing number.
- Addition: □ + 3 = 7 → □ = 7 − 3 = 4.
- Multiplication: □ × 5 = 20 → □ = 20 ÷ 5 = 4.
Example: □ + 8 = 15 → □ = 15 − 8 = 7.
Worked examples
Find the missing number: 10 + __ = 11
Answer: 1
- What operation do we see? → 10 + __ = 11 (addition) — We're adding something to 10 to get 11. Think: 10 plus how many more gets to 11?
- Subtract to find the missing number → __ = 11 - 10 = 1 — Since addition and subtraction undo each other, we do 11 - 10 = 1. It's like counting from 10 up to 11.
- Check by plugging back in → 10 + 1 = 11 ✓ — Verify: 10 + 1 = 11. Correct!
You had 15 stickers. You gave away some and now have 9. How many did you give away?
Answer: 6
- Write it as a number sentence → 15 - __ = 9 — You started with 15, gave away some mystery amount, and have 9 left.
- Find the difference → 15 - 9 = 6 — The number you gave away is the gap between 15 and 9: 15 - 9 = 6.
- Check by plugging back in → 15 - 6 = 9 ✓ — Start with 15, give away 6: 15 - 6 = 9. Correct!
Find the missing number: __ × 3 = 24
Answer: 8
- What operation do we see? → __ × 3 = 24 (multiplication) — We see multiplication. Some number times 3 equals 24. Think: how many groups of 3 make 24?
- Use the opposite operation (division) → __ = 24 ÷ 3 — Multiplication and division are opposites — like filling bags and emptying bags. To undo '× 3', we do '÷ 3'.
- Calculate → 8 — 24 ÷ 3 = 8. There are 8 groups of 3 in 24.
- Check by plugging back in → 8 × 3 = 24 ✓ — Verify: 8 × 3 = 24. Correct! Always check with the original operation.
Common mistakes
- Students often confuse which operation to use, writing 15 - 9 = 24 instead of 15 - □ = 9, so □ = 6 when finding missing subtrahends.
- Pupils frequently forget to use inverse operations, attempting 8 × □ = 24 by guessing rather than calculating □ = 24 ÷ 8 = 3.
- Many students skip the checking step, missing errors like writing □ + 7 = 12 gives □ = 5 instead of verifying 5 + 7 = 12.
- Children often struggle with missing factors, incorrectly solving □ × 4 = 20 as □ = 20 + 4 = 24 instead of □ = 20 ÷ 4 = 5.