Missing Number
Missing number problems present equations with one unknown value, typically represented by a box (□) or blank space. These problems require finding the value that makes the equation true using inverse operations. The box represents a specific number that, when placed correctly, balances the mathematical statement.
Why it matters
Missing number problems form the foundation for algebraic thinking, as required in Year 6 of the UK National Curriculum where pupils express missing number problems algebraically. These skills directly lead to solving linear equations at GCSE level, where x replaces the box symbol. In everyday life, missing number reasoning appears when calculating change (£20 - □ = £13.50), determining cooking portions (4 × □ = 16 biscuits), or working out journey times (45 minutes - 12 minutes = □). Shop assistants use this thinking when a till shows £8.40 due and a customer pays £10, requiring them to calculate £10 - £8.40 = £1.60 change. The inverse operation principle extends to more complex mathematics including quadratic equations and calculus.
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
Put a number in the box: [ ] + 1 = 8
Answer: 7
- The box is the mystery number → [ ] + 1 = 8 — The box is hiding a number. When we add 1 to it, we get 8. Let's figure out what's hiding!
- Use subtraction to 'undo' the addition → [ ] = 8 - 1 = 7 — Subtraction undoes addition, like erasing undoes drawing. 8 - 1 = 7.
- Check by plugging back in → 7 + 1 = 8 ✓ — Put 7 in the box: 7 + 1 = 8. It works!
You had 13 stickers. You gave away some and now have 3. How many did you give away?
Answer: 10
- Write it as a number sentence → 13 - __ = 3 — You started with 13, gave away some mystery amount, and have 3 left.
- Find the difference → 13 - 3 = 10 — The number you gave away is the gap between 13 and 3: 13 - 3 = 10.
- Check by plugging back in → 13 - 10 = 3 ✓ — Start with 13, give away 10: 13 - 10 = 3. Correct!
If 4 × 2 = 8, what is 8 ÷ 2?
Answer: 4
- Recognize the fact family → 4 × 2 = 8 — Multiplication and division are in the same 'fact family'. If 4 × 2 = 8, then dividing 8 by one number gives the other.
- Divide: 8 ÷ 2 → 4 — 8 ÷ 2 = 4. Multiplication and division always undo each other, just like addition and subtraction!
Common mistakes
- Using the same operation instead of the inverse: writing □ + 5 = 12 as □ = 12 + 5 = 17 instead of □ = 12 - 5 = 7
- Confusing the order in subtraction problems: solving 15 - □ = 8 as □ = 8 - 15 = -7 instead of □ = 15 - 8 = 7
- Mixing up multiplication and division inverses: finding □ in □ × 6 = 42 by calculating □ = 42 × 6 = 252 instead of □ = 42 ÷ 6 = 7