Websink Prep UKStep-by-step practice MathsLevel 4 chaptersMaths textbooksLevel 1Level 2Level 3Level 4Level 5Browse allPast papersFind a tutorBecome a tutor
Step-by-step practice: Maths · Level 4Chapter 9 · Solving problems with the four operations
Step-by-step Maths Level 4 · Solving problems with the four operations · Lesson 9.3

Step-by-step Maths Level 4: Missing-number problems

Part of the Step-by-step Maths Level 4 solving problems with the four operations chapter. Chapter overview · whole chapter on one page

9.3

Missing-number problems

Level 4
Solve a problem with a missing number by working backwards

In a missing-number problem, you know the answer but not the starting number. Work backwards.

Undo each step in the reverse order. Addition is undone by subtraction. Multiplication is undone by division.

Key ideas

  • Work backwards from the answer.
  • Undo each step with the opposite operation.
  • Check forwards to make sure.
Worked example 9.3.1
I think of a number. I add 350. The answer is 1200. What was my number?

Method. Work backwards: undo each step in the reverse order, then check forwards.

  1. Work backwards. Undo the addition by subtracting.
    1200 - 350 = 850
  2. Check forwards. Add the number back to check the answer.
    850 + 350 = 1200
  3. Write the answer. This was the number I started with.
    850

Check. Check: 850 + 350 = 1200.

Watch out. Undo the last step first.

Worked example 9.3.2
I think of a number. I multiply it by 6. The answer is 360. What was my number?

Method. Work backwards: undo each step in the reverse order, then check forwards.

  1. Work backwards. Undo multiplying by dividing.
    360 ÷ 6 = 60
  2. Check forwards. Multiply the number to check.
    60 × 6 = 360
  3. Write the answer. This was the number I started with.
    60

Check. Check: 60 × 6 = 360.

Watch out. Division undoes multiplication.

Worked example 9.3.3
I think of a number. I take away 40, then double the answer. The result is 220. What was my number?

Method. Work backwards: undo each step in the reverse order, then check forwards.

  1. Undo the doubling. Halve the result first.
    220 ÷ 2 = 110
  2. Undo the take away. Add back the 40 that was taken away.
    110 + 40 = 150
  3. Write the answer. This was the number I started with.
    150

Check. Check: 150 - 40 = 110, and 110 × 2 = 220.

Watch out. Work backwards, one step at a time.

Watch out

Watch out. If the last step is “double”, the first thing to undo is to halve. Undo the steps in reverse order.

Exam tip

Grown-up tip. Ask the child to follow their answer forwards through each step. Does it reach the answer in the question?

Exercise 9C  Practice: missing-number problems

Non-calculator
1
PSI think of a number. I add 725. The answer is 1356. What was my number?
2
PSI think of a number. I add 130. The answer is 1442. What was my number?
3
PSI think of a number. I multiply it by 4. The answer is 1264. What was my number?
4
PSI think of a number. I multiply it by 9. The answer is 6012. What was my number?
5
PSI think of a number. I take away 86, then double the answer. The result is 1986. What was my number?
6
PSI think of a number. I multiply it by 9. The answer is 5040. What was my number?
7
PSI think of a number. I add 1221. The answer is 1934. What was my number?
8
PSI think of a number. I add 2358. The answer is 6696. What was my number?
9
PSI think of a number. I multiply it by 8. The answer is 2568. What was my number?
10
PSI think of a number. I take away 112, then double the answer. The result is 3648. What was my number?
11
PSI think of a number. I add 2713. The answer is 5306. What was my number?
12
PSI think of a number. I multiply it by 3. The answer is 1122. What was my number?
13
PSI think of a number. I multiply it by 8. The answer is 6424. What was my number?
14
PSI think of a number. I take away 94, then double the answer. The result is 812. What was my number?
15
PSI think of a number. I add 468. The answer is 4277. What was my number?
16
PSI think of a number. I multiply it by 9. The answer is 1611. What was my number?

Websink Prep UK is an independent site. It is not affiliated with, endorsed by or sponsored by AQA, Pearson Edexcel, OCR, WJEC, Eduqas, CCEA, SQA, GL Assessment, CEM or the Department for Education. All exam board names and trademarks belong to their owners. Past papers are linked from the exam boards' own websites and are not hosted here.

About Websink Prep UK · Find a tutor · Privacy · Terms · Cookie settings