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Succeed with maths: part 2

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# 3.1 Doing some doing and undoing

Now you’ve had a look at an example, see how you get on with the next activity.

## Activity 7 Working out the number

Timing: Allow approximately 13 minutes

Try to work out what number was thought of in the following problems. You may find it helpful to use some doing-undoing diagrams to visualise, and keep track of these.

• a.Think of a number, subtract 3, and the answer is 2.

Figure 9 Doing-undoing diagram for part (a)

So, the initial number was 5.

Remember, you can check your answer by using it with the instruction to check you obtain the correct answer given. So, 5 − 3 = 2!

• b.Think of a number, multiply by 5, and the answer is 35.

Figure 10 Doing-undoing diagram for part (b)

So, the initial number was 7. (Check 7 × 5 = 35).

• c.Think of a number, add 4, double it, and the answer is 14.

Click on ‘reveal comment’ if you would like a hint

### Comment

When you have to deal with more than one operation, just take each step in turn. Write down the doing diagram and draw the undoing one underneath, working backwards to undo each operation.

Figure 11 Doing-undoing diagram for part (c)

So, working from the left in the undoing diagram, 14 ÷ 2 = 7 and 7 − 4 = 3.

If you like, you can write the output from each box on the arrow as shown in Figure 13 above.

So, the initial number was 3. (Check: 3 + 4 = 7, then 7 × 2 = 14).

• d.Think of a number, add 5, multiply by 3 and subtract 4. The answer is 17.