Succeed with maths: part 2
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.


This shows a figure containing a doing and undoing diagram for part (a).
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.


This shows a figure containing a doing and undoing diagram for part (b).
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


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.


This shows a figure containing a doing and undoing diagram for part (c).
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.


Described image
Figure 12 Doing and undoing diagrams to solve a multistep problem

So, if the answer is 17, undoing the steps by working from right to left gives:

Add 417 plus four equals 21
Divide by 321 division three equals seven
Subtract 5seven minus five equals two

So, the initial number was 2 this time. (Check: 2 + 5 = 7, then 7 × 3 = 21 and 21 − 4 = 17).

You may be wondering what is the point of all this doing/undoing business! Sometimes there is a need to change a formula so that you can work out something different from it. This is called rearranging the formula and does occur quite frequently in any subject area that uses formulas. The same technique that you have been looking at in this section on ‘undoing’ instructions can be used when rearranging formulas, as you’ll see in the next section.

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