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Teaching mathematics
Teaching mathematics

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Proportional problem 4: Printing press

A printing press takes exactly 12 minutes to print 14 dictionaries.

How many dictionaries can it print in 30 minutes?

Activity 16 Reflecting

Timing: Allow 5 minutes

Look at the learner’s incorrect response below.

How can you explain the thinking behind this approach?

  • The printing press can print 28 dictionaries.


This learner appears to have multiplied by 2, despite 12 not being half of 30. This is a common mistake made by learners, who have previously found that doubling has been an effective strategy. This is known as the magic doubling method, when learners use a doubling strategy but it is inappropriate to do so.

Similarly, learners often make mistakes by using multiplication but not by the correct factor.

It is important to offer learners a wide range of varied examples and to have discussions about strategies, identifying that some approaches will work for particular problems but not for others.

As mentioned in the first part of this week, teaching learners methods for solving ratio problems is not enough to develop their proportional reasoning. Learners need to be able to make decisions about when to use different strategies.