Teaching mathematics

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Proportional problem 2: Sharing the workload

It takes 3 workers 8 days to complete the foundations of a new building (Figure 22).

How long would it take if there was an extra worker?

Assume that all the workers will work at the same rate.

Figure 18 Building a brick wall

Activity 14 Reflecting

Timing: Allow 10 minutes

Look at the learner’s incorrect response below.

How could you explain to a learner that this approach is incorrect?

• There are 8 days of work completed by 3 workers.
• So, 8 ÷ 3 = 2 2/3 days of work per person.
• Now there are 4 workers, so:
• 4 2 2/3 = 10 2/3 days.

Discussion

This requires some logical thinking, relating the answer back to the original problem.

If it takes 3 workers 8 days to complete the job, would it take 4 workers more time to complete the same job?

No, it would take them less time, so this answer cannot be correct.

If learners have been working on ‘sharing in ratio’ problems, they may go into automatic mode and try to use the same approach with these types of problems, causing them to make mistakes. When working on problems with ratio and proportion, the context of the problem is important.

It will take 4 workers 6 days to complete the same work.

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