Teaching mathematics
Teaching mathematics

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Teaching mathematics

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.

Described image
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 multiplication 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.

three postfix times workers multiplication eight postfix times days equals 24 postfix times days of work in total postfix times
An extra worker equals four workers in total postfix times
four postfix times workers postfix multiplication question mark times days equals 24 postfix times days of work in total postfix times
equation left hand side 24 division four equals right hand side six postfix times days

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

TM_1

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