Mathematical symbols and their representation

5+5+5
Source:  http://www.telegraph.co.uk/news/newstopics/howaboutthat/11960777/Why-555-doesnt-always-make-15-Maths-exam-question-divides-the-internet.html

This post is a response to the article, ‘Why 5+5+5 doesn’t always make 15: Maths exam question divides the internet’.

Mathematical symbols convey information for the reader to interpret. In the example of question 1 shown above, is it fair for the child to have one mark deduced for ‘wrong’ representation?

When does ‘5 x 3 = 15’ be presented in form of 5 + 5 + 5 = 15 or 3 + 3 + 3 + 3 + 3 = 15?

5 x 3 = 15 in form of repeated addition; 3 + 3 + 3 + 3 + 3 = 15

  • 5 times of 3, when ‘times of’ is represented by the multiplication sign ‘x’
  • 5 groups of 3, when ‘groups of’ is represented by the multiplication sign ‘x’

5 x 3 = 15 in form of repeated addition; 5 + 5 + 5 = 15

  • 5 multiply 3 times, though this is usually not used in communication but the statement stands true.

Hence, both 3 + 3 + 3 + 3 + 3 = 15 and 5 + 5 + 5 = 15 are correct, depending on the interpretation of the reader. In the case of the paper setter, he/she interpret it as ‘5 times of 3’ / ‘5 groups of 3’. The child interpret it as ‘5 multiply 3 times’. Though the syllabus focuses on the former interpretation, that does not mean a child should be penalised for another logical interpretation.

If the required answer is  3 + 3 + 3 + 3 + 3 = 15, this question can be modified in the following suggestions:

  1. Solve 5 x 3 by completing the repeated addition statement.
    5 x 3 = 3 + 3 + ____________________ = __________. (Answer: 3 + 3 + 3 = 15)
  2. Based on the diagram below, solve 5 x 3 by using repeated addition.

5x3 (Answer: 3 + 3 + 3 + 3 + 3 = 15)

This kind of questions reminds me of a comic I posted before in my post ‘Do schools kill creativity?’

5fe5c91a25279e87ba650be9379344cb

What’s your thought?

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