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How would you teach your Primary 3 child to solve this past year GEP Selection Test Mathematics question?

Class 3A has 27 books and pencils. Class 3C has 39 books and pencils. How many books and pencils does Class 3B have?

At primary school level, such questions are commonly classified under the topic ‘Comparison & Replacement’ .

For adults, the intuitive approach would be to use algebra and simultaneous equations. However, if you’ve ever tried teaching a Primary 3 child to use algebra to solve problem sums, you’d probably agree that it’s a method few Primary 3 students can grasp.

Why do primary students find it difficult to employ algebra? We often forget that manipulating algebraic equations requires a whole suite of skills. These include forming correct equations based on the information given in a question, changing signs when shifting variables from one side of the equation to the other, determining common factors or multiples, and so on. Without mastering these fundamental skills, students inevitably encounter stumbling blocks when trying to use algebra to solve problem sums.

In many places (including Singapore), mathematics is taught to youngsters in spiraling stages of sophistication using the CPA approach. CPA stands for Concrete-Pictorial-Abstract. The Concrete stage refers to the manipulation of physical objects (such as blocks or fingers) in solving questions. The Pictorial stage refers to the use of visual representations to model problems. The bar modelling method is one such example. The Abstract stage refers to the use of abstract symbols to model problems. Algebra, with its use of x and y to represent variables, is taught during the Abstract stage.

So as you can see, this question, with its pictures of books and pencils, falls under the Pictorial category. This is appropriate given that it’s meant for Primary 3 students.

By observation, a student would realise that 3B has 1 more ‘book picture‘ compared to 3C. So, finding out how many actual books a book picture represents is key to solving the question. Since the only numbers given are for the total number of books and pencils that 3A and 3C have, the logical first step is to find some way of comparing those values.

The thinking process is this: if the number of pencil pictures is the same for 3A and 3C, then the difference in their total number of books and pencils would correspond to the difference in the number of book pictures. But since they are different (3A has 2 and 3C has 1), something must be done to make them comparable.

Video solution:

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