# Fun with mathematics

## This is the third of a four-part series of maths questions presented by Marshall Cavendish Education. The questions are targeted at pupils in upper primary, and the worked solutions and advice have been contributed by Associate Professor Lee Ngan Hoe, Assistant Head (Mathematics Education - Teaching) of the Mathematics & Mathematics Education Academic Group from the National Institute of Education (NIE) at Nanyang Technological University (NTU). Dr Lee is also the co-author of Shaping Maths and Maths Works!

• Try to understand the problem first. What is the problem about? What information is given to you, and how does it help you to better make sense of the given diagram? What else do you know given that the area of Triangle BEC is three times the area of Triangle AED? Did you use any other information that is not given in the question? If yes, why do you think the information is true for this question?

• Work out a plan to solve the problem. What can you do with the information given? What other information can you derive? Can you represent all this information on another diagram?

• Try to make sense of the answer. Is there a way to check it? What have you learnt from solving this problem?

• Refrain from telling the child what to do, for instance, by telling the child to "look at" the diagram. Instead, prompt the child to make sense of the given problem more holistically. You could start by asking: "Did you manage to get all the information about the problem?" or "Where else in the problem can you get more information?"

• Encourage the child to annotate the given diagram and draw additional diagrams where necessary to develop a plan to solve the problem. This makes it easier for the child to better visualise possible relationships that might exist between the unfamiliar.

• Help the child look for words to tap the necessary mathematics knowledge and skills. In this case, the skill needed is how to calculate the area of a triangle, which is determined by the formula ½ x base x height. There are several triangles in this problem. As a start, encourage the child to work out the areas of those triangles for which he or she can identify a base and corresponding height.

• In most problems where diagrams are involved, they are drawn to proportion but not to scale. Some children might make invalid conclusions about the diagram because of visual illusion.

QUESTION 4

Ken buys some mangoes. If he packs them equally into bags of 40, he will have seven mangoes left. If he packs them equally into five bags, he will need to buy more mangoes. What is the smallest number of mangoes he needs to buy?

The answer to Question 4 can be found online at http://www.straitstimes.com/tags/fun-with-mathematics

It will also be published in the Education pages of The Straits Times next Monday.

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A version of this article appeared in the print edition of The Straits Times on March 06, 2017, with the headline 'Fun with mathematics'. Print Edition | Subscribe