Singapore Primary Math Explained sc-math

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Updated: 14 July, 2007

Learning math is also about developing and improving pupils' mind. Cognitive skills such as reasoning and logic, abstract thinking, visualisation, perception, memory and concentration are learned mental processes. Pupils develop their mental skills as they learn to apply the various problem solving heuristics to solve challenging math problems.

Different problem solving heuristics involves different thinking skills. We should therefore encourage pupils to learn and practise the various ways of solving math problems as this would broaden their mind. They should not focus on a favourite strategy such as "guess and check" and disregard the other methods. Lack of proficiency in the various problem solving strategies will disadvantage pupils later on when they need a wide repertoire of problem solving skills to take on unfamiliar challenging problems.

As the pupils' cognitive skills improves, they will be able to make better sense of the available information and process them intelligently. Their overall intellectual and academic performance will therefore also improve.

"A mind that is stretched to a new idea, never returns to its original dimension."

Oliver Wendell Holmes (1809-1894)

Shown below are six solutions (with brief explanation) to the following math problem:

There are 300 boxes, some weighing 3 kg and some 5 kg. The total weight of the 5-kg boxes is 380 kg more than the total weight of the 3-kg boxes. What is the total weight of all the boxes?

The strategies used in the solutions are guess and check, logic and reasoning, looking for patterns, model drawing, algebra and scale drawing. Note that the last two solutions using algebra and scale drawing are probably not taught in Singapore's primary schools.

As we walk through the different solutions to the math problem, consider the thinking and reasoning that goes on in the pupil's mind when using a particular problem solving heuristic. The difference in the required mental skills between the various solutions may be subtle ("guess and check" and "logical thinking"), or obvious ("guess and check" and "model drawing").

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#1, 31 Jul 07 - 06:50pmbhchia

great way of looking at it.

another way of visualizing from reasoning is to start with mid-point of 150 boxes each, ie. 150 x 5 kg = 750kg and 150 x 3 kg = 450kg, which gives a delta of 300kg.but given condition is 380 kg (difference of 80kg) more of 5-kg boxes than 3-kg boxes, means more 5 kg boxes than 3-kg. since for every 3-kg box taken out we add a 5-kg, nett increase of one 5-kg and backing out one 3-kg results in a nett increase of 8kg..hence adding 10 boxes of 5-kg (10 x 8kg = 80kg) from 150 boxes, giving 160 x 5-kg and 140 x 3-kg...ie. 1220 kg in total.

160 x 5 = 800 kg

140 x 3 = 420 kg

diff = 380 kg.

cheers

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