Singapore Primary Math Explained sc-math

More than one way to solve math problems

Page 4 of 5

Please note that the next 2 solutions (algebra and scale drawing) are probably not taught in the primary schools.

Algebra

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?

Let x = number of 5-kg boxes
Let y = number of 3-kg boxes

5x − 3y = 380 ......(1)

x + y = 300
y = 300 − x

Substituting y with 300 − x in equation (1),
5x − 3(300 − x) = 380
5x − 900 + 3x = 380
8x = 380 + 900
x = 1280 ÷ 8
x = 160

Number of 5-kg boxes = 160
Number of 3-kg boxes = 300 − 160 = 140

Total weight of the boxes is 160 × 5 + 140 × 3 = 1220 kg.

According to the Singapore Primary Math syllabus, pupils are only taught introductory algebra (involving one variable) in primary six. The primary schools will therefore probably not be teaching this to the pupils as it is beyond the syllabus. However, pupils are NOT penalised for using algebra to solve math problems. They will be awarded full marks for a correct answer. I am showing algebra here as there are parents who use algebra when helping their child with math problems.

Diagrams - scale drawing/chart

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?

graph

The horizontal axis shows the number of 5-kg boxes (scale of 1 mm : 5 5-kg boxes). The left and right vertical axis shows the weight of the 3-kg boxes and 5-kg boxes respectively (scale of 1 mm : 20 kg). (Note: some may prefer to have a common vertical axis on the left for both the 3-kg and 5-kg boxes.) The red and blue sloping lines show the total weights of the 3-kg and 5-kg boxes respectively corresponding to the number of 5-kg boxes in the horizontal axis. The vertical distance between the blue and red lines represents the weight difference between the 5-kg and 3-kg boxes.

Based on the scale of 1 mm : 20 kg, we know that when the weight difference between the 5-kg boxes and 3-kg boxes is 380 kg, the distance between the blue and red line should be (380 ÷ 20) or 19 mm. As the 5-kg boxes weighs more than the 3-kg boxes, the blue line should also be "above" the red line.

We then slide a set square along the X-axis until the blue line (weight of 5-kg boxes) is 19 mm (380 kg) vertically above the red line (weight of 3-kg boxes) as shown in the diagram. The corresponding value of 160 at the X-axis shows that this weight difference of 380 kg occurs when there are 160 5-kg boxes.

Therefore,
Number of 5-kg boxes = 160
Number of 3-kg boxes = 300 − 160 = 140

Total weight of the boxes is 160 × 5 + 140 × 3 = 1220 kg.

(note: graph paper could be used as drawing aids to help pupils draw parallel and perpendicular lines.)

I've included scale drawing here because unlike the other methods it requires more than mental skills. It also requires the ability (fine motor skills) to plot, draw and measure accurately.

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page 1 of 1 1 comment

#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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