PSLE Math

Worked Example

There are 30 children going on a school trip. Each van can take 8 children. What is the least number of vans needed to take all the children?

Many children work out 30 ÷ 8 = 3 R 6 and answer 3 vans. But the 6 children left over still need a van, so the answer is 4 vans.

30 ÷ 8 = 3 R 6

3 vans + 1 more van = 4 vans

How we help: We teach your child to ask what the remainder means before writing the answer: sometimes it can be ignored, sometimes it needs one more group. Here, “R 6” is 6 children without a seat, so one more van is needed.

Worked Example

In a class, 34 of the pupils wear glasses. There are 12 more pupils who wear glasses than pupils who do not. How many pupils are in the class?

Many children treat 12 as the number of pupils who wear glasses and get 16. But 12 is the difference between the two groups, which is 2 units.

With glasses: 3 units; without: 1 unit

3 units − 1 unit = 2 units = 12, so 1 unit = 6

Class: 4 units = 4 × 6 = 24 pupils (not 16)

How we help: We use model drawing to show what a fraction means before your child calculates with it. Here, your child draws the class as 4 units, 3 with glasses and 1 without, and sees that the 12 is the difference of 2 units.

Worked Example

Mrs Tan spent 25 of her money on a dress and 14 of the remainder on a bag. The dress cost $45 more than the bag. How much money did she have at first?

A common mistake is to take 14 of all her money for the bag, which gives $300. But the 14 is of the remainder, so the bag is only 3 of 20 units, and she had $180 at first.

Dress = 25 of 20 units = 8 units

Bag = 14 of the 12 units left = 3 units

8 units − 3 units = 5 units = $45, so 1 unit = $9

At first: 20 units = $180 (not $300)

How we help: We teach your child to plan longer questions with a model, labelling what is left after each step. Here, they draw her money as 20 units, so that both the 25 and the 14 of the remainder are whole units.

Worked Example

In a school club, 40% of the pupils were boys. After 30 girls left the club, the ratio of the number of boys to the number of girls became 4 : 5. How many pupils were in the club at first?

Many children simplify 40 : 60 to 2 : 3 and compare it with 4 : 5, but those units are different sizes. Writing 40% : 60% as 4 : 6 keeps the boys at 4 units in both ratios, because the number of boys did not change.

Boys : girls = 40% : 60% = 4 : 6

Boys stay at 4 units; girls go from 6 units to 5 units

1 unit = 30 girls, so at first: 10 units = 300 pupils

How we help: We teach before-and-after models for changing ratios, with the unchanged quantity drawn the same length in both. Here, the boys stay at 4 units, so the 30 girls who left are 1 unit.