Tuesday, July 10, 2007: Solving (?) math problems with Celine Koh

After Berinderjeet Kaur's and Marshall Cavendish's presentations, the day still was not over. Most of us remained for a problem-solving session (lasting until 18:30) with Celine Koh, organizer of this week-long program and a former teacher of gifted students and current mathematics tutor. It was this session that introduced concretely to those previously not familiar with Primary Mathematics, what 'Singapore Math' is all about.

Following are the problems with which we, with our fried brains, struggled, and then Celine made it seem all so simple. Answers are not provided for the benefit of those who relish a challenge.

Grade 3

A mechanic fixed 12 wheels to 5 bicycles and tricycles. How many of them were bicycles and how many were tricycles?

Adapted from school exam paper

Grade 3/4

Mrs Tan is 31 years old and her daughter is 13 years old. How many years ago was Mrs Tan 3 times as old as her daughter?

Source: Challenge Problems Set B Question no. B52

Grade 4/5

Jane used 880g of a packet of sugar to bake a cake and 1/10 of the remaining sugar to make jelly.
She then had 3/7 of the packet of sugar left.
How much sugar was in the packet at first?

Adapted from school exam paper

Grade 5/6

Tim and Sally each have some money.
If Tim spends $80 per day and Sally spends $40 per day, Tim will have $500 left when Sally has spent all her money. If Tim spends $40 per day and Sally spends $80 per day, Tim will have $1100 left when Sally has spent all her money. Find the amount of money Sally has.

Adapted from school exam paper

Grade 5/6

Four toy cars cost as much as 3 dolls. Five toy cars cost $3.50 more than 2 dolls. Clare spent $14 on equal number of toy cars and dolls. How many toy cars did she buy?

Adapted from A* Maths Problems Whole Numbers and Decimals page 11 Question 5

Grade 5/6

John has a tank of fish.
The number of guppies is 25% of the total number of fish in the tank.
He buys as many guppies as he had.
Find the percentage of the angel fish now in the tank.

Adapted from PSLE Past year Questions

Grade 5/6

A jar contained some chocolates and sweets.
At first, the number of chocolates was 60% of the sweets.
After adding in another 10 chocolates and 10 sweets, the number of chocolates becomes 80% of the number of sweets.
How many sweets were there at first?

Adapted from school exam paper

Grade 5/6

Class A and Class B have the same number of pupils. The ratio of the number of boys in Class A to the number of boys in Class B is 3:2. The ratio of the number of girls in Class A to the number of girls in Class B is 3:5. Find the ratio of the number of boys to the number of girls in Class A.

Source: Challenge Problems Set C Question no. C66

Grade 6

The number of 20-cent coins to the number of 50-cent coins in a box was 3:2 Lyn took out four 50-cent coins and replaced them with 20-cent coins of the same value. After that the ratio of the number of 20-cent coins to the number of 50-cent coins became 7:2. How much money was there in the box?

Adapted from Challenge Problems Set C Question no. C67

Grade 6

There are two bags of stones labelled A and B. In Bag A, there are 350 black stones and 500 white stones. In Bag B, there are 400 black stones and 100 white stones. How many black and how many white stones should be transferred from Bag B to bag A so that 50% of the stones in Bag A and 75% of those in Bag B are black?

Source: A* Maths Problems Percentage page 9 Question 9

Many of the above resources can be purchased from a bookstore called Popular, introduced to us by our guide. Several members of the group, led by Cassy Turner and Tricia Salerno, made trips to Popular to buy more books, resulting in the need to purchase additional suitcases to transport them home.