Bar Model Method For A Challenging 2021 PSLE Question

Bar Model Method For A Challenging 2021 PSLE Question

 Ho Soo Thong  

 8 Oct 2021

“If I had an hour to solve a problem I’d spend 55 minutes thinking about the problem and 5 minutes thinking about solutions.” 

- Albert Einstein

 

We will focus on showing a bar model approach to a challenging 2021 PSLE question. This question involves Distributive Situations and the mathematics of Distributive Law. 

 

 

2021 Question – A Mix of 50-¢ Coins and 20-¢ Coins

Helen and Ivan had the same number of coins. 

Helen had a number of 50-cent coins and 64 20-cent coins. These coins had a mass of 1.134kg. 

Ivan had a number of 50-cent coins and 104 20-cent coins.

(a) Who has more money in coins and by how much?                                                         

(b) Given that each 50-cent coin is 2.7g more heavier than a 20-cent coin, what is the mass of Ivan’s coins in kilograms?                                                                                                      

Solution

Step A : Thinking about the problem.

Construct a bar model (Number of coins) to obtain an overall view of the problems involving two Distributive Situations.

 

Step B : Thinking about solutions. 

With Part-Whole and Comparison Concepts,  we divide each set of coins into 3 parts so as to obtain two identical pairs as shown. 

 

(a)   Helen have more money because she have more 50-cent coins by the amount 40×(50¢ – 20¢) = 1200¢ = $ 12

(b)   Each 50-¢ coin is 2.7g more heavier than a 20-¢ coin,

Mass of Helen’s coins - Mass of Ivan’s coins =  difference in total mass= 40×2.7 g = 108 g = 0.108 kg 

      Mass of Helen’s coins = 1.134 kg

Mass of Ivan’s coins = 1.134 kg – 0.108 kg = 1.026 kg

 

Note : It is not a difficult question for pupils understanding the mathematical situations and familiar with the solutions to the following two past year PSLE questions. 

More Distributive Questions – Variant of the above 2021 PSLE Question.

Question 1 (11/2/2016)

Four teams of students washed cars for charity.  They collected $ 10  for washing a small car and $ 15 for a big car. The table shows the number of cars washed by three of the teams. 

 

(a) Which of the three teams collected the most  money? What was the amount of money?

(b) Team D washed as many cars as Team A but collected $ 30 more. How many big cars did Team D wash?

Question 2 (17/2/2015) 

Three girls Amy, Beth and Cindy had the same number of coins. Amy and Beth each had a mix of fifty-cent and ten-cent coins. Amy had 9 ten-cent coins while Beth had 15 ten-cents coins. Cindy had only fifty-cent coins.

(a) Of the three girls who had the most money and who had the least?

(b) What was the difference in the total value of Amy and Beth’s coins.

(c) Beth used all her fifty-cent coins to buy some food. She then had $ 10 less in coins than Cindy. How many fifty-cent coins did Cindy have?