It seemed like déjà vu for the Primary 6 students who sat for the PSLE Maths paper in 2021 as they grappled with a seemingly incredibly complex question in Paper 2. Students may have recalled the much talked about ‘Circle question of 2019’ and it seemed to have made a comeback.
Reports on students showing great anxiety and stress upon completing the exams and why such a difficult question appeared have circulated widely. Many parents have pointed out that this question goes beyond the Primary 6 curriculum and are seeking answers.
Upon examining the question, we surmised that this question required students to use their logical thinking and clear reasoning skills, in addition to their mathematical techniques.
Let’s deep dive into the question that has puzzled many PSLE students:
Q: Kelly and Ivan had the same number of coins. Kelly had some 50-cent coins and 64 20-cent coins. Her coins had a total mass of 1.134 kg. Ivan had some 50-cent coins and 104 20-cent coins.
ai) Who has more money?
aii) What is the difference in the amount of money they had?
b) Given that a 50-cent coin is 2.7 g heavier than a 20-cent coin, find the total mass of Ivan’s coins. (Leave your answer in kilograms.)
We can draw a model with 2 bars of equal length to represent the equal number of coins that each of them has, labelling the number of 20-cent coins in each bar.
Find the difference in the number of 20-cent coins that Kelly and Ivan have:
104 – 64 = 40
Label the equal parts in the model:
This means that Ivan has 40 more 20-cent coins than Kelly, which also means that Ivan has 40 fewer 50-cent coins than Kelly.
When comparing the difference in value or mass, we simply focus on these 40 coins.
ai) Since Kelly has more 50-cent coins, she had more money.
aii) Difference in amount of money = 40 x (50¢ - 20¢)
= 1 200¢
= $12
b) Since Ivan has fewer 50-cent coins, his coins are lighter.
Difference in mass = 40 x 2.7g
= 108 g
= 0.108 kg
Mass of Ivan’s coins = 1.134 g – 0.108 kg
= 1.026 kg
Hindsight may be 20-20 but we hope that we have shed some light on the nature of one of this year’s most talked about Maths question.
At The Learning Lab, we always believe that rote learning is not the way to truly learn and master a subject. Our programme emphasises deep conceptual understanding and explicit teaching of skills such as systematic question analysis and teaching of multiple heuristics to solve all types of questions, including non-routine and higher-ordering thinking ones.
When students analyse problems similar to the one above, they are taught to pick out the keywords to identify the concept – when they see “equal number”, they should start off with a model with equal bars and label the information provided. With that, they will be able to identify the constant difference (difference in the number of 50-cent coins = difference in the number of 20-cent coins).
From coins to ribbons to even optimising the number of tables in a function hall, our in-house team of curriculum specialists design unique questions and worksheets to give students practice thinking in unusual contexts.
Our in-house team of curriculum specialists consistently curate worksheets that feature the challenging and unique questions found in past PSLE Maths papers for our Primary 4 and 5 students so they are better prepared for the national exam when their turn comes around.
Content mastery is certainly important in achieving academic success. However, what is equally, if not more vital, are the critical thinking and inferential skills as well as the dispositions that we at The Learning Lab impart to our students. This way, our students develop holistically and are able to manage their challenges ahead.
Click here to find out more about our Maths programmes.
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If you have any questions about our range of programmes or class schedules, you may contact us at 6733 8711 or drop us an email at enquiry@thelearninglab.com.sg.
The Learning Lab is now at locations. Find a location that suits your needs.
If you have any questions about our programmes, please email us at enquiry@thelearninglab.com.sg or call us at 6733 8711 and we will be happy to assist you.
The Learning Lab is now at locations. Find a location that suits your needs.
If you have any questions about our programmes, please email us at enquiry@thelearninglab.com.sg or call us at 6733 8711 and we will be happy to assist you.