Introduction
Rate questions are commonly tested in Primary 5 Math and often trip students up, especially when more than two quantities are involved.
In this blog post, weāll walk through a Rate question involving three variables: men, boats and days.
Weāll break the question down step-by-step using a table so your child can learn how to approach similar questions with confidence!
Alternatively, you can also watch my explainer video for free on our YouTube channel.
Let’s Analyse This Rate Question
Source: Maha Bodhi School ā 2018 P5 SA1 Examination Paper [Q14]
At first glance, this may look like a standard Rate question, but it involves three variables instead of the usual two. This means students will need to break down the problem into smaller, more manageable parts.
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Thought Process
Letās use a table to organise the information given in the first sentence into these known identities:
- Men
- Boat
- Days
But first, let us recap:
šĀ What Is Rate? š
It is the amount of a quantity per unit of another quantity.
This question has three variables, but when we are working with Rate, we work with two quantities at a time.
If we increase the number of men working, the number of boats built will increase in the same number of days.
Going back to the question, it asks: āWorking at the same rate, how many men are needed to build 5 boats in 1 day?ā
Let us work with two quantities at a time.
Which two shall we choose?
Since we need to find the number of men, let us look at boats first!
But itās tough to get from the number 2 to the number 5!
How about days? We can divide 4 by 4 to get to 1 day.
Letās apply this division to our boats too, while keeping the number of men at 10.
This new row means that 10 men can build half a boat in 1 day.
Now that the number of days is settled, how can we get from half a boat to 5 boats?
Let us multiply the number of boats by 10!
We can apply the same multiplication of 10 to the number of men. 10 multiplied by 10 will give you 100 men, and that answers the question of how many men are needed.
Final Answer
100 men can build 5 boats in 1 day.
Conclusion
To solve Rate questions with three quantities, it helps to work with two variables at a time.
In this question, we first fixed the number of days. Thereafter, we scaled the number of boats and men proportionally. Using a table and clear step by step made it easy to reach the final answer.
With regular practice and the right techniques, your child will get better at handling these multi-step questions.
Stay tuned for more P5 Math blog posts on Rate!
