Primary 5 · Mathematics
P5 rate
A rate question is one multiplication. The mark is lost before the multiplying starts, in a unit nobody converted. Here is the pattern, and the one question that catches it.
- Level
- P5
- Usually taught
- Term 3
- Covers
- 1 concept
What changes at P5
Rate is the first topic where your child handles two units at once: litres per minute, dollars per kilogram, pages per hour. The small word "per" is doing all of the work.
Once the two units agree, a rate question is a single multiplication. Nearly all the difficulty sits in making them agree first, which is why the working looks easy right up until the marks go.
The sentence that costs the mark
A tap fills a tank at 4.5 litres per minute. How much water flows in 1 h 20 min?
What the working usually does
4.5 litres ×20 minutes=90 litres
Multiplies by the minutes printed on the clock and leaves the hour out.
What the question asked
4.5 litres ×80 minutes=360 litres
Turns the whole duration into minutes first, because the rate is per minute.
Both are one clean multiplication and both give a believable tankful. Neither has an arithmetic error in it. The time is the only thing that went wrong, and it went wrong before any multiplying started.
The same question, worked properly
Match the units to the rate
the rate is per MINUTE, so the time has to be in minutesThis is the step that fails. The whole question turns on this line. A rate and a time in different units cannot be multiplied together, however tidy the sum looks.
Convert the time
1 h 20 min = 60 min + 20 min = 80 minAn hour is 60 minutes, not 100. This is where 1 h 20 min quietly becomes 1.2.
Multiply by the rate
80 min × 4.5 litres = 360 litresOnce the units agree, the arithmetic is the easy part of the question.
Check it back
360 litres ÷ 4.5 = 80 minDivide the answer by the rate and you should land back on the time you were given. The 90-litre answer gives 20 min, which is not what the question said.
How can you tell it has clicked?
You do not need to do the maths to check this. When a rate turns up, ask one thing: "per what?"
Then look at whether the time or the weight in the question is written in that same unit. A child who converts before multiplying has understood it. A child who multiplies the numbers in the order they appear has not, and the answer still looks tidy.
One thing to try tonight
Next time you fill a water bottle, time ten seconds of it and work out the rate per second together. Then ask how long the whole two-litre bottle would take.
The second question forces the unit check, which is the thing being examined. It takes a minute at the sink and needs no worksheet.
What your child will meet in this topic
- Rate
Most Singapore schools introduce this in Term 3, though schools do differ by a term either way. If your child’s school runs a different order, you can set it in the schedule on your dashboard.
What it leads to
Rate is the groundwork for the P6 water-tank questions, where a tank fills and drains at the same time and the units have to agree in more than one place at once.
The "per what" habit carries into any question that mixes units, which is most of the multi-step word problems in the P6 paper.
The methods your child will use here
Each one is the same method wherever it turns up, so it is worth learning once.
More in Primary 5
Other topics in the same year, so you can see what sits either side of this one.
Struggling with the working rather than the topic itself? How to help your child with problem sums
See how your child is doing on this topic
StudyLah marks each step separately, so you can see whether it was the setup or the arithmetic that cost the mark.