Primary 6 · Mathematics
P6 ratio
A ratio of 3 : 4 hides a total of 7, and the working that misses it still looks correct on the page. Here is the pattern, and the one question that checks for it.
- Level
- P6
- Usually taught
- Term 1
- Covers
- 3 concepts
What changes at P6
In Primary 6, a ratio describes how a quantity is split, not how big it is. 3 : 4 says nothing about size until the question also hands you one real amount: a total, one of the shares, or the difference between them.
That amount turns the terms into units, and units are what the rest of the topic runs on. Ratio, fractions and percentages then stop being three topics and become three notations for one split.
The sentence that costs the mark
A car park holds cars and motorcycles in the ratio 3 : 4. There are 28 vehicles in all. How many cars are there?
What the working usually does
3 out of4 parts=21 cars
Reads the second term as the whole, so takes three quarters of 28.
What the question asked
3 out of7 parts=12 cars
Adds the terms first, because 3 and 4 make 7 equal parts.
Neither column has an arithmetic error, and both end on a whole number of cars. That is what makes this one so hard to catch over a child's shoulder. The mistake happens before any calculating starts, in deciding what the 3 is being counted out of.
The same question, worked properly
Add the terms first
3 units + 4 units = 7 units in allThis is the step that fails. The whole topic turns on this line. Skip it and the 4 quietly becomes the total, which is the one error above.
Find one unit
7 units = 28 vehicles, so 1 unit = 28 ÷ 7 = 4 vehiclesThe MOE move that carries fractions, ratio and percentage alike.
Count the cars
cars = 3 units = 3 × 4 = 12 vehiclesThree of the seven units, not three of the four.
Check it back
motorcycles = 4 units = 16, and 12 + 16 = 28Worth teaching as a habit. The wrong answer fails this line instantly: 21 cars would leave 7 motorcycles, which is not the ratio the question gave.
How can you tell it has clicked?
You do not need to do the maths to check this. Point at any ratio in their homework and ask one thing: "how many equal parts altogether?"
If they add the terms without being prompted, it has landed. If they read the two numbers back to you separately, they are still seeing a pair rather than a split, and that holds up right until a total appears in the question.
One thing to try tonight
Downstairs in the carpark tonight, count the cars and the motorcycles in one row. Ask what the ratio is. Then ask how many vehicles that is altogether.
The second question is the whole intervention. It takes a minute, it needs no worksheet, and it lands on exactly the step that fails.
What your child will meet in this topic
- Ratio and Proportion
- Ratio with Fractions
- Ratio with Percent
Most Singapore schools introduce this in Term 1, 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
Ratio runs straight into percentage later in P6, and into the changing-ratio problems where one quantity stays fixed while the other moves. Same equal parts, longer question.
A child who adds the terms first without thinking about it tends to find those routine. The habit built here is most of the preparation for them.
The methods your child will use here
Each one is the same method wherever it turns up, so it is worth learning once.
The same topic in other years
It comes back each year and gets harder, so it helps to see what came before and what is coming.
More in Primary 6
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.