Primary 5 · Mathematics
P5 whole numbers and four operations
Every number in 5 + 3 × 10 is small, and the answer still comes out wrong more often than right. The reason is not the arithmetic. It is the order the two operations are done in.
- Level
- P5
- Usually taught
- Term 1
- Covers
- 3 concepts
What changes at P5
At Primary 5, the four operations get combined in one line: a sum with adding, multiplying, and sometimes brackets, all together. Your child has done each operation for years. The new skill is deciding which one to do first.
The order is fixed: brackets first, then multiplication and division, then addition and subtraction. Get the order right and the arithmetic is easy. Get it wrong and every number can be correct while the answer is not.
The sentence that costs the mark
Work out 5 + 3 × 10.
What the working usually does
add first5 + 3 × 10=80
Adds the 5 and 3 because they come first, then times 10. The arithmetic is fine, the order is not: × binds tighter than +.
What the question asked
times first5 + 3 × 10=35
Does 3 × 10 first, because × and ÷ come before + and −, then adds the 5. Thirty-five, not eighty.
Both are two clean operations on the same three numbers, and 80 is a believable answer. Nothing in the arithmetic is wrong. Only the order is, and the order is the whole topic.
The same question, worked properly
Look for brackets, then × and ÷
no brackets, so find the × firstScan the line: brackets first (none here), then multiplication and division. They are done before addition and subtraction, wherever they happen to sit in the line.
Do the multiplication first
3 × 10 = 30This is the step that fails. The 3 × 10 is worked as one amount before any adding, because × and ÷ bind tighter than + and −. Folding the 5 in first is the whole error.
Then the addition
5 + 30 = 35Now add the 5 to the block of thirty. Thirty-five, not eighty.
How can you tell it has clicked?
You do not need to do the sum to check this. Read 5 + 3 × 10 aloud and ask your child what they do first. The right answer is the 3 × 10, every time, before the adding.
A child who understands reaches for the multiplication first, wherever it sits in the line. A child who starts at the left and works across has the habit that quietly turns 35 into 80.
One thing to try tonight
Read the sum aloud with the multiplication as one chunk: "five, plus three tens." Said that way, nobody folds the five in first, because "three tens" is obviously one amount already.
Try it on any mixed sum in the homework. Say the × or ÷ part as a single thing first, then the rest. Understanding it that way sticks better than a memorised acronym.
What your child will meet in this topic
- Multiplying by 10s
- Dividing by 2-Digit
- Order of Operations
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
Order of operations runs under everything numerical that follows: fractions and decimals in one expression, then algebra in secondary school, where 5 + 3n means the same thing and the same order applies.
A child who does the multiplication first, by habit, carries that all the way up. A child who works left to right meets the same slip again the moment expressions get longer.
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 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.