Primary 5 · Mathematics

P5 fractions and division

One sentence pattern causes most of the lost marks in this topic. Here is what it looks like, and how to spot it at the kitchen table.

Level
P5
Usually taught
Term 1
Covers
6 concepts

What changes at P5

In Primary 5, fractions stop being about naming and comparing and start being about operating. Your child multiplies a fraction by a whole number, multiplies a fraction by another fraction, and handles questions where fractions sit alongside addition, subtraction and division in one go.

The real shift is that a fraction becomes a way of tracking a quantity through several steps, rather than the answer itself. That is a change in what the maths is for, not just a harder version of P4.

The sentence that costs the mark

Aiden had $60. He spent 25\frac{2}{5} of it on a book, then 13\frac{1}{3} of the remainder on lunch. How much did he spend on lunch?

What the working usually does

13\frac{1}{3} of$60=$20

Takes the third of the starting amount.

What the question asked

13\frac{1}{3} of$36=$12

Takes it of what was left after the book.

Both look like correct working, and neither has an arithmetic error. That is why this one is so hard to catch over a child's shoulder: the mistake is in the setup, and the setup is one word long.

A third of the remainder is one unit, not one of the original five.

The same question, worked properly

  1. Find one unit

    5 units = $60, so 1 unit = $60 ÷ 5 = $12

    The denominator of the first fraction chooses the unit. Fifths, so five units.

  2. Take out the book

    book = 2 units = $24

    Two of the five units. Most children are comfortable to here.

  3. Count what is actually left

    remainder = 3 units = $36

    This is the step that fails. The next fraction is of this, not of the $60. Skip this line and the answer becomes $20, with working that still looks tidy and correct.

  4. Take a third of the remainder

    13\frac{1}{3} of 3 units = 1 unit = $12

    This is why the model is worth drawing: a third of three units is one unit, and the answer arrives without any new arithmetic.

How can you tell it has clicked?

You do not need to be able to do the maths to check this. Ask your child to draw the question before solving it: a bar split into the parts the question describes.

If they can draw it, they have understood it. If they cannot draw it but still produce an answer, they have matched the question to one they have seen before, and that holds up right until the numbers move.

One thing to try tonight

Read the question aloud together and stop at every fraction to ask one thing: "a third of what?"

That is the whole intervention. It targets exactly the step that fails, it takes a minute, and it works even if you have not touched fractions in twenty years. If they cannot answer, go back one sentence and ask what was left at that point.

What your child will meet in this topic

  • Fraction × Whole
  • Fraction × Fraction
  • Mixed Fraction Maths
  • Fraction Units
  • Redistributing Fractions
  • Fractions of Remainder

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

This is the foundation for ratio and percentage, which arrive later in P5 and run through the whole of P6. All three are one idea (a part compared to a whole) in different notation.

A child who is comfortable asking "of what" here tends to find ratio straightforward. A child still guessing usually meets the same wall in P6, where the questions are longer and the guess travels further.

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.