Primary 3 · Mathematics

P3 fractions

The first fraction mistake most children make is calling 1/4 bigger than 1/3 because 4 is bigger than 3. Here is why the opposite is true, and how to show it at the kitchen table.

Level
P3
Usually taught
Term 3
Covers
4 concepts

What changes at P3

In Primary 3, fractions begin. Your child names a fraction, finds equal fractions like 1/2 and 2/4, compares two fractions, and adds or subtracts fractions that already share a bottom number. Comparing is where the first real misconception shows up.

The idea that carries everything later: the bottom number names the size of each piece, it is not a count that behaves like a whole number. Get that right in P3 and the heavier fraction work in P4 and P5 has something solid to stand on.

The sentence that costs the mark

Which is bigger, 13\frac{1}{3} or 14\frac{1}{4}?

What the working usually does

bigger bottom13\frac{1}{3} or 14\frac{1}{4}=14\frac{1}{4}

Picks 1/4 because 4 is bigger than 3. That is exactly how whole numbers work, so it feels safe and nothing looks careless.

What the question asked

bigger piece13\frac{1}{3} or 14\frac{1}{4}=13\frac{1}{3}

Picks 1/3 because thirds are bigger pieces. The same whole cut into fewer parts leaves each part larger.

Both answers look reasonable, and 4 really is bigger than 3, so the slip passes unnoticed. But cut one bar into 3 and another into 4, and the thirds are plainly the wider pieces. The bottom number counts the pieces, and more pieces means each one is smaller.

Two equal wholes, one cut into thirds and one into quarters. The shaded third is the wider piece, so 1/3 is the bigger share.

The same question, worked properly

  1. What the bottom number means

    3 equal pieces vs 4 equal pieces

    The bottom number, the denominator, says how many equal pieces the whole is cut into. Thirds cut it into 3, quarters into 4.

  2. More pieces means smaller pieces

    more pieces = smaller pieces

    This is the step that fails. Cut the same whole into 4 and each piece is smaller than cutting it into 3. This is the step the "4 is bigger than 3" habit skips, and it is where the mark is lost.

  3. So the third is the bigger share

    13>14\frac{1}{3} > \frac{1}{4}

    One third is bigger than one quarter. Draw two equal bars, one in thirds and one in quarters, and the shaded third is clearly the wider piece.

How can you tell it has clicked?

Ask which is bigger, 1/3 or 1/4. If they say 1/4 straight away, that is the exact slip: they read 4 as the bigger number. If they stop to picture the pieces, they have understood it.

The check that settles it: would you rather share a pizza between 3 people or 4? Fewer people, bigger slice. A child who sees that rarely leaves 1/4 as the bigger fraction.

One thing to try tonight

Share one chocolate bar between 3 people, then imagine sharing it between 4. With more people, each share is smaller. The bottom number is the number of people.

Then ask the one question that fixes it: more pieces, is each piece bigger or smaller? Once that answer is "smaller", the bigger-bottom mistake stops on its own.

What your child will meet in this topic

  • Equivalent Fractions
  • Comparing Fractions
  • Like Fractions
  • Unlike Fractions

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

Comparing fractions is the groundwork for equivalent fractions and for adding unlike fractions in P4, where the pieces have to be made the same size before they combine. The "what size is each piece" habit runs through all of it.

A child who compares by piece size rather than by the bottom number tends to stay accurate when fractions get multiplied and divided in P5 and P6, where the same misread costs a whole answer.

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 3

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.

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