Year 3 · Fractions of an amount
Is a third bigger than a quarter?
The homework asks which is more: a third of 12, or a quarter of 16. Your child answers a third of 12, straight away and without checking. As fractions they are right — a third is bigger than a quarter. As amounts, both come to 4.
Why the mistake is a smart one
Your child has recently learned something correct and reasonably hard: a third is bigger than a quarter, because splitting something into fewer pieces makes each piece larger. Share one pizza three ways and you get more than sharing it four ways.
They have applied that rule cleanly. The trouble is that the homework asked a different question — about amounts, not fractions — and the two starting numbers are not the same. The 12 and the 16 are doing the quiet work here, and nothing in the wording points at them.
Worth saying out loud: the fraction they picked really is the bigger fraction. They were not guessing.
The fix: three steps that untangle it
Counters, buttons or dried pasta on the table beat anything abstract here.
Step one — you cannot tell from the fractions alone. When the starting numbers are different, the only way to compare is to work out each amount separately. Put 12 things in one pile and 16 in another, so the difference is visible before any sharing starts.
Step two — a third of 12. The bottom number tells you how many equal groups to share into. A third means three groups, so deal the 12 counters into three piles, one at a time, like dealing cards. Count one pile: four.
Step three — a quarter of 16. A quarter means four groups, so deal the 16 counters into four piles. Count one pile: four again. More to share, shared more ways, same answer. Your child will often spot that before you say it.
What to say tonight
- “What does the bottom number tell us to do?”
- “Share the 12 into 3 equal groups — how many in each?”
- “Now do the same with 16 into 4 groups. What do you notice?”
How SmartMaths handles it
More than 80 Year 3 questions in our bank carry this exact mix-up — judging by the fraction instead of the amount is the most common error in the year. The wrong answer itself is labelled with it, so when a child taps “a third of 12” the app knows what they meant by it, not just that they were wrong.
It does not simply mark it. A calm panel opens over the question and walks the sharing method three steps at a time, deliberately on a second example rather than the child’s own, so they still get to finish theirs. If it has not landed, “Explain it differently” re-teaches the same question another way — a number line, a bar model, a quick sketch — until one of them clicks. The rest of the year is on our Year 3 maths practice page.
SmartMaths is very affordable tutor-style maths at home — it explains mistakes the way a tutor would; free trial at smartmaths.ai.
Common questions
How do you find a fraction of a number?
Share the total into as many equal groups as the bottom number says, then count as many groups as the top number says. For two thirds of 12, share into three groups of four and take two of them: eight.
Is a third bigger than a quarter?
As fractions of the same whole, yes — a third of a pizza is a bigger slice than a quarter of the same pizza. As amounts it depends what you are taking it of, which is exactly why a third of 12 and a quarter of 16 both come to 4.
What should a Year 3 child be able to do with fractions?
Find unit and simple non-unit fractions of amounts, recognise that the bottom number sets how many equal shares there are, and compare fractions that share a denominator. Understanding that the starting number changes the answer is part of that same step up.