From P4 to P5 Maths: What Actually Changes

8 September 2026 · by Larry

There is a version of this story that repeats every year. A child gets through P4 comfortably enough. Then a P5 paper comes home with more red on it than they have ever seen, and nobody can quite say what happened. They still know their tables. They can still do the sums when you set them out. But the questions have started beating them.

I wrote a while ago about what changes between P2 and P3, which is mostly about reading and about questions becoming multi-step. P4 to P5 is a different jump, and it catches a different child — often one who was doing fine before.

1. The numbers stop being whole

Up to P4, most of what a child handles is whole numbers, with fractions and decimals appearing as their own separate topics. From P5 the fractions, decimals, percentages and ratios stop being topics and become the ordinary furniture of every question.

The important part is not that each of those is harder. It is that they arrive together. A single question can give you a fraction, ask for a percentage and expect the answer as a decimal, and a child who is comfortable with all three separately can still lose the thread when they have to move between them mid-question.

If fractions were already shaky before this point, P5 is where that quietly becomes the whole problem. There is more on that in when fractions stop making sense, and it is worth going back to rather than pushing on.

2. "Of the remainder" — the phrase that eats the most marks

If you learn one thing to look out for this year, make it this one.

P4 questions tend to take a fraction of the original amount. P5 questions take a fraction of what is left, and then very often take a fraction of what is left after that. She spends a quarter of her money, then half of the remainder, then a third of what remains.

A child reading quickly takes every fraction of the starting amount, because that is what every question did last year. The working looks careful. The arithmetic is correct. The answer is wrong, and they cannot see why, because nothing they did was a mistake in the way they understand mistakes.

This is not really a maths error. It is a reading error with maths consequences, and the cure is a habit rather than more practice: every time the word "remainder" or "the rest" or "what was left" appears, stop and say out loud what the fraction is a fraction of. Not solve it. Just say it.

3. Questions start running backwards

Most P4 problems go forwards. You are given the start and asked for the end. You do the operations in the order the sentence gives them.

P5 hands you the end and asks for the beginning. You are told what she had left and asked what she started with. That sounds like a small difference and it is not, because every instinct a child has built so far says read left to right, do what it says. Working backwards means undoing operations in reverse order, and that is a genuinely new way of thinking rather than a harder version of an old one.

This is where drawing earns its place. A bar model turns a backwards question into a picture where the missing piece is visible, which is a completely different task from holding the reversal in your head. If bar models are new to you as a parent, our guide to bar models explains what your child is being taught to do.

4. The answer stops being most of the mark

A P5 problem is often worth several marks, and the final number is only one of them. The rest are for the working — for showing what you found first, what you did with it, and why.

Two consequences follow, and children find both of them unfair. A right answer with nothing written down loses marks it did not have to lose. And a wrong answer with clear, sound working keeps marks that would otherwise have gone. I wrote about the first of those in the right answer but the marks still went, and P5 is where it stops being an occasional annoyance and becomes most of the paper.

How to tell what is actually going wrong

Take one question they got wrong. Do not explain it, and do not let them solve it.

Ask them to draw it. A bar, a line, boxes, anything. Just the picture, no working, no answer.

What happens next tells you where the problem is:

• They cannot start the drawing. They have not understood what the question describes. This is comprehension, and more sums will not touch it.
• They draw it, but the parts are wrong — the second fraction is drawn against the whole bar instead of against the remaining piece. That is the remainder trap, and it is a specific, fixable habit.
• The drawing is right and they still cannot get an answer. Now it is method. This is the one that responds to being taught.
• Everything is right and the arithmetic slipped. That is the smallest of the four problems, even though it is the one that looks worst on the page.

Most parents assume they are dealing with the fourth, because a wrong number is what you can see. In P5 it is usually the second or the third.

Why more practice sometimes makes it worse

This is the year the instinct to buy another assessment book is strongest, and the year it is most likely to backfire.

A child who is misreading "of the remainder" and does thirty more questions is not getting better. They are getting faster and more confident at doing it the wrong way, and undoing a practised habit is harder than teaching a new one. Volume only helps once the method is right; before that it entrenches whatever is there.

Ten questions where they explain what they are doing beats fifty where they do not. That is a smaller evening, not a bigger one.

Two things that genuinely help

Read the question twice, with different jobs. The first read is for the story — who, what, what happened. The second read is only for one thing: what exactly is being asked for, and what is each fraction a fraction of? Children read once and start writing. The second read costs fifteen seconds and catches most of the remainder errors.

Put the answer back into the story. If she started with $60 and the answer says she spent $80, something is wrong regardless of the working. This is a habit almost no child has and almost every one of them can learn in a week. It catches the errors that are invisible from inside the working.

The part that is not about maths

P5 is around the age children start forming an opinion about whether they are "good at maths", and once that opinion sets it is much harder to shift than any topic on the syllabus. A run of poor papers at exactly the moment the subject genuinely got harder is a very easy thing to misread about yourself.

So it is worth saying out loud, more than once, that the questions changed. Not as reassurance — as a fact, because it is one. If that conversation is already happening in your house, when your child says they are bad at maths goes into it properly.

One practical note: schools differ in how subjects are arranged at this stage, and your child's own school is the right place to ask about that. It is a separate question from the maths itself, and it is worth keeping the two apart — the work in front of them tonight is the same either way.

The short version

P5 does not ask for harder arithmetic. It asks for fractions, decimals, percentages and ratios in the same breath, for fractions of remainders rather than of wholes, for questions that run backwards, and for working that earns most of the marks. A child can be perfectly competent at the sums and lose most of a paper to those four things.

Find out which one it is before buying anything. Ask them to draw the question. The drawing tells you more in two minutes than a term of extra worksheets.

Decimals, fractions and percentages start leaning on each other around here, and a shaky decimal place value shows up in all three. See decimals: the four slips.