Complaints that primary maths is hard tend to cluster at a particular point. A child who was fine through Years 1 and 2 changes expression around Year 3, and by Years 5 and 6 the gap is unmistakable. This is not a coincidence — it is how the curriculum is structured.

What gets layered on, year by year

Fractions are not a unit that is taught once and finished. A different layer is added each year.

• Year 3 — the concept of a fraction appears. This is the stage of grasping what "so many of a whole divided equally" means.
• Year 4 — addition and subtraction of fractions with the same denominator, with decimals arriving alongside.
• Year 5 — reducing and finding common denominators brings in fractions with different denominators, and then multiplication of fractions.
• Year 6 — division of fractions, extending into ratio and proportion.

What matters here is that if a lower storey is empty, the one above it collapses. A child who skipped past "why is a fraction written like that?" in Year 3 ends up memorising the rule for common denominators in Year 5, and gives up altogether on division in Year 6. On the surface it looks like "Year 5 maths is hard". The actual hole is two years below.

Getting the answer without understanding

The commonest misreading is that a correct answer means the child understood. Fraction arithmetic keeps producing correct answers for a long time on memorised procedure alone: find a common denominator and add; for division, flip and multiply. Nothing shows up at this stage.

The hole shows itself in word problems and after the move to middle school. When a situation has to be turned into an expression, and when letters and equations arrive, a student running on memorised procedure stops dead.

How to check — do not add more problems

The fastest way to check understanding is to ask for an explanation. It is more accurate than buying another workbook.

• "What is one half? Can you draw it and explain?"
• "Why do we need a common denominator? What happens if we do not?"
• "It says divide, so why does it turn into multiply?"
• "Which is bigger, two thirds or three fifths? Explain it without calculating."

If a child gets answers right but cannot answer these, that is the hole to fill. What is needed then is not moving on but going back.

How to go back without it feeling like a demotion

Dropping back a year is hard on a child. A few approaches reduce the sting.

• Start with physical objects. Folding paper, or dividing up a pizza or cake, builds the sense of "divided equally" first.
• Put fractions on a number line. This is practice in seeing a fraction as a size, and comparisons start to feel natural.
• Ask for two methods on one problem. If two methods come out, the child has understood.
• Do not time them. Timing at the concept stage sends a child straight back to memorising procedure.

Looking at the school's basic academic ability screening result alongside this narrows down which area falls short more quickly. That process is set out in Elementary School.

In summary

The point at which children let go of primary maths is generally fractions, and the cause is generally concept, not speed. The real hole is often not in the year currently being taught but one or two years below. Before adding another workbook, try "can you explain it?" first. That one question settles most of it.