Fractions With Guided Practice

The single error that costs the most marks

Put 1/3 + 1/4 in front of a Year 7 class and a predictable share of the room writes 2/7. It is not carelessness and it is not a gap in effort. It is a rule being carried across from somewhere it worked. In whole numbers you combine the things in front of you. In fraction multiplication you genuinely do go straight across the top and straight across the bottom. Addition is the one place that pattern fails, and nobody warns the child that it will.

The thinking behind 2/7 is also internally consistent, which is why telling a child they are wrong rarely fixes it. They have to see the contradiction themselves: 1/3 is already bigger than 2/7, so an addition has made the number smaller. That question does more than a correction.

Why equivalence sits underneath everything else

A fraction carries two meanings at once. Three quarters is three parts of a whole that was cut into four, and it is also 3 divided by 4. Children who only ever met the first meaning stall the moment fractions turn up as points on a number line or as operators, as in "three fifths of forty".

Equivalence is the bridge. Multiply the numerator and the denominator by the same number and the value does not move, which is why 3/4 and 6/8 are the same quantity written twice. Run it backwards and you are simplifying: 10/15 becomes 2/3 because five divides both parts. The error worth watching here is dividing the top and the bottom by different numbers, or by a number that does not go into both — 10/15 comes back as 2/5 or 5/3 and the child cannot see why it is wrong.

Making the denominators agree

Adding fractions that already match is the easy case: 3/8 + 2/8 is five of the same thing, so 5/8, and the denominator does not move because the size of the pieces has not changed. That sentence is the whole rule, and a child who can say it out loud will not add denominators later.

When the denominators differ, they have to be rewritten as the same size of piece first. For 1/3 + 1/4, the lowest common multiple of 3 and 4 is 12, so 1/3 becomes 4/12, 1/4 becomes 3/12, and the total is 7/12. Multiplying the two denominators together always produces a common denominator, though not always the lowest one; for 2/3 + 1/5 it happens to give the lowest, fifteen, and the answer is 13/15. Subtraction is the same procedure with one sign changed, so 3/4 − 1/3 is 9/12 − 4/12, which is 5/12.

What one wrong answer points back to

A wrong answer on an addition with unlike denominators is not one gap. It could be any of three earlier skills, and the maths check follows them rather than guessing.

That last column is the part parents find most useful. If the follow-up on the lowest common multiple also fails, the fractions lesson is not the problem — factors and multiples are, and no amount of fraction practice will fix it.

Multiplying and dividing feel wrong, and that is the clue

Two results offend everyone the first time. Multiplying 2/3 by 1/4 gives 1/6, which is smaller than either fraction. Dividing 1/2 by 1/4 gives 2, which is bigger than both. Neither is a trick. Multiplying by a fraction means taking a part of something, so the result shrinks. Dividing asks how many of the second fraction fit inside the first, and four quarters fit in a whole, so two fit in a half.

Children who learn "keep, change, flip" without that sentence will apply it to the wrong operation within a fortnight.

Where fractions come back later

Fractions are not a topic that ends. Three quarters is 0.75 and three fifths is 60 per cent, so percentage work inherits every fraction weakness intact. Finding 25 per cent of 60 is finding a quarter. Sharing £60 in the ratio 2 to 1 needs the same multiplicative thinking. And algebra puts letters on top of the same denominators, so a child who never settled 1/3 + 1/4 will not settle x/3 + x/4 either.

How practice works when a fraction question goes wrong

Help arrives in four steps rather than all at once: a nudge about where to look, then a question back, then a partly worked structure, then a full comparable example. A first wrong answer produces a different question on the same skill. A second brings a longer explanation. A third moves to a step-by-step walkthrough. The order matters, because the finished answer arriving early ends the thinking that the question existed to provoke.

What this page is not claiming

This is not a scheme of work and it is not aligned to any exam board specification. It covers the fraction skills the check actually tests, which stop well short of everything a secondary maths department teaches in a year.

FAQ: Questions parents ask about fractions

My child can do fractions on a worksheet but not in a word problem.

Then the fraction work is fine and the translation is not. Worksheets tell the child which operation to use by sitting it in a column of identical questions. A word problem does not. Practise turning sentences into calculations without doing the calculations at all.

Should I teach the cross-multiply shortcut?

Only after the common denominator method is secure. The shortcut gives a correct answer while hiding the reason, and the reason is what percentages, ratio and algebra will ask for later.

Are fraction walls too babyish for Year 7?

No. A child who cannot see that 1/3 is larger than 2/7 needs a picture more than they need another exercise. The visual is not remedial, it is the evidence.

How long should fraction practice take?

Short and repeated beats a long session. Getting a fraction question right three days after the last one is much stronger evidence than getting six right in a row on the same evening.