11 plus Fractions of Shapes questions

What a Fractions of Shapes question looks like

In the 11 plus, a Fractions of Shapes question shows your child a drawn figure divided into equal parts, with some of those parts shaded, and asks what fraction of it is shaded. The number they need is not written anywhere in the words: they have to count it off the figure first. That is what separates this topic from Fractions of Amounts, where the quantity is handed to them in the question, and it is why a child who is fluent with fractions on paper can still drop marks here.

The figures stay simple. A rectangle ruled into equal strips. A square cut into four. A circle divided into halves, or into eight, ten or twelve equal sectors. A triangle made of three smaller triangles, a hexagon made of six, a pentagon in five parts. Many are grids: a rectangle ruled into rows and columns, where the first job is working out how many small squares there are altogether. Totals run from two parts up to twenty-four, and there are five options with one right.

The asking varies more than the pictures do. Most questions want the shaded fraction, and most of those add “give your answer in its simplest form”. Several ask for the fraction that is NOT shaded. Some run the other way, giving the fraction and asking for a count: three quarters of a twenty-cell grid is shaded, so five cells are not. A few take two steps, shading a fraction and then shading more of the rest. One kind gives a child’s claim, such as “more than two thirds is shaded”, and asks whether it holds.

Example one: a rectangle in six equal strips

Picture a rectangle ruled into six equal strips side by side. The first three strips are shaded and the last three are white. What fraction is shaded, in its simplest form?

Count the parts first: six altogether, and three of them shaded. That is 3/6. Now simplify. The biggest number that goes into both 3 and 6 is 3: 3 divided by 3 is 1, and 6 divided by 3 is 2. The answer is 1/2.

The wrong option that catches children is 3/6 itself, correct but not finished. When the question says simplest form, an unsimplified answer scores nothing. The other tempting one is 6/3, from writing the two numbers the wrong way round.

Example two: a grid with four rows and five columns

Now picture a rectangle ruled into four rows and five columns, making twenty small squares. In each row the two cells on the left are shaded and the three on the right are white. What fraction is shaded, in its simplest form?

Do not count all twenty cells one by one. Four rows of five is 4 times 5, which is 20, and that is the bottom number. Two shaded in each of the four rows is 2 times 4, which is 8. So 8 out of 20 are shaded. Divide both by 4: 8 divided by 4 is 2, and 20 divided by 4 is 5. The answer is 2/5.

Two wrong options are built for it. One is 8/20, right but unsimplified. The other is 3/5, the white part of the grid, easy to reach for if your child has been looking at the twelve white cells rather than the eight shaded ones.

Example three: a circle in ten sectors

Picture a circle cut into ten equal sectors, like a cake cut into ten slices, with four of the slices shaded. What fraction of the circle is NOT shaded, in its simplest form?

The word NOT is the whole question. Four sectors are shaded, so the unshaded ones are 10 take away 4, which is 6. That gives 6/10. Both numbers divide by 2, so 6 divided by 2 is 3 and 10 divided by 2 is 5. The answer is 3/5.

The wrong option here is 2/5, a cruel one: it is the shaded fraction, 4/10, tidied up, so a child who counted carefully and simplified correctly still lands on it. Everything about it is right except which question it answers.

How to answer it

1. Count the total number of equal parts and write it as the bottom number. For a grid, multiply the rows by the columns rather than counting cell by cell, which is where miscounts start.
2. Count the shaded parts and write that as the top number. Count in a fixed order, along each row or round the circle, never hopping about.
3. Read the question again and check whether it wants the shaded parts or the unshaded ones. If unshaded, take the shaded count away from the total first.
4. Simplify if the question asks for the simplest form. Find the largest number that divides into both the top and the bottom, rather than halving over and over.
5. Sense-check against a half. If more than half the figure is coloured in, the answer has to be bigger than 1/2. That catches a flipped fraction on the spot.

Common mistakes

• Giving the right fraction unsimplified. 3/6 for 1/2, 8/20 for 2/5, 10/15 for 2/3. The unsimplified version is nearly always one of the five options, the most common way a correctly counted question is lost.
• Answering shaded when the question said unshaded. Both fractions appear in the options, and often both are simplified, so nothing about the wrong one looks wrong.
• Writing the fraction upside down. 6/3 instead of 1/2, 5/3 instead of 3/5. The parts shaded always go on top and the total always goes underneath.
• Using the rows or the columns as the total. With three rows and four columns, some children write the bottom number as 3 or 4 rather than 12. The total is every small square in the grid.
• Assuming every fraction simplifies. A grid of two rows and six columns with seven cells shaded gives 7/12, already as simple as it goes, because nothing divides into both 7 and 12.

How to practise 11 plus Fractions of Shapes questions

The useful thing to practise here is the counting, not the fractions. Most children in Year 5 can simplify 8/20 on sight, and the marks go instead on a miscounted grid or on answering the shaded half of a question that asked for the unshaded half. So when one comes back wrong, ask your child which part went wrong: the count, the reading, or the simplifying. Nine times out of ten it is one of the first two, and a child who knows that about themselves fixes it faster than one working through twenty more fraction sums. Short and regular beats long and occasional across eleven plus preparation, which is the pattern we set out in how much 11 plus practice a child needs each day. 11+ Daily has a Fractions of Shapes project alongside the other maths topics, on laptop, tablet or phone, and the full list sits on our 11 plus maths practice page. Every question is original to 11+ Daily, nothing is a past paper and nothing is licensed from another publisher, and the bank is re-checked in rounds.

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