11 plus Line Graphs & Pie Charts questions

What a Line Graphs & Pie Charts question looks like

A Line Graphs & Pie Charts question in the 11 plus puts one figure on the screen and asks a single thing about it, with five options underneath. About half use a line graph, half a pie chart. What separates the type from the paper’s other data questions is that no value is a bar standing on its own: a line graph tracks one quantity as it changes, so the slope and the flat stretches carry meaning as well as the points, and a pie chart prints no numbers, so every slice has to become a fraction of the whole before any arithmetic starts.

The line graphs run over time or over a scale: temperature through a day, a baby’s weight week by week, a town’s population by decade, pounds converted into euros. They ask for the value at one point, the point where a value is first reached, the change between two points, the steepest rise, a total across several points, and sometimes a time past the end of the line, where your child works out the rate and carries it on.

The pie charts use friendly shares: halves, thirds, quarters, fifths, sixths, or percentages such as 32% and 26%. Four jobs come up. Find a slice’s value from a stated total, work back from one slice to the total, find the slice that has not been labelled because the whole circle is 1 or 100%, or compare two slices.

Example one: reading two points off a line

Maya’s tablet time was recorded each week for six weeks. The line rises to week 5, then falls.

The question: how much more time did she spend on her tablet in week 4 than in week 2? The options are 40, 20, 30, 60 and 10 minutes.

Take one week at a time. Find week 4 along the bottom, go up to the line, then across to the minutes axis: 60. Do the same for week 2: 30. Subtract, 60 - 30 = 30 minutes.

The answer is 30 minutes.

The option that catches children is 60, from reading week 4 correctly and handing it in. “How much more” always needs two numbers and a subtraction. The other trap is 40, from reading week 5 by mistake. Writing each value down as it is read prevents that one.

Example two: the slice that is not labelled

Sixty children each chose one snack. The circle has three slices, two of them labelled.

The question: how many children chose chocolate? The options are 40, 20, 10, 30 and 15.

The whole circle is 1, so chocolate is what is left. Put both shares over the same bottom number: one half is three sixths, and three sixths and one sixth make four sixths. That leaves two sixths, which is one third. One third of 60 is 20.

The answer is 20 children.

Two wrong options are built to look right. Thirty is the crisps count, half of 60, found by a child who got a number but not the one asked for. Forty is everything except chocolate. Naming the fraction before touching the 60 keeps both away.

Example three: the flat parts of the line

A bus route was plotted as distance covered against time.

The question: for how long in total was the bus stopped? The options are 30, 15, 75, 60 and 45 minutes.

While a bus moves the distance covered goes up; while it is stopped the line goes flat. Look for every stretch where the number does not change. It stays at 5 km from 10:45 to 11:00, which is 15 minutes, and at 10 km from 11:15 to 11:45, which is 30 minutes. 15 + 30 = 45 minutes.

The answer is 45 minutes.

The tempting option is 30, from spotting the longer flat stretch and stopping there. One flat stretch is not the answer until the line has been read to the end.

How to answer it

1. Read the labels before the numbers: the words along the bottom, the words up the side, and what one step up the side is worth. On a pie chart, the slice labels and the total given.
2. Say what is wanted: one value, a change, a total, the steepest part, or a share. “How many more” and “in total” change the whole job.
3. On a line graph, go up from the bottom axis to the line first, then across to the side axis. Never straight across from the bottom axis, which is where the neighbouring value gets read by mistake. Write each number down.
4. On a pie chart, name the fraction before you use it. If a slice is unlabelled, take the labelled ones away from 1 or 100%. If a slice’s value is given, work out how many of it fit the circle and multiply.
5. Check the size of the answer: a difference must be smaller than the larger value, and one slice can never be more than the whole.

Common mistakes

• Tracing the line the wrong way. Going straight across from the bottom axis instead of up to the line and then across is the commonest error here, and it lands on a value sitting in the options.
• Reading the point next door. 8am instead of 10am, Tuesday instead of Wednesday, week 5 instead of week 4. The wrong options are built from these near misses.
• Rounding a point to the nearest gridline. If the side axis goes up in fifties and the point sits halfway between 150 and 200, it is 175, not 150.
• Judging a slice by eye. A slice that looks like a fifth is a sixth if the label says so. The printed fraction wins over the picture.
• Stopping one step early. Giving the winner’s votes when the question asked how many more they got. An option always waits for a half-finished answer.

How to practise 11 plus Line Graphs & Pie Charts questions

These are meant to be dependable marks in the eleven plus maths paper, so accuracy matters more than speed. Two habits do most of the work: tracing up to the line and then across, and naming a slice as a fraction before any number is used. When your child gets one wrong, ask which number they read rather than what they calculated. That is nearly always where it went.

11+ Daily has a Line Graphs & Pie Charts project inside its 11 plus maths practice, covering readings, changes, totals, flat and steep sections, and unlabelled slices. Every question is original to 11+ Daily, nothing is a past paper, nothing is licensed from another publisher, and the bank is re-checked in rounds. We have also written about how much 11 plus practice a child needs each day.

Questions parents ask