11 plus Bar Charts & Pictograms questions

What a Bar Charts & Pictograms question looks like

A Bar Charts & Pictograms question in the 11 plus shows a chart and asks one thing about the numbers in it, with five options underneath. It is either a bar chart, where each bar’s height is the number, or a pictogram, where a row of repeated symbols stands for the number and a key says what one symbol is worth. That is what separates this type from the paper’s other data questions: every number comes off a bar or a row of symbols, never off a line, a slice of a circle or a printed table.

They come in a few shapes. Read one bar, find the tallest or shortest, add several bars, take one away from another, or work back from a total to a bar that is missing. A few go further: numbers up the side left off and sizes given as a ratio, or bars covering groups such as 120 to 129 cm.

Roughly three in four are bar charts. The key is the biggest trap in the whole type: on a pictogram, one symbol never stands for one thing. It stands for 4, 6, 8, 12 or 15, and half symbols are everywhere.

Example one: a pictogram with a key

Four schools won medals at a sports day, drawn as rows of medal symbols. Each symbol stands for 6 medals, and half a symbol counts.

The question: how many more medals did School B win than School D? The options are 2, 9, 12, 15 and 18.

Work each school out on its own first. School B has four and a half symbols: 4 x 6 = 24, plus half of 6, which is 3, so 27 medals. School D has two: 2 x 6 = 12. Subtract, 27 - 12 = 15.

The answer is 15.

The option that catches children is 2, from subtracting symbols instead of medals: four and a half take away two leaves two and a half, and a child in a hurry writes 2. The key was read, then forgotten a line later.

Example two: bars that stop between the lines

A class scored points in a quiz each week for six weeks. The gridlines go up in tens, and two of the bars stop between them.

The question: what is the difference in points between Week 6 and Week 5? The options are 15, 10, 5, 25 and 20.

Read the two bars one at a time. Week 5 stops halfway between the 60 line and the 70 line, so it is 65. Week 6 stops halfway between 70 and 80, so it is 75. Subtract, 75 - 65 = 10.

The answer is 10.

The option to watch is 20, from snapping each bar to a gridline: Week 5 down to 60, Week 6 up to 80, and 80 - 60 = 20. Each bar is only 5 out, but the errors pull opposite ways, so the mistake doubles.

Example three: a chart with no numbers up the side

Five friends sent text messages in one day. The bars have no numbers up the side, so the question gives four values in words and says the five sent 100 messages between them.

The question: how many messages did Ella send? The options are 22, 20, 16, 18 and 14.

Ella’s bar cannot be read, so it has to come out of the total. Add the four you have: 28 + 14 = 42, then 64, then 82. Take that away from the total, 100 - 82 = 18.

The answer is 18.

The tempting option is 20, from one slip in the addition: a child who reaches 80 instead of 82 gets 100 - 80 = 20, and it sits in the list looking reasonable. Adding the four again in a different order settles it.

How to answer it

1. Read the labels before the numbers: the words along the bottom, the words up the side, and, on a pictogram, the key. That is the one children skip, and it decides every answer.
2. Mark what the question actually wants: one value, a total, a difference, the largest, or how many meet a rule. “How many more”, “in total” and “more than” change the whole job.
3. Write each number down as you read it off. Two numbers on paper are easier to compare than two bars.
4. If a bar stops between two gridlines, work out what one gap is worth, then take the fraction of it. Halfway up a gap of 10 is 5. Three quarters of a gap of 20 is 15.
5. Check the answer against the chart. A difference must be smaller than the larger of the two values, and a total no smaller than the tallest bar in it.

Common mistakes

• Counting symbols instead of counting things. Four and a half symbols take away two is two and a half symbols, not two and a half medals. Turn every count into a real number with the key first.
• Dropping the half symbol, or rounding it up. Two and a half symbols with a key of 4 is 10. Ignore the half and you get 8; round up and you get 12. Both sit in the options.
• Reading the nearest gridline instead of the bar. If the lines go up in tens and the bar stops halfway, the answer is not 40 and not 50, it is 45.
• Answering a different question. Giving one bar’s total when the question wanted the difference between two is the commonest error here, and it is always among the options.
• Giving the height of the tallest bar instead of what it stands for. If a chart counts how many pupils read 0, 1, 2 or 3 books and asks which number was most common, the answer is the label under the tallest bar.

How to practise 11 plus Bar Charts & Pictograms questions

These are among the most reliable marks in the eleven plus maths paper, so the aim is accuracy rather than speed. Two habits do most of the work: reading the key out loud before touching a pictogram, and writing each value down as it is read.

11+ Daily has a Bar Charts & Pictograms project inside its 11 plus maths practice, covering single values, totals, differences, pictograms with a key, and charts with no numbers up the side. 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.

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