Pictograms

Read a pictogram with its key, find totals and differences, draw part symbols, and work out a missing key.

In the exam for Edexcel IGCSE Maths 4MA1, Cambridge IGCSE Maths 0580, Cambridge O Level Maths 4024 · 24 real past-paper questions below

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What a Pictogram Is

A pictogram uses little symbols to show how many. The key tells you what one whole symbol is worth.

Part of a symbol is worth part of the key. With a key of 8:

You see	It is worth
one whole symbol	8
half a symbol	4
a quarter of a symbol	2
three quarters of a symbol	6

Rule

Read the key first. Every answer starts from it.

Reading One Row

The 1-mark question: how many on one day? Count the whole symbols, times by the key, then add the part symbol.

Key: one circle stands for 8 books. Tuesday shows 3 and a half circles.

Worked example

1
$Key: 1 circle = 8$ — Read the key first. Every circle is worth 8 books.
2
$3 \times 8 = 24$ — Tuesday has 3 whole circles. Each one is 8 books, so times 3 by 8.
3
$\frac{1}{2} \times 8 = 4$ — The half circle is worth half the key. Half of 8 is 4.
4
$24 + 4 = 28 books$ — Add the whole circles and the part circle. That is the number of books on Tuesday.

Common mistake

Counting symbols and stopping: 3.5 is the number of circles, not the number of books.

Key idea

Which day was least? Pick the shortest row. No sums needed.

Totals and How Many More

The 2-mark question: a total, or how many more on one day than another. Turn each row into a number first.

Worked example

1
$20 + 28 + 16 + 36 + 12$ — Turn each row into books (circles × 8), then write the five days, Monday to Friday, as one sum.
2
$= 112 books$ — Add them. This is the total for the whole week.
3
$2.5 + 3.5 + 2 + 4.5 + 1.5 = 14 circles$ — Check another way: count every circle in the pictogram, the halves too.
4
$14 \times 8 = 112$ — 14 circles at 8 books each gives the same 112, so the total is right.
5
$Thu - Fri = 36 - 12$ — “How many more on Thursday?” means take away. Use the books, not the circles.
6
$= 24 books$ — 36 − 12 = 24, so Thursday sold 24 more books than Friday.

Common mistake

Taking the rows away as symbols and forgetting the key: 4.5 − 1.5 = 3 circles is 24 books, not 3.

Key idea

“Sam says they sold more than 100 books. Is he right?” Work out the number, then write Yes or No with it: “Yes, 112 is more than 100.” A Yes or No on its own scores nothing.

Showing a Number on the Pictogram

The 1-mark question: "Show this on the pictogram." Divide the number by the key. The whole part is whole symbols. The rest is a part symbol.

Worked example

1
$12 \div 8 = 1.5$ — Friday is 12 books. Divide by the key to find how many circles that is.
2
$1.5 = 1 + \frac{1}{2}$ — Split it. The 1 is one whole circle, and the 0.5 is half a circle.
3
$draw 1 circle and \frac{1}{2} circle$ — Draw that in Friday's row. Check: 8 + 4 = 12.
4
$14 \div 8 = 1.75$ — Now suppose it were 14 books. Divide by the key again.
5
$1.75 = 1 + \frac{3}{4}$ — 0.75 is three quarters, so draw one whole circle and three quarters of a circle. Check: 8 + 6 = 14.

Common mistake

Drawing 12 circles, or a half circle for any leftover. The part must match: 6 out of 8 is three quarters.

A Missing Row From the Total

Exams often give the total and leave one row blank. Find the blank row's number, then draw it. This is often worth 3 marks.

Key: one symbol stands for 6 loaves. Monday 2½, Tuesday 1½, Wednesday 3 symbols. Thursday is blank. Monday to Thursday sold 57 loaves.

Worked example

1
$2.5 + 1.5 + 3 = 7 symbols$ — Count the symbols in the rows you can see: Monday, Tuesday and Wednesday.
2
$7 \times 6 = 42$ — Turn them into loaves with the key: 7 symbols at 6 loaves each.
3
$57 - 42 = 15$ — The 57 includes Thursday, so take the known rows away. Thursday is the 15 left over.
4
$15 \div 6 = 2.5$ — To draw it, divide by the key. 15 loaves is 2.5 symbols.
5
$draw 2 symbols and \frac{1}{2}$ — Draw 2 whole symbols and a half in Thursday's row. Check: 42 + 15 = 57.

Common mistake

Taking symbols away from loaves: 57 − 7 = 50 mixes two different things. Change symbols into loaves first.

Key idea

Write every line down. Most of the marks are for the working, and the drawing is marked from your own number. So one slip still leaves you most of the marks.

Finding a Missing Key

The 3 or 4-mark question: the key is not given, but one row's number is. Divide that number by the symbols in its row.

Worked example

1
$Mon = 2.5 circles = 20$ — The fact you are given: Monday's 2 whole circles and a half stand for 20 books.
2
$20 \div 2.5 = 8$ — Share the 20 books equally between the 2.5 circles. So one circle is 8 books.
3
$2.5 \times 8 = 20$ — Check: times back. It gives Monday's 20, so the key is right.
4
$14 \times 8 = 112$ — Now the key is known, any row or total follows. The pictogram has 14 circles in all, so 112 books.

Common mistake

Dividing 20 by 2 and ignoring the half circle. Count part symbols in the row too.

When you are told a difference instead

A toy shop: “Friday sold 18 more toys than Thursday.” Thursday has 1½ symbols, Friday 3¾. Find Monday, which has 2¾.

Worked example

1
$3.75 - 1.5 = 2.25 symbols$ — The 18 is the gap between the two rows, so find the gap in symbols too.
2
$18 \div 2.25 = 8$ — Divide the number by its symbols, as before. So one symbol is 8.
3
$Mon = 2.75 \times 8 = 22$ — Use the key on the row you are asked about. Monday has 2¾ symbols, so 22 toys.

Key idea

Symbols drawn as 4 small squares? Count small squares instead: Friday 15, Thursday 6, a gap of 9. So 9 small squares are 18, one small square is 2, and a whole symbol is 8.

Which Method? Read the Question

Find the key first, then match the wording.

You see	You do
How many on one day?	symbols × key
Which day most or least? The mode?	longest or shortest row
Total, or how many more?	each row as a number, then add or take away
Is he right?	work out the number, then Yes or No with it
Show this on the pictogram	number ÷ key, draw wholes and a part
Total given, one row blank	total − the other rows, then ÷ key to draw
Key missing, one row given	row's number ÷ its symbols
Key missing, a difference given	difference ÷ gap in symbols
Bars instead of symbols	Bar Charts and Composite Bar Charts

Key idea

For a total, count all the symbols first, then times by the key once: 14 × 8 = 112.

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