Lesson 3 of 8 · Grades 3 to 5
Picture graphs
A picture graph uses small pictures instead of bars. The key tells you what one picture is worth, so a few pictures can stand for a large number.
Pictures instead of numbers
A picture graph uses a small picture for each group of items. Instead of writing 10 books, it shows three stars and explains what one star is worth. The line that explains the picture is called the key, and the key is the most important part of the graph.
A picture graph is great for showing at a glance which row is longest. It also keeps the numbers small, because one picture can stand for 2, 5 or even 10 items. That is why you often see picture graphs in newspapers and on classroom walls.
Read the key first
Before you count anything, read the key. This graph has the key "Each star = 2 books". One star is worth 2, two stars are worth 4, and five stars are worth 10.
Show the data as a table
| Name | Stars | Books |
|---|---|---|
| Ana | 5 | 10 |
| Ben | 3.5 | 7 |
| Cara | 4 | 8 |
Each star stands for 2 books.
Ana drew 5 stars, so Ana read 5 × 2 = 10 books. Cara drew 4 stars, so Cara read 8 books. Ben drew 3 full stars and a half star. Three stars are worth 6 books, and a half star is worth half of 2, which is 1 book. Ben read 6 + 1 = 7 books.
Half a picture
A half picture always shows half of the key. If one star stands for 10 tickets, half a star stands for 5 tickets. If one star stands for 4 points, half a star stands for 2 points. The half picture is not half of the row, and it is not a mistake: it lets the graph show a number that sits between two whole pictures.
You can also work the other way. If the key is 4 tickets and a row shows 2 full stars and a half star, the value is 4 + 4 + 2 = 10 tickets. Always go back to the key before you decide what a picture is worth.
A bigger key
When the numbers are large, the key gets larger too. Here one star stands for 4 tickets, so a row of a few stars can show a large total.
Show the data as a table
| Name | Stars | Tickets |
|---|---|---|
| Blue | 3 | 12 |
| Green | 2.5 | 10 |
| Red | 4 | 16 |
Each star stands for 4 tickets.
Red sold the most tickets: 4 × 4 = 16. Blue sold 3 × 4 = 12, and Green sold 2.5 × 4 = 10, which is the same as 2 × 4 + 4 ÷ 2 = 8 + 2 = 10. The rows are easy to compare even though every number is a multiple of four.
Making your own key
To draw a picture graph, choose a key that makes the pictures a sensible number. If the biggest value is 20 and you want about five pictures, a key of 4 works well. If the biggest value is 50, a key of 10 keeps the row short. The key must stay the same for every row: a graph that changes its key halfway down cannot be read.
Worked example
Each star stands for 4 points. Amir has 3 full stars and half a star. How many points does Amir have?
Step 1: read the key. One star stands for 4 points.
Step 2: count the whole stars. 3 × 4 = 12 points.
Step 3: work out the half star. Half of 4 is 4 ÷ 2 = 2 points.
Step 4: add the parts. 12 + 2 = 14 points, and check that a half star can only ever add 2.
Answer: 14 points.
Watch out for this
Count the pictures first and multiply by the key afterwards. It is easy to read four stars as four items when each star is really worth 5. Also remember that a half star is half of the key, not half of the row.
Remember
- The key tells you what one picture is worth.
- Count the whole pictures, then multiply by the key.
- A half picture is half of the key.
- The key must be the same for every row.
Try it
Answer the five questions below. Work them out first, then open each answer to check.
-
Each star stands for 2 books. A shelf shows 6 stars. How many books is that?
Show answer
12 books. 6 × 2 = 12.
-
Each star stands for 5 stickers. A row shows 4 stars. How many stickers is that?
Show answer
20 stickers. 4 × 5 = 20.
-
Each star stands for 10 points. A row shows 3 stars. How many points is that?
Show answer
30 points. 3 × 10 = 30.
-
Each star stands for 4 tickets. A row shows 3 full stars and a half star. How many tickets is that?
Show answer
14 tickets. 3 × 4 = 12, and a half star is 4 ÷ 2 = 2. So 12 + 2 = 14.
-
Each star stands for 2 goals. The graph shows 10 goals. How many stars is that?
Show answer
5 stars. 10 ÷ 2 = 5.
Puzzle · Picture puzzle
Puzzle time
Each star stands for 4 tickets. The Blue team row has 3 full stars and 1 half star. How many tickets did the Blue team sell?
Show a hint
A whole star is worth 4 tickets. A half star is worth half of 4.
Show the answer
Answer: 14. Three whole stars are 3 × 4 = 12 tickets, and a half star is 4 ÷ 2 = 2 tickets. 12 + 2 = 14 tickets.