Lesson 4 of 8 · Grades 3 to 5
Bar graphs
A bar graph is a picture of numbers. The bar for each category stops at a height, and the numbered scale on the left turns that height into a number.
Bars with a numbered scale
A bar graph is a picture of numbers. Each category gets its own bar, and the bar stops at a height that matches its value. A numbered scale sits beside the graph, usually up the left side, so you can turn a height into a number.
The scale counts in equal steps. It might count 0, 1, 2, 3 and so on, or 0, 5, 10, 15 for larger numbers. The first number on the scale is almost always zero, because every bar is measured from the same starting line.
Reading one bar
This graph shows how many books a class read on each school day. To read a bar, find the category along the bottom, then follow the top of its bar across to the scale.
Show the data as a table
| Day | Books |
|---|---|
| Mon | 6 |
| Tue | 4 |
| Wed | 8 |
| Thu | 2 |
| Fri | 5 |
Wednesday reaches 8 on the scale, so the class read 8 books that day. Thursday reaches 2, which is the shortest bar. The numbers above the bars in this graph agree with the scale, so you can use either one to check the other.
Comparing bars
Bar graphs make comparisons easy because your eye can see which bar is taller. Wednesday is taller than Friday, so more books were read on Wednesday. Thursday is shorter than Tuesday, so fewer books were read on Thursday.
For a number answer, subtract the two values. Wednesday read 8 and Thursday read 2, so Wednesday was 8 − 2 = 6 books ahead. To find a total, add the bars: Monday 6 and Tuesday 4 make 6 + 4 = 10 books on those two days.
Reading between the lines
Sometimes the scale jumps in fives, and a bar stops between two printed numbers. This rainfall graph has a scale from 0 to 30 in steps of 5.
Show the data as a table
| Day | Rain (mm) |
|---|---|
| Mon | 15 |
| Tue | 25 |
| Wed | 10 |
| Thu | 30 |
| Fri | 20 |
Tuesday reaches exactly halfway between 20 and 30, so Tuesday had 25 mm of rain. Friday reaches 20, and Monday reaches halfway between 10 and 20, so Monday had 15 mm. When a bar lands on a line, read the number on that line; when it lands halfway, the value is halfway between the two numbers.
Adding a whole week
To find a grand total, read every bar and add the values together. The rainfall was 15 + 25 + 10 + 30 + 20 = 100 mm for the week. Check the addition in a different order to be sure: 15 + 25 = 40, and 40 + 10 + 30 + 20 = 100.
Worked example
The bar graph shows books read in May: Monday 6, Tuesday 4, Wednesday 8, Thursday 2 and Friday 5. How many books were read on Monday, Tuesday and Thursday altogether?
Step 1: read each bar named in the question. Monday is 6, Tuesday is 4 and Thursday is 2.
Step 2: add the three values. 6 + 4 = 10, and 10 + 2 = 12.
Step 3: check each bar again against the scale. Monday reaches 6, Tuesday reaches 4 and Thursday reaches 2.
Step 4: label the answer. The bars show books, so the total is 12 books.
Answer: 12 books.
Watch out for this
The top of a bar is the value, not the width of the bar. A wide bar does not mean a bigger number. Read every value by following the top of the bar across to the numbered scale.
Remember
- Each bar stands for one category.
- Follow the top of the bar across to the scale to read its value.
- The scale counts in equal steps, starting at zero.
- Add bars for a total and subtract to compare.
Try it
Answer the five questions below. Work them out first, then open each answer to check.
-
The graph shows books read each day. Wednesday is 8. How many books were read on Wednesday?
Show answer
8 books. Follow the top of the Wednesday bar across to the scale.
-
The daily numbers are Mon 6, Tue 4, Wed 8, Thu 2 and Fri 5. Which day had the most books?
Show answer
Wednesday, with 8 books. Its bar is the tallest of the five.
-
Monday is 6 books and Tuesday is 4 books. How many books on Monday and Tuesday together?
Show answer
10 books. 6 + 4 = 10.
-
Wednesday is 8 books and Thursday is 2 books. How many more books were read on Wednesday?
Show answer
6 books. 8 - 2 = 6.
-
The daily numbers are Mon 6, Tue 4, Wed 8, Thu 2 and Fri 5. How many books were read that week?
Show answer
25 books. 6 + 4 + 8 + 2 + 5 = 25.
Puzzle · Bar graph trap
Puzzle time
The bar graph shows the books read each day. Which day had exactly twice as many books as Thursday?
Show a hint
Read Thursday first, then double it. Find the day whose bar is exactly that height.
Show the answer
Answer: Fri. Thursday read 6 books. Twice 6 is 12, and Fri read 12 books, so Fri is the day.