Math Core

A bar graph uses bars instead of pictures. Longer bars mean bigger numbers, so you can compare groups at a glance. When the numbers get big, the graph uses a scale that counts by 2s, 5s or 10s instead of 1s.

Parts of a bar graph

Every bar graph has a title, a label for each bar, and a scale. The scale is the row of numbers along the side or bottom. It tells you how much each bar shows.

Definition

Scale

The scale of a bar graph is the set of numbers you read the bars against. The numbers go up by the same amount each time. A scale of 0, 5, 10, 15, 20 counts by 5s.

In this lesson, each bar is made of blue squares. One 🟦 is one step on the scale. If the scale counts by 5s, each 🟦 stands for 5.

Reading a scaled bar graph

To read a bar, find where it ends. Then read the number on the scale at that spot. With squares, you can skip count by the scale number, once for each square.

How to read a scaled bar graph

Find what the scale counts by.
Find where the bar ends. Skip count by the scale number to that spot.
Use the numbers to answer "how many more" or "how many in all."

Worked example: Favorite sports

Kids voted for a favorite sport. Scale: each 🟦 = 5 votes (0, 5, 10, 15, 20, 25, 30)

Sport	Votes
Soccer	🟦🟦🟦🟦
Basketball	🟦🟦🟦🟦🟦🟦
Swimming	🟦🟦🟦
Tennis	🟦

Soccer: count by 5s four times: 5, 10, 15, 20. 20 votes.
Basketball: $6 \times 5 = 30$ votes.
Swimming: $3 \times 5 = 15$ votes.
Tennis: 5 votes.

Basketball has the longest bar, so it got the most votes. How many more kids chose soccer than swimming? $20 - 15 = 5$ more kids.

Common mistake

Don't read the number of squares as the answer. A bar with 4 squares on a scale of 5 shows 20, not 4. Look at the scale before you read any bar.

Bars that end between numbers

On a real bar graph, the scale may only show every other number, like 0, 10, 20, 30. A bar can stop halfway between two lines. Then its value is the number halfway between them.

Worked example: Collecting cans

A class collected cans for three weeks. The scale is 0, 10, 20, 30, 40, 50.

The Week 1 bar ends right at 30.
The Week 2 bar ends halfway between 40 and 50.
The Week 3 bar ends right at 20.

How many cans did they collect in Week 2? How many in all three weeks?

Halfway between 40 and 50 is 45, so Week 2 shows 45 cans.

In all: $30 + 45 + 20 = 95$ cans.

Making a scaled bar graph

To draw a bar, divide the number by the scale. That tells you how many squares long the bar is.

Worked example: Library books

The class library has 16 story books, 10 comic books, 8 science books and 4 poem books. Make a bar graph with the scale each 🟦 = 2 books.

Story: $16 \div 2 = 8$ squares
Comics: $10 \div 2 = 5$ squares
Science: $8 \div 2 = 4$ squares
Poems: $4 \div 2 = 2$ squares

Kind of book	Books
Story	🟦🟦🟦🟦🟦🟦🟦🟦
Comics	🟦🟦🟦🟦🟦
Science	🟦🟦🟦🟦
Poems	🟦🟦

Check: story books is 8 squares, and $8 \times 2 = 16$ . ✓

Tip

To compare two bars fast, count how many more squares one bar has. Then multiply by the scale. Story has 4 more squares than Science, and $4 \times 2 = 8$ , so there are 8 more story books.

Practice

Practice 1

Scale: each 🟦 = 2 votes

Color	Votes
Red	🟦🟦🟦🟦🟦🟦🟦

How many votes did red get?

Type a number.

Practice 2

A bar graph has a scale of 0, 10, 20, 30, 40, 50, 60, 70. One bar ends halfway between 60 and 70. What number does that bar show?

Type a number.

Practice 3

Nora is making a bar graph where each 🟦 = 10 stickers. She has 80 stickers. How many squares long should her bar be?

Type a number.

Practice 4

This graph shows laps Omar ran. Scale: each 🟦 = 5 laps

Day	Laps
Monday	🟦🟦🟦
Tuesday	🟦🟦🟦🟦🟦🟦🟦🟦
Wednesday	🟦🟦🟦🟦🟦

How many more laps did Omar run on Tuesday than on Monday?

Type a number.

Practice 5

Tom looks at a bar graph with a scale that counts by 5s. One bar is 6 squares long. Tom says, "That bar shows 6." What does the bar really show?

Practice 6

Three classes counted how many books they brought for a book swap. Scale: each 🟦 = 4 books

Class	Books
3A	🟦🟦🟦🟦🟦
3B	🟦🟦🟦🟦🟦🟦
3C	🟦🟦🟦🟦

How many books did the three classes bring in all?

Type a number.

Practice 7

A fruit stand sold apples, pears and plums. Scale: each 🟦 = 3 pieces of fruit

Fruit	Sold
Apples	🟦🟦🟦🟦🟦🟦
Pears	🟦🟦
Plums	🟦🟦🟦

How many more apples were sold than pears and plums together?

Type a number.