# 6.8: Bar Graphs

**At Grade**Created by: CK-12

Look at the bar graph and the list of FACTS below. Can you label the bar graph correctly by writing the grade levels on the lines under the bars? In this concept, we will learn how to use bar graphs to correctly display information.

**FACTS**

- There are twice as many grade 1 students as grade 4 students.
- There are 10 more grade 1 students than grade 3 students.
- There are half as many grade 5 students as grade 3 students.
- The total number of student in the 5 grades is 175.

### Guidance

In order to interpret and use bar graphs like the one above, use the problem solving steps to help you.

- First,
**describe**what you see and what information you are given. - Next, identify what
**your job**is and what you are trying to solve. In these problems, your job will be to label the bar graph correctly, or correctly fill in missing bars. - Third, make a
**plan**for how you will solve. - Fourth,
**solve**the problem. - Last,
**check**your answer. Make sure your solution works with all of the facts.

#### Example A

Use the FACTS and the bar graph to figure out the names. Write the names on the lines under the bars.

**FACTS**

- Ella read half as many books as Dora.
- Cal read twice as many books as Abe.
- Bea didn’t read the greatest number of books.
- Together, Bea and Cal read 21 books.

**Solution:**

We can use problem solving steps to help.

**Describe:** The graph has 5 bars. The bars show numbers of books. The FACTS give information about the number of books each student has read.

**My Job:** Use the facts to figure out the student represented by each bar. Write the names under the bars.

**Plan:** Use the scale. Figure out the number of books for each bar. Find numbers that fit the FACTS. Label the bars with the students.

**Solve:** From left to right, the bars stand for 4, 6, 7, 9, and 12 books.

**Check:** Ella read half as many books as Dora. 4 is half of 8. Cal read twice as many books as Abe. 12 is twice 6. Bea didn't read the greatest number of books. 9 is less than 12. Bea and Cal read 21 books. 9+12=21.

#### Example B

Use the FACTS and the bar graph to figure out the names. Write the names on the lines under the bars.

**FACTS**

- Jack has half as many markers as Neil.
- Together, Jack and Mimi have the same number of markers as Leanne.
- Leanne has twice as many markers as Kent

**Solution:**

We can use problem solving steps to help.

**Describe:** The graphs has 5 bars. The bars show numbers of markers. The FACTS give information about the number of markers that each student has.

**My Job:** Use the facts to figure out the student represented by each bar. Write the students under the bars.

**Plan:** Use the scale. Figure out the number of markers for each bar. Find numbers that fit the FACTS. Label the bars with the students.

**Solve:** From left to right, the bars stand for 15, 20, 25, 30, and 40 markers.

**Check:** Jack has 15 markers which is half as many markers as Neil who has 30 markers. Together, Jack (15 markers) and Mimi (25 markers) have the same number of markers as Leanne (40 markers). Leanne, who has 40 markers, has twice as many markers as Kent, who has 20 markers.

#### Example C

Use the FACTS and the bar graph. Draw the missing bars.

**FACTS:**

- Lily has twice as many markers as Jan.
- Bob has 10 fewer markers than Kyle.
- Eric has half as many markers as Lily.

**Solution:**

We can use problem solving steps to help.

**Describe:** The bar graph shows numbers of markers. Three bars are missing. FACTS give information about the missing bars.

**My Job:** Use the FACTS. Draw the missing bars.

**Plan:** Figure out the number of markers for Jan and Kyle. Then use the FACTS.

- 1. Lily’s bar: Multiply Jan’s number of markers by 2. Draw Lily’s bar.
- 2. Bob’s bar: Subtract 10 from Kyle’s number of markers. Draw Bob’s bar.
- 3. Eric’s bar: Divide Lily’s number of markers by 2. Draw Eric’s bar.

**Solve:**

**Check:** Lily has \begin{align*}2 \times 30\end{align*}, or 60 markers. Bob has \begin{align*}45 - 10\end{align*}, or 35 markers. Eric has \begin{align*}60 \div 2\end{align*}, or 30 markers.

#### Concept Problem Revisited

**FACTS**

- There are twice as many grade 1 students as grade 4 students.
- There are 10 more grade 1 students than grade 3 students.
- There are half as many grade 5 students as grade 3 students.
- The total number of student in the 5 grades is 175.

We can use problem solving steps to help.

\begin{align*}& \mathbf{Describe:} && \text{The graph has} \ 5 \ \text{bars.}\!\\ &&& \text{The bars show numbers of students.}\!\\ &&& \text{The FACTS give information about the number of students in each grade.}\!\\ & \mathbf{My \ Job:} && \text{Use the facts to figure out the grade level represented by each bar.}\!\\ &&& \text{Write the grade levels under the bars.}\!\\ & \mathbf{Plan:} && \text{Use the scale. Figure out the number of students for each bar.}\!\\ &&& \text{Find numbers that fit the FACTS.}\!\\ &&& \text{Label the bars with the grades.}\!\\ & \mathbf{Solve:} && \text{From left to right, the bars stand for} \ 10, 25, 30, 50, \ \text{and} \ 60 \ \text{students.}\!\\ &&& \text{Fact} \ 2: \text{There are} \ 10 \ \text{more students in grade} \ 1 \ \text{than} \ 3.\!\\ &&& \qquad \qquad \text{The numbers} \ 50 \ \text{and} \ 60 \ \text{differ by} \ 10,\!\\ &&& \qquad \qquad \text{so grade} \ 1 \ \text{is} \ 60 \ \text{and grade} \ 3 \ \text{is} \ 50.\!\\ &&& \text{Fact} \ 3: 25 \ \text{is half of} \ 50 \ \text{and grade} \ 3 \ \text{is} \ 50. \ \text{So grade} \ 5 \ \text{is} \ 25.\!\\ &&& \text{Fact} \ 1: 60 \ \text{is twice} \ 30 \ \text{and grade} \ 1 \ \text{is} \ 60. \ \text{So grade} \ 4 \ \text{is} \ 30.\!\\ &&& \text{Fact} \ 4: \text{The only grade left is grade} \ 2, \ \text{so it must be} \ 10, \ \text{and} \ 10 \ \text{added to the total}\!\\ &&& \text{number of students in the other grades equals} \ 175.\!\\ &&& \qquad \qquad \text{Grade} \ 2 (10), \text{grade} \ 5 (25), \text{grade} \ 4 (30), \text{grade} \ 3 (50), \text{grade} \ 1 (60)\!\\ & \mathbf{Check:} && \text{Grade} \ 1 \ \text{is twice grade} \ 4: 2 \times 30 = 60.\!\\ &&& 10 \ \text{more students in grade} \ 1 \ \text{than grade} \ 3: 50 + 10 = 60.\!\\ &&& \text{Half as many in grade} \ 5 \ \text{than in grade} \ 3: 50 \div 2 = 25.\!\\ &&& \text{Total:} \ 10 + 25 + 30 + 50 + 60 = 175.\end{align*}

### Vocabulary

A ** bar graph** is a way of representing information in which different amounts are shown by the height of their rectangles (bars).

### Guided Practice

1. Use the FACTS and the bar graph to figure out the names. Write the names on the lines under the bars.

**FACTS**

- Grade 3 has 10 more pets than grade 1.
- Grade 5 has half as many pets as grade 4.
- Grade 2 has the same number of pets as grades 4 and 5 together.
- Grade 3 has the same number of pets as grades 1 and 5 together.

2. Use the FACTS and the bar graph to figure out the names. Write the names on the lines under the bars.

**FACTS**

- There are half as many rooms in Earl’s house as in Fran’s house.
- Hal’s and Ian’s houses have a total of 12 rooms.
- Hal’s house has twice as many rooms as Ian’s house.
- There is one more room in Gina’s house than in Earl’s house.
- Gina’s house has 2 more rooms than Ian’s house.

3. Use the FACTS and the bar graph. Draw the bars.

**FACTS:**

- Ella has 2 more pens than Abe.
- Dora has twice as many pens as Bea.
- Cal has half as many pens as Abe.

**Answers:**

1.

2.

3.

### Practice

1. Use the FACTS and the bar graph. Draw the bars.

**FACTS:**

- Mary has 10 more pencils than Neil.
- Lisa has half as many pencils as Mary.
- Owen and Patty have 45 pencils altogether.

2. Use the FACTS and the bar graph. Draw the bars.

**FACTS:**

- Edna has half as many sports cards as Frank.
- Helen has 3 more sports cards than George.
- George has twice as many sports cards as Iris.

3. Use the FACTS and the bar graph. Draw the bars.

**FACTS:**

- Fred has twice as many stickers as Henry.
- Gina has half as many stickers as Ida.
- Jenny has 30 fewer stickers than Ida.

4. Use the FACTS and the bar graph to figure out the names. Write the names on the lines under the bars.

**FACTS**

- Jenny has won 4 more games than Dave.
- Jessie has won half as many games as Jenny.
- Mike and Lucy have won the same number of games.

5. Use the FACTS and the bar graph to figure out the grades. Write the grades on the lines under the bars.

**FACTS**

- Grade 2 has the fewest number of homework problems per night.
- Grade 1 has twice as many homework problems as Grade 2.
- Grade 4 has 10 more homework problems per night than Grade 1.
- Grade 5 has 10 more homework problems per night than Grade 3.

### Image Attributions

Students interpret bar graphs and fill in missing parts of bar graphs using given facts. Students use problem solving steps to help.