# 6.18: Bar Graphs

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

**Teacher Notes**

Students interpret mathematical relationships presented in FACTS and complete bar graphs to match the facts. For each problem, the scale is provided for the vertical axis. Names of people or classes on the horizontal axis are deduced from the facts.

**Solutions**

Use the FACTS and the bar graph to figure out the grade levels.

Write the grade levels on the lines under the bars.

**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.

\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*}

1. 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.

2. 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