# 6.20: Missing Bars

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

**Teacher Notes**

In this section, some of the bars are missing from the graph. Students use the FACTS to deduce the nature of the missing bars.

**Solutions**

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.

\begin{align*}\mathbf{Describe:} \qquad \quad \ \text{The bar graph shows numbers of markers.}\!\\ {\;} \qquad \qquad \qquad \qquad \text{Three bars are missing.}\!\\ {\;} \qquad \qquad \qquad \qquad \text{FACTS give information about the missing bars.}\!\\ \mathbf{My \ Job:} \qquad \qquad \text{Use the FACTS. Draw the missing bars.}\!\\ \mathbf{Plan:} \qquad \qquad \quad \ \ \text{Figure out the number of markers for Jan and Kyle. Then use the FACTS.}\!\\ {\;} \qquad \qquad \qquad \qquad \qquad 1. \ \text{Lily's bar: Multiply Jan's number of markers by} \ 2. \ \text{Draw Lily's bar.}\!\\ {\;} \qquad \qquad \qquad \qquad \qquad 2. \ \text{Bob's bar: Subtract} \ 10 \ \text{from Kyle's number of markers. Draw Bob's bar.}\!\\ {\;} \qquad \qquad \qquad \qquad \qquad 3. \ \text{Eric's bar: Divide Lily's number of markers by} \ 2. \ \text{Draw Eric's bar.}\!\\ \mathbf{Solve:}\end{align*}

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

1. 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.

2. 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.