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6.20: Missing Bars

Difficulty Level: 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.


Use the FACTS and the bar graph.

Draw the missing bars.


  1. Lily has twice as many markers as Jan.
  2. Bob has 10 fewer markers than Kyle.
  3. 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.


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

2. Use the FACTS and the bar graph.

Draw the bars.


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

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