Read a double bar graph

3.MD.B.3 · take · grade 3

Archetype: Read and Scale a Data Graph · step in a 21-type progression

A class surveyed how many colored pencils and how many crayons the students own, sorted by color. The results are shown in a double bar graph in which each item displays two data sets (orange and yellow-green) side by side. For both colored pencils and crayons, an orange bar and a yellow-green bar are drawn next to each other.

For each item, compare the difference between the orange count and the yellow-green count, and determine which item — colored pencils or crayons — has the larger difference between the two colors.

The horizontal axis lists colored pencils and crayons, and each item shows a pair of bars, one orange and one yellow-green. The legend identifies the orange and yellow-green bars.

Show solution

Understand

A double bar graph shows two color counts (orange and yellow-green) for each of two items: colored pencils and crayons. For each item, find the difference between its two bars, then say which item has the larger orange-vs-yellow-green difference.

Givens

Each item (colored pencils, crayons) has an orange bar and a yellow-green bar side by side
A legend tells which bar is orange and which is yellow-green
The orange/yellow-green gap is visibly larger for crayons than for colored pencils

Unknowns

The difference between the two colors for each item
Which item has the larger between-color difference

Constraints

The difference is found per item by subtracting the shorter bar from the taller bar
Comparison is made between the two items' differences

Plan

#1 Draw a Diagram · also uses: #7 Identify Subproblems

The grouped bars are the diagram; for each item we solve a small subtraction subproblem (taller bar minus shorter bar), then compare the two gaps to pick the larger one.

Execute

#7 Identify Subproblems 3.MD.B.3

For each item, line up its orange bar and yellow-green bar and read the gap between their tops. That gap is the difference between the two color counts for that item.

\text{difference} = \text{taller bar} - \text{shorter bar}

The height gap between the paired bars is exactly how many more of one color there are.

#1 Draw a Diagram 3.MD.B.3

Set the two height gaps next to each other. The crayon pair shows a clearly wider gap between its orange and yellow-green bars than the colored-pencil pair does.

\text{gap}_{\text{crayon}} > \text{gap}_{\text{pencil}}

The bigger the visible gap between a paired item's bars, the bigger the difference between its two colors.

Answer: Crayons have the larger difference between the orange and yellow-green counts

Review

The crayon pair shows the wider visible separation between its two bars, so naming crayons as the item with the larger between-color difference matches what the graph displays.

Look for a pattern (tool 5): scan both pairs at once and pick the pair whose two bar-tops are spaced farthest apart, which is the crayon pair.

Standards · min grade 3

3.MD.B.3 Draw and interpret scaled picture graphs and bar graphs — Reading paired bars in a double bar graph and comparing within-item differences

💡 This only needs Grade 3 graph reading: the widest gap between a pair of bars wins!