Convert a table into a bar graph

3.MD.B.3 · adapt · grade 3

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

Mia surveyed her classmates about their favorite fruit and recorded the results in both a table and a bar graph. The table lists $3$ students for apples and $8$ students for bananas. The bar graph shows a bar of $3$ for apples and a bar of $8$ for bananas.

Find the data that is missing from the table by reading the graph, and find the data that is missing from the graph by reading the table, so that both the table and the bar graph are completed.

The bar graph's vertical axis shows the number of students, with gridlines marked at $0$ , $5$ , and $10$ . The horizontal axis lists apples and bananas. The apple bar has a height of $3$ and the banana bar has a height of $8$ .

Show solution

Understand

The same survey of favorite fruit is shown both as a table and as a bar graph. The table says apples 3 and bananas 8, and the bar graph shows an apple bar of 3 and a banana bar of 8. Use each representation to fill in what is missing in the other so both are complete.

Givens

Table: apples = 3, bananas = 8
Bar graph: apple bar height = 3, banana bar height = 8
Bar-graph gridlines are at 0, 5, and 10

Unknowns

The missing table entry (read from the graph)
The missing graph bar (read from the table)

Constraints

A table number and its matching bar height must be equal
Bar heights are read against the 0-5-10 scale

Plan

#15 Organize Information in More Ways · also uses: #1 Draw a Diagram

A table and a bar graph are two views of the same data. We translate between the two representations so each missing slot copies its partner's value.

Execute

#15 Organize Information in More Ways 3.MD.B.3

The apple bar rises to 3 and the banana bar rises to 8, so the table values are apples 3 and bananas 8.

\text{apple bar} = 3,\quad \text{banana bar} = 8

A bar's height tells you the count it stands for.

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

The table lists apples 3 and bananas 8, so the apple bar is drawn to 3 and the banana bar to 8.

3 \text{ (apple)},\ 8 \text{ (banana)}

To draw a bar, raise it to the number the table gives.

#15 Organize Information in More Ways 3.MD.B.3

Both views now agree: apples are 3 and bananas are 8 in the table and in the graph.

3 = 3,\quad 8 = 8

Two correct pictures of the same survey must show the same numbers.

Answer: Apples = 3 and bananas = 8 in both the table and the bar graph

Review

Both bars sit on the 0-5-10 scale (3 is below the 5 line, 8 is between 5 and 10), and the table and graph agree, so the completed pair is consistent.

Draw a diagram (tool 1): sketch each bar against the gridlines and check its top lines up with the matching table number.

Standards · min grade 3

3.MD.B.3 Draw and interpret scaled picture graphs and bar graphs — Translating between a frequency table and a bar graph to complete both

💡 This only needs Grade 3 graph reading: a table number and its bar are the same fact in two outfits!