This task is from Tools 4 NC Teachers. Given a table of data, students create a bar graph and then analyze and interpret data by answering questions. This task is remixable.

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Mrs. Cooper’s fourth grade class went on a field trip to Smokey Mountain to mine for gems. 

Each group chose 6 of their favorite gemstones to bring back to school to add to a class collection.  They decided to display the inventory of the collection in a bar graph.

Use the information below to determine how many of each kind of gemstone was collected.  Use graph paper to create a bar graph to display your findings.  <table can be viewed when file is downloaded> 

Part 1:  Students will use graph paper to create a bar graph that displays the data.  They will need to include a title and labels for the x-axis and y-axis. 

In this task, students will have to determine several things: 

·  Will the graph exhibit data vertically (with gemstones on the x-axis and numbers on the y-axis) or horizontally (with gemstones on the y-axis and numbers on the y-axis)? 

·  What is the best scale (1’s?  2’s?  5’s?) 

Part 2:  Students will analyze the data by responding the following questions:

1.  Which gemstone appears most often in the collection? (Emeralds)

2.  Which gemstone appears least often in the collection? (Calcite & Ruby are tied with 1 each.)

3.  How many kinds of gemstones does the collection have? (11)

4.  How many kinds of gemstones had less than 5 stones in the collection? (6)

5.  What scale did you choose to use when creating your graph? (answers will vary)

6.  Why did you choose to use that scale? (answers will vary)

7.  What challenges did you encounter as you created your graph?  What did you do to solve these challenges? (answers will vary)

Part 3:  Follow-up discussion

Display 4-6 graphs around the room and allow students to do a gallery walk to study the graphs.  Make sure that the graphs you display feature a variety of representations, including different scales and orientations.  Ask students to consider these prompts as they study the graphs:

1.  How does scale influence the graph?

2.  In this case, is one scale easier to read than another?

3.  In this case, does the orientation of the data matter?

4.  Do any of the graphs make you realize something that you didn’t consider when you were creating your own graph?

Once students have had a chance to reflect on the questions during the gallery walk, call them back together and begin your discussion of these prompts. As a result of your discussion, you want students to understand:

·    The scale is important. 

o  In using 1’s and 2’s, it is easier to interpret the value of the bars.  Because we have 6 gem types with a value less than 5, it is difficult to represent these values accurately on the graph. 

o  If possible, place a graph with a small scale (1’s or 2’s) beside a graph with a larger scale (5’s).  Prompt:  Look at the height (or length) of the bars.  Are they the same? (No) Is the number of gemstones the same? (Yes) Why are the lengths different?  (The scale is different.)  How can this unintentionally lead to a misunderstanding of the data or values in the bars? (People could think that because the size of the bars is different, the value of the bars in different.)

o  Follow up with:  Should we always use a small scale? (No) Can you think of a time when a large scale is more appropriate? (When dealing with numbers that are spread further apart.)

·    Orientation of the bars is not always important.

In this instance, it is not important to orient the bars in the graph horizontally or vertically.  The data you are displaying is not measurement data.   For instance, if you were displaying height of plants or distance run, the orientation helps someone to infer the situation being represented by the graph.