This task is from Tools 4 NC Teachers. Students create a bar graph based on data.  There are samples of student work to help teachers assess and also to help anticipate student responses. This is remixable.

Task Preview

Mr. Potter’s class has been researching moon phases in science.  They have created the chart below that shows the dates of the full moon, new moon, first quarter moon, and last quarter moon for each month.  Using the data in the chart, determine how many times during the year each moon phase occurred.  Create a bar graph to display your findings.  

<data in chart viewable when you download the file> 

Part 1:  Students will 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 moon phases on the x-axis and the number of occurrences on the y-axis) or horizontally (with the number of occurrences on the x-axis and the moon phases 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.  How many full moons occurred during the year? (13)

2.  How many new moons occurred during the year? (12)

3.  Summarize what you learned about these four phases of the moon by analyzing this data. (Every year is going to have at least 12 full moons, new moons, first quarter moons, last quarter moons.  Sometimes, there will be more instances depending on the number of days in the month.)

4.  Use what you know about the phases of the moon to explain why the facts you mentioned in question 3 happen. (It takes about one month (technically 27.3 days) for the moon to orbit the earth. As the moon is moving around the earth, we see different parts of the moon illuminated.)

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 the maximum number we are graphing is 13, we do not need to have a scale as large as 5 to be sure to include all of the data. 

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 phases 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.