### Purpose

To understand data tables and graphs. To understand the guidelines for making tables and graphs. To interpret graphs and determine which graph is best suited for the data.

### Context

Because students are exposed to visual displays of information on a daily basis, they should be able to interpret and understand this information and also be aware of possible bias. (*Benchmarks for Science Literacy*, p. 283.)

At this level, student communication of information should become more focused and quantitative. Students should come to think in a more focused and quantitative manner and expect that kind of thinking from others. They also should learn to question vague claims when quantitative ones are possible and relevant. (*Benchmarks for Science Literacy*, p. 295.)

The purpose of this lesson is to help students learn how to use and interpret graphs. The graphs will be pulled from a variety of sources, and the activities ask students to interpret graphs. Students need to start this lesson with the knowledge of what a graph is. They should also know how to observe and collect data.

### Motivation

Although students at this age should be aware of what a graph is, some may need a little refresher course. Start this lesson, then, by having a discussion about what graphs are.

Ask students these questions:

- What do you think a graph is?
- Can you tell me the names of the different types of graphs?
- Why do you think information is often presented in graphs instead of just in a list or table?

Encourage students to participate in the discussion and use their responses to generate a class list on the blackboard or flip chart.

Students may believe that a line plot, line graph, and bar graph are the same. To help familiarize students with different types of graphs and how they can be used to convey relevant information, direct students to Getting the Picture: Communicating Data Visually , part of the Annenberg/CPB website. (If you like, you can print out this article before class and hand it out to students to read in class.) Have students read through the text and see how the graphs in the article are used to help convey information.

Ask students the following questions about the article:

- Consider the census estimates that are presented for Massachusetts and Texas. Compare how the information is presented in the table to how it is presented in the first paragraph. What are some of the advantages to presenting the data in a table format versus the paragraph? What are some of the disadvantages?
- Next, look at the bar graphs. Do the bar graphs add anything to your interpretation of the data? If so, what?
- What are the graphs telling you?
- Can you describe in words what the table and graphs represent?
- What do you believe is the best way to illustrate the information in this article?

### Development

The purpose of this next activity is for students to predict and graph how many of one color of Skittles® candy are contained in a snack-size package. They will then collect and graph data. They are asked to hand in three items: data table, bar graph, and pie graph representing and illustrating Skittles® data.

Divide the class into groups of two or three. Ask each group to make a prediction about the total number of Skittles® in a bag and then the number of each color. Have students write their predictions in a table and then, using the data contained in the table, graph their predictions using Create a Graph, found on the National Center for Education Statistics website. Students can choose to graph their data using any of the three graphs demonstrated on the site: bar graph, pie chart, or line graph.

Ask students these questions about their graphs:

- What color did you predict would have more, have less?
- Why did you choose to use a bar/pie/line graph to show your data?
- Did the graph turn out as you expected?
- Do you believe this was the best graph to use to represent your data? Why or why not?
- Which type of graph do you believe best illustrated the data?
- What does the graph show you about your prediction?

Next, give each group one package of candy and a student data sheet for each group member. Even though students will work in groups, each student should fill out the What's In a Graph? Data Table and complete the assignment.

First, students will determine how many candies of each color are contained in the package by making a vertical 3-D graph with the candies and then counting the items in each column. Using the data they obtain from this exercise, tell students to again use the Create a Graph website to enter their information and make graphs from their data. Students should probably make the bar graph and pie chart so that they can see how these two graphs represent the information. The line graph probably would best be used to graph the total number of one color for each group (i.e., the number of red Skittles® in a bag listed by group).

Once students have completed their graphs, ask them these questions:

- After comparing your predictions and graphs with the actual numbers, were your predictions supported?
- Did you notice a pattern of particular colors as you compared the graphs?
- Which type of graph best illustrated the data?
- In looking at the bar graph, what color has the highest number? What color has the lowest number? Can you easily tell from the bar graph the percentage of each color in the bag?
- In looking at the pie chart, what color makes up the highest percentage of the bag? What color makes up the lowest percentage? Can you easily tell from the pie chart the number of each color in a bag?
- For the line graphs, look at your graph for the orange Skittles®. What group had the highest number of orange Skittles®? What group had the lowest number of orange Skittles®?
- What graph do you think would be the most helpful in determining the number of red Skittles® in a bag compared to the total number of Skittles®? What is the number of red Skittles® compared to the total number of Skittles®?
- What graph do you think would be the most helpful in determining the average number of yellow Skittles®? What is the average number of yellow Skittles®?

This exercise should give students a better idea about how graphs can be used to illustrate data and that different types of graphs represent certain types of data better than others.

### Assessment

To assess student understanding of graphs, students will gather data pertaining to their favorite sport, player, or team using the Sports Reference website or another similar sports site. Once students have gathered data from the site, they will develop a data table and two customized graphs. Students will then present their data table and graphs to the class.

Give students the What's In a Graph? Assessment sheet to help them evaluate their own graphs and/or those of their classmates. The purpose of this assessment is to determine if the students understand the following:

- how to communicate information to others and how to understand the relationships revealed by the information
- how to use and present data in a data table or chart correctly
- how to present data accurately using graphs

The assessment sheet is a simple rubric. There are several resources on the Internet that describe the use of rubrics in the K-12 classroom, a few of which are highlighted here.

To learn more about rubrics in general, see Make Room for Rubrics on the Scholastic site.

For specific examples of rubrics, more information, and links to other resources, check out the following sites:

- Kathy Schrock's Guide for Educators: Assessment & Rubric Information
- Assessment: Creating Rubrics
- Rubrics for Web Lessons

Finally, you can go to Teacher Rubric Makers on the Teach-nology.com website to create your own rubrics. At this site, you can fill out forms to create rubrics suitable for your particular students, and then print them instantly from your computer.

### Extensions

There are several other sites on the Internet that provide examples of graphs and tools for graphing data. One site, called Graphs, found at Math Forum, contains instructions for making bar graphs and pie charts using a ClarisWorks program. Using a spreadsheet program like ClarisWorks, students can create customized graphs.

For students who are more ambitious, the K-12 Education Curriculum section of the Center for Innovation in Engineering and Science Education website contains several activities that require collecting and graphing real-time data.