• Activities 1, 3, and 4 should be evaluated by appropriateness of presentation and strength of reasoning that supports the choice.
• Creation of word problems, graphs, and accompanying questions will demonstrate the quality of their representations of data. In word problems, look for originality and evaluate the graphs according to whether they are appropriate for the data they represent.

Distribute the Representations handout (M-6-3-2_Representations.docx and M-6-3-2_Representations KEY.docx). Briefly review the characteristics of each type of representation while students refer to the examples on the handout.

Activity 1: Choosing the Best Representation

Say, “We will divide up into groups of four or five students, and then we are going to look at four different problem situations. Discuss each situation with the members of your group and, using the Representations handout, try to choose the best representation of the data. Talk to each other about why that is the best representation and be prepared to share your reasons with the rest of the class.”

Write or project the following scenarios on the board:

1)      Elaine needs to analyze the amount of time she spends during the day on various tasks.

2)      Jeffrey wants to look at his grades in school over the past three years.

3)      Mrs. McAllum wants to analyze the amount of time in hours that students spend studying each week.

4)      Deborah wishes to examine the annual car sales for different dealers.

At the close of the activity, have students complete the “Use to…” column in the chart at the end of the Representations handout.

Activity 2: Analysis and Interpretations

Distribute the Analysis and Interpretations worksheet (M-6-3-2_Analysis&Interpretations.docx and
M-6-3-2_Analysis&Interpretations KEY.docx).

Part A—Students will analyze various representations and write conclusive statements, revealing their interpretations, within the given context. Students will also provide predictions where appropriate. The Analysis and Interpretations worksheet provides examples.

Part B—Students will analyze double-bar and double-line graphs to solve real-world problems. Project the following double-bar graph.

Ask the following questions and then discuss them with the class:

• “Which state offers the highest average yearly salary for a college graduate? For a non-college graduate?”
• “Which state offers the lowest average yearly salary for a college graduate? For a non-college graduate?”
• “Which state has the largest range in average yearly salary?”
• “What predictions can be made about the average yearly salaries of these states?”

Activity 3: Exploring More Data Representations

Distribute the Just Data handout (M-6-3-2_Just Data.docx and M-6-3-2_Just Data KEY.docx).

Provide time for students to explore the NCTM applets (see Related Resources) with graphs and histograms. They should input and experiment with data sets from the Just Data handout. Once students have had time to explore, they should identify the best representation of data for each data set on the Just Data handout. (Remind students to use the chart they completed at the end of the Representations handout.) Discuss student responses to which types of representations and data distributions they chose for each data set. Help students synthesize and summarize their conclusions.

Activity 4: Representing a Data Set of Your Choice

Instruct students to develop their own real-world problem, each with an accompanying data display and a list of three questions that can be answered from the display. Encourage students to use screenshots from the NCTM applets or use Microsoft Excel when creating their representations.

Extension:

• Include a technology activity that demonstrates how to create various graphs, charts, and tables with Microsoft Excel. [To create a chart in Excel, you start by entering the numeric data for the chart on a worksheet. Then you can plot that data into a chart by selecting the chart type that you want to use on the Office Ribbon (Insert tab, Charts group). Excel supports many types of charts to help you display data in ways that are meaningful to your audience. When you create a chart or change an existing chart, you can select from a variety of chart types (such as a column chart or a pie chart) and their subtypes (such as a stacked column chart or a pie in 3-D chart). You can also create a combination chart by using more than one chart type in your chart.]
• Routine: Look for data sets with larger variance, larger quantities, and values with negative numbers, decimals, and fractions for students who are more adept in numeration skills. For students with less developed skills, limit variance and numerical complexity.
• Small Group: These group activities are useful for encouraging students to help each other understand the differences between types of presentations.
• Technology: This lesson involves use of applets for demonstrative and interactive purposes. The extension includes creation of various graphs, charts, and tables.