The lesson covers data representation, analysis, and interpretation. Students will:
- create and evaluate various representations, such as a line graph, circle graph, bar graph, histogram, double-line graph, and double-bar graph.
- determine the proper representations for different situations.
- compare data sets and solve real-world problems.
- write conclusive statements and predictions.
- What makes a tool and/or strategy suitable for a certain task?
- How does the type of data effect the display method?
- How can we use probability and data analysis to make predictions?
- How may data be arranged and represented to reveal the relationship between quantities?
- Data Display: A graphical display showing data in a convenient way to draw conclusions.
- Just Data handout (M-6-3-2_Just Data and KEY)
- Analysis and Interpretations worksheet (M-6-3-2_Analysis&Interpretations and KEY)
- Representations handout (M-6-3-2_Representations and KEY)
- Activities 1, 3, and 4 should be evaluated based on the appropriateness of the presentation and the strength of the reasoning supporting the choice.
- The creation of word problems, graphs, and associated questions will demonstrate the quality of data representation. In word problems, search for originality and evaluate graphs based on whether they are appropriate for the data they represent.
Scaffolding, Active Engagement, Modeling and Explicit Instruction
W: This lesson teaches students how to select and analyze relevant data displays, and generate valid findings and predictions. To make appropriate data representation decisions, students must first understand and be able to represent the type of story the data is conveying the reader.
H: The lesson begins with a demonstration of new data representations, allowing students to rapidly visualize the types of data and see the displays. Include the following graphs: line, circle, bar, and histogram.
E: In doing Activities 1 and 2, students must first comprehend the similarities and differences between the cases. Then they must use their individual and collective knowledge to choose the most appropriate data presentation. In Activity 2, students learn the meaning of each display and extract specific information.
R: With the sample problem scenarios provided in Activity 1 and additional analysis and interpretation problems, students can revisit their understanding of the scenarios' nature, what they represent, and what each representation says about the scenario. Requiring students to justify their responses and offer predictions encourages them to reconsider their original understanding.
E: The last assignment, requiring students to create four real-world situations, brings together the important concepts of the lesson. Students must make a decision based on their own experiences or other available information. By participating in the selection process, students will select situations that meet the problems and reject those that do not.
T: Students with limited visual organizing skills may struggle to grasp double-bar graphs, which present numerous categories of data in small spaces. When discussing a specific data point, ensure that all students understand the one-to-one relationship between the individual data point and its location on the graph. To ensure that students understand why a data point is in a particular location on the graph, use the scale on the appropriate axis.
O: The layout of the lesson is designed in such a way as to preview many types of graphs available for use and allows students to choose the most appropriate one for each circumstance. Students are then asked to evaluate and analyze graphs, develop their own scenarios, and consider which presentation is most appropriate.
Distribute the Representations handout (M-6-3-2_Representations and KEY). Review the characteristics of each type of representation briefly while students look to the examples on the handout.
Activity 1: Choosing the Best Representation
Say, "We'll separate into groups of four or five students and look at four different problem situations. Discuss each situation with your group members and use the Representations handout to select the best representation of the data. Discuss why that is the greatest 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 how much time she spends on different tasks throughout the day.
2) Jeffrey wants to review his grades in school over the past three years.
3) Mrs. McAllum wants to examine the amount of time in hours that students spend studying each week.
4) Deborah wishes to investigate the annual car sales of several dealers.
After the activity, students should fill out the "Use to…" column in the chart at the end of the Representations handout.
Activity 2: Analysis and Interpretations
Provide the Analysis and Interpretations worksheet (M-6-3-2_Analysis&Interpretations and KEY).
Part A: Students will analyze numerous representations and write conclusive statements that indicate their interpretations within the given context. Students will also make predictions where appropriate. Examples can be found on the Analysis and Interpretation worksheet.
Part B: Students will use double-bar and double-line graphs to solve real-world situations. Project the following double-bar graph.
Ask and discuss the following questions with the class:
"Which state has the highest average annual salary for college graduates For a non-college graduate?"
"Which state has the lowest average annual salary for 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 and KEY).
Allow time for students to investigate the NCTM applets (see Related Resources) with graphs and histograms. They should enter and explore with the data sets from the Just Data handout. After students have had some time to explore, they should use the Just Data handout to determine the most suitable data representation for each data set. (Remind students to use the chart they created at the end of the Representations handout). Discuss student responses to the different 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 create their own real-world situation, complete with a data presentation and a list of three questions that may be answered using the data. Encourage students to use screenshots from NCTM applets or Microsoft Excel to create their representations.
Extension:
Include a technological activity that shows how to make various graphs, charts, and tables in Microsoft Excel. [To create a chart in Excel, first enter the numeric data for the chart on a worksheet. The data can then be plotted into a chart by selecting the chart type that you wants to use on the Office Ribbon. (Insert tab, Charts group). Excel provides a variety of charts to help you present data in ways that are meaningful to your audience. When you create a new chart or alter an existing one, you may choose from a number 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 may also make a combination chart by include more than one chart type in your chart.]
Routine: For students with stronger numeration skills, seek out data sets with larger variation, larger quantities, and values containing negative integers, decimals, and fractions. Limit variation and numerical complexity for students with lower skill levels.
Small Group: These group activities encourage students to help one another comprehend the differences between types of presentations.
Technology: This lesson makes use of applets for demonstration and interactive purposes. The extension supports the production of numerous graphs, charts, and tables.
