## Creating and Interpreting Graphs

### Debra Davis

#### Description

Students use data collected at the beginning of the lesson, such as their favorite brand of sneakers or favorite soft drinks, to create graphs and to interpret the results shown by each graph. Note: This lesson assesses only the creation and interpretation of two types of graphs.

#### Objectives

The student constructs and interprets displays of data, (including circle, line, bar, and box-and-whisker graphs) and explains how different displays of data can lead to different interpretations.

#### Materials

-Overhead, white/chalkboard or chart paper and appropriate markers
-Samples of various graphs to aid in discussion (transparencies, textbook, or poster form)
-Copies of handouts (See attached files)
-Transparency of practice activity sheet or prepared chart paper for demonstration purposes
-Transparency of checklist
-Transparency or chart paper template of frequency table
-Protractors
-Calculators

#### Preparations

1. Make copies of the activity sheets and the checklist for each student. (See attached file.)
2. Make needed transparencies. (See Materials list.)
3. Gather enough protractors and calculators if students do not have their own.
4. Collect samples of graphs. Some should be missing important components for demonstration purposes. Have at least one graph without any labels.

#### Procedures

Day 1

1. Show students an incomplete graph, such as a circle graph without the labels and title.

2. Ask: Can you tell me what this graph is about? What must I add to the graph to make it meaningful?

4. One at a time add components (title, labels, etc.). Ask again what the graph depicts.

5. Inform the class that today we are going to learn how to construct a circle graph. Before we begin, we will review the construction of bar graphs and discuss the components of a good graph.

6. Have different graphs available for display. Point out the qualities of good graphs: appropriate title and subtitles, consistent and appropriate scale, accurate angle measures for each percentage in the data, and appropriate labels.

7. As you look at each graph include a discussion about what the graph indicates about the data.

8. Distribute the practice activity sheet (see attached files), protractors, and calculators.

9. Review how to use a frequency table to create a bar graph.

10. Students work independently to complete the bar graph on the activity sheet. Check for completion.

11. Show students the steps for creating a circle graph. Demonstrate the steps as students complete the next graph on the activity sheet with you.

12. Be sure to review the components of a good graph discussed at the beginning of class and check that these components are represented on these two graphs.

13. Discuss the graphs with the class and interpret the displays. Give needed feedback. Write the interpretation of each graph for the students to copy onto their activity sheets.

14. Check for understanding.

15. Use the remaining time for students to complete the activity sheet.

16. Take up protractors and calculators.

17. Summarize today’s lesson. Students should finish activity sheet for homework if necessary.

Day 2

1. As a formative tool, check answers on yesterday’s activity sheet providing corrective feedback.

2. Inform students that today we are going to gather some data and as a class create a frequency table. Each student will then create two types of graphs from the set of data, and interpret the graphs they create.

3. Place a transparency of a blank frequency table on the overhead or display one on chart paper. (These two methods are preferred over the white or chalkboard if you have multiple classes.) Survey the class on their favorite brand of sneakers or favorite soft drinks. Complete the frequency table, tallying as you proceed around the classroom asking the question of each student. (You can substitute any appropriate survey item.) You may want to restrict the list to five or so categories. If more occur in your survey, you can discuss with class the option of creating an another category labeled [other] for infrequent answers.

4. Provide each student with the pre-printed circle and grids (see attached files), protractors, and calculators.

5. Display a copy of the checklist on the overhead or on the board. (See attached file.)

6. Remind students to refer to the checklist and to their completed activity sheets as needed.

7. Allow students time to create their graphs and write their interpretations of the data displays. Walk around and assist students providing feedback as needed.

8. Collect student work and materials.

9. Use the last ten minutes of class for several students to share their interpretations. Discuss the validity of their answers.

10. Evaluate students' graphs. (See Assessment.)

#### Assessments

Evidence:
Students create a circle graph and a bar graph from class-generated data. Students write a paragraph for each graph that interprets the display of the data. Formatively assess student progress as graphs are being produced, providing needed feedback. Before submitting their final products, students use the provided rubric to self-edit their work.

Criteria:
Each graph must have the following:
1. Appropriate title.
2. Appropriately labeled parts.
Bar graph must have an appropriate and consistent scale.
Circle graph must have correct angle measure for each category in data set.
Interpretation of the data is a clear and precise explanation of the data display.
Interpretation should include at least three different inferences about the data.

Assessment tool: Checklist (See attached file)

#### Extensions

This lesson can be extended to include line and box-and-whisker graphs, and these graphs used to explain how different displays of data can lead to different interpretations of the same data.

If all the different types of graphs have been taught in previous lessons, you can divide the students into groups of four students. Each group can create their own survey, collect the data from the class, and each student in the group can be made responsible for creating one of the graphs. The group can then use the four graphs to interpret the data and explain how the different displays can infer different information.

#### Attached Files

Creating and Interpreting Graphs: Bar Graph     File Extension: pdf

Creating and Interpreting Graphs: Circle Graph     File Extension: pdf

Creating and Interpreting Graphs Frequency Table     ;File Extension: pdf

Creating and Interpreting Graphs Checklist     File Extension: pdf

Creating and Interpreting Graphs Practice     File Extension: pdf