Misleading Graphs Lesson Plan

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Abstract

This lesson will challenge students to think creatively by having them design and build water balloon catchers from random scrap materials, while requiring them to take into consideration a multitude of variables including: cost, maintenance, total capacity, etc. After completing their water balloon catchers, students will collect data based on the performance of all catchers designed by the class. Students will then construct at least two bar graphs to be used in a commercial advocating the purchase of their group's catcher.

Standards (NCTM Grades: 3-5)

Algebra

Use mathematical models to represent and understand quantitative relationships

• model problem situations with objects and use representations such as graphs, tables, and equations to draw conclusions.

Data Analysis and Probability

Formulate questions that can be addressed with data and collect, organize, and display relevant data to answer them

• Design investigations to address a question and consider how data-collection methods affect the nature of the data set
• Collect data using observations, surveys, and experiments
• Represent data using tables and graphs such as line plots, bar graphs, and line graphs

Select and use appropriate statistical methods to analyze data

• Describe the shape and important features of a set of data and compare related data sets, with an emphasis on how the data are distributed
• Use measures of center, focusing on the median, and understand what each does and does not indicate about the data set
• Compare different representations of the same data and evaluate how well each representation shows important aspects of the data.

Understand and apply basic concepts of probability

• Describe events as likely or unlikely and discuss the degree of likelihood using such words as certain, equally likely, and impossible
• Predict the probability of outcomes of simple experiments and test the predictions

Student Prerequisites

• Technological:
  Students must be able to:
  • perform basic mouse manipulations such as point, click and drag
  • use a browser such as Netscape for experimenting with the activities

Teacher Preparation

Have a pretend store set up where students can "purchase" scrap materials.

Students will need:

• access to a browser.
• enough scrap materials so that each group is able to design and construct water balloon catchers.

Lesson Outline

1. Focus and Review
• Review vocabulary covered to this point.
• Review all types of graphs you have covered to this point.
• Explain the term misleading graph.
• Begin a discussion on how misleading graphs are used in advertising.

2. Objectives
Students will analyze and compare graphs in order to identify appropriate conclusions and determine if a particular graphical display is misleading.


3. Teacher Input
• Demonstrate how to use the Bar Graph and Histogram applets.

4. Guided Practice
• Allow time for the students to familiarize themselves with the applets while you circulate throughout the room answering any questions.

Teacher Input
• Have students turn off their monitor.
• Explain to the students their assignment:
  
  You are to work in pairs to construct a water balloon catcher. You have been alloted X amount of dollars to purchase supplies. (Have a store set up in the rear of the room. Materials can consist of almost any type of scrap you can collect from around the school, your home, or that your students collect and donate.) After these water balloon catchers are complete we will test them as a class. Each group will have the opportunity to drop 10 water balloons into their catcher in order to collect data on their group's catcher and their competitor's catchers based on:
  • How many water balloons landed in the catcher?
  • How many water balloons completely missed the catcher?
  • How many water balloons dropped into the catcher and bounced out?
  • Total number of balloons the catcher will hold at any given time.
  • Did the catcher require any maintenance?
  • Number of broken balloons.
  • Number of balloons caught without breaking.
  • Cost of balloon catcher.
  • Total cost of balloon catcher including maintenance fees.
  Once all the data has been collected you will design a commercial enticing people to purchase your water balloon catcher over your competitor's. You will need to include at least two graphs in your commercial. (These graphs can be misleading but are not required to be.)

5. Independent Practice
• Have the students construct their water balloon catchers.

Guided Practice
• Test the catchers and collect the data on the data sheet as a class.
Independent Practice
• Have the students design their graphs using the Bar Graph and/or the Histogram applets.
• Have students design their commercials.
• Have each group preform their commercial in front of the class.
• Have all the competing groups vote on which water balloon catcher they would buy based on the commercials (excluding their own).

6. Closure
• Select a few of the commercials to discuss.
• Discuss the graphs contained in the chosen commercials and why they may or may not be misleading.

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