Misleading Graphs

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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 Addressed:

Student Prerequisites

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

Teacher Preparation

  • access to a browser
  • access to a variety of scrap materials to design and construct water ballooon catchers
  • rulers and scissors

Key Terms

bar graphA diagram showing a system of connections or interrelations between two or more things by using bars
histogramA bar graph such that the area over each class interval is proportional to the relative frequency of data within this interval
line graphA diagram showing a system of connections or interrelations between two or more things by using lines
meanThe sum of a list of numbers, divided by the total number of numbers in the list. Also called arithmetic mean
median"Middle value" of a list. The smallest number such that at least half the numbers in the list are no greater than it. If the list has an odd number of entries, the median is the middle entry in the list after sorting the list into increasing order. If the list has an even number of entries, the median is equal to the sum of the two middle (after sorting) numbers divided by two. The median can be estimated from a histogram by finding the smallest number such that the area under the histogram to the left of that number is 50%
modeFor lists, the mode is the most common (frequent) value. A list can have more than one mode. For histograms, a mode is a relative maximum ("bump"). A data set has no mode when all the numbers appear in the data with the same frequency. A data set has multiple modes when two or more values appear with the same frequency.
pie graphA diagram showing a system of connections or interrelations between two or more things by using a circle divided into segments that look like pieces of pie
probabilityThe measure of how likely it is for an event to occur. The probability of an event is always a number between zero and 100%. The meaning (interpretation) of probability is the subject of theories of probability. However, any rule for assigning probabilities to events has to satisfy the axioms of probability

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

    Let the students know what they will be doing and learning today. Say something like this:

    • Today, class, we are going to learn about how graphs can sometimes be misleading.
    • We are going to use the computers to make our own graphs and learn how to analyze and compare those graphs, but please do not turn your computers on until I ask you to. I want to show you a little about these activities first.

  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.

  5. Independent Practice

    • Have students turn off their monitor.
    • Explain to the students their assignment and following the explanation have students construct their catchers:

      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.)

    • After students construct their water balloon catchers, they should collect data on the data sheet as a class.

      After the data has been collected,

      • 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.

Alternate Outline

This lesson can be rearranged in several ways if only one computer is available:

  • Have the students create their graphs on paper after showing them the applets on the computer
  • Have groups take turns creating their graphs on the computer so that everyone can use the applets

Suggested Follow-Up

This lesson can be followed up with the following lessons:

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