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.
Objectives
Upon completion of this lesson, students will:
Standards Addressed
Grade 3
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Statistics and Probability
- The student demonstrates an ability to classify and organize data.
- The student demonstrates an ability to analyze data (comparing, explaining, interpreting, or justifying conclusions).
Grade 4
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Statistics and Probability
- The student demonstrates an ability to classify and organize data.
- The student demonstrates an ability to analyze data (comparing, explaining, interpreting, evaluating; drawing or justifying conclusions).
Grade 5
-
Statistics and Probability
- The student demonstrates an ability to classify and organize data.
- The student demonstrates an ability to analyze data (comparing, explaining, interpreting, evaluating; drawing or justifying conclusions).
Grade 6
-
Statistics and Probability
- The student demonstrates an ability to classify and organize data.
- The student demonstrates an ability to analyze data (comparing, explaining, interpreting, evaluating; drawing or justifying conclusions).
Grade 7
-
Statistics and Probability
- The student demonstrates an ability to classify and organize data.
- The student demonstrates an ability to analyze data (comparing, explaining, interpreting, evaluating, making predictions; drawing or justifying conclusions).
Grade 8
-
Statistics and Probability
- The student demonstrates an ability to classify and organize data.
- The student demonstrates an ability to analyze data (comparing, explaining, interpreting, evaluating, making predictions, describing trends; drawing, formulating, or justifying conclusions).
Grade 9
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Statistics and Probability
- The student demonstrates an ability to analyze data (comparing, explaining, interpreting, evaluating, making predictions, describing trends; drawing, formulating, or justifying conclusions).
Grade 10
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Statistics and Probability
- The student demonstrates an ability to analyze data (comparing, explaining, interpreting, evaluating, making predictions, describing trends; drawing, formulating, or justifying conclusions).
Third Grade
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Measurement and Data
- Represent and interpret data.
Statistics and Probability
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Interpreting Categorical and Quantitative Data
- Summarize, represent, and interpret data on a single count or measurement variable
Grades 3-5
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Algebra
- Use mathematical models to represent and understand quantitative relationships
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Data Analysis and Probability
- Formulate questions that can be addressed with data and collect, organize, and display relevant data to answer them
- Select and use appropriate statistical methods to analyze data
Grade 5
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Number and Operations, Measurement, Geometry, Data Analysis and Probability, Algebra
- COMPETENCY GOAL 4: The learner will understand and use graphs and data analysis.
Grade 7
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Number and Operations, Measurement, Geometry, Data Analysis and Probability, Algebra
- COMPETENCY GOAL 4: The learner will understand and use graphs and data analysis.
Grade 8
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Number and Operations, Measurement, Geometry, Data Analysis and Probability, Algebra
- COMPETENCY GOAL 4: The learner will understand and use graphs and data analysis.
Introductory Mathematics
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Algebra
- COMPETENCY GOAL 4: The learner will understand and use graphs and data analysis.
-
Data Analysis and Probability
- COMPETENCY GOAL 3: The learner will understand and use graphs and data analysis.
5th Grade
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Data Analysis and Probability
- The student will demonstrate through the mathematical processes an understanding of investigation design, the effect of data-collection methods on a data set, the interpretation and application of the measures of central tendency, and the application of b
- The student will demonstrate through the mathematical processes an understanding of investigation design, the effect of data-collection methods on a data set, the interpretation and application of the measures of central tendency, and the application of basic concepts of probability.
7th Grade
-
Data Analysis and Probability
- The student will demonstrate through the mathematical processes an understanding of the relationships between two populations or samples.
5th Grade
-
Probability and Statistics
- 5.19 The student will find the mean, median, mode, and range of a set of data.
Student Prerequisites
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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 graph
A diagram showing a system of connections or interrelations between two or more things by using bars
histogram
A bar graph such that the area over each class interval is proportional to the relative frequency of data within this interval
line graph
A diagram showing a system of connections or interrelations between two or more things by using lines
mean
The 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%
mode
For 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 graph
A 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
probability
The 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
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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
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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.
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Teacher Input
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Guided Practice
Allow time for the students to familiarize themselves with the applets while you circulate throughout the room answering any questions.
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Independent Practice
- Have students turn off their monitor.
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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.)
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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).
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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: