Title: Using the Area on a Pie Chart to Calculate Probabilities Mathematics Content: Pie Charts; Area as Probability; Probabilities as Percents, Decimals & Fractions Objectives: To calculate probability using area. To use graphing technology to compare experimental probabilities. To express probabilities as percents, decimals, and fractions. Time: Approximately 3 4 fifty minute class periods MN Standards: Grade 7; Strand Data Analysis and Probability; Benchmark 7.4.2.1 Use reasoning with proportions to display and interpret data in circle graphs (pie charts) and histograms. Choose the appropriate data display and know how to create the display using a spreadsheet or other graphing technology. Grade 7; Strand Data Analysis and Probability; Benchmark 7.4.3.2 Calculate probability as a fraction of sample space or as a fraction of area. Express probabilities as percents, decimals and fractions. Materials: Graphing technology such as Excel, a fun size bag of M & M s for each student Instructor s Notes: Pre Test: The Pre Test below can be given as a brief way to assess students prior knowledge on how to make a pie chart as well as a calculate probability and write probabilities as fractions and decimals. M &M Activity: Probability as Area Worksheet looks at calculating a probability as an area question. This and M & M Probability Experiment could be worked on in groups or as a class. For the M & M Probability Experiment, the instructor can explain to their students how to create a pie chart using Excel. Students would create a pie chart that represents the percentages of each color their bag of M & M contains.appropriate topics to discuss during this experiment would be theoretical vs. experimental probability, predictions, sample size, and reviewing on interchanging decimals, percents, and fractions. Pie Chart/ Bar Graph Probabilities Activity: The Pie Chart/Bar Graph Probabilities Activity allows students to apply what they ve learned while taking another step with the M & M data. Students will create another pie chart answer to similar questions, while using the class s compiled M&M data. Instructor s may choose to have student s do a few questions of the Post Test/Activity individually, then discuss the end questions (about sample size) in a small group, and later as a class. Post Test: The Post Test is the same quiz as was given as a Pre Test.
Pie Chart/ Bar Chart Probabilities Pre-Test Name: Class: Hour: 1. You are handed a sheet of stickers that have pictures of various sport themes. On your sheet, you have seven basketball stickers, three volleyball stickers, nine soccer stickers, and twelve football stickers. a. Create a pie chart and bar graph to represent the percentages of each type of sticker you have. (You may use technology to help you.) b. If one sticker is chosen at random, what is the probability that is a soccer sticker? c. What percent of your stickers are basketball stickers? d. What fraction of your stickers are volleyball stickers?
Probability as Area Worksheet Name: After Farmer Jones passes away, his five children (Bill, Susan, Matthew, Carl, and Julie) are supposed to inherit an equal share of his 100 square acres. This is demonstrated in the Pie Chart below. 1. What is the area of the land they should each inherit? 2. If I am standing somewhere on Farmer Jones land, in terms of area, what is the probability that I am standing on the land that Julie will inherit? 3. What is the probability that I m on the land that Carl will inherit? Write as a fraction, then write as a decimal.
M & M Pie Chart Probability Experiment In a Fun Size pack of M & M s, you may have M & M s of the colors brown, red, blue, green, yellow and orange. Assume the same number of each color of M & M is created. Solely statistically speaking, what percent of each color would your bag contain? Write down the expected percent of each color by or on the graph below. Use the scenario and graph above to fill in the following table. (Remember, we are assuming the statistical percentages of each color.) Assume there are 18 M & M s in your bag. COLOR Number of Each Color Area of Particular Total Area Probability of Drawing Color (if one M & M is drawn randomly) Percent Fraction of Area for that 100 Decimal
Predictions! If you are handed a fun size bag of M & M s, do you think you will have the same number of each color? Why or why not? Just for fun, how many of each color of M & M do you think will be in your bag? Blue? Red? Green? Yellow? Brown? Orange? After you are finished with your predictions, open your bag, and fill in the actual numbers below. Blue? Red? Green? Yellow? Brown? Orange? Were your predictions close? Could you have made a better guess? Please explain. Sketch those Graphs! Sketch a Pie Graph and Box Plot of your M & M colors! Pie Graph 1. Arrange your M & M s in a circle inside the box to the right. 2. Trace around the outside of your M & M s to create a circle.
3. Create tick marks around the edge of your circle to separate each color. (You may then move your M & M s off to the side. But SAVE them so you are able to draw your upcoming box plot.) 4. Draw a dot in the center of your circle. (You do not need to measure this but try to be as accurate as possible.) 5. Use a ruler to carefully connect the center to each of your tick marks. Bar Graph Similarly, line up your M & M s to create a Bar Graph in the box below. Create a pie graph and a bar graph of your data using technology. List three observations about your M & M data that you can make by looking your graphs. 1.
2. 3. How is the pie chart of your M & M data different than the pie graph we used when we assumed each color was equally likely? List three differences. 1. 2. 3. Create a pie chart using technology to display the distribution of colors for your bag of M & M s. (Be sure to staple a printed copy of your chart to these worksheets.) Then, complete the chart, using your actual values) below. COLOR Number of Each Color Area of Particular Total Area Probability of Drawing Color (if one M & M is drawn randomly) Percent Fraction of Area for that 100 Decimal
Pie Chart/ Bar Graph Probabilities Activity Name: Class: Hour: Compile the class s M & M data. Use this data to complete following. 1. Create a pie chart and a bar graph to represent the distribution of the classes M & M colors. (Be sure to staple a print out of your graph to these worksheets.) 2. If the class s M & M s would ve been all together in a large bag and you randomly pulled out one M & M, what is the probability that it would be blue? 3. Complete the table below. COLOR Number of Each Color Area of Particular Total Area Probability of Drawing Color (if one M & M is drawn randomly) Percent Fraction of Area for that 100 Decimal
4. Name three similarities between (just) your M & M data and the classes M & M data. 1. 2. 3. 5. Name three differences you ve observed. 1. 2. 3.
6. Was (just) your data or the class s data more closely related to equal distribution? Why do you think this is? 7. Imagine everyone in the school had a pack of Fun Size M & M s and we combined all of the M & M s together. What do you think the pie chart representing these colors would look like? Explain your thoughts & create a sketch below. 8. How does sample size affect probability? Pie Chart Probabilities Post-Test Name: Class: Hour: 1. You are handed a sheet of stickers that have pictures of various sport themes. On your sheet, you have seven basketball stickers, three volleyball stickers, nine soccer stickers, and twelve football stickers. a. Create a pie chart and bar graph to represent the percentages of each type of sticker you have. (You may use technology to help you.)
b. If one sticker is chosen at random, what is the probability that is a soccer sticker? c. What percent of your stickers are basketball stickers? d. What fraction of your stickers are volleyball stickers?