Project Title: Proportional Reasoning in Real-Life Stories Challenge Brief In this investigation, you will determine whether three real-life stories describe proportional or non-proportional relationships by creating and examining tables of data and the related equation and graph that represent each story. Project Requirements: 1. Every group is complete the following for each story: Construct a data table Create a graph of the data Write an equation that corresponds with the data in the table and graph Answer the guiding questions 2. Creative Display of Work: Chart Paper Each group will be assigned one story to do the following: Write your scenario in large print. Include the data table, graph, and equation. In your own words, explain if the real-life scenario represents a proportional or nonproportional relationship. 3. Participation in Class Discussion Complete, ‘What Do You Think?’ Standards 7th Grade: (7.3) Patterns, relationships, and algebraic thinking. The student solves problems involving direct proportional relationships. The student is expected to (B) estimate and find solutions to application problems involving proportional relationships such as similarity, scaling, unit cost, and related measurement units. (7.5) Patterns, relationships, and algebraic thinking. The student uses equations to solve problems. The student is expected to (B) formulate problem situations when given a simple equation and formulate and equation when given a problem situation. th 8 Grade: (8.3) Patterns, relationships, and algebraic thinking. The student identifies proportional or nonproportional linear relationships in problem situations and solves problems. The student is expected to (A) compare and contrast proportional and non-proportional linear Relationships. Scenarios 1. Your principal has asked you to participate in a Race for the Cure, a fund-raising event to collect money for research to fight cancer. Your middle school will donate $20 for each mile you walk or run. 2. Your school plans to buy new computers at $525 per computer. The total number of computers that can be purchased depends on the amount of money in the budget allocated for the computers. 3. You are helping your mom plan a birthday party for your brother at a bowling alley. The shoe rental is $5 and each game costs$2.50. Race for the Cure Your principal has asked you to participate in a Race for the Cure, a fund-raising even to collect money for research to fight cancer. Your middle school will donate $20 for each mile you walk or run. a. Construct a table to determine the total amount of money you can raise depending on how many miles you will walk or run. Show how you determined the amount of the donation by recording the process you used to calculate the amount in a column labeled “Process”. b. Create a graph of your data. Describe how the graph is a representation of the table. (graph paper) c. Determine an equation that could be used to calculate the amount of money you can raise if you were to walk x miles. d. Does your equation represent the data in your graph? Explain your reasoning. e. In what way is the $20 per mile donation represented in the data table? In the equation? In the graph of the equation? f. a proportion to determine the money raised for walking or running 4 miles. Running or walking 8 miles? Running or walking 10 miles? Show your work. g. Were your answers for each problem already in the table, the equation, and your graph? Explain why or why not? h. Does the real-life problem represent a proportional relationship? Use the data from your table, equation, and graph to explain why or why not? Computer Purchases Your school plans to buy new computers at $525 per computer. The total number of computers that can be purchased depends on the amount of money in the budget allocated for the computers. a. Create a table to determine the cost of computers depending on the number of computers. b. Determine an equation that could be used to budget x computers. c. Use your equation to buy six additional computers. Enter the data in your table and graph the data. d. Does your equation represent the data in your graph? Explain your reasoning. e. In what way is the price of a computer represented in the data table? In the equation? In the graph of the equation? f. Set up a proportion to determine the cost of computers if the school bought 5 computers, eight computers, and ten computers. Show your work. g. Were your answers for each computer already in the table, the equation, and in your graph? Explain why or why not? h. Does this situation represent a proportional relationship? Why or why not? Use the data from your table, equation, proportion, and graph to explain. Party at the Bowling Alley You are helping your mom plan a birthday party for your brother at a bowling alley. The shoe rental is $5 and each game costs $2.50. a. Create a table to record what could be the cost per person for a different number of bowling games. b. Determine an equation that could be used to calculate the cost per person for x games. c. Use your equation to buy five additional games. Enter your data in the table and graph all the data. d. Does your equation represent the data you graphed? Explain your reasoning. e. Can you use a proportion to determine the cost of bowling 8 games? Explain your reasoning. f. In what way is the cost per game represented in the data table? In the equation? In the graph of the equation? g. In what way is the shoe rental price represented in the data table? In the equation? In the graph of the equation? h. Does this situation represent a proportional relationship? Why or why not? What Do You Think? 1. Compare and contrast data tables, equations, and graphs for the three stories you investigated. What is similar and what is different for the three tables? What is similar and what is different for the three graphs? What is similar and what is different for the three equations? 2. Identify characteristics of proportional and non-proportional relationships by analyzing the three data tables, graphs, and equations. Describe the properties of data in a table that represent a proportional relationship. Describe the properties of a graph that represents a proportional relationship. Describe the properties of an equation that represent a proportional relationship. Proportional Reasoning in Real-Life Stories Rubric 4 Explanation Use of Visuals Display of Work (chart paper) Mechanics Demonstrated Knowledge A complete response with a detailed explanation in all three scenarios. Clear data table, graph, and equation with detail in all three scenarios. Includes scenario, data table, graph, equation, & detailed explanation of proportional or non-proportional reasoning. Completes all three scenarios with no math errors or flaws in reasoning. Shows complete understanding of the scenarios, questions, proportional reasoning, and processes. Criteria 3 Good solid response with clear explanation in two out of the three scenarios. Clear data table, graph, & equation in all three scenarios. 2 Points 1 Explanations are unclear in any of the scenarios. Misses Key Points in all scenarios. Unclear data table, graph, & equation in any or all of the three scenarios. Missing data table, graph, or equation in any or all of the three scenarios. Includes scenario, data table, graph, equation & explanation of proportional or nonproportional reasoning. Includes scenario, data table, graph and equation. No product. No major math errors or serious flaws in reasoning. Some serious math errors or flaws in reasoning. Major errors or serious flaws in reasoning. Shows substantial understanding of the three scenarios, questions, proportional reasoning, and processes. Response shows some understanding of the scenarios. Response or no response shows complete lack of understanding.