# 4 G: Identify, analyze, and synthesize relevant external resources to pose or solve problems. 4 D: Interpret results in the context of a situation.

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1 MAT.HS.PT.4.TUITN.A.298 Sample Item ID: MAT.HS.PT.4.TUITN.A.298 Title: College Tuition Grade: HS Primary Claim: Claim 4: Modeling and Data Analysis Students can analyze complex, real-world scenarios and can construct and use mathematical models to interpret and solve problems. Secondary Claim(s): Claim 1: Concepts and Procedures Students can explain and apply mathematical concepts and interpret and carry out mathematical procedures with precision and fluency. Claim 2: Problem Solving Students can solve a range of well-posed problems in pure and applied mathematics, making productive use of knowledge and problem-solving strategies. Claim 3: Communicating Reasoning Students can clearly and precisely construct viable arguments to support their own reasoning and to critique the reasoning of others. Primary Content Domain: Statistics and Probability Secondary Content Functions, Algebra, Number and Quantity Domain(s): Assessment Target(s): 4 A: Apply mathematics to solve problems arising in everyday life, society, and the workplace. 4 E: Analyze the adequacy of and make improvements to an existing model or develop a mathematical model of a real phenomenon. 4 G: Identify, analyze, and synthesize relevant external resources to pose or solve problems. 4 B: Construct, autonomously, chains of reasoning to justify mathematical models used, interpretations made, and solutions proposed for a complex problem. 4 F: Identify important quantities in a practical situation and map their relationships (e.g., using diagrams, two-way tables, graphs, flowcharts, or formulas). 4 D: Interpret results in the context of a situation. 1 G: Create equations that describe numbers or relationships. 1 P: Summarize, represent, and interpret data on a singlecount or measurement variable. 2 B: Select and use appropriate tools strategically. 3 F: Base arguments on concrete referents such as objects, drawings, diagrams, and actions.

5 at the start of the performance task. To do this, teachers will compile the complete list of schools provided by the students. They will enter each school into the search tool provided below. Screen shots will be made of each school s tuition data. The screen shots will then be combined to form the simulated search tool to be used by the students when they begin Session 1 of the task. [Notes: Ideally, the simulated search should be laid out in a similar fashion to the search tool provided on this Web site listed below. The simulated search will be a subset of all schools found on this site. A sample screen shot is below. (It can be enlarged.) This is the school whose data are used in the sample response. A simulated search should be created to have only the data from the collective list of schools provided by the students. Students will locate the school they specifically chose, and ideally have these two tables displayed: In-state tuition & fees and Outof-state tuition & fees. Additional information: 1. If the simulated search can be computer based, scrolling over the bars from the bar graph will list both in- and out-of-state tuition and fees for the particular school. 2. If the simulation will not be available via computer, the output should be adjusted from what is shown in the screen shot below. (The screen shot below shows 2010 in-state tuition & fees displayed on top, followed by the in-state tuition and fees table.) The output should be adjusted to show the In-state tuition and fees on top and the Out-of-state tuition and fees underneath. 3. The data on this Web site is based on tuition and fees only. No additional expenses are reflected unless specifically noted. 4. This is the data students will use in Part A of the task.]

6 Session 1 [Note: Session 1 of the performance task consists of two Parts: A and B. Part A should be performed individually. Part B should be performed in pairs or small groups. The teacher should allow for the majority of Session 1 to be devoted to group work.] Your Assignment: College Tuition Based on your research during the last few days, you may have realized that the cost of a college education in the United States can be expensive. During this performance task, you will use a spreadsheet and your knowledge of functions and statistics to predict the future cost of college tuition.

7 Steps you will be following: To accomplish this, you will use a spreadsheet to help perform the following: 1. Gather data on the past year s tuition amounts. 2. Analyze the data and choose a model type that will best predict the future tuition total. 3. Develop a model equation based on the model type chosen. 4. Predict the total tuition amount for a 2-year or a 4-year college education in the near future. 5. Compare the predicted total tuition amount using the model equation with the total predicted tuition amount you calculated prior to the start of this task. 6. Compare tuition amounts at the college you chose with the average tuition amounts of all public 4-year colleges in the United States. 7. Predict the total tuition amount at a 2-year or a 4-year college education in the distant future. Part A Past Year s Tuition During the past few days, each of you chose a specific college or university to research. In order to predict the total tuition amount at that college or university, you must first research past year s tuition amounts for that school. You will use a computer to search for these data specific to the school you chose. Your search will provide you with the combined cost for tuition and school-related fees at your school over the past several years. Gather these data and enter them into a spreadsheet. The data must include the tuition and school-related fees, as one total dollar amount, for the past 10 years. [Note: With the data provided on the simulated searches in this example, that will be for the years ]

8 Part B Choosing a Model After you have collected your data and entered it into the spreadsheet, get into pairs or groups of 3 or 4. In your group, you will analyze each team member s data by determining the following: what the data look like graphically what outliers, if any, exist what model type, either linear or nonlinear, best fits the data As a group, decide which model type will be used to determine the function (model equation) that will predict each member s future tuition amounts at his/her chosen school. The model types may or may not be the same for all group members. Look for similarities and differences in each group member s data. Discuss some reasons why the data cause the model types for each group member to be the same or different. [Note: Allow 5-10 minutes at the end of Session 1 for a whole class discussion about what was discovered during the group work. Students should discuss the reasons they came up with for why the model types in their individual groups, and the class as a whole, may or may not be the same.] End of Session 1

11 Part D Comparing Individual Tuition and Average Tuition The following table shows actual data for the average tuition costs for all 4-year public universities in the United States. Use your spreadsheet to compare the data you found on your college s tuition amounts over a 10-year period with the data for the average tuition amounts at 4-year public colleges. Suppose the data for the average tuition amounts for all 4-year public colleges were used to create a new model equation. Also, suppose this model equation was used to predict the future college tuition amounts.

12 4. Which model equation would have a higher correlation factor: the model equation created from the average tuition amounts; or the model equation created from the tuition amounts at your chosen school? Explain why that model equation has a higher correlation factor. What does this suggest about how reliable each model is for predicting future college tuition amounts? Explain your reasoning. You may use a combination of diagrams, mathematical expressions/equations, and words. Part E Predicting Tuition for the Next Generation In this last part of the task, you will predict the total tuition amount someone in a future generation will be expected to pay. Use your spreadsheet and the model equation you determined for your college to predict the total tuition amount for a family that has a child born 10 years from now. You should assume that this child will:

13 attend the college you chose, begin college at age 18, and attend for the full length of time (either 2 or 4 years). 5. Show how you determined the predicted total college tuition amount for this person. You may use a combination of diagrams, mathematical expressions/equations, and words. Consider the two articles, Tuition Hikes of the Downturn and The State of the Union on college costs, you read prior to starting this task. 6. Use these articles to help justify why predicting college tuition costs too far into the future, beyond a few years, might not be reliable. Cite information from each article that supports your reasoning. [Note: Students should have both articles available during this portion of the task.] End of Session 2

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