Math Performance Task Teacher Instructions Stock Market Research Instructions for the Teacher The Stock Market Research performance task centers around the concepts of linear and exponential functions. Students demonstrate their understanding and application of functions by responding to questions and prompts. Read the student performance task, and familiarize yourself with the tasks the student will be asked to complete. Provide students with copies of the student performance task and a means (paper or electronic) to write their responses. The recommended time for completing the task is 30 to 60 minutes. Students complete the task individually. Assess student performance based on the accompanying rubric. Performance Task Skills Interpret a complicated linear or exponential expression by viewing one or more of its parts as a single entity Rearrange a formula to isolate a variable of interest where the formula is linear in that variable Interpret the meaning of the origin or scale for a graph or data display Solve a problem involving a linear or exponential equation in one variable Graph a linear or exponential equation using coordinate axes Graph an exponential function showing intercepts and end behavior Task Evidence Rating/Points 1. Interpret a linear expression. The student explains that 7.5 (the coefficient) represents the increase per year in the value of the stock. The student explains that 30 (the constant) represents the initial value of the stock. the meaning of the coefficient the constant 2. Rearrange an equation. Solve a problem involving a linear equation in one variable. The student writes the equation y 30 x =, or an equivalent form. 7.5 The student explains that it is easier to find a value of x when the equation is already solved for x. The student uses the equation to find that when y = 67.50, x = 5; it will take equation why rewriting the equation is helpful 1 point for finding the correct number of years 1 of 5
3. Solve a problem involving an exponential equation. 4. Solve a problem involving a linear or exponential equation. 5 years for the stock to have a value of $67.50. The student states that 1.3 represents the 30% increase per year. The student states that for x y = 8.3 (1.3), when x = 3, y = 18.24; the value of the stock after 3 years will be $18.24. The student makes a point of converting 24 months to 2 years. The student states that Virtual Game World s stock will have a value of $45.00 in 2 years. The student states that Robotics Unlimited s stock will have a value of $14.03 in 2 years. the meaning of 1.3 in the equation 1 point for stating that when x = 3, y = 18.24 1 point for converting the months to years before using the equation value of Virtual Game World s stock value of Robotics Unlimited s stock 5. Graph the equation. The student writes the ordered pairs (2, 45), (5, 67.5), and (10, 105) for the Virtual Game World table. The student writes the ordered pairs (2, 14.03), (3, 18.24), and (10, 114.42) for the Robotics Unlimited table. The student graphs each equation correctly. (See sample graph.) Virtual Game World table Robotics Unlimited table linear graph exponential graph 6. Interpret the meaning of the origin. The student says (0, 0) is not a point on either graph. The student states that x = 0 represents the initial time of purchase, y = 0 represents the initial value of the stocks, and the initial values are not $0. 1 point for saying that (0, 0) is not on either graph 1 point for giving a clear and accurate explanation of why or why not 7. Interpret the graph. The student states that when x = 0, the stock had an initial value of $8.30 per share. 1 point for correctly describing the meaning of the ordered pair 8. Solve a problem by interpreting the graph. The student correctly states that the point of intersection occurs at x = 9.5. The student explains that the point of intersection on the graph shows the time at which the stock values are the same. x-value 1 point for describing the intersection as the point of interest for determining when the stocks will be equal in 2 of 5
9. Analyze and interpret the information. Student selects Robotics Unlimited because based on the projected values, the stock will have a greater value than Virtual Game World s stock after ten years. value 0 2 points based on a complete recommendation Sample Response For the first ten years, Virtual Game World s stock will be worth more than Robotics Unlimited s stock. But, if the trends continue, after ten years Robotics Unlimited s stock will be worth more than Virtual Game World s stock. Since you plan to let your investment grow for at least 15 years, Alonso, you should invest in Robotics Unlimited. 3 of 5
Instructions for the Student Alonso wants to invest his savings in the stock market. He narrowed his choices to two companies Virtual Game World and Robotics Unlimited. He reads an article that predicts each company s future stock values. Help Alonso analyze the two companies. Determine which one he should invest in by answering the questions below. 1. The equation y = 7.5x + 30 models the projected value for one share of Virtual Game World stock. The variable y represents the value of one share of stock, and the variable x represents years invested. Let x = 0 represent year 0 or when you first buy the stock, and let x = 1 indicate one year after the stock purchase. Explain what the coefficient and constant mean in the context of the problem. 2. Alonso wants to know how long it would take for the Virtual Game stock to be worth $67.50. Rewrite the equation in terms of x. How does this help Alonso? Using your equation, find the number of years it will take for the stock value to be $67.50. 3. The equation y = 8.3(1.3) x models the projected value for one share of Robotics Unlimited stock. The variable x represents the number of years since purchase. The variable y represents the stock value. The initial value of the stock when x = 0 is $8.30 per share. The stock is expected to increase by 30% each year. What does 1.3 represent in the equation? Use the equation to determine the value of the Robotics Unlimited stock in 3 years. 4. What is the predicted value of each stock 24 months from the purchase date? 5. To better compare the two stocks, Alonso decided to graph the equations. Graph the two equations on the same grid. Complete a table of values for each equation to help you. Use the graph on the next page. Virtual Game World Year (x) 0 2 10 Value (y) 30 67.50 Robotics Unlimited Year (x) 0 2 3 10 Value (y) 8.3 4 of 5
6. Is the point (0, 0) on either of the graphs? Explain why or why not. 7. In the graph of y = 7.5x + 30, the y-intercept shows the initial value of the Virtual Game World stock as $30. What does the point (0, 8.3) on the graph for Robotics Unlimited represent? 8. After how many years will the values of the two stocks be the same? Use the graph in your analysis. Explain your answer. 9. Alonso plans to watch his investment grow for at least 15 years. Analyze the information about the two companies. Write a brief note to Alonso, making a recommendation about which stock he should choose. 5 of 5