Practice Set A Responses ~ Algebra/Data Analysis ~ Item 12


	Item 12 Practice Set A Responses

Park rangers determined that the current deer population in a park is 78. Ranger Jones predicted that the deer population will increase by 6 deer each year. Ranger Percy predicted that the deer population will increase by 8 deer each year. Complete the following in the Answer Book:

Complete the tables in the Answer Book for Ranger Jones and Ranger Percy.
For each ranger's prediction, write an expression that can be used to determine the deer population in the park n years from now.
What is the difference in the number of deer that Ranger Percy predicted will be in the park 10 years from now compared to Ranger Jones' 10-year prediction? Use mathematics to explain how you determined your answer. Use words, symbols, or both in your explanation.

Score Level 4 Paper
This response indicates application of a reasonable strategy that leads to a correct solution within the context of the problem. The student correctly completes the table for each ranger and gives correct expressions for Ranger Jones (6n+78) and for Ranger Percy (8n+78). The difference in the predicted number of deer in 10 years ("20 deer") is correct. The explanation supports the solution. ("On the graph where the points are at 10, then I know that that is my answer. Ranger J will be 138, and Ranger P will be 158.") This response demonstrates a complete understanding and analysis of the problem.
Score Level 1 Paper
This response indicates little application of a reasonable strategy. The tables are correctly completed; however, no expression is given. No attempt is made to determine the difference in the predicted number of deer in 10 years. This response demonstrates a minimal understanding and analysis of the problem. (Compare to this Level 1 anchor paper.)
Score Level 3 Paper
This response indicates application of a reasonable strategy that leads to some correct solutions. The table for Ranger Jones' predictions is correctly completed. The student correctly provides the prediction for the first year on Ranger Percy's table; however, the predictions for years two and three are incorrect. The representations, in the form of equations ("Ranger Jones y=78+6x…Ranger Percy y=78+8n"), are correct. The student indicates the difference in the total number of deer by comparing Ranger Jones' prediction ("138 deer") with Ranger Percy's ("158"). The explanation supports the solution ("by plugging ten into x and solving for y") This response demonstrates a clear understanding and analysis of the problem.
Score Level 2 Paper
This response indicates an incomplete application of a reasonable strategy. The tables are correctly completed. While the representations are essentially correct, in the form of equations, the student has not defined y, after changing it from n given in the item, and d is not defined. There is no indication that the student has responded to the third part of the question. This response demonstrates a conceptual understanding and analysis of the problem. (Compare to this Level 2 anchor paper.)
Score Level 3 Paper
This response indicates application of a reasonable strategy that leads to some correct solutions. The tables are correctly completed. The representations, in the form of equations (''Ranger Jones y=6n+78…Ranger Percy y=8n+78"), are correct. The difference in the predicted number of deer in 10 years (''Ranger Jones believes that there will be 50 fewer deer in the park than what Ranger Percy thinks") is incorrect. The symbolic explanation reveals a reasonable strategy. The student replaces n in each equation with 10 and solves for y, the predicted deer population. However, a mathematical error is made in the Ranger Jones' prediction when the student adds 60 and 78 and arrives at a total of 108, rather than 138. The student then concludes "Jones thinks that in 10 years there will be 108 deer and Percy thinks there will be 158." The difference of "50 fewer deer" is consistent with the student's numbers. This response demonstrates a clear understanding and analysis of the problem. (Compare to this Level 3 anchor paper.)
Score Level 4 Paper
This response indicates application of a reasonable strategy that leads to a correct solution within the context of the problem. The tables are correctly completed. Correct expressions for Ranger Jones (6N+ 78) and Ranger Percy (8N+ 78) are given. The difference in the predicted number of deer in 10 years (20) is correct. The explanation is clearly presented and fully developed; the student replaces the n in each equation with 10, solves for each ranger's prediction, and then finds the difference. This response demonstrates a complete understanding and analysis of the problem.
Score Level 1 Paper
This response indicates little application of a reasonable strategy. The table for Ranger Jones is correctly completed, but the table for Ranger Percy is incorrect for 3 years. No attempt is made to write an expression or determine the difference in the predicted number of deer in 10 years. This response demonstrates a minimal understanding and analysis of the problem. (Compare to this Level 1 anchor paper.)
Score Level 2 Paper
This response indicates an incomplete application of a reasonable strategy. The tables are correctly completed. The representations, in the form of equations set equal to d (defined as "deer"), are essentially correct. The student reverses the Ranger's names when labeling. There is no indication that the student has addressed the third part of the question. This response demonstrates a conceptual understanding and analysis of the problem.

Practice Set A Papers ~ Algebra/Data Analysis ~ Item 12

Complete the tables in the Answer Book for Ranger Jones and Ranger Percy.
For each ranger's prediction, write an expression that can be used to determine the deer population in the park n years from now.
What is the difference in the number of deer that Ranger Percy predicted will be in the park 10 years from now compared to Ranger Jones' 10-year prediction? Use mathematics to explain how you determined your answer. Use words, symbols, or both in your explanation.

Score Level 4 Paper

This response indicates application of a reasonable strategy that leads to a correct solution within the context of the problem. The student correctly completes the table for each ranger and gives correct expressions for Ranger Jones (6n+78) and for Ranger Percy (8n+78). The difference in the predicted number of deer in 10 years ("20 deer") is correct. The explanation supports the solution. ("On the graph where the points are at 10, then I know that that is my answer. Ranger J will be 138, and Ranger P will be 158.") This response demonstrates a complete understanding and analysis of the problem.

Score Level 1 Paper
This response indicates little application of a reasonable strategy. The tables are correctly completed; however, no expression is given. No attempt is made to determine the difference in the predicted number of deer in 10 years. This response demonstrates a minimal understanding and analysis of the problem. (Compare to this Level 1 anchor paper.)

Score Level 3 Paper

This response indicates application of a reasonable strategy that leads to some correct solutions. The table for Ranger Jones' predictions is correctly completed. The student correctly provides the prediction for the first year on Ranger Percy's table; however, the predictions for years two and three are incorrect. The representations, in the form of equations ("Ranger Jones y=78+6x…Ranger Percy y=78+8n"), are correct. The student indicates the difference in the total number of deer by comparing Ranger Jones' prediction ("138 deer") with Ranger Percy's ("158"). The explanation supports the solution ("by plugging ten into x and solving for y") This response demonstrates a clear understanding and analysis of the problem.

Score Level 2 Paper

This response indicates an incomplete application of a reasonable strategy. The tables are correctly completed. While the representations are essentially correct, in the form of equations, the student has not defined y, after changing it from n given in the item, and d is not defined. There is no indication that the student has responded to the third part of the question. This response demonstrates a conceptual understanding and analysis of the problem. (Compare to this Level 2 anchor paper.)

Score Level 3 Paper

This response indicates application of a reasonable strategy that leads to some correct solutions. The tables are correctly completed. The representations, in the form of equations (''Ranger Jones y=6n+78…Ranger Percy y=8n+78"), are correct. The difference in the predicted number of deer in 10 years (''Ranger Jones believes that there will be 50 fewer deer in the park than what Ranger Percy thinks") is incorrect. The symbolic explanation reveals a reasonable strategy. The student replaces n in each equation with 10 and solves for y, the predicted deer population. However, a mathematical error is made in the Ranger Jones' prediction when the student adds 60 and 78 and arrives at a total of 108, rather than 138. The student then concludes "Jones thinks that in 10 years there will be 108 deer and Percy thinks there will be 158." The difference of "50 fewer deer" is consistent with the student's numbers. This response demonstrates a clear understanding and analysis of the problem. (Compare to this Level 3 anchor paper.)

Score Level 4 Paper

This response indicates application of a reasonable strategy that leads to a correct solution within the context of the problem. The tables are correctly completed. Correct expressions for Ranger Jones (6N+ 78) and Ranger Percy (8N+ 78) are given. The difference in the predicted number of deer in 10 years (20) is correct. The explanation is clearly presented and fully developed; the student replaces the n in each equation with 10, solves for each ranger's prediction, and then finds the difference. This response demonstrates a complete understanding and analysis of the problem.

Score Level 1 Paper

This response indicates little application of a reasonable strategy. The table for Ranger Jones is correctly completed, but the table for Ranger Percy is incorrect for 3 years. No attempt is made to write an expression or determine the difference in the predicted number of deer in 10 years. This response demonstrates a minimal understanding and analysis of the problem. (Compare to this Level 1 anchor paper.)

Score Level 2 Paper

This response indicates an incomplete application of a reasonable strategy. The tables are correctly completed. The representations, in the form of equations set equal to d (defined as "deer"), are essentially correct. The student reverses the Ranger's names when labeling. There is no indication that the student has addressed the third part of the question. This response demonstrates a conceptual understanding and analysis of the problem.