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


	Item 12 Practice Set B 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 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 expressions (''Ranger Jones 6n+78…Percy 8n+78"), are correct. The student indicates the difference in the total number of deer predicted by comparing Ranger Percy's prediction ("158") with Ranger Jones' ("138"). However, an explanation is not provided. 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. The representations, in the form of equations, are correct. The variable d is not defined. The difference in the total number of predicted deer in 10 years ("20 deer") is correct. The symbolic explanation is fully developed and supports the solution. 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 tables are correctly completed. Although the student repeats the information given in the question, no expression is provided for either Ranger Jones or Ranger Percy. There is no indication that the student has responded to the third part of the question. This response demonstrates a minimal 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. The representations, in the form of equations (''Ranger Jones d=78+6n…Ranger Percy d=78+8n"), are correct, and the variable d is defined. The difference in the predicted number of deer in 10 years ("30") is incorrect. This response demonstrates a conceptual understanding and analysis of the problem. (Compare to this Level 2 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. The representations, in the form of expressions (''Ranger Jones 78+6n…Ranger Percy 78+8n"), are correct. The difference in the number of predicted deer in 10 years ("20 deer") is correct. The symbolic explanation is fully developed, clearly presented, and supports the solution. The student replaces the n in each equation with 10; solves for x, the predicted number of deer; 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 tables are correctly completed. The response to the second part of the question is a restatement of information given in the item. The student provides a predicted number of deer for Ranger Percy ("would be 156 deer") and Ranger Jones ("would be 144 deer"). However, these are incorrect predictions, and the student's incomplete explanation ("by just adding eight or 6 or 8 to the deer population that year") does not reveal the error. The difference between 156 and 144 is not "21." This response demonstrates a minimal 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. The representations, in the form of equations, are correct. The student has not defined x after changing it from n as given in the item. The equations are labeled for each ranger by their locations beneath the assigned tables. The numbers "132" and "158" indicate an attempt to arrive at a predicted number of deer for each ranger; however, the difference in the predicted number of deer in 10 years ("22 deer apart") is inconsistent with these numbers, and "132" is an incorrect prediction. This response demonstrates a conceptual understanding and analysis of the problem.
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 expressions, are correct, and the variable x is defined. The difference in the predicted number of deer in 10 years ("50 deer in 10 years is the difference of the 2 rangers predictions") is incorrect. The symbolic explanation reveals a reasonable strategy. The student replaces n in each equation with 10 and solves for the predicted deer population. For Ranger Percy's prediction, the student makes an error, arriving at a total of 182, rather than 158. The difference in deer population ("50 deer") is consistent with the student's numbers. This response demonstrates a clear understanding and analysis of the problem.

Practice Set B 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 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 expressions (''Ranger Jones 6n+78…Percy 8n+78"), are correct. The student indicates the difference in the total number of deer predicted by comparing Ranger Percy's prediction ("158") with Ranger Jones' ("138"). However, an explanation is not provided. 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. The representations, in the form of equations, are correct. The variable d is not defined. The difference in the total number of predicted deer in 10 years ("20 deer") is correct. The symbolic explanation is fully developed and supports the solution. 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 tables are correctly completed. Although the student repeats the information given in the question, no expression is provided for either Ranger Jones or Ranger Percy. There is no indication that the student has responded to the third part of the question. This response demonstrates a minimal 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. The representations, in the form of equations (''Ranger Jones d=78+6n…Ranger Percy d=78+8n"), are correct, and the variable d is defined. The difference in the predicted number of deer in 10 years ("30") is incorrect. This response demonstrates a conceptual understanding and analysis of the problem. (Compare to this Level 2 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. The representations, in the form of expressions (''Ranger Jones 78+6n…Ranger Percy 78+8n"), are correct. The difference in the number of predicted deer in 10 years ("20 deer") is correct. The symbolic explanation is fully developed, clearly presented, and supports the solution. The student replaces the n in each equation with 10; solves for x, the predicted number of deer; 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 tables are correctly completed. The response to the second part of the question is a restatement of information given in the item. The student provides a predicted number of deer for Ranger Percy ("would be 156 deer") and Ranger Jones ("would be 144 deer"). However, these are incorrect predictions, and the student's incomplete explanation ("by just adding eight or 6 or 8 to the deer population that year") does not reveal the error. The difference between 156 and 144 is not "21." This response demonstrates a minimal 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. The representations, in the form of equations, are correct. The student has not defined x after changing it from n as given in the item. The equations are labeled for each ranger by their locations beneath the assigned tables. The numbers "132" and "158" indicate an attempt to arrive at a predicted number of deer for each ranger; however, the difference in the predicted number of deer in 10 years ("22 deer apart") is inconsistent with these numbers, and "132" is an incorrect prediction. This response demonstrates a conceptual understanding and analysis of the problem.

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 expressions, are correct, and the variable x is defined. The difference in the predicted number of deer in 10 years ("50 deer in 10 years is the difference of the 2 rangers predictions") is incorrect. The symbolic explanation reveals a reasonable strategy. The student replaces n in each equation with 10 and solves for the predicted deer population. For Ranger Percy's prediction, the student makes an error, arriving at a total of 182, rather than 158. The difference in deer population ("50 deer") is consistent with the student's numbers. This response demonstrates a clear understanding and analysis of the problem.