Item 30 Mini Practice Set Responses    
Mike wants to know how many calories he can burn while jogging. The number of calories burned depends on the length of time Mike jogs. The table below shows the number of calories Mike burns while jogging.

Complete the following in the Answer Book:
  • Write an equation for a line of best fit. (If you choose to draw a graph, use the grid provided in the Answer Book.)
     
  • What is the slope of your line of best fit? What does the slope mean in the context of this problem?
     
  • Mike jogged for 60 minutes. According to your line of best fit, how many calories did he burn? Use mathematics to explain how you determined your answer. Use words, symbols, or both in your explanation.
     

Score Level 2 Paper

 

This response indicates an incomplete application of a reasonable strategy. Although the variables are not defined, an appropriate equation is given for the line of best fit. The slope is correct; however, the meaning of slope is not ("for every 10 minutes it will go up 9.811 in calories burned"). The correct context for slope would be that for every 1 minute 9.811 calories are burned. A correct answer ("588.708") for the number of calories burned and a clearly presented explanation (substitutes 60 for x in the equation) are given. This response demonstrates a conceptual understanding and analysis of the problem.

image of student response

Score Level 3 Paper

 

This response indicates application of a reasonable strategy that leads to a correct solution in the context of the problem. The variables are defined, and an appropriate equation for the line of best fit is provided. The slope and the meaning of slope ("means that Mike burns 9.81 calories per minute of jogging") are correct. A correct answer ("589") for the number of calories burned is given. The student substitutes 60 for x in the equation, providing a clearly presented and fully developed explanation. This response demonstrates a complete understanding and analysis of the problem.

image of student response

Score Level 1 Paper

 

This response indicates little attempt to apply a reasonable strategy. An appropriate equation for the line of best fit, a numerical answer for the slope, and the meaning of slope are not given. The student correctly answers ("587") for how many calories are burned, demonstrating some meaningful interaction, but no explanation is provided. Although a graph of the line of best fit is not required, the student plots the points from the table and connects the dots. This is not, however, a line of best fit. This response demonstrates a minimal understanding and analysis of the problem.

image of student response
 

Mini Practice Set Papers ~ Algebra/Data Analysis ~ Item 30

Mike wants to know how many calories he can burn while jogging. The number of calories burned depends on the length of time Mike jogs. The table below shows the number of calories Mike burns while jogging.

Complete the following in the Answer Book:
  • Write an equation for a line of best fit. (If you choose to draw a graph, use the grid provided in the Answer Book.)
     
  • What is the slope of your line of best fit? What does the slope mean in the context of this problem?
     
  • Mike jogged for 60 minutes. According to your line of best fit, how many calories did he burn? Use mathematics to explain how you determined your answer. Use words, symbols, or both in your explanation.
     

 

Score Level 2 Paper

 

This response indicates an incomplete application of a reasonable strategy. Although the variables are not defined, an appropriate equation is given for the line of best fit. The slope is correct; however, the meaning of slope is not ("for every 10 minutes it will go up 9.811 in calories burned"). The correct context for slope would be that for every 1 minute 9.811 calories are burned. A correct answer ("588.708") for the number of calories burned and a clearly presented explanation (substitutes 60 for x in the equation) are given. This response demonstrates a conceptual understanding and analysis of the problem.

image of student response

 

Score Level 3 Paper

 

This response indicates application of a reasonable strategy that leads to a correct solution in the context of the problem. The variables are defined, and an appropriate equation for the line of best fit is provided. The slope and the meaning of slope ("means that Mike burns 9.81 calories per minute of jogging") are correct. A correct answer ("589") for the number of calories burned is given. The student substitutes 60 for x in the equation, providing a clearly presented and fully developed explanation. This response demonstrates a complete understanding and analysis of the problem.

image of student response

 

Score Level 1 Paper

 

This response indicates little attempt to apply a reasonable strategy. An appropriate equation for the line of best fit, a numerical answer for the slope, and the meaning of slope are not given. The student correctly answers ("587") for how many calories are burned, demonstrating some meaningful interaction, but no explanation is provided. Although a graph of the line of best fit is not required, the student plots the points from the table and connects the dots. This is not, however, a line of best fit. This response demonstrates a minimal understanding and analysis of the problem.

image of student response