Item 27 Practice Set B Responses    
Students in a nutrition class decide to sell orange juice at their school's next sports event. To determine the price, the students record prices of orange juice from various stores in their city. The table below shows the price of different-sized bottles of juice.

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 equation? What does the slope mean in the context of this problem?
     
  • The students are selling 8-ounce bottles of orange juice. According to your line of best fit, what is the price of an 8-ounce bottle of juice? Use mathematics to explain how you determined your answer. Use words, symbols, or both in your explanation.

Score Level 2 Paper

 

This response indicates incomplete application of a reasonable strategy. An appropriate equation (y=.099x + .60) is given for the line of best fit. While the slope is correct, the meaning of slope is incorrect. The price of a bottle of juice ($1.392) is correct, and the explanation, substituting 8 for x in the equation and solving, is clearly presented. 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. An appropriate equation (y=.099x + .60) is given for the line of best fit. The slope and the meaning of slope (the cost per ounce in the bottle) are correct. The price of a bottle of juice ($1.40) is correct, and the explanation is logically sound (by plugging in 8 ounces in for x). Some definition of the variables is provided in the statement (x represents the bottle size in ounces); the fact that y is not specifically defined is a minor error. This response demonstrates a complete understanding and analysis of the problem. (Compare to this Level 3 anchor paper.)

image of student response

Score Level 1 Paper

 

This response indicates little application of a reasonable strategy. No equation is given for the line of best fit. No slope is provided. The meaning of slope is incomplete; the student does not include how much the cost is rising per ounce. An attempt is made to find a pattern from the given table in order to determine the price of a bottle of juice. Some relevant knowledge is given in the statement (price of the 8 ounce bottle should be 1.39 because you subtract .8 from 2.19; because from 8 oz to 16 oz there are 8 oz; from 16 oz to 24 oz there are 8 oz; the difference in the price is .8; subtract .8). This response demonstrates a minimal 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. An appropriate equation (y=.1x + .59) is given for the line of best fit. The omission of variable definitions is a minor error. The slope and the meaning of slope (the price increment is 10 cents per ounce) are both correct. The price of a bottle of juice is correct, and the explanation, substituting 8 for x in the equation, is clearly presented. This response demonstrates a complete understanding and analysis of the problem. (Compare to this Level 3 anchor paper.)

image of student response

Score Level 2 Paper

 

This response indicates incomplete application of a reasonable strategy. An appropriate equation (y=.099x + .602) is given for the line of best fit. While the slope is correct, the meaning of slope is incorrect. The price of a bottle of juice ($1.39) is correct, and the explanation is clearly presented (got $1.39 by replacing x with 8). 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. An appropriate equation (y=.1x + .60) is given for the line of best fit. Although the variables are not specifically defined, this is a minor error. The slope and the meaning of slope (the amount of money that increases as the bottle size increases an ounce) are both correct. The price for a bottle of juice ($1.40) is correct. The explanation is logically sound and supports the solution (plugged in 8 for x). This response demonstrates a complete understanding and analysis of the problem. (Compare to this Level 3 anchor paper.)

image of student response

Score Level 1 Paper

 

This response indicates little application of a reasonable strategy. No equation is given for the line of best fit. No slope is provided. The student supplies some relevant information about the meaning of slope (for every ounce of difference, there is a change of .10 cents) which is used to explain how the student determines an answer ($1.39) for the price of a bottle of juice. This response demonstrates a minimal understanding and analysis of the problem.

image of student response

Score Level 2 Paper

 

This response indicates incomplete application of a reasonable strategy. An appropriate equation (y=.1x + .6) is given for the line of best fit. While the slope is correct, the meaning of slope is incomplete. The student does not indicate that the slope represents the cost per ounce of orange juice. The price of a bottle of juice ($1.40) is correct, and the explanation is clearly presented (by plugging in the 8 for x and solving out the problem). This response demonstrates a conceptual understanding and analysis of the problem. (Compare to this Level 2 anchor paper.)

image of student response
 

Practice Set B Papers ~ Algebra/Data Analysis ~ Item 27

Students in a nutrition class decide to sell orange juice at their school's next sports event. To determine the price, the students record prices of orange juice from various stores in their city. The table below shows the price of different-sized bottles of juice.

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 equation? What does the slope mean in the context of this problem?
     
  • The students are selling 8-ounce bottles of orange juice. According to your line of best fit, what is the price of an 8-ounce bottle of juice? Use mathematics to explain how you determined your answer. Use words, symbols, or both in your explanation.

 

Score Level 2 Paper

 

This response indicates incomplete application of a reasonable strategy. An appropriate equation (y=.099x + .60) is given for the line of best fit. While the slope is correct, the meaning of slope is incorrect. The price of a bottle of juice ($1.392) is correct, and the explanation, substituting 8 for x in the equation and solving, is clearly presented. 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. An appropriate equation (y=.099x + .60) is given for the line of best fit. The slope and the meaning of slope (the cost per ounce in the bottle) are correct. The price of a bottle of juice ($1.40) is correct, and the explanation is logically sound (by plugging in 8 ounces in for x). Some definition of the variables is provided in the statement (x represents the bottle size in ounces); the fact that y is not specifically defined is a minor error. This response demonstrates a complete understanding and analysis of the problem. (Compare to this Level 3 anchor paper.)

image of student response

 

Score Level 1 Paper

 

This response indicates little application of a reasonable strategy. No equation is given for the line of best fit. No slope is provided. The meaning of slope is incomplete; the student does not include how much the cost is rising per ounce. An attempt is made to find a pattern from the given table in order to determine the price of a bottle of juice. Some relevant knowledge is given in the statement (price of the 8 ounce bottle should be 1.39 because you subtract .8 from 2.19; because from 8 oz to 16 oz there are 8 oz; from 16 oz to 24 oz there are 8 oz; the difference in the price is .8; subtract .8). This response demonstrates a minimal 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. An appropriate equation (y=.1x + .59) is given for the line of best fit. The omission of variable definitions is a minor error. The slope and the meaning of slope (the price increment is 10 cents per ounce) are both correct. The price of a bottle of juice is correct, and the explanation, substituting 8 for x in the equation, is clearly presented. This response demonstrates a complete understanding and analysis of the problem. (Compare to this Level 3 anchor paper.)

image of student response

 

Score Level 2 Paper

 

This response indicates incomplete application of a reasonable strategy. An appropriate equation (y=.099x + .602) is given for the line of best fit. While the slope is correct, the meaning of slope is incorrect. The price of a bottle of juice ($1.39) is correct, and the explanation is clearly presented (got $1.39 by replacing x with 8). 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. An appropriate equation (y=.1x + .60) is given for the line of best fit. Although the variables are not specifically defined, this is a minor error. The slope and the meaning of slope (the amount of money that increases as the bottle size increases an ounce) are both correct. The price for a bottle of juice ($1.40) is correct. The explanation is logically sound and supports the solution (plugged in 8 for x). This response demonstrates a complete understanding and analysis of the problem. (Compare to this Level 3 anchor paper.)

image of student response

 

Score Level 1 Paper

 

This response indicates little application of a reasonable strategy. No equation is given for the line of best fit. No slope is provided. The student supplies some relevant information about the meaning of slope (for every ounce of difference, there is a change of .10 cents) which is used to explain how the student determines an answer ($1.39) for the price of a bottle of juice. This response demonstrates a minimal understanding and analysis of the problem.

image of student response

 

Score Level 2 Paper

 

This response indicates incomplete application of a reasonable strategy. An appropriate equation (y=.1x + .6) is given for the line of best fit. While the slope is correct, the meaning of slope is incomplete. The student does not indicate that the slope represents the cost per ounce of orange juice. The price of a bottle of juice ($1.40) is correct, and the explanation is clearly presented (by plugging in the 8 for x and solving out the problem). This response demonstrates a conceptual understanding and analysis of the problem. (Compare to this Level 2 anchor paper.)

image of student response