Item 27 Practice Set A 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 1 Paper

 

This response indicates little application of a reasonable strategy. An equation (y = .10x + .75) is given for the line of best fit. Although the student does not specifically state the slope, the meaning of slope (each ounce costs about $.10) is correct. The price of a bottle of juice ($.76) is incorrect, and no explanation is supplied. 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. Because the student provides an expression, instead of an equation, the representation is not complete. The slope is correct; however, the meaning of slope is incorrect (for every .6 ounces it costs $.1). The price of a bottle of juice ($1.40) is correct, and the explanation is complete (by plugging in 8 ounces for x, then solving the equation). This response demonstrates a conceptual understanding and analysis of the problem.

image of student response

Score Level 1 Paper

 

This response indicates little application of a reasonable strategy. An appropriate equation (y=.09x + .60) is given for the line of best fit. The answer for slope contains an error; the student includes the variable "x." The meaning of slope is incorrect. The price of a bottle of juice is incorrect, and the attempted explanation shows serious flaws in reasoning. This response demonstrates a minimal understanding and analysis of the problem. (Compare to this Level 1 anchor paper.)

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 + .6) is given for the line of best fit. Although the student does not specifically define the variables, this is considered a minor error. The slope and the meaning of slope (for every ounce of orange juice, the price goes up $0.10) are both correct. The price of a bottle of juice ($1.40) is correct. The explanation is logically sound (found this by plugging 8 ounces in 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 2 Paper

 

This response indicates incomplete application of a reasonable strategy. An appropriate equation (y = .1x + .6) is provided for the line of best fit. Both the slope and the meaning of slope are incorrect. The price of a bottle of juice ($1.40) is given, and the explanation is clearly presented and supports the solution (substituting 8 for x in the equation and solving). 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=0.1x + 0.6) is given for the line of best fit. The slope and the meaning of slope (how much each extra ounce will cost) are correct. The price of a bottle of juice is correct ($1.40). The explanation is clearly presented (taking my original equation and substituting 8 for x). The definition of the variables (x stood for how many ounces; the price {y}) is given in the response to the last part of the question. 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. Because the slope (.80/8) would be a correct answer using the first two data points from the table, the student shows some relevant knowledge. The meaning of slope is incorrect, but demonstrates some relevant understanding (how much it increased by the size of the bottle). The price of a bottle of juice is incorrect, and the explanation does not support the solution. 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 is given for the line of best fit. The omission of variable definitions is a minor error. The slope and the meaning of slope (how much money you add for each ounce you increase) are correct. The price of a bottle of juice ($1.40) is correct. The explanation is logically sound and supports the solution (entered my equation in the y=part of my calculator; went to the table and scrolled down to where x equaled 8). This response demonstrates a complete understanding and analysis of the problem. (Compare to this Level 3 anchor paper.)

image of student response
 

Practice Set A 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 1 Paper

 

This response indicates little application of a reasonable strategy. An equation (y = .10x + .75) is given for the line of best fit. Although the student does not specifically state the slope, the meaning of slope (each ounce costs about $.10) is correct. The price of a bottle of juice ($.76) is incorrect, and no explanation is supplied. 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. Because the student provides an expression, instead of an equation, the representation is not complete. The slope is correct; however, the meaning of slope is incorrect (for every .6 ounces it costs $.1). The price of a bottle of juice ($1.40) is correct, and the explanation is complete (by plugging in 8 ounces for x, then solving the equation). This response demonstrates a conceptual understanding and analysis of the problem.

image of student response

 

Score Level 1 Paper

 

This response indicates little application of a reasonable strategy. An appropriate equation (y=.09x + .60) is given for the line of best fit. The answer for slope contains an error; the student includes the variable "x." The meaning of slope is incorrect. The price of a bottle of juice is incorrect, and the attempted explanation shows serious flaws in reasoning. This response demonstrates a minimal understanding and analysis of the problem. (Compare to this Level 1 anchor paper.)

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 + .6) is given for the line of best fit. Although the student does not specifically define the variables, this is considered a minor error. The slope and the meaning of slope (for every ounce of orange juice, the price goes up $0.10) are both correct. The price of a bottle of juice ($1.40) is correct. The explanation is logically sound (found this by plugging 8 ounces in 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 2 Paper

 

This response indicates incomplete application of a reasonable strategy. An appropriate equation (y = .1x + .6) is provided for the line of best fit. Both the slope and the meaning of slope are incorrect. The price of a bottle of juice ($1.40) is given, and the explanation is clearly presented and supports the solution (substituting 8 for x in the equation and solving). 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=0.1x + 0.6) is given for the line of best fit. The slope and the meaning of slope (how much each extra ounce will cost) are correct. The price of a bottle of juice is correct ($1.40). The explanation is clearly presented (taking my original equation and substituting 8 for x). The definition of the variables (x stood for how many ounces; the price {y}) is given in the response to the last part of the question. 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. Because the slope (.80/8) would be a correct answer using the first two data points from the table, the student shows some relevant knowledge. The meaning of slope is incorrect, but demonstrates some relevant understanding (how much it increased by the size of the bottle). The price of a bottle of juice is incorrect, and the explanation does not support the solution. 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 is given for the line of best fit. The omission of variable definitions is a minor error. The slope and the meaning of slope (how much money you add for each ounce you increase) are correct. The price of a bottle of juice ($1.40) is correct. The explanation is logically sound and supports the solution (entered my equation in the y=part of my calculator; went to the table and scrolled down to where x equaled 8). This response demonstrates a complete understanding and analysis of the problem. (Compare to this Level 3 anchor paper.)

image of student response