Item 36 Mini Practice Set Responses    
At a baseball game Sam bought 2 hamburgers and 1 order of French fries for a total of $3.75. Erica bought 1 hamburger and 2 orders of French fries for a total of $3.00.

Complete the following in the Answer Book:

  • Write an equation that represents Sam’s total cost. Write an equation that represents Erica’s total cost.
     
  • What is the cost of one hamburger? What is the cost of one order of French fries? Use mathematics to explain how you determined your answers. Use words, symbols, or both in your explanations. (If you choose to draw a graph, use the grid provided in the Answer Book to add to your written response.)
     
  • Use mathematics to justify your answers for the cost of one hamburger and the cost of one order of French fries.
     

Score Level 2 Paper

 

This response indicates an incomplete application of a reasonable strategy. The student provides the correct equations for both Sam's and Erica's total costs; however, the variables are not defined. The cost of one hamburger is correct, as is the cost of one order of fries. The explanation is incomplete ("plugging the costs for each into the equation and alterating different parts of the equation to make them equal the correct amount in each equation"). This response demonstrates a conceptual understanding and analysis of the problem. (Compare to this Level 2 anchor paper.)

image of student response

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 gives the correct equations for Sam's total cost ($3.75=2x+y) and Erica's total cost ($3.00=x+2y), and the variables are defined. The student provides the correct costs of one hamburger ($1.50) and one order of fries ($.75). The fully developed explanation is presented symbolically. The student fully justifies the solutions by inserting the values for x and y into each equation and simplifying, showing that the found values make each equation true. This response demonstrates a complete 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 correct solutions. The student gives the correct equations for Sam's total cost (2x+y=3.75) and Erica's total cost (1x+2y=3.00) , and the variables are defined. The student provides the correct costs of one hamburger ($1.50) and one order of fries ($.75). The symbolic explanation is fully developed and supports the solution. No justification is given. This response demonstrates a clear 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. While the student provides the correct equations for Sam's total cost (2h+1f=$3.75) and Erica's total cost (1h+2f=$3.00), the variables are not defined. The student does not solve for the cost of one hamburger or one order of fries, and no explanation or justification is provided. This response demonstrates a minimal understanding and analysis of the problem.

image of student response
 

Mini Practice Set Papers ~ Algebra/Data Analysis ~ Item 36

At a baseball game Sam bought 2 hamburgers and 1 order of French fries for a total of $3.75. Erica bought 1 hamburger and 2 orders of French fries for a total of $3.00.

Complete the following in the Answer Book:

  • Write an equation that represents Sam’s total cost. Write an equation that represents Erica’s total cost.
     
  • What is the cost of one hamburger? What is the cost of one order of French fries? Use mathematics to explain how you determined your answers. Use words, symbols, or both in your explanations. (If you choose to draw a graph, use the grid provided in the Answer Book to add to your written response.)
     
  • Use mathematics to justify your answers for the cost of one hamburger and the cost of one order of French fries.
     

 

Score Level 2 Paper

 

This response indicates an incomplete application of a reasonable strategy. The student provides the correct equations for both Sam's and Erica's total costs; however, the variables are not defined. The cost of one hamburger is correct, as is the cost of one order of fries. The explanation is incomplete ("plugging the costs for each into the equation and alterating different parts of the equation to make them equal the correct amount in each equation"). This response demonstrates a conceptual understanding and analysis of the problem. (Compare to this Level 2 anchor paper.)

image of student response

 

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 gives the correct equations for Sam's total cost ($3.75=2x+y) and Erica's total cost ($3.00=x+2y), and the variables are defined. The student provides the correct costs of one hamburger ($1.50) and one order of fries ($.75). The fully developed explanation is presented symbolically. The student fully justifies the solutions by inserting the values for x and y into each equation and simplifying, showing that the found values make each equation true. This response demonstrates a complete 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 correct solutions. The student gives the correct equations for Sam's total cost (2x+y=3.75) and Erica's total cost (1x+2y=3.00) , and the variables are defined. The student provides the correct costs of one hamburger ($1.50) and one order of fries ($.75). The symbolic explanation is fully developed and supports the solution. No justification is given. This response demonstrates a clear 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. While the student provides the correct equations for Sam's total cost (2h+1f=$3.75) and Erica's total cost (1h+2f=$3.00), the variables are not defined. The student does not solve for the cost of one hamburger or one order of fries, and no explanation or justification is provided. This response demonstrates a minimal understanding and analysis of the problem.

image of student response