Score Level 1 Anchor Paper

This response indicates little application of a reasonable strategy. The representation (75 = x(10) + y(15)), in the form of an equation rather than an inequality, is essentially correct. The student provides no response to the second or third parts of the question. The response demonstrates a minimal understanding and analysis of the problem.

Score Level 1 Anchor Paper

This response indicates little application of a reasonable strategy. The representation, in the form of an equation, is incorrect. The student provides the correct maximum number of shorts (3). The explanation supports the solution (because 2 shirts cost 20. Subtract 75-20=55, and 3 shirts cost 45. Subtract 55-45=5, so you can only buy 3). The student gives no response to the third part of the question. The response demonstrates a minimal understanding and analysis of the problem.

Score Level 2 Anchor Paper

This response indicates an incomplete application of a reasonable strategy. No representation is given. The student does provide the correct maximum number of shorts (3), and the explanation supports the solution. (I subtracted 75-20 to get 55, then I divided by 15, then got 3.) Although the student correctly lists all the number combinations of shirts and shorts that total exactly $75, a justification is not given. The response demonstrates a conceptual understanding and analysis of the problem.

Score Level 2 Anchor Paper

This response indicates application of a reasonable strategy that leads to some correct solutions. The representation (10x+15y=75), in the form of an equation rather than an inequality, is essentially correct. While the student provides the correct maximum number of shorts (3), an explanation is not given. A list of only two of the three combinations of shirts and shorts that total exactly $75 (3 shirts 3 shorts; 6 shirts 1 short) is supplied, and no justification is provided. The response demonstrates a conceptual understanding and analysis of the problem.

Score Level 3 Anchor Paper

This response indicates application of a reasonable strategy that leads to some correct solutions. The representation (75=x•10+y•15), in the form of an equation rather than an inequality, is essentially correct. The student gives the correct maximum number of shorts (3 pair of shorts). However, the calculations (Because if she bought 2 shirts that’s 20 dollars, and 3 pairs of shorts would be 45 dollars. And the total cost would be 65 plus tax), provide justification, rather than explanation. The student lists only one of the three combinations of shirts and shorts that total exactly $75 (3 shirts and 3 shorts). This solution is justified (3•10=30, 15•3=45, and 30+45=75). The response demonstrates a clear understanding and analysis of the problem.

Score Level 3 Anchor Paper

This response indicates application of a reasonable strategy that leads to some correct solutions. The student gives the correct inequality (10z+15x≤75). Although the student replaces x with z in the inequality and does not define z, it is evident from the response to the second bullet that z represents shirts. The correct maximum number of shorts (3) is given, and the explanation supports the solution. (If she buys 2 shirts, that is $20. 75-20=$55. One pair of shorts cost $15. So 55÷15=3.67). The student lists only one of the three combinations of shirts and shorts that total exactly $75 (3,3). This solution is justified (3 shorts cost $45; 3 shirts cost $30. 45+30=75). The response demonstrates a clear understanding and analysis of the problem.

Score Level 4 Anchor 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 inequality (10(x)+15(y) ≤75). The correct maximum number of shorts (3 pairs of shorts) is provided. The fully developed “guess and check” explanation is presented symbolically; the student replaces x in the inequality with 2 and then tries decreasing values for y until the solution is found. A correct list of all the number combinations of shirts and shorts that total exactly $75 is provided and fully justifies the solutions by inserting each of the values for x and y into the equation and simplifying, showing that the found values make the equation true. Note: the justification for 6,1 is done twice. The response demonstrates a complete understanding and analysis of the problem.

Score Level 4 Anchor 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 inequality (75≥10x+15y). The correct maximum number of shorts (3) is provided, and a fully developed explanation is presented symbolically. The student replaces x in the inequality with 2, then solves for y, and truncates to a whole number for the solution. A correct list of all the number combinations of shirts and shorts that total exactly $75 {(3,3) (6,1) (0,5)} is provided. The student fully justifies the solutions by inserting each of the values for x and y into the equation and simplifying, showing that the found values make the equation true. The response demonstrates a complete understanding and analysis of the problem.