Score Level 1 Anchor Paper

This response indicates little application of a reasonable strategy. The table is correctly completed. No expression for the relationship between the number of blocks and the surface area is given. Although the patterns used to complete the table are described, the student does not find either the volume or the surface area of a 10-block tower. This response demonstrates a minimal understanding and analysis of the problem.

Score Level 1 Anchor Paper

This response indicates little application of a reasonable strategy. While the table is correctly completed, the attempted equation is incorrect. No justification is given. Both the surface area (114) and the volume (36) of a 10-block tower are incorrect, and no explanations are provided. This 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. The table is correctly completed; however, no expression is given. The surface area (126) and the volume (40) of a 10-block tower are correct. Explanations are not provided. This response demonstrates a conceptual understanding and analysis of the problem.

Score Level 2 Anchor Paper

This response indicates an incomplete application of a reasonable strategy. The table is correctly completed. The representation, in the form of an expression (12x+6), is correct, and the variable is defined. No justification is provided. While an expression for finding the volume is given, the student makes no attempt to find either the volume or surface area of a 10-block tower. This 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 table is correctly completed. The representation, in the form of an equation (y=12x+6), is correct; however, a justification is not provided. Both the surface area (126) and the volume (40) of a 10-block tower are correct. The tabular explanation supports the solutions; the student extends the table to find the volume and surface area of ten blocks. This 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 table is correctly completed. The representation, in the form of an equation (y=12x+6), is correct, and the variables are defined. Although the student gives an explanation of the equation, the justification is incomplete. (I tested the equation with the data from the chart and it worked out.) The volume of a 10-block tower (40 cubic centimeters) is correct. The explanation supports the solution. The student describes the steps used on a graphing calculator and then summarizes (volume was found by multiplying 4 by the number of blocks used to build the tower). No surface area is provided. This 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 table is correctly completed. The representation, in the form of an equation (y=12x+6), is correct. The student provides an explanation of the equation followed by a justification. (If you plug any of the numbers we used for the x-axis, which is anything in List 1, you will find it correct. For example, if I plugged 2 {number of blocks} in as x, the equation would be y=12(2)+6. Y would equal 30 in this case, which is the correct surface area for 2 blocks.) The surface area of a 10-block tower (126 cm²) is correct, and the explanation supports the solution (going to the table, when x=10 and that shows that the surface area is 126 cm²). The volume (40 cm³) is correct; the explanation is clearly presented and supports the solution. The student finds an equation representing the relationship between the number of blocks and the volume and then uses the corresponding table in the graphing calculator to find the volume when x=10. This 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 table is correctly completed. The representation, in the form of an expression (12x+6), is correct, and the variable is defined. The symbolic justification is clearly presented, fully developed, and supports the solution. The student replaces the x in the expression with numbers 1 through 4 and solves for each, showing that the found solutions match the given numbers in the table. The surface area of a 10-block tower (126 cm²) is correct. The symbolic explanation is fully developed; the student replaces x in the expression with 10 and solves. The volume (40 cm³) is correct. The explanation is clearly presented and supports the solution. The student gives an expression representing the relationship between the number of blocks and the volume, replaces x with 10, and solves. This response demonstrates a complete understanding and analysis of the problem.