Anchor Papers ~ Algebra/Data Analysis ~ Item 12


	Item 12 Anchor Papers

Aisha used squares to make the pattern of figures below.

Complete the following in the Answer Book:

Using the pattern, draw Figure 5 and Figure 6 in the Answer Book.
Complete the table in the Answer Book to determine the perimeter of each figure.
Write an expression that can be used to determine the perimeter of the nth figure in this pattern.
If this pattern continues, which figure will have a perimeter of 140 centimeters? Use mathematics to explain how you determined your answer. Use words, symbols, or both in your explanation.

Score Level 1 Anchor Paper
This response indicates little application of a reasonable strategy. The figures are incorrectly drawn. While the table is correctly completed, no expression is given, and the figure with a perimeter of 140 units is not provided. 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. Figures 5 and 6 are correctly drawn. Although the table is correctly completed, no expression is given, and the figure with a perimeter of 140 units is not provided. 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. Figures 5 and 6 are accurately drawn, and the table is correctly completed. However, no expression is given. The student correctly determines that figure 35 will have a perimeter of 140 units, but an explanation is not provided. The 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. Figure 6 is accurately drawn; however, Figure 5 is not provided. While the table is correctly completed, no expression is given. The student correctly determines that figure 35 will have a perimeter of 140 units, and the explanation supports the solution. The student extends the pattern until the perimeter of 140 units is reached at figure 35. 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 student does not address the first part of the problem. The table is correctly completed, and the representation, in the form of an equation (P=4n) rather than an expression, is correct. The variable p is not defined. The student correctly determines that figure 35 will have a perimeter of 140 units. The explanation supports the solution. (I found this because for every figure times 4, gave me the perimeter {P=4n}; therefore, if I plug in 140 for the perimeter, I will get n=35.) 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. Figures 5 and 6 are accurately drawn, and the table is correctly completed. The representation, in the form of an equation (F(4)=P) rather than an expression, is correct. The variables are defined. The student correctly determines that figure 35 will have a perimeter of 140 units; however, an explanation is not given. 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. Figures 5 and 6 are accurately drawn, and the table is correctly completed. Although in the form of an equation set equal to "p," defined as the perimeter, the representation is correct. The student correctly determines that figure 35 will have a perimeter of 140 units. The fully developed explanation supports the solution. (I found this answer simply by placing 140 in the place of p in my expression, 140=4n. Then I divided both sides by four.) 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. Figures 5 and 6 are accurately drawn, and the table is correctly completed. The correct expression (4n) is given. The student correctly determines that figure 35 will have a perimeter of 140 units. The fully developed explanation supports the solution. (I placed what numbers I had to where they belong like 140=4n. Then I divided 140 by 4 to get 35.) The response demonstrates a complete understanding and analysis of the problem.

Anchor Papers ~ Algebra/Data Analysis ~ Item 12

Aisha used squares to make the pattern of figures below.

Complete the following in the Answer Book:

Using the pattern, draw Figure 5 and Figure 6 in the Answer Book.
Complete the table in the Answer Book to determine the perimeter of each figure.
Write an expression that can be used to determine the perimeter of the nth figure in this pattern.
If this pattern continues, which figure will have a perimeter of 140 centimeters? Use mathematics to explain how you determined your answer. Use words, symbols, or both in your explanation.

Score Level 1 Anchor Paper
This response indicates little application of a reasonable strategy. The figures are incorrectly drawn. While the table is correctly completed, no expression is given, and the figure with a perimeter of 140 units is not provided. 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. Figures 5 and 6 are correctly drawn. Although the table is correctly completed, no expression is given, and the figure with a perimeter of 140 units is not provided. 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. Figures 5 and 6 are accurately drawn, and the table is correctly completed. However, no expression is given. The student correctly determines that figure 35 will have a perimeter of 140 units, but an explanation is not provided. The 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. Figure 6 is accurately drawn; however, Figure 5 is not provided. While the table is correctly completed, no expression is given. The student correctly determines that figure 35 will have a perimeter of 140 units, and the explanation supports the solution. The student extends the pattern until the perimeter of 140 units is reached at figure 35. 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 student does not address the first part of the problem. The table is correctly completed, and the representation, in the form of an equation (P=4n) rather than an expression, is correct. The variable p is not defined. The student correctly determines that figure 35 will have a perimeter of 140 units. The explanation supports the solution. (I found this because for every figure times 4, gave me the perimeter {P=4n}; therefore, if I plug in 140 for the perimeter, I will get n=35.) 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. Figures 5 and 6 are accurately drawn, and the table is correctly completed. The representation, in the form of an equation (F(4)=P) rather than an expression, is correct. The variables are defined. The student correctly determines that figure 35 will have a perimeter of 140 units; however, an explanation is not given. 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. Figures 5 and 6 are accurately drawn, and the table is correctly completed. Although in the form of an equation set equal to "p," defined as the perimeter, the representation is correct. The student correctly determines that figure 35 will have a perimeter of 140 units. The fully developed explanation supports the solution. (I found this answer simply by placing 140 in the place of p in my expression, 140=4n. Then I divided both sides by four.) 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. Figures 5 and 6 are accurately drawn, and the table is correctly completed. The correct expression (4n) is given. The student correctly determines that figure 35 will have a perimeter of 140 units. The fully developed explanation supports the solution. (I placed what numbers I had to where they belong like 140=4n. Then I divided 140 by 4 to get 35.) The response demonstrates a complete understanding and analysis of the problem.