YBT Response Analysis

1. YBT Response Analysis

2. This response is a 2 because the computations are correct and the explanations are appropriate. However, the response does not address the general N cases of the problem.

3. This response is a 1. It draws the figure correctly, has the correct number of toothpicks in Figure 10, and identifies the correct number of toothpicks for Figure 20. However, the description of the general term indicates little understanding of the pattern. The area solutions also indicate misunderstanding.

4. This response is a 1 because the figure and the number of toothpicks for Figure 10 are correct. The response also shows understanding of the perimeter, even though the explanation is incomplete. The statements about area, however, show basic misunderstanding about the concept. There is also no attempt to describe or explain the general cases.

5. This response is a 2 because it has correct responses for each part of the question, but the examples and explanations for the general cases are missing or show little understanding.

6. This response is a 3 because it answers all parts of the question correctly and has appropriate supporting explanations. This response could be improved, however, if the equations for the general N cases had been stated.

7. This response is a 1 because it has the correct number of toothpicks for Figure 10 and the correct area for Figure5. It fails to earn a 2 because the general case is not expressed and some of the descriptions are vague. In addition, the conclusion about Figure 20 is incorrect.

8. This response is a 1 because it calculates the number of toothpicks for Figure 10, the area of Figure 5, and the area of Figure 20 correctly. The response indicates thought about the Nth case, but it never directly addresses or gives an expression for it. In addition, the response does not mention whether an area of 22 square units is reasonable for Figure 20.

9. This response is a 1. The student draws the correct figure and has a grasp on the concept of area, and seems to have some understanding about perimeter. The seventh term seems to be used as the Nth term but there is no reference to the Nth term. Only the area of the 20th figure is discussed the perimeter is ignored.

10. This response is a zero because only Figure 5 is drawn correctly. All the other answers are wrong, and the statements indicate misunderstanding of the concepts at hand.