Grade 8 / Case Study 1: MATH - WestEd

Grade 8 / Case Study 1

MATH SMARTER BALANCED PERFORMANCE TASK

Item 1

Student Response to Item 1

Analysis of Response to Item 1

How tall, in cm, is the stack of 8 cups? The response receives a full credit score of 1 point. The student gave the correct answer of 28.

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Grade 8 / Case Study 1

MATH SMARTER BALANCED PERFORMANCE TASK

Item 2

Student Response to Item 2

How tall, in cm, is 1 cup? Explain how you determined the height of 1 cup.

Analysis of Response to Item 2

This response receives a full credit score of 2 points. The student correctly calculated the height of one cup and provided a mathematically logical explanation as to how s/ he calculated the height. The student found the difference between stack one and stack two, divided the difference between the stack heights by 2, and found that each "lip" was 2 centimeters. In the above diagrams, s/he stated "2 cm = 1 lip" and computed 16 ? 2 = 14. S/he circled this computation to indicate the answer.

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Grade 8 / Case Study 1

MATH SMARTER BALANCED PERFORMANCE TASK

Item 3

Student Response to Item 3 Analysis of Response to Item 3

Your teacher thinks that instead of having to figure out these stacks each time, it would be useful to understand the general relationship. Write an equation expressing the relationship between the height of the stack and the number of cups in the stack. Let h represent the height of the stack, in cm, and n the number of cups in the stack.

This response receives a full credit score of 1 point. The student wrote a correct equation based on the calculations shown in the previous problem, where s/he determined a height of 14 ? 2 (another lip) = 12 centimeters for the base and a rate of growth of 2.

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Grade 8 / Case Study 1

MATH SMARTER BALANCED PERFORMANCE TASK

Item 4

Student Response to Item 4

Analysis of Response to Item 4

The catalog is advertising a stack of these cups that is 95 cm tall. Lori says, "That must be a misprint because a stack of that height is not possible." Do you agree or disagree with Lori? Explain your reasoning.

This response receives a full credit score of 2 points. The student agreed with Lori and provided a valid mathematical explanation as to why a stack of cups could not reach 95 centimeters. S/he worked backward in an equation using relevant values and arrived at a non-whole number, 41.5. Although there is a clear misuse of the equal sign in the extended equation, this had no impact on the score since this item is assessing communication of reasoning, not mathematical precision or an ability to set up an equation.

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Grade 8 / Case Study 1

MATH SMARTER BALANCED PERFORMANCE TASK

Item 5

Student Response to Item 5

Your teacher wants to sell School Spirit Cups with your school logo on them. She asks you to design this new cup such that a stack of 10 of them will be 125 cm tall.

Describe key measurements of the School Spirit Cups and explain how they will meet your teacher's specifications.

Analysis of Response to Item 5

This response receives a full credit score of 2 points. The student drew a picture showing the key measurements and then showed calculations in which 10 cup lips of 10 centimeters is equal to 100 centimeters, which added to the base of 25 centimeters gives a stack height of 125 centimeters. The mathematical calculation with labels makes this an adequate response.

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