Item: tVerbalRuleExtendModelGeometric1a

Stem:

Maddie has come up with an idea for a community project. During month 1 of the project, she performs three helpful tasks, one task for each of three people. She tutors her brother in math, rakes leaves for her neighbor, and replaces the chain on her friend's bicycle. In turn, she asks each person she helps to help out three new people during month 2. By the end of month 2, nine new tasks are accomplished, and nine people are each ready to help three new people during month 3. The plan is for the project to continue in this fashion.

If everyone participates as planned, how many new tasks would be accomplished in month 5?

Options:

1. 729

2. 81

3. 243

4. 15

5. 45

Key:

• Observable: 1. Score: 0; Evidence Value: 0.
  • Student:Sorry, that's not right, but you are close. You correctly figured out how many new tasks would be accomplished in month 6. In month 5, there will be 243 new tasks accomplished (35 = 243).
  • Teacher:The student probably raised the exponent by one too many. Instead of calculating the number of new tasks accomplished in month 5 (35 = 243), the student calculated the number of new tasks accomplished in month 6: 36 = 729
• Observable: 2. Score: 0; Evidence Value: 0.
  • Student:Sorry, that's not right, but you are close. You correctly figured out how many new tasks would be accomplished in month 4. In month 5, there will be 243 new tasks accomplished (35 = 243).
  • Teacher:The student probably raised the exponent by one too few. Instead of calculating the number of new tasks accomplished in month 5 (35 = 243), the student calculated the number of new tasks accomplished in month 4: 34 = 81
• Observable: 3. Score: 1; Evidence Value: 1.
  • Student:Correct, good job!
  • Teacher:Student has answered correctly: 35 = 243.
• Observable: 4. Score: 0; Evidence Value: 0.
  • Student:Sorry, that's not right. If three additional tasks were completed each month, your answer would be correct. But each month, each new participant performs three new tasks. In month 5, there will be 243 new tasks accomplished (35 = 243).
  • Teacher:The student multiplied 3 * 5 = 15, instead of rasing 3 to the 5th power (35 = 243).
• Observable: 5. Score: 0; Evidence Value: 0.
  • Student:Sorry, that's not right. By the end of the third month, 9 * 3 = 27 new tasks are completed. By the end of the fourth month, 27 * 3 = 81 new tasks are completed. In month 5, there will be 243 new tasks accomplished which is 35 = 243.
  • Teacher:The student probably multiplied 9 (the number of new tasks completed in month 2) by 5 (number of months).

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