Item: tVerbalRuleExtendModelGeometric1b

Stem:

You have an excellent recipe for chocolate chip cookies. By the end of a week, you've shared the recipe with four of your friends. During the second week, each of your friends share the recipe with four of their friends, so that sixteen new people now know about the recipe. During the third week, each of these 16 people share the recipe with four new friends.

Assuming this pattern continues, how many new friends will get the recipe during the 4th week?

Options:

1. 1,024

2. 64

3. 256

4. 32

5. 16

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 friends will get the recipe in week 5. In week 4, there will be 44 = 256 new recipes out there.
  • Teacher:The student probably raised the exponent by one too many. Instead of calculating the number of new friends who get the recipe in week 4 (44 = 256), the student calculated the number of new friends who get the recipe in week 5: 45 = 1,024
• Observable: 2. Score: 0; Evidence Value: 0.
  • Student:Sorry, that's not right, but you are close. You correctly figured out how many new friends would hear about the recipe in week 3. In week 4, there will be 44 = 256 new recipes out there.
  • Teacher:The student probably raised the exponent by one too few. Instead of calculating the number of new friends who get the recipe in week 4 (44 = 256), the student calculated the number of new friends who get the recipe in week 3: 43 = 64
• Observable: 3. Score: 1; Evidence Value: 1.
  • Student:Correct, good job!
  • Teacher:Student has answered correctly: 44 = 256.
• Observable: 4. Score: 0; Evidence Value: 0.
  • Student:Sorry, that's not right. By the end of week 3, 16 * 4 = 64 new friends have the recipe. So by the end of week 4, more than 64 new friends must have the recipe. In fact, by week 4, there will be 44 = 256 new recipes out there.
  • Teacher:The student probably multiplied 16 (the number of new friends who get the recipe in month 2) by 2.
• Observable: 5. Score: 0; Evidence Value: 0.
  • Student:Sorry, that's not right. If four additional friends got the recipe each month, your answer would be correct. But each month, each person gives the recipe to four new friends. In week 4, there will be 44 = 256 new recipes out there.
  • Teacher:The student multiplied 4 * 4 = 16, instead of raising 4 to the 4th power (44 = 256).

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