Item: tModelExtendTableGeometric2a

Stimulus:

At a certain bakery chain, fresh baked goods are prepared every morning. The number of pounds of baked goods that the bakery chain sells per hour, starting with the hour the bakeries open, is shown in the chart below.

Pounds of Baked Goods sold per hour

Stem:

If this pattern of sales continues, during which hour will the bakery chain first sell less than 15 pounds of baked goods?

Options:

1. 5

2. 6

3. 7

4. 8

Key:

• Observable: 1. Score: 0; Evidence Value: 0.
  • Student:Sorry, that's not right. The number of pounds of baked goods sold during the 5th hour is not below 15.
  • Teacher:The student may have made an arithmetic error in generating the next term for this geometric sequence, or may have an incomplete understanding of how to generate additional terms in a decreasing geometric sequence.
• Observable: 2. Score: 1; Evidence Value: 1.
  • Student:Correct, good job!
  • Teacher:The student's response is consistent with an understanding of how to generate successive terms in a decreasing geometric sequence.
• Observable: 3. Score: 0; Evidence Value: 0.
  • Student: Sorry, that's incorrect. Although you are correct that there are less than 15 pounds of baked goods sold in the 7th hour the bakeries are open, this is not the first hour in which this occurs.
  • Teacher: The student may have misinterpreted the question, and selected any hour for which the number of pounds of baked goods sold is less than 15, rather than selecting the first hour for which the number of pounds of baked goods is less than 15. It is also possible that the student has an incomplete understanding of how to generate successive terms in a decreasing geometric sequence.
• Observable: 4. Score: 0; Evidence Value: 0.
  • Student: Sorry, that's incorrect. Although you are correct that there are less than 15 pounds of baked goods sold in the 8th hour the bakeries are open, this is not the first hour in which this occurs.
  • Teacher: The student may have misinterpreted the question, and selected any hour for which the number of pounds of baked goods sold is less than 15, rather than selecting the first hour for which the number of pounds of baked goods is less than 15. It is also possible that the student has an incomplete understanding of how to generate successive terms in a decreasing geometric sequence.

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