Item: tModelExtendTableGeometric2b

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 45 pounds of baked goods?

Options:

1. 5

2. 6

3. 7

4. 8

Key:

• Observable: 1. 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: 2. Score: 0; Evidence Value: 0.
  • Student: Sorry, that's incorrect. Although you are correct that there are less than 45 pounds of baked goods sold in the 6th 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 45, rather than selecting the first hour for which the number of pounds of baked goods is less than 45. It is also possible that the student has an incomplete 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 45 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 45, rather than selecting the first hour for which the number of pounds of baked goods is less than 45. 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 45 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 45, rather than selecting the first hour for which the number of pounds of baked goods is less than 45. 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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