Item: tModelExtendTableGeometric3a

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:

Which equation best represents sales for the bakery chain, where n is the hour, an is the number of pounds of baked goods sold in the nth hour, and an+1 is the number of pounds of baked goods sold in the (n+1)th hour?

Options:

Key:

• Observable: 1. Score: 1; Evidence Value: 1.
  • Student:Correct, good job!
  • Teacher:The student answered correctly.
• Observable: 2. Score: 0; Evidence Value: 0.
  • Student:Sorry, that's incorrect. The equation you selected describes a situation where the number of pounds of baked goods sold decreases by a factor of 3 every hour. In the third hour, 96 pounds of baked goods are sold, and in the fourth hour, 48 pounds of baked goods are sold. Forty-eight is one-half of 96, not one-third of 96.
  • Teacher:The student selected an equation that assumes that number of pounds of baked goods sold decreases by a factor of 3 every hour.
• Observable: 3. Score: 0; Evidence Value: 0.
  • Student:Sorry, that's incorrect. The equation you selected describes a situation where the number of pounds of baked goods sold increases by a factor of 3 every hour. In the third hour, 96 pounds of baked goods are sold, and in the fourth hour, 48 pounds of baked goods are sold. So the number of pounds of baked goods sold is decreasing, not increasing.
  • Teacher:The student selected an equation that assumes that the number of pounds of baked goods sold increases by a factor of 3 every hour.
• Observable: 4. Score: 0; Evidence Value: 0.
  • Student:Sorry, that's incorrect. The equation you selected describes a situation where the number of pounds of baked goods sold increases by a factor of 2 every hour. In the third hour, 96 pounds of baked goods are sold, and in the fourth hour, 48 pounds of baked goods are sold. So the number of pounds of baked goods sold is decreasing, not increasing.
  • Teacher:The student selected an equation that assumes that the number of pounds of baked goods sold increases by a factor of 2 every hour.

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