Item: tExtendOtherRecursive2a

Stem:

1, 3, 7, 15, 31, . . .

Find the next two terms in the sequence shown above.

Options:

1. 33, 35

2. 41, 53

3. 63, 127

4. 83, 147

Key:

• Observable: 1. Score: 0; Evidence Value: 0.
  • Student:Sorry, that's not right. For problems like these, you need to find the pattern based on the differences between all the pairs of numbers. The pattern may not be a single common difference, as with arithmetic sequences. The correct numbers are 63 and 127.
  • Teacher:Student thinks there's a common difference of 2.
• Observable: 2. Score: 0; Evidence Value: 0.
  • Student:Sorry, that's not right. For problems like these, you need to find the pattern based on the differences between all the pairs of numbers. The pattern may not be a single common difference, as with arithmetic sequences. The correct numbers are 63 and 127.
  • Teacher:Student checked first two pairs and thinks there's an even progression (2, 4, 6, ... instead of 2, 4, 8, ...).
• Observable: 3. Score: 1; Evidence Value: 1.
  • Student:Correct, good job!
  • Teacher:The student got this item correct.
• Observable: 4. Score: 0; Evidence Value: 0.
  • Student:Sorry, that's not right. For problems like these, you need to find the pattern based on the differences between all the pairs of numbers. The pattern may not be a single common difference, as with arithmetic sequences. The correct numbers are 63 and 127.
  • Teacher:Not sure what the problem is.

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