98. Third graders are looking for patterns and rules in sets of whole numbers so they can predict what numbers will come next in the set. Which of the following shows an error in student reasoning?
Answer: B
B shows an error in student reasoning.
The reasoning behind option B is incorrect because the pattern described does not accurately reflect the actual sequence of numbers provided. The numbers 1, 4, 16, 25, and 36 do not follow a consistent rule of doubling the previous number and adding 1.
A) 12, 24, 36, 48, 60, ...
This option correctly identifies a pattern where each number increases by 12. The first number is 12, and the subsequent numbers are indeed following a consistent addition of 12, making the reasoning sound.
B) 1, 4, 16, 25, 36, ...
This option shows an error because the numbers do not result from doubling the previous number and adding 1. Instead, the sequence actually consists of perfect squares (1^2, 2^2, 4^2, 5^2, 6^2), indicating that the student's reasoning is flawed in identifying the underlying pattern.
C) 0, 1, 1, 2, 3, 5, 8, 13, ...
This option accurately reflects the Fibonacci sequence, where each number is the sum of the two preceding numbers. The reasoning is correct, as the first number is 0 and the second is 1, aligning perfectly with the established pattern of the sequence.
D) 1, -1, -3, -5, -7, ...
This option correctly identifies a pattern where each number decreases by 2. The first number is 1, and the subsequent numbers indeed follow a consistent subtraction of 2, demonstrating accurate reasoning.
Conclusion
Option B is definitively incorrect due to the misinterpretation of the sequence's pattern, while options A, C, and D correctly identify their respective patterns. This highlights the importance of accurately recognizing and articulating numerical relationships in order to predict subsequent numbers in a set.