Question

Which of the following student explanations uses reasoning that is most mathematically similar to Sergio's reasoning?

a.Since 24 is the same as 12 times 2 and 15 is the same as 5 times 3, I did 12 times 5 and got 60, then I did 2 times 3 and got 6, and 60 times 6 is 360.
b.To get 24 times 5, I did 20 times 5 and 4 times 5, which is 120 altogether, and then I needed 3 of that, and 120 times 3 is 360.
c.15 times 20 is the same as 30 times 10, and that gave me 300, and then I did 15 times 4 to get 60, and 300 plus 60 is 360.
d.24 divided by 2 is 12, and 15 times 2 is 30, so 24 times 15 is the same as 12 times 30, and so my answer is 360.

Answer 1

Option a uses reasoning most similar to Sergio's reasoning: breaking down the numbers and performing separate calculations before combining the results.

Step-by-step explanation:

The student explanation that uses reasoning most mathematically similar to Sergio's reasoning is option a.

Sergio's reasoning involves breaking down the numbers and performing separate calculations before combining the results. In option a, the student multiplies 12 (from 24) and 5 together to get 60, and then multiplies 2 (from 12) and 3 together to get 6. Finally, they multiply 60 and 6 to get the final answer of 360, which matches Sergio's reasoning.