Question

Ms. Duchamp asked her students to write explanations of how they found the answer to the problem 24×15. One student, Sergio, wrote, "I did 24 times 10 and got 240, then I did 24 times 5 and that's the same as 12 times 10 or 120, and then I put together 240 and 120 and got 360." Ms. Duchamp noticed that four other students found the same answer to the problem but explained their strategies differently. Which of the following student explanations uses reasoning that is most mathematically similar to Sergio's reasoning?

A. "I did 24 times 20 and got 480, then I did 24 times 3 and that's the same as 8 times 10 or 80, and then I put together 480 and 80 and got 560."
B. "I did 24 times 15 and got 360, then I did 24 times 5 and that's the same as 12 times 10 or 120, and then I put together 360 and 120 and got

Answer 1

The student explanation most similar to Sergio's method of partial products is Option A, where multiplication is broken down into easier steps and partial products are combined to obtain the final result.

Step-by-step explanation:

The student Sergio used a strategy called partial products to multiply 24 by 15. He first calculated 24×10 to get 240, then he calculated 24×5, which he simplified by thinking of it as 12×10 to get 120, and finally, he added the two products together to get 360. Among the given options, the reasoning that is most mathematically similar to Sergio's strategy is Option A:: "I did 24 times 20 and got 480, then I did 24 times 3 and that's the same as 8 times 10 or 80, and then I put together 480 and 80 and got 560." Just like Sergio, this student broke down the multiplication into easier steps, multiplied by a base number (either 10 or 20), and then recombined the partial products to get the final answer.