Make Math Moments Academy › Forums › MiniCourse Reflections › The Concept Holding Your Students Back › Lesson 82: Ratio and Rate Reasoning – Discussion › Reply To: Lesson 82: Ratio and Rate Reasoning – Discussion

In anticipating what my students would do with this task, a common misunderstanding would be for them to use additive thinking with the initial question: 25050= 200 ml of rice, so 50050= 450 ml of water. My question is, how could I guide students to use multiplicative thinking?
My initial reaction would be to get them to scale in tandem by asking them how much water would we need if we doubled the amount of rice? or how much rice would we need if we cut the amount of water in half, to try to get them to recognize the common factor that they are scaling by, in the hopes that they are recognizing by scaling both the water and rice by the same factor they’re using multiplicative thinking. What I think, though, is that I would have some students who would be able to do this, but still go to additive thinking as their first choice for solving the problem, and not realize the mistake in their thinking.
I think using rate reasoning could help in this situation, as I think many of my students would recognize that 250 is half of 500. After trying it out with many ratios (Is this a true statement? Does it work every time? What if we tried….?), I would bring them back to their answer of 450 ml of water and ask if this makes sense.