Wondering about how to give feedback

I am working on a ratio lesson. The context is making chocolate milk and they have to decide if a given mix will be less, equal, or more chocolaty than a given mix. I’m wondering how to give feedback. Ideas?

Eventually I am thinking making this a series of challenges-- but I struggle with the whole capture and history functions.

Maybe something like Desmos’ new Paint activity?

Color is tricky. The gradations I don’t think will pick up the level of precision we need at this point.

I did use the Paint activity with the students already. Very nice interaction and a nice stop on the way to understanding, but most of the kids are not “there” yet. In particular many students have not yet really grasped the transition to multiplicative thinking. For example, suppose you have ratios of milk:chocolate. One mix is 3:4 and another is 12:14, a large percentage of the kids will say that the second mix will taste more chocolaty since it has 2 more chocolate and the other mix only has 1 more chocolate. They are thinking additively rather than multiplicatively. The color difference would be small (57%:53%) and I don’t think it would be enough to convince them.

That said, the shift from additive to multiplicative thinking is tricky. I think that fostering this transition is at the core of middle school math (there are other ideas at the core too of course). I’ve found that it is pretty much always a good thing to check for— even with students who have made the transition.

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You can do a basic feedback similar to this (slide 8). Various images for various results.

Forgot the link: Secondary Math III Unit 3 Lesson 1: Evaluating Logarithms • Activity Builder by Desmos