Reply To: Lesson 9-1: Consolidating What We've Learned – Discussion

[Christina Michaels]

I don’t think my understanding of proportional relationships has necessarily evolved, but my way of teaching proportional relationships definitely has.

Before I was simply presenting students with equivalent ratios and expecting them to recongize the way they were changing. 3/4 is equivalent to 6/8 because both quantities are doubling.

Now, though I’m giving students lots of experiences using models and manipulatives. They’re drawing and using multiple representations, and THEY are the ones figuring out that the ratios are two quantities that are linked together and whatever is happening to one quantity, the same is happening to the other quantity. I’ve emphasized multiplicative thinking vs. additive thinking very explicitly and repeatedly and so we are using those ideas when we’re discussing what’s happening when we scale a ratio in tandem.

[Christina Michaels]

I don’t think my understanding of proportional relationships has necessarily evolved, but my way of teaching proportional relationships definitely has.

Before I was simply presenting students with equivalent ratios and expecting them to recongize the way they were changing. 3/4 is equivalent to 6/8 because both quantities are doubling.

Now, though I’m giving students lots of experiences using models and manipulatives. They’re drawing and using multiple representations, and THEY are the ones figuring out that the ratios are two quantities that are linked together and whatever is happening to one quantity, the same is happening to the other quantity. I’ve emphasized multiplicative thinking vs. additive thinking very explicitly and repeatedly and so we are using those ideas when we’re discussing what’s happening when we scale a ratio in tandem.