## Sunday, March 25, 2012

### PerCent "More" - Applying RATIOS DEEPLY

PROBLEM
Two thin cylindrical steel  disks have diameters of 35 in and 25 in. The area of the base of the larger is what % more than the smaller?

We would hope juniors in Alg 2 or Precalc would know the basic setup for % more, % increase/decrease or % change types, particularly since this is a middle school concept. Of course we know this is often not the case!

After having students work in small groups for a few minutes and watching them pushing calculator buttons you have someone come up and explain, asking questions and reviewing basics. As is typical, some students will use the diameters instead of the radii and get the right answer anyway. What are the "BIG IDEAS" here?

Write on the board (35/25)^2 = 49/25, then 24/25 = 96%.  No explanation. You give students in small groups 2 minutes to make sense of this and have 2 groups take turns explaining it to the class.A mental calculation?

Before you kneejerk reflexively react to this with " Even some of my honors students would struggle with that", I would like my readers to reflect on our obligation to stretch their minds and promote conceptual understanding.

IN NO WAY AM I SUGGESTING THAT IS THE METHOD MOST STUDENTS SHOULD USE!

SO WHAT ARE THE KEY MATH CONCEPTS USED IN MY EXPLANATION?

Of cou

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