Reflection: Developing a Conceptual Understanding More With Exponential Growth - Section 2: Direct Instruction


The segway from the iterative process of calculating percentage growth to using the formula is really crucial in this lesson.  Using the formula is not a tough sell because of the efficiency factor.  That said, it is important that students see the connection between the formula and the iterative process (MP8).   When I showed students the formula I asked them to think about why each number was being used.  The students were fine with putting the numbers in for the correct variable.  Then once we had 30,000(1+.06)^5 we discussed why each number was being used.  Several students commented about the fact that we are multiplying by 0.06 five times in the iterative process.  This helped them to see why this quantity was being multiplied by the initial value of 30,000.  Some students were still confused about the "1+".  Then one student spoke up and said, "If you want to figure out sales tax, you can multiply the number by 1.08.  That saves you from having to find the tax and then add it to the number."  This was the push the class needed to see why the formula used a 1+.  If we didn't have the 1+, we would just be left with the amount of growth but not the final amount.

Now that students had processed the formula and looked at it from a conceptual perspective, I felt comfortable having them use it as a tool to solve other problems.

  Developing a Conceptual Understanding: Let's be Efficient
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More With Exponential Growth

Unit 7: Exponential Functions
Lesson 5 of 13

Objective: SWBAT write a function that models percent increase of one quantity over a period of time.

Big Idea: Percent increase over time is modeled by an exponential growth function.

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