## Reflection: Intrinsic Motivation Special exponential "e" - Section 2: Discovering Euler's Number

Trying to find the biggest product brought out the competitiveness in 2 of my classes. In these classes I have some extremely bright student that the other students sometimes depend on when the class is learning new material.

Today after discussing whether we could divide the number by a decimal, I had students trying to get a better answer than each other. When one group put up an answer another group would immediately try to go out another decimal place. I actually had to stop the students to finish the activity.

I also had a student see how the size n/x portion for 20 and 10 were almost the same number. This student used that number 2.707 to quickly zoom into the largest product. He later explained what he did to the class.

The students also learned how the calculator can really assist in zooming in on the largest product. This video clip shows a student working to find a large product. When the student found the product she comments by saying "I got one" I then challenged the student to get a better answer by changing her scale in the table.

Intrinsic Motivation: Student Engagement

# Special exponential "e"

Unit 3: Exponential and Logarithmic functions
Lesson 2 of 11

## Big Idea: How can a number be divided so that raising the part to the power is was divided by gives you the largest product?

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Standards:
Subject(s):
Math, exponential function, Euler's number, PreCalculus, exponential function, logarithmic functions, equation solving, Properties of Logarithm
45 minutes

### Katharine Sparks

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