## Reflection: Discourse and Questioning Special exponential "e" - Section 3: Euler's number and exponential functions

Students showed a lot of conviction when they were organizing the functions. Here are 2 examples of organizing functions.

The first class organized by looking at the term with exponents. The students separated the functions with e then put a group together that had x without an exponent and finally a group where x was raised to a power. Some of the students in this class disagreed and wanted to put the 2 rational expression together but were convinced by the class to organize the data this way.

Another class organized more like I expected. They stated that the A=Pe^rt was different because it was the only function that had "multiple variables." At first the students did not know where they wanted the exponential y=e^x equation but a student said the exponent is x so it should go with the other exponential functions.

Some students did not want to put the linear equation with the other polynomial equations at first but a student explained to the class that the linear equation had an exponent of 1 on the x. This allowed the class to agree about the placement of the linear equation.

The students did struggle with this activity at first. They expected me to tell them how to organize the data. I reminded them that there are many ways to classify equations and as long as the class could defend the placement then the classification was correct.

In one class a students made the comment "we don't all think alike so we can see different ways to organize the equations."

Discourse and Questioning: Organizing Functions

# 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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