## Reflection: Developing a Conceptual Understanding Exponential Models Day 2 of 2 - Section 2: Modeling f(x) = a(b^x)

This set of lessons was so fun to write and even more fun to teach.  One of my biggest 'Aha' moments in aligning my curriculum to the Common Core has been how well students conceptually grasp topics when they are presented in context.  This is a switch in many mathematics classrooms.  Usually, students are taught a skill and then it is applied to a real-life context.  By switching this, I have found that a wider range of students really understanding the principles behind mathematical topics.  I remember hearing people say this early in my career and being very skeptical.  The key to success is that the presentation of the scenario is more open ended than your classic two trains going in opposite directions word problem.  That is also the challenge, to find worthy rich scenarios.

In today’s lesson, the students take the basic scenario, developed in the last lesson, and add an initial amount other than one.  I did a short physical demonstration of the model f(x)=2(2)x with my students, like yesterday, as this gave a physical representation of what happens in an exponential model.  One student and I each ‘infected’ one person to represent the first night, the four of us infected one person to represent the second night, and so on.  From this point we talked about them conceptually but the physical model really set the idea.

The one place that students struggled was the idea that f(x)=3x, for example, represents one original zombie with 2 victims totaling 3 zombies by the night’s end (Student Notes).   Often, students wouldn’t include the original zombie as part of the three.  A reminder of the physical demonstration did a lot to overcome this issue.

Developing a Conceptual Understanding: Building Transformations Through Context

# Exponential Models Day 2 of 2

Unit 8: Exponential and Logarithmic Functions
Lesson 4 of 15

## Big Idea: Aarrghhh...Brains...Zombies...and Exponential Functions! Discover Exponential Functions in this Zombie themed Lesson.

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Standards:
Subject(s):
Math, Algebra, exponential growth, Algebra 2, master teacher project, exponential models
50 minutes

### Amelia Jamison

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