## Reflection: Intervention and Extension Counting the Change: Linear, quadratic, or exponential? (Day 2 of 2) - Section 4: Isotope Problem

Overall, my students were not very successful on the isotope problem. I had a few students do well, but a majority of my students struggled. Most of my students solved the first problem correctly using the patterns they identified, such as this student: Counting the Change, Isotope question 1, student 1.jpg. I had a few students attempt to use a system of equations. Some were successful with this method: Counting the change, isotope question 1, student 3.jpg. Some were not successful: Counting the change, isotope question 1, student 2.jpg.

Not one of my students got the correct answer for question 2, part b. As I thought may happen, I got the same incorrect answer repeatedly. This was definitely the most popular wrong answer: Counting the change, isotope question 2, student 4.jpg. Most of my students wrote the equation as a function of half-lives, not as a function of time (or didn’t even attempt part b at all!). I did have a few students try a system of equations approach, but were just unsuccessful: Counting the change, isotope question 2, student 5.jpg.

Since many of my students had the same misconception. I am going to do a Favorite No activity at the start of class tomorrow using this student’s answer:Counting the change, isotope question 2, student 4.jpg. I mainly want to demonstrate to students how this equation won’t work for t. It is in terms of half-lives. Then I want to open it up to the class to help me write an equation that relates t and d. Then I also want students to take time to solve this using a system. Approaching this problem using a system of equations brings up some opportunities for discussion of exponential function properties and the rules of exponents. Help students to see that the cube root of one half is the same as writing one half to the power of one third.

Intervention and Extension: Student Work Analysis

# Counting the Change: Linear, quadratic, or exponential? (Day 2 of 2)

Unit 4: Exponential Functions and Equations
Lesson 6 of 14

## Big Idea: Students explore rates of change to identify function types and find patterns that help them to identify and define exponential functions.

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Standards:
Subject(s):
Math, Precalculus and Calculus, constant rate of change, PreCalculus, exponential function, percent change, comparing functions, function
50 minutes

### Tiffany Dawdy

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