Exponential Functions Unit in Algebra 1: Planning & Ideas
Exponential relationships were once one of those rushed topics I covered at the end of the year, but they turned into one of my favorite and most engaging units for Algebra I students. I hope I can share some ideas and lesson resources to help you plan your unit.
Looking at the Common Core State Standards, several standards need to be addressed as students learn about exponential functions. A key part of Algebra 1 is for students to distinguish situations that can be modeled with linear and exponential functions, so I like to keep linear relationships in the lessons as we study exponential. This also gives students a chance to deepen their understanding of linear functions.
Prerequisite Skills
Before we start any unit, I try to predict misconceptions and prerequisite skills that might hinder student success. For exponential functions, expressions involving percents are crucial. Many of my Algebra 1 students can find percent of a number or percent increase and decrease, but writing the expression using a decimal is a little trickier. For example, can they write an expression to find a 20% decrease? (x - 0.2x and 0.8x both work here.) They will need this skill to fluently work with exponential equations when we talk about growth and decay. I like to use this real world percent card sort to practice this skill before the exponential unit.
Introducing Thinking Exponentially
Understanding how things change exponentially is tough! Students are accustomed to thinking of linear relationships. To prepare them for this new mindset, I like to give them the options shown in the picture and ask which they would rather have. Option C offers a penny today and doubled each day for a month. To most students, this option seems like the worst choice. However, if they do the math, they will get a surprising glimpse of exponential growth! This intro activity provides them a table, graph, and an optional digital spreadsheet to see how the choices play out.
Distinguishing Linear from Exponential Relationships
The Common Core standards emphasize that students must be able to decide if a function is linear or exponential. I like to start by giving students real world stories and let them decide if they are linear or exponential relationships. In this card sort activity, they first sort scenarios as linear or exponential. Then, they choose the appropriate equation (since writing exponential equations is still new). Then they fill in a table of values and a graph to bring all the representations together.
Multiple Representations of Exponentials
Once students have worked with exponential functions for a bit, they are ready to explore more difficult problems using multiple representations. Can students take one piece of information (either a story, a graph, a table, or an equation), and figure out all the rest? In this multiple representations activity, they do just that! The word problems vary in difficulty as students figure out the missing information using what is given. If students can complete these, I know they have a solid understanding of exponential functions.
Get a free sample of this activity here.
The activities above make up the bulk of learning during the exponential functions unit. Following those are several practice activities before wrapping up with an assessment.
Looking for an outline to help plan your entire year of Algebra 1? Check out my free Scope and Sequence for Algebra 1.
