Review Lesson on Exponential Functions
Lesson 9 of 10
Objective: SWBAT create and interpret functions describing geometric and arithmetic sequences. SWBAT compare and contrast linear and exponential functions.
This lesson gives students time to practice and apply what they have learned about linear and exponential functions in this unit. I like the curriculum materials from the Mathematics Vision Project. The included Mathematics Vision Project Module is part of an integrated math sequence, but many of the lessons apply well to a Algebra I course unit on Linear and Exponential functions. The work for today's lesson can be found on pages 52-58 of the attached pdf file.
For today's Entry Ticket I have students complete the Table Puzzles on page 52 and the Graph Puzzles on page 53 in section 4.10 of the packet.
I like these exercises as it helps students continue to work on the relationship between equations and graphs. In addition to the prompts provided in the worksheet, I also ask students to identify each function as linear or exponential and explain their reasoning.
Teachers can create an opportunity for students to engage in Math Practice 3 by encouraging students to compare and contrast the strategies they used to create equations from the tables with a peer. Having students talk out their reasoning with a peer and to listen to a different perspective to approach problems can help lead to better conceptual understanding.
The lesson then turns to a review of solving exponential functions utilizing a graph. I hand out page 54 of the Mathematics Vision Project lesson 4.10.
During this portion of the lesson I review the first 2-3 problems with students in a guided practice format. When students respons, I am cognizant of asking them to elaborate their reasoning and to ask the "why" and not simply the "what" or answer.
After completing some examples of solving exponentials from a graph (#5 on the worksheet) and 1-2 examples of the Equation Puzzles I give students a 5-10 minutes to complete the worksheet in small groups. I like having students work in groups as it fosters all important social and interpersonal skills that will be valuable for college and careers.
Students continue working in groups and I hand out copies of pages 55-57 from the Mathematics Vision Project module on Linear and Exponential Functions.
I chose these particular worksheets for practice and review because they provide a nice mix of types of problems and concepts covered thus far in the unit on exponential functions. The problems are set up in a way where students are asked to shift and integrate their thinking. For example, rather than complete 20 problems on creating exponential functions and then spending another day creating sequences, students have to complete both types of problems. I think completing problems that cover similar concepts in different formats help students make the all important connections between, say exponential functions and geometric sequences.
During this time students work collaboratively in small groups to complete the worksheets. My role is to facilitate conversation, and I rotate amongst groups, being sure that students are on track and are at a getting a good balance of support and challenge.
Exit Ticket and Homework
To conclude the lesson I hand out page 58 of the Mathematics Vision Project module on Linear and Exponential functions on Simple and Compound Interest.
During the last few minutes of class I provide students with a short overview of simple and compound interest and answer any clarifying questions (many times students are unsure of what some of the variables stand for - for example some students may not make the connection that principal is a word for the beginning balance in interest question).
I then give groups time to complete any remaining group work. Students that complete the group work can begin the interest work. Either way, the simple and compound interest is due for homework next class. In this way, all students are engaged in mathematics for the duration of class, and also are given the time they need to process and practice the skills reviewed in class today.