I begin class with an example of an investment made for a child at birth. I gain student interest by suggesting that if the child had been them, they might have enough money now for college, or maybe a car. I explain that the initial deposit was $5000 and that the account has been paying 8.75% interest, compounded continuously since 1994. I ask if anyone remembers the compound interest formula and have them post it on the board, and if not I share it: A = P(e)^rt After a brief discussion of the symbols, I challenge my students to figure out how much money this child would have now. (MP1) After a few moments I randomly call on students to post their answers, until every student has responded. We critique the results as a class then move on to the next challenge - when will this account be worth $100,000? (MP1) These questions aren't specifically about end behavior or other key features, but they get my students looking at exponential graphs as math with meaning. When this question is answered, I do a quick review of exponential growth and decay, using bacterial growth and radioactive decay as examples, then check for understanding before moving on.
For this part of the lesson I tell my students that they will be working with their back partner and that they will have about 25 minutes to solve each problem and write an explanation. I explain that today, instead of sharing their work on the board or presenting to the class, I will be giving each team a large sheet of paper to put their work, solutions and explanations on and that these papers will be posted for a gallery walk at the end of the work session.
I distribute the growth and decay handout, ask if there are any questions, and repeat that they will have about 25 minutes for this assignment, including putting it on the large sheet of paper. (MP1, MP3) I anticipate that some students may struggle with setting up an appropriate viewing window on their calculator for each problem. For those students I try to ask leading questions like "What do you think the largest x and y values might be for this problem? What does that tell you about your window settings?"
When everyone is done or after about 25 minutes I ask my students to post their work around the room. I explain that we will be having a gallery walk to look over each team's work and that my expectations are that they stay at one poster until I say it's time to move on. I also explain that I want them to be looking for solutions that really impress them either because the solution solves the problem in a different way or has a clear and simple explanation.