I begin class by recapping for my students their success from yesterday, that they derived a formula to find the sum of a finite geometric series! I say that there are lots of mathematical formulas that have been developed to make mathematics simpler, not to make students crazy trying to memorize them. I emphasize that deriving the formula was just the first step, like setting up all your equipment before starting a science lab or getting all your ingredients ready before starting to bake cookies. The next step is to actually use the formula to answer questions. I pose the same question I started with yesterday about having to choose between a prize of $5000 per month for life or $100,000 as a lump sum now and invested at an annual rate of 1.4%. This time I say I'm only giving them five minutes to figure it out, because I know they can use their formula to look at the $100,000 investment, with the same parameter of 20 years. (MP1, MP2) Most students can easily complete this challenge, but as they work, I walk around looking for students who may need additional scaffolding and/or support. I try to identify if they are struggling with applying the formula, with understanding the problem or with using the calculator and address each problem.
When everyone is done I ask them to compare their results to the answers we got yesterday to confirm that the formula works, then ask if there are any questions. I answer any questions then tell my students that today they will have an opportunity to become proficient at using the formula they worked to derive yesterday.
You will need copies of the problem set for this section. Teamwork 15 minutes: I tell my students that they did such a great job demonstrating their mathematical abilities yesterday individually that today I'm giving the chance to demonstrate their talents as teams. I tell them they'll be working with their back partner to solve a set of real-world problems (MP1, MP2, MP4) and will get to present at least one problem to the class. (MP6) I tell them that I will randomly select teams to present, allowing each team to choose a problem to present (that has not already been selected). This does two things. It reduces the stress of presenting first by giving that team the choice of any of the problems and it keeps all teams focused on solving all the problems as well as they can since they don't know what choices will be available when they're selected to present. I distribute the problem set and ask if there are any questions. As my students are working I walk around offering encouragement and redirection or assistance as needed.
Presentations 15 minutes: As my students prepare to present I remind them as a class to be courteous and appropriate in their critiquing of each other. I select the first team and allow them to present,(MP6) with questions and critiques from their classmates as they go through their solution. (MP3) When every team has presented I offer bonus points for any team that presents any of the remaining problems (if there are any) If there are no takers, I walk my students through those final problems, accepting their critiques and questions as we go.
To close out this lesson I have my students individually apply the geometric sum formula to one final problem to demonstrate their competence and understanding. (MP1, MP2) This is an informal assessment that helps me see if I'm on track, as I explain in my Working the Formula video I look for the same kinds of problems I saw earlier; inability to decode the problem, difficulty in working the formula and problems using the calculator. There may be other areas of weakness I need to address, but these are the three I've seen most often. If my instruction and assistance during the earlier part of the lesson haven't helped, then I try to arrange some one-on-one time with students as needed.