I'll start by presenting a problem about speeding ticket fines in Connecticut. I'll probably say that our Assistant Principal received a speeding ticket in CT while visiting family over Thanksgiving Break. Since he is in charge of culture and discipline, I'm sure they'll get a kick out of a story of him receiving a speeding ticket.
The power point presents how the speeding fines are calculated. I'll then ask my students to figure out how much a fine would be if you drive 1,5, and 10 miles per hour over the speed limit. I will allow my students to work on these in pairs using whiteboards and markers. This is to give students a subtle hint that substitution is one way to solve an equation.
Next I will show the algebraic expression used to calculate the fines: F=10(S-55) + 40. I will ask students to tell me what they see in the equation. What is the F? What is the 10? (S-55)? and + 40. I have the verbal description showing at the same time to help students make the connection. This puts into practice MP2 and MP4. They will discuss these in brief turn-and-talks.
Finally, the problem will change where a certain fine is given. Students will be asked to determine how fast you must go to receive this fine. It is my hope that students use a variety of methods (and MP1) to solve this problem: guess-and-check, substitution, inverse operations, distributive property, tables, etc. I'll need to remind students not to erase their work so that we can discuss the various methods for solving the equation.
Here is the first chance for students to apply some of the discovered strategies in order to solve "pure" equations.
For problems GP1 and GP2, I expect to see students solve using substitution and inverse operations. If students struggle, I will also emphasize that each equation can be seen as a equation of two factors. So for 3(x+8) = 36, I will ask 3 times what number is 36? How can we determine what that number is? x + 8 must equal that number, so x = ? This is to focus students' attention on the structure of the problem (MP7) and may help them see that they may simply divide both sides by 3 as a first step. GP3 and GP4 are similar but they involve negative integers.
These problems will be solved by students independently. The problems mirror the guided problem solving problems, so students will be able to use that as a resource for solving. I will spend this time monitoring the class as they work. I may provide targeted help to students who I identified as struggling in earlier parts of the lesson. Otherwise each student will be expected to rely on his/her own self to solve these problems.
We will quickly review answer after a few minutes of working. I will look for at least two different methods for each problem so that I can bring these to students' attention again.
Here students will solve 4 problems that are very similar to the Guided Problem Solving and Independent Problem Solving sections. A successful exit ticket will have at least 3 correct answers.