# Speeding Tickets

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## Objective

SWBAT explore methods for solving problems and equations in the form p(x+q)=r

#### Big Idea

Students explore methods for solving equations in a problem solving context.

## Introduction

15 minutes

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.

## Guided Problem Solving

15 minutes

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.

## Independent Problem Solving

15 minutes

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.

## Exit Ticket

5 minutes

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.