## SolveProblemsEquationInForm_GPS.docx - Section 2: Guided Problem Solving

# Speeding Tickets

Lesson 9 of 20

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

*50 minutes*

#### Introduction

*15 min*

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.

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#### Guided Problem Solving

*15 min*

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.

#### Resources

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#### Independent Problem Solving

*15 min*

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.

#### Resources

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#### Exit Ticket

*5 min*

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.

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- LESSON 1: Simplifying Linear Expressions by Combining Like Terms
- LESSON 2: Expand Algebraic Expressions Using the Distributive Property
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- LESSON 4: Linear Expressions and Word Problems
- LESSON 5: Solving Addition and Subtraction Equations Using Models
- LESSON 6: Solve Addition and Subtraction Equations using Inverse Operations
- LESSON 7: Solve One-Step Equations Using Inverse Operations
- LESSON 8: Diagrams of Two-Step Equations
- LESSON 9: Speeding Tickets
- LESSON 10: Translate Verbal Statements to Inequalities
- LESSON 11: Graph Inequalities on a Number Line
- LESSON 12: Solve Inequalities Using Addition and Subtraction
- LESSON 13: Solve Inequalities Using Multiplication and Division
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