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* *Reflection: Staircase of Complexity
Solving for x - Section 3: Discussion

I really like how this task shows two equations that are essentially the same but the second one has two variables instead of one. I think this is a useful way for students to learn how to isolate x in both cases, rather than taking them on as two separate processes. Students who can solve multi-step equations for x when the answer is an integer often have trouble solving for a variable in terms of another variable. To me, this increase in complexity makes a lot of sense and I think it will make this work easier for students, both conceptually and in terms of the skill needed to solve.

*Adding in another variable*

*Staircase of Complexity: Adding in another variable*

# Solving for x

Lesson 12 of 14

## Objective: SWBAT solve linear equations in one variable and solve linear equations in two variables for one of the variables. SWBAT compare one variable and two variable equations with the same operations.

#### Introduction

*5 min*

Today's task asks students to build on the work they did in the previous lesson and build on solving linear equations in one variable to solving for x in the same equation with two variables. We start class by looking through Solving Equations, Literally together and I point out to students that the equations in the right column of the page are the same as the problems on the left except they have a y in them. I let them know they should solve both equations for x and think about their reasoning as they do so.

#### Resources

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#### Investigation

*30 min*

Next, students get to work in pairs or small groups on the equations. Some of my students will struggle with solving these equations so I reference the work we did previously in the Post-It Notes equations lesson. I might ask them to think about the first problem in terms of what would have happened at the cafeteria table in order to get this equation. I am looking for students to see that the last thing to have happened would be that the group divided into 5, so they'll have to undo this step by multiplying both sides by 5.

Students may also struggle when they see the y added into Question #2. I encourage them to think about their steps from Question #1 and see if they still apply. What's different about the equation because y is there? Can they still get x by itself?

Many of my students will also struggle with the last two problems. I encourage them to think about Question #9 as the same as the questions above but with letters instead of numbers. Can they still think about the operations they did above in the same way for the last two problems?

Lastly, many students freak out when they see the radical sign in Question #10. We may spend some time talking about inverse operations and how we can "undo" the radical sign. What would it mean to do the opposite of taking the square root of something?

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#### Discussion

*20 min*

I like to have students share out their equations side-by-side for our discussion today. I painted some of my classroom walls at whiteboards this year, so I divide up the students and spread them out around the room to put up their equations. We spend a lot of time on Questions 5 through 8, as many students will have trouble working with the 2/5 in Questions 5 and 6. Additionally, I like to have students explore the different ways to solve questions 7 and 8, and we can talk about the benefits or drawbacks of using the distributive property here. It can be fun to have students show two ways to solve Question #7 and then ask them to match up that same method with Question #8.

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#### Closing

*5 min*

Solving linear equations is a skill algebra students need to master. To that end, I want them to focus on some of the strategies they use to solve equations at the end of today's class. I ask them to write a reflection for the following prompt:

- What are some strategies you used today to solve linear equations?
- How do you think about equations with more than one letter in them?

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Solving Equations, Literally is licensed by © 2012 Mathematics Vision Project | MVP In partnership with the Utah State Office of Education Licensed under the Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported license.

http://www.mathematicsvisionproject.org/secondary-1-mathematics.html

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- UNIT 1: Introduction to Algebra: Focus on Problem Solving
- UNIT 2: Multiple Representations: Situations, Tables, Graphs, and Equations
- UNIT 3: Systems of Equations and Inequalities
- UNIT 4: Quadratics!
- UNIT 5: Data and Statistics
- UNIT 6: Arithmetic & Geometric Sequences
- UNIT 7: Functions

- LESSON 1: First Day of Class - The Marshmallow Challenge
- LESSON 2: How Does This Math Class Work? Creating a Positive Classroom Climate
- LESSON 3: Generating Student Discourse
- LESSON 4: What Makes Something a Pattern?
- LESSON 5: The Broken Eggs
- LESSON 6: Introduction to Functions
- LESSON 7: Tables, Words, and Equations
- LESSON 8: A Communication Challenge
- LESSON 9: Mystery Bags Game
- LESSON 10: Writing About Math in the Cafeteria
- LESSON 11: Post-It Note Equations
- LESSON 12: Solving for x
- LESSON 13: Inequalities: True or False?
- LESSON 14: The Great Inequality Debate