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# Practice with the Substitution Method

Lesson 8 of 13

## Objective: In this lesson students will have an opportunity to become fluent at solving systems of equations using the method of substitution. Students will be able to solve a variety of linear systems algebraically.

## Big Idea: Students need an opportunity to practice mathematical skills and procedures with examples that are challenging but still at their level. That is what this lesson provides. By the end of this lesson students should have fluency with solving system of equa

*45 minutes*

#### Independent Practice

*30 min*

There are two versions of this independent practice. When students are working on version A they can focus more on the process of solving a system using the substitution method. The algebraic manipulation required is not as difficult as in version B. Version A allows students to feel success and gain confidence which is extremely important. In version B, students also need to extend more effort to attend to precision*.*

**Things to watch out for:** With either version, one of the most common mistakes is not applying the distributive property correctly after the substitution in made. When a student has an error and is looking to find their mistake, that is usually the first place to look.

**Two teaching points: (1) **As mentioned before, I want to focus on process*. *I post the solution points (no work shown) to all of the excercises on each version so that students can see it is about focusing on the process and monitoring their own understanding. There is no reason to have students do 10 exercises the wrong way. If they are making mistakes they should find out why before moving on. **(2)** When students make mistakes (are not coming up with the correct solution) they need to be encouraged to go back through their work line by line to look for the error. If students have made an honest effort to find their error and still cannot I will examine their work and once I see the error I will tell them "it is somewhere in these three lines of work." This way they have more focus when determining the error but they still have to find it themselves. This is also part of the students monitoring their own understanding.* *

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#### Closure

*10 min*

**Ticket Out the Door**: 3-2-1: "Write down 3 things that you now understand about systems of equations, 2 questions that you still have (or two things you might think someone else would have a question about), and 1 thing you think is a *big idea *about solving systems." I break this closing activity up and do the 3 and 2 first before I give students the part about 1 big idea. It is really important that they have some time to think about what they want to say about the big idea before writing it down so that it "sounds smart." This is a quote I use when I don't want the students just writing whatever comes into their heads...they need to organize their thoughts before putting them on paper helping them to **construct a viable argument (MP3).**

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- LESSON 1: Introduction to systems of equations
- LESSON 2: What Does a System of Equations Really Look Like?
- LESSON 3: What is the "Point" of Solving a System?
- LESSON 4: Fitness Center Question
- LESSON 5: Cell Phone Plans
- LESSON 6: How are Systems of Equations related to Equations and Functions?
- LESSON 7: Solving Systems of Equations Without a Graph
- LESSON 8: Practice with the Substitution Method
- LESSON 9: Penny Problem
- LESSON 10: Practice Solving Systems Algebraically
- LESSON 11: Pulling the Systems Concepts All Together
- LESSON 12: An Interesting Lottery
- LESSON 13: Don't Sink The Boat