## Entry Ticket: Solving Systems with Substitution - Section 1: Entry Ticket

# Bring in the Sub!: Solving Systems of Equations in 2 Variables

Lesson 2 of 12

## Objective: SWBAT define variables and create equations to understand systems of equations. SWBAT apply the substitution method to solve systems of equations. SWBAT connect to, build on, and challenge a partner's ideas.

#### Entry Ticket

*15 min*

For today's **Entry Ticket **I have students complete a word problem that can be modeled by a system of linear equations.

I want students to practice the skills of defining variables and constructing equations from the previous lesson. The ticket also asks students to activate prior knowledge around graphing linear functions to find a common intersection/solution.

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Class then turns to active note-taking in **2-column note** form. During this time students are actively engaged in the note-taking process, asking questions, and discussing with peers as we review the Class Notes. Before I begin my presentation, I have the class brainstorm the meaning of the word "substitution." I want students to make connections to the term before we introduce the substitution method in class today.

The class perseveres through a number of examples of how to solve systems of equations using the substitution method. Although substitution is another form of combination, I like to teach it as a separate tool/strategy because I think students see it as a separate strategy.

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#### Collaborative Work

*20 min*

After reviewing the class notes for the day, students work in collaborative groups to complete 1-2 assigned word problems from Collaborative Work: Bring in the Sub! Applying the Substitution Method to Solve Systems. Each problem can be modeled by a system of linear equations. I try to use examples that students can relate to in the here and now, so the modeling (**MP.4)** in these problems helps make the math in the systems more tangible.

I find that assigning groups a small number of problems with high expectations of completeness helps students understand the concepts at a deeper level as opposed to having every students complete every problem in class. Each group is asked to document their work on one of the white boards in the room. I let the class know that we will be celebrating each other's work with a gallery walk after the group work.

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#### Gallery Walk and Revisions

*20 min*

When each group is completed documenting their work on the white boards, I have the class rotate between the different problems in a **Gallery Walk**.

I like to provide structure to this activity to make it time efficient - if there are 6 problems to present, give each group 3 minutes to review and provide feedback to one problem and then rotate.

One way to quickly generate constructive feedback from classmates is to have each group put their feedback on sticky notes. I like to give different groups different colored sticky notes so I can assess the detail and level of feedback each group is giving (and to be able to know which group made any inappropriate comments!).

I like the structure of this instructional activity because it gives students an opportunity to interact and share explanations and critiques (**MP.3)**. Having to present work on the white board pushes students to construct an argument in writing. The sticky notes gives students the perspective of their classmates on how they interpreted not only the problem, but how they thought about the problem.

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#### Exit Ticket

*15 min*

To conclude the lesson I have students complete an **Exit Ticket**. I want to assess where each student is at in his/her thinking about solving systems using the substitution method.

The Exit Ticket also provides another opportunity to assess student progress in defining variables and creating equations from a previous class. I want to intervene with additional support for any students who continue to struggle setting up the problems and/or with translating word problems into a system of equations.

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For homework tonight I assign practice problems from **Khan Academy **on **Solving Systems of Equations using Substitution**.

I like assigning practice problems through Khan Academy because there is built in support on the site - if students need a refresher/additional support on how to solve these types of problems, they can watch one of the step-by-step videos on the site.

Here is an example video students can use for support on their homework:

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- UNIT 1: Thinking Like a Mathematician: Modeling with Functions
- UNIT 2: Its Not Always a Straight Answer: Linear Equations and Inequalities in 1 Variable
- UNIT 3: Everything is Relative: Linear Functions
- UNIT 4: Making Informed Decisions with Systems of Equations
- UNIT 5: Exponential Functions
- UNIT 6: Operations on Polynomials
- UNIT 7: Interpret and Build Quadratic Functions and Equations
- UNIT 8: Our City Statistics: Who We Are and Where We are Going

- LESSON 1: Creating and Interpreting Equations to Solve Systems
- LESSON 2: Bring in the Sub!: Solving Systems of Equations in 2 Variables
- LESSON 3: The Whole is Greater than the Sum of Its Parts
- LESSON 4: Practice Session on Solving Systems
- LESSON 5: Graphing Systems of Equations
- LESSON 6: Solving Linear Equations in Two Variables
- LESSON 7: Solving Non-linear Systems of Equations
- LESSON 8: Graphing and Solving Systems of Inequalities
- LESSON 9: Job Offers and Cell Phone Plans: Making Informed Decisions with Mathematics
- LESSON 10: Study Session for Unit Test on Systems of Equations and Inequalities in 2 Variables
- LESSON 11: Unit Test: Systems of Equations and Inequalities in 2 Variables
- LESSON 12: Writing in Math Classroom, Part 2: Solving Equations & Inequalities in 2 Variables