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# Practice Session on Solving Systems

Lesson 4 of 12

## Objective: SWBAT define variables and create equations to model a system of equations SWBAT apply appropriate strategies to solve systems of equations

*90 minutes*

For today's lesson, students spend a lot of time working collaboratively on three main topics from the unit that students could use more practice on. This lesson can be taught as a progression with the students working at stations. Alternatively, students can focus on one of the three skills and rotate among the skills.

The three primary topics are:

- Rearranging and Substituting to Solve Systems
- Simple Elimination
- Multiplying and Combining/Eliminating.

I implement the lesson with all students working on the same skill at the same time. I do provide stations where students can rotate to mix up the class structure. The stations also make it possible to differentiate instruction. For example, students can stay at one station for the majority of the class if they require significant support in one area.

Check out the video below on suggestions on running the class in a station format.

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#### Entry Ticket

*15 min*

For today's **Entry Ticket **I give students two systems of linear equations to solve. The first is a system where substituting is setup and the second is a case where substitution or combination can be used to solve the system.

This entry ticket activates student's prior knowledge and gives a clue to the day's content and learning objectives.

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For **Focus Concept 1: Substitution Method, **the class practices solving systems involving rearranging/substituting to solve systems of equations. Since all students will complete this focus area together, I use the Entry Ticket from today's class as a bridge to a class discussion and review of solving systems with substitution.

After the class discussion, students have time to work collaboratively solving example problems from Khan Academy. If students have difficulty completing the problems, I refer them to this Khan Academy video for assistance: Solving Using Substitution. At the end of this mini-lesson, I have all students complete a problem on using the substitution method for the last 5 minutes or so of the lesson. The problem is:

*The monthly cost of two cell phone plans (M = cost of Motor Cell Phone plan and T = cost of Totally Wired cell phone plan) can be modeled with the system of equations below. Which cell phone company would you choose? Justify your answer.*

* 4M + 3T = 419*

* M + T = 173 *

**Instructional Note**: This class is set up as 3 mini lessons, each targeting a specific skill and providing direct instruction, group and individual practice for each of the three skills. You might use these activities differently, if you do not teach on a block schedule.

#### Resources

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For the **Focus Concept 2: Elimination Method, **the class practices solving systems involving simple elimination.

For this section, the class reviews one Khan Academy video providing an overview of solving systems using elimination:

After the class discussion of the video, students have time to work collaboratively solving example problems from Khan Academy (I encourage students to review instructional videos if they get stuck on a problem).

To assess individual understanding, I have all students complete a problem set on **Deltamath** that gives students a chance to practice the focus skill using technology and let's me as a teacher easily monitor and track student progress online.

If there is not enough time in class, sometimes I assign the Deltamath individual assignment for students to complete as homework. The class then moves on to the third and final Focus Concept mini lesson.

#### Resources

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The final mini-lesson for today's class is **Focus Concept 3: Elimination Method with Multiplication**. For this section, the class reviews one Khan Academy video providing an overview of the Focus Concept:

After the class discussion of the video, students have time to work collaboratively solving example problems from Khan Academy (I encourage students to review instructional videos if they get stuck on a problem).

To assess individual understanding, I have all students complete a problem set on **Deltamath** that gives students a chance to practice the focus skill using technology and let's me as a teacher easily monitor and track student progress online.

If there is not enough time in class, sometimes I assign the Deltamath individual assignment for students to complete as homework. The class then moves on to the third and final Focus Concept mini lesson.

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To recap the class I have students complete an **Exit Ticket** on what they learned today. I ask each student to write down the different stations they visited during class along with one strategy they learned and at least one area where they need additional practice.

I provide a rating scale because I find students have a difficult time articulating the level of difficulty they have for each problem and it helps to have some in between answers. I use the reflection sheet to guide an action plan for the night's homework assignment.

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For homework I have students review their reflection sheet and identify the one area that they are having the most difficult time with in regards to solving systems of equations. I then assign students to complete an additional 5-10 problems on Delta Math focusing on that skill. I also suggest that students review solutions on Deltamath.com or Khan Academy videos on the skill for additional practice.

I like the **Deltamath** website because I can track the number of problems students attempt as well as the number/percentage they get correct. It is an excellent way to organize and differentiate homework. It helps me to promote two main 2 intents of homework: practice and responsibility.

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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