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# Systems of Equations Day 2 of 2

Lesson 8 of 24

## Objective: Students will be able to justify why a given method is the best choice to solve system of equations.

## Big Idea: Engage students with Math Practice 5 (Use appropriate tools strategically) in this lesson on systems of equations.

*50 minutes*

#### Warm up and Homework Check

*10 min*

I include Warm ups with a Rubric as part of my daily routine. My goal is to allow students to work on **Math Practice 3** each day. Grouping students into homogeneous pairs provides an opportunity for appropriately differentiated math conversations. The lesson"s Warm Up- Systems of Equations Day 2 has students write a system of equations whose solution is (1,3). There will be many answers to this question as well as many strategies on how to produces these equations which will provide some excellent discussion.

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Solving systems is a foundation skill from Algebra 1 that students often need gentle reminders about, so the goal of this lesson is to present systems of equations to the students through the lens of **Math Practice 5** (Use appropriate tools strategically). After ensuring all students are familiar with the term system of equations, I give them an activity sheet that asks them to identify which of three separate methods of solution is the best choice. Specifics on this activity can be found in the PowerPoint - Systems of Equations, which includes detailed presentation notes.

My second goal for this formative assessment activity is to determine student comfort level for each method of solving systems of equations. I use a thumbs-up method to get information like this. I ask students to give me a thumbs-up if they know something really well, a side-thumb if they kind of know it, and a thumbs-down if they are really unsure. For classes where only a few students are unsure, I allow them to keep the activity sheets and arrange for a one-on-one session. If a larger number of students are unsure, I would do guided practice in class. For this practice I generate examples myself or use some from our Algebra 2 text.

Next, I ask them to determine the best method of solving a group of systems. I have students confer with their partner and then hold up one finger for graphing, two fingers for substitution, and three fingers for elimination (combination). I also call on students to explain their reasoning. I like this activity because there isn’t one best method. Students can have differing opinions and then have the opportunity to justify their choice (**Math Practice 3**).

Finally, students generate a list of the pros and cons for each method. This is done in with the groups formed in the original activity and then shared as a class.

Detailed presentation notes are included in the PowerPoint.

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#### Types of Solutions

*15 min*

My students have already looked at the graphical representation of no solution and infinite solutions in the lesson **Selling Cake Pops Day 4**. We are going to look at this again reinforce this information. I first ask them to do a think-pair-share on the question”How do you know if there is no solution to a system of equations?” We then do the same thing for the question “How do you know if there are infinite solutions to a system of equations?” The key is that they can recognize both the graphical and algebraic representations of these types of solutions. If the students are struggling with the algebraic portion, I may set up a simple system of either parallel or equivalent lines and have them solve it. Detailed presentation notes can be found in the PowerPoint located in Sections 2.

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#### Exit Ticket

*3 min*

I use an exit ticket each day to provide a quick formative assessment to judge the success of the lesson.

Today's Exit Ticket, located in the PowerPoint, asks the students to solve a system as well as explain the method they chose to use.

#### Resources

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The Assignment assignment has to distinct parts. The first part addressed the lesson’s objective where students choose a method (**Math Practice 5**) for solving a given system of equations. The second section is an extension (**Math Practice 1**) introducing non-linear systems and encouraging critical thinking as students compare and contrast linear and nonlinear systems.

#### Resources

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- UNIT 1: Modeling with Expressions and Equations
- UNIT 2: Modeling with Functions
- UNIT 3: Polynomials
- UNIT 4: Complex Numbers and Quadratic Equations
- UNIT 5: Radical Functions and Equations
- UNIT 6: Polynomial Functions
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- UNIT 9: Trigonometric Functions
- UNIT 10: Modeling Data with Statistics and Probability
- UNIT 11: Semester 1 Review
- UNIT 12: Semester 2 Review

- LESSON 1: Mathematical Modeling: Properties of Functions Day 1 of 2
- LESSON 2: Mathematical Modeling: Properties of Functions Day 2 of 2
- LESSON 3: Mathematical Modeling: Linear Functions
- LESSON 4: Mathematical Modeling: Linear Functions Design Project
- LESSON 5: Finding Equations of Parallel and Perpendicular Lines
- LESSON 6: Inverse Functions
- LESSON 7: System of Equations Day 1 of 2
- LESSON 8: Systems of Equations Day 2 of 2
- LESSON 9: Modeling Systems of Equations
- LESSON 10: Function Review
- LESSON 11: Function Mid Test
- LESSON 12: The Tortoise and The Hare Project Day 1
- LESSON 13: The Tortoise and The Hare Project Day 2
- LESSON 14: The Tortoise and The Hare Project Day 3
- LESSON 15: The Tortoise and the Hare Project Day 4
- LESSON 16: The Tortoise and the Hare Piece-wise Functions
- LESSON 17: Step Functions
- LESSON 18: Absolute Value Equations
- LESSON 19: Absolute Value Inequalities
- LESSON 20: Absolute Value Functions: Transformations Day 1
- LESSON 21: Absolute Value Functions: Transformations Day 2
- LESSON 22: Functions Test Review Day 1
- LESSON 23: Functions Test Review Day 2
- LESSON 24: Functions Test