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# Graphing Linear Systems of Equations (Day 1 of 2)

Lesson 1 of 9

## Objective: SWBAT solve linear systems of equations by graphing.

#### Do-Now

*10 min*

Today's class is the first lesson in the Systems of Equations unit. Students will first learn how to find the solution to a system by graphing. The purpose of this Do Now is to allow students an opportunity to practice converting equations in slope intercept form, since this skill will be used in the lesson.

Students will complete the Do-Now in 4 minutes, with volunteers coming up to the board to share their answers with the class.

Next, a student will read the objective, **"SWBAT solve linear systems of equations by graphing".**

#### Resources

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#### Opening

*10 min*

We will begin today's lesson by reviewing vocabulary using the Day 1 Graphing Systems PowerPoint and discussing new and familiar terms as we start our systems of equations unit. The video below shows how I will present these ideas in front of the class.

After the video, we will work on the Graphing Systems Day One worksheet.

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#### Notes & Guided Practice

*25 min*

As we begin to dig into systems of equations, students will follow along on today's presentation using guided notes. Students currently have an initial idea of an algebraic system. I will ask them to explore a concrete example on their own. We are working from Day 1 Graphing Systems.

**Slide 3:**** **I will display the first two lines of slide four on the board, which prompts students to graph the lines **y = x + 4** and **y = 2x - 1** on the graph at the top of their paper. After a brief pause, I will then reveal the rest of the text on the slide, and ask students to follow the rest of the instructions while sharing their responses with a partner.

After a few minutes, we will come back together as a whole group. I will ask students the following questions:

- What happened when both lines were graphed on the same coordinate plane?
- Where did the lines intersect?
- What happened when we tested the point into both equations?
- How does this result support our definition of a system?

**Slide 5:** Students will practice finding the solution to a system of equations by labeling the point of intersection for a given set of two lines. Problem #4 and #5 do not intersect at whole numbers, so I will ask the class to give a good estimate of the point of intersection. I think it is important for students to see examples like this early on in the unit. I want students to see that useful solutions can be estimated when the coordinates of the intersection point are not integers. I will inform students that we will eventually learn how to find an exact, non-estimated solution in cases like this. I will introduce the names for the methods substitution and elimination, as topics that will be coming up soon.

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#### Partner Practice - Matching

*25 min*

During today's Partner Practice, students will practice today's objective using this handout. Students will graph the system of equation in Column A, and then draw a line to its corresponding answer in Column B. I require students to verify each solution by plugging the solution into each equation. I will ask them to do this work on a separate sheet of paper.

**Teaching Note**: I created coordinate plane dry-erase boards by placing a sheet of graph paper into a clear sleeve (You can also use a sheet protector). Students write on the plastic sleeve with a marker.

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#### Closing

*10 min*

As the lesson comes to an end, I will ask students to give a 15-second summary of what we learned today, and to decide if we mastered our objective. I will then ask students to try to recall a time where we solved equations that had a common answer. Students will then complete an Exit Card. I will try to grade the Exit Cards directly after class. I will look for patterns in students' responses. I plan to group students by the percentage of correct questions for an intervention group during our next lesson.

#### Resources

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*Thanks for all your hard work - it takes time to put this all together. Since it is Valentine's Day <3 | 8 months ago | Reply*

Thank you so much for sharing your wonderful resources! The resources for this unit were a life-saver for me! I was given one day to plan a curriculum for summer school, and your activities, guided notes, and just everything were such a help in a stressful time. I really can't thank you enough!Â

| one year ago | Reply

thank you I wish I had had this a few weeks ago for my students.

Very clear to follow and the steps are logical, and lead the students through well.

| 2 years ago | Reply

Thank you for this lesson. Â The guided notes and examples were perfect for my Summer School students. Â They were extremely engaged in this lesson. Â You have a fan.

| 2 years ago | Reply

I really liked the closing lesson with the feedback comments. Â We have started to do unit feedback and homework feedback is a great idea!

Â Thanks :)

Mary

| 2 years ago | Reply*Responding to Nancy Jane Smith*

Hi Nancy, My full year should be live on the site within a couple of months.Â

| 2 years ago | Reply

Do you anticipate that you will have a school year's worth of lessons online soon? Â I am looking ahead and wondering if I need to look at one of the other contributors after we finish the units you have up. Â

| 2 years ago | Reply*expand comments*

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- UNIT 1: Welcome Back! - The First Week of School
- UNIT 2: Linear & Absolute Value Functions
- UNIT 3: Numeracy
- UNIT 4: Linear Equations
- UNIT 5: Graphing Linear Functions
- UNIT 6: Systems of Linear Equations
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- LESSON 1: Graphing Linear Systems of Equations (Day 1 of 2)
- LESSON 2: Graphing Linear Systems of Equations (Day 2 of 2)
- LESSON 3: Solving Linear Systems of Equations with Substitution (Day 1 of 3)
- LESSON 4: Solving Linear Systems of Equations with Substitution (Day 2 of 3)
- LESSON 5: Solving Linear Systems of Equations with Substitution (Day 3 of 3)
- LESSON 6: Solving Linear Systems of Equations with Elimination (Day 1 of 3)
- LESSON 7: Solving Linear Systems of Equations with Elimination (Day 2 of 3)
- LESSON 8: Solving Linear Systems of Equations with Elimination (Day 3 of 3)
- LESSON 9: Stacking Cups: Systems of Equations Real World Application