Graphing Linear Systems of Equations (Day 1 of 2)

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Objective

SWBAT solve linear systems of equations by graphing.

Big Idea

Students will discover that intersecting lines on a coordinate plane share a common solution, forming a system of equation.

Do-Now

10 minutes

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". 

Opening

10 minutes

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.

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

Notes & Guided Practice

25 minutes

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.

Partner Practice - Matching

25 minutes

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. 

Closing

10 minutes

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.