Graphing Linear Systems of Equations (Day 2 of 2)

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Objective

SWBAT solve linear systems of equations by graphing.

Big Idea

Students will use their knowledge of parallel lines to identify systems of equations with no solution.

Do-Now

10 minutes

As class begins students will complete the Do Now. Today's Do-Now students asks students to create equations of lines that are either parallel or perpendicular. This topic was taught during our last unit, but some students may still need a reminder to refer to their old notes if they have forgotten the relationship between parallel and perpendicular lines.

This activity is a great way to help students make a connection from previously learned material to today's objective since we will be identifying systems of equations with special solutions.

After reviewing the Do-Now as a whole group I will ask a volunteer to read the objective, "SWBAT solve linear systems of equations by graphing".

Before moving on, I will ask a volunteer to give a brief summary of what we learned about a systems of equations in our last class.

Notes + Guided Practice

30 minutes

Before beginning new material, I will return the exit cards from our last class to give students an opportunity to review their responses.

Students will then complete the Review on the top of today's guided note sheet. I will ask two students to come up to the front of the board to act as the instructor by talking through the process they used to graph and check the solutions for each system. 

Next, I will ask the class to recall the special solutions that we discovered when we solved linear equations. I will ask two students to name what they were, and to give an example of an equation that would fit the description of "no solutions" or "infinite solutions".

Then, I will tell the class that just like with linear equations, systems of equations can also have special solutions. I will tell students to turn-and-talk with a partner for 20 seconds about their prediction of what a system of equation with no, many, or one solution would look like. I will then set a timer on the board for 5 minutes, in which students will work with a partner to graph the three systems on the bottom of their paper. I will challenge the class to figure out which systems have no, many, or one solution. I will ask the students to justify their responses by filling in the explanation below each graph on their paper.

Lastly, we will review the three problems, and talk about each type of system:

  • Why does it make sense that a system with no solution does not intersect?
  • Could you tell if a system will have no solution before you graph it? How?
  • If we know that systems share a common solution, why does it make sense that coinciding lines have infinite solutions?
  • Would two coinciding lines still be considered a system of equations? Why or why not?
  • Could you identify a system of equations with infinite solution before you graphed it? How?

Students will then complete the six practice problems on the back of their notes with a partner. During this time, I will pull a small group of students who may be struggling with this concept based on in-class observations, and our last exit card.

Group Activity - Speed Dating

30 minutes

Before we began this group activity, I will ask the class if they know what speed dating is. Most will have seen it in a movie or on television, but for the ones that aren't sure, I will introduce what speed dating is and what the purpose of  an event like that is.

I then tell students that we will be speed dating in our class to figure out who their "Algebra BFF" is. Then, I give each student an equation to tape to the front of their shirt to act as their name-tag.

To complete this activity, students will circulate around the room with this paper. They will pair up with another student, and both students will introduce themselves to each other using the equation that is taped to their shirt. Next, both students will join to create a system of equations together, and then they will graph both lines on their paper. Last, they will record their shared solution, and decide whether or not they are BFF's using their own justifications and reasoning.

After about 20 minutes we will reconvene as a whole group to debrief the activity. This activity happened to fall near Valentine's Day, and was a big hit with my students. Please enjoy this fun video of the song my students started to sing as they searched for their BFF.

Closing

10 minutes

I will ask a volunteer student to give a brief summary of what we did today in class. I will ask another volunteer to compare and contrast linear equations and linear systems that have special solutions. Students will then complete an exit card.