# Oni's Equation Adventure- Day 4

## Objective

SWBAT understand that solutions to a system of two linear equations in two variables correspond to points of intersection of their graphs, because points of intersection satisfy both equations simultaneously.

#### Big Idea

Students graph two lines on the same coordinate grid to discover the solution that works for both equations. Then, they apply the concept to a real-world situation in Pizza Wars.

## Warm Up

8 minutes

For today's Warm Up assignment, students continue to practice using the structure of linear equations to direct the number of solutions. By filling different numbers in the blanks on each equation, they create equations that have one, no, or infinitely many solutions.

Once the time sounds after 5 minutes, I call for volunteers to share their numbers. Then, I model checking their work. Once all three equations have been created to satisfy the conditions required, we move to the day's learning objective.

## Learning Objective

5 minutes

Today's Learning Objective is language rich, so I take time to break down the objective and apply what is being said to an example.  Once I have done this, I ask students to "turn and talk" and explain the objective in their own words.

## Work Time, Part 1

10 minutes

Because students have already mastered the prerequisite skills for today's lesson, for Work Time, Part 1, I distribute a Solving Systems of Equations by Graphing worksheet for student practice. I demonstrate the first graph on the Smart board, then set the timer for students to complete the remainder of the graphs in 10 minutes. By limiting their work time, I keep the students focused on the task as I circulate and assist students as needed. Once the timer sounds, I remind students that the completed assignment should be turned in before the start of class tomorrow.

## Work Time, Part 2

14 minutes

Since students now have a better understanding of solving systems of linear equations by graphing, I introduce the Work Time, Part 2 assignment, Pizza Wars. This assignment requires students to write equations corresponding to a real-life situation. They then set up and graph the equations to determine the solution to the problem. I also as them to write in words a justification for their answer. I distribute the assignment, then set the timer for 14 minutes.

During this work time, I explain that students should seek help from their table mates before asking me for help (ASK3B4ME is a sign I have above my whiteboard). Students tend to strengthen their understanding far more from discussions with each other, so I want to create conditions that encourage this.

When the timer sounds, I bring the students' attention back to the Smart board for consensus building.

## Building Consensus

8 minutes

For lesson closure, we move to Building Consensus. I select student volunteers to share their equations for each pizza business and look for agreement from the class. Once agreement is had, I select a student to coach me in labeling the grid. I ask the class to listen carefully to my coach to make sure s/he does not miss any important detail.

I then select a student to plot each restaurant's line on the grid. I ask for students to give a thumbs-up signal if they agree with the answer displayed. I then ask students to "turn and talk" to their neighbor  for 1 minute and discuss how we might prove this answer algebraically. I eavesdrop and interject questions to student groups until I find a student who will share the idea of substituting the value back into each equation and solving.

I then ask students to reflect on their understanding of today's lesson and rate their learning on a 1-5 scale. I make note of any student who indicates a 2 or 1 so that I can pull them into small group tutoring during our schoolwide intervention time.