Oni's Equation Adventure-Day 6

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SWBAT solve systems of linear equations in two variables algebraically using elimination.

Big Idea

Now that students are comfortably graphing solutions to linear equations, they are ready to learn a new strategy: Elimination.

Warm Up

7 minutes

For today's Warm Up assignment, I have given students a system of equations that when solved, yields no solution. This is one of the special cases in the previous day's lesson (Day 5), so I wanted to give student some practice recognizing these.

As students work, I circulate through the class checking for understanding and watching for students who appear confident in their skills. I ask one of these students to share their solution once time is called.

When the timer sounds, I invite my pre-selected student to share her answer and ask for class agreement. I ask for any other answers and if one is volunteered, I ask how we might prove which answer is correct. I then ask the original student to share her approach to solving the problem and model her steps on the Smart board. Typically, students who found differing answers find their errors during this time. If not, however, I invite that student to share his/her approach. By allowing students with incorrect answers to share their ideas, I am modeling that I value multiple approaches as well as learning from our mistakes.

Once the class has reached consensus on the solution, I move directly to today's learning objective.

Learning Objective

6 minutes

After sharing today's Learning Objective, I explain to the students that solving systems by graphing is just one strategy we can use and that today, we will learn a second one called 'elimination'. I then ask that they watch and listen for the next few minutes while I do a "think aloud" as I solve the problem. This allows me to verbalize all the things I think about as I use elimination. After each step in the process, I stop and ask students to give me a "thumbs up" if they are following what is going on. This keeps the majority focused on what I am modeling. After I finish solving the first problem, I repeat the process with a second problem. At the end of my demonstration, I ask them to turn and talk with their partners about the process.

Work Time, Part 1

6 minutes

Once students have had an opportunity to verbalize the process they witnessed, I explain that I would like them to try out the strategy on their own by solving four systems problems using elimination. I reveal the four problems on the Smart board for Work Time, Part 1, and set the timer for six minutes.

Building Consensus, Part 1

6 minutes

When the timer for Work Time, Part 1, sounds I ask the class to come together for consensus building. While not all students may have finished the four problems, I have continued to monitor the work of the slower-paced so that they do not fall behind conceptually. 

I randomly select students (from the names cup) to share their answer on each of the four problems and seek consensus from the class. When it reached on all four problems, I then ask students to give me a quick understanding scale of 1-5 (1 = totally lost, 5 = I could teach someone this concept). I scan the room for any 1's or 2's and make mental note to group them with me during Work Time, Part 2.

Introducing Multiplication Property of Equality

4 minutes

Now that students understand the concept of elimination, I introduce a problem which doesn't combine to form a zero pair. I then introduce and demonstrate the concept of Mutiplication Property of Equality. Again, I do a think aloud, explaining my thought process as I progress to the solution. I then demonstrate another problem, but this time, I seek input from the class by asking questions along the way like, "Which variable would be easiest to eliminate?" or "How do I solve for x?"

Once we have found the solution to the second problem, I ask students to turn and talk to their partner about the extra step that is needed when solving a system of equations that has variables that do not combine to form a zero pair.

I want student to verbalize this understanding so they enter the next Work Time with a strong understanding of the the process.

Work Time, Part 2

10 minutes

Once we have solved both example problems using the multiplication property of equality, I distribute a half sheet assignment, Solving Systems by Elimination Practice for the students to solve. I then set the timer for 10 minutes for Work Time, Part 2.

Building Consensus, Part 2

6 minutes

When the timer sounds, I randomly select volunteers (from the cup of names) to share their solutions. I again work to gain consensus from the class so that students can look for and find their mistakes if they disagree. When class is over, I remind students to turn in their assignment for credit.

By looking at student responses on the Work Time, Part 2 assignment, I can categorize common errors and make note of them. I then use this data to select students to attend remediation class during our school-wide "Power Hour" which is held 3 days per week in place of Advisory class.