For today's Warm Up assignment, I provide students a system of equations to solve by graphing. I intentionally give one of the equations in slope-intercept from and the other in standard form. I want student to be able to recognize the forms and know how to convert, when necessary, for graphing.
Once the timer sounds after 5 minutes, I select a volunteer to give his solution. I the ask the class for confirmation. If the class concurs, I quickly graph the two equations on the grid to show the solution. If students don't agree, I ask for additional solutions, record each on the Smart board, and then ask a student to coach me through the process of converting the standard form equation for graphing. I then graph both equations, locate the solution, and record it. Typically, one of the solutions provided by the class is the correct solution, so I circle it for affirmation.
By taking time to check the answers, I can often clear up misconceptions held by students. I am, however, careful to record the names of struggling students on my observation clip board that can invite to morning intervention class (designed and carried out by all teachers in the school).
After reviewing the Warm Up assignment, I move to today's Learning Objective. I explain that although all our previous experiences with graphing systems have yielded one solution, during today's work, we will learn about special cases that results in no solutions or infinitely many, as previously learned while solving linear equations.
To assist students in understanding the special cases that can occur while solving systems of equations through graphing, I provide students a Systems by Graphing Foldble. In it, students solve each special cases as I show Systems by Graphing Examples. I then ask that they reflect and record why the system has a particular number of solutions. I can then look at student responses to quickly see who does not yet have a strong understanding. The foldable is glued into student journals for future reference and review.
Once students have a grasp of the special cases, for Work Time, I give them Solving Systems by Graphing Practice worksheet with 10 practice problems. Students have to convert equations to slope-intercept form, graph the equations, then decide if the system has one solution, no solution, or infinitely many solutions. I ask them to record their work in their journal so that they can refer back to it, if needed, during consensus building.
Once the timer sounds after 20 minutes, I call the class together for Building Consensus. I select students at random to tell me which problems (identified by letter) belong in each column. If disagreement arises, I record the system on the Smart board and ask students to coach me through solving each equation. I then graph the equations and indicate the solution. This gives disagreeing students an opportunity to see mistakes that were made in their own work so that they will hopefully learn from those errors.