For today's Warm Up assignment, I have provided three linear equations that students must simplify to determine if the equation has one solution, no solutions, or infinitely many solutions. I selected these to build on the previous day's lesson so I could be on the look out for any misconceptions or struggles students might be having during Warm Up and address them.
Once the timer sounds, I select student "volunteers" at random (from a cup of names) and ask for class consensus. If there is disagreement, I ask for that student to provide evidence to convince the class of his/her answer. I continue taking evidence from students as needed until we reach consensus as a class.
After Warm Up, I move quickly to today's Learning Objective, which is to identify structures of one variable linear equations that simplify to one solution, no solution, or infinitely many solutions. In the previous day's lesson, students had the opportunity to solve a variety of equations and sort them. Today, they will take those same equations and look for common attributes in each type.
For Work Time, Part 1, students, working with partners, will use the One-Step Equations Sort from the previous day's lesson to look for structures in each equation type that yield common solutions results. They will record these attributes in Solving equations with one variable foldable which we glued into journals on the previous day.
When the Work Time timer sounds, I explain it is time for Building Consensus by creating a class document about structures they discovered. I record them on the SmartBoard as students volunteer their ideas. I am careful to test each structure with a sample equation to check for accuracy. Students have often discovered a structure that is sometimes true, but not always, so I want to be sure they recognize the distinction. Once we have collected ideas for eight minutes, I explain that the document may be unfinished, but we are going to move on to the next work time, where we may discover additional structures which we can add.
For Work Time, Part 2, students work individually to complete four problems of "Creating Linear Equations" by filling in blanks so that each resulting equation yields the number of solutions required. These problems are scaffolded and increase in difficulty. I only provide seven minutes for this work and I spend this time circulating through the room asking any struggling student guiding questions to get or keep them working. I remind them to refer back to their foldable if they are stuck.
We close the day's lesson when the time sounds by Building Consensus again, this time around possible solutions to the equations they were presented.
As students volunteer solutions, I substitute them and ask the class to simplify with me. In this way, I am able to verbalize what I am doing and why and call attention, through questioning, what structures are at play. For example, I might ask why a student choose a particular coefficient to a variable.
Once we have listed several correct responses to each equation, I again return to our Consensus Chart from the previous Work Time so that we can add additional structures to our table for use throughout this unit.
After all classes have completed this activity, I record the structures on a anchor chart that remains posted in the classroom for reference.