I begin today's Launch with an equation that differs from ones that students have seen in our previous lessons. (This is a move that I sometimes make. I think it's a good idea to begin class with a problem that is a step above prior work.) I write this equation on the board and I walk around making sure everyone is on task and working independently on solving the equation. I want students to start with a strategy that makes sense to them.
There is more than one way of solving this equation. Once some students solve it a first way, I encourage them to figure out another way to solve the equation. I will also send a couple of students who have solved it in different ways up to the board to share their work for everyone to see. I expect that some students will successfully employ inverse operations. We have developed this strategy carefully over the last couple of lessons. Another method that I anticipate my students will try is to separate the left side of the equation into the sum of two fractions before trying to solve.
Now that we have begun class with an equation that can be solved multiple ways, I give students a worksheet that simulates two students who never seem to agree on an approach. The No way Rene Activity is designed to access and extend prior knowledge about simplifying algebraic expressions, while giving students the opportunity to engage in Mathematical Practices 3 and 6.
I want to make sure that my students can handle the problem of "cleaning up" messy solutions to equations:
In pursuing these threads, we are also continuing to pursue fluency with comprehension. And, it helps me to make progress towards the goal of helping my students to avoid common errors.
For the No way Rene Activity I judiciously and flexibly pair students up according to math ability, (see reflection) and stroll through the class listening carefully to discussions between group members. The problems are based on misconceptions I've seen in students in middle school. The activity emphasizes the idea that x can represent any number, and that the all numbers that are substituted for x, must make the algebraic expression true. For Part 1, I request that the students rewrite the equation correctly when possible. At the end of the activity, I randomly ask students to explain their the reasoning behind their work, for each problem.
As the end of class approaches, I project Closure Questions on the board and randomly call on students to answer each. I try calling on the students who probably think I will not call them, or students who I noticed were struggling as they did their activity.
Tonight's Homework involves 8 equations to solve where simplification must be completed successfully as part of the process of solving the equation.