For today's Warm Up assignment, I have given students three systems of equations to analyze and decide how many solutions they believe each will have. This is practice from the previous day's lesson where students identified specific characteristics of systems when they had one, none, or infinitely many solutions. As students selected and justified their answers, I monitored their work and made note on my observation clipboard of any struggling students so that I could provide them additional time with me on the concept the following day during our school's Power Hour (directed tutoring time held three days per week during advisory class).
Once the timer sounds, I select volunteers (from my cup of name sticks) to share an answer. I then seek class agreement or disagreement. I ask all students to justify their thinking so that they have the opportunity to construct viable arguments and critique the thinking of others (MP 3).
When we reach consensus on our answers, I move to today's learning objective.
Today's Learning Objective focuses on helping students acquire yet another strategy for solving linear systems of equations: Substitution. This strategy is typically very difficult for some students, so I am providing two example that we will analyze and process together. I want students to understand not only the "what is happening" when applying the strategy, but also the "why this is happening". I do this by first sharing the system that has one equation solved for y. This system is not intimidating to students because it mirrors problems they have seen since elementary school.
I begin by asking students to think about how they would find the value of x in the system. Once I have given them 15-20 seconds to process, I ask them to turn and talk to a neighbor about their plan. I select several students to present their plans to the class until we exhaust ideas. Then, I reveal the next system of equations that has both equations as y= equations. I follow the same procedures, asking student to analyze and then share their plans for solving.
Because the second system is not as intuitive for students, I strategically question students about what they know from the two equations such as, "Do we know the value of y in either equation?", "What does the equal sign in each equation mean?" and "How do the two equations relate to one another?" Through this line of questioning, we arrive at the idea that the two equations actually are equal to each other. I write this algebraically and ask students how we could solve for x. I then explain that we have just worked through two examples of substitution.
Once students have been introduced to the substitution strategy, I want them to practice applying it, so for Work Time, I give them Solving Systems by Substitution Practice, a five-question application opportunity that increases with difficulty with each problem. I designed this practice to scaffold naturally so all students have the opportunity to experience success early in the assignment, which builds their confidence for tackling the last two problems. I set the timer for 15 minutes and remind students to rely on each other to build understanding by remembering my request to ask the students at their tables for help first before seeking help from me (ASK3B4ME).
Once the timer sounds, I bring the class's attention back to the Smartboard for consensus building.
To close today's lesson, I want the class to agree on the practice assignment's answers by Building Consensus. Because students have already collaborated on their answers, most are very willing to share their work with the class. I select willing volunteers to give their answers and then ask for class agreement. If disagreement arises, I ask students to justify their thinking through the mathematics or their verbal description.
Once we have reached consensus on all five answers, I explain that we will spend the next few days practicing this strategy so we are as confident applying it as we are with the previous two strategies learned (graphing and elimination).