I plan for this Warm up to take about 5 minutes to complete, and about 5 minutes to review with the students. The two problems in the warm up are special cases of solving systems.
In today's Warmup I show how two special cases appear when applying algebraic methods to solve systems of equations:
I expect the students to apply their prior knowledge of graphing solutions to systems of equations to these two problems. I build off of this warm up to review the 3 possible solutions to a system of linear equations.
I model how I will go over the warm up in the video below:
In this lesson 2-column notes are an instructional method for students to connect writing out the steps on solving a system of equations on the right, and showing the work done algebraically on the left. The Elimination worksheet has the steps needed to solve the system of linear combinations and the problems to be worked . It is meant to help students retain the procedures and reasoning in solving a system of linear combinations by elimination. I encourage students to paraphrase the steps in their own words.
When teaching elimination, I refer back to a simpler example of adding opposites to create a sum of 0. I start with questioning, by asking students about simple sums of opposites:
What is 2 + -2, 3 + -3, 5 + -5?
Once students recognize the pattern that adding opposites creates a sum of 0, then we discuss how important it is to know multiplication facts to create those opposites. Students' prior knowledge of multiplication will help them to decide what number to multiply by to create an opposite. Students that struggle with creating opposites sometimes benefit by modeling division to identify the factor of the product needed to create an opposite.
I demonstrate how to use the 2-column notes with number 3 on the Steps to Elimination-worksheet before students begin the assignment because it is a system of equations that intersects at one point. I had not reviewed this type of problem with the students in this lesson yet. I instruct students to write out the steps on the right side of the notes, and to solve the system of equations algebraically on the left side. I encourage the students to paraphrase using their own words, but I did provide the steps on the worksheet for lower level students who struggle with writing the steps.
I use the Peer Checklist to increase feedback, student participation, and ownership of their own learning. Peer grading provides students immediate feedback, and provides a quick formative assessment for the teacher on solving a system of linear combinations. In order to use peer feedback, I provide students with a checklist to help each student focus on what needs to be checked. It does take more instructional time to train students on peer grading, but once students are trained, it is beneficial. Students are to use pens only if possible to grade, and put their pencils away in order to avoid students from erasing.
Most of the students grade accurately and are honest about their progress. I review the papers using my own judgement before entering any points into their grade. This method allows students to be involved in the assessment process. The advantage to the checklist is that it provides students with a view of what is being graded, similar to a rubric. Students are taking ownership of their own learning by taking feedback, and doing something with the feedback. It may be to identify a common mistake or misconception, to rework a problem, or to state what they learned after the feedback is provided.