The purpose of this lesson is for students to use two-column notes to organize, report steps, and show reasoning on Solving a System of Equations to increase comprehension. I have students use two-column notes to identify the main ideas and supporting details. Headings and subheading are also helpful when organizing two-column notes.
Students create two-column notes by drawing a line down their paper to create two columns. If students fold their paper in half, the crease in the paper is easy to follow to draw the line. The student may use the back of the paper or more pages if needed. The Students then read the assignment from the Purple Math website, "Systems of Linear Equations: Solving by Substitution." Students may also read a section from their textbook if the teacher prefers. The goal during the reading is for students to identify and write down the main ideas on the left and the key details on the right. Students answers may vary. Students also write the examples on the left with comments of supporting details on the right. These comments can include notes about what does substitution mean, how to substitute, when to use substitution, and how to identify the different types of solutions. Students may also write questions about certain steps, vocabulary, or difficulties of understanding on the right. I have provided an example of page 1 and page 2 of the two-column notes in the resource section.
After students have completed the note-taking from the reading, we discuss the main points, and key details needed to Solve a System of Equations by Substitution from the notes. I randomly call on students for input into the discussion. Students need to feel safe and comfortable with being wrong, and understand that student responses may be different. The class discussion is a vital part for two-column notes to be successful. It is the teacher's role to facilitate the discussion by building off of student comments and bringing it all together, as well as filling in gaps to meet the objective. Again, the objective is for the students to be able to solve a system of equations by Substitution for the 3 types of solutions. Along with knowing the method, students should be able to explain the meaning of Substitution and the solutions, when to use it, and why.
After the class discussion, and modeling the 3 examples using Substitution in the 2 column notes, I assign 8 problems. The 8 problems are independent practice on solving a System of Equations by Substitution. Students are required to use two-column notes in the assignment, writing out the math steps and reasoning in their own words. In the left column, the students are required to show their work mathematically and recording the steps and reasoning on the right.
I allow students more time to work in class with this lesson so that I can monitor the students progress. It also allows more one on one time with me and each student or small groups of students as I walk from table to table. When 10 minutes are left in the class, I will have them trade papers with another student to gain immediate feedback on the problems.
The Peer Checklist at the end of the lesson allows students immediate feedback on the problems missed. It also identifies if the student is missing a problem that has a certain type of solution. This takes about 5 minutes. When the paper is handed back to the student, I allow the other 5 minutes for the student to summarize what they learned today and to try to identify how to clear up any misconceptions or mistakes.
At the end of the peer feedback, students hand the feedback in with their paper. This provides me with an informative assessment on the progress of each student.
When looking at the formative assessment, I check to see if the students are struggling with a system with a certain solution, or a system with certain forms of equations.