Solving Systems of Equations

One of my favorite pages from this year was our Solving Systems of Equations page. In my opinion, this page was truly interactive. Students were sorting, classifying, and studying with these notes. YAY!!

This page took a few days to complete. First, we discussed solving systems graphically. After some exploration and activities, we completed THESE notes (new file link that the bottom). They were still connected as one piece of colored paper. Students then put those notes away in their handy-dandy pocket. We came back the next day and completed notes over solving by substitution and solving by elimination (new file link that the bottom). Students then put those in their pocket as well.

After making sure students were comfortable with solving systems, we started talking about one/none/infinitely-many solutions. Students were already thinking about these ideas because each colored set (graphically, substitution, elimination) had one system with each type of solution set. Here's where the fun part happened!

On page 103 of their notebook we took basic boring notes about what a system of equations is, the notation for a system, and what a solution point means. On page 104 we created a flipable pocket. The pocket is one full sheet and one half sheet of blank paper. Fold the full sheet in half width wise (hamburger style if you know what I mean) and then put the matching sized half sheet inside the larger, now folded paper. I know... it sounds confusing... it's really simple! Tape up the sides and fold the whole thing in half. You have four pocket areas. We only used three for our purposes. Do these pictures help at all??

 

 Anyway...

Students cut their colored papers apart and sorted into three piles: one solution, no solutions, and infinitely-many solutions. They looked for themes and commonalities within these new groups. We then had a class discussion about their observations and added general notes to the fronts of each pocket. We visually represented how one/none/infinitely-many looks on a graph and the type of solution when solved algebraically.

 ifinitely??? yeah... I dunno either...

The sorting and processing part really made things click for students. I also saw them studying with these notes later. They were able to take out all notes of the same color to study how to solve with a given method, or take our all notes within a pocket to study solution types.
Overall...success!

How have you done systems of equations in the past? Any great ideas to share??

New links that should *hopefully* work!