This page took a few days to complete. First, we discussed solving systems graphically. After some exploration and activities, we completed
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
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.
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.
How have you done systems of equations in the past? Any great ideas to share??
New links that should *hopefully* work!