This year I ran across a document in my Google Drive that Sonya New and I made in order to introduce solving systems of equations. I decided to do this on the first day back after Christmas break in order to get us "back on track." We have solved systems algebraically and had begun discussing the substitution and elimination methods the week before school let out.
I loved doing the assignment. I only had 6 groups but I still wanted to have them graph all 8 systems so a few groups had 2 systems to graph. I did not call them systems. I just told them to graph both lines on the same coordinate grid. I first allowed them to graph the lines on graph paper and then I had them put them on chart paper. Afterwards I assigned each group a different color marker to write with and had them do a gallery walk and put feedback on the graphs. If they agreed with the graph they put a check mark. If they thought there was an error they had to place an x and then tell what they thought was wrong. The last direction I gave them was to write down the solution to the system of equations. (We have been talking about solutions for systems of equations ALOT in class. I have even OPENED and CLOSED class MULTIPLE TIMES by randomly calling on a student and asking them, "What is the solution to a system of equations?" AND offered candy when they get it correct!! Many of them still don't know. I accept various answers: an x and a y that make both equations true, the point of intersection, an order pair that works for both.... It hurts my feelings but I still haven't gotten it to "sink in.") I had one student in the room that asked me if I meant for them to write the ordered pair down so eventually everyone caught on. Almost every group asked me what I meant by the solution but I would not tell them. I told them to discuss it within their groups because we had talked about it in depth before Christmas. Anyway...after they completed their gallery walk we "debriefed" as a class and settled any differences of opinion. It was a wonderful way to review graphing and reintroduce them to solving systems of equations - we had one no solution and one infinitely many solutions so we also discussed what those would look like algebraically. I did have them solve a couple of the solutions algebraically (using substitution) at the end of class.
Here is the document if you would like it.
1. Even my best students needed the graphing review. I had one of the top students in my class put his y-intercepts on the x axis!! I want to do a better job of spiraling my algebra class. I love that our Meaningful Math Algebra books include graphing in every single unit! I hope to incorporate more spiraling review as my warmups this semester.
2. It scares me how much my students forget AND it bothers me that I have to move on when I have so many who have clearly not retained what we have learned.
3. Many of them wrote that the solution was 5 and 2 when they really meant (5,2). They think I am being picky when I make them write the answer as an ordered pair.
4. Students like the opportunity to get out of their seats! I did have some really good student dialogue and I feel that it was a productive first day back after Christmas:)