My Algebra Honors students had a test last Friday on systems of equations in 2 variables. We had done a lot of work on this chapter and I knew that I didn’t want to assign them more of the same types of problems on our review day Wednesday. Instead I had the class work in groups of 3 and I gave each group a sheet of paper with two word problems written out. I told them that they had 50 minutes to solve these two problems using any strategy they wanted. They just had to justify their answer with math. I told the class that they are expected to explain their problem to the class toward the end of the period.
What I didn’t tell the class was that the problems involved 3 variables (an Algebra 2 concept) and that we hadn’t learned how to solve systems of equations in 3 variables. Instead I told them that I believed in them and I knew they would be able to solve them.
The students got to work solving the problems. As I walked around the groups I loved seeing all of the different strategies the students used. One group solved their problems on the white boards and every time they got stuck or realized they made a mistake they would start solving it again without erasing their work. They labeled each try as a “take” and would refer back to what they did before to help them figure out where they made mistakes. Finally “take 6” was successful and they were so proud of themselves for figuring it out.
They labeled their final, correct work as “Holy Ground” and they were so proud of themselves.
As this group worked I would hear them say things like “we’ve never solved equations with 3 variables before…I’m not sure how to set this up but I know Mrs. Schooler wouldn’t give us a problem we couldn’t solve.” I also heard a lot of comments about how their brain was growing from the mistakes they made! The groups for the most part worked without my help. At times if a group was really stuck I asked them some questions to get them thinking about the problem in a different way
and that was usually sufficient to get them working again.
As students presented their answers it was fascinating to see how almost every group solved both problems but even better was that not one group solved them the same exact way.
The students listened to each group present and they would exclaim that they hadn’t thought of solving it that way or telling another group they were impressed at how they approached the problem.
I surveyed the students after class asking them what they thought of the two problems and what approaches they used when they got stuck. Here were some of their responses:
“When we got stuck we would look back to see where we went wrong and we listened to each other’s advice.”
“Whenever we got stuck we would try a new strategy but left the old strategy on the board in case it helped us.”
I also asked the students how they felt after class. Here’s what they said:
“I felt accomplished and proud of myself because I got to figure out a hard problem without the teacher’s help. I also felt proud of my group because we worked really hard together to solve it.”
“I felt very challenged but in a good way.”
“I felt like I understood the problems a lot more after hearing how each group solved it.”
I was so proud of my students. They were given challenging problems to solve and were successful in solving them. They made connections to what they knew about systems of equations in 2 variables and applied it to 3 variables. This is a reminder to me that I need to always remember that my students are capable of so much and that if I am to prepare them to be strong mathematics students I need to give them more problems like this so I can help their brains grow.
