Friday, February 20, 2015

IMP Cookies - Solving Systems of Equations (Only One Variable and The Classic Way to Get the Point)

I love the way the Cookies unit starts with solving systems of inequalities and then works into solving systems of equations. In the Cookies and Inequalities portion of the unit the students are introduced to "real-world" problems where systems of inequalities can be used for solving them. The students practice writing constraints and then graphing the inequalities that go with them. In the real world problems often have more than one possible answer - much like is true of the feasible regions you get when graphing systems of inequalities.

Then, as you try to solve the Cookies unit problem or other problems in the unit involving minimums and maximums you discover that you need to find the "corners" where the lines intersect. We had our students just estimate using their graphs in order to find the points of intersection. However, it is neat to be able to introduce the topic of solving systems of equations by talking about how we really need to be more precise when we find the "corners" of the graph. For a couple of days this week our classes worked on an additional activity that helped them to explore the elimination method.

Today I first had my students do the Only One Variable activity. We had alot of fun with it because we integrated some technology too. Each group had an Ipad and they were projecting their screens using air server/airplay. I gave the group 3 minutes to work on the problem and then after the time was up they had to put something on their screen (they were using the Educreations app). It is so cool to be able to see several samples of student work on the board at the same time. We can critique the work without the class knowing whose work it is. We are able to celebrate different approaches for solving the problem. Also, we are able to talk about common mistakes. They love when they are working on a problem and I point out their work. I can say, "Hey, this person is really moving in the right direction."
Each group's problems projected simultaneously! Cool stuff!

Next we worked on The Classic Way to Get the Point which introduces the substitution method. Mrs. New and I had looked through the rest of this unit and we saw so many activities that give the students the opportunity to practice solving systems again and again. I used to teach these two methods of solving systems of equations separately. Then after covering each method I gave them some "mixed practice" where they had to choose the method to use.  However, I now like the idea of giving them some time to practice a few of each type and then let them decide which method to use as we go. The ACT and other tests are not going to tell them which method to use so they need to learn how to choose which method works better for each type of problem. There are several activities in this portion of the Cookies unit that give them a few more systems of equations to practice solving so hopefully by the time we revisit the topic several times my students will retain the information.