Connections

As a part of the Algebra 4 All State-wide project, myself and the other Algebra teachers at my school were asked to do a particular lesson with our classes and have another teacher observe the "math talk" aspects of our class. Being that we use Carnegie in our classrooms our students are used to working in groups and to helping one another. The fact that they helped each other and worked well in their groups was no surprise. However, they still managed to amaze me today!

I should start by explaining the project. My students were given a scenario about three college students who have created a budget. They all get paid on the first of the month and have to pay their rent on the last day of the month. My students were given a table showing three dates and the amount of money each student had left. They were asked to create a graph and then determine who could pay their rent. I didn't think my students would have difficulty with this part. We recently completed 1.10 Comparing US Shirts and Hot Shirts and they were familiar with graphing multiple scenarios on the same graph.

The hardest part of the problem was for students to write "a rule" to describe each student's spending. My students have not formally been introduced to slope or slope intercept form so I wasn't sure that they would be able to do it. When my first group of students were ready to try it I told them to think about the problems they had seen on the cognitive tutor. They remembered the problems with scenarios about companies that started with a set amount of money and were spending a particular amount each week. From that discussion, they decided that they needed to start their equation with the amount of money each student had and eventually they realized they needed to find out how much money each student was spending in one day. Without me telling them how to do it, several of my students were able to find the slope (although they didn't call it that)! I was so excited.

This made me realize that my students really are learning more than I realized by working on the Cognitive Tutor. I have to continue to make those connections more obvious by talking about them in class. Today's project was not from the Carnegie book or the Cognitive Tutor. However, students were able to take what they had learned (without any formal instruction on it) and apply it to a new situation. I was so elated that the teacher that was observing and I were giving each other high fives throughout the class. What an awesome way to end the week!