4/12/07

This rotation, the class that I'm teaching has 10 students in it, and half of them are special education students. Our school allows us to schedule and move students around in whatever way our teams want for our "core" learning time. For our team, that means we've got two hours and five minutes before lunch, and two hours and five minutes after lunch. As long as we cover all of the necessary curriculum, we can decide what classes to teach, when we want to teach them, and which students we want in those classes. We decided that some of our students would benefit from having a smaller math class.

The week after ISATs is always interesting. I love to play the game called "how much will my students remember?" Yesterday I was favorably impressed! I had my students pull out their ACE question packets from Investigation 1. (We copy all the ACE questions and put them into a packet for students, so they have easy access.) That's right — we went all the way back to the beginning! We played a review-type game using the dry erase boards for students to write down their work and answers. I pulled some of the ACE questions with more important content for us to review. We did questions 1 and 2 on page 12 in Moving Straight Ahead. All of my students were able to find the walking rates in these problems. But they are still having difficulty with labeling their answers. Only about half of the class labeled their answers. When I asked the others to go back and add labels, they were not able to correctly label their solutions. I took this time to review what the label should be when we are dividing:
___________ per _________________.
The label of the first number per the label of the second number.

We also spent some time reviewing how to graph information gained from tables. The majority of my students were able to correctly identify where the independent and the dependent variables go. The class came up with a way for everyone to remember which one goes where. The dependent variable goes up and down, because the independent variable is holding it up.

We practiced this a few times, and then started discussing how to look at a line and decide whether it is linear. The students indicated that we can look at a line and tell which one gets higher the fastest. This seemed like a good opportunity to go back to vocabulary and incorporate "rate of change."

We continued on with our review for the rest of class. Before students left class, they completed an exit slip based on the day's discussion. They had to draw a graph, label independent and dependent variables, and then label the line with the greatest rate of change. Eight of the students did this correctly. The other two did everything but the rate of change part correctly.

Later this week I plan to begin Investigation 2 with my class. The first question is finding the intersection point in a race between Emile and Henri. Students are given a small amount of information to start this problem, and are asked to find how long the race would have to run so that Henri could win it. It's a close race, not an obviously unfair one. Some of my students may have trouble starting this investigation, because they lack problem solving skills. Many have trouble finding somewhere to begin.

The idea behind this math program is to allow students to explore on their own, and then come back together as a whole class to summarize and discuss each problem. At times I have trouble deciding when it is appropriate to allow students to struggle, and how long I should let them struggle. I am thinking especially of my student Alonzo, when I ask myself these questions. He does not have the foundation in English, Spanish, or math to solve most seventh-grade math problems. How can I give him the support he needs? I always walk around the classroom and speak to groups of students and ask questions. But I wonder whether there are specific questions I should be asking Alonzo or his group, to help them break this problem down. I am considering suggesting a method to groups that have struggled for a while. I won't tell them where to begin, but I might say something like, "Why don't you try to make a table of the distance that the brothers cover?"

Today I'm giving a quiz on the information that we reviewed yesterday. Students will get a table of information and a blank graph. They'll have to graph the information, and correctly label and number each axis. There are four questions that follow the graph:

1. Which variable is the independent variable? The dependent variable? How do you know?
2. Describe the relationship between the two variables.
   (The differentiated quiz asks the same question, but gives a prompt: As the time increases, ______________________.)
3. Predict how much time it would take for 55 students to pass through the cafeteria line. Explain how you used the table or graph to determine your answer.
4. How many students would you expect to buy lunches in a 10-minute period? Explain how you used either the graph or the table to find your answer.