SWBAT add, subtract, multiply and divide functions.

Presentation will assist students in learning the notation of function operations.

5 minutes

Students are given 5 minutes to prepare for their presentations. This time is spent on reviewing information on the operation, determining who will present and reviewing the focus questions.

As the students are preparing I move around the room and check on groups. If a group had a lot to complete yesterday I verify the work is done. I check to see what technology each group will need. If students are using the projector, I have the group share the project in our class Google Drive folder so I can retrieve the document for presentation.

Because this is early in the year the students are learning not only the material but how to present so that other students will understand.

20 minutes

The Addition of Functions group goes first. I start with addition because it follows the progression of mathematical operation learned by students in elementary school. A basic presentation is one that only discusses the focus questions . Others extend the information and have many examples.

When each group completes its presentation, the class is able to question the group. Questions should focus on unclear ideas from the presentation. If I see some key idea missing or unclear and the class does not ask for clarification, then I will intercede with a question. I may say something like, "Can you tell me again how the domain of the answer compares to the domain of the orginal functions?" or "Why did you divide the x by x in the expression (x+1)/x?"

If the groups do not address common errors, I ask the class what are some mistakes they have made when doing this operation. Identifying common errors can be difficult for students. Some students do not realize they are making an error. Students don't think about looking for errors most of the time students are ask to find the correct answer.

I make sure students have the 2 to 5 practice problems the group have identified for the class to complete.

Here is an example of a group that made a Google presentation for Subtraction. The students then used the presentation as their notes for the oral presentation. Many groups wrote their presentation on the board as the talked. Here is an example of this type of presentation.

20 minutes

Each group has created some problems to complete. Students will work on these problems as the final activity for today's lesson.

With about 10 minutes left in class I put a closure problem on the board. I give the students 5 minutes to work on the problem in their groups. We then discuss the questions. Students will struggle with this because there are no rules for b(t) and d(t). Students are used to doing numerical problems. When an abstract problem is presented they are not sure what to do. Developing abstract reasoning is important for students planning to study more advanced mathematics. Some questions I will ask to help students:

- Why is this different than the problems you have worked on?
- Can you write a rule to represent the situation?
- Do you have to have an equation to answer this problem.

Understanding the r(5) will also cause problems. Students can find r(5) but they have trouble putting the answer into context which is a part of developing skills in precision. A student needs to understand the context of the answer so they can verify the reasonableness of their answer.

I work on reading the questions and look at when t=0. What year is that? So what if the 5 representing in r(5)? Can you tell me what r(t) represents? Now put it together.

When I do this scaffolding I am working with how I problem solve. Many students have never learned the skills.

Problem solving is not something that is natural for some students. Good problem solvers like good readers have skills that must be learned. When I ask the questions for r(5) I am showing students the questions I ask myself. This will help students learn how to read and interpret a problem.