SWBAT write equations for conics.

Through a poster students place wax paper designs made in previous lessons on a graph then determine the equation for the conic represented by the design.

10 minutes

Today we are starting a project that will be a major portion of the assessment for this unit. At the start of class, students receive the Wax Paper Poster information (also attached is alternate scoring guide for standard based grading) to read and annotate. I ask students to make note of any directions that are confusing and require clarification. Then, we review the directions as a class and I answer questions. I display several examples of posters from previous years to provide students a visual of what the end product might look like.

I like doing this project because it gives students a chance to really think about how to write equations. The project makes the students determine where to place the conic on a coordinate plane. Most activities require students to find an equation with a given graph or graph from a given equations. As the students complete this project they are demonstrating many mathematical practices (**MP1, MP2, MP4, MP5, MP6, **and** MP7)**.

Since the students need to put their wax paper designs on a coordinate plane, I have different types of graph paper. Students may also use rulers to make their own grids. I found my graph paper at MathBits. I have shared the files at the bottom of this section of the lesson.

Once students put their conic on a graph determine the key features and write equations for the conic. They will write the equations in both standard and general form for all four conics.

The first decision that students must make is how the conic should be placed on the grid so that writing the equation is easy. Some students realize by making their own scale for the graph will allow the key points to be located at what I call "nice numbers" (integers). Other students decide to put the center of all the conics at (0,0). Many times in calculus students are told to put the figure on a convenient grid. My students understand what is meant by this phrase after working on this project.

30 minutes

Students use the remainder of this class to organize their information for the poster.

In this activity, I have limited the number of question a group can ask. Many times students try to get me to do all the work for them and never talk to each other about what they are doing. When students have limited questions they will make sure to only ask questions that no one in their group or in other groups can answer. I will answer questions about the scoring guide and organizational ideas. Questions about how to find key features or how to write an equation are the questions are limited to 3.

Students may use their reference sheet, their textbooks or any other resource such as the Internet. Any research they do is fine since they will have to transfer the information they find to a graph they have produced. Interpreting the known facts to the design is an activity that is done many times by engineers, architects and other professionals.

5 minutes

With 5 minutes left, students clean up the materials they are using. I give the students the following questions to think about and answer. Each group turns in the responses for me to review.

- Where did your group end today?

- What is completed?
- What do you still need to do?

- What work do your group members need to complete before our next class?
- What is the first thing your group will need to do during our next class?

Many students do not think about how to finish projects in a timely fashion. The questions give students a way to prepare for the next class. It also shows me how much the students have completed and whether they are working together.

Each person has to be an active member of the group and everyone should be working on finding equations for the conics. The most efficient groups are the ones that have 4 people and each person works on one conic then they verify the solution with each other. If I notice a group expecting one person to do all the graphs and equations I ask each person in the group how they have divided the project up. If only one student is doing all the math. I ask the group if they think this person will be accurate and timely in getting **all** the work done. I may also tell a group that I will grade the students individually when one student is doing everything.

Making each student accountable to other in the group and to me helps with students that refuse to work. I also allow the students to pick the groups. I have students that are mainly high achievers it is interesting to see how students who usually do all the work flock together and those that do not work are left to be a group. If I was dividing the groups I would put the the students that are not team players together so they do not affect the work of the group.