I. Curricular Framework

Concept:

Classifying

Essential Question:

What is the application of conics to real life?

Bridge:

Models

Content:

Equations and Graphs for Conic Sections

Outcomes:

II. Standards Aligned

III. Instruction and Assessment

1. Connect: Connecting to the Concept Experientially

Objective: To create student curiosity about the conic sections as they appear in real life situations.

Activity: Students working in groups of four examine numbered exhibits. Exhibits will be posters containing pictures (found in magazines or newspapers) of conic sections as seen in real life, and objects (e.g., a horseshoe, ball, egg, vase, etc.) displayed on tables. Each group will classify the exhibits by grouping together similar pictures and objects. You will find that students will use different methods to classify your display.

Assessment: Involvement of students and their ability to work together.

2. Attend: Attending to the Connection

Objective: To enhance student ability to discuss what they have observed. To arouse curiosity for the material to be presented.

Activity: One student from each group reports on how his group classified the exhibits. The teacher lists the classifications on the board. General discussion follows after all groups have reported. It is not necessary to name all the conic sections at this point.

Assessment: Quality of discussion and participation.

Assessment, Phase One, Level of Engagement, Fascination:

3. Image: Creating a Mental Picture

Objective: To create the conic sections using waxed paper.

Activity: Following are the instructions for creating an ellipse, hyperbola, and parabola using waxed paper. Since students are familiar with the construction of a circle, it is not necessary to perform this construction. 1) Ellipse - Draw a circle of ink in the middle of a sheet of waxed paper. Fold the circle in half and crease the paper. On the fold line (diameter of the circle), mark a point about one inch inside the circle. Fold the waxed paper so that a point on the circle lies on the point. Crease the waxed paper. Rotate the paper keeping the circle on the point at all times, creasing the paper with each successive move until an ellipse is formed. 2) Hyperbola - Draw a circle in the middle of a sheet of waxed paper. Fold the circle about one inch outside the circle. Fold the waxed paper so that the circle lies on the point. Crease the paper. Rotate the paper keeping the circle on the point at all times, creasing the paper with each move until a hyperbola is formed. 3) Parabola - Draw a line across the middle of the waxed paper. Mark a point about one inch above the line. Fold the waxed paper so that the line lies on the point and crease. Rotate the paper keeping the line on the point at all times, creasing the paper after each move until a parabola is formed. After students have created their conic models, discuss the similarities between these shapes and the exhibits they previously classified in Activity 1.

Assessment: Student participation and attention.

Assessment, Phase Two, Seeing the Big Picture:

4. Inform: Receiving Facts & Knowledge

Objective: To teach concepts needed in order to understand conic sections.

Activity: Teach the following concepts: recognition of the equations and graphs of circles, ellipses, hyperbolas, and parabolas; graph the four conic sections; write the equations of the four conic sections. The graphing calculator may be easily used with this material.

Assessment: Student notetaking and level of questions, and teacher checking for understanding.

Assessment, Phase Three, Success with Acquiring Knowledge:

5. Practice: Developing Skills

Objective: To allow students to practice concepts and reinforce learning.

Activity: Students will work individually and in groups on problem sets, puzzles and play MATHO. They will write test summaries before each test.

Assessment: Quality of problem solving. Ability of students to work together and contribute to group effort.

Assessment, Phase Four, Success with Acquiring Skills:

6. Extend: Extending Learning to the Outside World

Objective: Students will increase their ability to choose from options based on curiosity and interest, and apply the concepts they have learned while enhancing their ability to plan a personalized learning project.

Activity: Students will be given project choices and timeline. These will be discussed in class. CONICS PROJECTS: 1.

7. Refine: Refining the Extension

Create a video, slide presentation, or photo album which illustrates the use of conics in everyday life. Material must be original, i.e., photographs instead of pictures cut from magazines. Know the type of conic you are videotaping or photographing. Minimum of 15 examples with at least three obvious examples of each of the four conic sections. 2.

8. Perform: Creative Manifestation of Material Learned

Investigate and explain the use of conics in the real world: conics used in construction (e.g., how to build a suspension bridge, build a whisper chamber or an amphitheater, etc.); satellite tracking; conics in space (missiles, astronomy, etc.); modern military use (role conics played in Desert Storm, etc.). Report should be a minimum of two pages, typed (double spaced) or four pages, handwritten with mandatory bibliography.

Assessment, Phase Five,Performance, Creative Use of Material Learned: