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# Cutting Conics

Lesson 1 of 13

## Objective: SWBAT identify the four conic sections and how they are actually sections of a cone.

## Big Idea: As an introduction to this unit, students actually cut cones to discover the four conic sections.

*30 minutes*

#### Introduction

*3 min*

**Overview:** This lesson is a quick investigative lesson leading into conic sections. This lesson will fall on a shortened schedule day for me. I could definitely see this being combined with the next day’s lesson if you have more time with your students.

**Preparation: **For today’s activity each student will need 5 paper cone cups, scissors, play dough, and 1 strand of linguini: Cutting Conics, supplies needed. The scissors are of course easy to come by and the linguini is cheap at the grocery store. But I have been having difficulty finding cheap paper cone cups and play dough. I will probably end up making the play dough. (Here is a link for play dough recipes) If I am not able to get the paper cone cups through my school I may also make copies of cone templates and have students cut them out and make their own cones. Then cut these cones apart. The other thought I had was the make laminated paper cones and have students fill the cones with play dough and then cut the play dough.

**Narrative: **After students gather their needed supplies, use pages 2-3 of the flipchart to introduce conic sections to students. Be careful not to mention any of the shapes that are created, but instead just refer to them generally as conic sections.

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Students should now work thorough their handout *Cutting Conics.* I would like every student to be making cuts (assuming I can get enough supplies). So every student will be completing their own work. I predict this activity to be pretty straight forward for students as long as they can recall some of the mathematical vocabulary (parallel, perpendicular, base, and central axis.) If students don’t see what shape the cuts make I am going to recommend that they flip the cup over and trace the cut section. I am guessing that many students are going to classify the cuts in question 1 and 2 as the same. It is important that they see that the cut in question 2 is not a perfect circle, but question 1 is. As I monitor the classroom, if I see incorrect answers (or not specific enough) I am going to ask students to trace their cuts. It is important that students are precise in their explanation of the cut sections (**MP6: Attend to precision**).

For our quick cutters… challenge them to name the shapes. Then challenge them to see if they can cut any other shapes with one cut.

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#### Closure: Name the Cuts

*7 min*

Present pages 4-5 of the flipchart and have students now name the conic sections they found. You could also use page 6 to present the ‘answers’ to insure all students can check their work and have identified the conics that they needed to.

#### Resources

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- UNIT 1: Basic Functions and Equations
- UNIT 2: Polynomial Functions and Equations
- UNIT 3: Rational Functions and Equations
- UNIT 4: Exponential Functions and Equations
- UNIT 5: Logarithmic Functions and Equations
- UNIT 6: Conic Sections
- UNIT 7: Rotations and Cyclical Functions
- UNIT 8: Cyclical Patterns and Periodic Functions
- UNIT 9: Trigonometric Equations
- UNIT 10: Matrices
- UNIT 11: Review
- UNIT 12: Fundamentals of Trigonometry

- LESSON 1: Cutting Conics
- LESSON 2: Name that Conic
- LESSON 3: Human Conics: Circles and Ellipses
- LESSON 4: Circles and Completing the Square (Day 1 of 2)
- LESSON 5: Circles and Completing the Square (Day 2 of 2)
- LESSON 6: Ellipses
- LESSON 7: Human Conics: Parabolas
- LESSON 8: Parabolas
- LESSON 9: Parabola Problem Partner Critiques
- LESSON 10: Hyperbolas
- LESSON 11: Non-Linear Systems of Equations
- LESSON 12: Conic Sections Test Review
- LESSON 13: Conic Sections Unit Test