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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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*I have an adaptation that I am going to use this year that I wanted to share! I am going to collaborate with the culinary class on campus and have them make a class set of scones in the shape of cones for a lesson that is called... wait for it... S'Conic Sections (Link: http://www.evilmadscientist.com/2013/sconic-sections/). I'm going to have them in teams of 4 so they can have a full set of the conic sections when they are done. They will physically cut the scones into the appropriate sections after they have determined where the cut needs to be made after they complete the NCTM Illuminations virtual conic section cutting exploration. (Link: https://illuminations.nctm.org/Activity.aspx?id=3506). | 9 months ago | Reply*

Great lesson. It's really hard using paper template cut-outs. The play-doe sticks to the paper, so cups are the way to go. Most Walmart stores don't carry the cups in store, so make sure you order them well in advance. Also, it might be a good idea to mold the play-doe to a cone using the paper, peeling the paper off, then using dental floss to make the cuts. Even with the "imperfect" cuts, students were able to visualize the conic section and they had lots of fun.

| 2 years ago | Reply

Thanks so much for the lessons! I used playdoh and dental floss, and that seemed to go okay. I had to explain a bit what cuts needed to be made where, but overall ok. Today I tried the cutting conics lesson with my Precalculus students, and it went mostly pretty well. I had a full class period, so I combined it a bit with your name that conic lesson. I'm excited to try some of the human conics next week.

| 3 years ago | Reply

Tiffany,

I like this lesson and have done a lesson similar with my students. I used the Playdoh to create the cones and then we used dental floss to make the cuts. It worked pretty well. I thought this might be an idea to try instead of the paper cones.

Thanks for sharing this lesson and your worksheet!

Lisa Scott

Mathematics Teacher

Billing, MT

| 3 years ago | Reply

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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
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- 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