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Playdough Conics

Playdough Conics. As teachers it is important for us to facilitate to students an understanding of conics in relation to its relevance for their overall learning.

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Playdough Conics

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  1. Playdough Conics • As teachers it is important for us to facilitate to students an understanding of conics in relation to its relevance for their overall learning. • Playdough conics is a lesson designed to give students hands on application as well as using something they are familiar with. Of course, this makes it “fun” for them.

  2. Learning Conics • Presented by Nicole Burgess, NBCT (Mathematics) and Kristyn Shaffer. Hume-Fogg Academic High School (Mathematics faculty) • Email: paula.burgess@mnps.org & kristyn.shaffer@mnps.org

  3. How to teach the lesson... • Ask students where they have seen conics used in their life experience • Student discovery of the sections. Talk about the four shapes...”conic sections”...that can be formed from a cone. Try to make them say the shapes. Students will probably be able to say a circle and an ellipse. You will have to help them discover the other two. • Student discovery of the “conic sections” of a cone. Have students make paper cuts. • Student discovery of the definition...”standard form”...for each conic section. • Student discovery of translation of conic sections. • Student application of what they have learned.

  4. Discovery of the conic sections : • Have students mold their playdough into a cone • Have students use their plastic knife to make the cut...(I usually begin with the circle)...have a student come up in front of the class to “lead” the students. It is important for students to take ownership of their learning. Have each student hold up their section and check for any students who need help. • Continue with their discovery of each cut. You may want to have students work with a buddy.

  5. Discovery of the definition • Have students place their conic section on the coordinate plane. (It is easiest to choose the origin!) Choose (0,0) and one other point. • Find the equation of the conic section by using the definition. Parabola: y = a(x – h)² + k Circle: (x – h)² + (y – k)² = r² Ellipse: or Hyberbola: or Be careful of your time factor!

  6. Discovery of Translation (Part 1) • Lay your conic section on the coordinate plane using the origin as the center or vertex. • Plug in your...vertex (Parabola) or plug in your center as well as radius length (Circle) or plug in a major length and minor length as well as a center (Ellipse) • Looking at your playdough on the coordinate plane that is now shaped into a conic section...plug in a coordinate on the conic section into the equation for x and y and see if the equation works.

  7. Discovery of Translation (Part 2) • Pick up your conic section and move it to any part on the coordinate plane and write the equation.

  8. Application • Make the Toyota Symbol and find the equations for the symbol. • Find the equation of a parabolic curve using leaves.

  9. Apply what you know!

  10. Hume-Fogg Academic High • Nine Week Project

  11. Task: Create a family album of the functions discussed in Algebra II. • Your family album pages should be neatly organized in a binder, photo album, or some other type of book/notebook. Sheet protectors of some kind are encouraged but not required. Neatness and organization is key. • The content for each function family must be accurate and will be graded accordingly.

  12. Procedure: • 1. Choose a theme for your album. • 2. Create a title page for your album. • 3. Create a page for each of the functions. • 4. You should find a picture of a real-world example of 5 of the functions and include those pictures with the appropriate function. These pictures should coincide with your theme. • 5. Decorate the front cover of your binder/notebook/album to reflect your theme. • 6. You are allowed to use your calculator to help you generate accurate information, but ALL GRAPHS MUST BE DONE BY HAND!!! • 7. All MATHEMATICS must be ACCURATE!!!

  13. 8. For each function, you need to include the following: • Graph of the parent function (must be done by hand on graph paper) • The equation must be written neatly or typed above the graph • T-chart for the parent function graph with ordered pairs listed for x-values -2, -1, 0, 1, 2 • You may choose additional points, but these points must be included on your T-chart • Domain and Range of the parent function (this is not the x-values you are choosing for your T-chart!) • X-intercepts and Y-intercepts of the parent function (if there are none, state that there are none!) • The graph must be done by hand and include the points from the T-chart.

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