Team Logo by Jason Kozel

Transformation 2013 Design Challenge 5E Lesson

Title:

Team Logo

Authored by: Additional content and revisions by: Subject:

Amin Lalani

Grade Level:

High School

Challenge Abstract:

Transformation 2013 Algebra Two

In this Design Challenge, students will take on the role of a logo designer for the Dallas Cowboys. The Students will explore how logo construction incorporates elliptical properties and they will apply their new knowledge to solve a real world problem

Meeting the Needs of STEM Education through Design Challenge

Design Challenge Title: Team Logo TEKS addressed: (2A.5) Algebra and geometry. The student knows the relationship between the geometric and algebraic descriptions of conic sections. The student is expected to: (B) sketch graphs of conic sections to relate simple parameter changes in the equation to corresponding changes in the graph; (C) identify symmetries from graphs of conic sections; (D) identify the conic section from a given equation;

Engage Activity Approximate time: 15 min On the day that you are planning on doing the engage activity, have students bring shirts, purses, pictures or any thing that has a logo. Students might not bring elliptical logos so bring items with elliptical logos, for example, Green Bay Packers shirt and Nike hat, etc. Use cues and questions to analyze logos. Tap into student’s prior knowledge on geometric shapes and symmetry. Students will refer to the ellipse as an oval. Make sure you convey the message that all ellipses are ovals, but an oval may or may not be an ellipse. Help students make that connection, and continue to encourage the students to use the correct “conic” terminology. Pose the following question before the engage activity and let the students know that they will get a chance in the second explore stage to solve this problem: The Cowboy’s logo designer has misplaced the elliptical stencil that is used to create the border of the team logos on the field. Come up with a tool that can be used to construct an ellipse to help the logo designer. The game starts in seven hours.

Engage Activity Products/Artifacts

Students will write in their journal addressing the following questions: -Where have you seen elliptical shapes? -How do you think ellipses are created and what kind of tools are used to make them so perfect? -Do you think math is involved in making this shape?

3 Materials/Equipment: - Overhead (to record student observation looking at different logos) - Logos Resources: Link to different types of logos. http://www.custombusinesslogos.com/EPS_Logos/logos.jpg http://www.epsvectorlogosoncd.com/graphics/color_company_logos_on_dvd.jpg ******The links have some logos that might not be appropriate for school. *********

Explore Activity 1 Approximate time: 60 min Have students work in groups of two. Materials: – Give each group 15 pieces of string that differ in color, but are all the same length. – Give students a sheet of graph paper that has a horizontal distance greater than the length of the string (all strings are the same size). – Ruler – Pencil – Tape/Glue – Scissors *You might consider having the students measure their own string to help incorporate additional 8th grade measurement TEKS.* Directions: 1. Instruct the students to place one string on top of the x-axis of the coordinate plane, centering the string at the origin as closely as possible. 2. Now, instruct the students to pick one point on the x-axis that falls between the origin and one end of the string. Ask them to plot that point using a pencil. 3. Once the students have plotted the point on the x-axis, have them find its reflection, with the y-axis being the line of symmetry, and plot that point using a pencil. 4. Instruct the students to take each string and cut them in different locations. This can be done one string at a time or all at once, whichever you choose. 5. Students will then take two strings that are the same color and place one endpoint of one string on one of the plotted points and one endpoint of the other string on the other plotted point. Tape/Glue each string securely at the plotted endpoints. 6. Students will then create an angle with the two unsecured endpoints and will tape/glue the string at the vertex of the angle that is formed. 7. Repeat this process for the remaining pieces of string, ensuring that angles are created in all four quadrants. Ask the students to use their pencil to connect each of the vertices…they should see the emerging ellipse. Explore I Activity Products/Artifacts

Students will create an ellipse on the graph paper using strings.

Materials/Equipment: The following materials are required for each group: – 15 different colored strings, all the same length – ruler – glue/tape – graph paper with x and y-axis drawn – Pencil – Scissors Resources: Look at the video to get an idea of how you can create an ellipse using the Explore Activity. http://www.sciences.univnantes.fr/physique/perso/gtulloue/conics/drawing/ellipse_string.html http://clem.mscd.edu/~talmanl/MOOVs/Ellipse1/Ellipse_NS.mov

Explain Activity Approximate time: 30 min Have the students share their finished products with the class by posting them at the front of the classroom. Give the students an opportunity to discuss the similarities and differences in the products. Introduce an ellipse that has all key parts of the ellipse identified…center, foci, vertices, co-vertices, major axis, minor axis, eccentricity. Work to ensure that the students are using the correct vocabulary terms. Consider introducing the equations of ellipses and reviewing the Pythagorean Theorem. Let the students know that this discussion will come into play later in the lesson. Ask the students what they know about ellipses and what they want to know about ellipses. Have the students fill in the KWL chart and record that information on the overhead. Then do a walkthrough and discuss the following: – How do the two points, known as the foci, affect the shape of the ellipse? Use this site to help students understand how the two points affect the shape. http://www.mathopenref.com/ellipseaxes.html – What is always true about the length of the two segments that have their vertex on the ellipse and the other endpoints on the x-axis? – Name the lines of symmetry? – What if the foci were located on the y-axis not the x-axis? How would that affect the shape of the ellipse? Explain I Activity Products/Artifacts

Students will use a KWL chart to fill in what they know and what they want to know about ellipses. .

Materials/Equipment: KWL chart for students KWL transparency Overhead to record all the “what I know and what I want to know” Resources: Print the KWL chart from this site http://www.eduplace.com/graphicorganizer/pdf/kwl.pdf Use this site to help students understand how the two points affect the shape. http://chickscope.beckman.uiuc.edu/explore/eggmath/shape/pins.html

Explore Activity 2 Approximate time: 60 min It is time to solve the design challenge. Have students work in groups of three to four. This is the challenge students will work on. The Cowboy’s logo designer has misplaced the elliptical stencil that is used to create the border of the team logos on the field. Come up with a tool that can be used to construct an ellipse to help the logo designer. The game starts in seven hours. Give students a picture of all the tools that they will receive (rope, thumbtacks, marker, ruler & compass). Ask student to design a plan to construct an ellipse whose major axis is x inches long using only the tools that are shown in the picture. Once the students design the plan, give each student a sheet of paper and ask the students to implement the design. Remember each group creates an ellipse whose major axis is x inches long. Bonus: For students, who complete the design challenge before other groups, ask them to scale their models up to “x” yards and identify concrete materials that could be used to carry out their design in the real world. Explore II Activity Products/Artifacts

Design plan and their final product.

Materials/Equipment: – One for each group: – Paper with directions and pictures of all the tools. In the directions, state how long their ellipse has to be (different for each group). – Rope different lengths (make sure if a group is creating an ellipse that is 6 inches long you have a rope that is a little longer than 6 inches). – Markers – Ruler – Compass – Push pins

Resources: None

Explain Activity Approximate time: 20 min Students will create a flow chart as a group to explain all the steps the logo designer can take to solve his problem. Ask students to identify tools that the designer might have available to him at the stadium. Students, as a group, will present their flow chart to the class. After every presentation, we will have a discussion.

Explain I Activity Products/Artifacts

Students will create a flow chart as a group to explain all the steps the logo designer can take to solve his problem.

Materials/Equipment: – Computer if students are using word or inspiration. – Overhead projector and a laptop if students want to project their word or inspiration file. – Posters – Markers

Resources: Free trial of inspiration for teacher and kidspiration software. http://www.mindservegroup.com/higher_ed/products.php

Elaborate Activity Approximate time: 20 min Students will use their knowledge of ellipses to find the distance from the center of the ellipse to the foci (the two points on the x-axis or the y-axis) given the minor axis and the major axis and solve real world problems.

Equals the length of the major axis major axis

Students should be able to use the Pythagorean Theorem to solve for x Ask students to write a paper on where you might see elliptical shapes and come up with a problem that can be solved using the properties you have learned. Teach students how to use their graphing calculators and or Java applet to graph ellipses.

Elaborate Activity Products/Artifacts

Present the paper to class.

Materials/Equipment: Foci worksheet on the last page Resources: Learn about eccentricity of ellipse http://www.mathwarehouse.com/ellipse/eccentricity-orbiting-planets.php

Evaluate Approximate time: Ongoing The following artifacts will be used for evaluation: – – – – – –

Two journal entries Flow chart Creating ellipse using string Design and implement of design challenge Foci worksheet Report

Evaluate Activity Products/Artifacts

All items mentioned above

Materials/Equipment:

Resources: Ellipse game to see if students can find the Foci of an ellipse. http://johnbanks.maths.latrobe.edu.au/Games/Ellipse/javaellipse.html