# Using Origami to Engage, Promote Geometryаа Understanding, and

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Using Origami to Engage, Promote Geometryаа Understanding, and

Using Origami to Engage, Promote Geometry Understanding, and Foster a Growth Mindset Session Day/Time: Friday, May 6, 2016, at 9:3011:00 a.m. Location: YCHuberEvans Presenter: Shelly Grothaus, Nature Hill Intermediate School Oconomowoc, WI [email protected] All materials created by Shelly Grothaus for this session are copyrighted. They are intended for individual classroom use. Our learning intentions We are learning to fold unit origami and see geometry concepts that connect to it. I will be successful when... ●I can brainstorm geometry words related to unit origami. ○I can try out a vocabulary method that promotes understanding. ●I can notice geometry concepts that can be taught using origami and find several concepts that relate to my grade level content. ○I can fill out a chart to analyze faces, edges, and vertices. ●I can build a unit piece, cube, and possibly a triangular hexahedron. ○ ( I may even be able to build a stellated octahedron or start it.) ●I can reflect on the benefits of using origami as a way to embed math and set goals for future steps I could possibly take to teach origami. Some may take additional steps: Our Norms for the Session Today ● Have a growth mindset while working on origami today. ● Take care of and reach out to the people next to us. ● Take the role of origami folder A and origami folder B when necessary. ● Stop on a three, two, one when I use the hand signal. It will save us much time and promote a respectful atmosphere. ● Simulate what it takes to teach up to 35 students origami at the same time. ● Put phones and technology to the side except during our work time. ● Engage, focus, and participate at a level that you would expect if students were watching you. ● Enjoy and learn Using Origami to Engage, Promote Geometry Understanding and Foster a Growth Mindset Agenda for Session ● Video Taking origami into the community and to cross grade level peers ● Norms for a successful session and growth mindset ● Learning intentions ● Why use origami? ● Related vocabulary Brainstorm session ○ Trying out the vocabulary handout ○ Share sentences ● Building the unit How to model origami in your class or with 30+ students without a trainwreck ○ Partner A (Green) builds ○ Partner member B (Pink) watches ○ Watch demo ○ Building the cube with white paper ● Fill out the “Analyzing Polyhedra for Math Concepts Chart” ○ Large size ○ Mini Try this with students as a next step (We won’t do today.) ○ Build and fill out chart ● Tetrahedron ○ Watch model and have a growth mindset ○ Build with colored paper ○ Fill out Analyzing Polyhedra for Math Concepts Chart Agenda Page 2 ● Tips for tight school schedules How do I find time to do origami in my classroom? ● Extensions for students ready to fly ○ Independent projects ○ Creating teaching videos ○ Finding additional unit origami pieces that have different shaped faces ● Work time choices ○ Colored cube ○ Stellated octahedron ○ Euler’s Formula Looking for patterns ● Closure ○ Benefits ○ Challenges ○ Growth mindset ● Reflection 10:53 ○ Next steps ○ Fill out reflection form and conference paperwork My goals for today’s session (Use the learning intentions and agenda to set your goals.) ________________________________________________________________________________________________ ________________________________________________________________________________________________ ________________________________________________________________________________________________ ________________________________________________________________________________________________ ________________________________________________________________________________________________ ________________________________________________________________________________________________ Growth Mindset and Origami Challenges Growth Mindset Findings from my Action Research ★ Teaching students about growth mindset impacted the challenges that students were willing to tackle in my advanced math class. ★ Those students surveyed who reported a growth mindset finished more of the challenging origami polyhedra than those who believe that their math intelligence is fixed. ○ For the first time since starting the advanced math class four years ago, all students finished the stellated icosahedron. ○ Most students in the class created more challenging additional origami pieces. ○ Those who reported a fixed mindset on the survey did not take on additional challenges. They tended to try to hide that they were stuck or didn’t know how to proceed. ★ Quote echoed in various wordings. ○ “I think that if I told myself at the beginning to ask questions, I would have had a lot smoother way through ‘this’. I really have to let myself know that asking questions doesn’t mean giving up. It means that I’m actually stronger.” ★ A way that I have grown as a teacher is to make my classroom a safe place for adolescent learners to admit that they don’t know something, are stuck, and need help. ○ Tips ★ Origami is the perfect tool for helping students learn the skills they need to have a growth mindset. ★ Student Quote ○ “When I made the cube, at first I didn’t think I could do it, but when I finished the cube easily, it changed my mindset. I think I could have had a better mindset at the very beginning. I wasn’t very enthusiastic, but I ended up loving it.” What can we and students learn mathematically from origami? Vocabulary Related to Unit Origami Brainstorm I am learning that paper folding is related to two and three dimensional geometry. I will be successful when I can… □ generate a list of vocabulary words related to origami. □ use the words in context □ understand properties of each term List Vocabulary Related to the Unit Materials Needed for Each of the Unit Origami Modules 1a. White Cube: Six pieces of white paper 1b. Colored Cube: Six pieces of paper – two each of three different colors https://www.youtube.com/watch?v=ztoLaug5AJE 2a. White Triangular Hexahedron: Three white pieces of paper 2b. Colored Triangular hexahedron: Three pieces of paper – one each of three different colors https://youtu.be/pjL8W9dPqk 3a. White Stellated Octahedron: Twelve sheets of white paper 3b. Stellated Octahedron: Twelve sheets of paper – four colors make three of each color https://youtu.be/VP3GiIwSfz0 4a. Stellated Icosahedron: Thirty sheets of white paper 4b. Stellated Icosahedron: Thirty sheets of paper – six colors make five of each Vocabulary Related to Unit Origami Brainstormed by Students I am learning that paper folding is related to two and three dimensional geometry. I will be successful when I can… □ generate a list of vocabulary words related to origami. □ use the words in context □ understand properties of each term List Vocabulary Related to the Unit half isosceles triangle onefourth 3D rectangle cube congruent right angle parallel lines symmetrical faces base edges height vertex/vertices overlapping right angle surface area right triangle parallel acute angle pyramids obtuse angle stellation surface area stellated icosahedron triangular hexahedron octahedron Student Origami Unit Reflection for ____________________________ Explain three important mathematical takeaways that you gained during our unit origami project. Explain how to find the surface area of a polyhedron with faces. In order to find the surface area of the ___________________________________________, a mathematician needs to... Describe your work ethic, use of time, and willingness to challenge yourself during this unit. Name ______________________________ Geometry Terms Related to Origami https://www.mathsisfun.com/definitions/face.html http://www.mathwords.com/a_to_z.htm Term Ex. faces ❏ Write a meaningful, Draw a sketch of the term. Show mathematical where it appears in your origami definition in your own piece. words. ❏ Use a resource to further understand the term. The flat polygon surfaces of a polyhedron Use the word in a sentence of at least 8 to 15 words. Demonstrate that you understand the concept in the context of the sentence. Underline each vocabulary word in the sentence. Box the capital letter and box the ending punctuation. ❏ ❏ Term ❏ Write a Draw a sketch of the term. Show meaningful, where it appears in your origami mathematical piece. definition in your own words. ❏ Use a resource to further understand the term. Use the word in a sentence of at least 8 to 15 words. Demonstrate that you understand the concept in the context of the sentence. Underline each vocabulary word in the sentence. Box the capital letter and box the ending punctuation. ❏ ❏ Analyzing Polyhedra for Math Concepts Name ______________________________ Analyzing Polyhedra for Math Concepts – Show all work on the designated handout. No calculators. Name of Number of Faces Number of Edges Number of Vertices Number of Polyhedron Pyramids Cube Mini Cube Triangular Hexahedron MiniTriangular Hexahedron Stellated Octahedron Stellated MiniOctahedron Surface Area in Sq.” Length _________ Width _________ X faces Length _________ Width _________ X faces Stellated Icosahedron Mini Stellated Icosahedron Name of Choice Piece 1 (Must be able to figure out surface area) Name of Choice Piece 2 (Must be able to figure out surface area) https://www.youtube.com/watch?v=r1anoTV9Htc Work space to show all work. Measure accurately. Label all units properly. Cube Stellated Octahedron Mini Cube Triangular Hexahedron MiniTriangular Hexahedron Mini Stellated Octahedron Stellated Icosahedron Mini Stellated Icosahedron Extra Work Space Name of Choice Piece 1 (Must be able to figure out surface area) Name of Choice Piece 2 (Must be able to figure out surface area) Name of Choice Piece 3 (Must be able to figure out surface area) Name __________________________________ Euler’s Formula Exploration Name of Polyhedron Number of Faces Number of Vertices Faces + Vertices Edges Patterns Noticed Cube Triangular Hexahedron Stellated Octahedron Stellated Icosahedron Choice Piece (Must have faces, vertices, and edges, like the previous pieces) Euler’s Formula Second Page What relationships do you see between vertices, faces, and edges? (Explain below.) _______________________________________________________________________________________________________________ _______________________________________________________________________________________________________________ _______________________________________________________________________________________________________________ _______________________________________________________________________________________________________________ _______________________________________________________________________________________________________________ What rule can be used to find the number of edges for any polyhedron? (This formula is called Euler’s Formula.) _______________________________________________________________________________________________________________ _______________________________________________________________________________________________________________ _______________________________________________________________________________________________________________ _______________________________________________________________________________________________________________ Euler’s formula : for any convex polyhedron, the number of vertices and faces together is exactly two more than the number of edges. Symbolically V−E+F=2. V + F – 2 = E Geometry Standards Related to Origami Listed by Grade Level Fifth Grade Possible Learning Intention/Target CCSS.MATH.CONTENT.5.G.B.3 I can identify properties of twodimensional faces of origami polyhedra. I can classify twodimensional figures into categories based on their properties. Standards and Learning Intentions Related to the Origami Mathematical Unit Sixth Grade CCSS.MATH.CONTENT.6.G.A.4 I can represent threedimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of 3D origami. I can apply these techniques in the context of solving realworld and mathematical problems related to the origami that I build. I can solve realworld and mathematical problems involving area, surface area, and volume. CCSS.MATH.CONTENT.6.G.A.1 I can find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving realworld origami problems. CCSS.MATH.CONTENT.6.G.A.2 I can find the volume of a right rectangular prism (origami cube) with fractional edge lengths by packing it with unit cubes of the appropriate unit fraction edge lengths, and show that the volume is the same as would be found by multiplying the edge lengths of the prism. Apply the formulas V = l w h and V = b h to find volumes of right rectangular prisms with fractional edge lengths in the context of solving realworld and mathematical problems. Standards and Learning Intentions Related to the Origami Mathematical Unit Seventh Grade CCSS.MATH.CONTENT.7.G.B.6 I can solve realworld and mathematical problems involving area, volume, and surface area of two and threedimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms related to origami. Standards and Learning Intentions Related to the Origami Mathematical Unit Eighth Grade I can explain congruence and similarity using origami physical models, transparencies, or geometry software. CCSS.MATH.CONTENT.8.G.A.1 I can verify experimentally the properties of rotations, reflections, and translations: CCSS.MATH.CONTENT.8.G.A.1.A I can compare lines that are taken to lines, and line segments to line segments of the same length using origami models. CCSS.MATH.CONTENT.8.G.A.1.B I can find and compare angles that are taken to angles of the same measure using origami models. CCSS.MATH.CONTENT.8.G.A.1.C I can notice similarity relationships related to parallel lines that are taken to parallel lines using origami models. Unfolding Mathematics with Unit Origami is a Very Helpful Book ISBN13: 9781559532754 ISBN10: 1559532750 Ordering Mini Paper for Unit Origami Remember that it’s easier to learn and fold with larger paper. Use the miniversion only when learners have been successful. http://www.officedepot.com/a/products/557783/TOPSNeonTwirlMemoPads400/ http://www.amazon.com/AssortedBrightColorsPaperNotes/dp/B00RDLWQC4 Closure What are the benefits of origami for students? What can they learn? What are my goals for possible next steps with origami? What action(s) would I need to take in order to meet my goals? 1 1 All materials created by Shelly Grothaus for this session are copyrighted. They are intended for individual classroom use. Please fill out this form and leave it on your table. Your feedback is appreciated. Using Origami to Engage, Promote Geometry Understanding, and Foster a Growth Mindset Shelly Grothaus Facilitator What did you find most helpful today? How likely are you to try some of the ideas from our session? Would you be interested in an advanced session of unit origami? Yes! 5 4 3 2 1 No Suggestions or ideas (Example: Advanced session on stellated icosahedron): Would you be interested in attending a future session on factor lattices? Yes! 5 4 3 2 1 No What suggestion(s) do you have for improving the session?