Presentation Topics for MA 202, Spring, 20051. Understanding Polygons (Grade level 6 with applications to earlier grades): “Building Polygons”, Investigation 2 of CONNECTED MATH, grade 6 (Geometry), “Shapes and Designs”. The presentation should solve the problems 2.1, 2.2, and 2.3. You may need to make up “polystrips”2. “Polygon Properties and Tiling”, Investigation 4 of CONNECTED MATH, “Shapes and Designs” grade 6 (Geometry). Make sure that you do Problems 4.2 and applications, connections, and extensions (p.47 -49)3*. Symmetries (Grades 4-8): See “Three Types of Symmetry”, Investigation 1 of CONNECTED MATH, “Kaleidoscopes, Hubcaps, and Mirrors”, grade 8 (Geometry). This presentation is required for those going into middle school teaching. This material is also covered in Section 13.2 ofLong and DeTemple. You should follow the CONNECTED MATH text but feel free to integrate the Long and DeTemple material. Cover as much of the investigation as you can in your time. Be sure to do Problem 1.2 (p. 9) and translational symmetry (p. 12) including Problem 1.4, and some of problems4,5,6, or 7.4. Use of Art for Mathematics education (grade level: K-5): See the article by Richard Millman and Ramona Speranza, "Artist's View of Points and Lines”, Mathematics Teacher Vol 84 (1991), 132-138. What mathematical concepts can you present to your students by using works of art? Remember: sculpture can give 3-D intuition, for example, even though it is not in the article. This is not about the applications of math to art (although that is fascinating) but rather how to use art to introduce math concepts to children. You will need to find some posters, slides or overheadsto do this. Visit the Fine Arts Library, explore and use your imagination. (If you cannot check out slides from that library, let me know and I will borrow them for you.)5*. A conjecture on area and perimeter (grade 5). See attached for description. First decide if the conjecture is true and then see your instructor(as a group) before settling on the rest of the project. Your presentation is about how you (as a teacher) would respond to the student in front of her class. What is your mathematical habit of the mind in responding? What doyou believe she is thinking about? How would you explain the mathematics?6. Volume of Cylinders and their surface area (Grade level: 4-6 or later): “Case 4: Slippery Cylinders” in Katherine Merseth, editor, WINDOWS ON TEACHING MATH. Work through the case and then explain conceptually the various responses of the students as well as the appropriate one. Do a “rice experiment”.7. Algebraic expressions (Grade level: non-College bound algebra II class). See “Case 1: Lost in Translation”, in Katherine Merseth, editor, WINDOWS ON TEACHING MATH. This Case Study deals with trying to explain moving to algebraic expressions from word descriptions to a class which has had math difficulties in the past. The algebra involves expressionslike 2- 5n = 12 + n.. Work through the case and then explain conceptually the various responses of the students as well as the appropriate one. The level of algebra is that of Chapter 8 of Long and DeTemple.8. Probability and Data Analysis (Early Childhood): See the article “Data Analysis and Probability in the Early Childhood Curriculum”, p. 147-166 of Juanita Copley, THE YOUNG CHILD AND MATHEMATICS. Your presentation must include an instruction principle and Assessment principle (see p. 166) and answer the question: What would be the math content of a similar project in the next grades and how would you structure it? What is it from MA 202 that is relevant to this article?9. Statistics- Averages (grade 4): This project discusses how to compute averages by non-standard means (pun intended). “Fourth Graders Invent Ways of Computing Averages”, Kamii, Pritchett, and Nelson in NCTM, PUTTING RESEARCH INTO PRACTICE, p. 232-237.10. Algebraic representations (Grades 4,5): Graphs and the stories they represent. Do Activity 5 of Dolan, Williamson, Muri, and ACTIVITIES FOR ELEMENTARY MATHEMATICS TEACHERS, p. 148. Now formulate content oriented questions based on each of the five graphs which will change the shape of the graph given. Be explicit about what the resulting graph will look like. Which of these can be described by algebraic “formulas”?11. Figures in Space (Grades 4-8): Present the material of Long and DeTemple, Section 11.3.12. Your choice (almost): Look at NLVM (see below), pick a manipulative that is relevant to MA 202 and explain its content and conceptual base to ourclass (audience: your fellow students). Please check with your instructor first to make sure that the topic and its mathematical depth are appropriate. (All grade levels).Remember: 1. Emphasis is on math content at the appropriate grade level throughout.2. Look at the National Library for Virtual Manipulatives for Interactive Mathematics (http://matti.usu.edu/nlvm/nav/vlibrary.html) and use one in your presentation or use another manipulative . You are not required to use NLVM’s manipulative.3. When there is student work in the article you read, you need to present it and explain conceptually why it is right (or wrong).4. All of the books and articles are on reserve in the Math Library, POT 065 under MA 202 and your instructor’s name. * There must be a presentation on each of these topics in each MA