Geometry for Teachers of Grades 6-8

  • Campus Pipeline To access WebCT (bulletin board and grades)
  • Course Overview
  • Dr. Sarah Greenwald's Syllabus

    Class Highlights

  • May 6 - Mon - Class #15 - Dr. Sarah 4:30-7:30pm
    Rhonda and Marissa provide snacks
    Meet in the Media Center
          Final projects due
          Extra credit crochet model of the hyperbolic plane due (for me to keep). Go to the website Construction of Hyperbolic Planes and scroll down to 2. How to Crochet the Hyperbolic Plane for directions.
    Read Hearing the Shape of a Drum article from NCTCM Centroid. Go through the Activity Sheets on Hearing the Shape of a Drum. Actually do the activities on a separate piece of paper and show work. Complete the Carolyn Gordon worksheet. Course evaluations. Final projects.

  • April 29 - Mon - No Class

  • April 27 - Sat - Classes #13, #14 at ASU in Boone - Dr. Sarah 9am - 4pm
    Each person brings money for lunch. Dr. Sarah provides snacks.
    We will meet in 203 and 308

    Collect hw (see Apr 15 for hw for today) Skim and finish 2D Universes and torus and Klein bottle games. The Shape of Space lab and worksheet. Build an icosahedron and a square and look at zometool activities.
    --Lunch from 12-1--
    Math Sciences Education Center Tour. Double Bubble Conjecture. Shape of the World Video. Review ideas via excerpts from Davide Cervone's Selected Course Notes. Work on final projects.
    Homework for May 6 Final Project -- You must develop one lesson for your topic that includes the use of geometer's sketchpad and a second lesson for this topic suitable for use in a classroom without technology access. You must type up your own lesson plans, notes for the teacher and solutions. In addition, you will reflect on the possible benefits and difficulties of implementation of your lessons and their relationship to the North Carolina Middle Grades 6-8 Mathematics Curriculum for Spatial Sense, Measurement, and Geometry and to the NCTM Principles and Standards for Geometry and Measurement.

    Plan on at least 1 hour and 15 minutes from Hickory. You can take 321 North past Lenoir, past Blowing Rock (stay on 321 Bypass instead of turning on 321 Business), and into Boone. Stay on 321, past the Lowes on the right, past the Burger King on the right, past the Wendy's on the left, past the Blockbuster on the left, until just past the Holmes Convocation Center on the left side. Turn left on Rivers street. On Rivers street, pass through 4 signals, and turn left at the 5th signal onto Bodenheimer/Depot. Immediately turn right into the parking lot. See the campus map. Cross Bodenheimer to enter into Walker Hall. Inside Walker Hall, go to the 2nd floor to 203. We will spend time in rooms 203 and 308.

  • April 22 - Mon - No Class

  • April 15 - Mon - Class #12 Dr. Sarah 4:30-7:30 pm
    Tracey and Anna provide snacks
    Meet in Media Center
    Collect hw (see Apr 8 for hw for today). Readings and Activities on Perspective Drawing and Projective Geometry,     perspective worksheet,     Homer,     2D Universes.
    Homework for April 27
    Go through these middle grades Sketchpad or dynamic software activities and write down a number of activities from (at least 3) different web pages that you would be interested in using in your classroom if you had the computers and the software. I want more than just the name of the activity - include a description of the software activities via printing them out or writing your own description. Also find at least 1 web page address and sketchpad activity that are not accessible from the link above by searching yourself. Be prepared to turn in the web page addresses and a descripiton of the activities. In addition, choose a topic for your final project that you would like to explore both with Sketchpad and without technology and be prepared to spend some time working on the Sketchpad part at ASU. This may be an activity that you have done in class before, which you now want to also explore with technology.

  • April 8 - Mon - Class #11 Dr. Sarah 4:30-7:30 pm
    Keith and Diana provide snacks
    Meet in the Art Room
    Collect hw (see Mar 25 for hw for today) Review problems 6 through e.c. #2 of Geometry of our Earth by calling on students. E.c. #3. Proof that the sum of the angles of a Euclidean triangle is 180 degrees. Paper Folding At the end of the last class, we proved that the sum of the angles of a spherical triangle is always larger than 180 degrees. Hence the Euclidean proof must fail on a sphere. What goes wrong with the proof in spherical geometry? Introduction to hyperbolic geometry via sketchpad (sum angles of a hyperbolic triangle, pythagorean thm, postulate 5, proposition 31, Playfair's axiom). Continue with history of geometry. Overview of spherical, Euclidean and hyperbolic geometry (non-Euclidean=spherical and hyperbolic). Escher model of hyperbolic geometry. Polygonal tiling models of the sphere, the plane and hyperbolic space. Heptagons, Septagons. Then begin the shape of space via Homer 3D..
    Homework for April 15 Write up a lesson plan for your students that incorporates Euclidean, hyperbolic AND spherical geometry in some (possibly small) way. This activity may take up a small portion of time or may take up the entire time increment that you teach. If you wish, you may assume an ideal and hypothetical classroom environment --- that you have access to a computer lab, globes, sketchpad and anything else you want for the purpose of this assignment, but the assignment should be aimed at your real-life students. Extra credit if you test out your activity and report back on student reactions. Your lesson plan (and extra credit) will be turned in to Dr. Sarah for grading. Extra credit for redoing the calculus computation for a sphere of radius r (instead of radius 1), with x going from -r to r. Extra credit for crocheting me a hyperbolic plane (see May 6 above for directions). Also, start thinking about a topic for your final project (see the final project description on my syllabus) that can be explored both with and without technology. This may be an activity that you have done in class before, which you now want to also explore with technology. You will have some time on Sat April 27 at ASU to work on your project, so you need to decide on a topic by then.

  • April 1- Mon - No Class

  • Mar 25 - Mon - Class #10 Dr. Sarah 4:30-7:30 pm
    Gary and Nicki provide snacks
    Review problems 0 through 5 of Geometry of our Earth by calling on students. Intro to Geometer's Sketchpad via Dr. Foley's Geometric Constructions and constructions via the corresponding Euclidean contructions and resulting inductive reasoning. Problem 6 Euclidean version in gsp. Problems 6-10 presentations and and help from Dr. Sarah on questions 6-10 and the extra credit questions (except for last e.c. question). Beachball activity. If time remains that continue with the history of geometry via discussion of Euclid's 5th postulate and Playfair's axiom.
    Homework for April 8 Using your beachball, review the answers to all of the geometry of the earth problems. Be prepared to orally respond to these questions using this manipulative at the beginning of class. In addition, click on Euclid's Elements from the main web page, find Book I, Proposition 4 via links from this Euclid's Element link, and print it out to turn in. Finally, check WebCT after April 1st for a message from me regarding your grade for the geometry of the earth assignment.

  • Mar 18 - Mon - Class #9 Dr. Sarah 4:30-7:30 pm
    Jill and Jennifer provide snacks
    Geometry of the Earth. Initial intuition, web searching, the final presentation, and help from Dr. Sarah. Dicuss the history of Euclid's Elements. Discuss the relationship to North Carolina Middle Grades 6-8 Mathematics Curriculum for Spatial Sense, Measurement, and Geometry (see the syllabus).
    Homework for March 25 Buy a light colored already inflated ball that you won't mind writing on with permanent marker during class. In addition, if you have masking tape, then bring that to class. Using your beachball, review the answers to the geometry of the earth problems 0 through 5 (but don't draw on your beachball). Be prepared to orally respond to these questions using this manipulative at the beginning of class.

  • Mar 11 - Mon - Class #8 Dr. Sarah 6-7:30 pm
    Dr. Sarah provides snacks
    First half of the class is Dr. McGalliard's final.
    Sign up sheet for snacks. What is geometry? Groups of 2 discuss this and then report back to the class. Introduction to the class web pages and WebCT, including bulletin board posting. Introduction to web searches. Search the web to find additional ideas on what geometry is.
    Homework for Mar 18 Using our discussions of geometry, look through your teaching materials from this year. What geometric activities are you using with your class this semester? You may answer this via photocopies of these activities and/or a typed summary of these activities.