Geometry for Teachers of Grades 6-8
To access WebCT (bulletin board and grades)
Dr. Sarah Greenwald's Syllabus
May 6 - Mon - Class #15 - Dr. Sarah 4:30-7:30pm
Rhonda and Marissa provide snacks
Meet in the Media Center
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
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.
Carolyn Gordon worksheet.
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
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
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
and a second lesson for this topic
suitable for use in a classroom without
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
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.
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,
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
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.
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
of hyperbolic geometry.
models of the sphere,
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
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
Your lesson plan (and extra credit) will be turned in to Dr. Sarah
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
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
Dr. Foley's Geometric Constructions
and constructions via the corresponding Euclidean contructions and
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).
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
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.