Date

CLASSWORK AND HOMEWORK
Work is due at the beginning of class
unless otherwise noted!

July 17  Mon 

July 18  Tues 
 Classwork Algebra
Linear equations: Egypt Rhind Papyrus, Babylon, China:
Egyptian Multiplication/Division
The origin of algebraic manipulation via
Linear Equations in One Unknown  Islamic Method worksheet from the
CD Linear Eqs
3233.
Chinese method of double false position of solving two linear equations
with two unknowns via Chinese Problems worksheet from the CD NegNums 4244.
System of Three Linear Equations  The Chinese Solution
from Algebra Activities from Many Cultures
Multicultural Origin of the Quadratic Formula
worksheet from
Algebra Activities from Many Cultures
History of Plimpton 322 via web search (Plimpton 322)
Brief history of the Pythagorean Theorem via a web search
(history of the pythagorean theorem):
site
and
site
Additional History of Math sites:
MacTutor History
of Mathematics Archive (Pythagorean site:wwwgroups.dcs.stand.ac.uk/)
Mathematicians of the
African Diaspora
Convergence: where
mathematics, history and teaching interact
Scarecrow's Theorem
Slide 1
Slide 2
Copyright Slide
Cubic equations: Europe  leading to sqrt(1)
Solutions to the quintic
Maple demo and fictional account of Galois
Begin Wednesday's classwork.
 Homework for Wednesday
Choose an NCTM standard related to algebra or geometry. Write down
that standard. Then find an activity related to that standard that is not
from our CD. You may find an activity in one of the books or from a web
search. Specify how the activity relates to the standard that you chose.
Continue working on the Reflective Journal
and CD assignments. Your CD project topic must be approved by Dr. Sarah by
Wednesday. Provide the Chapter and page number in addition to the title of
the activity.

July 19  Wed 
 Classwork Geometry
 What is geometry? Groups discuss and come back together.
 Brief history of early geometry knowledge including the
Babylonians, Egyptians, Greeks (Thales, Pythagoras, Plato, Euclid),
Chinese, and Africans.
Mention the Timeline for Geometry: Multicultural Highpoints
from Geometry Activities from Many Cultures
Skim LAV 6 section of the CD
on Origins of Length, Area, and Volume Measurement
Mention CD LAV 80 on Thales' Shadow Measurement Activity
Mention CD
Trig 80 and LAV 88 on Eratosthenes' Size of the Earth and
Trig 112 on AlBiruni's Calculation on the Size of the Earth
History of Euclid's elements including
Euclid's 5th postulate (prop 29 and later).
 Sum of the Angles in a Triangle:
Write out
Proposition 32 in modern language.
Discuss Euclid's historical proof,
paper folding,
and then an
Intro to Geometric Constructions
via a
construction in Sketchpad.
Dr. Sarah models the construction.
Discuss the history
(attributed to Pythagoras),
and compare and contrast the activities,
discussing the benefits and difficulties with using them in various classes.
**Then the group goes to the computer lab to try the Sketchpad construction.
 Pythagorean Theorem:
Discuss the Yale tablet and Babylonian Pythagorean knowledge.
Discuss the history of
Euclid Book 1 Proposition 47 and of it's importance in measurement.
Discuss Sketchpad demonstrations of the Pythagorean Theorem. From
Sketchpad, under File/open, go to
Desktop/205Math(yourcomputersnumber)/Applications/Sketchpad/ Samples/Sketches/Geometry/Pythagoras.gsp
Go through Behold Pythagoras! and Puzzled Pythagoras.
**Return to the classroom.
(Highlight
Euclid's Proof), discuss the historical differences in proofs,
and then Dr. Sarah's models the Pythagorean Theorem in Sketchpad.
Mention CD activities
LAV 124 Pythagorean Theorem,
LAV 130 Practical Pythagorean Theorem,
Geom 103 Pythagorean Project
Hand out A Chinese Proof of the Theorem from
Geometry Activities from Many Cultures
in order to complement the Sketchpad Behold Pythagoras! activity
Compare and contrast the methods used in the classroom.
 NonEuclidean Geometry:
Dynamic Geometry activities on the sphere and hyperbolic Poincare disk
Walter Fendt's Java Applet
and the sum of the angles and the Pythagorean Theorem
Escher worksheet
Sketchpad
Hyperbolic Sum of Angles
Sketchpad
Hyperbolic Pythagorean Theorem
Mention built in hyperbolic Sketchpad exploration and
Brad Findell's Elliptic/Spherical Toolkit for Sketchpad
Why Study
Hyperbolic Geometry? and a brief
history of
nonEuclidean geometry.
Hand out Explorers of NonEuclidean Geometry from
Geometry Activities from Many Cultures
Mention CD Trig 151 on Spherical Trig
Read through the
Shape of the Universe and discuss
 **Return to the computer lab. History of modern geometry
via web searches.
**Return to the classroom.
A brief history of
geometry education.
 Brief history of the connections and
differences between algebra and geometry
The Proof video
Mention the teacher's guide available at
NOVA Online
Powers
of twelve activity and the related
DXC history and
history of writers in the classroom
 Homework for Thursday
Complete the CD assignment.

July 20  Thur 
 Classwork CD presentations and Precursors to Calculus
 Finish up classwork from Wednesday
 CD presentations
 Ben Franklin's Will
 Begin calculus:
Discussion based on The Paradoxes of Zeno from From Agnesi to Zeno
 Archimedes:
Archimedes and pi via inscribed and circumscribed polygons.
Hand out the
Hypatia
worksheet
Examine the related NOVA website applet
Archimedes finding the area of a parabola in terms of the area of a
triangle and the quadrature of a parabola
Applications of series:
history of the approximation of Pi
and the number of known digits of Pi.
Apu and pi in Maple, and search for the world record on
the number of digits. Discuss Bailey and Borwein's series.
Archimedes computation of the area of a sphere as four
times the length of the great circle via oranges
Archimedes and the
volume of a sphere.
Read and discuss
Measuring Volumes
The
Archimedes Palimpsest
Analytic Geometry Notes
Create timeline  include names, year, and accomplishments
 Homework for Friday
Study for Assessment. Complete the Reflective Journal Assignment.

July 21  Fri 

July 29  Sat 
