1+History+of+Math

1st day (short) Expectations HW: Assignment worksheet here:

video activity: [|inspirations] How many things do you recognize? List as many as you can in 15 minutes - watch it several times if you need to... Read one article, and be prepared to discuss in class. __Zero The Biography of a Dangerous Idea,__ ch. 1 article __When Lions Battle__, Nicholas Tasaday article __Why History?__ by Underwood Dudley

Story of 1: - has some really good clips on history

12 Days

Part I: General introduction/overview (3 days)

Essential Question: Why is mathematics important to humans? Discussion Questions for class, journal, online: 1) How did religion influence the development of mathematics? 2) Compare / contrast the motivations for learning math in the east vs. west. 3) Share something you saw that you already knew about. Share something you saw that surprised you. 4) How was knowledge preserved, continued, disseminated throughout history? 5) Was math inevitable?

__Day 1__ Watch Inspirations one more time, pausing and talking about what they recognize. Jigsaw reading discussion using questions

HW: scavenger hunt - we give kids a list of big discoveries, important people, etc. - look up date, specific place, brief description

__Day 2__ kids put stuff on a map online at www.communitywalk.com Q: What do you notice? Does anything surprise you? Why do you think that is?

3 timelines? Europe, China, Middle East, show video of islam spread from Ascent of Man Ep5, at 18min (grace has)

HW: finish putting markers on map, read Mayan math article

__Day 3__ start video - The Story of Maths: Ep 1, first 15m, recognizing patterns, keeping records, etc.then 5m each of Egypt, Sumerians, Babylonians, Greeks

Ep. 2, 5m from China (weighing peaches, plums; eggs problem - for HW?) and India (include fractions/dividing by 0; weighing to solve system; House of Wisdom, symmetry tiling) HW: read article on Incan knots & watch video on website Video on Incan Knots: http://www.youtube.com/watch?v=ZvU-WVBXn9c&feature=BFa&list=SP18FC35BAE7676C38

__Day 4__ finishing videos Video montage since Renaissance - Fibonacci, Descartes, Newton, Euler, Gauss, France v. Germany, infinity Cantor, no HW (Rosh Hashanah)

HW: post a comment about one question 1) How did religion influence the development of mathematics? 2) Compare / contrast the motivations for learning math in the east vs. west. 3) How was knowledge preserved, continued, disseminated throughout history? 4) Was the development of math inevitable?

__Day 5__ Human's Intuition for math: 

See how good your intuition is by counting by 'seeing'. Click for demo, then set # of dots from 3 to 9. Have fun!)
 * 1: Read & Discuss: Excerpt from __Here's Looking at Euclid,__p. 1-8, then Play counting gameon website - what's the connection? (text for site:


 * 2: Read & discuss Number intuition article[[file:The Brain Humanity's Other Basic Instinct Math.pdf]], then watch video on website & discuss

Watch the video Brannon Lab Monkey research: What do you see in this video? What questions do you have about this monkey's ability to add?

number game blue vs. yellow dot test (testing your approximation): @http://www.nytimes.com/interactive/2008/09/15/science/20080915_NUMBER_SENSE_GRAPHIC.html
 * 3:

HW: start in class Number systems worksheet: analyze, compare, contrast ancient number symbols with current numbers & post response to big idea Q1: How did religion influence the development of math?

__Day 5__ article/video on different bases learn about and do math problems in a different base See PROMYS Pset 0 # P1, P2 - conversions PROMYS Pset 1 # P2 - addition of polynomials in different bases

__Day 6__ >
 * Station 1: Pi**
 * How Archimedes approximated pi activity worksheet with reading from PBS nova: http://www.pbs.org/wgbh/nova/physics/approximating-pi.html
 * Timeline of development of pi
 * Website of visual colors: website with visual of colors representing most digits of pi ever displayed
 * Factoids of pi from __The Joy of Pi__: David Blatner @ BHS Lib.
 * Station 2: Square Root 2**
 * 1 minutes Pythagoras square root of two clip
 * Babylonian square root of 2 clip
 * Estimating square root of 2 exercise
 * Reading about Babylonian clay tablet:[[file:Babylonian_sqrt2.pdf]]

Estimation: http://johncarlosbaez.wordpress.com/2011/12/02/babylon-and-the-square-root-of-2/

Example of a possible geometric proof that square root of 2 is irrational, much like what Pythagoras might have used: http://blog.plover.com/math/sqrt-2-new.html

zero: india - religious, everything / nothing vs. elsewhere is quantity
 * Stations 3: Zero and Infinity**
 * Reading from __Zero: The Biography of a Dangerous Idea__: p.19-23, The Fearsome Properties of Nothing
 * Video of __What the Ancients Knew__ (1 min 45sec): video
 * Video from Story of Maths about division of Zero

__Day 7__ computation - algorithms activities - try multiplication activities, tools - video of abacus contests, modern technology- video of development of computers egyptian multiplication, newton's method

__Day 8__ Proofs - Euclid, Pythagorean Theorem (video Ascent of Man, Ep. 5, 11 minutes in), Descartes/Philosophy, proof of rt2 is irrational, proof of rationals being same size as counting numbers, discuss idea of different levels of infinity Can also prove Given a,b,c element of Z: if a|b and b|c, then a|c (promys notes day 2)

//Zero: The Biography of a Dangerous Idea// proofs
 * Winston Churchill proof (Appendix A)
 * Cantor enumerates rational numbers (Appendix D)

Part IV: Their own research (3 days): Individual, written product get help from Ann setting up a page of resources

Choice 1: Investigate/do ancient math - Egyptian algorithms and computation - Greek constructions

Choice 2: Research and write about one of the following topics: Euclid, Brahmagupta, Rhind papyrus, Carl Gauss, Leonhard Euler

Choice 3: Choose a discussion question or theme from the unit and write an essay on it. Religion & Math, Eastern vs. Western culture & math, Human Intuition for math, human acquisition of knowledge, or a theme of your own choosing with approval of the teacher.

3-4 pages, at least 3 sources other than Wikipedia,

expectations of research, work, and plagiarism.

students view/share their final products on our website, somehow.

Zero: Biography of a Dangerous Idea p. 68 - evolution of our numerals image series of 7 youtube videos re: different mathematical models from ancient to modern times.

NOTES FOR NEXT YEAR: - give out big idea questions before watching videos; - watch all videos - give out ppt notes and big idea questions for each day of watching; - kids keep reading journal? - give out outline at start of unit.