Making Math: A Hands on History Beth Powell
|
|
- Melissa Burke
- 5 years ago
- Views:
Transcription
1 Making Math: A Hands on History Beth Powell My City School, San Francisco, CA bethciis@yahoo.com
2 Why Study the History of Math Full of Epic Failures Creates a Sense of Wonder Connections, Integration, and Creativity
3 Keep in Mind Inquiry and Exploration over Lecture Hands-on and Creative Engagement and Critical Thinking over Memorization
4 Ideas for Study People, Places, Mathematical Objects, History of a Number Students Can Pick Topic and Design a Lesson History of Math Fair Integrate with Current History Topics
5 Materials Babylonia: Clay and a Stylus or Reed Egypt: Papyrus and Soap Bars Guatemala: Sticks and Stones & Book Making Materials
6 Prehistoric Math Unit 1
7 Bruniquel Cave France 176,000 years old
8 Lebombo Africa 43,000 Years Old
9 Ishango Bone Africa 20,000 years old
10 Sketch of Lebombo Bone Sketch of Ishango Bone
11 Tally Systems Make Up Your Own!
12 Notes France What shapes do you notice? What do you think they used to make those shapes? Is this above ground or below ground? What is significant about where this was made? What do you think they did here? Africa What do you think these were made of? Why? What did you notice about the markings? What do you think they were used for? Timeline: What year (approximately) were each of these from?
13 Prehistoric Math Unit 2
14 1 2 3 Where South Africa Purpose Calendar? Age- 75,000 Years Old - Oldest Man Made Structure? Where East Bay, CA Purpose Unknown Age Unknown, Native Americans didn t build them? Where Syria to Saudi Arabia, Similar ones in Peru Purpose Ritual? Age Unknown - Prehistoric to 2000 years old Where Scotland Purpose Decoration? Age - Prehistoric Where Southern Africa Purpose Energy Grid? Age 180,000 Years Old Where - Jordan Purpose Unknown Age Prehistoric?
15 Sketch of Syrian Wheels Sketch of Jordan Circle
16 Notes Shapes What shapes do you notice? What do you think they used to make those shapes? Which locations would be easy to figure out the shape in person? Which shapes would be harder to notice from the ground? Purpose Why don t we know what all of these were used for? Why would people need a calendar? Any ideas what else these might be used for?
17 Prehistoric Math Unit 3
18 çatalhöyük Mound, Turkey Approximate Date: 7000 BC Lascaux Cave, France Approximate Date: 15,000 BC Chauvet Cave, France Approximate Date: 32,000 BC
19 Sketch of a Cave Drawing
20 Notes Drawings What animals do you see? Why do you think people drew these? Which cave has the oldest drawings? Origin of Numbers Which do you think came first paintings or numbers? Why? How would you describe the number of animals you see without using numbers? Without language? Guess which numbers are hard-wired into our brains.
21 Ancient Math: Babylonia Unit 1
22 Ancient Math: Civilization What do you think this is? What do you think it is made of? What common shapes do you see? What do you think they did about it?
23 Ancient Math Unit 1
24 Circle Time!! Small Circle: Diameter (D): Circumference (C): C divided by D: Medium Circle: Diameter (D): Circumference (C): C divided by D: Big Circle: Diameter (D): Circumference (C): C divided by D:
25 Find the Average of Your C/D Measurement Small Circle: C divided by D Medium Circle: C divided by D Big Circle: C divided by D Add those together Divide that by 3 You just found an approximate value of...
26 Approximate Values of Pi add your name to the list! BC Babylonia BC Egypt BC Greece to Archimedes BC China and Zu Chongzhi
27 Notes Circle Time! What two parts of the circle did you use to find pi? What did you do with those parts to find pi? What is the number that is always the same no matter how big or small a circle is? Pi Which place came up with the first calculation of pi that we know of? Who came up with the best approximation (the closest to the actual number) of pi? How many years did it take to get from the first approximation to the best approximation?
28 Ancient Math: Babylonia Unit 2
29 Ancient Math: Farming Once people settled down and starting farming, they had extra food that they needed to store. They built places where everyone stored their food together. Play the food storage game. What kind of problem did people need to solve? What do you think they did about it?
30 Olive Oil Stored in Jars and Amphora Oldest Known: 5800 BC Wine and Beer Stored in Amphora Oldest Known: 6000 BC Grains: Wheat, Barley, Amaranth Stored in Silos Oldest Known: 9500 BC
31 Notes Growing Food How did farming create the need for math? What type of information did people need to record? Why was it important to keep track of extra food? What was one kind of storage system people used?
32 Ancient Math: Babylonia Unit 3
33 Ancient Math: Clay Tokens What do you think these pictures represent? Give students time to discuss. Picture 1: Clay tokens each token represents a specific crop. For instance, if you stored 1 bushel of wheat, you d get 1 triangular token. We don t know for sure what each token represented. Picture 2: What would happen if you d tried to keep track of all these clay tokens? So people made an envelope. Picture 3: They finally figured out that they could make impressions of the tokens on the outside of the envelope so that they didn t have to break the envelope open to see what was inside. Guess how long it took to figure that out? About two thousand years! And they still put the tokens inside. Picture 4: Eventually, they realized they could just make markings in clay and get rid of the tokens. This eventually led to the first number system. What problem did they solve?
34
35 Notes Clay Tokens, Envelopes, and Tablets What were the tokens in Picture 1 used for? What does Picture 2 show? What was the big leap from Picture 2 to Picture 3? What does Picture 4 show?
36 Ancient Math: Babylonia Unit 4
37 Ancient Math: Base Sixty Ancient Babylonians were the first to divide the circle into 360 degrees They also gave us our 60 minutes and 60 seconds for time. What incredibly useful tool is made from a circle? They may have been among the first to use the wheel. Circular divisions were an important tool for sea explorations What shape was critical for the development of civilization?
38 What Numbers Are These?!?
39
40 Notes Write the numbers in Cuneiform on the tablets: First Number System!!! How many symbols are there? Does the position of the symbols matter? What did the Babylonian s use to write math? What type of problems and benefits do you see with this number system?
41 Ancient Math: Egypt Unit 1
42 Ancient Math: Egypt What do you know about Egypt? Pyramids, hieroglyphs, papyrus Let s see if you can figure out their numbers! Small group, then large group discussion. Use papyrus to create a project. Discuss what it is if needed. Use soap (instead of stone) to carve a project.
43 What Numbers Are These?!?
44 What numbers can you find? Name that number!
45 Notes What numbers can you write using hieroglyphs? 9: 47: 437: 1,573: Another Number System!!! How many symbols are there? Does the position of the symbols matter? 13,727: What did the Egyptians use to write or record math? 234,567: 1,273,645: What type of problems and benefits do you see with this number system?
46 Ancient Math: Egypt Unit 2
47 . Ancient Math: Egypt To find the product of 13 x 11, in one column, start from 1, doubling in each row until there are enough numbers in that column to add up to the number Then double the second number. Give students time to discover what to do from here. Add only the numbers in the left column that are needed and then add up the corresponding right column Example: 8, 4, and 1 add up to 13 so ( ) is the answer. 13 x X 11=143
48 One of the better preserved ancient scrolls from Egypt is the Ahmes Papyrus also known as the Rhind papyrus is from the 17 century BC. Its scribe (known only as Ahmes) had copied it from a school text which, he reported, had been a standard for nearly 400 years before his own time. It has tables to help a student with multiplication and division, showing methods that are very different from ours, but fascinating and (dare I say it?) useful even today. "One of the many puzzles on the Rhind papyrus: Seven houses contain seven cats. Each cat kills seven mice. Each mouse had eaten seven ears of grain. Each ear of grain would have produced seven hekats of wheat. What is the total of all of these?"
49 Multiplying Egyptian Style 11 X X X 15
50 Multiplying Egyptian Style 13 X X X 29
51 Ancient Math: Guatemala Unit 1
52 . Ancient Math: Guatemala Use sticks, rocks, and cacao beans to create a number system They had a very complex calendar that used another number system. Much of the history of the Maya was lost because a Catholic priest burned their manuscripts thinking it showed demons. See if you can figure out the numbers in the picture? Can you find any numbers? Teacher helps students discover the numbering system. For older students, introduce numbers above 20.
53 What numbers can you find?
54 MAYAN BOOKS Just as with modern books, paper was the most common material out of which codices (books) were made. The Maya made paper from the inner bark of fig trees. The large codices were folded like screens, covered with layer of starch, and then with a thin, white, paste. Subjects varied from religion, astronomy, agricultural cycles and history to prophecies. One or more themes occupied each page and in all cases, the contents related to the spiritual world.
55 Notes LARGE NUMBERS Rewrite using Mayan numbers: One More Number System!!! How many symbols are there? Does the position of the symbols matter? What number did the Maya used that the Egyptians and Babylonians didn t? What did the Maya use to write or record math? 368 What type of problems and benefits do you see with this number system? 567
56 Ancient Math: Babylonia Extra Info
57 YBC 7289 There are a number of remarkable facts about the tablet, which is one of the very oldest mathematical diagrams extant. Given our vast ignorance about the era, speculation is inevitable... We [may be] looking here at the very origins of mathematical reasoning. The Babylonians, unlike the early Greeks much later on, interpreted ratios of lengths as numbers. They weren't just finding a good (very good) approximation to the ratio of a diagonal to a side of a square. They knew that the ratio of the diagonal of a square to a side was a number whose square was 2. They possessed an algorithm for finding approximations to the square root of 2.
58 Mathematics Exercise Tablet Geometric Patterns Language: Akkadian Babylonian 1700 BC This large fragment is from a tablet containing mathematics exercises and questions, written in Akkadian. It dates back to around 1700 BC. The text in the lower right corner says: "The side of the square equals one. I have drawn four triangles in it. What is the surface area? Babylonian schools would train young scribes to learn geometry because they were required to draw up accurate deeds and calculate agricultural yields. This Tablet contained the student s geometry lesson, the measure of weight, and the medical tract that offered remedies for a variety of illnesses.
59 "This is one of the first clear examples of multiplication known to man," says Robert K. Englund, co-principal investigator at the Cuneiform Digital Library Initiative at University of California at Los Angeles. Clay tablet from ~3,100 BC showing how Babylonian landowners kept accounts. The face of the tablet is divided into five fields, each referring to a single parcel of agricultural land. Inside each field are symbols giving surface measurements of the parcels.
60 Ancient Math: Egypt Extra Info
61 . Ancient Math: Fractions Story of the Eye of Horus Egyptians only wrote fractions using unit fractions: 1/2, 1/4, 1/8, 1/16, 1/32 What do you notice about these fractions? How can you write 5/8 using fractions?
62 The Eye of Horus The Eye of Horus represents the combination of a human eye, with the cheek markings of a falcon. It was considered a powerful symbol for imparting protection and life. 2 parts 4 parts 8 parts Can you divide each circle into equal parts?
63 The Eye of Horus Divide each circle into equal parts. Shade in some of the parts in each circle. Label the fraction you created in each circle.
64
65
Mathematics in Ancient Egypt. Amber Hedgpeth. June 8, 2017
Mathematics in Ancient Egypt Amber Hedgpeth June 8, 2017 The culture of ancient Egypt is rich and fascinating, with its pharaohs, pyramids, and life around the Nile River. With a rich history of massive
More informationNumbers and Counting. Number. Numbers and Agriculture. The fundamental abstraction.
Numbers and Counting Number The fundamental abstraction. There is archaeological evidence of counters and counting systems in some of the earliest of human cultures. In early civilizations, counting and
More informationOh No! More on Fractals. The Koch Family of Curves. Unary and Binary. Homework #1 is due today at 11:59pm Give yourself sufficient time to make PDF
Great Theoretical Ideas In Computer Science Danny Sleator Lecture 3 CS 15-251 Jan 19, 2010 Spring 2010 Carnegie Mellon University Unary and Binary Oh No! Homework #1 is due today at 11:59pm Give yourself
More informationAMA1D01C Egypt and Mesopotamia
Hong Kong Polytechnic University 2017 Outline Cultures we will cover: Ancient Egypt Ancient Mesopotamia (Babylon) Ancient Greece Ancient India Medieval Islamic World Europe since Renaissance References
More informationGrade 6 Math Circles. Ancient Mathematics
Faculty of Mathematics Waterloo, Ontario N2L 3G1 Introduction Grade 6 Math Circles October 17/18, 2017 Ancient Mathematics Centre for Education in Mathematics and Computing Have you ever wondered where
More informationStudy Guide for Exam 1
Study Guide for Exam 1 Math 330: History of Mathematics October 2, 2006. 1 Introduction What follows is a list of topics that might be on the exam. Of course, the test will only contain only a selection
More informationGrade 6 Math Circles November 1 st /2 nd. Egyptian Mathematics
Faculty of Mathematics Waterloo, Ontario N2L 3G Centre for Education in Mathematics and Computing Grade 6 Math Circles November st /2 nd Egyptian Mathematics Ancient Egypt One of the greatest achievements
More informationMeasuring the Gardens of Eden, by Jenia Tevelev
Measuring the Gardens of Eden, by Jenia Tevelev 1 A map of the area around Gasur, near Kirkuk in northern Iraq, drawn up some time in the Sargonic period (2200 BCE). The central area, below the Rahium
More informationEGYPTIAN MATHEMATICS
EGYPTIAN MATHEMATICS TIMELINE Archaic Period (3100-2650 BC) Old Kingdom (2650-2134 BC) Large pyramids built; rich and productive period 1 st Intermediate Period (2200-2050) BC Chaotic Middle Kingdom (2050-1640
More informationEgyptian Mathematics
Egyptian Mathematics Dr. Carmen Bruni David R. Cheriton School of Computer Science University of Waterloo November 1st, 2017 Three Part Series Egyptian Mathematics Diophantus and Alexandria Tartaglia,
More informationDIRECTIONS: Complete each of the enclosed activities and then use what you learn along with prior knowledge to fill in the outline below:
DIRECTIONS: Complete each of the enclosed activities and then use what you learn along with prior knowledge to fill in the outline below: I. Geography of Sumer A. Located in modern-day B. Between two rivers
More informationEGYPTIAN RELIGION. Section 3
EGYPTIAN RELIGION Section 3 Religion was an important part of daily life in ancient Egypt. Egyptians believed their gods and goddesses controlled the workings of nature. They built temples to honor their
More informationπ is a mathematical constant that symbolizes the ratio of a circle s circumference to its
Ziya Chen Math 4388 Shanyu Ji Origin of π π is a mathematical constant that symbolizes the ratio of a circle s circumference to its diameter, which is approximately 3.14159265 We have been using this symbol
More informationI named this section Egypt and Babylon because the surviving documents from Egypt are older. But I m going to discuss Babylon first so sue me.
I. Ancient Times All the major ancient civilizations developed around river valleys. By 000 BC, there were civilizations thriving around the Nile (Egypt), the Tigris and Euphrates (Babylon), the Ganges
More informationGreece In 700 BC, Greece consisted of a collection of independent city-states covering a large area including modern day Greece, Turkey, and a multitu
Chapter 3 Greeks Greece In 700 BC, Greece consisted of a collection of independent city-states covering a large area including modern day Greece, Turkey, and a multitude of Mediterranean islands. The Greeks
More informationMesopotamia Here We Come
Babylonians Mesopotamia Here We Come Chapter The Babylonians lived in Mesopotamia, a fertile plain between the Tigris and Euphrates rivers. Babylonian society replaced both the Sumerian and Akkadian civilizations.
More informationBabylon/Mesopotamia. Mesopotamia = between two rivers, namely the Tigris and Euphrates.
Babylon/Mesopotamia Mesopotamia = between two rivers, namely the Tigris and Euphrates. Civilization dates from before 3000 BCE covering several empires with varying borders: Sumerians, Akkadians, Babylonians,
More informationMesopotamian Writing Mesopotamian Mathematics Conclusion. Mesopotamia. Douglas Pfeffer
n Writing n Mathematics Table of contents n Writing n Mathematics 1 n Writing 2 n Mathematics 3 Outline n Writing n Mathematics The Era and the Sources Cuneiform Writing 1 n Writing 2 n Mathematics 3 n
More informationChapter 3 The Science of Astronomy
Chapter 3 The Science of Astronomy 3.1 The Ancient Roots of Science Our goals for learning: In what ways do all humans employ scientific thinking? How did astronomical observations benefit ancient societies?
More informationMATHEMATICS AND ITS HISTORY. Jimmie Lawson
MATHEMATICS AND ITS HISTORY Jimmie Lawson Spring, 2005 Chapter 1 Mathematics of Ancient Egypt 1.1 History Egyptian mathematics dates back at least almost 4000 years ago. The main sources about mathematics
More informationLife and Death in Ancient Egypt
Level 4-5 Life and Death in Ancient Egypt Diana Ferraro Summary This book is about the lives of the ancient Egyptians and how they prepared for death. Contents Before Reading Think Ahead... 2 Vocabulary...
More informationMaya Achievements WRITING
Maya Achievements WRITING The Maya used the most advanced system of writing of the ancient Americans. They probably borrowed the idea of picture writing from another ancient American group known as the
More informationAfrican Invention of Mathematics. Egyptian Way of Calculating the Circle
African Invention of Mathematics and the Egyptian Way of Calculating the Circle drafts, written for a conference and a journal, illustrated 1979-2016 by Franz Gnaedinger 1 African Invention of Mathematics
More informationLIFE IN ANCIENT EGYPT LESSON 2 PG. 191
LIFE IN ANCIENT EGYPT LESSON 2 PG. 191 AGENDA 2/18 Finish #12 on Map Collect Map Lesson 1 Recap Lesson 2 Read + Notes (Graphic Organizer) HW: Read pg. 196-198;Finish Blue Questions (2) **Quest on Wednesday
More informationUpon Whose Shoulders We Stand: A History of Astronomy Up to 200 A.D. Dick Mallot 3/17/2005
Upon Whose Shoulders We Stand: A History of Astronomy Up to 200 A.D. Dick Mallot 3/17/2005 Who were these ancient astronomers? Where did real astronomy begin? What did we know about astronomy 2000+ years
More informationThe Ancient World. Chapter 1 The Beginnings of Human Society. What historical accomplishments is each civilization known for?
Chapter 1 The Beginnings of Human Society Chapter 1-Guiding Questions: What historical accomplishments is each civilization known for? How did physical geography affect the growth of ancient civilizations
More informationCHAPTER (multiply by 10) 2 10 (double first line) 4 20 (double third line) 8 40 (double fourth line) (halve first line)
CHAPTER 1 1. The answers are given in the answer section of the text. For the Egyptian hieroglyphics, 375 is three hundreds, seven tens and five ones, while 4856 is four thousands, eight hundreds, five
More informationIn Ancient Egypt, precious materials like gold and ivory were usually used in making
Question 1 Ancient Egyptian architecture is characterized by A. mud bricks held together with a limestone mortar. B. giant blocks of sandstone carved into large buildings. C. mostly wood construction made
More informationMath Round. Any figure shown may not be drawn to scale.
Indiana Academic Super Bowl Math Round 2019 Coaches Practice A Program of the Indiana Association of School Principals Students: Throughout this round we will be pronouncing mathematic symbols and concepts
More informationHow Long Does it Take to Complete the Lapbook? SAMPLE PAGE
Keep in mind that children of the same age can have very different academic and motor skills. Some children may have trouble writing in some of the smaller spaces of this lapbook. If this describes your
More informationMath Number 842 Professor R. Roybal MATH History of Mathematics 24th October, Project 1 - Proofs
Math Number 842 Professor R. Roybal MATH 331 - History of Mathematics 24th October, 2017 Project 1 - Proofs Mathematical proofs are an important concept that was integral to the development of modern mathematics.
More informationWhat is proof? Lesson 1
What is proof? Lesson The topic for this Math Explorer Club is mathematical proof. In this post we will go over what was covered in the first session. The word proof is a normal English word that you might
More informationLecture 1. The Dawn of Mathematics
Lecture 1. The Dawn of Mathematics The Dawn of Mathematics In ancient times, primitive people settled down in one area by water, built homes, and relied upon agriculture and animal husbandry. At some point,
More informationComparing and Contrasting Ancient Number Systems
By Mark Swanson Comparing and Contrasting Ancient Number Systems Question: How are ancient number systems and symbols of different civilizations similar and different? Why this Topic?: As a social studies
More informationHistory of π. Andrew Dolbee. November 7, 2012
History of Andrew Dolbee November 7, 01 The search for the ratio between a circle's circumference and its diameter, known as PI(), has been a very long one; appearing in some of the oldest mathematical
More informationLesson 32. The Grain of Wheat. John 12:20-26
L i f e o f C h r i s t from the gospel of J o h n Lesson 32 The Grain of Wheat John 12:20-26 Mission Arlington Mission Metroplex Curriculum 2010 Created for use with young, unchurched learners Adaptable
More informationName Period Date. GEO2.2: Area of Circles Derive the area formula for circles. Solve application problems that involve areas of circles.
Name Period Date GEOMETRY AND MEASUREMENT Student Pages for Packet 2: Circles GEO2.1 Circumference Use multiple representations to explore the relationship between the diameter and the circumference of
More informationHistory is not the accumulation of events of every kind which happened in the past. It is the science of human societies. Fustel de Coulanges
Delving into the past History is not the accumulation of events of every kind which happened in the past. It is the science of human societies. Fustel de Coulanges Photocopiable Rediscovering the past
More informationAncient Astronomy. Kickin it old school
Ancient Astronomy Kickin it old school Ancient Egypt Ancient Egyptians Only basic nocturnal timekeeping Yearly calendar secondary to Nile River Floods Sometimes needed a 13 th leap month Regulated by the
More informationMOR TIME TEACHERS. ONCE UPON A TIME Activity Overview BIG IDEA
MOR TIME 04 Activity Overview BIG IDEA OBJECTIVE BACKGROUND The geologic time scale can be challenging for students to understand. This activity explores how scientists divide the Earth s long history
More informationAncient Egypt The Pyramids
Non-fiction: Ancient Egypt The Pyramids Ancient Egypt The Pyramids Illustration by Rebekah Hanousek-Monge Most of us have seen pictures of the great pyramids of Egypt. Experts believe that these pyramids
More informationHistory EC LE UE MS. Knows the names and order of the Seasons of the Year and science behind it
History EC LE UE MS Time and Timelines : awareness of how the universe and life came to be and his/her place on the continuum. The child discovers interests, makes connections and draws inferences about
More informationDesigner(s): Emily Potts. Show-Me Standards
Designer(s): Emily Potts Title: The Great Pyramids Topic: Ancient Egypt Subject: History, Anthropology, Geography Grade(s): 6 th Show-Me Standards Knowledge Standards: Communication Arts 6: Participating
More informationMath Fundamentals for Statistics I (Math 52) Unit 7: Connections (Graphs, Equations and Inequalities)
Math Fundamentals for Statistics I (Math 52) Unit 7: Connections (Graphs, Equations and Inequalities) By Scott Fallstrom and Brent Pickett The How and Whys Guys This work is licensed under a Creative Commons
More informationGeography of the Americas
STATION ACTIVITY Geography of the Americas NAME: Directions: Using each station s text and maps, complete this graphic organizer. Olmec Mayans Aztecs Incas Where was this people group located? (include
More informationEuclidean Geometry. The Elements of Mathematics
Euclidean Geometry The Elements of Mathematics Euclid, We Hardly Knew Ye Born around 300 BCE in Alexandria, Egypt We really know almost nothing else about his personal life Taught students in mathematics
More informationNumber Systems. There are 10 kinds of people those that understand binary, those that don t, and those that expected this joke to be in base 2
Number Systems There are 10 kinds of people those that understand binary, those that don t, and those that expected this joke to be in base 2 A Closer Look at the Numbers We Use What is the difference
More informationTHE GRID SYSTEM. System of imaginary lines that give the exact position of a place on Earth
WORLD GEOGRAPHY THE GRID SYSTEM System of imaginary lines that give the exact position of a place on Earth LATITUDE Imaginary lines that travel horizontally around the earth measuring North and South Latitude
More informationPREVIEW 31. Teachers Curriculum Institute The Legacy of Ancient Greece 205
PREVIEW 31 Think about an event you would like to start, an invention you would like to create, or a discovery you would like to make that would be used by future generations. For example, you might like
More informationOrigins of Modern Astronomy
PHYS 1411 Introduction to Astronomy Origins of Modern Astronomy Chapter 4 Topics in Chapter 4 Chapter 4 talks about the history of Astronomy and the development of the model of the solar system. Brief
More informationCO480. Lecture 7. Alain Gamache. May 25th, University of Waterloo
CO480 Lecture 7 Alain Gamache University of Waterloo May 25th, 2017 Today s Lecture The problem: The division of loaves The place: Antic Egypt Egyptian Fractions The division of loaves Share 9 loaves of
More informationMayan Mathematics. Patrick Brown. History of Math
Mayan Mathematics Patrick Brown History of Math 2 Professor Van Opstall 8 July 2008 The Mayan civilization began around 2000 BCE in the southern region of what is now Mexico. At this time what is currently
More informationTraces and Ancient Egypt
August 26, 2018 Table of contents 1 2 Concepts and Relationships Early Number Bases Spacial Relationships Outline 1 2 Concepts and Relationships Early Number Bases Spacial Relationships Concepts and Relationships
More informationIndiana Academic Super Bowl. Math Round Senior Division Invitational 1. A Program of the Indiana Association of School Principals
Indiana Academic Super Bowl Math Round 2019 Senior Division Invitational 1 A Program of the Indiana Association of School Principals Students: Throughout this round we will be pronouncing mathematic symbols
More informationChapter 1 Primitive Man
Chapter 1 Primitive Man Oh, So Mysterious Egyptian Mathematics! Lewinter and Widulski The Saga of Mathematics 1 Hunter/gatherers Counted Simple Notches on wolf bone Groups of pebbles and stones Development
More informationChapter 0. Introduction. An Overview of the Course
Chapter 0 Introduction An Overview of the Course In the first part of these notes we consider the problem of calculating the areas of various plane figures. The technique we use for finding the area of
More informationAstronomical Distances. Astronomical Distances 1/30
Astronomical Distances Astronomical Distances 1/30 Last Time We ve been discussing methods to measure lengths and objects such as mountains, trees, and rivers. Today we ll look at some more difficult problems.
More informationExploring the Rhind Papyrus
Exploring the Rhind Papyrus Dana Hartnett and Lauren Koepfle, Miami University In this article, we introduce the ancient Rhind papyrus. The Rhind papyrus serves as the foundation of mathematics today as
More informationLinear Functions, Equations, and Inequalities
CHAPTER Linear Functions, Equations, and Inequalities Inventory is the list of items that businesses stock in stores and warehouses to supply customers. Businesses in the United States keep about.5 trillion
More information21st Century Global Learning
21st Century Global Learning A focus for 7th grade is on the ever-increasing global interactions in society. This focus includes a study of various societies and regions from every continent. We have already
More informationExam 1 is Feb. 1 (next Tuesday) This will cover everything we have done so far Earth motions The celestial sphere and observations from Earth Seasons
Ancient Astronomy Exam 1 is Feb. 1 (next Tuesday) This will cover everything we have done so far Earth motions The celestial sphere and observations from Earth Seasons Phases of the Moon Eclipses Ancient
More informationName: Date: Period: #: Chapter 1: Outline Notes What Does a Historian Do?
Name: Date: Period: #: Chapter 1: Outline Notes What Does a Historian Do? Lesson 1.1 What is History? I. Why Study History? A. History is the study of the of the past. History considers both the way things
More information1.2 MESOPOTAMIA. 10 Chapter 1 Egypt and Mesopotamia
10 Chapter 1 Egypt and Mesopotamia not surprising that these calculated angles closely approximate the actual angles used in the construction of the three major pyramids at Giza. The Moscow Papyrus, however,
More informationWritten in Stone UNIT 2 WEEK 1. Read the article Written in Stone before answering Numbers 1 through 5. Weekly Assessment Unit 2, Week 1 Grade 6 61
Read the article Written in Stone before answering Numbers 1 through 5. UNIT 2 WEEK 1 Written in Stone People need to communicate. The earliest human beings most likely communicated with sounds and gestures.
More informationIntroduction to Trigonometry: Grade 9
Introduction to Trigonometry: Grade 9 Andy Soper October 6, 2013 This document was constructed and type-set using P C T E X (a dielect of L A T E X) 1 1 Before you start 1.1 About these notes. These notes
More informationAlgebra I. Slide 1 / 178. Slide 2 / 178. Slide 3 / 178. The Number System & Mathematical Operations. Table of Contents
Slide 1 / 178 Slide 2 / 178 Algebra I The Number System & Mathematical Operations 2015-11-02 www.njctl.org Table of Contents Slide 3 / 178 Review of Natural Numbers, Whole Numbers, Integers and Rational
More informationNazca Lines Famous Places
PRE-READING A. WARM-UP QUESTIONS 1. Have you heard of the Nazca Lines? If yes, what are they? If no, what do you think they are, based on the picture? 2. Where are the Nazca Lines located? If you don t
More informationFoSSil Puzzler (1 Hour)
FoSSil Puzzler (1 Hour) Addresses NGSS Level of Difficulty: 2 Grade Range: 3-5 OVERVIEW Students will examine and sketch various trace fossils from an unknown creature and then construct an image of the
More informationAstronomical Distances
Astronomical Distances 13 April 2012 Astronomical Distances 13 April 2012 1/27 Last Time We ve been discussing methods to measure lengths and objects such as mountains, trees, and rivers. Astronomical
More informationMayan Math. Extra Credit Grade 6 mathematics Mr. Livingood and Mrs. Dettlinger. Extra Credit: Part 1 MAYAN AND ROMAN MATH SYMBOLS
Extra Credit Grade 6 mathematics Mr. Livingood and Mrs. Dettlinger Extra Credit: Part 1 MAYAN AND ROMAN MATH SYMBOLS Objective: Students will: explore how the Mayan and Roman people used mathematical symbols
More informationThe Timekeepers. Staging Divide the staging area into two parts: the watchmaker s shop and the land of dreams. Characters:
The Timekeepers An old watchmaker falls asleep at his workbench and has a dream. In the dream, people from the distant past appear to tell him about how they kept time. Staging Divide the staging area
More information18.2 Earth Cycles Days and years Calendars Years and days Leap years Calendars throughout human history 20,000 years ago. 7,000 BC. 4,000 BC.
18.2 Reading 18.2 Earth Cycles Do you ever wonder where our calendar comes from? Or why the Moon gradually changes its shape? Or why we have seasons? The answers have to do with the relative positions
More informationAlgebra I The Number System & Mathematical Operations
Slide 1 / 178 Slide 2 / 178 Algebra I The Number System & Mathematical Operations 2015-11-02 www.njctl.org Slide 3 / 178 Table of Contents Review of Natural Numbers, Whole Numbers, Integers and Rational
More informationEgyptian Fractions: Part I
Egyptian Fractions: Part I Prepared by: Eli Jaffe October 8, 2017 1 Cutting Cakes 1. Imagine you are a teacher. Your class of 10 students is on a field trip to the bakery. At the end of the tour, the baker
More informationStudent Outcomes. Lesson Notes. Classwork. Opening Exercises 1 3 (5 minutes)
Student Outcomes Students calculate the decimal expansion of using basic properties of area. Students estimate the value of expressions such as. Lesson Notes For this lesson, students will need grid paper
More informationFundamentals of Mathematics I
Fundamentals of Mathematics I Kent State Department of Mathematical Sciences Fall 2008 Available at: http://www.math.kent.edu/ebooks/10031/book.pdf August 4, 2008 Contents 1 Arithmetic 2 1.1 Real Numbers......................................................
More informationAfrican Women and the Origin of Mathematics
African Women and the Origin of Mathematics Lesson 1 Vocabulary Words: archaeology, excavation, radiocarbon dating, lunar The Ishango Bone In the late 1950s, a Belgian archaeologist named Jean de Heinzelin
More informationHistory of Math For the Liberal Arts CHAPTER 2. Egyptian Mathematics. Lawrence Morales. Seattle Central Community College
1 2 3 4 History of Math For the Liberal Arts 5 6 CHAPTER 2 7 8 Egyptian Mathematics 9 10 11 12 Lawrence Morales 13 14 15 Seattle Central Community College 2001, Lawrence Morales; MAT107 Chapter 2 - Page
More informationPACKERS PUZZLE. Teacher s Guide Getting Started. Kai Chung Tam Macau, People s Republic of China
Teacher s Guide Getting Started Kai Chung Tam Macau, People s Republic of China Purpose In this two-day lesson, students consider ways to estimate the number of spheres that will fit within a container.
More informationHistory of Geography. Origins of Geography. Natural Curiosity. Origins of Geography. Clay Tablets, Babylonia 8/29/2016 CLASSICAL GEOGRAPHY
History of Geography Prof. Anthony Grande Hunter College Geography Lecture design, content and presentation AFG 0616. Individual images and illustrations may be subject to prior copyright. Origins of Geography
More informationHandouts. CS701 Theory of Computation
Handouts CS701 Theory of Computation by Kashif Nadeem VU Student MS Computer Science LECTURE 01 Overview In this lecturer the topics will be discussed including The Story of Computation, Theory of Computation,
More information7 th Grade Algebra & Geometry Main Lesson Lesson Plan Outline
Day #1 7 th Grade Algebra & Geometry Main Lesson Lesson Plan Outline Ask students: "What do you think algebra is?" The essence of algebra is: It is the universal language of mathematics. Everywhere in
More informationText 3: Discoveries in Africa and Beyond. Topic 1: The Origins of Civilization (Prehistory B.C.E) Lesson 1: Learning About Our Past
Text 3: Discoveries in Africa and Beyond Topic 1: The Origins of Civilization (Prehistory - 300 B.C.E) Lesson 1: Learning About Our Past Discoveries in Africa and Beyond Since the 1870s, scholars have
More informationNo, not the PIE you eat.
March 14 is National Pi Day! No, not the PIE you eat. I'm talking about the mathematical constant, Pi, which is equal to approximately 3.14. 1 I wonder why Pi Day is on March 14? Here's a hint: Write March
More informationWhere, on Earth, are you?
Where, on Earth, are you? We all live on a big planet called Earth, of course. But where on Earth? And if you want to go to a different spot on Earth other than the spot you are in, how do you know which
More informationThe Origins of Mathematics. Mesopotamia
The Origins of Mathematics in Mesopotamia The ancient Egyptians made their number system more efficient by introducing more symbols. The inhabitants of Mesopotamia (our book calls them Babylonians) achieved
More informationResource and Activity Pack. Discussion questions Comprehension exercise Lesson plans Activities
Resource and Activity Pack Discussion questions Comprehension exercise Lesson plans Activities Discussion Questions 1. The ISS (International Space Station) is operated by fifteen different countries,
More informationMath in Our World. Section 4.1. Early and Modern Numeration Systems
Math in Our World Section 4.1 Early and Modern Numeration Systems Learning Objectives Define a numeration system. Work with numbers in the Egyptian system. Work with numbers in the Chinese system. Identify
More informationPatterns and relations Solving Equations Big Idea Learning Goals Essential Question Important Words
Patterns and RELATIONS Solving Equations Chapter 2 Big Idea Developing and solving equations can help me solve problems. Learning Goals I can use words to show number relationships. I can use equations
More informationLesson 7: The Mean as a Balance Point
Student Outcomes Students characterize the center of a distribution by its mean in the sense of a balance point. Students understand that the mean is a balance point by calculating the distances of the
More informationWho Loves the Sun? Iguanas!
Name Teacher Date / 5 ER.DFA2.2.R.RI.02: Identify and explain the main topic of a multiparagraph text as well as the focus of specific paragraphs within the text. Directions. Read the passage and select
More informationANCIENT EGYPTIAN MATHEMATICS
ANCIENT EGYPTIAN MATHEMATICS Searching for the Origins of Math Nida Haider University of Houston-MATH 4388 ANCEINT EGYPTAIN MATHEMATICS Searching for the Origins of Math In the study of mathematics, the
More informationKansas Archaeology Month
Activities for Discovering Prehistoric Trails TIME: 45 min. Kansas Archaeology Month Discovering Prehistoric Trails This lesson is divided into four sections: instructional goals, advanced preparation,
More informationEgyptian Fractions: Part I
Egyptian Fractions: Part I Prepared by: Eli Jaffe October 8, 2017 1 Cutting Cakes 1. Imagine you are a teacher. Your class of 10 students is on a field trip to the bakery. At the end of the tour, the baker
More informationWe are learning to describe how geography affected the growth of Mesopotamia.
Name Team/Rotation Middle East, Past and Present Learning Targets and Success Criteria We are learning to describe how geography affected the growth of Mesopotamia. We are looking for the reasons why rivers
More informationUnit 8 Practice Problems Lesson 1
Unit 8 Practice Problems Lesson 1 Problem 1 Find the area of each square. Each grid square represents 1 square unit. 17 square units. 0 square units 3. 13 square units 4. 37 square units Problem Find the
More informationA COMPARATIVE STUDY OF EARLY EGYPTIAN, BABYLONIAN AND MAYAN NUMBER SYSTEM. *K. C. Chowdhury 1 and A. Baishya 2
! """#$# A COMPARATIVE STUDY OF EARLY EGYPTIAN, BABYLONIAN AND MAYAN NUMBER SYSTEM *K. C. Chowdhury and A. Baishya!"#$"%#& '#() *+, & -. chowdhurykc@yahoo.com,skdas_jrt@yahoo.co.in (Received on: -08-;
More informationMAKE A STAR LANTERN. Learn about constellations by building a star lantern. NEMO Science Museum, ESERO NL / ESA.
MAKE A STAR LANTERN Learn about constellations by building a star lantern. NEMO Science Museum, ESERO NL / ESA Curriculum topic stars, constellations Big idea of science Earth is a very small part of the
More informationA100 Exploring the Universe: The Invention of Science. Martin D. Weinberg UMass Astronomy
A100 Exploring the Universe: The Invention of Science Martin D. Weinberg UMass Astronomy astron100-mdw@courses.umass.edu September 09, 2014 Read: Chap 3 09/09/14 slide 1 Problem Set #1: due this afternoon
More informationDave wrote to his 3 rd Grade teacher From: Dave Date: (month/date/year, time) Subject: Greeting from Egypt To: Mr./Mrs.
Worksheet 1a Dave s email to teacher (1) Dave wrote to his 3 rd Grade teacher From: Dave Date: (month/date/year, time) Subject: Greeting from Egypt To: Mr./Mrs. Dear Mr/Mrs. (teacher s last name), How
More information