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Exploring Numeration and Computation: From Ancient Systems to Modern Fun

Dive into the world of numeration and computation as we explore ancient number systems like the Babylonians, Romans, and Mayans, and their influence on modern mathematics. Discover the principles of additive and positional number systems, and learn about unique counting methods in various cultures. Engage with interactive activities that illustrate concepts like "three-ness" and collective counting. This exploration provides a rich understanding of how numeration has evolved and its applications in practical scenarios, ensuring a fun and educational experience for all.

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Exploring Numeration and Computation: From Ancient Systems to Modern Fun

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Presentation Transcript

  1. Chapter 3 Numeration And Computation

  2. 5

  3. America’s Funniest Home Videos • Tally’s on a staff • Pebbles in a pouch • Abstract idea of “three-ness” evolved • New Guinea • “iya” – one • “rarido” – two • Additive Number System

  4. Count! • Fe • Fi • Fo • Fum • Fiddle • Fruit • Folks • Fist

  5. Fe fiddle-fiddle-fe Fi fiddle-fiddle-fi Fo fiddle-fiddle-fo Fum fiddle-fiddle-fum Fiddle fiddle-fiddle-fiddle Fiddle-fe fiddle-fiddle-fiddle-fe Fiddle-fi fiddle-fiddle-fiddle-fi Fiddle-fo fiddle-fiddle-fiddle-fo Fiddle-fum fiddle-fiddle-fiddle-fum Fiddle-fiddle fiddle-fiddle-fiddle-fiddle

  6. Fe fi-fiddle-fe Fi fi-fiddle-fi Fo fi-fiddle-fo Fum fi-fiddle-fum Fiddle fo-fiddle Fiddle-fe fo-fiddle-fe Fiddle-fi fo-fiddle-fi Fiddle-fo fo-fiddle-fo Fiddle-fum fo-fiddle-fum Fi-fiddle fum-fiddle

  7. Written Number System

  8. Additive Number System M M M N N N N ^ ^ ^ ^ l l l M M N N N l l l l

  9. Use a Multiplier M M M N N N N ^ ^ ^ ^ l l l M M N N N l l l l

  10. Positional Number System M M M N N N N ^ ^ ^ ^ l l l M M N N N l l l l

  11. Egyptian Number SystemPage 144 • Additive System

  12. Million Man! • How Much is Million by David M. Schwartz • www.davidschwartz.com • If You Made a Million • The Magic of a Million Activity Book • Millions to Measure • If You Hopped Like a Frog • G is for Googol

  13. Millions Poster • Collecting a Million Pennies • Sharing “Millions” with the Elementary School • Collecting a Million Pennies in High School • Spending a Million Dollars

  14. Babylonian Number System

  15. Babylonian Number System

  16. Babylonian Number System < < < l l l l < < < < < < l l l l l l l < < l l l l < < < < l l l l l

  17. Mayan Number SystemPage 146 • As early as 200 BC, these resourceful people had developed a remarkably advanced society. • They were the first Native Americans to develop a system of writing and to manufacture paper and books. • Their calendar was very accurate, with a 365 day year and a leap year every fourth year.

  18. Mayan Number System

  19. Mayan Number System

  20. Roman Numerals

  21. Roman Numerals • Addition Principle • Subtraction Principle • The only things that can be subtracted are 1, 10, and 100 (I, X, and C). • You show subtraction by placing a smaller symbol to the left of a larger symbol. You may only subtract one symbol at a time. • You will write one place value at a time.

  22. Roman Numerals • Subtraction Principle • I can only be subtracted from V and X • X can only be subtracted from L and C • C can only be subtracted from D and M

  23. I II III IV (the one that comes before 5) V VI (the one that comes after 5) VII VIII IX (the one that comes before 10) X

  24. I X II XX III XXX IV XL V L VI LX VII LXX VIII LXXX IX XC X C

  25. I X C II XX CC III XXX CCC IV XL CD V L D VI LX DC VII LXX DCC VIII LXXX DCCC IX XC CM X C M

  26. Write 1469 using Roman Numerals

  27. Write MMMCMXCIX as a Hindu Arabic Number.

  28. Multiplication Principal • 649 =

  29. Multiplication Principal • 649 = DCXLIX • 649,000 = DCXLIX

  30. Multiplication Principal • 649 = DCXLIX • 649,000 = DCXLIX • 649,428 =

  31. Multiplication Principal • 649 = DCXLIX • 649,000 = DCXLIX • 649,428 = DCXLIXCDXXVIII • 649,000,000 =

  32. Multiplication Principal • 649 = DCXLIX • 649,000 = DCXLIX • 649,428 = DCXLIXCDXXVIII • 649,000,000 = DCXLIX

  33. Hindu-Arabic NumbersPage 149

  34. Homework QuestionsChapter 2

  35. Venn Diagram Lab Answers

  36. Test - Chapter 2 • http://mcis.jsu.edu/faculty/mjohnson/ms133r2.html

  37. Day 2

  38. Set Theory Test

  39. Base 10 Number System 10 digits: {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}

  40. Base 10 Number System hundredten millions thousands thousands thousands hundreds tens ones ____ , ____ ____ ____ , ____ ____ ____

  41. Base 10 Number System hundred ten hundredten millions millions millions thousands thousands thousands hundredstensones _________ , ______ ___ , _________

  42. Ones • Tens • Hundreds • Thousands • Ten Thousands • Hundred Thousands

  43. Millions • Ten Millions • Hundred Millions • Billions • Ten Billions • Hundred Billions

  44. Trillions • Ten Trillions • Hundred Trillions • Quadrillions • Ten Quadrillions • Hundred Quadrillions

  45. Quintillions • Ten Quintillions • Hundred Quintillions • Sextillions • Ten Sextillions • Hundred Sextillions

  46. Septillions • Ten Septillions • Hundred Septillions • Octillions • Ten Octillions • Hundred Octillions

  47. Nonillions • Ten Nonillions • Hundred Nonillions • Decillions • Ten Decillions • Hundred Decillions

  48. Googol 10,000,000,000,000,000,000,000,000, 000,000,000,000,000,000,000,000,000, 000,000,000,000,000,000,000,000,000, 000,000,000,000,000,000,000

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