1150 day 3

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1150 day 3

  1. 1. NumbersandNumberSystems
  2. 2. Numbers (as we know them) How many smileys are there? Thirteen 13 One group of ten Three singles
  3. 3. Hindu-Arabic System (what we use) •Numerals constructed from ten digits 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 •Place value based on powers of ten (base ten) 2 8 6 7 ____ ____ ____ ____ Expanded form 2867 = 2 · 1000 + 8 · 100 + 6 · 10 + 7 · 1 OR 2 · 103 + 8 · 102 + 6 · 101 + 7 · 100
  4. 4. EgyptianNumeration
  5. 5. Egyptian System •Modified tally system •No way to represent zero Page 166 1324 =
  6. 6. 1,333,331Egyptian Numbers from the Temple of Edfu
  7. 7. BabylonianNumeration
  8. 8. Babylonian System •Place value system based on groups of 60 •No way to represent zero Page 67
  9. 9. Cuneiform tablet from approximately 1800 B.C.
  10. 10. ______ ______ ______
  11. 11. = 3 · 10 + 2 = 32 = 12 · 60 + 23 Sixties Ones (units) = 720 + 23 = 743 = 1 · 3600 + 11 · 60 + 20 602 = 3600 + 660 + 20 60 1Or 3600 = 4280
  12. 12. ______ ______ ______ 602 60 1 Or 3600 3 60 203 42 = 180203 = 23 3 · 60 + 23
  13. 13. 4282 3600 ______ ______ ______ 682 602 60 1 Or 3600 11 60 6824282 = 600 1 · 3600 + 11 · 60 + 22 82 60 22
  14. 14. MayanNumeration
  15. 15. Mayan System •Place value system •Based on groups of 20 (with one exception) •Places are arranged vertically •Did have a symbol for zero Page 68
  16. 16. 20 · 20 · 18 or 720020 · 18 or 360201
  17. 17. = 14 2 · 360 720 0 · 20 +0 15 + 15 735
  18. 18. 1 · 7200 72000 · 360 +07 · 20 + 1405 +5 7345
  19. 19. 536 = 7200 536 176 360 160 1 · 360 176 16 8 · 20 16 · 1
  20. 20. RomanNumeration
  21. 21. Roman System •Additive system •Subtractive property – if a smaller symbol is to the left of a larger symbol, it is subtracted from the larger •No more than three of the same symbol in a row Page 69
  22. 22. DCCCXLIV500 + 300 + 40 + 4 = 844
  23. 23. Section 52 at the Coliseum in Rome
  24. 24. Natural (Counting) Numbers: {1, 2, 3, 4, …}Whole Numbers: {0, 1, 2, 3, …}The Natural Numbers are a subset of theWhole Numbers.
  25. 25. Whole Number addition 2+3=5addends sum
  26. 26. Models for whole-number addition 2+3=5Set Model
  27. 27. Models for whole-number addition 2+3=5Number Line Model 2 3
  28. 28. Properties of whole-number additionCommutative Property of Addition a+b=b+a 2+1=1+2Associative Property of Addition (a + b) + c = a + (b + c) (4 + 3) + 7 = 4 + (3 + 7)Identity Property of Addition a+0=a 7+0=7 0 is the additive identity
  29. 29. Whole Number subtraction 5–2=3minuend subtrahend difference Subtraction is related to addition: 5 – 2 = 3 if 5 = 2 + 3
  30. 30. Models for whole-number subtraction 5–2=3 Start with 5 starsTake-away Model Take away 2 3 stars left
  31. 31. Models for whole-number subtraction 5–2=3 Start with 5 starsComparison Model Compare with 2 circles 3 stars left
  32. 32. Models for whole-number subtraction 5–2=3Missing Addend Model 5–2=? 5=2+? ?=3

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