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. Fefiddle-fiddle-fe Fifiddle-fiddle-fi Fofiddle-fiddle-fo Fumfiddle-fiddle-fum Fiddlefiddle-fiddle-fiddle Fiddle-fefiddle-fiddle-fiddle-fe Fiddle-fifiddle-fiddle-fiddle-fi Fiddle-fofiddle-fiddle-fiddle-fo Fiddle-fumfiddle-fiddle-fiddle-fum Fiddle-fiddlefiddle-fiddle-fiddle-fiddle

6. Fefi-fiddle-fe Fifi-fiddle-fi Fofi-fiddle-fo Fumfi-fiddle-fum Fiddlefo-fiddle Fiddle-fefo-fiddle-fe Fiddle-fifo-fiddle-fi Fiddle-fofo-fiddle-fo Fiddle-fumfo-fiddle-fum Fi-fiddlefum-fiddle

7. Written Number System NumberSymbol

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 System Page 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 NumberSymbol 1 l 10 <

15. Babylonian Number System NumberSymbol 1 l 10 < 0

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 System Page 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 NumberSymbol 0 1 5

19. Mayan Number System

20. Roman Numerals Roman Symbol IVXLCDM Hindu Arabic 1510501005001000

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. IX IIXX IIIXXX IVXL VL VILX VIILXX VIIILXXX IXXC XC

25. IXC IIXXCC IIIXXXCCC IVXLCD VLD VILXDC VIILXXDCC VIIILXXXDCCC IXXCCM XCM

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 Numbers Page 149

34. Homework Questions Chapter 2

37. Venn Diagram Lab Answers

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

39. Day 2

40. Set Theory Test

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

42. Base 10 Number System hundred ten millions thousands thousands thousands hundreds tens ones ____, ____ ____ ____, ____ ____ ____

43. Base 10 Number System hundred ten hundred ten millions millions millions thousands thousands thousands hundreds tens ones ___ ___ ___, ___ ___ ___, ___ ___ ___

44. Ones Tens Hundreds Thousands Ten Thousands Hundred Thousands

45. Millions Ten Millions Hundred Millions Billions Ten Billions Hundred Billions

46. Trillions Ten Trillions Hundred Trillions Quadrillions Ten Quadrillions Hundred Quadrillions

47. Quintillions Ten Quintillions Hundred Quintillions Sextillions Ten Sextillions Hundred Sextillions

48. Septillions Ten Septillions Hundred Septillions Octillions Ten Octillions Hundred Octillions

49. Nonillions Ten Nonillions Hundred Nonillions Decillions Ten Decillions Hundred Decillions

50. 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

51. Googol-plex

52. The I Hate Mathematics Book by Marilyn Burns Math for Smarty Pants by Marilyn Burns Spaghetti and Meatballs for All! by Marilyn Burns The m&m’s Counting Book by Barbara Barbieri McGrath Counting Kisses by Karen Katz Math Potatoes by Greg Tang Millions of Cats by Wanda Ga’g

53. Expanded Notation Expanded Notation tells what the number means. 25,683

54. Expanded Notation 25,683 = 20,000 + 5,000 + 600 + 80 + 3 25,683 = (2 x 10,000) + (5 x 1000) + (6 x 100) + (8 x 10) + (3 x 1) 25,683 = (2 x 10 4 ) + (5 x 10 3 ) + (6 x 10 2 ) + (8 x 10 1 ) + (3 x 10 0 )

55. Reading Numbers 25, 638 “Twenty five thousand, six hundred thirty- eight”

56. Reading Numbers 25, 638, 304 “Twenty five million, six hundred thirty- eight thousand, three hundred four”

57. Models for Numeration Lab

58. 8 beans, 6 longs, 5 flats Exchange pieces for an equivalent collection (one that has the same number of beans) using the least number of pieces. 1 Long-flat, 1 Flat, 2 Longs, 3 beans

59. 2 Long-flats, 3 Longs, and 4 beans How many beans total? 269 beans

60. Make a collection of 42 beans using the least number of pieces possible.

62. Begin with 1 Long-flat. Trade in as needed to give away 12 beans. What’s left?

63. 4 Flats, 2 Longs, 3 Beans

64. Base Five Five Digits: {0, 1, 2, 3, 4} 125’s 25’s fives ones... _____ _____ _____ _____ _____ 5 4 5 3 5 2 5 1 5 0

65. Count in Base 5 1 2 3 4 10 11 12 13 14 20 21 22 23 24 30 31 32 33 34 40

66. Count in Base 5 1 2 3 4 10 11 12 13 14 20 21 22 23 24 30 31 32 33 34 40 41 42 43 44 100

67. Base Six Six Digits: {0, 1, 2, 3, 4, 5} 216’s 36’s six ones... _____ _____ _____ _____ _____ 6 4 6 3 6 2 6 1 6 0

68. Count in Base 6 1 2 3 4 5 10 11 12 13 14 15 20 21 22 23 24 25 30 31 32 33 34 35 40 41 42 43 44 45 50 51 52 53 54 55 100 101...

69. Base Twelve Twelve Digits: {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, T, E} 1728’s 144’s twelve ones... _____ _____ _____ _____ _____ 12 4 12 3 12 2 12 1 12 0

70. Count in Base Twelve 1 2 3 4 5 6 7 8 9 T E 10 11 12 13 14 15 16 17 18 19 1T 1E 20 21 22 23 24 25 26 27 28 29 2T 2E 30 31...

71. Base Two Two Digits; {0, 1} 8’s 4’s twos ones... _____ _____ _____ _____ _____ 2 4 2 3 2 2 2 1 2 0

72. Count in Base 2 1 10 11 100 101 110 111 1000 1001 1010 1011 1100 1101 1110 1111 10000 10001 10010 10011 10100 10101 10110 10111 11000 11001 11010 11011 11100 11101 11110 11111

73. 1324 five is read “one, three, two, four, base five” Expanded notation will tell us what it means. (This is the same thing as converting to base 10, because base 10 is what we understand.) 1324 five = (1x 5 3 ) + (3x 5 2 ) + (2 x 5 1 ) + (4 x 5 0 )

74. = (1 x 125) + (3 x 25) + (2 x 5) + (4 x 1) = 125 + 75 + 10 + 4 = 214 1324 five = 214 ten

75. 1324 five = (1x 5 3 ) + (3x 5 2 ) + (2 x 5 1 ) + (4 x 5 0 ) = (1 x 125) + (3 x 25) + (2 x 5) + (4 x 1) = 125 + 75 + 10 + 4 = 214 1324 five = 214 ten 1324 seven =

76. 1324 five = (1x 5 3 ) + (3x 5 2 ) + (2 x 5 1 ) + (4 x 5 0 ) = (1 x 125) + (3 x 25) + (2 x 5) + (4 x 1) = 125 + 75 + 10 + 4 = 214 1324 five = 214 ten 1324 seven =(1x 7 3 ) + (3x 7 2 ) + (2x 7 1 ) + (4x7 0 ) = (1 x 343) + (3 x 49) + (2 x 7) + (4 x 1) = 343 + 147 + 14 + 4 = 508 1324 seven = 508 ten

77. Start with base 10 382 = _______ five

78. Put 382 beans in groups of 5 382 = ______ five

79. 382 = ____2 five 76 longs and 2 beans left over.

80. Put 76 longs in groups of 5 382 = ____2 five 76 longs and 2 beans left over.

81. 382 = __ 12 five 76 longs and 2 beans left over. 15 flats, 1 long left over, 2 beans left over.

82. Put 15 flats in groups of 5 382 = __ 12 five 76 longs and 2 beans left over. 15 flats, 1 long left over, 2 beans left over.

83. Put 15 flats in groups of 5 382 = _ 012 five 76 longs and 2 beans left over. 15 flats, 1 long left over, 2 beans left over. 3 long-flats, 0 flats left over, 1 long left over, 2 beans left over.

84. Put 3 long-flats in groups of 5. Not enough – you are finished. 382 = 3012 five 76 longs and 2 beans left over. 15 flats, 1 long left over, 2 beans left over. 3 long-flats, 0 flats left over, 1 long left over, 2 beans left over.

85. Short Division 382 = _____ five 5 )382 (beans) (longs)

86. Short Division 382 = _____ five 5 )382 (beans)remainder 2 76 (longs)

87. Short Division 382 = _____ five 5 )382 (beans)remainder 2 5 )76 (longs)remainder 1 15 (flats)

88. Short Division 382 = _____ five 5 )382 (beans)remainder 2 5 )76 (longs)remainder 1 5 )15 (flats)remainder 0 3 (long-flats)

89. Short Division 382 = _____ five 5 )382 (beans)remainder 2 5 )76 (longs)remainder 1 5 )15 (flats)remainder 0 5 )3 (long-flats)remainder 3 0

90. Short Division 382 = _____ five 5 )382 (beans)remainder 2 5 )76 (longs)remainder 1 5 )15 (flats)remainder 0 5 )3 (long-flats)remainder 3 0 382 = 3012 five

91. Day 3

92. Homework Questions Page 154

93. Homework Questions Page 161

94. Go over Labs

95. Adding Bean Sticks 324 five + 243 five

97. Make Exchanges 324 five + 243 five

98. Make Exchanges 324 five + 243 five

99. 1122 five

100. Use your base five pieces to find each of the following: 1.43 five + 24 five

101. Use your base five pieces to find each of the following: 1.43 five + 24 five = 122 five 2.313 five + 233 five =

102. Use your base five pieces to find each of the following: 1.43 five + 24 five = 122 five 2.313 five + 233 five = 1101 five 3.304 five + 20 five +120 five + 22 five =

103. Use your base five pieces to find each of the following: 1.43 five + 24 five = 122 five 2.313 five + 233 five = 1101 five 3.304 five + 20 five +120 five + 22 five = 1021 five 4.1000 five + 100 five + 10 five =

104. Use your base five pieces to find each of the following: 1.43 five + 24 five = 122 five 2.313 five + 233 five = 1101 five 3.304 five + 20 five +120 five + 22 five = 1021 five 4.1000 five + 100 five + 10 five = 1110 five

105. Take away model Take away 3 beans 232 five – 143 five

107. Take away 4 longs 232 five – 143 five

109. Take away 1 flat 232 five – 143 five

111. 34 five

112. Use your bean sticks to complete the following: 1.1142 five – 213 five =

113. Use your bean sticks to complete the following: 1.1142 five – 213 five = 424 five 2.2331 five -124 five =

114. Use your bean sticks to complete the following: 1.1142 five – 213 five = 424 five 2.2331 five -124 five = 2202 five 3.4112 five – 143 five =

115. Use your bean sticks to complete the following: 1.1142 five – 213 five = 424 five 2.2331 five -124 five = 2202 five 3.4112 five – 143 five = 3414 five

116. LAB 1221 three + 122 three

117. Note your Final Answer 1221 three + 122 three 2120 three

118. Subtract 432 six – 144 six =

119. = 244 six

120. LAB

121. 201 three 2312 four 255 six +102 three +203 four +134 six 111 two 2333 four 11011 two +101 two +333 four +10101 two

122. 1221 three 2312 four 1001 four -122 three -203 four -112 four 1010 two 101 ten 1001 three -101 two -11 ten -112 three

123. Day 4

124. Homework Questions Page 177

125. Worksheet Questions

126. Scratch Addition 2395 789 5463 1284 985 +677

127. 4567 2396 569 392 1974 +568

128. Napier’s Bones

129. 64 x 36

131. 64 x 36 =2304

132. Lattice Multiplication 98 x 47

133. Lattice Multiplication 98 x 47 = 4606

134. Lattice Multiplication 576 x 49

135. Lattice Multiplication 576 x 49 = 28,224

136. Egyptian Multiplication 22 x 28

137. 22 x 28 = 616 128 256 4112 8224 16448 448 112 +56 616

138. 22 x 28 128 256 4112 8224 16448 22 x 28 = (16 + 4 + 2) x 28

139. 22 x 28 128 256 4112 8224 16448 22 x 28 = (16 + 4 + 2) x 28 = (16 x 28) + (4 x 28) + (2 x 28)

140. 22 x 28 = 616 128 256 4112 8224 16448 22 x 28 = (16 + 4 + 2) x 28 = (16 x 28) + (4 x 28) + (2 x 28) = 448 + 112 + 56 = 616

141. Egyptian Multiplication 48 x 65

142. Egyptian Multiplication 48 x 65 = 3120 165 2130 4260 8520 161040 322080 2080 +1040 3120

143. Russian Peasant Multiplication 32 x 45

144. Russian Peasant Multiplication 32 x 45 = 1440 3245 1690 8180 4360 2720 11440

145. 324532 x 45 1690 8180 4360 2720 11440

146. 324532 x 45 (16 x 2) x 45 1690 8180 4360 2720 11440

147. 324532 x 45 (16 x 2) x 45 16 x (2 x 45) 1690 8180 4360 2720 11440

148. 324532 x 45 (16 x 2) x 45 16 x (2 x 45) 169016 x 90 8180 4360 2720 11440

149. 324532 x 45 (16 x 2) x 45 16 x (2 x 45) 169016 x 90 (8 x 2) x 90 8 x (2 x 90) 8180 4360 2720 11440

150. 324532 x 45 (16 x 2) x 45 16 x (2 x 45) 169016 x 90 (8 x 2) x 90 8 x (2 x 90) 81808 x 180 4360 2720 11440

151. 324532 x 45 (16 x 2) x 45 16 x (2 x 45) 169016 x 90 (8 x 2) x 90 8 x (2 x 90) 81808 x 180 (4 x 2) x 180 4 x (2 x 180) 4360 2720 11440

152. 324532 x 45 (16 x 2) x 45 16 x (2 x 45) 169016 x 90 (8 x 2) x 90 8 x (2 x 90) 81808 x 180 (4 x 2) x 180 4 x (2 x 180) 43604 x 360 2720 11440

153. 324532 x 45 (16 x 2) x 45 16 x (2 x 45) 169016 x 90 (8 x 2) x 90 8 x (2 x 90) 81808 x 180 (4 x 2) x 180 4 x (2 x 180) 43604 x 360 (2 x 2) x 360 2 x (2 x 360) 2720 11440

154. 324532 x 45 (16 x 2) x 45 16 x (2 x 45) 169016 x 90 (8 x 2) x 90 8 x (2 x 90) 81808 x 180 (4 x 2) x 180 4 x (2 x 180) 43604 x 360 (2 x 2) x 360 2 x (2 x 360) 27202 x 720 11440

155. 324532 x 45 (16 x 2) x 45 16 x (2 x 45) 169016 x 90 (8 x 2) x 90 8 x (2 x 90) 81808 x 180 (4 x 2) x 180 4 x (2 x 180) 43604 x 360 (2 x 2) x 360 2 x (2 x 360) 27202 x 720 (1 x 2) x 720 1 x (2 x 720) 114401 x 1440

156. Russian Peasant Multiplication 48 x 65

157. Russian Peasant Multiplication 48 x 65 = 3120 4865 24130 12260 6520 31040 12080 2080 +1040 3120

158. 486548 x 65 24130 12260 6520 31040 12080

159. 486548 x 65 2413024 x 130 12260 6520 31040 12080

160. 486548 x 65 2413024 x 130 1226012 x 260 6520 31040 12080

161. 486548 x 65 2413024 x 130 1226012 x 260 65206 x 520 31040 12080

162. 486548 x 65 2413024 x 130 1226012 x 260 65206 x 520 310403 x 1040 12080

163. 486548 x 65 2413024 x 130 1226012 x 260 65206 x 520 310403 x 1040 (2 + 1) x 1040 12080

164. 486548 x 65 2413024 x 130 1226012 x 260 65206 x 520 310403 x 1040 (2 + 1) x 1040 (2x1040)+(1x1040) 12080

165. 486548 x 65 2413024 x 130 1226012 x 260 65206 x 520 310403 x 1040 (2 + 1) x 1040 (2x1040)+(1x1040) 12080(1x2080)+(1x1040)

166. Mental Math The ability to make accurate estimates and do mental arithmetic is increasingly important in today’s society. It is essential that the basic addition and multiplication facts be memorized since all other numerical calculations and estimations depend of this foundation.

167. Mental Math This should NOT be rote memorization of symbols. Students should experience the facts by frequent use of manipulatives, games, puzzles, and problem solving activities. In the same way, students learn basic properties of whole numbers and use them to “figure out” any fact they may have forgotten.

168. Mental Math One digit facts and the properties of whole numbers are the basis for mental calculations.

169. Mental Math Using Easy Combinations 35 + 7 + 15

170. Mental Math Using Easy Combinations Using Adjustments in Mental Calculations 57 + 84

171. Mental Math Using Easy Combinations Using Adjustments in Mental Calculations 57 + 84 83 - 48

172. Mental Math Using Easy Combinations Using Adjustments in Mental Calculations Working From Left to Right 352 + 647

173. Mental Math Using Easy Combinations Using Adjustments in Mental Calculations Working From Left to Right 352 + 647 739 - 224

174. Mental Math Using Easy Combinations Using Adjustments in Mental Calculations Working From Left to Right 352 + 647 739 – 224 4 x 235

175. 8 + 3 + 4 + 6 + 7 + 12 + 4 + 3 + 6 + 3

176. 25 x 8

177. 4 x 99

178. 57 - 25

179. 47 x 5

180. 286 + 347

181. 493 x 7

182. Rounding When we are asked to round 5,842 to the nearest thousand, it is because we want something close to 5,842 without any small pieces. We don’t want anything any smaller than a group of a thousand. 5,842 is between 5,000 and 6,000. Which one is it closest to?

183. 5,842 to the nearest thousand: 5,842 6,000

184. 67,498,499 to the nearest thousand: 67,498,499 is between 67,498,000 and 67,499,000 Which one is it closer to? To the nearest thousand: 67,498,499 ≈ 67,498,000

185. Round 524 to the nearest hundred: 524≈500 Round 587 to the nearest hundred: 587≈600 Round 549 to the nearest hundred: 549≈500 Round 550 to the nearest hundred: 550≈600 Round 551 to the nearest hundred: 551≈600

186. 5-Up Rule Page 201

187. Round 549 to the nearest hundred: 549≈500 Round 550 to the nearest hundred: 550≈500 Round 551 to the nearest hundred: 551≈600

188. Round 29,853 to the position indicated. Ten thousand: 30,000 Thousand: 30,000 Hundred: 29,900 Ten: 29,850

189. Approximate By Rounding 2,954 + 482 + 82 = Round to the nearest thousand 3,000 + 0 + 0 = Round to the nearest hundred 3,000 + 500 + 100 = Round to the left-most digit 3,000 + 500 + 80 =

190. Round to the left-most digit to find approximate answer. 2681 + 241 = 3000 + 200 = 3200 2681 – 241 = 3000 – 200 = 2800 2681 x 241 = 3000 x 200 = 600,000 57801 ÷ 336 = 60,000 ÷ 300 = 200

191. “I have... Who has... ?”

192. Math and Music The Magical Connection! Scholastic Parent and Child Magazine Spelling Phone Numbers School House Rock

193. “Skip to My Lou” Chorus:Times facts, they’re a breeze; Learn a few, then work on speed. Times facts, you’ll be surprised By just how fast you can memorize.

194. 3 time 7 is 21 Now, at last we’ve all begun. 4 times 7 is 28 Let’s sing what we appreciate. (Chorus) 5 times 7 is 35. Yes, by gosh, we’re still alive. 6 times 7 is 42. I forgot what we’re supposed to do. (Chorus)