Numeration

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Title: Numeration

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Title: Numeration

1
Chapter 3

Numeration
And
Computation

Americas Funniest Home Videos
Tallys 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

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

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

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

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

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

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

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

Write 1469 using Roman Numerals

Write MMMCMXCIX as a Hindu Arabic Number.

28
Multiplication Principal

29
Multiplication Principal

649 DCXLIX
649000 DCXLIX

30
Multiplication Principal

649 DCXLIX
649000 DCXLIX
649428

31
Multiplication Principal

649 DCXLIX
649000 DCXLIX
649428 DCXLIXCDXXVIII
649000000

32
Multiplication Principal

649 DCXLIX
649000 DCXLIX
649428 DCXLIXCDXXVIII
649000000 DCXLIX

33
Hindu-Arabic NumbersPage 149
34
Homework QuestionsChapter 2
35
(No Transcript)
36
(No Transcript)
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
___ ___ ___ ___ ___ ___ ___ ___ ___

Ones
Tens
Hundreds
Thousands
Ten Thousands
Hundred Thousands

Millions
Ten Millions
Hundred Millions
Billions
Ten Billions
Hundred Billions

Trillions
Ten Trillions
Hundred Trillions
Quadrillions
Ten Quadrillions
Hundred Quadrillions

Quintillions
Ten Quintillions
Hundred Quintillions
Sextillions
Ten Sextillions
Hundred Sextillions

Septillions
Ten Septillions
Hundred Septillions
Octillions
Ten Octillions
Hundred Octillions

Nonillions
Ten Nonillions
Hundred Nonillions
Decillions
Ten Decillions
Hundred Decillions

50
Googol

10000000000000000000000000
000000000000000000000000000
000000000000000000000000000
000000000000000000000

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 mms Counting Book
by Barbara Barbieri McGrath
Counting Kisses by Karen Katz
Math Potatoes by Greg Tang
Millions of Cats by Wanda Gag

53
Expanded Notation

Expanded Notation tells what the number means.
25683

54
Expanded Notation

25683 20000 5000 600 80 3
25683 (2 x 10000) (5 x 1000)
(6 x 100) (8 x 10) (3 x 1)
25683 (2 x 104) (5 x 103) (6 x 102)
(8 x 101) (3 x 100)

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.
61
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.

Whats left
63
4 Flats 2 Longs 3 Beans
64
Base Five

Five Digits 0 1 2 3 4
125s 25s fives ones
. . . _____ _____ _____ _____ _____
54 53 52 51 50

65
Count in Base 5

20 21 22 23 24 30
31 32 33 34 40
66
Count in Base 5
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
216s 36s six ones
. . . _____ _____ _____ _____ _____
64 63 62 61 60

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

69
Base Twelve

Twelve Digits 0 1 2 3 4 5 6 7 8 9 T
E
1728s 144s twelve ones
. . . _____ _____ _____ _____ _____
124 123 122 121 120

70
Count in Base Twelve
29 2T 2E 30 31 . . .

9 T E 10 11 12 13 14
15 16 17 18 19 1T 1E 20
21 22 23 24 25 26 27 28
71
Base Two

Two Digits 0 1
8s 4s twos ones
. . . _____ _____ _____ _____ _____
24 23 22 21 20

72
Count in Base 2

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

1324five 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.)
1324five (1x 53) (3x 52) (2 x 51) (4 x 50)

1324five (1x 53) (3x 52) (2 x 51) (4 x 50)
(1 x 125) (3 x 25) (2 x 5) (4 x 1)
125 75 10 4
214
1324five 214ten

1324five (1x 53) (3x 52) (2 x 51) (4 x 50)
(1 x 125) (3 x 25) (2 x 5) (4 x 1)
125 75 10 4
214
1324five 214ten
1324seven

1324five (1x 53) (3x 52) (2 x 51) (4 x 50)
(1 x 125) (3 x 25) (2 x 5) (4 x 1)
125 75 10 4
214
1324five 214ten
1324seven(1x 73) (3x 72) (2x 71) (4x70)
(1 x 343) (3 x 49) (2 x 7) (4 x 1)
343 147 14 4
508
1324seven 508ten

77
Start with base 10

382 _______five

78
Put 382 beans in groups of 5

382 ______ five

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.

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 Division382 _____five

5 )382 (beans)
(longs)

86
Short Division382 _____five

5 )382 (beans) remainder 2
76 (longs)

87
Short Division382 _____five

5 )382 (beans) remainder 2
5 )76 (longs) remainder 1
15 (flats)

88
Short Division382 _____five

5 )382 (beans) remainder 2
5 )76 (longs) remainder 1
5 )15 (flats) remainder 0
3 (long-flats)

89
Short Division382 _____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 Division382 _____five

5 )382 (beans) remainder 2
5 )76 (longs) remainder 1
5 )15 (flats) remainder 0
5 )3 (long-flats) remainder 3
0
382 3012five

91
Day 3
92
Homework QuestionsPage 154
93
Homework QuestionsPage 161
94
Go over Labs
95
Adding Bean Sticks

324five 243five

324five 243five

97
Make Exchanges

324five 243five

98
Make Exchanges

324five 243five

324five 243five
1122five

100
Use your base five pieces to find each of the
following

43five 24five

101
Use your base five pieces to find each of the
following

43five 24five 122five
313five 233five

102
Use your base five pieces to find each of the
following

43five 24five 122five
313five 233five 1101five
304five 20five 120five 22five

103
Use your base five pieces to find each of the
following

43five 24five 122five
313five 233five 1101five
304five 20five 120five 22five 1021five
1000five 100five 10five

104
Use your base five pieces to find each of the
following

43five 24five 122five
313five 233five 1101five
304five 20five 120five 22five 1021five
1000five 100five 10five 1110five

105
Take away modelTake away 3 beans

232five 143five

106

232five 143five

107
Take away 4 longs

232five 143five

108

232five 143five

109
Take away 1 flat

232five 143five

110

232five 143five

111

232five 143five
34five

112
Use your bean sticks to complete the following

1142five 213five

113
Use your bean sticks to complete the following

1142five 213five 424five
2331five -124five

114
Use your bean sticks to complete the following

1142five 213five 424five
2331five -124five 2202five
4112five 143five

115
Use your bean sticks to complete the following

1142five 213five 424five
2331five -124five 2202five
4112five 143five 3414five

116
LAB

1221three 122three

117
Note your Final Answer

1221three 122three
2120three

118
Subtract

432six 144six

119

432six 144six
244six

120
LAB
121

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

122

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

123
Day 4
124
Homework QuestionsPage 177
125
Worksheet Questions
126
Scratch Addition

2395
789
5463
1284
985
677

127

4567
2396
569
392
1974
568

128
Napiers Bones
129
64 x 36
130
64 x 36
131
64 x 36 2304
132
Lattice Multiplication98 x 47
133
Lattice Multiplication98 x 47 4606
134
Lattice Multiplication576 x 49
135
Lattice Multiplication576 x 49 28224
136
Egyptian Multiplication22 x 28
137
22 x 28 616

1 28
2 56
4 112
8 224
16 448
448
112
56
616

138
22 x 28

1 28
2 56
4 112
8 224
16 448
22 x 28 (16 4 2) x 28

139
22 x 28

1 28
2 56
4 112
8 224
16 448
22 x 28 (16 4 2) x 28
(16 x 28) (4 x 28) (2 x 28)

140
22 x 28 616

1 28
2 56
4 112
8 224
16 448
22 x 28 (16 4 2) x 28
(16 x 28) (4 x 28) (2 x 28)
448 112 56
616

141
Egyptian Multiplication48 x 65
142
Egyptian Multiplication48 x 65 3120

1 65
2 130
4 260
8 520
16 1040
32 2080
2080
1040
3120

143
Russian Peasant Multiplication32 x 45
144
Russian Peasant Multiplication32 x 45 1440

32 45
16 90
8 180
4 360
2 720
1 1440

145

32 45 32 x 45
16 90
8 180
4 360
2 720
1 1440

146

32 45 32 x 45
(16 x 2) x 45
16 90
8 180
4 360
2 720
1 1440

147

32 45 32 x 45
(16 x 2) x 45
16 x (2 x 45)
16 90
8 180
4 360
2 720
1 1440

148

32 45 32 x 45
(16 x 2) x 45
16 x (2 x 45)
16 90 16 x 90
8 180
4 360
2 720
1 1440

149

32 45 32 x 45
(16 x 2) x 45
16 x (2 x 45)
16 90 16 x 90
(8 x 2) x 90
8 x (2 x 90)
8 180
4 360
2 720
1 1440

150

32 45 32 x 45
(16 x 2) x 45
16 x (2 x 45)
16 90 16 x 90
(8 x 2) x 90
8 x (2 x 90)
8 180 8 x 180
4 360
2 720
1 1440

151

32 45 32 x 45
(16 x 2) x 45
16 x (2 x 45)
16 90 16 x 90
(8 x 2) x 90
8 x (2 x 90)
8 180 8 x 180
(4 x 2) x 180
4 x (2 x 180)
4 360
2 720
1 1440

152

32 45 32 x 45
(16 x 2) x 45
16 x (2 x 45)
16 90 16 x 90
(8 x 2) x 90
8 x (2 x 90)
8 180 8 x 180
(4 x 2) x 180
4 x (2 x 180)
4 360 4 x 360
2 720
1 1440

153

32 45 32 x 45
(16 x 2) x 45
16 x (2 x 45)
16 90 16 x 90
(8 x 2) x 90
8 x (2 x 90)
8 180 8 x 180
(4 x 2) x 180
4 x (2 x 180)
4 360 4 x 360
(2 x 2) x 360
2 x (2 x 360)
2 720
1 1440

154

32 45 32 x 45
(16 x 2) x 45
16 x (2 x 45)
16 90 16 x 90
(8 x 2) x 90
8 x (2 x 90)
8 180 8 x 180
(4 x 2) x 180
4 x (2 x 180)
4 360 4 x 360
(2 x 2) x 360
2 x (2 x 360)
2 720 2 x 720
1 1440

155

32 45 32 x 45
(16 x 2) x 45
16 x (2 x 45)
16 90 16 x 90
(8 x 2) x 90
8 x (2 x 90)
8 180 8 x 180
(4 x 2) x 180
4 x (2 x 180)
4 360 4 x 360
(2 x 2) x 360
2 x (2 x 360)
2 720 2 x 720
(1 x 2) x 720
1 x (2 x 720)
1 1440 1 x 1440

156
Russian Peasant Multiplication48 x 65
157
Russian Peasant Multiplication48 x 65 3120

48 65
24 130
12 260
6 520
3 1040
1 2080
2080
1040
3120

158

48 65 48 x 65
24 130
12 260
6 520
3 1040
1 2080

159

48 65 48 x 65
24 130 24 x 130
12 260
6 520
3 1040
1 2080

160

48 65 48 x 65
24 130 24 x 130
12 260 12 x 260
6 520
3 1040
1 2080

161

48 65 48 x 65
24 130 24 x 130
12 260 12 x 260
6 520 6 x 520
3 1040
1 2080

162

48 65 48 x 65
24 130 24 x 130
12 260 12 x 260
6 520 6 x 520
3 1040 3 x 1040
1 2080

163

48 65 48 x 65
24 130 24 x 130
12 260 12 x 260
6 520 6 x 520
3 1040 3 x 1040
(2 1) x 1040
1 2080

164

48 65 48 x 65
24 130 24 x 130
12 260 12 x 260
6 520 6 x 520
3 1040 3 x 1040
(2 1) x 1040
(2x1040)(1x1040)
1 2080

165

48 65 48 x 65
24 130 24 x 130
12 260 12 x 260
6 520 6 x 520
3 1040 3 x 1040
(2 1) x 1040
(2x1040)(1x1040)
1 2080 (1x2080)(1x1040)

166
Mental Math

The ability to make accurate estimates and do
mental arithmetic is increasingly important in
todays 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 5842 to the nearest
thousand it is because we want something close
to 5842 without any small pieces. We dont want
anything any smaller than a group of a thousand.
5842 is between 5000 and 6000. Which one is
it closest to

183