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Chapter 3

- Numeration
- And
- Computation

- 5

- 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

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

Written Number System

Additive Number System

- M M M N N N N l l l
- M M N N N l l l l

Use a Multiplier

- M M M N N N N l l l
- M M N N N l l l l

Positional Number System

- M M M N N N N l l l
- M M N N N l l l l

Egyptian Number SystemPage 144

- Additive System

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

Babylonian Number System

Babylonian Number System

Babylonian Number System

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.

Mayan Number System

Mayan Number System

Roman Numerals

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.

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.

Multiplication Principal

- 649

Multiplication Principal

- 649 DCXLIX
- 649,000 DCXLIX

Multiplication Principal

- 649 DCXLIX
- 649,000 DCXLIX
- 649,428

Multiplication Principal

- 649 DCXLIX
- 649,000 DCXLIX
- 649,428 DCXLIXCDXXVIII
- 649,000,000

Multiplication Principal

- 649 DCXLIX
- 649,000 DCXLIX
- 649,428 DCXLIXCDXXVIII
- 649,000,000 DCXLIX

Hindu-Arabic NumbersPage 149

Homework QuestionsChapter 2

(No Transcript)

(No Transcript)

Venn Diagram Lab Answers

Test - Chapter 2

- http//mcis.jsu.edu/faculty/mjohnson/ms133r2.html

Day 2

Set Theory Test

Base 10 Number System

- 10 digits 0, 1, 2, 3, 4, 5, 6, 7, 8, 9

Base 10 Number System

- hundred ten
- millions thousands thousands thousands

hundreds tens ones - ____ , ____ ____ ____ , ____ ____

____

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

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

Googol-plex

- 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

Expanded Notation

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

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 104) (5 x 103) (6 x 102)
- (8 x 101) (3 x 100)

Reading Numbers

- 25, 638
- Twenty five thousand, six hundred thirty-eight

Reading Numbers

- 25, 638, 304
- Twenty five million, six hundred thirty-eight

thousand, three hundred four

Models for Numeration Lab

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

2 Long-flats, 3 Longs, and 4 beans

How many beans total? 269 beans

Make a collection of 42 beans using the least

number of pieces possible.

Make a collection of 42 beans using the least

number of pieces possible.

- Begin with 1 Long-flat. Trade in as needed to

give away 12 beans.

Whats left?

4 Flats, 2 Longs, 3 Beans

Base Five

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

Count in Base 5

- 1
- 2
- 3
- 4
- 10
- 11
- 12
- 13
- 14

20 21 22 23 24 30

31 32 33 34 40

Count in Base 5

20 21 22 23 24 30

31 32 33 34 40

41 42 43 44 100

- 1
- 2
- 3
- 4
- 10
- 11
- 12
- 13
- 14

Base Six

- Six Digits 0, 1, 2, 3, 4, 5
- 216s 36s six ones
- . . . _____ _____ _____ _____ _____
- 64 63 62 61 60

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

- 1
- 2
- 3
- 4
- 5
- 10
- 11
- 12

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

Count in Base Twelve

29 2T 2E 30 31 . . .

- 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

Base Two

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

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

- 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

Start with base 10

- 382 _______five

Put 382 beans in groups of 5

- 382 ______ five

- 382 ____2 five
- 76 longs and 2 beans left over.

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.

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.

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.

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.

Short Division382 _____five

- 5 )382 (beans)
- (longs)

Short Division382 _____five

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

Short Division382 _____five

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

Short Division382 _____five

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

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

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

Day 3

Homework QuestionsPage 154

Homework QuestionsPage 161

Go over Labs

Adding Bean Sticks

- 324five 243five

- 324five 243five

Make Exchanges

- 324five 243five

Make Exchanges

- 324five 243five

- 324five 243five
- 1122five

Use your base five pieces to find each of the

following

- 43five 24five

Use your base five pieces to find each of the

following

- 43five 24five 122five
- 313five 233five

Use your base five pieces to find each of the

following

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

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

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

Take away modelTake away 3 beans

- 232five 143five

- 232five 143five

Take away 4 longs

- 232five 143five

- 232five 143five

Take away 1 flat

- 232five 143five

- 232five 143five

- 232five 143five
- 34five

Use your bean sticks to complete the following

- 1142five 213five

Use your bean sticks to complete the following

- 1142five 213five 424five
- 2331five -124five

Use your bean sticks to complete the following

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

Use your bean sticks to complete the following

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

LAB

- 1221three 122three

Note your Final Answer

- 1221three 122three
- 2120three

Subtract

- 432six 144six

- 432six 144six
- 244six

LAB

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

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

Day 4

Homework QuestionsPage 177

Worksheet Questions

Scratch Addition

- 2395
- 789
- 5463
- 1284
- 985
- 677

- 4567
- 2396
- 569
- 392
- 1974
- 568

Napiers Bones

64 x 36

64 x 36

64 x 36 2304

Lattice Multiplication98 x 47

Lattice Multiplication98 x 47 4606

Lattice Multiplication576 x 49

Lattice Multiplication576 x 49 28,224

Egyptian Multiplication22 x 28

22 x 28 616

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

22 x 28

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

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)

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

Egyptian Multiplication48 x 65

Egyptian Multiplication48 x 65 3120

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

Russian Peasant Multiplication32 x 45

Russian Peasant Multiplication32 x 45 1440

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

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

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

- 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

- 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

- 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

- 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

- 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

- 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

- 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

- 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

- 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

Russian Peasant Multiplication48 x 65

Russian Peasant Multiplication48 x 65 3120

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

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

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

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

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

- 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

- 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

- 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

- 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)

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.

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.

Mental Math

- One digit facts and the properties of whole

numbers are the basis for mental calculations.

Mental Math

- Using Easy Combinations
- 35 7 15

Mental Math

- Using Easy Combinations
- Using Adjustments in Mental Calculations
- 57 84

Mental Math

- Using Easy Combinations
- Using Adjustments in Mental Calculations
- 57 84
- 83 - 48

Mental Math

- Using Easy Combinations
- Using Adjustments in Mental Calculations
- Working From Left to Right
- 352 647

Mental Math

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

Mental Math

- Using Easy Combinations
- Using Adjustments in Mental Calculations
- Working From Left to Right
- 352 647
- 739 224
- 4 x 235

- 8 3 4 6 7 12 4 3 6 3

- 25 x 8

- 4 x 99

- 57 - 25

- 47 x 5

- 286 347

- 493 x 7

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 dont 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?

- 5,842 to the nearest thousand
- 5,842 6,000

- 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

- Round 524 to the nearest hundred
- 524500
- Round 587 to the nearest hundred
- 587600
- Round 549 to the nearest hundred
- 549500
- Round 550 to the nearest hundred
- 550600
- Round 551 to the nearest hundred
- 551600

5-Up RulePage 201

- Round 549 to the nearest hundred
- 549500
- Round 550 to the nearest hundred
- 550500
- Round 551 to the nearest hundred
- 551600

Round 29,853 to the position indicated.

- Ten thousand
- 30,000
- Thousand
- 30,000
- Hundred
- 29,900
- Ten
- 29,850

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

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

I have . . . Who has . . . ?

Math and MusicThe Magical Connection!

- Scholastic Parent and Child Magazine
- Spelling
- Phone Numbers
- School House Rock

Skip to My Lou

- Chorus Times facts, theyre a breeze
- Learn a few, then work on speed.
- Times facts, youll be surprised
- By just how fast you can memorize.

- 3 time 7 is 21
- Now, at last weve all begun.
- 4 times 7 is 28
- Lets sing what we appreciate.
- (Chorus)
- 5 times 7 is 35.
- Yes, by gosh, were still alive.
- 6 times 7 is 42.
- I forgot what were supposed to do.
- (Chorus)

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For a small fee you can get the industry's best online privacy or publicly promote your presentations and slide shows with top rankings. But aside from that it's free. We'll even convert your presentations and slide shows into the universal Flash format with all their original multimedia glory, including animation, 2D and 3D transition effects, embedded music or other audio, or even video embedded in slides. All for free. Most of the presentations and slideshows on PowerShow.com are free to view, many are even free to download. (You can choose whether to allow people to download your original PowerPoint presentations and photo slideshows for a fee or free or not at all.) Check out PowerShow.com today - for FREE. There is truly something for everyone!

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