Chapter 3
This presentation is the property of its rightful owner.
Sponsored Links
1 / 194

Chapter 3 PowerPoint PPT Presentation


  • 70 Views
  • Uploaded on
  • Presentation posted in: General

Chapter 3. Numeration And Computation. 5. 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. Count!. Fe Fi Fo Fum Fiddle Fruit Folks Fist.

Download Presentation

Chapter 3

An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -

Presentation Transcript


Chapter 3

Numeration

And

Computation


5


  • 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


  • Count!

    • Fe

    • Fi

    • Fo

    • Fum

    • Fiddle

    • Fruit

    • Folks

    • Fist


    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


    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


    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

    < < < l l l l < < < < < < l l l l l l l

    < < l l l l < < < < l l l l l


    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


    IX

    IIXX

    IIIXXX

    IVXL

    VL

    VILX

    VIILXX

    VIIILXXX

    IXXC

    XC


    IXC

    IIXXCC

    IIIXXXCCC

    IVXLCD

    VLD

    VILXDC

    VIILXXDCC

    VIIILXXXDCCC

    IXXCCM

    XCM


    • 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


    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

    hundredten

    millions thousands thousands thousands hundreds tens ones

    ____ , ____ ____ ____ , ____ ____ ____


    Base 10 Number System

    hundred ten hundredten

    millions millions millions thousands thousands thousands hundredstensones

    _________ , ______ ___ , _________


    • 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 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


    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.

    What’s left?


    4 Flats, 2 Longs, 3 Beans


    Base Five

    Five Digits: {0, 1, 2, 3, 4}

    125’s 25’s fives ones

    . . . _____ _____ _____ _____ _____

    5453525150


    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}

    216’s 36’s six ones

    . . . _____ _____ _____ _____ _____

    6463626160


    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}

    1728’s 144’s twelve ones

    . . . _____ _____ _____ _____ _____

    124123122121120


    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

    1

    2

    3

    4

    5

    6

    7

    8


    Base Two

    Two Digits; {0, 1}

    8’s 4’s twos ones

    . . . _____ _____ _____ _____ _____

    2423222120


    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

    1

    10

    11

    100

    101

    110

    111


    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 = ____2five

    76 longs and 2 beans left over.


    Put 76 longs in groups of 5

    382 = ____2five

    76 longs and 2 beans left over.


    382 = __ 12five

    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 = __ 12five

    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 = _ 012five

    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 = 3012five

    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


    201three2312four 255six

    +102three+203four+134six

    111two2333four 11011two

    +101two+333four+10101two


    1221three2312four 1001four

    -122three-203four -112four

    1010two101ten 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


    Napier’s 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

    128

    256

    4112

    8224

    16448

    448

    112

    +56

    616


    22 x 28

    128

    256

    4112

    8224

    16448

    22 x 28 = (16 + 4 + 2) x 28


    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)


    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


    Egyptian Multiplication48 x 65


    Egyptian Multiplication48 x 65 = 3120

    165

    2130

    4260

    8520

    161040

    322080

    2080

    +1040

    3120


    Russian Peasant Multiplication32 x 45


    Russian Peasant Multiplication32 x 45 = 1440

    3245

    1690

    8180

    4360

    2720

    11440


    324532 x 45

    1690

    8180

    4360

    2720

    11440


    324532 x 45

    (16 x 2) x 45

    1690

    8180

    4360

    2720

    11440


    324532 x 45

    (16 x 2) x 45

    16 x (2 x 45)

    1690

    8180

    4360

    2720

    11440


    324532 x 45

    (16 x 2) x 45

    16 x (2 x 45)

    169016 x 90

    8180

    4360

    2720

    11440


    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


    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


    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


    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


    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


    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


    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


    Russian Peasant Multiplication48 x 65


    Russian Peasant Multiplication48 x 65 = 3120

    4865

    24130

    12260

    6520

    31040

    12080

    2080

    +1040

    3120


    486548 x 65

    24130

    12260

    6520

    31040

    12080


    486548 x 65

    2413024 x 130

    12260

    6520

    31040

    12080


    486548 x 65

    2413024 x 130

    1226012 x 260

    6520

    31040

    12080


    486548 x 65

    2413024 x 130

    1226012 x 260

    65206 x 520

    31040

    12080


    486548 x 65

    2413024 x 130

    1226012 x 260

    65206 x 520

    310403 x 1040

    12080


    486548 x 65

    2413024 x 130

    1226012 x 260

    65206 x 520

    310403 x 1040

    (2 + 1) x 1040

    12080


    486548 x 65

    2413024 x 130

    1226012 x 260

    65206 x 520

    310403 x 1040

    (2 + 1) x 1040

    (2x1040)+(1x1040)

    12080


    486548 x 65

    2413024 x 130

    1226012 x 260

    65206 x 520

    310403 x 1040

    (2 + 1) x 1040

    (2x1040)+(1x1040)

    12080(1x2080)+(1x1040)


    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.


    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 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?


    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:

    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


    5-Up RulePage 201


    Round 549 to the nearest hundred:

    549≈500

    Round 550 to the nearest hundred:

    550≈500

    Round 551 to the nearest hundred:

    551≈600


    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, they’re a breeze;

    Learn a few, then work on speed.

    Times facts, you’ll be surprised

    By just how fast you can memorize.


    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)


  • Login