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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.

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Chapter 3

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
    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



    Additive 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
    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
    Positional Number System

    M M M N N N N ^ ^ ^ ^ l l l

    M M N N N l l l l


    Egyptian number system page 144
    Egyptian Number SystemPage 144

    • Additive System


    Million man
    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 system2
    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 system page 146
    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.





    Roman numerals1
    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 numerals2
    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





    Multiplication principal1
    Multiplication Principal

    • 649 = DCXLIX

    • 649,000 = DCXLIX


    Multiplication principal2
    Multiplication Principal

    • 649 = DCXLIX

    • 649,000 = DCXLIX

    • 649,428 =


    Multiplication principal3
    Multiplication Principal

    • 649 = DCXLIX

    • 649,000 = DCXLIX

    • 649,428 = DCXLIXCDXXVIII

    • 649,000,000 =


    Multiplication principal4
    Multiplication Principal

    • 649 = DCXLIX

    • 649,000 = DCXLIX

    • 649,428 = DCXLIXCDXXVIII

    • 649,000,000 = DCXLIX





    Test chapter 2
    Test - Chapter 2

    • http://mcis.jsu.edu/faculty/mjohnson/ms133r2.html




    Base 10 number system
    Base 10 Number System

    10 digits: {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}


    Base 10 number system1
    Base 10 Number System

    hundredten

    millions thousands thousands thousands hundreds tens ones

    ____ , ____ ____ ____ , ____ ____ ____


    Base 10 number system2
    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
    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



    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

    Expanded Notation tells what the number means.

    25,683


    Expanded notation1
    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
    Reading Numbers

    • 25, 638

    • “Twenty five thousand, six hundred thirty-eight”


    Reading numbers1
    Reading Numbers

    • 25, 638, 304

    • “Twenty five million, six hundred thirty-eight thousand, three hundred four”



    8 beans 6 longs 5 flats
    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
    2 Long-flats, 3 Longs, and 4 beans

    How many beans total?

    269 beans






    Base five
    Base beans.Five

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

    125’s 25’s fives ones

    . . . _____ _____ _____ _____ _____

    54 53525150


    Count in base 5
    Count in Base 5 beans.

    1

    2

    3

    4

    10

    11

    12

    13

    14

    20

    21

    22

    23

    24

    30

    31

    32

    33

    34

    40


    Count in base 51
    Count in Base 5 beans.

    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
    Base beans.Six

    Six Digits: {0, 1, 2, 3, 4, 5}

    216’s 36’s six ones

    . . . _____ _____ _____ _____ _____

    64 63626160


    Count in base 6
    Count in Base 6 beans.

    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
    Base beans.Twelve

    Twelve Digits: {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, T, E}

    1728’s 144’s twelve ones

    . . . _____ _____ _____ _____ _____

    124 123122121120


    Count in base twelve
    Count in Base Twelve beans.

    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
    Base beans.Two

    Two Digits; {0, 1}

    8’s 4’s twos ones

    . . . _____ _____ _____ _____ _____

    24 23222120


    Count in base 2
    Count in Base 2 beans.

    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


    1324 beans.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.)

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


    1324 beans.five= (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


    1324 beans.five= (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 =


    1324 beans.five= (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
    Start with base 10 beans.

    382 = _______five


    Put 382 beans in groups of 5
    Put 382 beans in groups of 5 beans.

    382 = ______ five


    382 = ____ beans.2five

    76 longs and 2 beans left over.


    Put 76 longs in groups of 5
    Put 76 longs in groups of 5 beans.

    382 = ____2five

    76 longs and 2 beans left over.


    382 = __ beans.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
    Put 15 flats in groups of 5 beans.

    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 51
    Put 15 flats in groups of 5 beans.

    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
    Put 3 long-flats in groups of 5. beans.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 division 382 five
    Short Division beans.382 = _____five

    5 )382 (beans)

    (longs)


    Short division 382 five1
    Short Division beans.382 = _____five

    5 )382 (beans) remainder 2

    76 (longs)


    Short division 382 five2
    Short Division beans.382 = _____five

    5 )382 (beans) remainder 2

    5 )76 (longs) remainder 1

    15 (flats)


    Short division 382 five3
    Short Division beans.382 = _____five

    5 )382 (beans) remainder 2

    5 )76 (longs) remainder 1

    5 )15 (flats) remainder 0

    3 (long-flats)


    Short division 382 five4
    Short Division beans.382 = _____five

    5 )382 (beans) remainder 2

    5 )76 (longs) remainder 1

    5 )15 (flats) remainder 0

    5 )3 (long-flats) remainder 3

    0


    Short division 382 five5
    Short Division beans.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 = 3012five


    Day 3
    Day 3 beans.


    Homework questions page 154
    Homework Questions beans.Page 154


    Homework questions page 161
    Homework Questions beans.Page 161


    Go over labs
    Go over Labs beans.


    Adding bean sticks
    Adding Bean Sticks beans.

    324five + 243five


    324 beans.five + 243five


    Make exchanges
    Make Exchanges beans.

    324five + 243five


    Make exchanges1
    Make Exchanges beans.

    324five + 243five


    324 beans.five + 243five

    1122five



    Use your base five pieces to find each of the following1
    Use your base five pieces to find each of the following: beans.

    • 43five + 24five = 122five

    • 313five + 233five =


    Use your base five pieces to find each of the following2
    Use your base five pieces to find each of the following: beans.

    • 43five + 24five = 122five

    • 313five + 233five = 1101five

    • 304five + 20five +120five + 22five =


    Use your base five pieces to find each of the following3
    Use your base five pieces to find each of the following: beans.

    • 43five + 24five = 122five

    • 313five + 233five = 1101five

    • 304five + 20five +120five + 22five = 1021five

    • 1000five + 100five + 10five =


    Use your base five pieces to find each of the following4
    Use your base five pieces to find each of the following: beans.

    • 43five + 24five = 122five

    • 313five + 233five = 1101five

    • 304five + 20five +120five + 22five = 1021five

    • 1000five + 100five + 10five = 1110five


    Take away model take away 3 beans
    Take away model beans.Take away 3 beans

    232five – 143five


    232 beans.five – 143five


    Take away 4 longs
    Take away 4 longs beans.

    232five – 143five


    232 beans.five – 143five


    Take away 1 flat
    Take away 1 flat beans.

    232five – 143five


    232 beans.five – 143five


    232 beans.five – 143five

    34five



    Use your bean sticks to complete the following1
    Use your bean sticks to complete the following: beans.

    • 1142five – 213five = 424five

    • 2331five -124five =


    Use your bean sticks to complete the following2
    Use your bean sticks to complete the following: beans.

    • 1142five – 213five = 424five

    • 2331five -124five = 2202five

    • 4112five – 143five =


    Use your bean sticks to complete the following3
    Use your bean sticks to complete the following: beans.

    • 1142five – 213five = 424five

    • 2331five -124five = 2202five

    • 4112five – 143five = 3414five


    LAB beans.

    1221three + 122three


    Note your final answer
    Note your Final Answer beans.

    1221three + 122three

    2120three


    Subtract
    Subtract beans.

    432six – 144six =


    432 beans.six – 144six =

    = 244six


    LAB beans.


    201 beans.three 2312four 255six

    +102three +203four +134six

    111two 2333four 11011two

    +101two +333four +10101two


    1221 beans.three 2312four 1001four

    -122three -203four -112four

    1010two 101ten 1001three

    -101two -11ten -112three


    Day 4
    Day 4 beans.


    Homework questions page 177
    Homework Questions beans.Page 177



    Scratch addition
    Scratch Addition beans.

    2395

    789

    5463

    1284

    985

    +677


    4567 beans.

    2396

    569

    392

    1974

    +568



    64 x 36
    64 x 36 beans.


    64 x 361
    64 x 36 beans.



    Lattice multiplication 98 x 47
    Lattice Multiplication beans.98 x 47


    Lattice multiplication 98 x 47 4606
    Lattice Multiplication beans.98 x 47 = 4606


    Lattice multiplication 576 x 49
    Lattice Multiplication beans.576 x 49


    Lattice multiplication 576 x 49 28 224
    Lattice Multiplication beans.576 x 49 = 28,224



    22 x 28 616
    22 x 28 = 616 beans.

    1 28

    2 56

    4 112

    8 224

    16 448

    448

    112

    +56

    616


    22 x 28
    22 x 28 beans.

    1 28

    2 56

    4 112

    8 224

    16 448

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


    22 x 281
    22 x 28 beans.

    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 6161
    22 x 28 = 616 beans.

    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 multiplication 48 x 65 3120
    Egyptian Multiplication beans.48 x 65 = 3120

    1 65

    2 130

    4 260

    8 520

    16 1040

    32 2080

    2080

    +1040

    3120



    Russian peasant multiplication 32 x 45 1440
    Russian Peasant Multiplication beans.32 x 45 = 1440

    32 45

    16 90

    8 180

    4 360

    2 720

    1 1440


    32 45 beans.32 x 45

    16 90

    8 180

    4 360

    2 720

    1 1440


    32 45 beans.32 x 45

    (16 x 2) x 45

    16 90

    8 180

    4 360

    2 720

    1 1440


    32 45 beans.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 beans.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 beans.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 beans.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 beans.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 beans.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 beans.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 beans.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 beans.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 multiplication 48 x 65 3120
    Russian Peasant Multiplication beans.48 x 65 = 3120

    48 65

    24 130

    12 260

    6 520

    3 1040

    1 2080

    2080

    +1040

    3120


    48 65 48 x 65 beans.

    24 130

    12 260

    6 520

    3 1040

    1 2080


    48 65 48 x 65 beans.

    24 130 24 x 130

    12 260

    6 520

    3 1040

    1 2080


    48 65 48 x 65 beans.

    24 130 24 x 130

    12 260 12 x 260

    6 520

    3 1040

    1 2080


    48 65 48 x 65 beans.

    24 130 24 x 130

    12 260 12 x 260

    6 520 6 x 520

    3 1040

    1 2080


    48 65 48 x 65 beans.

    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 beans.

    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 beans.

    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 beans.

    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
    Mental Math beans.

    • 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 math1
    Mental Math beans.

    • 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 math2
    Mental Math beans.

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


    Mental math3
    Mental Math beans.

    • Using Easy Combinations

      35 + 7 + 15


    Mental math4
    Mental Math beans.

    • Using Easy Combinations

    • Using Adjustments in Mental Calculations

      57 + 84


    Mental math5
    Mental Math beans.

    • Using Easy Combinations

    • Using Adjustments in Mental Calculations

      57 + 84

      83 - 48


    Mental math6
    Mental Math beans.

    • Using Easy Combinations

    • Using Adjustments in Mental Calculations

    • Working From Left to Right

      352 + 647


    Mental math7
    Mental Math beans.

    • Using Easy Combinations

    • Using Adjustments in Mental Calculations

    • Working From Left to Right

      352 + 647

      739 - 224


    Mental math8
    Mental Math beans.

    • Using Easy Combinations

    • Using Adjustments in Mental Calculations

    • Working From Left to Right

      352 + 647

      739 – 224

      4 x 235



    25 x 8 beans.


    4 x 99 beans.


    57 - 25 beans.


    47 x 5 beans.


    286 + 347 beans.


    493 x 7 beans.


    Rounding
    Rounding beans.

    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: beans.

    5,842 6,000


    67,498,499 to the nearest thousand: beans.

    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: beans.

    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 rule page 201
    5-Up Rule beans.Page 201


    Round 549 to the nearest hundred: beans.

    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
    Round 29,853 to the position indicated. beans.

    • Ten thousand:

      • 30,000

  • Thousand:

    • 30,000

  • Hundred:

    • 29,900

  • Ten:

    • 29,850


  • Approximate by rounding 2 954 482 82
    Approximate By Rounding beans. 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
    Round to the left-most digit to find approximate answer. beans.

    • 2681 + 241 =

      3000 + 200 = 3200

      • 2681 – 241 =

      3000 – 200 = 2800

      • 2681 x 241 =

      3000 x 200 = 600,000

    • 57801 ÷ 336 =

      60,000 ÷ 300 = 200



    Math and music the magical connection
    Math and Music beans.The Magical Connection!

    • Scholastic Parent and Child Magazine

    • Spelling

    • Phone Numbers

    • School House Rock


    Skip to my lou
    “Skip to My Lou” beans.

    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 beans.

    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)


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