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Additive Number System

- 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

Count!

- Fe
- Fi
- Fo
- Fum
- Fiddle
- Fruit
- Folks
- Fist

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

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

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

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 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

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

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

Test - Chapter 2

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

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

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

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”

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

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 beans.

Base beans.Five

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

125’s 25’s fives ones

. . . _____ _____ _____ _____ _____

54 53525150

Base beans.Six

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

216’s 36’s six ones

. . . _____ _____ _____ _____ _____

64 63626160

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 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 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

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 beans.

382 = _______five

Put 382 beans in groups of 5 beans.

382 = ______ five

382 = ____ beans.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 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 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. 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 beans.382 = _____five

5 )382 (beans) remainder 2

5 )76 (longs) remainder 1

15 (flats)

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 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 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 beans.

Homework Questions beans.Page 154

Homework Questions beans.Page 161

Go over Labs beans.

Adding Bean Sticks beans.

324five + 243five

324 beans.five + 243five

Make Exchanges beans.

324five + 243five

Make Exchanges beans.

324five + 243five

324 beans.five + 243five

1122five

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

- 43five + 24five

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 following: beans.

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

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 following: beans.

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

Take away model beans.Take away 3 beans

232five – 143five

232 beans.five – 143five

Take away 4 longs beans.

232five – 143five

232 beans.five – 143five

Take away 1 flat beans.

232five – 143five

232 beans.five – 143five

232 beans.five – 143five

34five

Use your bean sticks to complete the following: beans.

- 1142five – 213five =

Use your bean sticks to complete the following: beans.

- 1142five – 213five = 424five
- 2331five -124five =

Use your bean sticks to complete the following: beans.

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

Use your bean sticks to complete the following: beans.

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

LAB beans.

1221three + 122three

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 beans.

Homework Questions beans.Page 177

Worksheet Questions beans.

Napier’s Bones beans.

64 x 36 beans.

64 x 36 beans.

64 x 36 =2304 beans.

Lattice Multiplication beans.98 x 47

Lattice Multiplication beans.98 x 47 = 4606

Lattice Multiplication beans.576 x 49

Lattice Multiplication beans.576 x 49 = 28,224

Egyptian Multiplication beans.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

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

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 beans.48 x 65

Russian Peasant Multiplication beans.32 x 45

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 beans.48 x 65

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 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 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 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 Math beans.

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

Mental Math beans.

- Using Easy Combinations
35 + 7 + 15

Mental Math beans.

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

Mental Math beans.

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

83 - 48

Mental Math beans.

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

Mental Math beans.

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

739 - 224

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 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 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. beans. Thousand: Hundred: Ten:

- Ten thousand:
- 30,000

- 30,000

- 29,900

- 29,850

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. 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 beans.The Magical Connection!

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

“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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