Chapter 3 Numeration And Computation. 5 America’s Funniest Home Videos Tally’s on a staff...
-
Upload
lewis-osborne -
Category
Documents
-
view
220 -
download
1
Transcript of Chapter 3 Numeration And Computation. 5 America’s Funniest Home Videos Tally’s on a staff...
![Page 1: 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.](https://reader035.fdocuments.in/reader035/viewer/2022062308/56649eb45503460f94bbc77a/html5/thumbnails/1.jpg)
Chapter 3
Numeration
And
Computation
![Page 2: 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.](https://reader035.fdocuments.in/reader035/viewer/2022062308/56649eb45503460f94bbc77a/html5/thumbnails/2.jpg)
5
![Page 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.](https://reader035.fdocuments.in/reader035/viewer/2022062308/56649eb45503460f94bbc77a/html5/thumbnails/3.jpg)
• 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
![Page 4: 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.](https://reader035.fdocuments.in/reader035/viewer/2022062308/56649eb45503460f94bbc77a/html5/thumbnails/4.jpg)
Count!
• Fe• Fi• Fo• Fum• Fiddle• Fruit• Folks• Fist
![Page 5: 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.](https://reader035.fdocuments.in/reader035/viewer/2022062308/56649eb45503460f94bbc77a/html5/thumbnails/5.jpg)
Fe fiddle-fiddle-feFi fiddle-fiddle-fiFo fiddle-fiddle-foFum fiddle-fiddle-fumFiddle fiddle-fiddle-fiddleFiddle-fe fiddle-fiddle-fiddle-feFiddle-fi fiddle-fiddle-fiddle-fiFiddle-fo fiddle-fiddle-fiddle-foFiddle-fum fiddle-fiddle-fiddle-fumFiddle-fiddle fiddle-fiddle-fiddle-
fiddle
![Page 6: 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.](https://reader035.fdocuments.in/reader035/viewer/2022062308/56649eb45503460f94bbc77a/html5/thumbnails/6.jpg)
Fe fi-fiddle-feFi fi-fiddle-fiFo fi-fiddle-foFum fi-fiddle-fumFiddle fo-fiddleFiddle-fe fo-fiddle-feFiddle-fi fo-fiddle-fiFiddle-fo fo-fiddle-foFiddle-fum fo-fiddle-fumFi-fiddle fum-fiddle
![Page 7: 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.](https://reader035.fdocuments.in/reader035/viewer/2022062308/56649eb45503460f94bbc77a/html5/thumbnails/7.jpg)
Written Number System
Number Symbol
![Page 8: 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.](https://reader035.fdocuments.in/reader035/viewer/2022062308/56649eb45503460f94bbc77a/html5/thumbnails/8.jpg)
Additive Number System
M M M N N N N ^ ^ ^ ^ l l l
M M N N N l l l l
![Page 9: 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.](https://reader035.fdocuments.in/reader035/viewer/2022062308/56649eb45503460f94bbc77a/html5/thumbnails/9.jpg)
Use a Multiplier
M M M N N N N ^ ^ ^ ^ l l l
M M N N N l l l l
![Page 10: 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.](https://reader035.fdocuments.in/reader035/viewer/2022062308/56649eb45503460f94bbc77a/html5/thumbnails/10.jpg)
Positional Number System
M M M N N N N ^ ^ ^ ^ l l l
M M N N N l l l l
![Page 11: 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.](https://reader035.fdocuments.in/reader035/viewer/2022062308/56649eb45503460f94bbc77a/html5/thumbnails/11.jpg)
Egyptian Number SystemPage 144
• Additive System
![Page 12: 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.](https://reader035.fdocuments.in/reader035/viewer/2022062308/56649eb45503460f94bbc77a/html5/thumbnails/12.jpg)
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
![Page 13: 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.](https://reader035.fdocuments.in/reader035/viewer/2022062308/56649eb45503460f94bbc77a/html5/thumbnails/13.jpg)
• Millions Poster
• Collecting a Million Pennies
• Sharing “Millions” with the Elementary School
• Collecting a Million Pennies in High School
• Spending a Million Dollars
![Page 14: 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.](https://reader035.fdocuments.in/reader035/viewer/2022062308/56649eb45503460f94bbc77a/html5/thumbnails/14.jpg)
Babylonian Number System
Number Symbol
1 l
10 <
1
60x60x60
216,000
60x60
3600 60
![Page 15: 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.](https://reader035.fdocuments.in/reader035/viewer/2022062308/56649eb45503460f94bbc77a/html5/thumbnails/15.jpg)
Babylonian Number System
Number Symbol
1 l
10 <
0
1
60x60x60
216,000
60x60
3600 60
![Page 16: 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.](https://reader035.fdocuments.in/reader035/viewer/2022062308/56649eb45503460f94bbc77a/html5/thumbnails/16.jpg)
Babylonian Number System
< < < l l l l < < < < < < l l l l l l l
< < l l l l < < < < l l l l l
![Page 17: 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.](https://reader035.fdocuments.in/reader035/viewer/2022062308/56649eb45503460f94bbc77a/html5/thumbnails/17.jpg)
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.
![Page 18: 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.](https://reader035.fdocuments.in/reader035/viewer/2022062308/56649eb45503460f94bbc77a/html5/thumbnails/18.jpg)
Mayan Number System
Number Symbol
0
1
5
20x20x20x18
144,000
20x20x18
7200
20 x 18
360
20
1
![Page 19: 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.](https://reader035.fdocuments.in/reader035/viewer/2022062308/56649eb45503460f94bbc77a/html5/thumbnails/19.jpg)
Mayan Number System
![Page 20: 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.](https://reader035.fdocuments.in/reader035/viewer/2022062308/56649eb45503460f94bbc77a/html5/thumbnails/20.jpg)
Roman Numerals
Roman
Symbol
I V X L C D M
Hindu
Arabic
1 5 10 50 100 500 1000
![Page 21: 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.](https://reader035.fdocuments.in/reader035/viewer/2022062308/56649eb45503460f94bbc77a/html5/thumbnails/21.jpg)
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.
![Page 22: 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.](https://reader035.fdocuments.in/reader035/viewer/2022062308/56649eb45503460f94bbc77a/html5/thumbnails/22.jpg)
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
![Page 23: 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.](https://reader035.fdocuments.in/reader035/viewer/2022062308/56649eb45503460f94bbc77a/html5/thumbnails/23.jpg)
IIIIIIIV (the one that comes before 5)VVI (the one that comes after 5)VIIVIIIIX (the one that comes before 10)X
![Page 24: 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.](https://reader035.fdocuments.in/reader035/viewer/2022062308/56649eb45503460f94bbc77a/html5/thumbnails/24.jpg)
I XII XXIII XXXIV XLV LVI LXVII LXXVIII LXXXIX XCX C
![Page 25: 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.](https://reader035.fdocuments.in/reader035/viewer/2022062308/56649eb45503460f94bbc77a/html5/thumbnails/25.jpg)
I X CII XX CCIII XXX CCCIV XL CDV L DVI LX DCVII LXX DCCVIII LXXX DCCCIX XC CMX C M
![Page 26: 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.](https://reader035.fdocuments.in/reader035/viewer/2022062308/56649eb45503460f94bbc77a/html5/thumbnails/26.jpg)
• Write 1469 using Roman Numerals
![Page 27: 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.](https://reader035.fdocuments.in/reader035/viewer/2022062308/56649eb45503460f94bbc77a/html5/thumbnails/27.jpg)
• Write MMMCMXCIX as a Hindu Arabic Number.
![Page 28: 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.](https://reader035.fdocuments.in/reader035/viewer/2022062308/56649eb45503460f94bbc77a/html5/thumbnails/28.jpg)
Multiplication Principal
• 649 =
![Page 29: 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.](https://reader035.fdocuments.in/reader035/viewer/2022062308/56649eb45503460f94bbc77a/html5/thumbnails/29.jpg)
Multiplication Principal
• 649 = DCXLIX
• 649,000 = DCXLIX
![Page 30: 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.](https://reader035.fdocuments.in/reader035/viewer/2022062308/56649eb45503460f94bbc77a/html5/thumbnails/30.jpg)
Multiplication Principal
• 649 = DCXLIX
• 649,000 = DCXLIX
• 649,428 =
![Page 31: 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.](https://reader035.fdocuments.in/reader035/viewer/2022062308/56649eb45503460f94bbc77a/html5/thumbnails/31.jpg)
Multiplication Principal
• 649 = DCXLIX
• 649,000 = DCXLIX
• 649,428 = DCXLIXCDXXVIII
• 649,000,000 =
![Page 32: 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.](https://reader035.fdocuments.in/reader035/viewer/2022062308/56649eb45503460f94bbc77a/html5/thumbnails/32.jpg)
Multiplication Principal
• 649 = DCXLIX
• 649,000 = DCXLIX
• 649,428 = DCXLIXCDXXVIII
• 649,000,000 = DCXLIX
![Page 33: 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.](https://reader035.fdocuments.in/reader035/viewer/2022062308/56649eb45503460f94bbc77a/html5/thumbnails/33.jpg)
Hindu-Arabic NumbersPage 149
![Page 34: 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.](https://reader035.fdocuments.in/reader035/viewer/2022062308/56649eb45503460f94bbc77a/html5/thumbnails/34.jpg)
Homework QuestionsChapter 2
![Page 35: 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.](https://reader035.fdocuments.in/reader035/viewer/2022062308/56649eb45503460f94bbc77a/html5/thumbnails/35.jpg)
C
BA
![Page 36: 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.](https://reader035.fdocuments.in/reader035/viewer/2022062308/56649eb45503460f94bbc77a/html5/thumbnails/36.jpg)
BA
![Page 37: 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.](https://reader035.fdocuments.in/reader035/viewer/2022062308/56649eb45503460f94bbc77a/html5/thumbnails/37.jpg)
Venn Diagram Lab Answers
![Page 38: 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.](https://reader035.fdocuments.in/reader035/viewer/2022062308/56649eb45503460f94bbc77a/html5/thumbnails/38.jpg)
Test - Chapter 2
• http://mcis.jsu.edu/faculty/mjohnson/ms133r2.html
![Page 39: 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.](https://reader035.fdocuments.in/reader035/viewer/2022062308/56649eb45503460f94bbc77a/html5/thumbnails/39.jpg)
Day 2
![Page 40: 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.](https://reader035.fdocuments.in/reader035/viewer/2022062308/56649eb45503460f94bbc77a/html5/thumbnails/40.jpg)
Set Theory Test
![Page 41: 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.](https://reader035.fdocuments.in/reader035/viewer/2022062308/56649eb45503460f94bbc77a/html5/thumbnails/41.jpg)
Base 10 Number System
10 digits: {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}
![Page 42: 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.](https://reader035.fdocuments.in/reader035/viewer/2022062308/56649eb45503460f94bbc77a/html5/thumbnails/42.jpg)
Base 10 Number System
hundred ten
millions thousands thousands thousands hundreds tens ones
____ , ____ ____ ____ , ____ ____ ____
0123456 10101010101010
![Page 43: 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.](https://reader035.fdocuments.in/reader035/viewer/2022062308/56649eb45503460f94bbc77a/html5/thumbnails/43.jpg)
Base 10 Number System
hundred ten hundred ten
millions millions millions thousands thousands thousands hundreds tens ones
___ ___ ___ , ___ ___ ___ , ___ ___ ___
![Page 44: 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.](https://reader035.fdocuments.in/reader035/viewer/2022062308/56649eb45503460f94bbc77a/html5/thumbnails/44.jpg)
• Ones
• Tens
• Hundreds
• Thousands
• Ten Thousands
• Hundred Thousands
![Page 45: 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.](https://reader035.fdocuments.in/reader035/viewer/2022062308/56649eb45503460f94bbc77a/html5/thumbnails/45.jpg)
• Millions
• Ten Millions
• Hundred Millions
• Billions
• Ten Billions
• Hundred Billions
![Page 46: 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.](https://reader035.fdocuments.in/reader035/viewer/2022062308/56649eb45503460f94bbc77a/html5/thumbnails/46.jpg)
• Trillions
• Ten Trillions
• Hundred Trillions
• Quadrillions
• Ten Quadrillions
• Hundred Quadrillions
![Page 47: 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.](https://reader035.fdocuments.in/reader035/viewer/2022062308/56649eb45503460f94bbc77a/html5/thumbnails/47.jpg)
• Quintillions
• Ten Quintillions
• Hundred Quintillions
• Sextillions
• Ten Sextillions
• Hundred Sextillions
![Page 48: 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.](https://reader035.fdocuments.in/reader035/viewer/2022062308/56649eb45503460f94bbc77a/html5/thumbnails/48.jpg)
• Septillions
• Ten Septillions
• Hundred Septillions
• Octillions
• Ten Octillions
• Hundred Octillions
![Page 49: 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.](https://reader035.fdocuments.in/reader035/viewer/2022062308/56649eb45503460f94bbc77a/html5/thumbnails/49.jpg)
• Nonillions
• Ten Nonillions
• Hundred Nonillions
• Decillions
• Ten Decillions
• Hundred Decillions
![Page 50: 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.](https://reader035.fdocuments.in/reader035/viewer/2022062308/56649eb45503460f94bbc77a/html5/thumbnails/50.jpg)
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
10010
![Page 51: 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.](https://reader035.fdocuments.in/reader035/viewer/2022062308/56649eb45503460f94bbc77a/html5/thumbnails/51.jpg)
Googol-plex
googol10
![Page 52: 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.](https://reader035.fdocuments.in/reader035/viewer/2022062308/56649eb45503460f94bbc77a/html5/thumbnails/52.jpg)
The I Hate Mathematics Book by Marilyn BurnsMath for Smarty Pants by Marilyn BurnsSpaghetti and Meatballs for All! by Marilyn BurnsThe m&m’s Counting Book by Barbara Barbieri McGrathCounting Kisses by Karen KatzMath Potatoes by Greg TangMillions of Cats by Wanda Ga’g
![Page 53: 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.](https://reader035.fdocuments.in/reader035/viewer/2022062308/56649eb45503460f94bbc77a/html5/thumbnails/53.jpg)
Expanded Notation
Expanded Notation tells what the number means.
25,683
![Page 54: 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.](https://reader035.fdocuments.in/reader035/viewer/2022062308/56649eb45503460f94bbc77a/html5/thumbnails/54.jpg)
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)
![Page 55: 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.](https://reader035.fdocuments.in/reader035/viewer/2022062308/56649eb45503460f94bbc77a/html5/thumbnails/55.jpg)
Reading Numbers
• 25, 638
• “Twenty five thousand, six hundred thirty-eight”
![Page 56: 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.](https://reader035.fdocuments.in/reader035/viewer/2022062308/56649eb45503460f94bbc77a/html5/thumbnails/56.jpg)
Reading Numbers
• 25, 638, 304
• “Twenty five million, six hundred thirty-eight thousand, three hundred four”
![Page 57: 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.](https://reader035.fdocuments.in/reader035/viewer/2022062308/56649eb45503460f94bbc77a/html5/thumbnails/57.jpg)
Models for Numeration Lab
FLAT
LONG
BEAN
LONG-FLAT
![Page 58: 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.](https://reader035.fdocuments.in/reader035/viewer/2022062308/56649eb45503460f94bbc77a/html5/thumbnails/58.jpg)
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
![Page 59: 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.](https://reader035.fdocuments.in/reader035/viewer/2022062308/56649eb45503460f94bbc77a/html5/thumbnails/59.jpg)
2 Long-flats, 3 Longs, and 4 beans
How many beans total?
269 beans
![Page 60: 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.](https://reader035.fdocuments.in/reader035/viewer/2022062308/56649eb45503460f94bbc77a/html5/thumbnails/60.jpg)
Make a collection of 42 beans using the least number of pieces possible.
![Page 61: 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.](https://reader035.fdocuments.in/reader035/viewer/2022062308/56649eb45503460f94bbc77a/html5/thumbnails/61.jpg)
Make a collection of 42 beans using the least number of pieces possible.
![Page 62: 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.](https://reader035.fdocuments.in/reader035/viewer/2022062308/56649eb45503460f94bbc77a/html5/thumbnails/62.jpg)
Begin with 1 Long-flat. Trade in as needed to give away 12 beans.
What’s left?
![Page 63: 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.](https://reader035.fdocuments.in/reader035/viewer/2022062308/56649eb45503460f94bbc77a/html5/thumbnails/63.jpg)
4 Flats, 2 Longs, 3 Beans
![Page 64: 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.](https://reader035.fdocuments.in/reader035/viewer/2022062308/56649eb45503460f94bbc77a/html5/thumbnails/64.jpg)
Base Five
Five Digits: {0, 1, 2, 3, 4}
125’s 25’s fives ones
. . . _____ _____ _____ _____ _____
54 53 52 51 50
![Page 65: 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.](https://reader035.fdocuments.in/reader035/viewer/2022062308/56649eb45503460f94bbc77a/html5/thumbnails/65.jpg)
Count in Base 5
12341011121314
20
21
22
23
24
30
31
32
33
34
40
![Page 66: 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.](https://reader035.fdocuments.in/reader035/viewer/2022062308/56649eb45503460f94bbc77a/html5/thumbnails/66.jpg)
Count in Base 5
12341011121314
20
21
22
23
24
30
31
32
33
34
40
41
42
43
44
100
![Page 67: 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.](https://reader035.fdocuments.in/reader035/viewer/2022062308/56649eb45503460f94bbc77a/html5/thumbnails/67.jpg)
Base Six
Six Digits: {0, 1, 2, 3, 4, 5}
216’s 36’s six ones
. . . _____ _____ _____ _____ _____
64 63 62 61 60
![Page 68: 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.](https://reader035.fdocuments.in/reader035/viewer/2022062308/56649eb45503460f94bbc77a/html5/thumbnails/68.jpg)
Count in Base 612345101112
13
14
15
20
21
22
23
24
25
30
31
32
33
34
35
40
41
42
43
44
45
50
51
52
53
54
55
100
101
.
.
.
![Page 69: 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.](https://reader035.fdocuments.in/reader035/viewer/2022062308/56649eb45503460f94bbc77a/html5/thumbnails/69.jpg)
Base Twelve
Twelve Digits: {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, T, E}
1728’s 144’s twelve ones
. . . _____ _____ _____ _____ _____
124 123 122 121 120
![Page 70: 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.](https://reader035.fdocuments.in/reader035/viewer/2022062308/56649eb45503460f94bbc77a/html5/thumbnails/70.jpg)
Count in Base Twelve1
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
29
2T
2E
30
31
.
.
.
![Page 71: 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.](https://reader035.fdocuments.in/reader035/viewer/2022062308/56649eb45503460f94bbc77a/html5/thumbnails/71.jpg)
Base Two
Two Digits; {0, 1}
8’s 4’s twos ones
. . . _____ _____ _____ _____ _____
24 23 22 21 20
![Page 72: 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.](https://reader035.fdocuments.in/reader035/viewer/2022062308/56649eb45503460f94bbc77a/html5/thumbnails/72.jpg)
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
![Page 73: 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.](https://reader035.fdocuments.in/reader035/viewer/2022062308/56649eb45503460f94bbc77a/html5/thumbnails/73.jpg)
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)
![Page 74: 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.](https://reader035.fdocuments.in/reader035/viewer/2022062308/56649eb45503460f94bbc77a/html5/thumbnails/74.jpg)
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
![Page 75: 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.](https://reader035.fdocuments.in/reader035/viewer/2022062308/56649eb45503460f94bbc77a/html5/thumbnails/75.jpg)
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 =
![Page 76: 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.](https://reader035.fdocuments.in/reader035/viewer/2022062308/56649eb45503460f94bbc77a/html5/thumbnails/76.jpg)
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
![Page 77: 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.](https://reader035.fdocuments.in/reader035/viewer/2022062308/56649eb45503460f94bbc77a/html5/thumbnails/77.jpg)
Start with base 10
382 = _______five
![Page 78: 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.](https://reader035.fdocuments.in/reader035/viewer/2022062308/56649eb45503460f94bbc77a/html5/thumbnails/78.jpg)
Put 382 beans in groups of 5
382 = ______ five
![Page 79: 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.](https://reader035.fdocuments.in/reader035/viewer/2022062308/56649eb45503460f94bbc77a/html5/thumbnails/79.jpg)
382 = ____2 five
76 longs and 2 beans left over.
![Page 80: 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.](https://reader035.fdocuments.in/reader035/viewer/2022062308/56649eb45503460f94bbc77a/html5/thumbnails/80.jpg)
Put 76 longs in groups of 5
382 = ____2 five
76 longs and 2 beans left over.
![Page 81: 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.](https://reader035.fdocuments.in/reader035/viewer/2022062308/56649eb45503460f94bbc77a/html5/thumbnails/81.jpg)
382 = __ 12 five
76 longs and 2 beans left over.
15 flats, 1 long left over, 2 beans left over.
![Page 82: 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.](https://reader035.fdocuments.in/reader035/viewer/2022062308/56649eb45503460f94bbc77a/html5/thumbnails/82.jpg)
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.
![Page 83: 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.](https://reader035.fdocuments.in/reader035/viewer/2022062308/56649eb45503460f94bbc77a/html5/thumbnails/83.jpg)
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.
![Page 84: 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.](https://reader035.fdocuments.in/reader035/viewer/2022062308/56649eb45503460f94bbc77a/html5/thumbnails/84.jpg)
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.
![Page 85: 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.](https://reader035.fdocuments.in/reader035/viewer/2022062308/56649eb45503460f94bbc77a/html5/thumbnails/85.jpg)
Short Division382 = _____five
5 )382 (beans)
(longs)
![Page 86: 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.](https://reader035.fdocuments.in/reader035/viewer/2022062308/56649eb45503460f94bbc77a/html5/thumbnails/86.jpg)
Short Division382 = _____five
5 )382 (beans) remainder 2
76 (longs)
![Page 87: 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.](https://reader035.fdocuments.in/reader035/viewer/2022062308/56649eb45503460f94bbc77a/html5/thumbnails/87.jpg)
Short Division382 = _____five
5 )382 (beans) remainder 2
5 )76 (longs) remainder 1
15 (flats)
![Page 88: 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.](https://reader035.fdocuments.in/reader035/viewer/2022062308/56649eb45503460f94bbc77a/html5/thumbnails/88.jpg)
Short Division382 = _____five
5 )382 (beans) remainder 2
5 )76 (longs) remainder 1
5 )15 (flats) remainder 0
3 (long-flats)
![Page 89: 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.](https://reader035.fdocuments.in/reader035/viewer/2022062308/56649eb45503460f94bbc77a/html5/thumbnails/89.jpg)
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
![Page 90: 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.](https://reader035.fdocuments.in/reader035/viewer/2022062308/56649eb45503460f94bbc77a/html5/thumbnails/90.jpg)
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
![Page 91: 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.](https://reader035.fdocuments.in/reader035/viewer/2022062308/56649eb45503460f94bbc77a/html5/thumbnails/91.jpg)
Day 3
![Page 92: 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.](https://reader035.fdocuments.in/reader035/viewer/2022062308/56649eb45503460f94bbc77a/html5/thumbnails/92.jpg)
Homework QuestionsPage 154
![Page 93: 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.](https://reader035.fdocuments.in/reader035/viewer/2022062308/56649eb45503460f94bbc77a/html5/thumbnails/93.jpg)
Homework QuestionsPage 161
![Page 94: 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.](https://reader035.fdocuments.in/reader035/viewer/2022062308/56649eb45503460f94bbc77a/html5/thumbnails/94.jpg)
Go over Labs
![Page 95: 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.](https://reader035.fdocuments.in/reader035/viewer/2022062308/56649eb45503460f94bbc77a/html5/thumbnails/95.jpg)
Adding Bean Sticks
324five + 243five
![Page 96: 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.](https://reader035.fdocuments.in/reader035/viewer/2022062308/56649eb45503460f94bbc77a/html5/thumbnails/96.jpg)
324five + 243five
![Page 97: 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.](https://reader035.fdocuments.in/reader035/viewer/2022062308/56649eb45503460f94bbc77a/html5/thumbnails/97.jpg)
Make Exchanges
324five + 243five
![Page 98: 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.](https://reader035.fdocuments.in/reader035/viewer/2022062308/56649eb45503460f94bbc77a/html5/thumbnails/98.jpg)
Make Exchanges
324five + 243five
![Page 99: 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.](https://reader035.fdocuments.in/reader035/viewer/2022062308/56649eb45503460f94bbc77a/html5/thumbnails/99.jpg)
324five + 243five
1122five
![Page 100: 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.](https://reader035.fdocuments.in/reader035/viewer/2022062308/56649eb45503460f94bbc77a/html5/thumbnails/100.jpg)
Use your base five pieces to find each of the following:
1. 43five + 24five
![Page 101: 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.](https://reader035.fdocuments.in/reader035/viewer/2022062308/56649eb45503460f94bbc77a/html5/thumbnails/101.jpg)
Use your base five pieces to find each of the following:
1. 43five + 24five = 122five
2. 313five + 233five =
![Page 102: 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.](https://reader035.fdocuments.in/reader035/viewer/2022062308/56649eb45503460f94bbc77a/html5/thumbnails/102.jpg)
Use your base five pieces to find each of the following:
1. 43five + 24five = 122five
2. 313five + 233five = 1101five
3. 304five + 20five +120five + 22five =
![Page 103: 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.](https://reader035.fdocuments.in/reader035/viewer/2022062308/56649eb45503460f94bbc77a/html5/thumbnails/103.jpg)
Use your base five pieces to find each of the following:
1. 43five + 24five = 122five
2. 313five + 233five = 1101five
3. 304five + 20five +120five + 22five = 1021five
4. 1000five + 100five + 10five =
![Page 104: 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.](https://reader035.fdocuments.in/reader035/viewer/2022062308/56649eb45503460f94bbc77a/html5/thumbnails/104.jpg)
Use your base five pieces to find each of the following:
1. 43five + 24five = 122five
2. 313five + 233five = 1101five
3. 304five + 20five +120five + 22five = 1021five
4. 1000five + 100five + 10five = 1110five
![Page 105: 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.](https://reader035.fdocuments.in/reader035/viewer/2022062308/56649eb45503460f94bbc77a/html5/thumbnails/105.jpg)
Take away modelTake away 3 beans
232five – 143five
![Page 106: 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.](https://reader035.fdocuments.in/reader035/viewer/2022062308/56649eb45503460f94bbc77a/html5/thumbnails/106.jpg)
232five – 143five
![Page 107: 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.](https://reader035.fdocuments.in/reader035/viewer/2022062308/56649eb45503460f94bbc77a/html5/thumbnails/107.jpg)
Take away 4 longs
232five – 143five
![Page 108: 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.](https://reader035.fdocuments.in/reader035/viewer/2022062308/56649eb45503460f94bbc77a/html5/thumbnails/108.jpg)
232five – 143five
![Page 109: 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.](https://reader035.fdocuments.in/reader035/viewer/2022062308/56649eb45503460f94bbc77a/html5/thumbnails/109.jpg)
Take away 1 flat
232five – 143five
![Page 110: 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.](https://reader035.fdocuments.in/reader035/viewer/2022062308/56649eb45503460f94bbc77a/html5/thumbnails/110.jpg)
232five – 143five
![Page 111: 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.](https://reader035.fdocuments.in/reader035/viewer/2022062308/56649eb45503460f94bbc77a/html5/thumbnails/111.jpg)
232five – 143five
34five
![Page 112: 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.](https://reader035.fdocuments.in/reader035/viewer/2022062308/56649eb45503460f94bbc77a/html5/thumbnails/112.jpg)
Use your bean sticks to complete the following:
1. 1142five – 213five =
![Page 113: 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.](https://reader035.fdocuments.in/reader035/viewer/2022062308/56649eb45503460f94bbc77a/html5/thumbnails/113.jpg)
Use your bean sticks to complete the following:
1. 1142five – 213five = 424five
2. 2331five -124five =
![Page 114: 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.](https://reader035.fdocuments.in/reader035/viewer/2022062308/56649eb45503460f94bbc77a/html5/thumbnails/114.jpg)
Use your bean sticks to complete the following:
1. 1142five – 213five = 424five
2. 2331five -124five = 2202five
3. 4112five – 143five =
![Page 115: 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.](https://reader035.fdocuments.in/reader035/viewer/2022062308/56649eb45503460f94bbc77a/html5/thumbnails/115.jpg)
Use your bean sticks to complete the following:
1. 1142five – 213five = 424five
2. 2331five -124five = 2202five
3. 4112five – 143five = 3414five
![Page 116: 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.](https://reader035.fdocuments.in/reader035/viewer/2022062308/56649eb45503460f94bbc77a/html5/thumbnails/116.jpg)
LAB
1221three + 122three
LF
F F
F
![Page 117: 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.](https://reader035.fdocuments.in/reader035/viewer/2022062308/56649eb45503460f94bbc77a/html5/thumbnails/117.jpg)
Note your Final Answer
1221three + 122three
2120three
LF
F F
FF
LF
![Page 118: 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.](https://reader035.fdocuments.in/reader035/viewer/2022062308/56649eb45503460f94bbc77a/html5/thumbnails/118.jpg)
Subtract
432six – 144six =
F F F F
![Page 119: 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.](https://reader035.fdocuments.in/reader035/viewer/2022062308/56649eb45503460f94bbc77a/html5/thumbnails/119.jpg)
432six – 144six =
= 244six
F F F F
![Page 120: 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.](https://reader035.fdocuments.in/reader035/viewer/2022062308/56649eb45503460f94bbc77a/html5/thumbnails/120.jpg)
LAB
![Page 121: 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.](https://reader035.fdocuments.in/reader035/viewer/2022062308/56649eb45503460f94bbc77a/html5/thumbnails/121.jpg)
201three 2312four 255six
+102three +203four +134six
111two 2333four 11011two
+101two +333four +10101two
![Page 122: 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.](https://reader035.fdocuments.in/reader035/viewer/2022062308/56649eb45503460f94bbc77a/html5/thumbnails/122.jpg)
1221three 2312four 1001four
-122three -203four -112four
1010two 101ten 1001three
-101two -11ten -112three
![Page 123: 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.](https://reader035.fdocuments.in/reader035/viewer/2022062308/56649eb45503460f94bbc77a/html5/thumbnails/123.jpg)
Day 4
![Page 124: 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.](https://reader035.fdocuments.in/reader035/viewer/2022062308/56649eb45503460f94bbc77a/html5/thumbnails/124.jpg)
Homework QuestionsPage 177
![Page 125: 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.](https://reader035.fdocuments.in/reader035/viewer/2022062308/56649eb45503460f94bbc77a/html5/thumbnails/125.jpg)
Worksheet Questions
![Page 126: 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.](https://reader035.fdocuments.in/reader035/viewer/2022062308/56649eb45503460f94bbc77a/html5/thumbnails/126.jpg)
Scratch Addition
2395
789
5463
1284
985
+677
![Page 127: 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.](https://reader035.fdocuments.in/reader035/viewer/2022062308/56649eb45503460f94bbc77a/html5/thumbnails/127.jpg)
4567
2396
569
392
1974
+568
![Page 128: 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.](https://reader035.fdocuments.in/reader035/viewer/2022062308/56649eb45503460f94bbc77a/html5/thumbnails/128.jpg)
Napier’s Bones
82
2026
21
1
4
8
4
2
3
421
3
8
21
4
0
4
000
0000
6
6
6
![Page 129: 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.](https://reader035.fdocuments.in/reader035/viewer/2022062308/56649eb45503460f94bbc77a/html5/thumbnails/129.jpg)
64 x 36
82
2026
21
1
4
8
4
2
3
421
3
8
21
4
0
4
000
0000
6
6
6
![Page 130: 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.](https://reader035.fdocuments.in/reader035/viewer/2022062308/56649eb45503460f94bbc77a/html5/thumbnails/130.jpg)
64 x 36
82
2026
21
1
4
8
4
2
3
421
3
8
21
4
0
4
000
0000
6
6
6
22
1
43
18
6
![Page 131: 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.](https://reader035.fdocuments.in/reader035/viewer/2022062308/56649eb45503460f94bbc77a/html5/thumbnails/131.jpg)
64 x 36 =2304
82
2026
21
1
4
8
4
2
3
421
3
8
21
4
0
4
000
0000
6
6
6
2
30 4
22
1
43
18
6
![Page 132: 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.](https://reader035.fdocuments.in/reader035/viewer/2022062308/56649eb45503460f94bbc77a/html5/thumbnails/132.jpg)
Lattice Multiplication98 x 47
7
4
89
![Page 133: 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.](https://reader035.fdocuments.in/reader035/viewer/2022062308/56649eb45503460f94bbc77a/html5/thumbnails/133.jpg)
Lattice Multiplication98 x 47 = 4606
4
6
0 6
53 6
6
23
63
7
4
89
![Page 134: 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.](https://reader035.fdocuments.in/reader035/viewer/2022062308/56649eb45503460f94bbc77a/html5/thumbnails/134.jpg)
Lattice Multiplication576 x 49
9
4
675
![Page 135: 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.](https://reader035.fdocuments.in/reader035/viewer/2022062308/56649eb45503460f94bbc77a/html5/thumbnails/135.jpg)
Lattice Multiplication576 x 49 = 28,224
2
2 2
54
02
82
4
4
9
4
675
53
6
2
4
8
![Page 136: 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.](https://reader035.fdocuments.in/reader035/viewer/2022062308/56649eb45503460f94bbc77a/html5/thumbnails/136.jpg)
Egyptian Multiplication22 x 28
![Page 137: 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.](https://reader035.fdocuments.in/reader035/viewer/2022062308/56649eb45503460f94bbc77a/html5/thumbnails/137.jpg)
22 x 28 = 616
1 282 564 1128 22416 448
448112+56616
![Page 138: 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.](https://reader035.fdocuments.in/reader035/viewer/2022062308/56649eb45503460f94bbc77a/html5/thumbnails/138.jpg)
22 x 28
1 282 564 1128 22416 448
22 x 28 = (16 + 4 + 2) x 28
![Page 139: 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.](https://reader035.fdocuments.in/reader035/viewer/2022062308/56649eb45503460f94bbc77a/html5/thumbnails/139.jpg)
22 x 28
1 282 564 1128 22416 448
22 x 28 = (16 + 4 + 2) x 28= (16 x 28) + (4 x 28) + (2 x 28)
![Page 140: 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.](https://reader035.fdocuments.in/reader035/viewer/2022062308/56649eb45503460f94bbc77a/html5/thumbnails/140.jpg)
22 x 28 = 616
1 282 564 1128 22416 448
22 x 28 = (16 + 4 + 2) x 28= (16 x 28) + (4 x 28) + (2 x 28)= 448 + 112 + 56= 616
![Page 141: 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.](https://reader035.fdocuments.in/reader035/viewer/2022062308/56649eb45503460f94bbc77a/html5/thumbnails/141.jpg)
Egyptian Multiplication48 x 65
![Page 142: 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.](https://reader035.fdocuments.in/reader035/viewer/2022062308/56649eb45503460f94bbc77a/html5/thumbnails/142.jpg)
Egyptian Multiplication48 x 65 = 3120
1 652 1304 2608 52016 104032 2080
2080+1040 3120
![Page 143: 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.](https://reader035.fdocuments.in/reader035/viewer/2022062308/56649eb45503460f94bbc77a/html5/thumbnails/143.jpg)
Russian Peasant Multiplication32 x 45
![Page 144: 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.](https://reader035.fdocuments.in/reader035/viewer/2022062308/56649eb45503460f94bbc77a/html5/thumbnails/144.jpg)
Russian Peasant Multiplication32 x 45 = 1440
32 45
16 90
8 180
4 360
2 720
1 1440
![Page 145: 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.](https://reader035.fdocuments.in/reader035/viewer/2022062308/56649eb45503460f94bbc77a/html5/thumbnails/145.jpg)
32 45 32 x 45
16 90
8 180
4 360
2 720
1 1440
![Page 146: 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.](https://reader035.fdocuments.in/reader035/viewer/2022062308/56649eb45503460f94bbc77a/html5/thumbnails/146.jpg)
32 45 32 x 45(16 x 2) x 45
16 90
8 180
4 360
2 720
1 1440
![Page 147: 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.](https://reader035.fdocuments.in/reader035/viewer/2022062308/56649eb45503460f94bbc77a/html5/thumbnails/147.jpg)
32 45 32 x 45(16 x 2) x 4516 x (2 x 45)
16 90
8 180
4 360
2 720
1 1440
![Page 148: 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.](https://reader035.fdocuments.in/reader035/viewer/2022062308/56649eb45503460f94bbc77a/html5/thumbnails/148.jpg)
32 45 32 x 45(16 x 2) x 4516 x (2 x 45)
16 90 16 x 90
8 180
4 360
2 720
1 1440
![Page 149: 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.](https://reader035.fdocuments.in/reader035/viewer/2022062308/56649eb45503460f94bbc77a/html5/thumbnails/149.jpg)
32 45 32 x 45(16 x 2) x 4516 x (2 x 45)
16 90 16 x 90(8 x 2) x 908 x (2 x 90)
8 180
4 360
2 720
1 1440
![Page 150: 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.](https://reader035.fdocuments.in/reader035/viewer/2022062308/56649eb45503460f94bbc77a/html5/thumbnails/150.jpg)
32 45 32 x 45(16 x 2) x 4516 x (2 x 45)
16 90 16 x 90(8 x 2) x 908 x (2 x 90)
8 180 8 x 180
4 360
2 720
1 1440
![Page 151: 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.](https://reader035.fdocuments.in/reader035/viewer/2022062308/56649eb45503460f94bbc77a/html5/thumbnails/151.jpg)
32 45 32 x 45(16 x 2) x 4516 x (2 x 45)
16 90 16 x 90(8 x 2) x 908 x (2 x 90)
8 180 8 x 180(4 x 2) x 1804 x (2 x 180)
4 360
2 720
1 1440
![Page 152: 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.](https://reader035.fdocuments.in/reader035/viewer/2022062308/56649eb45503460f94bbc77a/html5/thumbnails/152.jpg)
32 45 32 x 45(16 x 2) x 4516 x (2 x 45)
16 90 16 x 90(8 x 2) x 908 x (2 x 90)
8 180 8 x 180(4 x 2) x 1804 x (2 x 180)
4 360 4 x 360
2 720
1 1440
![Page 153: 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.](https://reader035.fdocuments.in/reader035/viewer/2022062308/56649eb45503460f94bbc77a/html5/thumbnails/153.jpg)
32 45 32 x 45(16 x 2) x 4516 x (2 x 45)
16 90 16 x 90(8 x 2) x 908 x (2 x 90)
8 180 8 x 180(4 x 2) x 1804 x (2 x 180)
4 360 4 x 360(2 x 2) x 3602 x (2 x 360)
2 720
1 1440
![Page 154: 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.](https://reader035.fdocuments.in/reader035/viewer/2022062308/56649eb45503460f94bbc77a/html5/thumbnails/154.jpg)
32 45 32 x 45(16 x 2) x 4516 x (2 x 45)
16 90 16 x 90(8 x 2) x 908 x (2 x 90)
8 180 8 x 180(4 x 2) x 1804 x (2 x 180)
4 360 4 x 360(2 x 2) x 3602 x (2 x 360)
2 720 2 x 720
1 1440
![Page 155: 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.](https://reader035.fdocuments.in/reader035/viewer/2022062308/56649eb45503460f94bbc77a/html5/thumbnails/155.jpg)
32 45 32 x 45(16 x 2) x 4516 x (2 x 45)
16 90 16 x 90(8 x 2) x 908 x (2 x 90)
8 180 8 x 180(4 x 2) x 1804 x (2 x 180)
4 360 4 x 360(2 x 2) x 3602 x (2 x 360)
2 720 2 x 720(1 x 2) x 7201 x (2 x 720)
1 1440 1 x 1440
![Page 156: 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.](https://reader035.fdocuments.in/reader035/viewer/2022062308/56649eb45503460f94bbc77a/html5/thumbnails/156.jpg)
Russian Peasant Multiplication48 x 65
![Page 157: 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.](https://reader035.fdocuments.in/reader035/viewer/2022062308/56649eb45503460f94bbc77a/html5/thumbnails/157.jpg)
Russian Peasant Multiplication48 x 65 = 3120
48 6524 13012 2606 5203 10401 2080
2080 +1040
3120
![Page 158: 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.](https://reader035.fdocuments.in/reader035/viewer/2022062308/56649eb45503460f94bbc77a/html5/thumbnails/158.jpg)
48 65 48 x 65
24 130
12 260
6 520
3 1040
1 2080
![Page 159: 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.](https://reader035.fdocuments.in/reader035/viewer/2022062308/56649eb45503460f94bbc77a/html5/thumbnails/159.jpg)
48 65 48 x 65
24 130 24 x 130
12 260
6 520
3 1040
1 2080
![Page 160: 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.](https://reader035.fdocuments.in/reader035/viewer/2022062308/56649eb45503460f94bbc77a/html5/thumbnails/160.jpg)
48 65 48 x 65
24 130 24 x 130
12 260 12 x 260
6 520
3 1040
1 2080
![Page 161: 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.](https://reader035.fdocuments.in/reader035/viewer/2022062308/56649eb45503460f94bbc77a/html5/thumbnails/161.jpg)
48 65 48 x 65
24 130 24 x 130
12 260 12 x 260
6 520 6 x 520
3 1040
1 2080
![Page 162: 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.](https://reader035.fdocuments.in/reader035/viewer/2022062308/56649eb45503460f94bbc77a/html5/thumbnails/162.jpg)
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
![Page 163: 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.](https://reader035.fdocuments.in/reader035/viewer/2022062308/56649eb45503460f94bbc77a/html5/thumbnails/163.jpg)
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
![Page 164: 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.](https://reader035.fdocuments.in/reader035/viewer/2022062308/56649eb45503460f94bbc77a/html5/thumbnails/164.jpg)
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
![Page 165: 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.](https://reader035.fdocuments.in/reader035/viewer/2022062308/56649eb45503460f94bbc77a/html5/thumbnails/165.jpg)
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)
![Page 166: 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.](https://reader035.fdocuments.in/reader035/viewer/2022062308/56649eb45503460f94bbc77a/html5/thumbnails/166.jpg)
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.
![Page 167: 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.](https://reader035.fdocuments.in/reader035/viewer/2022062308/56649eb45503460f94bbc77a/html5/thumbnails/167.jpg)
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.
![Page 168: 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.](https://reader035.fdocuments.in/reader035/viewer/2022062308/56649eb45503460f94bbc77a/html5/thumbnails/168.jpg)
Mental Math
One digit facts and the properties of whole numbers are the basis for mental
calculations.
![Page 169: 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.](https://reader035.fdocuments.in/reader035/viewer/2022062308/56649eb45503460f94bbc77a/html5/thumbnails/169.jpg)
Mental Math
• Using Easy Combinations
35 + 7 + 15
![Page 170: 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.](https://reader035.fdocuments.in/reader035/viewer/2022062308/56649eb45503460f94bbc77a/html5/thumbnails/170.jpg)
Mental Math
• Using Easy Combinations
• Using Adjustments in Mental Calculations
57 + 84
![Page 171: 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.](https://reader035.fdocuments.in/reader035/viewer/2022062308/56649eb45503460f94bbc77a/html5/thumbnails/171.jpg)
Mental Math
• Using Easy Combinations
• Using Adjustments in Mental Calculations
57 + 84
83 - 48
![Page 172: 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.](https://reader035.fdocuments.in/reader035/viewer/2022062308/56649eb45503460f94bbc77a/html5/thumbnails/172.jpg)
Mental Math
• Using Easy Combinations
• Using Adjustments in Mental Calculations
• Working From Left to Right
352 + 647
![Page 173: 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.](https://reader035.fdocuments.in/reader035/viewer/2022062308/56649eb45503460f94bbc77a/html5/thumbnails/173.jpg)
Mental Math
• Using Easy Combinations
• Using Adjustments in Mental Calculations
• Working From Left to Right
352 + 647
739 - 224
![Page 174: 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.](https://reader035.fdocuments.in/reader035/viewer/2022062308/56649eb45503460f94bbc77a/html5/thumbnails/174.jpg)
Mental Math
• Using Easy Combinations• Using Adjustments in Mental Calculations• Working From Left to Right
352 + 647
739 – 224
4 x 235
![Page 175: 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.](https://reader035.fdocuments.in/reader035/viewer/2022062308/56649eb45503460f94bbc77a/html5/thumbnails/175.jpg)
8 + 3 + 4 + 6 + 7 + 12 + 4 + 3 + 6 + 3
![Page 176: 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.](https://reader035.fdocuments.in/reader035/viewer/2022062308/56649eb45503460f94bbc77a/html5/thumbnails/176.jpg)
25 x 8
![Page 177: 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.](https://reader035.fdocuments.in/reader035/viewer/2022062308/56649eb45503460f94bbc77a/html5/thumbnails/177.jpg)
4 x 99
![Page 178: 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.](https://reader035.fdocuments.in/reader035/viewer/2022062308/56649eb45503460f94bbc77a/html5/thumbnails/178.jpg)
57 - 25
![Page 179: 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.](https://reader035.fdocuments.in/reader035/viewer/2022062308/56649eb45503460f94bbc77a/html5/thumbnails/179.jpg)
47 x 5
![Page 180: 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.](https://reader035.fdocuments.in/reader035/viewer/2022062308/56649eb45503460f94bbc77a/html5/thumbnails/180.jpg)
286 + 347
![Page 181: 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.](https://reader035.fdocuments.in/reader035/viewer/2022062308/56649eb45503460f94bbc77a/html5/thumbnails/181.jpg)
493 x 7
![Page 182: 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.](https://reader035.fdocuments.in/reader035/viewer/2022062308/56649eb45503460f94bbc77a/html5/thumbnails/182.jpg)
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?
![Page 183: 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.](https://reader035.fdocuments.in/reader035/viewer/2022062308/56649eb45503460f94bbc77a/html5/thumbnails/183.jpg)
5,842 to the nearest thousand:
5,842 6,000
![Page 184: 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.](https://reader035.fdocuments.in/reader035/viewer/2022062308/56649eb45503460f94bbc77a/html5/thumbnails/184.jpg)
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
![Page 185: 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.](https://reader035.fdocuments.in/reader035/viewer/2022062308/56649eb45503460f94bbc77a/html5/thumbnails/185.jpg)
Round 524 to the nearest hundred:524≈500Round 587 to the nearest hundred:587≈600Round 549 to the nearest hundred:549≈500Round 550 to the nearest hundred:550≈600Round 551 to the nearest hundred:551≈600
![Page 186: 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.](https://reader035.fdocuments.in/reader035/viewer/2022062308/56649eb45503460f94bbc77a/html5/thumbnails/186.jpg)
5-Up RulePage 201
![Page 187: 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.](https://reader035.fdocuments.in/reader035/viewer/2022062308/56649eb45503460f94bbc77a/html5/thumbnails/187.jpg)
Round 549 to the nearest hundred:
549≈500
Round 550 to the nearest hundred:
550≈500
Round 551 to the nearest hundred:
551≈600
![Page 188: 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.](https://reader035.fdocuments.in/reader035/viewer/2022062308/56649eb45503460f94bbc77a/html5/thumbnails/188.jpg)
Round 29,853 to the position indicated.
• Ten thousand:• 30,000
• Thousand:• 30,000
• Hundred:• 29,900
• Ten:• 29,850
![Page 189: 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.](https://reader035.fdocuments.in/reader035/viewer/2022062308/56649eb45503460f94bbc77a/html5/thumbnails/189.jpg)
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 =
![Page 190: 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.](https://reader035.fdocuments.in/reader035/viewer/2022062308/56649eb45503460f94bbc77a/html5/thumbnails/190.jpg)
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
![Page 191: 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.](https://reader035.fdocuments.in/reader035/viewer/2022062308/56649eb45503460f94bbc77a/html5/thumbnails/191.jpg)
“I have . . . Who has . . . ?”
![Page 192: 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.](https://reader035.fdocuments.in/reader035/viewer/2022062308/56649eb45503460f94bbc77a/html5/thumbnails/192.jpg)
Math and MusicThe Magical Connection!
• Scholastic Parent and Child Magazine
• Spelling
• Phone Numbers
• School House Rock
![Page 193: 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.](https://reader035.fdocuments.in/reader035/viewer/2022062308/56649eb45503460f94bbc77a/html5/thumbnails/193.jpg)
“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.
![Page 194: 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.](https://reader035.fdocuments.in/reader035/viewer/2022062308/56649eb45503460f94bbc77a/html5/thumbnails/194.jpg)
3 time 7 is 21Now, at last we’ve all begun.4 times 7 is 28Let’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)