1 Numbers to 100 000

The distance around Earth’s equator is 40 075 kilometres.

The distance around Earth from pole to pole is 40 008 kilometres. Which distance is longer?

1Chapter

Numbers to 100 000

Lessons1.1 Numbersto1000001.2 ComparingNumbersto

1000001.3 Decomposingand

ComposingNumbers

Read, compare, and order numbers according to the place value of their digits. A number can be built or taken apart in different ways.

BIG IDEA

I wonder how big 40 000 really is.

1

Reading and writing numbers in standard, word, and expanded forms

Counting by ones, tens, hundreds, or thousands

Countbyones:5101,5102,5103,5104,…Countbytens:2001,2011,2021,2031,…Countbyhundreds:4200,4300,4400,4500,…Countbythousands:3800,4800,5800,6800,…

Determining the value of each digit in a number

Thousands Hundreds Tens Ones

4 7 2 8

standsfor standsfor standsfor standsfor 4thousands 7hundreds 2tens 8ones or4000 or700 or20 or8

Comparing numbers using a place-value chart

2910

Thousands Hundreds Tens Ones

2 9 1 0

2 6 8 82688

First,comparethethousands.Theyarethesame.Thencomparethehundreds.9hundredsisgreaterthan6hundreds.So,2910isgreaterthan2688.

RECALL PRIOR KNOWLEDGE

Standardform:1307Wordform:onethousandthreehundredsevenExpandedform:1000130017

2 Chapter 1 Numbersto100000

Express each number in standard form.

1 onehundrednine 2 eightthousandtwelve

3 2000170014013 4 500019011

Express each number in word form.

5 4691 6 2906

Express each number in expanded form.

7 64325 8 38055

Count by ones, tens, hundreds, or thousands.

9 5500,5600,5700, 10 9077,9078,9079,

11 5320,6320,7320, 12 4871,4881,4891,

Complete.

In5628,

13 Thedigit6isinthe place. 14 Thevalueofthedigit5is .

15 Thedigit2standsfor .

Compare the numbers.

16 Whichisgreater,3819or3918?

17 Whichisless,7052or936?

18 Whichisthegreatest,3625,4130,or4031?

Quick Check

Chapter 1 Numbersto1000003

LEARN Count by thousands.

TenThousands Thousands Hundreds Tens Ones


9000

10thousands51ten thousand

10000


1000,2000,3000,4000,5000,6000,7000,8000,9000,?

Goals• Countby1000and10000to100000.• Useplace-valuechartstoshownumbersto100000.• Readandwritenumbersto100000instandardform

andwordform.

1.1Lesson

Numbers to 100 000

Vocabularytenthousandhundredthousandstandardformwordform


Readthenumbers.Whatnumbercomesnext?

10000ortenthousand.

10tenthousands51hundred thousand

0 10000

1 ten

thou

sand

2 ten

thou

sand

s

3 ten

thou

sand

s

4 ten

thou

sand

s

5 ten

thou

sand

s

6 ten

thou

sand

s

7 ten

thou

sand

s

8 ten

thou

sand

s

9 ten

thou

sand

s

10 te

n tho

usand

s

50000 60000 70000 80000 90000 10000020000 30000 40000

LEARN Count by ten thousands.

Add1tenthousandto9tenthousandstoget10tenthousands.

10tenthousandsisthesameas1hundredthousand.Youwrite1hundredthousandas100000.

Hundred Thousands

Ten Thousands Thousands Hundreds Tens Ones

Hundred Thousands

Ten Thousands Thousands Hundreds Tens Ones

1 0 0 0 0 0

standsfor1hundred

thousandor100000

standsfor0ten

thousandsor0

standsfor0thousands

or0

standsfor0hundreds

or0

standsfor0tensor0

standsfor0onesor0

0 1000 5000 6000 7000 8000 9000 ?2000 3000 4000

Lesson 1.1 Numbersto1000005

LEARN Write numbers in standard form and word form.

Standardform:73486Wordform:seventy-threethousandfourhundredeighty-six


7 3 4 8 6


3 4 8 6

Standard form:3486Word form:threethousandfourhundredeighty-six

Count by ten thousands.

1 10000,20000, ,40000,50000,60000, ,80000,90000,

2 tenthousand,twentythousand,thirtythousand, ,fiftythousand, ,seventythousand,eightythousand,

,

GUIDED LEARNING


Express the number in word form.

4

Express the number in standard form.

5 Wordform:tenthousandtwohundredseventy-three

What are the missing headings?

3

1 2 0 5 9


6 8 1 7


Standardform:6817Wordform:

Standardform:

Standardform:12059Wordform:twelvethousandfifty-nine

GUIDED LEARNING



6 7048 7 90015

Express each amount of money in word form.

8 $86300 9 $70005


10 tenthousandsevenhundredthirty-two

11 fifty-twothousandninehundredfive

GUIDED LEARNING


8 6 7 2 1

First, read the ten thousands andthousands: eighty-six thousand.

Then read the remaining hundreds, tens,and ones: seven hundred twenty-one.

$86721isreadaseighty-sixthousandsevenhundredtwenty-onedollars.

b Howdoyouread$53023?

$53023isreadasfifty-threethousandtwenty-threedollars.

LEARN Read numbers to 100 000.Afactorymanagerearns$86721peryear.Aworkeratthefactoryearns$53023peryear.

a Howdoyouread$86721?


Workinpairs.

Activity 1Taketurnsreadingthesentencesaloud.Yourpartnerchecksthatthenumberineachsentencehasbeenreadcorrectly.

1 82759peopleattendedtheconcert.

2 Theorganizationraised$45085fromthecharityrun.

3 MountEverestis8848metresabovesealevel.

4 TheTrans-CanadaHighwayfromBritishColumbiatoNewfoundlandis7821kilometreslong.

Activity 2

5 Finda5-digitnumberthatdescribessomethingineverydaylife.Writeyournumberinstandardform.Explainwhatitdescribes.

6 Recordyournumberinaplace-valuechart.

7 Writeyournumberinwordform.

8 Whatstrategydidyouusetofindyour5-digitnumber?Compareyourstrategywithapartner’sstrategy.


HANDS-ON ACTIVITY


Look at the place-value chart. Then express the number in word form and standard form.


1 wordform: 2 standardform:


3 4815 4 $20505


5 fivethousandfivehundredeleven

6 forty-fivethousandeighty-ninedollars

Write the number in a place-value chart.

7 sixty-fourthousandfifty-two

Count by 10000. Write the missing numbers.

8 10443,20443, ,40443,50443, ,70443,80443

LET’S PRACTISE



LEARN Compare 5-digit numbers using greater than and less than.

Dairyfarmersuselitrestomeasurethevolumeofmilktheirfarmsproduce. Whichvolumeisgreater,93085litresor76105litres?

Comparethenumberoftenthousandsinthetwonumbers. 9tenthousandsisgreaterthan7tenthousands. So,93085litresisgreater than76105litres. 93085L>76105L

Whichvolumeisless,36520litresor37859litres?

First,comparethenumberoftenthousandsinthetwonumbers. Theyarethesame. Thencomparethenumberofthousandsinthetwonumbers. 6thousandsislessthan7thousands.

So,36520litresisless than37859litres. 36520L<37859L


9 3 0 8 5

7 6 1 0 5


3 6 5 2 0

3 7 8 5 9

1.2Lesson

Comparing Numbers to 100 000

Goals• Compareandordernumbersto100000.• Determineanumberthatisagivennumberof

place-valueunitsgreaterorlessthanagivennumber.

Vocabularygreaterthan(.) lessthan(,)order greatestleast

Lesson 1.2 ComparingNumbersto10000011

Order the numbers from least to greatest.

7 9456,73842,30512

8 41325,31425,51324,14325

9 27084,20784,27840,20874

Compare the numbers. Write > or < .

1 90847 69948 2 64515 65500

3 31256 31265 4 19283 19289

5 42100 41002 6 16935 16918

LEARN Order 5-digit numbers from greatest to least.

Threetownshavepopulationsof62357,9638,and28986.

Orderthepopulationsfromgreatesttoleast.


6 2 3 5 7

9 6 3 8

2 8 9 8 6

Comparethenumberoftenthousandsineachnumber.6tenthousandsisgreaterthan0tenthousandsand2tenthousands.62357isthegreatestpopulation.

2tenthousandsisgreaterthan0tenthousands.9638istheleastpopulation.

So,thepopulationsinorderfromgreatesttoleastare: 62357,28986,9638

GUIDED LEARNING

GUIDED LEARNING


Fill in the blanks.

10 Whichnumberisgreater,14651or14569?

isbetween14600and14700.

isbetween14500and14600.

istotherightof .

So, isgreaterthan .

11 Whichnumberisless,42154or42245?

istotheleftof .

So, islessthan .

GUIDED LEARNING

14500 14600 14700

42100 42150 42200 42250 42300

Whatstrategieshelpedyoudecidewheretoputeachnumberonthenumberline?

$67849islessthan$68000.$68794isgreaterthan$68000.So,$68794isgreaterthan$67849.

LEARN Compare numbers using a number line. Whichyearlysalaryisgreater,$67849or$68794?Useanumberlinetocomparethenumbers.

$67000 $68000 $69000

$67849 $68794


LEARN Use place value to determine a number that is greater or less than another number.

a Whatnumberis3000greaterthan36168?


3 6 1 6 8

3 9 1 6 8

39168is3000greaterthan36168.

b Whatnumberis200lessthan42387?


4 2 3 8 7

4 2 1 6 8

42168is200lessthan42387.

c Whatnumberis4000greaterthan26293?


2 6 2 9 3

2 10 2 9 3

30293is4000greaterthan26293.

3thousandsgreater

2hundredsless

Add4thousands.Regroup10thousandsas1tenthousand.

3 0


Use the number in the place-value chart to complete the sentences.


6 5 1 2 3

12 is4000greaterthan65123.


14 is20000lessthan65123.


What is the missing number?

16 30000lessthan34200is .


18 100greaterthan58967is .

19 12491is greaterthan12191.

20 36512is lessthan38512.

GUIDED LEARNING

d Whatnumberis500lessthan81255?


8 1 2 5 5

8 0 7 5 5

80755is500lessthan81255.

Regroup1thousandas10hundreds.Thensubtract5hundreds.

0 12


Workingroupsof4.

STEP

1 Use4setsofnumbercardsfrom0to9.

STEP

2 Shufflethenumbercards. Taketurnsdrawinguntileachpersonhas5cards.STEP

3 Arrangeyournumbercardstomakea5-digitnumber.

STEP

4 Compareyournumberwiththosemadebyothergroupmembers. Thenorderthenumbersfromgreatesttoleast.

Lookatthenumbersinthetable.

40432

30432

18432 19432 20432 21432 22432

10432

432

1 Whatdoyounoticeaboutthenumbersacrosstherowstartingwith18432?

2 Whatdoyounoticeaboutthenumbersdownthecolumnstartingwith40432?

3 Lookatthenumbersinthegreenboxes. Thenlookatthenumbersintheyellowboxes. Howaretheyalike?

4 Lookatthenumbersintheredboxes. Thenlookatthenumbersintheblueboxes. Howaretheyalike?

Materials:•numbercards

LET’S EXPLORE

HANDS-ON ACTIVITY


MATH JOURNAL

Lookatthenumbers.

1 Explainthestepsyouwouldtaketoorderthesedistancesfromleasttogreatest.

4509km 45km 45009km 450km

2 Explainthestepsyouwouldtaketoordertheseused-carpricesfromgreatesttoleast.

Howdoyouknowyouarecorrect?Explainhowyouknow.

$22375 $21357 $22099 $21408

Howdoesbreakingaproblemortaskintostepshelpyousolveit?Describeatimeyousolvedaproblemorcompletedataskbybreakingitintosteps.


Look at each place-value chart. Write greater than or less than.

1 TenThousands Thousands Hundreds Tens Ones

8 7 6 9

2 0 1 3 1

$8769is $20131.

2 TenThousands Thousands Hundreds Tens Ones

7 0 0 2 4

5 9 9 7 8

70024litresis 59978litres.

Complete the place-value chart. Order the numbers from greatest to least.


3 8372

4 51030

5 33443

6 Fromgreatesttoleast,thenumbersare , ,and .

LET’S PRACTISE


Compare the populations. Then complete.

7264379643

7 is7000lessthan .

8 7000greaterthan is .

Compare the masses of these blue whales. Then complete.

44678kg94678kg

9 50000greaterthan44678kilogramsis kilograms.

10 kilogramsis50000lessthan94678kilograms.

Use the number in the place-value chart to complete the sentences.


2 5 3 7 8








IknowthatmakingmistakesisOK.It’spartoflearning.


LEARN Each digit in a number has a place and a value.

Wordform:thirty-onethousandsevenhundredninety-eight

Fill in the blank.

1 In42653,thedigit isinthetenthousandsplace.

2 In63971,thedigit9isinthe place.


3 1 7 9 8

In31798, thedigit3 • isinthetenthousandsplace. • standsfor3tenthousands. • hasavalueof30000.

thedigit7 • isinthehundredsplace. • standsfor7hundreds. • hasavalueof700.

thedigit8 • isintheonesplace. • standsfor8ones. • hasavalueof8.

thedigit1• isinthethousandsplace.• standsfor1thousand.• hasavalueof1000.

thedigit9• isinthetensplace.• standsfor9tens.• hasavalueof90.

GUIDED LEARNING

1.3Lesson

Decomposing and Composing Numbers

Goals• Identifytheplacevalueofanydigitinnumbersto100000.• Readandwritenumbersto100000inexpandedform.• Decomposeandcomposenumbersto100000indifferent

ways.

Vocabularyexpanded formdecomposecompose


Writinganumberinexpandedformisonewaytodecomposeitintoparts.

LEARN Write numbers to 100 000 in expanded form.

The expanded form ofanumbershowsthevalueofeachdigit.


10 64245 thousands14hundreds12tens14ones

11 1829051tenthousand1 thousands12hundreds19tens

Complete the expanded form.

12 470935 1700019013

13 503285 130012018

14 694175 1 1 1 1

Standardform:31798Wordform:thirty-onethousandsevenhundredninety-eightExpandedformwithnumbersandwords:31798530000110001700190183179853tenthousands11thousand17hundreds19tens18ones

3 In20974,thedigitinthethousandsplaceis .

4 In56301,thevalueofthedigit3is .

5 In70569,thedigit7standsfor .

6 In82465,thedigit2standsfor .

What is the value of the digit 6 in each measurement?

7 63814kg 8 96781kg 9 20563kg

30000

8

3 1 7 9 81000

700

90

GUIDED LEARNING

Lesson 1.3 DecomposingandComposingNumbers21

FIND THE VALUE!GAME

Players:3 Materials:•10counters•blankplace-valuechart

STEP

1 Player1placesthecountersontheplace-valuecharttomakea5-digitnumber.Playersmaychoosenottouseallthecounters.

STEP

2 Player2writesthevalueofeachdigitinthe5-digitnumberlikethis:

STEP

3 Player3checkstheanswer.Player2gets1pointforeachdigitthatiswrittencorrectly.

STEP

4 Switchrolesandplayagain.Eachgroupplays6rounds.


Theplayerwiththehighestscorewins!


LEARN Compose a 5-digit number from its parts. Whatnumberhas5tenthousands,13thousands,21hundreds,14tens,and6ones?

Method 1

Useregroupingonaplace-valuechart.


5 13 21 14 6

Thenumberisnotinexpandedformbecausesomeplaceshavemorethan9units.Lookforwaystoregroup10smallunitsas1largerunit.Forexample,regroup10tensas1hundred.


5 13 21 14 6

6tenthousands15thousands12hundreds14tens16ones565246Thenumberis65246.

Method 2

Usementaladdition.

500001130001 21001 140165?

130002100

1406

63000

65100

65246

65240

50000

Thenumberis65246.

6 5 2

Youcomposeanumberwhenthepartsaregivenandyouputthemtogethertofigureoutthenumber.


LEARN Decompose a 5-digit number. Aswimmingpoolhas45628litresofwater.Whataresomewaystodecompose45628?

Method 1

Useexpandedform.


4 5 6 2 8

456285 4tenthousands15thousands16hundreds12tens18ones5 4000015000160012018

Method 2

Lookforwaystoregroup1largeunitas10smallerunits.Forexample,regroup1tenthousandas10thousands.


4 15 6 12 8

456285 3tenthousands115thousands15hundreds112tens18ones5 300001150001500112018

Method 3

Usementaladdition.

40000

4560045628

5600

28

4562854000015600128

3 5

Learningtodecomposenumbersindifferentwayshelpswithadding,subtracting,multiplying,anddividinglargenumbers.


Write the number. You can use a place-value chart.

15 3tenthousands124thousands19hundreds116tens123ones5

16 800001610011801 125

Write the missing numbers. You can use a place-value chart.

17 294435 1tenthousand1 thousands14hundreds13tens1 ones

18 719995700001 1 10021

GUIDED LEARNING

Workwithapartner.

1 Writeatleast5differentwaystodecomposethenumber100000.Tradewithanotherpairtocheckyouranswers.

2 ThelengthoftheSt.LawrenceRiverisabout1200kilometres.Howcanyouusethisdistancetohelpsomeoneunderstandhowlong100000kilometresis?

3 Finda5-digitreal-lifemeasurement.Howcanyouuseyourmeasurementtohelpsomeoneunderstandhowbig100000is?

HANDS-ON ACTIVITY

Materials:•place-valuecharts


Fill in the blanks.

1 In20675,thedigit0isinthe place.

2 In76501,thedigit isinthehundredsplace.

3 In39472,thedigit isinthetensplace,andthedigit isinthetenthousandsplace.

What is the value of the digit 5 in each number?

4 27058 5 85027

6 52708 7 23509

Write the number. You can use a place-value chart.

8 2tenthousands18thousands11hundred16tens17ones5

9 1tenthousand114thousands12hundreds115tens19ones5

10 20000126000130015995

What are the missing numbers?

11 409255 1 9001 2015

12 380055 300001 15

13 213915200001 1 91

14 321765 3tenthousands1 thousands11hundred17tens16ones

15 636025 5tenthousands1 thousands1 5hundreds1 tens1 2ones

16 940575 500001 157

LET’S PRACTISE


76

Tens Ones

TenThousands Thousands Hundreds

6

4

6000 4 70 000600014170000

Lookatthecolourcodesabove.Eachcolourcodeshowsaplacevalue.Usethecolourcodestodeterminethevalueofeachpuzzle.

Example

1

2

3

6 2

5 3 98

4 9 5 3

P RO B L E M S O LV I N G

76004

PUT ON YOUR THINKING CAP!


4 10000 20000

STEP

1 Copythenumberlineonasheetofpaper.

STEP

2 Dividethenumberlineinto10equalpartsandwritethevalueofeachpart.

STEP

3 Locateandwritethenumbers16500,19750,and12000onthenumberline.

5 16500 16600

STEP

1 Copythenumberlineonasheetofpaper.

STEP

2 Dividethenumberlineinto10equalpartsandwritethevalueofeachpart.

STEP

3 Locateandwritethenumbers16560,16510,and16575onthenumberline.

Workinpairs.

Ireadtheinformationinthesteps.ThenImadeaplantosolvetheproblem.First,Ineedtocomparethegivennumberswiththenumbersonthenumberline.


Write

Representing Numbers to 100 000

•Standardform:73486

•Wordform:seventy-threethousandfourhundredeighty-six

•Expandedform:7348657000013000140018016•Expandedformwithregrouping:734865720001140018016•Numbersthatareeasytoaddmentally:734865500001230001400186


7 3 4 8 6

Show Composeand

Decompose

You have learned ...

0 50000

73486

100000

Numbers to 100 000

CHAPTER WRAP UP


Compare

•Greaterthan:93085.76105

•Lessthan:36520,37859

•Fromgreatesttoleast:62357289869638

•Fromleasttogreatest:96382898662357

Comparing Numbers to 100 000

Order

Withoutregrouping:•20000morethan77642is97642.•300lessthan77642is77342.Withregrouping:•2000morethan59455is61455.•800lessthan27541is26741.

MakeNumbersThatAreGreaterorLess

Numbers to 100 000

Myfriendsaysmakingmistakesinmathishelpful.Whatdoyouthink?


Documents

1 Numbers to 100 000