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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
TenThousands Thousands Hundreds Tens Ones
9000
10thousands51ten thousand
10000
TenThousands Thousands Hundreds Tens Ones
1000,2000,3000,4000,5000,6000,7000,8000,9000,?
Goals• Countby1000and10000to100000.• Useplace-valuechartstoshownumbersto100000.• Readandwritenumbersto100000instandardform
andwordform.
1.1Lesson
Numbers to 100 000
Vocabularytenthousandhundredthousandstandardformwordform
4 Chapter 1 Numbersto100000
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
TenThousands Thousands Hundreds Tens Ones
7 3 4 8 6
TenThousands Thousands Hundreds Tens Ones
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
6 Chapter 1 Numbersto100000
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
TenThousands Thousands Hundreds Tens Ones
6 8 1 7
TenThousands Thousands Hundreds Tens Ones
Standardform:6817Wordform:
Standardform:
Standardform:12059Wordform:twelvethousandfifty-nine
GUIDED LEARNING
Lesson 1.1 Numbersto1000007
Express each number in word form.
6 7048 7 90015
Express each amount of money in word form.
8 $86300 9 $70005
Express each number in standard form.
10 tenthousandsevenhundredthirty-two
11 fifty-twothousandninehundredfive
GUIDED LEARNING
TenThousands Thousands Hundreds Tens Ones
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?
8 Chapter 1 Numbersto100000
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.
TenThousands Thousands Hundreds Tens Ones
HANDS-ON ACTIVITY
Lesson 1.1 Numbersto1000009
Look at the place-value chart. Then express the number in word form and standard form.
TenThousands Thousands Hundreds Tens Ones
1 wordform: 2 standardform:
Express each number in word form.
3 4815 4 $20505
Express each number in standard form.
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
TenThousands Thousands Hundreds Tens Ones
10 Chapter 1 Numbersto100000
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
TenThousands Thousands Hundreds Tens Ones
9 3 0 8 5
7 6 1 0 5
TenThousands Thousands Hundreds Tens Ones
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.
TenThousands Thousands Hundreds Tens Ones
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
12 Chapter 1 Numbersto100000
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
Lesson 1.2 ComparingNumbersto10000013
LEARN Use place value to determine a number that is greater or less than another number.
a Whatnumberis3000greaterthan36168?
TenThousands Thousands Hundreds Tens Ones
3 6 1 6 8
3 9 1 6 8
39168is3000greaterthan36168.
b Whatnumberis200lessthan42387?
TenThousands Thousands Hundreds Tens Ones
4 2 3 8 7
4 2 1 6 8
42168is200lessthan42387.
c Whatnumberis4000greaterthan26293?
TenThousands Thousands Hundreds Tens Ones
2 6 2 9 3
2 10 2 9 3
30293is4000greaterthan26293.
3thousandsgreater
2hundredsless
Add4thousands.Regroup10thousandsas1tenthousand.
3 0
14 Chapter 1 Numbersto100000
Use the number in the place-value chart to complete the sentences.
TenThousands Thousands Hundreds Tens Ones
6 5 1 2 3
12 is4000greaterthan65123.
13 is900greaterthan65123.
14 is20000lessthan65123.
15 is6000lessthan65123.
What is the missing number?
16 30000lessthan34200is .
17 is20000greaterthan53.
18 100greaterthan58967is .
19 12491is greaterthan12191.
20 36512is lessthan38512.
GUIDED LEARNING
d Whatnumberis500lessthan81255?
TenThousands Thousands Hundreds Tens Ones
8 1 2 5 5
8 0 7 5 5
80755is500lessthan81255.
Regroup1thousandas10hundreds.Thensubtract5hundreds.
0 12
Lesson 1.2 ComparingNumbersto10000015
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
16 Chapter 1 Numbersto100000
MATH JOURNAL
Lookatthenumbers.
1 Explainthestepsyouwouldtaketoorderthesedistancesfromleasttogreatest.
4509km 45km 45009km 450km
2 Explainthestepsyouwouldtaketoordertheseused-carpricesfromgreatesttoleast.
Howdoyouknowyouarecorrect?Explainhowyouknow.
$22375 $21357 $22099 $21408
Howdoesbreakingaproblemortaskintostepshelpyousolveit?Describeatimeyousolvedaproblemorcompletedataskbybreakingitintosteps.
Lesson 1.2 ComparingNumbersto10000017
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.
TenThousands Thousands Hundreds Tens Ones
3 8372
4 51030
5 33443
6 Fromgreatesttoleast,thenumbersare , ,and .
LET’S PRACTISE
18 Chapter 1 Numbersto100000
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.
TenThousands Thousands Hundreds Tens Ones
2 5 3 7 8
11 is3000greaterthan25378.
12 is200lessthan25378.
13 is800greaterthan25378.
What is the missing number?
14 20000lessthan62777is .
15 is600greaterthan56428.
16 500lessthan66350is .
IknowthatmakingmistakesisOK.It’spartoflearning.
Lesson 1.2 ComparingNumbersto10000019
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.
TenThousands Thousands Hundreds Tens Ones
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
20 Chapter 1 Numbersto100000
Writinganumberinexpandedformisonewaytodecomposeitintoparts.
LEARN Write numbers to 100 000 in expanded form.
The expanded form ofanumbershowsthevalueofeachdigit.
What is the missing number?
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.
TenThousands Thousands Hundreds Tens Ones
Theplayerwiththehighestscorewins!
22 Chapter 1 Numbersto100000
LEARN Compose a 5-digit number from its parts. Whatnumberhas5tenthousands,13thousands,21hundreds,14tens,and6ones?
Method 1
Useregroupingonaplace-valuechart.
TenThousands Thousands Hundreds Tens Ones
5 13 21 14 6
Thenumberisnotinexpandedformbecausesomeplaceshavemorethan9units.Lookforwaystoregroup10smallunitsas1largerunit.Forexample,regroup10tensas1hundred.
TenThousands Thousands Hundreds Tens Ones
5 13 21 14 6
6tenthousands15thousands12hundreds14tens16ones565246Thenumberis65246.
Method 2
Usementaladdition.
500001130001 21001 140165?
130002100
1406
63000
65100
65246
65240
50000
Thenumberis65246.
6 5 2
Youcomposeanumberwhenthepartsaregivenandyouputthemtogethertofigureoutthenumber.
Lesson 1.3 DecomposingandComposingNumbers23
LEARN Decompose a 5-digit number. Aswimmingpoolhas45628litresofwater.Whataresomewaystodecompose45628?
Method 1
Useexpandedform.
TenThousands Thousands Hundreds Tens Ones
4 5 6 2 8
456285 4tenthousands15thousands16hundreds12tens18ones5 4000015000160012018
Method 2
Lookforwaystoregroup1largeunitas10smallerunits.Forexample,regroup1tenthousandas10thousands.
TenThousands Thousands Hundreds Tens Ones
4 15 6 12 8
456285 3tenthousands115thousands15hundreds112tens18ones5 300001150001500112018
Method 3
Usementaladdition.
40000
4560045628
5600
28
4562854000015600128
3 5
Learningtodecomposenumbersindifferentwayshelpswithadding,subtracting,multiplying,anddividinglargenumbers.
24 Chapter 1 Numbersto100000
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
Lesson 1.3 DecomposingandComposingNumbers25
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
26 Chapter 1 Numbersto100000
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!
Chapter 1 Numbersto10000027
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.
28 Chapter 1 Numbersto100000
Write
Representing Numbers to 100 000
•Standardform:73486
•Wordform:seventy-threethousandfourhundredeighty-six
•Expandedform:7348657000013000140018016•Expandedformwithregrouping:734865720001140018016•Numbersthatareeasytoaddmentally:734865500001230001400186
TenThousands Thousands Hundreds Tens Ones
7 3 4 8 6
Show Composeand
Decompose
You have learned ...
0 50000
73486
100000
Numbers to 100 000
CHAPTER WRAP UP
Chapter 1 Numbersto10000029
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?
30 Chapter 1 Numbersto100000
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