Atthecompletionofthisunit,youwillbeableto:

multiplyanddividefractionsbywholenumbers,otherfractions,andmixednumbersusingmodels,drawingsandsymbols

estimateproductsandquotientsofwholenumbers,fractionsandmixednumbers

solveandcreateproblemsusingfractionoperations

calculatethevalueofexpressionsinvolvingfractions,usingtheproperorderofoperations

communicateclearlyaboutfractionoperations

Unit6:FractionOperations

Whatfractionofeachglassisfull?Assumethatthefullestglassisequalto1.

Howdothefractionscomparetoeachother?

Whichfractionswithadenominatorof8canberenamedinlowerterms?

Whichfractionscanbeaddedtogiveasumof1?

Whichfractionshaveadifferenceof1/2?

Theequation2+2/3=22/3tellsthesumoftheareasoftwoofthecolours.Whichcolours?Howdoyouknow?

redandblue4reds(1/2each)=22blues(1/3each)=2/3

Ifayellowhexagonhasanareaof1unit,whatistheareaofeachblock?

a)aredblock 1/2unit

b)ablueblock 1/3unit

c)agreenblock 1/6unit

Whatfractionscanyouusetodescribethepatternblockdesign?

a)1+4/2(2)=3

b)2/33/6=1/6

c)37/6(11/6)=15/6

d)4/23/6=23/6=13/6or11/2

Writeequationswithfractionsand/ormixednumberstodescribethefollowingareas.Makesureyousolveyourequations.Showyourwork.

a)theyellowandredpartsb)howmuchmoreisbluethangreenc)howmuchmoreisyellowandredthangreenandblued)howmuchmoreisredthangreen

Createyourowndesignusingthefollowing:

1.yellow,red,blue,andgreenpatternblocks

2.atotalofeightblocks

3.atleast2yellowblocks

4.atleastoneblockofeachothercolour

5.writefractionsand/ormixednumberstodescribeeacharea.Showyourwork.

6.Gototwootherdesignsandwrite3fractionequations(addingorsubtracting)forthosedesigns.

Aim: I can use repeated addition to multiply fractions by whole numbers

Multiplying a Whole Number by a Fraction

What does the fraction 3/4 mean?

How could you use a rectangle to model 3/4?

How could you use fraction strips to model 3/4?

How could you model 3/4 on a number line?

How could you model 3/4 using a grid and counters?

the number of parts being named

the number of equal parts into which the whole is divided

Fraction review:What is a denominator?

What is a numerator?

Think about it

Jana is having a party. After a few hours, she notices that 6 pitchers are each only 3/8 full. She decides to combine the leftovers to use few pitchers.

How many pitchers will the leftover lemonade fill completely?

Use a model to represent 8/8 of a pitcher.

Use this model to represent lemonade from the 6 partially full pitchers. Write as both an improper fraction and a mixed number.

When you add the above fractions, you will end up with 18/8 or 2 2/8 or 2 1/4.

Why could you write

3/8+ 3/8 + 3/8 + 3/8 +3/8 + 3/8 or 6 x 3/8 to describe the total amount of lemonade in the pitchers?

Draw 4 grids that are 6 by 2 in your notebook and show how you can represent 4 sets of 5/6.

How could you calculate 4 x 5/6 using grids and counters?Represent the answer as an improper fraction and as a mixed number.

4 x 5 = 4 x 5 = 20 6 6 6

or 3 2/6 or 3 1/3

You can also move the chips from the last grid in to fill the other three grids. This will show you your mixed number.

4 x 5/6 is four sets of 5/6

3 x 2 = 3 x 2 = 6 3 3 3

= 2

How can you calculate 3 x 2/3 using fraction strips? Write the product as an improper fraction and as a whole or mixed number.

5 x 3 = 5 x 3 = 15 = 7 1/2 2 2 2

How could you calculate 5 x 3/2 using a number line? Write the product as an improper fraction and as a whole or mixed number.

0 1 2 3 4 5 6 7 8 9 10

0 1 2 3 4 5 6 7 8 9 10

3/2 3/2 3/2 3/2 3/2

Jenniferpours2/3ofacupofwaterintoapotandrepeatsthis7times.Howmanycupsofwater,intotal,doesshepourintothepot?Useoneofthestrategies(grid,fractionstrips,ornumberline)toshowyouranswer.Writeitasamixednumber.

Yourassignment:Pages49and50#3,5,6,8,13and16

About1/10ofCanadianswhoare12andolderdownhillski.About2/5oftheseskiersarebetween

theagesof12and14.

WhatfractionoftheCanadianpopulationbetweentheagesof12and14aredownhillskiers?

IdentifytheKeyInformation

1/10Canadiansolderthan12ski.

2/5ofthe1/10areaged1214.

Whatfractionofthe1/10areaged1214?

MakeaPlan

Multiply2/5by1/10.

CarryoutthePlan

Thisiswhatwearelearningtoday!

1. Drawagridthatrepresentsthedenominator(5x10).

3.Thisrectangleis .

Itsareais2x1squaresoutofthetotal5x10squares.

4.

1/25Canadiansbetweentheagesof12and14downhillski.

Things to ponder...1.Howdoesthismodelshowbothand?

2.Howcanyouuseamodeltodeterminethenumeratoranddenominatorofaproduct?

3.Suggestapossibleprocedureformultiplyingtwofractionslessthan1.Whydoesthiswork?

To multiply 2 fractions less than one you can:

A.Drawthegrid.

B.Multiplythenumeratorsanddenominators.

e.g.

GridMethod

1.Drawagridwiththedimensionsofthedenominators.

2.Fillthegridwitharectanglethedimensionsofthenumerators.

3.Rewritethefractionasthe .

4.Writeinlowestterms.

e.g.

Multiplication

1.Multiplythenumeratorsanddenominators.

2.Rewriteinlowestterms.

Jacksonisawakefrom2/3oftheday.Hespends5/8ofthattimeathome.WhatfractionofthedayisJacksonawakeat

home?

TheGrade8classraised2/5ofthemoneyto

supporttheschool'swinterproduction.TheGrade8boysraised2/3oftheGrade8

money.Whatfractionofthewholeproductionfunddidthegrade8boysraise?

Aboriginalpeoplesmakeupabout3/20ofthepopulationofManitoba.Ofthose,onlyabout1/3areunder15.WhatfractionofManitoba'stotalpopulationismadeupof

Aboriginalpeoplesunder15?

OnetwentiethofManitoba'spopulationismadeupofAboriginalpeoplesundertheageof15.

Thegrade8boysraisedfourfifteenthsoftheproductionfund.

Jacksonisawakeforfivetwelfthsoftheday.

More Practice:

pg 54

1b, 2, 3, 4bc, 5, 6, 7, 8, 11 a

Aim: I can multiply mixed numbers and improper fractions.

Fraction Products and Multiplying Fractions Greater than 1

Thinkofastrategyyoumightusetosolvethisproblem?

A large tub of popcorn holds 2 1/2 times as much as a smaller tub. Aaron has 1 1/2 large tubs.He is pouring the popcorn into smaller tubs to give to friends.

How many small tubs will his popcorn fill?

smaller large

Thinkaboutwhywewouldsetupthemodelinthisway.Howdothenumbersinthisproblemhelpyoudecidehowlargetomaketherectangles?

AreaofAis1x2=2squareunits

AreaofBis1x1/2=1/2squareunit

AreaofCis1/2x2=1squareunit

AreaofDis1/2x1/2=1/4squareunit

Thetotalareais

2+1/2+1+1/4=33/4squareunitsHecouldfill33/4smalltubs.

Onestrategymightbetouseanareamodel.Weknowthisisamultiplicationproblembecausewehave11/2groupsof21/2.

AB

C D

1

1/2

2 1/2

Another strategy might be to set up a procedure.

Turn the problem into an equation. 1 1/2 groups of 2 1/2 becomes 1 1/2 x 2 1/2. Having a mixed number can make it difficult to solve, so turn each mixed number into an improper fraction. 1 1/2 is the same as 3/2, and 2 1/2 is the same as 5/2. By doing this, it will be easier to multiply.

3 5 2 2

x = 3 x 52 x 2

15 4

= = 3 34

Multiply the renamed fractions just like you would multiply fractions less than one.

2 1/2 x 3 1/3 = (2 x 3) + (2 x 1/3) + (1/2 x 3) + (1/2 x 1/3) = 6 + 2/3 + 3/2 + 1/6(make 6 common = 6 + 4/6 + 1 3/6 + 1/6denominator) = 7 + 8/6 or 8 2/6 or 8 1/3

Multiply 2 1/2 x 3 1/3 using area grids.

3 1/3

2

1/2

( 3 x 2)

3 x 1/2

1/3 x 2

1/3 x 1/2

Tomultiply21/2x31/3asaprocedure,youcandothefollowing:

212

52

3 13

=

= 103

52

10x 52 3

x=3 x10

=506 68 8= 3

2 1

Now,try5/8x61/2usingbothagridandaproceduretocalculate.Doyoucomeupwiththesameanswerforboth?

Usethestrategiesdiscussedinthislessontofindtheanswertotheproblem.

Miriam is making 3 1/2 dozen cookies. If 2/7 of the cookies have icing, how many dozen cookies have icing?

Today'sAssignment:

Pages61and62

#s5,7,8,10,12,14&16

Aim: I can use a sharing model to represent the quotient of a fraction divided by a whole number.

Dividing Fractions by Whole Numbers

Fourtenthsofthepossibledonorsstillhavetobecalled.Twoofthestudentsaregoingtosharethejob.

Whatfractionofallthepossibledonorswilleachstudentbecalling?

How

Thesameasthenumeratorofthefraction

Howdoyouknowhowmanycounterstouse?

Thenumberofsquaresisthesameasthedenominator.

Tofindthesolution,weneedtodividethefractionbyawholenumber.

Howdoweknowhowmanysquarestouseinthegridofthefraction?

4 10

2

4102=

210

WhenIdivideby2,Iseparatethemodelinto2equalgroups.WhenImultiplyby2,Iaddthemodel2times.

Whatdoyoudodifferentlytothegridmodelofthefractionwhenyoudivideitbyawholenumberthanwhenyoumultiplyitbyawholenumber?

4 10

2

Createagridandusethisstrategytosolvethisproblem.Remember,ifyouhave1/3,youaredividingby3.

Allison had art class 9 out of the 20 school days last month. She worked with a partner about 1/3 of the time. For what fraction of the school days did she work with a partner in art?

9 out of 20 is 9 209203 = =

320

9 3 20

Allison worked with a partner for 3 of the 20 days.

How do we divide a fraction if the numerator is not divisible by the whole number?

2/3 of a room still has to be tiled. Three workers are going to share the job. What fraction of the room will each worker tile if they all work at the same rate?

23 3 = 23

32 cannot be divided by 3 evenly. Since we are dividing fractions, we cannot have a decimal number. We need to find an equivalent fraction to 2/3 that can be divided by 3. An equivalent fraction to 2/3 would be 6/9. 6/9 can be divided by 3. 6__3

9 = 2

9

Assignment:Page71#s4,6,7,9and10

Dividing Fractions Using a Related Multiplication

Aim: Divide fractions using a related Multiplication.

Allison has 2 large cans of paint. Nikita has 7/8 of a large can of paint. Each student is pouring paint into small cans that hold 1/3 as much as the large ones.

How many small cans of paint will each student fill?

Allison Allison Nikita

Thinkofastrategyyoumightusetosolvethisproblem?

TofindouthowmanysmallcansIcanfill,Icandivide2by1/3

Ineededtodivide2by1/3toseehowmanysmallcans(1/3thesizeofthebigcans)wouldbefilledby2largecans.

2 = 2x

Thisiscalledtakingthereciprocal.Thereciprocalisthefractionthatresultsfromswitchingthenumeratorandthedenominatorofthefractionontherightsideoftheequation.

Flip rig

ht sid

e frac

tion

and Mu

ltiply

Ineededtodivide7/8by1/3toseehowmanysmallcanswouldbefilledbya7/8fulllargecan.

TofindouthowmanysmallcansIcanfill,Icandivide7/8by1/3

= x

Wecannowmultiplystraightacross

= =

Rahulhas2/3ofacontaineroftrailmix.Heisfillingsnackpacksthateachuseabout1/5ofacontainer.HowmanysnackcanRahulmake?

Trythiswithapartner

1) What is your initial amount?

2) What is the amount they are being divided into?

3) What is your equation going to look like?

4) Which equation do we flip?

Rahulhas2/3ofacontaineroftrailmix.Heisfillingsnackpacksthateachuseabout1/5ofacontainer.HowmanysnackcanRahulmake?

Thisisreallyaskingwhatis2/3dividedby1/5

HomeworkPg.8586#2,3af,6ad,9a,13

Attachments

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MSOfficePNG12818.png

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SMART Notebook

SMART Notebook

SMART Notebook

OrderofOperations2.10

Learner OutcomeUseorderofoperationsincalculationsinvolvingfractions

TheOrderofThings...

WithaPartner,try:(6+9) X (8 - 3) 25 + 7 - 4 X 2 =

Brackets

= 15 X 5 25 + 7 - 4 X 2

Multiply and Divide

= 75 25 + 7 - 4 X 2 Multiply and Divide

75 25 + 7 - 4 X 2 Multiply and Divide

= 3 + 7 - 8 Add and Subtract

= 3 + 7 - 8

Add and Subtract= 10 - 8

Add and Subtract= 2

NowTry...

EquililentFraction

Reciprical

Reduce

Target1Game

Thegoalistocreateanequationwhosesolutionisasclosetooneaspossible

Eachgroupcutsoutonefractionsheetandoneoperation

sheet

Ineachroundbothpartnerstake3

fractioncardsandtwooperationcards

Rearrangeyourfractionssotheyareasclosttoone

aspossible

ThepersonclosesttoonewinsthatroundThefirsttofiveroundswins!!

Solve

YourAssignment

Page90#1,3,6,7a13

Important Terms

Fraction: One number written over another. The operation is to divide the top the bottom

Numerator: Top number in a fraction

Denominator: Bottom number in a fraction

Mixed Fraction: Mix between a whole number and a fraction

Improper fraction: When the numerator is larger than the denominator

Chapter 2: Fractions January 26, 2011 3:41 PM

Chapter 2 Page 1

"How Many Times Does the bottom number fit into the top?" This will be your whole number (left of your fraction)

1.

Find what's left over (Whole number times bottom number, subtracted from original top number). Put that number as a fraction over the original denominator.

2.

Fraction Conversation NotesJanuary 31, 2011 8:28 AM

Chapter 2 Page 2

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January 31, 2011 5:40 PM

Chapter 2 Page 5

fractionaction

Inserted from:

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Chapter 2 Page 6

file://S:/XEROX-SCAN/fractionaction.PDF

fractionactionans Chapter 2 Page 7

fractionactionans

Inserted from:

Chapter 2 Page 8

file://S:/XEROX-SCAN/fractionactionans.PDF

Chapter 2 Page 9

Fraction DiagramsJanuary 31, 2011 5:36 PM

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February 3, 2011 9:00 AM

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Chapter 2 Page 15

2.1

Inserted from:

2.1February-06-11 11:32 AM

Chapter 2 Page 16

file://S:/Grade 8/GREVEBR/Math 8/CH 2/Scanning/2.1.PDF

Chapter 2 Page 17

2.2

Inserted from:

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file://S:/Grade 8/GREVEBR/Math 8/CH 2/Scanning/2.2.PDF

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2.3

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2.3February-06-11 11:32 AM

Chapter 2 Page 20

file://S:/Grade 8/GREVEBR/Math 8/CH 2/Scanning/2.3.PDF

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2.4

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2.4February-06-11 11:32 AM

Chapter 2 Page 22

file://S:/Grade 8/GREVEBR/Math 8/CH 2/Scanning/2.4.PDF

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2.5

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2.5February-06-11 11:32 AM

Chapter 2 Page 24

file://S:/Grade 8/GREVEBR/Math 8/CH 2/Scanning/2.5.PDF

Chapter 2 Page 25

February 9, 2011 9:11 AM

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Just like multiplying, convert all mixed fractions to improper fractions

Take the reciprocal of the fraction you are dividing by and change the division sign to multiplication

Top times top, bottom times bottom. Convert to a mixed fraction and reduce Done :)

Dividing Mixed FractionsFebruary-09-11 7:32 PM

Chapter 2 Page 29

Chapter 2 Page 30

Always Use BEDMAS to determine order of operations:

B - BracketsE - ExponentsD - Division M - Multiplication A - AdditionS - Subtraction

Order of OperationsFebruary-09-11 7:39 PM

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With a Partner:Cut out all fraction cards1.Place cards face down on a desk2.Each partner takes 3 fraction cards and 2 operation cards3.Each partner gets 1 set of brackets4.The goal is to arrange your fraction and operation cards to end up with an answer as close to 1 as possible

5.

Each win is worth 1 point, first to 5 points wins!6.

Math Game: Target 1February 11, 2011 8:51 AM

Chapter 2 Page 39

frac1

Inserted from:

February 17, 2011 9:03 AM

Chapter 2 Page 40

file://S:/XEROX-SCAN/frac1.PDF

frac2 Chapter 2 Page 41

frac2

Inserted from:

Chapter 2 Page 42

file://S:/XEROX-SCAN/frac2.PDF

Chapter 2 Page 43

Chapter 2 Page 44

introPage 1Page 2Page 3

21Page 1Page 2Page 3Page 4Page 5Page 6

22Page 1Page 2Page 3Page 4Page 5Page 6

25Page 1Page 2Page 3Page 4

26Page 1Page 2Page 3Page 4

29Page 1Page 2Page 3Page 4Attachments Page 1

30Page 1Page 2Page 3Page 4

Chapter 2