Volume, Capacity and Mass - Six Point Won! · If so, you have worked out the formula for volume: length x width x height = volume _____ Width Height Length Number of Cubes 48 48 48

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Volume, Capacity and Mass

Teacher Book – Series F

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Contents

Topic 1 – Volume and capacity

• millilitres and litres ____________________________________

• cubiccentimetresandcubicmetres _______________________

• displacement _________________________________________

• milk it maisie – create __________________________________

• think outside the box – create ____________________________

Topic 2 – Mass

• grams _______________________________________________

• kilograms ____________________________________________

• tonnes ______________________________________________

• spuds and carrots – solve _______________________________

• weighing it up – solve __________________________________

Date completed

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Volume, Capacity and Mass – Series F

Series Authors:

Rachel Flenley

Nicola Herringer

Contents

Section1–Answers(p.1-16)

• volume and capacity __________________________________ 1

• mass _______________________________________________ 9

Section2–Assessmentwithanswers(p.17-20)

• volume and capacity _________________________________ 17

• mass ______________________________________________ 19

Section3–Outcomes(p.21-23)

Copyright © 3P Learning Pty Ltd


SERIES TOPIC

1F 1

Colour the jugs to show these quantities:

Which unit would you use for measuring the capacity of each of these objects? Write L for litres or mL for millilitres:

Convert these amounts to millilitres:

a 8 L = b 2.5L =

c 9.5L = d 0.6L =

e 5.5mL = f 0.2L =

Express these amounts in litres:

a 2000mL= b 1500mL=

c 500mL = d 5000mL=

Capacityreferstotheamountacontainercanholdandisusuallyassociatedwithliquid.

1 000millilitres=1Litre 1 000mL=1L

Volume and capacity – millilitres and litres

4

5

2

3

1 When we convert:

a millilitres to litres we by 1 000

b litres to millilitres we by

a 2 ______ b 5 ______ c 1 ______ d 300 ____ e 4 ______ f 250 ____

a half a litre d900mLc 34 of a litreb

14 of a litre

÷

X 1000

2 L 1.5 L

0.5 L

8000 mL 2500 mL

9500 mL 600 mL

5500 mL 200 mL

5 L

L mL L mL L mL



SERIES TOPIC

2F 1

Volume and capacity – millilitres and litres

6

7

a Tylerhaspouredcordialsyrupintothisjug.How much water will he add to make 1 L of cordial drink?

b Thisjugcontainssomelemonade.Lucypoursinanother80mLoflemonade.Draw a line to showthenewamountofliquidinthejug.

Look at the pictures, then answer the questions below:

100

200

300

400

500

Answer these problems to do with mixing drinks:

50mL 600mL 300mL 1 L 5mL 200mL

True or False True or False

a The mug holds the same b The tea cup needs to be amountofliquidassixfull filled3timestoequalafull medicinecups. waterbottle.

c The medicine cup holds d More than 2 L of liquid is 10timesmoreliquidthan neededtofillthewater theteaspoon. bottlethreetimes.

e Thewaterbottleholdshalfas f The mug holds half as muchasthejuicebottle. muchasthewaterbottle.

g Thejuicebottleholdsthe h The tea cup holds one same amount of liquid as four tenth the amount the juice teacups. bottleholds.

800 mL

True True

True False

False True

False False



SERIES TOPIC

3F 1

Volumeistheamountofspaceoccupiedbyanobjectorsubstance. Commonlyusedvolumemeasurementsarethecubiccentimetreandthecubicmetre.

Volume and capacity – cubic centimetres and cubic metres

Onecubiccentimetreis1cmlong,1cmwideand1cmhigh.Thesymbol we use for cubic cm is cm3.1 cm x 1 cm x 1 cm = 1 cm3

Onecubicmetreis1mlong,1mwideand1mhigh.Thesymbol we use is m3.1 m x 1 m x 1 m = 1 m3

1 For this activity you will need 48 centicubes or centimetre blocks. Work with a friend and record your answers in the table as you go:

a Useall48cubestomakeablock4cubeswideand4cubeshigh.Beforeyoubegin,predicthowlongyouthinkitwillbe.Howlongisit?Recordyouranswerinthetablebelow.

b Nowuseall48cubestomakeablock12cubeslong.Beforeyoubeginpredicthowwideandhighitwillbe.Howwideandhighisit?

____________________________________________________________________________________

c Canyoumakeablockthatisstill12cubeslong,butisadifferentheightandwidth?

____________________________________________________________________________________

d Taketurnschoosingalengthbetween1and48.Theotherpersontriestomakeacubewiththatlength.Ifitcanbedone,addittothetable.Ifnot,listittotherightofthetable.Whydoyouthinktheselengthswon’t work?

____________________________________________________________________________________

e Canyouseeapatterninyourresults?

____________________________________________________________________________________

f Nowforeachrow,putamultiplicationsymbolbetweenthewidthandheightandthentheheightandlength.Putanequalssignbetweenthelengthandnumberofcubes.Dothenumbersentenceswork? Ifso,youhaveworkedouttheformulaforvolume:length x width x height = volume

____________________________________________________________________________________

Width Height Length Number of Cubes

48

48

48

48

48

48

Lengthsthatwon'twork:

___________________

___________________

___________________

___________________

___________________

12 x 1 x 4, 12 x 4 x 1, 12 x 2 x 2

12 x 2 x 2, 12 x 1 x 4, 12 x 4 x 1

Answers will vary

Answers will vary

Answers will vary

Answers will vary4

4

2

1

8

6

4

2

4

6

1

8

3

12

12

8

6

1



SERIES TOPIC

4F 1

Would you measure the volume of these objects in the given units? If not, suggest a better choice:

a swimming pool – cm3 ____________________ b brick – cm3 ______________________

c suitcase – cm3 ____________________ d restaurant – cm3 ______________________

e pencil case – cm3 ____________________ f lunch box – cm3 ______________________

g remote control – cm3 ____________________ h classroom – cm3 ______________________

a

x x =

c

x x =

e

x x =

b

x

x =

d

x

x =

f

x

x =

Tofindoutthevolumeofanobjectwithoutcountingeachblock,wecanmultiplythe length by the width bytheheight.

2

3

Using the formula l x w x h = v, calculate the volume of these boxes:

Length

Height

Width

l x w x h = v5x2x2=20cm3

1 m

1 m5m

2 m

3m

3m

6m

1 m

2 m

1 m

2 m

3m

6m

2 m

3m

4 m

2 m

3m

Volume and capacity – cubic centimetres and cubic metres

5 m35 1 1

12 m36 2 1

6 m33 2 1

18 m33 2 3

36 m33 2 6

24 m33 2 4

m3 Yes

Yes m3

Yes Yes

Yes m3



SERIES TOPIC

5F 1

Try this experiment. Work with a friend or in a small group. You’ll need the following equipment: a juice box, a lunch box, a measuring jug, a tote tray and some centicubes.

a Look at the capacity of your juice box.HowmanymLdoesithold?

__________________________

b Knowing what you do about the relationshipbetweenvolumeand capacity,whatdoyouthinkisthevolumeofthejuicebox?Writedownyourestimate.

____________________________________________________________________________________

c Drinkyourjuiceandthencarefullycutoffthelidofthejuicebox.Rinsetheboxout.Nowfillthejuiceboxwithcenticubes.Makesureyoukeepcountasyougo.Whatisthevolume?Isitthesameasyourestimate?Ifnot,whydoyouthinkthisis?

____________________________________________________________________________________

d Placeyourlunchboxinthetotetrayandcarefullyfillthelunchboxtotheverytopwithwater.Gentlysubmergeyourjuiceboxfilledwithcenticubesintothelunchbox.Makesureitisfullysubmerged.Watershouldoverflow.

e Takethejuiceboxoutofthelunchboxandcarefullytakethelunchboxoutofthetray.Pourthewaterthatoverflowedintothetrayintothemeasuringjug.Howmuchwateroverflowed?

____________________________________________________________________________________

f Wasitclosetothecapacityyoufoundinquestiona?

____________________________________________________________________________________

Use your measuring equipment and your knowledge of the relationship between volume and capacity to see if you can find a rock with a volume of 50 cm³.

a How much water will it displace? ________________________

b Whatsizerockdoyouthinkyouwillbelookingfor? ________________________

c Onceyouhavefoundone,wasitsmallerorlargerthanyouimagined? ________________________

Rememberthatvolumeistheamountofspaceoccupiedbyanobjectorsubstanceandcapacityistheamountanobjectwillhold.Wecanusedisplacementtocalculatebothvolumeandcapacity.Displacementistheamountoffluidthat ispushedawaywhenanobjectisplacedinthefluid.

Volume and capacity – displacement

1

2

Answers will vary

Answers will vary

Answers will vary

Answers will vary

Answers will vary

50 mL

Small

Answers will vary



SERIES TOPIC

6F 1

Wecanseetheconnectionbetweenvolumeandcapacity:

1 mL = 1 cm3

Volume and capacity – displacement

3

4

Calculate the volume (cm³) and capacity (mL) from these models made from centicubes:

a b c

Wandu, the work experience girl, has made these shapes out of centicubes. She has written their capacity underneath them. Is she right? Check her thinking.

a b c

5mL

6mL

6mL

Is she right? ________________ Is she right? _______________ Is she right? _______________

Volume = cm3

Capacity = mL

Volume = cm3

Capacity = mL

Volume = cm3

Capacity = mL

d e

7mL

12 mL

Is she right? ________________ Is she right? _______________

8 10 24

8 10 24

Yes

Yes

No

No

Yes



SERIES TOPIC

7F 1

Using the following fridge doormeasurements,workwith a friend to design and thenconstructamilkcarton.

Look carefully at the dimensions of the compartment on thediagram.

You’ll need to think carefully about the relationshipbetweenvolumeandcapacity.

Sketch your design and then constructyourcarton.Thisis a design prototype so it doesn’t actually have to hold the milk!

Whenplanning,itmayhelptolookatareallife fridgedoorcompartment.Nexttimeyouarein thesupermarket,lookatallthedifferenttypesofcartonsthereare.

Takeyourcartontoafridgeandtestitout.Doesitwork?

Milk it Maisie create

You have 4 teenage brothers who drink milk like it’s goingoutoffashion.

Tosavemoney,yourparentshaveboughtacow. Totheirdelight,Maisieproducesalotofmilk.Theyhave now asked you and a friend to design a 4 litre milkbottleorcartonthatwillfitinthefridgedoorcompartmenttoholdallthatmilk.

Youwillneedpaperorcardboard,aruler,scissors,tape,glue,staplerandanyothersuppliesyouthink maybeuseful.

What to do

10 cm

50 cm

50 cm

What to do next

Getting ready

Answers will vary

Possible dimensions include:

10 cm x 10 cm x 40 cm = 4000 cm3 = 4 L20 cm x 20 cm x 10 cm = 4000 cm3 = 4 L



SERIES TOPIC

8F 1

Think outside the box create

Inthisactivityyouaregoingtocreatedifferentshapedlidlessboxesusingthesamesizedpieceofpaper.

Youwillneed3sheetsofcmsquaredpaper,aruler,scissorsandsometape.

Youaregoingtocalculatethevolumeofeachbox.

Choosesomedifferentsizedpapersquaresandrepeattheprocess.Whatpatternsdoyoufind?Canyoumakevolumepredictionswithoutactuallymakingtheboxes?

Box 1:

Cuta12cmsquarepieceofpaper.

Makeyourfirstboxbycuttingonesquareoutfromeachcorner. Foldupthesidesandtapetheboxtogether.Whatisthevolume of the box? _____________

Box 2:

Cutoutanother12cmsquarepieceofpaper.Thistime,cutout 2cmx2cmsquaresineachcorner.Foldupthesidesandtape thatboxtogether.

Putthetwoboxessidebyside.Doyouthinktheyhavethesame volume? Does one box look bigger than the other? Calculatethevolumeofthe2ndbox.Wasyourpredictioncorrect? _____________

Box 3:

Takeathirdpieceofpaperandthistime,cutout3cmx3cmcorners. How does this change the look and the volume of the box? _____________

Makeatableofyourresults.

cutcut

cutcut

What to do

What to do next

Getting ready

This diagram shows howtocutbox1.

100 cm3

128 cm3

Box 1 10 cm x 10 cm x 1 cm = 100 cm3

Box 2 8 cm x 8 cm x 2 cm = 128 cm3

Box 3 6 cm x 6 cm x 3 cm = 108 cm3

108 cm3



SERIES TOPIC

9F 2

Massmeasureshowmuchmatterisinanobject.Weusuallymeasurethisbyfindingoutwhattheobjectweighs.Massandweightareslightlydifferentbutweoftenuseweighttermswhenwearetalkingaboutdaytodaymassmeasurements.Commonmeasurementsaregrams(g),kilograms(kg)andtonnes(t). Thereare1000ginakilogramand1000kginatonne.

Mass – grams

Before you begin this activity, make sure you get a feel for each of these weights. Your teacher will get you some of these weights to explore:

1

2

Choose 5 different objects to estimate and measure. Fill in the table below.

Object Estimate Mass

Athome,gothroughyourpantryorfridgeandfindsomeobjectsthatweigheither250grams, 500gramsor1000grams.Canyougetasenseofwhateachofthesemassesfeelslike?

Draw the item on the scale and the arrow to show the mass:

250 grams of macaroni 675 grams of chocolate buttons 950 grams rice

500g

100g1 g

Weight measures the force of gravity on an object and mass measures its inertia or the amount of matter that can ‘push back’. A brick weighs less in outer space where there is no gravity but its mass stays the same.

0100900

400600500

800 200

700 300

0100900

400600500

800 200

700 300

0100900

400600500

800 200

700 300

Answers will vary



SERIES TOPIC

10F 2

Mass – grams

3

4

5

Work out which cereal is the best value for money by calculating how much each would cost per kilo. Use the table below. ‘Great Grains’ is done for you.

Use the information to fill in the blanks in these statements:

a 20mL= g b 12 mL = g

c 75mL= g d 100mL= g

e 40mL= g f 155mL= g

g mL=20g h mL=45g

This section has already been completed. Check the thinking:

a 150mL= 150 g b 25mL = 250 g

c 500mL= 500 g d 10mL = 10 g

e 300mL= 30 g f 2 L = 200 g

GREATGRAINSGREATGRAINS

800 g

FRUITYFLAKESFRUITYFLAKES

500 g250 g

MUNCHMUESLIMUNCHMUESLI

$4.00 $8.00$3.60

Youshouldalreadyknowthisfact:

1millilitre(mL)ofwaterhasamassof1gram(g)

Weight Cost per kilogram

GreatGrains $3.60for250g $3.60x4=$14.40

Munch Muesli

Fruity Flakes

20 12

75 100

40 155

20 45

25 g

300 g 2000 g

$4.00 for 500 g $4.00 x 2 = $8.00

$8.00 for 800 g $8.00 ÷ 8 = $1.00 for 100 g so it is $10 per kg



SERIES TOPIC

11F 2

Mass – kilograms

1

2

3

How much does each person weigh?

Complete this table by writing each mass in grams and as a decimal. Remember to include the units of measurement:

Decimal Notation Grams Kilograms and Grams

4kg250g

1800g

3.75kg

Workers at a factory pack cartons that hold a net mass of 4 kg. Calculate the quantity of each item that can be packed per carton:

a Howmanytinsofsoupcanbepackedintoonecarton? _________________

b How many boxes of rice crackers can be packed into one carton? _________________

c How many bars of chocolate can be packed into a carton? _________________

d How many jars of jam can be packed into one carton? _________________

e Wouldacartoncontaining2tinsofsoupand10jarsofjamexceedthenetmass? _________________

a b c d

Mass = kg Mass = kg Mass = kg Mass = kg

15 20 85 90 70 75 5

10

SOUPRice Crackers

100 g

Chocolate Bar50g

J A M250 g

500 g

17

4.25 kg 4250 g

1.8 kg 1 kg 800 g

3 kg 750 g3750 g

86 73 9

8

40

80

16

No



SERIES TOPIC

12F 2

Use the information above to answer these questions. Record your answers in the table below.

Mass – kilograms

Airline Checked luggage allowance Excess luggage fee per kg

PacificAirways 23kg $15

ContinentalAir 20kg $14

Budgetways 20kg $12

NationalAirlines 25kg $18

Passenger Airline Luggage weight (kg) Amount over Excess luggage fee ($)

a Kim Budgetways

b Juan ContinentalAir

c Steve NationalAirlines

d Lisa PacificAirways

4

5 Answer the following problems to do with luggage allowance:

a MrandMrsChanaretravellingwithanairlinethathasaluggageallowanceof23kgperperson.Theirbagsweigh10kg,11kg,12kgand15kg.Willtheypayanexcessluggagefee?

____________________________________________________________________________________

b Sarahasaparcelthatweighs9.5kgandabagthatweighs10.2kg.Ifherairlinehasaluggageallowanceof20kg,willshepayanexcessfee?

____________________________________________________________________________________

c Bobisflyingwithanairlinethathasacheckedluggageallowanceof23kgandacarry-onluggageallowanceof7kg.Hissuitcaseweighs28.5kgandhiscarry-onluggageweighs1kg.Howmanykilogramsshouldhemovefromhissuitcasetohiscarry-onluggagetoavoidpayinganexcessfee?

____________________________________________________________________________________

a ThisisKim΄sbag.SheistravellingwithBudgetways.Willshepayafeeforexcessluggage?

c ThisisSteve΄sparcel.WillhepayanexcessluggagefeeifheisflyingwithNationalAirlines?

b ThisisJuan΄ssuitcase.IfheisflyingwithContinentalAirwillhepayafeeforexcessluggage?

d ThisisLisa΄ssuitcase.HerairlineisPacificAirways.Willshepayanexcessluggagefee?

20 kg 25 kg

20 kg 25 kg

20 kg 25 kg

20 kg 25 kg

22 kg $24

$42

$36

$7.50

23 kg

27 kg

23.5 kg

2 kg

3 kg

2 kg

0.5 kg

Yes – 2 kg over (24 kg per person)

No (19.7 kg)

5.5kg



SERIES TOPIC

13F 2

Mass – tonnes

1

2

3

Convert these measurements to kilograms (kg):

a 4 t = b 5t = c 2 t =

d 8 t = e 3t = f 3.5t =

g 20t= h 15t= i 25t =

j 45t= k 50t= l 80t =

Convert these amounts to tonnes (t):

a 1000kg = b 5000kg = c 4000kg =

d 8000kg = e 6000kg = f 2000kg =

g 9000kg = h 10000kg= i 15000kg=

j 50000kg= k 25000kg= l 65000kg=

Without using a calculator, convert these quantities from kilograms to tonnes. Check your answers with a calculator when you have finished.

Kilograms 2546 8500 3019 5854 10298 28131 55750

Tonnes 2.546

Tonnesareusedtomeasurelargeobjects.

1tonne=1000kilograms

1t=1000kg1 tonne 3tonnes

4000 kg 5000 kg 2000 kg

8000 kg 3000 kg 3500 kg

20000 kg 15000 kg 25000 kg

45000 kg

1 t 5 t 4 t

8 t 6 t 2 t

9 t 10 t 15 t

50 t

8.5 3.019 5.854 10.298 28.131 55.75(0)

25 t 65 t

50000 kg 80000 kg



SERIES TOPIC

14F 2

Mass – tonnes

Helicopter:3.2t Train:42t Truck:35t Campervan:3.5t

Four-wheelDrive:2t Bus:14t Car:1t Boat:20t

4 What is the difference between the mass of each pair of vehicles? Complete the first 3 problems. Now find a friend and take turns giving each other a pair of vehicle masses to calculate:

Vehicle 1 Vehicle 2 Difference in Tonnes

a Helicopter Four-wheeldrive

b Train Truck

c Boat Bus

d

e

f

g

5 Answer these word problems:

a A5-tonnetruckcancarryaloadof5tonnes.Howmany5-tonnetrucksareneededtodeliver65tonnesofsteeltoabuildingsite? ______________________________

b Howmanytonnesofsandcanbetransportedifa9-tonnetruckmakes 8 trips? ______________________________

c Thereare64passengersonabus.Iftheaverageweightofapassengeris60kilograms,whatisthetotalweightofthe passengers in tonnes? ______________________________

d Aforkliftiscarryingaboxthatweighs2.4tonnesandaboxthatweighs1.8tonnes.Iftheforklift’smaximumloadis5tonnes, shouldanother1.8tonneboxbeadded? ______________________________

1.2 t

Answers will vary

7 t

6 t

13 trucks

72 t

3.84 t

No – it will weigh 6 t



SERIES TOPIC

15F

Xxxxxxxx xxxxxxxx

2

Spuds and carrots solve

You have a job at a fancy restaurant but the chef is not happy with a mixup you made with the guacamole the other night – who knew wasabi paste could look so much likeavocado?Henowhasyouscrubbingoutthebinswithatoothbrush.Youwillnotbefreedfromthistaskuntilyousolvethefollowingproblem:

Whataboutifthepotatoesweighed260geachandthecarrotsremainthesameweight?(Therewillnolongerbeanidenticalamountofcarrotsandpotatoesinthebag.)

Thereisabagfilledwithpotatoesandcarrots.Itweighs 1kilogram.Thereisanequalnumberofcarrotsand potatoesinthebag.

Thepotatoeseachweigh140grams.Thecarrotsareall identicalandeachweighlessthanhalfthatamount.

How many spuds are in the bag? How many carrots?

What to do

What to do next

Getting ready

Perhaps making a table or list could help.

There are 5 potatoes and 5 carrots. We know

the weight of the potatoes and need to use

trial and error to work out the possible weight of the carrots.

They must weigh less than 70 g. We can use a list to find

complementary numbers.

2 potatoes (2 x 260 g) = 520 g (carrots 480 g)

3 potatoes (3 x 260 g) = 780 g (carrots 220 g)

potatoes carrots

1 140 g 60 g

2 280 g 120 g

3 420 g 180 g

4 560 g 240 g

5 700g 300 g

6 840 g 360 g



SERIES TOPIC

16F 2

Weighing it up solve

It’saslowdayatthezooand5zookeepersarestandingaroundtheelephantenclosure,shootingthebreeze.TheystartarguingabouttheweightofGertie,theirfavouriteelephant.Allfivemakeaprediction.Allarewrongwhichisfortunateasthelosersweregoing to have to dress up as a boy band and perform forthelunchcrowds.

YourjobistofindoutGertie’sactualweightusingthefollowingclues:

Theguesseswere: 4050kg

4070kg

4120kg

4130kg

4160kg

Rememberalloftheseguesseswerewrong.Howeveronlytwoguessesweremorethan30kgoutandthosetwowereoutby70kgand90kg.

HowmuchdoesGertieweigh?

What to do

Getting ready

Hmm… two guesses are more than 30 kg out. This means the other three must be close together.

They must either be at the top of the range or at the bottom of the range.

The difference between 70 and 90 is 20 – how can this clue help me?

Gertie weighs 4140 kg.

As 3 of the guesses are within 30 kg of each other, the closer guesses

must all sit either at the top or the bottom of the range.

Since the difference between 70 and 90 is 20, two of the guesses

must also have a difference of 20. These two numbers are 4120

and 4160.


17Series F Topic 1 Assessment

Skills Not yet Kind of Got it

• Converts between millilitres and litres

• Uses appropriate unit to measure volume and capacity

• Readscalibrationsona1litrejug

Nadia made a punch where she poured in 500 mL of pineapple juice, 700 mL of soda water and 400 mL of apple juice. How much punch did she make? ____________ L ____________ mL

Colour the jugs to show the flowing capacities:

Label each cubic centimetre model with its volume and capacity and appropriate unit.

Volume = ______________ Volume = ______________

Capacity = ______________ Capacity = ______________

How many cubic centimetre blocks will fit inside an empty box that is 6 cm long, 4 cm high and 2 cm wide? _________________

Write the following as millilitres:

a 6L = mL b 14 L = mL

c 812 L = mL d 2 L = mL

Volume and capacity Name ____________________

1

2

3

4

5

6

Write the following as litres:

a 3000mL = L b 7000mL= L

c 500mL = L d 4500mL= L

a half a litre b 14 of a litre c

34 of a litre d900mL


18Series F Topic 1 Assessment


• Converts between millilitres and litres

• Uses appropriate unit to measure volume and capacity

• Readscalibrationsona1litrejug

Nadia made a punch where she poured in 500 mL of pineapple juice, 700 mL of soda water and 400 mL of apple juice. How much punch did she make? ____________ L ____________ mL

Colour the jugs to show the flowing capacities:

Label each cubic centimetre model with its volume and capacity and appropriate unit.

Volume = ______________ Volume = ______________

Capacity = ______________ Capacity = ______________

How many cubic centimetre blocks will fit inside an empty box that is 6 cm long, 4 cm high and 2 cm wide? _________________

Write the following as millilitres:

a 6L = mL b 14 L = mL

c 812 L = mL d 2 L = mL

Volume and capacity Name ____________________

1

2

3

4

5

6

Write the following as litres:

a 3000mL = L b 7000mL= L

c 500mL = L d 4500mL= L

a half a litre b 14 of a litre c

34 of a litre d900mL

3

6000

7

250

0.5

8500

4.5

2000

48 blocks

10 cm3 6 cm3

10 mL 6 mL

1.6 1600


19


• Converts between grams and kilograms

• Readscalibrationsona1kilogramscale

• Converts between kilograms and tonnes

• Uses appropriate unit to measure mass

Complete this kilograms to tonnes conversion table:

Kilograms 1765 3890 1235 2456

Tonnes 7 8.765

Draw the following items on the scale and the arrow to show the mass:

Write the following as kilograms:

a 7000g= kg b 4000g= kg c 500g= kg

Write the following as grams:

a 5kg= g b 312 kg = g c 16kg= g

Mass Name ____________________

Series F Topic 2 Assessment

Write g or kg to show what to use to find the mass of each object:

a a baby b a pencil c a packed suitcase

d a die e a TV f an adult

1

2

4

5

6

3

425gcanofsoup 700gloafofbread 50gchocolatebar

0100900

400600500

800 200

700 300

0100900

400600500

800 200

700 300

0100900

400600500

800 200

700 300

List 3 things that we would weigh in tonnes:

__________________________ __________________________ __________________________


20


• Converts between grams and kilograms

• Readscalibrationsona1kilogramscale

• Converts between kilograms and tonnes

• Uses appropriate unit to measure mass

Complete this kilograms to tonnes conversion table:

Kilograms 1765 3890 1235 2456

Tonnes 7 8.765

Draw the following items on the scale and the arrow to show the mass:

Write the following as kilograms:

a 7000g= kg b 4000g= kg c 500g= kg

Write the following as grams:

a 5kg= g b 312 kg = g c 16kg= g

Mass Name ____________________

Series F Topic 2 Assessment

Write g or kg to show what to use to find the mass of each object:

a a baby b a pencil c a packed suitcase

d a die e a TV f an adult

1

2

4

5

6

3

425gcanofsoup 700gloafofbread 50gchocolatebar

0100900

400600500

800 200

700 300

0100900

400600500

800 200

700 300

0100900

400600500

800 200

700 300

List 3 things that we would weigh in tonnes:

__________________________ __________________________ __________________________

kg g kg

g

5000

7 4 0.5

3500 16000

kg kg

7000 8765

2.4561.2353.89(0)1.765

Answers will vary


21

Series F – Volume, Capacity and Mass

Series F Outcomes

RegionTopic 1 Volume and capacity

Topic 2 Mass

NSW

MS3.3 – Select and use the appropriate unit to estimate and measure volume and capacity including the volume of rectangular prisms

•construct regular prisms using cubic cm blocks and count to determine volume

•estimatethenmeasurethecapacityofrectangular prisms

•use the cubic metre as a formal unit•select the appropriate unit to measure volume

and capacity•findtherelationshipbetweenlength,width,

height and volume•demonstrate displacement•recordvolumeandcapacityto3decimal

places

MS3.4 – Select and use the appropriate unit and measuring device to find the mass of objects

•recognise the need for a unit larger than 1kg•convertbetweenkilograms,gramsandtonnes•select and use appropriate unit and measuring

device•recordmassusingdecimalnotationto3

decimal places•solveproblemsinvolvingdifferentunitsofmass(WM)

•associate gram measures with familiar objects (WM)

VIC

Number VELS Level 4

•usemetricunitstoestimateandmeasuremass,volumeandcapacity•measureasaccuratelyasneededforthepurposeoftheactivity•convert between metric units

QLD

M 4.1 Students choose appropriate units when estimating and measuring and explain relationships between dimensions when investigating volumes of prisms

•thelargertheunitthefewerrequiredtomeasureandviceversa−kilogramsandtonnes•relationshipsbetween−length,widthandheight,andvolumeofaprism

SA

3.4 – select appropriate attributes and systems to measure for a variety of purposes and report on how measurement is used in practice

3.5 – use a range of standard tools to measure relationships between distances and other measurable attributes to calculate size

•usetheappropriatemetricunitstomeasurecapacity,volume,andmass•measure for a variety of purposes•chooseappropriatetools(includingelectronic),strategiesandunitsofcomparisoninplanning

measurement•identifyrelationshipsbetweendistances,surfacesandvolumestodevelopanduseformulaeinordertoestimateandcalculatethevolumesofrectangularprisms

•estimatecapacitiesandmassesintermsofmetricunits•choosetheappropriatetools,technologiesandunitstomeasureforaparticularlevelofaccuracy,anddiscusseshowthetoolsusedaffecttheprecisionofmeasurements.


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Topic 2 Mass

WA

Level 4

The student selects appropriate attributes and chooses units of a sensible size for the descriptions and comparisons to be made. The student measures volume by counting cubes and mass and capacity by reading whole-number scales

•Theyexpressmeasuresofcapacityandmassusingcommonmetricprefixes,suchaskilo,milliandappropriatenotationsuchasmLandkg

•Studentscountunitsofvolumeinstraightforwardcases:forexample,theycanmeasurethevolume of arrangements composed of cubes and copy and build arrangements of cubes to order thembythenumberofcubesused.Theycancompareandorderlength,capacityandmassmeasurements provided in common standard units

NT

Learners recognise that the accuracy of measurement can be improved by subdividing the unit used. They perform and interpret calculations using measurement data in order to solve problems

M 3.1 Physical attributes

•performcalculationsonmeasurementsin order to convert between units and to determinethevolumeofrectangularprisms.

M 3.3 Graduated scales

•interpretunlabelledgraduationsrepresenting1/10thofaunitonalinearscale

•exploretherelationshipbetweenmLandcm³by displacing water in graduated containers with metric cubes

•use the technique of displacement to determine the volume of irregular objects

•findthevolumeofarectangularprismgiventhelineardimensions(length,widthandheight)

•recallandapplytherelationshipsbetweenvolume and capacity and convert between units in order to perform comparisons or calculations

•recordcapacityusingdecimalnotationto 3places,eg3.345L

•recalltherelationshipsbetweenunitsofcapacity,

•convertbetweenunitsofcapacity, eg3525mL=3.525L

•measure capacity using appropriate devices calibrated in millilitres

Learners recognise that the accuracy of measurement can be improved by subdividing the unit used. They perform and interpret calculations using measurement data in order to solve problems

•recognise that larger masses need a larger unit ofmass,thetonne

•record mass in tonnes from examples and in problems;usetheabbreviationt

•describetherelationshipbetweenunitsofmeasurement,ie1000kg=1tonne

•recordmassusingdecimalnotationto 3places,eg3.345t


Series F Outcomes


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Topic 2 Mass

ACT

17.LC.1 measurementattributesoflength,area,mass,capacity,volume,angleandtime

17.LC.2 informalandstandardunitsofmeasurementoftheseattributes,includingkilogram,gram,litre,millilitre,

17.LC.3 theconceptofconservation,includingdifferentwaysofrecordingthesamemeasurement

17.LC.4 theconceptofmeasurementsasapproximations,withthemeasurementcontextinfluencinglevelsofprecisionrequiredandwaysofrefiningmeasurements(e.g.bychangingunitsorinstruments)

17.LC.8 measure,compareandordermasses,capacitiesandvolumesbyselectingandusingsuitableunitsandinstruments,measuringtothenearestwholeunitandarrangingmeasurementsofthesameattributeinorderofmagnitude

17.LC.9 makereasonableestimatesbyapplyingstrategiesthatsuitthesituationsandobjects

17.LC.10 interpret and read the graduated scales of units on a range of measuring instruments

TAS

Standards 3-4, Stages 7-12

•explore the usefulness and value of standard units in a wide range of context

•use suitable strategies to measure how much a container holds including use of informal units

•readscalesingradationsoftenandexploringunlabelledgradations

•develop skills in measuring capacity•provideopportunitiestoquantifyattributessuchasvolume(capacity)forthepurposeof comparing and / or ordering and communicating

•introduce conversion of units of measure andidentifyingandlinkingdifferentformsofrecording metric measures

•choose and use appropriate measuring tools to the intended level of accuracy; using perimeter,areaandvolumerelationships;

•convert between standard units of measurementinstraightforwardcontexts–volume using litres and millilitres

•build understanding of volume as a concept that deals with three dimensions

•calculate volume of prisms •readscalesandmakingreasonableestimates

where measures fall between marked graduations

Standards 3-4, Stages 7-12

•Exploring the usefulness and value of standard units ina wide range of context

•Developing skills in measuring mass•Providingopportunitiestoquantifyattributes

such as mass the purpose of comparing and / ororderingandcommunicating

•Measuringandcomparemassesofdifferentobjects

•using appropriate instruments and balances•Makingreasonableestimatesofmassbased

on personal benchmarks •Introducing conversion of units of measure

and•identifyingandlinkingdifferentformsof

recordingmetric measures •Convertingbetweenstandardunitsofmeasurementinstraightforwardcontexts–mass

Series F Outcomes

Documents

Volume, Capacity and Mass - Six Point Won! · If so, you have worked out the formula for volume: length x width x height = volume _____ Width Height Length Number of Cubes 48 48 48