volume and capacity – millilitres and litres and capacity – millilitres and litres 1 when we...

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Volume, Capacity and Mass

SERIES TOPIC

1G 1

Capacity refers to the amount a container can hold and is usually associated with liquid.Common capacity measurements are millilitres and litres.

1000 millilitres = 1 litre 1000 mL = 1 L

Volume and capacity – millilitres and litres

1 When we convert:

a millilitres to litres, we by 1000

b litres to millilitres, we by

Convert these amounts to litres:

a 3 452 mL = b 7 895 mL =

c 10 000 mL = d 12 674 mL =

e 56 780 mL = f 235 mL =

2

3

Solve these word problems. They all involve conversion.

a Omarwasfillingupa3Lcontainerwithcordial.Heonlyhadasmall300mLjug.Howmanytimesdidhehavetofillthejugtototallyfillthecontainer?

____________________________________________________________________________________

b Ipoured375mLoutofa2Lmilkcontainer.Howmuchwasleft?Ithenpouredoutanother375mL. Howmuchisleftnow?

____________________________________________________________________________________

c Howmany315mLglassescanbefilledfroma1.7Ljug?Howmuchisleftover?

____________________________________________________________________________________

d Paulaismakingapunchforherparty.Sheuses1.5Loforangejuice,750mLpineapplejuice,1.25Loflemonadeand1.25Lofgingerale.Howmuchpunchdoesshehavealtogether?Howmany250mLcupswillshebeabletofill?

____________________________________________________________________________________

4

Convert these amounts to millilitres:

a 2.568 L = b 3.999 L =

c 10.566 L = d 1.78 L =

e 7.305 L = f 0.35 L =

÷

× 1000

3.452 L

2568 mL

7.895 L

3999 mL

10 L

10566 mL

12.674 L

1780 mL

56.78 L

7305 mL

0.235 L

350 mL

10

1.625 L, 1.250 L

5 glasses, 125 mL

4.750 L, 19 cups



SERIES TOPIC

2 G 1

Volume and capacity – millilitres and litres

5

6

7

8

How much liquid is in each jug? Answer in both litres and millilitres. The first one has been done for you.

Fill the jugs below to the amount shown:

Below is a recipe for the delicious summer drink, Lava Flow. The capacity measurements are expressed in cups or teaspoons. Express them in millilitres:

Lava FlowIngredients (for one drink)

•12 cupofpineapplejuice _______ mL

•12 cup of cream _______ mL

•12 a banana

•3teaspoonsofcoconutcream _______ mL

•4strawberries

•1cupice _______ mL

If you were going to make this drink for your entire class, what amounts of each ingredient would you need to purchase? Use a calculator if you wish. What is the most effective unit in which to express the amounts?

a ________ L

________ mL

b ________ L

________ mL

c ________ L

________ mL

d ________ L

_________ mL

e ________ L

________ mL

a 600 mL b 0.4 L c 1800 mL d 1.6 L e 500 mL

1 L

1 L 1 L2 L

1 L

2 L

1 L

1 L

1 L 1 L1 L 1 L

These capacity measurements are useful to know: 1 teaspoon = 5 mL 1 cup = 250 mL

0.5

500

MethodBlendallingredients(exceptstrawberries)untilsmooth.Putthestrawberriesinthebottomof atallglassandaddtheblendedmixture.Decoratewithadrizzleofstrawberrytopping.

1 L

0.9

900

0.3

300

1

1000

0.7

700

125

125

15

250

Teacher check



SERIES TOPIC

3G 1

Use the formula L × W × H = V to find the volume of these prisms. You may use a calculator.

a b c

d e f

Volume and capacity – cubic centimetres and cubic metres

1

2

Find the volume of these shapes by counting the cubes. Each cube is 1 cm³.

a Volume = ____________ cm3 b Volume = ____________ cm3 c Volume = ____________ cm3

Shape a b c d e f

Volume

15 cm

6.5 cm

8 cm

5 cm4 cm

2 cm

11 cm3.5 cm

7 cm

6 cm 1 cm

2 cm

5 cm4.5 cm

6 cm

4 cm2 cm

2 cm

Rememberthatvolumereferstotheamountofspaceoccupiedbyanobjectorsubstance.Commonlyusedvolumemeasurementsarethecubiccentimetreandthecubicmetre.

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

Onecubicmetreis1mlong,1mwideand1mhigh. The symbol we use is m3.1 m × 1 m × 1 m = 1 m3

Wecanfindoutthevolumeofarectangularprismorcubewithoutcountingeachblock.Wejustmultiplythelengthbythewidthbytheheight.

Length

Height

Width

L×W×H=V5 × 2 × 2 = 20 cm3

12 48 30

16 cm3 12 cm3 40 cm3 135 cm3 269.5 cm3 780 cm3



SERIES TOPIC

4 G 1

3

4

5

Use the formula L × W × H = V to find the volume of these prisms. You may use a calculator.

a b c d

Boxes of tissues are packed in cubic metre containers to be shipped to supermarkets. Use a calculator to work out how many of these boxes will fit into each container. You will first need to work out how many cubic centimetres are in a cubic metre.

Work with a friend on this activity. You may either physically build the towers or choose to talk through the problem together. You are building towers using centicubes. One of you makes your first level with 4 rows of 3 blocks. The other person starts with 5 rows of 4 blocks. The first one has been done for you.

a Fill in the table to show how the volume of thetowerswouldincreaseastheygrow.

b Your teacher says you can only have 200 cubes between you. You build the towers to the same height.Howmanylevelscouldyoueachbuild?

_____________________________________

_____________________________________

_____________________________________

Person 1 Person 2

1st level 12 cm3 20 cm3

2nd level cm3 cm3

3rd level cm3 cm3

4th level cm3 cm3

5th level cm3 cm3

6th level cm3 cm3

7th level cm3 cm3

8th level cm3 cm3

Shape a b c d

Volume

a

________________boxes

b

________________boxes

c

________________boxes

10 cm

20 cm10 cm

10 cm

10 cm10 cm

10 cm25 cm

10 cm

7.5 m

4 m

4 m

3.25 m3 m

4 m

4 m

3.5 m

5 m

4 m

3.5 m

10 m

Volume and capacity – cubic centimetres and cubic metres

120 m3 39 m3 70 m3 140 m3

500 1 000 400

24

36

48

60

72

84

96

40

60

80

100

120

140

160

Person 1 – 6th level

Person 2 – 6th level



SERIES TOPIC

5G 1

Now use the objects below (or something equivalent). Using displacement, find the volume and capacity of each object.

Objecta b c d e f g

Volume

Capacity

Volume and capacity – displacement

Rememberthatvolumeistheamountofspaceoccupiedbyanobjectorsubstanceandcapacityistheamountanobjectwillhold.Displacementistheamountoffluidthatispushedawaywhenanobjectisplacedinthefluid. We can use displacement to calculate both volume and capacity.

1

2

3

Try this experiment to find out about displacement. You will need a jug, a lunchbox, a tray and a model made from 100 centicubes. Work with a friend or in a small group.

1 Standthelunchboxinthetray.

2 Filltheboxtothetopwithwater.

3 Carefullysubmergethemodelinthewaterinthebox.

4 Pourthewaterthatoverflowedintothetrayintothemeasuringjug.HowmanymLequals100cm³?

___________________________________________

Checkyouranswerwiththatoftwoothergroups. Dotheyagreewithyou?

___________________________________________

Using what you now know about volume and displacement, how many millilitres of water would be displaced by objects with these volumes?

a 100 cm3 = __________ mL b 250 cm3 = __________ mL c 500 cm3 = __________ mL

d 8 cm3 = __________ mL e 1000 cm3 = __________ mL f 56 cm3 = __________ mL

g 86 cm3 = __________ mL h 4300 cm3 = __________ mL i 1.9 cm3 = __________ mL

Answers will vary

100 mL = 100 cm3

Answers will vary

100 250 500

8 1000 56

86 4300 1.9



SERIES TOPIC

6 G 1

a

Volume = _____________ cm3

Capacity = _____________ mL

Mass =_____________g

d

Volume = _____________ cm3

Capacity = _____________ mL

Mass =_____________g

b

Volume = _____________ cm3

Capacity = _____________ mL

Mass =_____________g

e

Volume = _____________ cm3

Capacity = _____________ mL

Mass =_____________g

c

Volume = _____________ cm3

Capacity = _____________ mL

Mass =_____________g

f

Volume = _____________ cm3

Capacity = _____________ mL

Mass =_____________g

Doyouremembertherelationshipbetweenvolume,massandcapacity?

1cm³=1mL=1g

Volume and capacity – linking mass, capacity and volume

1

2

3

Calculate the volume, mass and capacity of these shapes by counting the cubes. Each cube is 1 cm³.

Seven tenths of the human body is water. Weigh yourself in kg then use a calculator to help you work out the answers to the following:

a Howmuchofyourmassiswater? ____________________________

b Whatisthecapacityofthiswater? ____________________________

c Whatisthevolumeofthiswater? ____________________________

If you could drain yourself of all the water (not a good idea), what kind and size of container would be suitable and why?

____________________________________________________________

____________________________________________________________

____________________________________________________________

10

8 8 24

7 7

10

8 8 24

7 7

10

8 8 24

7 7

Answers will vary

Answers will vary

Answers will vary

Answers will vary



SERIES TOPIC

7G 1

Measuring mud investigate

Inthisactivityyouaregoingtousewhatyouknowabouttherelationshipbetweenmass and volume to calculate the volume of the water in mud. You will need a cup, some newspaper and a scale.

Workwithapartner.Thisexperimentmaytakeadayorsotocompleteandisprobably best done outside.

Collect a cupful of mud or damp soil. Make sure the mud is not too sloppy. Find its massbyweighingit.Howwillyoudothis?Perhapsyoucouldweightheemptycupandthensubtracttheweightofthecup.

Now spread out your mud onto sheets of newspaper and leave it to dry in the sun. It mayhelptoplaceweightsonthepaperortapeitdown.Youmayalsoneedtolabelyourexperimentsoitdoesn’tgetaccidentallycleanedup!

Once your mud has dried, carefully collect it and measure its mass. Remember to usethesamecup.Whydoyouneedtodothis?

Whatwasthevolumeofwaterinthemud?

Howdoyouknow?

Findarockthathasthesamevolumeasthelostwater.Howwill youdothis?Howwillyouknowthatithasthesamevolume?

What to do

What to do next

Getting ready

Answers will vary. Students may measure the mass

of the rock (mass = volume) or use displacement to

calculate capacity (capacity of displaced water = volume).

Answers will vary



SERIES TOPIC

8 G 1

Water, water, everywhere … investigate

Thisactivitycouldcomeinhandyshouldyoueverbestrandedinthebushsomewhere!Youwillneedagarbagebag,somestringandameasuringjug.Work inasmallgroup.

Youaregoingtopredict,collectandmeasuretheamountofwateratreebranchlosesthroughtranspiration(evaporation)overtheperiodofaday.Itisbesttobegintheexperimentasearlyinthedayaspossibleandtocollectthewateraslateinthedayasyoucan.Chooseanicesunnydayforyourexperiment.Abitofabreezewillhelp too.

Chooseaniceleafytreebranch.Howmuchwater do you think you will be able to collect fromit?Writedownyourpredictions.

Putyourbagoveryourselectedbranchandtieitoff.Now,makeapouchatthebottom ofthebagandtiethatofftoo.

Leavethebagoverthedayandcomeback to collect the water as late as you can.

Cut the pouch and carefully drain the water intoameasuringjug.Whatisthecapacityofthewateryouhavecollected?

Compareyourresultswiththeresultsofothergroups.Dotheydiffer?Why?

Repeatyourexperimentonanotherdayusingthesamebranch.Areyourresultsdifferenttothoseoftheoriginalexperiment?Whatwasdifferentaboutthe twodays?

What to do

What to do next

Getting ready

Answers will vary



SERIES TOPIC

9G 2

Massmeasureshowmuchmatterisinanobject.Weusuallymeasurethisbyfindingoutwhattheobjectweighs.Massandweightareslightlydifferentbutweoftenuseweighttermswhenwearetalkingaboutdaytodaymassmeasurements.Commonmeasurementsaregrams(g),kilograms(kg)andtonnes(t).Thereare1000gineachkilogramand1000kginatonne.

Mass – grams

1

2

3

4

This activity will help you get a feel for different masses. You̕ll need the objects in the table, a calibrated scale or a balance scale and some small masses (10 g, 50 g, or 100 g). Estimate, then measure the mass:

Item Estimate Mass

scissors

gluestick

calculator

lunchbox(full)

lunchbox(empty)

pencil case (full)

pencil case (empty)

Estimate and then measure how many of each of these objects are needed to balance 10 grams.

Centicubes 5¢ Coins Drawing pins

Estimate

Measure

Use your answers in question 1 to place the 7 items on the line in order of their individual mass.

Write each mass in grams, kilograms and grams and as a decimal.

Grams 1000g 350g

Kilograms and grams 2kg700g 5kg50g

Decimal notation 7.125kg 3.2kg

Lightest Heaviest

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.

Answers will vary

Answers will vary

Answers will vary

2700 g 7125 g 5050 g 3200 g

1 kg 7 kg 125 g 350 g 3 kg 200 g

1.0 kg 2.7 kg 0.35 kg 5.05 kg



SERIES TOPIC

10 G 2

Mass – grams and kilograms

There are 28 students in Mr Brown’s class. Being the dedicated and hardworking teacher that he is, he lugs their books home to mark each week.

a Eachmathsbookhasamassof550g.Heputsthemallinatotetraywhichhasamassof345g.Whatisthetotalmasshewillcarrytohiscar?

_____________________________________________________________

b Lastweekhetookhomethespellingbooksinthesametotetray.Thetotalmasswas9.445kg.Whatwasthemassofeachspellingbook?

_____________________________________________________________

c Nextweek,thefootballstartsagain.Theregoesthemarking.MrBrownwillnowbesittinginthegrandstandmunchingchipsandcheeringontheMightyBlues.Ifheconsumesfour375gbagsofchipsinaparticularlytensegame,howmuchdoesheeat?

_____________________________________________________________

1

2

3

Five children measured their mass.

a Usedecimalnotationtowritethemassesinkilogramsasshownonthescales:

A regular packet of cereal has a mass of 540 g. An average serving is 45 g. Answer these questions without a calculator.

a Howmanyaverageservingsarethereinonepacket? ___________________

b TherearefourpeopleinMichaela’sfamily.Eachhasanaverageserveperday. Howmanydayswilltheboxlast? ___________________

c Thelargestsizedboxhasamassof720g.Howlongwillthisboxlastherfamily? ___________________

d Michaela’sfamilyisgoingcampingfor2weeks.Theyneedtotakeall theirfoodwiththem.Theywanttotakeexactlytherightamountofcereal. Howmanyboxesofeachsizewilltheyneedtotake? ___________________

Minh

kg

Ben

kg

Heba

kg

Sara

kg

Yasmin

kg

b Noworderthechildrenfromlightesttoheaviest.

15 20 45 50 25 30 35 40 35

40

Lightest Heaviest

17 47.5 27 37 35.5

Minh Heba Yasmin Sara Ben

12

3 days

4 days

2 boxes of each

15.745 kg

325 g

1.5 kg



SERIES TOPIC

11G 2

Mass – tonnes

Tonnesareusedtomeasurethemassofheavierobjects.Anaveragecarhasamassofapproximately2tonnes.Anelephantcanhaveamassofupto6tonnes.

1tonne(t)=1000kg

1

2

When we convert:

a tonnestokilogramswe by 1000

b kilogramstotonneswe by

Convert these measurements from tonnes to kilograms:

a 5 t = kg b 16 t = kg

c 56.25 t = kg d 4.125 t = kg

e 0.5 t = kg f 13.05 t = kg

3 Use decimal notation to convert these kilograms into tonnes:

a 5000kg = t b 12245kg = t

c 44 567 kg = t d 6 009 kg = t

e 450 kg = t f 677 kg = t

5 Complete:

a 500kg+ = 1 t b 125kg+ = 1 t c 456kg+ = 1 t

2 tonnes 6 tonnes

4 1.5 2.5 120 440

4 Choose the correct unit of measurement (g, kg, t) for these objects:

Now order their masses from least to greatest:

Least Greatest

When converting between tonnes and kilograms we often have to move in and out of decimal numbers. Drawing the jumps can help.

6 7 8 kg = 0.678 t

÷

×

1000

5000 16000

56250 4125

500

5.0 12.245

44.567 6.009

0.450

t

120 g 440 g

500 kg 875 kg 544 kg

1.5 kg 2.5 t 4 t

kg t g g

0.677

13050



SERIES TOPIC

12 G 2

Mass – tonnes

6

7

8

9

Write each mass in kilograms, tonnes and kilograms, and as a decimal.

Kilograms 1000kg 350kg

Tonnes and kilograms 2t700kg 5t50kg

Decimal notation 7.125 t 3.2 t

The weighbridge on the expressway measures the mass of heavy vehicles.

a Calculatethemassofeachloadbysubtractingthetare(masswithoutaload) fromthetotalmassmeasuredontheweighbridge.Thefirstoneisdoneforyou.

Vehicle Total mass Tare Mass of load

Coach 17t200kg 13.1 t 4t100kg

Tow truck 3t878kg 2.75 t

Campervan 4t250kg 2.569 t

Cementmixer 20t456kg 12.842 t

Semi-trailer 11t300kg 8.675 t

b Whichvehiclehastheheaviestload? ____________________________

Louisa’s family did a big clean up at home and took the rubbish to the tip. The total mass of the car and the trailer was measured each time.

a Thecar’smasswas1.78t.Completethecharttoshow thetotalmassmeasuredeachtime

b Whatisthetotalamountofrubbishtakentothetip altogether?Answerintonnes.

___________________________________________

A 32 seater aeroplane was filled to capacity. The passengers had an average mass of 74 kg. The average mass of the luggage was 15 kg per person.

a Whatisthetotalmassofpassengersintonnes? __________________

b Whatisthetotalmassoftheluggage? __________________

c The aeroplane is licensed to carry 4 t. Howmuchextracargocantheynowtake? __________________

Load Mass of Load Total mass

1 675kg

2 935kg

3 798kg

The average was found by dividing the total mass by the number of people. So you can ‘undo’ this by multiplying.

2700 kg 7125 kg 5050 kg 3200 kg

1 t 0 kg 7 t 125 kg 0 t 350 kg 3 t 200 kg

1 t 2.7 t 0.35 t 5.05 t

1 t 128 kg

1 t 681 kg

7 t 614 kg

2 t 455 kg

2 t 715 kg

2 t 578 kg

2 t 625 kg

Cement mixer

2.408 t

2 t 368 kg

480 kg

1.152 t



SERIES TOPIC

13G 2

Whatisthemassof1millilitreofwater?

Mass – mass and capacity

1

2

3

Try this experiment to find out about the mass of water. You will need a measuring cup or jug, some balance scales and some weights.

1 Measurethemassofthemeasuringcup.

2 Pour 50 mL of water into the cup.

3 Measure the mass of the cup and water.

4 Calculatethemassofthewaterbysubtractingthemassofthecup.

5 Repeat for 100 mL, 250 mL, 500 mL and 1 L and record your results.

Amount of water 50 mL 100 mL 250 mL 500 mL 1 L

Mass

a Whathaveyoudiscovered?1mLofwater= gram.

b Whydidyouneedtosubtractthemassofthecup? ________________________________________

Without measuring, can you now calculate the mass of these amounts of water?

a 150mL =____________g b 467mL=____________g c 1.5L =__________kg

d 980 mL = ____________kg e 2.75 L = ____________kg f 8.45 L = __________g

Ben poured the same amount of water into five different containers. He then measured the mass of each of them. If you can work out the mass of each of the containers, Ben says your teacher will give you 5 early minutes. All the clues you need are in the table.

Container A B C D E

Mass of container filled with water

365g 678g 458g 1kg 1.3g

Mass of container 15g

How did you go? Did your teacher get the memo about the early minutes?

_______________________________________________________________________________________

_______________________________________________________________________________________

4

1 L

1

50 g 100 g 250 g 500 g 1 kg

328 g 108 g 650 g 950 g

150 467 1.5

0.98 2.75 8450

To find out the mass of the water.

Answers will vary



SERIES TOPIC

14 G 2

Try this experiment. You’ll need 10 centicubes, plasticine, a measuring cup and a tap. Push the centicubes gently but fully into the plasticine, then carefully remove them. Now, fill the holes with water. Finally, measure the amount of water.

a Howmuchwaterwasused? _____________________________________________________________

b Wasittheamountyouexpected?Ifnot,whydoyouthinkitisdifferent?

____________________________________________________________________________________

Mass – mass and capacity

5

6

Sean’s teacher asked him to conduct an experiment to find out more about the mass of water.

a Hestartedtodrawthisgraphandtable.Completebothforhim:

b Seanthendecidedtoseewhatwouldhappenwhenhesubmergedcenticubesinthewater.Thisgraphshowshowmuchwaterwasdisplacedashedidthis.Usethegraphtocompletethetable:

c UsetheinformationSeandiscoveredtocompletethefollowingtable:

Volume (cm³) 500cm³ 7cm³

Capacity (mL) 25 mL 1 200 mL

Mass (g) 350g 1kg

Cubic centimetres Water displaced

10 cm3

20 cm3

5 mL

14 mL

50 cm3

100 mL

850 cm3

Mass of water

05 10 15 20

5

10

15

20

Cubic centimetres (cm3)

Mill

ilitr

es (m

L)

Water displaced

Volume of water Mass of water

100 mL 100g

200 mL 200g

300 mL 300g

500 mL

600 mL

800 mL

1000 mL0

200

400

600

800

1000

100

100

Volume of water in mL

Mas

s in

g

200 300 400 500 600 700 800 900 1000

300

500

700

900

500 g

10 mL

5 cm3

350 cm3

500 mL 350 mL 1000 mL 7 mL

500 g 25 g 1200 g 7 g

25 cm3 1000 cm3 1200 cm3

14 cm3

100 cm3

600 g

20 mL

50 mL

850 mL

800 g

1000 g

Answers will vary

Answers will vary

0

200

400

600

800

1000

100

100

Volume of water in mL

Mas

s in

g

200 300 400 500 600 700 800 900 1000

300

500

700

900



SERIES TOPIC

15G 2

The chocolate challenge solve

This word problem requires you tocalculatetheweightoftwoidenticalchocolatebars.

Work with a friend to solve it. You only need a pencil, paper and your brains.

Youhavetwoidenticalchocolatebars.Youalsohaveasetofbalancescalesandtwoweights,onemeasuring100gandtheothermeasuring50g.

If you place one of the chocolate

bars on one side of the balance

scales, it is balanced by both

weightsand13 of the other

chocolate bar.

Howheavyiseachchocolatebar?

Couldyouwriteasimilarproblemforafriend?Usea200gweight,a100gweightand2identicalobjectsinyourproblem.

What to do

What to do next

100g

50g

100g

50g

Getting ready

Hmmm … I think algebra could be used here.

There are a number of ways to solve this problem. One way is:

1 bar = 150 g + 13 bar

This can be re framed as: 33 bar = 150 g + 13 bar

We remove 13 bar from both sides: 23 bar = 150 g

If we multiply both sides by 3 we have:

2 bars = 450 g

Then we divide by 2 to find the weight of one bar:

1 bar = 225 g



SERIES TOPIC

16 G 2

Cupcake creation solve

This word problem requires you to work out how many cupcakes you could make if you had a specifed amount ofingredients.

You can work alone or with a friend.

Hereisthemethod.Maybeyoucouldmaketheseathome.

Method

1. Preheat the oven to 200°C and grease a 12 cup muffin pan.

2. Sift the flour and add the caster sugar.

3. Make a hole in the centre of the mix and add milk, butter, vanilla and eggs.

4. Mix gently and when combined, spoon into the muffin pan.

5. Bake for 12–15 minutes. Let cakes cool in the pan for 5 minutes before transferring to a wire rack to cool.

6. Once cold, ice using 112 cups of icing sugar mixed with

1 tablespoon hot water and food colouring.

7. Decorate with sprinkles.

What to do

What to do next

Read the recipe (ontheright)for cupcakes:

This recipe makes 12 cupcakes.

Howmanycupcakescouldyoumakeif you had:

Ingredients

3kgself-raisingflour

720gcastersugar

1 L milk

600gbutter

5 teaspoons vanilla essence

Getting ready

48 cupcakes – enough of all ingredients for 4 batches. You will have flour, milk, and vanilla essence left over.

volume and capacity – millilitres and litres and capacity – millilitres and litres 1 when we...

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