Volume, Capacity and Mass - · PDF fileStudent Book SERIES G Name _____ Volume, Capacity and...

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Volume, Capacity and Mass

Teacher BookSERIES

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Series G – Volume, Capacity and Mass

Contents

Topic 1 – Volume and capacity• millilitres and litres ____________________________________

• cubiccentimetresandcubicmetres _______________________

• displacement _________________________________________

• linking mass, capacity and volume ________________________

• measuring mud – investigate ____________________________

• water, water, everywhere – investigate ____________________

Topic 2 – Mass• grams _______________________________________________

• grams and kilograms ___________________________________

• tonnes ______________________________________________

• mass and capacity _____________________________________

• the chocolate challenge – solve ___________________________

• cupcakecreation–solve ________________________________

Date completed

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Copyright ©

Series Authors:

Rachel Flenley

Nicola Herringer

Contents

Topic 1 – Volume and capacity (pp. 1–8)• millilitres and litres ____________________________________

• cubiccentimetresandcubicmetres _______________________

• displacement _________________________________________

• linking mass, capacity and volume ________________________

• measuring mud – investigate ____________________________

• water, water, everywhere – investigate ____________________

Topic 2 – Mass (pp. 9–16)• grams _______________________________________________

• grams and kilograms ___________________________________

• tonnes ______________________________________________

• mass and capacity _____________________________________

• the chocolate challenge – solve ___________________________

• cupcakecreation–solve ________________________________

Date completed

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Contents

Section1–Answers(pp.1–16)• volume and capacity __________________________________ 1

• mass _______________________________________________ 9

Section2–Assessmentwithanswers(pp.17–20)• volume and capacity _________________________________ 17

• mass ______________________________________________ 19

Section3–Outcomes(pp.21–23)

SERIES TOPIC

1G 1Copyright © 3P Learning


Capacity refers to the amount a container can hold and is usually associated with liquid.Common capacity measurements are millilitres and litres. 1000millilitres=1litre 1000mL=1L

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 3452mL = b 7895mL =

c 10000mL= d 12674mL=

e 56780mL= f 235mL =

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 2.568L = b 3.999L=

c 10.566L = d 1.78L =

e 7.305L = f 0.35L =

÷

× 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

G 12Copyright © 3P Learning


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

a600mL b0.4L c1800mL d1.6L e500mL

1 L

1 L 1 L2 L

1 L

2 L

1 L

1 L

1 L 1 L1 L 1 L

Thesecapacitymeasurementsareusefultoknow:1teaspoon =5mL 1cup =250mL

0.5

500

MethodBlendallingredients(exceptstrawberries)untilsmooth.Putthestrawberriesinthebottomof a tall glass and add the blended mixture. Decorate with a drizzle of strawberry topping.

1 L

0.9

900

0.3

300

1

1000

0.7

700

125

125

15

250

Teacher check

SERIES TOPIC



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,1 cm wide and 1 cm high. The symbol we use for cubic cm is cm3.1cm×1cm×1cm=1cm3

Onecubicmetreis1mlong,1 m wide and 1 m high. The symbol we use is m3.1m×1m×1m=1m3

Wecanfindoutthevolumeof a rectangular prism or cube withoutcountingeachblock.Wejustmultiplythelengthbythe width by the height.

Length

Height

Width

L×W×H=V5×2×2=20cm3

12 48 30

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

SERIES TOPIC



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 the towers would increase as they grow.

b Yourteachersaysyoucanonlyhave200cubesbetween you. You build the towers to the same height.Howmanylevelscouldyoueachbuild?

_____________________________________

_____________________________________

_____________________________________

Person 1 Person 2

1st level 12 cm3 20cm3

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

10cm

20cm 10cm

10cm

10cm10cm 10cm25cm

10cm

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



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 Stand the lunchbox in the tray.

2 Fill the box to the top with water.

3 Carefully submerge the model in the water in the box.

4 Pourthewaterthatoverflowedintothetrayintothemeasuringjug.HowmanymLequals100cm³?

___________________________________________

Check your answer with that of two other groups. Dotheyagreewithyou?

___________________________________________

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

a 100cm3 =__________mL b 250cm3 =__________mL c 500cm3=__________mL

d 8 cm3 =__________mL e 1000cm3=__________mL f 56cm3 =__________mL

g 86 cm3 =__________mL h 4300cm3=__________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



a

Volume =_____________cm3

Capacity=_____________mL

Mass =_____________g

d

Volume =_____________cm3


Mass =_____________g

b

Volume =_____________cm3


Mass =_____________g

e

Volume =_____________cm3


Mass =_____________g

c

Volume =_____________cm3


Mass =_____________g

f

Volume =_____________cm3


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



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.

Work with a partner. This experiment may take a day or so to complete and is probably best done outside.

Collect a cupful of mud or damp soil. Make sure the mud is not too sloppy. Find its massbyweighingit.Howwillyoudothis?Perhapsyoucouldweightheemptycupand then subtract the weight of the cup.

Now spread out your mud onto sheets of newspaper and leave it to dry in the sun. It may help to place weights on the paper or tape it down. You may also need to label your experiment so it doesn’t get accidentally cleaned up!

Onceyourmudhasdried,carefullycollectitandmeasureitsmass.Remembertousethesamecup.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



Water, water, everywhere … investigate

Thisactivitycouldcomeinhandyshouldyoueverbestrandedinthebushsomewhere!Youwillneedagarbagebag,somestringandameasuringjug.Work in a small group.

You are going to predict, collect and measure the amount of water a tree branch losesthroughtranspiration(evaporation)overtheperiodofaday.Itisbesttobeginthe experiment as early in the day as possible and to collect the water as late in the dayasyoucan.Chooseanicesunnydayforyourexperiment.Abitofabreezewillhelp too.

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

Put your bag over your selected branch and tieitoff.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

9GCopyright © 3P Learning

Volume, Capacity and Mass 2

Massmeasureshowmuchmatterisinanobject.Weusuallymeasurethisbyfindingoutwhattheobjectweighs.Massandweightareslightlydifferentbutweoftenuseweighttermswhenwearetalking about day to day mass measurements.Common measurements are grams (g), kilograms (kg) and tonnes (t).Thereare1000gineachkilogramand1000kginatonne.

Mass – grams

1

2

3

4

This activity will help you get a feel for different masses. You̕ ll 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

lunch box (full)

lunch box (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

G10Copyright © 3P Learning

Volume, Capacity and Mass2

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 Next week, the football starts again. There goes the marking. Mr Brown willnowbesittinginthegrandstandmunchingchipsandcheeringontheMightyBlues.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 There are four people in Michaela’s family. Each has an average serve per day. Howmanydayswilltheboxlast? ___________________

c Thelargestsizedboxhasamassof720g.Howlongwillthisboxlastherfamily? ___________________

d Michaela’s family is going camping for 2 weeks. They need to take all their food with them. They want to take exactly the right amount of cereal. Howmanyboxesofeachsizewilltheyneedtotake? ___________________

Minh

kg

Ben

kg

Heba

kg

Sara

kg

Yasmin

kg

b Now order the children from lightest to heaviest.

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



Mass – tonnes

Tonnesareusedtomeasurethemassofheavierobjects.Anaveragecarhasamassofapproximately2tonnes.Anelephantcanhaveamassofupto6tonnes.

1tonne(t)=1000kg

1

2

When we convert:

a tonnes to kilograms we by 1000

b kilograms to tonnes we by

Convert these measurements from tonnes to kilograms:

a 5t = kg b 16t = kg

c 56.25t= kg d 4.125t = kg

e 0.5t = kg f 13.05t = kg

3 Use decimal notation to convert these kilograms into tonnes:

a 5000kg = t b 12245kg = t

c 44567kg = t d 6009kg = t

e 450kg = t f 677kg = t

5 Complete:

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

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



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 7.125t 3.2t

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 13.1t 4t100kg

Tow truck 3t878kg 2.75t

Campervan 4t250kg 2.569t

Cement mixer 20t456kg 12.842kg

Semi-trailer 11t300kg 8.675t

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.Completethecharttoshowthetotalmassmeasuredeachtime

b Whatisthetotalamountofrubbishtakentothetipaltogether?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 Whatisthetotalmassofluggage? __________________

c Theaeroplaneislicensedtocarry4t.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



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 Measure the mass of the measuring cup.

2 Pour50mLofwaterintothecup.

3 Measure the mass of the cup and water.

4 Calculatethemassofthewaterbysubtractingthemassofthecup.

5 Repeatfor100mL,250mL,500mLand1Landrecordyourresults.

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

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 980mL = ____________ kg e 2.75L = ____________ kg f 8.450L = __________ 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 1 kg 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



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.Thisgraphshows how much water was displaced as he did this. Use the graph to complete the table:

c UsetheinformationSeandiscoveredtocompletethefollowingtable:

Volume (cm³) 500cm³ 7cm³

Capacity (mL) 25mL 1200mL

Mass (g) 350g 1 kg

Cubic centimetres Water displaced

10cm3

20cm3

5mL

14mL

50cm3

100mL

850cm3

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

100mL 100g

200mL 200g

300mL 300g

500mL

600mL

800mL

1000mL0

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



The chocolate challenge solve

This word problem requires you to calculate the weight of two identicalchocolatebars.

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 weights and 13 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



Cupcake creation solve

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

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 (on the right) for cupcakes:

This recipe makes 12 cupcakes.

Howmanycupcakescouldyoumakeif you had:

Ingredients3kgself-raisingflour720gcastersugar1Lmilk600gbutter5teaspoonsvanillaessence

Getting ready

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

17Series G Topic 1 Assessment

Copyright © 3P Learning

Volume and capacity Name ____________________

Skills Not yet Kind of Got it

• Convertsbetweenmillilitresandlitresusingdecimalnotation

• Uses appropriate unit to measure volume, capacity and mass

• Readscalibrationsona1litrejuginlitresandmillilitres

• Can describe what happens with displacement

Write the following as millilitres:

a 826L = mL b 12L = mL c 62L = mL

d 0.75L= mL e 2.25L= mL f 3.89L= mL

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

Volume =_______________

Capacity=_______________

Mass =_______________

Explain what would happen to the level of water in the jug if this centicube model is placed inside:

______________________________________________________________

______________________________________________________________

How much liquid is in each jug?

a b

_______________ L _______________ L

_______________ mL _______________ mL

Write the following as litres:

a 12345mL= L b 6438mL= L c 9264mL= L

d 7235mL = L e 276mL = L f 109mL = L

1

2

3

4

5

18 Series G Topic 1 Assessment


Volume and capacity Name ____________________


• Convertsbetweenmillilitresandlitresusingdecimalnotation

• Uses appropriate unit to measure volume, capacity and mass

• Readscalibrationsona1litrejuginlitresandmillilitres

• Can describe what happens with displacement

Write the following as millilitres:

a 826L = mL b 12L = mL c 62L = mL

d 0.75L= mL e 2.25L= mL f 3.89L= mL

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

Volume =_______________

Capacity=_______________

Mass =_______________

Explain what would happen to the level of water in the jug if this centicube model is placed inside:

______________________________________________________________

______________________________________________________________

How much liquid is in each jug?

a b

_______________ L _______________ L

_______________ mL _______________ mL

Write the following as litres:

a 12345mL= L b 6438mL= L c 9264mL= L

d 7235mL = L e 276mL = L f 109mL = L

1

2

3

4

5

12.345 6.438 9.264

7.235

826000 12000 62000

750 2250 3890

0.276 0.109

1 0.7

1000 700

7 cm3

7 mL

7 g

The level of the water would rise from 400 mL to 404 mL

19


Series G Topic 2 Assessment


• Convertsbetweengramsandkilogramsusingdecimalnotation

• Recognisestherelationshipbetweenvolume,massandcapacity

• Calculates with kilograms and tonnes

Calculate:

a 10×75kg= b 600kg+ =1t c 1t–560kg=

Complete the following table by writing the equivalent of each quantity:

Volume (cm³) 950cm3

Capacity (mL) 230mL 150mL 905mL

Mass (g) 700g 630g

Mass Name ____________________

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

Grams 250g 1234g



1

2

3

4

5

Draw a line to connect the equivalent masses:

Complete the following word problem:

A50seateraeroplanewasfilledtocapacity.Thepassengershadanaveragemass of74kg.Whatisthetotalmassofthepassengersintonnes? ___________________

3000kg

1500kg

1 t

8.2 t

0.75t

1.5t

8200kg

1000kg

750kg

3t

20


Series G Topic 2 Assessment


• Convertsbetweengramsandkilogramsusingdecimalnotation

• Recognisestherelationshipbetweenvolume,massandcapacity

• Calculates with kilograms and tonnes

Calculate:

a 10×75kg= b 600kg+ =1t c 1t–560kg=

Complete the following table by writing the equivalent of each quantity:

Volume (cm³) 950cm3

Capacity (mL) 230mL 150mL 905mL

Mass (g) 700g 630g

Mass Name ____________________

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

Grams 250g 1234g



1

2

3

4

5

Draw a line to connect the equivalent masses:

Complete the following word problem:

A50seateraeroplanewasfilledtocapacity.Thepassengershadanaveragemass of74kg.Whatisthetotalmassofthepassengersintonnes? ___________________

3000kg

1500kg

1 t

8.2 t

0.75t

1.5t

8200kg

1000kg

750kg

3t

2060 g

230 cm3 700 cm3 150 cm3 630 cm3 905 cm3

700 mL 950 mL 630 mL

230 g

750 kg 400 kg 440 kg

950 g 150 g 905 g

2 234 g 5250 g 6900 g

2 kg 234 g 0 kg 250 g 5 kg 250 g 1 kg 234 g

2.06 kg 0.25 kg 1.234 kg 6.9 kg

3.7 tonnes

21Series G Outcomes


Series G – Volume, capacity and mass

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

•constructregularprismsusingcubiccmblocks and count to determine volume

•estimatethenmeasurethecapacityofrectangular prisms

•usethecubicmetreasaformalunit•selecttheappropriateunittomeasure

volume and capacity•findtherelationshipbetweenlength,width,

height and volume•demonstratedisplacement•recordvolumeandcapacityto3decimalplaces

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

•recognisetheneedforaunitlargerthan1kg•convertbetweenkilograms,gramsandtonnes•selectanduseappropriateunitand

measuring device•recordmassusingdecimalnotationto3

decimal places•solveproblemsinvolvingdifferentunitsof

mass (WM)•associategrammeasureswithfamiliarobjects(WM)

VIC

Number VELS Level 4

•usemetricunitstoestimateandmeasuremass,volumeandcapacity•measureasaccuratelyasneededforthepurposeoftheactivity•convertbetweenmetricunits

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 practice3.5 – use a range of standard tools to measure relationships between distances and other measurable attributes to calculate size

•usetheappropriatemetricunitstomeasurecapacity,volume,andmass•measureforavarietyofpurposes•chooseappropriatetools(includingelectronic),strategiesandunitsofcomparisonin

planning measurement•identifyrelationshipsbetweendistances,surfacesandvolumestodevelopanduseformulaeinordertoestimateandcalculatethevolumesofrectangularprisms

•estimatecapacitiesandmassesintermsofmetricunits•choosetheappropriatetools,technologiesandunitstomeasureforaparticularlevelofaccuracy,anddiscusseshowthetoolsusedaffecttheprecisionofmeasurements

22 Series G Outcomes




Topic 2 Mass

WA

Level 4The 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,milliandappropriatenotationsuchasmLandkgStudentscountunitsofvolumeinstraightforwardcases:forexample,theycanmeasurethevolumeof arrangements composed of cubes and copy and build arrangements of cubes to order them by the number of cubes used. They can compare and order length, capacity and mass measurements 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•performcalculationsonmeasurements

in order to convert between units and to determine the volume of rectangular prisms

M 3.3 Graduated scales•interpretunlabelledgraduationsrepresenting

110 of a unit on a linear scale

•exploretherelationshipbetweenmLandcm³by displacing water in graduated containers with metric cubes

•usethetechniqueofdisplacementtodeterminethevolumeofirregularobjects

•findthevolumeofarectangularprismgiventhe linear dimensions (length, width and height)

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

•recordcapacityusingdecimalnotationto 3places,e.g.3.345L

•recalltherelationshipsbetweenunits of capacity

•convertbetweenunitsofcapacity, e.g.3525mL=3.525L

•measurecapacityusingappropriatedevicescalibrated 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

•recognisethatlargermassesneedalargerunit of mass, the tonne

•recordmassintonnesfromexamplesandinproblems;usetheabbreviationt

•describetherelationshipbetweenunitsofmeasurement,i.e.1000kg=1tonne

•recordmassusingdecimalnotationto 3places,e.g.3.345t

23Series G Outcomes




Topic 2 Mass

ACT

17.LC.1 measurementattributesoflength,area,mass,capacity,volume,angleandtime17.LC.2 informalandstandardunitsofmeasurementoftheseattributes,includingkilogram,gram,

litre, millilitre17.LC.3 theconceptofconservation,includingdifferentwaysofrecordingthesamemeasurement17.LC.4 theconceptofmeasurementsasapproximations,withthemeasurementcontext

influencinglevelsofprecisionrequiredandwaysofrefiningmeasurements(e.g.bychanging units or instruments)

17.LC.8 measure,compareandordermasses,capacitiesandvolumesbyselectingandusingsuitable units and instruments, measuring to the nearest whole unit and arranging measurementsofthesameattributeinorderofmagnitude

17.LC.9 makereasonableestimatesbyapplyingstrategiesthatsuitthesituationsandobjects17.LC.10 interpret and read the graduated scales of units on a range of measuring instruments

TAS

Standards 3–4, Stages 7–12

•exploretheusefulnessandvalueofstandardunits in a wide range of context

•usesuitablestrategiestomeasurehow much a container holds including use of informal units

•readscalesingradationsoftenandexploringunlabelledgradations

•developskillsinmeasuringcapacity•provideopportunitiestoquantifyattributes

such as volume (capacity) for the purpose of comparingand/ororderingandcommunicating

•introduceconversionofunitsofmeasureandidentifyingandlinkingdifferentforms of recording metric measures

•chooseanduseappropriatemeasuringtoolsto the intended level of accuracy; using perimeter,areaandvolumerelationships;

•convertbetweenstandardunitsofmeasurementinstraightforwardcontexts – volume using litres and millilitres

•buildunderstandingofvolumeasaconceptthat deals with three dimensions

•calculatevolumeofprisms•readscalesandmakingreasonableestimates

where measures fall between marked graduations

Standards 3–4, Stages 7–12

•exploringtheusefulnessandvalueofstandard units in a wide range of context

•developingskillsinmeasuringmass•providingopportunitiestoquantifyattributes

such as mass for the purpose of comparing and/ororderingandcommunicating

•measuringandcomparingmassesofdifferentobjects

•usingappropriateinstrumentsandbalances•makingreasonableestimatesofmassbased

on personal benchmarks •introducingconversionofunitsofmeasureandidentifyingandlinkingdifferentformsofrecording metric measures

•convertingbetweenstandardunitsofmeasurementinstraightforwardcontexts – mass

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