volume, capacity and mass - · pdf filestudent book series g name _____ volume, capacity and...
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Student BookSERIES
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Volume, Capacity and Mass
Teacher BookSERIES
G
Volume, Capacity and Mass
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
Volume, Capacity and Mass
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, Capacity and Mass
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
3G 1Copyright © 3P Learning
Volume, Capacity and Mass
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
G 14Copyright © 3P Learning
Volume, Capacity and Mass
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
5G 1Copyright © 3P Learning
Volume, Capacity and Mass
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
G 16Copyright © 3P Learning
Volume, Capacity and Mass
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 1Copyright © 3P Learning
Volume, Capacity and Mass
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
G 18Copyright © 3P Learning
Volume, Capacity and Mass
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
11GCopyright © 3P Learning
Volume, Capacity and Mass 2
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
G12Copyright © 3P Learning
Volume, Capacity and Mass2
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
13GCopyright © 3P Learning
Volume, Capacity and Mass 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 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
G14Copyright © 3P Learning
Volume, Capacity and Mass2
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
15GCopyright © 3P Learning
Volume, Capacity and Mass 2
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
G16Copyright © 3P Learning
Volume, Capacity and Mass2
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
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
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
Copyright © 3P Learning
Series G Topic 2 Assessment
Skills Not yet Kind of Got it
• 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
Kilograms and grams 2kg60g 6kg900g
Decimal notation 2.234kg 5.250kg
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
Copyright © 3P Learning
Series G Topic 2 Assessment
Skills Not yet Kind of Got it
• 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
Kilograms and grams 2kg60g 6kg900g
Decimal notation 2.234kg 5.250kg
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
Copyright © 3P Learning
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
Copyright © 3P Learning
Series G – Volume, capacity and mass
RegionTopic 1 Volume and capacity
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
Copyright © 3P Learning
Series G – Volume, capacity and mass
RegionTopic 1 Volume and capacity
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