4.3. Capacity*
MATHEMATICS
Grade 5
MEASUREMENT AND TIME
Module 53
CAPACITY
Capacity
Activity 1:
To solve problems that include the selection of standard units [LO 4.5.2, 4.6]
To measure accurately with the use of appropriate measuring instruments [LO 4.7.2]
DID YOU KNOW?
A liquid doesn’t have a particular shape, but takes on the shape of the container. We measure
liquid in litres and millilitres. Large quantities are measured in kilolitres.
Do you still remember?
1 000 mℓ = 1 litres
1 000 litres = 1 kℓ
1. You have now seen in the sections on length and mass that we use different measuring units for different situations. In the same way we also use specific units to determine various types of
capacity. In which measuring unit would you measure the content of the following?
1.1 eye drop .........................
1.2 petrol for Dad’s car .........................
1.3 a glass of fruit juice .........................
1.4 the dam that supplies water for your city? .........................
2. TO MAKE SURE OF AT HOME
2.1 A teaspoon can take ______ mℓ of liquid.
2.2 A medicine spoon can take ______ mℓ of liquid.
2.3 A tablespoon can take______ mℓ of liquid.
2.4 A teacup can take______ mℓ of liquid.
2.5 A coffee mug can take______ mℓ of liquid.
2.6 Dad’s car can take ______ litres of petrol in its tank.
2.7 Your swimming pool (if you have one) takes ______ kℓ water.
2.8 Your kettle holds______ litres of water
2.9 A small bottle of medicine takes______ mℓ
2.10 You bath in about ______ litres of water
3. Use the above answers to answer the following:
3.1 Every day Mom drinks five cups of tea. How many mℓ of tea is that? .....................
How many litres of tea does she drink daily? .....................
3.2 Dad drinks three mugs of coffee at work. How many mℓ of coffee is that? ..................
Write this as litres. .....................
If you have to drink two teaspoonfuls at a time, how many times will
you be able to take medicine before the bottle is empty? .....................
DID YOU KNOW?
The biggest waterfalls in the world are the Bogoma falls in the Congo River. Every second 17 000
kℓ flow over the edge of this waterfall! Can you say how many litres of water this is per second?
Activity 2:
To solve problems that include selecting, calculating and converting standard units [LO 4.6]
1. Complete the following tables:
Table 4.16.
1.1 ml
3 268 4
.............. 16
.............. 369
..............
litres 3, 268 .............. 0,98
.............. 1,423
.............. 0,006
Table 4.17.
1.2 litres 7 000 18
.............. 1 479
.............. 3,012
k ℓ
7
.............. 0,002
.............. 0,261
..............
2. Increase the following capacities by 75 mℓ:
2.1: 4,325 litres
2.2: 2,500 litres
2.3: 6,050 litres
2.4: 5,035 litres
4. Decrease the following capacities by 50 ℓ.
4.1: 16,750 kℓ
4.2: 13,085 kℓ
4.3: 18,900 kℓ
4.4: 17,658 kℓ
ADDITION AND SUBTRACTION:
When I add or subtract with units of length, mass and capacity it is easiest to convert everything to the smallest unit, e.g.
y = 5,094 m + 342 mm + 0,087 m + 9 mm
= 5 094 mm + 342 mm + 87 mm + 9 mm
5 094
342
87
+ 9
5 532
= 5 532 mm
y = 5,532 m
I also convert everything to the smallest unit before I subtract, e.g.
k = 9,075 ton – 4 328 kg
= 9 075 kg – 4 328 kg
9 075
− 4 328
4 747
= 4 747 kg
k = 4,747 t
5. Calculate the following:
5.1 c = 4,7 km + 876 m + 2,794 km + 65 m
5.2 e = 7,632 kg – 1 278 g
5.3 f = 2,03 kℓ + 432 litres + 0,869 kℓ + 38 litres
5.4 h = 19 litres – 2 347 mℓ
Activity 3:
To solve problems that include selecting, calculating and converting standard units [LO 4.6]
Choose a friend to work with you, and try to solve the following problems. You are NOT allowed
to use a pocket calculator! Ask your teacher for paper to work on.
1. The following items must be filled with petrol:
the school bus 85,6 litres
a motor-bike 14,65 litres
an empty can 893 mℓ
a pick-up van 64,4 litres
How many litres of petrol will be used altogether?
Write your answer as kℓ.
2. A family’s mass is made up as follows:
newly-born infant 2 667 g
sister 19,8 kg
mother 63,9 kg
2.1 What is the joint mass of the family in kg?
2.2 Write your answer in tons.
3. The Grade 5’s do textile painting on pieces of material that consist of the following lengths: 585 mm
1,024 m
362 mm
3.1 On how many mm of material have they painted altogether?
3.2 Give your answer in metres.
4. If an elephant has an average weight of 7 tons and a hippopotamus has an average weight of 1
500 kg, what is the difference in mass between them? Give your answer in kg first, and then in
tons.
5. A barrel contains approximately 9,5 litres of water. If I fill a 775 mℓ bottle from it, how much water is left in the barrel? Write your answer as litres.
6. There are 16,84 metres of material on a roll. If your mother cuts off 739 cm, how many metres of material are left on the roll?
Write your answer as mm.!
7. Use a pocket calculator to check your answers.
8. Now compare your answers with the rest of the class and have a class discussion on the best
way of solving the above-mentioned problems.
9. Give your answers to your teacher for assessment.
Assessment
Table 4.18.
LO 4
MeasurementThe learner will be able to use appropriate measuring units, instruments and
formulae in a variety of contexts.
We know this when the learner:
4.1 reads, tells and writes analogue, digital and 24-hour time to at least the nearest minute and second;
4.2 solves problems involving calculation and conversion between appropriate time units
including decades, centuries and millennia;
4.3 uses time-measuring instruments to appropriate levels of precision including watches and
stopwatches;
4.4 describes and illustrates ways of representing time in different cultures throughout history; 4.5 estimates, measures, records, compares and orders two-dimensional shapes and three-dimensional objects using S.I. units with appropriate precision for:
mass using grams (g) en kilograms (kg);
capacity using millimetres (mm), centimetres (cm), metres (m) en kilometres (km);
length using. millimetres (mm), centimetres (cm), metres (m) en kilometres (km);
length using. millimetres (mm), centimetres (cm), metres (m) en kilometres (km);
4.6 solves problems involving selecting, calculating with and converting between appropriate
S.I. units listed above, integrating appropriate contexts for Technology and Natural Sciences;
4.7 uses appropriate measuring instruments (with understanding of their limitations) to
appropriate levels of precision including:
bathroom scales, kitchen scales and balances to measure mass;
measuring jugs to measure capacity;
rulers, metre sticks, tape measures and trundle wheels to measure length.
Memorandum
ACTIVITY 1
1. 1.1 mℓ
1.2 ℓ
1.3 mℓ
1.4 kℓ
2. 2.1: 5
2.2: 5
2.3: 15
2.4: 200
2.5: 250
2.6 – 2.10 own answers
3. 3.1: 1 000
1 ℓ
3.2: 750
0,750
DID YOU KNOW?
17 000 000
ACTIVITY 2
2.1
Table 4.19.
mℓ
980
1 423
6
liter 0,004
0,016
0,369
2.2
Table 4.20.
liter
2
261
kℓ
0,018 1,479
3,012
3.
3.1: 4,342 ℓ
3.2: 2,575 ℓ
3.3: 6,125 ℓ
3.4: 5,110 ℓ
4.
4.1: 16,7 kℓ
4.2: 13,035 kℓ
:18,850 kℓ
:4.4 17,608 kℓ
:4.4 17,608 kℓ
5.
5.1: 8,435 km
8 435 m
5.2: 6 354 g
6,354 kg
5.3:3 369 ℓ
3,369 kℓ
5.4:16 653 mℓ
16,653 ℓ
4.4. Time*
MATHEMATICS
Grade 5
MEASUREMENT AND TIME
Module 54
TIME
Activity 1:
To solve problems that include calculating and converting appropriate time units [LO 4.2]
1. COMPETITION TIME!
In this activity your general knowledge will be tested. Let us see who can answer first – the boys or the girls! Each correct answer is worth 2 points. Points will be subtracted if learners shout out.
1.1 How many months are there in a year?
1.2 Which months have only 30 days?
1.3 Which months have 31 days?
1.4 How many days are there in a year?
1.5 How many days are there in a leap year?
1.6 How many days does February have in a leap year?
1.7 How many days are there in a school week?
1.8 How many seconds are there in a minute?
1.9 How many minutes are there in an hour?
1.10 How many hours are there in a day?
1.11 How many weeks are there in a year?
1.12 How many minutes are there in quarter of an hour?
1.13 How many seconds are there in three-quarters of a minute?
1.14 How many days does December have in a leap year?
Who won?
BRAIN-TEASERS!
How many years are there in a decade?
What is a millennium?
What is another word for a time period of 100 years?
Some people use v.a.e. and a.e. instead of BC (Before Christ) and AD (Anno Domini). What do
they mean?
DID YOU KNOW?
We use the Christian calendar that began with the birth of Jesus. The names of the months
originated from Roman times.E.g. August is named after the Roman emperor, Augustus Caesar,
who lived form 27 BC to 14 AD.
Activity 2:
To describe and illustrate the way in which time is represented in different cultures [LO 4.4]
1. CHALLENGE: SOME “RESEARCH” FOR YOUR PORTFOLIO!
Let us do some research into how time is indicated in other cultures. Ask your teacher for the
paper you will need to work on.
See whether you can find a Jewish or Muslim calendar.
Compare it to our calendar and make a list of the differences and similarities.
Tell your classmates how they differ, and in what way they are similar.
Give it to your teacher for assessment.
Exhibit it in the classroom for all to see.
Remember to file it neatly in your portfolio.
REMEMBER THESE ABBREVIATIONS
seconds : s
minutes : min
hour : h
day : d
week : wk
month : mo
year : a
DID YOU KNOW?
The symbol for hour (h), comes from the Latin word “hora” that means “hour”.
The symbol for year was originally “a”. This comes form the Latin word “annus”, which means
“year”.
Activity 3:
To use measuring instruments, including stop-watches, to measure time accurately [LO 4.3]
1. What is a stop-watch?
2. Work together with a friend and complete the table, using a stop-watch.
Table 4.21.
Time estimated Time measured Difference
1. Count up to 20
.....................
.....................
.....................
2. Tie your shoe lace
.....................
.....................
.....................
3. Open and close the classroom window. .....................
.....................
.....................
4. Write your name and surname.
.....................
.....................
.....................
5. Calculate 468 × 7
.....................
.....................
.....................
Activity 4:
To solve problems that include calculation and conversion of appropriate units of time
[LO 4.2]
1. Work together with a friend and calculate:
1.1 how many seconds there are in:
3 min: ......................... .........................
2 min: ......................... .........................
min: ......................... .........................
min: ......................... .........................
1 hour: ......................... .........................
1.2 how many minutes there are in:
2 hours:
1 hour:
hour:
3 hour:
a day:
1.3 How many hours there are in:
your school day:
1 week:
1 day:
360 min:
1.4 How many days there are in:
8 weeks:
264 hours:
year :
2 leap years
BRAIN-TEASER!
How many years are there in 2 centuries, 9 decades, 72 months and 156 weeks?
LET US LOOK AT WATCHES AND READ TIME!
Did you know?
Galileo, a famous scientist from Italy, studied pendulums. The first clocks were made by using
pendulums.
CHALLENGE
Make your own pendulum. Tie a piece of rope to a stone. Tie the end of the rope to a branch of a tree and let the stone swing to and fro.
Take a stop-watch and see how long it takes for the stone to swing to and fro 10 times.
..............................
Shorten the rope and time the 10 swings again. What do you notice? ..............................
Replace the stone with a lighter stone. Take the time for 10 swings again. What do you notice
now? ..............................
Activity 5:
To read, say and write analogue, digital and 24 hour time to at least the nearest minute and second
[LO 4.1]
It is of the utmost importance that we understand how to read time on the different watches,
because time is a major factor in our lives. It determines whether we are on time for appointments or not!
1. LET US HAVE A CLASS DISCUSSION
1.1 What is the difference between an “analogue” watch and a “digital” watch?
1.2 What is the function of the long hand and the short hand of the “analogue” watch?
1.3 When do we use “past” and “to” with the analogue watch?
1.4 What do the first two digits indicate on a digital watch?
1.5 What do the last two digits indicate on a digital watch?
1.6 What do the abbreviations “a.m.” and “p.m.” mean?
Do you still remember?
The international notation for time makes use of the 24 hour clock. We write it in the same way that time is indicated on a digital clock. Remember that there must always be 2 digits before and 2
digits after the colon!
2. Write the following in international time:
2.1 20 minutes before 6 in the morning
2.2 half past 6 in the evening
2.3 quarter to 4 in the afternoon
2.4 midnight
2.5 18 minutes before 3 in the morning
2.6 24 minutes before 9 in the evening
2.7 quarter past 5 in the afternoon
COURSE (LENGTH) OF TIME
REMEMBER!
There is a difference between “time” and “course of time” !
Time: e.g. What is the time? Eight o’clock.
Course of time: how long it takes, e.g. a journey from Cape Town to Worcester takes an hour and a half.
Activity 6:
To solve problems that include selecting, calculating with and converting standard units
[LO 4.6]
1. Split up into groups of three. Ask your teacher for paper to work on and try to find the answers to the following:
Mvesi leaves by taxi on a visit to his family in Middelburg, Cape. If he departs from Cape
Town and arrives in Middelburg at 17:05, how long did the journey take?
A participant in the Two Oceans marathon sets off at 06:15. It takes him 8 hours and 20
minutes to complete the race. At what time did he stop running?
Dudu is 11 years and 3 months of age. His father, Mr Sooliman, is 39 years and 11 months old.
What is their combined age?
Mr Katlego worked overseas for 9 months and 2 weeks, while Mrs Solomons toured overseas
for 4 months and 3 weeks. What is the difference in time that the two were not in South Africa?
2. Compare your answers to those of a different group.
3. Now illustrate on the board one of your calculations to the rest of the class.
4. Have a class discussion on the way in which the above-mentioned problems can be solved
successfully.
Activity 7:
To determine the equivalence and validity of different representations of the same problem
through comparison and discussion [LO 2.6.3]
1. In the previous activity you had the opportunity of solving problems in a way that made the
most sense to you. Now work through the following with a friend and look at the different
methods that were used.
The Grade 5’s are planning an outing to a crocodile farm. The buses will arrive at approximately 08:45 and will leave at 13:10. How long will they spend at the farm?
1.1 From 08:45 to 09:00 : 15 min
From 09:00 to 13:00 : 4 hours
From 13:00 to 13:10 : 10 min
Thus: Course of time: 4 h + 15 min + 10 min= 4 h 25 min
1.2 From 08:45 to 13:45 it is 5 hours
This is actually 35 minutes too much.
5 h – 35 min = 4 h 25 min
1.3 I calculate it in this way: 13 h 10 min = 12 h 70 min
− 08 h 45 min − 08 h 45 min
4 h 35 min
2. Whose method do you choose?
Why?
Activity 8:
To solve problems that include selecting, calculating with and converting standard units
[LO 4.6]
1. See whether you can solve the following on your own:
Study the tides in Table Bay.
Table 4.22.
Tides in Table bay
High tide
Today: 06:52 and 19:24
Tomorrow: 07:38 and 20:15
Low tide
Today: 00:54 and 12:40
Tomorrow: 01:41 and 13:40
1.1 How many hours and minutes will pass between “today’s” two high tide times?
1.2 How many hours and minutes pass between “tomorrow’s” two low tide times?
2. The taxi’s leave from Cape Town Station every 25 minutes. If the first taxi leaves at 06:15, write down the departure times of the 9 taxis that follow after the first one.
3. Write down the following in international time:
3.1 10 minutes earlier than 08:35 ..................................................
3.2 27 minutes earlier than 17:15 ..................................................
3.3 38 minutes earlier than 22:00 ..................................................
3.4 45 minutes earlier than 04:55 ..................................................
Activity 9:
To determine the equivalence and validity of different representations of the same problem
through comparison and discussion [LO 2.6.1]
1. In this activity you will again have the opportunity of trying to find different solutions to the same problem with your friends. Divide into groups of three. Discuss the following problem
and solutions (methods) and then explain them to a friend who doesn’t understand as well as
you do.
Loretta’s practice times for gymnastics are as follows Monday : 2 hours 40 min Wednesday : 1
hour 55 min Thursday : 3 hours 18 minHow much time does she spend practising altogether?
1.1 2 hours 40 min + 1 hour 55 min + 3 hours 18 min
2 h + 1 h + 3 h = 6 h
40 min + 55 min + 18 min = 113 min
= 1 h 53 min
Thus: 6 h + 1 h + 53 min = 7 h 53 min
1.2 I prefer to write the time below each other:
2 h 40 min
1 h 55 min
3 h 18 min
6 h 113 min
= 6 h + 1 h + 53 min (113 min = 1 h 53 min)
= 7 h 53 min
2. Whose method do you like best?
Why?
Activity 10:
To solve problems that include selecting, calculating with and converting standard units
[LO 4.6]
1. In the previous activities you were exposed to a variety of methods. Now use any method and
calculate:
1.1 3 weeks 5 days + 7 weeks 6 days + 9 weeks 2 days
1.2 8 days 17 hours + 5 days 21 hours + 4 days 19 hours
1.3 6 hours 45 min + 3 hours 38 min + 2 hours 54 min
1.4 5 min 29 seconds + 9 min 43 seconds + 4 min 42 seconds
1.5 7 years 9 months + 6 years 8 months + 5 years 11 months
Activity 11:
To determine the equivalence and validity of different representations of the same problem
through comparison and discussion [LO 2.6.1]
1. Look at the following problem and then discuss the solutions together as a class. Make sure that you understand each method very well.
Sven has been following the programme “Survivors” on TV and noticed that team A took 4 days
18 hours to cover a certain distance. Team B took 7 days 5 hours to complete the same distance.
How much longer did team B take?
1.1 I must calculate 7 days 5 hours – 4 days 18 hours.
4 days 18 hours to 5 days = 6 hours
5 days to 7 days 5 hours = 2 days 5 hours
2 days 5 hours + 6 hours = 2 days 11 hours
1.2 7 days 5 hours – 4 days 18 hours
7 days 5 hours = 6 days 29 hours (1 day = 24 hours)
6 days – 4 days = 2 days
29 hours – 18 hours = 11 hours
The answer is thus 2 days 11 hours
1.3 I answer it in this way:
6 5 + 24 = 29 (1 day = 24 hours) 7 days 5 hours
− 4 days 18 hours
2 days 11 hours (29 – 18)
Which method do you understand the best?
Activity 12:
To solve problems that include selecting, calculating with and converting standard units [LO 4.6]
1. Use all the knowledge