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Mathematics
GRADE 6
TOPIC: CAPACITY AND VOLUME
CONCEPTS & SKILLS TO BE ACHIEVED:
At the end of the lesson learners should be able to:
 look at a quantity of a substance and
 give a reasonably good estimate of its volume
 estimate using the standard units for measuring volume
(of which millilitres and litres are the most common).
Resources
Sasol Inzalo book, textbooks, DBE workbooks
Measuring jug or measuring cylinder; some coarse sand; gravel; rice
grains or dried beans; volume scales; various kinds of measuring
containers, syringes, measuring jugs, etc.; measuring spoons and
measuring cups; unusually shaped, clear plastic bottles; marking pen
DAY 1
LESSON PRESENTATION/DEVELOPMENT (20 MINUTES)
Introduction :
Capacity is the maximum volume that a container can hold.
This measuring jug has space for 250 ml of water, up to the 250 ml mark. We say the capacity of
the jug is 250 ml. You can see that the milk takes up 175 ml of the space in the jug. We
say the volume of the milk is 175 ml.
How much more milk must be added for the jug to reach its capacity?
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CLASSWORK: ACTIVITY 1
This measuring jug has space for 500 ml of water, up
to the 500 ml mark. We say the capacity of the jug
Capacity is 500𝓶𝓵
is 500 ml.
You can see that the water takes up 275 ml of the
Volume is 275𝓶𝓵
space in the jug. We say the volume of the water is
275 ml.
1. Estimate the volume of the potato.
To know what the volume of the potato is we need to know how much space it takes up.
We can do that by putting the potato in the jug with water as shown here.
2. Compare the water level in the jug without the potato,
and with the potato.
Can you now say what the volume of the potato is?
Objects such as cups, glasses, jugs, buckets, bottles and
cartons are called containers.
The wide bottle on the left will hold 120 ml of liquid (or sugar, or
flour or other material) when it is filled up to its shoulder.
The capacity of the wide bottle up to its shoulder is 120 ml. The
wide bottle in the picture contains 60 ml of oil. The volume of oil
in the bottle is 60 ml. The capacity of the narrow bottle up to its
shoulder is 20 ml.
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20 ml of oil is poured from the wide bottle into the narrow
bottle.
3. What is the volume of the oil in the wide bottle now?
4. What is the capacity of the wide bottle up to its shoulder?
5. How much oil must now be added to fill the wide bottle up
to its shoulder?
6. Each of these glasses can hold 100 ml of juice if it is filled right
to the top. Approximately how much juice is shown in each
glass?
Glass A
Glass B
Glass C
7. (a) Pour some water into a measuring jug and take the volume reading as in question 1.
(b) Estimate how many millilitres of sand you can hold in your hand, and write your estimate
down.
(c) Pour one handful of sand into the water in the jug and take a reading again so that you
can find out what the volume of the sand really is.
ACTIVITY 2: PRACTICAL
1.
Encourage learners to collect many different types of
containers with different capacities.
2.
These containers may be from different brands with
identical capacities but different shapes.
3.
Estimate the maximum capacities for each and practically investigate the capacities of
each.
4.
Repeat this with several other containers.
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HOMEWORK
ACTIVITY 3
1. Which of the following statements represents capacity or volume?
(a) Space taken up by a liquid
(b) space inside the object
2. Draw a diagram of a container which refers to (a) and (b) in number 1.
3. Give a definition of:
(a) Capacity
(b) volume
4. Using smaller containers with different capacities, investigate how many would be needed to
fill a bigger container.
Capacity
Number of containers needed to fill
250 𝓶𝓵 500 𝓶𝓵 750 𝓶𝓵
250 𝓶𝓵
1
1𝓵
1,5 𝓵
2𝓵
0
500 𝓶𝓵
750 𝓶𝓵
1𝓵
1,5 𝓵
2𝓵
5. Use the containers below to answer the questions.
Example
A
(a) Identify the gradation lines, (lines which show the
B
measurements) on the bottle.
Make a number line to show it.
(b) Calculate the space between each gradation.
C
D
E
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6.
Mark the capacity on the measuring cups and spoons using the labels provided.
100 ml
CUP A
7.
25 ml
CUP B
10 ml
CUP C
250 ml
CUP D
50 ml
SPOON A
5 ml
SPOON B
Complete table by writing how many cups will be used to fill a one litre jug with cups or
spoons of different sizes.
Express this in a fraction.
Cup or Spoon
CUP A
CUP B
CUP C
CUP D
SPOON A
SPOON B
Capacity
How many
will fill the jug
250 ml
4 cups will fill the jug
What fraction of the jug will be
filled by one cup or spoonful?
1
of the jug will be filled
4
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DAY 2
LESSON PRESENTATION/DEVELOPMENT (20 MINUTES)
Introduction :
Revise:
Capacity vs volume.
Containers and measurements
If the largest volume of water that can be held in a container is 1 litre, we say the container has
a capacity of 1 litre. Both volume and capacity are often measured in
millilitres, litres or kilolitres.
1 000 ml = 1 litre
In everyday life you
will come across the
The official symbols for litre are L and ℓ.
following notations:
Because the letter l is easily confused with the
Name
Symbols
number 1, we often write ℓ instead of l.
litre
l , L or ℓ
millilitre
ml, mL or mℓ
kilolitre
kl, kL or kℓ
1 kilolitre = 1 000 ℓ
ACTIVITY 4
The official symbols for kilolitre are kl and kL.
1. (a) How many millilitres are 1 kl?
(b) How many litres are 0,5 kl?
(c) How many millilitres are 0,1 kl?
Many of the water tanks used in towns and on farms are 1 kl
tanks; this means tanks with a capacity of 1 kl.
Doctors, nurses and other people who take care of sick
people often must measure out small volumes of
medicine. In some cases, they use
measuring spoons; in other cases
they use syringes. The largest
volume that can be accurately
measured is normally stated as the
capacity of a container.
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2. The picture shows the actual size of a small syringe.
(a) What do you think the capacity of this syringe is?
(b) How much medicine is in the syringe?
3. The pictures below do not show the actual sizes of
the syringes.
The bottom part of each syringe, up to the plunger, is filled with medicine.
All the syringes are marked in millilitres. There is 14 ml of medicine in Syringe A.
What volume of medicine is in each of the other syringes?
4. (a) What is the measuring capacity of each syringe?
(b) For each syringe, state how much more medicine can be drawn in to fill it up to its
measuring capacity.
(c) Which syringe contains the most medicine?
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When you take a reading on a
measuring jug, it is important
to have your eyes at the same
height than the level of the
liquid.
Why do you think this is
important?
5. What is the volume of liquid in each of the measuring cups below, and what is the
capacity of each cup?
A
B
C
D
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These pictures of two 500 ml measuring
cups are much smaller than the actual cups.
The measuring cup on the left has the
shape of part of a cone.
The cup on the right has the shape of a
cylinder.
6. Why are the intervals on the coneshaped cup above not spaced
equally? Think about it and write your
thoughts in a short paragraph.
You may find these pictures helpful to
guide your thoughts:
7. (a) Which spoon will you use to measure 30 ml of
medicine?
(b) Which combination of spoons will you use to
measure 20 ml of medicine accurately?
(c) Which combination of spoons will you use to
measure 10 ml of medicine accurately?
8. A tablespoon has a capacity of about 15 ml. How many tablespoons of water do you need to
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fill a cup with a capacity of 250 ml?
9. Imagine that measuring jugs such as the ones below have
some juice in them. State the volume of juice indicated by
each arrow. In e cases where the juice level is not at a
mark, you must estimate the volume.
10. Make rough sketches of the following:
(a) two containers with the same height, but with different capacities
(b) two containers with the same capacities, but with different heights
11. Does an empty container have a volume?
HOMEWORK: ACTIVITY 5
1.
(a) A cup has a capacity of 250 ml. The school term is 10 weeks long. You notice your
teacher drinks 3 cups of coffee per day. How much coffee is drunk during a term.
(b) Answer in litres.
2.
A hosepipe can use up to 30ℓ of water a minute.
How many ℓ of water would a hosepipe use in:
(a) 5 minutes
3.
(b) 712 minutes
(c) 12 hours
Complete the sentences.
(a) There are ____ 500mℓ in 6,5ℓ.
(b) There are ____ 250mℓ in 3ℓ.
(c) There are ____ 200mℓ in 2ℓ.
(d) There are ____ 750mℓ in 1,5ℓ.
4. Replace * with ˃ ˂ or =.
1
1
(a) 4kℓ * 200mℓ
(b) 5ℓ * 250mℓ
(c)
9
ℓ
10
* 900ℓ
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DAY 3
LESSON PRESENTATION/DEVELOPMENT (20 MINUTES)
Work with different units of measurement
Small quantities that a person may drink or eat, such as medicine, salt, sugar and milk, are
normally measured in millilitres.
Larger quantities, such as petrol and paint, are normally measured in litres.
Very large quantities, such as water in tanks or dams, are normally measured in kilolitres.
Remember:
• ml is a symbol for millilitre.
• ℓ is a symbol for litre.
• kl is a symbol for kilolitre.
• 1 000 ml is the same as 1ℓ.
• 1 000 ℓ is the same as 1 kl.
CLASSWORK: ACTIVITY 6
Study the diagram and complete the table that follows it.
1 litre = 1 000 millilitres
250𝓂ℓ
1
ℓ
4
500𝓂ℓ
1
ℓ
2
750𝓂ℓ
3
ℓ
4
1 000𝓂ℓ
1ℓ
𝓂ℓ
250 ml
375 ml
500 ml
750 ml
900 ml
1 000 ml
Whole numbers and common fractions
Fractional part of one litre
Fraction
Decimal Fraction/
Number
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CLASSWORK: ACTIVITY 7
1. With which unit (ml, ℓ or kl) will you measure the following?
(a) salt for dough of 10 loaves of bread
(b) water for the coffee flask
(c) petrol for the car
(d) water for the bathtub
(e) water in the Vaal dam
(f) a dose of cough mixture
2. (a) How many cups of 250 ml each do you need to fill a 5 ℓ bucket with water?
(b) How many buckets of 5 ℓ each can you fill with water from a full 2 kl water tank?
(c) How many 20 ℓ tanks can be filled from a dam that holds 6 kl?
3. (a) How many 5 ml spoonsful will fill a 250 ml cup?
(b) A 1 ℓ container holds 1 000 ml. How many 250 ml measuring cupsful will fill the container?
(c) How many 5 ml spoonful’s do you need to fill a 1 ℓ jug?
4. Write these volumes as fractions of 1 ℓ.
3
Example: 2 750 ml = 2 4ℓ
(a) 250 ml
(b) 800 ml
(c) 750 ml
(d) 100 ml
(e) 50 ml
(f) 1 500 ml
(g) 1 ℓ + 500 ml
(h) 3 050 ml
5. You know by now that decimals are just another way of expressing
fractions. Therefore, you
can also write the above volumes in decimal notation as litres. Try to do that!
6. Write each of the following in millilitres.
5
Example: 0,5 ℓ = 10ℓ = 500 ml
(a) 0,1 ℓ
(b) 0,6 ℓ
(c) 0,9 ℓ
(d) 1,4 ℓ
(e) 5,3 ℓ
(f) 10 ℓ
(g) 100 ℓ
(h) 500 ℓ
(i) one tenth of a kilolitre
(j) five tenths of a kilolitre
(k) 1 kl
(m) 2,7 kl
(l) 1,5 kl
(n) 0,25 kl
7. (a) During a drought, 1 kl of water is to be equally shared between 50 people.
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How much water will each person get?
(b) How much water will each person get if 1 kl is to be equally shared between 100 people?
(c) How much water will each person get if 1 kl is to be equally shared between 1 000 people?
When you do question 8, it will help you to keep in mind that fractions can be written in decimal
notation.
5
2
For example, 10 + 100 can be written as 0,3 + 0,02 which is 0,32.
8. Write each of the following in litres.
(a) one tenth of 1 kl
(b) 0,1 kl
(c) one hundredth of 1 kl
(d) one thousandth of 1 kl
(e) 0,01 kl
(f) 3,07 kl
(g) 0,11 kl
(h) 2,5 kl
(i) 2,11 kl
(j) 3,25 kl
(k) 4,35 kl
(l) 10,05 kl
(m) 600 kl
(n) 6 000 ml
1 000 ℓ = 1 kl. So 500 ℓ is half of 1 kl, which means that 500 ℓ = 0,5 kl.
1
4
250 ℓ is a quarter ( ) of 1 kl, which means that 250 ℓ = 0,25 kl.
1
100 ℓ is one tenth (10 ) of 1 kl, which means that 100 ℓ = 0,1 kl.
3
300 ℓ is three tenths (10) of 1 kl, which means that 300 ℓ = 0,3 kl.
1
)
100
10 ℓ is one hundredth (
of 1 kl, which means that 10 ℓ = 0,01 kl.
7
70 ℓ is seven hundredths (100) of 1 kl, which means that 70 ℓ = 0,07 kl.
ℓ is forty-six
hundredths
kl. ℓ? Write it in decimal notation.
9. 460
(a) How
many tenths
of a klofis1400
We can also say it is 4 tenths and 6 hundredths of 1 kl.
(b) How many hundredths of a kl is 360 ℓ? Write it in decimal notation.
This means that 460 ℓ = 0,4 kl + 0,06 kl which is 0,46 kl.
When we write 320 ℓ = 0,32 kl, we can say
we express 320 ℓ in kl.
HOMEWORK: ACTIVITY 8
10. Express each of the following in kl, as a fraction in common fraction notation and in
decimal notation.
(a) 250 ℓ
(b) 1 250 ℓ
(c) 2 750 ℓ
(d) 650 ℓ
(e) 150 ℓ
(f) 12 500 ℓ
(g) 370 ℓ
(h) 6 830 ℓ
(i) 80 000 ml
(j) 600 000 ml
11. (a) Write in ascending order:
639 ℓ
2,54 kl
45 100 ml
7,33 ℓ
8 kl
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(b) Write in descending order:
87 420 ml
0,25 kl
1
2
125 ℓ
1
4
6,89 ℓ
1 kl
12. Thuli adds 250 ml of concentrated fruit juice to 2 ℓ of water, to make drinks for the
athletes in a long-distance race.
(a) How much concentrated juice should she add to 5 ℓ of water?
(b) How many athletes can she provide with 400 ml of juice each, with the juice she
made by adding concentrate to 5 ℓ of water?
13. Diesoline is used to generate electricity at a small power station.
The power station uses 684 ℓ of diesoline each day. For how many days can the power
station operate if there is a stock of 9 765 ℓ of diesoline available?
14. The following volumes of milk are produced on a dairy farm on the first 10 days of
November:
1 287 ℓ
1 321 ℓ
1 108 ℓ
1 234 ℓ
1 276 ℓ
1 117 ℓ
1 198 ℓ
1 223 ℓ
1 298 ℓ
1 201 ℓ
Approximately how much milk, in total, do you think will be produced over the next 6 days?
Give detailed reasons for your estimate.
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DAY 4
CAPACITY AND VOLUME
INTRODUCTION
REVISE
CLASSWORK ACTIVITY 9
A. Study each container and complete the capacity in your writing book.
1)____ml
2)____ml 3)___ml 4)____ml 5)____ml 6)____ml 7)____ml 8)____ml
9)____ml 10)___ml
11)___ml 12)___ml 13)___ml 14)___ml 15)___ml 16)___ml 17)___ml 18)___ml 19)___ml 20)___ml
B. Study each of the two containers and write the difference in capacity between each
1)Difference =__ml 2)Difference =__ml 3)Difference =__ml 4)Difference =__ml 5) Difference =__ml 6) Difference =__ml
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7) Difference =__ml
8) Difference =__ml 9) Difference =__ml 10) Difference =__ml 11) Difference =__ml
CLASSWORK ACTIVITY 10
Solving Problems Involving Capacity
1. A 2,5 litre bottle of cola is shared between 5 friends, how much does each person get?
2. Michael drinks a 330 ml bottle of lemon water every day.
How much lemon water will he drink in one week? What is this in litres?
3. A Porsche uses 2,5 litres of fuel every 2 kilometres it travels.
How much fuel does it use if it travels 50 kilometres?
4. Susie has a jug of lemonade. She does not know how much lemonade she has, but she
Knows she can fill 12 glasses which have a capacity of 270 ml each.
How much lemonade does she have?
3
5. Jug A holds 1800 ml. Jug B holds 10 more. How much does jug B hold?
HOMEWORK: ACTIVITY 11
Solving Problems Involving Capacity
1. Michael drinks a 330ml bottle of lemon water every day. How much lemon water will he drink
during April? What is this as litres?
2. Jug A holds 3,75 litres of liquid. Jug B holds 1250 millilitres more. How much liquid does Jug B
hold?
1
3. James drinks 2,4 litres of water in a day. Stephen drinks 3 more. How much water does
Stephen drink? What is this in millilitres and litres?
4. A Porsche uses 2,5 litres of fuel every 2 kilometres it travels. How much fuel does Mr Rich use in
a working week if his journey to work from his house is 8 km? What is this in millilitres?
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1
2
5. Rochelle creates a Super Fruit Smoothie. It contains 10 of a litre of apple juice, 5of a litre of
1
orange juice and 8 of a litre of grape juice. Which jug is the most suitable for Rochelle to
serve her Smoothie in? Explain why you have chosen this jug.
Jug 1
0,3 litres
Jug 2
6 litres
Jug 3
750 ml
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DAY 5
CAPACITY AND VOLUME
REVISION:
𝓂ℓ ↔ ℓ
ℓ ↔ 𝑘ℓ
𝓂ℓ ↔ 𝑘ℓ
Converting litres to millilitres
How many millilitres are there in
a litre?
One thousand millilitres
Converting kilolitres to litres
How many litres are there in
a kilolitre?
One thousand litres
1 litre = 1 000 millilitres
How many millilitres are there
in?
(a) 2 litres
(b) 3 litres
(c) 14 litres
(d) 20 litres
1 kilolitre =1 000 litres
How many litres are there
in?
(a) 2 litres
(b) 3 litres
(c) 14 litres
(d) 20 litres
Converting kilolitres to millilitres
How many millilitres are there in a
kilolitre?
One thousand millilitres in a litre.
One thousand litres in a kilolitre.
1 000 x 1 000 = 1 000 000
One million millilitres in a kilolitre.
1 kilolitre =1 000 000 millilitres
Answer
(a) 2 000 ml
(b) 3 000 ml
(c) 14 000 ml
(d) 20 000 ml
Answer
(a) 2 000 kl
(b) 3 000 kl
(c) 14 000 kl
(d) 20 000 kl
Converting millilitres to litres
Converting litres to kilolitres
5
5𝓵 = 1 000 litres = 0,005 𝒌𝓵
50
50𝓵 = 1 000 litres = 0,05 𝒌𝓵
5 ml = 1 000 litres = 0,005 𝓵
50 ml = 1 000 litres = 0,05 𝓵
500 ml =
500
1 000
litres = 0,5 𝓵
500𝓵 =
Converting millilitres to kilolitres
5
5 ml = 1 000 000 𝒌𝓵 = 0,000005 𝒌𝓵
50
50 ml = 1 000 000 𝒌𝓵 = 0,00005 𝒌𝓵
5
1 000
litres = 0,5 𝒌𝓵
5
50
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DAY 5
Equivalent units for volume and capacity
If the contents of a 1 ℓ bottle are poured into a cube-shaped container with internal measurements
of 10 cm × 10 cm × 10 cm, it will fill the container exactly. Thus:
(10 cm × 10 cm × 10 cm) = 1 ℓ
or
Since
1 000 cm3 = 1 ℓ
1 ℓ = 1 000 ml
1 000 cm3 = 1 000 ml
∴ 1 cm3 = 1 ml
Since
[1 ℓ = 1 000 cm3]
[divide both sides by 1 000]
1 kl = 1 000 ℓ
= 1 000 × (1 000 cm3) [1 ℓ = 1 000 cm3]
= 1 000 000 cm3
= 1 m3 [1 000 000 cm3 = 1 m3]
This means that an object with a volume of 1 cm3 will take up the same amount of space as
1 ml of water. Or an object with a volume of 1 m3 will take up the space of 1 kl of water.
The following diagram shows the conversions in another way:
From the diagram on the previous page, you can see that:
• 1 ℓ = 1 000 ml; 1 ml = 0,001 ℓ
• 1 kl = 1 000 ℓ; 1 ℓ = 0,001 kl
• 1 ml = 1 cm3
• 1 ℓ = 1 000 cm3
• 1 kl = 1 000 000 cm3 or 1 m3
Remember these conversions:
1 ml = 1 cm3
1 kl = 1 m3
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CLASSWORK ACTIVITY 12
1. Convert the following to millilitres:
(a) 4 litres
(b) 4,5 litres
(c) 2 kilolitres
(d) 2,5 kilolitres
(e) 12 litres
(f) 6,25 litres
(g) 8 kilolitres
(h) 8,65 litres
(i) 4,65 litres
2. Convert the following to litres:
(a) 3 000 millilitres
(b) 3 400 millilitres
(c) 4 kilolitres
(d) 6,5 kilolitres
(e) 7,89 kilolitres
(f) 2 560 millilitres
(g) 15 600 millilitres
(h) 4,2 kilolitres
(i) 500 millilitres
3. Convert the following to kilolitres:
(a) 9 000 litres
(b) 7 500 millilitres
(c) 18 250 litres
(d) 6 000 000 litres
(e) 500 litres
(f) 8 500 000 millilitres
(g) 125 000 litres
(h) 6 550 000 millilitres
(i) 350 litres
4. Problem Solving
(1) My mother paid R5, 50 per 500 ml juice.
7
We drank 8 of the 2ℓ fruit juice.
(a) How much of his juice left? Give your answer in millilitres (ml).
(b) What is the cost of the juice that has been drunk?
(2) My dad’s wants to fill up his car. A litre of petrol costs R14,83. His car has a 40 litre tank.
(a) How much would he spend on petrol?
(b) In October 2020, the petrol will drop by 37 cents. How much will he save?
3. In Cape Town the cost of water is R127,13 for every 1000 litres.
(a) In your house, 3 000 litres was used. What is the cost spent on water?
(b) During the 2020 winter season, the water usage dropped by 1,75 kilolitres. How much
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water was saved?
HOMEWORK
ACTIVITY 12
Complete the following in your writing book.
1.
2.
Complete.
(a) 2kℓ = ____ℓ
(b) 5,5ℓ = ____mℓ
(c) 7 500mℓ = ____ℓ
(d) 1 350ℓ = ____kℓ
(e) 20ℓ = ____mℓ
(f) 6ℓ 200mℓ = ____mℓ
(g) 25% of 100ℓ = ____ℓ
(h) 10% of 50mℓ = ____mℓ
(i) 20% of 60ℓ = ____ℓ
Complete
Fraction
Decimal
ℓ/ mℓ
(a)
(b)
(c)
5,25ℓ
(d)
(e)
(f)
3ℓ 200mℓ
𝟏
1𝟐ℓ
3.
Pancake recipe for 10 pancakes:
250mℓ flour
125mℓ milk
150mℓ warm water
1 egg
10mℓ oil
5mℓ baking powder
How much milk will be needed for 60 pancakes for the class party.
4.
Every day, Miss Feni uses:
60ℓ of water to bath
6ℓ of water to wash dishes
2,5ℓ of water for cooking
1,5ℓ of water for drinking.
How much water does Miss Feni use in the month of June?
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5.
The ladies at the soup kitchen make 9ℓ of soup.
1 cup holds 250mℓ of soup.
How many people can have a cup of soup?
6.
(a) How many litres of oil did Tom’s Take away use from January to May?
Tom’s take away used 400ℓ of oil in the first 6 months of the year.
(b) How much oil was used in the month of June?
(c) Oil costs R18,50 per litre. How much did Tom pay for the 400ℓ ?
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MEMORANDUM
DAY 1 MEMO
ACTIVITY 1
1.
Learner to estimate
2.
225 ml
3.
The wide bottle had 60 ml of oil and has lost 20 ml that went into the narrow bottle.
The wide bottle, therefore, has 40 ml of oil.
4.
The capacity is 120 ml, as is stated in the shaded passage.
5.
You need another 80 ml to fill it up to 120 ml.
6.
Consider learners’ answers as they will vary: Glass A is about half-full, so the answer is
50 ml; Glass B contains about 90 ml juice; Glass C contains about 30 ml juice.
7.
The scales on the glasses on page 212 of the learner book, repeated below, show
volumes of A: 51 ml; B: 91 ml and C: 31 ml.
8.
(a) Pour water into the measuring jug or cylinder so that it is about 23
full. Ask a learner to read the water level on the scale, and then write the reading on the
board.
(b) Although the Learner Book suggests using sand, you can also use alternative
materials such as gravel, dried rice or beans – whatever is more accessible to you.
Pour the gravel, dried rice or beans into a learners hand and ask the learner to
estimate the volume. Then record the estimated volume.
(c) The learner puts all the gravel, beans or rice into the water and reads the new water
level on the scale. Subtract the old reading from the new reading: the difference is
the volume of the gravel, beans or rice. Ask the class if this volume is close to the
estimate.
ACTIVITY 2: PRACTICAL
ACTIVITY 3
1. (a) volume
(b) capacity
2. (a)
(b)
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3. (a) Capacity is the maximum volume a container can hold.
4.
Capacity
Number of containers needed to fill
250 𝓶𝓵
500 𝓶𝓵
750 𝓶𝓵
1𝓵
1,5 𝓵
2𝓵
250 𝓶𝓵
1
0
3
4
5
8
500 𝓶𝓵
2
1
0
2
3
4
750 𝓶𝓵
0
0
1
1+
2
2+
250ml
1𝓵
0
0
0
1
500ml
1+
2
500ml
1,5 𝓵
0
0
0
0
1
1+
500ml
5.
6.
2𝓵
0
A. 750 ml
B. 400ml
0
0
0
1
C.
CUP A
CUP B
CUP C
CUP D
SPOON A
SPOON B
250 ml
100 ml
50 ml
25 ml
10 ml
5 ml
Cup or Spoon
7.
0
Capacity
CUP A
250 ml
How many cups or
spoons
will the jug
4 cups will fill the jug
CUP B
100 ml
10
CUP C
50 ml
20
CUP D
25 ml
40
SPOON A
10 ml
100
SPOON B
5 ml
200
What fraction of the jug will be
filled by one cup or spoonful?
1
10
1
20
1
25
1
10
1
200
1
of the jug will be filled
4
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DAY 2 MEMO
ACTIVITY 4
1. (a) There are 1 000 millilitres in a litre. A kilolitre has 1 000 litres, thus a kilolitre has
1 000 × 1 000 millilitres, or 1 000 000 (one million) millilitres.
(b) 0,5 kilolitre is 0,5 × 1 000 litres, which is 500 litres.
(c) 0,1 kilolitres is 0,1 × 1 000 litres. Every litre is 1 000 millilitres, so 0,1 kilolitres is
0,1 × 1 000 × 1 000 millilitres, which is 0,1 × 1 000 000 millilitres, which is 100 000 millilitres.
2.
(a) The capacity is 5 ml, as shown on the scale, but it might be able to hold more than
5 ml of liquid if you pull the plunger far enough back.
(b) It seems that there is 2,5 ml to 3 ml of medicine in the syringe.
3.
Syringe A: 14 ml (The gaps or intervals on the scale are each 2 ml.)
1
1
Syringe B: 14 ml (The gaps or intervals on the scale are each 4 ml.)
Syringe C: 13 ml (The gaps or intervals on the scale are each 1 ml.)
1
1
Syringe D: 42 ml (The gaps or intervals on the scale are each 2 ml.)
4. (a) A: 20 and 15 ml; B: 2 ml; C: 20 and
1
10
1
5
ml; D: 6 ml
1
5
(b) Syringe A: 20 (and ) –14 ml of medicine already in the syringe = 6 (and ) ml
1
4
3
4
Syringe B: 2 ml − 1 ml = ml
Syringe C: 21 ml − 13 ml = 8 ml
1
1
Syringe D: 6 ml − 42ml = 12 ml
(c) Syringe A, because it contains 14 ml.
5. (a) Volume of liquid is about 190 ml, while the cup’s capacity is slightly more than 500 ml.
(b) Volume of liquid is about 420 ml, while the cup’s capacity is slightly more than 500 ml.
(c) Volume of liquid is about 280 ml, while the cup’s capacity is slightly more than 500 ml.
(d) Volume of liquid is about 350 ml, while the cup’s capacity is slightly more than 500 ml.
6. If the intervals or gaps between marks on the cone-shaped cup were equally spaced,
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you could not measure accurately with such a scale. The green cone slices in the
picture show what would happen: the slices are equal in thickness but not equal in
volume. The slices near the top have more volume than the slices at the bottom. So the
marks must be at greater spacing (i.e. wider intervals) near the bottom, to ensure that
the bottom slices have the same volume as the top slices. Ask learners to imagine
slicing the 500 ml cup they see on this page. Each slice must have a volume of 100 ml.
The bottom slice must be thicker than the top slice.
7. (a) Learners can suggest the following: Use the 15 ml spoon twice; use the 7,5 ml
spoon four times; use the 5 ml spoon six times; use the 2,5 ml spoon 12 times; use
the 1,5 ml spoon 20 times. (However, seeing that this is medicine and one would
want to measure the prescribed dosis as accurately as possible, it would be best to
use the 15 ml spoon twice. It would also be the quickest way.)
(b) Learners can suggest the following: Use the 15 ml and the 5 ml spoon; use the
7,5 ml spoon twice, and then use the 5 ml spoon.
(c) Use the 7,5 ml and the 2,5 ml spoons.
8. Ten tablespoons will be 150 ml of water and 20 tablespoons will be 300 ml of water,
so the answer must lie between 10 and 20 tablespoons. Let’s try 15 tablespoons:
15 ml × 15 = 225 ml. We are now getting closer to 250 ml! Let’s add one more
tablespoon: 225 ml + 15 ml = 240 ml. Now we need only another 10 ml and that is
2
2
about 3 of a tablespoon. The answer, therefore, is 16 and 3 tablespoons.
An approximated answer would be 17 tablespoons.
9. (a) 500 ml
(d) About 270 ml
(b) About 410 ml
(c) 300 ml
(e) About 170 ml
(f) About 170 ml
10. Learners must draw the following containers:
(a) Two containers with the same height, but one container will be wider than the
other. This means, therefore, that it will have a bigger capacity.
(b) One container must be taller and narrower than the other. Though it is taller it is
also narrower, and the narrowness compensates for the greater height.
11. Yes, an empty container is an object with its own volume, like a potato. Ask learners to
imagine a clay cup with very thick walls and a bottom. All the clay that was used to
make the cup has a volume. You can measure the volume of the cup in a larger
container, using the same method as with the potato at the beginning of this unit.
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ACTIVITY 5
1. (a) Daily coffee: 250 ml x 3 cups per day = 750 ml
Weekly coffee: 750 ml x 5 days = 3 750 ml
Term coffee intake: 3 750 x 10 weeks = 37 500 ml
(b) 37 500 ml = 37,5 litres per term
2.
(a) 30ℓ x 5 minutes = 150 ℓ
(c)
1 hour = 60 minutes
(b) 30ℓ x 712 minutes = 21 360 ℓ
12 hours = 720 minutes; therefor 24 hours = 1 440 minutes
30ℓ x 1 440 minutes = 43 200 ℓ= 43, 2 kℓ
3.
(a)
4.
(a)
13
(b)
1
kℓ > 200mℓ
4
12
(c) 10
(d) 2
(b) 5ℓ = 250mℓ
(c)
1
9
ℓ
10
< 900ℓ
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DAY 3 MEMO
ACTIVITY 6
𝓂ℓ
Whole numbers and common fractions
Fractional part of one litre
Fraction
1
4
3
8
1
2
3
4
9
10
1
1
250
1 000
375
1 000
500
1 000
750
1 000
900
1 000
1 000
1 000
250 ml
375 ml
500 ml
750 ml
900 ml
1 000 ml
Decimal Fraction/
Number
0,25
0,375
0,500/ 0,5
0,750/ 0,75
0,900/ 0,9
1,0
ACTIVITY 7
1. (a) millilitres – ml
(d) litres –ℓ
(b) millilitres –ml
(c) litres –ℓ
(e) kilolitres –kl
(f) millilitres –ml
2. (a) Four cups of 250 ml will give me 1 ℓ, so for 5 ℓ I need five times that amount, which is 20
cups.
(b) 2 kl is 2 000 ℓ. How many amounts of 5 ℓ can I get from 2 000 ℓ? The answer is 400
buckets.
(c) 6 kl is 6 000 ℓ. How many amounts of 20 ℓ can I get from 6 000 ℓ?
The answer is 6 000 ℓ ÷ 20 = 300 tanks.
3. (a) 250 ml ÷ 5 = 50 spoonfuls
(b) It will take 4 cupfuls to fill the container.
(c) 1 ℓ is 1 000 ml: 1 000 ml ÷ 5 ml = 200 spoonfuls
4. (a) 14 ℓ
(b) 8 10 or 45ℓ
(c) 34 ℓ
(d) 110 ℓ
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(e) 5 100 or 120 ℓ (f) 112ℓ
(g) 112ℓ
(h) 3 50 1 000 or 3 1 20 ℓ
5. (a) 0,25 ℓ
(b) 0,8 ℓ
(c) 0,75 ℓ
(d) 0,1 ℓ
(e) 0,05 ℓ
(f) 1,5 ℓ
(g) 1,5 ℓ
(h) 3,05 ℓ
6. (a) 0,1 ℓ = 1 10 ℓ = 100 ml
(b) 0,6 ℓ = 6 10 ℓ = 600 ml
(c) 0,9 ℓ = 910 ℓ = 900
(d) 1,4 ℓ = 1 4 10 ℓ = 1 400 ml
(e) 5,3 ℓ = 5 3 10 ℓ = 5 300 ml
(f) 10 ℓ = 10 000 ml
(g) 100 ℓ = 100 000 ml
(h) 500 ℓ = 500 000 ml
ml
(i) 1 10 kl = 100 ℓ = 100 000
ml
(j) 5 10 kl = 500 ℓ = 500 000 ml
(k) 1 kl = 1 000 ℓ = 1 000 000 ml (l) 1,5 kl = 1 500 ℓ = 1 500
000 ml
(m) 2,7 kl = 2 7 10 kl = 2 700 000 ml
(n) 0,25 kl = 14 kl = 250 000 ml
7. (a) 1 kl of water is 1 000 ℓ, so divided between 50 people, each person wil get 20 ℓ.
(Ask learners how many buckets of water this is.)
(b) The answer will be half of the answer in (a), i.e. 10 ℓ.
(c) Each person will get just 1 ℓ of water.
8. (a) 100 ℓ
(b) 100 ℓ
(c) 10 ℓ
(d) 1 ℓ
(e) 10 ℓ
(f) 3 070 ℓ
(g) 110 ℓ
(h) 2 500 ℓ
(i) 2 110 ℓ
(j) 3 250 ℓ
(k) 4 350 ℓ
(l) 10 050 ℓ
(m) 600 000 ℓ
9. (a) 0,4 kl
(n) 6 ℓ
(b) 0,36 kl
HOMEWORK: ACTIVITY 8
1
10. (a) 4kl = 0,25 kl
1
(b) 14kl = 1,25 kl
3
(c) 24kl = 2,75 kl
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65
(d) 100 kl = 0,65 kl
37
(g) 100 kl = 0,37 kl
(j)
6
10
15
(e) 100
1
kl = 0,15 kl
(f) 122kl = 12,5 kl
(h) 6 100 kl = 6,83 kl
(i) 100 kl = 0,08 kl
83
8
kl = 0,6 kl
11. (a) 7,33 ℓ; 45 100 ml; 639 ℓ; 2,54 kl; 8 kl
1
4
1
2
(b) 1 kl; 0,25 kl; 125 ℓ; 87 420 ml; 6,89
12. (a) 625 ml: If she must add 250 ml of concentrated juice to 2 ℓ of water, then she must
add 125 ml of concentrated juice to 1 ℓ of water.
So for 5 ℓ of water she adds 5 times 125 ml of concentrated juice, which is 625 ml.
(b) 14 athletes, because 5 000 ml water + 625 ml concentrate gives 5 625 ml.
At 400 ml per athlete, that will be enough for 14 servings.
13. 14 days
14. Learners’ answers will vary. For example, the total for 10 days is 12 263 ℓ. On average it
will be about 1 226 ℓ per day, i.e. approximately 7 357 ℓ in total over the next 6 days.
DAY 4 MEMO
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ACTIVITY 9
A.
(1) 38ml
(2) 16ml
(3) 32ml
(4) 4ml
(5) 14ml
(6) 28ml
(7) 6ml
(8) 12ml
(9) 18ml
(10) 22ml
(11) 600ml
(12) 100ml
(13) 850ml
(14) 250ml
(15) 950ml
(16) 500ml
(17) 1 000ml
(18) 650ml
(19) 350ml
(20) 750ml
(1) 5 ml
(2) 2ml
(3) 5ml
(4) 4ml
(5) 13ml
(6) 6ml
(7) 0,1ml
(8) 0,25ml
(9) 0,25ml
(10) 0,1ml
B.
(11) 0,4ml
ACTIVITY 10
(1) 2,5 ℓ ÷ 5 = 0,5
(2) 330ml x 7 days = 2 310ml = 2,310 ℓ
(3) (i) 50km ÷ 2 km = 25 km
(ii) 25km x 2,5 ℓ = 62,5 ℓ
Or 50km x 2,5 ℓ = 125 ℓ÷ 2 km= 62,5 ℓ
(4) 270ml x 12 glasses = 3 240ml or 3,24 ℓ
(5) Jug A: 1 800ml
Jug B = X 1 800ml = 1 800 ml ÷ 10 = 180 ml x 3 =540 ml
3
Jug B = Jug A + 10 more
= 1 800ml + 540 ml
= 2 340 ml or 2,34 ℓ
ACTIVITY 11
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1. April has 30 days. Michael drinks 330 ml per day for 30 days
= 330ml x 30= 9 900ml or 9,9 ℓ
2. Jug A: 3,75 ℓ
Jug B has 1 250ml or 1,25 ℓ more
Jug B= Jug A + 1 250ml
= 3,75 ℓ + 1,25 ℓ
= 5, 00/ 5 ℓ
3
3. James: 2,4 litres per day ;
Stephen =
3
10
x 2,4 litres
or
3
10
Stephen drinks 10 more
x 2 400ml
= 2,4 ÷ 10 x 3
or 2 400ml ÷ 10 x 3
= 0,24 ℓ x 3
or 240ml x 3
= 0, 72 ℓ
or
720ml
4. (i) 8km ÷ 2 km = 4 km
(ii) 4km x 2,5 ℓ = 10,0 ℓ
Or 8km x 2,5 ℓ = 20 ℓ÷ 2 km= 10,0 ℓ
5.
Apple Juice:
1
x 1 000ml = 1 000ml ÷ 10
10
= 100ml
Orange Juice:
2
x 1 000ml = 1 000ml ÷ 5 x 2 = 400ml
5
Grape Juice:
1
x 1 000ml = 1 000ml ÷ 8
8
= 125ml
Total smoothie: 100ml + 400ml + 125ml =625ml
Jug 3 will be chosen as its capacity is greater than the volume of the smoothie.
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DAY 5 MEMO
ACTIVITY 12
5. Convert the following to millilitres:
(b) 4 000ml
(b) 4 500ml
(c) 2 000 000ml
(e) 2 500 000ml
(e) 12 000ml
(f) 6 250 ml
(h) 8 000 000ml
(h) 8 650ml
(i) 4 650 ml
6. Convert the following to litres:
(b) 3 ℓ
(b) 3,4 ℓ
(c) 4 000 ℓ
(e) 6 500 ℓ
(e) 7 890 ℓ
(f) 2,56 ℓ
(h) 15,6 ℓ
(h) 4 200 ℓ
(i) 0,5 ℓ
7. Convert the following to kilolitres:
(b) 9kℓ
(b) 0,0075 kℓ
(c) 18,25 kℓ
(e) 6kℓ
(e)0,5 kℓ
(f) 8,5 kℓ
(h) 125 kℓ
(h) 6, 55 kℓ
(i) 0,35 kℓ
8.
1.
(a)
7
x 2 000ml = 2 000ml ÷ 8
8
(c)
R5,50 for every 500ml.
= 250ml x 7= 1 750ml drank.
1 750
250
1
=3
=3
500
500
2
1
3 2 x R5,50 =
2.
R19,25
(a) R14,83 x 40ℓ= R 593,20
(b) R14,83 – 37c = R14,46 x 40 ℓ = R578,40
R593,20 - R578,40 = R14,80.
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3. (a) R127,13 x 3 kℓ = R381,39
(b) 3 kℓ =3 0000 ℓ; 1,75kℓ = 1 750ℓ
3 000ℓ - 1 750 ℓ = 1 250 ℓ
ACTIVITY 13
2.
Complete.
(a) 2 000ℓ
(b) 5 500mℓ
(c) 7,5ℓ
(d) 1,35kℓ
(e) 20 000mℓ
(f) 6 200mℓ
(g) 25ℓ
(h) 5mℓ
(i) 12ℓ
2.
Fraction
Decimal
ℓ/ mℓ
1𝟐ℓ
𝟏
(c) 1,5
(d) 1 500ml
𝟏
5,25ℓ
(e) 5 250ml
𝟏
(f) 3,2 ℓ
3ℓ 200mℓ
(c) 5𝟒ℓ
(e) 3𝟓ℓ
6.
125mℓ milk x 6 = 750ml
7.
60ℓ + 6ℓ +2,5ℓ +1,5ℓ = 70ℓ
8.
9 000
= 36 cups
250
9.
(a) 75,25 + 56,5 + 49,25 + 68,5 + 71,75 = 321,25 ℓ
(b) 400 ℓ - 321,25 ℓ = 78,75ℓ
(c) R18,50 x 400 ℓ = R7 400