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Reg. No.: 2011/011959/07
Mathematics
Study guide 2/2
Grade 4
CAPS aligned
LESSON ELEMENTS
The guide consists of various lesson elements. Every element is important for the learning process and it indicates the skill that the learner needs to master.
ICON
LESSON ELEMENT
Think for yourself Tips
SAMPLE
Research Study
New concept or definition
Remember/Revise
Take note! Important Self-assessment Activity
UNIT 3
This unit covers 11 lessons (20 – 30). UNIT 3
TOPIC
Mental maths
LESSON 20
Capacity/Volume
LESSON 21
Common fractions
LESSON 22
Whole numbers: Counting, ordering, comparing and representing, and place value of digits (4-digit whole numbers)
Whole numbers: Addition and subtraction (4-digit whole numbers)
LESSON 23
Views of objects
LESSON 24
Properties of 2D shapes
LESSON 25
Data handling
LESSON 26
Numerical patterns
LESSON 27
Whole numbers: Addition and subtraction (4-digit whole numbers)
LESSON 28
Whole numbers: Multiplication (2-digit whole numbers by 2-digit whole numbers)
LESSON 29
Number sentences
LESSON 30
Transformations
Revision: Use the CAMI programme
LESSON 20: CAPACITY/VOLUME
In Grade 3 you learnt how to take measurements by pouring liquids into cups or measuring jugs and then reading the volume of liquid in them.
What is the difference between capacity and volume?
Your facilitator will show you two videos that will explain the difference between capacity and volume. •
goo.gl/U3VL7n
goo.gl/jgWhHG
Can you write down in your own words what the difference is between capacity and volume?
Capacity is how much space an object has inside. OR
SAMPLE
Capacity is the amount a container or something can hold when filled
Volume is the amount of space an object takes up.
An example of the difference between capacity and volume:
A glass can hold 250 mℓ of milk. You only pour 200 mℓ in the glass.
In this example, the glass’s capacity is 250 mℓ and the volume is 200 mℓ.
In lesson 13 we looked at which units are used to measure length. Capacity and volume are also measured in specific units.
Capacity and volume are measured in:
• millilitres (mℓ)
• litres (ℓ)
Examples of measuring instruments used to measure capacity and volume.
Measuring spoons
Measuring cups
Measuring jugs
Study the objects below. In what unit would you measure the capacity and volume of each object?
Decide between millilitres (mℓ) and litres (ℓ).
Litre is a larger unit than millilitre. 1 ℓ is 1 000 times more than 1 mℓ.
1 litre = 1 000 millilitres
You will measure the capacity and volume of larger objects in litres and to measure the capacity and volume of smaller objects in millilitres.
How do you convert between litres and millilitres?
SAMPLE
× 1 000
÷ 1 000
Examples of conversion
1. 3,2 ℓ = ____________ mℓ
To convert litres to millilitres, you must multiply by 1 000. 3,2 × 1 000 = 3 200 mℓ
2. 8 952 mℓ = ____________ ℓ
To convert from millilitres to litres, you must divide by 1 000. 8 952 ÷ 1 000 = 8,952 ℓ
The number of zeros in 10, 100 and 1 000 show the total number of place values, which will have an influence when you multiply or divide.
In Grade 4 we will not yet work with decimals, but it is important to know now that a comma (,) indicates decimal numbers.
When we multiply, the comma (,) moves the number of zeros that the number has to the right. When we divide, the comma (,) moves the number of zeros to the left.
If there is no comma (,) in the number, we picture an imaginary comma at the end of the number.
Study the examples again. Can you see how the number of zeros in the number has an influence on the place values (and how the comma moves between the place values)? It is an easy way to quickly multiply and divide by 10, 100 and 1 000.
In this example the number after the comma indicates the number of millilitres: 956 mℓ
5 , 956 litres
In this example the number before the comma indicates the number of full litres: 5 ℓ
This means 956 1 000 litres
ACTIVITY 51
DATE:
1. Write down the measurements of the water in each water jar and arrange them from small to large.
Question
Answer
2. Convert the measurements as indicated.
Question and answer
2.1 3 000 mℓ = __________ ℓ
2.2 3 500 mℓ = __________ and __________ ℓ
2.3 1 250 mℓ = __________ and __________ ℓ
2.4 5 750 mℓ = __________ and __________ ℓ
2.5 1 ℓ = __________ mℓ
2.6 1 500 mℓ = __________ ℓ and __________ mℓ
2.7 1 4 ℓ = __________ mℓ
2.8 3 4 ℓ = __________ mℓ
3. Complete the calculations.
Question and answer
3.1 1 000 mℓ – 500 mℓ = __________ mℓ
3.2 325 mℓ × 2 = __________ mℓ
3.3 240 mℓ ÷ 8 = __________ mℓ
3.4 The difference between 6 879 mℓ and 464 mℓ.
3.5 99 ℓ × 100
4. Round to the nearest litre or millilitre, as indicated.
Question
To the nearest 100 mℓ.
4.1
4.2
50 mℓ
To the nearest 100 mℓ.
325 mℓ
4.3 To the nearest ℓ.
1 ℓ 250 mℓ
To the nearest ℓ.
4.4
4.5
6 ℓ 760 mℓ
To the nearest ℓ.
510 mℓ
5. Read the scenarios and answer the questions that follow.
Question
Answer
Answer
A family of five buys a two litre bottle of cold drink every day. The three children each drink 250 mℓ of cold drink after lunch.
5.1
5.2
How much cold drink is left for the rest of the family after the children each drank a glass of cold drink in the afternoon?
How much cold drink does the family buy each week?
A water cooler contains 21 ℓ of water.
5.3
5.4
1 2 ℓ of water is added to the water cooler. How much water does it now contain?
Daniel fills his water bottle with 500 mℓ of water from the water cooler. How much water remains in the water cooler?
Dillian’s mom buys tomato sauce in bulk. She buys 5 ℓ of tomato sauce at the wholesaler and pours some of the sauce into two smaller containers. Each container is 500 mℓ.
5.5 How much tomato sauce remains in the large container?
5.6
5.7
If Dillian pours 125 mℓ of tomato sauce over his food from one of the 500 mℓ containers, how much tomato sauce remains in the container?
If Dillian’s brother, Tyron, takes the other 500 mℓ tomato sauce container and pours half of it over his food, how much tomato sauce remains in the container?
6. Study the containers and answer the questions that follow. The containers are not sized to scale – carefully consider the content of each container.
Question
Answer .
6.1 Which container will be able to hold the most water?
6.2 Which container will hold the least water?
6.3
Arrange the containers from large to small according to their capacity.
6.4
6.5
6.6
Which container’s volume is measured in litres (ℓ)?
Which container’s capacity is smaller than 1 litre?
Which container’s capacity is larger than 2 litres?
6.7 If container B’s capacity is 250 mℓ, how many containers of B can you pour into container E?
7. Paste pictures of containers that can hold more than 1 ℓ and less than 1 ℓ in the space provided.
Question and answer
More than 1 ℓ
Less than 1 ℓ
Self-assessment
Do you understand the work? Colour the faces that show what you can do.
CAPACITY AND VOLUME
Requirements
I can measure, estimate, indicate, order and compare the capacity and volume of 3D objects.
I know what measuring instruments to use to measure capacity and volume.
I know the units in which capacity and volume are measured and can use them.
I can solve problems of capacity and volume in context (word sums).
I can convert between litre and millilitre.
SAMPLE
LESSON 21: COMMON FRACTIONS
You started learning about fractions in unit 2.
Let’s have another look at what you know about fractions.
A fraction is when a whole number or object or shape is divided into equal parts. Each part is a fraction of the whole number or object or shape. Fractions are usually written as two numbers on top of one another, separated by a straight line.
What does this definition mean?
Object or shape
The given shape is a square.
If the square is divided into 4 equal parts, it looks like this:
We say that it is divided into 4 parts or into quarters
If 1 of the 4 parts is coloured, it looks like this:
If we write it mathematically, it looks like this:
There is a total of 4 parts. 1 part is coloured.
Every part of the fraction has a special name:
Numerator 1
4 Denominator
Study the examples of calculations with fractions.
1. Colour the following parts in the given shapes: 2 6
Each block in this shape represents one of the six parts: 1 6
To colour 2 6 of the shape, two parts should be coloured.
You can always add the parts to determine what you need to colour or calculate. To add fractions, the denominators must always be the same.
We will now compare fractions using the same symbols we used to compare whole numbers. Revise the symbols.
SMALLER < GREATER GREATER > SMALLER
Example
Use the symbols (< ; > ; =) to indicate the relationship between the fractions.
The first fraction shows 3 of 7 parts (three sevenths). The second fraction shows 5 of 7 parts (five sevenths). Three sevenths is smaller than five sevenths, therefore:
Do you see that the denominators are the same? This is very important when you compare fractions.
What happens when the denominators are not the same? You need to make them the same.
Do you see that the denominators are not the same?
Use the times tables to make the denominations the same.
Ask yourself: 4 × ? = 8
The answer is 4 × 2 = 8, but you cannot multiply the denominator only. If you multiply the denominator by a number, you must also multiply the numerator of that fraction:
3 4 and 6 8 are equivalent fractions. This means that 3 4 = 6 8 (Unit 1)
You can now compare the two fractions:
Before you compare or add any fractions, you must always make the denominators the same. When you multiply the denominator by a number, you must also multiply the numerator by the same number.
You will now apply what you have learnt so far. This lesson focuses on equivalent fractions.
Remember: When we do calculations with fractions (such as comparing or adding or subtracting), the denominators must be the same.
ACTIVITY 52
DATE:
1. Write the fractions in ascending order (from small to great).
Which fractions are smaller than 1? 2.2 Which fractions are greater than 1?
3. Use the fraction wall to identify the equivalent fractions.
Question and answer
4. Read the scenarios and answer the questions that follow.
Question
Answer
In a class of 20 learners, 8 learners write with BIC pens, 10 learners write with Staedtler pens and the rest write with Pilot pens.
4.1
4.2
4.3
What fraction of the learners write with Staedtler pens?
What fraction of the learners write with BIC pens?
What fraction of the learners write with BIC or Pilot pens?
Sandile and 3 of his friends (2 girls and 1 boy) share a packet of sweets between them. The 4 friends count the sweets and establish that there are 24 sweets in the packet.
4.4
4.5
If each boy gets 6 sweets, what fraction of the packet of sweets do they get altogether?
If each girl gets 3 sweets, what fraction of the packet of sweets do they get altogether?
4.6 What fraction of the packet of sweets remains?
• Comprehensive explanations of concepts in plain language.
• Practical, everyday examples with visuals and diagrams to help master concepts.
• Learners work at their own pace.
• Practical, everyday examples.
• Activities that test learners’ knowledge application and reasoning.
• The facilitator’s guide contains step-by-step calculations and answers.
