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MATHEMATICS STUDY GUIDE 2/2 Grade 4
A member of the FUTURELEARN group
Mathematics Study guide 2/2
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Grade 4
CAPS aligned
L Young
Study Guide 2/2 G04 ~ Mathematics
CONTENTS LESSON ELEMENTS.......................................................................................................... 3 UNIT 3 ................................................................................................................................. 4 LESSON 20: CAPACITY/VOLUME ................................................................................ 5 ACTIVITY 51 ......................................................................................................... 9 LESSON 21: COMMON FRACTIONS .......................................................................... 15 ACTIVITY 52 ....................................................................................................... 18 LESSON 22: WHOLE NUMBERS ................................................................................ 24 ACTIVITY 53 ....................................................................................................... 25 LESSON 23: VIEWS OF OBJECTS ............................................................................. 37 ACTIVITY 54 ....................................................................................................... 39 LESSON 24: PROPERTIES OF 2D SHAPES ............................................................. 45 ACTIVITY 55 ....................................................................................................... 49 LESSON 25: DATA HANDLING ................................................................................... 55 ACTIVITY 56 ....................................................................................................... 58 LESSON 26: NUMBER PATTERNS ............................................................................. 63 Input and output values ............................................................................................. 64 The associative property of multiplication .................................................................. 66 Types of number sequences ..................................................................................... 69 ACTIVITY 57 ....................................................................................................... 69 LESSON 27: WHOLE NUMBERS ................................................................................ 63 Order of subtraction ................................................................................................... 75 ACTIVITY 58 ....................................................................................................... 77 LESSON 28: WHOLE NUMBERS ................................................................................ 85 Distributive property of multiplication ......................................................................... 86 Dividing numbers into factors to multiply them .......................................................... 86 ACTIVITY 59 ....................................................................................................... 87 LESSON 29: NUMBER SENTENCES .......................................................................... 92 Pairs of equivalent number sentences ...................................................................... 96 ACTIVITY 60 ....................................................................................................... 97 LESSON 30: TRANSFORMATIONS .......................................................................... 102 ACTIVITY 61 ..................................................................................................... 103
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Study Guide 2/2 G04 ~ Mathematics
UNIT 4 ............................................................................................................................. 105 LESSON 31: WHOLE NUMBERS .............................................................................. 106 ACTIVITY 62 ..................................................................................................... 106 LESSON 32: MASS .................................................................................................... 120 ACTIVITY 63 ..................................................................................................... 123 LESSON 33: PROPERTIES OF 3D OBJECTS ......................................................... 131 ACTIVITY 64 ..................................................................................................... 134 LESSON 34: COMMON FRACTIONS ........................................................................ 139 ACTIVITY 65 ..................................................................................................... 142 LESSON 35: WHOLE NUMBERS .............................................................................. 139 ACTIVITY 66 ..................................................................................................... 151 LESSON 36: PERIMETER, SURFACE AREA AND VOLUME .................................. 155 Perimeter ................................................................................................................. 155 ACTIVITY 67 ..................................................................................................... 161 Surface area ............................................................................................................ 164 ACTIVITY 68 ..................................................................................................... 166 Volume .................................................................................................................... 168 LESSON 37: POSITION AND DISPLACEMENT ........................................................ 171 ACTIVITY 69 ..................................................................................................... 174 LESSON 38: TRANSFORMATIONS .......................................................................... 178 ACTIVITY 70 ..................................................................................................... 181 LESSON 39: GEOMETRIC PATTERNS ..................................................................... 184 ACTIVITY 71 ..................................................................................................... 186 LESSON 40: WHOLE NUMBERS .............................................................................. 191 ACTIVITY 72 ..................................................................................................... 191 LESSON 41: PROBABILITY ...................................................................................... 202 ACTIVITY 73 ..................................................................................................... 203 References: Unit 3 ..................................................................................................... 206 References: Unit 4 ..................................................................................................... 207
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Study Guide 2/2 G04 ~ Mathematics
Unit
3
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
Research
Study
New concept or definition
Remember/Revise
Take note! Important
Selfassessment
3
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Unit
Study Guide 2/2 G04 ~ Mathematics
3
UNIT 3 This unit covers 11 lessons: Lessons 20 â€“ 30. The table indicates the lesson topics as well as the time you will spend on each one.
UNIT 3 TOPIC Mental maths: Use the Train Your Brain Maths Grade 4 product
TIME AND NOTES 8 hours (divided into 10 minutes every day)
LESSON 20 Capacity/Volume
6 hours
LESSON 21 Common fractions
5 hours
LESSON 22 Whole numbers: Counting, ordering, comparing and representing, and place value of digits (4digit whole numbers) Whole numbers: Addition and subtraction (4digit whole numbers)
5 hours
LESSON 23 Views of objects
2 hours
LESSON 24 Properties of 2D shapes
4 hours
LESSON 25 Data handling
7 hours
LESSON 26 Numerical patterns
4 hours
LESSON 27 Whole numbers: Addition and subtraction (4digit whole numbers)
4 hours
LESSON 28 Whole numbers: Multiplication (2digit whole numbers by 2digit whole numbers)
5 hours
LESSON 29 Number sentences
3 hours
LESSON 30 Transformations
3 hours
Revision: Use the CAMI programme
4 hours
TOTAL
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60 hours
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Study Guide 2/2 G04 ~ Mathematics
Unit
3
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 the amount of space in an object. OR Capacity is the quantity that an object can contain (hold). Volume is the amount of space an object occupies. 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.
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Unit
Study Guide 2/2 G04 ~ Mathematics
3
Volume
Capacity
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
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Measuring cups
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Measuring jugs
Study Guide 2/2 G04 ~ Mathematics
Unit
3
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 actually 1 000 times larger than 1 mℓ.
1 litre = 1 000 millilitres Therefore, your choice will be to measure the capacity and volume of larger objects in litres and to measure the capacity and volume of smaller objects in millilitres.
If you look at the ratio between litres and millilitres, how would you convert between the two?
litres (ℓ)
× 1 000
millilitres (mℓ)
÷ 1 000
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Unit
Study Guide 2/2 G04 ~ Mathematics
3
Examples of conversion 3,2 â„“ = ____________ mâ„“ To convert litres to millilitres, you must multiply by 1 000. 3,2 Ă— 1 000 = 3 200 mâ„“
1.
8 952 mâ„“ = ____________ â„“ To convert from millilitres to litres, you must divide by 1 000. 8 952 Ăˇ 1 000 = 8,952 â„“
2.
The number of zeros in numbers such as 10, 100 and 1 000 show the total number of place values, which will have an influence when multiplication or division takes place. 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.
The number after the comma in this example indicates the number of millilitres: 956 mâ„“
5 , 956 litres The number before the comma in this example indicates the number of full litres: 5 â„“
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đ?&#x;—đ?&#x;—đ?&#x;—đ?&#x;—đ?&#x;—đ?&#x;—
This means đ?&#x;?đ?&#x;? đ?&#x;Žđ?&#x;Žđ?&#x;Žđ?&#x;Žđ?&#x;Žđ?&#x;Ž litres
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Study Guide 2/2 G04 ~ Mathematics
Unit
3
ACTIVITY 51
1.
Write down the measurements of the water in each water jar and arrange them from small to large. (Adapted: Gr 4 Kwartaal 3 Kapasiteit en Volume Klastoets 1. V.A.W.)
Question
Answer
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Unit
Study Guide 2/2 G04 ~ Mathematics
3
2.
Convert the following as indicated. Question and answer
3.
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
ℓ = __________ mℓ
2.8
3
ℓ = __________ mℓ
4 4
Calculate the following. Question and answer 3.1
1 000 mℓ – 500 mℓ = __________ mℓ
3.2
325 mℓ × 2 = __________ mℓ
3.3
240 mℓ ÷ 8 = __________ mℓ
The difference between 6 879 mℓ and 464 mℓ.
3.4
3.5
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99 ℓ × 100 10
Study Guide 2/2 G04 ~ Mathematics
4.
Unit
Round the following to the nearest litre or millilitre, as indicated. Question
5.
3
4.1
To the nearest 100 mℓ. 50 mℓ
4.2
To the nearest 100 mℓ. 325 mℓ
4.3
To the nearest ℓ. 1 ℓ 250 mℓ
4.4
To the nearest ℓ. 6 ℓ 76 mℓ
4.5
To the nearest ℓ. 510 mℓ
Answer
Read the scenarios and answer the questions that follow. Question
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
How much cold drink is left for the rest of the family after the children have each had a glass of cold drink in the afternoon?
5.2
How much cold drink does the family buy each week?
A watering dispenser contains 21 ℓ of water.
5.3
Another
1
2
ℓ of water is poured in. How
much water is now in the dispenser?
5.4
Daniel fills his water bottle with 500 mℓ of water from the water dispenser. How much water is now left in the dispenser?
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Unit
Study Guide 2/2 G04 ~ Mathematics
3
Dillian’s mom buys tomato sauce in bulk. She buys 5 ℓ of tomato sauce from the wholesaler. To make it easier to use, she pours it into two smaller containers. Each container is 500 mℓ.
6.
5.5
How much tomato sauce remains in the large container?
5.6
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?
5.7
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?
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 .
A
B
C
.
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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 according to their capacity – from large to small.
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D
E
Study Guide 2/2 G04 ~ Mathematics
7.
Unit
6.4
Which container’s volume are measured in litres (ℓ)?
6.5
Which container’s capacity is smaller than 1 litre?
6.6
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?
3
Find pictures on the internet or in magazines for advertisements of containers that can hold more and less than 1 ℓ. Question and answer More than 1 ℓ
Less than 1 ℓ
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Unit
Study Guide 2/2 G04 ~ Mathematics
3 Selfassessment
After you have completed this topic, you should be able to do the following. Look at the requirements (the things you must be able to do) and colour the face that best describes your skill or ability. 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 I can use them. I can solve problems of capacity and volume in context (word sums).
I can convert between litre and millilitre.
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Can I do it?
Study Guide 2/2 G04 ~ Mathematics
Unit
3
LESSON 21: COMMON FRACTIONS In unit 2 you started learning about fractions. Can you still remember what you learnt? Letâ€™s have another look at what you have already learnt.
A fraction is when a whole (it can be any whole number or an object or shape) is broken into equal parts. Each part is only a piece 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 4 15
1 part is coloured in.
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Unit
Study Guide 2/2 G04 ~ Mathematics
3
Every part of the fraction has a special name:
Numerator
1 4
Denominator
Look at the examples of calculations with fractions. 1.
2
Colour the following parts in the given shapes: 6. 1
Each block in this shape represents one of the six parts: 6. 1 6
2
1 6
1 6
1 6
1 6
1 6
To colour in 6 of the shape, two parts should be coloured. 1 6
1 6
1 6
1 6
1 6
1 6
1 1 2 + = 6 6 6
You can always add the parts together in order to know what to colour or calculate. To add fractions, the denominators must always be the same. We will now compare different fractions. Just as we used different symbols to compare whole numbers, we will use them with fractions. Revise the symbols.
< > =
SMALLER
LARGER
Bestudeer die vorms en beantwoord die volgende vrae.
LARGER EQUAL
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SMALLER EQUAL
Study Guide 2/2 G04 ~ Mathematics
Unit
3
Example Use the symbols (< ; > ; =) to indicate the relationship between the fractions.
3 5 ď Ż 7 7
The first fraction shows 3 out of 7 parts (three sevenths). The second fraction shows 5 out of 7 parts (five sevenths). Three sevenths is smaller than 5 sevenths, therefore:
3 5 < 7 7
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.
3 3 ď Ż 4 8
Do you see that the denominators are not the same? You can make the denominators the same by using the times tables. Ask yourself: 4 Ă— ? = 8
The answer is 4 Ă— 2 = 8, but you cannot only multiply the denominator. If you multiply the denominator by a number, you must also multiply the numerator of that fraction:
3 4
Now you can compare the two fractions:
6 = Ă— đ?&#x;?đ?&#x;? 8 Ă— đ?&#x;?đ?&#x;?
đ?&#x;‘đ?&#x;‘ đ?&#x;’đ?&#x;’
đ?&#x;”đ?&#x;”
and đ?&#x;–đ?&#x;– are equivalent
fractions. This means đ?&#x;‘đ?&#x;‘
đ?&#x;”đ?&#x;”
that đ?&#x;’đ?&#x;’ = đ?&#x;–đ?&#x;–. (Unit 1)
6 3 > 8 8
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Unit
Study Guide 2/2 G04 ~ Mathematics
3
Before you compare any fractions or even add them, 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 everything that you have learnt so far. This lesson focuses specifically on equivalent fractions. Remember: When we do calculations with fractions (such as comparing or adding or subtracting them), the denominators must be the same.
ACTIVITY 52
1.
Write the fractions in ascending order (from small to large). Question 1.1
1.2
1.3
1.4
1.5
2.
Answer
1 4 2 3 5 ; ; ; ; 5 5 5 5 5 2 7 3 1 ; ; ; 8 8 8 8 1 3 1 ; ; 4 8 8 1 4 3 ; ; 3 6 3 2 1 3 ; ; 3 2 3
Study the fractions and answer the questions. Question
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Answer
5 4 4 3 2 9 ; ; ; ; ; 6 7 4 5 2 9
2.1
Which fractions are smaller than 1?
2.2
Which fractions are larger than 1?
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Study Guide 2/2 G04 ~ Mathematics
3.
Unit
3
Use the fraction wall to identify the equivalent fractions. Question
3.1
3.2
3.3
3.4
3.5
3.6
3.7
3.8
3.9
Answer
4 = 8 4 4 = 8 2 2
=
3 6
=
4 6
1 = 2 4 2
1 = 3 6
2 = 6 12 2 = 4 8
4 = 12 3 19
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Unit
Study Guide 2/2 G04 ~ Mathematics
3 3.10
3.11
3.12
4.
1 = 2 8 2 = 6 3
4 = 12 6
Read the scenarios and answer the questions that follow. Question Answer In a class of 20 Grade 4 learners, there are 8 learners who write with BIC pens, 10 learners who write with Staedtler pens and the rest write with Pilot pens. 4.1
What fraction of the learners write with Staedtler pens?
4.2
What fraction of the learners write with BIC pens?
4.3
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. If each boy gets 6 sweets, what 4.4 fraction of the packet of sweets do they get altogether? If each girl gets 3 sweets, what 4.5 fraction of the packet of sweets do they get altogether? 4.6
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What fraction of the packet of sweets remains?
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Study Guide 2/2 G04 ~ Mathematics
5.
Unit
3
Write down number sentences for the images and calculate the answers. Question
Example
đ?&#x;?đ?&#x;? đ?&#x;?đ?&#x;? đ?&#x;‘đ?&#x;‘ + = đ?&#x;’đ?&#x;’ đ?&#x;’đ?&#x;’ đ?&#x;’đ?&#x;’
+ .
5.1
Answer
+ .
5.2
+ .
5.3 +
.
5.4
+ .
5.5
+ .
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Unit
Study Guide 2/2 G04 ~ Mathematics
3
6.
Use symbols (< ; > ; =) to indicate the relationship between the fractions. Question 4 1 8 4
6.1
4 3 8 2
6.2
1 3 2 6
6.3
1 2 2 4
6.4
2 2 10 5
6.5
7.
Answer
Complete the flow charts.
Question and answer
7.1
.
7.2
.
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1 6 2 6 3 6 4 6 5 6
______ ______ 1
+6
______ ______ ______
1 9 2 9 3 9 4 9 7 9
+
3 9 4 9 5 9 6 9 1
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Study Guide 2/2 G04 ~ Mathematics
Unit
7.3
.
1 6 1 3 2 3 4 6 3 3
3
______ ______ 1
+6
______ ______ ______
Selfassessment After you have completed this topic, you should be able to do the following. Look at the requirements (the things you must be able to do) and colour the face that best describes your skill or ability. FRACTIONS Requirements
Can I do it?
I can indicate common fractions on a diagram.
I can identify common fractions on a diagram.
I can compare common fractions and indicate their relationship.
I can calculate equivalent fractions.
I can do calculations (addition) with fractions.
I can solve fraction problems with calculations.
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Unit
Study Guide 2/2 G04 ~ Mathematics
3
LESSON 22: WHOLE NUMBERS • •
Counting, ordering, comparing and representing, and place value of digits (4digit whole numbers) Addition and subtraction (4digit whole numbers)
Everything that you have learnt up to now about whole numbers can occur in general calculations with whole numbers. You must be able to do the following: •
Count on and back in 2s, 3s, 5s, 10s, 25s, 50s and 100s – between 0 and 10 000. Order, describe and present 4digit whole numbers. Comparing and representing even and odd numbers up to 1 000. Recognise place values of 4digit whole numbers. Round to the nearest 10, 100 or 1 000.
• • • •
Take your time and go through the requirements with your facilitator. Revise these concepts and make sure that you have mastered all of them. In the next part of this lesson you will need to do and apply these requirements. Page back to lesson 1 and lesson 10 to refresh your memory. We are now going to use 4digit numbers to add and subtract whole numbers.
Ensure that you can use the following techniques when doing calculations: • • • • • •
Estimation Building up and breaking down numbers Rounding and compensation Doubling and halving Using a number line Using addition and subtraction as inverse operations to test your answers
By now you should be comfortable with all of the above techniques. If you are still uncertain about which technique to use, you now have the opportunity to practise and master the technique. If you have forgotten how to use any of the techniques, page back to lesson 9 in unit 1, and lessons 11 and 18 in unit 2 to refresh your memory.
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Study Guide 2/2 G04 ~ Mathematics
Unit
3
ACTIVITY 53
1.
Calculate the following. Question
1.1
5 000 + 300 + 50 + 7
1.2
1 000 + 50 + 3
1.3
9 000 + 900 + 9
Answer
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Unit
Study Guide 2/2 G04 ~ Mathematics
3
2.
1.4
5 000 + 100 + 20 + 3
1.5
4 000 + 500 + 6
The numbers are provided in words. Write the correct number in the answer column. Question
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Answer
2.1
Three thousand eight hundred and fiftyone
2.2
Seven thousand four hundred and three
2.3
5 Tens, 3 Units, 8 Thousands, 5 Hundreds
2.4
9 Units, 6 Thousands, 2 Tens
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Study Guide 2/2 G04 ~ Mathematics
3.
Unit
Use symbols (< ; > ; =) to indicate the relationship between the numbers. Question
4.
3
Answer
3.1
9 800 8 900
3.2
7 898 7 988
3.3
4 150 4 051
3.4
3 000 + 700 + 40 + 1 3 471
3.5
2 000 + 80 + 9 2 890
Round the numbers to the nearest 100. Between which multiples of 100 does each number appear? Complete the sentences.
Question and answer
Example
3 456 is between 3 400 and 3 500 and is rounded to 3 500.
5 345 is between __________ and __________ 4.1
and is rounded to __________.
9 873 is between __________ and __________ 4.2
and is rounded to __________.
1 230 is between __________ and __________ 4.3
and is rounded to __________.
3 731 is between __________ and __________ 4.4
and is rounded to __________.
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Unit
Study Guide 2/2 G04 ~ Mathematics
3
5.
Round the numbers to the nearest 1 000. Question
6.
5.1
7 686
5.2
5 132
5.3
9 823
5.4
2 912
5.5
4 444
Answer
Complete the table. Round the given number to 10, 100 and 1 000. Question and answer
Number
To the nearest 10
To the nearest 100
To the nearest 1 000
8 642 5 132 9 265 4 782 1 113 .
7.
What is the place value of the underlined digit? Question
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7.1
3 829
7.2
1 238
7.3
4 318
7.4
9 999
7.5
7 458
Answer
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