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MATHEMATICS STUDY GUIDE 2/2 Grade 4
A member of the FUTURELEARN group
Mathematics Study guide 2/2
1804-E-MAM-SG02
Í2$È-E-MAM-SG02UÎ
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 2-D 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 3-D 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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Unit
Study Guide 2/2 G04 ~ Mathematics
3
UNIT 3 This unit covers 11 lessons: Lessons 20 – 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 (4-digit whole numbers) Whole numbers: Addition and subtraction (4-digit whole numbers)
5 hours
LESSON 23 Views of objects
2 hours
LESSON 24 Properties of 2-D shapes
4 hours
LESSON 25 Data handling
7 hours
LESSON 26 Numerical patterns
4 hours
LESSON 27 Whole numbers: Addition and subtraction (4-digit whole numbers)
4 hours
LESSON 28 Whole numbers: Multiplication (2-digit whole numbers by 2-digit 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 mℓ = ____________ ℓ To convert from millilitres to litres, you must divide by 1 000. 8 952 á 1 000 = 8,952 ℓ
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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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 Self-assessment
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 3-D 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?