Grade 4 Study Guide 2/2 Mathematics by Impaq

Intermediate Phase Grade 4 • Study Guide 2/2

Mathematics Comprehensive explanations of concepts in simple language. Practical, everyday examples with visuals and diagrams to help master concepts. Learners work at their own pace. Activities that test learners’ knowledge application and reasoning. The facilitator’s guide contains step-by-step calculations and answers. Use in school or at home.

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Study Guide 2/2

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Mathematics Study guide 2/2

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Grade 4

Study Guide 2/2 G04 ~ Mathematics

Contents LESSON ELEMENTS.................................................................................................................................... 1 UNIT 3............................................................................................................................................................ 2 LESSON 20: CAPACITY/VOLUME........................................................................................................... 3 ACTIVITY 51...............................................................................................................................................7

LESSON 21: COMMON FRACTIONS......................................................................................................13 ACTIVITY 52............................................................................................................................................ 16 LESSON 22: WHOLE NUMBERS ...........................................................................................................22 ACTIVITY 53............................................................................................................................................ 23 LESSON 23: VIEWS OF OBJECTS...........................................................................................................32 ACTIVITY 54............................................................................................................................................ 34 LESSON 24: PROPERTIES OF 2D SHAPES..........................................................................................39 ACTIVITY 55............................................................................................................................................ 42 LESSON 25: DATA HANDLING...............................................................................................................47 ACTIVITY 56............................................................................................................................................ 50 LESSON 26: NUMBER PATTERNS.........................................................................................................55 Input and output values................................................................................................................................ 56 The associative property of multiplication........................................................................................... 58 Types of number sequences........................................................................................................................ 61 ACTIVITY 57............................................................................................................................................ 61 LESSON 27: WHOLE NUMBERS (Addition and subtraction [4-digit whole numbers]).....65 Order of subtraction........................................................................................................................................ 67 ACTIVITY 58............................................................................................................................................ 69

LESSON 28: WHOLE NUMBERS (Multiply [2-digit whole numbers by 2-digit whole numbers])..................................................................................................................................................77 Distributive property of multiplication.................................................................................................. 78 Dividing numbers into factors to multiply them................................................................................ 78 ACTIVITY 59............................................................................................................................................ 79 LESSON 29: NUMBER SENTENCES......................................................................................................83 Pairs of equivalent number sentences.................................................................................................... 87 ACTIVITY 60............................................................................................................................................ 88 LESSON 30: TRANSFORMATIONS........................................................................................................92 ACTIVITY 61............................................................................................................................................ 93 UNIT 4..........................................................................................................................................................95 LESSON 31: WHOLE NUMBERS............................................................................................................96 ACTIVITY 62............................................................................................................................................ 96 i

Study Guide 2/2 G04 ~ Mathematics

LESSON 32: MASS.................................................................................................................................. 108 ACTIVITY 63......................................................................................................................................... 110 LESSON 33: PROPERTIES OF 3D OBJECTS..................................................................................... 118 ACTIVITY 64......................................................................................................................................... 121 LESSON 34: COMMON FRACTIONS................................................................................................... 125 ACTIVITY 65......................................................................................................................................... 128 LESSON 35: WHOLE NUMBERS (Division [3-digit numbers by 1-digit number])............ 134 ACTIVITY 66......................................................................................................................................... 136 LESSON 36: PERIMETER, SURFACE AREA AND VOLUME.......................................................... 139 ACTIVITY 67......................................................................................................................................... 144 Surface area..................................................................................................................................................... 148 ACTIVITY 68......................................................................................................................................... 149 Volume............................................................................................................................................................... 151 LESSON 37: POSITION AND MOVEMENT....................................................................................... 154 ACTIVITY 69......................................................................................................................................... 156 LESSON 38: TRANSFORMATIONS..................................................................................................... 159 ACTIVITY 70......................................................................................................................................... 161 LESSON 39: GEOMETRIC PATTERNS............................................................................................... 164 ACTIVITY 71......................................................................................................................................... 166 LESSON 40: WHOLE NUMBERS (Addition and subtraction [4-digit whole numbers]).. 170 ACTIVITY 72......................................................................................................................................... 170 LESSON 41: PROBABILITY.................................................................................................................. 181 ACTIVITY 73......................................................................................................................................... 182 REFERENCES: UNIT 3........................................................................................................................... 185 REFERENCES: UNIT 4........................................................................................................................... 186

Study Guide 2/2 G04 ~ Mathematics

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 Self-assessment Activity 1

Unit

Study Guide 2/2 G04 ~ Mathematics

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

Study Guide 2/2 G04 ~ Mathematics

Unit

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

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.

Study Guide 2/2 G04 ~ Mathematics

Volume

Unit

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

Measuring cups

Measuring jugs

Study Guide 2/2 G04 ~ Mathematics

Unit

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?

× 1 000

litres (ℓ)

÷ 1 000

millilitres (mℓ)

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

8 952 mℓ = ____________ ℓ To convert from millilitres to litres, you must divide by 1 000. 8 952 ÷ 1 000 = 8,952 ℓ 5

Unit

Study Guide 2/2 G04 ~ Mathematics

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

956

This means _ 1 000 litres

Study Guide 2/2 G04 ~ Mathematics

Unit

ACTIVITY 51 1.

DATE:

Write down the measurements of the water in each water jar and arrange them from small to large. Question

Answer

Unit

Study Guide 2/2 G04 ~ Mathematics

Convert the measurements as indicated.

Question and answer

2.1

3 000 mℓ = __________ ℓ

2.3

1 250 mℓ = __________ and __________ ℓ

2.2 2.4 2.5 2.6 2.7 3.

2.8

3 500 mℓ = __________ and __________ ℓ 5 750 mℓ = __________ and __________ ℓ 1 ℓ = __________ mℓ

1 500 mℓ = __________ ℓ and __________ mℓ _ 14 ℓ = __________ mℓ _ 34 ℓ = __________ mℓ

Complete the calculations.

Question and answer

3.1

1 000 mℓ – 500 mℓ = __________ mℓ

3.3

240 mℓ ÷ 8 = __________ mℓ

3.2

325 mℓ × 2 = __________ mℓ

The difference between 6 879 mℓ and 464 mℓ.

3.4

3.5

99 ℓ × 100

Study Guide 2/2 G04 ~ Mathematics

Round to the nearest litre or millilitre, as indicated. Question

4.1 4.2 4.3 4.4 4.5 5.

Unit

Answer

To the nearest 100 mℓ. 50 mℓ

To the nearest 100 mℓ. 325 mℓ

To the nearest ℓ. 1 ℓ 250 mℓ

To the nearest ℓ. 6 ℓ 760 mℓ

To the nearest ℓ. 510 mℓ

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 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

_ 12 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?

Unit

Study Guide 2/2 G04 ~ Mathematics

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 5.6

5.7 6.

How much tomato sauce remains in the large container?

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?

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 6.2 6.3 © Optimi

Which container will be able to hold the most water?

Which container will hold the least water?

Arrange the containers from large to small according to their capacity.

Study Guide 2/2 G04 ~ Mathematics

6.4 6.5 6.6 6.7 7.

Unit

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?

If container B’s capacity is 250 mℓ, how many containers of B can you pour into container E?

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

Unit

Study Guide 2/2 G04 ~ Mathematics

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.

Can I do it?

Study Guide 2/2 G04 ~ Mathematics

Unit

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 4 13

1 part is coloured.

Unit

Study Guide 2/2 G04 ~ Mathematics

Every part of the fraction has a special name:

Numerator

1 4

Study the examples of calculations with fractions. 1.

Denominator

Colour the following parts in the given shapes: _ 26 Each block in this shape represents one of the six parts: _ 16

1 6

To colour _ 26 of the shape, two parts should be coloured.

1 1 2 + = 6 6 6

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 EQUAL

GREATER SMALLER EQUAL

Study Guide 2/2 G04 ~ Mathematics

Unit

Example Use the symbols (< ; > ; =) to indicate the relationship between the fractions.

3 7

5 7

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:

3 7

5 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 4

5 8

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:

You can now compare the two fractions:

3 4

x2 x2

6 8

= >

_ 43 and _ 86 are equivalent

fractions. This means 3

that _ 4 = _ 8 (Unit 1)

3 8

Unit

Study Guide 2/2 G04 ~ Mathematics

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 1.

Write the fractions in ascending order (from small to great). Question

1.1

_ 15 ; _ 25 ; _ 35 ; _ 54 ; _ 55

1.3

_ 14 ; _ 38 ; _ 18

1.2

1.4 1.5 2.

Answer

_ 28 ; _ 78 ; _ 38 ; _ 81 _ 13 ; _ 46 ; _ 33 _ 23 ; _ 12 ; _ 33

Study the fractions and answer the questions. Question

2.1 2.2 © Optimi

DATE:

_ 56 ; _ 74 ; _ 44 ; _ 35 ; _ 22 ; _ 99

Which fractions are smaller than 1? Which fractions are greater than 1? 16

Answer

Study Guide 2/2 G04 ~ Mathematics

Unit

Use the fraction wall to identify the equivalent fractions.

Question and answer 3.1 3.2 3.3 3.4 3.5 3.6

_ 4 = _ 8 4

3.7

_= _ 3

3.9

_ 4 = _ 8 2 2

3.8

_ 1 = _ 2 4

3.10

_ 1 = _ 3 6

3.12

4 _ 2 = _ 6

3.11

_ 2 = _ 6 12 _ 2 = _ 4 8

4 = _ _ 12 3 _ 1 = _ 2 8 _ 2 = _ 6 3

_ 4 = _ 12 6

Unit

Study Guide 2/2 G04 ~ Mathematics

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 4.6

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?

What fraction of the packet of sweets remains?

Study Guide 2/2 G04 ~ Mathematics

Unit

Write down number sentences for the images and calculate the answers. Question

Example

Answer

_ 2

+ 1_ = 3_ 4

5.1

5.2

5.3

+ .

5.4

5.5

Unit

Study Guide 2/2 G04 ~ Mathematics

Use symbols (< ; > ; =) to indicate the relationship between the fractions. Question and answer

6.1

6.3

1 2

3 6

7.2 .

1 2

6.4

3 2

Complete the flow charts.

7.1

1 4

4 8

6.2

4 8

2 10

6.5

2 4 2 5

Question and answer

_ 1 6 _ 2 6 _ 3 6 _ 4 6 _ 5 6

______ +_ 16

______ ______ ______ ______

1 _ 9 _ 2 9 _ 3 9 _ 4 9 _ 7 9

3 _ 9 _ 4 9 _ 5 9 _ 6 9 1

Study Guide 2/2 G04 ~ Mathematics

Unit

7.3 .

_ 1 6 _ 2 3 _ 2 3 _ 4 6 _ 3 3

______ +_ 61

______ ______ ______ ______

Self-assessment Do you understand the work? Colour the faces that show what you can do. 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.

Unit

Study Guide 2/2 G04 ~ Mathematics

LESSON 22: WHOLE NUMBERS • •

Counting, ordering, comparing and representing, and place value of digits (4-digit whole numbers) Addition and subtraction (4-digit whole numbers)

You must be able to do the following with whole numbers:

Count on and back in 2s, 3s, 5s, 10s, 25s, 50s and 100s – between 0 and 10 000.

• • • •

Order, describe and present 4-digit whole numbers.

Compare and represent even and odd numbers up to 1 000. Recognise place values of 4-digit 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 4-digit numbers to add and subtract whole numbers.

You must be able to 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.

Study Guide 2/2 G04 ~ Mathematics

Unit

ACTIVITY 53 1.

Question

1.1

5 000 + 300 + 50 + 7

1.3

9 000 + 900 + 9

1.4 2.

1.5

Answer

1 000 + 50 + 3

5 000 + 100 + 20 + 3 4 000 + 500 + 6

Write the number symbols for the number names in the answer column. Question

Answer

2.1

Three thousand eight hundred and fifty-one

2.3

5 Tens, 3 Units, 8 Thousands, 5 Hundreds

2.2

DATE:

Complete the addition sums.

1.2

2.4

Seven thousand four hundred and three 9 Units, 6 Thousands, 2 Tens

Use symbols (< ; > ; =) to indicate the relationship between the numbers. Question

3.1

9 800  8 900

3.3

4 150  4 051

3.2 3.4 3.5

Answer

7 898  7 988 3 000 + 700 + 40 + 1  3 471 2 000 + 80 + 9  2 890

Unit

Study Guide 2/2 G04 ~ Mathematics

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. 4.1

5 345 is between ____________ and ____________ and is rounded to ____________.

4.3

1 230 is between ____________ and ____________ and is rounded to ____________.

4.2

4.4

9 873 is between ____________ and ____________ and is rounded to ____________. 3 731 is between ____________ and ____________ and is rounded to ____________.

Round the numbers to the nearest 1 000. Question

5.1

7 686

5.3

9 823

5.2

5 132

5.4 6.

2 912

5.5

4 444

Complete the table. Round the given number to 10, 100 and 1 000. Question and answer

Number

To the nearest 10

8 642 5 132 9 265 4 782 .

Answer

1 113 24

To the nearest 100

To the nearest 1 000

Study Guide 2/2 G04 ~ Mathematics

Unit

What is the place value of the underlined digit? Question

7.1

3 829

7.3

4 318

Answer

1 238

7.2 7.4 8.

9 999

7 458

7.5

Complete the mixed sums. First give the estimated answer and then calculate the answer. You may use any valid method. Question

Answer

Estimated answer: ___________________ + ___________________ = ___________________ 8.1

3 876 + 5 734

Calculation:

Estimated answer: ___________________ + ___________________ = ___________________ Calculation: 8.2

8 979 – 3 887

Unit

Study Guide 2/2 G04 ~ Mathematics

Estimated answer: ___________________ + ___________________ = ___________________ Calculation: 8.3

8 215 + 1 110

Estimated answer: ___________________ + ___________________ = ___________________ Calculation: 8.4

6 452 – 4 132

Estimated answer: ___________________ + ___________________ = ____________________ Calculation: 8.5

5 892 – 1 695

Study Guide 2/2 G04 ~ Mathematics

Unit

Estimated answer: ___________________ + ___________________ = ___________________ Calculation: 8.6

3 123 + 4 891

Estimated answer: ___________________ + ___________________ = ____________________ Calculation: 8.7

6 869 – 1 038

Estimated answer: ___________________ + ___________________ = ___________________ Calculation: 8.8

5 352 + 2 555

Unit

Study Guide 2/2 G04 ~ Mathematics

Estimated answer: ___________________ + ___________________ = ___________________ Calculation: 8.9

2 856 + 2 182

Estimated answer: ___________________ + ___________________ = ___________________ Calculation: 8.10

Complete the following.

Question and answer

9.1

3 453 = (3 × ___________) + (4 × ___________) + (5 × ___________) + (3 × ___________)

9.3

4 123 = (1 000 × _________) + (100 × _________) + (10 × _________) + (1 × ________)

9.2 9.4

8 839 – 5 672

8 532 = (3 × ___________) + (8 × ___________) + (5 × ___________) + (2 × ___________)

1 075 = (1 000 × _________) + (100 × _________) + (10 × _________) + (1 × ________)

Grade 4 Study Guide 2/2 Mathematics

Articles inside

LESSON 22: WHOLE NUMBERS

LESSON 20: CAPACITY/VOLUME