Grade 4 Facilitators Guide Mathematics

Intermediate Phase Grade 4 • Facilitator’s Guide

Mathematics CAPS IEB Mathematics

• Comprehensive explanations of concepts in simple language. everyday examples with visuals and diagrams to help • Practical, 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.

home classroom college workplace

9 781990

Facilitator’s Guide

2004-E-MAM-FG01

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4

Mathematics Facilitator’s guide

CAPS aligned

L Young

2004-E-MAM-FG01

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Grade 4

Facilitator’s Guide G04 ~ Mathematics

Contents LESSON ELEMENTS.....................................................................................................................................1 INTRODUCTION...........................................................................................................................................2 TIME MANAGEMENT..................................................................................................................................2 ASSESSMENT REQUIREMENTS................................................................................................................7 YEAR PLAN....................................................................................................................................................8 UNIT 1.......................................................................................................................................................... 12 LESSON 1: WHOLE NUMBERS............................................................................................................... 13 Counting with whole numbers....................................................................................................................14 ACTIVITY 1...............................................................................................................................................16 Ordering whole numbers...............................................................................................................................19 ACTIVITY 2...............................................................................................................................................20 Place value............................................................................................................................................................22 ACTIVITY 3...............................................................................................................................................24 Comparing whole numbers...........................................................................................................................29 ACTIVITY 4...............................................................................................................................................30 Representing whole numbers......................................................................................................................33 ACTIVITY 5...............................................................................................................................................33 LESSON 2: NUMBER SENTENCES......................................................................................................... 34 ACTIVITY 6...............................................................................................................................................35 ACTIVITY 7...............................................................................................................................................36 ACTIVITY 8...............................................................................................................................................37 Pairs of equivalent number sentences.....................................................................................................39 ACTIVITY 9...............................................................................................................................................40 Addition and subtraction techniques.......................................................................................................41 Commutative property of addition............................................................................................................41 Associative property of addition................................................................................................................42 ACTIVITY 10.............................................................................................................................................43 Order of subtraction.........................................................................................................................................44 ACTIVITY 11.............................................................................................................................................45 LESSON 3: WHOLE NUMBERS............................................................................................................... 46 Addition with whole numbers.....................................................................................................................46 ACTIVITY 12.............................................................................................................................................46 ACTIVITY 13.............................................................................................................................................49 Subtraction of whole numbers....................................................................................................................51 ACTIVITY 14.............................................................................................................................................52 Estimation............................................................................................................................................................58 ACTIVITY 15.............................................................................................................................................60 Rounding...............................................................................................................................................................63 ACTIVITY 16.............................................................................................................................................65 ACTIVITY 17.............................................................................................................................................67 Compensation.....................................................................................................................................................68 Doubling and halving.......................................................................................................................................68 i

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Facilitator’s Guide G04 ~ Mathematics

ACTIVITY 18.............................................................................................................................................69 ACTIVITY 19.............................................................................................................................................71 Testing calculations with inverse operations........................................................................................72 ACTIVITY 20.............................................................................................................................................73 LESSON 4: NUMBER PATTERNS (Numeric patterns).................................................................... 75 ACTIVITY 21.............................................................................................................................................76 Input and output values.................................................................................................................................77 ACTIVITY 22.............................................................................................................................................77 ACTIVITY 23.............................................................................................................................................79 ACTIVITY 24.............................................................................................................................................80 The associative property of multiplication............................................................................................81 LESSON 5: WHOLE NUMBERS (Multiplication and division)..................................................... 84 Multiplication......................................................................................................................................................84 ACTIVITY 25.............................................................................................................................................92 Division..................................................................................................................................................................93 ACTIVITY 26.............................................................................................................................................94 ACTIVITY 27.............................................................................................................................................97

LESSON 6: TIME........................................................................................................................................ 98 ACTIVITY 28..........................................................................................................................................101 ACTIVITY 29..........................................................................................................................................104 LESSON 7: DATA HANDLING................................................................................................................106 Collecting, organising, analysing and interpreting data................................................................106 Pictograph.........................................................................................................................................................106 Pie chart..............................................................................................................................................................107 Bar graph...........................................................................................................................................................108 ACTIVITY 30..........................................................................................................................................109 LESSON 8: PROPERTIES OF 2D SHAPES..........................................................................................113 ACTIVITY 31..........................................................................................................................................116

LESSON 9: WHOLE NUMBERS (Multiplication of 2-digit numbers and division of 2-digit numbers by 1-digit numbers)...........................................................................................................118 ACTIVITY 32..........................................................................................................................................118 ACTIVITY 33..........................................................................................................................................120 ACTIVITY 34..........................................................................................................................................124 UNIT 2........................................................................................................................................................126 LESSON 10: WHOLE NUMBERS..........................................................................................................127 Counting with whole numbers.................................................................................................................128 ACTIVITY 35..........................................................................................................................................129 Ordering whole numbers............................................................................................................................132 ACTIVITY 36..........................................................................................................................................133 Place value.........................................................................................................................................................135 © Optimi

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Facilitator’s Guide G04 ~ Mathematics

ACTIVITY 37..........................................................................................................................................137 Comparing whole numbers........................................................................................................................140 ACTIVITY 38..........................................................................................................................................141 Representing whole numbers...................................................................................................................143 ACTIVITY 39..........................................................................................................................................143 Rounding............................................................................................................................................................143 ACTIVITY 40..........................................................................................................................................146 LESSON 11: WHOLE NUMBERS (Addition and subtraction)...................................................148 Commutative property of addition.........................................................................................................148 Associative property of addition.............................................................................................................149 Order of subtraction......................................................................................................................................151 ACTIVITY 41..........................................................................................................................................153 LESSON 12: COMMON FRACTIONS....................................................................................................156 ACTIVITY 42..........................................................................................................................................158 ACTIVITY 43..........................................................................................................................................160 LESSON 13: LENGTH..............................................................................................................................167 ACTIVITY 44..........................................................................................................................................168 LESSON 14: WHOLE NUMBERS (Multiply 2-digit numbers by 2-digit numbers)..............171 Distributive property of multiplication................................................................................................173 Dividing numbers into factors to multiply them..............................................................................173 ACTIVITY 45..........................................................................................................................................174 LESSON 15: PROPERTIES OF 3D OBJECTS......................................................................................179 ACTIVITY 46..........................................................................................................................................182 LESSON 16: GEOMETRIC PATTERNS................................................................................................185 ACTIVITY 47..........................................................................................................................................187 LESSON 17: SYMMETRY.......................................................................................................................189 ACTIVITY 48..........................................................................................................................................190 LESSON 18: WHOLE NUMBERS (Addition and subtraction)....................................................192 ACTIVITY 49..........................................................................................................................................192 LESSON 19: WHOLE NUMBERS (Dividing 3-digit numbers by 1-digit number)................196 ACTIVITY 50..........................................................................................................................................200 UNIT 3........................................................................................................................................................206 LESSON 20: CAPACITY/VOLUME.......................................................................................................207 ACTIVITY 51..........................................................................................................................................211 LESSON 21: COMMON FRACTIONS....................................................................................................216 ACTIVITY 52..........................................................................................................................................219 iii

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Facilitator’s Guide G04 ~ Mathematics

LESSON 22: WHOLE NUMBERS .........................................................................................................224 ACTIVITY 53..........................................................................................................................................225 LESSON 23: VIEWS OF OBJECTS.........................................................................................................232 ACTIVITY 54..........................................................................................................................................233 LESSON 24: PROPERTIES OF 2D SHAPES........................................................................................237 ACTIVITY 55..........................................................................................................................................240 LESSON 25: DATA HANDLING.............................................................................................................244 ACTIVITY 56..........................................................................................................................................246 LESSON 26: NUMBER PATTERNS.......................................................................................................251 Input and output values..............................................................................................................................252 The associative property of multiplication.........................................................................................254 Types of number sequences......................................................................................................................256 ACTIVITY 57..........................................................................................................................................257 LESSON 27: WHOLE NUMBERS (Addition and subtraction [4-digit whole numbers])...260 Order of subtraction......................................................................................................................................262 ACTIVITY 58..........................................................................................................................................264

LESSON 28: WHOLE NUMBERS (Multiply [2-digit whole numbers by 2-digit whole numbers])................................................................................................................................................269 Distributive property of multiplication................................................................................................269 Dividing numbers into factors to multiply them..............................................................................270 ACTIVITY 59..........................................................................................................................................271 LESSON 29: NUMBER SENTENCES....................................................................................................276 Pairs of equivalent number sentences..................................................................................................279 ACTIVITY 60..........................................................................................................................................280 LESSON 30: TRANSFORMATIONS......................................................................................................283 ACTIVITY 61..........................................................................................................................................284 UNIT 4........................................................................................................................................................285 LESSON 31: WHOLE NUMBERS..........................................................................................................286 ACTIVITY 62..........................................................................................................................................286 LESSON 32: MASS...................................................................................................................................295 ACTIVITY 63..........................................................................................................................................298 LESSON 33: PROPERTIES OF 3D OBJECTS......................................................................................304 ACTIVITY 64..........................................................................................................................................306 LESSON 34: COMMON FRACTIONS....................................................................................................310 ACTIVITY 65..........................................................................................................................................313 © Optimi

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Facilitator’s Guide G04 ~ Mathematics

LESSON 35: WHOLE NUMBERS (Division [3-digit numbers by 1-digit number]).............319 ACTIVITY 66..........................................................................................................................................321 LESSON 36: PERIMETER, SURFACE AREA AND VOLUME...........................................................325 ACTIVITY 67..........................................................................................................................................331 Surface area......................................................................................................................................................334 ACTIVITY 68..........................................................................................................................................335 Volume................................................................................................................................................................336 LESSON 37: POSITION AND MOVEMENT........................................................................................339 ACTIVITY 69..........................................................................................................................................341 LESSON 38: TRANSFORMATIONS......................................................................................................344 ACTIVITY 70..........................................................................................................................................346 LESSON 39: GEOMETRIC PATTERNS................................................................................................348 ACTIVITY 71..........................................................................................................................................350 LESSON 40: WHOLE NUMBERS (Addition and subtraction [4-digit whole numbers])...353 ACTIVITY 72..........................................................................................................................................353 LESSON 41: PROBABILITY...................................................................................................................359 ACTIVITY 73..........................................................................................................................................360 REFERENCES: UNIT 1............................................................................................................................362 REFERENCES: UNIT 2............................................................................................................................363 REFERENCES: UNIT 3............................................................................................................................364 REFERENCES: UNIT 4............................................................................................................................365 100 CHART...............................................................................................................................................366 ADDENDUM A..........................................................................................................................................367

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Facilitator’s Guide G04 ~ Mathematics

LESSON ELEMENTS The guide consists of various lesson elements. Every element is important for the learning process and 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

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Facilitator’s Guide G04 ~ Mathematics

INTRODUCTION Grade 4 learners are entering a new phase in their school careers and are being introduced to the concept of self-study for the first time. The study guide and the facilitator’s guide are written to guide learners and facilitators through the process and lay the foundation for future academic success. It is important to remember that the facilitator’s support is still crucial to help learners gain self-confidence to master the new challenges.

The study guide is written in a friendly and informal manner to involve learners and make the subject accessible and interesting. It consists of theory, activities and research activities. All activities in the study guide must be completed to help learners understand and apply the new knowledge.

After each lesson, learners must complete an individual self-assessment. Use the assessment to determine whether learners still need help with a particular lesson, and address the gap immediately. It may also be used to plan enrichment activities. Once learners have mastered the concepts in each lesson, additional enrichment activities may be completed.

The facilitator’s guide guides the facilitator to support the learners so that the theory of mathematics is well established at the end of each lesson. Many of the lessons have a practical component which the facilitator must present. Use the guidelines in the facilitator’s guide.

The study guide and facilitator’s guides are divided into four units. You are encouraged to complete one unit per term.

Do 10 minutes of mental arithmetic every day. Use the supplementary Train Your Brain Maths Grade 4 product.

The CAMI exercise programme (www.camiweb.com) is recommended for revision and additional practice.

This product consists of: • A facilitator’s guide • Two study guides: Units 1 and 2 are in study guide 1/2 and units 3 and 4 are in study guide 2/2.

• Train Your Brain Maths Grade 4 (for mental arithmetic)

TIME MANAGEMENT

The time allocation per topic is merely a guideline and may be adapted according to the learners’ pace.

It is important, however, to know which lessons must be completed before any test or exam can be attempted.

Learners must spend six hours per week on mathematics. Take note that this does not include all activities, assessments and examinations. If learners are working at a pace slower than the allotted time, make the necessary adjustments so that they can still complete all the work in time.

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Facilitator’s Guide G04 ~ Mathematics

It is also crucial that the learners do not progress to the next topic before they have a thorough understanding of the current topic. It is important to do revision until they have fully mastered the new concepts. Grade 4 is the start of a new phase and the last opportunity for learners to master the basics of mathematics.

Guidelines for time allocation per topic UNIT 1 TOPIC

TIME AND NOTES

Mental maths: Use the Train Your Brain Maths Grade 4 product

LESSON 1 Whole numbers: Counting, ordering, comparing and representing, and place value of digits (3-digit whole numbers) LESSON 2 Number sentences

LESSON 3 Whole numbers: Addition and subtraction (3-digit whole numbers) LESSON 4 Number patterns: Numeric patterns

LESSON 5 Whole numbers: Multiplication and division (1-digit whole number by 1-digit whole number) LESSON 6 Time

8 hours (divided into 10 minutes every day) 2 hours 3 hours 8 hours 4 hours 4 hours 6 hours

LESSON 7 Data handling

10 hours

LESSON 9 Whole numbers: • Multiply (2-digit whole numbers by 1-digit whole number) • Multiply (2-digit whole numbers by 2-digit whole numbers) • Divide (2-digit whole numbers by 1-digit whole number)

5 hours

LESSON 8 Properties of 2D shapes

Revision: Use the CAMI programme TOTAL

3

5 hours

5 hours

60 hours

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Facilitator’s Guide G04 ~ Mathematics

UNIT 2 TOPIC

TIME AND NOTES

Mental maths: Use the Train Your Brain Maths Grade 4 product

LESSON 10 Whole numbers: Counting, ordering, comparing and representing, and place value of digits (4-digit whole numbers)

7 hours (divided into 10 minutes every day) 1 hour

LESSON 11 Whole numbers: Addition and subtraction (4-digit whole numbers)

4 hours

LESSON 13 Length

7 hours

LESSON 12 Common fractions

LESSON 14 Whole numbers: Multiplication (2-digit whole numbers by 2-digit whole numbers) LESSON 15 Properties of 3D shapes LESSON 16 Geometric patterns

6 hours 5 hours 4 hours

LESSON 17 Symmetry

LESSON 18 Whole numbers: Addition and subtraction (4-digit whole numbers) LESSON 19 Whole numbers: Division (3-digit whole numbers by 1-digit whole number) Revision: Use the CAMI programme TOTAL

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6 hours

2 hours 4 hours 4 hours 4 hours

60 hours

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Facilitator’s Guide G04 ~ Mathematics

UNIT 3 TOPIC

TIME AND NOTES

Mental maths: Use the Train Your Brain Maths Grade 4 product 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)

8 hours (divided into 10 minutes every day) 6 hours 5 hours 5 hours

LESSON 23 Views of objects

2 hours

LESSON 25 Data handling

7 hours

LESSON 24 Properties of 2D shapes

4 hours

LESSON 26 Numerical patterns

LESSON 27 Whole numbers: Addition and subtraction (4-digit whole numbers)

LESSON 28 Whole numbers: Multiplication (2-digit whole numbers with 2-digit whole numbers) LESSON 29 Number sentences LESSON 30 Transformations

4 hours 4 hours 5 hours 3 hours 3 hours

Revision: Use the CAMI programme

4 hours

TOTAL

60 hours

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Facilitator’s Guide G04 ~ Mathematics

UNIT 4 TOPIC

TIME AND NOTES

Mental maths: Use the Train Your Brain Maths Grade 4 product

LESSON 31 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)

7 hours (divided into 10 minutes every day) 5 hours

LESSON 32 Mass

6 hours

LESSON 34 Common fractions

5 hours

LESSON 33 Properties of 3D objects

4 hours

LESSON 35 Whole numbers: Division (3-digit whole numbers by 1-digit whole number) LESSON 36 Perimeter, surface area and volume LESSON 37 Position and movement

7 hours 2 hours

LESSON 38 Transformations

3 hours

LESSON 39 Geometric patterns

LESSON 40 Whole numbers: Addition and subtraction (4-digit whole numbers) LESSON 41 Probability

Revision: Use the CAMI programme

2 hours 3 hours 2 hours 4 hours

TOTAL

60 hours

Find unit 1 and 2 in study guide 1/2 and unit 3 and 4 in study guide 2/2.

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3 hours

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Facilitator’s Guide G04 ~ Mathematics

ASSESSMENT REQUIREMENTS Formal assessment tasks and tests form part of a year-long formal assessment programme.

Formal assessment tasks and tests count 75% of the final mark and the November examinations count 25%.

The formal assessment programme indicates which components must be completed in each term (this includes the activities and investigations in the study guide).

Term (Unit)

Formal assessment

1

• •

1 × assignment 1 × test

2

3

• •

1 × test 1 × project

2

• •

2

4

TOTAL • •

Number of formal assessments per term/unit

• • •

1 × test 1 × June examination 1 × assignment 1 × research 1 × November examination

Total % contribution to final mark

2

75

3

25

9

100

The June examination covers all the work in term 1 and 2 (unit 1 and 2).

The November examination covers all the work in term 3 and 4 (unit 3 and 4).

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Unit

1

Facilitator’s Guide G04 ~ Mathematics

UNIT 1 This unit covers nine lessons: Lessons 1 to 9.

The table indicates the lesson topics as well as the time you will spend on each one.

UNIT 1

TOPIC

TIME AND NOTES

Mental maths: Use the Train Your Brain Maths Grade 4 product

LESSON 1 Whole numbers: Counting, ordering, comparing and representing, and place value of digits (3-digit whole numbers) LESSON 2 Number sentences

LESSON 3 Whole numbers: Addition and subtraction (3-digit whole numbers) LESSON 4 Number patterns: Numeric patterns

LESSON 5 Whole numbers: Multiplication and division (1-digit whole number by 1-digit whole number) LESSON 6 Time

LESSON 7 Data handling

2 hours 3 hours 8 hours 4 hours 4 hours 6 hours 10 hours

LESSON 8 Properties of 2D shapes

LESSON 9 Whole numbers: • Multiply (2-digit whole numbers by 1-digit whole number) • Multiply (2-digit whole numbers by 2-digit whole numbers) • Divide (2-digit whole numbers by 1-digit whole number) Revision: Use the CAMI programme TOTAL © Optimi

8 hours (divided into 10 minutes every day)

5 hours

5 hours 5 hours

60 hours 12

Facilitator’s Guide G04 ~ Mathematics

Unit

1

LESSON 1: WHOLE NUMBERS In this lesson learners will work with different notations of numbers for the first time. It is important to ensure that learners understand notations. It lays the foundation for the language of mathematics

and if learners are already comfortable with this, it can simplify the introduction of new mathematical

concepts. In this lesson, learners will work with whole numbers and do the following: • count • order • compare • represent • indicate place value (which is very important for the calculations that will be done later in the term) Do you know what a whole number is?

Whole numbers are numbers without fractions or decimals. Whole numbers are always positive and never negative. Remember: 0 is also a whole number.

Learners were introduced to whole numbers in Grade 3, even if they did not necessarily call them whole numbers. Ensure that learners know that a whole number is not a fraction. Different games may be used to reinforce this concept.

Example Write down different numbers, including fractions and whole numbers. Learners close their eyes and randomly point to a place on the page. They identify the number they chose as a whole number or not.

Examples of whole numbers {0; 1; 2; 3; 4; 5; 6; ...}

If numbers such as the above are placed in curly brackets { }, we call it a set of numbers.

This means that {0; 1; 2; 3; 4; 5; 6; ...} is a set of whole numbers.

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Unit

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Facilitator’s Guide G04 ~ Mathematics

Study the numbers in the table and circle the whole numbers.

-

15

5

0,9

101

10

24

-24

0

3

-4,1

-2

13 9

7

11 198 4

In this lesson, you will do the following with whole numbers: • count • order • compare • represent • indicate place value

Counting with whole numbers

It is very important that the learners count every day – both on (forwards) and back (backwards). In the beginning, learners may count with a 100 chart, but when they have completed the lesson, they must be able to count without any help. (See the 100 chart at the back of this facilitator’s guide.)

Counting must not only be seen as oral counting – learners must understand the calculations that are happening to count on or back.

Learners may use the following to count: •

countable objects (marbles, balls, beans, beads, etc.)

•

rows or diagrams, for example:

• •

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an abacus (available at any educational or plastics shop) number charts or tables

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Facilitator’s Guide G04 ~ Mathematics

Unit

1

In Grade 3 you learnt how to count with whole numbers.

Do you still remember how to count in 2s?

Let’s revise counting in 2s.

When you count in 2s, always add 2 to the previous number to get the next number.

+2

2

4

+2

6

+2

+2

8

10

+2

12

You can start with any number.

Study the numbers. Do you see that you can start at any number and count in whole numbers?

+2

63

65

+2

67

+2

+2

69

71

+2

73

In the above examples, you counted on or forwards.

Using whole numbers, you can also count back or backwards.

Study the following numbers and complete the missing numbers.

Count back in 3s.

–3

53

–3

50

–3

47

–3

–3

41

44

–3

38

–3

35

32

Now that your memory has been refreshed, you can apply what you have learnt.

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Unit

1

Facilitator’s Guide G04 ~ Mathematics

ACTIVITY 1 1.

2.

Write the set of whole numbers between 915 and 921. {916; 917; 918; 919; 920}

Indicate whether the numbers are whole numbers. Colour the correct circle.

Numbers

Whole number: yes or no?

658 14,3 53 3 1 412 3.

Study the number lines. You are not told what number to count with, nor whether you are counting on or back. Complete the number lines.

96;

101;

106;

111

...

3.2

416

413;

410;

407;

...

8;

108;

208

308;

...

3.4

12;

9;

6

3;

0

10;

35;

60;

85;

110

3.1

3.3

3.5

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Facilitator’s Guide G04 ~ Mathematics

4.

1

Unit

Andrew, Sibongile and Timmy like to play with marbles. They keep their marbles in bags.

Andrew’s bag can hold 10 marbles. Sibongile’s bag can hold 25 marbles. Timmy’s bag can only hold 3 marbles.

Look at the following example and count in 10s, 25s and 3s to determine how many marbles each child has.

Child

5.

Number of bags

Number of marbles

Andrew

30

Sibongile

25

Timmy

27

Complete the flow charts.

5.1

+ 50

81

+ 50

131

+ 50

181 + 50

31

231 5.2

– 25

387

– 25

362

– 25

337 – 25

412

312

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Unit

1

Facilitator’s Guide G04 ~ Mathematics

After each lesson learners must complete a self-assessment of the completed lesson. You may use the self-assessment to determine whether learners need additional help in the specific lesson, and to address the gap immediately. You may also use the self-assessment to plan enrichment activities. When learners have mastered each lesson, additional enrichment will still be hugely beneficial.

Self-assessment Do the learners understand the work? Let them colour the faces that show what they can do.

COUNTING IN WHOLE NUMBERS Requirements

Can the learners do it?

I can count on and back in 2s.

I can count on and back in 3s.

I can count on and back in 5s.

I can count on and back in 10s.

I can count on and back in 25s.

I can count on and back in 50s.

I can count on and back in 100s.

I can do all of the above up to the number 1 000.

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Facilitator’s Guide G04 ~ Mathematics

Unit

1

Ordering whole numbers Ordering means to arrange or organise numbers.

order = arrange

We can order or arrange numbers in different ways:

from GREAT to small OR

from small to GREAT

Study the number set.

{25; 2; 537; 119; 65} Arrange the numbers from great to small.

Step 1:

Choose the greatest number and write it down first.

The greatest number in this set is Step 2:

537.

Now cross out the greatest number in the number set.

{25; 2; 537; 119; 65}

You can no longer choose the number 537.

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Unit

Step 3:

1

Facilitator’s Guide G04 ~ Mathematics

From the remaining numbers, choose the greatest number and write it next to 537.

537; 119

Step 4:

Repeat steps 2 and 3 until you have crossed out all of the numbers.

When you are done, the set of numbers must look as follows:

{537; 119; 65; 25; 2} You have arranged the number set from greatest to smallest.

Can you arrange the following number set from small to great?

{913; 902; 35; 11; 1} Tip: Start by choosing the smallest number, not the greatest one.

Write your answer in the box below.

1; 11; 35; 902; 913

ACTIVITY 2 1.

Arrange the numbers from small to great.

Question

1.1

321 645 256 782 127

127; 256; 321; 645; 782

1.4

65 34 12 47 71

12; 34; 47; 65; 71

1.2 1.3 2.

Answer

1.5

56 72 201 114 98

56; 72; 98; 114; 201

527 471 298 638 138

138; 298; 471; 527; 638

147; 274; 355; 568; 724

724 568 147 274 355

Arrange the numbers from great to small.

Question

2.1

620 541 635 514 623

635; 623; 620; 541; 514

2.4

58 39 44 28 13

58; 44; 39; 28; 13

2.2 2.3 2.5 © Optimi

Answer

36 48 21 65 57

65; 57; 48; 36; 21

457 325 147 471 352

471; 457; 352; 325; 147

116; 110; 98; 76; 53

116 98 53 76 110

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Facilitator’s Guide G04 ~ Mathematics

3.

Build and arrange the numbers.

Question

3.1 3.2 3.3 3.4 3.5

1

Unit

Answer

Write down the numbers you can build with 1, 4 and 5 and arrange them from great to small.

Write down the numbers you can build with 7, 2 and 9 and arrange them from small to great.

Write down the numbers you can build with 8, 1 and 6 and arrange them from great to small.

Write down the numbers you can build with 9, 1 and 2 and arrange them from small to great.

541; 514; 451; 415; 154; 145

279; 297; 729; 792; 927; 972

861; 816; 681; 618; 186; 168

129; 192; 219; 291; 912; 921

Write down the numbers you can build with 9, 1 and 1 and arrange them from great to small.

911; 191; 119

Self-assessment Do the learners understand the work? Let them colour the faces that show what they can do.

ORDERING WHOLE NUMBERS Requirements

Can the learners do it?

I can arrange number sets from great to small.

I can arrange number sets from small to great.

I can build and arrange different numbers.

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Unit

1

Facilitator’s Guide G04 ~ Mathematics

Place value Place value is extremely important for developing number concept. If learners’ number concept is not

firmly established, they will find calculations difficult. Later in the term, calculations will already require a firm grasp of place value, which is why learners must spend enough time on this topic. Ensure that learners understand the concept really well.

Use additional resources to ensure the proper comprehension of place value, such as: • • •

100 charts

Flash cards

Dienes cubes

Various methods are covered in this topic. Learners must be aware of all the different methods, but they

are only required to use one method during assessment. The facilitator and learners together decide which method will work best.

Visit goo.gl/nBhGsR to find additional activities.

Place value helps us to determine the value of a digit.

Our number system (the numbers that we work with) contains digits from 0 to 9 only.

What do we do when we must work with numbers greater than 9?

We use place value to indicate when we are working with numbers greater than 9.

It means that the value of a digit is determined by its place or position in a number.

When we work with place value, we can think of each value as a box with high walls.

Hundreds

Tens

Units

In each box you can find the digits 0 to 9. As soon as the number becomes greater than 9, it jumps over the wall into the next box. © Optimi

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Facilitator’s Guide G04 ~ Mathematics

Unit

Hundreds

Tens

1

Units 7

The 7 in the Units box means that there are 7 Units. We can also write it as 7 x 1.

Can you see that there are no numbers in the Tens and Hundreds boxes?

This means that there are 0 x Tens and 0 x Hundreds in this number.

Let’s see what happens with a number greater than 9.

Hundreds

Tens

Units 13

There may only be one number in each box, but now there is a 1 and a 3 in the Units box.

What does the 13 mean? It consists of 10 + 3.

The 3 is in the Units box and it means 3 x 1, which is shown as 3.

The 10 jumps over the wall into the Tens box.

You CANNOT carry the full 10 across, because it then indicates 10 x Tens, which means 10 x 10, which equals 100. Therefore, only the 1 jumps across.

Hundreds

Tens 10

Units 3

1 × Tens means 1 × 10 = 10 If you want to indicate the place value of 13, it will look like this:

Hundreds

Tens 1

The same happens when there is a number greater than 9 in the Tens box.

Hundreds

Tens 84

23

Units 3

Units 2

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Unit

1

Facilitator’s Guide G04 ~ Mathematics

Since the 8 in the Tens box indicates 800, it must jump over the wall into the Hundreds box.

It means 8 x 100 = 800.

Hundreds 8

Tens 4

Units 2

It is not always as easy or practical to draw boxes to determine place value and it can take a lot of time.

There are three other methods to do the same without drawing boxes.

Use the number 534.

Write down where each digit would go, without drawing the blocks.

METHOD 1

5 Hundreds + 3 Tens + 4 Units METHOD 2 5 × 100 + 3 × 10 + 4 × 1 METHOD 3 500 + 30 + 4 These three methods are called expanded notation. When we write a number in expanded notation, we break down a number to show the place value of each digit.

Expanded notation ‘shows’ place value.

ACTIVITY 3 1.

Write the number names.

Question

1.1

495

1.4

751

1.2 1.3 1.5 © Optimi

122 463 99

Answer Four hundred and ninety-five

One hundred and twenty-two Four hundred and sixty-three Seven hundred and fifty-one Ninety-nine

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Facilitator’s Guide G04 ~ Mathematics

2.

Unit

Write the numbers in the correct column in the place value table.

Question

2.1

123

2.2

395

2.3

645

2.4

21

Answer

H

T

U

1

2

3

H

T

U

3

9

5

H

T

U

6

4

5

H

T

U

2

1

T

U

H 2.5 3.

1

4

4

Write the numbers in expanded notation. Use all three methods.

Question

Answer

METHOD 1: 2H + 6T + 5U 3.1

265

METHOD 2: 2 × 100 + 6 × 10 + 5 × 1 METHOD 3: 200 + 60 + 5 METHOD 1: 1H + 2T + 3U

3.2

123

METHOD 2: 1 × 100 + 2 × 10 + 3 × 1 METHOD 3: 100 + 20 + 3 METHOD 1: 3H + 9T + 5U

3.3

395

METHOD 2: 3 × 100 + 9 × 10 + 5 × 1 METHOD 3: 300 + 90 + 5

25

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Unit

1

Facilitator’s Guide G04 ~ Mathematics

METHOD 1: 2T + 7U 3.4

27

METHOD 2: 2 × 10 + 7 × 1 METHOD 3: 20 +7 METHOD 1: 3U

3.5

4.

METHOD 2: 3×1 METHOD 3: 3

Give the value of the underlined numbers.

Question

Answer

4.1

196

6

4.4

842

4.2 4.3 4.5

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3

542

500

154

50

90

92

800

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Facilitator’s Guide G04 ~ Mathematics

5.

Unit

1

Board game: Roll the dice and move the correct number of squares along on the board. Say the number of the block on which you land out loud. If you cannot say the number, move one block back. The first person to reach the finish block wins.

Start Finish 27

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Unit

1

Facilitator’s Guide G04 ~ Mathematics

Self-assessment Do the learners understand the work? Let them colour the faces that show what they can do.

PLACE VALUE Requirements

Can the learners do it?

I can break down numbers into Hundreds, Tens and Units.

I can give number names.

I can indicate place value.

I can do expanded notation (all three methods).

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Facilitator’s Guide G04 ~ Mathematics

Unit

1

Comparing whole numbers Use different sized physical objects to explain the concept of number comparison. You may also use place value – for example, 10 and 100 – to explain number comparison.

Additional resources: •

100 charts

•

visit goo.gl/tVXMwP to find additional exercises and activities

• •

physical objects flash cards

When we compare numbers, we study the numbers to determine what is asked.

When you compare numbers, you must look at the value of the digits.

Compare the following numbers: Circle the greatest number.

932 923 933

You already know how to compare numbers because you can order numbers. You also compare numbers when you complete sequences on number charts or number lines.

Example: Which whole numbers do the letters A and B represent?

25

A

29

31

B

Answer: A = 27 | B = 33 Example: Fill in the missing numbers on the number chart.

Answer:

29

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