Intermediate Phase Grade 5 • 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
2005-E-MAM-FG01
946400
5
Mathematics Facilitator’s guide
CAPS aligned
M Vos L Young
2005-E-MAM-FG01
Í4%È-E-MAM-FG01#Î
Grade 5
Facilitator’s Guide G05 ~ Mathematics
Contents LESSON ELEMENTS.................................................................................................................................... 1 INTRODUCTION.......................................................................................................................................... 2 TIME MANAGEMENT................................................................................................................................. 2 ASSESSMENT REQUIREMENTS............................................................................................................... 8 YEAR PLAN................................................................................................................................................... 9 UNIT 1..........................................................................................................................................................13 LESSON 1: WHOLE NUMBERS...............................................................................................................14 Counting with whole numbers...................................................................................................................15 ACTIVITY 1..............................................................................................................................................17 Ordering whole numbers..............................................................................................................................19 ACTIVITY 2..............................................................................................................................................21 Place value...........................................................................................................................................................22 ACTIVITY 3..............................................................................................................................................25 Comparing whole numbers..........................................................................................................................28 ACTIVITY 4..............................................................................................................................................29 Representing whole numbers.....................................................................................................................30 ACTIVITY 5..............................................................................................................................................31 LESSON 2: NUMBER SENTENCES.........................................................................................................32 ACTIVITY 6..............................................................................................................................................34 ACTIVITY 7..............................................................................................................................................35 ACTIVITY 8..............................................................................................................................................36 Pairs of equivalent number sentences....................................................................................................38 ACTIVITY 9..............................................................................................................................................39 Addition and subtraction techniques......................................................................................................40 Commutative property of addition...........................................................................................................40 Associative property of addition...............................................................................................................41 ACTIVITY 10............................................................................................................................................42 Order of subtraction........................................................................................................................................43 ACTIVITY 11............................................................................................................................................44 LESSON 3: WHOLE NUMBERS...............................................................................................................45 Addition with whole numbers....................................................................................................................45 ACTIVITY 12............................................................................................................................................45 ACTIVITY 13............................................................................................................................................47 Subtraction of whole numbers...................................................................................................................50 ACTIVITY 14............................................................................................................................................52 Estimation...........................................................................................................................................................56 ACTIVITY 15............................................................................................................................................58 Rounding..............................................................................................................................................................60 ACTIVITY 16............................................................................................................................................63 ACTIVITY 17............................................................................................................................................63 Compensation....................................................................................................................................................64 Doubling and halving......................................................................................................................................64 i
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Facilitator’s Guide G05 ~ Mathematics
ACTIVITY 18............................................................................................................................................65 ACTIVITY 19............................................................................................................................................67 Testing calculations with inverse operations.......................................................................................69 ACTIVITY 20............................................................................................................................................71
LESSON 4: NUMBER PATTERNS (Numeric patterns)....................................................................73 ACTIVITY 21............................................................................................................................................74 Input and output values................................................................................................................................75 ACTIVITY 22............................................................................................................................................75 ACTIVITY 23............................................................................................................................................77 ACTIVITY 24............................................................................................................................................79 The associative property of multiplication...........................................................................................80 LESSON 5: WHOLE NUMBERS (Multiplication and division).....................................................82 Multiplication.....................................................................................................................................................82 ACTIVITY 25............................................................................................................................................89 Division.................................................................................................................................................................90 ACTIVITY 26............................................................................................................................................92
LESSON 6: TIME........................................................................................................................................93 ACTIVITY 27............................................................................................................................................98 ACTIVITY 28......................................................................................................................................... 101 LESSON 7: DATA HANDLING...............................................................................................................105 ACTIVITY 29......................................................................................................................................... 109 LESSON 8: PROPERTIES OF 2D SHAPES.........................................................................................113 ACTIVITY 30......................................................................................................................................... 118 LESSON 9: CAPACITY AND VOLUME ................................................................................................120 ACTIVITY 31......................................................................................................................................... 124
UNIT 2.......................................................................................................................................................128 LESSON 10: WHOLE NUMBERS Counting, ordering, comparing and representing (6-digit whole numbers)....................................................................................................................................129 ACTIVITY 32......................................................................................................................................... 130 LESSON 11: WHOLE NUMBERS Addition and subtraction (5-digit whole numbers)..... 135 ACTIVITY 33......................................................................................................................................... 137 LESSON 12: COMMON FRACTIONS...................................................................................................145 ACTIVITY 34......................................................................................................................................... 149 ACTIVITY 35......................................................................................................................................... 154 LESSON 13: LENGTH.............................................................................................................................158 ACTIVITY 36......................................................................................................................................... 161 © Impaq
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Facilitator’s Guide G05 ~ Mathematics
LESSON 14: WHOLE NUMBERS Multiplication (3-digit whole numbers by 2-digit whole numbers).................................................................................................................................................166 ACTIVITY 37......................................................................................................................................... 168 LESSON 15: PROPERTIES OF 3D OBJECTS.....................................................................................170 ACTIVITY 38......................................................................................................................................... 174 LESSON 16: GEOMETRIC PATTERNS...............................................................................................177 ACTIVITY 39......................................................................................................................................... 179 LESSON 17: SYMMETRY......................................................................................................................181 ACTIVITY 40......................................................................................................................................... 183
LESSON 18: WHOLE NUMBERS Division (3-digit whole numbers by 2-digit whole numbers)................................................................................................................................................. 186 ACTIVITY 41......................................................................................................................................... 189 UNIT 3.......................................................................................................................................................192 LESSON 19: COMMON FRACTIONS...................................................................................................193 ACTIVITY 42......................................................................................................................................... 194 LESSON 20: MASS..................................................................................................................................198 ACTIVITY 43......................................................................................................................................... 201
LESSON 21: WHOLE NUMBERS Counting, ordering, comparing and representing, and place value of digits (6-digit whole numbers)............................................................................204 ACTIVITY 44......................................................................................................................................... 204 LESSON 22: WHOLE NUMBERS (Addition and subtraction)...................................................209 ACTIVITY 45......................................................................................................................................... 210 LESSON 23: VIEWS OF OBJECTS........................................................................................................215 ACTIVITY 46......................................................................................................................................... 217 LESSON 24: PROPERTIES OF 2D SHAPES.......................................................................................220 ACTIVITY 47......................................................................................................................................... 221 LESSON 25: TRANSFORMATIONS.....................................................................................................224 ACTIVITY 48......................................................................................................................................... 229 LESSON 26: TEMPERATURE...............................................................................................................233 ACTIVITY 49......................................................................................................................................... 235 LESSON 27: DATA HANDLING............................................................................................................238 ACTIVITY 50......................................................................................................................................... 239
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Facilitator’s Guide G05 ~ Mathematics
LESSON 28: NUMBER PATTERNS (Numerical patterns)...........................................................246 Input and output values............................................................................................................................. 247 The associative property of multiplication........................................................................................ 248 Types of number sequences..................................................................................................................... 251 ACTIVITY 51......................................................................................................................................... 252
LESSON 29: WHOLE NUMBERS Multiplication (3-digit whole numbers by 2-digit whole numbers)..............................................................................................................................................................255 ACTIVITY 52......................................................................................................................................... 255 UNIT 4.......................................................................................................................................................257 LESSON 30: WHOLE NUMBERS.........................................................................................................258 ACTIVITY 53......................................................................................................................................... 258 LESSON 31: WHOLE NUMBERS Addition and subtraction (5-digit whole numbers)..... 262 ACTIVITY 54......................................................................................................................................... 263 LESSON 32: PROPERTIES OF 3D OBJECTS.....................................................................................271 ACTIVITY 55......................................................................................................................................... 274 LESSON 33: COMMON FRACTIONS...................................................................................................278 ACTIVITY 56......................................................................................................................................... 279
LESSON 34: WHOLE NUMBERS Division (4-digit whole numbers by 2-digit whole numbers).................................................................................................................................................282 ACTIVITY 57......................................................................................................................................... 285 LESSON 35: PERIMETER, SURFACE AREA AND VOLUME .........................................................286 Perimeter.......................................................................................................................................................... 287 ACTIVITY 58......................................................................................................................................... 292 Surface area..................................................................................................................................................... 294 ACTIVITY 59......................................................................................................................................... 295 Volume............................................................................................................................................................... 296 LESSON 36: POSITION AND DISPLACEMENT................................................................................298 ACTIVITY 60......................................................................................................................................... 300 LESSON 37: TRANSFORMATIONS.....................................................................................................302 ACTIVITY 61......................................................................................................................................... 303 LESSON 38: GEOMETRIC PATTERNS...............................................................................................308 ACTIVITY 62......................................................................................................................................... 309 LESSON 39: NUMBER SENTENCES...................................................................................................311 ACTIVITY 63......................................................................................................................................... 312
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Facilitator’s Guide G05 ~ Mathematics
LESSON 40: PROBABILITY..................................................................................................................315 ACTIVITY 64......................................................................................................................................... 318 References...............................................................................................................................................320
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Facilitator’s Guide G05 ~ Mathematics
LESSON ELEMENTS The guide contains various lesson elements. Each element is important for the learning process and indicates the skill the learner must master. ICON
LESSON ELEMENT
ICON
LESSON ELEMENT
Think for yourself
Take note! Important
Tips
Self-assessment
Research
Activity
Study
Did you know?
New concept or definition
Tip
Remember/Revise
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Facilitator’s Guide G05 ~ Mathematics
INTRODUCTION By now, Grade 5 learners are familiar with the concept of self-study. The study guide and facilitator’s guide will help learners and facilitators to navigate the process and lay the foundation for future academic success. However, the facilitator’s role in supporting learners remains crucial to help build their confidence and master new challenges.
The study guide has a friendly and informal tone to involve learners and make the subject accessible and interesting. It contains theory, activities and research elements. It is important to complete all the activities in the study guide to help learners understand and apply new knowledge. There is an individual self-assessment after each lesson. Use this to determine whether a learner still requires help with a particular lesson or concept and to find a solution as soon as possible. The assessments can also be used to plan enrichment activities that can be completed once learners have mastered the concepts in each lesson. With the help of the facilitator’s guide, the facilitator can support learners so the theory of mathematics is well established at the end of each lesson. Many of the lessons have a practical component and there are recommended for these in the guide. Both guides are divided into four units. Aim to complete one unit per term.
Do 10 minutes of mental arithmetic every day. Use the supplementary Train Your Brain Maths Grade 5 product. The CAMI programme (www.camiweb.com) is recommended for revision and additional practise. The products include: • 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 5 (for mental arithmetic)
TIME MANAGEMENT
The time allocation per topic is a guideline and may be adapted according to the learners’ pace. Some topics are covered extensively but have shorter time allocation, for example, whole numbers in term 1. The learners studied whole numbers in Grade 4, and only do revision in Grade 5.
However, the topic is covered comprehensively to ensure the information is readily available should the facilitator identify gaps in the learners’ knowledge while doing revision. If this is the case, use the opportunity to repeat the work. Adjust the time allocation based on the learners’ mastery of the topic. From term 2, the learners are referred to previous lessons. The time allocation includes the revision to be completed before proceeding with the lesson. Do not go on to the next lesson or topic before the learners have a thorough understanding of the current topic, even if you exceed the recommended time. Continually adjust the time allocation to address the learners’ needs. © Impaq
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Facilitator’s Guide G05 ~ Mathematics
Keep in mind though that the required lessons must be completed before tests or exams can be attempted.
Learners must spend six hours per week on mathematics. This does not include all activities, assessments, and examinations. If learners are working at a slower pace, make the necessary adjustments to allow them to complete all the work in time.
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Facilitator’s Guide G05 ~ Mathematics
Guidelines for time allocation per topic UNIT 1 TOPIC
TIME AND NOTES
Mental maths: Use Train Your Brain Maths Grade 5
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)
8 hours (divided into 10 minutes each day) 2 hours 3 hours 5 hours
LESSON 4 Number patterns (Numeric patterns)
4 hours
LESSON 5 Whole numbers (Multiplication and division)
6 hours
LESSON 6 Time
6 hours
LESSON 7 Data handling
10 hours
LESSON 8 Properties of 2D shapes
7 hours
LESSON 9 Capacity and volume
5 hours
Revision: Use the CAMI programme
4 hours
TOTAL
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60 hours
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Facilitator’s Guide G05 ~ Mathematics
UNIT 2 TOPIC
TIME AND NOTES
Mental maths: Use Train Your Brain Maths Grade 5
LESSON 10 Whole numbers: Counting, ordering, comparing, and representing, and place value of digits (4-digit whole numbers)
7 hours (divided into 10 minutes each day) 1 hour
LESSON 11 Whole numbers: Addition and subtraction (5-digit whole numbers)
5 hours
LESSON 13 Length
6 hours
LESSON 12 Common fractions
LESSON 14 Whole numbers: Multiplication (3-digit whole numbers by 2-digit whole numbers) LESSON 15 Properties of 3D objects LESSON 16 Geometric patterns
5 hours
7 hours 6 hours 4 hours
LESSON 17 Symmetry
LESSON 18 Whole numbers: Division (4-digit whole numbers by 2-digit whole numbers) Revision: Use the CAMI programme
Assessment – examinations on all subjects
2 hours 8 hours 3 hours 6 hours
TOTAL
56 hours
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Facilitator’s Guide G05 ~ Mathematics
UNIT 3 TOPIC
TIME AND NOTES 8 hours (divided into 10 minutes each day)
Mental maths: Use Train Your Brain Maths Grade 5 LESSON 19 Common fractions
5 hours
LESSON 20 Mass
LESSON 21 Whole numbers: Counting, ordering, comparing and representing and place value of digits (6-digit whole numbers) LESSON 22 Whole numbers: Addition and subtraction LESSON 23 Views of objects
1 hours 5 hours 3 hours
LESSON 24 Properties of 2D shapes
4 hours
LESSON 25 Transformations
3 hours
LESSON 26 Temperature
2 hours
LESSON 27 Data handling
9 hours
LESSON 28 Number patterns
LESSON 29 Whole numbers: Multiplication (3-digit whole numbers by 2-digit whole numbers) Revision: Use the CAMI programme TOTAL
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5 hours
5 hours 7 hours 3 hours
60 hours
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Facilitator’s Guide G05 ~ Mathematics
UNIT 4 TOPIC
TIME AND NOTES
Mental maths: Use Train Your Brain Maths Grade 5
LESSON 30 Whole numbers: Counting, ordering, comparing and representing, and place value of digits (6-digit whole numbers)
7 hours (divided into 10 minutes each day) 1 hour
LESSON 31 Whole numbers: Addition and subtraction (5-digit whole numbers)
5 hours
LESSON 33 Common fractions
5 hours
LESSON 32 Properties of 3D objects
LESSON 34 Whole numbers: Division (4-digit whole numbers by 2-digit whole numbers) LESSON 35 Perimeter, surface area and volume LESSON 36 Position and movement
5 hours
7 hours 7 hours 2 hours
LESSON 37 Transformations
4 hours
LESSON 38 Geometric patterns
2 hours
LESSON 39 Number sentences
3 hours
LESSON 40 Probability
2 hours
Revision: Use the CAMI programme
4 hours
Assessment – examinations on all subjects
6 hours
TOTAL
55 hours
Find units 1 and 2 in study guide 1/2 and units 3 and 4 in study guide 2/2.
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Facilitator’s Guide G05 ~ Mathematics
ASSESSMENT REQUIREMENTS Formal assessment tasks and tests are part of the year-long formal assessment programme. Refer to the portfolio book or my.Impaq for the requirements.
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)
Number of formal assessments per term/unit
Formal assessment
1
• •
1 × assignment 1 × test
2
3
• •
1 × test 1 × project
2
2
4 • •
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• • • • •
1 × test 1 × June examination 1 × assignment 1 × research 1 × November examination
TOTAL
Total % contribution to the final mark
2
75
3
25
9
The June examination covers all the work in Terms 1 and 2 (units 1 and 2). The November examination covers all the work in Terms 3 and 4 (units 3 and 4).
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Facilitator’s Guide G05 ~ Mathematics
YEAR PLAN UNIT 1 TOPIC
DATE
DATE
STARTED
COMPLETED
Mental maths: Use Train Your Brain Maths Grade 5 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) LESSON 4 Number patterns (Numeric patterns) LESSON 5 Whole numbers (Multiplication and division) LESSON 6 Time LESSON 7 Data handling LESSON 8 Properties of 2D shapes LESSON 9 Capacity and volume Revision: Use the CAMI programme 9
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Facilitator’s Guide G05 ~ Mathematics
UNIT 2 TOPIC
Mental maths: Use Train Your Brain Maths Grade 5 LESSON 10 Whole numbers: Counting, ordering, comparing, and representing, and place value of digits (4-digit whole numbers) LESSON 11 Whole numbers: Addition and subtraction (5-digit whole numbers) LESSON 12 Common fractions LESSON 13 Length
LESSON 14 Whole numbers: Multiplication (3-digit whole numbers by 2-digit whole numbers) LESSON 15 Properties of 3D objects LESSON 16 Geometric patterns LESSON 17 Symmetry
LESSON 18 Whole numbers: Division (4-digit whole numbers by 2-digit whole numbers) Revision: Use the CAMI programme Assessment – examinations on all subjects © Impaq
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DATE
DATE
STARTED
COMPLETEDI
Facilitator’s Guide G05 ~ Mathematics
UNIT 3 TOPIC
DATE
DATE
STARTED
COMPLETED
Mental maths: Use Train Your Brain Maths Grade 5 LESSON 19 Common fractions LESSON 20 Mass
LESSON 21 Whole numbers: Counting, ordering, comparing and representing and place value of digits (6-digit whole numbers) LESSON 22 Whole numbers: Addition and subtraction LESSON 23 Views of objects
LESSON 24 Properties of 2D shapes LESSON 25 Transformations LESSON 26 Temperature
LESSON 27 Data handling
LESSON 28 Number patterns
LESSON 29 Whole numbers: Multiplication (3-digit whole numbers by 2-digit whole numbers) Revision: Use the CAMI programme
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Facilitator’s Guide G05 ~ Mathematics
UNIT 4 TOPIC Mental maths: Use Train Your Brain Maths Grade 5
LESSON 30 Whole numbers: Counting, ordering, comparing and representing, and place value of digits (6-digit whole numbers) LESSON 31 Whole numbers: Addition and subtraction (5-digit whole numbers) LESSON 32 Properties of 3D objects LESSON 33 Common fractions
LESSON 34 Whole numbers: Division (4-digit whole numbers by 2-digit whole numbers) LESSON 35 Perimeter, surface area and volume LESSON 36 Position and movement LESSON 37 Transformations
LESSON 38 Geometric patterns LESSON 39 Number sentences LESSON 40 Probability
Revision: Use the CAMI programme
Assessment – examinations on all subjects © Impaq
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DATE
DATE
STARTED
COMPLETED
Facilitator’s Guide G05 ~ Mathematics
1
Unit
UNIT 1 This unit covers lessons 1 to 9.
UNIT 1
TOPIC
TIME AND NOTES
Mental maths: Use Train Your Brain Maths Grade 5
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)
8 hours (divided into 10 minutes each day) 2 hours 3 hours 5 hours
LESSON 4 Number patterns (Numeric patterns)
4 hours
LESSON 5 Whole numbers (Multiplication and division)
6 hours
LESSON 6 Time
6 hours
LESSON 7 Data handling
10 hours
LESSON 8 Properties of 2D shapes
7 hours
LESSON 9 Capacity and volume
5 hours
Revision: Use the CAMI programme
4 hours
TOTAL
60 hours
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Unit
1
Facilitator’s Guide G05 ~ Mathematics
LESSON 1: WHOLE NUMBERS In this lesson, we look at whole numbers, which learners studied in Grade 4. Use this lesson for revision. You will see the time allocation is only 2 hours. If learners do not understand the content yet, you may spend more time as needed.
Revise the different notations of numbers. Make sure learners understand notations as it lays the foundation for the language of mathematics. If they are already comfortable with this, it can simplify the introduction of new concepts.
Learners will: • count • order • compare • represent • indicate place value (which is important for calculations later in the term)
Make sure learners have mastered the concepts before they start working with larger numbers in unit 2.
Do you still remember what a whole number is?
Whole numbers do not have 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 Grades 3 and 4. Make sure they know a whole number is not a fraction. Use different games 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; ...}
1 2
0,5
If numbers are placed in curly brackets { }, we call it a set of numbers. © Impaq
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Facilitator’s Guide G05 ~ Mathematics
Unit
1
This means that {0; 1; 2; 3; 4; 5; 6; ...} is a set of whole numbers. Learners must circle the whole numbers in the table.
-
33
15
1,9
153
10
100
-650
0
85
-8,98
-7
56 11
4
4 6 124 99
Counting with whole numbers Learners must count every day – both on (forwards) and back (backwards). Learners may use any of these to count: • countable objects (marbles, balls, beans, beads, etc.) • an abacus (available at any educational or plastics shop) • number charts or tables • rows or diagrams, for example:
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Unit
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Facilitator’s Guide G05 ~ Mathematics
In Grades 3 and 4, 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
+2
4
6
+2
+2
8
+2
10
12
You may start with any number. Study the numbers. Do you see you can start at any number and count in whole numbers?
+2
63
+2
65
67
+2
+2
69
+2
71
73
In the above examples, you counted on or forwards.
Using whole numbers, you can also count back or backwards. Study the numbers below and complete the missing numbers. Count back in 3s.
–3
53
–3
50
–3
47
–3
–3
41
44
–3
38
–3
32
35
You will now count with bigger numbers. Study the numbers and complete the missing numbers. You must determine whether you need to count on or back, and by how many. + 25
5 430
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+ 25
5 455
5 480
5 505
5 530
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5 555
5 580
5 605
5 630
Facilitator’s Guide G05 ~ Mathematics
Unit
Complete the missing numbers.
– 50
9 999
– 50
9 949
1
– 50
9 899
9 849
9 799
9 749
9 699
9 649
Let’s apply what you have learnt.
ACTIVITY 1 1.
Write the set of whole numbers between 1 915 and 1 921. {1 916; 1 917; 1 918; 1 919; 1 920} Point out to learners that the question requires the set of whole numbers between 1 915 and 1 921. Therefore, 1 915 and 1 921 are not included in the set.
2.
Indicate whether the numbers are whole numbers. Colour the correct circle. Numbers
Numbers
2.1
9 658
2.4
1
2.2
1 414,3
2.5
8 123
2.3 3.1 3.2 3.3 3.4 3.5
Whole number or not?
Whole number or not?
5 013 3
8 800; 8 650; 8 500; 8 350; ... Letter: P 1 000; 1 010; 1 020; 1 030; ... Letter: A 2 375; 4 750; 9 500; ... Letter: R 5 000; 6 000; 7 000 ... Letter: I 8 000; 9 000; 10 000; 11 000; ... Letter: S
The world’s largest treasure chest is in PARIS.
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Unit
4.
Facilitator’s Guide G05 ~ Mathematics
The Grade 5s made slime in their Life Skills class. Three learners put beads in their slime. Lucinda put 10 beads in each container, Marli put 150 beads in her containers and Sibongile put 50 beads in each of her containers. Study the representation and count in 2s, 3s, 5s, 10s, 25s or 50s to complete the table. Lucinda = 6 × 10 = 60 Marli = each container must contain 15 beads Sibongile = 5 × 50 = 250 *Learners may also only count in 10s or 50s in this question.
5.
Complete the flow charts. 5.1
– 10
3 180
– 10
3 170
– 10
3 160
– 10
3 190
3 150 5.2
+ 25
437
462
+ 25
+ 25
487
+ 25
412
512
After each lesson, learners complete a self-assessment. You may use the self-assessment to determine whether they need additional help in the specific lesson and to find a solution immediately. You may also use the self-assessment to plan enrichment activities. Even when learners have mastered each lesson, additional enrichment will still be beneficial.
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Facilitator’s Guide G05 ~ Mathematics
Unit
1
Self-assessment Do the learners understand the work? Let them colour the faces that show what they can do. COUNTING WITH 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 the above up to 10 000.
Ordering whole numbers In Grade 4, learners learnt how to arrange or place numbers in a specific order. Do they still remember how it works? Briefly revise ordering whole numbers. Ordering means to arrange or organise numbers. order = arrange
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Unit
1
Facilitator’s Guide G05 ~ Mathematics
We can order or arrange numbers in different ways:
from GREAT to small OR
from small to GREAT
Study the number set: {4 952; 4 592; 5 942; 2 924} Arrange the numbers from great to small. Step 1:
Step 2:
Choose the greatest number and write it down first. The greatest number in this set is 5 942.
Now cross out the greatest number in the number set.
{4 952; 4 592; 5 942; 2 924}
Step 3:
You can no longer choose the number 5 942.
From the remaining numbers, choose the greatest number and write it next to 5 942.
5 942; 4 952
Step 4:
Now repeat steps 2 and 3 until you have crossed out all the numbers.
When you are done, the set of numbers must look like this:
{5 942; 4 952; 4 592; 2 924} You have now arranged the number set from greatest to smallest.
Can you arrange the following number set from small to great?
{5 667; 5 676; 5 766; 6 756; 6 657}
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Facilitator’s Guide G05 ~ Mathematics
Unit
1
Tip: Start by choosing the smallest number, not the greatest one. Write your answer in the box below.
5 667; 5 676; 5 766; 6 657; 6 756
ACTIVITY 2 1.
Arrange the numbers from small to great.
2.
Arrange the numbers from great to small.
3.
1.1 1.2 1.3
2 067; 2 390; 4 533; 6 511; 8 812 3 113; 5 480; 6 749; 7 100; 7 214 2 607; 3 904; 5 110; 5 332; 8 121
2.1 2.2 2.3
8 420; 5 686; 4 312; 3 733; 1 088 9 124; 4 231; 3 420; 3 398; 2 607 4 865; 4 685; 4 658; 4 586; 4 568
1.4 1.5
4 335; 4 535; 4 553; 5 343; 5 433 1 199; 1 919; 1 991; 9 119; 9 191
2.4 2.5
3 211; 3 121; 2 311; 2 131; 2 113 9 555; 5 955; 5 595; 5 559
Build and arrange the numbers. You may build any 6 numbers for each question. Learners must use the given numbers to build any six numbers. Make sure they follow the criteria for each question: • Use the correct numbers • Build 6 numbers • Arrange them correctly
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 G05 ~ Mathematics
Place value Place value is crucial 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 they understand the concept well. Use additional resources to help learners understand 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 bit.ly/2WzJEV1 for additional exercises.
Place value helps us to determine the value of a digit. Our number system (the numbers 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.
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.
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Facilitator’s Guide G05 ~ Mathematics
Unit
Hundreds
Tens
1
Units 8
The 8 in the Units box means there are 8 Units. We can also write it as 8 × 1. Can you see there are no numbers in the Tens and Hundreds boxes? This means there are 0 × Tens and 0 × Hundreds in this number. Let’s see what happens with a number greater than 9.
Hundreds
Tens
Units 18
There may only be one number in each box, but now there is a 1 and an 8 in the Units box. What does the 18 mean? It consists of 10 + 8.
The 8 is in the Units box and it means 8 × 1, which is shown as 8. The 10 jumps over the wall into the Tens box.
You CANNOT carry the full 10 across, because it then indicates 10 × Tens, which means 10 × 10 which equals 100. Therefore, only the 1 jumps across.
Hundreds
Tens
Units
10
8
1 × Tens means 1 × 10 = 10 If you want to indicate the place value of 18, it will look like this:
Hundreds
Tens
Units
1
8
The same happens when there is a number greater than 9 in the Tens box.
Hundreds
Tens
Units
86
8
23
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Unit
1
Facilitator’s Guide G05 ~ Mathematics
Since the 8 in the Tens box indicates 800, it must jump over the wall into the Hundreds box. It means 8 × 100 = 800.
Hundreds
Tens
Units
8
6
8
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 368.
Write down where each digit would go, without drawing the blocks. METHOD 1
3 Hundreds + 6 Tens + 8 Units METHOD 2 3 × 100 + 6 × 10 + 8 × 1 METHOD 3 300 + 60 + 8 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.
You will now learn more place values, namely THOUSANDS, TEN THOUSANDS and HUNDRED THOUSANDS The methods and rules you studied in Grade 4 stay the same. Study the example.
Example Write the number in expanded notation. Clearly indicate the place value by using any of the options in the revision. 859 421
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24
Facilitator’s Guide G05 ~ Mathematics
1
Unit
To make it easier, we first place each number in its box:
Hundred Thousands
8
Ten Thousands
5
Thousands
Hundreds
9
4
Tens
Units
2 1
Write down where each digit would go, without drawing the blocks.
METHOD 1
8 Hundred Thousands + 5 Ten Thousands + 9 Thousands + 4 Hundreds + 2 Tens + 1 Units METHOD 2
8 × 100 000 + 5 × 10 000 + 9 × 1 000 + 4 × 100 + 2 × 10 + 1 × 1 METHOD 3
800 000 + 50 000 + 9 000 + 400 + 20 + 1 You will now work with the THOUSANDS place value only. You will learn more about the HUNDRED THOUSANDS place value later in the year.
ACTIVITY 3 1.
Write the number names. Question
Answer
1.1
4 953
Four thousand nine hundred and fifty-three
1.3
9 463
Nine thousand four hundred and sixty-three
7 199
Seven thousand one hundred and ninety-nine
1.2 1.4 1.5
1 222
One thousand two hundred and twenty-two
2 751
Two thousand seven hundred and fifty-one
25
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Unit
2.
3.
1
Facilitator’s Guide G05 ~ Mathematics
Write the numbers in the correct column in the place value table. Question
2.1
1 023
2.2
1 392
2.3
5 100
2.4
21
2.5
6
Answer
Th
H
T
U
1
0
2
3
Th
H
T
U
1
3
9
2
Th
H
T
U
5
1
0
0
Th
H
T
U
0
0
2
1
Th
H
T
U
0
0
0
6
Write the numbers in expanded notation. Use all three methods. Question
Answer
METHOD 1: 3Th + 2H + 6T + 5U 3.1
3 265
METHOD 2: 3 × 1 000 + 2 × 100 + 6 × 10 + 5 × 1 METHOD 3: 3 000 + 200 + 60 + 5 METHOD 1: 1Th + 2T + 3U
3.2
1 023
METHOD 2: 1 × 1 000 + 2 × 10 + 3 × 1 METHOD 3: 1 000 + 20 + 3 METHOD 1: 3Th + 9H + 5T + 5U
3.3
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3 955
METHOD 2: 3 × 1 000 + 9 × 100 + 5 × 10 + 5 × 1 METHOD 3: 3 000 + 900 + 50 + 5
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