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 © Optimi
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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. © Optimi
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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 © Optimi
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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 © Optimi
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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. © Optimi
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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
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Unit
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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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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
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2.
3.
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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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METHOD 2: 3 × 1 000 + 9 × 100 + 5 × 10 + 5 × 1 METHOD 3: 3 000 + 900 + 50 + 5
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Facilitator’s Guide G05 ~ Mathematics
Unit
1
METHOD 1: 4H + 2T 3.4
420
METHOD 2: 4 × 100 + 2 × 10 METHOD 3: 400 + 20 METHOD 1: 1T + 3U
3.5
4.
13
METHOD 3: 10 + 3
Give the value of the underlined numbers. 4.1
Question
Answer
1960
60
4.2
5 542
4.5
7 154
4.3
500 900
920
4.4 5.
METHOD 2: 1 × 10 + 3 × 1
8 000
8 426
50
Learners play the place value game. What do you need? • Place value tables (draw your own with Th, H, T and U): Th
•
H
T
U
Each player needs a place value table. One dice or a pack of cards (no face cards)
How to play 1. Players take turns to throw the dice or pick a card. 2. Each player writes the number on which the dice landed or on the card they picked in the column of their choice on their place value table. (The player decides where to write the number.) Example: Jenna picked a 6 and wrote it in the Tens column on her place value table: Th
H
T
U
6 3. 4.
Play until the place value tables of all the players are completed. The players compare their numbers. The player with the greatest number wins (or the smallest number – determine the rules beforehand). 27
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Facilitator’s Guide G05 ~ 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 Thousands, Hundreds, Tens and Units. I can give number names. I can indicate place value. I can do expanded notation (all three methods).
Comparing whole numbers Use different sized 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 • objects • flash cards
Visit bit.ly/31iHJ5S for additional exercises.
In Grade 4, you learnt what it means to compare numbers, how to compare numbers, and which symbols to use to compare numbers. When you compare numbers, you must look at the value of the digits.
Compare the following numbers and circle the greatest number:
4 953 4 593 4 539 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
Answer: A = 27 | B = 33 © Optimi
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Facilitator’s Guide G05 ~ Mathematics
Unit
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You can now compare numbers, say which number is the greatest and which is the smallest, and arrange them. But how do you indicate which number is the greatest or smallest without circling or underlining it?
We use the following symbols to indicate less than, greater than, and equal to:
<;>;=
The ‘small’ end always points to the smaller number. The ‘big’ end always points to the greater number.
4 565 < 4 655
OR
1 475 > 1 457
When two values are equal, we use the = to show they are the same:
8 432 = 8 432
Remember it like this:
r eate r g s i
than
is le
ss th
an
ACTIVITY 4 1.
Fill in <, > or = to show the relationship between the numbers. Question and answer
1.1
10 525 > 10 255
1.3
65 065 = 65 065
1.2 2.
1.4
21 121 > 20 121
1.5
11 954 > 11 459 14 010 > 14 001
Which number is greater? Circle the answer.
Answer
2.1
3 583
2.3
2 200
2.2
2.4
1 362
2.5
29
4 738 6 907
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3.
Facilitator’s Guide G05 ~ Mathematics
Answer the questions.
Question and answer
3.1
Thousands of people enjoy picnics in the Kirstenbosch National Botanical Garden in Cape Town each month. In December, 10 705 people picnicked and in January, 10 075 people picnicked. When did the least number of people picnic in the Botanical Garden?
3.2
Masetshaba sells ice cream at her kiosk on Hartenbos beach. In 2019, she sold 21 101 ice creams and in 2018 she sold 20 111 ice creams. In which year did she sell the most ice creams?
The least number of people had a picnic in January.
In 2019.
Self-assessment Do the learners understand the work? Let them colour the faces that show what they can do. COMPARING 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 complete missing numbers (in sequence and on number charts and number lines). I can use the correct symbols to indicate which numbers are greater than, smaller than or equal to other numbers (>, < or =).
Representing whole numbers Can you remember the different ways in which we represent numbers? •
Number sets
{.......}
•
Visual representation of numbers:
5 or
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Facilitator’s Guide G05 ~ Mathematics
•
Flow charts:
•
Symbols:
•
Number lines:
•
Place value:
1
Unit
<,>,= 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24
Th
H
T
U
4
2
6
5
METHOD 1 8 Hundred Thousands + 5 Ten Thousands + 9 Thousands + 4 Hundreds + 2 Tens + 1 Units METHOD 2
•
Expanded notation:
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
Can learners think of other representations?
ACTIVITY 5 1.
Choose any three representations to show the number 1 026. This is an open question, and learners may represent the number 1 026 in any way.
2.
Is 1 026 an odd or even number? An even number
4.
Round the number 1 026 to the nearest: 5 1 025 100 10 1 030 1 000
3.
Which number comes just before 1 026? 1 025 Is the answer an odd or even number? An odd number
31
1 000 1 000
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Facilitator’s Guide G05 ~ Mathematics
Self-assessment Do the learners understand the work? Let them colour the faces that show what they can do. REPRESENTING WHOLE NUMBERS Requirements
Can the learners do it?
I can represent whole numbers in different ways. I know the difference between even and odd numbers. I can round off numbers to the nearest 5, 10, 100 and 1 000.
LESSON 2: NUMBER SENTENCES Number sentences introduce operations with numbers (and in the senior and FET phases with variables). Once again, emphasise the concept using concrete, relevant examples. Learners in the intermediate phase sometimes work with number sentences in isolation. However, it is more common for learners to combine number sentences with other forms of representation; for example, mathematical problems that are simplified in words, as well as numbers and calculations represented in flow charts. It is important to include examples of mathematical problems that may be expressed as number sentences throughout the year. Also include number sentences in daily mental maths exercises.
You studied number sentences in Grade 4. In Grade 5, you will use number sentences to describe problems and solve number sentences through inspection and by trial and improvement. Briefly revise the Grade 4 work.
What are number sentences? A number sentence is an arrangement of numbers and symbols: 233 + 19 = 252 455 – 176 = 279 498 × 3 = 1 494 120 ÷ 2 = 60
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Facilitator’s Guide G05 ~ Mathematics
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You will not always work with number sentences. Sometimes a maths problem is expressed in words, and before you can solve it mathematically, you must first formulate a number sentence. Example: Your swimming lessons cost R3 900. Your mom makes 12 equal payments. How much is each payment? Start by reading the problem again and writing down the information: Total amount for lessons: R3 900
How many payments? 12 equal payments
The question does not ask how much your mom paid in total, but how much she must pay each month (12 payments). Write down the number sentence: 3 900 ÷ 12 = ?
Apply your Grade 4 calculation skills: 1
.
3
2
5
2
3
9
0
0
-
3
6
-
3
0
2
4
-
6
0
6
0 0
It means your mom must make 12 equal payments of R325 each. In this number sentence, we divided numbers.
You can also write a number sentence with + , – , × and ÷.
Example: Melanie has 36 blue marbles. Refilwe has 25 red marbles and 17 blue marbles. How many blue marbles do they have altogether?
If we want to solve the number sentence:
36 + 17 = ?
36 + 17 = 53
Melanie and Refilwe have 53 blue marbles altogether.
Write a few of your own number sentences. Evaluate learners’ answers and make sure they understand the concept. 33
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Facilitator’s Guide G05 ~ Mathematics
ACTIVITY 6 1.
Write a number sentence for each of the statements or questions. Question
1.1
1.2
1.3
1.4
1.5
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Rozelle plans to use different coloured plates for her birthday party. She wants 72 black plates, 96 gold plates, and silver plates. Rozelle needs 288 plates altogether. How many silver plates must she buy? Bulelwa bakes 108 cupcakes for Rozelle’s party. She has already baked 24 chocolate cupcakes and 48 strawberry cupcakes. How many vanilla cupcakes must she bake?
Paul collects coins. His brother gave him 38 coins, his mom gave him 33 coins and his sister gave him 35 coins. How many coins does Paul have now? Simphiwe takes the same route to school every day. He walks 4 blocks until he reaches the theatre, 8 blocks until he reaches the shop and 9 blocks until he reaches the school. If he has already walked 12 blocks, how many blocks must he still walk before he arrives at school? Heidi is at Gold Reef City and she wants to ride the rollercoaster, which costs 31 tickets. The bumper cars cost 16 tickets and the merry-go-round costs 33 tickets. Heidi had 17 tickets, but she lost 6 tickets on one of the rides. How many tickets does she still need to enjoy all the rides?
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Answer
72 + 96 + silver plates = 288 168 + silver plates = 288 Number of silver plates = 288 – 168 = 120 Rozelle must buy 120 silver plates. *Any valid method. 24 + 48 + vanilla = 108 72 + vanilla = 108 Number of vanilla cupcakes = 108 – 72 = 36 Bulelwa must bake 36 vanilla cupcakes for Rozelle’s birthday party. * Any valid method. 38 + 33 + 35 = Number of coins Number of coins = 106 Paul now has 106 coins. * Any valid method. 4 + 8 + 9 blocks. 4 + 8 + 9 = 21 blocks 21 blocks – 12 blocks (already walked) = 9 blocks Simphiwe must walk another 9 blocks before he arrives at school. * Any valid method. Heidi now has 17 – 6 tickets. 17 – 6 = 11 tickets Total number of tickets needed for the rides: 31 + 16 + 33 = 80 tickets needed in total. 80 tickets needed – 11 tickets (in Heidi’s possession) = 69 tickets Heidi still needs 69 tickets to enjoy all the rides. * Any valid method.
Facilitator’s Guide G05 ~ Mathematics
1
Unit
You can solve and complete number sentences by: • inspection • trial and improvement • checking the solution by substitution
Let us look at solving number sentences by inspection.
The inspection method is another name for ‘guess the answer’. If you look at a number sentence and must find the answer without making calculations, you will use inspection. In maths, we only solve simple number sentences by inspection. Example: Study the number sentence: 923 – 25 =
We are not going to draw any pictures to solve this number sentence. Use mental maths and decide on an answer. You will then see – by using inspection – that the answer is 898.
ACTIVITY 7 1.
Solve the number sentences using inspection. 1.1 1.2 1.3 1.4 1.5
Question
Answer
1 273 + 6 =
1 279
412 – 12 =
400
662 + 35 =
697
540 – 120 =
420
864
997 – 133 =
Now let us look at solving number sentences through trial and improvement.
Using this method, you will guess an answer, but you will write it down and then calculate the number sentence. If your answer is incorrect, you can try another answer and calculate the number sentence until it is correct or until the number sentence is TRUE. This number sentence is FALSE:
This number sentence is TRUE:
2 413 – 12 = 2 410
2 413 – 12 = 2 401
Example: Study the number sentence below and use trial and improvement to solve it. 3 156 –
= 3 149
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Facilitator’s Guide G05 ~ Mathematics
Attempt 1: Guess an answer that will make the number sentence TRUE. Guess that a 6 in the block will make the number sentence true. 3 156 – 6 = 3 149
Attempt 2: To choose 6 as the answer will make the number sentence FALSE. Guess another answer. Since 6 is not enough to subtract from 3 156 to get 3 149, you must choose a greater number. Use the number 7. 3 156 – 7 = 3 149
Using this method, it may take a few tries to solve the number sentence. It is time-consuming and not always the best choice.
ACTIVITY 8 1.
Solve the number sentences using trial and improvement. Question
Answer
1.1
1 458 – = 1 443
15
1.4
1 326 – = 1 316
1.2 1.3 1.5
239 + = 343
104
515 + = 1 415
900
14
985 + = 999
10
Checking the solution by substitution is very similar to trial and improvement. You must study the number sentence and then decide on an answer. You then replace the answer in the number sentence and do the calculation. The number sentence must be TRUE. Number sentences are also a way of showing equivalence. What does equivalence mean?
Equivalence is when one side of the number sentence is equal to the other side of the number sentence. In other words, showing that the number sentence is true. Equivalence
The left side of the number sentence is equivalent (equal to) the right side of the number sentence. It means the number sentence is true.
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Facilitator’s Guide G05 ~ Mathematics
Unit
1
Number sentences may also be used in flow charts and tables. Look at a few examples.
In the flow chart below, the number sentence is on the left-hand side and the equivalent value is on the right-hand side. Complete the flow chart so all the number sentences have equivalent values. 44 + 256 156 – 57
19 + 199
186 + 359 999 – 190
300 99
=
218 545 809
Addition and subtraction in number sentences You already know that addition and subtraction are opposites. If you add 14 sweets to the 6 you already have, you will have 20 sweets. To return to what you originally had, you are going to do the opposite. Instead of adding 14 sweets, you are going to subtract them. The 20 sweets minus the 6 sweets give you the original 14 sweets you had at the beginning. If you write this in a number sentence, it will look like this: Description in words
Number sentence
I have 14 sweets and add 6.
14 + 6 = 20
I have 20 sweets and subtract 6.
20 – 6 = 14
Can you think of more examples where addition and subtraction can be used as opposite calculations in number sentences? Learners must give their own examples. Let them go through this thought process on their own. Try not to help them but guide them if they really need help and let them think of more examples on their own.
You know addition and subtraction are opposites and they can be used to check the answers of number sentences. Multiplication and division are also opposites and used as inverse operations to test answers in number sentences. Study the examples: • 164 – 73 = 91 so 91 + 73 = 164 • 1 034 + 496 = 1 530 so 1 530 – 496 = 1 034 and 1 530 – 1 034 = 496 • 78 × 3 = 234 so 234 ÷ 3 = 78 and 234 ÷ 78 = 3 • 165 ÷ 3 = 55 so 55 × 3 = 165 37
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Unit
Facilitator’s Guide G05 ~ Mathematics
Special properties of +, –, × and ÷ • • • • • • • • •
358 – 358 = 0 2 264 – 0 = 2 264 237 – 4 + 4 = 237 927 + 366 – 366 = 927 8 216 ÷ 8 216 = 1 635 × 1 = 635 2 147 ÷ 2 147 = 1 125 ÷ 25 × 25 = 125 65 × 4 ÷ 4 = 65
Write down 5 of your own examples.
Learners must give their own examples. Let them go through the thought process on their own. Try not to help them but guide them if they really need help and let them think of more examples on their own.
Now that you have given your own examples, have another look at the number sentences above. What do you notice? Complete the sentences:
1.
When you subtract a number from itself, the answer is 0.
3.
Division is when you divide a number into equal parts or groups.
5.
When you multiply or divide a number by 1, the answer is the same/unchanged.
2.
4. 6.
When you add a number and then subtract that same number, you get the number you started with.
When you divide a number by itself, the answer is 1.
When you multiply or divide a number by the same number, you get the number you started with.
Pairs of equivalent number sentences
The word ‘equivalent’ means something is equal to something else or has the same value as something else.
Equivalent means equal to
Next, you will ensure that two number sentences are equivalent and not merely a number sentence with an equivalent answer. Look at the examples below. Example 1 Number sentence 1: 356 + 133 © Optimi
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Facilitator’s Guide G05 ~ Mathematics
1
Unit
You may use any of the methods in this unit to find the number sentence’s equivalent answer. Answer to number sentence 1: 489 Number sentence 2: 612 – 123
The equivalent answer to this number sentence is 489.
Do you see that both number sentences have the same answer? This means the two number sentences are also the same, which means we can say the two number sentences are equivalent. Number sentence 1 = Number sentence 2 356 + 133 = 612 – 123
Example 2 Number sentence 1: 105 – 81
When you study the number sentence, you may use any method to determine the equivalent answer. Answer to number sentence 1: 24 Number sentence 2: 105 + 81
The equivalent answer to this number sentence is 186.
Do you see that these number sentences DO NOT have the same answer? This means the two number sentences are NOT the same; therefore, we cannot say the two number sentences are equivalent. The number sentences are not equal to ( ≠ ) each other: Number sentence 1 ≠ Number sentence 2 105 – 81 ≠ 105 + 81
ACTIVITY 9 1.
Calculate the number sentences and determine whether they are equivalent. Question
1.1
Answer
Number sentence 1: 436 + 297
Number sentence 1: 436 + 297 = 733 Number sentence 2: 397 + 336 = 733 Number sentence 1 = Number sentence 2
Number sentence 2: 397 + 336
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Unit
1 1.2
1.3
1.4
1.5
1.6
1.7
Facilitator’s Guide G05 ~ Mathematics
Number sentence 1: 261 + 236
Number sentence 1: 261 + 236 = 497 Number sentence 2: 297 – 36 = 261 Number sentence 1 ≠ Number sentence 2
Number sentence 1: 245 – 115
Number sentence 1: 245 – 115 = 130 Number sentence 2: 249 – 119 = 130 Number sentence 1 = Number sentence 2
Number sentence 1: 304 – 10
Number sentence 1: 304 – 10 = 294 Number sentence 2: 300 + 14 = 314 Number sentence 1 ≠ Number sentence 2
Number sentence 1: 1 389 + 453
Number sentence 1: 1 389 + 453 = 1 842 Number sentence 2: 2 423 – 559 = 1 864 Number sentence 1 ≠ Number sentence 2
Number sentence 1: 5 412 + 336
Number sentence 1: 5 412 + 336 = 5 748 Number sentence 2: 6 489 – 741 = 5 748 Number sentence 1 = Number sentence 2
Number sentence 1: 4 500 + 278
Number sentence 1: 4 500 + 278 = 4 778 Number sentence 2: 5 008 – 379 = 4 629 Number sentence 1 ≠ Number sentence 2
Number sentence 2: 297 – 36 Number sentence 2: 249 – 119 Number sentence 2: 300 + 14 Number sentence 2: 2 423 – 559 Number sentence 2: 6 489 – 741 Number sentence 2: 5 008 – 379
Addition and subtraction techniques Commutative property of addition What does ‘commutative’ mean? Commutative comes from ‘commute’, which means to move around or to travel back and forth. When we refer to the commutative property of addition, we refer to numbers that are moved around.
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