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Mathematics
Facilitator’s guide
Grade 5
CAPS aligned
M Vos L Young
SAMPLE
SAMPLE
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
Think for yourself
Take note! Important Tips
Self-assessment
Research Activity Study
Did you know?
New concept or definition Tip
Remember/Revise
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)
SAMPLE
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.
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.
SAMPLE
Guidelines for time allocation per topic
UNIT 1 TOPIC
Mental maths: Use Train Your Brain Maths Grade 5
1
Whole numbers: Counting, ordering, comparing and representing, and place value of digits (3-digit whole numbers)
(divided into 10
UNIT 2
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
13
LESSON 14
Whole numbers: Multiplication (3-digit whole numbers by 2-digit whole numbers)
21 Whole numbers: Counting, ordering, comparing and representing and place value of digits (6-digit whole numbers)
UNIT 4
Mental maths: Use Train Your Brain Maths Grade 5
(divided into 10 minutes each day) 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)
32
of 3D objects
33
34
numbers: Division (4-digit whole numbers by 2-digit whole numbers)
Find units 1 and 2 in study guide 1/2 and units 3 and 4 in study guide 2/2.
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%.
Always refer to the assessment plan for the formal assessments that must be completed per term. (This excludes the activities and investigations in the study guide.)
SAMPLE
TOPIC
YEAR PLAN
UNIT 1
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
TOPIC
UNIT 2
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
SAMPLE
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
TOPIC
UNIT 3
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
TOPIC
UNIT 4
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
This unit covers lessons 1 to 9.
UNIT 1
UNIT 1
Mental maths: Use Train Your Brain Maths Grade 5
hours (divided into 10 minutes each day) LESSON 1
Whole numbers: Counting, ordering, comparing and representing, and place value of digits (3-digit whole numbers)
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.
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.
Counting with whole numbers
Learners must count every day – both on (forwards) and back (backwards).
• an abacus (available at any educational or plastics shop)
• number charts or tables
• rows or diagrams, for example:
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.
You may start with any number.
Study the numbers. Do you see you can start at any number and count in whole numbers?
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.
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.
Complete the missing numbers.
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 Whole number or not?
3.1 8 800; 8 650; 8 500; 8 350; ... Letter: P
3.2 1 000; 1 010; 1 020; 1 030; ... Letter: A
3.3 8 400; 8 950; 9 500; ... Letter: R
3.4 5 000; 6 000; 7 000 ... Letter: I
3.5 8 000; 9 000; 10 000; 11 000; ... Letter: S
The world’s largest treasure chest is in PARIS
Whole number or not?
4. 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.
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.
Self-assessment
Do the learners understand the work? Let them colour the faces that show what they can do.
COUNTING WITH WHOLE NUMBERS
Requirements
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
Can the learners do it?
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
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: Choose the greatest number and write it down first.
The greatest number in this set is 5 942
Step 2: Now cross out the greatest number in the number set.
{4 952; 4 592; 5 942; 2 924}
You can no longer choose the number 5 942.
SAMPLE
Step 3: 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}
Tip: Start by choosing the smallest number, not the greatest one.
3. 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
SAMPLE
Self-assessment
Do the learners understand the work? Let them colour the faces that show what they can do.
ORDERING WHOLE NUMBERS
Requirements
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.
Can the learners do it?
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
SAMPLE
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.
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.
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.
If you want to indicate the place value of 18, it will look like this:
The same happens when there is a number greater than 9 in the Tens box.
Since the 8 in the Tens box indicates 800, it must jump over the wall into the Hundreds box.
It means 8 × 100 = 800.
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
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.
To make it easier, we first place each number in its box:
8 5 9 4 2 1
Write down where each digit would go, without drawing the blocks.
