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Mathematics
Study guide 1/2
Grade 5
SAMPLE
SAMPLE
LESSON ELEMENTS
The guide contains various lesson elements. Each element is important for the learning process and indicates the skill you must master.
ICON
LESSON ELEMENT
ICON LESSON ELEMENT
Think for yourself Take note! Important
Self-assessment
Research Activity Study Did you know? New concept or definition Tip
Remember/Revise
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
LESSON 17 Symmetry
LESSON 18
Whole numbers: Division (3-digit whole numbers by 2-digit whole numbers)
Revision: Use the CAMI programme
TOPIC
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
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
FACT SHEET
Whole numbers
Whole numbers are numbers without fractions or decimals. Whole numbers are always positive and never negative. Remember: 0 is also a whole number.
Even numbers
• All numbers that are divisible by 2 without a remainder.
• Even number end with 2, 4, 6, 8 or 0.
Alternative words used for operations
Odd numbers
• All numbers that are not divisible by 2 without a remainder.
• Odd numbers end with 1, 3, 5, 7 or 9.
Decrease by Left Less than
Deduct Left over Minus
SAMPLE
Difference between/of Less Take away Fewer than Division
Divide Halve Percent
Divide equally How many times Quotient Goes into Out of Ratio of Half of Per Split into
Multiplication
Double Of Times
Increase by a factor of Product of Twice Multiply by
Rounding
Round to the nearest 5
Numbers ending with 3, 4, 5, 6 and 7 are rounded to 5.
Numbers ending with 1 and 2 are rounded to the previous ten (end with a 0).
Numbers ending with 8 and 9 are rounded to the next ten (end with a 0).
Numbers ending with 0 stays the same.
Round to the nearest 10
Numbers smaller than 5 are rounded to the previous ten (end with a 0).
Numbers ending with 5, 6, 7, 8 and 9 are rounded to the next ten (end with a 0).
Round 6 858 to the nearest 10:
Look at the tens column Th HTU
6 858 The ones column must help you decide (8 is greater than 5, therefore the number is rounded to the next ten and ends with a 0 the answer is 6 860.)
Round to the nearest 100
Numbers smaller than 5 are rounded to the previous hundred (end with a 0).
Numbers ending with 5, 6, 7, 8 and 9 are rounded to the next 100 (end with a 0).
Round 6 858 to the nearest 100:
Look at the hundreds column Th
6 858 The tens column must help you decide (5 and greater are rounded to the next 100 and end with a 0 the answer is 6 900.)
Apply the same method when you round to 1 000. (The hundreds column must help you decide.)
Properties
Commutative property: Numbers may be added or multiplied together in any order.
a + b = b + a a × b = b × a
10 + 8 = 8 + 10
12 × 3 = 3 × 12
18 = 18 36 = 36
Associative property: When you add or multiply numbers together, it does not matter how the numbers are grouped.
Distributive property: The distributive law of multiplication means that you can break down one or all of the numbers in a multiplication sum, multiply them separately and add the products together
The top number (numerator) counts how many of the bottom number (denominator) there are. You can remember the difference by seeing that the denominator is down below. The denominator determines what we name the fraction, for example, quarters, eighths, etc.
You may use a fractions wall to compare fractions.
SAMPLE
Important: Before you compare or add fractions, you must always make the denominators the same. It means that you determine the Least Common Denominator (LCD). When you multiply the denominator by a number, you must also multiply the numerator by the same number.
Time
1 minute = 60 seconds
1 hour = 60 minutes
24 hours = 1 day
7 days = 1 week
4 weeks = 1 month
12 months = 1 year
10 years = 1 decade
Analogue time Digital time Length
Conversions: Multiply or divide by 10, 100 and 1 000
Convert grams to kilograms.
4 000 g ÷ 1 000 = 4 kg
Picture a comma at the end of the number.
When you divide by 1 000, move the imaginary comma three place values to the left (because there are three zeros in 1 000).
4 0 0 0 , g ÷ 1 0 0 0 = 4 , 0 0 0 kg
Convert kilograms to grams.
4 kg × 1 000 = 4 000 g
When you multiply by 1 000, move the imaginary comma three place values to the right (because there are three zeros in 1 000).
4 , 0 0 0 kg × 1 0 0 0 = 4 0 0 0 g
2D shapes
Triangle
3 straight sides
3 angles
Rectangle
2 opposite long sides of equal length
2 opposite shorter sides of equal length
4 right angles (90°)
Square
4 straight sides of equal length
4 right angles (90°)
Circle
No angles
No straight sides (a curved side) Pentagon
5 straight sides and 5 angles
6 straight sides and 6 angles Heptagon
7 straight sides and 7 angles
3D objects
Rectangular prism
Sphere
Cube (square prism)
Square pyramid
SAMPLE
The base of the pyramid is a square and the other sides are triangles.
Triangular pyramid
The base of the pyramid is a triangle and the other sides are triangles.
Data handling
Write down all the shoe sizes from small to large
Make a mark for each data unit. Every fifth mark goes across the group of four marks to make a group of five. It is easier to count data in groups of five.
Frequency indicates the answer of the count. It shows how many units of data there are.
2
3 Every represents 6 teddy bears.
The mode is the value that occurs most often in a data set. The mode of the data set is: Shoe size 3
Grade 5 learners' maths test results
This unit covers lessons 1 to 9.
UNIT 1
UNIT 1
TOPIC
Mental maths
LESSON 1
Whole numbers: Counting, ordering, comparing and representing, and place value of digits (4-digit whole numbers)
LESSON 2
Number sentences
LESSON 3
Whole numbers (Addition and subtraction) (5-digit whole numbers)
LESSON 4
Number patterns (Numeric patterns)
LESSON 5
Whole numbers: Multiplication (2-digit whole number by a 2-digit whole number) and division (3-digit whole number by 1-digit whole number)
LESSON 6
Time
LESSON 7
Data handling
LESSON 8
Properties of 2D shapes
LESSON 9
Capacity and volume
Revision: Use the CAMI programme
LESSON 1: WHOLE NUMBERS
This lesson is a revision of Grade 4 work.
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.
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.
Study the numbers in the table and circle the whole numbers.
In this lesson, you will:
• count
• order
• compare
• represent and
• indicate place value of whole numbers
Counting with whole numbers
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 4 6 8 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?
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
DATE:
1. Write the set of whole numbers between 1 915 and 1 921.
2. Indicate whether the numbers are whole numbers. Colour the correct circle.
3. Logan is on a treasure hunt and discovers a message coded in numbers. If he can decipher the message, he will know where to find the largest treasure chest.
The message is written in a ‘letter-number’ code. It means the letters have been replaced with numbers. Complete the missing numbers to decipher the message.
Logan will find the world’s largest treasure chest in ______________________________________.
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.
Number of containers
Number of beads
*Draw the beads in each container. 150
Learner
Lucinda
Marli
Sibongile
Self-assessment
Do you understand the work? Colour the faces that show what you can do.
COUNTING WITH WHOLE NUMBERS
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 the number 10 000.
Ordering whole numbers
In Grade 4 you learnt how to order and arrange numbers in a specific order. Do you 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.
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 of 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.
Write your answer in the box below.
ACTIVITY 2
DATE:
1. 1. Arrange the numbers from small to great.
2. Arrange the numbers from great to small.
3. Build and arrange the numbers. You may build any 6 numbers for each question.
Question
Example
3.1
Write down the numbers you can build with 6, 3 and 2. Arrange them from small to great.
236; 263; 326; 362; 623; 632
Write down the numbers you can build with 1, 4, 3 and 5 and arrange them from great to small.
Write down the numbers you can build with 7, 2, 1 and 9 and arrange them from small to great.
3.2
Write down the numbers you can build with 6, 8, 1 and 6 and arrange them from great to small.
3.3
3.4
3.5
Write down the numbers you can build with 0, 9, 1 and 2 and arrange them from small to great. (Use 0 as a significant digit only, in other words, as a placeholder. Leading 0s – 0s used as the first digit in a number – are not significant.)
Write down the numbers you can build with 1, 9, 1 and 1 and arrange them from great to small.
Self-assessment
Do you understand the work? Colour the faces that show what you can do.
ORDERING WHOLE NUMBERS
Requirements Can I 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.
SAMPLE
• Omvattende verduidelikings van konsepte in eenvoudige taal.
• Praktiese, alledaagse voorbeelde met visuele voorstellings en diagramme wat leerders help om konsepte te bemeester.
• Leerders werk teen hul eie pas.
• Aktiwiteite wat leerders se toepassing van kennis en hul redeneervermoë uitdaag.
• Die fasiliteerdersgids bevat stapvirstapbewerkings en antwoorde.
