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Mathematics
Study guide 1/2
Grade 4
CAPS
LESSON ELEMENTS
The guide consists of various lesson elements. Every element is important for the learning process and indicates the skill that the learner needs to master.
ICON
LESSON ELEMENT
Think for yourself Tips
SAMPLE
Research Study
New concept or definition
Remember/Revise
Take note! Important Self-assessment
Activity
YEAR PLAN
UNIT 1
TOPIC
Mental maths: Use the Train Your Brain Maths Grade 4 product
LESSON 1
Whole numbers: Counting, ordering, comparing and representing, and place value of digits (3-digit whole numbers)
LESSON 2
Number sentences
LESSON 3
Whole numbers: Addition and subtraction (3-digit whole numbers)
LESSON 4
Number patterns: Numeric patterns
LESSON 5
Whole numbers: Multiplication and division (1-digit whole number by 1-digit whole number)
LESSON 6
Time
LESSON 7
Data handling
LESSON 8
Properties of 2-D shapes
LESSON 9
Whole numbers:
• Multiply (2-digit whole numbers by 1-digit whole number)
• Multiply (2-digit whole numbers by 2-digit whole numbers)
• Divide (2-digit whole numbers by 1-digit whole number)
Revision: Use the CAMI programme
UNIT 2
TOPIC
Mental maths: Use the Train Your Brain Maths Grade 4 product
LESSON 10
Whole numbers: Counting, ordering, comparing and representing, and place value of digits (4-digit whole numbers)
LESSON 11
Whole numbers: Addition and subtraction (4-digit whole numbers)
LESSON 12
Common fractions
LESSON 13
Length
LESSON 14
Whole numbers: Multiplication (2-digit whole numbers by 2-digit whole numbers)
LESSON 15
Properties of 3-D shapes
LESSON 16
Geometric patterns
LESSON 17
Symmetry
LESSON 18
SAMPLE
Whole numbers: Addition and subtraction (4-digit whole numbers)
LESSON 19
Whole numbers: Division (3-digit whole numbers by 1-digit whole number)
Revision: Use the CAMI programme
TOPIC
Mental maths: Use the Train Your Brain Maths Grade 4 product
LESSON 20
Capacity/Volume
LESSON 21
Common fractions
LESSON 22
Whole numbers: Counting, ordering, comparing and representing, and place value of digits (4-digit whole numbers)
Whole numbers: Addition and subtraction (4-digit whole numbers)
LESSON 23
Views of objects
LESSON 24
Properties of 2-D shapes
LESSON 25
Data handling
LESSON 26
Numerical patterns
LESSON 27
Whole numbers: Addition and subtraction (4-digit whole numbers)
LESSON 28
Whole numbers: Multiplication (2-digit whole numbers with 2-digit whole numbers)
LESSON 29
Number sentences
LESSON 30
Transformations
Revision: Use the CAMI programme
UNIT 4
TOPIC
Mental maths: Use the Train Your Brain Maths Grade 4 product
LESSON 31
Whole numbers: Counting, ordering, comparing and representing, and place value of digits (4-digit whole numbers)
Whole numbers: Addition and subtraction (4-digit whole numbers)
LESSON 32
Mass
LESSON 33
Properties of 3-D objects
LESSON 34
Common fractions
LESSON 35
Whole numbers: Division (3-digit whole numbers by 1-digit whole number)
LESSON 36
Perimeter, surface area and volume
LESSON 37
Position and movement
LESSON 38
Transformations
LESSON 39
Geometric patterns
LESSON 40
Whole numbers: Addition and subtraction (4-digit whole numbers)
LESSON 41
Probability
Revision: Use the CAMI programme
Find unit 1 and 2 in study guide 1/2 and unit 3 and 4 in study guide 2/2.
UNIT 1
This unit covers nine lessons (1 to 9).
UNIT 1
TOPIC
Mental maths
LESSON 1
Whole numbers: Counting, ordering, comparing and representing, and place value of digits (3-digit whole numbers)
LESSON 2
Number sentences
LESSON 3
Whole numbers: Addition and subtraction (3-digit whole numbers)
LESSON 4
Number patterns: Numeric patterns
LESSON 5
Whole numbers: Multiplication and division (1-digit whole number by 1-digit whole number)
LESSON 6
Time
LESSON 7
Data handling
LESSON 8
SAMPLE
Properties of 2-D shapes
LESSON 9
Whole numbers:
• Multiply (2-digit whole numbers by 1-digit whole number)
• Multiply (2-digit whole numbers by 2-digit whole numbers)
• Divide (2-digit whole numbers by 1-digit whole number)
Revision: Use the CAMI programme
LESSON 1: WHOLE NUMBERS
Do you know what a whole number is?
Whole numbers are numbers without fractions or decimals. Whole numbers are always positive and never negative. Remember: 0 is also a whole number.
Examples of whole numbers
{0; 1; 2; 3; 4; 5; 6; ...}
1 2 0,5
If numbers such as the above are placed in curly brackets { }, we call it a set of numbers.
This means that {0; 1; 2; 3; 4; 5; 6; ...} is a set of whole numbers.
Study the numbers in the table and circle the whole numbers.
In this lesson, you will do the following with whole numbers:
• count
• order
• compare
• represent
• indicate place value
Counting with whole numbers
In Grade 3 you learnt how to count with whole numbers. Do you still remember how to count in 2s?
Let’s revise counting in 2s. When you count in 2s, always add 2 to the previous number to get the next number. + 2 + 2 + 2 + 2 + 2 2 4 6 8 10 12
You can start with any number.
Study the numbers. Do you see that you can start at any number and count in whole numbers?
In the above examples, you counted on or forwards. Using whole numbers, you can also count back or backwards.
Study the following numbers and complete the missing numbers.
4. Andrew, Sibongile and Timmy like to play with marbles. They keep their marbles in bags.
Andrew’s bag can hold 10 marbles. Sibongile’s bag can hold 25 marbles. Timmy’s bag can only hold 3 marbles.
Look at the following example and count in 10s, 25s and 3s to determine how many marbles each child has. Child
Sibongile Timmy
5. Complete the flow charts.
Self-assessment
Do you understand the work? Colour the faces that show what you can do.
I can count on and back in 2s.
COUNTING IN WHOLE NUMBERS
I can count on and back in 3s.
I can count on and back in 5s.
I can count on and back in 10s.
I can count on and back in 25s.
I can count on and back in 50s.
I can count on and back in 100s.
I can do all of the above up to the number 1 000.
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
Study the number set.
{25; 2; 537; 119; 65}
SAMPLE
OR
from small to GREAT
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 537
Step 2: Now cross out the greatest number in the number set.
{25; 2; 537; 119; 65}
You can no longer choose the number 537.
Step 3: From the remaining numbers, choose the greatest number and write it next to 537.
537; 119
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 as follows:
{537;
119; 65; 25; 2}
You have now arranged the number set from greatest to smallest.
Can you arrange the following number set from small to great?
{913; 902; 35; 11; 1}
Tip: Start by choosing the smallest number, not the greatest one.
Write your answer in the box below.
1. Arrange
2. Arrange
3. Build and arrange the numbers.
Question Answer
Example
3.1
Write down the numbers that you can build with 6, 3 and 2 and arrange them from small to great.
Write down the numbers that you can build with 1, 4 and 5 and arrange them from great to small.
3.2
236; 263; 326; 362; 623; 632
3.3
Write down the numbers that you can build with 7, 2 and 9 and arrange them from small to great.
Write down the numbers that you can build with 8, 1 and 6 and arrange them from great to small.
3.4
3.5
Write down the numbers that you can build with 9, 1 and 2 and arrange them from small to great.
Write down the numbers that you can build with 9, 1 and 1 and arrange them from great to small.
Self-assessment
SAMPLE
Do you understand the work? Colour the faces that show what you 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.
Place value
Place value helps us to determine the value of a digit. Our number system (the numbers that we work with) contains digits from 0 to 9 only.
What do we do when we must work with numbers greater than 9?
We use place value to indicate when we are working with numbers greater than 9. It means that the value of a digit is determined by its place or position in a number.
When we work with place value, we can think of each value as a box with high walls.
Hundreds Tens Units
In each box you can find the digits 0 to 9. As soon as the number becomes greater than 9, it jumps over the wall into the next box.
The 7 in the Units box means that there are 7 Units. We can also write it as 7 x 1.
Can you see that there are no numbers in the Tens and Hundreds boxes? This means that there are 0 x Tens and 0 x Hundreds in this number.
Let’s see what happens with a number greater than 9. Hundreds
13
There may only be one number in each box, but now there is a 1 and a 3 in the Units box.
What does the 13 mean? It consists of 10 + 3.
The 3 is in the Units box and it means 3 x 1, which is shown as 3.
The 10 jumps over the wall into the Tens box.
You CANNOT carry the full 10 across, because it then indicates 10 x Tens, which means 10 x 10, which equals 100. Therefore, only the 1 jumps across. Hundreds
Units 10 3 1 × Tens means 1 × 10 = 10
If you want to indicate the place value of 13, it will look like this:
1 3
• Comprehensive explanations of concepts in plain language.
• Practical, everyday examples with visuals and diagrams to help master concepts.
• Learners work at their own pace.
• Practical, everyday examples.
• Activities that test learners’ knowledge application and reasoning.
• The facilitator’s guide contains step-by-step calculations and answers.
