Gauteng Province

Grade 9 Lesson Plan 1

Term 2
1. TOPIC: ALGEBRAIC EXPRESSIONS
2. DATE: 08 April 2024 DURATION: 1 hour
3. OBJECTIVES:
By the end of the lesson learners should know and be able to:
• recognize and identify conventions for writing algebraic expressions,
• identify and classify like and unlike terms in algebraic expressions,
• recognize and identify coefficients and exponents in algebraic expressions,
• recognize and differentiate between monomials, binomials and trinomials
4. RESOURCES: DBE workbook 2 & any other textbook
5. REVIEW AND CORRECTION OF HOMEWORK (Suggested time:5 minutes)
6. PRIOR KNOWLEDGE:
Revise algebraic language

7. MENTAL MATHS: (Suggested time:5 minutes)

8. ENGLISH ACROSS THE CURRICULUM: (Suggested time:10 minutes)

Terminology
Variables:
a number that can have different values as compared
to a constant that has a fixed value.
Constant:
a constant is a number on its own whose value does not
change.
Coefficient:
a constant attached to the front of a variable or group
of variables. The variable is multiplied by the coefficient.
Algebraic expression: a collection of quantities made up of constants and
variables joined by the four fundamental operations.
Term:
parts of an algebraic expression linked to each other by
the + or – symbols.
Monomial:
an algebraic expression that has only one term, for
example: 4x
Binomial:
an algebraic expression that has two terms, for example:
4x – 3y
Trinomial:
an algebraic expression that has three terms, eg.: 2𝑥 − 3𝑦 + 𝑧

Assessment Words
Describe
Equivalent
Determine
Substitute

9. INTRODUCTION (Suggested time:10 Minutes)

Discuss the following with learners and ask learners to provide suitable examples:
• the difference between an expression and an equation
• the concepts: constant, variable and coefficient
• definition of the term equivalent (expressions)
• conventions used in algebra

• an algebraic expression is made up of numbers, variables and operations signs, that

can also be described in words in some cases they can be described with flow diagrams.
an expression consists of terms that are combined using addition, subtraction,
multiplication and division.
Numeric expressions: 7 − 5; 100 ÷ 5 + 1; 6 × 10 − 2 + 5
algebraic expressions: 4 × 𝑥; 100𝑥 + 1; 3𝑥 − 2
• an equation tells us about the numeric relationship between quantities.
For example, say we have two boxes of balls and we know that there are 10 more balls
in the one box than in the other. Let’s use 𝑥 to indicate the number of balls in the first
box. Then there are 𝑥+ 10 balls in the second box. To find the total number of balls we
can make an equation: Total = 𝑥+ (𝑥 + 10), which gives: Total = 2𝑥+ 10. If we know that
there are 46 balls altogether, then we can say 2𝑥 + 10 = 46. When we solve this
equation, we get 𝑥 = 18. So we know there are 18 balls in one box and 28 balls in the
other.
 • equivalent expressions are algebraic expressions that have different sequences of
operations, but have the same numerical value for any given value of 𝑥.

• a convention is something that people have agreed to do in the same way. We write
3 × 𝑥 rather than 𝑥 × 3, and we write 3𝑥 rather than 𝑥3. In algebraic expressions, when
multiplying with variables the multiplication sign is often not shown: We normally write 4𝑥
instead of 4 × 𝑥 and 4(𝑥 − 5) instead of 4 × (𝑥 − 5)

• like terms are terms with the same variables and the same exponents.

10. LESSON PRESENTATION/ DEVELOPMENT (Suggested time:15 minutes)

Activity 1 NOTE STRUCTURE:

Complete the following table with the learners and discuss their ⚫ Emphasise
answers. algebraic language
and highlight key
Words Flow diagram Expression words “multiply,
subtract, from”.
 Multiply a number by 5𝑝 − 3 ⚫ Represent words
×5 −3
5 and then subtract 3 like “sum,
from the answer difference,
2(4𝑥 − 3) quotient, product”
in Maths symbols.
Let learners complete the table on page 117 in the Sasol-Inzalo
Book 1.

Activity 2
⚫ Emphasise the
2 3 2
Consider the 8𝑥 𝑦 + 5𝑥 𝑦 − 2 and discuss the following difference between
questions with the learners: an equation and
expressions
a) Why is 8𝑥 2 𝑦 + 5𝑥 3 𝑦 2 − 2 considered as an expression and not
⚫ Emphasise
an equation?
b) How many terms are in the expression? algebraic language
c) What is the number 8 called? “coefficient,
d) Write down the coefficient of 𝑥 3 constant, term,
e) What name is given to the number −2? descending”
f) What is the value 3 in this expression?
g) What is the term with the highest power of 𝑦?
h) Write the expression in descending order of 𝑦.
i) Determine the value of the expression if 𝑥 = 2 and 𝑦 = −1

Activity 3

With assistance of the learners rewrite the following applying

algebraic conventions:
𝑥×4+𝑥×𝑦−𝑦×3

Note:
Highlight the following misconceptions:
• 𝑥 + 𝑥 = 2𝑥 and NOT 𝑥 2 (note the convention is to write 2𝑥
rather than 𝑥2)
• 𝑥 2 + 𝑥 2 = 2𝑥 2 and NOT 2𝑥 4

Activity 4

Discuss the concepts monomial, binomial, trinomial and polynomial

⚫ Emphasise
with learners providing relevant example.
algebraic terms
Consider the following table and complete with learners the first “monomial,
row. Let leaners complete the rest of the table. binomial, trinomial”
 Expression Type of Symbol Constant Coefficient
expression used to of
represent
the
variable
2𝑥 2 + 3𝑥 Trinomial 𝑥 −10 the second
− 10 term is 6
𝑘 the first
− 15 term is
3

11. CLASSWORK/HOMEWORK
DBE workbook 2 Pg 12 no 1
13 no 2 - 4

12. SUPPORT
For learners at risk do support activities.

13. ADDITIONAL NOTES FOR TEACHERS

14. TEACHER REFLECTION:

15. LEARNER WORKSHEET
MENTAL MATHS

CLASSWORK
 Gauteng Province
Grade 9 Lesson Plan 2
Term 2
1. TOPIC: ALGEBRAIC EXPRESSIONS
2. DATE: 09 April 2024 DURATION: 1 hour
3. OBJECTIVES:
By the end of the lesson, learners should know and be able to
Use the commutative, associative and distributive laws for rational numbers and laws of
exponents to:
Add and subtract like terms in algebraic expressions

4. RESOURCES: DBE workbook 2 & any other textbook

5. REVIEW AND CORRECTION OF HOMEWORK (Suggested time:5 minutes)
6. PRIOR KNOWLEDGE:
• laws of exponents
• commutative, associative and distributive properties
• like and unlike terms

7. MENTAL MATHS: (Suggested time:5 minutes)

Simplify without using a calculator:

1. 3(3 + 2)
2. 3 – (5 + 11) + 13
3. (3 + 4) + 6 = 3 + (….. +……)
4. -5 × 3 = 3 × ……
5. 23 × 24
6. 35 ÷ 32

8. ENGLISH ACROSS THE CURRICULUM: (Suggested time:10 minutes)

Terminology
Commutative property
This law applies to addition and multiplication of numbers; it tells us that even if we change the
order of the numbers we still get the same answer.
4𝑥 + (−2𝑥) = −2𝑥 + 4𝑥
−5𝑥 × 3𝑦 = 3𝑦 × − 5𝑥
Associative property
This rule also applies to addition and multiplication; it allows us to group numbers when adding
or multiplying and still get the same answer.
3𝑥 + (−5𝑥) + 6𝑥 = [3𝑥 + (−5𝑥)] + 6𝑥 = 3𝑥 + [−5𝑥 + 6𝑥]
3𝑥 × (−5𝑥) × 6𝑥 = [3𝑥 × (−5𝑥)] × 6𝑥 = 3𝑥 × [−5𝑥 × 6𝑥]
Distributive property
When multiplying across addition or subtraction this property allows us to redistribute the
numbers and still get the same answer.
7(−5𝑥 + 2) = [7 × −5𝑥] + [7 × 2] = −35𝑥 + 14

Assessment Words
Group
Add
Subtract
Identify
9. INTRODUCTION (Suggested time:10 Minutes)

Activity 1
Allow learners to do the following activities:

1. Calculate the following:

a) 5(3 + 4)
b) 5 × 3 + 5 × 4
c) 6 × 3 + (4 + 6)
d) (6 + 4) + 3 × 6
e) 3 × (4 × 5)
f) (3 × 4) × 5

2. Which properties are applied in (a) and (b), (c) and (d), (e) and (f)
Note:
Learners should have noticed that the results of each pair of question are the same. This is
because operations with numbers have certain properties, namely the distributive,
commutative and associative properties.
10. LESSON PRESENTATION/ DEVELOPMENT (Suggested time:15 minutes)

Activity 1 NOTE STRUCTURE:

Let learners do the following activities individually and have a class
discussion.

a) 2𝑏 2 − 4𝑏 + 1 − 𝑏 2 − 𝑏 − 4𝑏 2 − 2𝑏 + 6 ⚫ Learners find the

Solution: equivalent
(2𝑏 2 − 𝑏 2 − 4𝑏 2 ) + (−4𝑏 − 𝑏 − 2𝑏) + (1 + 6) expressions by
(−3𝑏 2 ) + (−7𝑏) + (7) identifying and
−3𝑏 2 − 7𝑏 + 7
 b) 𝑥 2 𝑦 + 𝑥𝑦 + 3𝑥𝑦 − 𝑥𝑦 2 + 2𝑥 2 𝑦 − 4𝑥𝑦 grouping like terms
Solution: in the expression
(𝑥 𝑦 + 2𝑥 2 𝑦) + (𝑥𝑦 + 3𝑥𝑦 − 4𝑥𝑦) − 𝑥𝑦 2
2 ⚫ like terms can be
3𝑥 2 𝑦 + 0 − 𝑥𝑦 2 added and/or
3𝑥 2 𝑦 − 𝑥𝑦 2 subtracted
⚫ unlike terms
c) 3𝑥 2 + 13𝑥 + 7 + 2𝑥 2 − 8𝑥 − 12 cannot be added
Solution:
or subtracted
3𝑥 + 2𝑥 2 + 13𝑥 − 8𝑥 + 7 − 12
2
⚫ addition and
5𝑥 2 + 5𝑥 −5 subtraction
separate terms
11. CLASSWORK/HOMEWORK

12. SUPPORT
For learners at risk do support activities.

13. ADDITIONAL NOTES FOR TEACHERS

14. TEACHER REFLECTION:

15. LEARNER WORKSHEET
MENTAL MATHS
1. 3(3 + 2)=…….
2. 3 – (5 + 11) + 13= ……..
3. (3 + 4) + 6 = 3 + (….. +……)
4. -5 × 3 = 3 × ……
5. 23 × 24 = ……..
6. 35 ÷ 32 = …….
CLASSWORK

a)
b)
c)

a)
b)
c)
d)

a)
b)
c)

a)
b)
c)

a)
b)
c)
d)
e)
f)
 Gauteng Province
Grade 9 Lesson Plan 3
Term 2
1. TOPIC: ALGEBRAIC EXPRESSIONS
2. DATE: 10 April 2024 DURATION: 1 hour
3. OBJECTIVES:
By the end of the lesson, learners should know and be able to
Use the commutative, associative and distributive laws for rational numbers and laws of
exponents to:
Multiply integers and monomials by:
✓ monomials
✓ binomial
✓ trinomials
Divide the following by integers or monomials:
✓ monomials
✓ binomials
✓ trinomials

4. RESOURCES: DBE workbook 2 & any other textbook

5. REVIEW AND CORRECTION OF HOMEWORK (Suggested time:5 minutes)
6. PRIOR KNOWLEDGE:
• laws of exponents
• commutative, associative and distributive properties
• like and unlike terms

7. MENTAL MATHS: (Suggested time:5 minutes)

Simplify without using a calculator:

1. 7(-5 + 2) = [7 × (-5)] + [7 × 2] 2. -
4[(-2) – (-5)] = [(-4) × (-2)] – [(-4) × (-5)] 3.
a(b + c) = ab + ac

8. ENGLISH ACROSS THE CURRICULUM: (Suggested time:10 minutes)

Revise:
Terminology
Commutative property
This law applies to addition and multiplication of numbers; it tells us that even if we change the
order of the numbers we still get the same answer.
4𝑥 + (−2𝑥) = −2𝑥 + 4𝑥
−5𝑥 × 3𝑦 = 3𝑦 × − 5𝑥
Associative property
This rule also applies to addition and multiplication; it allows us to group numbers when adding
or multiplying and still get the same answer.
3𝑥 + (−5𝑥) + 6𝑥 = [3𝑥 + (−5𝑥)] + 6𝑥 = 3𝑥 + [−5𝑥 + 6𝑥]
3𝑥 × (−5𝑥) × 6𝑥 = [3𝑥 × (−5𝑥)] × 6𝑥 = 3𝑥 × [−5𝑥 × 6𝑥]
Distributive property
When multiplying across addition or subtraction this property allows us to redistribute the
numbers and still get the same answer.
7(−5𝑥 + 2) = [7 × −5𝑥] + [7 × 2] = −35𝑥 + 14

Assessment Words
Group
Add
Subtract
Identify
Multiply
Divide
9. INTRODUCTION (Suggested time:10 Minutes)

Activity 2
Discuss with learners the multiplication and division laws of exponents by using the following
problems:

a) 3𝑥 3 × 4𝑥 2 = 12𝑥 5
b) 𝑎2 𝑏 3 × 𝑎7 𝑏 5 = 𝑎9 𝑏 8
c) 𝑥 7 ÷ 𝑥 2 = 𝑥 5
𝑑2𝑒 5 𝑒2
d) =
𝑑7𝑒 3 𝑑2

10. LESSON PRESENTATION/ DEVELOPMENT (Suggested time:15 minutes)

NOTE STRUCTURE:

Multiply monomials:
Simplify: 5𝑥 2 𝑦 × −2𝑥 5 𝑦 2
Activity 1 = −10𝑥 7 𝑦 3
Demonstrate the following problems to the learners: ⚫ multiply the coefficients first
Simplify by using the distributive property. ⚫ Use laws of exponents to
multiply the variables
a) 3𝑥 2 × 5𝑥 3
 Solution: Multiply integer with a binomial:
15𝑥 5 Simplify: −5(𝑎 + 2𝑏)
= −5𝑎 − 10𝑏
b) 𝑎(𝑏 + 𝑐) ⚫ Use distributive property to
Solution: multiply
𝑎×𝑏+𝑎×𝑐 ⚫ Multiply (−5 × 𝑎) + (−5 × 2𝑏)
𝑎𝑏 + 𝑎𝑐
Multiply monomial with a
c) – 3(2𝑥 2 − 3𝑥 + 4) trinomial:
Solution:
Simplify: 5𝑎(3𝑎 + 8𝑏 − 𝑐)
(– 3 × 2𝑥 2 ) + (– 3 × −3𝑥) + (– 3 × +4)
= 15𝑎2 + 40𝑎𝑏 − 5𝑎𝑐
(– 6𝑥 2 ) + (9𝑥) + (– 9)
⚫ Use distributive property to
– 6𝑥 2 + 9𝑥 − 9
multiply
⚫ Multiply (5𝑎 × 3𝑎) + (5𝑎 ×
Activity 3
8𝑏) + (5𝑎 × −𝑐)
a) Demonstrate the following problem to the learners:

Divide monomials:
(6𝑎 + 9𝑏) ÷ 3
Simplify: 15𝑎 ÷ 3𝑏
Solution: 15𝑎
(6𝑎 ÷ 3) + (9𝑏 ÷ 3) =
3𝑏
2𝑎 + 3𝑏 5𝑎
=
𝑏

b) Show learners that this problem can also be written

6𝑎 + 9𝑏 Divide binomials:
in a fraction form i.e. 14𝑥 2 + 7𝑥
3 Simplify:
Solution: 14𝑥
14𝑥 2 7𝑥
6𝑎 9𝑏 = +
+ 14𝑥 14𝑥
3 3 1
=𝑥+
2𝑎 + 3𝑏 2

Divide trinomials:
4𝑥 2 𝑦4 −6𝑥𝑦 3 + 𝑦 2
Simplify:
4𝑥𝑦
4𝑥 2 𝑦 4 6𝑥𝑦 3 𝑦2
= − +
4𝑥𝑦 4𝑥𝑦 4𝑥𝑦

3𝑦 2 𝑦
= 𝑥𝑦 3 − +
2 4𝑥
11. CLASSWORK/HOMEWORK
Activity 1

Simplify:
1. −3𝑟 3 × −𝑟 × 5𝑟 2
2. −3𝑥(5𝑥 − 11)
3. 10(6𝑥 3 𝑦 − 7𝑥 2 𝑦 − 12𝑥)
Activity 2

Simplify:
−10𝑝12 𝑞8
1.
40𝑝7 𝑞
12𝑥 12 𝑦 10 −3𝑥(2𝑥 9 𝑦 12 )
2.
8𝑥 3 𝑦 10
3𝑥 20 𝑦 2 −9𝑥 4 𝑦 4 +𝑥𝑦 9
3.
9𝑥𝑦 2

12. SUPPORT
For learners at risk do support activities.

13. ADDITIONAL NOTES FOR TEACHERS

14. TEACHER REFLECTION:

15. LEARNER WORKSHEET

MENTAL MATHS
1. 7(-5 + 2) = [7 × (-5)] + [7 × 2]= ………….
2. -4[(-2) – (-5)] = [(-4) × (-2)] – [(-4) × (-5)]= ………….
3. a(b + c) = ab + ac = …………..
CLASSWORK
Simplify:
1. −3𝑟 3 × −𝑟 × 5𝑟 2

2. −3𝑥(5𝑥 − 11)

3. 10(6𝑥 3 𝑦 − 7𝑥 2 𝑦 − 12𝑥)

−10𝑝12 𝑞8
4.
40𝑝7 𝑞

12𝑥 12 𝑦 10 −3𝑥(2𝑥 9 𝑦 12 )
5.
8𝑥 3 𝑦 10

3𝑥 20 𝑦 2 −9𝑥 4 𝑦 4 +𝑥𝑦 9
6.
9𝑥𝑦 2
 Gauteng Province
Grade 9 Lesson Plan 4
Term 2
1. TOPIC: ALGEBRAIC EXPRESSIONS
2. DATE: 11 April 2024 DURATION: 1 hour
3. OBJECTIVES:
By the end of the lesson, learners should know and be able to
Use the commutative, associative and distributive laws for rational numbers and laws of
exponents to:
Add and subtract like terms in algebraic expressions
Multiply integers and monomials by:
✓ monomials
✓ binomial
✓ trinomials
Divide the following by integers or monomials:
✓ monomials
✓ binomials
✓ trinomials
Simplify algebraic expressions involving the above operations
4. RESOURCES: DBE workbook 2 & any other textbook
5. REVIEW AND CORRECTION OF HOMEWORK (Suggested time:5 minutes)
6. PRIOR KNOWLEDGE:
⚫ Algebraic language
⚫ laws of exponents
⚫ commutative, associative and distributive properties

7. MENTAL MATHS: (Suggested time:5 minutes)

Simplify without a calculator
(1) (-9)[(-1) + (-3)]
(2) -7[9 – (-2)]
(3) 12 + (13 – 1)
(4) 2(5𝑥 + 8) − 2𝑥 − 3
(5) (2𝑎 + 5) − (4𝑎 − 5)

8. ENGLISH ACROSS THE CURRICULUM: (Suggested time:10 minutes)

Revise:
Terminology
Commutative property
This law applies to addition and multiplication of numbers; it tells us that even if we change the
order of the numbers we still get the same answer.
4𝑥 + (−2𝑥) = −2𝑥 + 4𝑥
−5𝑥 × 3𝑦 = 3𝑦 × − 5𝑥
Associative property
This rule also applies to addition and multiplication; it allows us to group numbers when adding
or multiplying and still get the same answer.
3𝑥 + (−5𝑥) + 6𝑥 = [3𝑥 + (−5𝑥)] + 6𝑥 = 3𝑥 + [−5𝑥 + 6𝑥]
3𝑥 × (−5𝑥) × 6𝑥 = [3𝑥 × (−5𝑥)] × 6𝑥 = 3𝑥 × [−5𝑥 × 6𝑥]
Distributive property
When multiplying across addition or subtraction this property allows us to redistribute the
numbers and still get the same answer.
7(−5𝑥 + 2) = [7 × −5𝑥] + [7 × 2] = −35𝑥 + 14

Assessment Words
Group
Add
Subtract
Identify
Multiply
Divide
Simplify

9. INTRODUCTION (Suggested time:10 Minutes)

Activity 1
Discuss with learners questions below based on work covered in previous lessons:

10. LESSON PRESENTATION/ DEVELOPMENT (Suggested time:15 minutes)

Activity 1 NOTE STRUCTURE:

Learners do the activity as a follow

up lesson.
11. CLASSWORK/HOMEWORK

12. SUPPORT
For learners at risk do support activities.

13. ADDITIONAL NOTES FOR TEACHERS

14. TEACHER REFLECTION:

15. LEARNER WORKSHEET

MENTAL MATHS
Simplify without a calculator:
1. [(-1) + (-3)] = …………
2. -7[9 – (-2)] = ………….
3. 12 + (13 – 1) = …………..
4. 2(5𝑥 + 8) − 2𝑥 − 3 = …………..
5. (2𝑎 + 5) − (4𝑎 − 5) = ………..
 Gauteng Province
Grade 9 Lesson Plan 5
Term 2
1. TOPIC: ALGEBRAIC EXPRESSIONS
2. DATE: 12 April 2024 DURATION: 1 hour
3. OBJECTIVES:
By the end of the lesson, learners should know and be able to
determine the squares, cubes, square roots and cube roots of single algebraic terms or like
algebraic terms
4. RESOURCES: DBE workbook 2 & any other textbook
5. REVIEW AND CORRECTION OF HOMEWORK (Suggested time:5 minutes)
6. PRIOR KNOWLEDGE:
• squares
• cubes
• square roots
• cube roots
• laws of exponents

7. MENTAL MATHS: (Suggested time:5 minutes)

1. Write in exponential form:
(a) 2 × 2
(b) (b) 2 × 2 × 2
2. Simplify without a calculator:
(a) √4
3
(b) (b) √27
(c) (c) √16 + 9
3. Complete:
(a) (𝑦 𝑚 )𝑛 = ⋯
(b) (𝑥𝑦)𝑚 = ⋯

8. ENGLISH ACROSS THE CURRICULUM: (Suggested time:10 minutes)

Revise:
Terminology
Commutative property
This law applies to addition and multiplication of numbers; it tells us that even if we change the
order of the numbers we still get the same answer.
4𝑥 + (−2𝑥) = −2𝑥 + 4𝑥
−5𝑥 × 3𝑦 = 3𝑦 × − 5𝑥
Associative property
This rule also applies to addition and multiplication; it allows us to group numbers when adding
or multiplying and still get the same answer.
 3𝑥 + (−5𝑥) + 6𝑥 = [3𝑥 + (−5𝑥)] + 6𝑥 = 3𝑥 + [−5𝑥 + 6𝑥]
3𝑥 × (−5𝑥) × 6𝑥 = [3𝑥 × (−5𝑥)] × 6𝑥 = 3𝑥 × [−5𝑥 × 6𝑥]
Distributive property
When multiplying across addition or subtraction this property allows us to redistribute the
numbers and still get the same answer.
7(−5𝑥 + 2) = [7 × −5𝑥] + [7 × 2] = −35𝑥 + 14

Assessment Words
Group
Add
Subtract
Identify
Multiply
Divide
Simplify

9. INTRODUCTION (Suggested time:10 Minutes)

Ask the learners to give the mathematical meaning of the following concepts and provide
examples of it:
square, cube, square root and cube root

• A square number is a number that you get when a number is multiplied by itself once
e.g. 4 × 4 = 16. Therefore 16 is a square number.
• The square root is a value that multiplies by itself once to give the original number
e.g. 4 × 4 = 16. Therefore √16 = 4

Note:
Discuss the following misconceptions with the learners:
32 = 3 × 3 not 3 × 2
3×2=2+2+2
(3𝑥)2 = 3𝑥 × 3𝑥
=3×𝑥×3×𝑥
=3×3×𝑥×𝑥
= 9𝑥 2

• A cube number is a number you get when a number is multiplied by itself two times e.g.
3 × 3 × 3 = 27. Therefore 27 is a cube number
• A cube root is a value that multiplies by itself two times to give the original number
3
e.g. 3 × 3 × 3 = 27. Therefore √27 = 3

10. LESSON PRESENTATION/ DEVELOPMENT (Suggested time:15 minutes)

NOTE STRUCTURE:
Let the learners complete the following activities individually as part
of revision:

Activity 1

Determine the value of each without the use of a calculator:

3
a) √25 b) √144 c) √64
3
d) √216
• The square root of
Discuss the following with learners and with their assistance a product of
complete the activities square numbers is
equal to the
e.g. √ 25 × 9 = √25 × √9 product of the
square roots
=5 ×3

= 15

• Discuss the misconceptions with learners. • The square of the

sum of square
numbers is not
√25 + 9 ≠ √25 + √9
equal to the sum of
the square roots.
√34 ≠ 5+3

√34 ≠ 8
• The square of the
√100 − 64 ≠ √100 − √64 difference of
square numbers is
not equal to the
√36 ≠ 10 − 8
difference of the
square roots.
√36 ≠ 2
• The square root of
81 √81 9 a quotient of
√ = =
4 √4 2 square numbers is
equal to the
Activity 2 quotient of the
square root.
Demonstrate the following problems to learners.
• Change the
a) √0,49 decimal fraction
49 into an improper
=√
100 fraction
√49 • Determine the
=
√100 square root of both
 7 the numerator and
=
10 the denominator
= 0,7 • Convert the
improper fraction
Learners to determine the cube root: into a proper
b) 3√0,0027 fraction

Activity 3
Discuss with learners questions below:

11. CLASSWORK/HOMEWORK
Activity 1
1. Simplify the following

(a) √𝑥 12
(b)
(c)
(d) √125𝑥 2 + 44𝑥 2
(e)
3
(f) √−27𝑥 3
(g)

2. Say whether the equation is true or false. Give a reason for your answer.

√7𝑥 2 × 7𝑥 2 = 7𝑥 2

3. Simplify the following:

 a) (25𝑥 − 16𝑥)2
b) (2𝑥 3 )3

12. SUPPORT
For learners at risk do support activities.

13. ADDITIONAL NOTES FOR TEACHERS

14. TEACHER REFLECTION:

15. LEARNER WORKSHEET

MENTAL MATHS
1. Write in exponential form:
(a) 2 × 2 = …….
(b) 2 × 2 × 2 = ……
2. Simplify without a calculator:
(a) √4 = ……..
3
(b) √27 = ……
(c) √16 + 9 = ……
3. Complete:
(a) (𝑦 𝑚 )𝑛 = ⋯
(b) (𝑥𝑦)𝑚 = ⋯

CLASSWORK
1. Simplify the following
(a) √𝑥 12

(b)
(c)

(d) √125𝑥 2 + 44𝑥 2

(e)

3
(f) √−27𝑥 3

(g)

2. Say whether the equation is true or false. Give a reason for your answer.

√7𝑥 2 × 7𝑥 2 = 7𝑥 2

3. Simplify the following:

(a) (25𝑥 − 16𝑥)2

(b) (2𝑥 3 )3
 Gauteng Province
Grade 9 Lesson Plan 6
Term 2
1. TOPIC: ALGEBRAIC EXPRESSIONS
2. DATE: 15 April 2024 DURATION: 1 hour
3. OBJECTIVES
By the end of the lesson, learners should know and be able to:
❖ multiply integers and monomials by:
o monomials
o binomial
o trinomials

4. RESOURCES: DBE workbook & any other textbook

5. REVIEW AND CORRECTION OF HOMEWORK (suggested time:5 minutes)
• PRIOR KNOWLEDGE: types of expressions- monomial, binomials
• variables
• coefficient
• laws of exponents
• factors
• distributive law
6. MENTAL MATHS: (Suggested time:10 minutes)

7. ENGLISH ACROSS THE CURRICULUM: (Suggested time:5 minutes)

Terminology
A binomial is a polynomial with exactly 2 terms e.g. 𝑥 + 2 or 𝑥 2 + 3𝑥
A trinomial is a polynomial with exactly 3 terms e.g. 𝑥 2 + 2𝑥 + 1
A polynomial is an algebraic expression involving a sum of powers in
one or more variables multiplied by coefficients.
Assessment Words
Determine the following, Simplify the expression

8. INTRODUCTION (Suggested time:10 Minutes)

Educator - Write the following Algebraic Expression on the board:
Remind learners of the properties of whole numbers(Distributive property).
An Algebraic Expression is made up of numbers, variables and operations signs, that can also
be described in words in some cases they can be described with flow diagrams.
Allow learners to do the following activities:
1. Calculate the following:
a) 5(3 + 4)
b) 5 × 3 + 5 × 4
c) 6 × 3 + (4 + 6)
d) (6 + 4) + 3 × 6
e) 3 × (4 × 5)
f) (3 × 4) ×5
2. Which properties are applied in (a) and (b), (c) and (d), (e) and (f)
9. LESSON PRESENTATION/ DEVELOPMENT (Suggested time:15 minutes)
Example 1
= −3(𝑥 3 + 2𝑥 2 − 2) (Use the Distributive property to expand/multiply) NOTE STRUCTURE:
Remind learners about
= (−3 × 𝑥 3 ) + (−3 × 2𝑥 2 ) + (−3 × −2)
laws of exponents.
= −3𝑥 3 − 6𝑥 2 + 6 (simplify)
Utilization of the
Distributive law to
Example 2
simplify.
𝑥(2𝑥 4 + 𝑥 3 − 3𝑥 2 + 𝑥 − 13)
laws of exponents
= 2𝑥 4+1 + 𝑥 3+1 − 3𝑥 2+1 + 𝑥 1+1 − 13𝑥 0+1
applicable
5 4 3 2
= 2𝑥 + 𝑥 − 3𝑥 + 𝑥 − 13𝑥 (𝑥 𝑎 )𝑏 = 𝑥 𝑎𝑏
Find solutions to the following activities with learners. 𝑥 𝑎 × 𝑥 𝑏 = 𝑥 𝑎+𝑏
Multiplication is
Present and do the following activities with the learners distributed over
addition and
Activity 1 subtraction. You may
have used this property
a) −2𝑥( 𝑥 4 + 3𝑥 3 − 𝑥 2 + 𝑥 − 1) − (𝑥 5 + 2𝑥 3 + 𝑥 2 + 𝑥) before to multiply
b) (𝑥 + 3)(𝑥 − 5 ) numbers:
c) (𝑥 + 3)2 Engage in discussion
and work with the
learners to find
Solutions solutions in activities a
a) −2𝑥( 𝑥 4 + 3𝑥 3 − 𝑥 2 + 𝑥 − 1) − (𝑥 5 + 2𝑥 3 + 𝑥 2 + 𝑥) –d
= −2𝑥 5 − 6𝑥 4 + 2𝑥 3 − 2𝑥 2 + 2𝑥 − 𝑥 5 − 2𝑥 3 − 𝑥 2 − 𝑥 a) Emphasise that:
= (−2𝑥 5 − 𝑥 5 ) + (−6𝑥 4 ) + (+2𝑥 3 − 2𝑥 3 ) + (−2𝑥 2 − 𝑥 2 ) + • like terms can
(2𝑥 − 𝑥) be added and/or
= −3𝑥 5 − 6𝑥 4 − 3𝑥 2 + 𝑥 subtracted
 b) (𝑥 + 3)(𝑥 − 5 ) • unlike terms
= (𝑥 × 𝑥) + (𝑥 × −5) + (3 × 𝑥) + (3 × −5) cannot be
= 𝑥 2 − 5𝑥 + 3𝑥 − 15 added or
= 𝑥 2 − 2𝑥 − 15 subtracted
• addition and
(𝑥 + 2) 2 subtraction
c)
= (𝑥 + 2)(𝑥 + 2) separate terms
= 𝑥 2 + 2𝑥 + 2𝑥 + 4 • multiplication
= 𝑥 2 + 4𝑥 + 4z and division
combine terms
• the denominator
cannot be equal
to zero

10. CLASSWORK/ HOMEWORK (Suggested time:15 minutes)

Learners do the following activities in their classwork books:

Simplify:

2x5 +6x4 −8x3 −2x2 + 4x

a)
2x

b) 𝑥(2𝑥 4 + 𝑥 3 − 3𝑥 2 + 𝑥 − 13)

c) (𝑥 − 3)2

11. SUPPORT
For learners at risk do support activities. (Choose questions from DBE workbook)

12. ADDITIONAL NOTES FOR TEACHERS

13. TEACHER REFLECTION:

14. LEARNER WORKSHEET
MENTAL MATHS

15. CLASSWORK
Simplify:

2x5 +6x4 −8x3 −2x2 + 4x

(a)
2x

(b) 𝑥(2𝑥 4 + 𝑥 3 − 3𝑥 2 + 𝑥 − 13)

(c) (𝑥 − 3)2
 Gauteng Province
Grade 9 Lesson Plan 7
Term 2
1. TOPIC: ALGEBRAIC EXPRESSIONS
2. DATE: 16 April 2024 DURATION: 1 hour
3. OBJECTIVES
By the end of the lesson, learners should know and be able to:
❖ Divide the following by integers or monomials:
o monomials
o binomials
o trinomials
❖ simplify algebraic expressions involving the above operations.

4. RESOURCES: DBE workbook & any other textbook

5. REVIEW AND CORRECTION OF HOMEWORK (suggested time:5 minutes)
• PRIOR KNOWLEDGE: types of expressions- monomial, binomials
• variables
• coefficient
• laws of exponents
• factors
6. distributive law
7. MENTAL MATHS: (Suggested time:10 minutes)
Make 24 with all 4 numbers on the card. You can add, subtract, multiply or divide. You have
to use all four numbers. Each number may be used only once.
For example: if the numbers are 2, 2, 6, 8:
You could make 24 by explaining (8-2) x (6-2) = 24.
(There might be more than one solution) Don’t get mixed up with a 6 and a 9 - every number
is underlined, so you can clearly see the difference!

8. ENGLISH ACROSS THE CURRICULUM: (Suggested time:5 minutes)

Terminology
A binomial is a polynomial with exactly 2 terms e.g. 𝑥 + 2 or 𝑥 2 + 3𝑥
A trinomial is a polynomial with exactly 3 terms e.g. 𝑥 2 + 2𝑥 + 1
A polynomial is an algebraic expression involving a sum of powers in
one or more variables multiplied by coefficients.
Factorization or factoring consists of writing a number or another mathematical object as a
product of several factors, usually smaller or simpler objects of the same kind. For example,
3 × 5 is an integer factorization of 15, and (𝑥 – 2)(𝑥 + 2) is a polynomial factorization of 𝑥 2 – 4.
Assessment Words
Determine the following, Simplify the expression

9. INTRODUCTION (Suggested time:10 Minutes)

Educator –
Revise the following with learners:
Simplify

a) −3(𝑥 3 + 2𝑥 2 − 2 ) − 𝑥(3𝑥 + 1)
b) (𝑥 + 2)(𝑥 − 3 )
𝑥3 𝑥2
c) +
𝑥2 𝑥4
d) 2(𝑥 − 3)2 − 3(𝑥 + 1)
e) √36𝑥 2

10. LESSON PRESENTATION/ DEVELOPMENT (Suggested time:15 minutes)

If 𝑥(𝑥 − 2) = 𝑥 2 − 2𝑥 then 𝒙 and (𝒙 − 𝟐) are factors of 𝒙𝟐 − 𝟐𝒙.
We also notice that 𝒙 appears in both terms. NOTE STRUCTURE:
Engage in discussion
2
If we look at 𝑥 − 2𝑥 and work with the
= 𝑥. 𝑥 − 2. 𝑥 learners to find
solutions in activities a
In this case 𝒙 is the highest common factor (HCF) of 𝒙𝟐 − 𝟐𝒙.
–d
The focus of this lesson is to find the factors of algebraic expressions.
In other words, the reverse
process of multiplication.
Find solutions to the following activities with learners.
Simplify the following algebraic expressions Emphasise that:
• like terms can be
2𝑝3 −𝑝𝑥 2 added and/or
a)
𝑝
subtracted
−8𝑥 4 +4𝑥 3 𝑦 −2𝑥 2
b)
2𝑥 • unlike terms cannot
c) 𝑥(−2𝑥) − 3𝑥(4𝑥 − 𝑥 2 ) + 6(𝑥 3 + 2𝑥 2 + 5) be added or
8𝑥 3 2𝑥 3 −𝑥 2 2𝑥 4 +4𝑥 3 −2𝑥 2 subtracted
d) + +
−2 𝑥 2𝑥
• addition and
subtraction
Solution
separate terms
• multiplication and
2𝑝3 −𝑝𝑥 2
a) division combine
𝑝
2𝑝3 𝑝𝑥 2 terms.
= − • the denominator
𝑝 𝑝
2
= 2𝑝 − 𝑥 2 cannot be equal to
zero.
−8𝑥 3 4𝑥 3 𝑦 2𝑥 2
b) + −
2𝑥 2𝑥 2𝑥
= −4𝑥 2 + 2𝑥 2 𝑦 − 𝑥

c) 𝑥(−2𝑥) − 3𝑥(4𝑥 − 𝑥 2 ) + 6(𝑥 3 + 2𝑥 2 + 5)

= −2𝑥 2 − 12𝑥 2 + 3𝑥 3 + 6𝑥 3 + 12𝑥 2 + 30
= (3𝑥 3 + 6𝑥 3 ) + (−2𝑥 2 − 12𝑥 2 + 12𝑥 2 ) + 30
= 9𝑥 3 − 2𝑥 2 + 30

8𝑥 3 2𝑥 3 −𝑥 2 2𝑥 4 +4𝑥 3 −2𝑥 2
d) + +
−2 𝑥 2𝑥
8𝑥 3 2𝑥 3 𝑥2 2𝑥 4 4𝑥 3 2𝑥 2
= + − + + −
−2 𝑥 𝑥 2𝑥 2𝑥 2𝑥
3 2 3 2
= −4𝑥 + 2𝑥 − 𝑥 + 𝑥 + 𝑥 − 𝑥
= (−4𝑥 3 + 𝑥 3 ) + (2𝑥 2 + 𝑥 2 ) + (−𝑥 − 𝑥)
= −3𝑥 3 + 3𝑥 2 − 2𝑥
11. CLASSWORK/ HOMEWORK (Suggested time:15 minutes)
Learners do the following activities in their classwork books:
Simplify

12𝑥 2 𝑦−6𝑥𝑦 2
a)
3𝑥𝑦
b) −2(4𝑥 − 2𝑥 2 ) − 6 + 5𝑥(3𝑥 2 − 𝑥 + 5)
15𝑚3 + 3𝑚2
c)
3

27𝑚5 + 9𝑚4 −12𝑚3 15𝑚3 − 3𝑚2

d) + +1
−3𝑚 3
12. SUPPORT
For learners at risk do support activities. (Choose questions from DBE workbook)

13. ADDITIONAL NOTES FOR TEACHERS

14. TEACHER REFLECTION:

15. LEARNER WORKSHEET

MENTAL MATHS
Make 24 with all 4 numbers on the card. You can add, subtract, multiply or divide. You have
to use all four numbers. Each number may be used only once.
For example: if the numbers are 2, 2, 6, 8:
You could make 24 by explaining (8-2) x (6-2) = 24.
(There might be more than one solution) Don’t get mixed up with a 6 and a 9 - every number
is underlined, so you can clearly see the difference!

16. CLASSWORK
Simplify:

12𝑥 2 𝑦−6𝑥𝑦 2
a)
3𝑥𝑦
b) −2(4𝑥 − 2𝑥 2 ) − 6 + 5𝑥(3𝑥 2 − 𝑥 + 5)

15𝑚3 + 3𝑚2
c)
3

27𝑚5 + 9𝑚4 −12𝑚3 15𝑚3 − 3𝑚2

d) + +1
−3𝑚 3
 Gauteng Province
Grade 9 Lesson Plan 8
Term 2
1. TOPIC: ALGEBRAIC EXPRESSIONS
2. DATE: 17 April 2024 DURATION:1 hour
3. OBJECTIVES
By the end of the lesson, learners should know and be able to:
• multiply binomial by binomial
4. RESOURCES: DBE workbook & any other textbook
5. REVIEW AND CORRECTION OF HOMEWORK (suggested time:5 minutes)
• PRIOR KNOWLEDGE: types of expressions- monomial, binomials
• variables
• coefficient
• laws of exponents
• factors
• distributive law
6. MENTAL MATHS: (Suggested time:10 minutes)
make 24 with all 4 numbers on the card. You can add, subtract, multiply or divide. You have
to use all four numbers. Each number may be used only once.
For example: if the numbers are 2, 2, 6, 8:
You could make 24 by explaining (8-2) x (6-2) = 24.
(There might be more than one solution)Don't get mixed up with a 6 and a 9 - every number
is underlined, so you can clearly see the difference!

7. ENGLISH ACROSS THE CURRICULUM: (Suggested time:5 minutes)

Terminology
A binomial is a polynomial with exactly 2 terms e.g. 𝑥 + 2 or 𝑥 2 + 3𝑥
A trinomial is a polynomial with exactly 3 terms e.g. 𝑥 2 + 2𝑥 + 1
A polynomial is an algebraic expression involving a sum of powers in
one or more variables multiplied by coefficients.
Assessment Words
Determine the following, Simplify the expression

8. INTRODUCTION (Suggested time:10 Minutes)

Consider the product (𝑎 + 𝑏)(𝑐 + 𝑑) . We can use the distributive, commutative and associative
laws to multiply the two binomials.

This is done using what we can call the FOIL method.

Here you must first multiply the first terms in each bracket. Then you multiply the outer
terms, then the inner terms and finally the last terms.
9. LESSON PRESENTATION/ DEVELOPMENT (Suggested time:15 minutes)
Example 1
Expand and simplify the following: NOTE STRUCTURE:
(a) (x 3)(x 4) Remind learners about
Whenever a monomial
Solution is raised to a further
power, it is important
to work through the
following steps:
Step 1: Evaluate the
signs using the fact
that (−)𝑒𝑣𝑒𝑛 𝑛𝑢𝑚𝑏𝑒𝑟
and (−)𝑜𝑑𝑑 𝑛𝑢𝑚𝑏𝑒𝑟
For example: (−1)4
( 1)( 1)( 1)( 1)
(−1)4 (1)4 1
(−1)5
( 1)( 1)( 1)( 1)( 1)
(−1)5 (−1)5 1
b) Step 2: Raise the
coefficient to the
given power by
using the laws of
exponents
c) .Emphasise that:
• like terms can
be added and/or
subtracted
• unlike terms
cannot be
 © (𝑥 + 2)(𝑥 − 2) added or
2
= 𝑥 − 𝟐𝒙 + 𝟐𝒙 − 4 subtracted
= 𝑥2 − 4 • addition and
subtraction
separate terms
• multiplication
and division
(Remember additive combine terms.
inverse of −𝟐𝒙 𝒊𝒔 + 𝟐𝒙 • the denominator
which will give you 0) cannot be equal
to zero.
10. CLASSWORK/ HOMEWORK (Suggested time:15 minutes)
Learners do the following activities in their classwork books:
Expand and simplify:

11. SUPPORT
For learners at risk do support activities. (Choose questions from DBE workbook)

12. ADDITIONAL NOTES FOR TEACHERS

13. TEACHER REFLECTION:

14. LEARNER WORKSHEET

MENTAL MATHS
make 24 with all 4 numbers on the card. You can add, subtract, multiply or divide. You have
to use all four numbers. Each number may be used only once.
For example: if the numbers are 2, 2, 6, 8:
You could make 24 by explaining (8-2) x (6-2) = 24.
 (There might be more than one solution)Don't get mixed up with a 6 and a 9 - every number
is underlined, so you can clearly see the difference!

15. CLASSWORK
Expand and simplify:
 Gauteng Province
Grade 9 Lesson Plan 9
Term 2
1. TOPIC: ALGEBRAIC EXPRESSIONS
2. DATE: 18 April 2024 DURATION: 1 hour
3. OBJECTIVES
By the end of the lesson, learners should know and be able to

✓ Determine the numerical value of algebraic expressions by substitution,

DBE workbook (Page 72 – 92), Sasol-Inzalo workbook (Page 152
4. RESOURCES:
– 143), textbook, ruler, pencil, eraser, calculators,
5. REVIEW AND CORRECTION OF HOMEWORK (suggested time:5 minutes)
Simplify:

(1) 3(5𝑥 2 )2 = 𝟑(𝟐𝟓𝒙𝟒 ) = 𝟕𝟓𝒙𝟒

2
3𝑥 2 𝟗𝒙𝟒 𝒙𝟒
(2) ( ) = =
6𝑦 𝟑𝟔𝒚𝟐 𝟒𝒚𝟐

(3) √144𝑥 4 × 9𝑦 2 = 𝟏𝟐𝒙𝟐 × 𝟑𝒚 = 𝟑𝟔𝒙𝟐 𝒚

(4) √16𝑥 4 + 9𝑥 4 = √𝟐𝟓𝒙𝟒 = 𝟓𝒙𝟐

3
(5) √27𝑥 6 = 𝟑𝒙𝟐

PRIOR KNOWLEDGE:
• Squares,
• Cubes,
• square/cube Roots
• Exponents
6. MENTAL MATHS: (Suggested time:10 minutes)
𝑥 -2 5 -1
𝑦 4 -3 2
𝑥+𝑦
7+𝑥−𝑦
(2𝑦)(4𝑥) + 5
7. ENGLISH ACROSS THE CURRICULUM: (Suggested time:5 minutes)
Terminology
Exponent -
Power
Square Square roots
Cubes/ Cube Roots
Base
Assessment Words
Determine the following, Simplify the expression.
8. INTRODUCTION (Suggested time:10 Minutes)
Educator –
Revise the following with learners:
Simplify:
(1) 3(5𝑥 2 )2 = 𝟑(𝟐𝟓𝒙𝟒 ) = 𝟕𝟓𝒙𝟒

2
3𝑥 2 𝟗𝒙𝟒 𝒙𝟒
(2) ( ) = =
6𝑦 𝟑𝟔𝒚𝟐 𝟒𝒚𝟐

(3) √144𝑥 4 × 9𝑦 2 = 𝟏𝟐𝒙𝟐 × 𝟑𝒚 = 𝟑𝟔𝒙𝟐 𝒚

(4) √16𝑥 4 + 9𝑥 4 = √𝟐𝟓𝒙𝟒 = 𝟓𝒙𝟐

3
(5) √27𝑥 6 = 𝟑𝒙𝟐

9. LESSON PRESENTATION/ DEVELOPMENT (Suggested time:15 minutes)

Educator asks learners to discuss what substitution is with
examples NOTE STRUCTURE:
Determine the squares,
• Substitution: cubes, square roots
and cube roots of
When we determine the numerical value of an expression we single algebraic
replace the variable with a constant. terms or like
algebraic terms,
Examples:
(1) If 𝑥 = −3 𝑎𝑛𝑑 𝑦 = 5, find the values of:
(1.1) 𝑥 + 𝑦
= −3 + 5 = 2

(1.2) (𝑦 − 𝑥)(𝑥 − 𝑦)
= [5 − (−3)][−3 − (5)] = [8][−8] = −64
5𝑥
(1.3)
4𝑦
5(−3) −15 3
= = = −
4(5) 20 4
(2) If 𝑥 = 2 and 𝑦 = 5𝑥 − 7, find the value of 𝑦
 ∴ 𝑦 = 5(2) − 7 ∴𝑦=3

(3) Calculate the area of the rectangle with sides 2𝑥 and (𝑥 + 1)

given that 𝑥 = 6
𝐴 =𝑙 ×𝑏 ∴ 𝐴 = 2𝑥 × (𝑥 + 1) ∴ 𝐴 = 2𝑥 2 + 2𝑥

(Activity 1)

Educator asks learners to discuss the following substitutions in their

respective groups

• Substitution in square and cube roots

Example: If 𝑥 = 3 𝑎𝑛𝑑 𝑦 = 4, calculate the value of each of the
following
(a) √𝑥 2 + 𝑦 2 = √32 + 42 = √25 = 5
3 3
(b) √𝑥 3 = √33 = 3
• Substitution in formulae
Example: Calculate the perimeter of the following shapes if 𝑥 = 4

(a) 𝑥+3 (b)

𝑥+1 5𝑥 7𝑥

5𝑥
𝑃 = 2(𝑙 + 𝑏) ∴ 𝑃 = 2(𝑥 + 3 + 𝑥 + 1) 𝑃 = 5𝑥 + 5𝑥 + 7𝑥
∴ 𝑃 = 2(2𝑥 + 4) ∴ 𝑃 = 17𝑥
∴ 𝑃 = 2[2(4) + 4] = 24 P = 17(4) = 68

10. CLASSWORK/ HOMEWORK (Suggested time:15 minutes)

Learners do the following activities in their classwork books:
(1) Given 𝑦 = 𝑥 2 − 4, calculate 𝑦 when 𝑥 = −7
(2) Given that 𝑥 = 3, find the perimeter of a triangle with sides 5𝑥; 7𝑥 𝑎𝑛𝑑 3𝑥
(3) If 𝑎 = 4 and 𝑏 = 2𝑎, find the value of 𝑏. Use the formula of 𝑏 to find 𝑐, if 𝑐 = 2𝑏 − 2𝑎
11. SUPPORT
For learners at risk do support activities. (Choose questions from DBE workbook)

12. ADDITIONAL NOTES FOR TEACHERS

13. TEACHER REFLECTION:

14. LEARNER WORKSHEET

MENTAL MATHS
Complete the table:
𝑥 -2 5 -1
𝑦 4 -3 2
𝑥+𝑦
7+𝑥−𝑦
(2𝑦)(4𝑥) + 5
15. CLASSWORK
Substitute:
(1) Given 𝑦 = 𝑥 2 − 4, calculate 𝑦 when 𝑥 = −7

(2) Given that 𝑥 = 3, find the perimeter of a triangle with sides 5𝑥; 7𝑥 𝑎𝑛𝑑 3𝑥

(3) If 𝑎 = 4 and 𝑏 = 2𝑎, find the value of 𝑏. Use the formula of 𝑏 to find 𝑐, if 𝑐 = 2𝑏 − 2𝑎
 Gauteng Province
Grade 9 Lesson Plan 10
Term 2
1. ALGEBRAIC EXPRESSIONS
2. DATE: 19 April 2024 DURATION: 1 hour
3. OBJECTIVES
✓ By the end of the lesson learners should know and be able to:
factorise algebraic expressions that involve common factors.
DBE workbook (Page 72 – 92), Sasol-Inzalo workbook
4. RESOURCES:
(115 – 143), textbook, ruler, pencil, eraser, calculators,
5. REVIEW AND CORRECTION OF HOMEWORK (suggested time:5 minutes)
Simplify:

(6) 3(5𝑥 2 )2 = 𝟑(𝟐𝟓𝒙𝟒 ) = 𝟕𝟓𝒙𝟒

2
3𝑥 2 𝟗𝒙𝟒 𝒙𝟒
(7) ( ) = =
6𝑦 𝟑𝟔𝒚𝟐 𝟒𝒚𝟐

(8) √144𝑥 4 × 9𝑦 2 = 𝟏𝟐𝒙𝟐 × 𝟑𝒚 = 𝟑𝟔𝒙𝟐 𝒚

(9) √16𝑥 4 + 9𝑥 4 = √𝟐𝟓𝒙𝟒 = 𝟓𝒙𝟐

3
(10) √27𝑥 6 = 𝟑𝒙𝟐

PRIOR KNOWLEDGE:
• types of expressions- monomial, binomials
• variables
• coefficient
• laws of exponents
• factors
• H.C.F
• distributive law
6. MENTAL MATHS: (Suggested time:10 minutes)
𝑥 -2 5 -1
𝑦 4 -3 2
𝑥+𝑦
7+𝑥−𝑦
(2𝑦)(4𝑥) + 5
7. ENGLISH ACROSS THE CURRICULUM: (Suggested time:5 minutes)
Terminology
Exponent -
Power
Square Square roots
Cubes/ Cube Roots
Base
Assessment Words
Determine the following, Simplify the expression.
8. INTRODUCTION (Suggested time:10 Minutes)
Revise with learners by asking them the following questions:
Expand
f) 2[( 𝑥 + 2 ) + 3]
g) 3𝑥[(𝑥 − 2 ) + (𝑦 + 1)]

9. LESSON PRESENTATION/ DEVELOPMENT (Suggested time:15 minutes)

Discuss the following with learners NOTE

𝑎𝑐 + 𝑎𝑑 + 𝑏𝑐 + 𝑏𝑑 STRUCTURE:

Common factor

𝑎(𝑐+𝑑) + 𝑏 (𝑐 + 𝑑 )

( 𝑎 + 𝑏 )(𝑐 + 𝑑 )

Ask learners to identify what is common on the given expressions

a) 𝑏𝑥 − 𝑐𝑥 + 3𝑏 − 3𝑐
b) 𝑎𝑥 − 𝑏𝑥 − 𝑏𝑦 + 𝑎𝑦

Solutions

a) = (𝑏𝑥 − 𝑐𝑥) + (3𝑏 − 3𝑐)

= 𝑥(𝑏 − 𝑐) + 3(𝑏 − 𝑐)
= (𝑥 + 3)(𝑏 − 𝑐)

b) = (𝑎𝑥 − 𝑏𝑥) − (𝑏𝑦 − 𝑎𝑦)

= 𝑥(𝑎 − 𝑏) − 𝑦( 𝑏 − 𝑎)
= 𝑥(𝑎 − 𝑏) + 𝑦( 𝑎 − 𝑏) (change of sign in the second term)
= (𝑥 + 𝑦)( 𝑎 + 𝑏)
10. CLASSWORK/ HOMEWORK (Suggested time:15 minutes)
Learners do the following activities in their classwork books:

Factorise the following expressions.

a) 2𝑥 2 − 8𝑥
b) 𝑚𝑥 − 𝑚𝑦 + 5𝑥 − 5𝑦
c) 4𝑝(𝑐 − 𝑑) − 7(−𝑑 + 𝑐)
d) 3𝑚 − 3𝑑 − 4𝑑𝑒 + 4𝑚𝑒
(4) 𝑡𝑣 − 𝑢𝑣 − 𝑡𝑤 + 𝑢𝑤
11. SUPPORT
For learners at risk do support activities. (Choose questions from DBE workbook)

12. ADDITIONAL NOTES FOR TEACHERS

13. TEACHER REFLECTION:

14. LEARNER WORKSHEET

MENTAL MATHS
Complete the table:
𝑥 -2 5 -1
𝑦 4 -3 2
𝑥+𝑦
7+𝑥−𝑦
(2𝑦)(4𝑥) + 5

15. CLASSWORK
Factorise the following expressions:
(1) 2𝑥 2 − 8𝑥

(2) 𝑚𝑥 − 𝑚𝑦 + 5𝑥 − 5𝑦
(3) 4𝑝(𝑐 − 𝑑) − 7(−𝑑 + 𝑐)

(4) 3𝑚 − 3𝑑 − 4𝑑𝑒 + 4𝑚𝑒

(5) 𝑡𝑣 − 𝑢𝑣 − 𝑡𝑤 + 𝑢𝑤
 Gauteng Province
Grade 9 Lesson Plan 11
Term 2
1. TOPIC: ALGEBRAIC EXPRESSIONS
2. DATE: 22 April 2024 DURATION: 1 hour
3. OBJECTIVES
✓ By the end of the lesson learners should know and be able to factorise algebraic
expressions that involve difference of two squares.
DBE workbook (Page 72 – 92), Sasol-Inzalo
4. RESOURCES: workbook (115 – 143), textbook, ruler, pencil,
eraser, calculators,
5. REVIEW AND CORRECTION OF HOMEWORK (suggested time:5 minutes)
PRIOR KNOWLEDGE:
• types of expressions- monomial, binomials
• variables
• coefficient
• laws of exponents
• factors
• H.C.F
• distributive law
• Numerator
• Fraction
• Denominator
6. MENTAL MATHS: (Suggested time:10 minutes)

7. ENGLISH ACROSS THE CURRICULUM: (Suggested time:5 minutes)

Terminology
Exponent
Power
Square roots
Cubes/ Cube Roots
Base
Assessment Words
Determine the following, Simplify the expression.
8. INTRODUCTION (Suggested time:10 Minutes)
Revise with learners by asking them the following questions:

Activity 1

Determine:
a) √𝑥 2
 b) √𝑝6

Activity 2
Expand:
h) (𝑥 − 2)( 𝑥 + 2)
i) (2𝑥 − 1)( 2𝑥 + 1)
j) (2𝑥 + 4)(2𝑥 − 4)

9. LESSON PRESENTATION/ DEVELOPMENT (Suggested time:15 minutes)

Discuss the following with learners:
• Before you can simplify an algebraic fraction, it must have only one term NOTE
in both the numerator and denominator. STRUCTURE:
Factorise fully at the top and the bottom of the fraction to get one term in If the brackets
each. have opposite
• Simplify by dividing factors that are the same. signs and the
2𝑝2 +4𝑝 same
Example: variables and
3𝑝+6
2𝑝(𝑝 + 2) constants, the
=
3(𝑝 + 2) middle terms
2𝑝 will
=
3 always add up
Fraction Example: to 0. When
you see this
pattern,
you can work
quickly by just
multiplying
Firsts
and Lasts in
each bracket.

4𝑥 2 − 16

Step 1.

1. Are these two terms?

2. Are both coefficients (4 and 16) perfect squares?
3. Are all variables raised to an even power? (2, 4, 6,…)
4. Does one term have a positive coefficient and another term have
negative coefficient?
If your answer in all questions above is YES, then the expression is a
difference of two squares.

Step 2
Begin factorising by writing ( )( )
Now find the square root of 4𝑥 2 , √4 = 2 and √𝑥 2 = 𝑥
(2𝑥 )( 2𝑥 )
Consider 16 and find square root, √16 = 4
(2𝑥 4)(2𝑥 4)

Step 3
Now add plus sign to the middle of the first set of brackets and a
negative sign in the middle of the second set of brackets or vice versa.
(2𝑥 + 4)(2𝑥 − 4)

Step 4
Expand to check if you get the original expression
10. CLASSWORK/ HOMEWORK (Suggested time:15 minutes)
Learners do the following activities in their classwork books:

Factorise the following expressions

a) 25𝑎2 − 9
b) 1 − 16𝑥 2
c) 2𝑥 2 − 2
d) (𝑥 + 𝑦)2 − 𝑏 2
1
e) 4𝑥 6 −
9
f) −(𝑥 + 𝑦)2 + 1

11. SUPPORT
For learners at risk do support activities. (Choose questions from DBE workbook)

12. ADDITIONAL NOTES FOR TEACHERS

13. TEACHER REFLECTION:

14. LEARNER WORKSHEET
CLASSWORK
Factorise the following expressions:
(1) 25𝑎2 − 9

(2) 1 − 16𝑥 2

(3) 2𝑥 2 − 2

(4) (𝑥 + 𝑦)2 − 𝑏 2

1
(5) 4𝑥 6 −
9

(6) −(𝑥 + 𝑦)2 + 1

 Gauteng Province
Grade 9 Lesson Plan 12
Term 2
1. TOPIC: ALGEBRAIC EXPRESSIONS
2. DATE: 23 April 2024 DURATION: 1 hour
3. OBJECTIVES:
By the end of the lesson, learners should know and be able to
- Factorize quadratic trinomials of the form: 𝑥 2 + 𝑏𝑥 + 𝑐
4. RESOURCES: DBE workbook 2 & any other textbook
5. REVIEW AND CORRECTION OF HOMEWORK (Suggested time:5 minutes)
6. PRIOR KNOWLEDGE:
• Prime factors
• Factors
• HCF
• Products
• Multiplication of binomials
• Multiplication of Integers

7. MENTAL MATHS: (Suggested time:5 minutes)

Be the first player to make 24 𝑤𝑖𝑡ℎ 𝑎𝑙𝑙 4 numbers on the card.
You can add, subtract, multiply or divide. You have to use all four numbers. Each number may
be used only once.
For example: if the numbers are 2, 2, 6, 8:
You could make 24 by explaining (8 − 2) 𝑥 (6 − 2) =

8. ENGLISH ACROSS THE CURRICULUM: (Suggested time:10 minutes)

Revise:
Terminology
Commutative property
This law applies to addition and multiplication of numbers; it tells us that even if we change the
order of the numbers we still get the same answer.
4𝑥 + (−2𝑥) = −2𝑥 + 4𝑥
−5𝑥 × 3𝑦 = 3𝑦 × − 5𝑥
Associative property
This rule also applies to addition and multiplication; it allows us to group numbers when adding
or multiplying and still get the same answer.
3𝑥 + (−5𝑥) + 6𝑥 = [3𝑥 + (−5𝑥)] + 6𝑥 = 3𝑥 + [−5𝑥 + 6𝑥]
3𝑥 × (−5𝑥) × 6𝑥 = [3𝑥 × (−5𝑥)] × 6𝑥 = 3𝑥 × [−5𝑥 × 6𝑥]
Distributive property
When multiplying across addition or subtraction this property allows us to redistribute the
numbers and still get the same answer.
7(−5𝑥 + 2) = [7 × −5𝑥] + [7 × 2] = −35𝑥 + 14

Assessment Words
Factorize
Determine
Factor
9. INTRODUCTION (Suggested time:10 Minutes)
Let learner do the following activity as part of revision:
Determine the product of the following:
a) (𝑥 + 2)(𝑥 + 3)
b) 3(𝑥 − 2)(𝑥 − 3)
c) (𝑥 − 2)(𝑥 + 3)
d) (𝑥 + 2)(𝑥 − 3)
Indicate Key words/phrases like : The product is the answer we get when multiplying
Expressions above are in factor form (i.e. the expressions are factorized)
Do corrections with the learners:
a) 𝑥 2 + 2𝑥 + 3𝑥 + 6 = 𝑥 2 + 5𝑥 + 6
b) 3(𝑥 2 − 2𝑥 − 3𝑥 + 6) = 3(𝑥 2 − 5𝑥 + 6) = 3𝑥 2 − 15𝑥 + 18
c) 𝑥 2 + 𝑥 − 6
d) 𝑥 2 − 𝑥 − 6
10. LESSON PRESENTATION/ DEVELOPMENT (Suggested time:15 minutes)

Explain the following to the learners: NOTE STRUCTURE:

STEPS for
𝑥 2 + 5𝑥 + 6 factorizing a
The above expression is not in factor form, but is a product of 2 quadratic
binomials as seen from the introduction above trinomial
- Take out
Write the above trinomial in factor form: the HCF if
possible.
- If the expression
(or the factor in the
bracket) is in the
form 𝒙𝟐 + 𝒃𝒙 + 𝒄it
 is a quadratic
trinomial and may
factorise into two
brackets.
- List the pairs of
factors of the last
term
- Check if any pair
adds up to _ (the
coefficient of the
middle term).
These factors will
be the constant
terms in the
brackets.

11. CLASSWORK/HOMEWORK
Activity 1
4. Factorize the following trinomials

(h) 𝑥 2 − 14𝑥 + 48

(i) 𝑥 2 − 4𝑥 − 45

(j) 𝑥 2 + 28𝑥 − 32

(k) 𝑥 2 − 𝑥 − 2

12. SUPPORT
For learners at risk do support activities.

13. ADDITIONAL NOTES FOR TEACHERS

14. TEACHER REFLECTION:

15. LEARNER WORKSHEET
MENTAL MATHS

Be the first player to make 24 𝑤𝑖𝑡ℎ 𝑎𝑙𝑙 4 numbers on the card.

You can add, subtract, multiply or divide. You have to use all four numbers. Each number may
be used only once.
For example: if the numbers are 2, 2, 6, 8:
You could make 24 by explaining (8 − 2) 𝑥 (6 − 2) =

16. CLASSWORK
4. Simplify the following
(a) 𝑥 2 − 14𝑥 + 48

(h) 𝑥 2 − 4𝑥 − 45

(i) 𝑥 2 + 28𝑥 − 32

(l) 𝑥 2 − 𝑥 − 2
 Gauteng Province
Grade 9 Lesson Plan 13
Term 2
1. TOPIC: Algebraic Expressions
2. DATE: 24 April 2024 DURATION: 1 hour
3. OBJECTIVES
By the end of the lesson, learners should know and be able to:
• factorise algebraic expressions that involve trinomials of 𝑥 2 + 𝑏𝑥 + 𝑐 𝑎𝑛𝑑 𝑎𝑥 2 + 𝑏𝑥 +
𝑐, where a is a common factor
4. RESOURCES: DBE workbook & any other textbook
5. REVIEW AND CORRECTION OF HOMEWORK (suggested time:5 minutes)
• PRIOR KNOWLEDGE: types of expressions- trinomial
• variables
• coefficient
• laws of exponents
• Highest Common Factors
6. MENTAL MATHS: (Suggested time:10 minutes)

7. ENGLISH ACROSS THE CURRICULUM: (Suggested time:5 minutes)

Terminology
A binomial is a polynomial with exactly 2 terms e.g. 𝑥 + 2 or 𝑥 2 + 3𝑥
A trinomial is a polynomial with exactly 3 terms e.g. 𝑥 2 + 2𝑥 + 1
A polynomial is an algebraic expression involving a sum of powers in
one or more variables multiplied by coefficients.
Assessment Words
Determine the following, Simplify the expression

8. INTRODUCTION (Suggested time:10 Minutes)

Educator - Write the following Algebraic Expression on the board:
Revise the following with learners:
Expand
a) 2(𝑥 2 + 4𝑥 + 8)
b) (𝑥 + 2)(𝑥 + 5)
9. LESSON PRESENTATION/ DEVELOPMENT (Suggested time:15 minutes)
Complete the following activity with learners:
Factorise the following trinomial: 𝒙𝟐 + 𝟕𝒙 + 𝟏𝟐 NOTE
STRUCTURE:
How many terms are there in the 3 terms Factorisation of an
above expression? expression is the
reverse of
What are the factors of the first 𝒙 𝒙
expanding an
term? expression.
List the pairs of factors of the 12 6 4
last term / constant. 1 2 3
Which pair of factors when 4
added gives the coefficient of 3
the middle term? 4+𝟑=𝟕
Put both factors of the first term (𝒙 + 𝟒)(𝒙 + 𝟑)
and last term into each of these NB. The signs may not
brackets (𝒙 ±? )(𝒙± ? ) always be positive
Expand the factors to check if 𝒙×𝒙+𝟑×𝒙+𝟒×𝒙
they give you the original +𝟒×𝟑
trinomial 𝒙𝟐 + 𝟑𝒙 + 𝟒𝒙 + 𝟏𝟐
𝒙𝟐 + 𝟕𝒙 𝟏𝟐

10. CLASSWORK/ HOMEWORK (Suggested time:15 minutes)

Learners do the following activities in their classwork books following the procedure in the
example above:
 Factorise the following expressions.
a) 𝑥 2 + 5𝑥 + 6
b) 𝑥 2 − 5𝑥 + 6
c) 2𝑥 2 + 10𝑥 + 12
d) −2𝑏 2 + 6𝑏 − 4

11. SUPPORT
For learners at risk do support activities. (Choose questions from DBE workbook)

12. ADDITIONAL NOTES FOR TEACHERS

13. TEACHER REFLECTION:

14. LEARNER WORKSHEET

CLASSWORK
Factorise the following expressions:
(1) 𝑥 2 + 5𝑥 + 6

(2) 𝑥 2 − 5𝑥 + 6

(3) 2𝑥 2 + 10𝑥 + 12

(4) −2𝑏 2 + 6𝑏 − 4
 Gauteng Province
Grade 9 Lesson Plan 14
Term 2
1. TOPIC: Algebraic Expressions
2. DATE: 25 April 2024 DURATION:1 hour
3. OBJECTIVES
By the end of the lesson, learners should know and be able to:
• simplify algebraic expressions that involve factorisation by common factor, difference of
two squares and trinomial factorisation.
• Simplify algebraic fractions using factorisation
4. RESOURCES: DBE workbook & any other textbook
5. REVIEW AND CORRECTION OF HOMEWORK (suggested time:5 minutes)
• PRIOR KNOWLEDGE: types of expressions- trinomial
• variables
• coefficient
• laws of exponents
• Highest Common Factors
6. MENTAL MATHS: (Suggested time:10 minutes)

7. ENGLISH ACROSS THE CURRICULUM: (Suggested time:5 minutes)

Terminology
A binomial is a polynomial with exactly 2 terms e.g. 𝑥 + 2 or 𝑥 2 + 3𝑥
A trinomial is a polynomial with exactly 3 terms e.g. 𝑥 2 + 2𝑥 + 1
A polynomial is an algebraic expression involving a sum of powers in
one or more variables multiplied by coefficients.
Assessment Words
Determine the following, Simplify the expression

8. INTRODUCTION (Suggested time:10 Minutes)

Revise the following with learners:

Activity 1
What factorisation method would you use in the following?
c) 2𝑥 + 6𝑦
d) 𝑎(𝑥 − 𝑦) + 7(𝑦 − 𝑥)
e) 9𝑥 2 − 1
f) 𝑥2 + 1
g) 3𝑥 2 − 3𝑥 − 18
𝑎2 −1
h) × (2𝑎 − 4)
𝑎2 −𝑎−2
9. LESSON PRESENTATION/ DEVELOPMENT (Suggested time:15 minutes)
Present the following solution to learners and let them answer
question based on the solution. NOTE STRUCTURE:
Factorisation of an
Activity 1 expression is the
𝑥 2 −2𝑥−3 reverse of expanding
Alakhe and Ido have to determine the value of for
𝑥−3 an expression.
𝑥 = 4.6
without the use of a calculator.

Alake’s solution Ido’s solution

𝑥 2 −2𝑥−3 𝑥 2 − 2𝑥 − 3
𝑥−3
(4,6)2 −2(4,6)−3
𝑥−3
= =
4,6−3
21,16−9,2−3 (𝑥−3)(𝑥+1)
= 𝑥−3
4,6−3

=
8,196 =𝑥+1
1,6 = 4,6 + 1
= 5,6 = 5,6

NB: the focus is not

in the circled part.

Which solution do you prefer and why?

10. CLASSWORK/ HOMEWORK (Suggested time:15 minutes)

Learners do the following activities in their classwork books following the procedure in the
example above:

Simplify the following expressions fully:

3𝑥 −3𝑦
a)
6𝑥 − 6𝑦

𝑥 2 +6𝑥 𝑥 2 +2𝑥−3
b) ×
𝑥+3 1−𝑥

𝑥 2 +11𝑥+30 𝑥 2 −4
c) ×
𝑥 2 +4𝑥−12 −𝑥−5

11. SUPPORT
For learners at risk do support activities. (Choose questions from DBE workbook)
12. ADDITIONAL NOTES FOR TEACHERS

13. TEACHER REFLECTION:

14. LEARNER WORKSHEET

CLASSWORK
Factorise the following expressions fully:
3𝑥 −3𝑦
(1)
6𝑥 − 6𝑦

𝑥 2 +6𝑥 𝑥 2 +2𝑥−3
(2) ×
𝑥+3 1−𝑥

𝑥 2 +11𝑥+30 𝑥 2 −4
(3) ×
𝑥 2 +4𝑥−12 −𝑥−5
 Gauteng Province
Grade 9 Lesson Plan 15
Term 2
1. TOPIC: ALGEBRAIC EXPRESSIONS
2. DATE: 26 April 2024 DURATION: 1 hour
3. OBJECTIVES:
By the end of the lesson, learners should know and be able to
Manipulate algebraic Expressions
4. RESOURCES: DBE workbook 2 & any other textbook
5. REVIEW AND CORRECTION OF HOMEWORK (Suggested time:5 minutes)
6. PRIOR KNOWLEDGE:
• Algebraic Expressions

7. MENTAL MATHS: (Suggested time:5 minutes)

You can add, subtract, multiply or divide. You have to use all four numbers. Each number may
be used only once.
For example: if the numbers are 2, 2, 6, 8:
You could make 24 by explaining (8 − 2) 𝑥 (6 − 2) =

8. ENGLISH ACROSS THE CURRICULUM: (Suggested time:10 minutes)

Revise:
Terminology
Commutative property
This law applies to addition and multiplication of numbers; it tells us that even if we change the
order of the numbers we still get the same answer.
4𝑥 + (−2𝑥) = −2𝑥 + 4𝑥
−5𝑥 × 3𝑦 = 3𝑦 × − 5𝑥
Associative property
This rule also applies to addition and multiplication; it allows us to group numbers when adding
or multiplying and still get the same answer.
3𝑥 + (−5𝑥) + 6𝑥 = [3𝑥 + (−5𝑥)] + 6𝑥 = 3𝑥 + [−5𝑥 + 6𝑥]
3𝑥 × (−5𝑥) × 6𝑥 = [3𝑥 × (−5𝑥)] × 6𝑥 = 3𝑥 × [−5𝑥 × 6𝑥]
Distributive property
When multiplying across addition or subtraction this property allows us to redistribute the
numbers and still get the same answer.
7(−5𝑥 + 2) = [7 × −5𝑥] + [7 × 2] = −35𝑥 + 14
Assessment Words
Group
Add
Subtract
Identify
Multiply
Divide
Simplify
Factorize

9. INTRODUCTION (Suggested time:10 Minutes)

Ask the learners to do the following activity:

1) Simplify where possible and explain why it is not possible to simplify the expressions:
a. 𝑥 + 2 =
b. 𝑥 2 − 2𝑥 − 3
2) Write down the coefficient of x in the following:
a. 3𝑥 4 − 2𝑥 3 + 4𝑥 2 − 𝑥 + 3

10. LESSON PRESENTATION/ DEVELOPMENT (Suggested time:15 minutes)

Let the learners complete the following activities individually as part of NOTE
revision: STRUCTURE:

Activity 1
• Make copies
Simplify the following expressions: of the
worksheets
a) for the
learners to
b) work on, as
c) either
classwork or
d) homework. It
e) is important
for learners to
Activity 2 present their
own work.
11. CLASSWORK/HOMEWORK
Activity 3
Factorize fully.

1.
2.
3.
Activity 4

Activity 5
Simplify the following expressions:

1.

2.
12. SUPPORT
For learners at risk do support activities.

13. ADDITIONAL NOTES FOR TEACHERS

14. TEACHER REFLECTION:

15. LEARNER WORKSHEET
MENTAL MATHS
You can add, subtract, multiply or divide. You have to use all four numbers. Each number may
be used only once.
For example: if the numbers are 2, 2, 6, 8:
You could make 24 by explaining (8 − 2) 𝑥 (6 − 2) =

CLASSWORK
(j)

(k)

(l)

(m)

(n)
Factorize fully.

1.

2.

3.

Simplify the following expressions:

1.

2.
 Gauteng Province
Grade 9 Lesson Plan 16
Term 2
1. TOPIC: ALGEBRAIC EQUATIONS
2. DATE: 29 April 2024 DURATION: 1 hour
3. OBJECTIVES:
By the end of the lesson, learners should be able to:

• set up equations to describe problem situation.

4. RESOURCES: Textbooks, Sasol-Inzalo book 1
5. REVIEW AND CORRECTION OF HOMEWORK (suggested time:5 minutes)

Homework provides an opportunity for teachers to track learners’ progress in the mastery of
mathematics concepts and to identify the problematic areas which require immediate
attention. Therefore it is recommended that you place more focus on addressing errors from
learner responses that may later become misconceptions.

6. PRIOR KNOWLEDGE

• Basic Mathematics operations,

• Substitution,
• Number sentences,
• Algebraic expressions
• Equation
7. MENTAL MATHS: (Suggested time:5 minutes)
Complete the table
Verbal description Algebraic
language
The sum of a number and two 𝑥+2
A number that is five more than 𝑎
The difference between two and a
number
A number increased by seven
8. ENGLISH ACROSS THE CURRICULUM: (Suggested time:5 minutes)
Vocabulary
Number Sentences Difference
Operations more than
Sum increase
Terminology
Number Sentences: A Number Sentence represents an equation that includes numbers and
operation symbols.

A statement compares two expressions using relationship signs such as equal to (=), not equal
to (≠), greater than (>), less than (<), less than or equal to (≤), etc. When we deal with
equations, we use the equal sign.
Assessment Words
Solve Interpret
Write Justify
9. INTRODUCTION (Suggested time:10 Minutes)
Educator asks learners the steps to follow when dealing with problem solving

• Problem solving steps

Word problems can be written as mathematical statements so that they can be solved
mathematically.
Steps to follow:
Step 1: Identify what you have been asked to solve.
Step 2: Let this value be x or any other variable
Step 3: Identify what you have been given.
Step 4: Write a number sentence:
Step 5: Substitute your values and solve/calculate.
Step 6: Write your answer with the correct SI units.

10. LESSON PRESENTATION/ DEVELOPMENT (Suggested time:15 minutes)

Example 1: NOTE STRUCTURE:
Translate the following problem into an equation and
then solve it. Educator asks learners the steps to
follow when dealing with problem
Think of a number, multiply it by 2, and then add 3. If solving
the answer is 15, find the original number.
• Problem solving steps
x The number
Word problems can be written as
2x + 3 = 15 Multiply by 2, add 3, the
answer is 15 mathematical statements so that they
can be solved mathematically.
2x + 3 − 3 = 15 − 3 Solving this equation
Steps to follow:
∴ 2x = 12
The number is 6 Step 1: Identify what you have been
∴x=6
asked to solve.
Step 2: Let this value be x or any
other variable
Example 2:
Step 3: Identify what you have been
If we add the ages of a mother and her son, the total of given.
their ages is 60. The mother is currently 4 times as old Step 4: Write a number sentence:
as her son. Find their ages. Step 5: Substitute your values and
solve/calculate.
Let the son be x years old. Step 6: Write your answer with the
correct SI units.
The mother is 4x years old.

∴ x + 4x = 60

∴ 5x = 60

∴ x = 12
The son is 12 years old and the mother is 4 × 12 = 48
years old.
Educator asks learners to do the following example in
pairs

11. CLASSWORK/ HOMEWORK (Suggested time:15 minutes)

Activity 1
Two numbers added together equal 20. The difference between the numbers is 4. Find the
numbers.

Activity 2
A Father is currently 5 times as old as his son. If the difference between their ages is 36 years,
how old is the son now?
HOMEWORK
1.The sum of the ages of two brothers is 70 years. In 10 years’ time, Thabo will be twice as old
as Tshepo was 8 years ago. How old are Thabo and Tshepo now?

12. SUPPORT:
For learners at risk do support activities. (Choose questions from activities provided)

13. ADDITIONAL NOTES FOR TEACHERS:

14. TEACHER REFLECTION:

15. LEARNER WORKSHEET

MENTAL MATHS CLASSWORK HOMEWORK

Complete the table Activity 1 1.The sum of the ages of

two brothers is 70 years. In
Verbal Algebraic Two numbers added 10 years’ time, Thabo will be
description language together equal 20. The twice as old as Tshepo was
difference between the 8 years ago. How old are
The sum of a 𝑥+2 numbers is 4. Find the
number and two Thabo and Tshepo now?
numbers.
A number that is Activity 2
five more than 𝑎
A Father is currently 5
The difference times as old as his son. If
between two and the difference between
a number their ages is 36 years, how
old is the son now?
A number
increased by
seven
 Gauteng Province
Grade 9 Lesson Plan 17
Term 2
1. TOPIC: ALGEBRAIC EQUATIONS
2. DATE: 30 April 2024 DURATION: 1 hour
3. OBJECTIVES:
By the end of the lesson, learners should be able to:

• set up equations to describe problem situation

• analyse and interpret equations that describe a given situation
4. RESOURCES: Textbooks, Sasol-Inzalo book 1
5. REVIEW AND CORRECTION OF HOMEWORK (suggested time:5 minutes)

Homework provides an opportunity for teachers to track learners’ progress in the mastery of
mathematics concepts and to identify the problematic areas which require immediate
attention. Therefore it is recommended that you place more focus on addressing errors from
learner responses that may later become misconceptions.

• PRIOR KNOWLEDGE

• addition, subtraction, multiplication and division of integers

• simplifying algebraic expression
• multiplication table up to at least 12 × 12
6. MENTAL MATHS: (Suggested time:5 minutes)
Complete the table
Verbal description Algebraic
language
The sum of a number and two 𝑥+2
A number that is five more than 𝑎
The difference between two and a
number
A number increased by seven
7. ENGLISH ACROSS THE CURRICULUM: (Suggested time:5 minutes)
Vocabulary
Number Sentences Difference
Operations more than
Sum increase
Terminology
Number Sentences: A Number Sentence represents an equation that includes numbers and
operation symbols.
A statement compares two expressions using relationship signs such as equal to (=), not equal
to (≠), greater than (>), less than (<), less than or equal to (≤), etc. When we deal with
equations, we use the equal sign.
Assessment Words
Solve Interpret
Write Justify
8. INTRODUCTION (Suggested time:10 Minutes)
Divide learners into small groups. Give them 4 expressions and 4 equations like the ones
below:

3𝑥 + 15 𝑥−1=9

3𝑝 − 9 = 𝑝 𝑥2 + 4

4𝑦 𝑚=3

𝑥 2 = 10 𝑎𝑛 − 𝑑

Ask them to group the expressions together and the equations together. Ask them to identify
how the equations differ from the expressions.

Note: When learners can identify an equation then they are ready to move on and setting up
equations to describe situations.
Guide learners in setting up an equation that has 5 as a solution.

Start by writing the solution 𝑥=5

Add 3 to both sides 𝑥+3=8

Multiply both sides by 3 3𝑥 + 9 = 24

What is the equation?

Note: Encourage the learners to use their own words to read an equation formed, for
example, 3 multiplied by ‘what’ and add 9 should give me 24.
9. LESSON PRESENTATION/ DEVELOPMENT (Suggested time:15 minutes)

Activity 1 • Complete Andile’s

work, working in
Andile worked to get the equation 3(𝑥 + 4) = 21 but he rubbed out
pairs
part of his work as follows:

Start by writing the solution 𝑥 = ______

______________________ 𝑥 + 4 = ______

Multiply both sides by 3 3(𝑥 + 4) = ______

Complete Andile’s writing to solve the equation.

After having completed the example and activity 1, ask the

• discuss in pairs how
learners if it is possible to move from the equation to the
to move from the
solution because previously they have been moving from the
equation to the
solution to the equation referring to their own equations
solution and present
obtained in activity 1 above. The response should be YES. Ask
their findings to the
them how that can be done. Give them few minutes to think
whole class
about it and eventually present the following examples on the

board.

Activity 2

Translate each of the following situations into mathematical

equation. Do not solve the equation. Use the letter 𝑥 for the
unknown number:

a) If we multiply a number by 2 and then add 5, the answer is

43.
2𝑥 + 5 = 43

b) If we divide a number by 5 and then add 8, the answer is 30.

 𝑥
+ 8 = 30
5

Note: Give the learners different numbers per pair to use to

form an equation. Move around as they are doing it and after
few minutes allow them to present the equation while
facilitating the process. After doing that, present number two
In pairs translate the
below to them and let learners complete it.
situations given into
equations
10. CLASSWORK/ HOMEWORK (Suggested time:15 minutes)

1) Create an equation that has your birth date as the solution. Use more than one
operation.

2) Shaun is 7 years older than Mike. Let Shaun’s age be 𝑥. Express each of the following in
terms of 𝑥.
a) Mike’s age
b) Shaun’s age in 2 years’ time
c) Mike’s age in 2 years’ time

3) In 2 years’, time, Shaun will be twice as old as Mike. Set up an equation that expresses
this situation.
4) For each of the following situations, choose the equation that describes the situation and
write down the letter that corresponds to the correct option.
4.1. A number increased by 11 gives 20.
A 11𝑥 = 20
B 𝑥 + 11 = 20
C 𝑥 − 11 = 20
D none of the above
4.2. If you subtract 8 from a number, you get 14
A 8 − 𝑥 = 14
B 𝑥 = 14 − 8
C 𝑥 − 8 = 14
D none of the above
4.3. A certain number is doubled and added to 23. The answer is 31.
A 2𝑥 + 23 = 31
B 2(𝑥 + 23) = 31
C 𝑥 = 2(23 + 31)
D none of the above
11. HOMEWORK
The primary purpose of Homework is to give each learner an opportunity to demonstrate
mastery of mathematics skills taught in class. Therefore Homework should be purposeful and
the principle of ‘Less is more’ is recommended, i.e. give learners few high quality activities that
address variety of skills than many activities that do not enhance learners’ conceptual
understanding.
Carefully select appropriate activities from the Sasol-Inzalo books, workbooks and/or
textbooks for learners’ homework. The selected activities should address different cognitive
levels.

Homework:
Translate each of the following into mathematical equations. Do not solve the equation. Use
the letter 𝑥 for the unknown number:

a) If you subtract 9 from 8 multiplied by the number, you get 42.

Sam is 7 years older than his younger brother. The sum of their ages is 23. If Sam is 𝑥 years old,
set up an equation to express this situation.
12. SUPPORT
For learners at risk do support activities. (Choose questions from activities provided)

13. ADDITIONAL NOTES FOR TEACHERS

14. TEACHER REFLECTION:

15. LEARNER WORKSHEET

MENTAL MATHS CLASSWORK HOMEWORK

Complete the table 1.Tickets for the Gr12 1. Thirty-five shots were fired at a
dinner and dance costs target. Each time the target is
Verbal Algebraic 𝑅250 per couple and 𝑅150 hit the keeper has to pay R2,50.
description language for a single person. Twice For every missed target he has
The product as many couple tickets to pay R1,50. If he makes a
of two and were sold as single ones. profit of R35, how many times
a number Let 𝑥 be the single tickets did he hit the target?
sold. The total income for Number of times missed 30 − x
A number the ticket sales was
that is half R65 000 .
the sum of
2 and 3
The a) What equation would 25 x − 15(30 − x) = 350
quotient if 𝑥 you use to find 𝑥? 25 x − 450 + 15 x = 350
is divided b) Calculate how many 25 x + 15 x = 350 + 450
by two single tickets were 40 x = 800
sold.
A number x = 20
c) How many people
that is He makes 20 hits
attended the dance
decreased 2. To rent a room in a certain
altogether?
by nine building, you have to pay a
deposit of R400 and then R80
2. Henry has a certain per day.
amount of pocket money. a) How much money do you
2 need to rent the room for 10
His sister, Lucy, gets of
3
days?
the amount of money that
b) How much money do you
Henry gets. Altogether they
need to rent the room for 15
get R600 pocket money.
days?
a) R80 x 10 + R400 = R800
+ R400 = R1 200
R80 x 15 + R400 = R1 200 + R400 =
R1 600
 Gauteng Province
Grade 9 Lesson Plan 18
Term 2
1. TOPIC: ALGEBRAIC EQUATIONS
2. DATE: 02 May 2024 DURATION: 1 hours
3. OBJECTIVES:
By the end of the lesson, learners should be able to:

• set up equations to describe problem situations

• solve equations by:
- inspection
- using additive and multiplicative inverses
4. RESOURCES: DBE workbook, Sasol-Inzalo workbook, textbook, calculator.
5. REVIEW AND CORRECTION OF HOMEWORK (suggested time:5 minutes)

Homework provides an opportunity for teachers to track learners’ progress in the mastery of
mathematics concepts and to identify the problematic areas which require immediate attention.
Therefore it is recommended that you place more focus on addressing errors from learner
responses that may later become misconceptions.

• PRIOR KNOWLEDGE

•set up equations to describe problem situations

•solve equations by:
- inspection
- using additive and multiplicative inverses
6. MENTAL MATHS: (Suggested time:5 minutes)
Complete the following table. Substitute the given x-values into the equation until you find the
value that makes the equation true;

Equation LHS if Is LHS = LHS if Is LHS = Correct Is LHS = Correct

𝑥=4 RHS? 𝑥=5 RHS? Solution RHS? Solution
3𝑥 – 4 = 11
2𝑥 + 7 = 19
13 – 5𝑥 = -7
7. ENGLISH ACROSS THE CURRICULUM: (Suggested time:5 minutes)
Vocabulary
Number Sentences Difference
Operations more than
Sum increase
Terminology
Number Sentences: A Number Sentence represents an equation that includes numbers and
operation symbols.
A statement compares two expressions using relationship signs such as equal to (=), not equal
to (≠), greater than (>), less than (<), less than or equal to (≤), etc. When we deal with
equations, we use the equal sign.
Assessment Words
Solve Interpret
Write Justify
8. INTRODUCTION (Suggested time:10 Minutes)
Show learners how equations are formed/built up:
(Building an equation) (Solving an equation)
Action on Equivalent Action on Equivalent
both sides Equations both sides Equations
Solution (1) 𝑥=3 Equation (1) 3𝑥 + 2 = 11
x3 3𝑥 = 9 -2 3𝑥 + 2 - 2 = 11-2
3𝑥 = 9
+2 3𝑥 + 2 = 11 ÷3 3𝑥 9
=
3 3
𝑥=3

Solution (2) 𝑥 = -9 Equation (2) 3(𝑥+2) = 𝑥 - 12

x2 2𝑥 = -18 Apply distr. 3𝑥 + 6 = 𝑥 - 12
Law on LHS
+6 2𝑥 + 6 = -12 -𝑥 3𝑥 + 6 = 𝑥 – 12
3𝑥-𝑥 + 6= 12
2𝑥 + 6 = -12
+𝑥 3𝑥 + 6 = 𝑥 - 12 -6 2𝑥 + 6-6 = -12+6
2𝑥 = - 18
factorise 3(𝑥+2) = 𝑥 - 12 ÷2 2𝑥 −18
=
2 2
𝑥=-9
9. LESSON PRESENTATION/ DEVELOPMENT (Suggested time:15 minutes)

Example
Solve the following equation: 2𝑏 + 2 = 6𝑏 – 14
2𝑏 + 2 = 6𝑏 - 14 NOTE STRUCTURE:
2𝑏 + 2 - 2 = -14 - 2 subtract 2 on both sides
2𝑏 = -16
2𝑏 −16 divide by 2 on both sides
=
2 2

𝑏=-8
Example
Solve the following equation: 3(2𝑟 – 3) = 5 - 2(𝑟 – 5)
3(2𝑟 – 3) = 5 - 2(𝑟 – 5) NOTE STRUCTURE:
6𝑟 – 9 = 5 – 2𝑟 + 10 Multiplying into the brackets
6𝑟 – 9 = 15 – 2𝑟
6𝑟 – 9 + 9 = 15 – 2𝑟 + 9 Adding 9 on both sides
6𝑟 = 24 – 2𝑟
6𝑟 + 2𝑟 = 24 -2𝑟 + 2𝑟 Adding 2r on both sides
8𝑟 = 24
8𝑟 24 Divide both sides by 8
=
8 8

𝑟=3
10. CLASSWORK/ HOMEWORK (Suggested time:15 minutes)
CLASSOWORK
Solve for unknown variable below
𝑎) 4(2𝑚 − 5) = 2(𝑚 + 1)

𝑏) 3(𝑥 − 1) − 4𝑥 = 5 − 2(𝑥 + 1)

𝑐) (2𝑥 + 1)2 = (2𝑥 − 3)(𝑥 + 5) − 3

HOMEWORK

11. SUPPORT

12. ADDITIONAL NOTES FOR TEACHERS

13. TEACHER REFLECTION:

14. LEARNER WORKSHEET

MENTAL MATHS

Complete the following table. Substitute the given x-values into the equation until you find the
value that makes the equation true;

Equation LHS if 𝑥= Is LHS = LHS if 𝑥 = Is LHS = Correct Is LHS Correct

4 RHS? 5 RHS? Solution = RHS? Solution
3𝑥 – 4 = 11
2𝑥 + 7 = 19
13 – 5𝑥 = -
7
Classwork Homework

Solve for the unknown

𝑎) 4(2𝑚 − 5) = 2(𝑚 + 1)

𝑏) 3(𝑥 − 1) − 4𝑥 = 5 − 2(𝑥 + 1)

𝑐) (2𝑥 + 1)2 = (2𝑥 − 3)(𝑥 + 5) − 3

 Gauteng Province
Grade 9 Lesson Plan 19
Term 2
1. TOPIC: ALGEBRAIC EQUATIONS

2. DATE: 03 May 2024 DURATION: 1 hour

3. OBJECTIVES:
By the end of the lesson, learners should be able to:

• solve equations using laws of exponents

GDE ATP Term 2
4. RESOURCES:
DBE workbook, Sasol-Inzalo workbook, textbook, calculator
5. REVIEW AND CORRECTION OF HOMEWORK (suggested time:5 minutes)

Homework provides an opportunity for teachers to track learners’ progress in the mastery of
mathematics concepts and to identify the problematic areas which require immediate attention.
Therefore it is recommended that you place more focus on addressing errors from learner
responses that may later become misconceptions.

6. PRIOR KNOWLEDGE

• Solve simple equations algebraically or by inspection

• Determine additive and multiplicative inverses
• Use substitution to determine values of unknowns
• Exponential laws
7. MENTAL MATHS: (Suggested time:5 minutes)
Solve for 𝒂:
a) 5𝑎 = 25
b) 3𝑎 = 33
𝑐) 2𝑎 = 64
8. ENGLISH ACROSS THE CURRICULUM: (Suggested time:5 minutes)
Vocabulary
Number Sentences Difference
Operations more than
Sum increase
Terminology
Number Sentences: A Number Sentence represents an equation that includes numbers and
operation symbols.
A statement compares two expressions using relationship signs such as equal to (=), not equal
to (≠), greater than (>), less than (<), less than or equal to (≤), etc. When we deal with
equations, we use the equal sign.
Assessment Words
Solve Interpret
Write Justify
9. INTRODUCTION (Suggested time:10 Minutes)
Discuss the following examples with the learners:

Example 1.

Solve for 7𝑥 = 79
Since the bases are the same set the exponents equal to each other
∴ 𝑥=9

10. LESSON PRESENTATION/ DEVELOPMENT (Suggested time:15 minutes)

Example 2 NOTE STRUCTURE:

Solve for 3𝑥 = 243
Rewrite 243 in exponential form: 243 = 3.3.3.3.3 = 35
3 𝑥 = 35
Ignore the bases and simply set the exponents equal to
each other
𝑥 =5

Example 3
Solve for 2𝑥+1 = 2−4
Ignore the bases and simply set the exponents equal to
each other
𝑥 + 1 = -4
Solve for the variable
∴ 𝑥 = -5
11. CLASSWORK (Suggested time:15 minutes)

Solve the following equations without using a calculator:

𝑎) 3𝑥−2 = 3−5

𝑏) 22𝑥+2 = 16

𝑐) 33𝑥 = 36

12. HOMEWORK
Solve the following equations without using a calculator

𝑎) 2𝑥 = 2

𝑏) 22𝑥+2 = 16
𝑐) 9𝑥 = 81

13. SUPPORT
For learners at risk do support activities. (Choose questions from activities provided)

14. ADDITIONAL NOTES FOR TEACHERS

15. TEACHER REFLECTION:

16. LEARNER WORKSHEET

Mental Maths Classwork Homework

a) 5𝑎 = 25 Solve the following equations Solve the following equations

without using a calculator: without using a calculator

b) 3𝑎 = 33 𝑎) 3𝑥−2 = 3−5 𝑎) 2𝑥 = 2

c) 2𝑎 = 64 𝑏) 22𝑥+2 = 16 𝑏) 22𝑥+2 = 16

𝑐) 33𝑥 = 36 𝑐) 9𝑥 = 81
 Gauteng Province
Grade 9 Lesson Plan 20
Term 2
1. TOPIC: ALGEBRAIC EQUATIONS
2. DATE: 06 May 2024 DURATION: 1 hour
3. OBJECTIVES:
By the end of the lesson, learners should be able to:

• use substitution in equations to generate tables of ordered pairs.

GDE ATP Term 2
4. RESOURCES: DBE workbook, Sasol-Inzalo workbook, textbook,
calculator.
5. REVIEW AND CORRECTION OF HOMEWORK (suggested time:5 minutes)

Homework provides an opportunity for teachers to track learners’ progress in the mastery of
mathematics concepts and to identify the problematic areas which require immediate attention.
Therefore it is recommended that you place more focus on addressing errors from learner
responses that may later become misconceptions.

6. PRIOR KNOWLEDGE

• Solve simple equations algebraically or by inspection

• Determine additive and multiplicative inverses
• Use substitution to determine values of unknowns
7. MENTAL MATHS: (Suggested time:5 minutes)

Complete the table below to show some of the input and output numbers of the relationship
described by the formula
= 2𝑥 − 3

Input -5 0 2 4 6 8
Output
8. ENGLISH ACROSS THE CURRICULUM: (Suggested time:5 minutes)
Vocabulary
Number Sentences Difference
Operations more than
Sum increase
Terminology
Number Sentences: A Number Sentence represents an equation that includes numbers and
operation symbols.
A statement compares two expressions using relationship signs such as equal to (=), not equal
to (≠), greater than (>), less than (<), less than or equal to (≤), etc. When we deal with equations,
we use the equal sign.
Assessment Words
Solve Interpret
Write Justify
9. INTRODUCTION (Suggested time:10 Minutes)
Educator asks learners the steps to follow when dealing with problem solving

• Problem solving steps

Word problems can be written as mathematical statements so that they can be solved
mathematically.
Steps to follow:
Step 1: Identify what you have been asked to solve.
Step 2: Let this value be x or any other variable
Step 3: Identify what you have been given.
Step 4: Write a number sentence:
Step 5: Substitute your values and solve/calculate.
Step 6: Write your answer with the correct SI units.

10. LESSON PRESENTATION/ DEVELOPMENT (Suggested time:15 minutes)

In the relationship 𝑦 = 2𝑥 − 1, 𝑥 is called the independent NOTE STRUCTURE:
variable, because any value for 𝑥 can be chosen randomly or
independently. However, 𝑦 is called the dependent variable,
because the value of 𝑦 depends on the value of 𝑥

We will select a few values for 𝑥 and then calculate the values
of 𝑦 corresponding to these values of 𝑥. We will use a table to
represent the information. Each value of 𝑥 and its
corresponding 𝑦 value can be written in ordered pairs

Determine the value for 𝑦, for the given values of 𝑥 if 𝑦 = 2 𝑥 - 1

-𝑥 -2 -1 0 1 2
𝑦 -5 -3 -1 1 3

Write the outcome as ordered pairs:

{(-2; -5); (-1; -3); (0; -1); (1; 1); (2; 3)}

Whole class activity

Determine the value for y for the given values of 𝑥 if 𝑦 = 3𝑥

-𝑥 -2 1 2
𝑦 -3 0

Write the outcome as ordered pairs:

11. CLASSWORK/ HOMEWORK (Suggested time:15 minutes)

Complete the table below for 𝑥 and y values for the equation:

a) Determine the value for y for the given values of 𝑥 if 𝑦 = 2𝑥²

-𝑥 -2 -1 0 1 2
𝑦

Write the outcome as ordered pairs:

b) Determine the value for y for the given values of 𝑥 if 𝑦 = -𝑥²

-𝑥 -3 -1 0 2 3
𝑦

Write the outcome as ordered pairs:

12. HOMEWORK

a) Complete the table below for 𝑥 and y values for the equation: 𝑦 = 2𝑥² - 3

-𝑥 -2 -1 0 3 7
y

b) Complete the table below for 𝑥 and y values for the equation: 𝑦 = 𝑥² - 2

-𝑥 -3 -2 0 2 4
𝑦

13. SUPPORT
For learners at risk do support activities. (Choose questions from activities provided)

14. ADDITIONAL NOTES FOR TEACHERS

15. TEACHER REFLECTION

16. LEARNER WORKSHEET
Mental Maths Classwork Homework

Complete the table below to show Complete the table below for 𝑥 a) Complete the table below for 𝑥
and y values for the equation:
some of the input and output and y values for the equation:
numbers of the relationship a) Determine the value for y 𝑦 = 2𝑥² - 3
for the given values of 𝑥 if 𝑦 =
described by the formula
2𝑥²
𝑦 = 2𝑥 − 3 -𝑥 -2 -1 0 3 7
-𝑥 -2 -1 0 1 2 y
Input -5 0 2 4 6 8 𝑦 b) Complete the table below for 𝑥
Output and y values for the equation:
Write the outcome as ordered
𝑦 = 𝑥² - 2
pairs:

b) Determine the value for y for -𝑥 -3 -2 0 2 4

the given values of 𝑥 if 𝑦 = -𝑥² 𝑦

-𝑥 -3 -1 0 2 3
𝑦

Write the outcome as ordered

pairs:
 Gauteng Province
Grade 9 Lesson Plan 21
Term 2
1. TOPIC: ALGEBRAIC EQUATIONS
2. DATE: 07 May 2024 DURATION: 1 hour
3. OBJECTIVES:
By the end of the lesson, learners should be able to:

• Use substitution in equations to generate tables of ordered pairs.

4. RESOURCES: Textbooks, Sasol-Inzalo book 1
5. REVIEW AND CORRECTION OF HOMEWORK (suggested time:5 minutes)

Homework provides an opportunity for teachers to track learners’ progress in the mastery of
mathematics concepts and to identify the problematic areas which require immediate attention.
Therefore it is recommended that you place more focus on addressing errors from learner
responses that may later become misconceptions.

6. PRIOR KNOWLEDGE

• Solve simple equations algebraically or by inspection

• Determine additive and multiplicative inverses
• Use substitution to determine values of unknowns

7. MENTAL MATHS: (Suggested time:5 minutes)

1. The sum of a number and 15 is 63. Find the number.

2.What number divided by 12 gives an answer of 72.
3. What number divided by 12 gives an answer of 72.
4. What number when multiplied by 15 gives -90.
8. ENGLISH ACROSS THE CURRICULUM: (Suggested time:5 minutes)
Vocabulary
Number Sentences Difference
Operations more than
Sum increase
Terminology
Number Sentences: A Number Sentence represents an equation that includes numbers and
operation symbols.
A statement compares two expressions using relationship signs such as equal to (=), not equal
to (≠), greater than (>), less than (<), less than or equal to (≤), etc. When we deal with
equations, we use the equal sign.
Assessment Words
Solve Interpret
Write Justify
9. INTRODUCTION (Suggested time:10 Minutes)
a) Complete the table below for 𝑥 and y values for the equation:
𝑦 = 2𝑥² − 3

-𝑥 -2 -1 0 3 7
𝑦 -3 -1 -3 15 95

b) Complete the table below for 𝑥 and y values for the equation:
𝑦 = 𝑥² − 2

-𝑥 -3 -2 0 2 4
𝑦 9 4 -2 2 14
10. LESSON PRESENTATION/ DEVELOPMENT (Suggested time:15 minutes)

NOTE STRUCTURE:
1. Tom is 6 years older than John and John is 4 years older than
Sam. The sum of their ages is 83. How old is John. Educator asks learners
the steps to follow
when dealing with
Model Let 𝑥 be? Sam’s age problem solving
Then ? John’s age is “𝑥 + 4”
• Problem solving
And Tom’s age will be (𝑥+4) + 6 = 𝑥 + 10 steps
Word problems can be
Hence 𝑥 + (𝑥+4) + (𝑥+10) = 83 written as mathematical
statements so that they
Analysis 𝑥 + (𝑥+4) + (𝑥+10) = 83 can be solved
mathematically.
3𝑥 + 14 = 83 Steps to follow:
Step 1: Identify what
3𝑥 = 69 you have been asked
to solve.
𝑥 = 23
Step 2: Let this value
John’s 𝑥+ 4 = 23 + 4 = 27years be x or any other
age variable
Step 3: Identify what
you have been
given.
Step 4: Write a number
 sentence:
Step 5: Substitute your
2. Sophie is 6 years older than Simphiwe. In 3 years’, time Sophie will values and
solve/calculate.
be
Step 6: Write your
twice as old as Simphiwe. How old is Sophie now? answer with the correct
SI units.
Model Let 𝑥 be? Simphiwe

Sophie’s age is “𝑥+6”

Then in 3 yrs time Sophie = (𝑥+6) + 3

Simphiwe = 𝑥 + 3

Analysis (𝑥+6) + 3 = 2(𝑥+3)

𝑥+9 = 2𝑥 + 6

𝑥 – 2𝑥 = 6 - 9

-𝑥 = - 3

𝑥=3

Sophie’s age 3 + 6 = 9 years

Check in 3 Simphiwe = 3+ 3 = 6, and Sophie = 9 + 3 =

yrs time 12
(Sophie is twice as old as Simphiwe)

11. CLASSWORK/ HOMEWORK (Suggested time:15 minutes)

a) Printing Shop A charges 45c per page and R12 for binding a book. Printing shop B
charges 35c per page and R15 for binding a book. How many pages will the two shops
charge the same?

b) Firm A calculates the cost of a job using the formula Cost = 500 + 30t, where t is the
number of days it takes to complete the job.

Homework

Firm B calculates the cost of a job using the formula Cost = 260 + 48t, where t is the number of
days it takes to complete the job.

a) What would Firm A charge for a job that takes 10 days?

b) How long would Firm B take to complete a job for which their charge is R596?
Here is a specific job for which firms charge the same and take the same time to
complete. How long does this job take?
12. SUPPORT

13. ADDITIONAL NOTES FOR TEACHERS

14. TEACHER REFLECTION:

15. LEARNER WORKSHEET

Mental Maths Classwork Homework

1. The sum of a number and Printing Shop A charges 45c Firm A calculates the cost of a
15 is 63. per page and R12 for binding job using the formula Cost =
Find the number. a book. Printing shop B 500 + 30t, where t is the
charges 35c per page and number of days it takes to
R15 for binding a book. How complete the job.
many pages will the two
shops charge the same? Firm B calculates the cost of a
2. What number divided by job using the formula Cost =
12 gives an answer of 72. 260 + 48t, where t is the
number of days it takes to
complete the job.

3. What number must added a) What would Firm A

to 8 to get the charge for a job that
takes 10 days?
answer of -23. What b) How long would Firm B
number when multiplied take to complete a job
for which their charge is
by 15 gives -9 R596?
Here is a specific job for which
firms charge the same and
take the same time to
complete. How long does this
job take?
 Gauteng Province
Grade 9 Lesson Plan 22
Term 2
1. TOPIC: ALGEBRAIC EQUATIONS
2. DATE: 08 May 2024 DURATION: 1 hours
3. OBJECTIVES:
By the end of the lesson learners should know and be able to extend solving equations
to include:
• using factorisation.
• equations of the form: a product of factors = 0
GDE ATP Term
4. RESOURCES:
DBE workbook, Sasol-Inzalo workbook, textbook, calculator.
5. REVIEW AND CORRECTION OF HOMEWORK (suggested time:5 minutes)

Homework provides an opportunity for teachers to track learners’ progress in the mastery of
mathematics concepts and to identify the problematic areas which require immediate attention.
Therefore it is recommended that you place more focus on addressing errors from learner
responses that may later become misconceptions.

6. PRIOR KNOWLEDGE

• Solve simple equations algebraically or by inspection

• Determine additive and multiplicative inverses
• Use substitution to determine values of unknowns
7. MENTAL MATHS: (Suggested time:5 minutes)

8. ENGLISH ACROSS THE CURRICULUM: (Suggested time:5 minutes)

Vocabulary
Number Sentences Difference
Operations more than
Sum increase

Terminology
Number Sentences: A Number Sentence represents an equation that includes numbers and
operation symbols.

A statement compares two expressions using relationship signs such as equal to (=), not equal
to (≠), greater than (>), less than (<), less than or equal to (≤), etc. When we deal with equations,
we use the equal sign.
Assessment Words
Solve Interpret
Write Justify
9. INTRODUCTION (Suggested time:10 Minutes)
Present the following to the learners:
𝒂𝒙² + 𝒃𝒙 + 𝒄 = 𝟎

is known as a quadratic equation in standard form

(𝒂, 𝒃, and c can have any value, except that a can't be 0.)
10. LESSON PRESENTATION/ DEVELOPMENT (Suggested time:15 minutes)

Present the following to the learners: NOTE STRUCTURE:

𝒂𝒙² + 𝒃𝒙 + 𝒄 = 𝟎

is known as a quadratic equation in standard form

(𝒂, 𝒃, and c can have any value, except that a can't be 0.)

Remember for all purposes for Grade 9 we are only solving

equations with a value of 𝒂 = 𝟏

To factorise a quadratic is to find what to multiply to get the

quadratic. (We need to find the factors)

Multiplying (𝑎 + 4)(𝑎 – 1) together is called expanding

In fact, expanding and factorising are opposites

Expand

(𝑎 + 4)(𝑎 – 1) 𝑎² + 3𝑎 − 4

Factorising

Explain to the learners that the product of the first terms of the
factors must be equal to the 𝑥 2 term of the trinomial

𝒙𝟐 + 5𝑥 + 6 = (𝒙 + 2)(𝒙 + 3) meaning that 𝑥 . 𝑥 = 𝑥 2

The product of the last terms of the factors must be equal to the
last term (the constant term) of the trinomial

𝑥 2 + 5𝑥 + 𝟔 = (𝑥 + 𝟐)(𝑥 + 𝟑) meaning that 2 . 3 = 6

The sum of the inner and outer products must be equal to the 𝑥
term of the trinomial

𝑥 2 + 5𝑥 + 6 = (𝑥 + 2)(𝑥 + 3) meaning that (2 + 3)𝑥 =

5𝑥
The factors are of the form: (𝑥. 𝑥) + (𝑎 + 𝑏)𝑥 + (𝑎. 𝑏) = (𝑥 +
𝑎)(𝑥 + 𝑏)
(remember FOIL)

Example 1:

Solve 𝑎² − 7𝑎 + 12 = 0

(𝑎 − 3)(𝑎 – 4) = 0

𝑎 − 3 = 0 𝑜𝑟 𝑎 – 4 = 0

𝑎 = 3 𝑜𝑟 𝑎 = 4

11. CLASSWORK (Suggested time:15 minutes)

Determine the values of the x which will make the following
statements to be true:

12. HOMEWORK
Determine the values of the x which will make the
following statements to be true:

13. SUPPORT
For learners at risk do support activities. (Choose questions from activities provided)

14. ADDITIONAL NOTES FOR TEACHERS

15. TEACHER REFLECTION:

16. LEARNER WORKSHEET
CLASSWORK
Determine the values of the x which will make the following
statements to be true:

HOMEWORK
Determine the values of the x which will make the following
statements to be true:
 Gauteng Province
Grade 9 Lesson Plan 23
Term 2
1. TOPIC: ALGEBRAIC EQUATIONS
2. DATE: 09 May 2024 DURATION: 1 hours
3. OBJECTIVES:
By the end of the lesson learners should know and be able to extend solving equations
to include:
• analyse and interpret equations that describe a given situation
• set up equations to describe problem situations
• solve equations by:
- inspection
- using additive and multiplicative inverses
• solve equations using laws of exponents
• Use substitution in equations to generate tables of ordered pairs.
• using factorisation.
• equations of the form: a product of factors = 0
GDE ATP Term
4. RESOURCES:
DBE workbook, Sasol-Inzalo workbook, textbook, calculator.
5. REVIEW AND CORRECTION OF HOMEWORK (suggested time:5 minutes)

Homework provides an opportunity for teachers to track learners’ progress in the mastery of
mathematics concepts and to identify the problematic areas which require immediate attention.
Therefore it is recommended that you place more focus on addressing errors from learner
responses that may later become misconceptions.

6. PRIOR KNOWLEDGE

• Solve simple equations algebraically or by inspection

• Determine additive and multiplicative inverses
• Use substitution to determine values of unknowns
7. ENGLISH ACROSS THE CURRICULUM: (Suggested time:5 minutes)
Vocabulary
Number Sentences Difference
Operations more than
Sum increase

Terminology
Number Sentences: A Number Sentence represents an equation that includes numbers and
operation symbols.
A statement compares two expressions using relationship signs such as equal to (=), not equal
to (≠), greater than (>), less than (<), less than or equal to (≤), etc. When we deal with equations,
we use the equal sign.
Assessment Words
Solve Interpret
Write Justify

8. LESSON PRESENTATION/ DEVELOPMENT (Suggested time:15 minutes)

9. SUPPORT
For learners at risk do support activities. (Choose questions from activities provided)

10. ADDITIONAL NOTES FOR TEACHERS

11. TEACHER REFLECTION