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FIRST TERM
WEEKLY LESSON NOTES
WEEK 6
Week Ending: 10-11-2023 DAY: Subject: Mathematics
Duration: 100MINS Strand: Number

Class: B9 Class Size: Sub Strand: SURDS

Content Standard: Indicator: Lesson:
B9.1.2.4 Demonstrate understanding of surds as
B9.1.2.4.1 Identify simple and compound
real numbers, the process of adding and
subtracting of surds
surds. 1 of 2
Core Competencies:
Performance Indicator:
Communication and Collaboration (CC)
Learners can identify and simplify simple and compound surds. Critical Thinking and Problem solving (CP)
References: Mathematics Curriculum Pg. 169
New words: Surds, Simple Surd, Compound, Radicand

Phase/Duration Learners Activities Resources

PHASE 1: Display the following numbers on the board: √3, √18, √2, √50.
STARTER
Ask learners, "What do these numbers have in common, and how
might they be different from each other?"

Share performance indicators and introduce the lesson.

PHASE 2: NEW Briefly discuss what surds are (numbers that can't be simplified to Number cards
LEARNING remove a square root).

Explain the terminology: the number under the square root sign is
called the 'radicand'.

Define a simple surd as a square root whose radicand cannot be

further simplified.

Provide examples, such as √2 or √3, and explain why these are

simple surds (because they don't have factors which are perfect
squares, apart from 1).

Define a compound surd as a square root whose radicand can be

simplified further by factoring out perfect squares.

Use examples to illustrate. For instance, √18 can be written as

√(9x2) or 3√2.

Guide learners through the process of simplifying a few compound

surds.
Example: Simplify the compound surd: √72.
Solution
To simplify the compound surd √72, you can simplify it as follows:
 √72 = √(36 * 2)
Now, simplify the square root of 36, which is 6:
√(6 * 2) = 6√2

So, the simplified form of √72 is 6√2.

Distribute a set of cards to each student or small groups, where

each card has a surd written on it.
Example: √50, √18, √98, √54, √75, etc.

Ask learners to sort these cards into two piles: simple surds and
compound surds.

After sorting, encourage learners to pick a compound surd and

simplify it.
Example: Simplify √162
solution
√162 = √(9 * 18)
We can start by factoring 162 as = √9=3 and √18=(9*2)
= 3*3√2

So, the simplified form of √162 is 9√2

Assessment
1. Simplify the compound surd: √72.
2. Is √5 a simple or compound surd? Explain your answer.
3. Simplify √45.
4. Simplify √80.
5. Simplify √28.
6. Simplify √63.
7. Simplify √112.
8. Simplify √200.
PHASE 3: Use peer discussion and effective questioning to find out from
REFLECTION learners what they have learnt during the lesson.

Take feedback from learners and summarize the lesson.

Week Ending: 10-11-2023 DAY: Subject: Mathematics
Duration: 100MINS Strand: Number

Class: B9 Class Size: Sub Strand: SURDS

Content Standard: Indicator: Lesson:
B9.1.2.4 Demonstrate understanding of surds as
B9.1.2.4.2 Explain the identities/rules of
real numbers, the process of adding and
subtracting of surds surds 1 of 2

Performance Indicator: Core Competencies:

Communication and Collaboration
Learners can understand the fundamental identities and rules of
(CC) Critical Thinking and Problem
surds and apply them in mathematical expressions. solving (CP)
References: Mathematics Curriculum Pg. 169
New words: Surds, Simple Surd, Rationalizing, Radicand

Phase/Duration Learners Activities Resources

PHASE 1: Begin with a math puzzle. Display the following expressions on the
STARTER board: √4, √9, √16, and √25.

Ask learners, "What do you notice about these numbers, and how
can you describe this pattern?"

Share performance indicators and introduce the lesson.

PHASE 2: NEW Revise with learners on the definition of surds as square roots that Number cards
LEARNING cannot be simplified to whole numbers.

Explain that the number under the square root sign is called the
'radicand.'

Identity: Rule 1- √a * √b = √(a * b):

Introduce the product rule, explaining that when you multiply two
surds with the same index (e.g., both √a), you can simplify them by
multiplying the radicands.

Provide examples and guide learners through the process: √3 * √5 =

√(3 * 5) = √15.

Identity: Rule 2- √a / √b = √(a / b):

Introduce the quotient rule, explaining that when you divide two
surds with the same index, you can simplify them by dividing the
radicands.
Provide examples and guide learners: √12 / √3 = √(12 / 3) = √4 = 2.

𝑏 𝑏 √a b√a
Identity: Rule 3 - = * =
√a √a √a a
Introduce Rule 3, explaining that it's used when you have a surd in
the denominator of a fraction.

Walk through the steps: b/(√a) = b/(√a) * (√a)/(√a) = (b√a)/a.

Provide examples and let students practice.
Example 1:
Simplify 5 / √3.
Solution:
5 / √3 = 5 / √3 * √3 / √3 = (5√3) / 3

Example 2:
Simplify 2 / √6.
Solution:
2 / √6 = 2 / √6 * √6 / √6 = (2√6) / 6 = √6 / 3

Identity: Rule 4 - a√c + b√c = (a + b)√c:

Introduce Rule 4, explaining that it's used when adding or subtracting
surds with the same index and radicand.

Walk through the steps: a√c + b√c = (a + b)√c. Provide examples

and let students practice.

Example 1:
Simplify 4√5 + 3√5 using Rule 4.
Solution:
4√5 + 3√5 = (4 + 3)√5 = 7√5

Example 2:
Simplify √7 + 2√7 using Rule 4.
Solution:
√7 + 2√7 = (1 + 2)√7 = 3√7

𝑐 𝑐 𝑎−𝑏√n
Identity: Rule 5 - : = *
a+b√n a+b√n 𝑎−𝑏√n

Introduce Rule 5, explaining that it's used for rationalizing the

denominator when the denominator contains a sum.

Walk through the steps: c/(a+b√n) = c/(a+b√n) * (a-b√n)/(a-b√n).

Provide examples and let students practice.

Example 1:
Rationalize the denominator in the expression 5 / (3 + √2).
Solution:
5 / (3 + √2) = 5 / (3 + √2) * (3 - √2) / (3 - √2) = (5 * (3 - √2)) / (3^2 -
(√2)^2) = (15 - 5√2) / (9 - 2) = (15 - 5√2) / 7
 Example 2:
Rationalize the denominator in the expression 2 / (1 + √5).
Solution:
2 / (1 + √5) = 2 / (1 + √5) * (1 - √5) / (1 - √5) = (2 * (1 - √5)) / (1^2 -
(√5)^2) = (2 - 2√5) / (1 - 5) = (2 - 2√5) / -4 = -(1/2) + (1/2)√5

𝑐 𝑐 𝑎+𝑏√n
Identity: Rule 6 - = * :
a−b√n a−b√n 𝑎+𝑏√n

Introduce Rule 6, explaining that it's used for rationalizing the

denominator when the denominator contains a difference.

Walk through the steps: c/(a-b√n) = c/(a-b√n) * (a+b√n)/(a+b√n).

Provide examples and let students practice

Example 1:
Rationalize the denominator in the expression 3 / (2 - √3)
Solution:
3 / (2 - √3) = 3 / (2 - √3) * (2 + √3) / (2 + √3) = (3 * (2 + √3)) / (2^2 -
(√3)^2) = (6 + 3√3) / (4 - 3) = (6 + 3√3) / 1 = 6 + 3√3

Example 2:
Rationalize the denominator in the expression 4 / (1 - √2).
Solution:
4 / (1 - √2) = 4 / (1 - √2) * (1 + √2) / (1 + √2) = (4 * (1 + √2)) / (1^2 -
(√2)^2) = (4 + 4√2) / (1 - 2) = (4 + 4√2) / -1 = -4 - 4√2

Provide learners with a set of surd expressions to simplify using the

rules discussed.

Encourage group work and peer learning. Allow learners to check

their work collaboratively.

Assessment
1. Apply the product rule to simplify √2 * √8.
2. Use the quotient rule to simplify √15 / √5.
3. Rationalize the denominator in the expression 1 / √2.
4. Simplify the expression 4√7 / √2 using the surd rules.
5. What is the result of applying Rule 4 to 5√3 + 2√3?
6. Use Rule 5 to rationalize the denominator in the expression 7 /
(1 + √5).
7. Apply Rule 6 to rationalize the denominator in 3 / (2 - √6).
PHASE 3: Use peer discussion and effective questioning to find out from
REFLECTION learners what they have learnt during the lesson.

Take feedback from learners and summarize the lesson.