First Term Mathematics revision for SS 1

Class: SS 1
Term: First Term
Week: 11
Age: 15 years
Duration: 60 minutes
Subject: General Mathematics
Curriculum Theme: Revision
Focal competence: Integration of the term’s curriculum competencies
Key competencies/values: Critical Thinking; Communication
Skills:

• Curriculum skills covered in Weeks 1-10

Previous Lesson: Base 16 Numbers and Their Representation
Topic: Revision and Consolidation
Subject Matter: core term topics, taught skills, common misconceptions, revision exercises

Specific Objectives

By the end of the lesson, pupils/students should be able to:

Cognitive Domain

• Recall the key concepts taught during the term.
• Identify common misconceptions in core topics.
• Solve problems related to the term’s curriculum.

Psychomotor Domain

• Apply the term’s knowledge and skills in written tasks.
• Demonstrate problem-solving techniques in practical exercises.

Affective Domain

• Participate actively in revision exercises.
• Show confidence in tackling mathematical problems.

Reference Materials

The following resources were used in planning this lesson:

• 2025 New Revised Senior Secondary Education Curriculum (SSEC)
• Relevant State Unified Scheme of Work
• Essential Mathematics for Senior Secondary Schools 1
• The HeadTeacher Scheme of work For The New Revised Senior Secondary Education Curriculum (SSEC)

Instructional Materials

The teacher will teach this lesson with the aid of:

• Class notes and approved textbooks
• Past questions/revision exercises
• Whiteboard/Chalkboard
• Markers/Chalk
• Calculators (where permitted)

Rationale for the Lesson

This revision lesson is important for consolidating students’ understanding of all topics covered in the First Term. It helps to reinforce learned concepts, address any lingering misconceptions, and prepare students for examinations. Effective revision ensures that students can confidently apply their mathematical skills to new problems.

Prerequisite/Previous Knowledge

Students should have a foundational understanding of all Mathematics topics covered from Week 1 to Week 10 of the First Term.

Lesson Content/Board Summary

Revision and Consolidation

Number Bases

Number bases are systems of counting where the number of unique digits (including zero) used to represent numbers is equal to the base. Common bases include base 10 (decimal), base 2 (binary), base 8 (octal), and base 16 (hexadecimal).

Conversion of Number Bases

To convert from base 10 to another base, repeatedly divide the base 10 number by the new base and record the remainders. Read the remainders from bottom to top.

To convert from another base to base 10, multiply each digit by the base raised to the power of its position (starting from 0 from the right).

Example 1 (Base 10 to Base 2)

Question: Convert (25_{10}) to base 2.

Solution:

Step 1: Divide 25 by 2 repeatedly.

(25 div 2 = 12) remainder (1)

(12 div 2 = 6) remainder (0)

(6 div 2 = 3) remainder (0)

(3 div 2 = 1) remainder (1)

(1 div 2 = 0) remainder (1)

Step 2: Read remainders from bottom up.

Answer: (11001_2)

Example 2 (Base 5 to Base 10)

Question: Convert (324_5) to base 10.

Solution:

Step 1: Expand the number using powers of the base.

(324_5 = (3 times 5^2) + (2 times 5^1) + (4 times 5^0))

Step 2: Calculate the values.

(= (3 times 25) + (2 times 5) + (4 times 1))

(= 75 + 10 + 4)

Step 3: Sum the values.

(= 89)

Answer: (89_{10})

Indices (Exponents)

Indices are used to show that a number is multiplied by itself a certain number of times. For example, in (a^n), (a) is the base and (n) is the index or exponent.

Laws of Indices

1. Multiplication Law: (a^m times a^n = a^{m+n})
2. Division Law: (a^m div a^n = a^{m-n})
3. Power Law: ((a^m)^n = a^{mn})
4. Zero Index: (a^0 = 1) (where (a neq 0))
5. Negative Index: (a^{-n} = frac{1}{a^n})
6. Fractional Index: (a^{1/n} = sqrt[n]{a}) and (a^{m/n} = (sqrt[n]{a})^m)

Example 3

Question: Simplify ((2x^3y^2)^2 times x^{-1}y^4)

Solution:

Step 1: Apply the power law to the first term.

((2x^3y^2)^2 = 2^2 times (x^3)^2 times (y^2)^2 = 4x^6y^4)

Step 2: Multiply the result by the second term.

(4x^6y^4 times x^{-1}y^4)

Step 3: Apply the multiplication law for indices.

(= 4 times x^{6+(-1)} times y^{4+4})

(= 4x^5y^8)

Answer: (4x^5y^8)

Logarithms

Logarithms are the inverse of exponentiation. If (b^y = x), then (log_b x = y). Here, (b) is the base, (x) is the number, and (y) is the logarithm.

Laws of Logarithms

1. Product Law: (log_b (MN) = log_b M + log_b N)
2. Quotient Law: (log_b (frac{M}{N}) = log_b M – log_b N)
3. Power Law: (log_b (M^p) = p log_b M)
4. Logarithm of 1: (log_b 1 = 0)
5. Logarithm of Base: (log_b b = 1)
6. Change of Base: (log_b x = frac{log_a x}{log_a b})

Example 4

Question: Evaluate (log_3 27 + log_3 9)

Solution:

Step 1: Express the numbers as powers of the base.

(27 = 3^3)

(9 = 3^2)

Step 2: Substitute into the expression.

(log_3 (3^3) + log_3 (3^2))

Step 3: Apply the power law of logarithms ((log_b (M^p) = p log_b M)).

(= 3 log_3 3 + 2 log_3 3)

Step 4: Use the law (log_b b = 1).

(= 3(1) + 2(1))

(= 3 + 2)

Step 5: Simplify.

(= 5)

Answer: (5)

Basic Algebra and Equations

Revision includes simplifying algebraic expressions, solving linear equations, and understanding basic algebraic terms like variables, constants, and coefficients.

Solving Linear Equations

To solve a linear equation, isolate the variable by performing the same operation on both sides of the equation.

Example 5

Question: Solve for (x): (3(x+2) – 5 = 2x + 7)

Solution:

Step 1: Expand the bracket.

(3x + 6 – 5 = 2x + 7)

Step 2: Simplify both sides.

(3x + 1 = 2x + 7)

Step 3: Collect like terms (move (2x) to the left and (1) to the right).

(3x – 2x = 7 – 1)

Step 4: Simplify to find (x).

(x = 6)

Answer: (x = 6)

Teaching Methods/Instructional Techniques

Discussion, Question and Answer, Explanation, Guided Practice, Problem Solving, Individual Practice

Instructional Procedures

Step 1: Introduction

Time: 5 minutes

Teaching Skill: Activating Prior Knowledge

Teacher’s Activity: The teacher welcomes the students and explains that today’s lesson is a revision of key topics covered in the First Term. The teacher asks students to briefly mention one topic they found challenging or interesting during the term.

Pupils’ Activity: Students respond by mentioning various topics and prepare for the revision.

Learning Point: Term topics recall

Step 2: Review of Number Bases

Time: 10 minutes

Teaching Skill: Explanation/Demonstration

Teacher’s Activity: The teacher reviews the concept of number bases, focusing on conversions between different bases (e.g., base 10 to other bases and vice versa). The teacher works through Example 1 and Example 2 from the Board Summary on the board, explaining each step clearly and addressing common errors.

Pupils’ Activity: Students actively listen, ask questions for clarification, and follow the worked examples.

Learning Point: Number base conversions

Step 3: Practice on Number Bases

Time: 5 minutes

Teaching Skill: Guided Practice

Teacher’s Activity: The teacher provides a quick practice question on number base conversion for students to attempt individually or in pairs. E.g., “Convert (1011_2) to base 10” or “Convert (30_{10}) to base 3”. The teacher walks around to provide support.

Pupils’ Activity: Students attempt the practice questions and discuss their solutions with peers.

Learning Point: Number base application

Step 4: Review of Indices

Time: 10 minutes

Teaching Skill: Explanation/Problem Solving

Teacher’s Activity: The teacher reviews the laws of indices, writing them on the board. The teacher then works through Example 3 from the Board Summary, emphasizing the correct application of each law. Misconceptions about negative and fractional indices are clarified.

Pupils’ Activity: Students recall the laws of indices and observe the step-by-step solution to the example, asking questions where necessary.

Learning Point: Laws of indices

Step 5: Review of Logarithms

Time: 10 minutes

Teaching Skill: Explanation/Demonstration

Teacher’s Activity: The teacher introduces the concept of logarithms as the inverse of indices and reviews the laws of logarithms. The teacher works through Example 4 from the Board Summary, demonstrating how to apply the laws to simplify logarithmic expressions.

Pupils’ Activity: Students pay attention to the explanation and worked example, noting the relationship between indices and logarithms.

Learning Point: Laws of logarithms

Step 6: Review of Basic Algebra and Equations

Time: 10 minutes

Teaching Skill: Problem Solving/Guided Practice

Teacher’s Activity: The teacher revises simplifying algebraic expressions and solving linear equations. The teacher works through Example 5 from the Board Summary, guiding students through collecting like terms and isolating the variable. The teacher provides a similar problem for students to solve.

Pupils’ Activity: Students participate in solving the example and attempt the practice problem, applying algebraic rules.

Learning Point: Algebraic equation solving

Step 7: Evaluation/Review

Time: 5 minutes

Teaching Skill: Questioning/Assessment

Teacher’s Activity: The teacher evaluates the learning by asking the following questions:

1. Convert (17_{10}) to base 2.
2. Simplify (y^5 times y^{-2}).
3. Evaluate (log_2 8).
4. Solve for (x): (4x – 3 = 2x + 5).

Pupils’ Activity: Pupils answer orally and in writing.

Learning Point: Term concepts application

Step 8: Conclusion

Time: 5 minutes

Teaching Skill: Consolidation

Teacher’s Activity: The teacher summarises the key topics revised (Number Bases, Indices, Logarithms, and Basic Algebra) and encourages students to continue practicing these concepts using their textbooks and past questions. The teacher reminds them of the importance of consistent practice for mastery.

Pupils’ Activity: Students listen to the summary and prepare for the next lesson.

Learning Point: Key concepts reinforced

Lesson Keywords

• Number Base – A system for representing numbers.
• Index (Exponent) – A number that indicates how many times the base number is multiplied by itself.
• Logarithm – The power to which a base must be raised to produce a given number.
• Algebra – A branch of mathematics dealing with symbols and the rules for manipulating these symbols.
• Equation – A statement that two mathematical expressions are equal.

Differentiation

For students who are struggling, the teacher can provide simpler, step-by-step revision exercises and offer one-on-one guidance during practice sessions. For advanced learners, the teacher can provide more complex problems or challenge them to explain concepts to their peers, fostering deeper understanding and critical thinking.

Suggested Lesson Videos

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