Liberia - Grade 11 - Mathematics

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Subject: Mathematics

Semester: 1

Period: 1

Week: 4

WEEK 4

Class: Grade 11
Age: 16 years
Duration: 40 minutes per period
Subject: Mathematics
Topic: Logarithms
Focus: Revision of Logarithms of Numbers Greater Than One, Characteristics, and Calculation with Logarithmic Tables and Calculators.

SPECIFIC OBJECTIVES:
By the end of the lesson, students should be able to:

Revise logarithms of numbers greater than one and understand their properties.
Understand and apply the characteristics of logarithms of numbers greater than one and less than one.
Convert numbers to standard form and use logarithms for multiplication, division, powers, and roots.
Solve simple logarithmic equations.
Understand the accuracy of results obtained from a logarithm table and calculator.

INSTRUCTIONAL TECHNIQUES:
• Question and answer
• Guided demonstration
• Discussion
• Practice exercises
• Use of analogies and real-life examples

INSTRUCTIONAL MATERIALS:
• Logarithm tables
• Booklets containing solution charts of logarithms
• Flex banners showing logarithms and antilogarithms of numbers
• Whiteboard and markers

PERIOD 1 & 2: Revision of Logarithms of Numbers Greater Than One

PRESENTATION:

Step	Teacher's Activity	Student's Activity
Step 1 - Introduction	Revise the definition and properties of logarithms for numbers greater than 1 (log x > 0). Explain the law of logarithms: log(a × b) = log a + log b, and the law of powers: log(a^b) = b × log a.	Students listen attentively and ask questions if needed.
Step 2 - Characteristics	Explain that logarithms of numbers greater than one are positive, and the logarithms of numbers less than one are negative. Show examples with values like log 10 = 1 and log 1000 = 3.	Students observe the characteristics and take notes.
Step 3 - Demonstration	Solve problems involving multiplication and division of logarithms, using the logarithm table for numbers greater than 1. For example, log 50 + log 2.	Students follow along with the calculations and copy the steps.
Step 4 - Practice	Assign several multiplication and division problems using the logarithm table (e.g., log 2 + log 5, log 100 ÷ log 10).	Students work in pairs to solve the problems and check each other’s solutions.

NOTE ON BOARD:
Logarithm Rules:

log (a × b) = log a + log b
log (a ÷ b) = log a - log b
log (a^b) = b × log a

EVALUATION (5 Exercises):

Calculate log 50 + log 2.
Find log 500 ÷ log 10.
Find log 1000 - log 100.
Simplify log 100 + log 5.
What is log 10?

CLASSWORK (5 Questions):

Simplify log 200 + log 5.
Calculate log 50 ÷ log 10.
What is the value of log 2 × log 5?
Simplify log 1000 ÷ log 10.
What is the value of log 500?

ASSIGNMENT (5 Tasks):

Find log 300 + log 20.
Calculate log 250 ÷ log 5.
Find the value of log 10^3.
Solve log 1000 - log 100.
Explain why log 1 equals 0.

PERIOD 3 & 4: Logarithms of Numbers Less Than One, Multiplication, Division, Powers, and Roots

PRESENTATION:

Step	Teacher's Activity	Student's Activity
Step 1 - Introduction	Introduce logarithms for numbers less than one (log x < 0). Discuss that log (0.1) = -1, and the logarithm of a number between 0 and 1 is negative.	Students take notes and discuss real-life examples.
Step 2 - Calculation	Demonstrate how to multiply, divide, and find powers and roots using logarithms. Example: log (a^b) = b × log a.	Students observe the demonstration and ask clarifying questions.
Step 3 - Practice with Roots	Show how to find square roots and cube roots using logarithms. Example: √100 = 10^log100/2.	Students practice with examples and check their answers.
Step 4 - Guided Practice	Solve several problems involving logarithmic operations (e.g., log 25 × log 4, log 81 ÷ log 9).	Students work in groups to solve problems and discuss solutions.

NOTE ON BOARD:
For Powers and Roots:

log (a^b) = b × log a
log (√a) = log a / 2
log (³√a) = log a / 3

EVALUATION (5 Exercises):

Calculate log (0.1) + log (0.5).
Find log (0.25) × log (0.4).
Simplify log (0.2^3).
Find the square root of 100 using logarithms.
Solve log (0.05) ÷ log (0.2).

CLASSWORK (5 Questions):

Calculate log (0.5) + log (0.2).
Find log (0.1) × log (0.2).
Simplify log (0.2^4).
Find the cube root of 100 using logarithms.
Calculate log (0.25 ÷ 0.5).

ASSIGNMENT (5 Tasks):

Find the value of log (0.75) + log (0.25).
Solve log (0.125) × log (0.5).
Simplify log (0.2^5).
Find the square root of 200 using logarithms.
Solve log (0.5 ÷ 0.25).

PERIOD 5: Solving Simple Logarithmic Equations and Accuracy of Results

PRESENTATION:

Step	Teacher's Activity	Student's Activity
Step 1 - Introduction	Explain how to solve simple logarithmic equations such as log x = 2 or log x = log 3. Demonstrate solving equations with logarithmic properties.	Students pay attention and take notes.
Step 2 - Practice	Solve problems like log x = 2 and log x = log 5. Also, solve equations involving addition and subtraction of logarithms.	Students practice solving logarithmic equations.
Step 3 - Using Logarithm Table and Calculator	Demonstrate using a logarithm table and calculator to find values of logs and antilogs. Discuss accuracy and possible errors in calculations.	Students practice using the logarithm table and calculator for accuracy.
Step 4 - Guided Practice	Provide additional problems for students to solve, including solving logarithmic equations and using logarithmic tables.	Students work individually or in pairs to solve equations and check accuracy.

NOTE ON BOARD:
Solving Logarithmic Equations:

For log x = 2, x = 10^2 = 100.
For log x = log 5, x = 5.

EVALUATION (5 Exercises):

Solve log x = 2.
Solve log x = log 3.
Solve log x = 4.
Solve log x = log 7.
Solve log x = 1.

CLASSWORK (5 Questions):

Solve log x = 3.
Solve log x = log 10.
Solve log x = 0.
Solve log x = 2.
Solve log x = log 5.

ASSIGNMENT (5 Tasks):

Solve log x = 5.
Solve log x = log 2.
Solve log x = log 100.
Solve log x = 0.5.
Use a calculator to find log 2 and log 3.