Mathematics - Senior Secondary 1 - Logarithms (II)

Logarithms (II)

Get it on Google Play
Get it on the Apple App Store
  1. Home
  2. Comprehensive Lesson Plan and Notes
  3. Senior Secondary 1
  4. Logarithms (II)

TERM: 1ST TERM

WEEK: 7
Class: Senior Secondary School 1
Age: 15 years
Duration: 40 minutes of 5 periods
Subject: Mathematics
Topic: Logarithm (II)
Focus: Calculations Involving Multiplication and Division, Reading Logarithm and Antilogarithm Tables.

SPECIFIC OBJECTIVES:

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

  1. Use logarithm and antilogarithm tables for multiplication and division calculations.
  2. Understand how to interpret values from logarithm and antilogarithm tables.
  3. Perform complex calculations involving multiplication and division using logarithmic tables.
  4. Apply logarithmic operations to solve real-life problems.

INSTRUCTIONAL TECHNIQUES:

  • Guided demonstration
  • Question and answer
  • Practice exercises
  • Discussion
  • Real-life applications

 

INSTRUCTIONAL MATERIALS:

  • Logarithm table chart
  • Antilogarithm table chart
  • Flex banner with logarithmic table booklet
  • Whiteboard and markers

 

PERIOD 1 & 2: Introduction to Logarithms (II)

PRESENTATION:

Step

Teacher’s Activity

Student’s Activity

Step 1 - Review of Logarithms

Briefly reviews logarithmic principles learned in the previous lesson. Explains how logarithms simplify complex multiplication and division.

Students listen and recall previous lesson concepts, ask clarifying questions.

Step 2 - Using the Logarithmic Table

Introduces the logarithmic table chart. Guides students on how to read and use the table for multiplication and division. Explains the concept of a logarithmic scale.

Students observe and practice reading the table. They take notes on how the table simplifies calculations.

Step 3 - Demonstrating Multiplication Using Logarithms

Shows how multiplication can be simplified using logarithms: For example, log(AB) = log(A) + log(B).

Students watch the demonstration and practice solving similar multiplication problems using the logarithmic table.

Step 4 - Demonstrating Division Using Logarithms

Explains division using logarithms: log(A/B) = log(A) - log(B). Guides students through an example.

Students practice division using the logarithmic table, noting the differences in the calculation process.

NOTE ON BOARD

Multiplication with Logarithms: log(AB) = log(A) + log(B) Division with Logarithms: log(A/B) = log(A) - log(B)

Students copy the notes into their notebooks.

EVALUATION (5 exercises):

  1. What is the product of 10 × 100 using logarithms?
  2. How would you divide 1000 by 10 using logarithms?
  3. If log(2) = 0.3010 and log(3) = 0.4771, what is log(6)?
  4. What is the logarithmic value of 125 using the logarithmic table?
  5. Using the table, find the logarithmic value of 450.

CLASSWORK (5 questions):

  1. Multiply 15 × 200 using logarithms.
  2. Divide 5000 by 100 using logarithms.
  3. Find the logarithmic value of 72 using the table.
  4. Using logarithms, calculate 12 × 14.
  5. Find the division of 500 by 25 using logarithms.

ASSIGNMENT (5 tasks):

  1. Use logarithms to find the product of 8 and 250.
  2. Divide 2000 by 10 using logarithms.
  3. What is log(1000)?
  4. Multiply 75 × 30 using logarithms.
  5. Solve 625 ÷ 25 using logarithms.

 

PERIOD 3 & 4: Logarithmic and Antilogarithmic Tables for Multiplication and Division

PRESENTATION:

Step

Teacher’s Activity

Student’s Activity

Step 1 - Introduction to Antilogarithms

Introduces the concept of antilogarithms. Explains how antilogarithms are the inverse of logarithms and can be used for finding the original value of a number from its logarithm.

Students listen and make notes about the inverse relationship between logarithms and antilogarithms.

Step 2 - Reading the Antilogarithmic Table

Guides students through the process of using the antilogarithmic table to find the original number from its logarithmic value.

Students practice reading from the antilogarithmic table, understanding how to find the corresponding value.

Step 3 - Example Problem (Multiplication)

Demonstrates multiplication using both logarithms and antilogarithms. For example, log(AB) = log(A) + log(B), then use the antilogarithmic table to find the original number.

Students observe and practice solving multiplication problems with both logarithms and antilogarithms.

Step 4 - Example Problem (Division)

Demonstrates division using logarithms: log(A/B) = log(A) - log(B), then uses the antilogarithmic table to find the original value of the result.

Students practice division problems using both logarithms and antilogarithms.

NOTE ON BOARD

Antilogarithms: If log(A) = B, then A = antilog(B).

Students copy the notes into their notebooks.

EVALUATION (5 exercises):

  1. Using the antilogarithmic table, find the value of 10^2.
  2. Using logarithms, calculate the product of 12 and 200. Then use the antilogarithmic table to find the result.
  3. Using logarithms and antilogarithms, divide 3000 by 15.
  4. If log(15) = 1.1761, what is the original value of 15?
  5. Use the antilogarithmic table to find the original value of 10^4.

CLASSWORK (5 questions):

  1. Find the antilogarithmic value of 3.2.
  2. Multiply 150 × 250 using logarithms, then use the antilogarithmic table to find the result.
  3. Divide 1000 by 25 using logarithms and antilogarithms.
  4. If log(5) = 0.69897, what is the antilogarithmic value of 0.69897?
  5. Using the logarithmic and antilogarithmic tables, solve 500 ÷ 4.

ASSIGNMENT (5 tasks):

  1. Using logarithms and antilogarithms, calculate 40 × 50.
  2. Solve 9000 ÷ 30 using logarithms and antilogarithms.
  3. Find the value of 10^3 using the antilogarithmic table.
  4. Multiply 30 × 40 using logarithms, then find the result using the antilogarithmic table.
  5. If log(100) = 2, what is the antilogarithmic value?

 

PERIOD 5: Application of Logarithms in Real-Life Problems

PRESENTATION:

Step

Teacher’s Activity

Student’s Activity

Step 1 - Review of Applications

Reviews real-life applications of logarithms and antilogarithms in fields like chemistry, physics, and engineering.

Students listen and engage in discussion about how logarithms are used in real life.

Step 2 - Word Problems

Guides students through a few practical word problems that involve logarithmic calculations. For example, calculating the pH level of a substance using logarithms.

Students participate in the discussion and solve word problems.

Step 3 - Group Activity

In groups, students will solve word problems that involve logarithms and antilogarithms.

Students collaborate in groups to solve problems and share solutions.

Step 4 - Class Discussion

Facilitates a class discussion on the importance of logarithms in real-life scenarios.

Students discuss and summarize the applications of logarithms in real life.

NOTE ON BOARD

Real-life applications include calculating the pH of solutions, Richter scale for measuring earthquakes, and population growth.

Students copy down examples of real-life applications.

EVALUATION (5 exercises):

  1. Calculate the pH of a solution if the hydrogen ion concentration is 1 × 10^-4 M.
  2. Use logarithms to find the Richter scale value of an earthquake with an intensity of 10^3.
  3. Calculate the population growth using logarithms over a period of 5 years.
  4. Solve a word problem involving exponential decay.
  5. Use logarithms to solve for the time it takes for a radioactive substance to decay to half of its original amount.

CLASSWORK (5 questions):

  1. Use logarithms to calculate the pH of a solution.
  2. Solve for the Richter scale value given the intensity of an earthquake.
  3. Calculate the logarithmic value of a population increase over time.
  4. Use logarithms to determine the half-life of a substance.
  5. Solve a word problem on exponential growth using logarithms.

ASSIGNMENT (5 tasks):

  1. Find the pH of a solution with a concentration of 1 × 10^-6 M.
  2. Calculate the population growth of a species over 10 years.
  3. Use logarithms to determine the half-life of a substance.
  4. Solve a word problem on exponential decay.

Research another real-life application of logarithms in science or engineering.