Mathematics - Senior Secondary 1 - Standard Form (AX10^n)

Standard Form (AX10^n)

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TERM: 1ST TERM

WEEK: 5

Class: Senior Secondary School 1
Age: 15 years
Duration: 40 minutes of 5 periods
Subject: Mathematics
Topic: Standard Form (AX10^n)
Focus: Writing Numbers in Index Form, Adding, Subtracting, Multiplying, Dividing Numbers in Standard Form, and Square Roots of Numbers in Standard Form.

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

  1. Write numbers in index (standard) form.
  2. Add two numbers and express the results in standard form.
  3. Subtract one number from another in standard form.
  4. Multiply numbers in standard form.
  5. Divide numbers in standard form, including finding the square root of such numbers.

INSTRUCTIONAL TECHNIQUES:

  • Direct Instruction
  • Guided Practice
  • Discussion
  • Analogy and real-life connections
  • Demonstration

INSTRUCTIONAL MATERIALS:

  • Whiteboard and markers
  • Charts on standard form and its rules
  • Scientific calculators
  • Worksheets for exercises
  • Flashcards with example problems

PERIOD 1 & 2: Writing Numbers in Standard Form (AX10^n)

PRESENTATION:

Step

Teacher’s Activity

Student’s Activity

Step 1 - Introduction

Introduces the concept of standard form (scientific notation). Explains that numbers can be written in the form A × 10^n, where A is a number between 1 and 10, and n is an integer.

Students listen and ask clarifying questions.

Step 2 - Writing Numbers in Standard Form

Demonstrates how to write large and small numbers in standard form. Example: 3500 = 3.5 × 10^3, 0.0045 = 4.5 × 10^-3.

Students observe and take notes on how to write numbers in standard form.

Step 3 - Guided Practice

Provides several examples and guides students in writing numbers in standard form.

Students work through examples with guidance.

Step 4 - Class Practice

Assigns practice problems for students to write in standard form.

Students complete problems individually or in pairs.

NOTE ON BOARD:

  • Numbers in standard form: A × 10^n
  • Where A is between 1 and 10, and n is an integer.

EVALUATION (5 exercises):

  1. Write 70000 in standard form.
  2. Write 0.00035 in standard form.
  3. Write 550000 in standard form.
  4. Write 0.09 in standard form.
  5. Write 124000 in standard form.

CLASSWORK (5 questions):

  1. Write 456000 in standard form.
  2. Write 0.000056 in standard form.
  3. Write 9000000 in standard form.
  4. Write 0.000012 in standard form.
  5. Write 36000000 in standard form.

ASSIGNMENT (5 tasks):

  1. Write 130000000 in standard form.
  2. Write 0.000009 in standard form.
  3. Write 78400000 in standard form.
  4. Write 0.0042 in standard form.
  5. Find a real-life example of a number that could be written in standard form.

 

PERIOD 3 & 4: Adding and Subtracting Numbers in Standard Form

PRESENTATION:

Step

Teacher’s Activity

Student’s Activity

Step 1 - Introduction

Explains how to add and subtract numbers in standard form. The base of the powers of 10 must be the same. If they are not, convert the numbers to the same power of 10 first.

Students listen and ask questions.

Step 2 - Addition in Standard Form

Demonstrates adding two numbers in standard form (e.g., (3 × 10^4) + (4 × 10^4) = 7 × 10^4).

Students observe and take notes on the process.

Step 3 - Subtraction in Standard Form

Demonstrates subtracting numbers in standard form (e.g., (6 × 10^5) - (2 × 10^5) = 4 × 10^5).

Students watch the example and practice.

Step 4 - Guided Practice

Assigns problems to students, working with addition and subtraction of numbers in standard form.

Students work through problems individually or in pairs.

NOTE ON BOARD:

  • Addition/Subtraction: Ensure that powers of 10 are the same before adding or subtracting.
  • Example: (2 × 10^3) + (4 × 10^3) = 6 × 10^3.
  • Example: (5 × 10^6) - (3 × 10^6) = 2 × 10^6.

EVALUATION (5 exercises):

  1. Add (3 × 10^5) and (2 × 10^5).
  2. Subtract (5 × 10^4) from (8 × 10^4).
  3. Add (4 × 10^6) and (6 × 10^6).
  4. Subtract (3 × 10^3) from (7 × 10^3).
  5. Add (1 × 10^2) and (5 × 10^2).

CLASSWORK (5 questions):

  1. Add (6 × 10^5) and (2 × 10^5).
  2. Subtract (4 × 10^7) from (9 × 10^7).
  3. Add (3 × 10^4) and (7 × 10^4).
  4. Subtract (8 × 10^6) from (5 × 10^6).
  5. Add (9 × 10^2) and (2 × 10^2).

ASSIGNMENT (5 tasks):

  1. Add (2 × 10^3) and (5 × 10^3).
  2. Subtract (4 × 10^6) from (8 × 10^6).
  3. Add (7 × 10^2) and (3 × 10^2).
  4. Subtract (3 × 10^4) from (5 × 10^4).
  5. Create a real-life situation where you might add or subtract numbers in standard form.

PERIOD 5: Multiplying and Dividing Numbers in Standard Form

PRESENTATION:

Step

Teacher’s Activity

Student’s Activity

Step 1 - Introduction

Explains how to multiply and divide numbers in standard form. For multiplication, multiply the coefficients and add the exponents. For division, divide the coefficients and subtract the exponents.

Students listen attentively.

Step 2 - Multiplication in Standard Form

Demonstrates multiplying two numbers in standard form: (2 × 10^3) × (4 × 10^2) = (2 × 4) × 10^(3+2) = 8 × 10^5.

Students observe and take notes on how to multiply numbers in standard form.

Step 3 - Division in Standard Form

Demonstrates dividing two numbers in standard form: (6 × 10^5) ÷ (2 × 10^2) = (6 ÷ 2) × 10^(5-2) = 3 × 10^3.

Students watch and take notes on the division method.

Step 4 - Guided Practice

Provides several multiplication and division problems for students to practice.

Students work through examples individually or in pairs.

NOTE ON BOARD:

  • Multiplication: (A × 10^m) × (B × 10^n) = (A × B) × 10^(m+n)
  • Division: (A × 10^m) ÷ (B × 10^n) = (A ÷ B) × 10^(m-n)

EVALUATION (5 exercises):

  1. Multiply (3 × 10^4) and (2 × 10^3).
  2. Divide (8 × 10^6) by (2 × 10^3).
  3. Multiply (4 × 10^5) and (5 × 10^2).
  4. Divide (6 × 10^7) by (3 × 10^3).
  5. Multiply (7 × 10^2) and (9 × 10^1).

CLASSWORK (5 questions):

  1. Multiply (5 × 10^3) and (3 × 10^2).
  2. Divide (9 × 10^6) by (3 × 10^2).
  3. Multiply (2 × 10^4) and (7 × 10^5).
  4. Divide (10 × 10^8) by (5 × 10^3).
  5. Multiply (6 × 10^2) and (8 × 10^3).

ASSIGNMENT (5 tasks):

  1. Multiply (3 × 10^3) and (2 × 10^6).
  2. Divide (8 × 10^5) by (4 × 10^2).
  3. Multiply (5 × 10^4) and (7 × 10^3).
  4. Divide (9 × 10^7) by (3 × 10^3).

Find the square root of (9 × 10^4) in standard form.