Mathematics - Senior Secondary 1 - Approximation

Approximation

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TERM: 2ND TERM

WEEK: 2

Class: Senior Secondary School 1
Age: 15 years
Duration: 40 minutes of 5 periods
Subject: Mathematics
Topic: Approximation
Focus: Rounding up and rounding down of numbers to significant figures, decimal places, and nearest whole numbers. Application of approximation to everyday life. Percentage error.

 

SPECIFIC OBJECTIVES:

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

  1. Round numbers up or down to the nearest significant figures and decimal places.
  2. Apply approximation in real-life scenarios.
  3. Calculate percentage error and understand its relevance.

 

INSTRUCTIONAL TECHNIQUES:

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

 

INSTRUCTIONAL MATERIALS:

  • Whiteboard and markers
  • Charts illustrating rounding rules
  • Flashcards with numbers for rounding practice
  • Worksheets with problems on approximation and percentage error
  • Incomplete table showing various numbers for approximation (to be completed in class)

 

PERIOD 1 & 2: Rounding Numbers to Significant Figures and Decimal Places

PRESENTATION:

Step

Teacher’s Activity

Student’s Activity

Step 1 - Introduction

Introduces the concept of rounding numbers to significant figures and decimal places. Explains why approximation is important.

Students listen attentively and ask clarifying questions.

Step 2 - Rounding to Significant Figures

Demonstrates rounding numbers to significant figures. Provides examples: rounding 234.567 to 2 significant figures results in 230, and rounding 0.00456 to 2 significant figures results in 0.0046.

Students observe and take notes on the process of rounding to significant figures.

Step 3 - Rounding to Decimal Places

Demonstrates rounding numbers to decimal places. Example: rounding 45.6789 to 2 decimal places results in 45.68.

Students practice rounding numbers to decimal places on their own with examples.

Step 4 - Guided Practice

Provides several numbers for students to round to both significant figures and decimal places.

Students work through the examples and ask questions where needed.

NOTE ON BOARD:

  • Rounding to Significant Figures: Retain the first few digits of the number, adjusting others to 0.
  • Rounding to Decimal Places: Round based on the desired number of decimal places.

 

EVALUATION (5 Exercises):

  1. Round 568.923 to 3 significant figures.
  2. Round 0.00756 to 2 significant figures.
  3. Round 123.4567 to 2 decimal places.
  4. Round 987.654 to the nearest whole number.
  5. Round 0.00009876 to 3 significant figures.

CLASSWORK (5 Questions):

  1. Round 4567 to 2 significant figures.
  2. Round 0.3456 to 3 decimal places.
  3. Round 9.876 to the nearest whole number.
  4. Round 0.0089 to 2 significant figures.
  5. Round 453.6789 to 1 decimal place.

 

ASSIGNMENT (5 Tasks):

  1. Round 0.000678 to 3 significant figures.
  2. Round 987.654 to 1 decimal place.
  3. Round 12345 to 4 significant figures.
  4. Round 0.123456 to 2 decimal places.
  5. Provide an example of when rounding to significant figures is useful in real life.

 

PERIOD 3 & 4: Application of Approximation to Everyday Life

PRESENTATION:

Step

Teacher’s Activity

Student’s Activity

Step 1 - Introduction

Explains how approximation is used in everyday life, e.g., estimating prices, distances, or quantities.

Students listen and think about examples from their daily experiences.

Step 2 - Everyday Applications

Shows real-life examples where approximation is applied (e.g., estimating the total cost of shopping, calculating time, or measuring distances in rough terms).

Students discuss and share their own real-life examples.

Step 3 - Guided Practice

Provides scenarios for students to apply rounding in practical situations (e.g., rounding up a price to the nearest Naira).

Students work on scenarios in groups, applying rounding to estimate costs and other real-life calculations.

NOTE ON BOARD:

  • Approximation is essential when exact values are not required, especially in budgeting, estimating quantities, and calculations involving time or distance.

EVALUATION (5 Exercises):

  1. Estimate the cost of 3 items priced at N234.99, N456.78, and N789.65 (round to the nearest Naira).
  2. A bus travels 134.76 km. Estimate the distance to the nearest 10 km.
  3. Round N189.45 to the nearest Naira and explain its use in estimating total expenses.
  4. Estimate the total time for 3 tasks that take 15.7 minutes, 22.8 minutes, and 7.9 minutes (round to nearest minute).
  5. Round 9.999 to the nearest whole number and explain when this would be practical in real life.

 

CLASSWORK (5 Questions):

  1. Estimate the cost of 4 items priced at N120.50, N75.30, N90.40, and N160.20 (round to nearest Naira).
  2. Round the total time for tasks of 45.6 minutes, 30.2 minutes, and 12.3 minutes to the nearest 5 minutes.
  3. Round the price of a product N432.89 to the nearest 10 Naira.
  4. Estimate the cost of fuel for a trip where 12.7 liters are needed and the price of fuel is N145.67 per liter (round to nearest Naira).
  5. Estimate the weight of an item weighing 12.34 kg, rounded to the nearest kilogram.

 

ASSIGNMENT (5 Tasks):

  1. Estimate the total cost of 5 items priced at N150.60, N230.80, N85.90, N100.40, and N56.10 (round to the nearest Naira).
  2. A person walked 45.75 km today. Estimate this distance to the nearest 5 km.
  3. Round the cost of a meal priced at N987.65 to the nearest 50 Naira.
  4. Calculate the total time spent on 3 activities (28.4 minutes, 46.2 minutes, 11.6 minutes) and round to the nearest 5 minutes.
  5. Explain how approximation can help in estimating the quantity of items needed for an event.

 

      5. If the actual value is 500 and the approximate value is 505, calculate the percentage error.

 

CLASSWORK (5 Questions):

  1. Calculate the percentage error when the actual value is 200 and the approximate value is 195.
  2. Find the percentage error if the actual value is 78 and the approximate value is 80.
  3. Calculate the percentage error for actual value 120 and approximate value 118.
  4. If the actual value is 45 and the approximate value is 50, calculate the percentage error.
  5. Find the percentage error when the actual value is 150 and the approximate value is 145.

 

ASSIGNMENT (5 Tasks):

  1. Calculate the percentage error for actual value 1000 and approximate value 1020.
  2. Find the percentage error when the actual value is 62 and the approximate value is 60.
  3. Calculate the percentage error for actual value 220 and approximate value 215.
  4. If the actual value is 85 and the approximate value is 90, calculate the percentage error.

Explain why percentage error is important in scientific measurements.