Whole Numbers Continued: Problem Solving in Quantitative Aptitude Reasoning Using Large Numbers Mathematics JSS 1 First Term Lesson Notes Week 2

Mathematics JSS 1 First Term Lesson Notes Week 2

Subject: Mathematics
Class: JSS 1
Term: First Term
Week: 2
Age: 11-12 years
Topic: Whole Numbers Continued: Problem Solving in Quantitative Aptitude Reasoning Using Large Numbers
Sub-topic: Solving Problems Involving Large Numbers
Duration: 40 minutes

Behavioural Objectives:

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

1. Understand and apply problem-solving strategies using large numbers.
2. Solve quantitative aptitude reasoning problems involving large numbers.
3. Use arithmetic operations like addition, subtraction, multiplication, and division with large numbers.

Keywords:

• Problem-solving
• Large numbers
• Quantitative reasoning
• Arithmetic operations

Set Induction (5 minutes):

The teacher presents a real-life scenario involving large numbers, such as calculating the population of a country, and asks students how they would solve related problems.

Entry Behaviour:

Students have knowledge of counting and writing numbers in millions, billions, and trillions.

Learning Resources and Materials:

1. Problem-solving worksheets
2. Flashcards with arithmetic operations on large numbers
3. Calculator (optional)

Building Background/Connection to Prior Knowledge:

Students already understand large numbers and their place values. This lesson will extend their ability to use those numbers in problem-solving contexts.

Embedded Core Skills:

• Critical thinking
• Problem-solving
• Numeracy
• Analytical reasoning

Instructional Materials:

1. Chalkboard or whiteboard
2. Worksheets with quantitative aptitude problems
3. Place value tables
4. Arithmetic operation charts

Content:

Problem Solving with Large Numbers:

1. Addition and Subtraction of Large Numbers:
   • Example 1: Add 4,567,000 to 2,345,000.
     Solution: 4,567,000 + 2,345,000 = 6,912,000.
   • Example 2: Subtract 1,234,000 from 5,678,000.
     Solution: 5,678,000 – 1,234,000 = 4,444,000.
2. Multiplication and Division of Large Numbers:
   • Example 1: Multiply 3,000,000 by 5.
     Solution: 3,000,000 × 5 = 15,000,000.
   • Example 2: Divide 1,000,000,000 by 1000.
     Solution: 1,000,000,000 ÷ 1,000 = 1,000,000.
3. Word Problems Involving Large Numbers:
   • Problem: If Nigeria has a population of 200,000,000 people and each person drinks an average of 1 litre of water daily, how many litres of water are consumed in one year?
     Solution: 200,000,000 × 365 = 73,000,000,000 litres of water consumed annually.
4. Using Arithmetic in Real-life Situations:
   • Example: Calculate the total cost if a company buys 50 trucks at 1,500,000 Naira each.
     Solution: 50 × 1,500,000 = 75,000,000 Naira.

Topic: Ordering Large Numbers

Introduction

When dealing with large numbers, it is essential to understand how to compare and arrange them in either ascending or descending order. This helps in situations like ranking numbers, determining the largest or smallest values, and organizing data.

Worked Examples

Example 1: Finding the smallest and largest number

Given the following numbers:

• 2,675,571
• 3,498,567
• 2,670,781
• 3,497,859

Step 1: Compare numbers starting with 2.

Comparing the numbers starting with 2, 2,670,781 is smaller than 2,675,571.

Step 2: Compare numbers starting with 3.

Comparing the numbers starting with 3, 3,497,859 is smaller than 3,498,567.

Thus, the smallest number is 2,670,781 and the largest number is 3,498,567.

Example 2: Arranging numbers in ascending order

Arrange these numbers in ascending order:

• 13,456,786
• 24,567,432
• 38,479,871
• 24,558,011
• 13,498,069
• 38,478,817

Step 1: Group the numbers starting with 1:

• 13,456,786
• 13,498,069

In ascending order: 13,456,786, 13,498,069

Step 2: Group the numbers starting with 2:

• 24,558,011
• 24,567,432

In ascending order: 24,558,011, 24,567,432

Step 3: Group the numbers starting with 3:

• 38,478,817
• 38,479,871

In ascending order: 38,478,817, 38,479,871

Final ascending order: 13,456,786, 13,498,069, 24,558,011, 24,567,432, 38,478,817, 38,479,871

Example 3: Arranging numbers in descending order

Arrange the following numbers in descending order:

• 89728567
• 89704567
• 89693670
• 89776909
• 89735890

Step 1: Compare the numbers by their digits:

1. 89776909 (Highest)
2. 89735890
3. 89728567
4. 89704567
5. 89693670 (Lowest)

In descending order:
89776909, 89735890, 89728567, 89704567, 89693670

Example 4: Using a mixture of digits and words with large numbers

Sometimes, large numbers are written using a mixture of digits and words to make them easier to read and understand.

For example:

• £30,000,000 becomes £30 million.
• N75,000,000,000 becomes N75 billion.
• £3,400,000,000,000 becomes £3.4 trillion.

Example 5: Changing units of large numbers

When working with large numbers in various units, it’s important to convert between units properly.

Convert the following:

1. 173 cm to millimeters:
   Since 1 cm = 10 mm,
   173 cm = 173 × 10 = 1,730 mm
2. 5.9 km to millimeters:
   1 km = 1,000,000 mm,
   5.9 km = 5.9 × 1,000,000 = 5,900,000 mm or 5.9 million mm
3. 200 meters to millimeters:
   1 meter = 1,000 mm,
   200 meters = 200 × 1,000 = 200,000 mm

Evaluations

1. Arrange the following numbers in ascending order:
   89728567, 89704567, 89693670, 89776909, 89735890.
2. Arrange the following numbers in descending order:
   217679057, 497378939, 234656452, 21023404895, 2100998969.
3. Convert the following:
   • 5000 kg to grams
   • 1250 liters to milliliters
4. Write the following numbers as a mixture of digits and words:
   • 780,000 barrels
   • 900,000 km
   • $900,000,000
5. Write these numbers in digits:
   • $312 billion
   • £0.85 trillion
   • 212 million liters

Reading Assignment

• Essential Mathematics for JSS1 by AJS Oluwasanmi, pages 23-35.
• New General Mathematics for JSS 1 by M. F Macrae, pages 15-20.

Weekend Assignment

1. What is the value of 1.2 km in meters?
   • (a) 120 m
   • (b) 1,200 m
   • (c) 12,000 m
   • (d) 120,000 m
2. Which of the following numbers is the largest?
   • (a) 727345565
   • (b) 727245565
   • (c) 727445565
   • (d) 726778876
3. $114 million in digits only is:
   • (a) $1,200,000
   • (b) $1,140,000
   • (c) $1,250,000
   • (d) $125,000
4. Le 5,600,000 in digits and words is:
   • (a) Le 56 million
   • (b) Le 5.6 billion
   • (c) Le 0.56 billion
   • (d) Le 5.6 million
5. 13,500,000 mm in km is:
   • (a) 13.5 km
   • (b) 1.35 km
   • (c) 1350 km
   • (d) 13,500 km

Theory

1. Write these numbers in digits only:
   • (a) Le 0.5 billion
   • (b) $9.1 million
2. Write down the missing numbers:
   • 100,987,331, 101,987,331, 102,987,331, __________, __________, 105,987,331
   • 980,231,680, 980,231,682, __________, 980,231,686, __________, 980,231,690

1. Add 4,000,000 to 6,000,000. The answer is ______.
   a) 10,000,000
   b) 5,000,000
   c) 2,000,000
   d) 15,000,000
2. Subtract 1,234,000 from 9,876,000. The answer is ______.
   a) 8,642,000
   b) 7,642,000
   c) 6,642,000
   d) 9,642,000
3. Multiply 4,500,000 by 2. The result is ______.
   a) 9,000,000
   b) 7,000,000
   c) 8,000,000
   d) 6,000,000
4. Divide 12,000,000 by 3. The result is ______.
   a) 2,000,000
   b) 3,000,000
   c) 4,000,000
   d) 5,000,000
5. Subtract 3,000,000 from 10,000,000. The answer is ______.
   a) 7,000,000
   b) 5,000,000
   c) 8,000,000
   d) 9,000,000
6. Multiply 6,000,000 by 4. The result is ______.
   a) 24,000,000
   b) 20,000,000
   c) 25,000,000
   d) 30,000,000
7. Divide 100,000,000 by 1,000. The result is ______.
   a) 1,000,000
   b) 100,000
   c) 10,000
   d) 1,000
8. If you subtract 500,000 from 2,000,000, you get ______.
   a) 1,500,000
   b) 2,500,000
   c) 1,000,000
   d) 500,000
9. Add 7,890,000 to 3,210,000. The sum is ______.
   a) 10,000,000
   b) 11,100,000
   c) 12,100,000
   d) 11,000,000
10. Multiply 1,000,000 by 12. The result is ______.
    a) 11,000,000
    b) 12,000,000
    c) 13,000,000
    d) 14,000,000
11. Divide 4,500,000 by 5. The result is ______.
    a) 900,000
    b) 1,000,000
    c) 1,500,000
    d) 850,000
12. Subtract 2,500,000 from 6,000,000. The answer is ______.
    a) 2,500,000
    b) 4,000,000
    c) 3,500,000
    d) 3,000,000
13. Multiply 3,000,000 by 10. The result is ______.
    a) 30,000,000
    b) 25,000,000
    c) 20,000,000
    d) 15,000,000
14. Divide 9,000,000 by 3. The result is ______.
    a) 3,000,000
    b) 4,000,000
    c) 2,000,000
    d) 1,000,000
15. Add 2,340,000 to 1,450,000. The sum is ______.
    a) 4,000,000
    b) 3,500,000
    c) 3,790,000
    d) 3,790,000

1. What is quantitative reasoning?
   Quantitative reasoning involves using math to solve problems logically.
2. What are large numbers in mathematics?
   Large numbers are numbers in millions, billions, or more.
3. How do I add large numbers?
   Align the numbers by place value and add them starting from the right.
4. Can we use calculators to solve large numbers?
   Yes, calculators can help solve large numbers more quickly.
5. What is the population problem involving large numbers?
   It is solving math problems related to population figures using large numbers.
6. How do I multiply large numbers?
   Multiply the digits and then count the zeros.
7. What is the easiest way to subtract large numbers?
   Align the numbers by place value and subtract each column.
8. Why is place value important in large numbers?
   Place value helps us understand the position of digits in large numbers.
9. Can I divide large numbers by smaller numbers?
   Yes, large numbers can be divided by smaller numbers to get a smaller quotient.
10. What is the best method to solve quantitative aptitude problems?
    Understanding the question, using arithmetic, and checking the result are key methods.
11. How do you solve problems involving large numbers in real life?
    Apply basic arithmetic operations and use logic to arrive at the solution.
12. What are real-life examples of large numbers?
    Examples include population figures, national budgets, or company profits.
13. What operations are used with large numbers?
    Addition, subtraction, multiplication, and division.
14. What happens if I make a mistake when adding large numbers?
    The answer will be incorrect, so always double-check your calculations.
15. Can I solve large number problems without a calculator?
    Yes, though it might take more time. Practice helps you solve large number problems faster.

Presentation:

Step 1: The teacher revises the previous lesson on large numbers and their place values.
Step 2: The teacher explains how to solve problems using large numbers in addition, subtraction, multiplication, and division.
Step 3: The teacher gives real-life examples and allows students to solve similar problems in class.

Teacher’s Activities:

• Demonstrates solving quantitative reasoning problems with large numbers.
• Provides examples of how large numbers are used in everyday situations.
• Engages students in solving problems individually and in groups.

Learners’ Activities:

• Participate in problem-solving activities.
• Use arithmetic operations to solve problems with large numbers.
• Work in pairs to check their answers.

Assessment:

Solve the following problems:

1. Add 5,000,000 to 3,000,000.
2. Subtract 1,500,000 from 7,000,000.
3. Multiply 2,000,000 by 4.
4. Divide 9,000,000 by 3.
5. Solve this word problem: If a factory produces 3,000,000 boxes of products per month, how many boxes will it produce in a year?

Evaluation Questions:

1. What is the result of adding 4,000,000 and 6,000,000?
2. How do you subtract large numbers accurately?
3. What is 10,000,000 divided by 2?
4. How can you solve problems involving large numbers in real life?
5. Multiply 7,000,000 by 3.

Conclusion:

The teacher goes around to mark students’ work, corrects errors, and provides additional explanations where necessary.