Whole Numbers Basic 6 Mathematics Lesson Note

a. Reading and Writing Numbers in Millions up to Billions

Understanding Large Numbers

When we count beyond thousands, we move to millions and billions. Each group of three digits represents a new period.

Number Periods:

• Units: Ones, Tens, Hundreds
• Thousands: Thousands, Ten thousands, Hundred thousands
• Millions: Millions, Ten millions, Hundred millions
• Billions: Billions, Ten billions, Hundred billions

Place Value Chart:

Billions | Millions | Thousands | Units

H T U   | H T U   | H T U    | H T U

Examples of Reading Numbers:

1. 5,234,567

• Reading: Five million, two hundred and thirty-four thousand, five hundred and sixty-seven

2. 12,045,300

• Reading: Twelve million, forty-five thousand, three hundred

3. 3,000,000,000

• Reading: Three billion

4. 25,600,000,000

• Reading: Twenty-five billion, six hundred million

Writing Numbers in Figures:

Examples:

• Seven million, five hundred thousand = 7,500,000
• Forty-three billion, two hundred million = 43,200,000,000
• Six million, twenty-five thousand, four hundred = 6,025,400

Exercise A – Reading Numbers

Write these numbers in words:

1. 8,456,789 = ________________________________
2. 15,000,000 = ________________________________
3. 2,300,500,000 = ________________________________
4. 456,000,000 = ________________________________
5. 7,050,200 = ________________________________

Exercise B – Writing Numbers in Figures

Write these numbers in figures:

1. Nine million, four hundred thousand = ________________
2. Twelve billion, three hundred million = ________________
3. Five million, sixty-seven thousand, eight hundred = ________________
4. Twenty-eight billion = ________________
5. Four million, five hundred thousand, twenty = ________________

b. Skip Counting in Thousands, Millions and Billions

What is Skip Counting?

Skip counting means counting by a certain number each time instead of counting by ones.

Skip Counting by Thousands:

Examples:

• Count by 1,000: 1,000, 2,000, 3,000, 4,000, 5,000…
• Count by 5,000: 5,000, 10,000, 15,000, 20,000, 25,000…
• Count by 10,000: 10,000, 20,000, 30,000, 40,000, 50,000…

Skip Counting by Millions:

Examples:

• Count by 1 million: 1,000,000, 2,000,000, 3,000,000…
• Count by 5 million: 5,000,000, 10,000,000, 15,000,000…
• Count by 10 million: 10,000,000, 20,000,000, 30,000,000…

Skip Counting by Billions:

Examples:

• Count by 1 billion: 1,000,000,000, 2,000,000,000, 3,000,000,000…
• Count by 2 billion: 2,000,000,000, 4,000,000,000, 6,000,000,000…

Exercise C – Skip Counting

Complete these skip counting patterns:

1. By 2,000: 2,000, 4,000, 6,000, _____, _____, _____
2. By 50,000: 50,000, 100,000, 150,000, _____, _____, _____
3. By 3 million: 3,000,000, 6,000,000, 9,000,000, _____, _____, _____
4. By 5 million: 5,000,000, 10,000,000, _____, _____, 25,000,000
5. By 10 billion: 10,000,000,000, _____, 30,000,000,000, _____

Exercise D – Find the Pattern

Identify the skip counting pattern and fill in the missing numbers:

1. 4,000, 8,000, 12,000, _____, 20,000 Pattern: Skip by _____
2. 7,000,000, 14,000,000, 21,000,000, _____ Pattern: Skip by _____
3. 15,000,000,000, 30,000,000,000, _____, 60,000,000,000 Pattern: Skip by _____

c. Place Value and Value of Whole Numbers

Understanding Place Value

The place value of a digit depends on its position in the number. The value is what the digit is actually worth in that position.

Place Value Chart Example: 5,234,567,890

Breaking it down:

• 5 is in the billions place = 5,000,000,000
• 2 is in the hundred millions place = 200,000,000
• 3 is in the ten millions place = 30,000,000
• 4 is in the millions place = 4,000,000
• 5 is in the hundred thousands place = 500,000
• 6 is in the ten thousands place = 60,000
• 7 is in the thousands place = 7,000
• 8 is in the hundreds place = 800
• 9 is in the tens place = 90
• 0 is in the units place = 0

Standard Form vs Expanded Form:

Standard Form: 45,678,230 

Expanded Form: 40,000,000 + 5,000,000 + 600,000 + 70,000 + 8,000 + 200 + 30

Exercise E – Place Value

For the number 6,789,345,120, find:

1. The digit in the billions place = _____
2. The digit in the ten millions place = _____
3. The digit in the hundred thousands place = _____
4. The place value of 9 = _____
5. The value of 4 = _____

Exercise F – Expanded Form

Write these numbers in expanded form:

1. 234,567,000 = ________________________________
2. 8,905,400 = ________________________________
3. 15,000,000,000 = ________________________________

Exercise G – Standard Form

Write these expanded forms in standard form:

1. 7,000,000 + 500,000 + 60,000 + 3,000 + 400 + 20 + 5 = ________________
2. 20,000,000,000 + 8,000,000,000 + 300,000,000 = ________________
3. 4,000,000 + 80,000 + 7,000 + 600 = ________________

d. Quantitative Reasoning

1. Number Patterns: Finding the next number in a sequence.

Example: 2, 6, 18, 54, _____ 

Solution: Each number is multiplied by 3, so 54 × 3 = 162

2. Comparing Numbers: Using symbols: > (greater than), < (less than), = (equal to)

Example: Compare 45,000,000 and 4,500,000 

Solution: 45,000,000 > 4,500,000

3. Word Problems: Solving real-life situations using mathematical operations.
4. Logical Reasoning: Using mathematics to make decisions and solve problems.

Exercise H – Number Patterns

Find the next two numbers in each pattern:

1. 5, 10, 20, 40, _____, _____
2. 1,000, 3,000, 9,000, 27,000, _____, _____
3. 100, 200, 400, 800, _____, _____
4. 2,000,000, 4,000,000, 8,000,000, _____, _____

Exercise I – Comparing Numbers

Use >, < or = to compare these numbers:

1. 234,000,000 _____ 243,000,000
2. 5,600,000 _____ 5,060,000
3. 12,000,000,000 _____ 1,200,000,000
4. 789,000 _____ 789,000
5. 45,300,000 _____ 45,030,000

Exercise J – Word Problems

Solve these quantitative reasoning problems:

1. Population Problem: Lagos State has a population of 15,000,000 people. Kano State has 13,500,000 people. How many more people live in Lagos than in Kano? Answer: ________________________________
2. Money Problem: A bank has ₦5,000,000,000 in deposits. If they lend out ₦3,250,000,000, how much money remains in the bank? Answer: ________________________________
3. Distance Problem: The distance from Lagos to Abuja is 756,000 meters. Express this distance in words. Answer: ________________________________

Exercise K – Logical Reasoning

Answer these reasoning questions:

1. If you skip count by 50,000 starting from 100,000, what will be the 6th number in the sequence? Answer: ________________________________
2. A number has 7 in the millions place, 3 in the hundred thousands place, and 0 in all other places. What is the number? Answer: ________________________________
3. Which is greater: 15 million or 1.5 billion? By how much? Answer: ________________________________

Exercise L – Real-World Applications

Use quantitative reasoning to solve:

1. School Enrollment: A school district has 125,000 students. If 15,000 new students enroll next year, what will be the total enrollment?
2. Budget Planning: Nigeria’s annual budget is ₦17,000,000,000,000 (17 trillion naira). Write this number in words.
3. Technology: A computer can process 2,500,000 calculations per second. How many calculations can it process in 4 seconds?

Answer Key

Exercise A:

1. Eight million, four hundred and fifty-six thousand, seven hundred and eighty-nine
2. Fifteen million
3. Two billion, three hundred million, five hundred thousand
4. Four hundred and fifty-six million
5. Seven million, fifty thousand, two hundred

Exercise B:

1. 9,400,000
2. 12,300,000,000
3. 5,067,800
4. 28,000,000,000
5. 4,500,020

Exercise C:

1. 8,000, 10,000, 12,000
2. 200,000, 250,000, 300,000
3. 12,000,000, 15,000,000, 18,000,000
4. 15,000,000, 20,000,000
5. 20,000,000,000, 40,000,000,000

Exercise D:

1. 16,000; Pattern: Skip by 4,000
2. 28,000,000; Pattern: Skip by 7,000,000
3. 45,000,000,000; Pattern: Skip by 15,000,000,000

Exercise E:

1. 6
2. 8
3. 3
4. Ten millions place
5. 40,000

Exercise H:

1. 80, 160 (multiply by 2)
2. 81,000, 243,000 (multiply by 3)
3. 1,600, 3,200 (multiply by 2)
4. 16,000,000, 32,000,000 (multiply by 2)

Exercise I:

1. <
2. =

Exercise J:

1. 1,500,000 people
2. ₦1,750,000,000
3. Seven hundred and fifty-six thousand meters