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Lesson 1 ~30 min Unit 3 · Number +85 XP

Place Value and Large Numbers

Lesson 1 ΓÇö Place Value and Large Numbers

Today's hook: Before we dive in, try this challenge. Write the largest number you can think of using only three digits. How do you know it's the biggest possible?
0/5QUESTS
Think First
warm-up

Before we dive in, try this challenge. Write the largest number you can think of using only three digits. How do you know it's the biggest possible?

Warm-up Puzzle: If you write the digits 7, 2, and 9 in some order, what is the largest number you can make? What is the smallest? What makes one number larger than another?

Record your answer in your workbook.
1
The Big Idea
+5 XP

Every digit in a number has a place value based on its position. Understanding place value lets us read, write, and compare numbers of any size ΓÇö from single digits to millions and beyond.

Our number system is base-10 (decimal), meaning each place is 10 times the place to its right.

Australia's population is approximately 26 million. Place value helps us make sense of numbers this large.

Place Value Chart 5 2 7 4 1 8 Ones Tens Hundreds Thousands Ten Thousands Hundred Thousands $\\times 1$ $\\times 10$ $\\times 100$ $\\times 1000$ $\\times 10\\,000$ $\\times 100\\,000$ 527,418
Key Insight
Our number system is base-10 (decimal), meaning each place is 10 times the place to its right.
Real World
Australia's population is approximately 26 million. Place value helps us make sense of numbers this large.
Remember
Keep practising these skills!
What to write in your book
  • The big idea and key formula for this lesson.
  • One worked example to copy into your book.
2
What You'll Master
objectives
Know

Key facts

  • The place value of each digit in whole numbers up to millions
  • How to read and write large numbers in words and digits
  • The pattern of powers of 10 in our number system
Understand

Deep concepts

  • That each place value position is 10 times the position to its right
  • Why zero is essential as a placeholder in our number system
  • How to compare and order numbers using place value
Can do

Skills

  • Read and write numbers up to millions
  • Partition numbers into their place value components
  • Compare and order large numbers
  • Solve problems involving place value reasoning
3
Words You Need
vocabulary
Place ValueThe value of a digit depending on its position in a number. For example, in 347, the 4 has a place value of 40 (tens).
DigitAny of the symbols 0, 1, 2, 3, 4, 5, 6, 7, 8, or 9 used to write numbers.
PeriodA group of three digits in a large number, separated by commas or spaces. Example: millions, thousands, ones.
PartitioningBreaking a number into its place value parts. For example, $4,728 = 4000 + 700 + 20 + 8$.
Base-10 SystemOur number system where each place value is 10 times larger than the place to its right.
Placeholder ZeroA zero that holds a place to show there is no value in that position. In 4,052, the zero shows there are no hundreds.
4
Spot the Trap
heads-up
Γ£ù
❌ Confusing "and" in number words
Γ£ô
Students often write "five thousand and two hundred" instead of "five thousand, two hundred." Use "and" only between hundreds and tens/ones, not between periods.
Γ£ù
❌ Ignoring placeholder zeros
Γ£ô
In 40,506, both zeros are essential. Removing either changes the number completely. Always check every position when reading or writing numbers.
Γ£ù
❌ Comparing from the wrong end
Γ£ô
When comparing numbers, always start from the leftmost (highest place value) digit, not the rightmost. 89,999 is still less than 90,000 because 8 < 9 in the ten-thousands place.
5
Understanding Place Value
+5 XP

In our number system, the position of each digit determines its value. This is called place value.

Consider the number 6,347,521:

Millions

The digit 6 is in the millions place, so it represents $6 \\times 1,000,000 = 6,000,000$

Hundred Thousands

The digit 3 represents $3 \\times 100,000 = 300,000$

Ten Thousands

The digit 4 represents $4 \\times 10,000 = 40,000$

Thousands

The digit 7 represents $7 \\times 1,000 = 7,000$

Hundreds

The digit 5 represents $5 \\times 100 = 500$

Tens

The digit 2 represents $2 \\times 10 = 20$

Ones

The digit 1 represents $1 \\times 1 = 1$

What to write in your book
  • Key points from the "Understanding Place Value" section.
  • Any formulas or rules introduced here.
Quick check ΓÇö which one is right?
6
Reading and Writing Large Numbers
+5 XP

Large numbers are grouped into periods of three digits, starting from the right. We use spaces or commas to separate periods.

📖 Worked Example: Writing Numbers in Words

Write 4,508,732 in words.

Step 1: Break the number into periods: 4 | 508 | 732

This gives us: 4 millions, 508 thousands, 732 ones.

Step 2: Read the millions period: "four million"

Step 3: Read the thousands period: "five hundred and eight thousand"

Step 4: Read the ones period: "seven hundred and thirty-two"

Step 5: Combine: "Four million, five hundred and eight thousand, seven hundred and thirty-two"

Remember

We use "and" between the hundreds and the tens/ones within each period. We never say "and" where the comma or space is.

What to write in your book
  • Key points from the "Reading and Writing Large Numbers" section.
  • Any formulas or rules introduced here.
True or false?
This statement is true based on what you just learned.
7
Partitioning Numbers
+5 XP

Partitioning means breaking a number into the value of each digit. This helps us understand what a number is really made of.

📖 Worked Example: Partitioning

Partition the number 83,547 into its place value parts.

Step 1: Identify each digit and its place value.

$8$ is in the ten-thousands place

$3$ is in the thousands place

$5$ is in the hundreds place

$4$ is in the tens place

$7$ is in the ones place

Step 2: Write each digit multiplied by its place value.

$83{,}547 = (8 \\times 10{,}000) + (3 \\times 1{,}000) + (5 \\times 100) + (4 \\times 10) + (7 \\times 1)$

Step 3: Simplify each part.

$83{,}547 = 80{,}000 + 3{,}000 + 500 + 40 + 7$

What to write in your book
  • Key points from the "Partitioning Numbers" section.
  • Any formulas or rules introduced here.
Quick check ΓÇö which one is right?
8
Comparing Numbers
+5 XP

To compare two numbers, start from the highest place value and work to the right until you find a difference.

📖 Worked Example: Comparing Numbers

Which is larger: 45,892 or 45,972?

Step 1: Line up the numbers by place value and compare from the left.

Ten-thousands: Both have 4 Γ£ô

Thousands: Both have 5 Γ£ô

Step 2: Move to the hundreds place.

$45{,}892$ has 8 hundreds

$45{,}972$ has 9 hundreds

Step 3: Since $9 > 8$, we can conclude:

$45{,}972 > 45{,}892$

Symbol

$>$ means "greater than", $<$ means "less than", $=$ means "equal to"

What to write in your book
  • Key points from the "Comparing Numbers" section.
  • Any formulas or rules introduced here.
9
The Power of Zero
+5 XP

Zero is not "nothing" ΓÇö it is a placeholder that tells us a position is empty. Without zero, we could not tell 4,052 from 452.

The Importance of Zero 4,052 means 4 thousands + 0 hundreds + 5 tens + 2 ones 452 means 4 hundreds + 5 tens + 2 ones The zero changes 452 into four thousand and fifty-two!
Did You Know?

The concept of zero as a placeholder was developed in ancient India around the 5th century. It revolutionised mathematics!

What to write in your book
  • Key points from the "The Power of Zero" section.
  • Any formulas or rules introduced here.
10
Ordering Numbers
+5 XP

To place numbers in ascending order (smallest to largest) or descending order (largest to smallest), compare them digit by digit from the left.

📖 Worked Example: Ordering Numbers

Place these numbers in ascending order: 8,412, 8,241, 8,421, 8,124

Step 1: All numbers have 8 thousands, so compare the hundreds digit.

$8{,}412$ → 4 hundreds

$8{,}241$ → 2 hundreds

$8{,}421$ → 4 hundreds

$8{,}124$ → 1 hundred

Step 2: The smallest hundreds digit is 1, then 2, then 4 (appears twice).

So far: $8{,}124$ is smallest, then $8{,}241$

Step 3: For the two numbers with 4 hundreds, compare the tens digit.

$8{,}412$ has 1 ten

$8{,}421$ has 2 tens

So $8{,}412 < 8{,}421$

Answer: $8{,}124 < 8{,}241 < 8{,}412 < 8{,}421$

What to write in your book
  • Key points from the "Ordering Numbers" section.
  • Any formulas or rules introduced here.
📖 Worked Example: Writing Numbers in Words
+15 XP per step

Write 4,508,732 in words.

Step 1: Break the number into periods: 4 | 508 | 732

This gives us: 4 millions, 508 thousands, 732 ones.

📖 Worked Example: Partitioning
+15 XP per step

Partition the number 83,547 into its place value parts.

Step 1: Identify each digit and its place value.

$8$ is in the ten-thousands place

$3$ is in the thousands place

$5$ is in the hundreds place

$4$ is in the tens place

$7$ is in the ones place

📖 Worked Example: Comparing Numbers
+15 XP per step

Which is larger: 45,892 or 45,972?

Step 1: Line up the numbers by place value and compare from the left.

Ten-thousands: Both have 4 Γ£ô

Thousands: Both have 5 Γ£ô

📖 Worked Example: Ordering Numbers
+15 XP per step

Place these numbers in ascending order: 8,412, 8,241, 8,421, 8,124

Step 1: All numbers have 8 thousands, so compare the hundreds digit.

$8{,}412$ → 4 hundreds

$8{,}241$ → 2 hundreds

$8{,}421$ → 4 hundreds

$8{,}124$ → 1 hundred

ΓÜí
Brain Trainer
+5 XP

Quick-fire drills ΓÇö test your recall!

1
1. Value of 6 in 45,623?
600
2
2. 8,000 + 300 + 50 + 7 = ?
8,357
3
3. Write 20,405 in words
Twenty thousand, four hundred and five
4
4. Which is larger: 78,291 or 78,921?
78,921
5
5. How many thousands in 45,000?
45
6
6. Partition 93,847
90,000 + 3,000 + 800 + 40 + 7
7
7. 700,000 + 5,000 + 30 + 9 = ?
705,039
8
8. Digit in the ten-thousands place of 847,321?
4
9
9. Write "six hundred twelve thousand, forty" in digits
612,040
10
10. Place 52,318; 52,813; 52,138 in ascending order
52,138; 52,318; 52,813

Quick Check · 5 questions

1
What is the value of the digit 7 in the number 3,742,856?
+10 XP
2
Which number is the largest?
+10 XP
3
How is the number 5,020,400 written in words?
+10 XP
4
What is 7,000,000 + 50,000 + 300 + 8 written as a single number?
+10 XP
5
Which statement is true?
+10 XP
Short Answer 1
+10 XP

Write the number 12,045,607 in words.

+3 XPAnswered? Claim your points
Show solution

Solution: Twelve million, forty-five thousand, six hundred and seven.

Break into periods: 12 | 045 | 607. Twelve million, forty-five thousand, six hundred and seven.

Short Answer 2
+10 XP

Partition the number 945,302 into its place value parts using expanded notation.

+3 XPAnswered? Claim your points
Show solution

Solution:

$945{,}302 = (9 \\times 100{,}000) + (4 \\times 10{,}000) + (5 \\times 1{,}000) + (3 \\times 100) + (0 \\times 10) + (2 \\times 1)$

$= 900{,}000 + 40{,}000 + 5{,}000 + 300 + 0 + 2$

Short Answer 3
+10 XP

Arrange these numbers in descending order (largest first): 723,541, 732,451, 723,451, 732,541

+3 XPAnswered? Claim your points
Show solution

Solution: $732{,}541 > 732{,}451 > 723{,}541 > 723{,}451$

All have 7 hundred thousands. Compare ten thousands: 3 > 2, so the 732,___ numbers come first. Then compare thousands within each group.

🚀
Stretch Challenge
+15 XP

Using each of the digits 1, 2, 3, 4, 5, and 6 exactly once, what is the largest number you can make? What is the smallest? What is the difference between them?

Solution: Largest = 654,321. Smallest = 123,456. Difference = 654,321 − 123,456 = 530,865.

I am a 7-digit number. My millions digit is 4. My hundred-thousands digit is half my millions digit. My ten-thousands digit is the sum of my first two digits. My thousands digit is 0. My hundreds digit equals my millions digit. My tens digit is 1. My ones digit is 3 more than my tens digit. What number am I?

Solution: 4 | 2 | 6 | 0 | 4 | 1 | 4 = 4,260,414

A palindromic number reads the same forwards and backwards (e.g., 12,321). How many 5-digit palindromic numbers exist? Explain your reasoning.

Solution: A 5-digit palindrome has the form ABCBA. A can be 1-9 (9 choices), B can be 0-9 (10 choices), C can be 0-9 (10 choices). Total = $9 \\times 10 \\times 10 = 900$ palindromic numbers.

Daily Challenge: Teach the concept to a friend or family member.
+20 XP
← →
Watch Me Solve It · Partitioning Numbers
+15 XP per step
Q2
PROBLEM
Partition 83,547 into its place value parts.
  1. 1
    Identify each digit
    8 → ten-thousands; 3 → thousands; 5 → hundreds; 4 → tens; 7 → ones
  2. 2
    Write expanded notation
    83,547 = (8 × 10,000) + (3 × 1,000) + (5 × 100) + (4 × 10) + (7 × 1)
  3. 3
    Simplify
    83,547 = 80,000 + 3,000 + 500 + 40 + 7
Answer80,000 + 3,000 + 500 + 40 + 7
What to write in your book
True or false?
In the number 4,052, the zero is just a placeholder and removing it would not change the value.
Watch Me Solve It · Comparing Numbers
+15 XP per step
Q3
PROBLEM
Which is larger: 45,892 or 45,972?
  1. 1
    Compare from the left
    Ten-thousands: 4 = 4 ✓; Thousands: 5 = 5 ✓
  2. 2
    Move to the hundreds place
    45,892 → 8 hundreds; 45,972 → 9 hundreds
  3. 3
    Decide
    45,972 > 45,892
    Since 9 > 8, the number with 9 hundreds is larger.
Answer45,972 > 45,892
What to write in your book