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Lesson 1 ~25 min Unit 1 · Number +85 XP

Place Value and Whole Numbers

Read, write and compare whole numbers up to millions. Understand how each digit's position determines its value.

Today's hook: Imagine you have $4,560,231 in your bank account. Every digit matters — the 4 means millions, the 5 means hundred-thousands. Get one digit wrong and you could be off by a fortune!
0/5QUESTS
Think First
warm-up

Before you read on — quickly: Which number is larger: 4,560,231 or 4,506,321? How do you know? Try it, then check your reasoning as you go.

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

Every digit in a number has a value based on its position. This is called place value. The place value system uses periods of three digits (hundreds, thousands, millions) separated by commas.

In the number 4,560,231, each digit's position tells us its worth. The 4 is in the millions place, so it represents 4,000,000. The 5 is in the hundred-thousands place, so it represents 500,000. Understanding place value is the foundation for all number work.

4,560,231 4 560 231 MILLIONS THOUSANDS UNITS 4,000,000 + 560,000 + 231 Each period = 3 digits Commas separate periods
Periods: Millions | Thousands | Units
Read each period
Read each 3-digit group as a number, then say the period name.
Zeros are placeholders
They hold the position so other digits keep their value.
Start from the left
Always read from the largest place value first.
2
What You'll Master
objectives

Know

  • The value of each digit in numbers up to millions
  • How commas separate periods of three digits
  • The words for each place value position

Understand

  • How place value determines a digit's worth
  • Why zero is essential as a placeholder
  • Why comparing from the left is always correct

Can Do

  • Read and write large whole numbers in words and digits
  • Compare two large numbers using place value
  • Identify the value of any digit in a number
3
Words You Need
vocabulary
Place valueThe value of a digit based on its position in a number.
DigitAny of the symbols 0–9 used to write numbers.
PeriodA group of three digits in a large number, separated by commas.
MillionsThe period to the left of the first comma (1,000,000).
Greater than (>)The symbol showing one number is larger than another.
Less than (<)The symbol showing one number is smaller than another.
4
Spot the Trap
heads-up

Wrong: "The more digits a number has, the larger it is." 100 has more digits than 99, but 999 > 100.

Right: Start comparing from the highest place value (leftmost digit). The first different digit decides.

Wrong: Writing "five thousand and sixty-two" as 5,602 instead of 5,062.

Right: Use a place value table or say the number out loud. 5,062 = 5 thousands + 0 hundreds + 6 tens + 2 ones.

5
Reading Large Numbers
+5 XP

To read a large number, split it into periods (groups of three digits from the right), then read each period as a 3-digit number followed by the period name.

The number 4,560,231 splits into three periods: 4 (millions), 560 (thousands), and 231 (units). Read it as: "Four million, five hundred and sixty thousand, two hundred and thirty-one."

4,560,231 4 560 231 million thousand (units) "Four million, five hundred and sixty thousand, two hundred and thirty-one" Split → Read → Name
4 | 560 | 231 → "Four million..."
Split into periods
Start from the right, group digits in threes.
Say it out loud
Reading aloud catches errors your eyes miss.
Use commas as guides
Each comma signals a new period name.
6
Writing Numbers in Words
+5 XP

To write a number in words, work period by period from left to right. Write each period as a 3-digit number in words, then add the period name.

Write 7,030,052 in words. Split: 7 | 030 | 052. Read each: "Seven" + "million" + "thirty" + "thousand" + "and" + "fifty-two". Result: "Seven million, thirty thousand and fifty-two." Note the and before the last part.

7,030,052 Split into periods 7 030 052 "Seven million, thirty thousand and fifty-two" 030 → "thirty" NOT "thirty zero"
7,030,052 = "Seven million, thirty thousand and fifty-two"
Watch the zeros
030 is "thirty" not "thirty zero". Skip leading zeros.
Use "and"
The word "and" goes before the tens/units part.
Period names
Million, thousand, (units). These are your anchors.
7
Comparing Numbers
+5 XP

To compare two numbers, line up the digits and compare from the left. The first place where the digits differ tells you which number is larger. The > symbol means "greater than" and < means "less than". The open end always faces the larger number.

Compare 5,678,901 and 5,687,109. Line up: millions match (5=5), hundred-thousands match (6=6), but ten-thousands differ: 7 < 8. So 5,687,109 is larger. The alligator eats the bigger number: 5,678,901 < 5,687,109.

5,678,901 vs 5,687,109 5 6 7 8 9 5 6 8 7 1 DIFFER! 7 < 8 at the ten-thousands So 5,687,109 is LARGER 5,678,901 < 5,687,109
First different digit decides
Line up by place
Use a table if it helps — digits must be in matching columns.
Left has most power
Millions beat thousands, thousands beat hundreds.
The alligator rule
> and < open toward the bigger number.
Watch Me Solve It · Write in words
+15 XP per step
Q1
PROBLEM
Write 12,045,600 in words.
  1. 1
    Split into periods
    12 | 045 | 600
    Start from the left. Three periods: millions, thousands, units.
  2. 2
    Read each period
    12 → "twelve million", 045 → "forty-five thousand", 600 → "six hundred"
  3. 3
    Combine with commas and "and"
    "Twelve million, forty-five thousand and six hundred"
    No "and" needed before the thousands period — only before the final units part.
AnswerTwelve million, forty-five thousand and six hundred
Watch Me Solve It · Find the digit value
+15 XP per step
Q2
PROBLEM
What is the value of the digit 8 in 28,934,105?
  1. 1
    Identify the position of the digit
    28,934,105 — the 8 is in the millions period
    Split: 28 | 934 | 105. The 8 sits in the millions group.
  2. 2
    Determine the place value
    The 8 is in the millions column
  3. 3
    Calculate the value
    8 × 1,000,000 = 8,000,000
    The digit 8 in the millions place represents eight million.
Answer8,000,000 (eight million)
Watch Me Solve It · Compare two numbers
+15 XP per step
Q3
PROBLEM
Compare 9,876,543 and 9,865,743. Which is larger? Use >, <, or =.
  1. 1
    Line up the digits by place value
    9,876,543
    9,865,743
    Both have 7 digits. Start comparing from the left.
  2. 2
    Compare digit by digit from the left
    Millions: 9 = 9 ✓
    Hundred-thousands: 8 = 8 ✓
    Ten-thousands: 7 > 6 ← this decides!
  3. 3
    Write the comparison
    9,876,543 > 9,865,743
    The first different digit (7 vs 6) at the ten-thousands place tells us the answer.
Answer9,876,543 > 9,865,743
9
Common Pitfalls
heads-up
Confusing place value with face value
In 5,000, the digit 5 has a place value of 5,000 (five thousand), not just 5. The face value is always just the digit itself. The place value depends on position.
Fix: Ask "Where does this digit sit?" not "What number is this?"
Forgetting zero as a placeholder
In 3,005, there are zero hundreds and zero tens. The zeros hold those positions so the 3 stays in the thousands place and the 5 stays in the ones place.
Fix: Without the zeros, 3,005 would become 35 — a completely different number!
Comparing from the right instead of the left
Students sometimes start from the ones column. But 9,876,543 and 9,865,743 both end in 543 and 743 — the ones place would suggest the second is larger, which is wrong!
Fix: Always start from the left (largest place value). The leftmost different digit is the decider.
Copy Into Your Books

Place Value Table

  • Millions → Hundred-Thousands → Ten-Thousands → Thousands → Hundreds → Tens → Ones
  • Each position is 10× the one to its right
  • Commas separate every 3 digits (periods)

Reading Numbers

  • Split into periods (groups of 3)
  • Read each period as a 3-digit number
  • Add the period name after each
  • Use "and" before the final units part

Writing in Words

  • Write periods as words: million, thousand
  • Hyphenate numbers 21–99
  • Skip leading zeros (030 = thirty)
  • Check by reading aloud

Comparing Numbers

  • Line up digits by place value
  • Compare from left to right
  • First different digit decides
  • > opens toward the larger number

How are you completing this lesson?

D
Brain Trainer · Place Value
4 problems

Four drill problems to sharpen your place-value skills. Work each, then reveal the answer.

  1. 1 Write 7,005,020 in words.

    Split: 7 | 005 | 020. Read: "Seven million, five thousand and twenty."Seven million, five thousand and twenty
  2. 2 What is the value of 6 in 16,284,573?

    The 6 is in the millions place (16 | 284 | 573). Value = 6 × 1,000,000.6,000,000 (six million)
  3. 3 Arrange from smallest to largest: 1,111,111   1,101,111   1,110,111

    Compare from left: all start 1,1. At hundred-thousands: 0 < 1. Then 1,101,111 vs 1,110,111: ten-thousands 0 < 1.1,101,111 < 1,110,111 < 1,111,111
  4. 4 Write "three million and twelve" as a number.

    3 million + 0 thousand + 12. Need zeros as placeholders for hundred-thousands, ten-thousands, thousands, hundreds, and tens.3,000,012
Complete in your workbook.
1
What is the value of 9 in 29,384?
+10 XP
2
Which is the largest number?
+10 XP
+10 XP, +5 coins" data-feedback-wrong="Watch the zeros. 080 = "eighty" not "eight hundred". The zero hundreds means we skip that word.">
3
Write 5,080,060 in words.
+10 XP
4
Which number is "three million, four thousand and five"?
+10 XP
5
What is 10,000 less than 5,678,901?
+10 XP
Show Your Working
9 marks total
Apply Medium 3 MARKS

Q6. Write 20,307,080 in words. Explain your process step by step.

Answer in your workbook.
Understand Easy 2 MARKS

Q7. Find the value of the underlined digit: 372,908. Explain how you know.

Answer in your workbook.
Reason Hard 4 MARKS

Q8. Find a number between 4,500,000 and 4,600,000 where the digit 7 is worth 70,000. Give two different examples and explain your reasoning.

Answer in your workbook.
Comprehensive Answers

Quick Check

1. A — 9,000. The 9 is in the thousands place.

2. A — 4,210,000. At hundred-thousands: 2 > 1 > 0.

3. B — "Five million, eighty thousand and sixty." 080 = eighty.

4. C — 3,004,005. Three million + four thousand + five.

5. A — 5,668,901. Subtract 10,000: the 78 becomes 68.

Show Your Working Model Answers

Q6 (3 marks): Split into periods: 20 | 307 | 080 [1]. Read each: "Twenty million" + "three hundred and seven thousand" + "and eighty" [1]. Answer: "Twenty million, three hundred and seven thousand and eighty" [1].

Q7 (2 marks): The 7 is in the ten-thousands place [1]. Its value is 7 × 10,000 = 70,000 (seventy thousand) [1].

Q8 (4 marks): The digit 7 must be in the ten-thousands place for it to be worth 70,000. The number must be between 4,500,000 and 4,600,000, so it starts with 4,57_. Two examples: 4,570,000 and 4,571,234 [2 for correct examples]. Any number 4,570,000 ≤ n ≤ 4,579,999 works because the 7 is in the ten-thousands place [2 for explanation].

Stretch Challenge · +25 XP, +10 coins

The Digit Puzzle

Using the digits 3, 0, 5, 7, 2, 1, 8 each exactly once, make the largest possible number and the smallest possible number. What is the difference between them?

Reveal solution

Largest: arrange digits from largest to left: 8,753,210. Smallest: smallest non-zero digit first, then the rest: 1,023,578. Difference: 8,753,210 − 1,023,578 = 7,729,632.

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Quick Review

Periods

Millions | Thousands | Units

Read by period

Read each 3-digit group, add period name

Write in words

Use periods, skip leading zeros, use "and"

Compare left to right

First different digit decides

Zero matters

Placeholder — keeps other digits in position

Commas

Separate every 3 digits from the right

Interactive: Square Root Estimator

Develop your number sense by estimating square roots. A square has a certain area — can you guess its side length?

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