Learning Objectives: Expanded Form in Mathematics for Grade 1

Master expanded form: tens and ones decomposition, visual representations, and step-by-step solutions through these 5 detailed exercises.

Solution: Exercises 1 to 3
1 Basic tens and ones
Exercise 1
Write the expanded form of: 24
Definition:

Expanded form: Writing a number as the sum of its place values. For 2-digit numbers: Tens + Ones

Method:
  1. Identify the digit in the tens place
  2. Identify the digit in the ones place
  3. Write each digit with its place value
  4. Connect with addition sign
2
4
→
20
+
4
=
24
Step 1: Identify place values

In 24: Tens digit = 2, Ones digit = 4

Step 2: Calculate place values

Tens place: 2 × 10 = 20, Ones place: 4 × 1 = 4

Step 3: Write expanded form

24 = 20 + 4

24 = 20 + 4
Final answer:

24 = 20 + 4

Applied rules:

• Place value: Each digit has a value based on its position

• Tens rule: Tens digit × 10

• Ones rule: Ones digit × 1

• Expanded form: Sum of place values

2 Decomposition with visual aids
Exercise 2
Write the expanded form of: 37
Definition:

Expanded form: Breaking a number into parts showing each digit's value based on position

3
7
→
30
+
7
=
37
Step 1: Identify digits and positions

In 37: Tens digit is 3, Ones digit is 7

Step 2: Calculate each place value

3 tens = 3 × 10 = 30, 7 ones = 7 × 1 = 7

Step 3: Combine with addition

37 = 30 + 7

37 = 30 + 7
Final answer:

37 = 30 + 7

Applied rules:

• Position matters: Leftmost digit is tens, rightmost is ones

• Value calculation: Digit × Place value (10 for tens, 1 for ones)

• Sum formation: Add all calculated values together

3 Multiple examples
Exercise 3
Write the expanded form of: 52
Definition:

Expanded form: Expressing a number as the sum of each digit multiplied by its place value

5
2
→
50
+
2
=
52
Step 1: Analyze the number

52 has two digits: 5 in tens place, 2 in ones place

Step 2: Calculate place values

5 tens = 5 × 10 = 50, 2 ones = 2 × 1 = 2

Step 3: Write the expanded form

52 = 50 + 2

52 = 50 + 2
Final answer:

52 = 50 + 2

Applied rules:

• Digit identification: Recognize tens and ones positions

• Value computation: Multiply each digit by its place value

• Sum representation: Show the number as a sum of its parts

Rules and methods, laws,...
\(AB = A \times 10 + B \times 1\)
Expanded Form Formula
Tens Rule
\(A \times 10\)
Multiply tens digit by 10
Ones Rule
\(B \times 1\)
Multiply ones digit by 1
Expanded Form
\(A \times 10 + B \times 1\)
Sum of place values
Key definitions:

Place value: The value of a digit based on its position in a number

Expanded form: Writing a number as the sum of each digit's place value

Tens place: The second digit from the right (multiplied by 10)

Ones place: The rightmost digit (multiplied by 1)

Complete methodology:
  1. Identify digits: Recognize each digit in the number
  2. Determine positions: Identify tens and ones places
  3. Calculate values: Multiply each digit by its place value
  4. Express as sum: Add the calculated values
  5. Verify: Check that the sum equals the original number
Tip 1: Remember: Tens place is always the second digit from the right.
Tip 2: Think of tens as groups of 10, ones as individual units.
Tip 3: Always check your answer by adding the expanded parts.
Solution: Exercises 4 to 5
4 Advanced decomposition
Exercise 4
Write the expanded form of: 68
Definition:

Expanded form: Breaking down a number to show the value of each digit based on its position

6
8
→
60
+
8
=
68
Step 1: Identify each digit

68 has digits: 6 (tens place) and 8 (ones place)

Step 2: Calculate place values

6 tens = 6 × 10 = 60, 8 ones = 8 × 1 = 8

Step 3: Form the expanded expression

68 = 60 + 8

Step 4: Verify the result

60 + 8 = 68 ✓

68 = 60 + 8
Final answer:

68 = 60 + 8

Applied rules:

• Position identification: Tens digit is leftmost, ones digit is rightmost

• Value multiplication: Tens digit × 10, Ones digit × 1

• Addition principle: Sum of place values equals original number

5 Comprehensive example
Exercise 5
Write the expanded form of: 93
Definition:

Expanded form: Expressing a number as the sum of each digit multiplied by its place value

9
3
→
90
+
3
=
93
Step 1: Recognize the digits

93 has two digits: 9 in tens place and 3 in ones place

Step 2: Compute place values

9 tens = 9 × 10 = 90, 3 ones = 3 × 1 = 3

Step 3: Write the expanded form

93 = 90 + 3

Step 4: Validate the answer

90 + 3 = 93 ✓

93 = 90 + 3
Final answer:

93 = 90 + 3

Applied rules:

• Digit analysis: Identify each digit's position

• Value calculation: Multiply by respective place values

• Sum formation: Combine with addition operation

• Verification: Confirm the sum equals the original number

Key Concepts: Laws, Methods, Rules, Definitions
\(AB = A \times 10 + B \times 1\)
General Expanded Form Formula
Key definitions:

Place value: The value of a digit based on its position in a number

Expanded form: Writing a number as the sum of each digit's place value

Tens place: The second digit from the right, multiplied by 10

Ones place: The rightmost digit, multiplied by 1

Standard form: The regular way we write numbers (e.g., 24)

Word form: Writing numbers using words (e.g., twenty-four)

Complete methodology:
  1. Digit identification: Recognize each digit in the number
  2. Position determination: Identify tens and ones places
  3. Value calculation: Multiply each digit by its place value
  4. Expression formation: Write the sum of calculated values
  5. Verification: Check that the sum equals the original number
Tip 1: Remember: Tens digit × 10, Ones digit × 1
Tip 2: Think of tens as bundles of 10, ones as single items
Tip 3: Always add the expanded parts to verify your answer
Tip 4: Practice with visual aids like base-10 blocks
Common errors: Confusing tens and ones positions, forgetting to multiply by place value, miscounting digits.
Memory aid: "Teens are tens" - the first digit is always tens place in 2-digit numbers.
Essential rules to remember:

• Place value rule: In 2-digit numbers, left digit is tens, right digit is ones

• Multiplication rule: Tens digit × 10, Ones digit × 1

• Addition rule: Sum of expanded parts equals original number

• Verification rule: Always check by adding expanded parts

Visual Guide: Expanded Form

🔢
Example: 45
4
5
→
40
+
5
=
45
4 tens + 5 ones
Example: 72
7
2
→
70
+
2
=
72
7 tens + 2 ones
Expanded Form Process
1
Identify Digits
2
Find Place Values
3
Multiply
4
Add Together

Questions & Answers

Question: I don't understand why we write 24 as 20 + 4. Why not just keep it as 24?

Answer: Great question! Writing 24 as 20 + 4 helps us understand what the number really means:

  • The digit 2 in 24 represents 2 tens, which is 20
  • The digit 4 in 24 represents 4 ones, which is 4
  • So 24 is made up of 20 + 4

Think of it like this: if you have 24 apples, you could group them as 2 groups of 10 apples (20 apples) plus 4 individual apples. This understanding helps you with bigger numbers later!

Expanded form shows us that each digit has a special value based on where it sits in the number.

Question: My child is confused about the difference between tens and ones. How can I explain this better?

Answer: Here's a helpful way to explain tens and ones:

  • Tens: Think of them as "groups of 10" - like packs of 10 pencils
  • Ones: Think of them as "individual items" - like single pencils

Use physical objects: Take 34 items (like blocks or candies). Make 3 groups of 10, and you'll have 4 left over. So 34 = 3 groups of 10 (30) + 4 singles (4).

You can also use the counting: "ten, twenty, thirty" (that's the 3 tens) "thirty-one, thirty-two, thirty-three, thirty-four" (that's the 4 ones).

Question: What happens when I have a number like 50? Does it still work the same way?

Answer: Yes, it works the same way! Let's look at 50:

  • In 50: Tens digit = 5, Ones digit = 0
  • 5 tens = 5 × 10 = 50
  • 0 ones = 0 × 1 = 0
  • So 50 = 50 + 0

Even though the ones digit is 0, we still count it! Zero means "none," so 50 has 5 tens and 0 ones.

This pattern works for every 2-digit number: the first digit is always tens, the second digit is always ones, even if one of them is zero.

Detailed Summary: Expanded Form Learning Objectives

Key Definitions
  • Place Value: The value of a digit based on its position in a number (tens, ones, etc.)
  • Expanded Form: Writing a number as the sum of each digit's place value (e.g., 24 = 20 + 4)
  • Tens Place: The second digit from the right, representing groups of 10
  • Ones Place: The rightmost digit, representing individual units
  • Standard Form: The regular way we write numbers (e.g., 24)
Core Rules & Principles
  • Position Rule: In 2-digit numbers, left digit is tens, right digit is ones
  • Multiplication Rule: Tens digit × 10, Ones digit × 1
  • Addition Rule: Sum of expanded parts equals original number
  • Verification Rule: Always check by adding expanded parts
  • Zero Rule: Zero in any place still has value (e.g., 50 = 50 + 0)
Step-by-Step Methods
  • Step 1: Identify each digit in the number
  • Step 2: Determine the place value of each digit
  • Step 3: Calculate the value of each digit (multiply by place value)
  • Step 4: Write the sum of all calculated values
  • Step 5: Verify by adding the expanded parts
Examples & Applications
  • Simple: 15 = 10 + 5 (1 ten + 5 ones)
  • Medium: 37 = 30 + 7 (3 tens + 7 ones)
  • Advanced: 84 = 80 + 4 (8 tens + 4 ones)
  • With zero: 60 = 60 + 0 (6 tens + 0 ones)
  • Verification: 20 + 3 = 23 ✓
Tips & Common Pitfalls
  • Tip: Remember "Teens are Tens" - the first digit is always tens
  • Tip: Think of tens as groups of 10, ones as individual items
  • Pitfall: Don't confuse tens and ones positions
  • Pitfall: Forget to multiply by place value
  • Always verify: Add expanded parts to check original number
Key Notes & Memory Aids
  • Formula: AB = A×10 + B×1 (where A=tens, B=ones)
  • Pattern: Every 2-digit number follows this format
  • Visualization: Use base-10 blocks or drawings
  • Practice: Work with many examples to build fluency
  • Foundation: This concept builds for larger numbers