Solved Exercises on Expanded Forms Over Contracted Forms for Grade 1

Master expanded forms over contracted forms: place value decomposition, number representation, and mathematical expressions through these 5 detailed exercises.

Solution: Exercises 1 to 3
1 Basic Comparison
Exercise 1
Compare 24 in expanded form vs. contracted form.
Which shows the value of each digit?
Definition:

Contracted form: The standard way we write numbers (24).

Expanded form: Writing a number to show the value of each digit by adding the value of its digits (20 + 4).

Method:
  1. Identify the number in contracted form (24)
  2. Break down each digit by its place value
  3. Write the expanded form showing each digit's value
  4. Compare the two forms
Contracted Form
24
→
Expanded Form
20 + 4
CONTRACTED
24
→
EXPANDED
20+4
Step 1: Identify the contracted form

24 is the contracted form

Step 2: Identify each digit's place value

2 is in tens place = 2 × 10 = 20

4 is in ones place = 4 × 1 = 4

Step 3: Write the expanded form

Expanded form: 20 + 4

Step 4: Compare the forms

Contracted form (24) doesn't show digit values clearly

Expanded form (20 + 4) shows each digit's value

Final answer:

The expanded form (20 + 4) shows the value of each digit, while the contracted form (24) does not.

Applied rules:

• Comparison rule: Expanded form reveals the actual value of each digit

• Place value rule: Each position has a specific value

• Visualization rule: Expanded form makes place value visible

Tip: Expanded form helps understand what each digit represents.
2 Expanded Shows More Information
Exercise 2
Why is expanded form more helpful than contracted form?
Use 57 as an example.
Definition:

Expanded form superiority: Expanded form provides more insight into the value of each digit compared to contracted form.

Contracted Form
57
→
Expanded Form
50 + 7
CONTRACTED
57
→
EXPANDED
50+7
Step 1: Look at the contracted form

57 - this just shows the number

Step 2: Break down using place value

5 is in tens place = 5 × 10 = 50

7 is in ones place = 7 × 1 = 7

Step 3: Write the expanded form

Expanded form: 50 + 7

Step 4: Compare benefits

Contracted form: Quick, but hides digit values

Expanded form: Shows exactly what each digit represents

Final answer:

Expanded form (50 + 7) is more helpful because it shows that 5 represents 50 and 7 represents 7, making place value clear.

Applied rules:

• Transparency rule: Expanded form makes digit values transparent

• Educational rule: Expanded form aids in understanding place value

• Clarity rule: Expanded form removes ambiguity about digit values

3 Place Value Understanding
Exercise 3
Explain how expanded form helps understand place value using 83.
Show both forms.
Definition:

Place value understanding: Expanded form demonstrates how each digit's position determines its value.

Contracted Form
83
→
Expanded Form
80 + 3
CONTRACTED
83
→
EXPANDED
80+3
Step 1: Identify the contracted form

83 is the contracted form

Step 2: Identify each digit's place value

8 is in tens place = 8 × 10 = 80

3 is in ones place = 3 × 1 = 3

Step 3: Write the expanded form

Expanded form: 80 + 3

Step 4: Explain how expanded form helps

Shows that the 8 in 83 represents 80 (8 tens)

Shows that the 3 in 83 represents 3 (3 ones)

Final answer:

Expanded form (80 + 3) helps understand place value by showing that 8 in the tens place represents 80 and 3 in the ones place represents 3.

Applied rules:

• Position rule: Each position has a specific value (ones, tens)

• Value revelation rule: Expanded form reveals the true value of each digit

• Educational benefit rule: Expanded form enhances place value comprehension

Rules and methods, laws,...
24 = 20 + 4
Expanded vs. Contracted
🔒
Contracted Form
Standard number notation (24)
🔓
Expanded Form
Value breakdown (20 + 4)
📊
Place Value
Digit position value
Key definitions:

Contracted form: The standard way we write numbers (24, 57, 83)

Expanded form: Writing a number as the sum of the values of its digits (20 + 4, 50 + 7, 80 + 3)

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

Tens: Groups of 10 (the left digit in a two-digit number)

Ones: Single units (the right digit in a two-digit number)

Complete methodology:
  1. Identify contracted form: Look at the standard number (24)
  2. Determine place value: Tens and ones for two-digit numbers
  3. Calculate value: Multiply each digit by its place value
  4. Express in expanded form: Add the calculated values together
  5. Compare benefits: Understand why expanded form is superior
Tip 1: Expanded form reveals what each digit actually represents.
Tip 2: Use expanded form to understand place value better.
Tip 3: Contracted form is for quick writing, expanded form is for learning.
Benefits of expanded form: Shows digit values clearly, aids understanding, prevents confusion.
Limitations of contracted form: Hides true value of digits, may cause misunderstanding.
Formulas to know by heart:

• Two-digit number AB = (A × 10) + B (expanded form)

• Tens value = tens digit × 10

• Ones value = ones digit × 1

• Expanded form > Contracted form for learning

Detailed Summary of Expanded Forms Over Contracted Forms
Key Concepts and Definitions:
  • Contracted Form: The standard way we write numbers (24, 57, 83)
  • Expanded Form: Writing a number as the sum of the values of its digits (20 + 4, 50 + 7, 80 + 3)
  • Place Value: The value of a digit based on its position in the number
  • Digit Value: What each digit actually represents in a number
  • Position Importance: How the location of a digit determines its value
Core Rules and Principles:
  • Visibility Rule: Expanded form makes digit values visible, contracted form hides them
  • Educational Superiority: Expanded form is better for learning and understanding
  • Value Revelation: Expanded form reveals the true value of each digit
  • Place Value Rule: Each position has a specific value (ones, tens, hundreds)
  • Comparison Rule: Expanded form provides more information than contracted form
Step-by-Step Method:
  1. Identify the contracted form: Look at the standard number (e.g., 24)
  2. Determine place values: Identify tens and ones positions
  3. Calculate digit values: Multiply each digit by its place value
  4. Write expanded form: Add the calculated values (20 + 4)
  5. Compare forms: Understand why expanded form is superior for learning
Examples:
  • Simple: 24 (contracted) vs. 20 + 4 (expanded)
  • Medium: 57 (contracted) vs. 50 + 7 (expanded)
  • Advanced: 83 (contracted) vs. 80 + 3 (expanded)
Tips and Tricks:
  • Learning Tip: Use expanded form to understand what digits represent
  • Memory Aid: "Expanded" means more detail, "Contracted" means less detail
  • Practice Strategy: Convert between forms to strengthen understanding
  • Visual Aid: Use base-10 blocks to see the difference
Key Notes for Memorization:
  • Expanded > Contracted: For understanding and learning
  • 24 ≠ 2 + 4: It's 20 + 4 (place value matters)
  • Digit Position: Determines its actual value
  • Learning Priority: Master expanded form before relying on contracted form
Solution: Exercises 4 to 5
4 Advantages of Expanded Form
Exercise 4
List 3 advantages of expanded form over contracted form.
Use 49 as an example.
Definition:

Advantages of expanded form: Benefits that make expanded form superior to contracted form for learning and understanding.

Contracted Form
49
→
Expanded Form
40 + 9
CONTRACTED
49
→
EXPANDED
40+9
Step 1: Identify the contracted form

49 is the contracted form

Step 2: Convert to expanded form

4 in tens place = 4 × 10 = 40

9 in ones place = 9 × 1 = 9

Expanded form: 40 + 9

Step 3: List advantages of expanded form

1. Shows actual value of each digit (4 = 40, 9 = 9)

2. Makes place value clear and visible

3. Helps prevent confusion about digit values

Final answer:

Three advantages of expanded form over contracted form for 49 (40 + 9):

  1. Shows that the 4 represents 40 (not just 4)
  2. Makes place value relationships clear
  3. Prevents confusion about digit values
Applied rules:

• Educational advantage rule: Expanded form enhances learning

• Clarity rule: Expanded form removes ambiguity

• Value visibility rule: Expanded form makes digit values visible

5 Real-World Application
Exercise 5
Explain why expanded form is better than contracted form when counting objects.
Use 72 as an example.
Definition:

Real-world application: Using expanded form in practical situations like counting objects to understand quantities better.

Contracted Form
72
→
Expanded Form
70 + 2
CONTRACTED
72
→
EXPANDED
70+2
Step 1: Consider counting scenario

If counting 72 objects, contracted form just says "72"

Step 2: Analyze with expanded form

72 = 70 + 2 means 7 groups of 10 and 2 singles

Step 3: Compare benefits

Contracted: Just a number (72)

Expanded: Shows organization (7 tens + 2 ones)

Step 4: Explain real-world advantage

Expanded form helps organize counting into groups

Final answer:

Expanded form (70 + 2) is better than contracted form (72) when counting because it shows the organization: 7 groups of 10 and 2 individual items, making it easier to count and verify.

Applied rules:

• Organization rule: Expanded form shows grouping structure

• Practical advantage rule: Expanded form aids real-world counting

• Verification rule: Expanded form makes it easier to check accuracy

Place Value Concepts: Expanded vs. Contracted Forms
24 = 20 + 4
Expanded vs. Contracted
Key definitions:

Place value: The value of a digit based on its position in the number (tens, ones)

Contracted form: Standard number notation (24, 57, 83)

Expanded form: Writing a number as the sum of the values of its digits (20 + 4, 50 + 7, 80 + 3)

Tens: Groups of 10 (the left digit in a two-digit number)

Ones: Single units (the right digit in a two-digit number)

Complete methodology:
  1. Identify the contracted form: Look at the standard number
  2. Determine place value: Tens place (left) or ones place (right)
  3. Calculate value: Multiply each digit by its place value
  4. Express in expanded form: Add the calculated values together
  5. Understand advantages: See why expanded form is superior for learning
Tip 1: Use expanded form to understand what digits really represent.
Tip 2: Remember: tens digit × 10, ones digit × 1.
Tip 3: Practice converting between forms to strengthen understanding.
Tip 4: Use expanded form for learning, contracted form for efficiency.
Benefits of expanded form: Shows digit values clearly, enhances understanding, prevents confusion about place value.
Exam preparation: Know how to convert between forms, understand why expanded form is valuable.
Formulas to know by heart:

• Two-digit number AB = (A × 10) + B (expanded form)

• Tens value = tens digit × 10

• Ones value = ones digit × 1

• Expanded form provides more educational value than contracted form

🔒
Contracted Form
Quick notation (24)
🔓
Expanded Form
Value breakdown (20 + 4)
📊
Place Value
Digit position value

Questions & Answers

Question: Why do we need expanded form if we already have the normal way of writing numbers like 24?

Answer: Great question! The normal way (24) is called "contracted form" and it's quick for writing. But "expanded form" (20 + 4) helps us understand what each digit really means:

  • The "2" in 24 doesn't just mean 2 - it means 20 (2 tens)!
  • The "4" in 24 means 4 ones
  • So 24 = 20 + 4, not 2 + 4

Expanded form teaches us about place value - that the position of a digit changes its value. This is important for understanding bigger numbers later!

Question: When should my child use expanded form versus contracted form?

Answer: Here's when to use each form:

  • Use expanded form when learning: To understand place value, to see what digits represent, to solve problems
  • Use contracted form for efficiency: When writing answers quickly, when the context is clear
  • Transition: Start with expanded form to build understanding, then move to contracted form once the concept is mastered

Think of expanded form as training wheels - they help learn, but once you're confident, you can ride without them.

Question: How does expanded form help me when I count things?

Answer: Expanded form helps you organize counting! For example, if you're counting 57 toys:

  • Contracted form (57): Just tells you the total
  • Expanded form (50 + 7): Shows you have 5 groups of 10 toys and 7 extra toys

This makes counting easier because you can group items into tens and count the groups, then add the extras. It also helps you check your work!