Expanded Form and Written Form for Grade 1

Complete guide to expressing numbers in expanded form and written form with detailed exercises and visual learning tools.

Exercise Solutions: Number Forms
1 Converting to Expanded Form
Exercise 1
Write 45 in expanded form and explain each part.
Definition:

Expanded form: Writing a number to show the value of each digit separately. For example, 45 = 40 + 5

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

Method:
  1. Identify each digit in the number
  2. Determine the place value of each digit
  3. Write each digit with its place value
  4. Join them with addition signs
Number
45
Expanded
40 + 5
Step 1: Identify digits

In 45, we have digit 4 and digit 5

Step 2: Determine place values

The 4 is in the tens place, so its value is 4 × 10 = 40

The 5 is in the ones place, so its value is 5 × 1 = 5

Step 3: Write expanded form

45 = 40 + 5

45 = 40 + 5
Final answer:

45 in expanded form is 40 + 5

Applied rules:

• Tens place rule: Multiply digit by 10

• Ones place rule: Digit stays the same

• Expanded form rule: Add all place values together

Tip: Think of expanded form as breaking the number into its building blocks!
2 Converting to Written Form
Exercise 2
Write 67 in written form and explain how to spell it.
Definition:

Written form: Writing a number using words instead of digits. For example, 67 = sixty-seven

Number
67
Written Form
sixty-seven
Step 1: Identify tens and ones

67 has 6 tens (sixty) and 7 ones (seven)

Step 2: Spell the tens part

6 tens = sixty

Step 3: Spell the ones part

7 ones = seven

Step 4: Join with hyphen

sixty-seven

67 = sixty-seven
Final answer:

67 in written form is sixty-seven

Applied rules:

• Hyphen rule: Numbers 21-99 use hyphens (except multiples of 10)

• Spelling rule: Learn the correct spelling of number words

• Combination rule: Tens part + ones part

3 Mixed Conversion Practice
Exercise 3
Write 83 in both expanded form and written form.
Definition:

Expanded form: Shows place value breakdown (83 = 80 + 3)

Written form: Shows number in written words (eighty-three)

Number
83
Expanded
80 + 3
Written Form
eighty-three
Step 1: For expanded form

8 tens = 80, 3 ones = 3, so 83 = 80 + 3

Step 2: For written form

8 tens = eighty, 3 ones = three, joined as eighty-three

Step 3: Verification

80 + 3 = 83 ✓ and eighty-three = 83 ✓

83 = 80 + 3 = eighty-three
Final answer:

Expanded form: 80 + 3, Written form: eighty-three

Applied rules:

• Place value rule: Each digit has specific value based on position

• Hyphen rule: Numbers 21-99 connect tens and ones with hyphens

• Verification rule: Check that forms equal original number

Number Forms Comparison
NUMBER FORMS VISUAL GUIDE
STANDARD FORM
26
(Digits)
EXPANDED FORM
20 + 6
(Place Values)
WRITTEN FORM
twenty-six
(Written Words)
TENS PLACE
2
20
ONES PLACE
6
6
26 = 20 + 6 = twenty-six
All Forms Equal
Memory Tip: S-E-W for Standard, Expanded, Written forms!
Practice Tip: Say number names out loud to remember spelling!
Advanced Conversion Exercises
4 Converting Written Form to Standard
Exercise 4
Convert "ninety-one" to standard form and expanded form.
Definition:

Converting written form: Translating written number words back to digits

Written Form
ninety-one
Standard
91
Expanded
90 + 1
Step 1: Identify the parts

"ninety" = 9 tens = 90, "one" = 1 one = 1

Step 2: Write in standard form

ninety-one = 91

Step 3: Write in expanded form

91 = 90 + 1

Step 4: Verify

90 + 1 = 91 and ninety-one = 91 ✓

ninety-one = 91 = 90 + 1
Final answer:

Standard form: 91, Expanded form: 90 + 1

Applied rules:

• Word-to-digit rule: Learn number word equivalents

• Place value rule: Tens and ones positions determine value

• Verification rule: Check that conversions are accurate

5 Comprehensive Practice
Exercise 5
Complete the table: 54 = ___ (expanded), ___ (written), ___ (visual representation).
Definition:

Multiple representations: Same number shown in different formats

Number
54
Expanded
50 + 4
Written Form
fifty-four
Step 1: Expanded form

5 tens = 50, 4 ones = 4, so 50 + 4

Step 2: Written form

5 tens = fifty, 4 ones = four, joined as fifty-four

Step 3: Verification

50 + 4 = 54, and fifty-four = 54 ✓

Step 4: Visual representation

5 groups of 10 blocks + 4 individual blocks

54 = 50 + 4 = fifty-four
Final answer:

Expanded: 50 + 4, Written: fifty-four, Visual: 5 tens blocks + 4 ones blocks

Applied rules:

• Consistency rule: All forms represent the same value

• Place value rule: Position determines digit value

• Visualization rule: Concrete objects help understand abstract concepts

Detailed Learning Summary: Number Forms Mastery
COMPREHENSIVE NUMBER FORMS SUMMARY
Core Definitions

Standard Form: Numbers written using digits (e.g., 23, 47, 89)

Expanded Form: Numbers written to show place value of each digit (e.g., 23 = 20 + 3)

Written Form: Numbers written using words (e.g., twenty-three)

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

Essential Rules and Laws

Place Value Rule: Each position is 10 times the value of the position to its right

Hyphen Rule: Numbers 21-99 join tens and ones with hyphens (e.g., thirty-four)

Equivalence Rule: All forms represent the same numerical value

Conversion Rule: Each form can be converted to another using place value understanding

Step-by-Step Methods

Method 1 - Standard to Expanded:

  1. Identify each digit in the number
  2. Determine the place value of each digit
  3. Write each digit with its place value
  4. Join with addition signs

Method 2 - Standard to Written Form:

  1. Identify the tens digit and its word equivalent
  2. Identify the ones digit and its word equivalent
  3. Join with hyphen for numbers 21-99

Method 3 - Written to Standard:

  1. Translate word parts to digits
  2. Combine using place value
  3. Write as standard form
Concrete Examples

Simple Example: 12 = 10 + 2 = twelve

Medium Example: 37 = 30 + 7 = thirty-seven

Advanced Example: 68 = 60 + 8 = sixty-eight

Complex Example: 94 = 90 + 4 = ninety-four

Tips and Memory Aids

Tip 1: S-E-W for Standard, Expanded, Written forms

Tip 2: "Teens" (13-19) have unique names

Tip 3: Hyphens connect tens and ones (21-99)

Tip 4: Count by tens to reinforce place value

Common Pitfalls to Avoid

Pitfall 1: Forgetting to hyphenate compound numbers (43 = forty-three, not forty three)

Pitfall 2: Confusing place values (4 in 45 is 40, not 4)

Pitfall 3: Misreading written forms (fifty vs. fifteen)

Pitfall 4: Adding instead of multiplying place values

Key Takeaways for Memorization

Remember: Each digit's position determines its value

Memorize: Number words from one to one hundred

Practice: Daily conversion between forms

Master: The relationship between digits and their written equivalents

Number Forms Questions & Answers

Question: My students confuse "fifty" and "fifteen". How can I help them distinguish these?

Answer: This is a very common confusion! Here are effective strategies:

  • Teach the pattern: "fifteen" ends in "teen" (like 13-19), while "fifty" ends in "ty" (like 40, 50, 60...)
  • Use visual cues: Write "fifteen" and "fifty" side by side, highlighting the "teen" vs "ty" endings
  • Connect to place value: "Fifteen" = 1 ten + 5 ones, "Fifty" = 5 tens
  • Create memory phrases: "Teens are in their teens (13-19)" vs "Tys are in the twenties, thirties, forties, fifties, etc."

Practice with multiple examples: thirteen/thirty, fourteen/fourty, sixteen/sixty to reinforce the pattern.

The key is emphasizing the suffix patterns that distinguish the ranges!

Question: My child writes "fifty and four" instead of "fifty-four". Is this wrong?

Answer: While "fifty and four" shows good conceptual understanding, the standard mathematical convention is "fifty-four" with a hyphen.

  • Numbers 21-99 use hyphens to connect the tens and ones parts
  • "Fifty-four" is one word representing the complete number 54
  • "Fifty and four" suggests two separate numbers being combined
  • This convention helps distinguish between single numbers and mathematical operations

Praise your child's understanding of the place value concept, then gently introduce the standard format.

Use the phrase: "We write it as one word with a hyphen: fifty-four!"

Question: Why do we need to learn all these different ways to write numbers? Isn't standard form enough?

Answer: Different forms serve different purposes and strengthen mathematical understanding!

  • Standard form: Quick, efficient for calculations
  • Expanded form: Shows place value understanding, helps with addition/subtraction
  • Written form: Used in reading, writing, formal documents, helps with spelling

Expanded form especially helps you understand that 26 really means 20 + 6, which makes bigger math easier later!

It's like learning to say, write, and show a word in different ways - it makes you stronger at understanding it!

Each form gives you a different view of the same number, like looking at it from different angles!