Expanded Form Worksheets for Grade 1: Learning Place Value

Master expanded form: breaking down numbers into their place value components. Includes 5 detailed exercises with step-by-step solutions, definitions, rules, and methods for young learners.

Solution: Exercises 1 to 3
1 Basic Two-Digit Number
Exercise 1
Write 15 in expanded form.
Definition:

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

Method for expanded form:
  1. Look at each digit in the number
  2. Figure out what place each digit is in (ones or tens)
  3. Multiply each digit by its place value
  4. Add all the parts together
Number
15
Place Values
10 + 5
Step 1: Look at each digit

15 has two digits: 1 and 5

Step 2: Figure out the place values

1 is in the tens place (so 1 × 10 = 10), 5 is in the ones place (so 5 × 1 = 5)

Step 3: Write in expanded form

15 = 10 + 5

1
Tens
1 × 10 = 10
5
Ones
5 × 1 = 5
15 = 10 + 5
Final answer:

15 in expanded form is 10 + 5

Applied rules:

• Place value rule: Each digit's value depends on its position

• Expanded form rule: Sum of each digit × its place value

• Tens place: The number on the left in a two-digit number

2 Two-Digit Number
Exercise 2
Write 23 in expanded form.
Definition:

Two-digit number expanded form: T × 10 + O × 1

Number
23
Expanded
20 + 3
Step 1: Look at each digit

23 has: 2 in tens place, 3 in ones place

Step 2: Calculate place values

2 × 10 = 20, 3 × 1 = 3

Step 3: Write expanded form

23 = 20 + 3

2
Tens
2 × 10 = 20
3
Ones
3 × 1 = 3
23 = 20 + 3
Final answer:

23 in expanded form is 20 + 3

Applied rules:

• Tens rule: 2nd digit from right represents tens

• Ones rule: Rightmost digit represents ones

• Place value progression: Each position to the left is 10 times greater

3 Larger Two-Digit Number
Exercise 3
Write 47 in expanded form.
Definition:

Two-digit number expanded form: T × 10 + O × 1

Number
47
Expanded
40 + 7
Step 1: Look at each digit

47 has: 4 in tens place, 7 in ones place

Step 2: Calculate place values

4 × 10 = 40, 7 × 1 = 7

Step 3: Write expanded form

47 = 40 + 7

4
Tens
4 × 10 = 40
7
Ones
7 × 1 = 7
47 = 40 + 7
Final answer:

47 in expanded form is 40 + 7

Applied rules:

• Pattern rule: Same method works for any two-digit number

• Place value rule: Left digit is tens, right digit is ones

• Verification rule: Add expanded parts to check answer

Rules and methods, laws,...
12 = 10 + 2
Basic Expanded Form
Ones Place
Digit × 1
Rightmost digit
Tens Place
Digit × 10
Left digit in 2-digit number
Key definitions:

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

Standard form: Regular way of writing numbers (e.g., 12)

Expanded form: Breaking a number into the sum of its place values

Complete methodology:
  1. Count digits: Look at how many digits are in the number
  2. Identify positions: Recognize which digit is in tens and ones places
  3. Calculate values: Multiply each digit by its corresponding place value
  4. Combine: Add all the products together
  5. Verify: Check that the sum equals the original number
Tip 1: Think of tens as groups of 10, ones as single units.
Tip 2: Use fingers or objects to count and group by tens.
Tip 3: Practice with smaller numbers first, then move to bigger ones.
Tip 4: Always check your answer by adding the expanded parts.
Common errors: Mixing up tens and ones, forgetting to multiply by place value.
Memorization aid: Think of place values as: Ones (right), Tens (left).
Formulas to know by heart:

• Ones place: Digit × 1

• Tens place: Digit × 10

• Expanded form: Sum of (Digit × Place Value)

Solution: Exercises 4 to 5
4 Number with Zero
Exercise 4
Write 30 in expanded form.
Definition:

Numbers ending in zero: Include zero place values in expanded form.

Number
30
Expanded
30 + 0
Simplified
30
Step 1: Look at each digit

30 has: 3 in tens place, 0 in ones place

Step 2: Calculate place values

3 × 10 = 30, 0 × 1 = 0

Step 3: Write expanded form

30 = 30 + 0, which simplifies to just 30

3
Tens
3 × 10 = 30
0
Ones
0 × 1 = 0
30 = 30 + 0 = 30
Final answer:

30 in expanded form is 30 + 0 (or just 30)

Applied rules:

• Zero rule: Include zero place values in expanded form

• Simplification: Adding zero doesn't change the value

• Place value rule: Zero still holds its place value position

5 Mixed Practice
Exercise 5
Write 58 in expanded form.
Definition:

Two-digit number expanded form: T × 10 + O × 1

Number
58
Expanded
50 + 8
Step 1: Look at each digit

58 has: 5 in tens place, 8 in ones place

Step 2: Calculate place values

5 × 10 = 50, 8 × 1 = 8

Step 3: Write expanded form

58 = 50 + 8

5
Tens
5 × 10 = 50
8
Ones
8 × 1 = 8
58 = 50 + 8
Final answer:

58 in expanded form is 50 + 8

Applied rules:

• Consistency rule: Same method works for any two-digit number

• Place value rule: Left digit is tens, right digit is ones

• Verification rule: Add expanded parts to confirm answer

Place Value and Expanded Form Rules, Methods, and Definitions
24 = 20 + 4
Expanded Form Pattern
Key definitions:

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

Standard form: Regular way of writing numbers (e.g., 24)

Expanded form: Breaking a number into the sum of its place values

Ones: Single units (rightmost digit)

Tens: Groups of ten (second digit from right)

Complete methodology:
  1. Analyze the number: Count digits and identify positions
  2. Assign place values: Match each digit to its place value
  3. Calculate products: Multiply each digit by its place value
  4. Write sum: Express as addition of all place values
  5. Verify result: Add components to check if they equal original number
Tip 1: Remember: Ones are singles, Tens are groups of 10.
Tip 2: Use base-10 blocks or draw circles to visualize place values.
Tip 3: When converting back to standard form, add all expanded parts.
Tip 4: Practice counting by tens: 10, 20, 30, 40, 50...

Common errors: Mixing up tens and ones places, forgetting to multiply by place values.
Practice tip: Use expanded form to understand number relationships and comparisons.
Formulas to know by heart:

• Ones place: Digit × 1

• Tens place: Digit × 10

• Expanded form: Sum of (Digit × Place Value)

Questions & Answers

Question: My grade 1 students struggle with understanding why we multiply digits by place values in expanded form. How can I make this clearer for young learners?

Answer: Great question! For grade 1 students, focus on concrete, visual representations:

  • Use manipulatives: Base-10 blocks where rods represent tens and small cubes represent ones
  • Draw pictures: Draw groups of 10 objects and single objects
  • Use real-world examples: Compare to packs of crayons (tens) and loose crayons (ones)
  • Count together: Show that 2 tens means counting by 10s twice: 10, 20

Example: For 23, show 2 groups of 10 sticks and 3 single sticks. This makes the "20 + 3" concept tangible!

Question: My child gets confused between tens and ones. How can I help them remember which is which?

Answer: Try these memory aids for grade 1 students:

  • Visual positioning: "Tens are on the LEFT, Ones are on the RIGHT"
  • Size comparison: "Tens are bigger because they're groups of 10"
  • Finger counting: Use 10 fingers for tens, 1 finger for ones
  • Rhyme: "Tens are big, ones are small, left side big, right side all"

Practice daily with simple numbers like 12, 15, 23 to build confidence.

Question: Why do we need to learn expanded form? When will I ever use this in real life?

Answer: Expanded form helps you understand numbers better! Here are some fun ways you'll use it:

  • Counting money: Understanding that $23 is $20 + $3 bills
  • Shopping: Comparing prices like $15 vs $20
  • Playing games: Understanding scores and points
  • Measuring: Understanding that 2 feet and 3 inches is 24 + 3 inches
  • Future math: Essential foundation for bigger numbers and harder math

Think of expanded form as learning the "parts" that make up numbers - just like knowing the ingredients in your favorite snack!

Detailed Summary: Place Value and Expanded Form

Key Concepts & Definitions

Place Value: The value of a digit based on its position in a number. Each position has a different value.

Standard Form: The regular way we write numbers (like 12, 23, 45).

Expanded Form: Writing a number as the sum of each digit multiplied by its place value.

Ones Place: The rightmost digit represents single units.

Tens Place: The second digit from the right represents groups of ten.

Core Rules & Laws

Place Value Rule: Each digit's value depends on its position in the number.

Position Rule: In two-digit numbers, the left digit is tens, the right digit is ones.

Multiplication Rule: Multiply each digit by its place value (1 for ones, 10 for tens).

Addition Rule: Sum all the place values to get the expanded form.

Verification Rule: Adding the expanded parts should equal the original number.

Step-by-Step Methods
  1. Identify digits: Look at each digit in the number
  2. Determine positions: Figure out which digit is in tens place and which is in ones place
  3. Calculate place values: Multiply each digit by its place value (tens × 10, ones × 1)
  4. Write expanded form: Add the calculated values together
  5. Verify answer: Add the expanded parts to make sure they equal the original number
Examples (Simple to Advanced)
Simple: 12 = 10 + 2
Medium: 25 = 20 + 5
Advanced: 47 = 40 + 7
With zero: 30 = 30 + 0
Challenge: 99 = 90 + 9
Memory Tip: Tens are BIGGER because they represent groups of 10, ones are SMALLER because they represent single units.
Position Trick: LEFT digit = tens, RIGHT digit = ones (in two-digit numbers).
Verification: Always add your expanded parts to check if they equal the original number.
Practice: Use objects, drawings, or fingers to visualize tens and ones.
Real Life: Expanded form helps with counting money, measuring, and comparing numbers.
Common Pitfalls & Tips

Common Mistakes: Mixing up tens and ones positions, forgetting to multiply by place value, skipping the verification step.

Helpful Tips: Use visual aids like base-10 blocks, count by tens aloud, practice with real objects, always check your work.

Success Strategy: Start with smaller numbers, gradually increase difficulty, celebrate small victories to build confidence.