Expanded Correction in Place Value for Grade 1

Master place value and expanded form with 5 detailed exercises, definitions, rules, and visual learning tools.

Solution: Exercises 1 to 3
1 Expanded Form Basics
Exercise 1
Write 23 in expanded form and explain its place value.
Definition:

Expanded form: Writing a number to show the value of each digit. For example, 23 = 20 + 3

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

Method:
  1. Identify the digits in the number
  2. Determine the place value of each digit
  3. Write each digit with its place value
  4. Add all parts together
Number
23
Expanded
20 + 3
Step 1: Identify digits

In 23, we have digit 2 and digit 3

Step 2: Determine place values

The 2 is in the tens place, so its value is 2 × 10 = 20

The 3 is in the ones place, so its value is 3 × 1 = 3

Step 3: Write expanded form

23 = 20 + 3

23 = 20 + 3
Final answer:

23 in expanded form is 20 + 3

Applied rules:

• Tens place rule: Multiply digit by 10

• Ones place rule: Digit stays the same

• Expanded form: Add all place values together

Tip: Remember "TOES" - Tens, Ones, Every digit has a place!
2 Two-Digit Expanded Form
Exercise 2
Convert 47 to expanded form and represent it visually.
Definition:

Expanded form: Shows the value of each digit separately. 47 = 40 + 7

Number
47
Expanded
40 + 7
Step 1: Break down the number

47 has 4 tens and 7 ones

Step 2: Calculate place values

4 tens = 4 × 10 = 40

7 ones = 7 × 1 = 7

Step 3: Write in expanded form

47 = 40 + 7

47 = 40 + 7
Final answer:

47 in expanded form is 40 + 7

Applied rules:

• Place value rule: Each position has a specific value

• Base ten system: Uses groups of ten

• Digit value: Position determines value

3 Three-Digit Introduction
Exercise 3
Show 124 in expanded form using base ten blocks concept.
Definition:

Three-digit expanded form: 124 = 100 + 20 + 4

Base ten blocks: Visual representation using hundreds, tens, and ones

Number
124
Expanded
100 + 20 + 4
Step 1: Identify each digit

1 is in hundreds place, 2 is in tens place, 4 is in ones place

Step 2: Calculate place values

1 hundred = 1 × 100 = 100

2 tens = 2 × 10 = 20

4 ones = 4 × 1 = 4

Step 3: Combine in expanded form

124 = 100 + 20 + 4

124 = 100 + 20 + 4
Final answer:

124 in expanded form is 100 + 20 + 4

Applied rules:

• Hundreds place: Multiply by 100

• Tens place: Multiply by 10

• Ones place: Keep as is

Visual Learning: Place Value Infographic
PLACE VALUE CONCEPT
🎯
ONES PLACE
×1
🔟
TENS PLACE
×10
💯
HUNDREDS PLACE
×100
HUNDREDS
1
100
TENS
2
20
ONES
4
4
124 = 100 + 20 + 4
Expanded Form
Memory Tip: "H-T-O" for Hundreds, Tens, Ones
Visual Tip: Think of blocks - big blocks for hundreds, sticks for tens, dots for ones
Solution: Exercises 4 to 5
4 Converting Standard to Expanded
Exercise 4
Convert 89 to expanded form and draw the representation.
Definition:

Standard form to expanded: Breaking down a number to show place value of each digit

Number
89
Expanded
80 + 9
Step 1: Identify digit positions

8 is in the tens place, 9 is in the ones place

Step 2: Calculate place values

8 tens = 8 × 10 = 80

9 ones = 9 × 1 = 9

Step 3: Write expanded form

89 = 80 + 9

Step 4: Verification

Add back: 80 + 9 = 89 ✓

89 = 80 + 9
Final answer:

89 in expanded form is 80 + 9

Applied rules:

• Position rule: Leftmost digit is highest place value

• Multiplication rule: Tens × 10, Hundreds × 100

• Addition rule: Sum of place values equals original number

5 Mixed Practice
Exercise 5
Write 56 in expanded form and explain why it works.
Definition:

Expanded form explanation: Shows how numbers are built from place values

Number
56
Expanded
50 + 6
Step 1: Analyze the number

56 has two digits: 5 and 6

Step 2: Assign place values

5 is in tens place: 5 × 10 = 50

6 is in ones place: 6 × 1 = 6

Step 3: Write expanded form

56 = 50 + 6

Step 4: Explain the concept

This works because our number system is base ten, where each position is worth 10 times more than the position to its right

56 = 50 + 6
Final answer:

56 in expanded form is 50 + 6, showing 5 tens and 6 ones

Applied rules:

• Base ten system: Each place value is 10 times the previous

• Positional notation: Value depends on position

• Decomposition: Breaking numbers into component parts

Key Concepts: Place Value & Expanded Form
23 = 20 + 3
Expanded Form Example
Key definitions:

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

Expanded form: Writing a number to show the value of each digit separately

Standard form: The normal way we write numbers (like 23)

Complete methodology:
  1. Identify digits: Look at each digit in the number
  2. Assign positions: Determine which place each digit occupies
  3. Calculate values: Multiply each digit by its place value
  4. Combine: Add all the values together
Tip 1: Use "HTO" - Hundreds, Tens, Ones to remember the order.
Tip 2: Count zeros to determine place value (10, 100, 1000...).
Tip 3: Always verify by adding expanded parts to get the original number.
Common errors: Forgetting place values, misidentifying digit positions, adding incorrectly.
Visual aids: Use base ten blocks, place value charts, or drawing representations.
Essential rules:

• Ones place: multiply by 1

• Tens place: multiply by 10

• Hundreds place: multiply by 100

• Thousands place: multiply by 1000

Questions & Answers

Question: My child is struggling to understand why 23 is equal to 20 + 3. How can I explain expanded form more clearly?

Answer: Great question! Here's a concrete approach:

  • Use physical objects like popsicle sticks or small toys. Have 23 items and group them into 2 groups of 10 and 3 individual items
  • Draw 23 circles and circle groups of 10 to show 2 tens and 3 ones
  • Think of money: 23 cents could be 2 dimes (20 cents) and 3 pennies (3 cents)

The key is showing that 23 is made up of 2 tens (20) and 3 ones (3), so 20 + 3 = 23.

Make it visual and hands-on - first graders learn better with concrete examples!

Question: How do I introduce place value to students who don't understand the concept of grouping by tens?

Answer: Start with concrete manipulatives:

  • Use unifix cubes or snap cubes - have students make groups of 10
  • Introduce the concept of "trading": 10 ones can be traded for 1 ten stick
  • Create a "bank" game where students deposit 10 singles for a ten rod
  • Use real-world examples: eggs come in dozens (groups of 12), but we count money in tens

Progress from concrete (manipulatives) to pictorial (drawings) to abstract (numbers only). This progression helps solidify understanding.

Spend extra time on counting by tens (10, 20, 30...) before moving to mixed numbers.

Question: Why do we need to learn expanded form? It seems harder than just writing the number normally.

Answer: Expanded form is like taking apart a toy to see how it works! Here's why it's helpful:

  • It helps you understand what each digit really means (the 2 in 23 means 20, not just 2)
  • It makes bigger addition and subtraction easier later on
  • It helps you compare numbers (knowing 35 is 30 + 5 helps you see it's bigger than 28 which is 20 + 8)
  • It builds the foundation for multiplication and division

Think of it as learning the "secret code" of numbers - once you know it, math becomes much easier!

Just like learning the alphabet helps you read words, expanded form helps you understand numbers!