Expanded form: Writing a number to show the value of each digit separately. For example, 23 = 20 + 3
Place value: The value of a digit based on its position in a number.
- Identify each digit in the number
- Determine the place value of each digit
- Write each digit with its place value
- Join them with addition signs
In 23, we have digit 2 and digit 3
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
23 = 20 + 3
23 in expanded form is 20 + 3
• Tens place rule: Multiply digit by 10
• Ones place rule: Digit stays the same
• Expanded form rule: Add all place values together
Expanded form: Writing a number to show the value of each digit separately. For example, 47 = 40 + 7
In 47, we have digit 4 and digit 7
4 tens = 4 × 10 = 40
7 ones = 7 × 1 = 7
47 = 40 + 7
47 in expanded form is 40 + 7
• Place value rule: Each position has specific value
• Base ten rule: Tens place is 10 times the ones place
• Verification rule: Add expanded parts to check
Expanded form: Shows place value breakdown (85 = 80 + 5)
Verification: Checking that expanded parts equal original number
8 tens = 80, 5 ones = 5, so 85 = 80 + 5
80 + 5 = 85 ✓
85 in expanded form is 80 + 5, verified by adding 80 + 5 = 85
• Place value rule: Each digit has specific value based on position
• Verification rule: Check that forms equal original number
• Base ten system: Uses groups of ten
Teen numbers: Numbers 11-19 are composed of 1 ten and some ones
In 16, we have digit 1 and digit 6
1 ten = 1 × 10 = 10
6 ones = 6 × 1 = 6
16 = 10 + 6
10 + 6 = 16 ✓
16 in expanded form is 10 + 6, showing 1 ten and 6 ones
• Teen number rule: Numbers 11-19 have 1 ten and extra ones
• Place value rule: Each position has specific value
• Verification rule: Check that parts equal whole number
Round numbers: Numbers like 10, 20, 30... represent exact tens with zero ones
7 tens = 70, 0 ones = 0, so 70 = 70 + 0
70 represents seven groups of ten with zero extra ones
70 + 0 = 70 ✓
70 in expanded form is 70 + 0, showing seven tens and zero ones
• Round number rule: Multiples of 10 have zero ones
• Place value rule: Tens place shows number of tens
• Zero rule: Zero ones means no additional single units
Verification: Checking that expanded parts equal the original number
9 tens = 90, 4 ones = 4
94 = 90 + 4
90 + 4 = 94 ✓
94 in expanded form is 90 + 4, verified by adding 90 + 4 = 94
• Verification rule: Always check your answer
• Place value rule: Each digit's position determines value
• Base ten rule: Uses groups of ten
Expanded Form: Writing a number to show the value of each digit separately (e.g., 23 = 20 + 3)
Place Value: The value of a digit based on its position in a number
Tens Place: The second digit from the right, representing groups of 10
Ones Place: The rightmost digit, representing individual units
Place Value Rule: Each position is 10 times the value of the position to its right
Tens Rule: The tens digit represents groups of 10 (multiply by 10)
Ones Rule: The ones digit keeps its face value
Verification Rule: The sum of expanded parts equals the original number
Method 1 - Standard to Expanded:
- Identify each digit in the number
- Determine the place value of each digit
- Write each digit with its place value
- Join with addition signs
Method 2 - Verification:
- Add the expanded parts together
- Check if the sum equals the original number
- If yes, the expanded form is correct
Simple Example: 12 = 10 + 2
Medium Example: 38 = 30 + 8
Advanced Example: 64 = 60 + 4
Complex Example: 97 = 90 + 7
Tip 1: "Left is tens, right is ones"
Tip 2: Tens digit × 10 = actual value
Tip 3: Always add expanded parts to verify
Tip 4: Use base ten blocks to visualize
Pitfall 1: Forgetting that the tens digit represents groups of 10 (3 in 35 = 30, not 3)
Pitfall 2: Adding instead of multiplying place values
Pitfall 3: Not verifying the answer by adding expanded parts
Pitfall 4: Confusing place values with face values
Remember: Each digit's position determines its value
Memorize: Tens place = digit × 10, Ones place = digit × 1
Practice: Daily conversion exercises
Master: The relationship between digits and their expanded equivalents
Expanded Form Examples and Solutions Questions & Answers
Question: How can I ensure students understand both the examples and solutions equally well?
Answer: Focus on the process and reasoning:
- Provide clear step-by-step solutions for each example
- Have students verbalize the process as they solve
- Ask students to explain their thinking
- Use multiple representations (visual, numeric, verbal)
The goal is for students to understand the underlying process, not just copy the solution.
Encourage students to check their own work using the verification method!
Question: My child understands the examples but struggles with the solutions. How can I help?
Answer: This often happens when students focus on the final answer rather than the process:
- Emphasize the steps involved in reaching the solution
- Practice with fewer examples but focus on understanding the process
- Have your child explain each step aloud
- Use visual aids to reinforce the concept
Help your child understand that the solution is just the result of following the correct process.
Practice the steps until the process becomes automatic!
Question: Why do we need to write the solution steps? Can't I just get the answer?
Answer: Writing solution steps helps you in many ways:
- You understand how to solve similar problems in the future
- You can catch mistakes along the way
- You can explain your thinking to others
- You build logical thinking skills
The steps show your thinking process and help you learn the method.
Following the steps helps you solve ANY expanded form problem!