Show all solution steps.
Expanded solution: A complete solution that shows every step needed to find the answer, including identification, calculation, and verification.
- Identify the number (35)
- Identify place values (tens, ones)
- Calculate value of each digit
- Write expanded form
- Verify the solution
The number is 35
3 is in the tens place
5 is in the ones place
3 tens = 3 × 10 = 30
5 ones = 5 × 1 = 5
35 = 30 + 5
30 + 5 = 35 ✓
The expanded form of 35 is 30 + 5
• Step-by-step rule: Show all solution steps clearly
• Place value rule: Each position has a specific value
• Verification rule: Always check your answer
Show all steps and verification process.
Complete verification: Checking that the expanded form adds up to the original number to ensure accuracy.
The number is 64
6 is in the tens place
4 is in the ones place
6 tens = 6 × 10 = 60
4 ones = 4 × 1 = 4
64 = 60 + 4
60 + 4 = 64 ✓
The answer is correct!
The expanded form of 64 is 60 + 4, verified by adding 60 + 4 = 64
• Verification rule: Always check that expanded parts sum to original number
• Completeness rule: Show all solution steps
• Accuracy rule: Verification ensures correct answers
Show traditional method and word form.
Multiple approaches: Solving the same problem using different methods to deepen understanding.
Step 1: 8 tens = 8 × 10 = 80
Step 2: 2 ones = 2 × 1 = 2
Step 3: 82 = 80 + 2
Step 1: Eighty-two = eighty + two
Step 2: Eighty-two = 80 + 2
80 + 2 = 82 ✓
82 = 80 + 2 (verified through multiple approaches)
• Different approaches rule: Same problem can be solved multiple ways
• Consistency rule: All approaches should yield same result
• Verification rule: Multiple approaches increase confidence in answer
Expanded solution: A complete solution showing all steps to find the answer
Place value: The value of a digit based on its position in the number
Verification: Checking that the solution is correct
Tens: Groups of 10 (the left digit in a two-digit number)
Ones: Single units (the right digit in a two-digit number)
- Identify the problem: What number do you need to expand?
- Determine place values: Tens and ones for two-digit numbers
- Calculate digit values: Multiply each digit by its place value
- Write expanded form: Add the calculated values together
- Verify solution: Check that expanded parts sum to original number
• Two-digit number AB = (A × 10) + B
• Tens value = tens digit × 10
• Ones value = ones digit × 1
• Verification: Expanded parts should sum to original number
- Expanded Solution: A complete solution showing all steps to find the answer
- Place Value: The value of a digit based on its position in the number
- Verification: Checking that the solution is correct by confirming expanded parts sum to original number
- Step-by-Step Process: Following a logical sequence to solve problems
- Multiple Approaches: Solving the same problem using different methods
- Completeness Rule: Show all solution steps clearly
- Verification Rule: Always check that expanded parts equal the original number
- Place Value Rule: Each position has a specific value (tens, ones)
- Accuracy Rule: Verification ensures correct answers
- Systematic Rule: Follow a consistent method for all problems
- Identify: Determine what number needs to be expanded
- Determine Place Values: Identify tens and ones positions
- Calculate Digit Values: Multiply each digit by its place value
- Write Expanded Form: Add the calculated values together
- Verify Solution: Check that expanded parts sum to original number
- Simple: 35 = 30 + 5
- Medium: 64 = 60 + 4
- Advanced: 82 = 80 + 2
- Write Clearly: Keep each step separate and clear
- Always Verify: Add expanded parts to confirm original number
- Use Visuals: Draw blocks or charts to help understand
- Check Work: Use multiple approaches when possible
- IDCAV Method: Identify, Determine, Calculate, Add, Verify
- Two-digit ABCD = (A × 10) + D for any two-digit number
- Verification Essential: Always add expanded parts to check
- Place Matters: Left digit is tens, right digit is ones
Show solution, identify common errors, and correct them.
Error correction: Identifying and fixing common mistakes in expanded form solutions.
Step 1: Identify number - 57
Step 2: Place values - 5 tens, 7 ones
Step 3: Calculate - 5 × 10 = 50, 7 × 1 = 7
Step 4: Write - 57 = 50 + 7
Step 5: Verify - 50 + 7 = 57 ✓
Error 1: 57 = 5 + 7 (wrong - ignores place value)
Error 2: 57 = 50 + 70 (wrong - wrong ones value)
Error 3: 57 = 5 + 70 (wrong - mixed up values)
Always remember: tens digit × 10, ones digit × 1
The expanded form of 57 is 50 + 7. Common error is forgetting that 5 tens = 50, not 5.
• Error identification rule: Recognize common mistakes
• Correction rule: Show why common errors are wrong
• Verification rule: Always check final answer
Include numeric, word, and verification formats.
Comprehensive solution: Providing the answer in multiple formats to demonstrate complete understanding.
Step 1: 9 tens = 9 × 10 = 90
Step 2: 1 one = 1 × 1 = 1
Step 3: 91 = 90 + 1
Ninety-one = ninety + one
Ninety-one = 90 + 1
90 + 1 = 91 ✓
91 = [9 tens] + [1 one]
Numeric: 91 = 90 + 1
Word: Ninety-one = ninety + one
Verified: 90 + 1 = 91 ✓
• Multi-format rule: Present solution in various formats
• Consistency rule: All formats should yield same result
• Verification rule: Check answer across all formats
Place value: The value of a digit based on its position in the number (tens, ones)
Expanded solution: A complete solution showing all steps to find the answer
Verification: Checking that the solution is correct by confirming expanded parts sum to original number
Tens: Groups of 10 (the left digit in a two-digit number)
Ones: Single units (the right digit in a two-digit number)
- Identify the problem: What number do you need to expand?
- Determine place value: Tens place (left) or ones place (right)
- Calculate value: Multiply each digit by its place value
- Express in expanded form: Add the calculated values together
- Verify solution: Check that expanded parts sum to original number
• Two-digit number AB = (A × 10) + B
• Tens value = tens digit × 10
• Ones value = ones digit × 1
• Verification: Expanded parts should sum to original number
Questions & Answers
Question: Why do I need to show all the steps when solving expanded form problems? Can't I just write the answer?
Answer: Showing all steps is very important for several reasons:
- Understanding: It helps you understand what you're doing, not just getting the answer
- Mistake catching: If you make an error, showing steps helps you find where you went wrong
- Learning: It builds good habits for solving harder problems later
- Checking: Teachers can see your thinking and help if needed
Think of it like showing your work in a recipe - it helps you learn and improves your skills!
Question: How can I help my child develop good expanded solution habits?
Answer: Here are effective strategies to help your child develop good expanded solution habits:
- Model the process: Show them how you solve problems step by step
- Create templates: Use worksheets with labeled steps to guide them
- Encourage verbalization: Have them explain each step out loud
- Practice regularly: Daily short practice sessions build habits
- Celebrate progress: Praise careful work, not just correct answers
Focus on the process, not just the final answer. Good habits developed now will help in future math learning.
Question: What should I do if I make a mistake in my expanded solution?
Answer: Making mistakes is completely normal and helpful for learning! Here's what to do:
- Don't panic: Mistakes help you learn better
- Check your work: Go back through each step carefully
- Look for patterns: Are you making the same type of mistake?
- Ask for help: Talk to your teacher or parent about the mistake
- Try again: Use what you learned to solve it correctly
Remember: The most important thing is to learn from mistakes, not avoid them!