Khan Academy approach: Multi-step subtraction word problem requiring students to identify the initial amount and calculate the total amount taken away before subtracting.
- Read the problem carefully
- Identify the starting amount (initial books)
- Calculate the total amount taken away (books borrowed)
- Subtract the total taken from the starting amount
- Check your answer
Initial books: 247
Borrowed on Monday: 89 books
Borrowed on Tuesday: 45 books
89 + 45 = 134 books borrowed total
247 - 134 = ?
| Hundreds | Tens | Ones |
|---|---|---|
| 2 | 4 | 7 |
| - 1 | - 3 | - 4 |
7 - 4 = 3 ones
4 - 3 = 1 ten
2 - 1 = 1 hundred
There are 113 books left in the library.
Always break multi-step problems into smaller parts. First, add all the amounts being subtracted, then subtract from the total.
Khan Academy approach: Sequential subtraction problem where students must subtract amounts one at a time or combine them first.
Fruit stand started with 350 apples
Wednesday: 127 apples, Thursday: 86 apples
Total sold: 127 + 86 = 213 apples
350 - 213 = ?
| Hundreds | Tens | Ones |
|---|---|---|
| 3 | 5 | 0 |
| - 2 | - 1 | - 3 |
We cannot subtract 3 from 0, so we borrow from tens place
5 tens becomes 4 tens, 0 ones becomes 10 ones
10 - 3 = 7 ones
4 - 1 = 3 tens
3 - 2 = 1 hundred
The fruit stand has 137 apples now.
When subtracting and you encounter a smaller number on top, always borrow from the next higher place value. This is called regrouping.
Khan Academy approach: Mixed operations problem involving subtraction followed by addition, demonstrating the importance of following the sequence of events.
Dealership started with 425 cars
January: 158 cars, February: 97 cars
Total sold: 158 + 97 = 255 cars
425 - 255 = 170 cars remaining
| Hundreds | Tens | Ones |
|---|---|---|
| 4 | 2 | 5 |
| - 2 | - 5 | - 5 |
Since 5<5 in ones place and 2<5 in tens place, we need to borrow from hundreds: 425 becomes 3 hundreds, 12 tens, 5 ones, then 3 hundreds, 11 tens, 15 ones
15-5=10, 11-5=6, 3-2=1 → 160+10=170
170 + 65 = 235 cars
The dealership has 235 cars now.
For problems with multiple operations, solve them in the order the events occurred. Follow the sequence: sold cars (subtract), then received cars (add).
Subtraction: Taking away one number from another to find the difference.
Minuend: The number being subtracted from (larger number).
Subtrahend: The number being subtracted (smaller number).
Difference: The result of the subtraction operation.
Word Problem: A math question written in sentences that tells a story.
Regrouping/Borrowing: Taking from a higher place value when the top digit is smaller than the bottom digit.
Multi-step Problem: A problem requiring multiple operations to reach the solution.
Place Value: The value of a digit based on its position (ones, tens, hundreds, etc.).
Khan Academy Method: Systematic approach emphasizing understanding, visualization, and step-by-step problem solving.
Subtraction Rule: Minuend - Subtrahend = Difference
Order Matters: We always subtract the smaller number from the larger number.
Checking Rule: Difference + Subtrahend = Minuend (always verify your answer).
Borrowing Rule: When the top digit is smaller than the bottom digit, borrow 1 from the next place value.
Zero Rule: Any number minus zero equals itself (e.g., 500 - 0 = 500).
Same Number Rule: Any number minus itself equals zero (e.g., 375 - 375 = 0).
Commutative Property: Subtraction is NOT commutative (a - b ≠ b - a).
Khan Academy Principle: Break complex problems into smaller, manageable steps.
- Read Carefully: Read the whole problem slowly and understand what's happening
- Identify Information: Find the starting amount and what is being taken away
- Determine Operations: Look for clue words that indicate which operations are needed
- Organize Data: For multi-step problems, identify all amounts being subtracted
- Align Place Values: Write numbers vertically with proper alignment
- Subtract Right to Left: Start with the ones place and work left
- Regroup if Needed: If top digit is smaller, borrow from next place value
- Check: Add your answer to the subtrahend to verify you get the minuend
- Answer Question: Make sure your answer matches what the problem asked
Simple Subtraction: 45 - 12 = 33 (no regrouping needed)
With Regrouping: 62 - 28 = 34 (regroup ones place)
Multi-step: Started with 100, spent 25, then 15 → 100-(25+15)=60
Mixed Operations: Had 50, spent 12, earned 8 → 50-12+8=46
Word Clues: "left," "remain," "how many more," "difference," "take away," "give," "sell," "away," "lose," "used," "cost," "available," "unsold," "remaining"
Count Backwards: Start with the bigger number and count backwards by the smaller number.
Use Place Value Charts: Boxes for hundreds, tens, and ones to organize the numbers.
Check with Addition: Always add your answer to the number you took away to verify.
Look for Keywords: Words like "left," "remaining," "less," "fewer" mean subtraction.
Borrowing Reminder: When borrowing, decrease the top digit in the next place value by 1.
Multi-step Strategy: Add all the amounts being subtracted first, then subtract from the total.
Estimation: Round numbers to estimate the answer and check reasonableness.
Khan Academy Approach: Visualize the problem with drawings or models when stuck.
Wrong Order: Subtracting the big number from the small number (e.g., 28 - 62 instead of 62 - 28).
Missing Keywords: Not recognizing words that indicate subtraction is needed.
Forgetting to Borrow: Not borrowing when the top digit is smaller than the bottom digit.
Mistake in Borrowing: Forgetting to decrease the top digit in the next place value.
Not Checking: Forgetting to verify the answer makes sense in the context.
Ignoring Context: Getting the math right but not answering the question asked.
Place Value Errors: Misaligning digits when setting up the problem.
Multi-step Confusion: Performing operations in the wrong order.
Formula to Remember: Total - Taken Away = What's Left
Always Bigger - Smaller: Subtract the smaller number from the bigger number.
Check Your Work: Difference + Subtrahend = Minuend
Keywords List: left, remain, fewer, less, take away, give, sell, cost, spend, lose, away, used, available, unsold, remaining
Borrowing Rule: When top number is smaller than bottom, borrow 1 from next place value.
Khan Academy Method: Break complex problems into smaller, sequential steps.
Fact Families: Know that 62 - 28 = 34 means 34 + 28 = 62.
Level 1: Subtract with pictures and objects (concrete)
Level 2: Subtract using number lines (visual)
Level 3: Single-digit mental subtraction (abstract)
Level 4: Two-digit subtraction without borrowing
Level 5: Two-digit subtraction with borrowing
Level 6: Three-digit subtraction with borrowing
Level 7: Multi-step word problems
Level 8: Mixed operations problems
Level 9: Four-digit subtraction with regrouping
Level 10: Decimal subtraction
Common Core: CCSS.MATH.CONTENT.2.OA.A.1 - Use addition and subtraction within 100 to solve one- and two-step word problems.
Operations: Fluently add and subtract within 100 using strategies based on place value.
Problem Types: Result unknown, change unknown, start unknown scenarios.
Strategies: Mental math, place value decomposition, properties of operations.
Relating Operations: Understanding that subtraction is the inverse of addition.
Khan Academy Approach: Emphasis on conceptual understanding, visualization, and real-world applications.
Self-Paced Learning: Mastery-based progression allowing students to advance when ready.
Minuend: The number being subtracted from (larger number)
Subtrahend: The number being subtracted (smaller number)
Difference: The result of the subtraction operation
Word problem: A mathematical problem expressed in ordinary language
Borrowing/Regrouping: Taking 1 from a higher place value when the top digit is smaller
- Read the problem: Understand the context and what is being asked
- Identify numbers: Find the starting amount and amount being taken away
- Choose operation: Determine if subtraction is needed
- Align place values: Write numbers vertically with proper alignment
- Solve: Perform the subtraction calculation (borrow if needed)
- Check: Verify the answer makes sense in the context
• Subtraction finds the difference between two numbers
• The minuend is always greater than or equal to the subtrahend
• Word problems require careful reading to identify operations
• Checking: Difference + Subtrahend = Minuend
• Key words indicating subtraction: left, fewer, less, take away, remain, away, lost, gave, used, sold, cost, available, remaining
• When borrowing: 1 ten = 10 ones, 1 hundred = 10 tens
• Khan Academy approach: Visualize, break down, and check your work
Khan Academy emphasizes mastery learning, where students progress only after demonstrating understanding. This approach ensures solid foundations before advancing to more complex concepts.
Questions & Answers
Question: How do I know when a word problem needs subtraction instead of addition?
Answer: Look for these clue words that signal subtraction:
- Words like "left," "remaining," "how many are left," "how many more to go"
- "Gave away," "ate," "used," "spent," "lost," "took away"
- Questions asking "How many didn't..." or "How many are still..."
For example: "Sam had 10 balloons, he gave 3 to his friend. How many does he have left?" The word "left" signals subtraction.
Addition usually has words like "total," "altogether," "more," "added," "combined," "in all."
Question: My child is struggling with Khan Academy subtraction word problems. Any tips?
Answer: Khan Academy's approach emphasizes understanding over memorization. Here are effective strategies:
- Visualize: Encourage your child to draw pictures or use objects to represent the problem
- Break it down: Help them identify each piece of information in the problem separately
- Practice regularly: Consistency is key - even 10-15 minutes daily helps
- Watch videos: Khan Academy videos provide excellent step-by-step explanations
- Work backwards: After solving, check if the answer makes sense in the context
- Use hints: Don't hesitate to use Khan Academy's hint system when stuck
Remember, Khan Academy focuses on mastery, so it's better to fully understand one concept before moving to the next.
Question: I sometimes get confused about which number to subtract from which. How can I remember?
Answer: Think of it this way:
- Start with the BIGGER number: This is what you have at first
- Then subtract the SMALLER number: This is what gets taken away
- Remember: We always take away from what we already have
- Check: Your answer should be smaller than the number you started with
- Khan Method: Draw a picture showing the starting amount and cross out what's taken away
Example: "I had 8 cookies and ate 3. How many left?"
Start with: 8 (bigger), Take away: 3 (smaller), So: 8 - 3 = 5. Check: 5 is smaller than 8 ✓