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Chapter 3: Subtraction with Regrouping

When you don't have enough, exchange from the next box!

CBSE: Subtraction with/without regrouping • ICSE: Place value exchange • Cambridge: Stage 3
👨‍👩‍👧 Parent/Teacher notes at bottom

📋 What You'll Learn

  1. Part 1: Subtracting when you have enough
  2. Part 2: Subtracting when you need to exchange
  3. Part 3: Chain exchanges (many boxes need help)
  4. Practice: Predicting where you need exchange
  5. Quiz: Thinking questions

💡 The Big Idea

Step 1 of 6
🐢 No speed pressure • 🧠 Understand, don't memorize • 💬 Exchange is just renaming
✅

Part 1: No Exchange Needed

1
8,547 − 2,315
Ones: 7−5=2 ✓ Tens: 4−1=3 ✓ Hundreds: 5−3=2 ✓ Thousands: 8−2=6 ✓
All have enough. No exchange needed. Answer: 6,232
Start With
8,547
−
Take Away
2,315
Exchange Forecast:
Th
H
T
O
Enough!
Thousands
6
8−2
Hundreds
2
5−3
Tens
3
4−1
Ones
2
7−5
Answer
6,232
✨
Check each box first. If you have enough everywhere, just subtract directly!
🔄

Part 2: With Exchange

2
5,234 − 2,567
Ones: 4−7? Not enough! → Exchange 1 ten for 10 ones. Now 14−7=7 ✓
Tens: 2−6? Not enough! → Exchange 1 hundred for 10 tens. Now 12−6=6 ✓
Hundreds: 1−5? Not enough! → Exchange 1 thousand for 10 hundreds. Now 11−5=6 ✓
Thousands: 4−2=2 ✓ Answer: 2,667
TENS
3 → 2
→
ONES
4 → 14
Before
5,234
🔒
Same total!
After
5,234
🔒
Exchange never changes the total. 1 ten = 10 ones. Same value, different boxes!
🔄🔄

Part 3: Chain Exchange! — Many boxes need help

3
🎯 Many Exchanges Needed!
Let's try: 4,003 − 1,567

Ones: 3−7? Not enough! Need to exchange from tens.
But tens has 0! So first exchange from hundreds.
But hundreds has 0 too! So first exchange from thousands!

Work from left to right. Stay calm. One exchange at a time.
Exchange Forecast:
Th
H
T
O
Chain exchange!
Th
4
−1
H
0
−5
T
0
−6
O
3
−7
🔗
If one box is empty, exchange from the next bigger box first. Keep going until you have enough.
🔮

Practice: Exchange Predictor — Think before you subtract

4
0
Correct
0
Streak
5,234 − 2,567
Will the ONES box need exchange?
✅ Yes, need exchange
❌ No, have enough
➖

Practice: Subtract Numbers — Find the difference

5
0
Correct
Start
7,423
−
Take Away
3,856
🔧

Exchange Rescue — Find the mistake

6
0
Fixed
7,423 − 3,856 = ?
One of these answers is WRONG. Which one?
3,467
Answer A
3,567
Answer B
🧘

Calm Subtractor — Who solved it better?

7
6,234 − 2,567
Who got it right?
🏃
Speedy Sam
"Done in 10 seconds!"
3,777
🐢
Careful Cara
"Let me check each box..."
3,667
📝

Thinking Quiz — Check your understanding

8
0
Score
0
Total
Loading question...
👨‍👩‍👧 For Parents & Teachers
▼

🎯 What This Chapter Teaches

Exchange (often called "borrowing") happens because a place value box doesn't have enough. We avoid the word "borrow" because it implies something is taken away. Instead, we explain: exchange is just renaming. 1 ten becomes 10 ones. The total never changes.

💬 What to Say

  • "Do you have enough ones to subtract?"
  • "Can you predict which boxes will need exchange?"
  • "Did the total change after exchanging?"
  • "How would you explain exchange to a friend?"

🚫 What NOT to Say

  • "Just borrow from the tens" — This hides the WHY
  • "Do it faster" — Speed creates errors and anxiety
  • "Cross out and add 10" — Procedure without understanding

✅ Signs of Understanding

  • Predicts which boxes need exchange BEFORE calculating
  • Explains WHY exchange happens, not just HOW
  • Understands the total never changes after exchanging
  • Can find and fix errors in others' work