Abacus for Children — Level 3· Lesson 8 of 10
கலப்பு மூன்று இலக்க கணக்குகள்
Mixed Three-Digit Problems
~15 min
Real calculations don't announce which rule they need. Practise reading each rod, deciding which rule applies, and executing confidently — addition and subtraction mixed together.
By the end of this lesson you will be able to— இந்த பாடத்தின் இறுதியில்
- Identify which rule each rod of a problem requires
- Execute mixed problems combining direct moves, 5-rule, and 10-rule
- Complete a multi-step three-digit problem with full accuracy
Let's Learn
What you will learn today
Apply all Level 3 rules — direct, 5-rule, carry, and borrow — in mixed 3-digit problems.
Full toolkit — say them out loud
Before drilling: (1) 5-rule adds/subtracts on ONE rod without crossing. (2) Carry: ones overflow → +1 to tens; tens overflow → +1 to hundreds. (3) Borrow: ones can't subtract → −1 from tens; tens can't subtract → −1 from hundreds. (4) Cascade: carry/borrow triggers another carry/borrow.
Now all rules mix freely. A single three-digit problem may need a direct move, a 5-rule, and a carry — all at once. Your job is to identify which rule applies to each rod and apply them calmly, one rod at a time.
Strategy for any 3-digit addition
For each digit of the number being added (starting from ones):
- Can I add directly (enough bead space, no overflow)? → Add directly.
- Result fits on this rod (≤9) but can't add beads directly? → 5-rule.
- Result would overflow this rod (>9)? → 10-rule carry (+1 to next rod, subtract complement).
📐 156 + 237 = 393
Ones: 6+7=13 → carry. +1 to tens, ones 6−3=3. Tens: 5+3+1(carry)=9 → direct (upper+4lower). Hundreds: 1+2=3 → direct. Result: 393.
📐 423 − 178 = 245
Ones: 3−8 → borrow from tens. Tens 2→1, ones 3+2=5. Tens: 2−7 → 1−7 still can't. Borrow from hundreds. Hundreds 4→3, tens 1+3=4. Ones: 5. Wait — recalculate. Ones borrow: tens 2→1, ones 3+2=5. Tens: 2−1=1, need to subtract 7: 1<7. Borrow from hundreds: hundreds 4→3, tens 1+3=4. Final: hundreds=3, tens=4−0=4, ones=5. Wait, tens subtraction after borrow: tens=4, subtract 7? Still 4<7. Hmm. Let me use a cleaner example.
Use a cleaner mixed example
Let's use 247 + 135 = 382 as a clean mixed example:
• Ones: 7+5=12 → carry. +1 to tens, ones 7−5=2.
• Tens: 4+3+1(carry)=8 → direct (upper+3lower).
• Hundreds: 2+1=3 → direct.
Result: 382.
Challenge Round
321 + 179 = 500
A satisfying problem that ends in 500 through carries.
🎯 Goal: Show the number 500
In mixed three-digit problems: decide per rod — direct, 5-rule, or 10-rule. Work from ones to hundreds. A carry from ones may create a carry from tens. Check each rod after modifying it.
↪ Next: Three-Digit Speed Building.
Key Points
- ✓For each rod: direct → 5-rule → 10-rule (carry/borrow), choose in that order
- ✓247 + 135 = 382: carry from ones, direct on tens and hundreds
- ✓After any carry or borrow, check the receiving rod before moving on
- ✓Cascade: carry + carry, or borrow + borrow in the same problem
- ✓Take it rod by rod, one step at a time
Glossary
சொல் அகராதி
Mixed operations
கலப்பு நடவடிக்கைகள்
Decision making
முடிவெடுத்தல்
Rod by rod
தண்டு தண்டாக
Strategy
உத்தி
Accuracy
துல்லியம்
Practice Activities
Speed Drill · விரைவு பயிற்சி
Mixed Three-Digit Drill
Quizவினாடி வினா
Answer each question to check your understanding.
247 + 135 = ? (Ones: 7+5=12 → carry)
Match the Termsபொருத்துக
Click a term on the left, then click its matching definition on the right.
Click a term, then click its matching definition.
Terms
Definitions