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Progress Pack Answer Keys
Progress Pack Answer Keys
Course: Abacus for Children — Levels 2–3
Complete answer keys for all Progress Pack drills with technique explanations and scoring guide.
Abacus Progress Pack — Complete Answer Keys
Answers, techniques, and common error patterns for all four drill types. Use this for marking and for understanding how each problem should be solved.
5-Complement Drills — Answers
| # | Problem | Answer | Technique |
|---|---|---|---|
| 1 | 4 + 1 | 5 | Direct add |
| 2 | 3 + 2 | 5 | Direct add |
| 3 | 3 + 3 | 6 | 5-rule: +5, -2 |
| 4 | 4 + 2 | 6 | 5-rule: +5, -3 |
| 5 | 4 + 3 | 7 | 5-rule: +5, -2 |
| 6 | 4 + 4 | 8 | 5-rule: +5, -1 |
| 7 | 3 + 4 | 7 | 5-rule: +5, -1 |
| 8 | 2 + 3 | 5 | Direct (reaches 5) |
| 9 | 2 + 4 | 6 | 5-rule: +5, -1 |
| 10 | 1 + 4 | 5 | Direct (reaches 5) |
| 11 | 1 + 3 | 4 | Direct add |
| 12 | 3 + 1 | 4 | Direct add |
| 13 | 2 + 2 | 4 | Direct add |
| 14 | 4 + 1 | 5 | Direct (reaches 5) |
| 15 | 1 + 2 | 3 | Direct add |
| 16 | 5 - 1 | 4 | 5-rule: -5, +4 |
| 17 | 5 - 2 | 3 | 5-rule: -5, +3 |
| 18 | 5 - 3 | 2 | 5-rule: -5, +2 |
| 19 | 5 - 4 | 1 | 5-rule: -5, +1 |
| 20 | 6 - 1 | 5 | Direct remove |
| 21 | 6 - 2 | 4 | 5-rule: -5, +3 |
| 22 | 6 - 3 | 3 | 5-rule: -5, +2 |
| 23 | 7 - 2 | 5 | Direct remove |
| 24 | 7 - 3 | 4 | 5-rule: -5, +2 |
| 25 | 7 - 4 | 3 | 5-rule: -5, +1 |
| 26 | 8 - 3 | 5 | Direct remove |
| 27 | 8 - 4 | 4 | 5-rule: -5, +1 |
| 28 | 9 - 4 | 5 | Direct remove |
| 29 | 6 - 4 | 2 | 5-rule: -5, +1 |
| 30 | 9 - 1 | 8 | Direct remove |
Common Error Patterns (5-Complement)
- Removing the number being added instead of the 5-complement
- Trying direct add when only 5-rule works (e.g., 4+2 by pushing 2 more)
- In subtraction: adding wrong complement (e.g., 5-comp of 3 is 2, not 3)
10-Complement Drills — Answers
| # | Problem | Answer | Technique |
|---|---|---|---|
| 1 | 9 + 1 | 10 | Direct (carry to tens) |
| 2 | 9 + 2 | 11 | 10-rule: +10, -8 |
| 3 | 9 + 3 | 12 | 10-rule: +10, -7 |
| 4 | 9 + 4 | 13 | 10-rule: +10, -6 |
| 5 | 9 + 5 | 14 | 10-rule: +10, -5 |
| 6 | 9 + 6 | 15 | 10-rule: +10, -4 |
| 7 | 9 + 7 | 16 | 10-rule: +10, -3 |
| 8 | 9 + 8 | 17 | 10-rule: +10, -2 |
| 9 | 9 + 9 | 18 | 10-rule: +10, -1 |
| 10 | 8 + 2 | 10 | Direct (carry to tens) |
| 11 | 8 + 3 | 11 | 10-rule: +10, -7 |
| 12 | 8 + 4 | 12 | 10-rule: +10, -6 |
| 13 | 8 + 5 | 13 | 10-rule: +10, -5 |
| 14 | 8 + 6 | 14 | 10-rule: +10, -4 |
| 15 | 8 + 7 | 15 | 10-rule: +10, -3 |
| 16 | 7 + 3 | 10 | Direct (carry to tens) |
| 17 | 7 + 4 | 11 | 10-rule: +10, -6 |
| 18 | 7 + 5 | 12 | 10-rule: +10, -5 |
| 19 | 7 + 6 | 13 | 10-rule: +10, -4 |
| 20 | 7 + 7 | 14 | 10-rule: +10, -3 |
| 21 | 7 + 8 | 15 | 10-rule: +10, -2 |
| 22 | 7 + 9 | 16 | 10-rule: +10, -1 |
| 23 | 6 + 4 | 10 | Direct (carry to tens) |
| 24 | 6 + 5 | 11 | 10-rule: +10, -5 |
| 25 | 6 + 6 | 12 | 10-rule: +10, -4 |
| 26 | 6 + 7 | 13 | 10-rule: +10, -3 |
| 27 | 6 + 8 | 14 | 10-rule: +10, -2 |
| 28 | 6 + 9 | 15 | 10-rule: +10, -1 |
| 29 | 5 + 5 | 10 | Direct (carry to tens) |
| 30 | 5 + 6 | 11 | 10-rule: +10, -4 |
| # | Problem | Answer | Technique |
|---|---|---|---|
| 31 | 11 - 9 | 2 | 10-rule: -10, +1 |
| 32 | 11 - 8 | 3 | 10-rule: -10, +2 |
| 33 | 11 - 7 | 4 | 10-rule: -10, +3 |
| 34 | 11 - 6 | 5 | 10-rule: -10, +4 |
| 35 | 12 - 9 | 3 | 10-rule: -10, +1 |
| 36 | 12 - 8 | 4 | 10-rule: -10, +2 |
| 37 | 12 - 7 | 5 | 10-rule: -10, +3 |
| 38 | 13 - 9 | 4 | 10-rule: -10, +1 |
| 39 | 13 - 8 | 5 | 10-rule: -10, +2 |
| 40 | 13 - 7 | 6 | 10-rule: -10, +3 |
| 41 | 14 - 9 | 5 | 10-rule: -10, +1 |
| 42 | 14 - 8 | 6 | 10-rule: -10, +2 |
| 43 | 15 - 9 | 6 | 10-rule: -10, +1 |
| 44 | 15 - 8 | 7 | 10-rule: -10, +2 |
| 45 | 16 - 9 | 7 | 10-rule: -10, +1 |
Common Error Patterns (10-Complement)
- Removing the addend instead of the 10-complement (e.g., for 9+4, removing 4 instead of 6)
- Forgetting to carry to the tens rod after the ones rod swap
- In subtraction: adding the subtrahend instead of its 10-complement
Carry/Borrow Operations — Answers
Page 1: 2-digit + 1-digit
Page 2: 2-digit + 2-digit
Page 3: Subtraction with borrow
Page 4: 3-digit cascading
Error Checking — Answers
| # | Error? | Correct Ans | Rule Violated |
|---|---|---|---|
| 1 | YES* | 6 | Wrong method (direct instead of 5-rule), but answer is coincidentally correct |
| 2 | YES | 7 | Wrong 5-complement: removed 3 instead of 2 |
| 3 | YES | 8 | Wrong 5-complement: removed 2 instead of 1 |
| 4 | YES* | 3 | Wrong method (direct remove impossible), but answer is coincidentally correct |
| 5 | YES | 4 | Wrong 5-complement: added 2 instead of 1 |
| 6 | YES | 13 | Removed addend (4) instead of 10-complement (6) |
| 7 | YES | 15 | Removed addend (7) instead of 10-complement (3) |
| 8 | YES | 13 | Removed addend (6) instead of 10-complement (4) |
| 9 | NO | 4 | No error |
| 10 | YES | 6 | Added subtrahend (8) instead of 10-complement (2) |
| 11 | NO | 43 | No error |
| 12 | YES | 83 | Forgot to add carry to tens column |
| 13 | NO | 25 | No error |
| 14 | YES | 27 | Used original tens (6) instead of borrowed tens (5) |
| 15 | YES | 202 | Forgot cascaded carry to hundreds |
| 16 | YES* | 11 | Used 5-rule when 10-rule was needed (answer happens to be correct) |
| 17 | NO | 243 | No error |
| 18 | NO | 114 | No error |
| 19 | YES | 122 | Carry from ones to tens was calculated but not applied in final tens total |
| 20 | NO | 146 | No error |
* Problems marked YES* have correct final answers but incorrect methods. Award half credit if the child identifies the wrong method even though the answer matched.
Scoring Guide
| Drill Type | Excellent | Good | Needs Work |
|---|---|---|---|
| 5-Complement (60) | 54+ | 42-53 | Below 42 |
| 10-Complement (60) | 54+ | 42-53 | Below 42 |
| Carry/Borrow (40) | 36+ | 28-35 | Below 28 |
| Error Checking (20) | 18+ | 14-17 | Below 14 |
If scores are “Excellent” across all drills
Your child has mastered complement rules and carry/borrow mechanics. They are ready for Abacus Level 3 (mixed operations, 3+ digit mental calculation). Print the drills once more in 2 weeks as a retention check.
If scores are “Good”
Print one fresh copy of the drill(s) in the “Good” range and repeat in 3-4 days. Focus specifically on the pages where errors occurred. One more round usually pushes scores to Excellent.
If scores are “Needs Work”
Go back to the corresponding Abacus Level 2 lesson and work through the guided teaching together. Then redo the drill starting from Page 1. Do not skip ahead — the pages are scaffolded for a reason.
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Practice creates permanence.
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