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Progress Pack Answer Keys

Course: Abacus for Children — Levels 2–3

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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

Pages 1-4 (60 problems). Key technique: when lower beads are full, use the 5-complement swap.

#	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

Pages 1-4 (60 problems). Key technique: when ones rod overflows, carry to tens and remove 10-complement.

#	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

Subtraction (Page 3)

#	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

Speed Drill (Page 4)

46. 9+6=1547. 11-7=448. 8+5=1349. 14-9=550. 7+7=1451. 13-8=552. 6+8=1453. 12-6=654. 9+9=1855. 15-7=856. 8+8=1657. 11-5=658. 7+6=1359. 16-9=760. 6+9=15

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

1.17+5= 22(carry: Y)

2.28+4= 32(carry: Y)

3.19+3= 22(carry: Y)

4.36+7= 43(carry: Y)

5.45+8= 53(carry: Y)

6.24+9= 33(carry: Y)

7.33+8= 41(carry: Y)

8.16+6= 22(carry: Y)

9.47+5= 52(carry: Y)

10.29+7= 36(carry: Y)

Page 2: 2-digit + 2-digit

11.15+17= 32

12.23+18= 41

13.34+27= 61

14.46+15= 61

15.28+34= 62

16.37+25= 62

17.19+23= 42

18.44+18= 62

19.26+36= 62

20.38+24= 62

Page 3: Subtraction with borrow

21.21-7= 14(borrow: Y)

22.32-8= 24(borrow: Y)

23.40-6= 34(borrow: Y)

24.53-9= 44(borrow: Y)

25.25-17= 8(borrow: Y)

26.34-16= 18(borrow: Y)

27.41-23= 18(borrow: Y)

28.50-28= 22(borrow: Y)

29.63-37= 26(borrow: Y)

30.72-45= 27(borrow: Y)

Page 4: 3-digit cascading

31.105+97= 202

32.213+89= 302

33.150-63= 87

34.247+56= 303

35.300-127= 173

36.198+45= 243

37.256-79= 177

38.189+123= 312

39.400-213= 187

40.315+97= 412

Error Checking — Answers

20 problems. “Correct” means the student's work had no error.

#	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.

பயிற்சி நிரந்தரத்தை ஏற்படுத்துகிறது.

Practice creates permanence.

Part of these learning packs

Abacus Progress Pack

16 printable pages for Levels 2–3 — complement rules, carry/borrow operations, and error-checking templates with parent answer keys

Every page has an answer key explaining which rule applies and why. Check work confidently.

These packs include this resource alongside other printables, tools, and study guides — curated for a specific goal. View all packs →

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