What This Drill Trains
Compensation Mix is a professional-level fluency check: addition and subtraction problems that reward rounding tricks rather than slow digit grinding. At this stage you should choose a friendly path quickly, compute, and adjust without losing the original question. That flexibility is what separates practiced mental calculators from people who only know one algorithm.
How to Think During the Round
Scan for near-round numbers first (x8, x9, x1, x2 away from a ten or hundred). Round, compute, adjust. If both numbers are awkward, keep one intact and move the other in tens-sized chunks. Narrate the adjustment so it cannot vanish under time pressure.
You have 90 seconds. Accuracy still outranks raw speed: one calm method repeated well beats a streak of guesses. After the timer ends, notice which problems felt sticky — that short review is where real improvement happens.
Worked Examples
Study these before you press Start. Try to recreate the thinking without looking at the answer first.
198 + 47
Thinking: 200 + 47 = 247; subtract the extra 2 → 245.
Answer: 245
305 − 98
Thinking: 305 − 100 = 205; add back 2 → 207.
Answer: 207
76 + 89
Thinking: 76 + 90 = 166; subtract 1 → 165.
Answer: 165
Common Mistakes
- Rounding both numbers and then adjusting only once.
- Losing the sign of the compensation on subtraction problems.
- Spending longer choosing a trick than it would take to decompose normally.
Practice Tips
- If a problem is already friendly, skip compensation — simple is allowed.
- Practice naming the rounded problem in one breath before calculating.
- Review the compensation technique lesson when adjustments feel inconsistent.
Suggested Session Plan
- Read the method section once if this skill is new.
- Cover the answers and re-solve the three worked examples aloud.
- Start the timed round and stick to one strategy.
- Replay once, then write down any fact or pattern you missed.
- If the same error repeats, open the full lesson for more examples and a practice set with an answer key.
Full explanation, extra worked examples, and practice problems for this skill: open the related stage lesson .
Prefer a structured curriculum instead of random drills? Browse all learning stages or read the complete mental arithmetic guide . More timed drills live on the games hub.