Case math does not improve by rereading a cheat sheet. It improves when you time a set, write the miss, and rerun the same miss tomorrow. This page owns the practice loop. Tricks live on shortcuts. Formulas with units live on the formulas page.
The grade in the room is: equation out loud, units attached, a number inside 10%, a so-what. Practice those four, not “being good at math.”
A weekly loop that actually moves the needle
| Day | Minutes | What you do |
|---|---|---|
| Mon / Wed / Fri | 12 | Timed set: 8–10 items, no calculator, answers hidden |
| After each set | 5 | Error log: type of miss, not “I was sloppy” |
| Tue / Thu | 8 | Re-drill only the miss types from the log |
| Sat | 25 | One full case; pause only to write the equation |
Miss types worth tagging: wrong base, unit skip (days vs years), percent of a percent, forgot (1 − utilization), dropped 000s, rounded twice the same way. If you cannot name the type, you will repeat it.
Do not mix this with learning a new framework in the same hour. Math automaticity and structure are different muscles.
Worked practice item: PE portco kiln
Use this as a single timed item (90 seconds to equation, 90 seconds to number, 30 seconds to so-what). Then check.
Facts. Harbor Partners owns Ridge Kiln. Nameplate 2,400 tonnes clinker / day. Planned run days 330 / year. Last year actual uptime 91% of planned days (the rest is unplanned stops). Energy $38 / tonne. A new contractor promises 96% uptime for +$1.2m / year. Clinker contribution excluding energy is $41 / tonne. Energy is extra. Harbor asks: is the contractor worth it?
Equation (say it). Annual tonnes = 2,400 t/day × 330 day/year × uptime. Extra tonnes = Δuptime × that planned block. Extra contribution = extra tonnes × (41 − 38) = extra tonnes × $3 / t. Compare to $1.2m.
Math. Planned block = 2,400 × 330 = 792,000 t. At 91%: 792,000 × 0.91. 792 × 0.9 = 712.8; 792 × 0.01 = 7.92; total 720kt (720,720 t). At 96%: 792,000 × 0.96 = 760kt (760,320 t). Delta ≈ 39.6kt.
Contribution on the delta: 39,600 × $3 = $119k. Contractor costs $1.2m. The contractor destroys ~$1.08m.
So-what. Do not buy 5 points of uptime at that price when energy leaves only $3/t on the table. Either cut energy (the real lever) or negotiate the contractor below ~$100k. A candidate who computed tonnes and forgot contribution minus energy would have said 39.6kt × $41 = $1.6m and wrongly hired the contractor.
That last sentence is why practice must include the so-what, not only the multiply.
How to write an error log that works
One line per miss:
2026-08-12 | kiln | used 365 days not 330 | unit / calendar | drill: capacity × days × util
The third column is the behavior. “I panicked” is not a behavior. “I used 365 when the prompt said 330” is.
Once a week, tally tags. If “wrong base” is 40% of misses, spend Thursday only on “percent of what.” The quick math drill is built for that isolation. Do not “do more mixed cases” until the tag shrinks.
When this practice method is the wrong tool
The night before a live round. Cramming 40 mixed problems raises anxiety and does not rewire a miss type. Sleep. Do eight items in your weakest tag.
When the leak is structure, not arithmetic. If you freeze before the equation exists, you need structure, not more division.
When you already compute fast and skip the so-what. Then practice interpretation: take a finished number and write the recommendation in one sentence. Arithmetic sets will make that worse by rewarding speed alone.
The mistake that is unique to “practicing math”
Only checking the answer key’s final integer. You can land on 720kt with the right tonnes and still have used the wrong contribution. Grade the equation in the log. If the equation was wrong and the number luckily matched, log a miss.
The other unique fail is practicing on a calculator and expecting the room to feel the same. The room is pen, rounding, and an interviewer asking “what if uptime is 88%.” Build that question into every set: after you finish, shock one input by 10% and resay the verdict.
A 10-item set you can copy
Write answers on paper. Then grade.
- 15% of 8.4m
- 240 × 365 (then 240 × 330)
- $48 × 12,400
- 490,000 / 340
- 1.8% × 12 versus “compound, direction only”
- Margin if profit $14m on $210m revenue
- CAGR: 80 → 120 in 4 years (approx)
- 2,400 × 330 × 0.91
- Payback: $2.4m / $0.9m
- 86% occupancy × 420 beds × 365 / 4.2 day stay (admissions order of magnitude)
Items 8–10 are the ones that leak units. That is the point.
Time the set, log the miss type
Run a quick-math session the same way you will in the room: equation, units, so-what.