5.4 Estimation, Calculator Discipline, and Checking Your Work
Key Takeaways
- OPM permits a calculator and scratch paper on the Occupational Math Assessment and advises preparing your testing station with both plus a pencil or pen.
- OPM's tips also recommend drawing diagrams to visualise scenarios and double-checking your work before clicking RECORD ANSWER if time permits.
- Estimating before calculating gives you an independent magnitude check that catches keying errors and misplaced decimal points.
- Because answers cannot be revised after submission, verification must happen before you click RECORD ANSWER.
- Five minutes per question is ample for a single calculation plus a check, so the dominant risk is careless submission rather than running out of time.
5.4 Estimation, Calculator Discipline, and Checking Your Work
Quick Summary: OPM's Occupational Math preparation tips are: review math concepts; prepare your testing station with all allowed materials, including scratch paper, a pencil or pen, and a calculator; use diagrams whenever possible to help visualise different scenarios; and double-check your work before clicking RECORD ANSWER if time permits. With five minutes per question, time almost always permits.
What a calculator does and does not fix
A calculator eliminates one category of error — arithmetic slips — and leaves three untouched:
| Error type | Fixed by calculator? |
|---|---|
| Arithmetic slip (7 × 8 = 54) | Yes |
| Wrong operation chosen | No |
| Wrong number keyed in | No |
| Misplaced decimal point on entry | No |
The last two are worse with a calculator than without, because a calculator displays a wrong answer with the same authority as a right one. Mental arithmetic gives you a rough feel for magnitude as you go; a keypad does not.
The defence is estimation.
Estimate first, calculate second
Before keying anything, round the numbers to something you can handle in your head and get an approximate answer. Then calculate exactly and check the two agree in magnitude.
An office spends $47.60 per week on supplies for each of 23 workstations. What is the weekly total?
- Estimate: about $50 × about 20 = about $1,000.
- Calculate: 47.60 × 23 = 1,094.80.
- Check: $1,094.80 is close to $1,000. Accept.
If the display had read 109.48 or 10,948, the estimate would have flagged it instantly. That is the entire value of the habit, and it costs about five seconds.
Rounding for estimation
- Round to one or two significant figures: 47.60 → 50, 1,455 → 1,500, 0.0725 → 0.07.
- Round in opposite directions when you can, so errors partly cancel: for 47.6 × 23, rounding one up to 50 and one down to 20 keeps the estimate honest.
- For percentages, use easy anchors. 10% is a decimal shift; 5% is half of that; 25% is a quarter; 33% is about a third.
A department's budget of $186,000 is cut by 12%. Estimate the cut.
10% of 186,000 = 18,600. Add another 2%, which is a fifth of the 10% figure, about 3,720. Estimate ≈ 22,320. Exact: 0.12 × 186,000 = 22,320. Here the estimate is exact, which is common with clean percentages.
Using scratch paper properly
OPM tells you to prepare scratch paper, and the tip about drawing diagrams is a hint about how to use it.
- Write the target first. One line at the top: what quantity, in what units.
- List givens with units. One per line.
- Show intermediate results with labels. Not a column of bare numbers — write "online = 160" rather than "160". Labelled intermediates prevent you from submitting an intermediate value as the final answer, which is a leading error pattern.
- Draw the situation when it is spatial or proportional: a rectangle for an area problem, a bar split into parts for a fraction-of-a-total problem, a simple timeline for a scheduling problem.
The verification routine
From Section 2.2: you cannot review or change answers once submitted. So verification is not optional and it cannot be deferred. Before every RECORD ANSWER click, run four checks.
1. Did I answer the asked quantity? Compare your result against the target you wrote at the top of your working. If the question asked what remains and your line says "spent", you have the wrong number.
2. Is the magnitude plausible? Compare against your estimate.
3. Are the units right? Dollars against dollars, hours against hours, a count against a count. A percentage answer expressed as 0.15 when the options are percentages should read 15%.
4. Does the selected option match my working? Read the option text again, not the letter position. Distractors are built from predictable errors — the intermediate value, the wrong-direction difference, the early-rounded figure — so an option that "looks familiar" may be familiar precisely because it is a trap.
Reverse-checking
When a check is cheap, do it.
- Division: multiply back. If 4.68 ÷ 0.4 = 11.7, then 11.7 × 0.4 should return 4.68.
- Subtraction: add back. If 18,400 − 10,590 = 7,810, then 7,810 + 10,590 should return 18,400.
- Percentage: apply in reverse. If 22,320 is 12% of the budget, then 22,320 ÷ 0.12 should return 186,000.
- Algebra: substitute the solution into the original equation (Section 7.1).
Time budgeting
A realistic allocation for a five-minute item:
| Phase | Time |
|---|---|
| Read the question and write the target | 30 seconds |
| List givens and choose the operation | 45 seconds |
| Estimate | 10 seconds |
| Calculate | 45 seconds |
| Verify against the four checks | 45 seconds |
| Total | about 3 minutes |
That leaves roughly two minutes of slack for a harder item. There is no reason to hurry, and no benefit to finishing early.
A calculator display reads 109.48 for the weekly cost of 23 workstations at $47.60 each. What does an estimate reveal?
Why does labelling intermediate results on scratch paper reduce errors on Occupational Math items?
A candidate calculates that a 12% cut to a budget is $22,320. What is the cheapest reverse check?