Checking a conclusion means comparing your number with what the situation allows: units, size and limits. It takes about ten seconds and catches a large share of avoidable errors.
It is the last skill in three-science numerical fluency and works with units, rates, gradients and measurement limits. All data is invented.
What are the three questions?
- Unit: does the unit match what was asked (a rate, a total, a percentage)?
- Size: is the number in a believable range for this situation?
- Limit: does it break a rule, such as more than 100% or a negative count?
Keep a few anchor values in mind: a person walks at about 1.5 m/s, a jog is about 3 to 4 m/s, and a percentage of a whole is between 0 and 100.
Worked example (invented data)
A runner covers 1.2 km in 5 min. A student calculates the speed as 1200 ÷ 5 = 240 m/s. Find the error and the correct speed.
Step 1, size check: 240 m/s is far beyond anything a runner can do, so something is wrong.
Step 2, find the cause: 1200 m was divided by 5 minutes, not seconds. The units were mixed, so the answer is neither m/s nor m/min.
Step 3, correct: 5 min = 300 s, and 1200 ÷ 300 = 4 m/s.
Step 4, recheck: 4 m/s is a brisk jog, which fits. ✓
The mistake to watch for
Mistaken answer: “Percentage yield = 6.4 ÷ 5.0 × 100 = 128%, so the reaction made more than expected.”
The student reported the number without questioning it.
Yield above 100% breaks the limit that a reaction cannot give more product than the theoretical maximum (5.0 g here). The correction is to recheck the data for an error, such as a transposed digit, before writing a conclusion. If the invented data really says 6.4 g, the sensible comment is that the sample may not be dry or pure.
Check yourself
Try these without a calculator, then open each answer.
1. A student states that a 70 kg person has a weight of 70 N. Using g = 10 N/kg, find the weight and say whether 70 N is plausible.
Show answer
Weight = 70 × 10 = 700 N. A value of 70 N is far too small for a person, so it is not plausible. The student used mass as weight.
2. A count shows 15 of 60 cells in a stage of division. A student writes 250%. Give the correct percentage.
Show answer
15 ÷ 60 × 100 = 25%. The student inverted the fraction, giving a percentage above 100% for a part of a whole.
3. A heater supplies 8400 J to 200 g of water (specific heat capacity 4.2 J/(g °C)). Find the temperature rise and decide whether it is sensible.
Show answer
ΔT = 8400 ÷ (200 × 4.2) = 8400 ÷ 840 = 10 °C. A 10 °C rise for this energy is sensible.
Where this leads next
Put all five skills together in the numerical fluency practice set. Keep your slips in the mistake log and retest queue so that each type of error gets a fresh question later.
When a sense-check is the only thing between you and full marks, a short run of one-to-one sessions can make it automatic. See online one-to-one Co-ordinated Sciences tuition.