Chapter Summary and Practice

Problem
Build a complete investigation for the claim that lamp A makes bean seedlings grow three times better than lamp B.

1. 1.Define the vague phrase. Let ‘growth’ mean mean dry biomass gained after 21 days; height alone could be misleading if plants become tall and weak.
2. 2.Form a focused question: under otherwise similar conditions, how does lamp type affect mean dry biomass gained by bean seedlings in 21 days?
3. 3.Build a model: light affects photosynthesis and growth, while water, carbon dioxide, temperature, nutrients and starting condition also matter.
4. 4.State assumptions: seedlings are from the same variety, pots and soil are comparable, and lamps are positioned to provide the intended treatment.
5. 5.Make a prediction before testing: the mean biomass gain under lamp A will be approximately three times that under lamp B.
6. 6.Use groups of several seedlings. Change lamp type; measure biomass gain; keep variety, water, soil, pot size, temperature and duration similar.
7. 7.Record units, for example grams of dry biomass per plant. Compare group means and variation rather than selecting the tallest plant.
8. 8.Interpret evidence. If the ratio is near one rather than three, the advertisement’s specific claim is not supported under the tested conditions.
9. 9.State limitations: one plant variety, one distance, one duration and one growth measure do not justify claims about every indoor plant.
10. 10.Connect disciplines: biology explains growth, physics measures light, chemistry concerns nutrients and pigments, mathematics compares data, and technology concerns lamp design and energy use.

Problem
A student reports that a school bus travelled 12 km in 30 min at an average speed of 400 m/s. Diagnose the answer systematically.

1. 1.Estimate first: 12 km in half an hour should be about 24 km/h, a normal city speed—not hundreds of metres per second.
2. 2.Convert distance: 12 km = 12,000 m.
3. 3.Convert time: 30 min = 1800 s.
4. 4.Use the relationship: v = d/t = 12,000 m ÷ 1800 s ≈ 6.67 m/s.
5. 5.Convert for a second check: 6.67 m/s × 3.6 ≈ 24 km/h.
6. 6.Locate a likely error: the student mixed kilometres, minutes, metres and seconds or misplaced a factor during conversion.
7. 7.Report the corrected result with suitable precision: average speed ≈ 6.7 m/s or 24 km/h.
8. 8.Interpret the model: this is average speed for the journey and does not mean the bus moved at one constant speed throughout.

Problem
A person says, ‘My method predicts rain. If it rains, it worked; if it does not rain, invisible forces delayed the rain.’ Why is this not a useful scientific test?

1. 1.Identify the problem: every possible result is reinterpreted as success.
2. 2.No observation has been named that could challenge the claim.
3. 3.Replace the vague claim with a measurable prediction containing conditions, location and time.
4. 4.Record the prediction before the outcome occurs.
5. 5.Compare many predictions with observations using one scoring rule.
6. 6.A scientific claim must take the risk of being wrong; otherwise evidence cannot distinguish it from an invented explanation.

Problem
Question: Why did the crushed paper fall closer to the steel ball than the flat paper?

1. 1.Claim: crushing the paper reduced the effect of air resistance relative to its weight.
2. 2.Evidence: the crushed and flat paper had the same material and mass, but the crushed paper had a much smaller exposed area and fell faster.
3. 3.Reasoning: a broad flat sheet experiences greater drag from air, while the compact shape makes the gravity-only model a better approximation.
4. 4.Limitation: the result depends on shape, size, air and drop conditions; it does not mean air resistance becomes exactly zero.