Five Fair-Test Designs and One $20 Budget
Mr. Iyer's fifth graders are investigating whether fertilizer affects bean plant growth. Each of five groups designs its own test. Group 1 puts one plant in a sunny window with 10 mL of fertilizer solution and one in a dark closet with 10 mL of water. Group 2 uses two plants, both in the window, one with 10 mL of fertilizer and one with 10 mL of water, but the fertilized plant is in a smaller pot. Group 3 measures plant height daily for two weeks. Group 4 measures 'how healthy it looks' on a 1–5 scale. Group 5 uses five plants per condition. The class has two weeks, a windowsill that holds about twelve pots, and $20. Mr. Iyer wants students to critique the designs, then run one class investigation and report results with an honest statement of uncertainty.
1. Evaluate each group's design. Which confounds or weaknesses must be fixed before the class runs a single investigation, and which are acceptable?
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Group 1 confounds two variables at once - light and fertilizer - so any difference could be attributed to either. This is the most serious flaw and the most teachable, because the fix is simple: hold light constant.
Group 2 has the right instinct (same location, same volume, one variable changed) but the smaller pot confounds root space and soil volume with the fertilizer treatment. Change the pot.
Group 3 is not wrong, only incomplete: measuring height daily for two weeks is a reasonable operational measure, but height alone ignores leaf number or color, and a single plant per condition gives no replication.
Group 4's 'how healthy it looks' is not a fair-test flaw, it is a measurement problem. Subjective ratings can be used if they are operationalized, for example counting yellow leaves or rating against a photographed reference scale, with two observers.
Group 5 has the strongest structure - five plants per condition gives replication and some sense of variability - but replication does not rescue a confounded design, so the physical setup still has to be fixed.
The fix list before running the class test: constant light, identical pots and soil volume, equal water volume, at least three plants per condition, and a measurement protocol that includes a quantitative and an operationalized qualitative measure.
2. The class has twelve windowsill spots and $20. Propose a class design and justify the allocation of plants and materials.
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With twelve spots and two conditions, the natural allocation is six pots per condition, but the budget and two-week window argue for a slightly different split.
Six and six uses the whole sill and gives real replication, but identical pots, soil, and fertilizer may exceed $20 if pots must be purchased. Cheaper: use saved or donated pots of the same size and spend the budget on seed, soil, and fertilizer. If only six matched pots are available, three per condition is the minimum defensible design and should be explained to students as a budget-driven compromise, not as ideal.
Seed variability is a real confounder that students often miss: different seeds germinate at different rates. If possible, start all seeds a week before the investigation and assign similar-sized seedlings to conditions, or use fast-germinating beans and randomize which seedling goes to which pot. Randomization does not remove variability, but it stops variability from lining up systematically with the treatment.
Water volume must be identical by measuring cup, not by judgment, and the fertilizer concentration must match the label so the treatment is a defined dose rather than 'some fertilizer.' The remaining money should go to a cheap ruler and masking tape for a height chart on the window frame, so measurements are taken from a fixed reference point rather than from the soil surface each time.
3. What claim can the class legitimately make after two weeks, and how should they report the uncertainty? What would make the claim stronger?
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With three to six plants per condition over two weeks, the class can claim a pattern in their own classroom conditions, not a general law about fertilizer. The honest phrasing is comparative and bounded: 'In our windowsill, with this soil, this fertilizer concentration, and this amount of light, the fertilized plants were taller on average by about X cm after fourteen days.' That is a real claim and it is defensible.
Reporting uncertainty should include the spread, not just the mean. Students should compute or at least eyeball the range or typical difference from the average for each group and see whether the ranges overlap. If the tallest unfertilized plant exceeds the shortest fertilized plant, the class should say the difference is consistent but not clean-cut. That experience - seeing overlap and still having a best estimate - is more valuable than a tidy result.
Two weeks is also short enough that germination timing can dominate height differences, which should be named as a limitation.
What would strengthen the claim: more plants, a longer growing period, repeated trials with a second batch of seeds, and a measured rather than estimated light level. A follow-up question worth asking is whether the fertilizer effect would persist at higher concentrations, which turns the result into a new testable question rather than a conclusion.