Words to know
independent variable
The factor the investigator deliberately changes (e.g. fertilizer concentration).
dependent variable
The factor that is measured to see the effect (e.g. plant height or dry mass).
controlled variables
Factors kept the same for all groups so that only the independent variable differs.
control group
A group that does not get the treatment (or gets a standard one), used for comparison.
replicate
A repeat of a treatment (more plants or more trials) to make results more reliable.
operational definition
A precise statement of how a variable will be measured, e.g. "height from soil surface to the tip of the tallest leaf, in cm".
outlier
A data value that is very different from the others, often caused by an error or unusual event.
random error / systematic error
Random error varies unpredictably between measurements; systematic error shifts all measurements in the same direction.
From "I wonder" to evidence
You've now met many factors that affect plant growth: light, water, nutrients, temperature, soil, hormones. Knowing that they matter is a start. Scientists ask how much they matter, and they find out with carefully designed investigations. In this lesson you'll learn to design a fair, reliable plant growth inquiry, the way the curriculum asks you to, and then carry one out at home over about three weeks.
Remember from Grades 9 and 10
You have used the words hypothesis, independent variable, dependent variable and controlled variables before, and drawn line and bar graphs. Grade 11 adds more care: operational definitions, replicates, outliers, error analysis and significant figures.
Step 1: a testable question
A good question names one factor to change and one thing to measure:
- Weak: "How does fertilizer affect plants?" (Which fertilizer? Which effect?)
- Strong: "How does the concentration of an all-purpose fertilizer (0, 1, 2 and 4 g/L) affect the height of radish seedlings after 21 days?"
Other good factors from the curriculum: nutrient quantity, light quantity (distance from a lamp, hours per day) or quality (coloured filters), temperature, and water retention or percolation (soil type, watering amount).
Step 2: a hypothesis with a reason
Use "If ..., then ..., because ...": If the fertilizer concentration increases, then the seedlings will grow taller, up to a point, because more nitrogen is available for proteins and chlorophyll; but at the highest concentration growth will decrease, because salty soil water makes it harder for roots to absorb water. A hypothesis must be testable and based on science you know.
Step 3: plan the variables
- Independent variable: fertilizer concentration (0, 1, 2, 4 g/L).
- Dependent variable, with an operational definition: height from the soil surface to the tip of the tallest leaf, measured with a ruler to the nearest 0.1 cm on day 21. (Even better: dry mass, which measures all growth, but it destroys the plants.)
- Controlled variables: seed variety and batch, pot size, type and amount of soil, volume and timing of watering, light (same window or lamp), temperature, planting depth, number of seeds.
- Control group: 0 g/L (plain water), for comparison.
- Replicates: at least 5 plants per group, so one unusual plant can't decide the result. Randomly assign pots to positions, and rotate them, so no group always gets the best spot.
Step 4: carry it out safely and record carefully
Write a numbered procedure someone else could follow. Label everything. Record raw data in a table as you go, with units in the headings. Note anything unusual (a broken stem, a pot that dried out) in an observations column.
Safety: wash hands after handling soil and fertilizer; keep fertilizer away from children and pets; follow the label; don't use pesticides.
Worked exampleLet's analyse the fertilizer data
Heights (cm) of 5 radish seedlings per group after 21 days: 0 g/L: 6.1, 5.8, 6.4, 5.9, 6.3. 1 g/L: 8.2, 7.9, 8.6, 8.1, 8.4. 2 g/L: 9.0, 9.4, 3.1, 9.2, 8.9 (notes: the 3.1 cm plant had a broken stem on day 8). 4 g/L: 7.1, 6.8, 7.4, 6.9, 7.3. Calculate the mean and range for each group, and decide what to do with the 3.1 cm value.
- 0 g/L: sum = 30.5, mean = 30.5 ÷ 5 = 6.1 cm; range 5.8 to 6.4 cm.
- 1 g/L: sum = 41.2, mean = 8.24 → 8.2 cm; range 7.9 to 8.6 cm.
- 2 g/L: the 3.1 cm plant is an outlier with a known cause (broken stem), not an effect of fertilizer, so it is fairly excluded and reported. Mean of the other four = (9.0 + 9.4 + 9.2 + 8.9) ÷ 4 = 36.5 ÷ 4 = 9.125 → 9.1 cm; range 8.9 to 9.4 cm. (Including it would give 7.9 cm, which would hide the real trend.)
- 4 g/L: sum = 35.5, mean = 7.1 cm; range 6.8 to 7.4 cm.
- Significant figures: heights were measured to 0.1 cm, so means are reported to 0.1 cm.
- Graph choice: the independent variable is numerical and continuous, so use a line graph (or scatter plot) with concentration on the x-axis, not a bar graph.
Means: 6.1, 8.2, 9.1 and 7.1 cm for 0, 1, 2 and 4 g/L. The outlier is excluded because it had a known, unrelated cause, and the exclusion is reported.
Step 5: analyse and conclude
- Describe the trend: height increased from 6.1 cm (0 g/L) to 9.1 cm (2 g/L), then fell to 7.1 cm at 4 g/L.
- Compare with the hypothesis: the results support it: growth rose with nutrients up to an optimum, then dropped at a high concentration.
- Calculate a percent change to show the size of an effect: from 0 to 2 g/L, (9.1 − 6.1) ÷ 6.1 × 100% ≈ 49% taller.
- Be careful with claims: you only tested four concentrations, so the true optimum could be anywhere between about 1 and 4 g/L. One species, one soil and one season limit how far you can generalize.
Step 6: evaluate errors and bias (A1.8)
- Random errors (vary from plant to plant): reading the ruler at a slight angle, natural variation between seeds. Reduce them with more replicates.
- Systematic errors (push all results one way): a ruler that starts 2 mm from its end; always measuring the "best-looking" plant first. Reduce them with careful technique and checking equipment.
- Bias: if you expect the fertilizer to work, you might water the fertilized plants a little more without meaning to. Using measured volumes, random positions and, if possible, having someone else measure without knowing which group is which (a blind measurement) reduces bias.
Step 7: communicate (A1.11)
A lab report usually has: title, question, hypothesis, materials, procedure, data (tables and graphs), analysis, conclusion, evaluation (errors and improvements) and references.
Hands-on activityYour own three-week growth inquiry
Choose one factor to test (pick what you can control at home):
- Nutrient quantity: 0, ½ and 1 times the label strength of a houseplant fertilizer.
- Light quantity: 4, 8 and 12 hours under the same lamp (use a timer), or distance from a window.
- Light quality: clear, red and blue cellophane tents over small pots (same light source).
- Water retention/percolation: sand, potting soil and garden soil, watered the same.
- Temperature: a cool room versus a warm room (record temperatures).
You need: 12 to 15 small pots or cups with drainage holes (poke holes with a grown-up's help), potting soil, fast seeds (radish, bean, pea or lettuce), a ruler, a measuring cup, labels, and optionally a kitchen scale.
- Write your question and hypothesis (If..., then..., because...).
- List your IV, DV (with an operational definition) and at least five controlled variables. Identify your control group.
- Plant 2 seeds per pot, at least 4 pots per group. After a week, thin to 1 seedling per pot.
- Measure and record every 3 to 4 days for 3 weeks in a table with units.
- Calculate means and ranges, make an appropriate graph, and write a conclusion and evaluation (errors, bias, improvements).
What to look for: a clear trend between groups, with small ranges within each group. If the ranges overlap a lot, the difference may not be real; more replicates would help. Wash hands after handling soil and fertilizer, and store fertilizer out of reach of children and pets.
Check your understandingQuiz
1. In an experiment on how light hours affect bean growth, the dependent variable is:
2. Which is the best hypothesis?
3. Why use several plants per treatment?
4. An outlier caused by a broken stem should be:
5. Which graph best shows plant height at fertilizer concentrations of 0, 1, 2 and 4 g/L?
6. A balance that always reads 0.3 g too high causes:
For parents and teachersBig idea: F2.2 asks students to design and carry out an inquiry into factors affecting plant growth (nutrients, light quantity and quality, temperature, water retention or percolation). This lesson also teaches the scientific investigation skills of strand A: questions and hypotheses (A1.1), controlled inquiry (A1.5), organizing data (A1.6), error and bias (A1.8), conclusions (A1.10), communication (A1.11) and precision (A1.13).
How to help: The three-week inquiry is the centrepiece. Help your teen choose a factor that is easy to control at home, set a regular measuring schedule (e.g. Monday and Thursday), and resist changing the plan midway. Ask: "What is the only thing that's different between the groups?" Radishes, beans and peas are reliable and fast.
Common difficulties:
- Changing more than one variable at a time (the most common flaw).
- Using only one plant per group.
- Reporting means with too many decimal places.
- Dropping inconvenient data without a reason. Outliers need a known cause and must be reported.