Scientific Method & Graphing - Key Terms

Scientific Method and Measurements – Study Notes (Ch. 1.1)

  • These notes consolidate key ideas for Quiz 2 on the Scientific Method and vocabulary from Chapter 1.1, including graphing, data analysis, measurement, and CER (Claim-Evidence-Reasoning).
  • Structure mirrors the required competencies: identify and apply the 5 steps, understand controlled experiments, organize and analyze data, construct and read graphs, measure with metric units, and draw conclusions from data.

The 5 Steps of the Scientific Method (as presented)

  • Observing and Asking Questions

    • Involves careful sensory observation and formulating questions that can be investigated empirically.
    • Example: Observing that a plant’s growth varies with fertilizer and asking, "Does a higher nitrogen level accelerate growth?"

  • Inferring and Hypothesizing

    • Make inferences from observations and propose testable explanations or predictions (hypotheses).
    • A hypothesis is a tentative answer or educated forecast that can be tested by experiments.

  • Designing Controlled Experiments

    • Plan experiments to test the hypothesis while controlling variables.
    • Key idea: only one independent variable should be altered at a time to observe its effect on the dependent variable.

  • Collecting Data

    • Gather quantitative (numbers) and qualitative (descriptions) data using appropriate tools and units.
    • Ensure data collection is reliable, repeatable, and well-documented.

  • Analyzing Connections

    • Analyze data to identify patterns, trends, and relationships.
    • Draw conclusions from data, graphs, and written descriptions.
    • Determine whether results support or refute the hypothesis and consider sources of error.

  • Connections to the broader process:

    • Data, graphs, and paragraphs all contribute to a coherent conclusion.
    • Results may lead to new questions and iterative refinements of the hypothesis.

Parts of a Controlled Experiment (definitions + examples)

  • Independent Variable (IV)

    • The variable deliberately changed by the experimenter.
    • Example: Amount of fertilizer applied to plants (e.g., 0 g, 5 g, 10 g).

  • Dependent Variable (DV)

    • The variable measured and observed in response to the IV.
    • Example: Plant height after two weeks.

  • Control Variables (Constants)

    • Variables kept constant to ensure that observed effects are due to the IV only.
    • Examples: Light exposure, soil type, pot size, amount of water, ambient temperature.

  • Control Group

    • A baseline group that does not receive the experimental treatment, used for comparison.
    • Example: Plants receiving 0 g fertilizer.

  • Experimental Group

    • The group(s) that receive the experimental treatment(s).
    • Example: Plants receiving 5 g or 10 g fertilizer.

  • Practical note:

    • A well-designed experiment often includes multiple experimental groups and a single control group to establish dose–response relationships and baseline behavior.

Data Organization and Analysis

  • Constructing a Data Table
    • Organize data to compare IV levels with corresponding DV measurements.
    • Typical columns: Trial, Independent Variable (IV) Level, Dependent Variable (DV) Value, Observations/Notes.
    • Ensure units are specified (e.g., cm, g, mL).
  • Calculating Averages
    • When repeating trials, compute the mean (average) of DV measurements.
    • Formula: ar{x} = \frac{1}{n} \sum{i=1}^{n} xi
    • Example: If DV values across 4 trials are 6.2, 6.8, 6.5, 6.9 cm, then \bar{x} = \frac{6.2+6.8+6.5+6.9}{4} = 6.6\,\text{cm}
  • Percent Change
    • Assess relative change between initial and final DV values.
    • Formula: \text{percent change} = \frac{xf - xi}{x_i} \times 100\%
    • Example: If initial height is 4.0 cm and final height is 5.2 cm, percent change is \frac{5.2-4.0}{4.0} \times 100\% = 30\%

Graphing Skills (construction and interpretation)

  • Create a graph based on a set of data
    • Title: Provide a concise description of the data set.
    • Axis Labels: Label x-axis (independent variable) and y-axis (dependent variable) with units.
    • Units: Include units for all measurements.
    • Scale: Choose a scale that covers the data range and makes trends visible.
    • Key: If multiple data sets are plotted, include a legend/key.
    • Correct graph type: Choose line graph for continuous data; bar graph for discrete categories.
  • Reading graphs and data tables
    • Identifying specific data points: Read corresponding values from the graph or table.
    • Describing trends or patterns: Note increasing/decreasing trends, plateaus, or fluctuations.
    • Describing relationships between variables: Correlations, causation caveats, positive/negative relationships.

Measurements in Science and the Metric Ladder

  • Tools for metric measurements
    • Mass: balance scales, triple-beam balance, digital scale.
    • Volume: graduated cylinder, beaker, volumetric flask.
    • Temperature: thermometer (Celsius or Kelvin scale).
    • Length: ruler, meter stick.
  • The Metric Ladder (order of magnitude)
    • Base units: meter (m) for length, liter (L) for volume, gram (g) for mass.
    • Prefixes on either side of the base unit (10x steps):
    • Larger scales: kilo- (k), hecto- (h), deca- (da)
    • Smaller scales: deci- (d), centi- (c), milli- (m)
    • Example relationships: 1 m = 100 cm = 1000 mm; 1 L = 1000 mL; 1 g = 1000 mg.
  • Converting metric measurements using the ladder method
    • Procedure: Move the decimal point left or right to convert between units, using the ladder as a guide.
    • Example conversions:
    • From cm to m: 150 cm → 1.50 m (move decimal 2 places left).
    • From L to mL: 0.75 L → 750 mL (move decimal 3 places right).
    • From g to kg: 500 g → 0.500 kg (move decimal 3 places left).
    • Quick checks:
    • Count steps between units to determine how many decimal places to move.
    • Ensure the final value has appropriate significant figures based on measurement precision.

Data Interpretation and CER (Connection to Evidence and Reasoning)

  • Be able to draw conclusions from data, graphs, and paragraphs
    • Use the collected data to state a clear claim.
    • Support the claim with specific evidence from data (values, trends, observations).
    • Explain why the data supports the claim using scientific reasoning and relevant concepts.
    • Consider sources of error and limitations of the study.
  • CER (Claim-Evidence-Reasoning) framework
    • Claim: A concise statement answering the question or hypothesis.
    • Evidence: Data and observations that support the claim (e.g., specific measurements, graph trends).
    • Reasoning: The logic that connects the evidence to the claim, invoking scientific principles or concepts.
    • Example structure:
    • Claim: Fertilizer at 10 g increases plant height more than 0 g after two weeks.
    • Evidence: Average height for 10 g group = 12.4 cm; 0 g group = 8.1 cm; trend shows positive correlation with fertilizer amount.
    • Reasoning: Increased nutrient availability from fertilizer promotes growth; comparing to control isolates the effect of the fertilizer while other factors are constant.
  • Real-world relevance and ethical considerations
    • Applications in agriculture, medicine, and environmental science.
    • Reliability and validity: sample size, replication, measurement accuracy, and potential biases.
    • Practical implications: scaling results, safety considerations, and cost-benefit analyses.

Quick Reference Formulas and Key Concepts

  • Averages: ar{x} = \frac{1}{n} \sum{i=1}^{n} xi
  • Percent change: \text{percent change} = \frac{xf - xi}{x_i} \times 100\%
  • Relationship of SI prefixes (examples):
    • 1\,\text{m} = 100\,\text{cm} = 1000\,\text{mm}
    • 1\,\text{L} = 1000\,\text{mL}
    • 1\,\text{g} = 1000\,\text{mg}
  • Graph types and purposes:
    • Line graphs: continuous data over time or ordered categories.
    • Bar graphs: discrete categories or groups.

Practice Ideas (to solidify understanding)

  • Design a simple controlled experiment:

    • IV: amount of sunlight (e.g., 4 h, 8 h, 12 h)
    • DV: plant height after 14 days
    • Controls: water, soil type, pot size, temperature
    • Data table: record height for each trial; compute mean height per sunlight level; create a line graph of height vs. sunlight hours.

  • Calculate averages and percent change from a small data set:

    • Data: 5.0 g, 7.2 g, 6.8 g
    • Average: \bar{x} = \frac{5.0+7.2+6.8}{3} = 6.333…\text{ g}
    • Initial vs final: 4.0 cm to 5.5 cm → percent change: \frac{5.5-4.0}{4.0} \times 100\% = 37.5\%

  • CER example prompt:

    • Given fertilizer data, write a claim that fertilizer increases growth, cite specific average heights, and justify with a reason linking nutrients to cell expansion and photosynthesis.

  • Note on common pitfalls:

    • Confounding variables: failing to control all but IV.
    • Small sample sizes leading to high variability.
    • Misinterpreting correlation as causation.

These notes cover: identifying and applying the five steps of the scientific method, parts and examples of controlled experiments, data organization and analysis (averages and percent change), graph construction and interpretation, metric measurements and ladder conversions, and drawing conclusions via data-driven reasoning (CER). They align with the content for Quiz 2 and Chapter 1.1.