TOOL 3: Mathematics
T3.1 Applying general mathematics
T3.2 Using units, symbols and numerical values
T3.3 Processing Uncertainties
T3.4 Graphing
T3.1 Applying general mathematics
- Use basic arithmetic and algebraic calculations to solve problems
- Carry out calculations involving: decimals, fractions, percentages, ratios, proportions, frequencies (including allele frequencies), densities, approximations and reciprocals
- Calculate measures of central tendency: mean, median and mode
- Apply measures of dispersion: range, standard deviation (SD), standard error (SE), interquartile range (IQR)
- Use and interpret scientific notation (for example, 3.5 × 106)
- Use approximation and estimation
- Calculate scales of magnification
- Calculate rates of change from graphical or tabulated data
- Understand direct and inverse proportionality between variables, as well as positive and negative correlations between variables
- Calculate and interpret percentage change and percentage difference
- Distinguish between continuous and discrete variables
- Calculating the actual size from a micrograph that has a scale bar
- Apply the Simpson reciprocal index
- Apply the Lincoln index
- Apply the chi-squared test.
- Chi-Square independence
- Chi-square association
- Apply the t-test
T3.2 Using units, symbols and numerical values
- Apply and use International System of Units (SI) prefixes and units or non-SI metric units
- Express quantities and uncertainties to an appropriate number of decimal places
T3.3 Processing Uncertainties
- Understand the significance of uncertainties in raw and processed data
- Record uncertainties in measurements as a range (±) to an appropriate level of precision
- Express ranges, degrees of precision, standard error or standard deviations as error bars
- Express measurement and processed uncertainties to an appropriate number of decimal places or level of precision
- Apply the coefficient of determination (R2) to evaluate the fit of a trend line
- Interpret values of the correlation coefficient (r) and identify correlations as positive or negative
- Apply and interpret appropriate tests of statistical significance (for example, chi-squared test)
T3.4 Graphing
- Sketch graphs, with labeled but unscaled axes, to qualitatively describe trends
- Construct and interpret tables, charts and graphs for raw and processed data including bar charts, histograms, scatter graphs, line and curve graphs, logarithmic graphs, pie charts, and box-and-whisker plot
- Plot linear and non-linear graphs showing the relationship between two variables with appropriate scales and axes
- Draw lines or curves of best fit
- Interpret features of graphs including gradient, changes in gradient, intercepts, maxima and minima
- Draw and interpret uncertainty/error bars
- Extrapolate and interpolate graphs
- Design dichotomous keys
- Represent energy flow in the form of food chains, food webs and pyramids of energy
- Represent familial genetic relationships using pedigree charts