Identify and justify whether properties (closure, identity, inverse, commutative and associative) hold for a given set and operations; e.g., even integers and multiplication.
Compare, order and determine equivalent forms for rational and irrational numbers.
Explain the effects of operations such as multiplication or division, and of computing powers and roots on the magnitude of quantities.
Demonstrate fluency in computations using real numbers.
Estimate the solutions for problem situations involving square and cube roots.
Create a scatterplot for a set of bivariate data, sketch the line of best fit, and interpret the slope of the line of best fit.
Analyze and interpret frequency distributions based on spread, symmetry, skewness, clusters and outliers.
Describe and compare various types of studies (survey, observation, experiment), and identify possible misuses of statistical data.
Describe characteristics and limitations of sampling methods, and analyze the effects of random versus biased sampling; e.g., determine and justify whether the sample is likely to be representative of the population.
Make inferences about relationships in bivariant data, and recognize the difference between evidence of relationship (correlation) and causation.
Use counting techniques and the Fundamental Counting principle to determine the total number of possible outcomes for mathematical situations.
Describe, create and analyze a sample space and use it to calculate probability.
Identify situations involving independent and dependent events, and explain differences between, and common misconceptions about, probabilities associated with those events.
Use theoretical and experimental probability, including simulations or random numbers, to estimate probabilities and to solve problems dealing with uncertainty; e.g., compound events, independent events, simple dependent events.