How to learn High school: Mathematics

Iowa academic standards: Mathematics, High school

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1. Statistics and Probability · Represent data on two quantitative variables on a scatter plot and describe how the variables are related. ★

1. Scatter Graphs & Correlation: Describe simple mathematical relationships between two variables using scatter graphs, identify positive, negative, or no correlation, and use a line of best fit to make predictions

2. Functions · Distinguish between situations that can be modeled with linear functions and with exponential functions.

1. Linear Function Graphs: Recognise that a linear function produces a straight-line graph, understand the relationship between an equation of the form y = mx + c and its graphical representation, and interpret gradient and y-intercept in context

3. Functions · Graph functions expressed symbolically and show key features of the graph by hand in simple cases and using technology for more complicated cases.

1. Quadratic Graphs: Recognise that quadratic functions produce curved (parabolic) graphs, distinguish them from linear graphs, and use plotted quadratic graphs to estimate values and find approximate solutions

4. Algebra · Solve quadratic equations in one variable. (A1 and A2)

1. Solving Linear Equations: Use algebraic methods to solve linear equations in one variable, including equations that require rearrangement, expanding brackets, and collecting terms on both sides; solve equations with rational number coefficients

5. Algebra · Choose and produce an equivalent form of an expression or equation to reveal and explain properties of the quantity represented by the expression. ★ (A1 and A2)

1. Algebraic Transformations: Model situations or procedures by translating them into algebraic expressions or formulae and by using graphs; move between word problems, algebraic representations, tables, and graphical representations
2. Factorising Expressions: Factorise algebraic expressions by taking out common factors — identify the highest common factor of all terms and write the expression as a product, e.g., 6x + 9 = 3(2x + 3)

6. Functions · Find inverse functions.

1. Simple formulae: Understand and use standard mathematical formulae; rearrange formulae to change the subject, performing inverse operations to isolate a different variable

7. Statistics and Probability★ · Weigh the possible outcomes of a decision by assigning probabilities to payoff values and finding expected values. ★

1. The Probability Scale: Understand probability as a measure on a scale from 0 (impossible) to 1 (certain); use the language of probability including likely, unlikely, certain, and impossible
2. Experimental probability: Record, describe, and analyse the frequency of outcomes from probability experiments to develop an understanding of relative frequency as an estimate of probability