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How to learn High school: Mathematics

Georgia academic standards: Mathematics, High school

0 of 29 concepts ready to learn · Markdown, for your AI

1. Modeling and Analyzing Quadratic Functions · Create and analyze exponential expressions and equations to represent and model real-life phenomena; solve exponential equations in mathematically applicab

  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
  2. Estimating answers (age 13+): Use graphs of linear and quadratic functions to estimate output values for given inputs, find approximate solutions to equations, and interpret graphical information in real-world contexts

2. Investigating Rational and Irrational Numbers · Investigate rational and irrational numbers and rewrite expressions involving square roots and cube roots.

  1. Number Sets & Infinity: Appreciate the infinite nature of the sets of integers, real numbers, and rational numbers; position integers on a number line and distinguish between rational and irrational numbers

3. Analyzing Linear Inequalities · Create, analyze, and solve linear inequalities in two variables and systems of linear inequalities to model real-life phenomena.

  1. Simultaneous Equations: Understand that two linear equations can be solved simultaneously by finding the point where their graphs intersect, and interpret this graphically and algebraically as the pair of values satisfying both equations
  2. Numbers on a number line: Understand inequalities as statements comparing expressions, represent solutions on a number line, and solve simple linear inequalities using the same inverse-operation methods as equations

4. Modeling Linear Functions · Construct and interpret arithmetic sequences as functions, algebraically and graphically, to model and explain real-life phenomena. Use formal notation to represent linear

  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

5. Geometric & Spatial Reasoning · Develop an introductory understanding of the unit circle; solve trigonometric equations using the unit circle.

  1. Trigonometry basics: Use the trigonometric ratios sin, cos, and tan in right-angled triangles to find unknown sides and angles, including setting up the correct ratio for a given problem

6. Patterning & Algebraic Reasoning · Represent data with matrices, perform mathematical operations, and solve systems of linear equations leading to real-world linear programming applications.

  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
  2. 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

7. Functional & Graphical Reasoning · Analyze the behaviors of rational functions to model applicable, mathematical problems.

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

8. Data & Statistical Reasoning · Communicate descriptive and inferential statistics by collecting, critiquing, analyzing, and interpreting real-world data.

  1. Comparing measurements: Describe, interpret, and compare distributions of a single variable using appropriate measures of central tendency (mean, median, mode) and spread (range), including the effect of outliers
  2. 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
  3. Proportional Reasoning Vocabulary: Know and use advanced vocabulary of multiplicative reasoning — direct proportion, inverse proportion, ratio, rate, unit rate, compound unit, scale factor — accurately in problem-solving contexts

9. PC Geometric & Spatial Reasoning · Analyze the behaviors of conic sections and polar equations to model contextual mathematical problems.

  1. Coordinate Transformations: Identify properties of translations, rotations, and reflections; describe and perform these transformations on given figures, and understand that the image is congruent to the original

10. Data & Statistical Reasoning · Collect, analyze, and interpret univariate quantitative data to answer statistical investigative questions that compare groups to solve real-life problems; Represent biv

  1. Scatter Graphs: Plot bivariate data on a scatter graph with correctly labelled axes and appropriate scales; describe the correlation (positive, negative, none) and draw an estimated line of best fit where appropriate

11. Mathematical Modeling · Apply mathematics to real-life situations; model real-life phenomena using mathematics.

  1. Compound Units: Use compound units such as speed (distance ÷ time), unit pricing (cost ÷ quantity), and density (mass ÷ volume); solve problems involving compound units

12. Patterning & Algebraic Reasoning · Analyze the chances for success or failure in order to make decisions.

  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

13. Data & Statistical Reasoning · Collect, analyze, interpret, summarize, and construct displays of data to make predictions within real-world applications.

  1. Tree diagrams: Generate theoretical sample spaces for single and combined events using listing, tables, and tree diagrams, and calculate theoretical probabilities as the number of favourable outcomes divided by the total number of equally likely outcomes

14. Geometric & Spatial Reasoning · Apply properties of polygons, circles, and trigonometry to model and explore real-world applications.

  1. Properties of triangles and quadrilaterals: Derive and illustrate properties of triangles, quadrilaterals, and circles using appropriate language, including interior angles, diagonals, symmetry, and relationships between side lengths

15. Numerical Reasoning · Utilize fractions, decimals, percents, and ratios to write and solve a variety of financial problems.

  1. Percentages as Fractions: Define percentage as 'number of parts per hundred'; interpret percentages and percentage changes as a fraction or a decimal; express one quantity as a percentage of another; compare quantities using percentages; work with percentages greater than 100%

16. Data & Statistical Reasoning · Make sense of and reason about variation in data using graphs, tables and probability models to solve problems and draw appropriate conclusions from solutions.

  1. Sets & Venn Diagrams: Enumerate sets and their unions and intersections systematically using tables, grids, and Venn diagrams to organise and count outcomes

17. Geometric & Spatial Reasoning · Reason deductively and inductively about figures and their properties and make sense of geometric situations using measurements in real-world contexts.

  1. Proportion: Recognise and solve problems involving direct proportion (as one quantity increases, the other increases at a constant rate) and inverse proportion (as one increases, the other decreases), including graphical and algebraic representations
  2. Angles in triangles (age 11+): Derive and apply formulae for the area of triangles, parallelograms, and trapezia, and for the volume of cuboids and other prisms (including cylinders), connecting each formula to its geometric reasoning
  3. Estimating by rounding: Use approximation through rounding to estimate answers and calculate possible resulting errors expressed using inequality notation a < x ≤ b; understand upper and lower bounds of rounded values

18. Probabilistic Reasoning · Solve problems involving the probability of compound events to make informed decisions; interpret expected value and measures of variability to analyze probability distributi

  1. Complementary events: Understand and apply the rule that probabilities of all mutually exclusive outcomes sum to one; use this to find the probability of a complementary event (P(not A) = 1 − P(A))

19. Geometric & Spatial Reasoning · Examine and apply theorems involving circles; describe and derive arc length and area of a sector; and model and explain real-life situations involving circles.

  1. Circles: Circumference & Area: Calculate the circumference and area of circles using the formulae C = πd (or 2πr) and A = πr², and solve problems involving perimeters and areas of composite shapes that include circular parts

20. Geometric & Spatial Reasoning · Describe dilations in terms of center and scale factor and use these terms to describe properties of dilations; use the precise definition of a dilation to describe sim

  1. Coordinates (age 12+): Understand similarity as a relationship where one shape is an enlargement of another; construct similar shapes by enlargement with a given scale factor and centre, with and without coordinate grids

21. Geometric & Spatial Reasoning · Establish facts between angle relations and generate valid arguments to defend facts established. Prove theorems and solve geometric problems involving lines and angles

  1. Angles with parallel lines: Understand and use the relationship between parallel lines cut by a transversal: corresponding angles, alternate interior angles, and co-interior (same-side interior) angles; use these to find unknown angles
  2. Understanding angles (age 12+): Use ruler and compasses to perform standard constructions: perpendicular bisector of a line segment, perpendicular to a line from or at a given point, and bisecting an angle