Geometry: Concepts and Connections (Georgia's K-12 Mathematics Standards)

Mathematical Modeling (MM)

• G.MM.1 Apply mathematics to real situations and build models of real-life phenomena.
  • G.MM.1.1 Explain real problems by using a mathematical model.
  • G.MM.1.2 Create models that explain situations in science, social science, the arts and humanities.
  • G.MM.1.3 Use abstract and quantitative reasoning to make decisions from data and situations.
  • G.MM.1.4 Use a range of representations and structures to show and solve real-life problems.

Patterning & Algebraic Reasoning (PAR)

• G.PAR.2 Interpret the structure of polynomials and calculate with them in geometric settings.
  • G.PAR.2.1 Interpret polynomial expressions of different degrees that stand for geometric quantities.
  • G.PAR.2.2 Calculate with polynomials and show that, like integers, they are closed under these operations.
  • G.PAR.2.3 Add, subtract and multiply polynomials in one variable using algebraic reasoning.

Geometric & Spatial Reasoning (GSR)

• G.GSR.3 Use transformations to define translations, rotations and reflections and to describe symmetry and congruence.
  • G.GSR.3.1 Use the symmetry of regular polygons to define rotations, reflections and translations.
  • G.GSR.3.2 Check by experiment that rigid motions keep lines, lengths, angles and parallel lines the same.
  • G.GSR.3.3 Draw transformed figures, predict the effect of transformations and describe sequences that show congruence.
  • G.GSR.3.4 Explain triangle congruence criteria using rigid motions and use them to solve problems and prove results.
• G.GSR.4 Establish facts about angles, build valid arguments and prove theorems about lines and angles.
  • G.GSR.4.1 Use undefined terms such as point and line to write precise definitions, notation and proofs.
  • G.GSR.4.2 Classify quadrilaterals on the coordinate plane by proving simple theorems algebraically.
  • G.GSR.4.3 Make formal geometric constructions with a range of tools and methods.
  • G.GSR.4.4 Prove and use theorems about lines and angles to solve problems.
  • G.GSR.4.5 Reason about triangle angle sums, exterior angles, angles made by transversals and AA similarity.
• G.GSR.5 Describe dilations by center and scale factor and use similarity to prove relationships.
  • G.GSR.5.1 Check the properties of dilations by experiment.
  • G.GSR.5.2 Use similarity transformations to decide whether two figures are similar.
  • G.GSR.5.3 Use properties of similarity transformations to establish triangle similarity criteria and solve problems.
  • G.GSR.5.4 Write formal proofs to justify and use theorems about triangles.
• G.GSR.6 Use side ratios in similar right triangles to define sine, cosine and tangent and solve modeling problems.
  • G.GSR.6.1 Explain how side ratios in similar right triangles define the trigonometric ratios of acute angles.
  • G.GSR.6.2 Explain and use the link between the sine and cosine of complementary angles.
  • G.GSR.6.3 Use trigonometric ratios and the Pythagorean Theorem to find sides and angles in applied problems.
• G.GSR.7 Explore radian measure and special right triangles.
  • G.GSR.7.1 Understand a radian as the ratio of arc length to radius.
  • G.GSR.7.2 Explain how radians and degrees are related and convert between them fluently.
  • G.GSR.7.3 Use special right triangles on the unit circle to find trig values, reference angles and coordinates.
• G.GSR.8 Use circle theorems, derive arc length and sector area, and model situations with circles.
  • G.GSR.8.1 Use angle relationships formed by chords, tangents, secants and radii of circles.
  • G.GSR.8.2 Use similarity to derive arc length and sector area formulas and solve problems.
  • G.GSR.8.3 Write and graph the equation of a circle in standard form.
• G.GSR.9 Give informal arguments for formulas, solve volume problems and relate 2-D and 3-D objects.
  • G.GSR.9.1 Use volume formulas for prisms, cylinders, pyramids, cones and spheres, including oblique solids.
  • G.GSR.9.2 Use measures and properties of shapes to describe objects and estimate volumes.
  • G.GSR.9.3 Use density based on area and volume in modeling problems.

Probabilistic Reasoning (PR)

• G.PR.10 Solve compound-probability problems to make decisions and interpret expected value and variability.
  • G.PR.10.1 Describe events as subsets of a sample space using union, intersection and complement, and use the Addition Rule.
  • G.PR.10.2 Use and interpret the general Multiplication Rule with two-way tables or tree diagrams.
  • G.PR.10.3 Use conditional probability to interpret risk, including false positives and negatives in screening tests.
  • G.PR.10.4 Define permutations and combinations and use them to find probabilities of compound events.
  • G.PR.10.5 Interpret the probability distribution of a random variable and its expected value.
  • G.PR.10.6 Build probability distributions from theoretical or observed probabilities and find expected value.
  • G.PR.10.7 Calculate the expected value of a random variable and interpret it as the mean of the distribution.
  • G.PR.10.8 Compare payoffs and make decisions using expected value and variability.

Data & Statistical Reasoning (DSR)

• G.DSR.11 Use two-way frequency tables from real situations to find probabilities and model categorical data.
  • G.DSR.11.1 Build and summarize two-way frequency tables for categorical data.
  • G.DSR.11.2 Use data in two-way tables to calculate and interpret probabilities.