Georgia Math Standards
G.PAR.2.1: Interpret polynomial expressions of varying degrees that represent a quantity in terms of its given geometric framework.
Modeling the Factorization of ax2+bx+c
Modeling the Factorization of x2+bx+c
Quadratics in Factored Form
Quadratics in Polynomial Form
G.PAR.2.2: Perform operations with polynomials and prove that polynomials form a system analogous to the integers in that they are closed under these operations.
Addition and Subtraction of Functions
Addition of Polynomials
Factoring Special Products
Modeling the Factorization of ax2+bx+c
Modeling the Factorization of x2+bx+c
G.PAR.2.3: Using algebraic reasoning, add, subtract, and multiply single variable polynomials.
Addition and Subtraction of Functions
Addition of Polynomials
Factoring Special Products
Modeling the Factorization of ax2+bx+c
Modeling the Factorization of x2+bx+c
G.GSR.3.1: Use geometric reasoning and symmetries of regular polygons to develop definitions of rotations, reflections, and translations.
Reflections
Rotations, Reflections, and Translations
Translations
G.GSR.3.2: Verify experimentally the congruence properties of rotations, reflections, and translations: lines are taken to lines and line segments to line segments of the same length; angles are taken to angles of the same measure; parallel lines are taken to parallel lines.
Reflections
Rotations, Reflections, and Translations
Translations
G.GSR.3.3: Use geometric descriptions of rigid motions to draw the transformed figures and to predict the effect on a given figure. Describe a sequence of transformations from one figure to another and use transformation properties to determine congruence.
Rotations, Reflections, and Translations
Translations
G.GSR.3.4: Explain how the criteria for triangle congruence follow from the definition of congruence in terms of rigid motions. Use congruency criteria for triangles to solve problems and to prove relationships in geometric figures.
Chords and Arcs
Congruence in Right Triangles
Proving Triangles Congruent
G.GSR.4.1: Use the undefined notions of point, line, line segment, plane, distance along a line segment, and distance around a circular arc to develop and use precise definitions and symbolic notations to prove theorems and solve geometric problems.
G.GSR.4.3: Make formal geometric constructions with a variety of tools and methods.
Constructing Congruent Segments and Angles
Constructing Parallel and Perpendicular Lines
Segment and Angle Bisectors
G.GSR.4.4: Prove and apply theorems about lines and angles to solve problems.
Constructing Congruent Segments and Angles
Constructing Parallel and Perpendicular Lines
Investigating Angle Theorems
Segment and Angle Bisectors
G.GSR.4.5: Use geometric reasoning to establish facts about the angle sum and exterior angle of triangles, about the angles created when parallel lines are cut by a transversal, and the angle-angle criterion for similarity of triangles.
Constructing Congruent Segments and Angles
Proving Triangles Congruent
Triangle Angle Sum
G.GSR.5.1: Verify experimentally the properties of dilations.
G.GSR.5.2: Given two figures, use and apply the definition of similarity in terms of similarity transformations.
G.GSR.5.3: Use the properties of similarity transformations to establish criterion for two triangles to be similar. Use similarity criteria for triangles to solve problems and to prove relationships in geometric figures.
G.GSR.5.4: Construct formal proofs to justify and apply theorems about triangles.
G.GSR.6.1: Explain that by similarity, side ratios in right triangles are properties of the angles in the triangle, leading to definitions of trigonometric ratios for acute angles.
Sine, Cosine, and Tangent Ratios
G.GSR.6.2: Explain and use the relationship between the sine and cosine of complementary angles.
G.GSR.6.3: Use trigonometric ratios and the Pythagorean Theorem to solve for sides and angles of right triangles in applied problems.
Pythagorean Theorem
Pythagorean Theorem with a Geoboard
Sine, Cosine, and Tangent Ratios
G.GSR.7.1: Explore and interpret a radian as the ratio of the arc length to the radius of a circle.
G.GSR.7.2: Explore and explain the relationship between radian measures and degree measures and convert fluently between degree and radian measures.
G.GSR.7.3: Use special right triangles on the unit circle to determine the values of sine, cosine, and tangent for 30° (pi/6), 45° (pi/4) and 60° (pi/3) angle measures. Use reflections of triangles to determine reference angles and identify coordinate values in all four quadrants of the coordinate plane.
Cosine Function
Sine Function
Tangent Function
G.GSR.8.1: Identify and apply angle relationships formed by chords, tangents, secants and radii with circles.
Chords and Arcs
Inscribed Angles
G.GSR.8.3: Write and graph the equation of circles in standard form.
G.GSR.9.1: Use volume formulas for prisms, cylinders, pyramids, cones, and spheres to solve problems including right and oblique solids.
Measuring Volume
Prisms and Cylinders
Pyramids and Cones
G.PR.10.2: Apply and interpret the general Multiplication Rule conceptually to independent events of a sample space, P(A and B) = [P(A)] × [P(B|A)] = [P(B)] × [P(A|B)] using contingency tables or tree diagrams.
Independent and Dependent Events
G.PR.10.4: Define permutations and combinations and apply this understanding to compute probabilities of compound events and solve meaningful problems.
G.PR.10.5: Interpret the probability distribution for a given random variable and interpret the expected value.
G.PR.10.6: Develop a probability distribution for variables of interest using theoretical and empirical (observed) probabilities and calculate and interpret the expected value.
Lucky Duck (Expected Value)
Probability Simulations
G.PR.10.7: Calculate the expected value of a random variable and interpret it as the mean of a given probability distribution.
Correlation last revised: 5/26/2022