Gizmos for Georgia - Mathematics: Analytic Geometry (GA--Standards of Excellence adopted 2015)

This correlation lists the recommended Gizmos for this state's curriculum standards. Click any Gizmo title below for more information.

MGSE9-12.A.SSE: : Seeing Structure in Expressions

MGSE9-12.A.SSE.1a: : Interpret parts of an expression, such as terms, factors, and coefficients, in context.

MGSE9-12.A.SSE.1b: : Given situations which utilize formulas or expressions with multiple terms and/or factors, interpret the meaning (in context) of individual terms or factors.

MGSE9-12.A.SSE.2: : Use the structure of an expression to rewrite it in different equivalent forms.

MGSE9-12.A.SSE.3a: : Factor any quadratic expression to reveal the zeros of the function defined by the expression.

MGSE9-12.A.SSE.3b: : Complete the square in a quadratic expression to reveal the maximum and minimum value of the function defined by the expression.

MGSE9-12.A.SSE.1a: : Interpret parts of an expression, such as terms, factors, and coefficients, in context.

MGSE9-12.A.SSE.1b: : Given situations which utilize formulas or expressions with multiple terms and/or factors, interpret the meaning (in context) of individual terms or factors.

MGSE9-12.A.SSE.2: : Use the structure of an expression to rewrite it in different equivalent forms.

MGSE9-12.A.SSE.3a: : Factor any quadratic expression to reveal the zeros of the function defined by the expression.

MGSE9-12.A.SSE.3b: : Complete the square in a quadratic expression to reveal the maximum and minimum value of the function defined by the expression.

MGSE9-12.A.APR: : Arithmetic with Polynomials and Rational Expressions

MGSE9-12.A.APR.1: : Add, subtract, and multiply polynomials; understand that polynomials form a system analogous to the integers in that they are closed under these operations.

MGSE9-12.A.CED: : Creating Equations

MGSE9-12.A.CED.1: : Create equations and inequalities in one variable and use them to solve problems. Include equations arising from quadratic functions.

MGSE9-12.A.CED.2: : Create quadratic equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. (The phrase “in two or more variables” refers to formulas like the compound interest formula, in which A = P(1 + r/n)nt has multiple variables.)

MGSE9-12.A.CED.4: : Rearrange formulas to highlight a quantity of interest using the same reasoning as in solving equations.

MGSE9-12.A.CED.1: : Create equations and inequalities in one variable and use them to solve problems. Include equations arising from quadratic functions.

MGSE9-12.A.CED.2: : Create quadratic equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. (The phrase “in two or more variables” refers to formulas like the compound interest formula, in which A = P(1 + r/n)nt has multiple variables.)

MGSE9-12.A.CED.4: : Rearrange formulas to highlight a quantity of interest using the same reasoning as in solving equations.

MGSE9-12.A.REI: : Reasoning with Equations and Inequalities

MGSE9-12.A.REI.4a: : Use the method of completing the square to transform any quadratic equation in x into an equation of the form (x – p)² = q that has the same solutions. Derive the quadratic formula from ax² + bx + c = 0.

MGSE9-12.A.REI.4b: : Solve quadratic equations by inspection (e.g., for x² = 49), taking square roots, factoring, completing the square, and the quadratic formula, as appropriate to the initial form of the equation (limit to real number solutions).

MGSE9-12.A.REI.4a: : Use the method of completing the square to transform any quadratic equation in x into an equation of the form (x – p)² = q that has the same solutions. Derive the quadratic formula from ax² + bx + c = 0.

MGSE9-12.A.REI.4b: : Solve quadratic equations by inspection (e.g., for x² = 49), taking square roots, factoring, completing the square, and the quadratic formula, as appropriate to the initial form of the equation (limit to real number solutions).

MGSE9-12.F.IF: : Interpreting Functions

MGSE9-12.F.IF.4: : Using tables, graphs, and verbal descriptions, interpret the key characteristics of a function which models the relationship between two quantities. Sketch a graph showing key features including: intercepts; interval where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior.

MGSE9-12.F.IF.5: : Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes.

MGSE9-12.F.IF.6: : Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph.

MGSE9-12.F.IF.7a: : Graph quadratic functions and show intercepts, maxima, and minima (as determined by the function or by context).

MGSE9-12.F.IF.8a: : Use the process of factoring and completing the square in a quadratic function to show zeros, extreme values, and symmetry of the graph, and interpret these in terms of a context.

MGSE9-12.F.IF.4: : Using tables, graphs, and verbal descriptions, interpret the key characteristics of a function which models the relationship between two quantities. Sketch a graph showing key features including: intercepts; interval where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior.

MGSE9-12.F.IF.5: : Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes.

MGSE9-12.F.IF.6: : Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph.

MGSE9-12.F.IF.7a: : Graph quadratic functions and show intercepts, maxima, and minima (as determined by the function or by context).

MGSE9-12.F.IF.8a: : Use the process of factoring and completing the square in a quadratic function to show zeros, extreme values, and symmetry of the graph, and interpret these in terms of a context.

MGSE9-12.F.BF: : Building Functions

MGSE9-12.F.BF.1a: : Determine an explicit expression and the recursive process (steps for calculation) from context.

MGSE9-12.F.BF.3: : Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and f(x + k) for specific values of k (both positive and negative); find the value of k given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them.

MGSE9-12.F.BF.1a: : Determine an explicit expression and the recursive process (steps for calculation) from context.

MGSE9-12.F.BF.3: : Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and f(x + k) for specific values of k (both positive and negative); find the value of k given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them.

MGSE9-12.G.CO: : Congruence

MGSE9-12.G.CO.6: : Use geometric descriptions of rigid motions to transform figures and to predict the effect of a given rigid motion on a given figure; given two figures, use the definition of congruence in terms of rigid motions to decide if they are congruent.

MGSE9-12.G.CO.8: : Explain how the criteria for triangle congruence (ASA, SAS, and SSS) follow from the definition of congruence in terms of rigid motions. (Extend to include HL and AAS.)

MGSE9-12.G.CO.9: : Prove theorems about lines and angles.

MGSE9-12.G.CO.10: : Prove theorems about triangles.

MGSE9-12.G.CO.11: : Prove theorems about parallelograms.

MGSE9-12.G.CO.13: : Construct an equilateral triangle, a square, and a regular hexagon, each inscribed in a circle.

MGSE9-12.G.CO.6: : Use geometric descriptions of rigid motions to transform figures and to predict the effect of a given rigid motion on a given figure; given two figures, use the definition of congruence in terms of rigid motions to decide if they are congruent.

MGSE9-12.G.CO.8: : Explain how the criteria for triangle congruence (ASA, SAS, and SSS) follow from the definition of congruence in terms of rigid motions. (Extend to include HL and AAS.)

MGSE9-12.G.CO.9: : Prove theorems about lines and angles.

MGSE9-12.G.CO.10: : Prove theorems about triangles.

MGSE9-12.G.CO.11: : Prove theorems about parallelograms.

MGSE9-12.G.CO.13: : Construct an equilateral triangle, a square, and a regular hexagon, each inscribed in a circle.

MGSE9-12.G.SRT: : Similarity, Right Triangles, and Trigonometry

MGSE9-12.G.SRT.1a: : The dilation of a line not passing through the center of the dilation results in a parallel line and leaves a line passing through the center unchanged.

MGSE9-12.G.SRT.1b: : The dilation of a line segment is longer or shorter according to the ratio given by the scale factor.

MGSE9-12.G.SRT.2: : Given two figures, use the definition of similarity in terms of similarity transformations to decide if they are similar; explain, using similarity transformations, the meaning of similarity for triangles as the equality of all corresponding pairs of angles and the proportionality of all corresponding pairs of sides.

MGSE9-12.G.SRT.4: : Prove theorems about triangles.

MGSE9-12.G.SRT.5: : Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures.

MGSE9-12.G.SRT.6: : Understand 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.

MGSE9-12.G.SRT.8: : Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems.

MGSE9-12.G.SRT.1a: : The dilation of a line not passing through the center of the dilation results in a parallel line and leaves a line passing through the center unchanged.

MGSE9-12.G.SRT.1b: : The dilation of a line segment is longer or shorter according to the ratio given by the scale factor.

MGSE9-12.G.SRT.2: : Given two figures, use the definition of similarity in terms of similarity transformations to decide if they are similar; explain, using similarity transformations, the meaning of similarity for triangles as the equality of all corresponding pairs of angles and the proportionality of all corresponding pairs of sides.

MGSE9-12.G.SRT.4: : Prove theorems about triangles.

MGSE9-12.G.SRT.5: : Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures.

MGSE9-12.G.SRT.6: : Understand 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.

MGSE9-12.G.SRT.8: : Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems.

MGSE9-12.G.C: : Circles

MGSE9-12.G.CO.8: : Explain how the criteria for triangle congruence (ASA, SAS, and SSS) follow from the definition of congruence in terms of rigid motions. (Extend to include HL and AAS.)

MGSE9-12.G.CO.9: : Prove theorems about lines and angles.

MGSE9-12.G.CO.10: : Prove theorems about triangles.

MGSE9-12.G.CO.11: : Prove theorems about parallelograms.

MGSE9-12.G.CO.13: : Construct an equilateral triangle, a square, and a regular hexagon, each inscribed in a circle.

MGSE9-12.G.C.1: : Understand that all circles are similar.

MGSE9-12.G.C.2: : Identify and describe relationships among inscribed angles, radii, chords, tangents, and secants. Include the relationship between central, inscribed, and circumscribed angles; inscribed angles on a diameter are right angles; the radius of a circle is perpendicular to the tangent where the radius intersects the circle.

MGSE9-12.G.C.5: : Derive using similarity the fact that the length of the arc intercepted by an angle is proportional to the radius, and define the radian measure of the angle as the constant of proportionality; derive the formula for the area of a sector.

MGSE9-12.G.C.1: : Understand that all circles are similar.

MGSE9-12.G.C.2: : Identify and describe relationships among inscribed angles, radii, chords, tangents, and secants. Include the relationship between central, inscribed, and circumscribed angles; inscribed angles on a diameter are right angles; the radius of a circle is perpendicular to the tangent where the radius intersects the circle.

MGSE9-12.G.C.5: : Derive using similarity the fact that the length of the arc intercepted by an angle is proportional to the radius, and define the radian measure of the angle as the constant of proportionality; derive the formula for the area of a sector.

MGSE9-12.G.GPE: : Expressing Geometric Properties with Equations

MGSE9-12.G.GPE.1: : Derive the equation of a circle of given center and radius using the Pythagorean Theorem; complete the square to find the center and radius of a circle given by an equation.

MGSE9-12.G.GMD: : Geometric Measurement and Dimension

MGSE9-12.G.GMD.1a: : Give informal arguments for the formulas of the circumference of a circle and area of a circle using dissection arguments and informal limit arguments.

MGSE9-12.G.GMD.1b: : Give informal arguments for the formula of the volume of a cylinder, pyramid, and cone using Cavalieri’s principle.

MGSE9-12.G.GMD.3: : Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems.

MGSE9-12.G.GMD.1a: : Give informal arguments for the formulas of the circumference of a circle and area of a circle using dissection arguments and informal limit arguments.

MGSE9-12.G.GMD.1b: : Give informal arguments for the formula of the volume of a cylinder, pyramid, and cone using Cavalieri’s principle.

MGSE9-12.G.GMD.3: : Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems.

MGSE9-12.S.ID: : Interpreting Categorical and Quantitative Data

MGSE9-12.S.ID.6a: : Decide which type of function is most appropriate by observing graphed data, charted data, or by analysis of context to generate a viable (rough) function of best fit. Use this function to solve problems in context. Emphasize quadratic models.

MGSE9-12.S.ID.6a: : Decide which type of function is most appropriate by observing graphed data, charted data, or by analysis of context to generate a viable (rough) function of best fit. Use this function to solve problems in context. Emphasize quadratic models.

MGSE9-12.S.CP: : Conditional Probability and the Rules of Probability

MGSE9-12.S.CP.1: : Describe categories of events as subsets of a sample space using unions, intersections, or complements of other events (or, and, not).

MGSE9-12.S.CP.2: : Understand that if two events A and B are independent, the probability of A and B occurring together is the product of their probabilities, and that if the probability of two events A and B occurring together is the product of their probabilities, the two events are independent.

MGSE9-12.S.CP.3: : Understand the conditional probability of A given B as P (A and B)/P(B). Interpret independence of A and B in terms of conditional probability; that is, the conditional probability of A given B is the same as the probability of A, and the conditional probability of B given A is the same as the probability of B.

MGSE9-12.S.CP.6: : Find the conditional probability of A given B as the fraction of B’s outcomes that also belong to A, and interpret the answer in context.

MGSE9-12.S.CP.1: : Describe categories of events as subsets of a sample space using unions, intersections, or complements of other events (or, and, not).

MGSE9-12.S.CP.2: : Understand that if two events A and B are independent, the probability of A and B occurring together is the product of their probabilities, and that if the probability of two events A and B occurring together is the product of their probabilities, the two events are independent.

MGSE9-12.S.CP.3: : Understand the conditional probability of A given B as P (A and B)/P(B). Interpret independence of A and B in terms of conditional probability; that is, the conditional probability of A given B is the same as the probability of A, and the conditional probability of B given A is the same as the probability of B.

MGSE9-12.S.CP.6: : Find the conditional probability of A given B as the fraction of B’s outcomes that also belong to A, and interpret the answer in context.

Correlation last revised: 9/16/2020

Georgia - Mathematics: Analytic Geometry

GA--Standards of Excellence | Adopted: 2015

MGSE9-12.A.SSE: : Seeing Structure in Expressions

MGSE9-12.A.SSE.1a: : Interpret parts of an expression, such as terms, factors, and coefficients, in context.

MGSE9-12.A.SSE.1b: : Given situations which utilize formulas or expressions with multiple terms and/or factors, interpret the meaning (in context) of individual terms or factors.

MGSE9-12.A.SSE.2: : Use the structure of an expression to rewrite it in different equivalent forms.

MGSE9-12.A.SSE.3a: : Factor any quadratic expression to reveal the zeros of the function defined by the expression.

MGSE9-12.A.SSE.3b: : Complete the square in a quadratic expression to reveal the maximum and minimum value of the function defined by the expression.

MGSE9-12.A.APR: : Arithmetic with Polynomials and Rational Expressions

MGSE9-12.A.APR.1: : Add, subtract, and multiply polynomials; understand that polynomials form a system analogous to the integers in that they are closed under these operations.

MGSE9-12.A.CED: : Creating Equations

MGSE9-12.A.CED.1: : Create equations and inequalities in one variable and use them to solve problems. Include equations arising from quadratic functions.

MGSE9-12.A.CED.4: : Rearrange formulas to highlight a quantity of interest using the same reasoning as in solving equations.

MGSE9-12.A.REI: : Reasoning with Equations and Inequalities

MGSE9-12.A.REI.4a: : Use the method of completing the square to transform any quadratic equation in x into an equation of the form (x – p)² = q that has the same solutions. Derive the quadratic formula from ax² + bx + c = 0.

MGSE9-12.A.REI.4b: : Solve quadratic equations by inspection (e.g., for x² = 49), taking square roots, factoring, completing the square, and the quadratic formula, as appropriate to the initial form of the equation (limit to real number solutions).

MGSE9-12.F.IF: : Interpreting Functions

MGSE9-12.F.IF.5: : Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes.

MGSE9-12.F.IF.6: : Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph.

MGSE9-12.F.IF.7a: : Graph quadratic functions and show intercepts, maxima, and minima (as determined by the function or by context).

MGSE9-12.F.IF.8a: : Use the process of factoring and completing the square in a quadratic function to show zeros, extreme values, and symmetry of the graph, and interpret these in terms of a context.

MGSE9-12.F.BF: : Building Functions

MGSE9-12.F.BF.1a: : Determine an explicit expression and the recursive process (steps for calculation) from context.

MGSE9-12.G.CO: : Congruence

MGSE9-12.G.CO.6: : Use geometric descriptions of rigid motions to transform figures and to predict the effect of a given rigid motion on a given figure; given two figures, use the definition of congruence in terms of rigid motions to decide if they are congruent.

MGSE9-12.G.CO.8: : Explain how the criteria for triangle congruence (ASA, SAS, and SSS) follow from the definition of congruence in terms of rigid motions. (Extend to include HL and AAS.)

MGSE9-12.G.CO.9: : Prove theorems about lines and angles.

MGSE9-12.G.CO.10: : Prove theorems about triangles.

MGSE9-12.G.CO.11: : Prove theorems about parallelograms.

MGSE9-12.G.CO.13: : Construct an equilateral triangle, a square, and a regular hexagon, each inscribed in a circle.

MGSE9-12.G.SRT: : Similarity, Right Triangles, and Trigonometry

MGSE9-12.G.SRT.1a: : The dilation of a line not passing through the center of the dilation results in a parallel line and leaves a line passing through the center unchanged.

MGSE9-12.G.SRT.1b: : The dilation of a line segment is longer or shorter according to the ratio given by the scale factor.

MGSE9-12.G.SRT.4: : Prove theorems about triangles.

MGSE9-12.G.SRT.5: : Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures.

MGSE9-12.G.SRT.6: : Understand 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.

MGSE9-12.G.SRT.8: : Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems.

MGSE9-12.G.C: : Circles

MGSE9-12.G.C.1: : Understand that all circles are similar.

MGSE9-12.G.C.5: : Derive using similarity the fact that the length of the arc intercepted by an angle is proportional to the radius, and define the radian measure of the angle as the constant of proportionality; derive the formula for the area of a sector.

MGSE9-12.G.GPE: : Expressing Geometric Properties with Equations

MGSE9-12.G.GPE.1: : Derive the equation of a circle of given center and radius using the Pythagorean Theorem; complete the square to find the center and radius of a circle given by an equation.

MGSE9-12.G.GMD: : Geometric Measurement and Dimension

MGSE9-12.G.GMD.1a: : Give informal arguments for the formulas of the circumference of a circle and area of a circle using dissection arguments and informal limit arguments.

MGSE9-12.G.GMD.1b: : Give informal arguments for the formula of the volume of a cylinder, pyramid, and cone using Cavalieri’s principle.

MGSE9-12.G.GMD.3: : Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems.

MGSE9-12.S.ID: : Interpreting Categorical and Quantitative Data

MGSE9-12.S.ID.6a: : Decide which type of function is most appropriate by observing graphed data, charted data, or by analysis of context to generate a viable (rough) function of best fit. Use this function to solve problems in context. Emphasize quadratic models.

MGSE9-12.S.CP: : Conditional Probability and the Rules of Probability

MGSE9-12.S.CP.1: : Describe categories of events as subsets of a sample space using unions, intersections, or complements of other events (or, and, not).

MGSE9-12.S.CP.2: : Understand that if two events A and B are independent, the probability of A and B occurring together is the product of their probabilities, and that if the probability of two events A and B occurring together is the product of their probabilities, the two events are independent.

MGSE9-12.S.CP.6: : Find the conditional probability of A given B as the fraction of B’s outcomes that also belong to A, and interpret the answer in context.