Alabama Common Core
G.CO.2: Represent transformations in the plane using, e.g., transparencies and geometry software; describe transformations as functions that take points in the plane as inputs and give other points as outputs. Compare transformations that preserve distance and angle to those that do not (e.g., translation versus horizontal stretch).
Function Machines 1 (Functions and Tables)
Function Machines 2 (Functions, Tables, and Graphs)
Function Machines 3 (Functions and Problem Solving)
G.CO.3: Given a rectangle, parallelogram, trapezoid, or regular polygon, describe the rotations and reflections that carry it onto itself.
Bisectors in Triangles
Reflections
Rotations, Reflections and Translations
G.CO.4: Develop definitions of rotations, reflections, and translations in terms of angles, circles, perpendicular lines, parallel lines, and line segments.
Reflections
Rotations, Reflections and Translations
Translations
G.CO.5: Given a geometric figure and a rotation, reflection, or translation, draw the transformed figure using, e.g., graph paper, tracing paper, or geometry software. Specify a sequence of transformations that will carry a given figure onto another.
Reflections
Rotations, Reflections and Translations
Translations
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.
Dilations
Reflections
Rotations, Reflections and Translations
G.CO.7: Use the definition of congruence in terms of rigid motions to show that two triangles are congruent if and only if corresponding pairs of sides and corresponding pairs of angles are congruent.
Congruence in Right Triangles
Dilations
Proving Triangles Congruent
Reflections
Rotations, Reflections and Translations
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.
Congruence in Right Triangles
Dilations
Proving Triangles Congruent
Reflections
Rotations, Reflections and Translations
G.CO.9: Prove theorems about lines and angles.
Investigating Angle Theorems - Activity A
Simplifying Trigonometric Expressions
G.CO.10: Prove theorems about triangles.
Bisectors in Triangles
Simplifying Trigonometric Expressions
Triangle Angle Sum - Activity A
Triangle Inequalities
G.CO.11: Prove theorems about parallelograms.
Parallelogram Conditions
Simplifying Trigonometric Expressions
G.CO.12: Make formal geometric constructions with a variety of tools and methods (compass and straightedge, string, reflective devices, paper folding, dynamic geometric software, etc.).
Construct Parallel and Perpendicular Lines
Constructing Congruent Segments and Angles
G.CO.13: Construct an equilateral triangle, a square, and a regular hexagon inscribed in a circle.
Classifying Triangles
Isosceles and Equilateral Triangles
G.SRT.14: Verify experimentally the properties of dilations given by a center and a scale factor:
G.SRT.14.a: A dilation takes a line not passing through the center of the dilation to a parallel line, and leaves a line passing through the center unchanged.
G.SRT.14.b: The dilation of a line segment is longer or shorter in the ratio given by the scale factor.
Dilations
Perimeters and Areas of Similar Figures
Similar Figures - Activity A
Similar Polygons
G.SRT.15: 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.
Dilations
Perimeters and Areas of Similar Figures
Reflections
Rotations, Reflections and Translations
Similar Figures - Activity A
Similar Polygons
Triangle Angle Sum - Activity A
G.SRT.16: Use the properties of similarity transformations to establish the AA criterion for two triangles to be similar.
Investigating Angle Theorems - Activity A
Perimeters and Areas of Similar Figures
Similar Figures - Activity A
Similar Polygons
G.SRT.17: Prove theorems about triangles.
Bisectors in Triangles
Perimeters and Areas of Similar Figures
Similar Polygons
G.SRT.18: Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures.
Congruence in Right Triangles
Perimeters and Areas of Similar Figures
Proving Triangles Congruent
Similar Figures - Activity A
Similar Polygons
G.SRT.19: 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.
Sine and Cosine Ratios - Activity A
Sine, Cosine and Tangent
Tangent Ratio
Triangle Angle Sum - Activity A
G.SRT.20: Explain and use the relationship between the sine and cosine of complementary angles.
Cosine Function
Sine Function
Sine and Cosine Ratios - Activity A
Sine, Cosine and Tangent
Unit Circle
G.SRT.21: Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems.
Distance Formula - Activity A
Geoboard: The Pythagorean Theorem
Pythagorean Theorem - Activity A
Pythagorean Theorem - Activity B
Sine and Cosine Ratios - Activity A
G.SRT.24: Understand and apply the Law of Sines and the Law of Cosines to find unknown measurements in right and non-right triangles (e.g., surveying problems, resultant forces).
G.C.25: Prove that all circles are similar.
Perimeters and Areas of Similar Figures
G.C.26: Identify and describe relationships among inscribed angles, radii, and chords.
Chords and Arcs
Inscribing Angles
G.C.27: Construct the inscribed and circumscribed circles of a triangle, and prove properties of angles for a quadrilateral inscribed in a circle.
Bisectors in Triangles
Classifying Quadrilaterals - Activity B
Parallelogram Conditions
G.C.29: 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.
Area of Parallelograms - Activity B
Chords and Arcs
Inscribing Angles
G.GPE.30: 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.
G.GPE.31: Use coordinates to prove simple geometric theorems algebraically.
Simplifying Trigonometric Expressions
G.GPE.32: Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems (e.g., find the equation of a line parallel or perpendicular to a given line that passes through a given point).
Construct Parallel and Perpendicular Lines
Slope - Activity B
G.GPE.33: Find the point on a directed line segment between two given points that partitions the segment in a given ratio.
Perimeters and Areas of Similar Figures
Similar Figures - Activity A
G.GPE.34: Use coordinates to compute perimeters of polygons and areas of triangles and rectangles, e.g., using the distance formula.
Area of Parallelograms - Activity A
Bisectors in Triangles
Distance Formula - Activity A
Geoboard: The Pythagorean Theorem
Pythagorean Theorem - Activity A
Pythagorean Theorem - Activity B
Rectangle: Perimeter and Area
G.GMD.36: Give an informal argument for the formulas for the circumference of a circle, area of a circle, volume of a cylinder, pyramid, and cone.
Circle: Circumference and Area
Perimeter, Circumference, and Area - Activity B
Prisms and Cylinders - Activity A
Pyramids and Cones - Activity A
G.GMD.37: Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems.
Prisms and Cylinders - Activity A
Pyramids and Cones - Activity A
G.GMD.39: Identify the shapes of two-dimensional cross-sections of three-dimensional objects, and identify three-dimensional objects generated by rotations of two-dimensional objects.
G.MG.40: Use geometric shapes, their measures, and their properties to describe objects (e.g., modeling a tree trunk or a human torso as a cylinder).
Classifying Quadrilaterals - Activity B
Classifying Triangles
Parallelogram Conditions
Special Quadrilaterals
G.MG.41: Apply concepts of density based on area and volume in modeling situations (e.g., persons per square mile, BTUs per cubic foot).
Area of Parallelograms - Activity B
Prisms and Cylinders - Activity A
S.CP.43: Understand the conditional probability of A given B as P(A and B)/P(B), and interpret independence of A and B as saying that 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.
Probability Simulations
Theoretical and Experimental Probability
S.CP.44: Construct and interpret two-way frequency tables of data when two categories are associated with each object being classified. Use the two-way table as a sample space to decide if events are independent and to approximate conditional probabilities.
Box-and-Whisker Plots
Compound Independent Events
Compound Independent and Dependent Events
Describing Data Using Statistics
Histograms
Line Plots
Scatter Plots - Activity A
Stem-and-Leaf Plots
S.CP.45: Recognize and explain the concepts of conditional probability and independence in everyday language and everyday situations.
Compound Independent Events
Compound Independent and Dependent Events
S.CP.46: 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 terms of the model.
S.CP.49: Use permutations and combinations to compute probabilities of compound events and solve problems.
Compound Independent Events
Compound Independent and Dependent Events
Permutations
Permutations and Combinations
S.MD.50: Use probabilities to make fair decisions (e.g., drawing by lots, using a random number generator).
Probability Simulations
Theoretical and Experimental Probability
S.MD.51: Analyze decisions and strategies using probability concepts (e.g., product testing, medical testing, pulling a hockey goalie at the end of a game).
Correlation last revised: 3/17/2015