A | B | C | D | E | F | G | H | I | J | K | L | M | N | O | P | Q | R | S | T | U | V | W | X | Y | Z | |
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1 | Geometry | |||||||||||||||||||||||||

2 | A.APR.1 | Arithmetic With Polynomials And Rational Expressions | Perform Arithmetic Operations On Polynomials | Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials. | ||||||||||||||||||||||

3 | G.CO.1 | Congruence | Experiment With Transformations In The Plane | Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment, based on the undefined notions of point, line, distance along a line, and distance around a circular arc. | ||||||||||||||||||||||

4 | G.C.1 | Circles | Understand And Apply Theorems About Circles | Prove that all circles are similar. | ||||||||||||||||||||||

5 | G.C.2 | Circles | Understand And Apply Theorems About Circles | Identify and describe relationships among inscribed angles, radii, and chords. 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. | ||||||||||||||||||||||

6 | G.C.3 | Circles | Understand And Apply Theorems About Circles | Construct the inscribed and circumscribed circles of a triangle, and prove properties of angles for a quadrilateral inscribed in a circle. | ||||||||||||||||||||||

7 | G.C.4 | Circles | Understand And Apply Theorems About Circles | (+) Construct a tangent line from a point outside a given circle to the circle. | ||||||||||||||||||||||

8 | G.C.5 | Circles | Find Arc Lengths And Areas Of Sectors Of Circles | 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. | ||||||||||||||||||||||

9 | G.CO.10 | Congruence | Prove Geometric Theorems | Prove theorems about triangles. Theorems include: measures of interior angles of a triangle sum to 180°; base angles of isosceles triangles are congruent; the segment joining midpoints of two sides of a triangle is parallel to the third side and half the length; the medians of a triangle meet at a point. | ||||||||||||||||||||||

10 | G.CO.11 | Congruence | Prove Geometric Theorems | Prove theorems about parallelograms. Theorems include: opposite sides are congruent, opposite angles are congruent, the diagonals of a parallelogram bisect each other, and conversely, rectangles are parallelograms with congruent diagonals. | ||||||||||||||||||||||

11 | G.CO.12 | Congruence | Make Geometric Constructions | Make formal geometric constructions with a variety of tools and methods (compass and straightedge, string, reflective devices, paper folding, dynamic geometric software, etc.). Copying a segment; copying an angle; bisecting a segment; bisecting an angle; constructing perpendicular lines, including the perpendicular bisector of a line segment; and constructing a line parallel to a given line through a point not on the line. | ||||||||||||||||||||||

12 | G.CO.13 | Congruence | Make Geometric Constructions | Construct an equilateral triangle, a square, and a regular hexagon inscribed in a circle. | ||||||||||||||||||||||

13 | G.CO.2 | Congruence | Experiment With Transformations In The Plane | 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). | ||||||||||||||||||||||

14 | G.CO.3 | Congruence | Experiment With Transformations In The Plane | Given a rectangle, parallelogram, trapezoid, or regular polygon, describe the rotations and reflections that carry it onto itself. | ||||||||||||||||||||||

15 | G.CO.4 | Congruence | Experiment With Transformations In The Plane | Develop definitions of rotations, reflections, and translations in terms of angles, circles, perpendicular lines, parallel lines, and line segments. | ||||||||||||||||||||||

16 | G.CO.5 | Congruence | Experiment With Transformations In The Plane | 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. | ||||||||||||||||||||||

17 | G.CO.6 | Congruence | Understand Congruence In Terms Of Rigid Motions | 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. | ||||||||||||||||||||||

18 | G.CO.7 | Congruence | Understand Congruence In Terms Of Rigid Motions | 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. | ||||||||||||||||||||||

19 | G.CO.8 | Congruence | Understand Congruence In Terms Of Rigid Motions | Explain how the criteria for triangle congruence (ASA, SAS, and SSS) follow from the definition of congruence in terms of rigid motions. | ||||||||||||||||||||||

20 | G.CO.9 | Congruence | Prove Geometric Theorems | Prove theorems about lines and angles. Theorems include: vertical angles are congruent; when a transversal crosses parallel lines, alternate interior angles are congruent and corresponding angles are congruent; points on a perpendicular bisector of a line segment are exactly those equidistant from the segment’s endpoints. | ||||||||||||||||||||||

21 | G.GMD.1 | Geometric Measurement And Dimension | Explain Volume Formulas And Use Them To Solve Problems | Give an informal argument for the formulas for the circumference of a circle, area of a circle, volume of a cylinder, pyramid, and cone. Use dissection arguments, Cavalieri’s principle, and informal limit arguments. | ||||||||||||||||||||||

22 | G.GMD.3 | Geometric Measurement And Dimension | Explain Volume Formulas And Use Them To Solve Problems | Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems.★ | ||||||||||||||||||||||

23 | G.GMD.4 | Geometric Measurement And Dimension | Visualize Relationships Between Two-Dimensional And Three- Dimensional Objects | Identify the shapes of two-dimensional cross-sections of three- dimensional objects, and identify three-dimensional objects generated by rotations of two-dimensional objects. | ||||||||||||||||||||||

24 | G.GPE.1 | Expressing Geometric Properties With Equations | Translate Between The Geometric Description And The Equation For A Conic Section | 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. | ||||||||||||||||||||||

25 | G.GPE.4 | Expressing Geometric Properties With Equations | Use Coordinates To Prove Simple Geometric Theorems Algebraically | Use coordinates to prove simple geometric theorems algebraically. | ||||||||||||||||||||||

26 | G.GPE.5 | Expressing Geometric Properties With Equations | Use Coordinates To Prove Simple Geometric Theorems Algebraically | 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). | ||||||||||||||||||||||

27 | G.GPE.6 | Expressing Geometric Properties With Equations | Use Coordinates To Prove Simple Geometric Theorems Algebraically | Find the point on a directed line segment between two given points that partitions the segment in a given ratio. | ||||||||||||||||||||||

28 | G.GPE.7 | Expressing Geometric Properties With Equations | Use Coordinates To Prove Simple Geometric Theorems Algebraically | Use coordinates to compute perimeters of polygons and areas of triangles and rectangles, e.g. using the distance formula.★ | ||||||||||||||||||||||

29 | G.MG.1 | Modeling With Geometry | Apply Geometric Concepts In Modeling Situations | Use geometric shapes, their measures, and their properties to describe objects (e.g. modeling a tree trunk or a human torso as a cylinder).★ | ||||||||||||||||||||||

30 | G.MG.2 | Modeling With Geometry | Apply Geometric Concepts In Modeling Situations | Apply concepts of density based on area and volume in modeling situations (e.g. persons per square mile, BTUs per cubic foot).★ | ||||||||||||||||||||||

31 | G.MG.3 | Modeling With Geometry | Apply Geometric Concepts In Modeling Situations | Apply geometric methods to solve design problems (e.g. designing an object or structure to satisfy physical constraints or minimize cost; working with typographic grid systems based on ratios).★ | ||||||||||||||||||||||

32 | G.SRT.1 | Similarity, Right Triangles, And Trigonometry | Understand Similarity In Terms Of Similarity Transformations | Verify experimentally the properties of dilations given by a center and a scale factor: | ||||||||||||||||||||||

33 | G.SRT.1.a | Similarity, Right Triangles, And Trigonometry | Understand Similarity In Terms Of Similarity Transformations | 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. | ||||||||||||||||||||||

34 | G.SRT.1.b | Similarity, Right Triangles, And Trigonometry | Understand Similarity In Terms Of Similarity Transformations | The dilation of a line segment is longer or shorter in the ratio given by the scale factor. | ||||||||||||||||||||||

35 | G.SRT.11 | Similarity, Right Triangles, And Trigonometry | Apply Trigonometry To General Triangles | (+) 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). | ||||||||||||||||||||||

36 | G.SRT.2 | Similarity, Right Triangles, And Trigonometry | Understand Similarity In Terms Of Similarity Transformations | 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. | ||||||||||||||||||||||

37 | G.SRT.3 | Similarity, Right Triangles, And Trigonometry | Understand Similarity In Terms Of Similarity Transformations | Use the properties of similarity transformations to establish the AA criterion for two triangles to be similar. | ||||||||||||||||||||||

38 | G.SRT.4 | Similarity, Right Triangles, And Trigonometry | Prove Theorems Involving Similarity | Prove theorems about triangles. Theorems include: a line parallel to one side of a triangle divides the other two proportionally, and conversely; the Pythagorean Theorem proved using triangle similarity. | ||||||||||||||||||||||

39 | G.SRT.5 | Similarity, Right Triangles, And Trigonometry | Prove Theorems Involving Similarity | Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures. | ||||||||||||||||||||||

40 | G.SRT.6 | Similarity, Right Triangles, And Trigonometry | Define Trigonometric Ratios And Solve Problems Involving Right Triangles | 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. | ||||||||||||||||||||||

41 | G.SRT.7 | Similarity, Right Triangles, And Trigonometry | Define Trigonometric Ratios And Solve Problems Involving Right Triangles | Explain and use the relationship between the sine and cosine of complementary angles. | ||||||||||||||||||||||

42 | G.SRT.8 | Similarity, Right Triangles, And Trigonometry | Define Trigonometric Ratios And Solve Problems Involving Right Triangles | Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems.★ | ||||||||||||||||||||||

43 | S.CP.2 | Conditional Probability And The Rules Of Probability | Understand Independence And Conditional Probability And Use Them To Interpret Data | Understand that two events A and B are independent if the probability of A and B occurring together is the product of their probabilities, and use this characterization to determine if they are independent. | ||||||||||||||||||||||

44 | S.CP.5 | Conditional Probability And The Rules Of Probability | Understand Independence And Conditional Probability And Use Them To Interpret Data | Recognize and explain the concepts of conditional probability and independence in everyday language and everyday situations. | ||||||||||||||||||||||

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