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Hale County Schools Geometry Pacing Guide GLENCOE GEOMETRY Month Taught August September November CCRS (2010 COS) Quality Core Correlations GEOMETRY 1. Know precise definitions of angle, circle, perpendicular C.1.a Using Logic and Proof to Reason Mathematically; Logic and Proof; Use definitions, line, parallel line, and line segment based on the basic postulates, and theorems about points, undefined notions of point, line, distance along a line, segments, lines, angles, and planes to write proofs and distance around a circular arc. [G-CO1] and to solve problems. STI Achievement Services Resources Date Tested 1-1 3-1 1-2 3-2 1-3 10-1 1-4 Page 1 Hale County Schools Geometry Pacing Guide Month Taught CCRS (2010 COS) October 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). [G-CO2] October 3. Given a rectangle, parallelogram, trapezoid, or regular polygon, describe the rotations and reflections that carry it onto itself. [G-CO3] STI Achievement Services Quality Core Correlations G.1.e Relating Geometric Ideas to the Coordinate Plane; Coordinate Geometry; Determine the effect of reflections, rotations, translations, and dilations and their compositions on the coordinate plane Resources Date Tested 9-2 9-3 9-4 9-6 9-5 Page 2 Hale County Schools Geometry Pacing Guide Month Taught October September October CCRS (2010 COS) 4. Develop definitions of rotations, reflections, and translations in terms of angles, circles, perpendicular lines, parallel lines, and line segments. [G-CO4] 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. [G-CO5] Quality Core Correlations C.1.a Using Logic and Proof to Reason Mathematically; 1. Logic and Proof; Use definitions, basic postulates, and theorems about points, segments, lines, angles, and planes to write proofs and to solve problems. E.1.e Comparing Congruent and Similar Geometric Figures; Similarity and Congruence; Identify and draw images of transformations and use their properties to solve problems. E.1.a Comparing Congruent and Similar Geometric Figures; Similarity and Congruence; Determine points or lines of symmetry and apply the properties of symmetry to figures. E.1.e Comparing Congruent and Similar Geometric Figures; Similarity and Congruence; Identify and draw images of transformations and use their properties to solve problems. Resources 9-1 9-2 9-3 4-6 9-1 9-2 0-3 9-4 September 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. [G-CO6] E.1.a Comparing Congruent and Similar Geometric Figures; Similarity and Congruence; Determine points or lines of symmetry and apply the properties of symmetry to figures. 4-6 4-7 September 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. [G-CO7] C.1.g Using Logic and Proof to Reason Mathematically; Logic and Proof; Use the principle that corresponding parts of congruent triangles are congruent to solve problems. 4-3 4-7 STI Achievement Services Date Tested Page 3 Hale County Schools Geometry Pacing Guide Month Taught CCRS (2010 COS) Quality Core Correlations Resources Date Tested E.1.b Comparing Congruent and Similar Geometric Figures; Similarity and Congruence; Identify congruent figures and their corresponding parts October 8. Explain how the criteria for triangle congruence, angleside-angle (ASA), side-angle-side (SAS), and side-sideside (SSS), follow from the definition of congruence in terms of rigid motions. [G-CO8] September 9. 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; and points on a perpendicular bisector of a line segment are exactly those equidistant from the segment’s endpoints. [G-CO9] C.1.f Using Logic and Proof to Reason Mathematically; Logic and Proof; Prove that two triangles are congruent by applying the SSS, SAS, ASA, AAS, and HL congruence statements. 9-6 C.1.a Using Logic and Proof to Reason Mathematically; Logic and Proof; Use definitions, basic postulates, and theorems about points, segments, lines, angles, and planes to write proofs and to solve problems. 2-7 2-8 3-2 3-5 C.1.e Using Logic and Proof to Reason Mathematically; Logic and Proof; Read and write different types and formats of proofs including twocolumn, flowchart, paragraph, and indirect proofs. D.1.c Identifying, Classifying, and Applying the Properties of Geometric Figures in Space; Points, Lines, Planes, and Space; Identify corresponding, same-side interior, same-side exterior, alternate interior, and alternate exterior angle pairs formed by a pair of parallel lines and a transversal and use these special angle pairs to solve problems (e.g., solve equations, use in proofs) C.1.b Using Logic and Proof to Reason Mathematically; Logic and Proof; Use inductive reasoning to make conjectures and deductive reasoning to arrive at valid conclusions. STI Achievement Services Page 4 Hale County Schools Geometry Pacing Guide Month Taught CCRS (2010 COS) Quality Core Correlations Resources Date Tested D.1.b Identifying, Classifying, and Applying the Properties of Geometric Figures in Space; Points, Lines, Planes, and Space; Identify vertical, adjacent, complementary, and supplementary angle pairs and use them to solve problems (e.g., solve equations, use in proofs) September 10. Prove theorems about triangles. Theorems include measures of interior angles of a triangle sum to 180º, October 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, and the medians of a triangle meet at a point. [G-CO10] C.1.e Using Logic and Proof to Reason Mathematically; Logic and Proof; Read and write different types and formats of proofs including twocolumn, flowchart, paragraph, and indirect proofs. D.2.b Identifying, Classifying, and Applying the Properties of Geometric Figures in Space; Polygons; Identify medians, altitudes, perpendicular bisectors, and angle bisectors of triangles and use their properties to solve problems. D.2.j Identifying, Classifying, and Applying the Properties of Geometric Figures in Space; Polygons; Apply the Isosceles Triangle Theorem and its converse to triangles to solve mathematical and realworld problems. STI Achievement Services 4-2 4-4 4-5 4-6 4-8 5-1 5-2 5-3 5-4 5-5 5-6 8-1 Page 5 Hale County Schools Geometry Pacing Guide Month Taught October CCRS (2010 COS) 11. 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. [G-CO11] Quality Core Correlations C.1.e Using Logic and Proof to Reason Mathematically; Logic and Proof; Read and write different types and formats of proofs including twocolumn, flowchart, paragraph, and indirect proofs. Resources Date Tested 6-2 6-3 6-4 C.1.i Using Logic and Proof to Reason Mathematically; Logic and Proof; Use properties of special quadrilaterals in a proof. D.2.g Identifying, Classifying, and Applying the Properties of Geometric Figures in Space; Polygons; Identify and classify quadrilaterals, including parallelograms, rectangles, rhombi, squares, kites, trapezoids, and isosceles trapezoids, using their properties. 12. Make formal geometric constructions with a variety of August September tools and methods such as compass and straightedge, November string, reflective devices, paper folding, and dynamic geometric software. Constructions include 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. [G-CO12] STI Achievement Services D.1.a Identifying, Classifying, and Applying the Properties of Geometric Figures in Space; Points, Lines, Planes, and Space; Identify and model plane figures, including collinear and noncollinear points, lines, segments, rays, and angles using appropriate mathematical symbols. D.1.c Identifying, Classifying, and Applying the Properties of Geometric Figures in Space; Points, Lines, Planes, and Space; Identify corresponding, same-side interior, same-side exterior, alternate interior, and alternate exterior angle pairs formed by a pair of parallel lines and a transversal and use these special angle pairs to solve problems (e.g., solve equations, use in proofs). 1-2 1-3 1-4 1-5 1-6 2-7 3-5 3-6 4-1 4-6 10-5 Page 6 Hale County Schools Geometry Pacing Guide Month Taught CCRS (2010 COS) Quality Core Correlations Resources Date Tested D.1.d Identifying, Classifying, and Applying the Properties of Geometric Figures in Space; Points, Lines, Planes, and Space; Use construction techniques, including straightedge and compass, to bisect and trisect segments and to create parallel and perpendicular lines, perpendicular bisectors, and angle bisectors. November 13. Construct an equilateral triangle, a square, and a regular hexagon inscribed in a circle. [G-CO13] 10-5 Extend October 14. Verify experimentally the properties of dilations given by a center and a scale factor. [G-SRT1] 9-6 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-SRT1a] 14.b. The dilation of a line segment is longer or shorter in the ratio given by the scale factor. [G-SRT1b] STI Achievement Services Page 7 Hale County Schools Geometry Pacing Guide Month Taught October CCRS (2010 COS) 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. [G-SRT2] Quality Core Correlations C.1.h Using Logic and Proof to Reason Mathematically; Logic and Proof; Use several methods, including AA, SAS, and SSS, to prove that two triangles are similar, corresponding sides are proportional, and corresponding angles are congruent Resources Date Tested 7-2 7-6 . E.1.c Comparing Congruent and Similar Geometric Figures; Similarity and Congruence; Identify similar figures and use ratios and proportions to solve mathematical and real- world problems (e.g., finding the height of a tree using the shadow of the tree and the height and shadow of a person) E.1.d Comparing Congruent and Similar Geometric Figures; Similarity and Congruence; Use the definition of similarity to establish the congruence of angles, proportionality of sides, and scale factor of two similar polygons October 16. Use the properties of similarity transformations to establish the angle-angle (AA) criterion for two triangles to be similar. [G-SRT3] STI Achievement Services C.1.h Using Logic and Proof to Reason Mathematically; Logic and Proof; Use several methods, including AA, SAS, and SSS, to prove that two triangles are similar, corresponding sides are proportional, and corresponding angles are congruent. 9-6 Extend Page 8 Hale County Schools Geometry Pacing Guide Month Taught CCRS (2010 COS) Quality Core Correlations Resources 17. Prove theorems about triangles. Theorems include a line parallel to one side of a triangle divides the other two proportionally, and conversely; and the Pythagorean Theorem proved using triangle similarity. [G-SRT4] D.2.e Identifying, Classifying, and Applying the Properties of Geometric Figures in Space; Polygons; Apply the Pythagorean Theorem and its converse to triangles to solve mathematical and real-world problems. 7-3 7-4 7-5 8-1 September 18. Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric October figures. [G-SRT5] D.2.d Identifying, Classifying, and Applying the Properties of Geometric Figures in Space; Polygons; Solve problems involving the relationships formed when the altitude to the hypotenuse of a right triangle is drawn. 4-3 4-4 4-5 7-3 7-4 7-5 7-6 8-1 October E.1.e Comparing Congruent and Similar Geometric Figures; Similarity and Congruence; Identify and draw images of transformations and use their properties to solve problems. Date Tested E.1.g. Comparing Congruent and Similar Geometric Figures; Similarity and Congruence; Determine the geometric mana between two numbers and use it to solve problems (e.g., find the lengths of segments in right triangles.) October 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. [G-SRT6] STI Achievement Services H.1.b Investigating and Applying Basic Ideas of Trigonometry; Introduction to Trigonometry; Find the sine, cosine, and tangent rations of acute angles given the side lengths of right triangles. 8-3 8-4 Page 9 Hale County Schools Geometry Pacing Guide Month Taught CCRS (2010 COS) Quality Core Correlations Resources October 20. Explain and use the relationship between the sine and cosine of complementary angles. [G-SRT7] H.1.b Investigating and Applying Basic Ideas of Trigonometry; Introduction to Trigonometry; Find the sine, cosine, and tangent rations of acute angles given the side lengths of right triangles. 8-4 October 21. Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems.* [G-SRT8] D.2.e Identifying, Classifying, and Applying the Properties of Geometric Figures in Space; Polygons; Apply the Pythagorean Theorem and its converse to triangles to solve mathematical and real-world problems. 8-2 8-5 Date Tested H.1.b Investigating and Applying Basic Ideas of Trigonometry; Introduction to Trigonometry; Find the sine, cosine, and tangent rations of acute angles given the side lengths of right triangles. H.1.c. Investigating and Applying Basic Ideas of Trigonometry; Introduction to Trigonometry; Use trigonometric ratios to find the sides or angles of right triangles and to solve real- world problems (e.g. use angles of elevation and depression to find missing measures). H.1.a Investigating and Applying Basic Ideas of Trigonometry; Introduction to Trigonometry; Apply properties of 45-45- 90 and 30-60-90 triangle to determine lengths of right triangles. STI Achievement Services Page 10 Hale County Schools Geometry Pacing Guide Month Taught October CCRS (2010 COS) 22. (+) Derive the formula A = ( 1/ 2) ab sin(C) for the area of a triangle by drawing an auxiliary line from a vertex perpendicular to the opposite side. [GSRT9] Quality Core Correlations D.2.d Identifying, Classifying, and Applying the Properties of Geometric Figures in Space; Polygons; Solve problems involving the relationships formed when the altitude to the hypotenuse of a right triangle is drawn. Resources Date Tested 8-6 D.2.f Identifying, Classifying, and Applying the Properties of Geometric Figures in Space; Polygons; Identify and use Pythagorean triples in right triangles to find lengths of the unknown side. F.2.a Using Length, Area, Perimeter, and Volume to Find Quantities and Solve Problems; Lateral Area, Surface Area, and Volume; Find the lateral area, surface area, and volume of prisms, cylinders, cone, and pyramids in mathematical and real-world settings. October 23. (+) Prove the Law of Sines and the Law of Cosines and use them to solve problems. [G-SRT10] STI Achievement Services D.2.f Identifying, Classifying, and Applying the Properties of Geometric Figures in Space; Polygons; Identify and use Pythagorean triples in right triangles to find lengths of the unknown side. 8-6 Page 11 Hale County Schools Geometry Pacing Guide Month Taught CCRS (2010 COS) Quality Core Correlations Resources October 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-SRT11] 8-6 November 25. Prove that all circles are similar. [G-C1] 10-1 November 26. 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. [G-C2] D.3.a Identifying, Classifying, and Applying the Properties of Geometric Figures in Space; Circles; Identify and define lines segments associated with circles (e.g., radii, diameters, chords, secants, tangents) Date Tested 10-2 10-3 10-4 D.3.b Identifying, Classifying, and Applying the Properties of Geometric Figures in Space; Circles; Determine the measure of central and inscribed angles and their intercepted arcs. D.3.c Identifying, Classifying, and Applying the Properties of Geometric Figures in Space; Circles; Find segment lengths, angle measures, and intercepted arc measures formed by chords, secants, and tangents intersecting inside and outside circles November 27. Construct the inscribed and circumscribed circles of a triangle, and prove properties of angles for a quadrilateral inscribed in a circle. [G-C3] STI Achievement Services D.2.b Identifying, Classifying, and Applying the Properties of Geometric Figures in Space; Polygons; Identify medians, altitudes, perpendicular bisectors, and angle bisectors of triangles and use their properties to solve problems. 10-4 10-5 Extend Page 12 Hale County Schools Geometry Pacing Guide Month Taught CCRS (2010 COS) Quality Core Correlations Resources Date Tested D.3.d Identifying, Classifying, and Applying the Properties of Geometric Figures in Space; Circles; Solve problems using inscribed and circumscribed polygons. November 28. (+) Construct a tangent line from a point outside a given circle to the circle. [G-C4] D.3.c Identifying, Classifying, and Applying the Properties of Geometric Figures in Space; Circles; Find segment lengths, angle measures, and intercepted arc measures formed by chords, secants, and tangents intersecting inside and outside circles. 10-5 November 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. [G-C5] F.1.d Using Length, Area, Perimeter, and Volume to Find Quantities and Solve Problems; Area and Perimeter; Find arc lengths and circumferences of circles from given information (e.g., radius, diameter, coordinates) 11-3 F.1.e Using Length, Area, Perimeter, and Volume to Find Quantities and Solve Problems; Area and Perimeter; Find the area of a circle and the area of a sector of a circle from given information (e.g., radius, diameter, coordinates) November 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-GPE1] G.1.d Relating Geometric Ideas to the Coordinate Plane; Coordinate Geometry; Write equations for circles in standard form and solve problems using equations and graphs 10-8 D.1.e Identifying, Classifying, and Applying the Properties of Geometric Figures in Space; Points, Lines, Planes, and Space; Locate, describe, and draw a locus in a plane or space. STI Achievement Services Page 13 Hale County Schools Geometry Pacing Guide Month Taught CCRS (2010 COS) Quality Core Correlations September 31. Use coordinates to prove simple geometric theorems algebraically. [G-GPE4] Example: Prove or disprove that October a figure defined by four given points in the coordinate plane is a rectangle; prove or disprove that the point (1, 3) lies on the circle centered at the origin and containing the point (0, 2). September 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). [G-GPE5] Resources Date Tested 4-8 6-4 6-5 6-6 C.1.d Using Logic and Proof to Reason Mathematically; Logic and Proof; Use various methods to prove that two lines are parallel or perpendicular (e.g., using coordinates, angle measures) 3-2 3-4 D.1.f Identifying, Classifying, and Applying the Properties of Geometric Figures in Space; Points, Lines, Planes, and Space; Apply properties and theorems of parallel and perpendicular lines to solve problems. G.1.a Relating Geometric Ideas to the Coordinate Plane; Coordinate Geometry; Use slope to distinguish between and write equations for parallel and perpendicular lines. G.1.c Relating Geometric Ideas to the Coordinate Plane; Coordinate Geometry; Use coordinate geometry to solve problems about geometric figures (e.g., segments, triangles, quadrilaterals) STI Achievement Services Page 14 Hale County Schools Geometry Pacing Guide Month Taught October November CCRS (2010 COS) Quality Core Correlations Resources 33. Find the point on a directed line segment between two G.1.c Relating Geometric Ideas to the Coordinate Plane; Coordinate Geometry; Use coordinate given points that partitions the segment in a given ratio. geometry to solve problems about geometric figures [G-GPE6] 8-7 10-8 34. Use coordinates to compute perimeters of polygons and areas of triangles and rectangles, e.g., using the distance formula.* [G-GPE7] 1-6 11-1 Date Tested (e.g., segments, triangles, quadrilaterals) August And November F.2.a Using Length, Area, Perimeter, and Volume to Find Quantities and Solve Problems; Lateral Area, Surface Area, and Volume; Find the lateral area, surface area, and volume of prisms, cylinders, cone, and pyramids in mathematical and real-world settings. G.1.c Relating Geometric Ideas to the Coordinate Plane; Coordinate Geometry; Use coordinate geometry to solve problems about geometric figures (e.g., segments, triangles, quadrilaterals) August 35. Determine areas and perimeters of regular polygons, including inscribed or circumscribed polygons, given the coordinates of vertices or other characteristics. G.1.c Relating Geometric Ideas to the Coordinate Plane; Coordinate Geometry; Use coordinate geometry to solve problems about geometric figures (e.g., segments, triangles, quadrilaterals) 1-6 November December 36. Give an informal argument for the formulas for the circumference of a circle; area of a circle; and volume of a cylinder, pyramid, and cone. Use dissection arguments, Cavalieri’s principle, and informal limit arguments. [G-GMD1] D.4.a Identifying, Classifying, and Applying the Properties of Geometric Figures in Space; Solids; Identify and classify prisms, pyramids, cylinders, cones, and spheres and use their properties to solve problems. 11-3 12-4 12-5 12-6 F.2.a Using Length, Area, Perimeter, and Volume to Find Quantities and Solve Problems; Lateral Area, Surface Area, and Volume; Find the lateral area, surface area, and volume of prisms, cylinders, cone, and pyramids in mathematical and real-world settings. STI Achievement Services Page 15 Hale County Schools Geometry Pacing Guide Month Taught CCRS (2010 COS) Quality Core Correlations Resources Date Tested F.2.b Using Length, Area, Perimeter, and Volume to Find Quantities and Solve Problems; Lateral Area, Surface Area, and Volume; Use cross sections of prisms, cylinders, pyramids, and cones to solve volume problems. E.1.f. Comparing Congruent and Similar Geometric Figures; Similarity and Congruence; Apply relationships between perimeters of similar figures, areas of similar figures, and volumes of similar figures, in terms of scale factor, to solve mathematical and real-world problems. E.1.h. Comparing Congruent and Similar Geometric Figures; Similarity and Congruence; Identify and give properties of congruent or similar solids. August December 37. Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems.* [G-GMD3] D.4.a Identifying, Classifying, and Applying the Properties of Geometric Figures in Space; Solids; Identify and classify prisms, pyramids, cylinders, cones, and spheres and use their properties to solve problems. 1-7 12-3 12-5 12-6 F.2.a Using Length, Area, Perimeter, and Volume to Find Quantities and Solve Problems; Lateral Area, Surface Area, and Volume; Find the lateral area, surface area, and volume of prisms, cylinders, cone, and pyramids in mathematical and real-world settings. STI Achievement Services Page 16 Hale County Schools Geometry Pacing Guide Month Taught CCRS (2010 COS) Quality Core Correlations Resources Date Tested F.2.c Using Length, Area, Perimeter, and Volume to Find Quantities and Solve Problems; Lateral Area, Surface Area, and Volume; Find the surface area and volume of a sphere in mathematical and real-world settings. November December 38. Determine the relationship between surface areas of similar figures and volumes of similar figures. D.4.a Identifying, Classifying, and Applying the Properties of Geometric Figures in Space; Solids; Identify and classify prisms, pyramids, cylinders, cones, and spheres and use their properties to solve problems. F.2.a Using Length, Area, Perimeter, and Volume to Find Quantities and Solve Problems; Lateral Area, Surface Area, and Volume; Find the lateral area, surface area, and volume of prisms, cylinders, cone, and pyramids in mathematical and real-world settings. F.2.c Using Length, Area, Perimeter, and Volume to Find Quantities and Solve Problems; Lateral Area, Surface Area, and Volume; Find the surface area and volume of a sphere in mathematical and real-world settings. October December 39. Identify the shapes of two-dimensional cross-sections of three-dimensional objects, and identify threedimensional objects generated by rotations of twodimensional objects. [G-GMD4] STI Achievement Services D.4.b Identifying, Classifying, and Applying the Properties of Geometric Figures in Space; Solids; Describe and draw cross sections of prisms, cylinders, pyramids, and cones 11-1 11-2 11-3 11-4 11-5 12-1 12-2 12-3 12-4 12-5 12-6 12-7 12-8 9-3 Extend 12-1 Page 17 Hale County Schools Geometry Pacing Guide Month Taught August October November December CCRS (2010 COS) 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).* [G-MG1] Quality Core Correlations D.1.a Identifying, Classifying, and Applying the Properties of Geometric Figures in Space; Points, Lines, Planes, and Space; Identify and model plane figures, including collinear and noncollinear points, lines, segments, rays, and angles using appropriate mathematical symbols. Resources Date Tested 1-7 Extend 6-1 11-5 12-3 E.1.h. Comparing Congruent and Similar Geometric Figures; Similarity and Congruence; Identify and give properties of congruent or similar solids. November 41. Apply concepts of density based on area and volume in modeling situations (e.g., persons per square mile, British Thermal Units (BTUs) per cubic foot).* [G-MG2] 11-2 Extend September October November December 42. 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).* [G-MG3] 2-5 3-6 5-1 5-2 5-5 11-2 6-6 STI Achievement Services 7-1 7-7 8-2 10-3 11-4 12-2 13-4 Page 18 Hale County Schools Geometry Pacing Guide Month Taught December CCRS (2010 COS) STATISTICS AND PROBABILITY 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. [S-CP3] Quality Core Correlations Resources 13-5 December 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. [S-CP4] 13-5 December 45. Recognize and explain the concepts of conditional probability and independence in everyday language and everyday situations. [S-CP5] Example: Compare the chance of having lung cancer if you are a smoker with the chance of being a smoker if you have lung cancer. 13-5 December 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-CP6] 13-5 December 47. Apply the Addition Rule, P(A or B) = P(A) + P(B) - P(A and B), and interpret the answer in terms of the model. [S-CP7] 13-6 STI Achievement Services Date Tested Page 19 Hale County Schools Geometry Pacing Guide Month Taught CCRS (2010 COS) Quality Core Correlations Resources December 48. (+) Apply the general Multiplication Rule in a uniform probability model, P(A and B) = P(A)P(B|A) = P(B)P(A|B), and interpret the answer in terms of the model. [S-CP8] 13-4 December 49. (+) Use permutations and combinations to compute probabilities of compound events and solve problems. [S-CP9] 13-2 December 50. (+) Use probabilities to make fair decisions (e.g., drawing by lots, using a random number generator). [SMD6] F.1.c. Using Length, Area, Perimeter, and Volume to Find Quantities and Solve Problems1. Area and Perimeter; Use area to solve problems involving geometric probability. 13-4 December 51. (+) Analyze decisions and strategies using probability concepts (e.g., product testing, medical testing, pulling a hockey goalie at the end of a game). [S-MD7] F.1.c. Using Length, Area, Perimeter, and Volume to Find Quantities and Solve Problems1. Area and Perimeter; Use area to solve problems involving geometric probability. 13-3 STI Achievement Services Date Tested Page 20