Cherokee County Schools

Mathematics Course of Study

Geometry

Geometry provides students with knowledge about shapes and properties and assists with the development of spatial sense, critical for further study in mathematics and for everyday life. Because of its importance in the development of mathematical empowerment, this course is required for all students. To better meet the needs of students of varying abilities, school systems may offer Geometry (140 hours/one credit) or Geometry A and B (280 hours/two credits).

Traditionally, writing proofs has been a major emphasis in Geometry. While in recent years this focus has diminished, Geometry continues to provide an excellent context for developing students’ abilities to reason and write proofs. In this course, students are engaged in problematic situations in which they form conjectures, determine the validity of these conjectures, and defend their conclusions to classmates. Emphasis is placed on the power of deductive reasoning, expressed either informally or formally in a variety of formats. The use of technology as a powerful mathematical tool is also encouraged. Technology may be used for exploring geometric situations or may be incorporated into technological applications such as dynamic geometry software to support classroom instruction.

Please use this document to plan mathematics lessons. The content standards define what students should know and be able to do at the conclusion of the course or grade. The order in which standards are listed within a course or grade is not intended to convey a sequence for instruction. Each standard is aligned with the appropriate student assessment and correlated with textbooks adopted by Cherokee County Schools. Bullets denote content that is related to the standards and required for instruction. Examples clarify certain components of content standards or bullets and are not exhaustive. Technology is integrated throughout the document.

NOTE: Most high school mathematics classes described in the new Alabama course of study are designed to help a student pass the graduation exam and are not college prep courses. Geometry is no exception. Therefore, this course must be correlated to both the AHSGE objectives and the COS. Since these sets of objectives do not match real well, this course will require two tables with correlations. These correlations will be for both the Prentice Hall and Saxon series. Since Saxon math uses an integrated approach, some explanation will be provided.

Geometry is integrated throughout the Saxon series. The geometry skills needed to succeed on achievement tests and college entrance examinations are included in the Algebra 1 and Algebra 2 textbooks. Students who finish Algebra 2 will have completed the equivalent of one semester of what is traditionally informal geometry. Students who continue and complete the Advanced Math book will have completed on full year of Euclidean geometry.

(Source: Saxon Publishers Teacher’s Resource Booklet for Upper Grades Mathematics, pg 7)

Methods to obtain a Geometry credit using Saxon according to Saxon:

1. Complete Saxon Algebra 1 and Prentice Hall Geometry

2. Complete Saxon Algebra 1, Algebra 2, and Advanced Math

Method 1 is the preferred method for students on a standard diploma.

Method 2 is for advanced diploma students. However, it does not satisfy the Alabama requirement by stating a student has passed a geometry course. To solve this problem, Saxon has designed the Algebra 2 and Advanced Math book to solve this problem. Together, these books have been written for three courses: Algebra 2, Geometry with Pre-Calculus, and Pre-Calculus.

(Source: Saxon Publishers Teacher’s Resource Booklet for Upper Grades Mathematics, pg 7-8)

Therefore, in order to correlate this course for Saxon, all three books will be used.

Correlation to the COS

Alabama Course of Study		Saxon Algebra 1	Saxon Algebra 2		Saxon Advanced Mathematics		Prentice Hall Geometry
1. Determine the equation of a line parallel or perpendicular to a second line through a given point.		Lessons 51,75,81,98 106,107	Lessons A,1,8,12,13,14 20,25,31,49		Lessons 10,37,39		Section 3.6
2. Justify theorems related to pairs of angles, including angles formed by parallel and perpendicular lines, vertical angles, adjacent angles, complementary angles, and supplementary angles. Example: proving vertical angles congruent			Lessons A,1,11,25,30,31 49,125,127		Lessons 1,4,8,15		Sections 2.5,3.1,3.2
3. Verify the relationships among different classes of polygons by using their properties. Example: showing that a square has all the properties of both a rectangle and a rhombus Determining the missing lengths of sides or measures of angles in similar polygons.			Lessons B,1,22,24,26,32 35,37,39,124 126		Lessons 1,3,5,8,17,30 72,73		Sections 4.1,6.1,6.2,6.3 6.4,6.5,8.2,8.3
Alabama Course of Study		Saxon Algebra 1	Saxon Algebra 2		Saxon Advanced Mathematics		Prentice Hall Geometry
4. Determine the measure of interior and exterior angles associated with polygons. · Verifying the formulas for the measures of interior and exterior angles of polygons inductively and deductively					Lessons 3,12,73		Sections 3.3,3.4
5. Solve real-life and mathematical problems using properties and theorems related to circles, quadrilaterals, and other geometric shapes. Example: finding the center of a solid wooden wheel using the perpendicular bisectors of two chords Determine the equation of a circle given its center and radius.					Lessons 2,3,11,12,13,14 30,33,42,48,54 58,63,68,71,73 78,89,93,106 123,125		Sections 4.5,5.1,5.2,5.3,5.5 6.1,6.2,6.3,6.4,6.5 7.6,11.1,11.2,11.3 11.4,11.5
6. Apply the Pythagorean Theorem to solve application problems, expressing answers in simplified radical form or as decimal approximations, using Pythagorean triples when applicable.		Lessons 15,20,97,98	Lessons 1,10,30,31,88 124,128		Lessons 3,17,33,35,37 93		Section 7.2
Alabama Course of Study		Saxon Algebra 1	Saxon Algebra 2		Saxon Advanced Mathematics		Prentice Hall Geometry
7. Use the ratios of the sides of special right triangles to find lengths of missing sides. · Deriving the ratios of the sides of 30-60-90 and 45-45-90 triangles			Lessons 66,79		Lessons 20,27,29,32,36 39,48		Section 7.3
8. Deduce relationships between two triangles, including proving congruence or similarity of the triangles from given information, using the relationships to solve problems and to establish other relationships. Determining the geometric mean to find missing lengths in right triangles.		Lessons 15,20	Lessons 1,22,24,26		Lessons 3,8,9,17,20,27 91,99
9. Use inductive reasoning to make conjectures and deductive reasoning to justify conclusions. Recognizing the limitations of justifying a conclusion through inductive reasoning.		Lessons 30,32,83,92 114	Lessons 4,5,22,29,34,47 52,61,74,92,101 111,120		Lessons 7,9,15		Ch 1 Sec 1 Ch 2 Sec 2-5 Ch 3 Sec 1,2,5,6,7 Ch 4 Sec 1-7 Ch 5 Sec 1-5 Ch 6 Sec 1-7 Ch 7 Sec 1,4-8 Ch 8 Sec 1-6 Ch 9 Sec 1-3 Ch 11 Sec 5
Alabama Course of Study	Saxon Algebra 1			Saxon Algebra 2		Saxon Advanced Mathematics		Prentice Hall Geometry
10. Find the missing measures of sides and angles in right triangles by applying the right triangle definitions of sine, cosine, and tangent.				Lessons 1,43,44,49		Lessons 8,14,29,32,72 76,81,91,96,97		Sections 9.1,9.2,9.3
11. Determine the areas and perimeters of regular polygons, including inscribed or circumscribed polygons, given the coordinates of vertices or other characteristics.				Lessons B,22,24,128		Lessons 2,5,56,73		Sections 1.7,7.1,7.3,7.4 7.5,8.6
12. Apply distance, midpoint, and slope formulas to solve problems and to confirm properties of polygons. Examples: finding the area of a rectangle given the coordinates of its vertices, showing that the median of a trapezoid is half the sum of the bases				Lessons 14,20,87,88		Lessons 1,2,5,10,33,35 37,39,48,56,58		Sections 1.6,3.5,6.2,6.6

Alabama Course of Study	Saxon Algebra 1	Saxon Algebra 2	Saxon Advanced Mathematics	Prentice Hall Geometry
13. Identify the coordinates of the vertices of the image of a given polygon that is translated, rotated, reflected, or dilated. Example: rotating a triangle a given a number of degrees around a specific point, comparing the vertices of the image and pre-image.	Lessons 2,110	Lessons B,32	Lessons 22,31,47,57,66 68,106	Sections 12.1,12.2,12.3 12.4,12.7
14. Classify polyhedrons according to their properties, including the number of faces. Example: identifying a polyhedron having 6 vertices and 12 edges Identifying Euclidean solids	Lessons 60,72,91	Lessons A,B	Lesson 2	Sections 10.1,10.3,10.4
15. Calculate measures of arcs and sectors of a circle from given information.	Lessons 3,8	Lessons B,56,128	Lessons 1,11,13,56	Sections 7.6,7.7
Alabama Course of Study	Saxon Algebra 1	Saxon Algebra 2	Saxon Advanced Mathematics	Prentice Hall Geometry
Examples: finding the area of a sector given its arc length and radius, finding the arc length of a sector given its area and radius, finding the area or arc length given the measure of the central angle and the radius
16. Calculate surface areas and volumes of solid figures, including spheres, cones, and pyramids. · Developing formulas for surface area and volume of spheres, cones, and pyramids · Calculating specific missing dimensions of solid figures from surface area or volume · Determining the relationship between the surface areas of similar figures and volumes of similar figures	Lessons 3,8	Lesson B	Lessons 2,5	Sections 10.2,10.3,10.4 10.5,10.6,10.7 10.8

Alabama Course of Study	Saxon Algebra 1	Saxon Algebra 2	Saxon Advanced Mathematics	Prentice Hall Geometry
17. Analyze sets of data from geometric contexts to determine what, if any, relationships exist. Example: Collect data and create a scatterplot comparing the perimeter and area of various rectangles. Determine whether a line of best fit can be drawn. 17. Analyze sets of data from geometric contexts to determine what, if any, relationships exist. · Distinguishing between conclusions drawn when using deductive and statistical reasoning · Calculating probabilities arising in geometric contexts Example: finding the probability of hitting a particular ring on a dart board whose rings are formed by equally spaced concentric circles	Lessons 45,52,65,85,120	Lesson 129	Lessons 34,38,41,45,55 61,70,75,83,92