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SUBJECT: Geometry STRAND: Language of Geometry CONTENT STANDARDS: Standard 1: Students will develop the language of geometry including specialized vocabulary, reasoning, and application of theorems, properties, and postulates. BIG IDEA PRIMARY SLE PRIMARY SLE RELATED SLEs ASSESSMENT 1 2 3 4 OBJECTIVES Logic and Reasoning LG.1.G.1 Define, compare and contrast inductive reasoning and deductive reasoning for making predictions based on real world situations venn diagrams matrix logic conditional statements (statement, inverse, converse, and contrapositive) *figural patterns LG.1.G.3 Describe relationships derived from geometric figures or figural patterns LG.1.G.6 Give justification for conclusions reached by deductive reasoning *State and prove key basic theorems in geometry (i.e., the Pythagorean theorem, the sum of the measures of the angles of a triangle is 180° , and the line joining the midpoints of two sides of a triangle is parallel to the third side and half it’s length 1. 2. 3. 4. 5. Compare and contrast inductive and deductive reasoning. Use Venn Diagrams to solve problems. Use Matrix Logic to solve problems. Identify the inverse, converse and contrapositive of a statement. Recognize and describe relationships derived from figural patterns. X SUBJECT: Geometry STRAND: Language of Geometry CONTENT STANDARDS: Standard 1: Students will develop the language of geometry including specialized vocabulary, reasoning, and application of theorems, properties, and postulates. BIG IDEA PRIMARY SLE PRIMARY SLE RELATED SLEs ASSESSMENT 1 2 3 4 OBJECTIVES Points, Lines, & Planes LG.1.G.2 Represent points, lines, and planes pictorially with proper identification, as well as basic concepts derived from these undefined terms, such as segments, rays, and angles 1. 2. 3. 4. 5. 6. Represent points pictorially with proper identification. Represent lines pictorially with proper identification. Represent rays pictorially with proper identification. Represent line segments pictorially with proper identification Represent angles pictorially with proper identification. Represent planes pictorially with proper identification. X SUBJECT: Geometry STRAND: Language of Geometry CONTENT STANDARDS: Standard 1: Students will develop the language of geometry including specialized vocabulary, reasoning, and application of theorems, properties, and postulates. BIG IDEA PRIMARY SLE PRIMARY SLE RELATED SLEs ASSESSMENT 1 2 3 4 OBJECTIVES Angle Relationships LG.1.G.4 Apply, with and without appropriate technology, definitions, theorems, properties, and 1. Solve problems involving complementary angles. X postulates related to such topics as complementary, supplementary, vertical angles, linear pairs, and angles formed by perpendicular lines LG.1.G.5 Explore, with and without appropriate technology, the relationship between angles formed by two lines cut by a transversal to justify when lines are parallel M.3.G.5 *Identify and apply properties of and theorems about parallel and perpendicular lines to prove other theorems and perform basic Euclidean constructions 2. 3. 4. 5. 6. 7. Solve problems involving supplementary angles Solve problems involving vertical angles. Solve problems involving linear pairs of angles. Solve problems involving angles formed by perpendicular lines. Solve problems involving parallel lines cut by a transversal. Perform basic Euclidean constructions. SUBJECT: Geometry STRAND: Coordinate Geometry and Transformations CONTENT STANDARDS: Standard 5: Students will specify locations, apply transformations and describe relationships using coordinate geometry. BIG IDEA PRIMARY SLE PRIMARY SLE RELATED SLEs ASSESSMENT 1 2 OBJECTIVES Slope and Equations of Lines CGT.5.G.1 Use coordinate geometry to find the distance between two points, the midpoint of a segment, and the slopes of parallel, perpendicular, horizontal, and vertical lines 1. CGT.5.G.2 *Write the 3. 2. Identity horizontal and vertical lines by calculating the slope. Determine if sets of lines are parallel or perpendicular by calculating their slope. Write the equation X 3 4 equation of a line parallel to a line through a given point not on the line CGT.5.G.3 *Write the equation of a line perpendicular to a line through a given point CGT.5.G.4 *Write the equation of the perpendicular bisector of a line segment 4. 5. of a line parallel to a line through a point not on the line. Write the equation of a line perpendicular to a line through a given point. Write the equation of the perpendicular bisector of a line segment. SUBJECT: Geometry STRAND: Relationships between two- and three- dimensions CONTENT STANDARDS: Standard 4: Students will analyze characteristics and properties of two- and three-dimensional geometric shapes and develop mathematical arguments about geometric relationships. STRAND: Coordinate Geometry and Transformations CONTENT STANDARDS: Standard 5: Students will specify locations, apply transformations and describe relationships using coordinate geometry. BIG IDEA PRIMARY SLE PRIMARY SLE RELATED SLEs ASSESSMENT 1 2 3 OBJECTIVES Properties of Polygons R.4.G.1 Explore and verify the properties of quadrilaterals 1. 2. R.4.G.2 Solve problems using properties of polygons: sum of the measures of the interior angles of a polygon interior and exterior angle measure of a regular polygon or irregular 3. Use properties of quadrilaterals to solve problems. Solve problems involving the sum of the measures of the interior angles of a polygon. Solve problems involving the interior and exterior angle measures of regular and irregular polygons. X 4 polygon number of sides or angles of a polygon 4. CGT.5.G.5 Determine, given a set of points, the type of figure based on its properties (parallelogram, isosceles triangle, trapezoid) 5. 6. Solve problems involving the number of sides and angles of polygons. Classify figures given the set of points that form the vertices of the figure. Prove theorems about polygons SUBJECT: Geometry STRAND: Relationships between two- and three- dimensions CONTENT STANDARDS: Standard 4: Students will analyze characteristics and properties of two- and three-dimensional geometric shapes and develop mathematical arguments about geometric relationships. BIG IDEA PRIMARY SLE PRIMARY SLE RELATED SLEs ASSESSMENT 1 2 3 OBJECTIVES Non-Euclidean Geometrics R.4.G.9 *Explore nonEuclidean geometries, such as spherical geometry and identify its unique properties which result from a change in the parallel postulate 1. Identify unique properties which result when the parallel postulate is not included as one of the postulates for a geometry. 4 X SUBJECT: Geometry STRAND: Triangles CONTENT STANDARDS: Standard 2: Students will identify and describe types of triangles and their special segments. They will use logic to apply the properties of congruence, similarity, and inequalities. The students will apply the Pythagorean Theorem and trigonometric ratios to solve problems in real world situations. BIG IDEA PRIMARY SLE PRIMARY SLE RELATED SLEs ASSESSMENT 1 2 3 4 OBJECTIVES Special Segments of Triangles T.2.G.3 Identify and use the special segments of triangles (altitude, 1. Identify altitudes of triangles and use them to solve X median, angle bisector, perpendicular bisector, and midsegment) to solve problems 2. 3. 4. 5. problems. Identity medians of triangles and use them to solve problems. Identify angle bisectors of triangles and use them to solve problems. Identity perpendicular bisectors of triangles and use them to solve problems. Identity midsegments of triangles and use them to solve problems. SUBJECT: Geometry STRAND: Triangles CONTENT STANDARDS: Standard 2: Students will identify and describe types of triangles and their special segments. They will use logic to apply the properties of congruence, similarity, and inequalities. The students will apply the Pythagorean Theorem and trigonometric ratios to solve problems in real world situations. STRAND: Coordinate Geometry and Transformations CONTENT STANDARDS: Standard 5: Students will specify locations, apply transformations and describe relationships using coordinate geometry. BIG IDEA PRIMARY SLE PRIMARY SLE RELATED SLEs ASSESSMENT 1 2 3 4 OBJECTIVES Pythagorean Theorem & Related Topics T.2.G.2 Investigate the measures of segments to determine the existence of triangles (triangle inequality theorem) T.2.G.4 Apply the 1. 2. Prove the Pythagorean Theorem Use the Pythagorean Theorem and its converse to solve X Pythagorean Theorem and its converse in solving practical problems CGT.5.G.1 Use coordinate geometry to find the distance between two points, the midpoint of a segment, and the slopes of parallel, perpendicular, horizontal, and vertical lines 3. 4. 5. problems Find the distance between two points in a rectangular coordinate system. Find the coordinates of the midpoint of a line segment in the coordinate plane. Apply the triangle inequality to solve problems. SUBJECT: Geometry STRAND: Triangles CONTENT STANDARDS: Standard 2: Students will identify and describe types of triangles and their special segments. They will use logic to apply the properties of congruence, similarity, and inequalities. The students will apply the Pythagorean Theorem and trigonometric ratios to solve problems in real world situations. STRAND: Measurement CONTENT STANDARDS: Standard 3: Students will measure and compare, while using appropriate formulas, tools, and technology to solve problems dealing with length, perimeter, area and volume. BIG IDEA PRIMARY SLE PRIMARY SLE RELATED SLEs ASSESSMENT 1 2 3 4 OBJECTIVES Proportional Reasoning T.2.G.1 Apply congruence (SSS …) and similarity (AA ...) correspondences and properties of figures to find missing parts of geometric figures and provide logical justification 1. M.3.G.4 Use (given similar geometric objects) proportional reasoning to solve practical problems 3. 2. Find missing measures of figures based on congruence relationships. Find missing measures of figures based on similarity relationships. Use properties of parallel lines and proportional reasoning to find lengths of segments. X (including scale drawings) M.3.G.5 *Identify and apply properties of and theorems about parallel and perpendicular lines to prove other theorems and perform basic Euclidean constructions SUBJECT: Geometry STRAND: Triangles CONTENT STANDARDS: Standard 2: Students will identify and describe types of triangles and their special segments. They will use logic to apply the properties of congruence, similarity, and inequalities. The students will apply the Pythagorean Theorem and trigonometric ratios to solve problems in real world situations. BIG IDEA PRIMARY SLE PRIMARY SLE RELATED SLEs ASSESSMENT 1 2 3 4 OBJECTIVES Trigonometry T.2.G.5 Use the special right triangle relationships (30˚-60˚90˚ and 45˚-45˚-90˚) to solve problems 1. 2. T.2.G.6 Use trigonometric ratios (sine, cosine, tangent) to determine lengths of sides and measures of angles in right triangles including angles of elevation and angles of depression T.2.G.7 *Use similarity of right triangles to express the sine, cosine, and tangent of an angle in a right triangle as a ratio of given lengths of sides 3. 4. 5. Use trigonometric ratios to find the measures of sides of right triangles to solve problems. Use trigonometric ratios to find the measures of angles in right triangles to solve problems. Use trigonometric ratios to solve problems involving angles of elevation. Use trigonometric ratios to solve problems involving angles of depression. Use the special right triangle relationships to solve problems. X SUBJECT: Geometry STRAND: Measurement CONTENT STANDARDS: Standard 3: Students will measure and compare, while using appropriate formulas, tools, and technology to solve problems dealing with length, perimeter, area and volume. BIG IDEA PRIMARY SLE PRIMARY SLE RELATED SLEs ASSESSMENT 1 2 3 4 OBJECTIVES Perimeter & Area M.3.G.1 Calculate probabilities arising in geometric contexts (Ex. Find the probability of hitting a particular ring on a dartboard.) M.3.G.2 Apply, using appropriate units, appropriate formulas (area, perimeter, surface area, volume) to solve application problems involving polygons, prisms, pyramids, cones, cylinders, spheres as well as composite figures, expressing solutions in both exact and approximate forms 1. 2. 3. 4. 5. 6. Solve problems involving perimeter of polygons. Solve problems involving the circumference of circles. Solve problems involving perimeter of composite figures. Solve problems involving area of polygons. Solve problems involving area of circles. Solve problems involving area of composite figures. X SUBJECT: Geometry STRAND: Relationships between two- and three- dimensions CONTENT STANDARDS: Standard 4: Students will analyze characteristics and properties of two- and three-dimensional geometric shapes and develop mathematical arguments about geometric relationships. STRAND: Coordinate Geometry and Transformations CONTENT STANDARDS: Standard 5: Students will specify locations, apply transformations and describe relationships using coordinate geometry. BIG IDEA PRIMARY SLE PRIMARY SLE RELATED SLEs ASSESSMENT 1 2 3 OBJECTIVES 4 Circles R.4.G.5 Investigate and use the properties of angles (central and inscribed) arcs, chords, tangents, and secants to solve problems involving circles 1. 2. R.4.G.6 Solve problems using inscribed and circumscribed figures CGT.5.G.6 Write, in standard form, the equation of a circle given a graph on a coordinate plane or the center and radius of a circle 3. 4. 5. 6. 7. 8. 9. Write the equation of a circle in standard form given a coordinate graph of the circle. Write the equation of a circle in standard form given the coordinates of the center of the circle and the radius of the circle Use properties of central angles o a circle to solve problems. Use properties of central angles of circles to solve problems. Use properties of angles inscribed in circles to solve problems. Use properties of arc of circles to solve problems. Use properties of chords of circles to solve problems. Use properties of line tangent to circles to solve problems. Use properties of lines secant to circles to solve problems. X 10. Solve problems using inscribed figures 11. Solve problems using circumscribed figures. SUBJECT: Geometry STRAND: Measurement CONTENT STANDARDS: Standard 3: Students will measure and compare, while using appropriate formulas, tools, and technology to solve problems dealing with length, perimeter, area and volume. BIG IDEA PRIMARY SLE PRIMARY SLE RELATED SLEs ASSESSMENT 1 2 3 4 OBJECTIVES Surface Area & M.3.G.2 Apply, using X 7. Solve problems Volume appropriate units, appropriate formulas (area, perimeter, surface area, volume) to solve application problems involving polygons, prisms, pyramids, cones, cylinders, spheres as well as composite figures, expressing solutions in both exact and approximate forms M.3.G.3 Relate changes in the measurement of one attribute of an object to changes in other attributes (Ex. How does changing the radius or height of a cylinder affect its surface area or volume?) 8. 9. 10. 11. 12. 13. 14. involving surface area of prisms. Solve problems involving surface area of pyramids. Solve problems involving surface area of cones. Solve problems involving surface area of cylinders. Solve problems involving surface area of spheres. Solve problems involving the surface area of composite objects. Solve problems involving volume of prisms. Solve problems 15. 16. 17. 18. 19. 20. involving volume at pyramids. Solve problems involving volume of cones. Solve problems involving volume of cylinders Solve problems involving volume of spheres. Solve problems involving volume of composite objects. Relate changes in the measurement of one attribute of an object to changes in the measurement of other attributes. Use area models to calculate probabilities. SUBJECT: Geometry STRAND: Relationships between two- and three- dimensions CONTENT STANDARDS: Standard 4: Students will analyze characteristics and properties of two- and three-dimensional geometric shapes and develop mathematical arguments about geometric relationships. STRAND: Coordinate Geometry and Transformations CONTENT STANDARDS: Standard 5: Students will specify locations, apply transformations and describe relationships using coordinate geometry. BIG IDEA PRIMARY SLE PRIMARY SLE RELATED SLEs ASSESSMENT 1 2 3 OBJECTIVES Transformations R.4.G.3 Identify and explain why figures tessellate R.4.G.4 Identify the 1. Draw and interpret the results of transformations and successive 4 X attributes of the five Platonic Solids CGT.5.G.7 Draw and interpret the results of transformations and successive transformations on figures in the coordinate plane translations reflections rotations (90˚, 180˚, clockwise and counterclockwis e about the origin) dilations (scale factor) 2. 3. transformations on figures in the coordinate plane. Identify and explain why figures tessellate. Identify the attributes of the five Platonic Solids. SUBJECT: Geometry STRAND: Relationships between two- and three- dimensions CONTENT STANDARDS: Standard 4: Students will analyze characteristics and properties of two- and three-dimensional geometric shapes and develop mathematical arguments about geometric relationships. BIG IDEA PRIMARY SLE PRIMARY SLE RELATED SLEs ASSESSMENT 1 2 3 OBJECTIVES 2-D Representation of 3-D Objects R.4.G.4 Identify the attributes of the five Platonic Solids R.4.G.7 Use orthographic drawings (top, front, side) and isometric drawings (corner) to represent three-dimensional objects R.4.G.8 Draw, examine, and classify crosssections of three- 1. 2. 3. Use orthographic drawings to represent three dimensional objects. Use isometric drawings to represent threedimensional objects. Draw, examine and classify crosssections of threedimensional objects. 4 X dimensional objects