Geometry CP Curriculum Pacing Guide

Transcription

1 The mathematical processes provide the framework for teaching, learning, and assessing in all high school mathematics core courses. Instructional programs should be built around these processes. Standard G-1: Indicators G-1.1 The student will understand and utilize the mathematical processes of problem solving, reasoning and proof, communication, connections, and representation. Demonstrate an understanding of the axiomatic structure of geometry by using undefined terms, definitions, postulates, theorems, and corollaries G-1.2 G-1.3 G-1.4 G-1.5 G-1.6 G-1.7 G-1.8 G-1.9 G-1.10 Communicate knowledge of geometric relationships by using mathematical terminology appropriately. Apply basic rules of logic to determine the validity of the converse, inverse, and contrapositive of a conditional statement. Formulate and test conjectures by using a variety of tools such as concrete models, graphing calculators, spreadsheets, and dynamic geometry software Use inductive reasoning to formulate conjectures. Use deductive reasoning to validate conjectures with formal and informal proofs, and give counterexamples to disprove a statement. Understand the historical development of geometry. Connect geometry with other branches of mathematics. Demonstrate an understanding of how geometry applies to in real-world contexts (including architecture, construction, farming, and astronomy). Demonstrate an understanding of geometric relationships (including constructions through investigations by using a variety of tools such as straightedge, compass, Patty Paper, dynamic geometry software, and handheld computing devices). Anderson School District Five Page 1 Copyright July 1, 2012

2 Anderson School District Five Page 2 Copyright July 1, 2012

3 First Nine Weeks BASICS OF GEOMETRY G-1: The students will understand and utilize the mathematical processes of problem solving, reasoning and proof, communication, connections, and representation. G-2: The student will demonstrate through the mathematical processes an understanding of the properties of basic geometric figures and the relationships between and among them. G-3: The student will demonstrate through the mathematical processes an understanding of the properties and special segments of triangles and the relationships between and among triangles. Basics of Geometry Standards/ Indicators Concepts/Essential Knowledge Activities G-1.4 Formulate and test conjectures by using a variety of tools such as concrete models, graphing calculators, spreadsheets, and dynamic geometry software G-1.5 Use inductive reasoning to formulate conjectures. Inductive Reasoning (1.5 days) inductive reasoning conjecture conclusion counterexample patterns G-2.1 Infer missing elements of visual or numerical geometric patterns (including triangular and rectangular numbers and the number of diagonals in polygons). Anderson School District Five Page 3 Copyright July 1, 2012

4 First Nine Weeks Basics of Geometry Standards/ Indicators SC G-1.1 SC G-1.2 G-CO.1 G-CO.2 Demonstrate an understanding of the axiomatic structure of geometry by using undefined terms, definitions, postulates, theorems, and corollaries. Communicate knowledge of geometric relationships by using mathematical terminology appropriately. Know precise definitions of angle, circle, perpendicular line, parallel line, and lines segment, based on the undefined notions of point, line, distance along a line, and distance around a circular arc. 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). Concepts/Essential Knowledge Terminology (1.5 days) point line plane space intersection coplanar collinear dimensions rays segments opposite rays vertex, angle acute obtuse right straight interior exterior postulate theorem congruence parallel skew Activities Exploring Points and Planes Planes and Space Activity Index Cards Plane Intersection Anderson School District Five Page 4 Copyright July 1, 2012

5 First Nine Weeks Basics of Geometry Standards/ Indicators SC G-1.4 SC G-1.10 G-CO.12 Formulate and test conjectures by using a variety of tools such as concrete models, graphing calculators, spreadsheets, and dynamic geometry software. Demonstrate an understanding of geometric relationships (including constructions through investigations by using a variety of tools such as straightedge, compass, Patty Paper, dynamic geometry software, and handheld computing devices). 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. Concepts/Essential Knowledge Basic Constructions (0.5 day) ruler straightedge protractor compass distance segment bisectors midpoint perpendicular lines perpendicular bisector Activities Basic Constructions SC G-2.5 G-CO.9 Carry out a procedure to create geometric constructions (including the midpoint of a line segment, the angle bisector, the perpendicular bisector of a line segment, the line through a given point that is parallel to a given line, and the line through a given point that is perpendicular to a given line). 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. Anderson School District Five Page 5 Copyright July 1, 2012

6 First Nine Weeks Basics of Geometry Standards/ Indicators G-2.4 Use direct measurement to determine the length of a segment, degree of an angle, and distance from a point to a line. Concepts/Essential Knowledge Protractor/Measurement (0.5 day) protractor degree ruler distance congruence angle classifications straight angle Activities G-3.1 G-3.2 Carry out a procedure to compute the perimeter of a triangle. Carry out a procedure to compute the area of a triangle. Perimeter, Circumference, Area (1.0 day) squares rectangles triangles circles Perimeter, Circumference and Area Practice G-3.3 Analyze how changes in dimensions affect the perimeter or area of triangles. Review and Test (1.5 days) Anderson School District Five Page 6 Copyright July 1, 2012

7 First Nine Weeks ANGLES AND LINES G-6: The student will demonstrate through the mathematical processes an understanding of transformations, coordinate geometry, and vectors. G-2: The student will demonstrate through the mathematical processes an understanding of the properties of basic geometric figures and the relationships between and among them Angles and Lines Standards/ Indicators Concepts/Essential Knowledge Activities SC G-6.2 G-GPE.4 G-GPE.7 Use the midpoint formula to solve problems 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. Distance formula/ Midpoint formula Addition postulates (2.0 days) distance formula midpoint formula segment bisector angle addition segment addition Midpoint of Segment Angle Additions Segment Addition SC G-2.5 G-CO.12 Carry out a procedure to create geometric constructions (including the midpoint of a line segment, the angle bisector, the perpendicular bisector of a line segment, the line through a given point that is parallel to a given line, and the line through a given point that is perpendicular to a given line). 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. Angle pairs/ bisectors Perpendicular lines (1.0 day) adjacent angles vertical angles linear pairs, complementary supplementary Angle Bisectors Vertical Angles Review and Test (1.0 day) Anderson School District Five Page 7 Copyright July 1, 2012

8 First Nine Weeks Angles and Lines Standards/ Indicators Concepts/Essential Knowledge Activities SC G-2.2 SC G-2.3 G-CO.9 Apply properties of parallel lines, intersecting lines, and parallel lines cut by a transversal to solve problems. Use the congruence of line segments and angles to solve problems 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. Review and Test (1.0 day) Parallel lines/transversals/ Special angle pairs (5.0 days) transversal corresponding angles alternate interior same-side interior angles alternate exterior Discovering Parallel Lines Parallel Lines Practice City Project Write on the Desk Anderson School District Five Page 8 Copyright July 1, 2012

9 First Nine Weeks DEDUCTIVE REASONING G-1: The students will understand and utilize the mathematical processes of problem solving, reasoning and proof, communication, connections, and representation. G-2: The student will demonstrate through the mathematical processes an understanding of the properties of basic geometric figures and the relationships between and among them. Deductive Reasoning Standards/ Indicators Concepts/Essential Knowledge Activities G-1.3 Apply basic rules of logic to determine the validity of the converse, inverse, and contrapositive of a conditional statement. Conditional/converse (1.0 day) hypothesis conclusion p and q symbols conditional converse biconditional SC G-1.6 G-CO.12 Use deductive reasoning to validate conjectures with formal and informal proofs, and give counterexamples to disprove a statement. 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. Inverse/Contrapositive/ Negation Laws of detachment and syllogism (1.5 days) negation inverse contrapositive law of detachment and syllogism truth value p and q symbols Practice LOD and LOS Anderson School District Five Page 9 Copyright July 1, 2012

10 First Nine Weeks Deductive Reasoning Standards/ Indicators Concepts/Essential Knowledge Activities SC G-2.3 G-CO.9 Use the congruence of line segments and angles to solve problems. 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. Properties of equality/congruence (1.0 day) transitive reflexive symmetric proof Review and Test (1.0 day) Create a Proof Proof Practice Proof Activity First Nine Weeks Exam (1.5 days) Anderson School District Five Page 10 Copyright July 1, 2012

11 Second Nine Weeks PROPERTIES OF TRIANGLE G-3: The student will demonstrate through the mathematical processes an understanding of the properties and special segments of triangles and the relationships between and among triangles. G-4: The student will demonstrate through the mathematical processes an understanding of the properties of quadrilaterals and other polygons and the relationships between and among them. Properties of Triangle Standards/ Indicators Concepts/Essential Knowledge Activities SC G-3.6 G-CO.10 Apply the triangle sum theorem to solve problems. Prove theorems about triangles. Theorems include: measures of interior angles of a triangle sun 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. Triangle Sum Theorem Triangle Sum Activity Triangle Sum with Algebra Triangle Sum Practice Triangle Sum Theorem SC G-3.4 G-CO.12 Apply properties of isosceles and equilateral triangles to solve problems. 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. Triangle classifications (1.0 day) legs base vertex base angles Anderson School District Five Page 11 Copyright July 1, 2012

12 Second Nine Weeks Properties of Triangle Standards/ Indicators Concepts/Essential Knowledge Activities SC G-3.10 G-SRT.6 Use the Pythagorean theorem and its converse to solve problems. 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. Pythagorean Theorem (1.5 days) simplifying radicals Pythagorean theorem and converse Pythagorean Theorem with Algebra Pythagorean Theorem Pythagorean Theorem and Converse Pythagorean Spiral G-SRT.7 G-SRT.8 SC G-6.1 G-GPE.7 Explain and use the relationship between the sine and cosine of complementary angles. Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems. Use the distance formula to solve problems Use coordinates to compute perimeters of polygons and areas of triangles and rectangles, e.g., using the distance formula. G-3.1 G-3.2 G-3.3 Carry out a procedure to compute the perimeter of a triangle Carry out a procedure to compute the area of a triangle Analyze how changes in dimensions affect the perimeter or area of triangles Area (0.5 day) area and perimeter of triangles dimensions Review and Test (1.5 days) Anderson School District Five Page 12 Copyright July 1, 2012

13 Second Nine Weeks TRIANGLE CONGRUENCY G-3: The student will demonstrate through the mathematical processes an understanding of the properties and special segments of triangles and the relationships between and among triangles G-1: The students will understand and utilize the mathematical processes of problem solving, reasoning and proof, communication, connections, and representation. Triangle Congruency G-3.8 G-3.9 Apply congruence and similarity relationships among triangles to solve problems Apply theorems to prove that triangles are either similar or congruent. Corresponding Parts, Triangle Congruence Test, SSS, SAS, ASA, AAS, HL, Overlapping Triangles (3.5 days) congruence corresponding hypothesis SSS SAS ASA AAS HL overlapping CPCTC Building Congruent Triangles Congruent Triangle Patty Congruent Triangle Project Triangle Congruency Practice Anderson School District Five Page 13 Copyright July 1, 2012

14 Second Nine Weeks Triangle Congruency SC G-1.6 G-CO.11 Use deductive reasoning to validate conjectures with formal and informal proofs, and give counterexamples to disprove a statement. 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. Proofs in general (1.5 days) Triangle Congruency Proofs Triangle Congruency Proofs Quiz Fill in the Blank Triangle Proofs 1 Fill in the Blank Triangle Proofs 2 Triangle Congruency Quiz 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.). 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. Review and Test (1.0 day) Anderson School District Five Page 14 Copyright July 1, 2012

15 Second Nine Weeks RELATIONSHIPS WITHIN TRIANGLES G-3: The student will demonstrate through the mathematical processes an understanding of the properties and special segments of triangles and the relationships between and among triangles G-1: The students will understand and utilize the mathematical processes of problem solving, reasoning and proof, communication, connections, and representation. Relationships within Triangles SC G-3.5 G-CO.10 SC G-3.7 G-CO.10 Use interior angles, exterior angles, medians, angle bisectors, altitudes, and perpendicular bisectors to solve problems. Prove theorems about triangles. Theorems include: measures of interior angles of a triangle sun 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. Apply the triangle inequality theorem to solve problems Prove theorems about triangles. Theorems include: measures of interior angles of a triangle sun 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. Special segments of triangles/points of concurrency, Perpendicular bisectors, circumcenter, Angle bisectors, incenter, Medians/centroid, Altitudes/orthocenter (2.0 days) perpendicular bisector concurrent point of concurrency median centroid circumcenter circumscribed incenter inscribed altitude orthocenter midsegment Triangle inequality (2.0 days) relationship between sides and angles requirements for side lengths Anderson School District Five Page 15 Copyright July 1, 2012 Relationships in Triangles Graphic Organizer Construction of Concurrency Points Concurrency Word Search Points of Concurrency Worksheet Stained Glass Project (Review all Triangle Topics) Triangle Inequalities Exploring Activity Triangle Angle and Side Ordering Activity

16 Second Nine Weeks Relationships within Triangles G-1.7 Understand the historical development of geometry Historical Development of Geometry Project (2.5 days) a cumulative project displaying how geometry has developed over the years (timeline) Review and Test (1.0 day) History Paper Works Cited OR History Project Works Consulted History of Geometry Rubric Second Nine Weeks Exam (1.5 days) Anderson School District Five Page 16 Copyright July 1, 2012

17 Third Nine Weeks QUADRILATERALS G-4: The student will demonstrate through the mathematical processes an understanding of the properties of quadrilaterals and other polygons and the relationships between and among them. G-2: The student will demonstrate through the mathematical processes an understanding of the properties of basic geometric figures and the relationships between and among them Quadrilaterals SC G-4.1 G-CO.11 Carry out a procedure to compute the perimeter of quadrilaterals, regular polygons, and composite figures. 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. Types of quadrilaterals Area (1.0 day) parallelograms rectangle rhombus square kite trapezoid isosceles trapezoid perimeter area composite figures Introduction to Polygons SC G-4.5 G-CO.11 Apply the properties and attributes of quadrilaterals and regular polygons and their component parts to solve problems. 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. Properties of parallelograms Coordinate geometry (3.5 days) diagonals properties and converses polygon angle sum exterior angles Property Check List Fill in Properties of Quadrilaterals Parallelogram Worksheet Honors Parallelogram Jigsaw Activity Parallelogram Worksheet Shape Tree Diagram Trapezoid and Kite Worksheet Sidewalk Chalk Shapes Anderson School District Five Page 17 Copyright July 1, 2012

18 Third Nine Weeks Quadrilaterals G-4.2 G-4.4 Carry out a procedure to find the area of quadrilaterals, regular polygons, and composite figures. Analyze how changes in dimensions affect the perimeter or area of quadrilaterals and regular polygons. Area (1.0 day) area of quadrilaterals regular polygons composite figures ratios of perimeters and areas Review and Test (1.0 day) Anderson School District Five Page 18 Copyright July 1, 2012

19 Third Nine Weeks SIMILARITY G-2: The student will demonstrate through the mathematical processes an understanding of the properties of basic geometric figures and the relationships between and among them G-4: The student will demonstrate through the mathematical processes an understanding of the properties of quadrilaterals and other polygons and the relationships between and among them. Similarity SC G-2.6 G-SRT.5 SC G-4.1 G-CO.11 Use scale factors to solve problems involving scale drawings and models Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures. Carry out a procedure to compute the perimeter of quadrilaterals, regular polygons, and composite figures. 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. Ratio/proportions Perimeter and area (2.5 days) proportions scale factor scale models perimeter, area composite figures regular polygons apothem House Project Similarity Comic Strip Project Investigating Ratios Activity Anderson School District Five Page 19 Copyright July 1, 2012

20 Third Nine Weeks Similarity G-4.2 G-4.4 G-4.6 Carry out a procedure to find the area of quadrilaterals, regular polygons, and composite figures. Analyze how changes in dimensions affect the perimeter or area of quadrilaterals and regular polygons. Apply congruence and similarity relationships among shapes (including quadrilaterals and polygons) to solve problems. Ratio/proportions Perimeter and area (3.0 days) area of quadrilaterals, regular polygons (given apothem and perimeter/side length) composite figures apothem ratios of perimeters and areas similarity ratio area ratio Review and Test (1.0 day) Anderson School District Five Page 20 Copyright July 1, 2012

21 Third Nine Weeks SPECIAL RIGHT TRIANGLES G-3: The student will demonstrate through the mathematical processes an understanding of the properties and special segments of triangles and the relationships between and among triangles. Special Right Triangles SC G-3.11 G-SRT.6 Use the properties of and triangles to solve problems 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. Radicals (1 day) simplest radical form approximations Special Right Triangles 1 Special Right Triangles 2 Investigating Similar Right Triangles Investigating Special Right Triangles G-SRT.7 Explain and use the relationship between the sine and cosine of complementary angles. G-SRT.8 Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems. SC G-3.10 G-SRT.6 G-SRT.7 Use the Pythagorean theorem and its converse to solve problems 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. Explain and use the relationship between the sine and cosine of complementary angles. Pythagorean Theorem and Converse Review (2.0 days) Pythagorean theorem radicals Pythagorean triple acute obtuse right Pythagorean Theorem and Converse G-SRT.8 Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems. Anderson School District Five Page 21 Copyright July 1, 2012

22 Third Nine Weeks TRIGONOMETRY G-3: The student will demonstrate through the mathematical processes an understanding of the properties and special segments of triangles and the relationships between and among triangles G-6: The student will demonstrate through the mathematical processes an understanding of transformations, coordinate geometry, and vectors. Trigonometry SC G-3.12 G-SRT.6 Use trigonometric ratios (including sine, cosine, and tangent) to 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. Sine, cosine, tangent Angles of elevation and depression (2.0 days) opposite, adjacent, hypotenuse, sine, cosine, tangent, angle of elevation, angle of depression, inverse trig functions Is the Handicap Ramp Legal? A Day at the Park Measuring Height with Trigonometry Water Balloon Launch Trigonometry Word Problems Trigonometry Practice Investigating Trigonometry Ratios G-SRT.7 G-SRT.8 Explain and use the relationship between the sine and cosine of complementary angles. Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems. Anderson School District Five Page 22 Copyright July 1, 2012

23 Third Nine Weeks Trigonometry G-6.5 Carry out a procedure to represent the sum of two vectors geometrically by using the parallelogram method. Vectors (1.5 days) magnitude direction initial point terminal point notation vector addition G-6.6 Carry out a procedure to determine the magnitude and direction of the resultant of two vectors by using a scale drawing and direct measurement resultant graphing magnitude direction G-6.7 Carry out a procedure to compute the magnitude of the resultant of two perpendicular vectors by using the Pythagorean theorem. Pythagorean theorem perpendicular horizontal vertical G-6.8 Carry out a procedure to determine the direction of the resultant of two perpendicular vectors by using a scale drawing and direct measurement inverse trig functions Review and Test (1 day) Third Nine Weeks Exam (1.5 days) Anderson School District Five Page 23 Copyright July 1, 2012

24 Third Nine Weeks Anderson School District Five Page 24 Copyright July 1, 2012

25 Fourth Nine Weeks REGULAR POLYGONS G-4: The student will demonstrate through the mathematical processes an understanding of the properties of quadrilaterals and other polygons and the relationships between and among them Regular Polygons SC G-3.5 G-CO.10 Use interior angles, exterior angles, medians, angle bisectors, altitudes, and perpendicular bisectors to solve problems. Prove theorems about triangles. Theorems include: measures of interior angles of a triangle sun 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. Interior/exterior angles of polygons exterior angles interior angles sum of interior angles of a polygon {(n- 2)180} Investigating the Sum of the Interior G-4.3 SC G-4.5 G-CO.11 G-4.6 Apply procedures to compute measures of interior and exterior angles of polygons Apply the properties and attributes of quadrilaterals and regular polygons and their component parts to solve problems. 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. Apply congruence and similarity relationships among shapes (including quadrilaterals and polygons) to solve problems. Properties (1.0 day) properties of quad, kite trapezoid rhombus isosceles trapezoid rectangle square regular polygon scale factors proportions similar polygons Anderson School District Five Page 25 Copyright July 1, 2012

26 Fourth Nine Weeks Regular Polygons SC G-4.1 G-CO.11 Carry out a procedure to compute the perimeter of quadrilaterals, regular polygons, and composite figures. 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. Perimeter/area/general area review (1.5 days) perimeter of regular polygons and composite figures Areas of Regular Polygons Area of Polygon Worksheet Class Quilt Deriving the Formula of a Regular Polygon G-4.2 G-2.7 Carry out a procedure to find the area of quadrilaterals, regular polygons, and composite figures. Use geometric probability to solve problems area of regular polygons finding apothem/lengths with trig/right triangles Geometric Probability (1.0 day) Review and Test (1.0 day) Anderson School District Five Page 26 Copyright July 1, 2012

27 Fourth Nine Weeks THREE DIMENSIONAL FIGURES G-7: The student will demonstrate through the mathematical processes an understanding of the surface area and volume of three-dimensional objects. Three Dimensional Figures G-7.6 G-7.5 Apply a procedure to draw an isometric view of a three-dimensional object Apply a procedure to draw a top view, front view, and side view of a three-dimensional object. Nets 3-D Drawings dimensions isometric drawing nets orthographic drawing Making Nets of 3 Dimensional G-7.1 SC G-7.2 G-GMD.1 G-GMD.3 Carry out a procedure to compute the surface area of three-dimensional objects (including cones, cylinders, pyramids, prisms, spheres, and hemispheres). Carry out a procedure to compute the volume of three-dimensional objects (including cones, cylinders, pyramids, prisms, spheres, hemispheres, and composite objects). Give an informal argument for the formulas for the circumference of a circle, volume of a cylinder, pyramid, and cone. Use dissection arguments, Cavalieri s principle, and informal limit arguments. Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems. Surface area and volume Pyramids, prisms Spheres, cylinders, cones (4.0 days) surface area and lateral area of cones cylinders pyramids prisms spheres slant height oblique/right altitude bases Euler s formula vertex face edge cross sections volume of cylinders pyramids Crush and Run 3D Review (1st 2 Stages) Review Surface Area Review Volume Review Surface Area and Volume Student Formula Sheet Household Item Project Investigating Surface Area Anderson School District Five Page 27 Copyright July 1, 2012

28 Fourth Nine Weeks Three Dimensional Figures G-7.3 G-7.4 Analyze how changes in dimensions affect the volume of objects (including cylinders, prisms, and spheres). Apply congruence and similarity relationships among geometric objects to solve problems. prisms spheres slant height oblique/right altitude, bases change dimensions and analyze effects similarity ratio volume ratio Review and Test (1.0 day) Anderson School District Five Page 28 Copyright July 1, 2012

29 Fourth Nine Weeks CIRCLES G-5: The student will demonstrate through the mathematical processes an understanding of the properties of circles, the lines that intersect them, and the use of their special segments. Circles SC G-5.5 G-C.2 Apply the properties of the component parts of a circle (including radii, diameters, chords, sectors, arcs, and segments) to solve problems. 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. Basic Definitions (1.0 day) circle radii diameters chords sectors arcs segments standard form for a circle Properties of Chords Worksheet Properties of Intercepted Arcs Worksheet Intersecting Chords Worksheet SC G-5.1 G-GMD.1 G-GMD.3 Carry out a procedure to compute the circumference of circles Give an informal argument for the formulas for the circumference of a circle, volume of a cylinder, pyramid, and cone. Use dissection arguments, Cavalieri s principle, and informal limit arguments. Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems. Circumference/Area (1.0 day) diameter radius pi circumference Anderson School District Five Page 29 Copyright July 1, 2012

30 Fourth Nine Weeks Circles SC G-5.2 G-GMD.1 G-GMD.3 Carry out a procedure to compute the area of circles Give an informal argument for the formulas for the circumference of a circle, volume of a cylinder, pyramid, and cone. Use dissection arguments, Cavalieri s principle, and informal limit arguments. Circumference/Area (1.0 day) diameter radius pi area of circle G-5.3 Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems. Analyze how a change in the radius affects the circumference or area of a circle relationship between length of radius and circumference/area SC G-5.4 G-C.2 G-C.5 Carry out a procedure to compute the length of an arc or the area of a sector of a circle. 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. 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. Arc length, area of sectors (1.5 days) arc central angle measure arc length sector segment Circle Intro/Printable Circle Intro/Circle Intro Answer Goat Farmer Pizza Problem Anderson School District Five Page 30 Copyright July 1, 2012

31 Fourth Nine Weeks Circles SC G-5.7 G-C.2 Apply the properties of central angles, inscribed angles, and arcs of circles to solve problems. 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. Central angles, inscribed angles, arcs of circles (1.0 day) central angle inscribed angle circumscribed angle Exploring Inscribed Angles SC G-5.6 G-C.2 Apply the properties of lines that intersect circles (including two secants, two tangents, and a secant and a tangent) to solve problems. 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. Review and Test (1.0 day) Properties of secants and tangents (2.0 days) secant tangent Tangents and Circles Circle Review Circle Review 2 Anderson School District Five Page 31 Copyright July 1, 2012

32 Fourth Nine Weeks TRANSFORMATIONS G-7: The student will demonstrate through the mathematical processes an understanding of the surface area and volume of three-dimensional objects. Transformations SC G-6.3 G-CO.1 G-CO.2 Apply transformations translation, reflection, rotation, and dilation to figures in the coordinate plane by using sketches and coordinates. Know precise definitions of angle, circle, perpendicular line, parallel line, and lines segment, based on the undefined notions of point, line, distance along a line, and distance around a circular arc. 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). Translations, reflections, rotations, dilations (2.5 days) translation reflection rotation dilation preimage image isometry composition of transformations types of symmetry tessellations Making a Tessellation with Patty Paper Penrose Tiles Quiz - Transformations Anderson School District Five Page 32 Copyright July 1, 2012

33 Fourth Nine Weeks Transformations G-6.4 G-CO.1 Apply transformations (including translation and dilation) to figures in the coordinate plane by using matrices. Know precise definitions of angle, circle, perpendicular line, parallel line, and lines segment, based on the undefined notions of point, line, distance along a line, and distance around a circular arc. Translations, reflections, rotations, dilations (2.5 days) matrix row column scalar multiplication dilation enlargement reductions Wind Chime Project 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). Review and Test (1.0 day) Vocabulary Book/Word List for Vocabulary Fourth Nine Weeks Exam (2.5 days) Anderson School District Five Page 33 Copyright July 1, 2012

34 Fourth Nine Weeks Anderson School District Five Page 34 Copyright July 1, 2012