Download West Windsor-Plainsboro Regional School District Geometry Honors

West Windsor-Plainsboro Regional School District
Geometry Honors & Accelerated Grade 9
Unit 1: Logic and Laws of Inference Content Area: Mathematics Course & Grade Level: Geometry Honors and Accelerated, 9 Summary and Rationale Geometry (Honors and Accelerated) is a course for mathematically gifted ninth‐grade students who have completed an enriched Advanced Algebra II curriculum. It consists of a college preparatory course in Euclidean plane and solid geometry, considered mostly from a traditional (synthetic approach), but with coordinate and transformational approaches and non‐Euclidean geometries studied as well. Conjecturing, proof, and real world problem solving are essential aspects of the course. Heavy use is made of The Geometer’s Sketchpad software in class demonstrations and computer lab work. Discovery and small‐group learning methods will be used regularly as learning methods throughout the course. Basic course topics include: properties of angles, parallel lines, triangles, quadrilaterals, polygons, circles, and solids; algebra review, coordinate geometry, transformations, constructions, area, perimeter, volume, congruence, similarity, inductive and deductive reasoning, and axiomatic systems. Enrichment topics include: tessellations, fractals, non‐Euclidean geometries, logic and locus. Recommended Pacing 15 days State Standards Standard 4.G‐CO
CPI # Cumulative Progress Indicator (CPI) 9 Prove theorems about lines and angles. 10 Prove theorems about triangles . 11 Prove theorems about parallelograms. Instructional Focus
Unit Enduring Understandings  Students will understand how to use inductive and deductive reasoning. Unit Essential Questions  How does logic build a foundation for formal proof using deductive reasoning? Objectives Students will know:  Vocabulary: biconditional, converse, contrapositive, tautology, truth table, flow proof, Laws of Inference, inductive reasoning, deductive reasoning Students will be able to:  Express a statement in symbolic form  Develop a truth table based on an argument  Determine whether a statement is tautology through the development of a truth table  Apply the Laws of Inference  Analyze conditional statements and rewrite them in different forms  Demonstrate elementary deductive reasoning Resources
Core Text: Geometry for Enjoyment and Challenge, Rhoad, Milauskas, Whipple 1996 Suggested Resources: Unit 2: Introduction to Geometry Content Area: Mathematics Course & Grade Level: Geometry Honors and Accelerated, 9 Summary and Rationale Geometry (Honors and Accelerated) is a course for mathematically gifted ninth‐grade students who have completed an enriched Advanced Algebra II curriculum. It consists of a college preparatory course in Euclidean plane and solid geometry, considered mostly from a traditional (synthetic approach), but with coordinate and transformational approaches and non‐Euclidean geometries studied as well. Conjecturing, proof, and real world problem solving are essential aspects of the course. Heavy use is made of The Geometer’s Sketchpad software in class demonstrations and computer lab work. Discovery and small‐group learning methods will be used regularly as learning methods throughout the course. Basic course topics include: properties of angles, parallel lines, triangles, quadrilaterals, polygons, circles, and solids; algebra review, coordinate geometry, transformations, constructions, area, perimeter, volume, congruence, similarity, inductive and deductive reasoning, and axiomatic systems. Enrichment topics include: tessellations, fractals, non‐Euclidean geometries, logic and locus. Recommended Pacing 15 days State Standards Standard 4.G‐CO Congruence CPI # Cumulative Progress Indicator (CPI) 1 Know precise definitions of angle, circle, perpendicular line, parallel line, based on the undefined notions of point, line, distance along a line, and distance around a circular arc. 12 Make formal geometric constructions with a variety of tools and methods (compass and straightedge, string, reflective devices, paper folding, dynamic geometric software, etc.). Standard 4.G‐MG Modeling with Geometry CPI # Cumulative Progress Indicator (CPI) 2 Apply concepts of density based on area and volume in modeling situations. Instructional Focus
Unit Enduring Understandings  Build a foundation for the development of Euclidean geometry  Extend algebraic skills to problem solving with geometric concepts  Communicate mathematical ideas effectively in a variety of modalities Unit Essential Questions  How can spatial relationships be described by careful use of geometric language?  How do geometric relationships help to solve problems and/or make sense of phenomena?  What situations can be analyzed using transformations and symmetries?  How can we best represent geometric relationships? Objectives Students will know:  Undefined terms: point, line, plane  Terms: equidistant, distance, collinear, coplanar, intersection, segment, ray, angle, length, congruent, midpoint, bisector, postulate, theorem 
Postulates: Ruler and Protractor Postulate, Segment and Angle Addition Postulate, Point‐Line‐Plane Postulates  Theorems: Line Intersection Theorems Students will be able to:  Use knowledge of points, lines, and planes appropriately  Apply concepts of collinearity and betweeness in problem solving  Develop paragraph proofs involving basic geometric concepts  Use deductive structure to develop proofs of basic geometric concepts  Use Geometer’s Sketchpad to demonstrate conjectures of basic geometric concepts  Solve problems and form predictions involving probability measures Resources
Core Text: Geometry for Enjoyment and Challenge, Rhoad, Milauskas, Whipple 1996 Suggested Resources: Unit 3: Basic Concepts and Proofs Content Area: Mathematics Course & Grade Level: Geometry Honors and Accelerated, 9 Summary and Rationale Geometry (Honors and Accelerated) is a course for mathematically gifted ninth‐grade students who have completed an enriched Advanced Algebra II curriculum. It consists of a college preparatory course in Euclidean plane and solid geometry, considered mostly from a traditional (synthetic approach), but with coordinate and transformational approaches and non‐Euclidean geometries studied as well. Conjecturing, proof, and real world problem solving are essential aspects of the course. Heavy use is made of The Geometer’s Sketchpad software in class demonstrations and computer lab work. Discovery and small‐group learning methods will be used regularly as learning methods throughout the course. Basic course topics include: properties of angles, parallel lines, triangles, quadrilaterals, polygons, circles, and solids; algebra review, coordinate geometry, transformations, constructions, area, perimeter, volume, congruence, similarity, inductive and deductive reasoning, and axiomatic systems. Enrichment topics include: tessellations, fractals, non‐Euclidean geometries, logic and locus. Recommended Pacing 15 days State Standards Standard 4.G‐CO Congruence CPI # Cumulative Progress Indicator (CPI) 1 Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment, based on the undefined notions of point, line, distance around a circular arc. 3 Develop definitions of rotations, reflections, and translations in terms of angles, circles, perpendicular lines, parallel lines, and line segments. 4 Develop definitions of rotations, reflections, and translations in terms of angles, circles, perpendicular lines, parallel lines, and line segments. 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; points on a perpendicular bisector of a line segment are exactly those equidistant from the segment’s endpoints. Instructional Focus
Unit Enduring Understandings  Students will understand how to use parallelism and perpendicularity concepts to deduce relationships (both directly & indirectly) of quadrilaterals Unit Essential Questions  How can spatial relationships be described by careful use of geometric language?  How do geometric relationships help to solve problems and/or make sense of phenomena?  How can we best represent and verify geometric/algebraic relationships? Objectives Students will know:  Terms: parallel, perpendicular, polygons, classification of triangles & quadrilaterals, planes  Notation: parallel, perpendicular, triangle, segment, ray, line, quadrilaterals Students will be able to:  Write indirect proofs  Prove lines parallel  Parallel line concepts to develop relationships in parallelograms and other quadrilaterals  Apply various properties of quadrilaterals in proofs  Prove quadrilaterals are parallelograms  Prove special types of quadrilaterals  Prove theorems involving perpendicularity of a line and plane  Prove theorems involving parallel planes Resources
Core Text: Geometry for Enjoyment and Challenge, Rhoad, Milauskas, Whipple, 1996 Suggested Resources: Unit 4: Constructions and Congruent Triangles Content Area: Mathematics Course & Grade Level: Geometry Honors & Accelerated, 9 Summary and Rationale In this unit, students will explore the properties of congruent triangles and how to show that two triangles are congruent. An examination of angle bisectors and perpendicular bisectors leads to a discussion of reflections and symmetry. Recommended Pacing 20 days State Standards Standard 4.G‐CO Congruence CPI # Cumulative Progress Indicator (CPI) 6 Use geometric descriptions of rigid motions to transform figures and to predict the effect of a given rigid motions on a given figure; given two figures, use the definition of congruence in terms of rigid motions to decide if they are congruent. 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. 8 Explain how the criteria for triangle congruence (ASA, SAS, and SSS) follow from the definition of congruence in terms of rigid motions. Instructional Focus
Unit Enduring Understandings  Continue the development of Euclidean geometry  Extend algebraic skills to problem solving with geometric concepts  Communicate mathematical ideas effectively in a variety of modalities  Geometry properties can be used to construct geometric figures  Geometric relationships provide a means to make sense of a variety of phenomena  Reasoning and/or proof can be used to verify or refute conjectures or theorems in geometry  Coordinate geometry can be used to represent and verify geometric/algebraic relationships Unit Essential Questions  How can spatial relationships be described by careful use of geometric language?  How do geometric relationships help to solve problems and/or make sense of phenomena?  How can we best represent and verify geometric/algebraic relationships? Objectives Students will know:  Terms: congruent, corresponding parts, isosceles triangle, parts of an isosceles triangle, parts of a right triangle, median, altitude, perpendicular bisectors, equidistant, distance from a point to a line  Postulates: SSS Postulate, SAS Postulate, ASA Postulate  Theorems: Isosceles Triangle Theorem, Converse of Isosceles Triangle Theorem, AAS Theorem, HL Theorem, theorems about perpendicular bisectors and angle bisectors  Corollaries: Corollaries dealing with equilateral, equiangular, and isosceles triangles Students will be able to: 
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Perform basic constructions and relate these to triangle congruence Use Geometer’s Sketchpad to explore triangle congruence and construction Identify the corresponding parts of congruent figures Prove two triangles congruent by using SSS Postulate, the SAS Postulate and the ASA Postulate Deduce information about segments and angles after proving that two triangles are congruent Apply the theorems and corollaries about isosceles triangles Use the AAS Theorem to prove two triangles congruent Use the HL Theorem to prove two right triangles are congruent Prove that two overlapping triangles are congruent Prove two triangles congruent by first proving two other triangles congruent Apply the definitions of median and altitude of a triangle and the perpendicular bisector of a segment State and apply the theorems about a point on the perpendicular bisector of a segment, and the converse State and apply the theorem about a point on the bisector of an angle, and the converse Resources
Core Text: Geometry for Enjoyment and Challenge, Rhoad, Milauskas, Whipple, 1996 Suggested Resources: Unit 5: Parallel Lines and Planes Content Area: Mathematics Course & Grade Level: Geometry Honors and Accelerated, 9 Summary and Rationale Students will study the angles formed when two lines are cut by a third line, called the transversal. Throughout the unit, they will be introduced to several theorems and postulates related to parallel and perpendicular lines. Recommended Pacing 13 days State Standards Standard 4.G‐CO Congruence CPI # Cumulative Progress Indicator (CPI) 1 Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment, based on the undefined notions of point, line, distance around a circular arc. 3 Develop definitions of rotations, reflections, and translations in terms of angles, circles, perpendicular lines, parallel lines, and line segments. 4 Develop definitions of rotations, reflections, and translations in terms of angles, circles, perpendicular lines, parallel lines, and line segments. 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; points on a perpendicular bisector of a line segment are exactly those equidistant from the segment’s endpoints. Instructional Focus
Unit Enduring Understandings  Continue the development of Euclidean geometry  Extend algebraic skills to problem solving with geometric concepts  Communicate mathematical ideas effectively in a variety of modalities  Geometry properties can be used to construct geometric figures  Geometric relationships provide a means to make sense of a variety of phenomena  Reasoning and/or proof can be used to verify or refute conjectures or theorems in geometry  Coordinate geometry can be used to represent and verify geometric/algebraic relationships Unit Essential Questions  How can spatial relationships be described by careful use of geometric language?  How do geometric relationships help to solve problems and/or make sense of phenomena?  How can we best represent and verify geometric/algebraic relationships? Objectives Students will know:  Terms: parallel lines, parallel planes, transversal, alternate interior angles, same side interior angles, corresponding angles, corollary, triangle, exterior angle of a triangle, remote interior angles of a triangle, convex polygons, regular polygons, exterior/interior angles of convex polygons, spherical geometry, inductive reasoning  Postulates: Postulates dealing with parallel lines and proving lines parallel 
Theorems: Theorems dealing with parallel lines and proving lines parallel, sum of the measures of the three angles of a triangle, measure of exterior angle of a triangle, theorems dealing with angles of a polygon  Corollaries: Corollaries dealing with angles of a triangle. Students will be able to:  Distinguish between intersecting lines, parallel lines, and skew lines  State and apply the theorem about the intersection of two parallel planes by a third plane  Identify the angles formed when two lines are cut by a transversal  State and apply the postulates and theorems about parallel lines  State and apply the theorems about a parallel and a perpendicular to a given line through a point outside the line  Classify triangles according to sides and to angles  State and apply the theorem and the corollaries about the sum of the measures of the angles of a triangle  State and apply the theorem about the measure of an exterior angle of a triangle  Recognize and name convex polygons and regular polygons  Find the measure of the interior angles and exterior angles of convex polygons  Understand and use inductive reasoning Resources
Core Text: Geometry for Enjoyment and Challenge, Rhoad, Milauskas, Whipple, 1996 Suggested Resources: Unit 6: Similar Polygons Content Area: Mathematics Course & Grade Level: Geometry Honors and Accelerated, 9 Summary and Rationale The concept of similarity is explored in this unit. Students will use ratios and proportions in connections with similar polygons. Recommended Pacing 15 days State Standards Standard 4.G‐SRT Similarity, Right Triangles, and Trigonometry CPI # Cumulative Progress Indicator (CPI) 2 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. 3 Use the properties of similarity transformations to establish the AA criterion for two triangles to be similar. 5 Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures. Standard 4.G‐MG Modeling with Geometry CPI # Cumulative Progress Indicator (CPI) 1 Use geometric shapes, their measures, and their properties to describe objects. Instructional Focus
Unit Enduring Understandings  Continue the development of Euclidean geometry  Extend algebraic skills to problem solving with geometric concepts  Communicate mathematical ideas effectively in a variety of modalities  Geometry properties can be used to construct geometric figures  Geometric relationships provide a means to make sense of a variety of phenomena  Reasoning and/or proof can be used to verify or refute conjectures or theorems in geometry  Coordinate geometry can be used to represent and verify geometric/algebraic relationships Unit Essential Questions  How can spatial relationships be described by careful use of geometric language?  How do geometric relationships help to solve problems and/or make sense of phenomena?  How can we best represent and verify geometric/algebraic relationships? Objectives Students will know:  Terms: ratio, proportion, means, extremes, similar, scale factor (similarity ratio)  Properties of proportions  Postulate: AA Postulate  Theorems: SAS Theorem, SSS Theorem, Triangle Proportionality Theorem, Triangle Angle Bisector Theorem  Corollary: Corollary dealing with parallel lines and proportional segments Students will be able to:  Use Geometer’s Sketchpad to explore the comparison between a geometric mean and an arithmetic mean  Study and use the concepts of similarity between polygons  Use related theorems to prove triangles are/are not similar  Explore and utilize the properties of congruence and proportionality of similar triangles  Investigate and prove theorems related to proportionality Resources
Core Text: Geometry for Enjoyment and Challenge, Rhoad, Milauskas, Whipple, 1996 Suggested Resources: Unit 7: The Pythagorean Theorem and Right Triangles Content Area: Mathematics Course & Grade Level: Geometry Honors & Accelerated, 9 Summary and Rationale This unit investigates the relationship between the sides lengths of special right triangles, and the use of the three main trigonometric ratios. Recommended Pacing 20 days State Standards Standard 4.G‐SRT Similarity, Right Triangles, and Trigonometry CPI # Cumulative Progress Indicator (CPI) 6 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. 7 Explain and use the relationship between the sine and cosine of complementary angles. 8 Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems. 10 Prove the Law of Sines and Cosines and use them to solve problems. Instructional Focus
Unit Enduring Understandings  Continue the development of Euclidean geometry  Extend algebraic skills to problem solving with geometric concepts  Communicate mathematical ideas effectively in a variety of modalities  Geometry properties can be used to construct geometric figures  Geometric relationships provide a means to make sense of a variety of phenomena  Reasoning and/or proof can be used to verify or refute conjectures or theorems in geometry  Coordinate geometry can be used to represent and verify geometric/algebraic relationships  Measurements can be used to describe, compare, and make sense of phenomena Unit Essential Questions  How can spatial relationships be described by careful use of geometric language?  How do geometric relationships help to solve problems and/or make sense of phenomena?  How can we best represent and verify geometric/algebraic relationships?  How can measurements be used to solve problems? Objectives Students will know:  Terms: geometric mean, sine, cosine, tangent, angle of depression, angle of elevation  Theorems: Theorem about the similar triangles formed by the altitude to the hypotenuse, Pythagorean Theorem, converse of the Pythagorean Theorem, theorems about the lengths of the sides of an acute/ obtuse triangle, 45˚ ‐ 45˚ ‐ 90˚ Theorem, 30˚‐ 60˚ ‐ 90˚ Theorem  Corollaries: Corollaries about the altitude drawn to the hypotenuse of a right triangle and the geometric mean
Students will be able to:  Apply properties of radicals to problem solving  Apply solutions of quadratics to problem solving 
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Investigate and prove relationships that occur when an altitude is drawn to a hypotenuse Develop and use the Distance Formula in problem solving Explore relationships of right triangle families Investigate and prove relationships that exist in special right triangles Apply knowledge of the Pythagorean Theorem and it’s proof to problem solving situations Explore the concept of right triangle trigonometry and how these ratios are used in problem solving Resources
Core Text: Geometry for Enjoyment and Challenge, Rhoad, Milauskas, Whipple, 1996 Suggested Resources: Unit 8: Circles Content Area: Mathematics Course & Grade Level: Geometry Honors & Accelerated, 9 Summary and Rationale All students will develop spatial sense and the ability to use geometric properties, relationships, and measurement to model, describe, and analyze phenomena. Recommended Pacing 20 days State Standards Standard 4.G‐C Circles CPI # Cumulative Progress Indicator (CPI) 2 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. 3 Construct the inscribed and circumscribed circles of a triangle, and prove properties of angles for a quadrilateral inscribed in a circle. 4 Construct a tangent line from a point outside a given circle to the circle. Instructional Focus
Unit Enduring Understandings  Continue the development of Euclidean geometry  Extend algebraic skills to problem solving with geometric concepts  Communicate mathematical ideas effectively in a variety of modalities  Geometry properties can be used to construct geometric figures  Geometric relationships provide a means to make sense of a variety of phenomena  Reasoning and/or proof can be used to verify or refute conjectures or theorems in geometry  Coordinate geometry can be used to represent and verify geometric/algebraic relationships Unit Essential Questions  How can spatial relationships be described by careful use of geometric language?  How do geometric relationships help to solve problems and/or make sense of phenomena?  How can we best represent and verify geometric/algebraic relationships? Objectives Students will know:  Terms: circle, center, radius, chord, diameter, secant, tangent, point of tangency, sphere, congruent circles, concentric circles, inscribed and circumscribed circles, great circle, common tangents, tangent circles, central angle, arc, minor and major arc, semicircle, measure of an arc, adjacent arcs, congruent arcs, inscribed angle, intercepted arc  Postulate: Arc Addition Postulate  Theorems: Theorems dealing with tangents and chords (and their converses), same circles and congruent circles, inscribed angles, tangent‐tangent angles, tangent‐chord angles, chord‐chord angles, tangent‐secant angles. Theorems dealing with segments of a circle including chord‐chord segments, tangent‐secant segments, secant‐secant segments.  Corollaries: Corollaries dealing with tangents and inscribed angles Students will be able to:  Define a circle, a sphere and terms related to them  Recognize inscribed (circumscribed) polygons and circumscribed (inscribed) circles  Apply theorem that relate tangents and radii  Define and apply properties of arcs and central angles  Apply theorems about chords of a circle  Solve problems and prove statements involving inscribed angles and angles formed by chords, secants and tangents of a circle  Solve problems involving lengths of chords, secant segments and tangent segments Resources
Core Text: Geometry for Enjoyment and Challenge, Rhoad, Milauskas, Whipple, 1996 Suggested Resources: Unit 9: Area Content Area: Mathematics Course & Grade Level: Geometry Honors & Accelerated, 9 Summary and Rationale All students will develop spatial sense and the ability to use geometric properties, relationships, and measurement to model, describe, and analyze phenomena. Recommended Pacing State Standards Standard 4.G‐GPE Expressing Geometric Properties with Equations CPI # Cumulative Progress Indicator (CPI) 7 Use coordinates to compute perimeters of polygons and areas of triangles and rectangles, e.g. Using the distance formula. Standard 4.G‐MG Modeling with Geometry CPI # Cumulative Progress Indicator (CPI) 1 Use geometric shapes, their measures, and their properties to describe objects. 3 Apply geometric methods to solve design problems. Standard 4.G‐GMD Geometric Measurement and Dimension 1 Give an informal argument for the formulas for the circumference of a circle, area of a circle, volume of a cylinder, pyramid, and cone. Instructional Focus
Unit Enduring Understandings  Continue the development of Euclidean geometry  Extend algebraic skills to problem solving with geometric concepts  Communicate mathematical ideas effectively in a variety of modalities  Geometry properties can be used to construct geometric figures  Geometric relationships provide a means to make sense of a variety of phenomena  Reasoning and/or proof can be used to verify or refute conjectures or theorems in geometry  Coordinate geometry can be used to represent and verify geometric/algebraic relationships Unit Essential Questions  How can spatial relationships be described by careful use of geometric language?  How do geometric relationships help to solve problems and/or make sense of phenomena?  How can we best represent and verify geometric/algebraic relationships? Objectives Students will know:  Terms: area, center, radius, central angle and apothem of a regular polygon, circumference, arc length, sector, segment of a circle, geometric probability  Formulas: Area formulas for rectangles, parallelograms, triangles, rhombuses, trapezoids, regular polygons, circles, sectors of a circle; circumference of a circle  Postulate: Area of a square = s2, Area Congruence Postulate, Area Addition Postulate  Theorems: Theorems for finding area of plane and similar figures and perimeter of similar figures Students will be able to:  Understand what is meant by the area of a polygon  Know and use the formulas for the areas of rectangles, parallelograms, triangles, rhombuses, trapezoids and regular polygons  Know and use the formulas for circumference and area of circles, for arc length and areas of sectors of a circle  Find the ratio of the areas of two triangles  Understand and apply the relationships between scale factors, perimeters and areas of similar figures  Use areas to solve problems involving geometric probability Resources
Core Text: Geometry for Enjoyment and Challenge, Rhoad, Milauskas, Whipple, 1996 Suggested Resources: Unit 10: Surface Area and Volume Content Area: Mathematics Course & Grade Level: Geometry Honors & Accelerated, 9 Summary and Rationale All students will develop spatial sense and the ability to use geometric properties, relationships, and measurement to model, describe, and analyze phenomena. Recommended Pacing 20 days State Standards Standard 4.GMD Geometric Measurement and Dimension CPI # Cumulative Progress Indicator (CPI) 1 Give an informal argument for the formulas for the circumference of a circle, area of a circle, volume of a cylinder, pyramid, and cone. 2 Give an informal argument using Cavalieri's principle for the formulas for the volume of a sphere and other solid figures. 3 Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems. Standard 4.G‐MG Modeling with Geometry CPI # Cumulative Progress Indicator (CPI) 2 Apply concepts of density based on area and volume in modeling situations. 3 Apply geometric methods to solve design problems. Instructional Focus
Unit Enduring Understandings  Continue the development of Euclidean geometry  Extend algebraic skills to problem solving with geometric concepts  Communicate mathematical ideas effectively in a variety of modalities  Geometry properties can be used to construct geometric figures  Geometric relationships provide a means to make sense of a variety of phenomena  Reasoning and/or proof can be used to verify or refute conjectures or theorems in geometry  Coordinate geometry can be used to represent and verify geometric/algebraic relationships Unit Essential Questions  How can spatial relationships be described by careful use of geometric language?  How do geometric relationships help to solve problems and/or make sense of phenomena?  How can we best represent and verify geometric/algebraic relationships? Objectives Students will know:  Terms: prism, base, altitude, lateral face, lateral edge, right prism, oblique prism, lateral area, total area, cube, volume, regular pyramid, vertex, slant height, cylinder, cone, sphere, similar solids  Theorems: Theorems dealing with lateral area, total area and volume of prisms, pyramids, cylinders and cones. Theorems with area and volume of spheres. Theorems involving ratios of two similar solids. Students will be able to: 
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Identify the parts of prisms, pyramids, cones and cylinders Develop the concept of surface area of polyhedral and examine the properties of polyhedral Investigate and use surface area of circular solids Find the lateral areas, total areas and volumes of right prisms, regular pyramids, right cylinders, right cones Find the area and volume of a sphere State and apply the properties of similar solids Resources
Core Text: Geometry for Enjoyment and Challenge, Rhoad, Milauskas, Whipple, 1996 Suggested Resources: Unit 11: Coordinate Geometry Content Area: Mathematics Course & Grade Level: Geometry Honors & Accelerated, 9 Summary and Rationale All students will develop spatial sense and the ability to use geometric properties, relationships, and measurement to model, describe, and analyze phenomena. Recommended Pacing 15 days State Standards Standard 4.G‐CO Congruence CPI # Cumulative Progress Indicator (CPI) 1 Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment, based on the undefined notions of point, line, distance around a circular arc. 3 Develop definitions of rotations, reflections, and translations in terms of angles, circles, perpendicular lines, parallel lines, and line segments. 4 Develop definitions of rotations, reflections, and translations in terms of angles, circles, perpendicular lines, parallel lines, and line segments. 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; points on a perpendicular bisector of a line segment are exactly those equidistant from the segment's endpoints. Instructional Focus
Unit Enduring Understandings  Build a foundation for the development of Euclidean geometry  Extend algebraic skills to problem solving with geometric concepts  Communicate mathematical ideas effectively in a variety of modalities  Coordinate geometry can be used to represent and verify geometric/algebraic relationships  Students will understand the link between algebraic skills and geometric reasoning Unit Essential Questions  How can we understand the link between algebraic skills and geometric reasoning?  How can we best represent and verify geometric/algebraic relationships? Objectives Students will know:  Terms: y‐intercept, slope, parallel, perpendicular  Formulas: midpoint, distance, slope, standard, slope‐intercept, and point‐slope forms of lines Students will be able to:  Graph a point given its coordinates and determine the coordinates of a point given its graph  Apply the midpoint formula  Find the slope of a line given coordinates of two points on the line  Determine whether two lines are parallel, perpendicular, or neither when given the slopes of two lines  Graph a line given its equation 
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Write an equation of a line in standard, slope‐intercept and point‐slope forms Apply the distance formula Manipulate geometric figures using Geometer Sketchpad Resources
Core Text: Geometry for Enjoyment and Challenge, Rhoad, Milauskas, Whipple, 1996 Suggested Resources: Unit 12: Transformations Content Area: Mathematics Course & Grade Level: Geometry Honors, 9 Summary and Rationale All students will develop spatial sense and the ability to use geometric properties, relationships, and measurement to model, describe, and analyze phenomena. Recommended Pacing 12 days State Standards Standard 4.G‐CO Congruence CPI # Cumulative Progress Indicator (CPI) 2 Represent transformations in the plane; describe transformations as functions that take points in the place as inputs and give other points as outputs. Compare transformations that preserve distance and angle to those that do not. 3 Given a rectangle, parallelogram, trapezoid, or regular polygon, describe the rotations and reflections that carry it onto itself. 4 Develop definitions of rotations, reflections, and translations in terms of angles, circles, perpendicular lines, parallel lines, and line segments. 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. Instructional Focus
Unit Enduring Understandings  Continue the development of Euclidean geometry  Extend algebraic skills to problem solving with geometric concepts  Communicate mathematical ideas effectively in a variety of modalities  Geometry properties can be used to construct geometric figures  Geometric relationships provide a means to make sense of a variety of phenomena  Reasoning and/or proof can be used to verify or refute conjectures or theorems in geometry  Coordinate geometry can be used to represent and verify geometric/algebraic relationships Unit Essential Questions  How can spatial relationships be described by careful use of geometric language?  How do geometric relationships help to solve problems and/or make sense of phenomena?  How can we best represent and verify geometric/algebraic relationships? Objectives Students will know:  Terms: image, preimage, mapping, one‐to‐one mapping, transformation, isometry, congruence mapping, reflection, translation, glide reflection, vector, magnitude, rotation, dilation, expansion, contraction, similarity mapping, composite, identity, inverse, symmetry (line, point, rotational, translational, glide reflection, bilateral, plane), tessellations  Notation: Notation for mappings and composition of mappings, reflections, translations, rotations, dilations, inverse and identities  Theorems: Theorems dealing with isometries (reflection, translation, rotation). Theorems dealing with dilations and compositions of mappings  Corollaries: Corollaries dealing with isometries, dilations and compositions of mappings Students will be able to:  Recognize and use the terms image, preimage, mapping, one‐to‐one mapping, transformation, isometry and congruence mapping  Recognize the properties of the basic mappings  Locate images of figures by reflection, translation, glide reflection, rotation and dilation  Locate the images of figures by compositions of mappings  Recognize the terms identity and inverse in relation to mappings  Describe the symmetry of figures and solids Resources
Core Text: Geometry for Enjoyment and Challenge, Rhoad, Milauskas, Whipple, 1996 Suggested Resources: