Geometry Honors Dunmore School District Dunmore, PA
Geometry Honors Prerequisite: Successful Completion of Algebra I Honors K This course is designed for the student who has successfully completed Algebra I Honors K. The course content is designed to strengthen algebraic skills as students study all properties and applications of one dimensional and twodimensional geometric figures. This course is intended to develop visual, pictorial, and analytical thinking skills which emphasize modeling as a strategy to solving real world application problems. After completion of the course, students will be allowed to enroll in Honors Algebra II or Algebra II. Geometry Honors Page 1
Year-at-a-glance Subject: Geometry Honors Grade Level: 9th Date Completed: 2/23/2017 1 st Quarter Fraction Computation Topic Resources Standards M07.A-N.1.1 CC.2.1.7.E.1 Radical Computation Geometry Formulas Kuta Softwre - M08.A-N.1.1 CC.2.1.8.E.1 M07.C-G.2 G.2.2.2 CC.2.2.HS.C.1 CC.2.3.HS.A.3 CC.2.3.HS.A.9 Geometry Honors Page 2
Literal Equations Shaded Area Pythagorean Theorem/Pythagorean Triples Dunmore School District CC.2.2.HS.D.8, A1.1.2.1.1, A1.1.2.1.2, A1.1.2.1.3, A2.1.3.1.1, A2.1.3.1.2, A2.1.3.1.3, A2.1.3.1.4, A2.1.3.2.1, A2.1.3.2.2 M07.C-G.2 G.2.2.2 CC.2.2.HS.C.1 CC.2.3.HS.A.3 CC.2.3.HS.A.9 G.2.1. G.2.3 CC.2.3.8.A.3 CC.2.3.HS.A.11 CC.2.3.8.A.1 CC.2.3.HS.A.12 CC.2.3.HS.A.14. G.2.2.3. CC.2.3.HS.A.8 CC.2.3.HS.A.9 Geometry Honors Page 3
Midpoint, Distance, Slope Perimeter/Area Special Right Triangles Dunmore School District G.2.1.2.3 CC.2.3.8.A.3 CC.2.3.HS.A.11 M07.C-G.2 G.2.2.2 CC.2.2.HS.C.1 CC.2.3.HS.A.3 CC.2.3.HS.A.9 G.2.1.1. CC.2.2.HS.C.9 CC.2.3.HS.A.7 CC.2.3.HS.A.7 Geometry Honors Page 4
Right Triangle Trigonometry Dunmore School District G.2.1.1.2 CC.2.2.HS.C.9 CC.2.3.HS.A.7 Geometry Honors Page 5
2 nd Quarter Topic Resources Standards Introduction to Geometry: Vocabulary/Postulates G.1.2.1 CC.2.3.8.A.2 CC.2.3.HS.A.3 CC.2.3.HS.A.13 Angles: Naming, Measuring, Adding, Subtracting Three Dimensional Drawings G.1.2.1 G.1.2.1 CC.2.3.8.A.2 CC.2.3.HS.A.3 CC.2.3.HS.A.13 Geometry Honors Page 6
Pairs of Angles/Missing Angle Puzzles Dunmore School District Holt) McDougal G.1.2.1 Introduction to Constructions: Duplicating Segments/Segment Addition/Segment Subtraction/Centroid/Circumcenter/ Orthocenter/Incenter G.1.3.1.1 G.1.2.1 CC.2.3.8.A.2. CC.2.3.HS.A.3 CC.2.3.HS.A. TI-84 Cabri Jr. G.1.3.1.1 G.1.2.1 CC.2.3.8.A.2. CC.2.3.HS.A.3 CC.2.3.HS.A. Geometry Honors Page 7
Transformations: Translations/Reflections/Rotations Dunmore School District G.1.3.1 CC.2.3.HS.A.1 CC.2.3.HS.A.2. CC.2.3.HS.A. CC.2.3.HS.A.6 Geometry Honors Page 8
3 rd Quarter Inductive Reasoning Linear Function Patterns/Graphing Calculator Pascal s Triangle/Fibonacci Sequence Topic Resources Standards G.2.1.2 G.1.3.2.1 CC.2.3.HS.A.11 G.2.1.2 G.1.3.2.1 CC.2.3.HS.A.11 G.2.1.2 G.1.3.2.1 CC.2.3.HS.A.11 Geometry Honors Page 9
Logic: Conditional Statements/Truth Tables Parallel Lines/Perpendicular Lines: Geometric Figures Classifying Triangles/All Triangle Facts/interior Angle Sum/Exterior Angle Sum/Midsegments Dunmore School District G.2.1.2 G.1.3.2.1 CC.2.3.HS.A.11 G.2.2.1 CC.2.3.8.A.2 CC.2.3.HS.A.3 CC.2.3.HS.A.11 G.1.2.1 CC.2.3.8.A.2 CC.2.3.HS.A.3. CC.2.3.HS.A.13 Geometry Honors Page 10
Congruent Triangles Dunmore School District G.1.3.1 CC.2.3.HS.A.1 CC.2.3.HS.A.2 CC.2.3.HS.A.5 CC.2.3.HS.A.6 Geometry Honors Page 11
4 th Quarter Congruent Triangle Proofs Similar Triangles Topic Resources Standards G.1.3.1 CC.2.3.HS.A.1 CC.2.3.HS.A.2 CC.2.3.HS.A.5 CC.2.3.HS.A.6 G.1.3.1 G.1.3.1.2 G.2.2.3.1 G.2.3.2.1 CC.2.3.HS.A.1 CC.2.3.HS.A.2 CC.2.3.HS.A.5 CC.2.3.HS.A.6 Quadrilaterals: Rectangles/Squares/Rhombus/Trapezoids/Kites Area/Perimeter/shaded Area G.1.3.1 CC.2.3.HS.A.1 CC.2.3.HS.A.2 CC.2.3.HS.A.5 CC.2.3.HS.A.6 Geometry Honors Page 12
Polygons: Inductive Reasoning Interior Angle Sum, Exterior Angle Sum, Find Number of Sides Dunmore School District G.1.3.1 G.1.2.1.4 G.2.2.2.2 G.2.2.2.3 CC.2.3.HS.A.1 CC.2.3.HS.A.2 CC.2.3.HS.A.5. CC.2.3.HS.A.6 Circles: Parts/Solve for Missing Radii, Diameters, Central Angles, Inscribed Angles, Missing Arcs, Missing Angles, Missing Segments Review and Final Exam G.1.1.1 G.1.1.1.1 G.1.1.1.2 G.1.1.1.3 G.1.1.1.4 G.2.2.2.1 G.2.2.2.5 CC.2.3.HS.A.8 CC.2.3.HS.A.9 CC.2.3.HS.A.13 Geometry Honors Page 13
General Topic Anchor Descriptor Eligible Content, Essential Knowledge, PA Core Standards Skills & Vocabulary Resources & Activities Assessments Suggested Time (In Days) Prerequisite Skills M07.A-N.1.1 Solve real-world and mathematical problems involving the four operations with rational numbers. CC.2.1.7.E.1 Apply and extend previous understandings of operations with fractions to operations with rational numbers. M08.A-N.1.1 Apply concepts of rational and irrational numbers. CC.2.1.8.E.1 Distinguish between rational and irrational numbers using their properties. Fractions M07.A-N.1.1.3 Apply properties of operations to multiply and divide rational numbers, including real-world contexts; demonstrate that the decimal form of a rational number terminates or eventually repeats. Radicals M08.A-N.1.1.4 Use rational approximations of irrational numbers to compare and order irrational numbers. A1.1.1.1.2 Simplify square roots (e.g., 24 = 2 6). Geometry: Common Core Critical Thinking Questions Worksheets (Gift Sheets) Teacher prepared tests, quizzes, etc. Series available assessments online. 46 Days *Combine/Multiply/Divide Radicals Introduction to Formulas Literal Equations Geometry Honors Page 14
CC.2.2.HS.D. Apply inverse operations to solve equations or formulas for a given variable. A1.1.2.1.1, A1.1.2.1.2, A1.1.2.1.3, A2.1.3.1.1, A2.1.3.1.2, A2.1.3.1.3, A2.1.3.1.4, A2.1.3.2.1, A2.1.3.2.2 M07.C-G.2 Solve real-world and mathematical problems involving angle measure, circumference, area, surface area, and volume. G.2.2.2 Use and/or develop procedures to determine or describe measures of perimeter, circumference, and/or area. (May require conversions within the same system.) CC.2.2.HS.C.1 Use the concept and notation of functions to interpret and apply them in terms of their context. CC.2.3.HS.A.3 Verify and apply geometric theorems as they relate to geometric figures. CC.2.3.HS.A.9 Extend the concept of similarity to determine arc lengths and areas of sectors of circles. M07.C-G.2.2.2 Solve realworld and mathematical problems involving area, volume, and surface area of two and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms. Use Formulas to Find Shaded Area G.2.2.2.1 Estimate area, perimeter, or circumference of an irregular figure. G.2.2.4.1 Use area models to find probabilities. G.2.2.2.2 Find the measurement of a missing length, given the perimeter, circumference, or area. G.2.2.2.4 Develop and/or use strategies to estimate the area of a compound/composite figure. G.2.3.1.1 Calculate the surface area of prisms, cylinders, cones, pyramids, and/or spheres. Formulas Geometry Honors Page 15
G.2.2.4 Apply probability to practical situations. CC.2.3.HS.A.14 Apply geometric concepts to model and solve realworld problems. G.2.1.2 Solve problems using analytic geometry. CC.2.3.8.A.3 Understand and apply the Pythagorean theorem to solve problems. CC.2.3.HS.A.11 Apply coordinate geometry to prove simple geometric theorems algebraically. G.2.3.1 Use and/or develop procedures to determine or describe measures of surface area and/or volume. (May require conversions within the same system.) are provided on a reference sheet. G.2.3.1.2 Calculate the volume of prisms, cylinders, cones, pyramids, and/or spheres. Formulas are provided on a reference sheet. G.2.3.1.3 Find the measurement of a missing length given the surface area or volume. Pythagorean Theorem G.2.1.1.1 Use the Pythagorean theorem to write and/or solve problems involving right triangles. G.2.1.2.1 Calculate the distance and/or midpoint between two points on a number line or on a coordinate plane. CC.2.3.8.A.1 Apply the concepts of volume of cylinders, cones, and spheres to solve real world and mathematical problems. CC.2.3.HS.A.12 Explain volume formulas and use them to solve problems. Pythagorean Triples Midpoint, Distance, Slope G.2.1.2.3 Use slope, distance, and/or midpoint between two points on a coordinate plane to Geometry Honors Page 16
CC.2.3.HS.A.14 Apply geometric concepts to model and solve realworld problems. G.2.2.3 Describe how a change in one dimension of a twodimensional figure affects other measurements of that figure. CC.2.3.HS.A.8 Apply geometric theorems to verify properties of circles. CC.2.3.HS.A.9 Extend the concept of similarity to determine arc lengths and areas of sectors of circles. G.2.1.1 Solve problems involving right triangles. CC.2.2.HS.C.9 Prove the Pythagorean identity and use it to calculate trigonometric ratios. CC.2.3.HS.A.7 Apply trigonometric ratios to solve problems involving right triangles. establish properties of a two dimensional shape. Special Right Triangles G.1.2.1.1 Identify and/or use properties of triangles. G.1.2.1.3 Identify and/or use properties of isosceles and equilateral triangles. G.1.2.1.4 Identify and/or use properties of regular polygons. Trigonometric Functions G.2.1.1.2 Use trigonometric ratios to write and/or solve problems involving right triangles. Vocabulary: Rational Numbers Irrational Numbers Sine Cosine Tangent CC.2.3.HS.A.7 Apply trigonometric ratios to solve problems involving right triangles. Geometry Honors Page 17
Foundations of Geometry G.1.2.1 Recognize and/or apply properties of angles, polygons, and polyhedral CC.2.3.8.A.2 Understand and apply congruence, similarity, and geometric transformations using various tools. CC.2.3.HS.A.3 Verify and apply geometric theorems as they relate to geometric figures. CC.2.3.HS.A.13 Analyze relationships between twodimensional and threedimensional objects. G.1.3.1 Use properties of congruence, correspondence, and similarity in problem solving settings involving two and three dimensional figures. CC.2.3.HS.A.1 Use geometric figures and their properties to represent transformations in the plane. G.1.3.1.1 Identify and/or use properties of congruent and similar polygons or solids. Constructions: Duplicating segments Segment addition Segment subtraction Midpoint Perpendicular bisectors Triangles Medians Altitudes Angle bisectors Circumcenter Centroid Incenter Orthocenter Right angles Various angle degree measures Nine point circle Transformations Translations Reflections Rotations Vocabulary: Geometry: Common Core Critical Thinking Questions Worksheets (Gift Sheets) Cabri Jr. Construction Software on Graphing Calculator Teacher prepared tests, quizzes, etc. Series available assessments online. 47 Days CC.2.3.HS.A.2 Apply rigid transformations to determine and explain congruence. point line plane Geometry Honors Page 18
CC.2.3.HS.A.5 Create justifications based on transformations to establish similarity of plane figures. CC.2.3.HS.A.6 Verify and apply theorems involving similarity as they relate to plane figures. G.2.2.1 Use and/or compare measurements of angles. CC.2.3.8.A.2 Understand and apply congruence, similarity, and geometric transformations using various tools. G.2.2.1 Use and/or compare measurements of angles. line segment collinear noncollinear coplanar noncoplanar endpoint rays opposite rays postulate coordinate distance length congruent segments between midpoint bisects perpendicular bisector CC.2.3.8.A.2 Understand and apply congruence, similarity, and geometric transformations using various tools. CC.2.3.HS.A.3 Verify and apply geometric theorems as they relate to geometric figures. G.2.2.1 Use and/or compare measurements of angles. Angle Vertex Interior of Angle Exterior of an Angle Angle Measure Degree Acute Angle Right Angle Obtuse Angle Straight Angle Adjacent Angles Geometry Honors Page 19
CC.2.3.HS.A.1 Use geometric figures and their properties to represent transformations in the plane. CC.2.3.HS.A.2 Apply rigid transformations to determine and explain congruence. Linear Pair Complementary Angles Supplementary Angles Vertical Angles Define Sketch, Draw, Construct CC.2.3.HS.A.5 Create justifications based on transformations to establish similarity of plane figures. Geometric Reasoning G.2.1.2 Solve problems using analytic geometry. CC.2.3.8.A.3 Understand and apply the Pythagorean theorem to solve problems. CC.2.3.HS.A.11 Apply coordinate geometry to prove simple geometric theorems algebraically. Pattern Discovery Linear Functions Quadratic Functions Conditional statements Conditional statements Hypothesis Conclusion Inverse Converse Contrapositive Biconditional Statements Geometry: Common Core Critical Thinking Questions Teacher prepared tests, quizzes, etc. Series available assessments online. 20 Days Truth Tables G.1.3.2.1 Write, analyze, complete, or identify formal proofs (e.g., direct and/or indirect proofs/proofs by contradiction). Worksheets (Gift Sheets) Geometry Honors Page 20
Congruence Proofs Vocabulary: Lines - G.2.2.1 Use and/or compare measurements of angles. CC.2.3.8.A.2 Understand and apply congruence, similarity, and geometric transformations using various tools. CC.2.3.HS.A.3 Verify and apply geometric theorems as they relate to geometric figures CC.2.3.HS.A.11 Apply coordinate geometry to prove simple geometric theorems algebraically. inductive reasoning deductive reasoning conjectures inverse converse, contrapositive biconditional statements G.2.2.1.1 Use properties of angles formed by intersecting lines to find the measures of missing angles. G.2.2.1.2 Use properties of angles formed when two parallel lines are cut by a transversal to find the measures of missing angles. G.2.1.2.2 Relate slope to perpendicularity and/or parallelism (limit to linear algebraic equations). Geometry: Common Core Critical Thinking Questions Worksheets (Gift Sheets) Teacher prepared tests, quizzes, etc. Series available assessments online. 8 Days Algebraic Equations with Parallel and Perpendicular Lines Geometry Honors Page 21
Vocabulary: parallel lines perpendicular lines transversals alternate interior angles alternate exterior angles corresponding angles same side interior Triangles G.1.2.1 Recognize and/or apply properties of angles, polygons, and polyhedra. CC.2.3.8.A.2 Understand and apply congruence, similarity, and geometric transformations using various tools. CC.2.3.HS.A.3 Verify and apply geometric theorems as they relate to geometric figures. CC.2.3.HS.A.13 Analyze relationships between twodimensional and threedimensional objects. G.1.2.1.1 Identify and/or use properties of triangles. G.1.2.1.3 Identify and/or use properties of isosceles and equilateral triangles. G.1.3.1.1 Identify and/or use properties of congruent and similar polygons or solids. Classifying Triangles Triangle Inequalities Area of Triangles: 5 Methods Interior Angle Sum Exterior Angle Sum Remote Interior Angles Congruent Triangles Congruence Shortcuts CPCTC Geometry: Common Core Critical Thinking Questions Worksheets (Gift Sheets) Teacher prepared tests, quizzes, etc. Series available assessments online. 20 Days Geometry Honors Page 22
Congruence Proofs Isosceles Triangles Triangle Theorems Midsegments Similar Triangles G.1.3.1 Use properties of congruence, correspondence, and similarity in problem solving settings involving two and three dimensional figures. CC.2.3.HS.A.1 Use geometric figures and their properties to represent transformations in the plane. CC.2.3.HS.A.2 Apply rigid transformations to determine and explain congruence. CC.2.3.HS.A.5 Create justifications based on transformations to establish similarity of plane figures. CC.2.3.HS.A.6 Verify and apply theorems involving similarity as they relate to plane figures. G.1.3.1.2 Identify and/or use proportional relationships in similar figures. G.2.2.3.1 Describe how a change in the linear dimension of a figure affects its perimeter, circumference, and area (e.g., How does changing the length of the radius of a circle affect the circumference of the circle?). G.2.3.2.1 Describe how a change in the linear dimension of a figure affects its surface area or volume (e.g., How does changing the length of the edge of a cube affect the volume of the cube?). Properties of similar triangles Similarity shortcuts Proportions Geometric Mean Geometry: Common Core Critical Thinking Questions Worksheets (Gift Sheets) Teacher prepared tests, quizzes, etc. Series available assessments online. 10 Days Geometry Honors Page 23
Quadrilaterals and Polygons G.1.2.1 Recognize and/or apply properties of angles, polygons, and polyhedra. CC.2.3.8.A.2 Understand and apply congruence, similarity, and geometric transformations using various tools. CC.2.3.HS.A.3 Verify and apply geometric theorems as they relate to geometric figures. CC.2.3.HS.A.13 Analyze relationships between twodimensional and threedimensional objects. G.1.2.1.2 Identify and/or use properties of quadrilaterals. G.1.2.1.3 Identify and/or use properties of isosceles and equilateral triangles. G.1.2.1.4 Identify and/or use properties of regular polygons. G.1.2.1.5 Identify and/or use properties of pyramids and prisms. G.2.2.2.2 Find the measurement of a missing length, given the perimeter, circumference, or area. Geometry: Common Core Critical Thinking Questions Worksheets (Gift Sheets) 11 Days G.2.2.2.3 Find the side lengths of a polygon with a given perimeter to maximize the area of the polygon. Parallelograms Rectangles Squares Rhombi Trapezoids Kites Polygons Geometry Honors Page 24
Circles. G.1.1.1 Identify and/or use parts of circles and segments associated with circles, spheres, and cylinders. CC.2.3.HS.A.8 Apply geometric theorems to verify properties of circles. CC.2.3.HS.A.9 Extend the concept of similarity to determine arc lengths and areas of sectors of circles. CC.2.3.HS.A.13 Analyze relationships between twodimensional and threedimensional objects. G.1.1.1.1 Identify, determine, and/or use the radius, diameter, segment, and/or tangent of a circle. G.1.1.1.2 Identify, determine, and/or use the arcs, semicircles, sectors, and/or angles of a circle. G.1.1.1.3 Use chords, tangents, and secants to find missing arc measures or missing segment measures. G.1.1.1.4 Identify and/or use the properties of a sphere or cylinder. G.2.2.2.1 Estimate area, perimeter, or circumference of an irregular figure. Geometry: Common Core Critical Thinking Questions Worksheets (Gift Sheets) Teacher prepared tests, quizzes, etc. Series available assessments online. 10 Days G.2.2.2.5 Find the area of a sector of a circle. Parts of a Circle: Central Angles Inscribed Angles Properties of Arcs and Chords Tangents Secants Annulus Geometry Honors Page 25
Review and Final Exam Preparation Dunmore School District Shaded Area: Inscribed and Circumscribed Polygons Sectors Segments 8 Days Geometry Honors Page 26