Geometry Dunmore School District Dunmore, PA
Geometry Prerequisite: Successful completion Algebra I This course is designed for the student who has successfully completed Algebra I. 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 Page 1
Year-at-a-glance Subject: Geometry Grade Level: 10th 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 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 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 Page 3
Midpoint, Distance, Slope Perimeter/Area 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 Special Right Triangles G.2.1.1. CC.2.2.HS.C.9 CC.2.3.HS.A.7 CC.2.3.HS.A.7 Geometry 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 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 Page 6
Pairs of Angles/Missing Angle Puzzles Dunmore School District 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 Page 7
Transformations: Translations/Reflections/Rotations Dunmore School District Critical Thinking Questions 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 Page 8
3 rd Quarter Inductive Reasoning Topic Resources Standards G.2.1.2 G.1.3.2.1 CC.2.3.HS.A.11 Linear Function Patterns/Graphing Calculator G.2.1.2 G.1.3.2.1 CC.2.3.HS.A.11 Pascal s Triangle/Fibonacci Sequence G.2.1.2 G.1.3.2.1 CC.2.3.HS.A.11 Geometry Page 9
Logic: Conditional Statements/Truth Tables Dunmore School District G.2.1.2 G.1.3.2.1 CC.2.3.HS.A.11 Parallel Lines/Perpendicular Lines: Geometric Figures G.2.2.1 CC.2.3.8.A.2 CC.2.3.HS.A.3 CC.2.3.HS.A.11 Classifying Triangles/All Triangle Facts/interior Angle Sum/Exterior Angle Sum/Midsegments G.1.2.1 CC.2.3.8.A.2 CC.2.3.HS.A.3. CC.2.3.HS.A.13 Geometry 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 Page 11
4 th Quarter Congruent Triangle Proofs 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 Similar Triangles ) 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 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 Page 13
2.3. Geometry General Topic Anchor Descriptor PA Core Standards Eligible Content, Essential Knowledge, Skills & Vocabulary 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. Resources & Activities Assessments Suggested Time (In Days) Geometry: Common Core Critical Thinking Questions Worksheets (Gift Sheets) Teacher prepared tests, quizzes, etc. Series available assessments online. 46 Days A1.1.1.1.2 Simplify square roots (e.g., 24 = 2 6). 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, *Combine/Multiply/Divide Radical Introduction to Formulas Literal Equations Geometry Page 14
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. G.2.2.4 Apply probability to practical situations. CC.2.3.HS.A.14 Apply geometric concepts to model and solve realworld problems. 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, Geometry Page 15
G.2.1.2 Solve problems using analytic geometry. and/or spheres. Formulas are provided on a reference sheet. 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.) 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. 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. 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. Pythagorean Triples Midpoint, Distance, Slope G.2.1.2.3 Use slope, distance, and/or midpoint between two points on a Geometry Page 16
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. CC.2.3.HS.A.7 Apply trigonometric ratios to solve problems involving right triangles. coordinate plane to 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 Geometry 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. CC.2.3.HS.A.2 Apply rigid transformations to determine and explain congruence. 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: Point Line Plane Line Segment 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 Geometry 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. 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. Collinear Noncollinear Coplanar Noncoplanar Endpoint Rays Opposite Rays Postulate Coordinate Distance Length Congruent Segments Between Midpoint Bisects Perpendicular Bisector angle vertex interior of angle exterior of an angle angle measure degree acute angle right angle obtuse angle straight angle adjacent angles linear pair Geometry Page 19
G.2.2.1 Use and/or compare measurements of angles. 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. 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 Truth Tables G.1.3.2.1 Write, analyze, complete, or identify formal proofs (e.g., direct and/or Geometry: Common Core Critical Thinking Questions Worksheets (Gift Sheets) Teacher prepared tests, quizzes, etc. Series available assessments online. 20 Days Geometry Page 20
Indirect proofs/proofs by contradiction). Congruence Proofs Vocabulary: inductive reasoning deductive reasoning conjectures inverse converse contrapositive biconditional statements 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. 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 Geometry Page 21
Algebraic Equations with Parallel and Perpendicular Lines 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. 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 Geometry: Common Core Critical Thinking Questions Teacher prepared tests, quizzes, etc. Series available assessments online. 20 Days Geometry Page 22
CC.2.3.HS.A.13 Analyze relationships between twodimensional and threedimensional objects. Interior Angle Sum Exterior Angle Sum Remote Interior Angles Congruent Triangles Congruence Shortcuts CPCTC Congruence Proofs Isosceles Triangles Triangle Theorems Midsegments Worksheets (Gift Sheets) 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. 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?). Geometry: Common Core Critical Thinking Questions Worksheets (Gift Sheets) Teacher prepared tests, quizzes, etc. Series available assessments online. 10 Days Geometry Page 23
CC.2.3.HS.A.6 Verify and apply theorems involving similarity as they relate to plane figures. Properties of Similar Triangles Similarity Shortcuts Proportions Geometric Mean 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 Geometry 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. Rhombi Trapezoids Kites Polygons 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 Geometry Page 25
Review and Final Exam Preparation Dunmore School District Properties of Arcs and Chords Tangents Secants Annulus Shaded Area: Inscribed and Circumscribed Polygons Sectors Segments 8 Days Geometry Page 26