# Algebra II/Geometry Curriculum Guide Dunmore School District Dunmore, PA

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1 Algebra II/Geometry Dunmore School District Dunmore, PA

2 Algebra II/Geometry Prerequisite: Successful completion of Algebra 1 Part 2 K Algebra II/Geometry is intended for students who have successfully completed Algebra I Part 2 K. This course is intended to introduce students to the Pennsylvania Common Core standards covered in Algebra II and Geometry. The core standards in this course provide the students with a solid foundation to be successful in future mathematics courses and on the SAT Exam. Algebra II/Geometry Page 1

3 Year-at-a-glance Subject: Algebra II/Geometry Grade Level: 11 Date Completed: 6/6/ st Quarter Topic Resources Standards Real Numbers, Algebra, and Problem Solving Chapter 1 1-1,1-2,1-3,1-4,1-5,1-6,1-7,1-8 A , CC.2.1.HS.F.2, CC.2.1.HS.F.1, A , A , and Inequalities Chapter 2 2-1,2-2,2-3,2-4,2-5,2-6,2-7 Relations, Functions, and Graphs Exponential Functions Logarithmic Functions Chapter 3 3-1,3-2,3-3,3-4,3-5,3-6,3-7 A , A , CC.2.2.HS.D.8, CC.2.2.HS.D 9, A , A , CC.2.1.HS.F.3, CC.2.2.HS.C.2, A , A , A Systems of and Inequalities and Problem Solving Chapter 4 4-1,4-2,4-3,4-6,4-7 CC.2.2 HS. D.7, CC.2.2.HS.D.10, A Algebra II/Geometry Page 2

4 2 nd Quarter Topic Resources Standards Polynomials and Polynomial Chapter 5 5-1,5-2,5-3,5-4,5-5,5-6,5-7 Rational Expressions and Chapter 6 6-1,6-2,6-3,6-4,6-6,6-7,6-8 CC.2.2.HS.D.4, CC.2.2.HS.D.5, CC.2.2.HS.D.3 A , A CC.2.2.HS.D.1, CC.2.2.HS.D.2, CC.2.2.HS.D.6, CC.2.1.HS.F.4, A , A Powers, Roots, and Complex Numbers Chapter 7 7-1,7-2,7-3,7-4,7-5,7-6,7-7,7-8,7-9,7-10 CC.2.1.HS.F.6, CC.2.1.HS.F.7, A , A , A , A Algebra II/Geometry Page 3

5 3 rd Quarter Topic Resources Standards Quadratic Chapter 8 8-1,8-2,8-3,8-4,8-5,8-6 CC.2.2.HS.C.5, A Quadratic Functions and Transformations Chapter 9 9-1,9-2,9-3,9-4,9-7 Geometry Introduction CC.2.2.HS.C.4, A , A G Angles Chapter G.1.2.1, G.2.2.1, G , G Algebra II/Geometry Page 4

6 4 th Quarter Topic Resources Standards Lines with Transversals Chapter 3 3-1,3-2 G.2.2.1, G , G , G Triangles and Congruence Chapter 4 4-3,4-4,4-5,4-6,4-7,4-9 Similarity Relationships Chapter 7 7-1,7-2,7-3,7-4,7-5 Trigonometric Ratios Chapter 8 8-1,8-2 Extending Perimeter, Circumference, and Area Chapter ,10-4 Spatial Reasoning Chapter ,11-3,11-4 Circles Chapter ,12-2,12-4,12-5,12-7 G.1.2.1, CC A.2, CC.2.3.HS.A.3, CC.2.3.HS.A.13, G , G , G 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 , G , G 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 , G , G , G , G M07.C-G.2, G.2.2.2, M07.C-G.2.2.2, G , G , G , G G.2.3.1, CC A.1, CC.2.3.HS.A.12, CC.2.3.HS.A.14, G , G G.1.1.1, CC.2.3.HS.A.8, CC.2.3.HS.A.9, CC.2.3.HS.A.13, G , G , G , G , G Review and Final Exam Textbooks Review Packets Algebra II/Geometry Page 5

7 General Topic Anchor Descriptor PA Core Standards Eligible Content, Essential Knowledge, Skills & Vocabulary Real Numbers, Algebra, and Problem Solving A Use Exponents, roots, and/or absolute value to represent equivalent forms or to solve problems. CC.2.1.HS.F.2 Apply properties of rational and irrational numbers to solve real world or mathematical problems. CC.2.1.HS.F.1 Apply and extend the property of exponents to solve problems. A Use exponential expressions to represent rational numbers. A Simplify/evaluate expressions involving positive and negative exponents and/or roots (may contain all types of real numbers). Algebraic Expressions Commutative Property Associative Property Distributive Property Exponential Notation Order of Operations Resources & Activities Assessments Suggested Time (In Days) Approved textbook Algebra 2 with Trigonometry Chapter Real Numbers and 1-2 Multiplication and Division 1-3 Algebraic Expressions and Properties of Numbers 1-4 The Distributive Property 1-5 Solving 1-6 Writing 1-7 Exponential Notation 1-8 Properties of Exponents 10 days Algebra II/Geometry Page 6

8 and Inequalities A Use Exponents, roots, and/or absolute value to represent equivalent forms or to solve problems. A Describe and/or determine change. CC.2.2.HS.D.8 Apply inverse operations to solve equations and formulas for a given variable. CC.2.2.HS.D 9 Use reasoning to solve equations and justify the solution. A Simplify/evaluate expressions involving multiplying with exponents, powers of powers, and powers of products. A Use algebraic processes to solve a formula for a given variable. A Write, solve, and/or apply linear or exponential growth and decay. Principle of Zero Products Guidelines to Solve Word Problems Solution Sets Compound Inequality Conjunctions Disjunctions Absolute Value Number Line Algebra 2 with Trigonometry Chapter More on Solving 2-2 Using 2-3 Solving Formulas 2-4 Solving Inequalities 2-5 Using Inequalities 2-6 Compound Inequalities 2-7 Absolute Value 14 days Algebra II/Geometry Page 7

9 Relations, Functions, and Graphs Exponential Functions Logarithmic Functions Systems of and Inequalities and Problem Solving CC.2.1.HS.F.3 Apply quantitative reasoning to choose and interpret units and scales in formulas, graphs, and data displays. CC.2.2.HS.C.2 Graph and analyze functions and use their properties to make connections between the different representations. CC.2.2 HS. D.7 Create and graph equations or inequalities to describe numbers and relationships. CC.2.2.HS.D.10 Represent, solve and interpret equations/inequalities and systems of equations/inequalities algebraically and graphically. A Determine the domain, range, or inverse function. A Create, interpret, and/or use the equation, graph, or table of a polynomial function. A Create, interpret, and/or use the equation, graph, or table of exponential functions. A Determine how a change in one variable relates to a change in the second variable. Substitution Method Linear Combinations Consistent System Dependent System Algebra 2 with Trigonometry Chapter Relations and Ordered Pairs 3-2 Graphs (Guidelines) 3-3 Functions 3-4 Graphs of Linear 3-5 Slope 3-6 More of Lines 3-7 Parallel and Perpendicular 3-9 Composition of Function Algebra 2 with Trigonometry Chapter Systems of I Two Variables 4-2 Solving a System of 4-3 Using a System of Two 4-6 Consistent and Dependent Systems 4-7 Systems of Inequalities 12 days 14 days Algebra II/Geometry Page 8

10 Polynomials and Polynomial Rational Expressions and CC.2.2.HS.D.4 Understand the relationship between zeros and factors of polynomials to make generalizations about functions and their graphs. CC.2.2.HS.D.5 Use polynomial identities to solve problems. CC.2.2.HS.D.3 Extend the knowledge of arithmetic operations and apply to polynomials. CC.2.2.HS.D.1 Interpret the structure of expressions to represent a quantity in terms of its context. A Factor algebraic expressions, including difference of squares and trinomials. ( In the form ax 2 + bx + c where (a) is not equal to zero). A Simplify rational algebraic expressions. Monomial Binomial Trinomial Additive Inverses F.O.I.L. Factoring Principle of Zero Products Factoring (Sum and Difference of two cubes) A Simplify rational expressions. A Solve equations involving rational and/or radical expressions. Algebra 2 with Trigonometry Chapter Polynomials and Functions 5-2 Addition and Subtraction of Polynomials 5-3 Multiplication of Polynomials 5-4 Factoring 5-5 More Factoring 5-6 Factoring (A General Strategy) 5-7 Solving by Factoring Algebra 2 with Trigonometry Chapter Multiplying and Simplifying 14 days 13 days Algebra II/Geometry Page 9

11 Powers, Roots, and Complex Numbers CC.2.2.HS.D.2 Write expressions in equivalent forms to solve problems. CC.2.2.HS.D.6 Extend the knowledge of rational functions to rewrite in equivalent forms. CC.2.1.HS.F.4 Use units as a way to understand problems and guide CC.2.1.HS.F.6 Extend the knowledge of arithmetic operations and apply to complex numbers. Vocabulary Reciprocals Common Denominator Least Common Multiple Complex Rational Expression Rational Equation A Simplify/write square roots in terms of i. 6-2Addition and Subtraction 6-3 Complex Rational Expressions 6-4 Division of Polynomials 6-6 Solving Rational 6-7 Using Rational 6-8 Formulas Algebra 2 with Trigonometry Chapter 7 15 days CC.2.1.HS.F.7 Apply concepts of complex numbers in polynomial identities and quadratic equations to solve problems A Simplify/evaluate expressions involving powers of i. A Add and subtract complex numbers. A Multiply and divide complex numbers. 7-1 Radical Expressions 7-2 Multiplying and Simplifying 7-3 Operations with Radical Expressions 7-4 More Operations with Radical Expressions 7-5 Rational Numbers as Exponents 7-6 Solving radical 7-7 Imaginary and Complex Numbers Algebra II/Geometry Page 10

13 Geometry Introduction G Recognize and/or apply properties of angles, polygons, and polyhedral. Axis of Symmetry Transformation Translation Horizontal Vertical Vertex Minimum Maximum Standard Form Point Line Plane Line Segment Collinear Noncollinear Coplanar Noncoplanar Endpoint Rays Opposite Rays Postulate Coordinate Distance Length Congruent Segments Between Midpoint Bisects Perpendicular Bisector 2 days Algebra II/Geometry Page 12

14 Angles G Recognize and/or apply properties of angles, polygons, and polyhedral G Use and/or compare measurements of angles. G Use properties of angles formed by intersecting lines to find the measures of missing angles. G Use properties of angles formed when two parallel lines are cut by a transversal to find the measures of missing angles Chapter Pairs of Angles Teacher produced worksheets 16 days Angle Vertex Interior of Angle Exterior of an Angle Angle Measure Degree Acute Angle Right Angle Obtuse Angle Straight Angle Adjacent Angles Linear Pair Complementary Angles Supplementary Angles Vertical Angles Algebra II/Geometry Page 13

15 Lines with Transversals G Use and/or compare measurements of angles. G Use properties of angles formed by intersecting lines to find the measures of missing angles. G Use properties of angles formed when two parallel lines are cut by a transversal to find the measures of missing angles. Chapter Lines and Angles 3-2 Angles Formed by Parallel Lines and Transversals Teacher produced worksheets 7 days G Relate slope to perpendicularity and/or parallelism (limit to linear algebraic equations). Parallel Lines Perpendicular Lines Skew Lines Parallel Planes Transversal Corresponding Angles Alternate Interior Angles Alternate Exterior Angles Same-Side Interior Angles Algebra II/Geometry Page 14

16 Triangles and Congruence G Recognize and/or apply properties of angles, polygons, and polyhedra. CC 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 Identify and/or use properties of triangles. G Identify and/or use properties of isosceles and equilateral triangles. G Identify and/or use properties of congruent and similar polygons or solids. Classifying Triangles Interior Angle Exterior Angle Remote Interior Angle Corresponding Angles Corresponding Sides Congruent Polygons Triangle Rigidity Included Angle Included Side Hypotenuse CPCTC Isosceles Triangle Legs Vertex Angle Base Base Angles SSS SAS ASA AAS HL Chapter Angle Relationships in Triangles 4-4 Congruent Triangles 4-5 Triangle Congruence: SSS and SAS 4-6 Triangle Congruence: ASA, AAS, and HL 4-7 Triangle Congruence: CPCTC 4-9 Isosceles and Equilateral Triangles Teacher Produced Worksheets 12 days Algebra II/Geometry Page 15

17 Similarity Relationships G Use properties of congruence, correspondence, and similarity in problemsolving 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. Dunmore School District G Identify and/or use proportional relationships in similar figures. G 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 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?). Similar Similar Polygons Similarity Ratio Similarity Transformation Reflexive Property of Similarity Symmetric Property of Similarity Transitive Property of Similarity Chapter Ratios in Similar Polygons 7-2 Similarity in Transformations 7-3 Triangle Similarity: AA,SSS, and SAS 7-4 Applying Properties of Similar Triangles 7-5 Using Proportional Relationships Teacher Produced Worksheets Algebra II/Geometry Page 16 5 days

18 Trigonometric Ratios 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 Identify and/or use properties of triangles. G Identify and/or use properties of isosceles and equilateral triangles. G Identify and/or use properties of regular polygons. G Use trigonometric ratios to write and/or solve problems involving right triangles. G Identify and/or use properties of congruent and similar polygons or solids Chapter Similarity in Right Triangles 8-2 Trigonometric Ratios Teacher Produced Worksheets 3 days Geometric Mean Altitude Trigonometric Ratios Sine Cosine Tangent Algebra II/Geometry Page 17

19 Extending Perimeter, Circumference, and Area M07.C-G.2 Solve real-world and mathematical problems involving angle measure, circumference, area, surface area, and volume. G Use and/or develop procedures to determine or describe measures of perimeter, circumference, and/or area. (May require conversions within the same system.) M07.C-G 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. G Estimate area, perimeter, or circumference of an irregular figure. G Use area models to find probabilities. Chapter Composite Figures 10-4 Perimeter and Area in the Coordinate Plane Teacher Produced Worksheets 4 days G Find the measurement of a missing length, given the perimeter, circumference, or area. G Develop and/or use strategies to estimate the area of a compound/composite figure. Composite Figure Perimeter Area Distance Formula Irregular Figure Algebra II/Geometry Page 18

20 Spatial Reasoning G Use and/or develop procedures to determine or describe measures of surface area and/or volume. (May require conversions within the same system.) CC A.1 Apply the concepts of volume of cylinders, cones, and spheres to solve real world and mathematical problems. G Calculate the volume of prisms, cylinders, cones, pyramids, and/or spheres. Formulas are provided on a reference sheet. G Find the measurement of a missing length given the surface area or volume. Chapter Volumes of Prisms and Cylinders 11-3 Volume of Pyramids and Cones 11-4 Spheres Teacher Produced Worksheets 3 days CC.2.3.HS.A.12 Explain volume formulas and use them to solve problems. Circles CC.2.3.HS.A.14 Apply geometric concepts to model and solve real world problems G 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. G Identify, determine, and/or use the radius, diameter, segment, and/or tangent of a circle. G Identify, determine, and/or use the arcs, semicircles, sectors, and/or angles of a circle. G Use chords, tangents, and secants to find missing arc measures or missing segment measures. Chapter Lines that Intersect Circles 12-2 Arcs and Chords 12-4 Inscribed Angles 12-5 Angle Relationships in Circles 12-7 Circles in the Coordinate Plane Teacher Produced Worksheets 5 days Algebra II/Geometry Page 19

21 CC.2.3.HS.A.13 Analyze relationships between twodimensional and threedimensional objects. G Estimate area, perimeter, or circumference of an irregular figure. G Find the area of a sector of a circle Review and Final Exam Interior of a Circle Exterior of a Circle Chord Secant Tangent Point of Tangency Congruent Circles Concentric Circles Tangent Circles Central Angle Arc Minor Arc Major Arc Semicircle Adjacent Arcs Congruent Arcs Inscribed Angles Intercepted Arc Subtends Tangent Secant Final Exam 5 days Algebra II/Geometry Page 20

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