Common Core State Standards for Mathematics High School

Transcription

1 Using the Program for Success Common Core State Standards for Mathematics High School The following shows the High School Standards for Mathematical Content that are taught in Pearson s Prentice Hall Geometry Common Core Edition Included are all of the standards that make up Achieve s Pathway for Algebra 2 and all of the assessed standards from the PARCC Model Content Frameworks. Standards that are part of Achieve s Pathway are indicated with an (A) on the standard code, while those that are part of the PARCC Model Content Frameworks are indicated with (P) on the standard code. Standards that begin with(1) indicate additional mathematics that students should learn in order to take advanced courses such as calculus, advanced statistics, or discrete mathematics. Congruence Geometry Experiment with transformations in the plane G-CO.A.1 Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment, based on the undefined notions of point, line, distance along a line, and distance around a circular arc. G-CO.A.2 Represent transformations in the plane using, e.g., transparencies and geometry software; describe transformations as functions that take points in the plane as inputs and give other points as outputs. Compare transformations that preserve distance and angle to those that do not (e.g., translation versus horizontal stretch). G-CO.A.3 Given a rectangle, parallelogram, trapezoid, or regular polygon, describe the rotations and reflections that carry it onto itself. G-CO.A.4 Develop definitions of rotations, reflections, and translations in terms of angles, circles, perpendicular lines, parallel lines, and line segments. G-CO.A.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. Where to Find 1-2, 1-3, 1-4, 1-6, 3-1, , CB 9-1, 9-2, 9-3, 9-4, 9-6 CB , 9-2, , 9-2, CB 9-2, 9-3, 9-4 T44 Common Core State Standards

2 Understand congruence in terms of rigid motions G-CO.B.6 Use geometric descriptions of rigid motions to transform figures and to predict the effect of a given rigid motion on a given figure; given two figures, use the definition of congruence in terms of rigid motions to decide if they are congruent. G-CO.B.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. G-CO.B.8 Explain how the criteria for triangle congruence (ASA, SAS, and SSS) follow from the definition of congruence in terms of rigid motions. Prove geometric theorems G-CO.C.9 Prove G-CO.C.10 Prove G-CO.C.11 Prove Make geometric constructions G-CO.D.12 Make Geometry 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. theorems about triangles. Theorems include: measures of interior angles of a triangle sum to 180 ; base angles of isosceles triangles are congruent; the segment joining midpoints of two sides of a triangle is parallel to the third side and half the length; the medians of a triangle meet at a point. theorems about parallelograms. Theorems include: opposite sides are congruent, opposite angles are congruent, the diagonals of a parallelogram bisect each other and its converse, rectangles are parallelograms with congruent diagonals. formal geometric constructions with a variety of tools and methods (compass and straightedge, string, reflective devices, paper folding, dynamic geometric software, etc.). Copying a segment; copying an angle; bisecting a segment; bisecting an angle; constructing perpendicular lines, including the perpendicular bisector of a line segment; and constructing a line parallel to a given line through a point not on the line. Where to Find 9-1, 9-2, 9-3, 9-4, , 3-2, , 4-5, 5-1, , 6-3, 6-4, , CB 3-2, 3-6, 4-4, CB 4-5, 5-2, CB 6-9, CB 7-5 G-CO.D.13 (A) (P) Construct an equilateral triangle, a square, and a regular hexagon inscribed in a circle. 3-6, 4-5, 10-3 Common Core State Standards T45 MMON CORE COMMON CORE COMMON CORE COM

3 Using the Program for Success Similarity, Right Triangles, and Trigonometry Understand similarity in terms of similarity transformations G-SRT.A.1 Verify experimentally the properties of dilations given by a center and a scale factor: CB 9-6 G-SRT.A.1a A dilation takes a line not passing through the center of the dilation to a parallel line, and CB 9-6 leaves a line passing through the center unchanged. G-SRT.A.1b The dilation of a line segment is longer or shorter in the ratio given by the scale factor. CB 9-6 G-SRT.A.2 Given two figures, use the definition of similarity in terms of similarity transformations to decide 9-7 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 side. G-SRT.A.3 Use the properties of similarity transformations to establish the AA criterion for two triangles to be similar. 9-7 Prove theorems involving similarity G-SRT.B.4 Prove theorems about triangles. Theorems include: a line parallel to one side of a triangle divides the other two proportionally and its converse; the Pythagorean Theorem proved using triangle similarity. 7-5, 8-1 G-SRT.B.5 Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures. Define trigonometric ratios and solve problems involving right triangles G-SRT.C.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. G-SRT.C.7 (A) (P) Explain and use the relationship between the sine and cosine of complementary angles. 8-3 G-SRT.C.8 Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems. Apply trigonometry to general triangles G-SRT.D.9 (1) Derive the formula A ab sin(c) for the area of a triangle by drawing an auxiliary line from a vertex perpendicular to the opposite side. 4-2, 4-3, 4-4, 4-5, 4-6, 4-7, 5-1, 5-2, 5-4, 6-1, 6-2, 6-3, 6-4, 6-5, 6-6, 7-2, 7-3, 7-4 CB 8-3 G-SRT.D.10 (A) (P) (1) Prove the Laws of Sines and Cosines and use them to solve problems. 8-5, 8-6 G-SRT.D.11 (1) Geometry Understand and apply the Law of Sines and the Law of Cosines to find unknown measurements in right and non-right triangles (e.g., surveying problems, resultant forces). Where to Find 8-1, 8-2, 8-3, 8-4, CB , 8-6 T46 Common Core State Standards

4 Circles Understand and apply theorems about circles G-C.A.1 Prove that all circles are similar G-C.A.2 Identify G-C.A.3 Construct 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. the inscribed and circumscribed circles of a triangle, and prove properties of angles for a quadrilateral inscribed in a circle. G-C.A.4 (A) (P) (1) Construct a tangent line from a point outside a given circle to the circle Find arc lengths and areas of sectors of circles G-C.B.5 Derive using similarity the fact that the length of the arc intercepted by an angle is proportional to the radius, and define the radian measure of the angle as the constant of proportionality; derive the formula for the area of a sector. Expressing Geometric Properties with Equations Translate between the geometric description and the equation for a conic section G-GPE.A.1 Derive Geometry the equation of a circle of given center and radius using the Pythagorean Theorem; complete the square to find the center and radius of a circle given by an equation. Where to Find 10-6, CB 10-6, 12-2, , , 10-7 G-GPE.A.2 (A) Derive the equation of a parabola given a focus and directrix. CB 12-5 Use coordinates to prove simple geometric theorems algebraically G-GPE.B.4 Use coordinates to prove simple geometric theorems algebraically. 6-9 G-GPE.B.5 Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric 3-8, 7-3, 7-4 problems (e.g., find the equation of a line parallel or perpendicular to a given line that passes through a given point). G-GPE.B.6 Find the point on a directed line segment between two given points that partitions the 1-3, 1-7 segment in a given ratio. G-GPE.B.7 Use coordinates to compute perimeters of polygons and areas of triangles and rectangles, e.g., using the distance formula. 6-7, Common Core State Standards T47 MMON CORE COMMON CORE COMMON CORE COM

5 Geometry Where to Find Geometric Measurement and Dimension Explain volume formulas and use them to solve problems G-GMD.A.1 Give G-GMD.A.2 (A) an informal argument for the formulas for the circumference of a circle, area of a circle, volume of a cylinder, pyramid, and cone. Use dissection arguments, Cavalieri s principle, and informal limit arguments. (1) Give an informal argument using Cavalieri s principle for the formulas for the volume of a sphere and other solid figures. 11-4, CB G-GMD.A.3 (A) (P) Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems. 11-4, 11-5, 11-6 Visualize relationships between two-dimensional and three-dimensional objects G-GMD.B.4 Identify the shapes of two-dimensional cross-sections of three-dimensional objects, and identify three-dimensional objects generated by rotations of two-dimensional objects. Modeling with Geometry Apply geometric concepts in modeling situations 11-1, 12-6 G-MG.A.1 Use G-MG.A.2 Apply G-MG.A.3 Apply geometric shapes, their measures, and their properties to describe objects (e.g., modeling a tree trunk or a human torso as a cylinder). concepts of density based on area and volume in modeling situations (e.g., persons per square mile, BTUs per cubic foot). geometric methods to solve design problems (e.g., designing an object or structure to satisfy physical constraints or minimize cost; working with typographic grid systems based on ratios). 8-3, 10-1, 10-2, 10-3, 11-2, 11-3, 11-4, 11-5, 11-6, T48 Common Core State Standards

6 Conditional Probability and the Rules of Probability Understand independence and conditional probability and use them to interpret data S-CP.A.1 (A) Describe events as subsets of a sample space (the set of outcomes) using characteristics (or categories) of the outcomes, or as unions, intersections, or complements of other events ( or, and, not ). S-CP.A.2 (A) Understand that two events A and B are independent if the probability of A and B occurring together is the product of their probabilities, and use this characterization to determine if they are independent. S-CP.A.3 (A) Understand the conditional probability of A given B as P(A and B)/P(B), and interpret independence of A and B as saying that the conditional probability of A given B is the same as the probability of A, and the conditional probability of B given A is the same as the probability of B. S-CP.A.4 (A) Construct and interpret two-way frequency tables of data when two categories are associated with each object being classified. Use the two-way table as a sample space to decide if events are independent and to approximate conditional probabilities. S-CP.A.5 (A) Recognize and explain the concepts of conditional probability and independence in everyday language and everyday situations. Use the rules of probability to compute probabilities of compound events in a uniform probability model S-CP.B.6 (A) Find the conditional probability of A given B as the fraction of B s outcomes that also belong to A, and interpret the answer in terms of the model. S-CP.B.7 (A) Apply the Addition Rule, P(A or B) 5 P(A) 1 P(B) 2 P(A and B), and interpret the answer in terms of the model. S-CP.B.8 (A) S-CP.B.9 (A) (1) Apply the general Multiplication Rule in a uniform probability model, P(A and B) 5 P(A)P(B A) 5 P(B)P(A B), and interpret the answer in terms of the model. (1) Use permutations and combinations to compute probabilities of compound events and solve problems. Using Probability to Make Decisions Use probability to evaluate outcomes of decisions S-MD.B.6 (A) (1) Use probabilities to make fair decisions (e.g., drawing by lots, using a random number generator). S-MD.B.7 (A) Statistics and Probability (1) Analyze decisions and strategies using probability concepts (e.g., product testing, medical testing, pulling a hockey goalie at the end of a game). Where to Find , 13-2, , , CB , CB 13-7 Common Core State Standards T49 MMON CORE COMMON CORE COMMON CORE COM

7 Using the Program for Success Geometry Pacing Guide This Pacing Chart is provided as a guide to help you customize your course. It shows the lessons that address the standards in the Achieve Pathways as well as those that are assessed in the PARCC End-of- Course Assessment as defined in the Model Content Frameworks. You can design your geometry course using the information provided. The suggested number of days for each chapter is based on a traditional 45-minute class period and on a 90-minute block period. The total of 160 days of instruction leaves time for assessments, projects, assemblies, preparing for your state test, or other special days that vary from school to school. KEY = Geometry Content = Prerequisite Content = Content for Enrichment Common Core State Standards PARCC Achieve Chapter 1 Tools of Geometry Traditional 10 Block Nets and Drawings for Visualizing Geometry Prepares for G-CO.A Points, Lines, and Planes G-CO.A Measuring Segments G-CO.A.1, G-GPE.B Measuring Angles G-CO.A Exploring Angle Pairs Prepares for G-CO.A.1 Concept Byte: Compass Designs Prepares for G-CO.D Basic Constructions G-CO.A.1, G-CO.D.12 Concept Byte: Exploring Constructions Prepares for G-CO.D Midpoint and Distance in the Coordinate Plane Prepares for G-GPE.B.4 and G-GPE.B.7; also G-GPE.B.6 Review: Classifying Polygons Prepares for G-MG.A Perimeter, Circumference, and Area N-Q.A.1 Concept Byte: Comparing Perimeters and Areas Prepares for G-MG.A.2 T50 Geometry Pacing Guide

8 Common Core State Standards PARCC Achieve Chapter 2 Reasoning and Proof Traditional 12 Block Patterns and Inductive Reasoning Prepares for G-CO.C.9, G-CO.C.10, and G-CO.C Conditional Statements Prepares for G-CO.C.9, G-CO.C.10, and G-CO.C.11 Concept Byte: Logic and Truth Tables Prepares for G-CO.C.9, G-CO.C.10, and G-CO.C Biconditionals and Definitions Prepares for G-CO.C.9, G-CO.C.10, and G-CO.C Deductive Reasoning Prepares for G-CO.C.9, G-CO.C.10, and G-CO.C Reasoning in Algebra and Geometry Prepares for G-CO.C.9, G-CO.C.10, and G-CO.C Proving Angles Congruent G-CO.C.9 Chapter 3 Parallel and Perpendicular Lines Traditional 12 Block Lines and Angles G-CO.A.1, Prepares for G-CO.D.12 Concept Byte: Parallel Lines and Related Angles G-CO.D.12, Prepares for G-CO.C Properties of Parallel Lines G-CO.C Proving Lines Parallel Extends G-CO.C Parallel and Perpendicular Lines G-MG.A.3 Concept Byte: Perpendicular Lines and Planes Extends G-CO.A Parallel Lines and Triangles G-CO.D.10 Concept Byte: Exploring Spherical Geometry Extends G-CO.A Constructing Parallel and Perpendicular Lines G-CO.D.12, G-CO.D Equations of Lines in the Coordinate Plane Prepares for G-GPE.B Slopes of Parallel and Perpendicular Lines G-GPE.B.5 Chapter 4 Congruent Triangles Traditional 16 Block Congruent Figures Prepares for G-SRT.B.5 Concept Byte: Building Congruent Triangles Prepares for G-SRT.B Triangle Congruence by SSS and SAS G-SRT.B Triangle Congruence by ASA and AAS G-SRT.B.5 Concept Byte: Exploring AAA and SSA Extends G-SRT.B Using Corresponding Parts of Congruent Triangles G-CO.D.12, G-SRT.B.5 Concept Byte: Paper-Folding Conjectures G-CO.D Isosceles and Equilateral Triangles G-CO.C.10, G-CO.D.13, G-SRT.B.5 Algebra Review: Systems of Linear Equations Reviews A-REI.C Congruence in Right Triangles G-SRT.B Congruence in Overlapping Triangles G-SRT.B.5 Geometry Pacing Guide T51 MMON CORE COMMON CORE COMMON CORE COM

9 Common Core State Standards PARCC Achieve Chapter 5 Relationships Within Triangles Traditional 16 Block 8 Concept Byte: Investigating Midsegments Prepares for G-CO.C Midsegments of Triangles G-CO.C.10, G-SRT.B Perpendicular and Angle Bisectors G-CO.C.9, G-CO.D.12, G-SRT.B.5 Concept Byte: Paper Folding Bisectors Prepares for G-C.A Bisectors in Triangles G-C.A.3 Concept Byte: Special Segments in Triangles Prepares for G-CO.C Medians and Altitudes G-CO.C.10, G-SRT.B Indirect Proof Extends G-CO.C.10 Algebra Review: Solving Inequalities Reviews A.CED.A Inequalities in One Triangle Extends G-CO.C Inequalities in Two Triangles Extends G-CO.C.10 Chapter 6 Polygons and Quadrilaterals Traditional 18 Block 9 Concept Byte: Exterior Angles of Polygons Prepares for G-SRT.B The Polygon-Angle Sum Theorems G-SRT.B Properties of Parallelograms G-CO.C.11, G-SRT.B Proving That a Quadrilateral Is a Parallelogram G-CO.C.11, G-SRT.B Properties of Rhombuses, Rectangles, and Squares G-CO.C.11, G-SRT.B Conditions for Rhombuses, Rectangles, and G-CO.C.11, G-SRT.B.5 Squares 6-6 Trapezoids and Kites G-SRT.B Polygons in the Coordinate Plane G-GPE.B Applying Coordinate Geometry Prepares for G-GPE.B.4 Concept Byte: Quadrilaterals in Quadrilaterals G-CO.D Proofs Using Coordinate Geometry G-GPE.B.4 T52 Geometry Pacing Guide

10 Common Core State Standards PARCC Achieve Chapter 7 Similarity Traditional 10 Block Ratios and Proportions Prepares for G-SRT.B.5 Algebra Review: Solving Quadratic Equations Reviews A-CED.A Similar Polygons G-SRT.B.5 Concept Byte: Fractals Extends G-SRT.B Proving Triangles Similar G-SRT.B.5, G-GPE.B Similarity in Right Triangles G-SRT.B.5, G-GPE.B.5 Concept Byte: The Golden Ratio Extends G-SRT.B.5 Concept Byte: Exploring Proportions in Triangles G-CO.D Proportions in Triangles G-SRT.B.4 Chapter 8 Right Triangles and Trigonometry Traditional 10 Block 6 Concept Byte: The Pythagorean Theorem Prepares for G-SRT.B The Pythagorean Theorem and Its Converse G-SRT.4, G-SRT.C Special Right Triangles G-SRT.C.8 Concept Byte: Exploring Trigonometric Ratios G-SRT.C Trigonometry G-SRT.C.7, G-SRT.C.8, G-MG.A.1 Concept Byte: Measuring From Afar G-SRT.C Angles of Elevation and Depression G-SRT.C Law of Sines G-SRT.D.10, G-SRT.D Law of Cosines G-SRT.D.10, G-SRT.D.11 Geometry Pacing Guide T53 MMON CORE COMMON CORE COMMON CORE COM

11 Common Core State Standards PARCC Achieve Chapter 9 Transformations Traditional 10 Block 5 Concept Byte: Tracing Paper Transformations G-CO.A Translations G-CO.A.2, G-CO.A.4, G-CO.A.5, G-CO.B.6 Concept Byte: Paper Folding and Reflections G-CO.A Reflections G-CO.A.2, G-CO.A.4, G-CO.A.5, G-CO.B Rotations G-CO.A.2, G-CO.A.4, G-CO.A.5, G-CO.B.6 Concept Byte: Tracing Paper Transformations G-CO.A Compositions of Isometries G-CO.A.2, G-CO.A.5, G-CO.B Triangle Congruence G-CO.B.6, G-CO.B.7, G-CO.B.8 Concept Byte: Exploring Dilations G-SRT.A.1a, G-SRT.A.1b 9-6 Dilations G-CO.A Similarity Transformations G-SRT.A.2, G-SRT.A.3 Chapter 10 Area Traditional 12 Block 6 Concept Byte: Transforming to Find Area Prepares for G-GMD.A Areas of Parallelograms and Triangles G-GPE.7, G-MG.A Areas of Trapezoids, Rhombuses, and Kites G-MG.A Areas of Regular Polygons G-CO.D.13, G-MG.A Perimeters and Areas of Similar Figures Prepares for G-GMD.A Trigonometry and Area G-SRT.C Circles and Arcs G-CO.A.1, G-C.A.1, G-C.A.2, G-C.A.5 Concept Byte: Circle Graphs G-C.A.2 Concept Byte: Exploring the Area of a Circle G-GMD.A Areas of Circles and Sectors G-C.B.5 Concept Byte: Inscribed and Circumscribed Figures Extends G-GPE.B Geometric Probability Prepares for S-CP.A.1 T54 Geometry Pacing Guide

12 Common Core State Standards PARCC Achieve Chapter 11 Surface Area and Volume Traditional 16 Block Space Figures and Cross Sections G-GMD.B.4 Concept Byte: Perspective Drawing Extends G-GMD.B.4 Concept Byte: Literal Equations Reviews A-CED.A Surface Areas of Prisms and Cylinders G-MG.A Surface Areas of Pyramids and Cones G-MG.A Volumes of Prisms and Cylinders G-GMD.A.1, G-GMD.A.2, G-GMD.A.3, G-MG.A.1 Concept Byte: Finding Volume Prepares for G-GMD.A Volumes of Pyramids and Cones G-GMD.A.3, G-MG.A Surface Areas and Volumes of Spheres G-GMD.A.3, G-MG.A.1 Concept Byte: Exploring Similar Solids Prepares for G-MG.A Areas and Volumes of Similar Solids G-MG.A.1, G-MG.A.2 Chapter 12 Circles Traditional 10 Block Tangent Lines Prepares for G-C.A.2 Concept Byte: Paper Folding With Circles Prepares for G-C.A Chords and Arcs G-C.A Inscribed Angles G-C.A.2, G-C.A.3, G-C.A.4 Concept Byte: Exploring Chords and Secants Extends G-C.A Angle Measures and Segment Lengths Extends G-C.A Circles in the Coordinate Plane G-GPE.A.1 Concept Byte: Equation of a Parabola G-GPE.A Locus: A Set of Points G-GMD.B.4 Chapter 13 Probability Traditional 10 Block Experimental and Theoretical Probability S-CP.A.1, S-CP.A Probability Distributions and Frequency Tables S-CP.A.4, S-CP.A Permutations and Combinations Prepares for S-CP.B Compound Probability and Probability of Multiple S-CP.B.7, S-CP.B.8, S-CP.B.9 Events 13-5 Probability Models S-CP.A Conditional Probability Formulas S-CP.A.2, S-CP.A.3, S-CP.A.5, S-CP.A Modeling Randomness S-MD.B.6, S-MD.B.7 Concept Byte: Probability and Decision Making S-MD.B.6, S-MD.B.7 Geometry Pacing Guide T55 MMON CORE COMMON CORE COMMON CORE COM