, VersaTiles (R), High School Level, Book 2, VersaTiles (R), High School Level, Book 3,, VersaTiles (R), High School Level, Book 5 Grades: 9, 10, 11, 12 State: Georgia Common Core Standards Subject: Mathematics Publisher: ETA hand2mind GA.CC.MP. GA.CC.9-12.N. MCC9-12.N.Q. EXPECTATION MCC9 12.N.Q.1. Mathematical Practices Common Core Georgia Performance Standards Mathematics Grades 9 12 - Adopted 2011 The Standards for Mathematical Practice reflect various forms of expertise and mathematical habits of mind that students develop throughout their mathematics education. VersaTiles is designed to help students become more fluent and more efficient in various mathematical skills (e.g., computational algorithms, applications of formulae, mathematical vocabulary). While there will be opportunities for teachers to elicit evidence of the Standards for Mathematical Practice if they extend VersaTiles activities into class discussions, math journals, or other formats, the activities themselves are designed primarily as skill practice. Thus, the correlation presented here shows coverage of the mathematics content standards. Number and Quantity Quantities Reason quantitatively and use units to solve problems. Use units as a way to understand problems and to guide the solution of multi step problems; choose and interpret units consistently in formulas; choose and interpret the scale and the origin in graphs and data displays. GA.CC.9-12.A. MCC9-12.A.CED. VersaTiles (R), High School Level, Book 2 VersaTiles (R), High School Level, Book 2: Similarity, Congruence, and Trigonometry, page 22-23 (Areas and Perimeter Formulas) VersaTiles (R), High School Level, Book 2: Similarity, Congruence, and Trigonometry, page 24 (Those Changing Dimensions) Algebra Creating Equations Create equations that describe numbers or relationships EXPECTATION MCC9 12.A.CED.1. Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. : Structure & Proof, page 06-07 (Using Algebra with Parallel EXPECTATION MCC9 12.A.CED.2. Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. : Structure & Proof, page 06-07 (Using Algebra with Parallel : Connecting Algebra &, page 06-07 (Slope and EXPECTATION MCC9 12.A.CED.3. Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or non viable options in a modeling context. For example, represent inequalities describing nutritional and cost constraints on combinations of different foods.
GA.CC.9-12.A. MCC9-12.A.REI. EXPECTATION MCC9 12.A.REI.1. : Structure & Proof, page 06-07 (Using Algebra with Parallel Algebra Reasoning with Equations and Inequalities Understand solving equations as a process of reasoning and explain the reasoning Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method. GA.CC.9-12.A. MCC9-12.A.REI. EXPECTATION MCC9 12.A.REI.3. : Structure & Proof, page 06-07 (Using Algebra with Parallel Algebra Reasoning with Equations and Inequalities Solve equations and inequalities in one variable Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. GA.CC.9-12.F. MCC9 12.F.IF. EXPECTATION MCC9 12.F.IF.6. : Structure & Proof, page 06-07 (Using Algebra with Parallel Functions Interpreting Functions Interpret functions that arise in applications in terms of the context Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph. GA.CC.9-12.F. MCC9 12.F.IF. EXPECTATION MCC9 12.F.IF.7. GRADE MCC9 12.F.IF.7a. EXPECTATION GA.CC.9-12.F. MCC9 12.F.BF. EXPECTATION MCC9 12.F.BF.1. : Connecting Algebra &, page 04 (Slippery Slopes) : Connecting Algebra &, page 06-07 (Slope and : Connecting Algebra &, page 21 (Quadrilateral Query) : Connecting Algebra &, page 22-23 (Polygon Functions Interpreting Functions Analyze functions using different representations Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases. Graph linear and quadratic functions and show intercepts, maxima, and minima. : Connecting Algebra &, page 24 (Parabolic Functions Building Functions Build a function that models a relationship between two quantities Write a function that describes a relationship between two quantities.
GRADE MCC9 12.F.BF.1a. EXPECTATION GA.CC.9-12.F. MCC9 12.F.TF. EXPECTATION MCC9 12.F.TF.3. Determine an explicit expression, a recursive process, or steps for calculation from a context. : Structure & Proof, page 06-07 (Using Algebra with Parallel Functions Trigonometric Functions Extend the domain of trigonometric functions using the unit circle (+) Use special triangles to determine geometrically the values of sine, cosine, tangent for π/3, π/4 and π/6, and use the unit circle to express the values of sine, cosine, and tangent for π x, π + x, and 2π x in terms of their values for x, where x is any real number. MCC9-12.G.CO. EXPECTATION MCC9 12.G.CO.1. VersaTiles (R), High School Level, Book 2 VersaTiles (R), High School Level, Book 2: Similarity, Congruence, and Trigonometry, page 12 (Sine, Cosine, and Tangent Ratios) VersaTiles (R), High School Level, Book 2: Similarity, Congruence, and Trigonometry, page 13 (Trigonometric Ratios) VersaTiles (R), High School Level, Book 2: Similarity, Congruence, and Trigonometry, page 16-17 (Angles of Elevation and Depression) VersaTiles (R), High School Level, Book 2: Similarity, Congruence, and Trigonometry, page 18 (Law of Congruence Experiment with transformations in the plane 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. : Structure & Proof, page 01 (Terms of ) : Structure & Proof, page 02 (What Kind of Lines?) : Structure & Proof, page 03 (Angle Measures) : Structure & Proof, page 04-05 (Aren't These Angle Pairs Special?) : Structure & Proof, page 06-07 (Using Algebra with Parallel : Structure & Proof, page 08 (All About Angles) : Structure & Proof, page 09 (Angle Pairs) : Structure & Proof, page 10-11 (Moving Around) : Structure & Proof, page 12-13 (Converse, Inverse, and Contrapositive) : Structure & Proof, page 14 (Let the Truth Be Told) : Structure & Proof, page 15 (Conditionals and Logical Equivalents) : Structure & Proof, page 16-17 (Laws of Logic and Indirect Proof) : Structure & Proof, page 18 (Name That Triangle) : Structure & Proof, page 19 (They're all 180 Degrees) : Structure & Proof, page 20 (Altitudes, Bisectors, and Medians) : Structure & Proof, page 21 (Triangle Relationships) : Structure & Proof, page 22-23 (Medians, Altitudes, and Bisectors) : Structure & Proof, page 24 (Special Quadrilaterals) VersaTiles (R), High School Level, Book 2 VersaTiles (R), High School Level, Book 2: Similarity, Congruence, and Trigonometry, page 01 (To Be or Not To Be a Triangle?) VersaTiles (R), High School Level, Book 2: Similarity, Congruence, and Trigonometry, page 02-03 (Opposites Attract) VersaTiles (R), High School Level, Book 2: Similarity, Congruence, and Trigonometry, page 04-05 (Proving Triangles Congruent)
VersaTiles (R), High School Level, Book 2: Similarity, Congruence, and Trigonometry, page 06 (CPCTC) VersaTiles (R), High School Level, Book 2: Similarity, Congruence, and Trigonometry, page 07 (Oh, So Similar) VersaTiles (R), High School Level, Book 2: Similarity, Congruence, and Trigonometry, page 08 (The Pythagorean Theorem) VersaTiles (R), High School Level, Book 2: Similarity, Congruence, and Trigonometry, page 09 (Proportional Segments) VersaTiles (R), High School Level, Book 2: Similarity, Congruence, and Trigonometry, page 10-11 (Geometric Mean) VersaTiles (R), High School Level, Book 2: Similarity, Congruence, and Trigonometry, page 12 (Sine, Cosine, and Tangent Ratios) VersaTiles (R), High School Level, Book 2: Similarity, Congruence, and Trigonometry, page 13 (Trigonometric Ratios) VersaTiles (R), High School Level, Book 2: Similarity, Congruence, and Trigonometry, page 14-15 (Special Right Triangles) VersaTiles (R), High School Level, Book 2: Similarity, Congruence, and Trigonometry, page 16-17 (Angles of Elevation and Depression) VersaTiles (R), High School Level, Book 2: Similarity, Congruence, and Trigonometry, page 18 (Law of VersaTiles (R), High School Level, Book 2: Similarity, Congruence, and Trigonometry, page 19 (Angles in Polygons) VersaTiles (R), High School Level, Book 2: Similarity, Congruence, and Trigonometry, page 20-21 (Congruent and Similar Polygons) VersaTiles (R), High School Level, Book 2: Similarity, Congruence, and Trigonometry, page 22-23 (Areas and Perimeter Formulas) VersaTiles (R), High School Level, Book 2: Similarity, Congruence, and Trigonometry, page 24 (Those Changing Dimensions) VersaTiles (R), High School Level, Book 3 VersaTiles (R), High School Level, Book 3: Three-Dimensions, page 01 (Naming Three-Dimensional Figures) VersaTiles (R), High School Level, Book 3: Three-Dimensions, page 02-03 (Nothing but Net) VersaTiles (R), High School Level, Book 3: Three-Dimensions, page 04-05 (Where Should We Meet?) VersaTiles (R), High School Level, Book 3: Three-Dimensions, page 06 (Euler's Formula) VersaTiles (R), High School Level, Book 3: Three-Dimensions, page 07 (Volume of Prisms) VersaTiles (R), High School Level, Book 3: Three-Dimensions, page 08-09 (Volume of Pyramids) VersaTiles (R), High School Level, Book 3: Three-Dimensions, page 10 (Volume of Cylinders) VersaTiles (R), High School Level, Book 3: Three-Dimensions, page 11 (Volume of Cones) VersaTiles (R), High School Level, Book 3: Three-Dimensions, page 12-13 (Surface Area of Prisms and Cylinders) VersaTiles (R), High School Level, Book 3: Three-Dimensions, page 14-15 (Surface Area of Pyramids and Cones) VersaTiles (R), High School Level, Book 3: Three-Dimensions, page 16 (On the Ball) VersaTiles (R), High School Level, Book 3: Three-Dimensions, page 17 (Surface Area and Volume of Spheres) VersaTiles (R), High School Level, Book 3: Three-Dimensions, page 18-19 (Congruent and Similar Solids) VersaTiles (R), High School Level, Book 3: Three-Dimensions, page 20-21 (Cavalieri's Principle) VersaTiles (R), High School Level, Book 3: Three-Dimensions, page 22-23 (Out and About) VersaTiles (R), High School Level, Book 3: Three-Dimensions, page 24 (Dynamic Dimensions) : Connecting Algebra &, page 01 (Point It Out) : Connecting Algebra &, page 02 (Halfway There) : Connecting Algebra &, page 03 (The End Is in Sight) : Connecting Algebra &, page 04 (Slippery Slopes) : Connecting Algebra &, page 05 (Linear Relationships) : Connecting Algebra &, page 06-07 (Slope and : Connecting Algebra &, page 08-09 (Distance Formula) : Connecting Algebra &, page 10-11 (Around the Edge) : Connecting Algebra &, page 12-13 (Areas of Rectangles and Triangles) : Connecting Algebra &, page 14 (Translations) : Connecting Algebra &, page 15 (Reflections) : Connecting Algebra &, page 16-17 (Rotations)
: Connecting Algebra &, page 18-19 (Dilations) : Connecting Algebra &, page 20 (Double : Connecting Algebra &, page 21 (Quadrilateral Query) : Connecting Algebra &, page 22-23 (Polygon : Connecting Algebra &, page 24 (Parabolic EXPECTATION MCC9 12.G.CO.2. VersaTiles (R), High School Level, Book 5 VersaTiles (R), High School Level, Book 5: Circles & Probability, page 01 (Parts of Circles) VersaTiles (R), High School Level, Book 5: Circles & Probability, page 02-03 (Circumference and Area of Circles) VersaTiles (R), High School Level, Book 5: Circles & Probability, page 04-05 (Around the Bend) VersaTiles (R), High School Level, Book 5: Circles & Probability, page 06-07 (Segment Lengths) VersaTiles (R), High School Level, Book 5: Circles & Probability, page 08-09 (Angle Properties) VersaTiles (R), High School Level, Book 5: Circles & Probability, page 10-11 (Arc and Angle Measures) VersaTiles (R), High School Level, Book 5: Circles & Probability, page 12-13 (Triangle Similarity) VersaTiles (R), High School Level, Book 5: Circles & Probability, page 14-15 (A Round of Graphing) VersaTiles (R), High School Level, Book 5: Circles & Probability, page 16 (Equations of Circles) VersaTiles (R), High School Level, Book 5: Circles & Probability, page 17 (Circle Graphs and Central Angles) VersaTiles (R), High School Level, Book 5: Circles & Probability, page 18 (Independent Events) VersaTiles (R), High School Level, Book 5: Circles & Probability, page 19 (That Depends) VersaTiles (R), High School Level, Book 5: Circles & Probability, page 20-21 (Is That Fair?) VersaTiles (R), High School Level, Book 5: Circles & Probability, page 22-23 (Geometric Probability) VersaTiles (R), High School Level, Book 5: Circles & Probability, page 24 (Permutations and Combinations) 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). : Structure & Proof, page 10-11 (Moving Around) EXPECTATION MCC9 12.G.CO.3. : Connecting Algebra &, page 14 (Translations) : Connecting Algebra &, page 15 (Reflections) : Connecting Algebra &, page 16-17 (Rotations) : Connecting Algebra &, page 18-19 (Dilations) : Connecting Algebra &, page 20 (Double Given a rectangle, parallelogram, trapezoid, or regular polygon, describe the rotations and reflections that carry it onto itself. : Structure & Proof, page 10-11 (Moving Around) EXPECTATION MCC9 12.G.CO.4. : Connecting Algebra &, page 15 (Reflections) : Connecting Algebra &, page 16-17 (Rotations) : Connecting Algebra &, page 20 (Double Develop definitions of rotations, reflections, and translations in terms of angles, circles, perpendicular lines, parallel lines, and line segments. : Structure & Proof, page 10-11 (Moving Around) : Connecting Algebra &, page 14 (Translations) : Connecting Algebra &, page 15 (Reflections) : Connecting Algebra &, page 16-17 (Rotations) : Connecting Algebra &, page 20 (Double
EXPECTATION MCC9 12.G.CO.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. : Structure & Proof, page 10-11 (Moving Around) MCC9-12.G.CO. EXPECTATION MCC9 12.G.CO.6. : Connecting Algebra &, page 14 (Translations) : Connecting Algebra &, page 15 (Reflections) : Connecting Algebra &, page 16-17 (Rotations) : Connecting Algebra &, page 20 (Double Congruence Understand congruence in terms of rigid motions 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. : Structure & Proof, page 10-11 (Moving Around) EXPECTATION MCC9 12.G.CO.7. : Connecting Algebra &, page 14 (Translations) : Connecting Algebra &, page 15 (Reflections) : Connecting Algebra &, page 16-17 (Rotations) : Connecting Algebra &, page 18-19 (Dilations) : Connecting Algebra &, page 20 (Double 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. VersaTiles (R), High School Level, Book 2 VersaTiles (R), High School Level, Book 2: Similarity, Congruence, and Trigonometry, page 04-05 (Proving Triangles Congruent) VersaTiles (R), High School Level, Book 2: Similarity, Congruence, and Trigonometry, page 06 (CPCTC) EXPECTATION MCC9 12.G.CO.8. : Connecting Algebra &, page 22-23 (Polygon Explain how the criteria for triangle congruence (ASA, SAS, and SSS) follow from the definition of congruence in terms of rigid motions. MCC9-12.G.CO. EXPECTATION MCC9 12.G.CO.9. VersaTiles (R), High School Level, Book 2 VersaTiles (R), High School Level, Book 2: Similarity, Congruence, and Trigonometry, page 04-05 (Proving Triangles Congruent) VersaTiles (R), High School Level, Book 2: Similarity, Congruence, and Trigonometry, page 06 (CPCTC) VersaTiles (R), High School Level, Book 2: Similarity, Congruence, and Trigonometry, page 20-21 (Congruent and Similar Polygons) Congruence Prove geometric theorems 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.
: Structure & Proof, page 04-05 (Aren't These Angle Pairs Special?) : Structure & Proof, page 06-07 (Using Algebra with Parallel : Structure & Proof, page 08 (All About Angles) VersaTiles (R), High School Level, Book 2 VersaTiles (R), High School Level, Book 2: Similarity, Congruence, and Trigonometry, page 09 (Proportional Segments) VersaTiles (R), High School Level, Book 2: Similarity, Congruence, and Trigonometry, page 10-11 (Geometric Mean) EXPECTATION MCC9 12.G.CO.10. Prove theorems about triangles. Theorems include: measures of interior angles of a triangle sum to 180 degrees; 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. GA.CC.9-12.G. MCC9-12.G.CO. : Structure & Proof, page 19 (They're all 180 Degrees) : Structure & Proof, page 20 (Altitudes, Bisectors, and Medians) : Structure & Proof, page 21 (Triangle Relationships) : Structure & Proof, page 22-23 (Medians, Altitudes, and Bisectors) VersaTiles (R), High School Level, Book 2 VersaTiles (R), High School Level, Book 2: Similarity, Congruence, and Trigonometry, page 01 (To Be or Not To Be a Triangle?) VersaTiles (R), High School Level, Book 2: Similarity, Congruence, and Trigonometry, page 02-03 (Opposites Attract) VersaTiles (R), High School Level, Book 2: Similarity, Congruence, and Trigonometry, page 04-05 (Proving Triangles Congruent) VersaTiles (R), High School Level, Book 2: Similarity, Congruence, and Trigonometry, page 06 (CPCTC) VersaTiles (R), High School Level, Book 2: Similarity, Congruence, and Trigonometry, page 07 (Oh, So Similar) VersaTiles (R), High School Level, Book 2: Similarity, Congruence, and Trigonometry, page 10-11 (Geometric Mean) VersaTiles (R), High School Level, Book 2: Similarity, Congruence, and Trigonometry, page 14-15 (Special Right Triangles) Congruence Make geometric constructions EXPECTATION MCC9 12.G.CO.12. Make 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. MCC9-12.G.SRT. EXPECTATION MCC9 12.G.SRT.1. : Structure & Proof, page 20 (Altitudes, Bisectors, and Medians) Similarity, Right Triangles, and Trigonometry Understand similarity in terms of similarity transformations Verify experimentally the properties of dilations given by a center and a scale factor: GRADE MCC9 12.G.SRT.1a. A dilation takes a line not passing through the center of the dilation to a parallel line, and leaves a line passing EXPECTATION through the center unchanged. : Connecting Algebra &, page 18-19 (Dilations) : Connecting Algebra &, page 20 (Double
GRADE MCC9 12.G.SRT.1b. The dilation of a line segment is longer or shorter in the ratio given by the scale factor. EXPECTATION MCC9-12.G.SRT. EXPECTATION MCC9 12.G.SRT.2. : Connecting Algebra &, page 18-19 (Dilations) : Connecting Algebra &, page 20 (Double Similarity, Right Triangles, and Trigonometry Understand similarity in terms of similarity transformations 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. : Structure & Proof, page 21 (Triangle Relationships) : Structure & Proof, page 22-23 (Medians, Altitudes, and Bisectors) VersaTiles (R), High School Level, Book 2 VersaTiles (R), High School Level, Book 2: Similarity, Congruence, and Trigonometry, page 07 (Oh, So Similar) VersaTiles (R), High School Level, Book 2: Similarity, Congruence, and Trigonometry, page 10-11 (Geometric Mean) VersaTiles (R), High School Level, Book 2: Similarity, Congruence, and Trigonometry, page 20-21 (Congruent and Similar Polygons) VersaTiles (R), High School Level, Book 2: Similarity, Congruence, and Trigonometry, page 24 (Those Changing Dimensions) VersaTiles (R), High School Level, Book 3 VersaTiles (R), High School Level, Book 3: Three-Dimensions, page 18-19 (Congruent and Similar Solids) : Connecting Algebra &, page 22-23 (Polygon MCC9-12.G.SRT. EXPECTATION MCC9 12.G.SRT.4. VersaTiles (R), High School Level, Book 5 VersaTiles (R), High School Level, Book 5: Circles & Probability, page 12-13 (Triangle Similarity) Similarity, Right Triangles, and Trigonometry Prove theorems involving similarity Prove theorems about triangles. Theorems include: a line parallel to one side of a triangle divides the other two proportionally, and conversely; the Pythagorean Theorem proved using triangle similarity. EXPECTATION MCC9 12.G.SRT.5. : Structure & Proof, page 21 (Triangle Relationships) : Structure & Proof, page 22-23 (Medians, Altitudes, and Bisectors) Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures. : Structure & Proof, page 21 (Triangle Relationships) : Structure & Proof, page 22-23 (Medians, Altitudes, and Bisectors) VersaTiles (R), High School Level, Book 2 VersaTiles (R), High School Level, Book 2: Similarity, Congruence, and Trigonometry, page 04-05 (Proving Triangles Congruent)
VersaTiles (R), High School Level, Book 2: Similarity, Congruence, and Trigonometry, page 06 (CPCTC) VersaTiles (R), High School Level, Book 2: Similarity, Congruence, and Trigonometry, page 07 (Oh, So Similar) VersaTiles (R), High School Level, Book 2: Similarity, Congruence, and Trigonometry, page 10-11 (Geometric Mean) VersaTiles (R), High School Level, Book 2: Similarity, Congruence, and Trigonometry, page 20-21 (Congruent and Similar Polygons) : Connecting Algebra &, page 22-23 (Polygon MCC9-12.G.SRT. EXPECTATION MCC9 12.G.SRT.6. VersaTiles (R), High School Level, Book 5 VersaTiles (R), High School Level, Book 5: Circles & Probability, page 12-13 (Triangle Similarity) Similarity, Right Triangles, and Trigonometry Define trigonometric ratios and solve problems involving right triangles 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. EXPECTATION MCC9 12.G.SRT.7. VersaTiles (R), High School Level, Book 2 VersaTiles (R), High School Level, Book 2: Similarity, Congruence, and Trigonometry, page 08 (The Pythagorean Theorem) VersaTiles (R), High School Level, Book 2: Similarity, Congruence, and Trigonometry, page 12 (Sine, Cosine, and Tangent Ratios) VersaTiles (R), High School Level, Book 2: Similarity, Congruence, and Trigonometry, page 13 (Trigonometric Ratios) VersaTiles (R), High School Level, Book 2: Similarity, Congruence, and Trigonometry, page 14-15 (Special Right Triangles) VersaTiles (R), High School Level, Book 2: Similarity, Congruence, and Trigonometry, page 16-17 (Angles of Elevation and Depression) VersaTiles (R), High School Level, Book 2: Similarity, Congruence, and Trigonometry, page 18 (Law of Explain and use the relationship between the sine and cosine of complementary angles. EXPECTATION MCC9 12.G.SRT.8. VersaTiles (R), High School Level, Book 2 VersaTiles (R), High School Level, Book 2: Similarity, Congruence, and Trigonometry, page 12 (Sine, Cosine, and Tangent Ratios) VersaTiles (R), High School Level, Book 2: Similarity, Congruence, and Trigonometry, page 13 (Trigonometric Ratios) VersaTiles (R), High School Level, Book 2: Similarity, Congruence, and Trigonometry, page 16-17 (Angles of Elevation and Depression) VersaTiles (R), High School Level, Book 2: Similarity, Congruence, and Trigonometry, page 18 (Law of Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems. GA.CC.9-12.G. MCC9-12.G.SRT. VersaTiles (R), High School Level, Book 2 VersaTiles (R), High School Level, Book 2: Similarity, Congruence, and Trigonometry, page 08 (The Pythagorean Theorem) VersaTiles (R), High School Level, Book 2: Similarity, Congruence, and Trigonometry, page 12 (Sine, Cosine, and Tangent Ratios) VersaTiles (R), High School Level, Book 2: Similarity, Congruence, and Trigonometry, page 13 (Trigonometric Ratios) VersaTiles (R), High School Level, Book 2: Similarity, Congruence, and Trigonometry, page 14-15 (Special Right Triangles) VersaTiles (R), High School Level, Book 2: Similarity, Congruence, and Trigonometry, page 16-17 (Angles of Elevation and Depression) VersaTiles (R), High School Level, Book 2: Similarity, Congruence, and Trigonometry, page 18 (Law of Similarity, Right Triangles, and Trigonometry
Apply trigonometry to general triangles EXPECTATION MCC9 12.G.SRT.10. (+) Prove the Laws of Sines and Cosines and use them to solve problems. VersaTiles (R), High School Level, Book 2 VersaTiles (R), High School Level, Book 2: Similarity, Congruence, and Trigonometry, page 18 (Law of EXPECTATION MCC9 12.G.SRT.11. (+) 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). MCC9-12.G.C. EXPECTATION MCC9 12.G.C.2. VersaTiles (R), High School Level, Book 2 VersaTiles (R), High School Level, Book 2: Similarity, Congruence, and Trigonometry, page 18 (Law of Circles Understand and apply theorems about circles 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. EXPECTATION MCC9 12.G.C.4. VersaTiles (R), High School Level, Book 5 VersaTiles (R), High School Level, Book 5: Circles & Probability, page 06-07 (Segment Lengths) VersaTiles (R), High School Level, Book 5: Circles & Probability, page 08-09 (Angle Properties) VersaTiles (R), High School Level, Book 5: Circles & Probability, page 10-11 (Arc and Angle Measures) VersaTiles (R), High School Level, Book 5: Circles & Probability, page 12-13 (Triangle Similarity) VersaTiles (R), High School Level, Book 5: Circles & Probability, page 17 (Circle Graphs and Central Angles) (+) Construct a tangent line from a point outside a given circle to the circle. VersaTiles (R), High School Level, Book 3 VersaTiles (R), High School Level, Book 3: Three-Dimensions, page 16 (On the Ball) VersaTiles (R), High School Level, Book 3: Three-Dimensions, page 17 (Surface Area and Volume of Spheres) MCC9-12.G.C. EXPECTATION MCC9 12.G.C.5. VersaTiles (R), High School Level, Book 5 VersaTiles (R), High School Level, Book 5: Circles & Probability, page 01 (Parts of Circles) VersaTiles (R), High School Level, Book 5: Circles & Probability, page 06-07 (Segment Lengths) VersaTiles (R), High School Level, Book 5: Circles & Probability, page 08-09 (Angle Properties) VersaTiles (R), High School Level, Book 5: Circles & Probability, page 10-11 (Arc and Angle Measures) VersaTiles (R), High School Level, Book 5: Circles & Probability, page 12-13 (Triangle Similarity) Circles Find arc lengths and areas of sectors of circles 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. GA.CC.9-12.G. MCC9-12.G.GPE. VersaTiles (R), High School Level, Book 5 VersaTiles (R), High School Level, Book 5: Circles & Probability, page 04-05 (Around the Bend) Expressing Geometric Properties with Equations Translate between the geometric description and the equation for a conic section EXPECTATION MCC9 12.G.GPE.1. Derive 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.
VersaTiles (R), High School Level, Book 5 VersaTiles (R), High School Level, Book 5: Circles & Probability, page 14-15 (A Round of Graphing) VersaTiles (R), High School Level, Book 5: Circles & Probability, page 16 (Equations of Circles) EXPECTATION MCC9 12.G.GPE.2. Derive the equation of a parabola given a focus and directrix. : Connecting Algebra &, page 24 (Parabolic EXPECTATION MCC9 12.G.GPE.3. (+) Derive the equations of ellipses and hyperbolas given the foci, using the fact that the sum or difference of distances from the foci is constant. GA.CC.9-12.G. MCC9-12.G.GPE. VersaTiles (R), High School Level, Book 3 VersaTiles (R), High School Level, Book 3: Three-Dimensions, page 04-05 (Where Should We Meet?) Expressing Geometric Properties with Equations Use coordinates to prove simple geometric theorems algebraically EXPECTATION MCC9 12.G.GPE.5. Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems (e.g., find the equation of a line parallel or perpendicular to a given line that passes through a given point). : Connecting Algebra &, page 05 (Linear Relationships) : Connecting Algebra &, page 06-07 (Slope and : Connecting Algebra &, page 21 (Quadrilateral Query) : Connecting Algebra &, page 22-23 (Polygon EXPECTATION MCC9 12.G.GPE.6. Find the point on a directed line segment between two given points that partitions the segment in a given ratio. : Connecting Algebra &, page 02 (Halfway There) : Connecting Algebra &, page 03 (The End Is in Sight) : Connecting Algebra &, page 08-09 (Distance Formula) : Connecting Algebra &, page 10-11 (Around the Edge) : Connecting Algebra &, page 12-13 (Areas of Rectangles and Triangles) : Connecting Algebra &, page 21 (Quadrilateral Query) : Connecting Algebra &, page 22-23 (Polygon EXPECTATION MCC9 12.G.GPE.7. Use coordinates to compute perimeters of polygons and areas of triangles and rectangles, e.g., using the distance formula. : Structure & Proof, page 10-11 (Moving Around) : Connecting Algebra &, page 02 (Halfway There) : Connecting Algebra &, page 03 (The End Is in Sight) : Connecting Algebra &, page 08-09 (Distance Formula) : Connecting Algebra &, page 10-11 (Around the Edge) : Connecting Algebra &, page 12-13 (Areas of Rectangles and Triangles)
GA.CC.9-12.G. MCC9-12.G.GMD. : Connecting Algebra &, page 14 (Translations) : Connecting Algebra &, page 15 (Reflections) : Connecting Algebra &, page 16-17 (Rotations) : Connecting Algebra &, page 18-19 (Dilations) : Connecting Algebra &, page 20 (Double : Connecting Algebra &, page 21 (Quadrilateral Query) : Connecting Algebra &, page 22-23 (Polygon : Connecting Algebra &, page 24 (Parabolic Geometric Measurement and Dimension Explain volume formulas and use them to solve problems EXPECTATION MCC9 12.G.GMD.3. Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems. GA.CC.9-12.G. MCC9-12.G.GMD. VersaTiles (R), High School Level, Book 3 VersaTiles (R), High School Level, Book 3: Three-Dimensions, page 07 (Volume of Prisms) VersaTiles (R), High School Level, Book 3: Three-Dimensions, page 08-09 (Volume of Pyramids) VersaTiles (R), High School Level, Book 3: Three-Dimensions, page 10 (Volume of Cylinders) VersaTiles (R), High School Level, Book 3: Three-Dimensions, page 11 (Volume of Cones) VersaTiles (R), High School Level, Book 3: Three-Dimensions, page 17 (Surface Area and Volume of Spheres) VersaTiles (R), High School Level, Book 3: Three-Dimensions, page 20-21 (Cavalieri's Principle) VersaTiles (R), High School Level, Book 3: Three-Dimensions, page 22-23 (Out and About) VersaTiles (R), High School Level, Book 3: Three-Dimensions, page 24 (Dynamic Dimensions) Geometric Measurement and Dimension Visualize relationships between two dimensional and three dimensional objects EXPECTATION MCC9 12.G.GMD.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. GA.CC.9-12.S. MCC9-12.S.CP. EXPECTATION MCC9 12.S.CP.2. VersaTiles (R), High School Level, Book 3 VersaTiles (R), High School Level, Book 3: Three-Dimensions, page 04-05 (Where Should We Meet?) Statistics and Probability Conditional Probability and the Rules of Probability Understand independence and conditional probability and use them to interpret data 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. GA.CC.9-12.S. MCC9-12.S.MD. EXPECTATION MCC9 12.S.MD.6. VersaTiles (R), High School Level, Book 5 VersaTiles (R), High School Level, Book 5: Circles & Probability, page 18 (Independent Events) Statistics and Probability Using Probability to Make Decisions Use probability to evaluate outcomes of decisions (+) Use probabilities to make fair decisions (e.g., drawing by lots, using a random number generator). VersaTiles (R), High School Level, Book 5 VersaTiles (R), High School Level, Book 5: Circles & Probability, page 20-21 (Is That Fair?)