Carnegie Learning Middle School Materials West Virginia Standards: Integrated Math II

Transcription

1 West Virginia Standards: d Math II d 1 5: Exponential 5.5 Radical Because It's Cliché 2: Linear and Exponential Relationships 7: Rational Exponents 1: Properties of Rational Exponents Extend the properties of exponents to rational exponents M.2HS.1 d 1 15: Real Number System 5: Exponential 15.3 Imagine the Possibilities 15.4 It's Not Complex -- It's Solutions are Complex! 5.5 Radical Because It's Cliché 5.6 Checkmate! 2: Linear and Exponential Relationships 7: Rational Exponents 2: Rewriting Expressions with Radical and Rational Exponents M.2HS.2 32: Polynomials and s 15: Real Number System 13.6 Could It Be Groovy to Be a Square? 15.3 Imagine the Possibilities Use properties of rational and irrational numbers M.2HS.3 15: Real Number System 15.1 The Real Numbers For Realsies! 15.2 Getting Real, and Knowing How 1

2 West Virginia Standards: d Math II Perform arithmetic operations with complex numbers M.2HS.4 M.2HS.5 I I 4: 4: 4.6 Now It's Getting Complex But It's Really Not Difficult 4.6 Now It's Getting Complex But It's Really Not Difficult 2: 2: 2: Operations with Complex Numbers 2: Operations with Complex Numbers 1: Introduction to Complex Numbers 2: Simplifying Radicals with Negative Radicands 3: Simplifying Powers of I 3: Adding and Subtracting Complex Numbers 4: Multiplying Complex Numbers 1: Searching for Patterns 3.1 Patterns They're Grrrowing 3.2 Are They Saying the Same Thing? 1: Power 2: Exploring Power 3: Building on the Coordinate Plane Perform arithmetic operations with complex numbers M.2HS.6 I 4: 5: Polynomial 4.1 Shape and Structure 5.1 Planting the Seeds 5.3 Function Makeover 5.6 Closing Time 3: Polynomial 3: Polynomial Operations 1: Adding Polynomials with Higher Orders 3: Multiplying Polynomials 6: Polynomial Expressions and Equations 6.2 The Great Polynomial Divide 2

3 West Virginia Standards: d Math II Interpret function that arise in applications in terms of a context M.2HS.7 M.2HS.8 12: Introduction to 12: Introduction to 16: Other and Inverses 12.1 Up and Down or Down and Up 12.2 Just U and I 12.3 Walking the. Curve? 12.4 Are You Afraid of Ghosts? 12.5 Just Watch That Pumpkin Fly 12.6 The Form is "Key" 12.3 Walking the Curve? 16.4 Take the Egg Plunge! 6: s 2: Models in General Form 1: Modeling Projectile Motion from Ground 2: Recognizing Key Features of Projectile Motion Graphs M.2HS.9 12: Introduction to 12.2 Just U and I Analyze functions using different representati ons M.2HS.10 16: Other and Inverses 11: Mathematical Modeling 16.4 Take the Egg Plunge! 11.3 People, Tea, and Carbon Dioxide 11.4 BAC is BAD News 3

4 West Virginia Standards: d Math II M.2HS.10. a d 1 1: Quantities and Relationships 12: Introduction to 14: Solving Equations and Inequalities 1.3 There are Many Ways to Represent 1.4 Function Families for 200, Alex 12.3 Walking the Curve? 12.4 Are You Afraid of Ghosts? 12.5 Just Watch that Pumpkin Fly 12.6 The Form is "Key" 12.7 More Than Meets the Eye 14.2 It's Watching and Tracking 6: s 5: forms of s 4: Sketching M.2HS.10. b 16: Other and Inverses 16.1 I Graph In Pieces 16.2 Step by Step 4

5 West Virginia Standards: d Math II M.2.HS.11 * In I for Polynom ials, not specifical ly Quadrati cs M.2HS.11. a M.2HS.11. b d 1 I 3: Searching For Patterns 3.1 Patterns They're Grrrowing 3.2 Are They Saying the Same Thing? 2: Linear and Exponential Relationships 4: Exponential 3: Properties of Exponents 12: Graphs of Exponential and Logarithmic 12.1 Small Investment, Big Reward M.2HS.12 6: s 6: Forms of s 5: Comparing in Different Forms 5

6 West Virginia Standards: d Math II M.2HS.13 See IM1 standard M.1HS.2 0 Build a Function that models a relationship between two quantities M.2HS.13. a M.2HS.13. b See IM1 standard M.1HS.2 0.a 13: Polynomials and s *Includes more than just linear and exponential 13.1 Controlling the Populations 7: Inverse 1: Function Operations 2: Adding and Subtracting Linear 6

7 West Virginia Standards: d Math II M.2HS.14 12: Introduction to 12.7 More Than Meets the Eye 6: s 3: Linear and Transformations 1: Shifting Vertically 2: Reflecting and Dilating using Graphs 3: Shifting Horizontally 4: Transforming using Tables of Values 5: Using Multiple Transformations Build new functions from existing functions M.2HS.15 16: Other and Inverses 16.3 The Inverse Undoes What the Function Does 16.4 Taking the Egg Plunge 7: Inverse 2: Inverses of 1: Recognizing Graphs of Inverses 2: Calculating Inverses of Linear 7

8 West Virginia Standards: d Math II Construct and Compare linear, quadratic, and exponential models and solve problems M.2HS.16 * already covered exponen tial in IM1 nothing specific for Quadrati cs M.2HS.17 12: Introduction to 12.2 Just U and I 12.3 Walking the Curve? Interpret the structure of expressions M.2HS.17. a * Exponen tial already covered in IM1 see M.1HS.4. a 8

9 West Virginia Standards: d Math II 12: Introduction to 12.4 Are You Afraid of Ghosts? 12.5 Just Watch that Pumpkin Fly! 12.6 The Form is "Key" M.2HS.17. b * Exponen tial already covered in IM1 see M.1HS.4. b M.2HS.18 13: Polynomials and s 13.5 What Makes You So Special? Write Expressions in equivalent forms to solve problems M.2HS.19 M.2HS.19. a 12: Introduction to 12.4 Are You Afraid of Ghosts? 6: s 6: Forms of s 6: s 6: Forms of s 2: Converting s to Factored Form 1: Converting s to General Form 9

10 West Virginia Standards: d Math II 13: Polynomials and s 13.3 What Factored Into It? 13.4 Zeroing In 13.5 What Makes You So Special M.2HS.19. b 13: Polynomials and s 13.7 Another Method 6: s 6: Forms of s 1: Converting s to General Form M.2HS.19. c d 1 2: Linear and Exponential Relationships 7: Rational Exponents 3: Transforming Exponential Expressions Create equations that describe numbers or relationship s M.2HS.20 12: Introduction to 12.1 Up and Down or Down and Up 12.2 Just U and I 12.3 Walking the. Curve? 12.4 Are You Afraid of Ghosts? 6: s 1: Models in Factored Form 1: Modeling Area as Product of Monomial and Binomial 2: Modeling Area as Product of Two Binomials 3: Maximizing Area 10

11 West Virginia Standards: d Math II 13: Polynomials and s 14: Solving Equations and Inequalities 13.1 Controlling the Population 13.6 Could it Be Groovy to Be a Square? 13.1 Ladies and Gentlemen: Please Welcome the Formulas! 13.3 They're a Lot More Than Just Sparklers 13.4 You Must Have a System 12: Introduction to 12.1 Up and Down or Down and Up 12.2 Just U and I 12.3 Walking the. Curve? 12.4 Are You Afraid of Ghosts? M.2HS.21 14: Solving Equations and Inequalities 14.1 Ladies and Gentlemen: Please Welcome the Formulas! 14.3 They're a Lot More Than Just Sparklers 14.4 You Must Have a System 11

12 West Virginia Standards: d Math II M.2HS.22 16: Other and Inverses 16.4 Take the Egg Plunge! M.2HS.23 Solve Equations and inequalities in one variable M.2HS.23. a 14: Solving Equations and Inequalities 14.1 Ladies and Gentlemen: Please Welcome the Formulas! 6: s 5: Expression Factoring 7: Completing the Square M.2HS.23. b 13: Polynomials and s 13.4 Zeroing In 13.6 Could it Be Groovy to Be a Square? 13.7 Another Method 6: s 7: Equation Solving 2: Solving Equations by Factoring 3: Solving Equations 12

13 West Virginia Standards: d Math II Use complex numbers in polynomial identities and equations M.2HS.24 M.2HS.25 M.2HS.26 I I I 14: Solving Equations and Inequalities 4: 4: 4: 14.2 It's Watching and Tracking 4.7 You Can't Spell "Fundamental Theorem of Algebra" without F-U-N! 4.6 Now It's Getting Complex But It's Really Not Difficult 4.7 You Can't Spell "Fundamental Theorem of Algebra" without F-U-N! 4.7 You Can't Spell "Fundamental Theorem of Algebra" without F-U-N! 2: 2: Operations with Complex Numbers 5: Solving Equations with Complex Roots Solve Systems of Equations M.2HS.27 14: Solving Equations and Inequalities 14.4 You Must Have a System 13

14 West Virginia Standards: d Math II M.2HS.28 19: Probability 19.1 These are a Few of My Favorite Things 19.2 It's in the Cards Understand independen ce and conditional probability and use them to interpret data M.2HS.29 M.2HS.30 19: Probability 20: More Probability and Counting 19.3 And? 19.5 And, OR, and More! 20.2 It all Depends 9: Probability 9: Probability 1: Independence and Conditional Probability 1: Independence and Conditional Probability 1: Independent Events 2: Conditional Probability M.2HS.31 20: More Probability and Counting 20.1 Left, Left, Left, Right, Left 9: Probability 1: Independence and Conditional Probability 3: Understanding Frequency Tables 4: Constructing and Interpreting Frequency Tables M.2HS.32 20: More Probability and Counting 20.2 It all Depends 9: Probability 1: Independence and Conditional Probability 5: Recognizing Concepts of Conditional Probability 14

15 West Virginia Standards: d Math II M.2HS.33 20: More Probability and Counting 20.2 It all Depends 9: Probability 1: Independence and Conditional Probability 6: Calculating Compound Probabilities M.2HS.34 19: Probability 19.4 Or? 9: Probability 1: Independence and Conditional Probability 6: Calculating Compound Probabilities M.2HS.35 19: Probability 19.3 And? 19.5 And, OR, and More! M.2HS.36 20: More Probability and Counting 20.3 Counting 20.4 Trials Use Probability to evaluate outcomes of decisions M.2HS.37 M.2HS.38 20: More Probability and Counting 20: More Probability and Counting 20.5 To Spin or Not to Spin 20.5 To Spin or Not to Spin Understand similarity in terms of similarity transformati ons M.2HS.39 M.2HS.39. a 4: Similarity Through a Transformation 4.1 Big and Small 15

16 West Virginia Standards: d Math II M.2HS.39. b 4: Similarity Through a Transformation 4.1 Big and Small M.2HS.40 4: Similarity Through a Transformation 4.1 Big and Small M.2HS.41 4: Similarity Through a Transformation 8: Trigonometry 4.2 Similar Triangles or Not? 8.1 Three Angles Measure 8.2 The Tangent Ratio Prove Geometric Theorems M.2HS.42 2: Introduction to Proofs 2.1 A Little Dash of Logic 2.2 And Now From a New Angle 2.3 Forms of Proof 2.4 What's Your Proof 2.5 A Reversed Condition 1: Angles, Segments and Lines 1: Angle Properties 1: Calculating and Justifying Angle Measures 2: Calculating Angle Measures 5: Congruence Through Transformations 5.7 Any Other Theorems You Forgot to Mention 2: Introduction to Proofs with Segments and Angles 2: Completing Measure Proofs 3: Connecting Steps in Angle Proofs 4: Using Angle Theorems 16

17 West Virginia Standards: d Math II 7: Properties of Quadrilaterals 7.5 Exterior and Interior Angle Interactions 3: Lines Cut By a Transversal 1: Classifying Angles Formed by Transversals 2: Calculating Angles formed by Transversals 3: Calculating Angles Formed by Multiple Transversals 4: Parallel Lines Theorems 1: Proving Parallel lines Theorems 2: Proving the Converse of Parallel Lines Theorems 3: Properties of Triangles 3.1 Inside Out 3.2 Trade Routes and Pasta, Anyone? 3.3 Stamps Around the World 3.4 More Stamps, Really? 3: Triangle Congruence 2: Proving Triangles Congruent using SAS and SSS 3: Proving Triangles Congruent using AAS and ASA 4: Proving Triangles Congruent using HL and HA 5: Using Triangle Congruence 6: Proving Theorems Using Congruent Triangles M.2HS.43 d 2 5: Congruence Through Transformations 5.3 It's All About The Sides 5.4 Make Sure the Angle is Included 5.5 Angle to the Left of Me, Angle to the Right of Me 5.6 Sides Not Included 5.7 Any Other Theorems You 2: Triangles 4: Triangle Theorems 1: Proving Triangle Theorems 2: Using Triangle Theorems 17

18 West Virginia Standards: d Math II Forgot to Mention 6: Using Congruence Theorems 6.1 Time to Get Right 6.2 CPCTC 6.3 Congruence Theorems 6.4 Making Some Assumptions d I 6: Parallelograms 1: Properties of Parallelograms 1: Understanding Parallelograms 2: Determining Parts of Quadrilaterals and Parallelograms with Numbers 3: Determining Parts of Quadrilaterals and Parallelograms with Expressions M.2HS.44 7: Properties of Quadrilaterals 7.1 Squares and Rectangles 7.2 Parallelograms and Rhombi 7.3 Kites and Trapezoids 2: Triangles 5: Parallelogram Proofs 1: Proofs About Parallelograms 18

19 West Virginia Standards: d Math II Prove Theorems Involving Similarity M.2HS.45 M.2HS.46 4: Similarity Through a Transformation 4: Similarity Through a Transformation 4.3 Keep It In Proportion 4.4 Geometric Mean 4.5 Proving the Pythagorean Theorem 4.1 Big and Small 4.2 Similar Triangles or Not? 4.3 Keep It In Proportion 4.4 Geometric Mean 4.6 Indirect Measurement 2: Triangles 2: Triangles 2: Similar Triangles 3: Proofs Using Similar Triangles 1: Special Right Triangles 2: Similar Triangles 1: Introduction to Special Right Triangles 2: Calculating the Lengths of Sides of Special Right Triangles 1: Calculating Corresponding Parts of Similar Triangles 8: Trigonometry 8.1 Three Angles Measure 8.2 The Tangent Ratio 1: Special Right Triangles 2: Calculating Lengths of Sides of Special Right Triangles Use Coordinates to prove simple geometric theorems algebraically M.2HS.47 d I 12: Geometry on the Coordinate Plane 1: Tools of Geometry 12.2 Treasure Hunt 1.3 Stuck in the Middle 4: Tools of Geometry 2: Distances on the Coordinate Plane 3: Partitioning Segments Proportionately 19

20 West Virginia Standards: d Math II 8: Trigonometry 8.1 Three Angles Measure 8.2 The Tangent Ratio 3: Triangles and Trigonometry 1: Trigonometric Ratios 1: Introduction to Trigonometric Ratios M.2HS.48 M.2HS.49 8: Trigonometry 8.5 We Compliment Each Other! 3: Triangles and Trigonometry 1: Trigonometric Ratios 2: Relating Sine and Cosine of Complementary Angles Define trigonometri c ratios and solve problems involving right triangles M.2HS.50 8: Trigonometry 7: Properties of Quadrilaterals 8.3 The Sine Ratio 8.4 The Cosine Ratio 8.5 We Compliment Each Other 10.1 Squares and Rectangles 10.3 Kites and Trapezoids 10.4 Interior Angles of a Polygon 10.5 Exterior and Interior Angle Measurements 3: Similarity, Right Triangles, and Trigonometry 2: Right Triangles and Trigonometric Ratio 1: Determining Side Lengths Using One Trigonometric Ratio 2: Determining Side Lengths Using Multiple Trigonometric Ratios 18: Circles and Parabolas 18.2 Bring on the Algebra 18.3 Is that Point on the Circle? 20

21 West Virginia Standards: d Math II Prove and apply trigonometri c identities M.2HS.51 8: Trigonometry 8.6 Time to Derive M.2HS.52 9: Circles 9.1 Riding a Ferris Wheel 4: Circles 1: Properties of Circles 1: Introduction to Circles M.2HS.53 9: Circles 9.1 Riding a Ferris Wheel 9.2 Take the Wheel 9.3 Manhole Covers 9.4 Color Theory 4: Circles 2: Angles in Circles 1: Determining Central and Inscribed Angles in a Circle 2: Determining Chords in a Circle 3: Determining Interior and Exterior Angles in Circles M.2HS.54 10: Arcs and Sectors of Circles 10.1 Replacement for a Carpenter's Square 4: Circles 2: Angles in Circles 4: Angles of an Inscribed Quadrilateral M.2HS.55 9: Circles 9.5 Solar Eclipses 21

22 West Virginia Standards: d Math II Find arc lengths and areas of sectors of circles M.2HS.56 10: Arcs and Sectors of Circles 10.2 Gears 10.3 Playing Darts 4: Circles 3: Arc Length 1: Relating Arc Length and Radius 2: Calculating Area of a Sector Translate between the geometric description and the equation for a conic section M.2HS.57 M.2HS.58 18: Circles and Parabolas 18: Circles and Parabolas 18.2 Bring on the Algebra 18.4 The Parabola 18.5 Simply Parabolic 8: Conics 1: Equation of a Circle 8: Conics 2: Equation of a Parabola 1: Deriving the Equation of a Circle 2: Determining the Radius and Center of a Circle 1: Deriving the Equation of a Parabola 22

23 West Virginia Standards: d Math II Use Coordinates to prove simple geometric theorems algebraically M.2HS.59 d I 12: Geometry on the Coordinate Plane 15: Connecting Algebra and Geometry with Polygons 17: Shapes on the Coordinate Plane 18: Circles and Parabolas 12.4 Did You Find a Parking Space? 15.1 Name That Triangle! 15.2 Name That Quadrilateral! 15.3 IS that Point on the Circle 17.1 It's All About the Slope 17.3 And I know That Quadrilateral Too! 18.1 The Coordinate Plane 18.3 Is That Point on the Circle Explain Volume Formulas and use them to solve problems M.2HS.60 11: Three- Dimensional Figures 4.3 Cavaleirei's Principles M.2HS.61 11: Three- Dimensional Figures 11.6 Turn up the 3: Three- Dimensional Shapes 2: Volume 1: Calculating Volume of Cylinders 2: Calculating Volume of Pyramids 3: Calculating Volume of Cones 4: Calculating Volume of Spheres 23