Indexes Cross-Referencing Your State Standards |
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I-1 | |
Quick Reference Guide |
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xvii | |
Acknowledgments |
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xxv | |
Letter to High School Mathematics Teachers |
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xxvii | |
Letter to High School Principals |
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xxix | |
Introduction |
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A Brief History of Current State Standards |
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xxxi | |
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College and Career Ready Standards for Mathematics |
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xxxi | |
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xxxii | |
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Major Work of High School |
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xxxiii | |
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Terminology Used in This Book |
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xxxiii | |
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The Common Core Standards for Mathematical Practice (Processes) |
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xxxiv | |
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Effective Mathematical Teaching Practices |
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xxxvi | |
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xxxvii | |
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xxxix | |
Part 1. Modeling |
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Conceptual Category Overview |
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2 | (1) |
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3 | (4) |
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Reflection Questions: Modeling |
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7 | (3) |
Part 2. Number and Quantity |
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Conceptual Category Overview |
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10 | (1) |
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Direct Connections to Number and Quantity in the Middle Grades |
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11 | (1) |
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11 | (1) |
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Number and Quantity-Overarching Key Vocabulary |
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11 | (1) |
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Domain: The Real Number System (N.RN) |
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12 | (10) |
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12 | (1) |
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Cluster A: Extend the properties of exponents to rational exponents. |
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13 | (4) |
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Cluster B: Use properties of rational and irrational numbers. |
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17 | (2) |
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19 | (2) |
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Reflection Questions: The Real Number System |
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21 | (1) |
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22 | (7) |
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Cluster A: Reason quantitatively and use units to solve problems. |
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22 | (4) |
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26 | (2) |
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Reflection Questions: Quantities |
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28 | (1) |
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Domain: The Complex Number System (N.CN) |
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29 | (18) |
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29 | (1) |
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Cluster A: Perform arithmetic operations with complex numbers. |
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30 | (4) |
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Cluster B: Represent complex numbers and their operations on the complex plane. |
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34 | (5) |
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Cluster C: Use complex numbers in polynomial identities and equations. |
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39 | (5) |
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44 | (2) |
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Reflection Questions: The Complex Number System |
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46 | (1) |
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Domain: Vector & Matrix Quantities (N.VM) |
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47 | (29) |
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47 | (1) |
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Cluster A: Represent and model with vector quantities. |
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48 | (4) |
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Cluster B: Perform operations on vectors. |
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52 | (4) |
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Cluster C: Perform operations on matrices and use matrices in applications. |
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56 | (12) |
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68 | (5) |
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Reflection Questions: Vector and Matrix Quantities |
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73 | (3) |
Part 3. Algebra |
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Conceptual Category Overview |
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76 | (1) |
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Direct Connections to Algebra in the Middle Grades |
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76 | (2) |
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77 | (1) |
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Algebra-Overarching Key Vocabulary |
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77 | (1) |
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Domain: Seeing Structure in Expressions (A.SSE) |
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78 | (11) |
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79 | (1) |
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Cluster A: Interpret the structure of expressions. |
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80 | (3) |
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Cluster B: Write expressions in equivalent forms to solve problems. |
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83 | (4) |
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87 | (1) |
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Reflection Questions: Seeing Structure in Expressions |
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88 | (1) |
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Domain: Arithmetic With Polynomials and Rational Expressions (A.APR) |
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89 | (16) |
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89 | (1) |
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Cluster A: Perform arithmetic operations on polynomials. |
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90 | (2) |
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Cluster B: Understand the relationship between zeros and factors of polynomials. |
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92 | (4) |
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Cluster C: Use polynomial identities to solve problems. |
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96 | (4) |
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Cluster D: Rewrite rational expressions. |
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100 | (3) |
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103 | (1) |
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Reflection Questions: Arithmetic With Polynomials and Rational Expressions |
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104 | (1) |
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Domain: Creating Equations (A.CED) |
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105 | (9) |
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105 | (1) |
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Cluster A: Create equations that describe numbers or relationships. |
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106 | (6) |
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112 | (1) |
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Reflection Questions: Creating Equations |
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113 | (1) |
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Domain: Reasoning With Equations and Inequalities (A.REI) |
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114 | (28) |
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114 | (1) |
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Cluster A: Understand solving equations as a process of reasoning and explain the reasoning. |
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115 | (5) |
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Cluster B: Solve equations and inequalities in one variable. |
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120 | (6) |
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Cluster C: Solve systems of equations. |
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126 | (7) |
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Cluster D: Represent and solve equations and inequalities graphically. |
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133 | (5) |
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138 | (2) |
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Reflection Questions: Reasoning With Equations and Inequalities |
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140 | (2) |
Part 4. Functions |
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Conceptual Category Overview |
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142 | (1) |
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Direct Connections to Functions in the Middle Grades |
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143 | (1) |
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143 | (1) |
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Functions-Overarching Key Vocabulary |
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143 | (1) |
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Domain: Interpreting Functions (F.IF) |
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144 | (31) |
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144 | (1) |
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Cluster A: Understand the concept of a function and use function notation. |
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145 | (6) |
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Cluster B: Interpret functions that arise in application in terms of the context. |
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151 | (5) |
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Cluster C: Analyze functions using different representations. |
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156 | (15) |
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171 | (3) |
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Reflection Questions: Interpreting Functions |
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174 | (1) |
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Domain: Building Functions (F.BF) |
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175 | (16) |
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175 | (1) |
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Cluster A: Build a function that models a relationship between two quantities. |
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176 | (6) |
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Cluster B: Build new functions from existing functions. |
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182 | (6) |
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188 | (2) |
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Reflection Questions: Building Functions |
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190 | (1) |
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Domain: Linear, Quadratic, and Exponential Models (F.LE) |
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191 | (17) |
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191 | (1) |
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Cluster A: Construct and compare linear, quadratic, and exponential models and solve problems. |
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192 | (11) |
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Cluster B: Interpret expressions for functions in terms of the situation they model. |
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203 | (2) |
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205 | (2) |
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Reflection Questions: Linear, Quadratic, and Exponential Models |
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207 | (1) |
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Domain: Trigonometric Functions (F.TF) |
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208 | (24) |
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208 | (2) |
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Cluster A: Extend the domain of trigonometric functions using the unit circle. |
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210 | (9) |
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Cluster B: Model periodic phenomena with trigonometric functions. |
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219 | (6) |
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Cluster C: Students probe identities involving trigonometric functions and use them to solve problems. |
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225 | (3) |
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228 | (2) |
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Reflection Questions: Trigonometric Functions |
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230 | (2) |
Part 5. Geometry |
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Conceptual Category Overview |
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232 | (1) |
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Direct Connections to Geometry in the Middle Grades |
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233 | (2) |
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233 | (1) |
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Geometry-Overarching Key Vocabulary |
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233 | (2) |
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Domain: Congruence (G.CO) |
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235 | (29) |
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236 | (1) |
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Cluster A: Experiment with transformations in the plane. |
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237 | (11) |
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Cluster B: Understand congruence in terms of rigid motions. |
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248 | (5) |
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Cluster C: Prove geometric theorems. |
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253 | (4) |
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Cluster D: Make geometric constructions. |
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257 | (4) |
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261 | (2) |
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Reflection Questions: Congruence |
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263 | (1) |
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Domain: Similarity, Right Triangles, and Trigonometry (G.SRT) |
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264 | (25) |
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265 | (1) |
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Cluster A: Understand similarity in terms of similarity transformations. |
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266 | (6) |
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Cluster B: Prove theorems involving similarity. |
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272 | (4) |
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Cluster C. Define trigonometric rations and solve problems involving right triangles. |
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276 | (4) |
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Cluster D: Apply trigonometry to general triangles. |
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280 | (5) |
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285 | (3) |
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Reflection Questions: Similarity, Right Triangles, and Trigonometry |
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288 | (1) |
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289 | (15) |
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289 | (1) |
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Cluster A: Understand and apply theorems about circles. |
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290 | (7) |
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Cluster B: Find arc lengths and areas of sectors of circles. |
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297 | (3) |
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300 | (3) |
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Reflection Questions: Circles |
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303 | (1) |
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Domain: Expressing Geometric Properties With Equations (G.GPE) |
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304 | (16) |
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304 | (1) |
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Cluster A: Translate between the geometric description and the equation for a conic section. |
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305 | (7) |
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Cluster B: Use coordinates to prove simple geometric theorems algebraically. |
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312 | (5) |
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317 | (2) |
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Reflection Questions: Expressing Geometric Properties With Equations |
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319 | (1) |
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Domain: Geometric Measurement and Dimension (G.GMD) |
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320 | (13) |
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320 | (1) |
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Cluster A: Explain volume formulas and use them to solve problems. |
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321 | (7) |
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Cluster B: Visualize relationships between two-dimensional and three-dimensional objects. |
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328 | (2) |
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330 | (2) |
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Reflection Questions: Measurement and Dimension |
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332 | (1) |
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Domain: Modeling With Geometry (G.MG) |
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333 | (11) |
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333 | (1) |
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Cluster A: Apply geometric concepts in modeling situations. |
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334 | (4) |
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338 | (3) |
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Reflection Questions: Modeling With Geometry |
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341 | (3) |
Part 6. Statistics and Probability |
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Conceptual Category Overview |
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344 | (1) |
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Direct Connections to Statistics and Probability in Middle Grades |
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344 | (2) |
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345 | (1) |
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Statistics and Probability-Overarching Key Vocabulary |
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345 | (1) |
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Domain: Interpreting Categorical and Quantitative Data (S.ID) |
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346 | (34) |
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346 | (3) |
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Cluster A: Summarize, represent, and interpret data on a single count or measurement variable. |
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349 | (9) |
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Cluster B: Summarize, represent, and interpret data on two categorical and quantitative variables. |
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358 | (10) |
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Cluster C: Interpret linear models. |
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368 | (8) |
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376 | (3) |
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Reflection Questions: Interpreting Categorical and Quantitative Data |
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379 | (1) |
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Domain: Making Inferences and Justifying Conclusions (S.IC) |
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380 | (19) |
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380 | (1) |
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Cluster A: Understand and evaluate random processes underlying statistical experiments. |
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381 | (5) |
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Cluster B: Make inferences and justify conclusions from sample surveys, experiments, and observational studies. |
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386 | (9) |
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395 | (3) |
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Reflection Questions: Making Inferences and Justifying Conclusions |
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398 | (1) |
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Domain: Conditional Probability and the Rules of Probability (S.CP) |
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399 | (22) |
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399 | (2) |
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Cluster A: Understand independence and conditional probability and use them to interpret data. |
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401 | (10) |
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Cluster B: Use the rules of probability to compute probabilities of compound events in a uniform probability model. |
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411 | (7) |
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418 | (2) |
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Reflection Questions: Conditional Probability and the Rules of Probability |
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420 | (1) |
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Domain: Using Probability to Make Decisions (S.MD) |
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421 | (17) |
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421 | (1) |
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Cluster A: Calculate expected values and use them to solve problems. |
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422 | (6) |
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Cluster B: Use probability to evaluate outcomes of decisions. |
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428 | (5) |
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433 | (2) |
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Reflection Questions: Using Probability to Make Decisions |
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435 | (3) |
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Table 1 Standards for Mathematical Practice |
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438 | (3) |
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Table 2 Effective Teaching Practices |
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441 | (3) |
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Reproducible 1 Blank Sample Planning Page |
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444 | (2) |
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Reproducible 2 The Real Number System |
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446 | (1) |
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Reproducible 3 Seeing Structure in Expressions |
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447 | (1) |
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Reproducible 4 Reasoning With Equalities and Inequalities |
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448 | (2) |
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Reproducible 5 Interpreting Functions |
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450 | (1) |
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Reproducible 6 Building Functions |
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451 | (1) |
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Reproducible 7 Linear and Exponential Functions Cards |
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452 | (1) |
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Reproducible 8 Trigonometric Functions |
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453 | (1) |
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Reproducible 9 Exploring the Values of the Trigonometry Ratios |
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454 | (2) |
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Reproducible 10 Real and Nonsense Words |
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456 | (1) |
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Reproducible 11 Disjoint vs. Independent Activity |
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457 | (2) |
Additional Resources and References |
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459 | (2) |
About the Authors |
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461 | |