Acknowledgments |
|
xxiii | |
Letter to High School Mathematics Teachers |
|
xxv | |
Letter to High School Principals |
|
xxvii | |
Introduction: A Brief History of the Common Core |
|
xxix | |
The Common Core State Standards for Mathematics |
|
xxix | |
Instructional Shifts |
|
xxx | |
Major Work of High School |
|
xxx | |
Common Core Word Wall |
|
xxxi | |
The Common Core Standards for Mathematical Practice |
|
xxxii | |
Effective Mathematical Teaching Practices |
|
xxxiv | |
How to Use This Book |
|
xxxv | |
Reflection Questions |
|
xxxvi | |
|
|
|
Conceptual Category Overview |
|
|
2 | (1) |
|
|
3 | (4) |
|
Reflection Questions: Modeling |
|
|
7 | (3) |
|
Part 2 Number and Quantity |
|
|
|
Conceptual Category Overview |
|
|
10 | (1) |
|
Direct Connections to Number and Quantity in the Middle Grades |
|
|
11 | (1) |
|
|
11 | (1) |
|
Number and Quantity---Overarching Key Vocabulary |
|
|
11 | (1) |
|
Domain: The Real Number System (N.RN) |
|
|
12 | (10) |
|
|
12 | (1) |
|
Cluster A Extend the properties of exponents to rational exponents |
|
|
13 | (4) |
|
Cluster B Use properties of rational and irrational numbers |
|
|
17 | (2) |
|
|
19 | (2) |
|
Reflection Questions: The Real Number System |
|
|
21 | (1) |
|
|
22 | (7) |
|
Cluster A Reason quantitatively and use units to solve problems |
|
|
22 | (4) |
|
|
26 | (2) |
|
Reflection Questions: Quantities |
|
|
28 | (1) |
|
Domain: The Complex Number System (NGN) |
|
|
29 | (18) |
|
|
29 | (1) |
|
Cluster A Perform arithmetic operations with complex numbers |
|
|
30 | (4) |
|
Cluster B Represent complex numbers and their operations on the complex plane |
|
|
34 | (5) |
|
Cluster C Use complex numbers in polynomial identities and equations |
|
|
39 | (5) |
|
|
44 | (2) |
|
Reflection Questions: The Complex Number System |
|
|
46 | (1) |
|
Domain: Vector & Matrix Quantities (N.VM) |
|
|
47 | (29) |
|
|
47 | (1) |
|
Cluster A Represent and model with vector quantities |
|
|
48 | (4) |
|
Cluster B Perform operations on vectors |
|
|
52 | (4) |
|
Cluster C Perform operations on matrices and use matrices in applications |
|
|
56 | (12) |
|
|
68 | (5) |
|
Reflection Questions: Vector and Matrix Quantities |
|
|
73 | (3) |
|
|
|
Conceptual Category Overview |
|
|
76 | (1) |
|
Direct Connections to Algebra in the Middle Grades |
|
|
76 | (2) |
|
|
77 | (1) |
|
Algebra---Overarching Key Vocabulary |
|
|
77 | (1) |
|
Domain: Seeing Structure in Expressions (A.SSE) |
|
|
78 | (11) |
|
|
79 | (1) |
|
Cluster A Interpret the structure of expressions |
|
|
80 | (3) |
|
Cluster B Write expressions in equivalent forms to solve problems |
|
|
83 | (4) |
|
|
87 | (1) |
|
Reflection Questions: Seeing Structure in Expressions |
|
|
88 | (1) |
|
Domain: Arithmetic With Polynomials and Rational Expressions (AAPR) |
|
|
89 | (16) |
|
|
89 | (1) |
|
Cluster A Perform arithmetic operations on polynomials |
|
|
90 | (2) |
|
Cluster B Understand the relationship between zeros and factors of polynomials |
|
|
92 | (4) |
|
Cluster C Use polynomial identities to solve problems |
|
|
96 | (4) |
|
Cluster D Rewrite rational expressions |
|
|
100 | (3) |
|
|
103 | (1) |
|
Reflection Questions: Arithmetic With Polynomials and Rational Expressions |
|
|
104 | (1) |
|
Domain: Creating Equations (A.CED) |
|
|
105 | (9) |
|
|
105 | (1) |
|
Cluster A Create equations that describe numbers or relationships |
|
|
106 | (6) |
|
|
112 | (1) |
|
Reflection Questions: Creating Equations |
|
|
113 | (1) |
|
Domain: Reasoning With Equations and Inequalities (A.REI) |
|
|
114 | (28) |
|
|
114 | (1) |
|
Cluster A Understand solving equations as a process of reasoning and explain the reasoning |
|
|
115 | (5) |
|
Cluster B Solve equations and inequalities in one variable |
|
|
120 | (6) |
|
Cluster C Solve systems of equations |
|
|
126 | (7) |
|
Cluster D Represent and solve equations and inequalities graphically |
|
|
133 | (5) |
|
|
138 | (1) |
|
Reflection Questions: Reasoning With Equations and Inequalities |
|
|
139 | (3) |
|
|
|
Conceptual Category Overview |
|
|
142 | (1) |
|
Direct Connections to Functions in the Middle Grades |
|
|
143 | (1) |
|
|
143 | (1) |
|
Functions---Overarching Key Vocabulary |
|
|
143 | (1) |
|
Domain: Interpreting Functions (F.IF) |
|
|
144 | (31) |
|
|
144 | (1) |
|
Cluster A Understand the concept of a function and use function notation |
|
|
145 | (6) |
|
Cluster B Interpret functions that arise in application in terms of the context |
|
|
151 | (5) |
|
Cluster C Analyze functions using different representations |
|
|
156 | (15) |
|
|
171 | (3) |
|
Reflection Questions: Interpreting Functions |
|
|
174 | (1) |
|
Domain: Building Functions (F.BF) |
|
|
175 | (16) |
|
|
175 | (1) |
|
Cluster A Build a function that models a relationship between two quantities |
|
|
176 | (6) |
|
Cluster B Build new functions from existing functions |
|
|
182 | (6) |
|
|
188 | (2) |
|
Reflection Questions: Building Functions |
|
|
190 | (1) |
|
Domain: Linear, Quadratic, and Exponential Models (F.LE) |
|
|
191 | (17) |
|
|
191 | (1) |
|
Cluster A Construct and compare linear, quadratic, and exponential models and solve problems |
|
|
192 | (11) |
|
Cluster B Interpret expressions for functions in terms of the situation they model |
|
|
203 | (2) |
|
|
205 | (2) |
|
Reflection Questions: Linear, Quadratic, and Exponential Models |
|
|
207 | (1) |
|
Domain: Trigonometric Functions (F.TF) |
|
|
208 | (24) |
|
|
208 | (2) |
|
Cluster A Extend the domain of trigonometric functions using the unit circle |
|
|
210 | (9) |
|
Cluster B Model periodic phenomena with trigonometric functions |
|
|
219 | (6) |
|
Cluster C Students probe identities involving trigonometric functions and use them to solve problems |
|
|
225 | (3) |
|
|
228 | (2) |
|
Reflection Questions: Trigonometric Functions |
|
|
230 | (2) |
|
|
|
Conceptual Category Overview |
|
|
232 | (1) |
|
Direct Connections to Geometry in the Middle Grades |
|
|
233 | (2) |
|
|
233 | (1) |
|
Geometry---Overarching Key Vocabulary |
|
|
233 | (2) |
|
Domain: Congruence (G.CO) |
|
|
235 | (29) |
|
|
236 | (1) |
|
Cluster A Experiment with transformations in the plane |
|
|
237 | (11) |
|
Cluster B Understand congruence in terms of rigid motions |
|
|
248 | (5) |
|
Cluster C Prove geometric theorems |
|
|
253 | (4) |
|
Cluster D Make geometric constructions |
|
|
257 | (4) |
|
|
261 | (2) |
|
Reflection Questions: Congruence |
|
|
263 | (1) |
|
Domain: Similarity, Right Triangles, and Trigonometry (G.SRT) |
|
|
264 | (25) |
|
|
265 | (1) |
|
Cluster A Understand similarity in terms of similarity transformations |
|
|
266 | (6) |
|
Cluster B Prove theorems involving similarity |
|
|
272 | (4) |
|
Cluster C Define trigonometric rations and solve problems involving right triangles |
|
|
276 | (4) |
|
Cluster D Apply trigonometry to general triangles |
|
|
280 | (5) |
|
|
285 | (3) |
|
Reflection Questions: Similarity, Right Triangles, and Trigonometry |
|
|
288 | (1) |
|
|
289 | (15) |
|
|
289 | (1) |
|
Cluster A Understand and apply theorems about circles |
|
|
290 | (7) |
|
Cluster B Find arc lengths and areas of sectors of circles |
|
|
297 | (3) |
|
|
300 | (3) |
|
Reflection Questions: Circles |
|
|
303 | (1) |
|
Domain: Expressing Geometric Properties With Equations (G.GPE) |
|
|
304 | (16) |
|
|
304 | (1) |
|
Cluster A Translate between the geometric description and the equation for a conic section |
|
|
305 | (7) |
|
Cluster B Use coordinates to prove simple geometric theorems algebraically |
|
|
312 | (5) |
|
|
317 | (2) |
|
Reflection Questions: Expressing Geometric Properties With Equations |
|
|
319 | (1) |
|
Domain: Geometric Measurement and Dimension (G.GMD) |
|
|
320 | (13) |
|
|
320 | (1) |
|
Cluster A Explain volume formulas and use them to solve problems |
|
|
321 | (7) |
|
Cluster B Visualize relationships between two-dimensional and three-dimensional objects |
|
|
328 | (2) |
|
|
330 | (2) |
|
Reflection Questions: Measurement and Dimension |
|
|
332 | (1) |
|
Domain: Modeling With Geometry (G.MG) |
|
|
333 | (11) |
|
|
333 | (1) |
|
Cluster A Apply geometric concepts in modeling situations |
|
|
334 | (4) |
|
Reflection Questions: Modeling With Geometry |
|
|
338 | (1) |
|
|
339 | (5) |
|
Part 6 Statistics and Probability |
|
|
|
Conceptual Category Overview |
|
|
344 | (1) |
|
Direct Connections to Statistics and Probability in Middle Grades |
|
|
344 | (2) |
|
|
345 | (1) |
|
Statistics and Probability---Overarching Key Vocabulary |
|
|
345 | (1) |
|
Domain: Interpreting Categorical and Quantitative Data (S.ID) |
|
|
346 | (34) |
|
|
346 | (3) |
|
Cluster A Summarize, represent, and interpret data on a single count or measurement variable |
|
|
349 | (9) |
|
Cluster B Summarize, represent, and interpret data on two categorical and quantitative variables |
|
|
358 | (10) |
|
Cluster C Interpret linear models |
|
|
368 | (8) |
|
|
376 | (3) |
|
Reflection Questions: Interpreting Categorical and Quantitative Data |
|
|
379 | (1) |
|
Domain: Making Inferences and Justifying Conclusions (S.IC) |
|
|
380 | (19) |
|
|
380 | (1) |
|
Cluster A Understand and evaluate random processes underlying statistical experiments |
|
|
381 | (5) |
|
Cluster B Make inferences and justify conclusions from sample surveys, experiments, and observational studies |
|
|
386 | (9) |
|
|
395 | (3) |
|
Reflection Questions: Making Inferences and justifying Conclusions |
|
|
398 | (1) |
|
Domain: Conditional Probability and the Rules of Probability (S.CP) |
|
|
399 | (22) |
|
|
399 | (2) |
|
Cluster A: Understand independence and conditional probability and use them to interpret data |
|
|
401 | (10) |
|
Cluster B Use the rules of probability to compute probabilities of compound events in a uniform probability model |
|
|
411 | (7) |
|
|
418 | (2) |
|
Reflection Questions: Conditional Probability and the Rules of Probability |
|
|
420 | (1) |
|
Domain: Using Probability to Make Decisions (S.MD) |
|
|
421 | (17) |
|
|
421 | (1) |
|
Cluster A Calculate expected values and use them to solve problems |
|
|
422 | (6) |
|
Cluster B Use probability to evaluate outcomes of decisions |
|
|
428 | (5) |
|
|
433 | (2) |
|
Reflection Questions: Using Probability to Make Decisions |
|
|
435 | (3) |
|
|
|
Table 1 Standards for Mathematical Practice |
|
|
438 | (3) |
|
Table 2 Effective Teaching Practices |
|
|
441 | (3) |
|
|
|
Reproducible 1 Blank Sample Planning Page |
|
|
444 | (2) |
|
Reproducible 2 The Real Number System |
|
|
446 | (1) |
|
Reproducible 3 Seeing Structure in Expressions |
|
|
447 | (1) |
|
Reproducible 4 Reasoning With Equalities and Inequalities |
|
|
448 | (2) |
|
Reproducible 5 Interpreting Functions |
|
|
450 | (1) |
|
Reproducible 6 Building Functions |
|
|
451 | (1) |
|
Reproducible 7 Linear and Exponential Functions Cards |
|
|
452 | (1) |
|
Reproducible 8 Trigonometric Functions |
|
|
453 | (1) |
|
Reproducible 9 Exploring the Values of the Trigonometry Ratios |
|
|
454 | (2) |
|
Reproducible 10 Real and Nonsense Words |
|
|
456 | (1) |
|
Reproducible 11 Disjoint vs. Independent Activity |
|
|
457 | (2) |
Additional Resources and References |
|
459 | (2) |
About the Authors |
|
461 | |