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E-raamat: Your Mathematics Standards Companion, High School: What They Mean and How to Teach Them

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  • Sari: Corwin Mathematics Series
  • Ilmumisaeg: 06-Feb-2018
  • Kirjastus: Corwin Press Inc
  • Keel: eng
  • ISBN-13: 9781544317434
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  • Formaat: PDF+DRM
  • Sari: Corwin Mathematics Series
  • Ilmumisaeg: 06-Feb-2018
  • Kirjastus: Corwin Press Inc
  • Keel: eng
  • ISBN-13: 9781544317434

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Transforming the standards into learning outcomes just got a lot easier

This expansion of the popular Common Core Mathematics Companions provides a Cross-Referencing Index for states implementing their own specific mathematics standards.  This index allows you to see in an instant which of your standards are the same as CCSS-M, which differ and how—and which page number to turn to for standards-based teaching ideas.

Beyond that? It’s the same great go-to guide for guide for teaching, planning, assessing, collaborating, and designing powerful high school mathematics curriculum, in any state or district.

Arvustused

"Your Mathematics Standards Companion, High School: What They Mean and How to Teach Them completes the set of books designed to support classroom teachers in implementing College and Career Ready Standards for K12. You will find an overview of both the content and practice standards as well as a detailed explanation of each standard including examples of classroom practice. As you use this book to help in planning and building your mathematics program it truly will become your planning companion!" -- Linda Gojak, Past President "Your Mathematics Standards Companion, High School: What They Mean and How to Teach Them is a welcome addition to the series! Providing the connections for the standards within the grade level, below grade level, and across conceptual categories helps teachers better plan supports for student learning. Using the series with districts helps to paint the whole K12 picture when planning curriculum and opening the doors of communication across the grade levels." -- Michele Mailhot, Mathematics Specialist "Finally, Your Mathematics Standards Companion is available for high school! The attention this volume brings to modeling and leveraging technology will be extremely valuable, and the focus on student misconceptions and common mistakes will help teachers create classroom communities that use misconceptions and mistakes as opportunities for student learning. Overall, the book provides multiple opportunities to deepen teachers understanding of their state standards and their ability to bring those standards alive in their classrooms." -- Cathy Martin, Director of PreK12 Mathematics "I like how this book gives specific advice for each standard on what teachers can do to support student learning and what students do to demonstrate mastery of a standard. There are clear teacher moves outlined in the text, along with questions and examples that encourage the teacher to reflect on their work and what they see from students." -- Brian Shay, Math Teacher and Chairperson "High school mathematics standards are daunting to wade through. This book is a lifesaver for teachers to quickly identify vertical alignments and efficiently discuss what students should be thinking at every step along the way. The bullets for "What the Teacher Does" and "What the Students Do" are great for identifying key learning goals and experiences to build lessons around, and provide insight into potential misconceptions." -- Mary Velez, Math Teacher

Indexes Cross-Referencing Your State Standards I-1
Quick Reference Guide xvii
Acknowledgments xxv
Letter to High School Mathematics Teachers xxvii
Letter to High School Principals xxix
Introduction
A Brief History of Current State Standards
xxxi
College and Career Ready Standards for Mathematics
xxxi
Instructional Shifts
xxxii
Major Work of High School
xxxiii
Terminology Used in This Book
xxxiii
The Common Core Standards for Mathematical Practice (Processes)
xxxiv
Effective Mathematical Teaching Practices
xxxvi
How to Use This Book
xxxvii
Reflection Questions
xxxix
Part
1. Modeling
Conceptual Category Overview
2(1)
Sample Planning Page
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)
Suggested Materials
11(1)
Number and Quantity-Overarching Key Vocabulary
11(1)
Domain: The Real Number System (N.RN)
12(10)
N.RN-Key Vocabulary
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)
Sample Planning Page
19(2)
Reflection Questions: The Real Number System
21(1)
Domain: Quantities (N.Q)
22(7)
Cluster A: Reason quantitatively and use units to solve problems.
22(4)
Sample Planning Page
26(2)
Reflection Questions: Quantities
28(1)
Domain: The Complex Number System (N.CN)
29(18)
N.CN-Key Vocabulary
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)
Sample Planning Page
44(2)
Reflection Questions: The Complex Number System
46(1)
Domain: Vector & Matrix Quantities (N.VM)
47(29)
N.VM-Key Vocabulary
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)
Sample Planning Page
68(5)
Reflection Questions: Vector and Matrix Quantities
73(3)
Part
3. Algebra
Conceptual Category Overview
76(1)
Direct Connections to Algebra in the Middle Grades
76(2)
Suggested Materials
77(1)
Algebra-Overarching Key Vocabulary
77(1)
Domain: Seeing Structure in Expressions (A.SSE)
78(11)
A. SSE-Key Vocabulary
79(1)
Cluster A: Interpret the structure of expressions.
80(3)
Cluster B: Write expressions in equivalent forms to solve problems.
83(4)
Sample Planning Page
87(1)
Reflection Questions: Seeing Structure in Expressions
88(1)
Domain: Arithmetic With Polynomials and Rational Expressions (A.APR)
89(16)
A.APR-Key Vocabulary
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)
Sample Planning Page
103(1)
Reflection Questions: Arithmetic With Polynomials and Rational Expressions
104(1)
Domain: Creating Equations (A.CED)
105(9)
ACED-Key Vocabulary
105(1)
Cluster A: Create equations that describe numbers or relationships.
106(6)
Sample Planning Page
112(1)
Reflection Questions: Creating Equations
113(1)
Domain: Reasoning With Equations and Inequalities (A.REI)
114(28)
A.REI-Key Vocabulary
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)
Sample Planning Page
138(2)
Reflection Questions: Reasoning With Equations and Inequalities
140(2)
Part
4. Functions
Conceptual Category Overview
142(1)
Direct Connections to Functions in the Middle Grades
143(1)
Suggested Materials
143(1)
Functions-Overarching Key Vocabulary
143(1)
Domain: Interpreting Functions (F.IF)
144(31)
F.IF-Key Vocabulary
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)
Sample Planning Page
171(3)
Reflection Questions: Interpreting Functions
174(1)
Domain: Building Functions (F.BF)
175(16)
F.BF-Key Vocabulary
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)
Sample Planning Page
188(2)
Reflection Questions: Building Functions
190(1)
Domain: Linear, Quadratic, and Exponential Models (F.LE)
191(17)
F. LE-Key Vocabulary
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)
Sample Planning Page
205(2)
Reflection Questions: Linear, Quadratic, and Exponential Models
207(1)
Domain: Trigonometric Functions (F.TF)
208(24)
F.TF-Key Vocabulary
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)
Sample Planning Page
228(2)
Reflection Questions: Trigonometric Functions
230(2)
Part
5. Geometry
Conceptual Category Overview
232(1)
Direct Connections to Geometry in the Middle Grades
233(2)
Suggested Materials
233(1)
Geometry-Overarching Key Vocabulary
233(2)
Domain: Congruence (G.CO)
235(29)
G.CO-Key Vocabulary
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)
Sample Planning Page
261(2)
Reflection Questions: Congruence
263(1)
Domain: Similarity, Right Triangles, and Trigonometry (G.SRT)
264(25)
G.SRT-Key Vocabulary
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)
Sample Planning Page
285(3)
Reflection Questions: Similarity, Right Triangles, and Trigonometry
288(1)
Domain: Circles (G.C)
289(15)
G.C-Key Vocabulary
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)
Sample Planning Page
300(3)
Reflection Questions: Circles
303(1)
Domain: Expressing Geometric Properties With Equations (G.GPE)
304(16)
G. GPE-Key Vocabulary
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)
Sample Planning Page
317(2)
Reflection Questions: Expressing Geometric Properties With Equations
319(1)
Domain: Geometric Measurement and Dimension (G.GMD)
320(13)
G.GMD-Key Vocabulary
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)
Sample Planning Page
330(2)
Reflection Questions: Measurement and Dimension
332(1)
Domain: Modeling With Geometry (G.MG)
333(11)
G.MG-Key Vocabulary
333(1)
Cluster A: Apply geometric concepts in modeling situations.
334(4)
Sample Planning Page
338(3)
Reflection Questions: Modeling With Geometry
341(3)
Part
6. Statistics and Probability
Conceptual Category Overview
344(1)
Direct Connections to Statistics and Probability in Middle Grades
344(2)
Suggested Materials
345(1)
Statistics and Probability-Overarching Key Vocabulary
345(1)
Domain: Interpreting Categorical and Quantitative Data (S.ID)
346(34)
S.ID-Key Vocabulary
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)
Sample Planning Page
376(3)
Reflection Questions: Interpreting Categorical and Quantitative Data
379(1)
Domain: Making Inferences and Justifying Conclusions (S.IC)
380(19)
S.IC-Key Vocabulary
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)
Sample Planning Page
395(3)
Reflection Questions: Making Inferences and Justifying Conclusions
398(1)
Domain: Conditional Probability and the Rules of Probability (S.CP)
399(22)
S.CP-Key Vocabulary
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)
Sample Planning Page
418(2)
Reflection Questions: Conditional Probability and the Rules of Probability
420(1)
Domain: Using Probability to Make Decisions (S.MD)
421(17)
S.MD-Key Vocabulary
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)
Sample Planning Page
433(2)
Reflection Questions: Using Probability to Make Decisions
435(3)
Resources
Table 1 Standards for Mathematical Practice
438(3)
Table 2 Effective Teaching Practices
441(3)
Reproducibles
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
Frederick L. Dillon is an author and national mathematics curriculum and professional learning consultant based near Cleveland, Ohio. He is a retired teacher with 35 years of classroom experience, having taught grades 7 through college. Fred is a frequent speaker at national, state, and local conferences and institutes. He is active at the local, state, and national level in professional organizations, including serving on the board of directors for the National Council of Teachers of Mathematics (NCTM). Fred was a recipient of the Presidential Award for Excellence in Science and Mathematics Teaching and the Christopherson-Fawcett Award from OCTM for Lifetime Contributions to Mathematics Education.

W. Gary Martin is Emily R. and Gerald S. Leischuck Endowed Professor in the Department of Curriculum and Teaching at Auburn University, where he teaches undergraduate and graduate courses in mathematics education and serves as co-director of the Mathematics Teacher Education Partnership (www.MTE-Partnership.org), a national coalition of universities seeking to improve the preparation of secondary mathematics teachers. He has been a writer on multiple standards documents, including Principles and Standards for School Mathematics (National Council of Teachers of Mathematics [ NCTM], 2000), Focus in High School Mathematics: Reasoning and Sense Making (NCTM, 2009), and Principles to Actions: Ensuring Mathematical Success for All (NCTM, 2014). Most recently, he was the lead writer for high school on the Standards for Preparing Teachers of Mathematics (Association of Mathematics Teacher Educators, 2017). He has presented extensively on mathematics education, particularly the teaching and learning of geometry, mathematics curriculum and standards, and mathematics teacher preparation. Previously, Martin served as the director of research for NCTM and has also held positions at the University of Hawai?i and Northern Illinois University. He began his career as a high school mathematics teacher, a role that remains central to his professional identity.

Basil Conway IV is an associate professor of mathematics education in the College of Education and Health Professions at Columbus State University and serves as the mathematics education graduate programs director. He serves on numerous doctoral committees as both a chair and methodologist. He earned his BS, MS, and PhD. in mathematics education from Auburn University in 2005, 2012, and 2015, respectively. He also completed his MS in statistical science at Colorado State University in 2010.



 Basil previously spent 10 years teaching in public middle and high schools before he became a teacher educator. During this time, he also worked as an instructor at a local junior college. Over the past 17 years of service in teaching mathematics and future teachers of mathematics, he has served in various local mathematics education leadership positions and organizations including Transforming East Alabama Mathematics (TEAM-Math), Auburn Universitys Teacher Leader Academy, East Alabama Council for Teachers of Mathematics, Woodrow Wilson Fellow, National Mathematics and Science Initiative, and A+ College Ready. He has published works related to teaching mathematics for social justice in numerous books and journals and has a special interest in statistics education.

 Basils lens for teaching and student learning draws heavily from Vygotskys theory of social constructivism in which language and culture play essential roles in human intellectual development. Thus, he believes the co-construction of knowledge is paramount in the development of students social, religious, and mathematical identities. He believes teachers, parents, other students, cultural norms, and other cultural communicative devices play a critical role in shaping students knowledge of themselves, faith, and mathematics.

Marilyn E. Strutchens is the Emily R. and Gerald S. Leischuck Endowed Professor for Critical Needs and the Mildred Cheshire Fraley Distinguished Professor of Mathematics Education in the Department of Curriculum and Teaching at Auburn University and coordinator of secondary mathematics education. She is also the Director of the Professional Mathematics Learning Communities Project between TEAM-Math and the Alabama Mathematics, Science, and Technology Initiative. She teaches courses in mathematics education. Strutchens is a member of the Board of Directors for the National Council of Teachers of Mathematics and serves on the Advisory Committee for the Education and Human Resource Directorate for the National Science Foundation. She has held positions at the University of Maryland at College Park and the University of Kentucky. Her research interests include mathematics teacher preparation, equity issues in mathematics education, and teacher leader development. Recently, she was one of the writers for the Standards for Preparing Teachers of Mathematics (Association of Mathematics Teacher Educators [ AMTE], 2017). She was the series editor for AMTEs Second Monograph Series, editor for the special equity issue of the Journal of Mathematics Teacher Education published in February 2012, and has co-edited several National Council of Teachers of Mathematics (NCTM) books including, Focus on High School Mathematics: Fostering Reasoning and Sense Making for All Students, The Learning of Mathematics: 69th NCTM Yearbook, and Changing the Faces of Mathematics: Perspectives on African Americans. She has also authored and co-author several book chapters and journal articles. In addition, she has given numerous presentations. In addition, she was the AMTE 2017 Judith Jacobs Lecturer.