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E-raamat: Your Mathematics Standards Companion, Grades 6-8: What They Mean and How to Teach Them

  • Formaat: PDF+DRM
  • Sari: Corwin Mathematics Series
  • Ilmumisaeg: 25-May-2017
  • Kirjastus: Corwin Press Inc
  • Keel: eng
  • ISBN-13: 9781544304878
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  • Formaat: PDF+DRM
  • Sari: Corwin Mathematics Series
  • Ilmumisaeg: 25-May-2017
  • Kirjastus: Corwin Press Inc
  • Keel: eng
  • ISBN-13: 9781544304878

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Transforming the standards into learning outcomes just got a lot easier

In this expansion of the original popular Common Core Mathematics Companion, you can see in an instant how teaching to your state standards should look and sound in the classroom. Under the premise that math is math, the authors provide a Cross-Referencing Index for states implementing their own specific mathematics standards, showing 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.

It’s all here, page by page:

  • Get the inside scoop on which standards connect, what key vocabulary means, and time-saving tables showing where to focus instruction for each grade 
  • Write curriculum for: ratios and proportional relationships, the number system, expressions and equations, functions, geometry, and statistics & probability
  • Use the What to Teach pages to deliver powerful standards-based lessons 
  • Learn effective techniques to create an environment where all students can experience math break-throughs
  • Incorporate the Standards for Mathematical Practice to improve  students’ ability to problem solve, construct viable arguments, use tools strategically, attend to precision, and more
  • Cross-referenced index listing the standards in the following states, explaining what is unique to the standards of each state

Your Mathematics Standards Companion is your one-stop guide for teaching, planning, assessing, collaborating, and designing powerful mathematics curriculum.

 
Indexes Cross-Referencing Your State Standards 1(1)
Quick Reference Guide xv
Acknowledgments xxiii
Letter to Grades 6-8 Teachers xxv
Letter to Middle School Principals xxvii
Introduction xxix
A Brief History of Current State Standards xxix
College and Career Ready Standards for Mathematics xxix
Instructional Shifts xxx
Terminology Used in This Book xxxi
Effective Teaching Practices xxxiii
How to Use This Book xxxiv
Reflection Questions xxxv
Part 1 Ratios and Proportional Relationships
Domain Overview
2(1)
Suggested Materials for This Domain
3(1)
Key Vocabulary
3(3)
Grade 6
Cluster A Understand ratio concepts and use ratio reasoning to solve problems
6(6)
Sample Planning Page: Ratios and Proportional Relationships, Grade 6, Cluster A
12(2)
Planning Page
14(2)
Grade 7
Cluster A Analyze proportional relationships and use them to solve real-world and mathematical problems
16(9)
Sample Planning Page: Ratios and Proportional Relationships, Grade 7, Cluster A
25(2)
Planning Page
27(3)
Reflection Questions: Ratios and Proportional Relationships
28(2)
Part 2 The Number System
Domain Overview
30(1)
Suggested Materials for This Domain
31(1)
Key Vocabulary
31(2)
Grade 6
Cluster A Apply and extend previous understandings of multiplication and division to divide fractions by fractions
33(3)
Cluster B Compute fluently with multi-digit numbers and find common factors and multiples
36(6)
Cluster C Apply and extend previous understandings of numbers to the system of rational numbers
42(8)
Sample Planning Page: The Number System, Grade 6, Cluster C
50(2)
Planning Pages
52(4)
Grade 7
Cluster A Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers
56(11)
Sample Planning Page: The Number System, Grade 7, Cluster A
67(2)
Planning Page
69(1)
Grade 8
Cluster A Know that there are numbers that are not rational, and approximate them by rational numbers
70(4)
Sample Planning Page: The Number System, Grade 8, Cluster A
74(2)
Planning Page
76(4)
Reflection Questions: The Number System
77(3)
Part 3 Expressions and Equations
Domain Overview
80(1)
Suggested Materials for This Domain
81(1)
Key Vocabulary
81(3)
Grade 6
Cluster A Apply and extend previous understandings of arithmetic to algebraic expressions
84(7)
Cluster B Reason about and solve one-variable equations and inequalities
91(5)
Cluster C Represent and analyze quantitative relationships between dependent and independent variables
96(2)
Sample Planning Page: Expressions and Equations, Grade 6, Cluster C
98(2)
Planning Pages
100(3)
Grade 7
Cluster A Use properties of operations to generate equivalent expressions
103(3)
Cluster B Solve real-life and mathematical problems using numerical and algebraic expressions and equations
106(6)
Sample Planning Page: Expressions and Equations, Grade 7, Cluster A
112(2)
Planning Pages
114(2)
Grade 8
Cluster A Work with radicals and integer exponents
116(6)
Cluster B Understand the connections between proportional relationships, lines, and linear equations
122(4)
Cluster C Analyze and solve linear equations and pairs of simultaneous linear equations
126(4)
Sample Planning Page: Expressions and Equations, Grade 8, Cluster A
130(1)
Planning Pages
131(5)
Reflection Questions: Expressions and Equations
134(2)
Part 4 Functions
Domain Overview
136(1)
Suggested Materials for This Domain
137(1)
Key Vocabulary
137(1)
Grade 8
Cluster A Define, evaluate, and compare functions
138(4)
Cluster B Use functions to model relationships between quantities
142(3)
Sample Planning Page: Functions, Grade 8, Cluster A
145(2)
Planning Pages
147(5)
Reflection Questions: Functions
149(3)
Part 5 Geometry
Domain Overview
152(1)
Suggested Materials for This Domain
153(1)
Key Vocabulary
153(2)
Grade 6
Cluster A Solve real-world and mathematical problems involving area, surface area, and volume
155(6)
Sample Planning Page: Geometry, Grade 6, Cluster A
161(1)
Planning Page
162(2)
Grade 7
Cluster A Draw, construct, and describe geometrical figures and describe the relationships between them
164(4)
Cluster B Solve real-life and mathematical problems involving angle measure, area, surface area, and volume
168(4)
Sample Planning Page: Geometry, Grade 7, Cluster B
172(2)
Planning Pages
174(2)
Grade 8
Cluster A Understand congruence and similarity using physical models, transparencies, or geometry software
176(9)
Cluster B Understand and apply the Pythagorean Theorem
185(4)
Cluster C Solve real-world and mathematical problems involving volume of cylinders, cones, and spheres
189(2)
Sample Planning Page: Geometry, Grade 8, Cluster A
191(2)
Planning Pages
193(5)
Reflection Questions: Geometry
196(2)
Part 6 Statistics and Probability
Domain Overview
198(1)
Suggested Materials for This Domain
199(1)
Key Vocabulary
199(2)
Grade 6
Cluster A Develop understanding of statistical variability
201(6)
Cluster B Summarize and describe distributions
207(5)
Sample Planning Page: Statistics and Probability, Grade 6, Cluster B
212(2)
Planning Pages
214(2)
Grade 7
Cluster A Use random sampling to draw inferences about a population
216(3)
Cluster B Draw informal comparative inferences about two populations
219(3)
Cluster C Investigate chance processes and develop, use, and evaluate probability models
222(8)
Sample Planning Page: Statistics and Probability, Grade 7, Cluster C
230(2)
Planning Pages
232(4)
Grade 8
Cluster A Investigate patterns of association in bivariate data
236(6)
Sample Planning Page: Statistics and Probability, Grade 8, Cluster A
242(2)
Planning Page
244(4)
Reflection Questions: Statistics and Probability
245(3)
Resources
Table 1 Standards for Mathematical Practice
248(3)
Table 2 Effective Teaching Practices
251(3)
Reproducibles
Reproducible 1 Percent Wheel
254(1)
Reproducible 2 Frayer Model
255(1)
Reproducible 3 Net of a Cube
256(1)
Reproducible 4 Example for MAD (Mean Absolute Deviation)
257(2)
Additional Resources 259(2)
About the Authors 261
Ruth Harbin Miles coaches rural, suburban, and inner-city school mathematics teachers.  Her professional experiences include coordinating the K-12 Mathematics Teaching and Learning Program for the Olathe, Kansas, Public Schools for more than 25 years; teaching mathematics methods courses at Virginias Mary Baldwin College; and serving on the Board of Directors for the National Council of Teachers of Mathematics, the National Council of Supervisors of Mathematic, and both the Virginia Council of Teachers of Mathematics and the Kansas Association of Teachers of Mathematics.  Ruth is a co-author of five Corwin books including A Guide to Mathematics Coaching, A Guide to Mathematics Leadership, Visible Thinking in the K-8 Mathematics Classroom, The Common Core Mathematics Standards, and Realizing Rigor in the Mathematics Classroom.  As co-owner of Happy Mountain Learning, Ruth specializes in developing teachers content knowledge and strategies for engaging students to achieve high standards in mathematics.

After teaching mathematics in grades K-8 for 20 years, Lois served as the middle school mathematics specialist for the Virginia Department of Education. Here she worked on curriculum and teacher professional learning. She served the Virginia Council of Teachers of Mathematics and was a board member for the local Jefferson Council of Teachers of Mathematics. After receiving her doctorate in curriculum and instruction at The University of Virginia, she began serving as adjunct faculty to Mary Baldwin College and is in her 15th year working with pre-service teachers. Currently Lois is an International Fellow with the Charles A. Dana Center working with classroom teachers in the Department of Defense Schools helping them implement their College and Career Readiness Standards. Among her recognitions are a Fulbright Teacher Exchange and Virginia Middle School Mathematics Teacher of the Year.