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E-raamat: Common Core Mathematics Companion: The Standards Decoded, Grades 6-8: What They Say, What They Mean, How to Teach Them

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  • Formaat: PDF+DRM
  • Sari: Corwin Mathematics Series
  • Ilmumisaeg: 18-Feb-2016
  • Kirjastus: Corwin Press Inc
  • Keel: eng
  • ISBN-13: 9781506341637
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Common Core Mathematics Companion: The Standards Decoded, Grades 6-8: What They Say, What They Mean, How to Teach ThemSuurem pilt
  • Formaat: PDF+DRM
  • Sari: Corwin Mathematics Series
  • Ilmumisaeg: 18-Feb-2016
  • Kirjastus: Corwin Press Inc
  • Keel: eng
  • ISBN-13: 9781506341637
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"The Common Core Mathematics Companion 6-8 offers a practical guide for implementing the CCSS Math Standards. Teachers will appreciate the misconception alerts and ideas for differentiation." 
— Jay McTighe, Author and Consultant

When it comes to math, standards-aligned is achievement-aligned…

In the short time since The Common Core Mathematics Companions, Grades K-2 and 3-5 burst on the scene, they have been lauded as the best resources for making critical math ideas easy to teach. With this brand-new 6-8 volume, middle school math success is at your fingertips. 

Page by page, the authors lay out the pieces to a cutting-edge curriculum, helping you to: 

  • 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 

The Common Core Mathematics Companion, Grades 6–8 has what every middle school needs to provide students with the foundation for the concepts and skills they will be expected to know in grade 9–12. 

Ruth Harbin Miles is a mathematics coach, with special expertise in developing teachers’ content knowledge and strategies for engaging students to achieve high mathematics standards. A serving member on the Board of Directors for the National Council of Teachers of Mathematics and the National Council of Supervisors of Mathematics, Ruth is a co-author with Linda Gojak of The Common Core Mathematics Companions, K–2 and 3–5 (Corwin). 

Lois Williams, Ed.D., who taught mathematics in grades K–8 for 20 years, is currently an adjunct professor at Mary Baldwin College and an International Fellow with the Charles A. Dana Center, training teachers in the College and Career Readiness Standards She has been honored with a Fulbright Teacher Exchange and the Virginia Middle School Mathematics Teacher of the Year award.

 

Arvustused

"The Common Core Mathematics Companion, 6-8 should be readily available for every teacher of mathematics.  It provides a succinct and organized way to bring the theoretical standards down to practical application for enhanced student achievement."



  -- Betty Brandenburg, Retired Educator "The Common Core Mathematics Companion 6-8 offers a practical guide for implementing the CCSS Math Standards.

Teachers will appreciate the misconception alerts and ideas for differentiation."





  -- Jay McTighe, author and consultant "The sample lesson-planning section provides a framework that prompts teachers to ask higher-order-thinking questions and ways to differentiate instruction. The sample planning page is also a great resource for administrators to gain an understanding of what mathematics should look and sound like in the classroom. Both the teacher and the administrator can have meaningful conversations about related standards and student learning." -- Teaching Children Mathematics

Acknowledgments xxiii
Letter to Grades 6--8 Teachers xxv
Letter to Middle School Principals xxvii
Introduction xxix
A Brief History of the Common Core xxix
The Common Core State Standards for Mathematics xxix
Instructional Shifts xxix
Major Work of Grades 6--8 xxx
Common Core Word Wall xxxi
The Common Core Standards for Mathematical Practice 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(1)
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(1)
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(3)
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(2)
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(3)
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(1)
Reflection Questions: Statistics and Probability
245(3)
Resources
Table 1 Standards for Mathematical Practice
248(3)
Table 2 Effective Teaching Practices
251(7)
CCSS Where to Focus Grade 6 Mathematics
253(1)
CCSS Where to Focus Grade 7 Mathematics
254(1)
CCSS Where to Focus Grade 8 Mathematics
255(3)
Reproducibles
Reproducible 1 Percent Wheel
258(1)
Reproducible 2 Frayer Model
259(1)
Reproducible 3 Net of a Cube
260(1)
Reproducible 4 Example for MAD (Mean Absolute Deviation)
261(2)
Additional Resources 263(2)
About the Authors 265
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.
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