# Common Core Mathematics in a PLC at Work: Grades 6-8

This teacher guide illustrates how to sustain successful implementation of the Common Core State Standards for mathematics, grades 6–8. Discover what students should learn and how they should learn it at each grade level. Comprehensive research-affirmed analysis tools and strategies will help you and your collaborative team develop and assess student demonstrations of deep conceptual understanding and procedural fluency.

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## Chapter 1: Using High-Performing Collaborative Teams for Mathematics |
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—NGA & CCSSO Students arrive at middle school with many challenges, and grades 6–8 teachers are expected to ensure all students achieve proficiency in the rigorous Standards for mathematics content as well as the Standards for Mathematical Practice described in the CCSS. How can you successfully help your middle school students achieve these expectations? One of the characteristics of high-performing and high-impact schools that are successfully closing achievement gaps is their focus on teacher collaboration as a key to improving instruction and reaching all students (Education Trust, 2005; Kersaint, 2007). A collaborative culture is one of the best ways for teachers to acquire both the instructional knowledge and skills required to meet this challenge, as well as the energy and support necessary to reach all students (Leithwood & Seashore Louis, 1998). Seeley (2009) characterizes this challenge by noting, “Alone we can accomplish great things. … But together, with creativity, wisdom, energy, and, most of all commitment, there is no end to what we might do” (pp. 225–226). |
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## Chapter 2: Implementing the Common Core Standards for Mathematical Practice |
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—NGA & CCSSO The CCSS for mathematics include standards for student proficiency in mathematical practice as well as content standards for developing student understanding. According to the CCSS, “The Standards for |
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## Chapter 3: Implementing the Common Core Mathematics Content in Your Curriculum |
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—Daro, McCallum, & Zimba Chapter 2 addressed one of the two types of Common Core standards—the Standards for Mathematical Practice—and illustrated instructional practices that promote students’ proficiency in these practices. This chapter analyzes the second type of standard—the Standards for Mathematical Content. As you read this chapter, keep in mind that the Standards for Mathematical Practice and the Standards for Mathematical Content |
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## Chapter 4: Implementing the Teaching-Assessing-Learning Cycle |
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—Dylan Wiliam The focus of this chapter is to illustrate the appropriate use of ongoing student assessment as part of an interactive, cyclical, and systemic collaborative team When led well, ongoing unit-by-unit mathematics assessments—whether in-class, during the lesson checks or end-of-unit assessment instruments like tests, quizzes, or projects—serve as a feedback bridge within the teaching-assessing-learning cycle. The cycle requires your team to identify core learning targets or standards for the unit, create cognitively demanding common mathematics tasks that reflect the learning targets, create in-class formative assessments of those targets, and design common assessment instruments to be used during and at the end of a unit of instruction. |
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## Chapter 5: Implementing Required Response to Intervention |
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—Roland Barth As the curriculum is written, the learning targets are set, and your assessments are in place, your instructional processes need to meet the needs of |
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## Epilogue: Your Mathematics Professional Development Model |
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Implementing the Common Core State Standards for mathematics presents you with both new challenges and new opportunities. The unprecedented adoption of a common set of mathematics standards by nearly every state provides the opportunity for U.S. educators to press the reset button on mathematics education (Larson, 2011). Collectively, you and your colleagues have the opportunity to rededicate yourselves to ensuring all students are provided with exemplary teaching and learning experiences, and you have access to the supports necessary to guarantee all students the opportunity to develop mathematical proficiency. The CCSS college and career aspirations and vision for teaching, learning, and assessing students usher in an opportunity for unprecedented implementation of research-informed practices in your school or district’s mathematics program. In order to meet the expectations of the five fundamental paradigm shifts described in this book, you will want to assess your current practice and reality as a school against the roadmap to implementation described in figure E.1 (page 180). |
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## Appendix A: Standards for Mathematical Practice |
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The Standards for Mathematical Practice describe varieties of expertise that mathematics educators at all levels should seek to develop in their students. These practices rest on important “processes and proficiencies” with longstanding importance in mathematics education. The first of these are the NCTM process standards of problem solving, reasoning and proof, communication, representation, and connections. The second are the strands of mathematical proficiency specified in the National Research Council’s report |
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## Appendix B: Standards for Mathematical Content, Grade 6 |
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In Grade 6, instructional time should focus on four critical areas: (1) connecting ratio and rate to whole number multiplication and division and using concepts of ratio and rate to solve problems; (2) completing understanding of division of fractions and extending the notion of number to the system of rational numbers, which includes negative numbers; (3) writing, interpreting, and using expressions and equations; and (4) developing understanding of statistical thinking. (1) Students use reasoning about multiplication and division to solve ratio and rate problems about quantities. By viewing equivalent ratios and rates as deriving from, and extending, pairs of rows (or columns) in the multiplication table, and by analyzing simple drawings that indicate the relative size of quantities, students connect their understanding of multiplication and division with ratios and rates. Thus students expand the scope of problems for which they can use multiplication and division to solve problems, and they connect ratios and fractions. Students solve a wide variety of problems involving ratios and rates. |
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## Appendix C: Standards for Mathematical Content, Grade 7 |
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In Grade 7, instructional time should focus on four critical areas: (1) developing understanding of and applying proportional relationships; (2) developing understanding of operations with rational numbers and working with expressions and linear equations; (3) solving problems involving scale drawings and informal geometric constructions, and working with two- and three-dimensional shapes to solve problems involving area, surface area, and volume; and (4) drawing inferences about populations based on samples. (1) Students extend their understanding of ratios and develop understanding of proportionality to solve single- and multi-step problems. Students use their understanding of ratios and proportionality to solve a wide variety of percent problems, including those involving discounts, interest, taxes, tips, and percent increase or decrease. Students solve problems about scale drawings by relating corresponding lengths between the objects or by using the fact that relationships of lengths within an object are preserved in similar objects. Students graph proportional relationships and understand the unit rate informally as a measure of the steepness of the related line, called the slope. They distinguish proportional relationships from other relationships. |
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## Appendix D: Standards for Mathematical Content, Grade 8 |
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In Grade 8, instructional time should focus on three critical areas: (1) formulating and reasoning about expressions and equations, including modeling an association in bivariate data with a linear equation, and solving linear equations and systems of linear equations; (2) grasping the concept of a function and using functions to describe quantitative relationships; (3) analyzing two- and three-dimensional space and figures using distance, angle, similarity, and congruence, and understanding and applying the Pythagorean Theorem. (1) Students use linear equations and systems of linear equations to represent, analyze, and solve a variety of problems. Students recognize equations for proportions ( |

Details

- Title
- Common Core Mathematics in a PLC at Work: Grades 6-8
- Authors
- Briars, Diane J., David Foster
- Isbn
- 9781936764105
- Publisher
- Solution Tree Press
- Imprint
- Price
- 33.99
- Street date
- October 26, 2012

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- 9781936764129
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