Grades 6-8 (Volume III)
A practical, comprehensive, developmentally appropriate approach to effective mathematical instruction in grades 6 to 8.
New to This Edition
Key content changes include:
- The use of color in the figures, tables, and text helps to enhance and clarify the concepts presented.
- Activities corresponding to the CCSS have been added. Numerous problem-based tasks, designed to engage students in doing mathematics, are presented in the activities and now connect to the appropriate CCSSs. Most include adaptation and accommodation suggestions for English language learners and students with special needs. Appendix D includes a table listing all of the activities at a glance.
- Tables of Common Errors and Misconceptions help readers avoid or move beyond common problems in learning mathematics. Each chapter in Part 2 includes a new table addressing chapter-related mathematical topics. The tables often include examples of student work or responses that reflect the common errors.
- Part 1 focuses on important “hot” topics that address ideas for creating a classroom environment in which all children succeed. By design, the chapters are shorter in length than the content chapters in Part 2, but are full of effective strategies and ideas. These chapters are ideal for use in professional development workshops, book study, or professional learning community (PLC) discussions.
Major changes to chapters in Part 1 include:
- Chapter 1: A new table that relates NCTM’s process standards (2000) and CCSS-M’s mathematical practices (CCSSO, 2010), clarification about the difference between modeling mathematics and modeling with mathematics, and an additional emphasis on the characteristics of productive classrooms that promote student understanding
- Chapter 2: A new section on the eight mathematics teaching practices from Principles to Actions (NCTM, 2014); a new section on “Evaluating and Adapting Tasks”; a new section on growth versus fixed mindsets and their relationship to productive struggle and learning from mistakes; a new section on aspects of questioning that helps teachers think, in particular, about the level of questions asked and the pattern of questions used; and more detail pertaining to the three-phases (before, during, and after) to better highlight that these phases occur during (not after) the lesson.
- Chapter 4: This chapter was revised to better highlight differentiated tasks for whole-classroom instruction. New team-building activities for working in groups are also included.
Major changes in the chapters in Part 2 include:
- Chapter 8: Includes a new learning progression for counting that identifies increasingly sophisticated levels of reasoning and includes:
- Several new activities focusing on developing early counting skills, and
- A new section on thinking about zero.
- Chapter 9: Features an increased focus on helping children write equations from word problems, using both computational and semantic forms. Also included are:
- An improved section on helping children analyze contextual problems by detailing strategies that can help children prepare to solve problems, and
- A new section about helping children solve multistep problems, including the use of hidden questions to help children progress from one-step to multistep problems.
- Chapter 10: Includes an increased focus on assessing basic facts, presents the risks of using timed tests, and offers a collection of alternative assessment ideas.
- Chapter 12: Includes an expanded discussion of the written records of computing multiplication and division problems including lattice multiplication, open arrays, and partial quotients.
- Chapter 13: Features more focused sections on generalization with number, place value, and algorithms to better illustrate how to connect arithmetic to algebra. Included is an enhanced section on repeating patterns.
- Chapter 14: Looks at an increased focus on moving from the part-whole meaning of fractions to an iterative notation of fractions. Included are new activities and references to technology, and a new table providing a quick overview of three types of models—area, length, and set—defining the wholes and their related parts for each model.
- Chapter 16: The Geometry chapter is now reorganized around the four geometry strands (shapes and properties, location, transformations, visualization) to provide more cohesiveness. Examples of appropriate activities help clarify each level as it’s introduced.
- Chapter 17: In the chapter on Data, the new addition of driving questions (Hourigan and Leavy, 2015/2016) is introduced as a way to motivate involvement in the processes of doing statistics. There is an increased emphasis on helping children consider the shape of the data as they engage in the analysis and interpretation phases of doing statistics.