Grades 3-5 (Volume II)
A practical, comprehensive, developmentally appropriate approach to effective mathematical instruction in grades 3 to 5.
New to This Edition
Key content changes include:
- A shift in topics to correspond to the Common Core State Standards (CCSS) and other new state standards, among them: a considerable emphasis on multiplicative thinking, rational numbers, and the development of the mathematical practices. This includes:
- 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.
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- Basic Facts: Chapter 9 includes an increased focus on assessing basic facts, presenting the risks of using timed tests and presenting a collection of alternative assessment ideas.
- Whole Number Computation: Chapter 11 includes an expanded discussion of the written records of computing multiplication and division problems including lattice multiplication, open arrays, and partial quotients.
- Fraction Operations: Chapter 11 uses a developmental approach capitalizing on learning trajectories ad expands the discussion of developing meaning for each operation with more examples and activities.
- Algebra: Chapter 15 carefully bridges the connection between arithmetic and algebra with increased attention to relational thinking and the structure of equations. Significant attention is paid to content described in the CCSS, including generalizing arithmetic, use of symbols, structure in the number system, and functional thinking.
- Measurement: Includes an increased emphasis on converting units in the same measurement system, a new section on perimeter, which focuses on the third grade, and new activities and additional activity sheets across all measurement topics.
Major changes to specific chapters 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” that includes suggestions for adapting tasks to increase their potential for learning; 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 3: Supported by the recent position statement from professional organizations (NCSM and AMTE) about assessment for learning (AFL), this chapter was revised to be more explicit about how to collect evidence from students on their progress, interpret that evidence, make informed decisions about the next instructional steps and provide actionable feedback to students. There is also an expanded section on using writing to learn mathematics.
- Chapter 4: This chapter was revised to better highlight differentiated tasks for whole-classroom instruction. You will also find new team-building activities to enhance your children’s interactions with each other when working in groups.
- Chapter 6: Chapter 6 has several new features including a printable set of cards, each with a Strategy for Making Math Accessible for learners who struggle. This resource can be used when planning core instruction modifications or interventions for students with special needs. There is also a Mathematics Integration Plan Template to support planning for gifted students or students with a high interest in exploring mathematical topics in relation to other subject areas or perspectives.