Mathematics for Elementary Teachers with Activities, 5th edition

About the Book 

Teaches students to know more than just how, but to be able to explain why.

• Organization Around Operations instead of different types of numbers which provides two key advantages.
• A more advanced, unified perspective, which emphasizes that a given operation (addition, subtraction, multiplication, or division) retains its meaning across all the different types of numbers.
• Fractions, decimals, and percents—traditional weak spots—can be studied repeatedly throughout a course, rather than only at the end. The repeated coverage of fractions, decimals, and percents allows students to gradually become used to reasoning with these numbers, so they aren’t overwhelmed when they get to multiplication and division of fractions and decimals.
• Emphasizes key concepts and principles, and guides prospective teachers in giving explanations that draw on these key concepts and principles. In this way, teachers will come to organize their knowledge around the key concepts and principles of mathematics so they will be able to help their students do likewise.
• Addresses the eight CCSSM Standards for Mathematical Practice as well as covering the CCSM content standards. A Common Core icon at the beginning of a section indicates that a section addressed at a particular grade level. New CCSS references in the margin indicates that content within the section address the specific standard(s) noted. Common Core standards have also been noted on every activity. These icons and the Common Core material have been designed to not be a distraction for states that have not adopted the CCSSM.
• Visual representations, including number lines, double number lines, strip diagrams (also known as tape diagrams), and base-ten drawings are used repeatedly throughout the book and help prospective teachers learn to explain and make sense of mathematical ideas, solution methods, and standard notation.
• Class Activities were written as part of the text and are central and integral to full comprehension.

Pedagogical features 

• Class Activities were written as part of the text and are central and integral to full comprehension.
• Practice problems allow students to apply principles with examples and explanation. Answers to Practice Problems appear immediately after the problem so students can check their understanding before moving on to the Problems.  
• Problems give students opportunities to explain the mathematics they have learned without seeing the answer. More challenging problems are indicated with a purple asterisk.
• Common Coreicons indicates that the section addresses the Common Core State Standards for Mathematics at the given grade level.
• NEW! CCSS References in the margin connect content from the section to specific CCSS standards.
• UPDATED! From The Field Boxes include more detail on literature related to the mathematical content in the section with an added focus on related research.
• Section Summary and Study Items at the end of each section help students organize their thinking and focus on key ideas. Chapter Summaries pull together ideas from each section.

About the Book

• In the previous edition, a Common Core icon indicated that a section addressed the Common Core State Standards at a particular grade level. New to this edition are CCSS references in the margin that address these specific standards. Common Core standards have also been noted on every activity. These icons and the Common Core material have been designed to not be a distraction for states that have not adopted the CCSSM.
• Due to reviewer feedback, the geometry chapters have been heavily revised with updated discussion, precise language and definitions and new art. 
• The art program was re-worked to enhance clarity and explanations. 
• QR codes in the margins open some of the Common Core videos. (Complete access to the videos requires MML access.)  
• Practice and Problems have been updated and revised where necessary. More challenging problems that require students to think deeply are indicated with a purple asterisk. 
• The From the Field feature has been expanded to include more on educational research and children’s literature as it relates to mathematics. 
• Videos and animations have been added to the MyLab™ Math course to provide additional support for students.

Content changes for the 5th edition

• Chapter 1 introduces the term “place value parts” to highlight base-ten structure, as recommended by Professors Roger Howe and Karen Fuson. New base-ten drawings better show the structure of repeated bundling in groups of ten.
• Based on research, Chapter 2 has an improved discussion in the text and new activities that use measurement to highlight how fractions are numbers. This “measurement sense of fraction” continues to be developed in revised fraction multiplication and division activities in Chapters 5 and 6 and in revised activities on developing equations for proportional relationships in Chapter 7.
• Chapter 3 extends the discussion of addition and subtraction on number lines by including the case of subtraction as a difference or unknown addend.
• Based on research, Chapter 4 has a revised introduction to multiplication to better highlight how multiplication is about coordinating numbers and sizes of equal groups of quantities. New color-coordinated math drawings continue into Chapters 5, 6, and 7 to highlight connections across multiplication, division, and proportional relationships, and across whole numbers and fractions.
• Chapter 4 also clarifies that there are different written methods for implementing the standard multiplication algorithm (e.g., the partial-products method). Revisions to the activities promote more active reasoning about arrays to develop the standard multiplication algorithm.
• Chapter 5 has an improved discussion and revised activities on how the definition of multiplication in Chapter 4 continues to apply to the case of fractions.
• Chapter 6 clarifies that there are different written methods for implementing the standard division algorithm (e.g., a version of the scaffold method). The Class Activity on interpreting the standard division algorithm in terms of bundled toothpicks has been improved. It now starts with simpler examples.
• Based on research, Chapter 6 highlights cases of equivalent division problems in fraction (and decimal) division.
• Based on research, Chapter 7 develops different ways of reasoning about multiplication and division with quantities to solve ratio and proportion problems. There is a new section on proportional relationships, which includes ways of reasoning about strip diagrams and variable parts to develop equations, including for lines through the origin in a coordinate plane. The section on inversely proportional relationships now puts more emphasis on reasoning about multiplication and division with quantities.
• In Chapter 9, some Class Activities and problems were revised and moved for a more coherent and streamlined development. The section on sequences now includes graphs and equations for arithmetic sequences as part of the development of linear relationships, which started in Chapter 7 with proportional relationships. The sections on functions and linear functions now build more explicitly on proportional relationships and arithmetic sequences.
• Chapter 10 now starts with a discussion of lines and angles, including more angle terminology to facilitate clear communication, and a new Class Activity on folding paper to create angles. Class Activities on categories of shapes are revised for a better focus on relationships among categories.
• Chapter 11 now better highlights how measurement concepts underlie the process of measurement.
• Chapter 12 includes more opportunities for problem solving, including with shearing. The section on circles has an improved discussion of the relationship between the diameter and circumference of circles that extends ideas about proportional relationships developed in Chapter 7. The section on the Pythagorean theorem now includes a discussion of its converse.
• In Chapter 13 revised art clarifies the locations of bases in solid shapes.
• In Chapter 14 revisions to the art, text, Class Activities, and problems offer better opportunities to explore what various transformations do to points, lines, line segments, angles, and shapes. New and revised Class Activities and problems provide opportunities to use a compass and straightedge to construct the results of transformations and to construct lines and angles with desired properties. There are additional problems about applying congruence.
• Chapter 14 also makes stronger connections to ratio and proportional relationships discussed in Chapter 7, including a new section on dilations and similarity that builds on ideas about proportional relationships in Chapter 7, and a more explicit discussion of how similarity applies to lines and their slope.
• Based on research, Chapter 15 includes revised text, Class Activities, and problems about reasoning to draw inferences from random samples.
• In Chapter 15, examples have been updated using more current data. Revisions to the text, Class Activities, and problems provide better opportunities for comparing distributions.
• Chapter 16 has a better exposition of probabilities of events in uniform probability models.