Activity Manual for Problem Solving Approach to Mathematics for Elementary School Teachers, A

Description

1. An Introduction to Problem Solving
   • 1-1 Mathematics and Problem Solving
   • 1-2 Explorations with Patterns
   • Chapter 1 Review
2. Introduction to Logic and Sets
   • 2-1 Reasoning and Logic: An Introduction
   • 2-2 Describing Sets
   • 2-3 Other Set Operations
   • Chapter 2 Review
3. Numeration Systems and Whole Number Operations
   • 3-1 Numeration Systems
   • 3-2 Addition of Whole Numbers
   • 3-3 Subtraction of Whole Numbers
   • 3-4 Multiplication of Whole Numbers
   • 3-5 Division of Whole Numbers
   • Chapter 3 Review
4. Number Theory
   • 4-1 Divisibility
   • 4-2 Prime and Composite Numbers
   • 4-3 Greatest Common Divisor and Least Common Multiple
   • Module A: Clock and Modular Arithmetic–online
   • Chapter 4 Review
5. Integers
   • 5-1 Addition and Subtraction of Integers
   • 5-2 Multiplication and Division of Integers
   • Chapter 5 Review
6. Rational Numbers and Proportional Reasoning
   • 6-1 The Set of Rational Numbers
   • 6-2 Addition, Subtraction, and Estimation with Rational Numbers
   • 6-3 Multiplication, Division, and Estimation with Rational Numbers
   • 6-4 Proportional Reasoning
   • Chapter 6 Review
7. Decimals, Percents, and Real Numbers
   • 7-1 Terminating Decimals
   • 7-2 Operations on Decimals
   • 7-3 Repeating Decimals
   • 7-4 Percents
   • 7-5 Real Numbers
   • Chapter 7 Review
8. Algebraic Thinking
   • 8-1 Variables
   • 8-2 Equals Relation and Equations
   • 8-3 Functions
   • 8-4 Equations in a Cartesian Coordinate System
   • Module B: Using Real Numbers in Equations–online
   • Chapter 8 Review
9. Probability
   • 9-1 Determining Probabilities
   • 9-2 Multistage Experiments and Modeling Games
   • 9-3 Simulations and Applications in Probability
   • 9-4 Permutations and Combinations in Probability
   • Chapter 9 Review
10. Data Analysis/Statistics: An Introduction
    • 10-1 Designing Experiments/Collecting Data
    • 10-2 Displaying Data: Part I
    • 10-3 Displaying Data: Part II
    • 10-4 Measures of Central Tendency and Variation
    • Chapter 10 Review
11. Introductory Geometry
    • 11-1 Basic Notions
    • 11-2 Curves, Polygons, and Symmetry
    • 11-3 More About Angles
    • 11-4 Geometry in Three Dimensions
    • Module C: Networks–online
    • Chapter 11 Review
12. Congruence and Similarity with Constructions
    • 12-1 Congruence Through Constructions
    • 12-2 Additional Congruence Theorems
    • 12-3 Additional Constructions
    • 12-4 Similar Triangles and Other Similar Figures
    • Module D: Trigonometry Ratios via Similarity–online
    • Chapter 12 Review
13. Area, Pythagorean Theorem, and Volume
    • 13-1 Linear Measure
    • 13-2 Areas of Polygons and Circles
    • 13-3 The Pythagorean Theorem, Distance Formula, and Equation of a Circle
    • 13-4 Surface Areas
    • 13-5 Volume, Mass, and Temperature
    • Chapter 13 Review 890
    • Technology Modules
    • Module E: Spreadsheets–online
    • Module F: Graphing Calculators–online
    • Module H: GeoGebra–online
14. Transformations
    • 14-1 Translations, Rotations, and Tessellations
    • 14-2 Reflections and Glide Reflections
    • 14-3 Dilations 935
    • Chapter 14 Review

Credits

Answers to Problems

Additional Instructor Answers (Annotated Instructor’s Edition only)

• More relevant and engaging Chapter Opener Problems use examples from social media.
• Completely reorganized Chapter 3 (Numeration Systems and Whole Number Operations) adheres more closely to the way operations are taught in elementary school. 
• Reorganized and upgraded Mathematical Connections in the exercise sets reflect current thinking in mathematics education.
• StatCrunch^® is referenced where relevant to enable students to interact with data.
• Many new solved examples and new problems in assessments appear throughout each chapter. 
• Tighter connection to the Common Core State Standards is achieved through enhanced treatment of many topics. Examples include:
• Chapter 1: Expanded the Four-Step Polya Problem-Solving Process with input from Standards for Mathematical Practice. The process is referred to in examples throughout the chapter and the book. The section on patterns has been shortened.
• Chapter 2: The section on valid reasoning has been revised. Logical reasoning is now an integral part of Chapter 2.
• Chapter 5: Now includes a definition of addition for integers that uses absolute value—included because it is one of the techniques used in operations on integers in CCSS.
• Chapter 6: As called for in CCSS, a section on Using Bar Models to Solve Rational Proportion Problems has been added.
• Chapter 8: Algebraic Thinking is streamlined, with greater emphasis on variables and equation solving.
• Chapter 10: Reorganization and the inclusion of misuses throughout the chapter more clearly follow recommendations of statistical educators.
• Chapter 13: Due to the central role of measurement in geometry, Chapter 13 on Area, Pythagorean Theorem, and Volume has been moved to come before Chapter 14 on Transformations.
• More comprehensive chapter summary charts are included.

Also available with MyLab Math

New media assets available in MyLab™ Math all include assignable questions. New assets include:

• Completely new section lecture videos that incorporate the various resources found in the MyLab Math course, such as animations and IMAP videos.
• Common Core in Action videos.
• Animations library.
• Math Education Insights videos.
• Common Core Assessment Analysis questions that enable students to analyze real CCSS assessment questions.
• Mindset materials that support students in developing a math mindset and an understanding of how important it is to do so with their future students.

Rick Billstein is a Professor of Mathematics at the University of Montana. He has worked in mathematics teacher education at this university for over 40 years and his current research is in the areas of curriculum development and mathematics teacher education. He teaches courses for future teachers in the Mathematics Department. He served as the site director for the Show-Me Project, an NSF-funded project supporting the dissemination and implementation of standards-based middle grades mathematics curricula. He worked on the NSF grant Tinker Plots to develop new data analysis software and he serves on the Advisory Boards for several other national projects. From 1992-1997, he directed the NSF-funded Six Through Eight Mathematics (STEM) middle school mathematics curriculum project and is now directing the Middle Grades MATH Thematics Phase II Project. Dr. Billstein has published articles in over 20 different journals, and has co-authored over 40 books, including ten editions of A Problem Solving Approach to Mathematics for Elementary Teachers. He typically does about 25 regional and national presentations per year and has worked in mathematics education at the international level. He presently serves on the Editorial Board of NCTM’s Mathematics Teaching in the Middle School. Dr. Billstein was recently awarded the George M. Dennison Presidential Faculty Award for Distinguished Accomplishment at the University of Montana.

Dr. Barbara Boschmans teaches in the Department of Mathematics and Statistics at Northern Arizona University. She received her BsEd (1995), MAT (1997), and EdD (2003) in Mathematics Education from Northern Arizona University. She has taught at Arizona State University (AZ), Plymouth State University (NH), and Northern Arizona University (AZ). Dr. Boschmans has taught a variety of mathematics and mathematics education courses. She has been a frequent speaker at local, state, national, and international conferences. She has been a board member of the New Hampshire Teachers of Mathematics and the Arizona Association of Teachers of Mathematics. Dr. Boschmans is interested in bringing a joy and appreciation of mathematics to preservice and inservice elementary teachers and changing non-STEM students’ fixed mindset to a growth mindset.

Shlomo Libeskind is a professor in the mathematics department at the University of Oregon in Eugene, Oregon, and has been responsible there for the mathematics teaching major since 1986. In addition to teaching and advising pre-service and in-service teachers, Dr. Libeskind has extensive writing experience (books, articles, and workshop materials) as well as in directing mathematics education projects. In teaching and in writing, Dr. Libeskind uses a heuristic approach to problem solving and proof; in this approach the reasonableness of each step in a solution or proof is emphasized along with a discussion on why one direction might be more promising than another. As part of his focus on the improvement of the teaching of mathematics, Dr. Libeskind is also involved at many levels locally, nationally, and worldwide in the evaluation of mathematics teacher preparation programs. In his home state, he is actively involved in schools and councils, as well as in reviewing materials for the state standards for college admission. Most recently (spring 2008) he visited teacher colleges in Israel as a Fulbright Fellow. During this visit he conducted observations and critiques of the preparation of mathematics teachers at several colleges in Northern Israel. Dr. Libeskind received his Bachelor’s and Master’s Degrees in Mathematics at the Technion (Israel Institute of Technology) and his PhD in Mathematics at the University of Wisconsin, Madison.

Johnny W. Lott began his teaching career in the public schools of DeKalb County, Georgia, outside Atlanta. There he taught mathematics in grades 8-12. He also taught one year at the Westminster Schools, grades 9-12, and one year in the Pelican, Alaska, school, grades 6-12. Johnny is the co-author of several books and has written numerous articles and other essays in the “Arithmetic Teacher”, “Teaching Children Mathematics”, “The Mathematics Teacher”, “School Science and Mathematics”, “Student Math Notes”, and “Mathematics Education Dialogues”. He was the Project Manager for the “Figure This!” publications and website developed by the National Council of Teachers of Mathematics (NCTM) and was project co-director of the State Systemic Initiative for Montana Mathematics and Science (SIMMS) Project. He has served on many NCTM committees, has been a member of its Board of Directors, and was its president from April 2002-April 2004. Dr. Lott is Professor Emeritus from the Department of Mathematical Sciences at The University of Montana, having been a full professor. He is currently the Director of the Center for Excellence in Teaching and Learning, Professor of Mathematics, and Professor of Education at the University of Mississippi. Additionally, he is on the Steering Committee of the Park City Mathematics Institute, works with the International Seminar, the Designing and Delivering Professional Development Seminar, and is editor for its high school publications. His doctorate is in mathematics education from Georgia State University.

Focusing on the Standards for Mathematical Practice

• The Activity Manual includes classroom-tested activities and a pouch of perforated, printed color manipulatives.
• Activity Manual annotations in the Annotated Instructor’s Edition clarify when specific activities should be used for each lesson, making it easier to teach a more hands-on course.
• The manual is available as a value-pack option. Ask your Pearson representative for details.
• Now Try This exercises follow key examples to help students in their learning, facilitate the development of critical-thinking and problem-solving skills, and stimulate class discussion. Answers are in both the Annotated Instructor’s Edition and student text.
• Thirteen eManipulatives, available in MyLab Math, allow students to investigate, explore, practice, build conceptual understanding, and solve specific problems, without the mess or cost of physical manipulatives.
• Annotations in the student edition indicate where these eManipulatives are relevant. Exercises related to the eManipulatives are assignable within MyLab Math.
• Chapter openers from social media are thought-provoking and set the tone to prepare students for the material ahead.
• Problem-Solving Strategies are highlighted in italics and are used throughout the text to help students put the strategies to work.

Teaching the Mathematics in the Context of Common Core 

• Common Core State Standards (CCSS) are cited in sections to focus student attention and provide a springboard for discussion.
• More exercises have been added, particularly in the reorganized Mathematical Connections exercise sets.
• Connecting Mathematics to the Classroom exercises require interpretation and analysis of the thinking of typical K-8 students.
• Updated – School book pages are included to show how various topics are introduced to the K-8 pupil. Icons within the text link the narrative to the appropriate school book page. Students are asked to complete many of the activities on the student pages so they can see what is expected in elementary school.

Assessing the Mathematics Content and Procedures

• Extensive Problem Sets are organized into three categories for maximum instructor flexibility when assigning homework that address the standards.
• Assessment A has problems with answers in the text, so students can check their work.
• Assessment B contains parallel problems to those in Assessment A, but answers are not given in the student text.
• Mathematical Connections problems include the following categories: Connecting Mathematics to the Classroom, Review Problems, Cooperative Learning, and NAEP sample questions.
• MyLab Math offers hundreds of assignable, algorithmic exercises. The 13th Edition MyLab Math course contains even more assignable exercises to meet students’ needs. Assignable exercise types include:
• Over 2000 algorithmically generated exercises parallel those in the text.
• Lecture video exercises allow instructors to assign the videos with confidence students will watch them. Exercises are included for New Math Education Insight Videos, Common Core in Action Videos, and Integrated Mathematics and Pedagogy (IMAP) videos.
• New – Common Core Assessment Analysis exercises require analysis and interpretation of Sample CCSS exercises.

Also available with MyLab Math 

MyLab™ Math is the teaching and learning platform that empowers you to reach every student. By combining trusted author content with digital tools and a flexible platform, MyLab Math personalizes the learning experience and improves results for each student. Learn more about MyLab Math.

Reach every student with MyLab Math 

Deliver trusted content

• Over 2000 exercises correlated to the textbook provide immediate feedback, to give students unlimited opportunities for practice. Common Core Assessment Analysis questions were built to require analysis and interpretation of sample CCSS examples. Additional exercises complement the various media elements in the course, such as Animations, Common Core in Action videos, Math Education Insight videos, IMAP videos, eManipulatives, and more.
• Course-specific resources and interactive features–Resources all feature assignable questions, and include:

• New – Completely new section lecture videos that incorporate the various resources found in the MyLab Math course, such as animations and IMAP videos
• New – Videos and animations, available in MyLab Math, to help students grasp concepts and real life applications, including Common Core in Action videos and Math Education Insights videos
• Integrating Mathematics and Pedagogy (IMAP) videos feature elementary school children working problems. Margin notes in the student edition indicate where these videos are relevant. 
• New – Common Core Assessment Analysis questions that enable students to analyze real CCSS assessment questions
• New – Mindset materials that support students in developing a math mindset and an understanding of how important it is to do so with their future students.

• Conceptual understanding
• Thirteen eManipulatives, available in MyLab Math, allow students to investigate, explore, practice, build conceptual understanding, and solve specific problems, without the mess or cost of physical manipulatives.

• Annotations in the student edition indicate where these eManipulatives are relevant. Exercises related to the eManipulatives are assignable within MyLab Math.
• StatCrunch^® is integrated into the MyLab Math course and accompanying eText as an aid to learning. StatCrunch is a powerful web-based statistical software that allows users to perform complex analyses, share data sets, and generate compelling reports of their data.

Additional information

Dimensions	29.53 × 334.64 × 433.07 in
Imprint	Pearson
Format	gen
ISBN-13	09780134995618
ISBN-10	0134995619
Author	Dan Dolan, Jim Williamson, Mari Muri
Subjects	mathematics, higher education, Service Math, Math for Teachers