# The Craft of Word Problems

## CONTENTS OF CURRICULUM UNIT 04.05.07

- Introduction
- Definitions of Math Properties
- Commutative Properties of Addition and Multiplication
- Inverse Properties of Addition and Subtraction
- Associative Properties
- Distributive Property
- Reviewing Properties
- Rules for Properties of the Real Numbers
- Lesson Plan I
- Lesson Plan II
- Lesson Plan III
- Appendix A: Using Basic Properties To Solve Problems In Math
- Appendix B Glossary of Math Terms for Basic Properties
- Reading List
- Teacher Resources
- Bibliography

### Unit Guide

## Using Basic Properties to Solve Problems in Math

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## Reading List

Mathematical Puzzles of Sam Loyd (Selected and edited by M. Gardner) Dover Publications, New York, 1959. Martin Gardner offers a selection of the best mathematical puzzles of Sam Loyd, taken from the long out-of-print “Cyclopedia.” Many of Loyd’s most famous puzzles are included in this book such as “Horse of a Different Color which sold millions.

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Singapore Primary Mathematics Text 6A, 6B,
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U.S. Edition, Curriculum Planning and Development Division, Ministry of Education, Singapore Federal Publications. The main features of this book are the use of the Concrete -Pictorial-Abstract approach. The book encourages active thinking processes, communication of mathematical ideas and problem solving. It consists of six units which are divided in parts. Each part starts with a meaningful task, practice and review designed to help students.

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Knowing and Teaching Elementary Mathematics
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, by Liping MA Lawrence Erlbaum Associates, Mahwah, NJ, 1999. This book describes the nature and development of the “profound understanding of fundamental mathematics” that elementary teachers need to become accomplished mathematics teachers, and suggests why such teaching knowledge is much more common in China than in the United States, despite the fact that Chinese teachers have less formal education than U.S. teachers.

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Teaching Problems and the Problems of Teaching
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, by M. Lampert, Yale University Press, New Haven, CT, 2001. This book is about teaching with problems and the problem in teaching. It identifies problems that must be addressed in teaching.

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Thinking Mathematically, by T. Carpenter
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, M.L. Franke, and L.Levi Heinemann, Portsmouth, NH, 2003. In this book, the authors revealed how children’s developing knowledge of the powerful unifying ideas of mathematics can deepen their understanding of arithmetic and provide a solid foundation for learning algebra. It provides numerous examples of classroom dialogues that indicate how algebraic ideas emerge in children’s thinking and what problems and questions help to elicit them.

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Houghton Mifflin Mathematics
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, Houghton Mifflin Co. Boston MA. 2002. This is a traditional textbook in math that consists of a problem solving plan that can help students to become better problem solvers. There are many strategies that can be used to solve problems.

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Math 4 today: 10-Minute Daily Skills Book
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, McGrow-Hill Children’s Publishing, Good Apple 1998.
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Math 4 Today
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is a comprehensive easy to use supplement to any fourth through fifth-grade math curriculum. In only ten minutes each day, several essential skills are reviewed during a four-day period and evaluated on the fifth day. The book is designed on a continuous spiral so that concepts are repeated weekly. Complete answer keys are provided for 54 weeks worth of reproducible worksheets. Great practice for standardized tests!