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Understanding Numbers in Elementary School Mathematics

Hung-Hsi Wu University of California, Berkeley, CA
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Hardcover ISBN: 978-0-8218-5260-6
Product Code: MBK/79
List Price: $88.00 MAA Member Price:$79.20
AMS Member Price: $70.40 Electronic ISBN: 978-1-4704-1210-4 Product Code: MBK/79.E List Price:$83.00
MAA Member Price: $74.70 AMS Member Price:$66.40
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List Price: $132.00 MAA Member Price:$118.80
AMS Member Price: $105.60 Click above image for expanded view Understanding Numbers in Elementary School Mathematics Hung-Hsi Wu University of California, Berkeley, CA Available Formats:  Hardcover ISBN: 978-0-8218-5260-6 Product Code: MBK/79  List Price:$88.00 MAA Member Price: $79.20 AMS Member Price:$70.40
 Electronic ISBN: 978-1-4704-1210-4 Product Code: MBK/79.E
 List Price: $83.00 MAA Member Price:$74.70 AMS Member Price: $66.40 Bundle Print and Electronic Formats and Save! This product is available for purchase as a bundle. Purchasing as a bundle enables you to save on the electronic version.  List Price:$132.00 MAA Member Price: $118.80 AMS Member Price:$105.60
• Book Details

2011; 551 pp
MSC: Primary 97; 00;

This is a textbook for pre-service elementary school teachers and for current teachers who are taking professional development courses. By emphasizing the precision of mathematics, the exposition achieves a logical and coherent account of school mathematics at the appropriate level for the readership. Wu provides a comprehensive treatment of all the standard topics about numbers in the school mathematics curriculum: whole numbers, fractions, and rational numbers. Assuming no previous knowledge of mathematics, the presentation develops the basic facts about numbers from the beginning and thoroughly covers the subject matter for grades K through 7.

Every single assertion is established in the context of elementary school mathematics in a manner that is completely consistent with the basic requirements of mathematics. While it is a textbook for pre-service elementary teachers, it is also a reference book that school teachers can refer to for explanations of well-known but hitherto unexplained facts. For example, the sometimes-puzzling concepts of percent, ratio, and rate are each given a treatment that is down to earth and devoid of mysticism. The fact that a negative times a negative is a positive is explained in a leisurely and comprehensible fashion.

Solutions to the activities are available electronically on the Supplemental Materials page.

Pre-service elementary school teachers and current teachers interested in a logical and coherent account of school mathematics.

• Part 1. Whole numbers
• Chapter 1. Place value
• Chapter 2. The basic laws of operations
• Chapter 3. The standard algorithms
• Chapter 4. The addition algorithm
• Chapter 5. The subtraction algorithm
• Chapter 6. The multiplication algorithm
• Chapter 7. The long division algorithm
• Chapter 8. The number line and the four operations revisited
• Chapter 9. What is a number?
• Chapter 10. Some comments on estimation
• Chapter 11. Numbers in base $b$
• Part 2. Fractions
• Chapter 12. Definitions of fraction and decimal
• Chapter 13. Equivalent fractions and FFFP
• Chapter 14. Addition of fractions and decimals
• Chapter 15. Equivalent fractions: further applications
• Chapter 16. Subtraction of fractions and decimals
• Chapter 17. Multiplication of fractions and decimals
• Chapter 18. Division of fractions
• Chapter 19. Complex fractions
• Chapter 20. Percent
• Chapter 21. Fundamental Assumption of School Mathematics (FASM)
• Chapter 22. Ratio and rate
• Chapter 23. Some interesting word problems
• Chapter 24. On the teaching of fractions in elementary school
• Part 3. Rational numbers
• Chapter 25. The (two-sided) number line
• Chapter 26. A different view of rational numbers
• Chapter 27. Adding and subtracting rational numbers
• Chapter 28. Adding and subtracting rational numbers redux
• Chapter 29. Multiplying rational numbers
• Chapter 30. Dividing rational numbers
• Chapter 31. Ordering rational numbers
• Part 4. Number theory
• Chapter 32. Divisibility rules
• Chapter 33. Primes and divisors
• Chapter 34. The Fundamental Theorem of Arithmetic (FTA)
• Chapter 35. The Euclidean algorithm
• Chapter 36. Applications
• Chapter 37. Pythagorean triples
• Part 5. More on decimals
• Chapter 38. Why finite decimals are important
• Chapter 39. Review of finite decimals
• Chapter 40. Scientific notation
• Chapter 41. Decimals
• Chapter 42. Decimal expansions of fractions

• Reviews

• [This book] delivers the mathematical knowledge that elementary-grades teachers need.

American Educator
• Requests

Review Copy – for reviewers who would like to review an AMS book
Desk Copy – for instructors who have adopted an AMS textbook for a course
Examination Copy – for faculty considering an AMS textbook for a course
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
2011; 551 pp
MSC: Primary 97; 00;

This is a textbook for pre-service elementary school teachers and for current teachers who are taking professional development courses. By emphasizing the precision of mathematics, the exposition achieves a logical and coherent account of school mathematics at the appropriate level for the readership. Wu provides a comprehensive treatment of all the standard topics about numbers in the school mathematics curriculum: whole numbers, fractions, and rational numbers. Assuming no previous knowledge of mathematics, the presentation develops the basic facts about numbers from the beginning and thoroughly covers the subject matter for grades K through 7.

Every single assertion is established in the context of elementary school mathematics in a manner that is completely consistent with the basic requirements of mathematics. While it is a textbook for pre-service elementary teachers, it is also a reference book that school teachers can refer to for explanations of well-known but hitherto unexplained facts. For example, the sometimes-puzzling concepts of percent, ratio, and rate are each given a treatment that is down to earth and devoid of mysticism. The fact that a negative times a negative is a positive is explained in a leisurely and comprehensible fashion.

Solutions to the activities are available electronically on the Supplemental Materials page.

Pre-service elementary school teachers and current teachers interested in a logical and coherent account of school mathematics.

• Part 1. Whole numbers
• Chapter 1. Place value
• Chapter 2. The basic laws of operations
• Chapter 3. The standard algorithms
• Chapter 4. The addition algorithm
• Chapter 5. The subtraction algorithm
• Chapter 6. The multiplication algorithm
• Chapter 7. The long division algorithm
• Chapter 8. The number line and the four operations revisited
• Chapter 9. What is a number?
• Chapter 10. Some comments on estimation
• Chapter 11. Numbers in base $b$
• Part 2. Fractions
• Chapter 12. Definitions of fraction and decimal
• Chapter 13. Equivalent fractions and FFFP
• Chapter 14. Addition of fractions and decimals
• Chapter 15. Equivalent fractions: further applications
• Chapter 16. Subtraction of fractions and decimals
• Chapter 17. Multiplication of fractions and decimals
• Chapter 18. Division of fractions
• Chapter 19. Complex fractions
• Chapter 20. Percent
• Chapter 21. Fundamental Assumption of School Mathematics (FASM)
• Chapter 22. Ratio and rate
• Chapter 23. Some interesting word problems
• Chapter 24. On the teaching of fractions in elementary school
• Part 3. Rational numbers
• Chapter 25. The (two-sided) number line
• Chapter 26. A different view of rational numbers
• Chapter 27. Adding and subtracting rational numbers
• Chapter 28. Adding and subtracting rational numbers redux
• Chapter 29. Multiplying rational numbers
• Chapter 30. Dividing rational numbers
• Chapter 31. Ordering rational numbers
• Part 4. Number theory
• Chapter 32. Divisibility rules
• Chapter 33. Primes and divisors
• Chapter 34. The Fundamental Theorem of Arithmetic (FTA)
• Chapter 35. The Euclidean algorithm
• Chapter 36. Applications
• Chapter 37. Pythagorean triples
• Part 5. More on decimals
• Chapter 38. Why finite decimals are important
• Chapter 39. Review of finite decimals
• Chapter 40. Scientific notation
• Chapter 41. Decimals
• Chapter 42. Decimal expansions of fractions
• [This book] delivers the mathematical knowledge that elementary-grades teachers need.

American Educator
Review Copy – for reviewers who would like to review an AMS book
Desk Copy – for instructors who have adopted an AMS textbook for a course
Examination Copy – for faculty considering an AMS textbook for a course
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
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