Problems in Algebra for Teachers
1st Edition
Published on 10. January 2018
194 pages
978-1-64113-397-5 (ISBN)
Description
The book is a collection of problems in school mathematics specifically written for the teachers. It is an attempt to enrich prospective and current teachers with the deep knowledge of school mathematics and to develop their reasoning and proving skills. Also, it is supposed to help them to anticipate and analyze their students' errors and use them as teachable moments.
The book is intended to be used in mathematics education courses (or professional development) for pre-service or in-service secondary school teachers. It can be used in graduate and undergraduate courses, in accordance with the orientations of different teacher preparation programs. Additionally, it can be used for the independent studies. One can also imagine situations in which teachers might use certain problems from this problem book directly in working with students, but this would constitute a supplementary use of the book.
The book is intended to be used in mathematics education courses (or professional development) for pre-service or in-service secondary school teachers. It can be used in graduate and undergraduate courses, in accordance with the orientations of different teacher preparation programs. Additionally, it can be used for the independent studies. One can also imagine situations in which teachers might use certain problems from this problem book directly in working with students, but this would constitute a supplementary use of the book.
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Alexander Karp | Julia Viro
Problems in Algebra for Teachers
Book
10/2018
Information Age Publishing
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Alexander Karp | Julia Viro
Problems in Algebra for Teachers
Book
10/2018
Information Age Publishing
€111.30
Shipment within 3-4 weeks
Content
- Cover
- Problems in Algebra for Teachers
- Problems in Algebra for Teachers
- Copyright
- CONTENTS
- FOREWORD
- I: PROBLEMS
- 1: NUMBERS AND ALGEBRAIC EXPRESSIONS
- CALCULATIONS WITH WHOLE NUMBERS
- CALCULATIONS WITH FRACTIONS
- CALCULATIONS WITH FRACTIONS
- Example
- Calculate
- Solution
- CALCULATIONS INVOLVING RADICALS
- COMPARING EXPRESSIONS INVOLVING RADICALS
- Example 1
- Calculate
- Solution
- Example 2
- Compare the numbers (without using a calculator)
- Solution
- RATIONAL AND IRRATIONAL NUMBERS
- EQUALITY OF ALGEBRAIC EXPRESSIONS
- FACTORIZATION
- Example
- Factor the following expressions
- Solution
- CONDITIONAL IDENTITIES
- Example
- Solution
- EXPRESSIONS WITH RADICALS
- WORD PROBLEMS AND ALGEBRAIC EXPRESSIONS
- 2: LINEAR AND PIECEWISE LINEAR FUNCTIONS, LINEAR EQUATIONS
- LINEAR FUNCTION
- Graphing a Linear Function
- Increasing and Decreasing Linear Functions
- Example
- Proof
- Piecewise Linear Functions
- Example
- Some Graphs With Absolute Values
- Example
- Solution
- LINEAR EQUATIONS
- Example
- Solution
- Example
- Solution
- Answer
- Equations With Absolute Values
- Example
- Solution
- Answer
- Example
- Solution
- Answer
- A Few More Graphs With Absolute Values
- Example
- Solution
- 3: QUADRATIC 3FUNCTIONS. QUADRATIC EQUATIONS
- SIMPLEST QUADRATIC EQUATIONS
- COMPLETING THE SQUARE AND QUADRATIC FORMULA
- DISCRIMINANT
- Example
- Solution
- FACTORING THE QUADRATIC TRINOMIAL THE THEOREM ON THE RELATION BETWEEN ROOTS AND COEFFICIENTS IN AN EQUATION
- WORD PROBLEMS SOLVED BY QUADRATIC EQUATIONS
- GRAPH OF THE QUADRATIC TRINOMIAL
- Example
- Solution
- MORE ABOUT THE GRAPH OF THE QUADRATIC TRINOMIAL
- MORE COMPLEX EQUATIONS REDUCIBLE TO QUADRATIC FORM
- Example
- ANALYSIS OF QUADRATIC EQUATIONS
- Example
- Solution
- 4: INEQUALITIES
- ON INEQUALITIES AND THEIR PROPERTIES
- Example
- Proof
- PROVING INEQUALITIES
- Example
- Proof
- Example
- Proof
- Example
- Proof
- SOLVING INEQUALITIES
- Example
- Solution
- Method of Intervals
- Example
- Solution
- WORD PROBLEMS SOLVED WITH INEQUALITIES
- INEQUALITIES WITH PARAMETERS
- Example
- Solution
- Example
- Solution
- 5: FUNCTIONS AND GRAPHS
- NOTION OF A FUNCTION AND FUNCTIONAL NOTATIONS
- Example
- Solution
- DOMAIN AND RANGE
- Example
- Solution
- Example
- Solution
- Example
- Solution
- INCREASING FUNCTIONS AND DECREASING FUNCTIONS
- Example
- Solution
- Example
- Solution
- MAXIMA AND MINIMA OF A FUNCTION
- Example
- Solution
- SYMMETRIES OF GRAPHS
- Example
- Solution
- COMPOSITIONS OF FUNCTIONS AND INVERSE FUNCTIONS
- Example
- Solution
- Example
- Solution
- GRAPHING FUNCTIONS USING TRANSFORMATIONS
- Example
- Solution
- Example
- Solution
- GRAPHS OF FUNCTIONS INVOLVING ABSOLUTE VALUE
- Example
- Solution
- INEQUALITIES WITH TWO VARIABLES ON A COORDINATE PLANE
- Example
- Solution
- LOCI
- Example
- Solution
- 6: SOME MORE COMPLICATED EQUATIONS
- EQUATIONS THAT CAN BE SOLVED BY INTRODUCING A NEW VARIABLE
- Example
- Solution
- EQUATIONS THAT CAN BE SOLVED BY FACTORING
- Example 1
- Solution
- Example 2
- Solution
- EQUATIONS THAT CAN BE SOLVED BY USING THE PROPERTIES OF FUNCTIONS
- Example
- Solutions
- EQUATIONS WITH RADICALS
- Example
- Solution
- SYSTEMS OF EQUATIONS
- Example
- Solution
- Example
- Solution
- EQUIVALENCE OF EQUATIONS AND IMPLICATIONS OF EQUATION
- 7: MATH CONTEST PROBLEMS
- COMBINATORICS AND COUNTING
- Example 1
- Solution
- Example 2
- Solution
- Example 3
- Solution
- EVEN AND ODD NUMBERS
- DIVISIBILITY AND REMAINDERS
- Example 1
- Solution
- Solution
- Example
- Solution
- Example
- Solution
- Example
- Proof
- Example
- Solution
- DIOPHANTINE EQUATIONS
- Example 1
- Solution
- Example 2
- Solution
- THE PIGEONHOLE PRINCIPLE
- Example 1
- Solution
- Example 2
- Solution
- Example 3
- Solution
- INVARIANTS
- Example 1
- Solution
- Example 2
- Solution
- II: ANSWER KEY AND SOLUTIONS
- ANSWER KEY AND SOLUTIONS CHAPTER 1
- Problem
- Solution
- ANSWER KEY AND SOLUTIONS CHAPTER 2
- ANSWER KEY AND SOLUTIONS CHAPTER 3
- ANSWER KEY AND SOLUTIONS CHAPTER 4
- ANSWER KEY AND SOLUTIONS CHAPTER 5
- ANSWER KEY AND SOLUTIONS CHAPTER 6
- ANSWER KEY AND SOLUTIONS CHAPTER 7
- ABOUT THE AUTHORS
