100 commonly asked questions in math class : answers that promote mathematical understanding, grades 6-12 /: answers that promote mathematical understanding, grades 6-12. (2013)

• Record Type: Book
• Other Titles: One hundred commonly asked questions in math class; Hundred commonly asked questions in math class
• Further Information: Note: Alfred S. Posamentier, William Farber, Terri L. Germain-Williams, Elaine Paris, Bernd Thaller, Ingmar Lehmann.
• Other Names: Posamentier, Alfred S
• Contents: About the Authors; Introduction; Chapter One. General Questions; 1. Why do I have to learn mathematics?; 2. Is there a language connection between mathematical terms and common English words?; 3. How many leaves are on a tree?; 4. Why do we have to learn about the history of mathematics?; 5. Who introduced the Hindu-Arabic numbers to the Western world, and when?; 6. What are the three famous problems of antiquity?; 7. What are the Fibonacci numbers?; 8. What is the golden ratio?; 9. Is there a smallest number, and is there a largest number?; 10. Why is infinity not a number?; 11. How large is infinity?; 12. Is there anything larger than infinity?; 13. Can the union of two sets ever be equal to the intersection of the two sets?; 14. How can we determine how many subsets a given set has?; 15. How can we avoid making an error in a "proof" that leads to a generalization?; 16. How does a calculator function?; 17. Which is correct--my calculating, the calculator, or the computer?; 18. What are conic sections?; 19. What is a mathematical group?; 20. What is a mathematical ring?; 21. What is a mathematical field?; 22. What are the three famous laws that Johannes Kepler discovered about planetary motion involving the ellipse?; Notes; Chapter Two. Arithmetic Questions; 23. What is the difference between a number and a digit?; 24. What are the differences between cardinal, ordinal, and nominal numbers?; 25. What are the natural numbers, and does the number zero belong to the natural numbers?; 26. How can we remember the order of operations using PEMDAS?; 27. What is a fraction?; 28. What is a rational number?; 29. How can one convert a decimal number to a fraction?; 30. What is so special about the Pascal triangle?; 31. How can the product of two numbers be smaller than both of its factors?; 32. If the temperature rises from 80 degrees F to a temperature of 88 degrees F, why is it wrong to say it became 10% warmer?; 33. How do the values of the following differ? (order of operations); 34. Why is division by zero not permissible?; 35. Why is x multiplied by 0 = 0?; 36. What is 0!?; 37. What is the largest number that can be represented in the decimal system with three digits (and without using any other symbols)?; 38. What is a prime number?; 39. Does the number 1 belong to the prime numbers?; 40. How many prime numbers are there?; 41. What is a palindrome?; 42. What are successive percentages?; Notes; Chapter Three. Algebra Questions; 43. Why is the product of two negative numbers positive?; 44. Why must a and b be positive in order for the following to hold true?; 45. Why is it advantageous to rationalize the denominator?; 46. What is meant by the "absolute value" of a variable?; 47. What is a variable? A term? An expression? An equation?; 48. How can we have students realize that the average of rates is not simply the arithmetic mean?; 49. Why does 0.99999 . . . = 1?; 50. Is a road with a slope of 20% twice as steep as a road with a 10% slope?; 51. Is there a number that differs from its reciprocal by 1?; 52. What is a determinant, and how can it be used to solve a system of linear equations?; 53. How do the arithmetic, geometric, and harmonic means compare in magnitude?; 54. What is a function?; 55. What is meant by the inverse of a function?; 56. Can a function be equal to its inverse?; 57. What is a 1-1 onto function?; 58. Where does the quadratic formula come from?; 59. What is a parabola?; 60. How can you find the turning point of a parabola?; 61. What is an ellipse?; 62. What is a hyperbola?; 63. When does one use the Law of Sines?; 64. When does one use the Law of Cosines?; 65. What is the difference between y = arccos x and y = cos-1 x?; 66. What is a vector?; 67. Why can a vector not be divided by a vector?; 68. What is i?; 69. What is e?; Notes; Chapter Four. Geometry Questions; 70. Why is the diagonal of a square longer than its side?; 71. How can you demonstrate that the circumference of a circle is 2 pi r?; 72. How can you demonstrate that the area of a circle is equal to pi r squared?; 73. Can a triangle contain two right angles?; 74. Why must the sum of any two sides of a triangle be greater than the third side?; 75. How do the terms "acute angle" and "obtuse angle" relate to the English language?; 76. Can trigonometry be used to prove the Pythagorean theorem?; 77. How is the distance formula derived?; 78. How can the Pythagorean theorem be used to determine if an angle of a triangle is acute or obtuse?; 79. What is a Platonic solid?; 80. What is a golden rectangle?; 81. What is a golden triangle?; 82. From which point in a triangle is the sum of the distances to the three vertices smallest?; 83. What is the sum of the distances from a point in a triangle to its three sides?; 84. What is President James A. Garfield's proof of the Pythagorean theorem?; 85. What is the nine-point circle?; 86. How can the Pythagorean theorem be proved by paper folding?; 87. How can we prove that the sum of the measures of the angles of any triangle is 180 degrees using paper folding?; 88. What figure is created by joining the midpoints of any quadrilateral?; 89. How can the concurrency of the medians of a triangle be proved in one step?; Notes; Chapter Five. Probability Questions; 90. What is the fundamental principle of counting?; 91. What does it mean when the probability of an event is 1? Is 0?; 92. What are mutually exclusive events?; 93. What is the probability of either or both of two events happening?; 94. What is the difference between combinations and permutations?; 95. What is the difference between correlation and causation?; 96. What is the Pascal triangle?; 97. What is binomial probability?; 98. What is the birthday problem?; 99. How can algebra help us to understand a probability question?; 100. What kind of averages are batting averages?; Index;
• Publisher Details: Thousand Oaks : Corwin
• Publication Date: 2013
• Extent: 1 online resource (232 pages)
• Subjects: 510.71/2; Mathematics -- Study and teaching (Middle school); Mathematics -- Study and teaching (Secondary); Mathematics -- Problems, exercises, etc
• Languages: English
• ISBNs: 9781483333991
• Related ISBNs: 148333399X
• Access Rights: Legal Deposit; Only available on premises controlled by the deposit library and to one user at any one time; The Legal Deposit Libraries (Non-Print Works) Regulations (UK).
• Access Usage: Restricted: Printing from this resource is governed by The Legal Deposit Libraries (Non-Print Works) Regulations (UK) and UK copyright law currently in force.