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Title:
100 commonly asked questions in math class : answers that promote mathematical understanding, grades 6-12 / Alfred S. Posamentier, William Farber, Terri L. Germain-Williams, Elaine Paris, Bernd Thaller, Ingmar Lehmann.
Author:
Posamentier, Alfred S.
Publication Information:
Thousand Oaks, California : Corwin, [2013]
Call Number:
QA139 .P65 2013
Abstract:
100 ways to get students hooked on math! It happens to the best of us: that one question thats got you stumped. Or maybe you have the answer, but its not all that compelling or convincing. Al Posamentier and his coauthors to the rescue with this handy reference containing fun answers to students 100 most frequently asked math questions. Even if you already have the answers, Als explanations are certain to keep kids hookedand thats what its all about. The questions are all organized around the Common Cores math content standards and relate directly to Numbers and Quantity, Functions, Algebra, Geometry, and Statistics and Probability.
ISBN:
9781452243085
Physical Description:
xiv, 217 pages : illustrations ; 26 cm
Contents:
Machine generated contents note: ch. 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? --

Contents note continued: 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 -- ch. 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? --

Contents note continued: 32.If the temperature rises from 80°F to a temperature of 88°F, why is it wrong to say it became 10% warmer? -- 33.How do the values of the following differ: abc, (ab)c, (ab)c, abc? -- 34.Why is division by zero not permissible? -- 35.Why is x 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 -- ch. 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? [√]a [√]b = [√]ab? -- 45.Why is it advantageous to rationalize the denominator? -- 46.What is meant by the "absolute value" of a variable? --

Contents note continued: 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? --

Contents note continued: 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 -- ch. 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]r2? -- 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? --

Contents note continued: 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° 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 -- ch. 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? --

Contents note continued: 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?.
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