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E-book
Author Puritz, Christian

Title Explaining and Exploring Mathematics : Teaching 11- to 18-year-olds for understanding and enjoyment
Published Florence : Taylor and Francis, 2016

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Description 1 online resource (227 pages)
Contents 880-01 Explaining and Exploring Mathematics- Front Cover; Explaining and Exploring Mathematics; Title Page; Copyright Page; Contents; Introduction; Part I: 11-14 years old; Chapter 1: Decimals and multiplication by 10, etc.; Chapter 2: Multiplying and dividing by decimals; Chapter 3: Adding fractions; Chapter 4: Multiplying and dividing by fractions; and by 0; Exercise; Chapter 5: Using patterns with negative numbers, or do two minuses really make a plus?; Chapter 6: Use hundreds and thousands, not apples and bananas! Helping beginners make sense of algebra; Chapter 7: Angles and polygons
880-01/(S Chapter 8: Special quadrilateralsChapter 9: Basic areas; Chapter 10: Circles and π; Chapter 11: Starting trigonometry; Chapter 12: Square of a sum and sum of squares, leading to Pythagoras' theorem; Chapter 13: The difference of two squares; Chapter 14: Another look at (a -- b)(a + b); Chapter 15: Number museum: how many factors; Part II: 14-16 years old; Chapter 16: The difference of two squares revisited; Chapter 17: The m, d method: an alternative approach to quadratics; Exercise; Answers; Chapter 18: Negative and fractional indices; A concluding problem; Chapter 19: A way to calculate π
Chapter 20: Pyramids and conesChapter 21: Volume and area of a sphere; Chapter 22: Straight line graphs and gradients; Chapter 23: Percentage changes; Chapter 24: Combining small percentage changes; The product and quotient rules; The derivative of x; Area under y = x; Conclusion; Chapter 25: Angle properties of circles; Chapter 26: Trigonometry with general triangles; Chapter 27: Irrational numbers; Chapter 28: Minimising via reflection; Chapter 29: Maximum area with given perimeter; Chapter 30: Farey sequences: fractions in order of size
Chapter 31: Touching circles and Farey sequences againPart III: 16-18 years old; Chapter 32: Remainder theorem and factorising polynomials; Chapter 33: Adding arithmetic series; Exercise; Chapter 34: d why? by dx: or what is differentiation for?; Chapter 35: Integration without calculus; Chapter 36: Integration using calculus; Chapter 37: Summing series: using differencing instead of induction; Exercise; Chapter 38: GPs, perfect numbers and loan repayment; Chapter 39: Binomial expansion and counting; Chapter 40: How to make your own logarithms; Chapter 41: The mysterious integral of 1/x
Chapter 42: Differentiating exponential functionsChapter 43: Why do the trig ratios have those names?; Chapter 44: Compound angle formulae; Chapter 45: Differentiating the trigonometric ratios; Chapter 46: Fermat centre of a triangle; Index
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Subject Mathematics -- Study and teaching (Secondary)
Mathematics -- Study and teaching (Secondary)
Form Electronic book
ISBN 9781317191315
1317191315