Introduction \ 1. A Tale of Two Numbers: Finding factors and using ratio \ 2. Acting Your Age?: Solving simultaneous equations and drawing straight-line graphs \ 3. Arc Drawings: Finding the area and perimeter of sectors of circles \ 4. Area of a Triangle: Using the sine rule and the equation 'area = ½ absinC' \ 5. Bearings: Calculating and measuring bearings and back-bearings \ 6. Beat the Calculator!: Using calculators and simplifying algebraic expressions \ 7. Being Human: Estimating quantities and working with given data \ 8. Being Irrational: Understanding and manipulating irrational numbers \ 9. Building a Wall: Moving the centre of enlargement and investigating what happens \ 10. Cake-Cutting Contest: Finding areas of sectors of circles and using circle theorems \ 11. Circle Theorems: Understanding circle theorems \ 12. Circular Argument: Finding the circumference of a circle \ 13. Congruence: Understanding the conditions for congruence of two triangles \ 14. Connect Four: Practising algebraic substitution and looking for connections \ 15. Constructions: Constructing triangles given side-side-side \ 16. Counting Squares: Estimating and calculating with large numbers \ 17. Cutting a Square: Investigating angles on parallel lines \ 18. Equable Sectors: Finding the area and perimeter of sectors of circles and using scatter-graphs \ 19. Equivalent Fractions: Using equivalence of fractions to solve problems \ 20. Factorizing Quadratics: Understanding when monic quadratics will factorize \ 21. Fill it Up!: Generating and describing quadratic (and other) sequences \ 22. Fly on the Wall: Exploring Pythagoras' Theorem in three dimensions \ 23. Functions: Understanding the concept and notation of mathematical functions \ 24. Golden Rectangles: Designing a questionnaire involving ratio calculations \ 25. Graphical Linear Inequalities: Shading inequalities in two variables \ 26. Graphical Solutions of Equations: Solving equations by drawing a suitable line on a curve \ 27. Histograms: Understanding why grouped bar charts can be misleading \ 28. Identities: Manipulating algebra and solving quadratic equations \ 29. Indices: Simplifying quantities with integer indices \ 30. Inverse Functions: Understanding inverse functions by drawing 'function-machine' diagrams \ 31. Kim's Game: Adding and subtracting directed numbers and collecting terms \ 32. Many Faces: Finding equivalent algebraic expressions \ 33. Maximum Product: Estimating products and multiplying integers \ 34. Monkeying Around: Estimating values and using standard form \ 35. Odd Ones Out: Exploring the properties of numbers, shapes and so on \ 36. Ordering Fractions: Adding and subtracting fractions \ 37. Percentage Increases and Decreases: Working with repeated percentage changes \ 38. Pint Cone: Finding the surface area and volume of a cone \ 39. Polygon Areas: Using the area of a triangle to find the area of other polygons \ 40. Prime Numbers: Using the sieve of Eratosthenes 41. Prime-Generating Formulae: Practising algebraic substitution and looking for primes \ 42. Probability Pi: Investigating digit frequency and drawing pie charts \ 43. Properties of Circles: Establishing and working with circle theorems \ 44. Proportionality: Examining direct and inverse proportion \ 45. Pythagoras' Theorem: Proving Pythagoras' Theorem by dissection \ 46. Quadratic Probabilities: Using the quadratic formula and understanding the role of the discriminant \ 47. Quadratics in Disguise: Rearranging and factorizing quadratic equations \ 48. Radical Equations: Manipulating indices to solve equations \ 49. Randomness: Exploring patterns of heads and tails when throwing a fair coin \ 50. Rationalizing Denominators: Manipulating surds \ 51. Recurring Decimals: Converting recurring decimals to simplified fractions \ 52. Reverse Percentages: Finding the 'old' amount before a specified percentage change \ 53. Rounding: Introducing the 'floor' and 'ceiling' functions \ 54. Set Theory: Making sense of set notation \ 55. Similarity: Proving similarity and using it to solve problems \ 56. Simpson's Paradox: Handling data and exploring ratio \ 57. Solving Quadratic Equations: Critiquing learners' work and comparing different methods \ 58. Straight-Line Graphs: Understanding the effects of m and c in y = mx + c and of k in x = k on the graphs \ 59. Surds: Manipulating surds and understanding irrational numbers \ 60. Surface Area and Volume of a Cuboid: Maximizing the number of cubes that can be wrapped with one sheet of paper \ 61. Surface Area and Volume of a Sphere: Proving the formulae without using calculus \ 62. Tetraphobia: Exploring linear sequences with 'missing' terms \ 63. The Cosine Rule: Proving the cosine rule \ 64. The Sine Rule: Proving the sine rule \ 65. Throwing a Coin: Designing an experiment to estimate a probability \ 66. Trial and Improvement: Investigating exponential equations \ 67. Trigonometry: Introducing sin, cos and tan via measurement \ 68. Twenty Questions: Developing a strategy to find a missing number \ 69. Vectors: Adding and subtracting vectors \ 70. Winner Takes All!: Understanding and using conditional probability \ Other Resources \ Index