Colin Foster teaches mathematics at a secondary school in Coventry, UK.

'The problems in this book would enrich the mathematical learning of any class; they are clear and challenging whilst being easily differentiable. Colin Foster has produced a resource that will extend the mathematical learning of any student, helping them to engage with mathematics, instead of just doing mathematics.' James Robinson, Teacher of Mathematics, Ripley St Thomas School, UK

• Introduction 1. Amazing Ways: Counting the numbers of routes through a word maze 2. Dividing Cakes: Partitioning fractions in different ways 3. Draw a Picture: Drawing pictures using mathematical graphs 4. Ever-Increasing Circles: Approximating the area of a circle by counting dots 5. Factor Trees: Exploring patterns in prime factor trees 6. Fiddling Averages: Investigating how averages can be manipulated 7. Folding: Finding connections relating to flat folds 8. Four Numbers: Generating and solving linear equations 9. Four Weights: Making as many values as possible from four numbers 10. Four-Star Hotels: Deducing the contents of a grid from the sums of columns and rows 11. Fuel: Maximizing the amount of fuel that can be transferred across a desert 12. Have a Megaday!: Converting time units and using standard prefixes 13. How Far?: Devising a statistical experiment 14. Infinity: Exploring a converging sequence 15. Investigating Mirrors: Finding out what happens when you reflect more than once 16. Journey Through a Word: Using bearings and distance to describe a route 17. Ladders: Solving simultaneous equations and drawing straight-line graphs18. Make Twenty-Four: Using priority of operations to construct calculations19. Meeting Up: Finding out how straight lines relate to their equations 20. Mystery Messages: Using frequency analysis to crack a substitution code 21. Newspaper Pages: Investigating the pagination of newspapers and books 22. One Cut: Categorizing the outcomes from one fold and one cut of a square 23. Palindromic Numbers: Solving problems relating to palindromic numbers 24. Percentage Puzzles: Practising mental percentage calculations 25. Pizza Slices: Finding the areas and perimeters of circular sectors 26. Rectilinear Shapes: Exploring angles and line segments in rectilinear shapes 27. Regular Polygons: Understanding necessary and sufficient conditions in geometry28. Seven Divided by Three: Partitioning integers and finding patterns 29. Shape Riddles: Understanding inclusive definitions 30.Shapes Within Shapes: Relating numerical sequences to geometrical properties 31. Sharing Camels: Using fractions to solve a remainder problem 32. Simultaneous Investigation: Finding simultaneous equations with integer solutions 33. Sinusoids: Examining the sine and cosine graphs 34. Squares and Remainders: Exploring the divisibility properties of square numbers 35. Squares and Roots: Finding out how square numbers and surds behave 36. Star Polygons: Calculating angles in star polygons and drawing them 37. Street Race: Using travel graphs to solve problems 38. Symmetrical Possibilities: Finding examples of shapes with specified symmetries 39. Take a Breath: Estimating and calculating using large numbers 40. The Playground Problem: Solving a practical minimization problem 41.The Tailor's Rule of Thumb: Testing statistical hypotheses relating to body proportions 42. The Totient Function: Investigating patterns in reducible fractions 43. Three Consecutive Numbers: Using algebra to prove relationships 44. Transforming Graphs: Carrying out transformations on straight-line graphs 45. Transport Problems: Solving complicated problems in the best possible way 46. Trapped Squares: Exploring patterns relating to straight-line graphs 47. Travel Arrangements: Making and interpreting travel graphs 48. Triangle Angles: Using simple trigonometry to solve not-so-simple triangles 49. Vanishing Lines: Explaining an optical illusion using gradient 50. Water: Calculating volumes and lengths and finding connections Other ResourcesIndex