Mathematical Reasoning and Investigation

• Acknowledgements
• Acknowledgement of country
• Accessibility Information
• Introduction
• What can you learn from the book?
• What if I get stuck?
• I. The Hero's Journey
• 1. The Hero's Journey
• 2. Entry
• 3. Attack
• 4. Problems!
• 5. Review: the hero's return
• II. Fundamental concepts in mathematical reasoning
• 6. Algebra
• 7. Properties of addition and multiplication
• 8. Order of operations
• 9. Describing relationships with variables
• 10. Using expressions to solve problems
• 11. Working with fractions
• III. Algorithms
• 12. What is an algorithm?
• 13. Scratch
• 14. Conditional instructions (if-then rules)
• 15. Loops
• 16. Assigning values to variables and solving problems with Scratch
• IV. Interpreting visual information
• 17. Interpreting graphs from points
• 18. Are graphs just pictures?
• 19. Sketching graphs from words
• 20. Sketching graphs from pictures
• 21. Looking at gradients
• V. Sequences and progressions
• 22. Patterns and sequences
• 23. Arithmetic progressions
• 24. Sums of progressions
• 25. Geometric progressions
• 26. Summing geometric progressions
• VI. Geometry
• 27. Introduction to Geometry
• 28. Triangles
• 29. Circles
• 30. Volume
• VII. Measurement
• 31. Measurement
• 32. The algebra of ratio
• 33. The metric system
• 34. Scientific notation
• 35. Base conversion
• VIII. Graphs and networks
• 36. Graphs and networks
• 37. Graph theory
• 38. Euler paths and Euler cycles
• 39. Minimum spanning trees
• 40. Graph colouring and chromatic numbers
• IX. Simulation
• 41. Simulation
• 42. Computer simulation
• 43. Probability intuition
• 44. The normal distribution
• 45. Where does the Normal Distribution Model come from?
• 46. Mean of a distribution
• 47. Other distributions
• X. Probability
• 48. Estimating probability
• 49. Success fractions and sample space
• 50. Tree diagrams and independent events
• 51. Conditional probabilities
• 52. Venn diagrams
• Conclusion
• Reuse and attributions

Mathematical Reasoning and Investigation is designed to help you develop the ability to use mathematics to solve the kinds of problems that don't come with answers in the back of the book. We like to think of it as a mathematics book for people who think they're not good at mathematics. The work will be useful for anyone wanting to develop their own skills in reasoning and problem solving using mathematics, and for teachers and preservice teachers hoping to help their students to develop these same skills.