Sharpening Understandings Table of Contents
Teachers are busy people and we have designed Sharpening Understandings with that in mind. Each Whetstone is a four-page gem, containing ideas, connections, understandings and applications. The four-page booklets are designed to be photocopied and used as guided lesson material for students (provided that the teacher who owns the book is teaching those students, there is no issue regarding copyright).
Mathematical Whetstones topics have been mapped to the applicable unit in the Australian Curriculum Senior Mathematics Course.
The Algebra Group
1. Algebra and Indices
2. Quadratic equations, Completing the square
3. Quadratics: Factors and Formula
4. Coordinate Geometry, Basic ideas
1. Algebra and Indices
2. Quadratic equations, Completing the square
3. Quadratics: Factors and Formula
4. Coordinate Geometry, Basic ideas
The Relations Group
5. Mappings
6. Continuity and Smoothness
7. Equivalence and other relations
5. Mappings
6. Continuity and Smoothness
7. Equivalence and other relations
The Trigonometry Group
8. Common ratios
9. Angles and applications
10. Radians and applications
11. The Sine Rule
12. The Cosine Rule
13. The Area of a Triangle Rule
14. Angles of Any Magnitude: Definitions
15. Angles of any Magnitude: Ratios and Angles
16. Compound Angles
17. Functions and Modelling: Part 1
18. Functions and Modelling: Part 2
8. Common ratios
9. Angles and applications
10. Radians and applications
11. The Sine Rule
12. The Cosine Rule
13. The Area of a Triangle Rule
14. Angles of Any Magnitude: Definitions
15. Angles of any Magnitude: Ratios and Angles
16. Compound Angles
17. Functions and Modelling: Part 1
18. Functions and Modelling: Part 2
The Vectors Group
19. History and Arrows
20. Algebra
21. Linear Independence
22. Plane Geometry Proofs
23. Basis and Scalar Product
24. The Vector or Cross Product
25. Projections and Functions
The Probability Group
26. Probability, Basics
27. Probability, Two Events: Part 1
28. Probability, Two events: part 2
The Counting and Combinatorics Group
29. Counting
30. The Binomial
31. The Inclusion-Exclusion Principle
32. Derangements
33. The Pigeon Hole Principle
The Plane Geometry Group
34. Euclid’s Elements
35. Circles 1
36. Circles 2
37. Quadrilaterals
The Other Functions Group
38. Rational Functions
39. Exponential Functions
40. Logarithms, Introduction
41. Logarithms, Functions
The AP and GP Group
42. Sequences and Series
43. Arithmetic and Geometric Sequences
44. Arithmetic and Geometric Series
45. Geometric Progression, Applications 1
46. Geometric Progression, Applications 2
Matrices
47. Basics
48. Solving Systems
49. Transformations 1
50. Transformations 2
51. Transformations 3
The Calculus Group
52. Rates of Change
53. Differentiation and Integration
54. The Fundamental Theorem
55. The Derivative
56. Trigonometric Functions
57. Logarithm and Exponential Functions
The Integration Techniques Group
58. Integration Techniques: 1
59. Integration Techniques: 2
The Complex Numbers Group
60. The Story of the Cubic
61. The Basics
62. Geometry
63. Polynomials
64. Solutions and Subsets
The Differential Equations Group
65. First Order
66. Homogeneous
67. Direction Fields and the Logistic equation
68. Euler’s method
69. Rectilinear Motion
70. Forces 1
71. Forces 2
72. Simple Harmonic Motion
73. Projectile Motion
Statistics
74. Random Variables and Expected Value
75. Discrete Distributions
76. Continuous Distributions
Sampling
77. Introduction
78. Distributions
79. Confidence Intervals
80. Proportions
19. History and Arrows
20. Algebra
21. Linear Independence
22. Plane Geometry Proofs
23. Basis and Scalar Product
24. The Vector or Cross Product
25. Projections and Functions
The Probability Group
26. Probability, Basics
27. Probability, Two Events: Part 1
28. Probability, Two events: part 2
The Counting and Combinatorics Group
29. Counting
30. The Binomial
31. The Inclusion-Exclusion Principle
32. Derangements
33. The Pigeon Hole Principle
The Plane Geometry Group
34. Euclid’s Elements
35. Circles 1
36. Circles 2
37. Quadrilaterals
The Other Functions Group
38. Rational Functions
39. Exponential Functions
40. Logarithms, Introduction
41. Logarithms, Functions
The AP and GP Group
42. Sequences and Series
43. Arithmetic and Geometric Sequences
44. Arithmetic and Geometric Series
45. Geometric Progression, Applications 1
46. Geometric Progression, Applications 2
Matrices
47. Basics
48. Solving Systems
49. Transformations 1
50. Transformations 2
51. Transformations 3
The Calculus Group
52. Rates of Change
53. Differentiation and Integration
54. The Fundamental Theorem
55. The Derivative
56. Trigonometric Functions
57. Logarithm and Exponential Functions
The Integration Techniques Group
58. Integration Techniques: 1
59. Integration Techniques: 2
The Complex Numbers Group
60. The Story of the Cubic
61. The Basics
62. Geometry
63. Polynomials
64. Solutions and Subsets
The Differential Equations Group
65. First Order
66. Homogeneous
67. Direction Fields and the Logistic equation
68. Euler’s method
69. Rectilinear Motion
70. Forces 1
71. Forces 2
72. Simple Harmonic Motion
73. Projectile Motion
Statistics
74. Random Variables and Expected Value
75. Discrete Distributions
76. Continuous Distributions
Sampling
77. Introduction
78. Distributions
79. Confidence Intervals
80. Proportions