- 1. Lesson 1: The Visual Area Argument of Pythagoras
Students will discover and apply the rule that for any right-angled triangle, the area of the square on the longest side equals the sum of the areas of the squares on the two shorter sides.
- 2. Lesson 2: Formalising Pythagoras and Finding the Hypotenuse
Students will identify the hypotenuse of a right-angled triangle, translate the visual area rule into the algebraic formula $a^2 + b^2 = c^2$, and calculate the length of the hypotenuse.
- 3. Lesson 3: Finding a Shorter Side and Exact Values
Students will use Pythagoras' Theorem with subtraction to calculate a shorter side, and write non-whole number answers in exact surd form.
- 4. Lesson 4: The Converse of Pythagoras
Students will apply the converse of Pythagoras' Theorem to verify whether a given triangle contains a right angle by testing its side lengths.
- 5. Lesson 5: Strategic Competence: Hidden Right-Angled Triangles
Students will construct auxiliary lines to reveal hidden right-angled triangles within isosceles triangles, rectangles, trapeziums, and coordinate grids, and apply Pythagoras' Theorem to solve problems.
- 6. Lesson 6: Trigonometric Functions as Machines
Students will understand sine, cosine, and tangent as mathematical function machines that take an angle as an input and produce a numerical output, and use a calculator to evaluate direct and inverse trigonometric functions.
- 7. Lesson 7: Relativity of Sides & Discovering the Tangent Ratio
Students will correctly label the Opposite, Adjacent, and Hypotenuse sides relative to a reference angle, and discover that the ratio of Opposite divided by Adjacent is constant for any given angle (the Tangent).
- 8. Lesson 8: Applying Tangent (TOA)
Students will utilize the TOA mnemonic and a structured 4-step method to solve for missing side lengths and missing angles using the Tangent ratio.
- 9. Lesson 9: Discovering and Applying Sine & Cosine (SOH CAH)
Students will discover the Sine and Cosine ratios, complete the SOH CAH TOA mnemonic, and use them to calculate missing side lengths and angles.
- 10. Lesson 10: The Metacognition of Ratio Selection
Students will utilize the "Ticking Method" to accurately and independently select between Sine, Cosine, and Tangent for any given right-angled triangle problem.
- 11. Lesson 12: Trigonometric Interconnectivity: Gradient and the Unit Circle
Students will connect the Tangent ratio to the gradient of a line, and relate Sine and Cosine to Cartesian coordinates (x, y) using the Unit Circle.
- 12. Lesson 13: Deriving Exact Trigonometric Values
Students will geometrically construct two special triangles to derive the exact fractional and surd values for sine, cosine, and tangent of 30°, 45°, and 60° without a calculator.
- 13. Lesson 14: Master Class: Method Selection and Mixed Problem Solving
Students will independently select between Pythagoras' Theorem and Trigonometry to solve ambiguous geometric diagrams and sequence multiple steps to solve compound shape problems.
