Deeper Understanding of Pythagoras' Theorem - Progression Points

Dimension

Level

Progression Point

Measurement, chance and data

5.25

• Use of Pythagoras’ theorem to calculate the length of a side other than a hypotenuse

5.5

• Use of Pythagoras’ theorem to calculate the length of a side other than a hypotenuse

5.75

• Use of Pythagoras theorem in three-dimensional applications

6.0 Standard

… Students use Pythagoras’ theorem and trigonometric ratios (sine, cosine and tangent) to obtain lengths of sides, angles and the area of right-angled triangles.

Structure

4.75

• Solution of equations such as x² = 17 as required in measurement situations; for example, using Pythagoras’ theorem

Number

5.0 Standard

… Students calculate squares and square roots of rational numbers that are perfect squares (for example, √0.81 = 0.9 and √⁹/₁₆ = ³/₄).

Using technology they find square and cube roots of rational numbers to a specified degree of accuracy (for example, ³√200 = 5.848 to three decimal places).

5.5

• Simplification of surds;
  for example, √(12) = 2√(3)

6.0 Standard

… Students carry out exact arithmetic computations involving fractions and irrational numbers such as square roots (for example, √18 = 3√2, √(³/₂) = √⁶/₂) and multiples and fractions of π (for example π + ^π/₄ = 5^π/₄).

They use appropriate estimates to evaluate the reasonableness of the results of calculations involving rational and irrational numbers, and the decimal approximations for them.

Working mathematically

6.0 Standard

… Students follow formal mathematical arguments for the truth of propositions.