Mathematical Arguments - Progression Points

Dimension

Level

Progression Point

Working mathematically

3.75

• Students construct and record short informal mathematical arguments, such as explaining short cuts for multiplying by 11 or 99.

4.5

• Students extend mathematical arguments, such as finding angle sum of a pentagon by extending the argument that angle sum of quadrilateral is 360° because it can be split into two triangles. They explain mathematical relationships by extending patterns.

4.75

• They link known facts together logically, such as parallelograms have rotational symmetry, therefore they have equal opposite angles.

5.0 Standard

... Students formulate conjectures and follow simple mathematical deductions (for example, if the side length of a cube is doubled, then the surface area increases by a factor of four, and the volume increases by a factor of eight).

5.25

• Students formulate and test conjectures and present informal logical arguments for their truth, such as the product of three consecutive integers divides by 2, 3 and 6.

5.75

• Students follow a formal mathematical argument of several steps presented by the teacher, such as Pythagoras’ theorem. They identify gaps in reasoning.

6.0 Standard

... They follow formal mathematical arguments for the truth of propositions (for example, ‘the sum of three consecutive natural numbers is divisible by 3’).

Space

5.5

• They can determine congruence and similarity of triangles using geometric properties of lines and angles.