Real World Investigations - Progression Points

Dimension

Level

Progression Point

Working Mathematically

1.0 Standard

… Students use diagrams and materials to investigate mathematical and real life situations.

1.5

• Understanding of how to follow a sequence of steps in a procedure

2.25

• Use of materials and models to solve problems and explain answers

2.75

• Use of materials and models to illustrate and test generalisations

3.0 Standard

… Students test the truth of mathematical statements and generalisations. For example, in:

• number (which shapes can be easily used to show fractions)
• computations (whether products will be odd or even, the patterns of remainders from division)
• number patterns (the patterns of ones digits of multiples, terminating or repeating decimals resulting from division)
• shape properties (which shapes have symmetry, which solids can be stacked)
• transformations (the effects of slides, reflections and turns on a shape)
• measurement (the relationship between size and capacity of a container).

3.25

• Consideration of problems with a similar mathematical structure as a problem solving strategy
• Use of familiar problems to focus on strategies to help in solving an unfamiliar problem

3.75

• Application of a set of questions linked to an area of investigation

4.0 Standard

… Students recognise and investigate the use of mathematics in real (for example, determination of test results as a percentage) and historical situations (for example, the emergence of negative numbers).

They engage in investigations involving mathematical modelling.

4.5

• Identification of the mathematical information needed to solve a problem or carry out an investigation

4.75

• Communication of the results of a mathematical investigation in an appropriate form

5.0 Standard

… Students develop simple mathematical models for real situations (for example, using constant rates of change for linear models).

They analyse the reasonableness of points of view, procedures and results, according to given criteria, and identify limitations and/or constraints in context.

6.0 Standard

… Students choose, use and develop mathematical models and procedures to investigate and solve problems set in a wide range of practical, theoretical and historical contexts (for example, exact and approximate measurement formulas for the volumes of various three dimensional objects such as truncated pyramids).