Using Diagrams and Models - Progression Points

Dimension

Level

Progression Point

Working Mathematically

0.5

• Selection of appropriate materials for illustrating a mathematical problem or its solution
• Use of drawing to represent problems and solutions

1.0 Standard

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

1.5

• Formulation and testing of conjectures using models that involve, for example, objects, patterns, shapes and numbers

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
• Rephrasing of a problem or representing it using a physical model, diagram, list or table as a problem solving strategy

3.5

• Application of mathematics to model and solve simple practical problems; for example, the construction of a pair of stilts

3.75

• Knowledge of interpretation of maps, graphs and models

4.0 Standard

… Students engage in investigations involving mathematical modelling.

They use calculators and computers to investigate and implement algorithms (for example, for finding the lowest common multiple of two numbers), explore number facts and puzzles, generate simulations (for example, the gender of children in a family of four children), and transform shapes and solids.

5.0 Standard

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

They develop generalisations by abstracting the features from situations and expressing these in words and symbols.

Number

1.0 Standard

… Students use materials to model addition and subtraction by the aggregation (grouping together) and disaggregation (moving apart) of objects.

2.0 Standard

…Students model the place value of the natural numbers from 0 to 1000.

2.25

• use of money as a model for grouping and unpacking lots of 10s

2.5

• development and use of fraction notation and recognition of equivalent fractions such as 1/2 = 4/8 , including the ordering of fractions using physical models

3.0 Standard

… Students develop fraction notation and compare simple common fractions such as 3/4 > 2/3 using physical models.

They add and subtract simple common fractions with the assistance of physical models.

3.25

• multiplication of fractions by fractions through use of the rectangle area model (grid)

4.0 Standard

… Students model integers (positive and negative whole numbers and zero), common fractions and decimals.

4.75

• representation of subtraction of integers through the use of a physical model, and of integer subtraction as an equivalent integer addition, and as the difference between integers

Space

2.75

• construction of a model for an angle using rotation of lines

5.25

• use of two-dimensional nets and line-segment models to investigate regular, semi-regular and irregular solids