Fractions for Algebra and Arithmetic - Progression Points

Dimension

Level

Progression Points

Number

2.75

• 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

3.25

• Use of brackets to determine order of operations
• Multiplication of fractions by fractions through use of the rectangle area model (grid)

4.0 Standard

… Students add, subtract, and multiply fractions and decimals (to two decimal places) and apply these operations in practical contexts, including the use of money.

4.25

• Division of fractions using multiplication by the inverse

4.5

• Use of calculations involving operations with mixed numbers

5.0 Standard

… Students use technology for arithmetic computations involving several operations on rational numbers of any size.

5.75

• Rationalisation of expressions where division by a square root is involved; for example, √(5)/ √(3) = ^√(15)/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).

Working Mathematically

5.75

• Representation and manipulation of symbolic expressions using technology

Structure

3.50

• Consistent and correct use of conventions for order of operations

5.25

• Factorisation of algebraic expressions by extracting a common factor

5.5

• Expansion of products of algebraic factors, for example, (2x + 1)(x − 5) = 2x² − 9x − 5
• Equivalence between algebraic forms; for example, polynomial, factorised and turning point form of quadratics
• Use of inverse operations to re-arrange formulas to change the subject of a formula

6.0 Standard

… Students use irrational numbers such as, π, φ and common surds in calculations in both exact and approximate form.