Structure of Algebraic Expressions - Progression Points

Dimension

Level

Progression Point

Structure

2.25

• Use of ‘=’ to indicate equivalence or the result of a computation

2.5

• Construction of number sentences

3.0 Standard

… Students understand the meaning of the ‘=’ in mathematical statements and technology displays (for example, to indicate either the result of a computation or equivalence).

They construct number sentences with missing numbers and solve them.

3.25

• Use of add and subtract as inverse operations to solve simple word equations such as ‘I am thinking of a number. If I add 6 I get 18, what number did I start with?’
• Use of trial and error to find a missing number in a number sentence; for example, 4 × ? + 6 = 22

3.5

• Use of division and multiplication as inverses; for example, multiplication by 25 can be carried out as ‘multiplication by 100 followed by division by 4’

4.0 Standard

… Students recognise that addition and subtraction, and multiplication and division are inverse operations.

They use words and symbols to form simple equations.

They solve equations by trial and error.

4.25

• Interpretation of a letter as a symbol for any one of a set of numbers and use in symbolic description of relationships

4.5

• Use of inequality, equality, approximately equal and not equal, including in symbolic expressions
• Translation from verbal description to algebraic representation, and of the structure of algebraic expressions; for example, if $500 is shared between n people, each receives 500/n
• Solution of simple linear equations using tables, graphs and inverse operations (backtracking)

4.75

• Graphical representation of simple inequalities such as y ≤ 2x + 4

5.0 Standard

… Students solve simple equations (for example, 5x + 7 = 23, 1.4x − 1.6 = 8.3, and 4x2 − 3 = 13) using tables, graphs and inverse operations.

They recognise and use inequality symbols.

They solve simple inequalities such as y ≤ 2x + 4 and decide whether inequalities such as x2 > 2y are satisfied or not for specific values of x and y.

5.5

• Equivalence between algebraic forms; for example, polynomial, factorised and turning point form of quadratics

6.0 Standard

… Students solve equations of the form f(x) = k, where k is a real constant (for example, x(x + 5) = 100) and simultaneous linear equations in two variables (for example, {2x − 3y = −4 and 5x + 6y = 27} using algebraic, numerical (systematic guess, check and refine or bisection) and graphical methods.