Manipulating Symbols - 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
• Calculations using notation such as ‘3 + 5 − 2 =’

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).

3.25

• Use of trial and error to find a missing number in a number sentence; for example, 4 × ? + 6 = 22

4.0 Standard

… Students 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

5.0 Standard

… Students use inverses to rearrange simple mensuration formulas, and to find equivalent algebraic expressions (for example, if P = 2L + 2W, then W = P/2 − L. If A = πr² then r = √A/π for r > 0).

5.5

• Use of inverse operations to re-arrange formulas to change the subject of a formula

5.75

• Formulation of pairs of simultaneous equations and their graphical solution

6.0 Standard

... Students apply the algebraic properties (closure, associative, commutative, identity, inverse and distributive) to computation with number, to rearrange formulas, rearrange and simplify algebraic expressions involving real variables.

They verify the equivalence or otherwise of algebraic expressions (linear, square, cube, exponent, and reciprocal), for example, 4x − 8 = 2(2x − 4) = 4(x − 2); (2a − 3)² = 4a² − 12a + 9; (3w)³ = 27w³; (x³y) /xy² = x²y −1; 4/xy = 2/x × 2/y.