Equivalence in Number Sentences - Progression Points

Dimension

Level

Progression Point

Structure

2.25

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

2.5

• Variation of order and grouping of addition (commutative and associative property) to facilitate computations; for example, 3 + 5 + 7 + 5 = 3 + 7 + 5 + 5 = 10 +10 = 20
• Construction of number sentences.
• Calculations using notation such as ‘3 + 5 − 2 =’

2.75

• Use of distributive property in calculations; for example, 6 × 37 = 6 × 30 + 6 × 7

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 use number properties in combination to facilitate computations (for example, 7 + 10 + 13 = 10 + 7 + 13 = 10 + 20).

They multiply using the distributive property of multiplication over addition (for example, 13 × 5 = (10 + 3) × 5 = 10 × 5 + 3 × 5).

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 establish equivalence relationships between mathematical expressions using properties such as the distributive property for multiplication over addition (for example, 3 × 26 = 3 × (20 + 6)).

They 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.