Missing Number Sentences - 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).

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?'

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.

4.5

• 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

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.

5.25

• solution of equations by graphical methods

5.5

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

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.

Number

1.25

• use of written number sentences to summarise addition

1.75

• development and use of a 'fact family' linking 25 + 5 = 30 to 5 + 25 = 30, 30 − 5 = 25 and 30 − 25 = 5

2.25

• use of written number sentences such as 20 ÷ 4 = 5 to summarise sharing (partition) and 'how many?' (quotition) processes

2.75

• use of fact families (5 × 7 = 35, 35 ÷ 7 = 5) to solve division problems

Working Mathematically

2.25

• use of materials and models to solve problems and explain answers

2.5

• selection of appropriate situations for the use of a guess-check-improve strategy
• explanation and comparison of alternative computation methods

2.75

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

4.75

• numerical and graphical solution of algebraic problems using technology