Properties of Operations - Progression Points

Dimension

Level

Progression Point

Structure

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

2.75

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

3.0 Standard

… Students 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).

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)).

5.0 Standard

… Students apply the commutative, associative, and distributive properties in mental and written computation (for example, 24 × 60 can be calculated as 20 × 60 + 4 × 60 or as 12 × 12 × 10).

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

1.5

• use of the number properties (commutative and associative) of addition in mental computation, and recognition of complements to ten; for example, 3 + 4 + 7 + 6 = 3 + 7 + 4 + 6 = 10 + 10 = 20

2.0 Standard

… Students use commutative and associative properties of addition and multiplication in mental computation (for example, 3 + 4 = 4 + 3 and 3 + 4 + 5 can be done as 7 + 5 or 3 + 9).

2.5

• use of strategies such as ‘near doubles’, ‘adding 9’ and ‘build to next 10’ to solve addition and subtraction problems
• use of written methods for whole number problems of addition and subtraction involving numbers up to 99

2.75

• use of algorithms for the addition and subtraction of numbers to two decimal places
• representation of multiplication as a rectangular array and as the area of a rectangle

3.75

• multiplication by increasing and decreasing by a factor of two; for example,
  24 × 16 = 48 × 8 = 96 × 4 = 192 × 2 = 384 × 1 = 384