Mathematics Developmental Continuum P-10

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Identifying Factors and Multiplication - Progression Points

Dimension

Level

Progression Point

Number

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
  • Automatic recall of number facts from 2, 5 and 10 multiplication tables

2.75
  • Representation of multiplication as a rectangular array and as the area of a rectangle

3.0 Standard

… Students compute with numbers up to 30 using all four operations.

They provide automatic recall of multiplication facts up to 10 × 10.

They devise and use written methods for:

  • multiplication by single digits (using recall of multiplication tables) and multiples and powers of ten (for example, 5 × 100, 5 × 70)

3.25
  • Representation of square numbers using a power of 2; for example, 9 = 32

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
  • Use of inverse relationship between multiplication and division to validate calculations
  • Creation of sets of multiples of numbers and their representation in index form; for example, 3, 9, 27 written as 
    31, 32, 33 respectively

4.0 Standard

… Students interpret numbers and their factors in terms of the area and dimensions of rectangular arrays (for example, the factors of 12 can be found by making rectangles of dimensions 1 × 12, 2 × 6, and 3 × 4).

They identify square, prime and composite numbers.

They create factor sets (for example, using factor trees) and identify the highest common factor of two or more numbers.

They recognise and calculate simple powers of whole numbers (for example, 24 = 16).

4.5
  • Construction of factor trees for the expression of numbers in terms of powers of prime factors

Structure

2.25
  • Knowledge of the effect of multiplying by ten on the location of the decimal point in a number

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’