Multiplication and Division - Progression Points

Dimension

Level

Progression Point

Number

1.25

• Drawing of diagrams to show sharing of up to 20 items

1.5

• Counting by 2s, 5s and 10s from 0 to a given target …

2.0 Standard

... Students skip count by 2s, 4s and 5s from 0 to 100 starting from any natural number.

Students describe and calculate simple multiplication as repeated addition, such as 3 × 5 = 5 + 5 + 5; and division as sharing, such as 8 shared between 4.

They 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).

2.25

• Use of money as a model for grouping and unpacking lots of 10s
• Use of written number sentences such as 20 ÷ 4 = 5 to summarise sharing (partition) and ‘how many?’ (quotition) processes

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
• Use of fact families to solve division problems, for example 5 × 7 = 35, 35 ÷ 7 = 5

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: whole number problems of addition and subtraction involving numbers up to 999; multiplication by single digits (using recall of multiplication tables) and multiples and powers of ten (for example, 5 × 100, 5 × 70 ); division by a single-digit divisor (based on inverse relations in multiplication tables).

3.25

• Appropriate selection and use of mental and written algorithms to add, subtract, multiply and divide (by single digits) natural numbers
• Multiplication of fractions by fractions through use of the rectangle area model (grid)

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
• Recognition that multiplication can either enlarge or reduce the magnitude of a number (multiplication by fractions or decimals)
• Use of inverse relationship between multiplication and division to validate calculations

4.0 Standard

... Students explain and use mental and written algorithms for the addition, subtraction, multiplication and division of natural numbers (positive whole numbers).

They add, subtract and multiply fractions and decimals (to two decimal places) …

4.25

• Use of index notation to represent repeated multiplication
• Division of fractions using multiplication by the inverse

4.75

• Addition, multiplication and division of integers

5.75

• Division and multiplication of numbers in index form, including application to scientific notation