Fact Families (Multiplications 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.

They 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 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

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