Early Division Ideas - Progression Points

Dimension

Level

Progression Point

Number

1.25

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

1.75

• Identification of half of a set of objects, including recognition of the need for 1/2 when sharing an odd number of objects

2.0 Standard

… Students describe simple fractions such as one half, one third and one quarter in terms of equal sized parts of a whole object, such as a quarter of a pizza, and subsets such as half of a set of 20 coloured pencils.

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.

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

3.0 Standard

… Students devise and use written methods for: division by a single-digit divisor (based on inverse relations in multiplication tables).

3.75

• Use of inverse relationship between multiplication and division to validate calculations

Working Mathematically

2.75

• Selection of multiplication and division as more efficient processes than repeated addition and subtraction

Structure

3.0

… Students recognise that the sharing of a collection into equal-sized parts (division) frequently leaves a remainder.