Multiplication and Division are investigated additively in K-2, when students skip count.

From Year 3 onwards, students investigate Multiplication and Division multiplicatively, using the distributive property, and also investigate the relationship between division and fractions. (See the diagram below.)

Students begin investigating fraction concepts – halves of shapes – in Kindergarten/Prep/Reception (FD 1).

Students begin to investigate multiplication and division formally in Year 1, dividing in 2 ways – into ‘groups of …’ and into ‘… equal groups’ (MD 1). They investigate dividing by 2 by dividing into ‘groups of 2’ and into ‘2 equal groups’, relating dividing into ‘2 equal groups’ with halving groups (MD 2, FD 2, PA 9). Students investigate dividing in ‘groups of …’ and find the total by skip counting (MD 3, 4, PA 8).

Students begin to investigate dividing into arrays (MD 5) in Year 2, and multiplying coins (MD 6, MF 8). They investigate dividing in 2 ways – into ‘groups of …’ and into ‘… equal groups’, recording number sentences (MD 7) and related dividing by 4 by dividing into ‘4 equal groups’ with quartering groups (MD 8, FD 4).

Students begin to investigate multiplication and division multiplicatively in Year 3, investigating multiplying and dividing by 10 related to multiplicative place value (MD 9). They investigate multiplying and dividing by 2, 4, 3 and 5 using the distributive property (MD 10, 11, 12, 13), relating dividing with finding a fraction and the meaning of the denominator (FD 7).

Students continue to investigate multiplication and division multiplicatively in Year 4, investigating multiplying and dividing by 9, 6, 8 and 7 using the distributive property (MD 14, 15, 16, 17), again relating dividing with finding a fraction and the meaning of the denominator (FD 7). Students investigate Patterns and Algebra concepts of skip counting number patterns and multiplication and division problems (MD 18, 19, PA 23, 25).

Students investigate highest common factors, equivalent division calculations and divisibility tests (MD 20, 21, 22, PA 26) in Year 5. They investigate the meaning of the vinculum (FD 19) to divide the remainder to create a fraction (MD 22, FD 20). Students investigate multiplying two-digit numbers using the distributive property (MD 24).

Students investigate additive and multiplicative place value of numbers of any size (PV 28, FD 25) in Year 6 and use their understanding to investigate multiplying and dividing by decimals (PV 29, MD 25, FD 26). They use their understanding of the relationship between division and fractions to explain that division is multiplication by a fraction (MD 26, FD 27). Students investigate square and triangular numbers, prime and composite numbers, and order of operations and grouping symbols (AS 33, MD 27, 28, 29, PA 29, 31).