# Multiplicative Thinking Professional Learning Courses

Multiplicative Thinking is critically important because it underpins so much of mathematics. Children who do not develop the ability to think multiplicatively, find it difficult to move beyond primary school mathematics. Unless we explicitly teach children to think multiplicatively, it may not happen for many children – indeed many adults think additively.

Multiplicative Thinking involves using mathematical meta-language to explain, and working conceptually with, relative magnitude, as ‘times bigger / times smaller’, ‘times as many / times more / times fewer’.

Multiplicative Thinking is involved in multiplication and division, fractions, place value of whole numbers and decimals, and metric measurement.

The 2 ways to divide are quotitive (‘groups of …’) and partitive (“… equal groups)’. Partitive division is useful when dividing by whole numbers, and quotitive division is useful when dividing by fractions.

Arrays in mathematics are equal rows. Arrays may be seen additively (repeated addition) or multiplicatively (partitioned into parts). Seeing arrays multiplicatively links to area, and is a visual representation of the distributive property.

The distributive property means we make our multiplication (and division because division is just multiplication by a fraction) simpler, by distributing it over addition. The distributive property is the most important property a child will ever learn – it is the basis of a large portion of future mathematics learning.

Fluency is knowing how a number can be composed and decomposed, and using that information to be flexible and efficient with solving problems – not rote memorisation. Developing fluency in ‘tables’ using the distributive property allows children to learn so much more than just the ‘tables’.

### TPL4USCOURSE: MULTIPLICATIVE THINKING

This self-paced, research-based, practical course is for teachers seeking to deepen their understanding of multiplicative thinking, and their capacity to explicitly teach their students to think multiplicatively.

### TPL4USCOURSE: FROM ARRAYS TO THE DISTRIBUTIVE PROPERTY

This self-paced, research-based, practical course is for teachers seeking to deepen their understanding of multiplying and dividing using multiplicative thinking, and their capacity to explicitly teach their students to think multiplicatively as they multiply and divide.