Multiplication and Division Growth Points

As students move through the Multiplication and Division growth points they become increasingly able to create mental images of quantities that are constructed multiplicatively. In growth points 0 and 1, students count one by one to find the solution in situations involving multiple groups when all objects are modelled or perceived. In growth point 2, students begin to transition to using multiplicative structures to model a solution, to partial modelling and using abstract imagery to solve a range of problems at growth point 3 and above.

To support students from moving from concrete materials to becoming flexible in using more advanced multiplicative strategies, it is important to screen concrete models to build students mental imagery for the shift to imagining the multiplicative structure in partial models in growth point 3 in order to remove concrete models at growth point 4 and beyond.

The following table provides teachers with a framework to identify the strategies a student uses to solve problems.