 # Multiplication and Division Models

### Multiplicative models are useful for developing  students’ conceptual understanding of multiplication and division situations. They can help students focus on the meaning of a problem and draw out the links between different forms of textual, visual, structural and symbolic representations.  # Arrays

### Arrays make it easier for students to focus on these three quantities at the same time, and to link multiplication and division. 1. ### Different array visualisations help students move from additive (equal group) thinking to multiplicative thinking (proportions or scaling). 1. ### Arrays are also useful for developing conceptual understanding of the commutative and distributive properties of multiplication.     ### We will look at these properties  in greater depth in the next post. # Number lines

### A basic knowledge of forwards and backwards skip counting is a useful foundation for understanding and working with the equal groups (repeated addition) multiplicative structure. Number lines help students develop their skip counting skills and   understandings. Empty or partially empty number lines are particularly useful as students need to mentally construct and test the viability of their own numerical sequences, checking and revising their thinking as they go. # Bar models

### Let’s look at an example of this in action. Below is a problem where the the number of parts and the total are known and students need to identify the size of the parts. The information is presented as a word problem and students must extract the mathematical information and decide where each piece fits in the model. The model provides useful organisational clues.   # Mathletics Resources

### Here are some array model activities available in Mathletics. If you would like to add some to your courses and you are not sure how, contact your account manager directly or call 1300 850 331.   