# Multiplication & Division

All of these concepts involve proportional and multiplicative relationships and the bar model is particularly valuable for representing these types of problems and for making the connections between these concepts visible and accessible.

**Multiplication**

Notice how each section of the bars in the problem below has a value of 4 and not 1. This many-to-one correspondence, or unitising is important and occurs early, for example in the context of money, where one coin has a value of 2p for example. It is also a useful principle in the modelling of ratio problems.

**Peter has 4 books Harry has five times as many books as Peter. How many books has Harry?**

4 × 5 = 20

Harry has 20 books

**Division**

When using the bar model for division it is the image of sharing rather than grouping which is highlighted in this representation.

**Mr Smith had a piece of wood that measured 36 cm. He cut it into 6 equal pieces. How long was each piece?**

36 ÷ 6 = 6

Each piece is 6 cm