Central principles

Comparison and ordering

The foundation of all aspects of measurement is direct comparison, putting two and then more than two objects (or events) in order according to the attribute in question. The language of comparison is of central importance here.

Two objects are placed side by side and pupils determine which is the longer, which is the shorter. Two items are placed in the pans of a balance and pupils determine which is the heavier, which is the lighter. Water is poured from one container to another to determine which holds more, which holds less. Two pupils perform specified tasks, starting simultaneously, and observe which takes a longer time, which takes a shorter time. No units are involved at this stage, simply direct comparison leading to putting two or more objects or events in order.

Teaching Point

Always introduce new aspects of measurement through direct comparison and activities involving ordering.

Recording the results of comparison and ordering can be an opportunity to introduce the inequality signs (< and >). So, for example, ‘A is longer than B’ can be recorded as A > B, and ‘B is shorter that A’ as B < A. This introduces in a practical context an important principle of inequalities that can be expressed formally as follows:

If A > B, then B < A.

If A < B, then B > A.