## Introduction

A measurement results from dividing a continuous quantity, such as length, area or volume, into identical units and determining the number of units. This allows continuous quantities to be compared with other quantities of the same type.

To measure a continuous quantity, such as the length of a desk, the length has to be partitioned into units that can be counted by either repeating the unit along the length, or subdividing the length into units of a given size. That is, after identifying the endpoints of the length to be measured and the unit to quantify the distance between the endpoints, this unit is used repeatedly end to end (alongside the object being measured) to determine the accumulated number of units corresponding to the length. We call using the unit repeatedly end to end iterating the unit.

Learning how spatially organised units fit together, and how they may be counted systematically, is basic to understanding the measurement of length, area and volume. As we move from length to area and volume we increase the need to coordinate units of units. However, in each case to obtain a precise measurement, units must be aligned or packed so that there are no gaps or overlaps.

Iterating a unit to measure length