In early years, people living in community was away to keep safe by pulling resources, but to get jobs done most effectively and to make sure that goods were share fairly tools were needed. The first mathematical tools developed were to help them measure.
Another way of measuring that was developed was to find the heights of tree. People needed to know if the wood would be large enough. One of this tools called a Thedolite.
Some of the early ways of measuring the height of tall structures are still in use today. They require very little equipment and can be used out in forests where special equipment is hard to come by.
They would walk far enough from the tree to find a place where they were just able to see the top of the tree ( from their upside down position) . The distance from this place to the base of the tree was approximately the height of the tree.
Length
Length is the most necessary measurement in everyday life, and units of length in many countries still reflect humanity's first elementary methods.
The inch is a thumb. The foot speaks for itself. The yard relates closely to a human pace, but also derives from two cubits (the measure of the forearm).
The mile is in origin the Roman mille passus- a 'thousand paces', approximating to a mile because the Romans define a pace as two steps, bringing the walker back to the same foot.
With measurements such as these, it is easy to explain how far away the next village is and to work out whether an object will get through a doorway.
The solution is a rod or bar, of an exact length, kept in a central public place. From this 'standard' other identical rods can be copied and distributed through the community. In Egypt and Mesopotamia these standards are kept in temples. The basic unit of length in both civilizations is the cubit, based on a forearm measured from elbow to tip of middle finger.
Weight
For measurements of weight, the human body provides no such easy approximations as for length. But nature steps in. Grains of wheat are reasonably standard in size. Weight can be expressed with some degree of accuracy in terms of a number of grains - a measure still used by jewellers.
As with measurements of length, a lump of metal can be kept in the temples as an official standard for a given number of grains. Copies of this can be cast and weighed in the balance for perfect accuracy. But it is easier to deceive a customer about weight, and metal can all too easily be removed to distort the scales. An inspectorate of weights and measures is from the start a practical necessity, and has remained so.
Volume
Among the requirements of traders or tax collectors, a reliable standard of volume is the hardest to achieve. Nature provides some very rough averages, such as goatskins. Baskets, sacks or pottery jars can be made to approximately consistent sizes, sufficient perhaps for many everyday transactions.
But where the exact amount of any commodity needs to be known, weight is the measure more likely to be relied upon than volume.
Time
Time, a central theme in modern life, has for most of human history been thought of in very imprecise terms.
The day and the week are easily recognized and recorded - though an accurate calendar for the year is hard to achieve. The forenoon is easily distinguishable from the afternoon, provided the sun is shining, and the position of the sun in the landscape can reveal roughly how much of the day has passed. By contrast the smaller parcels of time - hours, minutes and seconds - have until recent centuries been both unmeasurable and unneeded.