Warm-Up Activity: Measuring Ourselves

Using your own body, determine:

•How many hands tall are you?

•How many finger-widths tall is your head?

•How many finger-widths is it from your elbow to the tip of your finger?

Compare your results with your neighbors.

A Concise and Abbreviated History of Measurement

Units of measurement based on the human body

Diagram of Yup’ik (Alaska Native) units of length

Relief carving of Ancient Greek measurement using hand span and foot

Diagram of Egyptian definitions of cubit and palm

image credit: Jerry Lipka et al

photo credit: Xavier de Jauréguiberry

The Smoot

The Harvard Bridge between Boston and Cambridge, MA. The Harvard Bridge is 364.4 Smoots in length, plus or minus an ear.

Oliver Smoot being used to measure the Harvard Bridge in 1958.

photo credit: Denimadept creative commons photo credit: MIT museum via Dave Schumaker

With trade and taxation came the need for standardized units

Standard weights for measuring gold dust used by the Asante of Ghana

photo credit: Claudia Zaslavsky

Standardized weights from the Indus river valley

photo credit: John Hill creative commons

photo credit: Andrew Robinson

A bronze ruler from the Han dynasty in China

Systems of measurement commonly used in the US:

The English or Imperial System

image credit: Ian Whitelaw

photo credit: Andrew RobinsonThe early English inch was defined as the length of three barleycorns laid end-to-end King George the III of England’s

standard weights from 1773.

Systems of measurement commonly used in the US:

The Metric System

Since 1983, the meter has been defined as the distance that light travels in 1 299,792458th of a second

Commemorative stamp showing the French Republic measuring one quarter of the earth’s circumference – the original idea behind the meter

Systems of measurement commonly used in the US:

More about the metric system

The Canadian Standard Kilogram. The kilogram is the only unit in the metric system defined by an actual object.

photo credit: Harry Turner, National Reseach Council of Canada

The nickel has a mass of 5 grams

A cube of water with sides each 1 cm has a mass of 1 gram

1 cm

1 cm

1 cm

Bibliography

Lipka, Jerry, Tod Shockey and Barbara Adams. “Bridging Yup’ik Ways of Measuring to Western Mathematics” in Learning and Teaching Measurement: 2003 Yearbook. Ed. Douglas Clements and George Bright. The National Council of Teachers of Mathematics, Inc, Reston, VA. 2003

Robinson, Andrew. The Story of Measurement. Thames and Hudson Ltd, London, UK. 2007

Tavernor, Robert. Smoot’s Ear: The Measure of Humanity. Yale University Press, New Haven, CT. 2007

Whitelaw, Ian. A Measure of All Things: the story of man and measurement. Quid publishing, Hove, England. 2007

Zaslavsky, Claudia. Africa Counts: Number and Pattern in African Culture. Prindle, Weber, and Schmidt Inc, Boston, MA. 1973

Your turn: Discussion

In groups of 2 or 3, discuss the following questions:

•Why do we measure?

•How do we choose what to use to measure?

Think not only in general, but also in the context of your work in your program.