Reinventing the Timepiece

For over 4000 years, devices have been used to measure and keep track of time. The current sexagesimal system of measurement dates to 2000 BC. This is a base 60 numbers system developed in an ancient civilization called Sumer in Mesopotamia. The Ancient Egyptians divided the day into two 12-hour periods and used large obelisks to track the movement of the Sun.

Since the timepiece has undergone so many changes, why shouldn’t the Mathletes endeavor to reinvent the timepiece? So, we did.

I first talked about Archimedes who was known for being able to draw the most perfect circle freehand. I had the children explore their circle drawing skills. It was fun to watch their different methods. Some sought to use their fingers or the whiteboard marker as a radius; very clever.

The next challenge was to draw the 12 vertices of a dodecagon. These are 12 points equally spaced around a circle. Most of them again tried to do this free hand finding that there was usually space left over in between the last and the first point. We did have some students make the connection to the clock or compass and I suggested to them that they should think of 12 as north, 6 as south, 3 as east and 9 as west. Then they could easily space the remaining numbers in between to finish their dodecagon (12 sided polygon).

I then challenged them to reinvent the timepiece by taking my watch off and throwing it across the room. Luckily it is the type of watch worn by the Navy Seals and does not damage.

We looked at a wonderful math clock I have in my classroom which has equations of all operations representing the first 12 digits. We then brainstormed as to other ways to represent the numbers. See the attached pdf called Clock Reinventing the Timepiece Examples.pdf. It has a picture of the math clock, a list of ideas and pages of examples of clocks using Roman Numerals (although that has been done for centuries), polygons, equations using subtraction, addition, multiplication and division, Mayan numbers, and dice. You could also use Chinese, Hebrew or any other numbered characters. The pdf also has pictures of several clocks created by Mathletes using square roots, the periodic table of elements, and even a clock made from a triangular pyramid.

The children spent part of the class using the Clock Worksheet.pdf to explore many different clocks. The ones that can be a lot of fun are using a theme of multiples of ____. So if they choose multiples of 7, they can start with 7 at the one spot and then 14, 21, 28, and so on. You can check their work by looking at the 12 spot and multiplying 7 x 12 to see if they ended up with 84.

This week they should create as many clocks as possible. Use color and even brass fasteners to make hands. Most of all, have fun. Remember, Mathlete Dollars are awarded for effort; accuracy and mastery will come.