Family Mathematics Problem Solving
Sponsored by
The Somerville Mathematics Fund

The Family Mathematics problems are written for adults and children to work on together. They are not meant as another homework to be turned in to your child’s teacher, instead it is an opportunity for you to work together to solve a mathematical problem. The week of October 6 through 10, 2003 is National Metric Week. In honor of National Metric Day, October 10th, our family mathematics problems this month relate to the story of the metric system. We hope you will enjoy working together to solve these problems. The solutions will be printed in next week’s Somerville Journal. Enjoy.
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The Somerville Mathematics Fund was founded in 2000 to celebrate and encourage mathematics achievement in the city of Somerville. We offer scholarships to students and grants to teachers.
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From October 2003    
All Grades



Family Mathematics Problem Solving: All Grades

Meandering Towards Metrics

Initially the systems of measurement that people used were based on familiar things such as foot, yard (nose tip to fingertip), hand, cubit (elbow to tip of longest finger), or barleycorn. The first people to standardize measurements were the Egyptians; the royal cubit dates to about 3000 B.C.E.

 

Gabriel Mouton was the first westerner to propose a decimal system of measurement which would take one minute of the earth’s circumference as a unit of length which could be repeatedly further divided by tenths. Here are the clues to find out what year Mouton proposed this system:

• the number formed by the thousands and hundreds digits is the fourth power of the smallest prime number
• the tens digit is the fourth prime number
• the sum of the digits is 14

 

On June 19, King Louis XVI of France met with a committee of twelve mathematicians and scientists and approved the development of the metric system. The next day the king was imprisoned when trying to flee the country. A year later, from prison, the king issued an order for the engineers Jean Delambre and Pierre Méchain to make the necessary measurements to determine the official length of a meter (one ten-millionth part of a meridional quadrant of the earth). Here are the clues to find out what year King Louis XVI met with the mathematicians:

• if the tens digit were two less, then the number would be a palindrome
• the hundreds digit is one less than the only one-digit even cube

 

When the metric system was officially adopted by the Republic of France, the system’s motto was “For all people, for all time.” Thirty-eight years later, it was made the only system of measurement in France. Here are the clues to find out when the metric system was adopted initially by France:

• the tens, units and thousands digits are odd square numbers
• the hundreds digit is one less than the smallest prime number cubed
• the sum of the digits is 26

When the United States was a new country, they needed to agree upon their systems of money and measurement. Thomas Jefferson was one of the people advocating a decimal system, however, our congress chose to go with the English system.
When Greenleaf’s New Practical Arithmetic was published, David Scott, the principal of one of New York City’s public schools predicted: “The introduction of the Metric System has my warm approval; I envy the school-master of thirty years hence, who by it will be relieved of that stupefying incubus” (he was referring to the English system of measurement). This was the same year that the Congress of the United States approved the use of the metric system. Here are the clues to find out when the congress approved but did not mandate the use of the metric system:

• the tens and units digits are each the product of the two smallest primes
• the sum of the digits is 21

 

The Metric Conversion Act was passed requiring all federal agencies in the United States to have converted to the metric system of measurement. Here are the clues to find what year the USA decided to convert to metric:

• the hundreds, tens and units digits are consecutive odd numbers in descending order
• the year is a multiple of five

 

President Jimmy Carter appointed the first nominees to the U. S. Metric Board two years after the law was passed; but the board was eliminated five years later by budget cuts. A year before the deadline mandated by the Metric Conversion Act passed, President George Bush signed an executive order requiring all agencies to submit detailed metric conversion plans to the Commerce Department. On September 30, the deadline passed for all federal agencies in the U.S. to convert to the metric system. Here are the clues to find out which year the U.S. was to have converted to the metric system:

• if the units digit were one less, the number would be a palindrome
• the sum of the digits is 21

 

Unfortunately, the deadline passed without the U.S. government agencies converting completely to the metric system. On October 1, the New York Times carried the front page story entitled: “Missing What Didn’t Add Up, NASA Subtracted an Orbiter.” On September 23, the Mars Climate Orbiter unexpectedly disappeared. It was off course by about 60 miles at the end of its 416,000,000 mile journey to Mars because of confusion over units of measure. The engineers at Lockheed Martin Corporation who built the orbiter used the English unit of pounds when making calculations of thrust, while NASA scientists assumed that the information was calculated in newtons, a metric measurement. The misinformation was used in the computers used to calculate the position and direction of the spacecraft. Here is the clue to find out the year NASA made a $125,000,000 mistake because not everyone was using the same system of measurement:

• the sum of the digits is 28.






 

 




Other Problem Solving Sources:
http://mathforum.org/pow/
http://www.figurethis.org/index40.htm
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