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. This Month’s Family Mathematics Problems have been around for many years. We hope you will enjoy working together to solve these problems. The solutions are printed in the Somerville Journal. Enjoy
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 June 2003    
4th and 5th Grades
6th Grades
7th and 8th Grades

Problems from the Good Old Days!

Family Mathematics Problem Solving: 4th and 5th Grades

The Cabbage, the Wolf and the Goat

In 804, Alcuin of York died. He was the personal tutor of the emperor Charlemagne. He wrote a mathematics book called Propositions for Sharpening Youths. Here is one of the problems you would have worked on if you lived 1200 years ago:

A man must ferry a wolf, a goat and a head of cabbage across a river. The available boat, however, can only carry the man and one other thing. The goat cannot be left alone with the cabbage, nor the wolf with the goat. How should the man ferry his three items across the river?

Family Mathematics Problem Solving: 6th Grade

Noah’s Descendents

If you were a student in school 185 years ago instead of today, you might have used The Scholar’s Arithmetic by Jacob Willets (Poughkeepsie New York, 1817). There are calculators today, but back then, calculators had not been invented. Here is one of the problems in that book for you to solve--if you want to use a calculator that is ok:

If the Posterity of Noah, which consisted of 6 persons at the flood, increased so as to double their number in 20 years, how many inhabitants were in the world 2 years before the death of Shem, who lived 502 years after the flood?
Family Mathematics Problem Solving: 7th and 8th Grades
The Cost of Housing

If you were a student in school 130 years ago instead of today, you might have used The National Arithmetic by Benjamin Greenleaf (Boston, 1869).
Here is a “practical” problem of determining the cost of a house. The students who originally solved this problem could not use a calculator, but you can.

A gentleman offered a house for sale on the following terms: for the first door he should charge 10 cents, for the second 20 cents, for the third 40 cents, for the forth 80 cents, and so on in a geometrical ratio. If there were 40 doors, what was the price of the house?




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