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, instead it is an opportunity for you to work together to solve a mathematical problem. This Month’s Family Mathematics Problems are about large numbers. We hope you will enjoy working together to solve these problems. A link for the solutions is listed below.
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 December 2001    


Family Mathematics Problem Solving: Grades 4 and 5

A Million Minutes

You know how long a minute is. Close your eyes and have someone time you to see if you can estimate when one minute has passed. Before you start the calculations for this problem, take a guess. Who in your family has been alive for one million minutes? Have any of the children lived that long? What about the parents or would you need to go to the grandparents to find someone who is so “ancient”?
Bonus: Has anyone in your family been alive for a billion minutes?

Family Mathematics Problem Solving: Grade 6

Six Million Paperclips

There was a recent story in the news about Whitwell Middle School in Marion, Tennessee where the students were studying the Holocaust and paperclips. During World War II, people in Norway wore paperclips on their collars as a sign of protest against the Nazis. The students are collecting stories from Holocaust survivors as well as trying to collect six million paperclips, one for each victim of the Holocaust. Recently it was reported that they had already collected two million paperclips.
If they were to collect only the smaller standard size paperclip, and to make a paperclip chain with all 6,000,000 of them, how long would their chain be? Would it be as long as a mile? If more than a mile, how many miles?
Family Mathematics Problem Solving: Grades 7 and 8

Six Million Pennies

Instead of collecting paperclips, what if someone started out to collect six million pennies. Norman Salsitz is trying to do just this. He wants to collect six million pennies to be used to help the Righteous Gentiles, the people who risked their lives to help the Jews during World War II. Even though we call them copper pennies, starting in 1982, pennies are only 2.5% copper (97.5% zinc). Each penny as a mass of about 2.5 grams. The U.S. mint makes 13 billion pennies each year; there are 130,000,000,000 of them in circulation, so there should be plenty available for this project.
If Norman Salsitz lined up the six million pennies end to end, how long would the line of pennies be? If he stacked them instead, how high would the stack be? The two million paperclips already collected by the Whitwell students (see the 6th grade problem) weigh about 600 pounds. How many times heavier are six million pennies than six million paperclips?