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 are about large numbers. We hope you will enjoy working together to solve these problems. The solutions are listed on another page.
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.
For more information, call 617-666-0666 (evenings)
or e-mail voolich@aol.com

From December 2001
 Solutions
  


Family Mathematics Problem Solving: Grades four and five

A Million Minutes
There are 60 minutes in an hour and 24 hours in a day, so every day has 1440 minutes. 1,000,000 ÷ 1440 is a little more than 694.4 days. So, shortly before your second birthday, you had already lived for one million minutes. Now for a billion minutes: 1,000,000,000 ÷ 365 is about 1,902.6 years and 1,000,000,000 ÷ 365.25 is about 1901.3 years, so no one in your family has been alive that long! What a difference a few zeros makes.

Family Mathematics Problem Solving: Grade six

Six Million Paperclips
If you make a paperclip chain, you will find that a 5 clip chain is 6 inches long, so a six clip chain is 12 inches long. 6,000,000 ÷ 10 = 600,000 chains
600,000 x 12 inches = 7,200,000 inches = 7,200,000 ÷ 12 inches/foot = 600,000 feet = 600,000 ÷ 5280 feet/mile gives an answer a little bit bigger than 113.6 miles.
Family Mathematics Problem Solving: Grades seven and eight

Six Million Pennies
If you line up pennies end-to-end along the side of a ruler, you should find that 4 pennies are about 3 inches long.
To find out how long a line of 6,000,000 pennies is:
6,000,000 ÷ 4 x 3 = 4,500,000 inches = 4,500,000 ÷ 12 = 375,000 feet = 375,000 ÷ 5280 gives a little more than 71 miles.
You need to measure a stack of pennies, you should have found there are about 18 pennies in an inch tall stack.
To find out how tall a stack of 6,000,000 pennies is:
6,000,000 ÷ 18 = 333,333 1/3 inches = 333,333 1/3 ÷ 12 = 27,777.8 feet = 27,777.8 ÷ 5280 is a little less than 5.3 miles high.
Each penny weighs about 2.5 grams. There are 28.35 grams in an ounce and 16 ounces in a pound.
6,000,000 x 2.5 ÷ 28.35 ÷ 16 = 33,068.78 pounds.
If 2,000,000 paperclips weigh about 600 pounds, then 6,000,000 paper clips will weigh about 18 pounds.
33,068.78 ÷ 18 is about 18.4. So the pennies are about 18.4 times as heavy as the paperclips.