The teens found a book with metallic foil pages. A variety of mysterious symbols covered the pages. Although none of the symbols looked familiar to the teens, they did notice that several symbols appeared more frequently than others. These symbols seemed to be used to ``number'' the pages. The first thirteen pages were numbered in the following way:

1. If the teens are correct, what is the base of this strange numeration system? Make a key indicating the face value of each basic digit.
2. To test their theory, one teen counted the pages until she reached the one labeled . How many pages did she count?
3. The book had a total of 127 pages. How was the last page numbered?
4. The last page was actually numbered but after carefully examining the book, the teens discovered that several pages had been torn out. How many pages were missing?
5. (Something totally different) The two Voyager spacecraft each carried a 12-inch phonograph record containing images and sounds selected to portray the diversity of life and culture on Earth. Visit the website http://vraptor.jpl.nasa.gov/voyager/record.html.
   1. Follow the link to Images and then click on Mathematical definitions. Write a paragraph explaining how this image describes our numeration system. You should address the following questions: Is it clear from the image that we use ten basic digits to write all numerals. Does the image show how we use the idea of place value? To what base is our base-ten system compared? What symbols are used as basic digits in the other base?
   2. Comment on some of the other images and sounds on the phonograph. What do you think should have been included or not included?