### Binary "Bits" For All!

In 1988 David Macaulay's classic *The Way Things Work* was published. In 1998, he followed up this very successful book with *The New Way Things Work*, which includes a chapter entitled "The Digital Domain." This chapter begins with a very entertaining explanation of bits and binary arithmetic in a story that involves crating up pumpkins from a pumpkin patch. I had the good fortune to come across this story just before going to an elementary school to introduce the concept of binary numbers.

The plan was to teach children in 5th, 4th, and 2nd grade how digitized data is represented, using the "Count the Dots" activity in *CS Unplugged*:

http://www.csunplugged.org

The story was a great lead in, but I had no idea how timely the lesson was until after I presented it. Without realizing the connection, I brought big round, scalloped edge, orange sticky notes with me to use as dots on sheets of paper showing 1, 2, 4, and 8 dots. The sticky notes looked just like pumpkins! Moreover, the timing of the lesson, in the latter part of October shortly before Halloween, couldn't have been better, to attach the idea of pumpkins and binary numbers to something familiar in the childrens' experience. Even the 2nd graders got it.

Just a few more notes: The 5th graders had no problem including 16 dots on a sheet of paper, so we could represent larger values with them, but 2nd graders are not ready for that. 2nd graders are, however, good at doubling, so even though they haven't started multiplying in their math lessons, they do get the binary concept. I made individual sets of small cards for each child so they could practice representing numbers in binary, individually or in pairs. In the future, I will have the students build the large sheets of paper with the orange sticky note dots with me to increase their understanding. I will also have them make their own sets of individual cards and draw pumpkins on the cards for the dots. I showed YouTube videos (links from CS Unplugged and MathManiaCS) demonstrating counting in binary. The kids enjoy that and it is something they can try for themselves, counting on their fingers. Another link goes to a page where a clever piano keys activity for binary numbers is found.

A great introduction to binary numbers that can be used in an introductory programming class at the high school level can be found at:

http://apcentral.collegeboard.com/apc/members/courses/teachers_corner/45338.html

And more motivation comes with the Cisco Binary Game:

http://forums.cisco.com/CertCom/game/binary_game_page.htm

Be careful...this one is addictive!

Macauly, David. *The New Way Things Work*, Houghton Mifflin Company. (1998).

ISBN 10: 0-395-93647-3.

http://www.csunplugged.org

http://www.mathmaniacs.org

http://www.mathmaniacs.org/lessons/01-binary/Binary_Piano/

Contributed by Kathy Larson