Form groups of size three or four persons. You may not work alone!  You should start this group activity by introducing each member of the group. You may also want to choose one person to write down the group's discussion on the provided transparency as you go so that it can be displayed on the classroom's overhead projector.

Counting m&m's

Your first task is very important to the survival of the human race. Given a bag of m&m's, you must provide a precise procedure for determining which color is represented by the most m&m's and which by the least (i.e., the most generic and most rare colors in the bag). It has been said that brown m&m's are the most common ones, while green m&m's are the most rare (and thus taste the best). Individual groups will attempt to answer this question for their bag; as a class, we will try to make a more significant statement.

Note that it is typically easy for a human to look at ten things and say which is the largest, or the tallest, or the brightest. Humans can visually compare many things at once. And it will be especially tempting for you to do this with a bunch of brightly colored candies in front of you. 

To develop this procedure, try imagining finding the tallest thing in a completely dark room. Or think about an animal in a snow covered forest; how does that animal the best meal or the best shelter? In other words, without being able to simply see the answer. You can assume your counting computer knows how to:

• report if one number is smaller than, equal to, or larger than another
• report if one color is the same as or different from another 
• make a pile of things
• report how many things are in a pile
• remember a number or a pile

Making Comparisons

Early on in our lives, we learn that some numbers are bigger than others. At this point, it is impossible to say how we do this task. It is just something we know. Computers know this fundamental ordering of numbers as well --- it is "hard-wired" into them when they are created. However, there are many things that we must still figure out how to compare when we encounter them (or perhaps remind ourselves). It is these things for which we can formulate algorithms.

You should describe how to compare the following things:

• volume of two boxes
• density of two oddly shaped things, like a king's crown for example 
• speed of two cars
• value of cost of two differently sized items
• height of two buildings in different cities, or at least not so close that you can see them together
• which of two boxes of different shape completely holds a collection of oddly shaped items
• lung capacity of two people
• alphabetic order of two words (you may assume you know if one letter is alphabetically before another)
• can you think of other interesting comparisons?

For extra credit, describe how to fill a bucket with exactly four gallons of water given only two buckets: one that holds exactly three gallons of water and one that holds exactly five gallons. For maximum credit, you must complete your description before the bomb in the classroom goes off :)