Situation 1: You are ordering bulbs online for the next growing season. You have previously worked out how many bulbs you need for a new flowerbed. Online, you discover a company that is offering a 2 for 1 sale. You think, "Why not?" and order twice the number of bulbs planned, reasoning that you'll simply double the size of the flowerbed. Question: Assuming that the larger bed will be similar to the original design, what will be the increase in dimensions from the smaller bed to the larger bed?

Situation 2: You are preparing to cut down a tree in your yard. The tree seems pretty tall, and you don't want to actually fell it until you have a pretty decent estimate of its height. Then you notice that both you and the tree are casting a shadow. Your shadow is 3.5 feet long, the shadow of the tree is 19 feet long. If you are 6 feet tall, how tall is the tree?

Situation 3: The school board has declared that boundaries between schools should be set such that each student goes to the school that is closest to where he/she lives. How should this be accomplished?

Situation 4: You are researching car rental prices, and have found that the same car is offered by two different rental companies. Company 1 (Wrent a Wreck Wrentals) has a daily rate of $29.95 and charges $0.30 per mile, while company 2 (Take a Chance Cars) has a daily rate of $49.95 but only charges $0.10 per mile. If you know that you will drive at most 50 miles in one day, which company is cheaper? Is it different if you drive 140 miles in one day?

Situation 5: A lifeguard at a local beach sees that a swimmer is having difficulty getting in to shore. The swimmer grabs on to a marker buoy and calls for help. Since the lifeguard can run faster than she can swim, how far down the beach should the lifeguard run before entering the surf so as to get to the swimmer in the least amount of time? Assume that the running speed of the lifeguard is 7 meters per second, while her swimming speed is 3 meters per second.

There may be many common elements to these five situations, but the one that is significant for this presentation, is that they can all be modeled using dynamic geometry software such as The Geometer's Sketchpad or Cabri. These programs give us the opportunity to have electronic chalk boards on which to demonstrate geometric concepts. In the lab, these programs allow students to discover and/or review theorems, postulates and definitions. But should these programs be limited to the geometry classroom? Couldn't they also have a place in the elementary, middle, and upper high school classroom as a problem-solving tool?

For convenience, I have chosen to use Geometer's Sketchpad to create my sketches. I have printed each sketch and will include these in a handout, so that you can concentrate on the problem-solving aspects of each sketch. So that each problem can be addressed in a timely fashion, the sketches are finished products. (In other words, you don't get to see me fumble my way through the creation process.) The advantage of saving time will, I hope, outweigh the disadvantage of you, the student, not being able to participate directly in the problem solving experience. My goal is to demonstrate the versatility of these programs in the context of the general classroom as opposed to the geometry classroom alone.