Chocolate Bar Saves the Day
The problem we were assigned in the mechanical engineering class seemed quite simple. Using two yardsticks and five weights, we were supposed to determine the weight of each of the weights, and then we needed to attach one of the yard sticks to the table like a diving board and measure how far the end was from the floor each time we hung one of the weights from it. However, there were two catches. We had to change the inches in the distance measurement to centimeters and we had to calculate the weight of each of the weights because these figures were not provided.
The first problem was not too difficult to solve. As long as someone in the group knew either the number of feet in a mile or the number of centimeters per inch, we could use division or multiplication to get our answers.
The second problem proved to be more challenging. But we were given another tool to assist us in finding its solution -- a pure chocolate Hershey's candy bar? Amazingly, this proved to be enough.
First, the students, who had been placed in groups, noted that the candy bar weighed 2.6 ounces. Next, various forms of scales were tried using the candy bar, the weights, and one of the yardsticks. One of the ways that groups finally reached the solution was by using a yard stick as a lever. It was balanced on a large weight, kind of like a seesaw. The candy bar was placed on one end and a weight was placed on the other. Then either the candy bar or the weight was moved toward the center. Next, the distance between the object that was furthest from the center was put over the distance of the object that was closest. The closest object was the heavier. Next, we figured out what fraction of the candy bar's weight or how many times its weight the ratio was. After that, it was all basic multiplication.
To get the distance of the end of the yardstick from the floor when a weight was put on it, we simply used the other yardstick to measure the distance and converted the distance to centimeters.
The problem was interesting and challenging, and although not everyone figured out how to solve it or did the mathematics correctly, everyone was on the right track.