Ms. Warburton's Lesson: The Seesaw Method

In this lesson involving mixtures, Ms. Warburton was able to take a concept that seemed complex and difficult, and gave her students two methods to attack and solve the problems. One method is called the “Mixture Picture” and the other is called the “Seesaw Method.” I appreciated her introduction to mixture questions by declaring that “Mixture problems are perhaps the most dreaded type of problem in Algebra 1.” She stated it as very matter of fact, which of course brought a sense of impending doom. She followed this statement by reading a mixture question involving multiple percentages and volumes out loud to the class, in order to further prove how challenging these problems are. It was evident in the students faces and reactions that they were in “done for.” She then used her teaching virtuosity and began to unfold the problem before them. By using a demonstration in which they could see the results and
using simple words like “strong” and “weak” to describe the solutions, she was able to bring the topic down to a more conceptual level. Yet again, the reactions of the students to demonstration made it clear that there was the beginning of understanding. Ms. Warburton took the example question that had previously read aloud and showed her students how to easily organize the information in pictorial form; a graphic organizer of sorts. This is what she referred to as the Mixture Picture. In many instances, a picture is truly worth a thousand words and students tend to have a much easier time making the appropriate mathematical connections if they can “see it.” This method gives them a simple, clear, and easily reproducible way to organize the information given them in a problem and to begin to look at the relationships between the numbers. Placing the desired percentage in the center of the picture and the strong and weak solutions to either side, the students can more easily see the difference in values or “how far away” each solution is from the desired mixture. And by including the individual volume, (known and/or unknown,) of each solution beneath the respective percentages, the organizational structure of the diagram is completed. Often times, the numbers will work out in such a way that students will be able to see the ratios between them and can solve the problem right from this picture. But, as Ms. Warburton stated, the numbers might not always be so easy to work with; in which case, another approach may need to be used. The next method presented by Ms.
Warburton she called the Seesaw Method. This results in an equation that can be used for the more complex problems, (such as when the numbers and ratios don’t work so easily.) She began by sketching a seesaw with different sized people on it and asked how they could be balanced. Several students came up with the (correct) answer. At this point I would suggest to Ms. Warburton that another demonstration or even a manipulative for the students could have been introduced. Having students try to balance two small unequal masses (like 100 grams and 200 grams) on a ruler resting on a simple fulcrum (like a marker) would take only a few minutes, but could be very effective for the students, especially the tactile learners. In any case; she continued by showing that the product of weight and distance from fulcrum for both sides would be equal when the seesaw is balanced. At this point she shows how the same equation can be used for mixtures, revealing how something that seems complex and difficult can become very
simple. The students felt a sense of success by working through what was perceived as a difficult problem. Ms. Warburton masterfully walked them through the emotional spectrum from fear and trepidation to feelings of pride and accomplishment. At the close of the lesson, there was clear evidence of elation by these students, which seemed to be the norm for Ms. Warburton’s class.