Thinking MEANingfully:
The Sweet Tooth Candy Company
The First 100 Days of School !!
Exploring Fraction Concepts
with the Geoboard
The setup for this problem is excellent for younger students. Last friday the Sweet Tooth Candy Company ran into a quality control problem and the amount of candy in each bag is no longer constant. The students of the class are given bags of candy and asked to first estimate and then count the number of pieces of candy in their bags. Next the students are asked to go about the class and compare with other students and make the amount of candy in each bag equal. This helped bring home the idea that the average is really the leveling off of the bigger and smaller bags. The students are asked to keep track of their exchanges, and eventually graph this information. The goal of this activity is for the participants to see that these adjusted bags are a very good representation of the mean. Also, if the students graph the number of pieces of candy that were in the bags at the beginning, it is possible to show another representation of the mean as a line through the graph.
Above the line are enough entries to fill the empty spots below it. Many of the Measuring Up teachers used this activity in their own classes and had their students not only graph the initial amounts of candy in the bags, but then placed unifix blocks over their graph.
The students were given a number chart listing the numbers from 1 to 100 in squares, and were asked to start counting the squares by threes, and color in the squares.
Next the participants were asked to find patterns in the chart they filled out. Then they discussed their patterns with the others in their group. This discussion is very important for the participants, and finally the students. To recognize the similarities and differences in the patterns that different people find is the goal. This also helps them try to verbalize their mathematical thoughts. Then they were asked to explain if these patterns will continue on further if the chart perhaps went up to 120. Finally, they were asked to think about what would happen if they had counted by six instead of three.
The Geoboards are available for various mathematical, conceptual representations. The particular case which was practiced as well as observed on a video was fractions. The number 1/8 was used by the project participants. The video looked at 1/2 with elementary school students. There are many different ways that these fractions can be shaped by using rubber bands to single off sections of the Geoboard. It gives the students the understanding that area equality does not necessarily mean congruence, that is the areas are the same size, but the figures look very different.
