step into my classroom: pre-algebra at ECA, quarter three

My pre-algebra classes have been moving along at a steady pace since Christmas break. In an attempt to solidify some concepts for them during third quarter I relied on several projects to give them a chance to spread their wings and apply the skills they've been learning.

The eighth graders began quarter three with a rather complex unit on geometry and measurement. We relearned the names of the geometric solids, then learned how to find the surface area and volume of each. For some this was a very challenging chapter, as not every student is strong in visual-spatial skills. I had them build each figure out of paper to help them make the connection between a flat, two-dimensional shape and a three-dimensional shape.

Upon finishing that unit they completed a fun project in which they were the owners of an ice cream cone factory and had to make some decisions about what kind of cones to produce and sell. They were given a set of figures to work with and then had to use the formulas for volume and lateral surface area to investigate the affect height and diameter have on the end results. Finally, they had to design the ultimate ice cream cone and explain, mathematically, why it was the ideal cone. Some chose their cones based on volume and how much ice cream it could hold, while others tried to choose a surface area that would facilitate the perfect "cream-to-crunch" ratio. They summarized their work and conclusions in poster format and added some fun color and drawings to give it some flair. Who says math has to be all numbers?

The next unit took us in a totally opposite direction - data and probability! Another chapter that came easier for some, but was more challenging for those who struggle with critical thinking. After learning all the ins and outs of data collection, sample types, and bias, the 8th graders were set loose on the student population of ECA to conduct a survey. They had to write two unbiased questions, one that would require a categorical reply and one for numerical. They had to explain how they would randomly select 30 students from our 1-12 school. Some just put all the name in a hat while others did a stratified approach - either separating them by gender, grade level, or "school level" (elementary, middle, and high). After choosing the appropriate data displays they had to analyze their results and determine whether they had accurately represented the entire population. They also had to make some suggestions as to why the results turned out the way they did - and I was quite impressed with some of their ideas. One student's question was, "How many siblings do you have?" and she made the observation that many of her randomly selected participants were actually siblings with each other, which skewed her results significantly.

Finally, we did a fun probability activity on St. Patrick's Day - partly as an excuse for me to give them candy and partly as a chance for them to once again demonstrate and solidify the concepts we'd been studying. The students were given a random mixture of Skittles and M&M's, and after taking inventory of their candies they had to determine the probability of various events.

We had just learned how to find the probability of disjoint, overlapping, and complementary events. So, they had to write three examples of each, then find the probability of each example they'd written. The next day, they corrected their own work by presenting their problems for the rest of the class to solve.

Overall, third quarter was a challenging, but engaging time for the eighth graders. Hopefully something from this quarter with stick with them!