I focused on surface area this week with my juniors in my catch-all-test-prep-this-should-definitely-be-illegal class. (To put my two cents in on forcing students to take Algebra 2 as well as a PSSA prep class… well a post for another time I suppose). The past two weeks we were covering area and perimeter and I was astounded at the lack of understanding. Many misconceptions were evident but the most alarming was the inability to use the test prep formula sheet. For example, many students were unable to identify the triangle on their paper and match it to the triangle on the formula sheet and thus find the correct formula. I thought it might be because they were using a right triangle and the height was measured different, but when the test came and I matched the shapes to their formula sheet I was still surprised at the number of students who could not match the shapes. Thus the test on area and perimeter became a test on something totally different.
Only about 5 students in each class were still struggling with identifying parts of a shape and the rest of the students were starting to get frustrated and bored. I decided to move forward and try to squash area misconceptions during surface area, since we would still continue to use the area formulas for the shapes again and again.
Why I believe this unit worked so effectively had to with the use of scaffolding in their warm-ups, manipulatives, and lots of classwork practice time with limited homework. For each day I focused on two shapes and had the warmup focus on finding the area of the 2-D shapes that would ultimately make up the 3-D solids. For example, for the rectangular solid their warm-up was to find the area of three rectangles that later in the lesson we would put together to build the 3-D solid.
I made sure that for each shape they saw the deconstruction of the solid into their familiar shapes and I had cut out my own nets and taped and colored them to pass around the classroom for further understanding. What captivated the students most was asking them what shapes they believed made up the 3-D solid. For example with the cylinder they all noticed the two circles for the bases but most did not guess that the “middle” was actually a rectangle. When we got to the cone it was pretty cool how excited they were to guess what the 2-D shape would be. I used that as a great moment to say, “This is a funky shape- which is why it has a funky formula.” So the students didn’t really moan and groan at the obnoxious cone formula because they saw (sort of) where it came from.
Finally I made sure to have a practice sheet for the last 15 minutes of class everyday. I wanted students to practice the formulas in front of me and immediately after learning about it. I also read this blog about Results Only Learning Environment and the role of homework. Since homework completion and cheating are two huge obstacles to overcome I decided to focus on classwork and if students needed more time they could complete the rest of the worksheet at home. This way I could monitor who is doing their own work, the struggles they are having as well as ensure they are getting the practice I desire.
Overall I was very pleased with this unit and hoping to follow some of these teaching themes that worked to help me in the Volume Unit I start on Wednesday. All suggestions, resources, and what you’ve done in the past for surface area and volume would be greatly appreciated as well!
mathemagical molly 