The Largest Container

A vod presentation by Annenberg Media, Learner.org, by Suzanne Duncan a 7th and 8th grade class discusses length, width, and height of volume of a rectangular prism and area in a container.  shows a lesson “The Largest Container.”

Moving her arms in the air, Ms. Duncan defines the volume as a cylinder as a circle moving through space (height). Maximizing the idea of surface area and volume she asked the students to design the largest area possible out of a sheet of paper. What elements come to mind? Volume. Surface area. Once students had a possible solution they were encouraged to flatten out their shape, and write out the dimensions, and their computation of surface area and volume (so their thinking doesn’t get lost).

Causes for intervention in helping students correct for computational errors: 1) running out of time in the lesson, (stop where you are and move to the next phase), 2) adjusting to individual needs and learning dispositions. 3) redirect after students have had the opportunity to explore and discover on their own, preferably through small group engagement and whole class sharing.

As the topic of volume and formulas is too advanced for a 2/3 split classroom, I can restructure this lesson for my students by modeling and constructing a cube and a rectangle from a blank sheet of paper. An essential question may offer, “How many sides are in a cube?” Can you prove it? Can you build a cube? Sharing the many different possibilities in a class poster can encourage discussion and knowledge transfer. I can introduce vocabulary of length, width and height and touch upon concept of surface area.

Ms. Duncan holds a strong belief that mathematics is for all students. Moving from teaching a select few, who either understood the concepts or didn’t, to reaching and teaching all students, gave Ms. Duncan a sense of pride and accomplishment. Re-charging her batteries at the end of a 15 year career, she believes today that all students are naturally gifted learners. According to Gardner (1993), student intelligences can be categorized as follows: Verbal-linguistic (word smart), Visual-spatial (picture smart), Musical-rhythmic (music smart), Body-kinesthetic (body smart),  Interpersonal (people smart), Intrapersonal (self smart), Naturalist (nature smart). Considering the multiplicities of how all people learn, an important goal of education is to apply knowledge outside of school in the social and cultural settings of our greater life.