Reaching for the Stars
Not that long ago I spent some time at Impact Academy in our Geometry classroom. Our geometry teacher has been working hard to develop a personalized learning approach as a way to leverage the technology. As part of this venture, we have been designing innovative technology-enhanced projects that will provide our students with multiple opportunities to apply their mathematical skills. We endeavor to create interesting and engaging problems that require students to analyze and problem solve in ways that challenge them to go beyond the traditional algorithmic applications of mathematical concepts, and in this case geometry concepts.
This particular project that I observed is called the “Skyscaping.”
The “Skyscraping” is a project designed so that students can explore, learn about and apply 3-dimensional measurements – the challenge being to create a design for a skyscraper. This gives students an opportunity to think about area, volume and surface area of complex shapes. Groups of 3 or 4 students conduct investigations about various types of skyscrapers around the world – including the current tallest building in the world, the Burg Khalifa in Dubai – and make decisions about which architectural features they want to emphasize in their designs: aesthetics, sustainability, height, cost or a combination of the four.
After examining the important techniques of vertical tapering and radial symmetry, groups then begin designing the buildings. Each student is responsible for an individual design and section of the building.
Each section is a combination of at least three basic geometric shapes with the center atrium having no more than a 72-degree radial symmetry, meaning at least a 5-sided pentagonal atrium, and maintaining radial symmetry around the center.
The sections must also logically stack on top of each other using vertical tapering to ensure stability and height needs. Once the hand-drawn designs are made, students then use an on-line architectural application, AutoCad 360, to draw and measure their sections.
At this point, students can begin the process of calculating how big their section and ultimately the entire building will be. Groups are also responsible for calculating an estimate cost for the structure based on location and anticipated building usage.
Groups then create a media file (Google Presentation, PowerPoint, Key Note or other software) for an in-class oral presentation of their findings.
The documentation, including videos of “Skyscrapers 2012” (a visual tour of the current and anticipated tallest buildings in the world) and “MI4: Ghost Protocol” (where Tom Cruise does his own stunt work by jumping and climbing around the Burg Khalifa), can be found at www.ia-geometry.weebly.com under the tab “Skyscraping.” You can also view some of the student presentations under “Group PowerPoint Layout.”