Scaling, Go Figure!
Students see what happens to lengths, perimeters and areas when scaling. This scaling example shows doubling and tripling.
Students learn how different characteristics of shapes—side lengths, perimeter and area—change when the shapes are scaled, either enlarged or reduced. Student pairs conduct a “scaling investigation” to measure and calculate shape dimensions (rectangle, quarter circle, triangle; lengths, perimeters, areas) from a bedroom floorplan provided at three scales. They analyze their data to notice the mathematical relationships that hold true during the scaling process. They see how this can be useful in real-world situations like when engineers design wearable or implantable biosensors. This prepares students for the associated activity in which they use this knowledge to help them reduce or enlarge their drawings as part of the process of designing their own wearables products. Pre/post-activity quizzes, a worksheet and wrap-up concepts handout are provided.
A hot engineering trend is the design of “wearables”—smart electronic devices and sensors that are embedded into clothing, accessories and implants to detect physical activity, blood sugar levels, sweat composition and/or other quantifiables. At Michigan State University, mechanical engineer Peter Lillehoj’s lab is creating a self-powered sewn sensor patch to provide ways for diabetics to monitor blood sugar (glucose) without finger pricks and for other purposes such as monitoring wound healing. To do this, robust, flexible electrochemical sensors are embroidered onto medical-grade gauze and placed on wounds to make quick biomarker measurements. In tandem, materials engineers research and invent new materials, even tissues, fabrics and threads, with the desired properties for specific applications. In this activity, students learn about dimensions and scale, which they apply in the associated activity when they draw their designs for prototype wearables.
After this lesson, students should be able to:
- Explain how the perimeters and areas of shapes change when they are enlarged and reduced.
- Enlarge or reduce the sizes of shapes given specific scale factors.
- Solve problems involving perimeter and area.