Help students understand scale factor by having them re-create their own scale drawing.  We have some images cut out that students can use, or they can bring their own logo/image that they brought from home.  We have students follow the step by step google slide show and break it down as follows:Day 1: Create grid on student's image and determine scale.  Start on grid lines which are on a large white piece of paper and based on the selected scale factor.Day 2: Complete grid lines on paper and model how students are to re-create their drawing one square at a time.  It may also be a good idea to have students label rows and columns (A, B, C... and 1, 2, 3...) so they can easily reference each square.  Students may be ready to start drawing.Day 3 & 4: Work Days-spent recreating their drawing while representing the scale factor and coloring/painting when completed.Day 5: Present

Students build scale models of objects of their choice. In class they measure the original object and pick a scale, deciding either to scale it up or scale it down. Then they create the models at home. Students give two presentations along the way, one after their calculations are done, and another after the models are completed. They learn how engineers use scale models in their designs of structures, products and systems. Two student worksheets as well as rubrics for project and presentation expectations and grading are provided.

Challenged with a hypothetical engineering work situation in which they need to figure out the volume and surface area of a nuclear power plant’s cooling tower (a hyperbolic shape), students learn to calculate the volume of complex solids that can be classified as solids of revolution or solids with known cross sections. These objects of complex shape defy standard procedures to compute volumes. Even calculus techniques depend on the ability to perform multiple measurements of the objects or find functional descriptions of their edges. During both guided and independent practice, students use (free GeoGebra) geometry software, a photograph of the object, a known dimension of it, a spreadsheet application and integral calculus techniques to calculate the volume of complex shape solids within a margin of error of less than 5%—an approach that can be used to compute the volumes of big or small objects. This activity is suitable for the end of the second semester of AP Calculus classes, serving as a major grade for the last six-week period, with students’ project results presentation grades used as the second semester final test.