Measuring the dimensions of nano-circuits requires an expensive, high-resolution microscope with integrated video camera and a computer with sophisticated imaging software, but in this activity, students measure nano-circuits using a typical classroom computer and (the free-to-download) GeoGebra geometry software. Inserting (provided) circuit pictures from a high-resolution microscope as backgrounds in GeoGebra's graphing window, students use the application's tools to measure lengths and widths of circuit elements. To simplify the conversion from the on-screen units to the real circuits' units and the manipulation of the pictures, a GeoGebra measuring interface is provided. Students export their data from GeoGebra to Microsoft® Excel® for graphing and analysis. They test the statistical significance of the difference in circuit dimensions, as well as obtain a correlation between average changes in original vs. printed circuits' widths. This activity and its associated lesson are suitable for use during the last six weeks of the AP Statistics course; see the topics and timing note below for details.

The Course includes the concept of probability distribution mainly binomial, poisson and normal distribution. In this course students will understood how to solve probability distribution problems using definition and open source software's like GeoGebra and excel

Este material destiná-se a professores que atuam na Educação Superior e visa apresentar uma introdução a práticas educacionais fazendo uso de Recursos Educacionais abertos

Students are introduced to the technology of flexible circuits, some applications and the photolithography fabrication process. They are challenged to determine if the fabrication process results in a change in the circuit dimensions since, as circuits get smaller and smaller (nano-circuits), this could become very problematic. The lesson prepares students to conduct the associated activity in which they perform statistical analysis (using Excel® and GeoGebra) to determine if the circuit dimension sizes before and after fabrication are in fact statistically different. A PowerPoint® presentation and post-quiz are provided. This lesson and its associated activity are suitable for use during the last six weeks of the AP Statistics course; see the topics and timing note for details.

Working as if they are engineers aiming to analyze and then improve data collection devices for precision agriculture, students determine how accurate temperature sensors are by comparing them to each other. Teams record soil temperature data during a class period while making changes to the samples to mimic real-world crop conditions—such as the addition of water and heat and the removal of the heat. Groups analyze their collected data by finding the mean, median, mode, and standard deviation. Then, the class combines all the team data points in order to compare data collected from numerous devices and analyze the accuracy of their recording devices by finding the standard deviation of temperature readings at each minute. By averaging the standard deviations of each minute’s temperature reading, students determine the accuracy of their temperature sensors. Students present their findings and conclusions, including making recommendations for temperature sensor improvements.

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.