Students learn about regular polygons and the common characteristics of regular polygons. They relate their mathematical knowledge of these shapes to the presence of these shapes in the human-made structures around us, especially trusses. Through a guided worksheet and teamwork, students explore the idea of dividing regular polygons into triangles, calculating the sums of angles in polygons using triangles, and identifying angles in shapes using protractors. They derive equations 1) for the sum of interior angles in a regular polygon, and 2) to find the measure of each angle in a regular n-gon. This activity extends students’ knowledge to engineering design and truss construction. This activity is the middle step in a series on polygons and trusses, and prepares students for the Polygon and Popsicle Trusses associated activity.

Students learn about the fundamental strength of different shapes, illustrating why structural engineers continue to use the triangle as the structural shape of choice. Examples from everyday life are introduced to show how this shape is consistently used for structural strength. Along with its associated activity, this lesson empowers students to explore the strength of trusses made with different triangular elements to evaluate the various structural properties.

Students learn about and use a right triangle to determine the width of a "pretend" river. Working in teams, they estimate of the width of the river, measure it and compare their results with classmates.

Students investigate the relationships between angles and side lengths in right triangles with the help of materials found in the classroom and a mobile device. Using all or part of a meter stick or dowel and text books or other supplies, students build right triangles and measure the angles using a clinometer application on an Android® (phone or tablet) or iOS® device (iPhone® or iPad®). Then they are challenged to create a triangle with a given side length and one angle. The electronic device is used to measure the accuracy of their constructions.

This lesson focuses on ultrasound wavelengths and how sound frequencies are used by engineers to help with detection of specific distances to or in materials. Students gain an understanding about how ultrasonic waves are reflected and refracted. Students also see how ultrasound technology is used in medical devices. The activity following this lesson allows students to test their knowledge by using the Sunfounder Ultrasonic sensor and Arduino Mega Microcontroller.

This video is meant to be a fun, hands-on session that gets students to think hard about how machines work. It teaches them the connection between the geometry that they study and the kinematics that engineers use -- explaining that kinematics is simply geometry in motion. In this lesson, geometry will be used in a way that students are not used to. Materials necessary for the hands-on activities include two options: pegboard, nails/screws and a small saw; or colored construction paper, thumbtacks and scissors. Some in-class activities for the breaks between the video segments include: exploring the role of geometry in a slider-crank mechanism; determining at which point to locate a joint or bearing in a mechanism; recognizing useful mechanisms in the students' communities that employ the same guided motion they have been studying.

Students learn how to quickly and efficiently interpret graphs, which are used for everyday purposes as well as engineering analysis. Through a practice handout completed as a class and a worksheet completed in small groups, students gain familiarity in talking about and interpreting graphs. They use common graph terminology such as independent variable, dependent variable, linear data, linear relationship and rate of change. The equation for calculating slope is explained. The focus is on students becoming able to clearly describe linear relationships by using the language of slope and the rate of change between variables. At lesson end, students discuss the relationship between variables as presented by the visual representation of a graph. Then they independently complete a homework handout.

Learn how to add vectors. Drag vectors onto a graph, change their length and angle, and sum them together. The magnitude, angle, and components of each vector can be displayed in several formats.

Learn how to add vectors. Drag vectors onto a graph, change their length and angle, and sum them together. The magnitude, angle, and components of each vector can be displayed in several formats.

For this maker challenge, students become biomedical engineers who design, create, and test a medical device that measures a patient’s pulse using a microcontroller, LED, and light sensor. Students use data collected from the device they build to determine how to best visualize the results, so that a doctor can view the patient’s pulse on the computer screen. During the challenge, students learn about basic coding, the capabilities of microcontrollers, how sensors gather data, how the human circulatory system works, and how to plot real data. Finally, students are challenged to make their systems portable so that they create wearable health technology. This is a great project for a high school senior design team project.

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.

Prepared with pre-algebra or algebra 1 classes in mind, this module leads students through the process of graphing data and finding a line of best fit while exploring the characteristics of linear equations in algebraic and graphic formats. Then, these topics are connected to real-world experiences in which people use linear functions. During the module, students use these scientific concepts to solve the following hypothetical challenge: You are a new researcher in a lab, and your boss has just given you your first task to analyze a set of data. It being your first assignment, you ask an undergraduate student working in your lab to help you figure it out. She responds that you must determine what the data represents and then find an equation that models the data. You believe that you will be able to determine what the data represents on your own, but you ask for further help modeling the data. In response, she says she is not completely sure how to do it, but gives a list of equations that may fit the data. This module is built around the legacy cycle, a format that incorporates educational research feindings on how people best learn.

Students collect a large set of data (approximately 60 sets) of individual student’s water use and learn how to use spreadsheets to graph the data and find mean, median, mode, and range. They compared their findings to the national average of water use per person per day and use it to evaluate how much water a municipality would need in the event of a recovery from a water shutdown. This analysis activity introduces students to the concept of central tendencies and how to use spreadsheets to find them.

This set of problems for Linear Algebra in the open-source WeBWorK mathematics platform was created under a Round Eleven Mini-Grant for Ancillary Materials Creation. The problems were created for an implementation of the CC-BY Lyrix open textbook A First Course in Linear Algebra. Also included as an additional file are the selected and modified Lyryx Class Notes for the textbook.

Topics covered include:

Linear Independence
Linear Transformations
Matrix of a Transformation
Isomorphisms
Eigenvalues and Eigenvectors
Diagonalization
Orthogonality

These open-source mathematics homework problems are programmed for the WeBWorK mathematics platform and correspond to chapters in OpenStax Calculus Volume I. They were created through a Round Eight Textbook Transformation Grant.

These open-source mathematics homework problems are programmed for the WeBWorK mathematics platform and correspond to chapters in OpenStax Introductory Statistics. They were created through a Round Eight Textbook Transformation Grant.

Students apply their knowledge of scale and geometry to design wearables that would help people in their daily lives, perhaps for medical reasons or convenience. Like engineers, student teams follow the steps of the design process, to research the wearable technology field (watching online videos and conducting online research), brainstorm a need that supports some aspect of human life, imagine their own unique designs, and then sketch prototypes (using Paint®). They compare the drawn prototype size to its intended real-life, manufactured size, determining estimated length and width dimensions, determining the scale factor, and the resulting difference in areas. After considering real-world safety concerns relevant to wearables (news article) and getting preliminary user feedback (peer critique), they adjust their drawn designs for improvement. To conclude, they recap their work in short class presentations.

Students learn about infrared energy and how it is used to sense the surrounding environment. They review where infrared falls on the electromagnetic spectrum and learn how infrared sensors work, as well as various ways engineers and scientists create and apply infrared technology to study science and collect information for security, communications, medical, research and other purposes. Pre/post-quizzes and a take-home assignment are provided. Learning the concepts prepares students to conduct the associated activity in which they design and program Arduino-controlled robots that use IR sensors to follow a line and make designated stops, much like the automated guided vehicles used in industry and commerce.

Students first explore different materials to see what types reduce the most amount of sound when placed in a box. Each group is assigned a different material and they fill their box with that specific material. Students measure the sound level of a tone playing from inside the box using a decibel reader from outside the box. Students share this data with the class and analyze which types of materials absorb the most sound and which reflect the most sound.