In this activity, students explore how trebuchets were used during the Middle Ages to launch projectiles over or through castle walls as well as how they are used today in events such as Punkin’ Chunkin’. Students work as teams of engineers and research how to design and build their own trebuchets from scratch while following a select number of constraints. They test their trebuchets, evaluate their results through several quantitative analyses, and present their results and design process to the class.

Students work as engineers to design and test trebuchets (in this case LEGO® MINDSTORMS® robots) that can launch objects. During the testing stage, they change one variable at a time to study its effect on the outcome of their designs. Specifically, they determine how far objects travel depending on their weights. As students learn about the different components of robot design and the specific function controls, they determine what design features are important for launching objects.

Examines a number of famous trials in European and American history. Considers the salient issues (political, social, cultural) of several trials, the ways in which each trial was constructed and covered in public discussion at the time, the ways in which legal reasoning and storytelling interacted in each trial and in later retellings of the trial, and the ways in which trials serve as both spectacle and a forum for moral and political reasoning. Students have an opportunity to study one trial in depth and present their findings to the class.

This task gives students a chance to explore several issues relating to rigid motions of the plane and triangle congruence. As an instructional task, it can help students build up their understanding of the relationship between rigid motions and congruence.

The purpose of this task is to emphasize the adjective "geometric" in the "geometric" series, namely, that the algebraic notion of a common ratio between terms corresponds to the geometric notion of a repeated similarity transformation.

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.

This task provides a good opportunity for group work and class discussions where students generate and compare equivalent expressions. In class discussion, students should be asked to connect the terms of an expression with quantities shown in the diagram.

This course addresses the design of tribological systems: the interfaces between two or more bodies in relative motion. Fundamental topics include: geometric, chemical, and physical characterization of surfaces; friction and wear mechanisms for metals, polymers, and ceramics, including abrasive wear, delamination theory, tool wear, erosive wear, wear of polymers and composites; and boundary lubrication and solid-film lubrication. The course also considers the relationship between nano-tribology and macro-tribology, rolling contacts, tribological problems in magnetic recording and electrical contacts, and monitoring and diagnosis of friction and wear. Case studies are used to illustrate key points.

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.

In this task students must investigate this conjecture to discover that it does not work in all cases: Pick any two integers. Look at the sum of their squares, the difference of their squares, and twice the product of the two integers you chose. Those three numbers are the sides of a right triangle.

This course describes the large-scale circulation systems of the tropical atmosphere and analyses the dynamics of such systems. Topics include: Radiative-convective equilibrium; the Hadley and walker circulation; monsoons; tropical boundary layers; theory of the response of the tropical atmosphere to localized sea-surface temperature anomalies; intraseasonal oscillations; equatorial waves; El Ni–o/Southern Oscillation; easterly waves; and tropical cyclones.

In this lesson students read a series of documents about the American and Mexican reasons for and against the 1846 U.S.-Mexico War. As they read the documents students identify when the authors employ various foreign policy ideologies such as Manifest Destiny, Racial and Cultural Superiority, and Self Defense. This lesson was designed to be implemented with a Smartboard, but it can be completed without this technology.

Students learn how to identify the major features in a topographical map. They learn that maps come in a variety of forms: city maps, road maps, nautical maps, topographical maps, and many others. Map features reflect the intended use. For example, a state map shows cities, major roads, national parks, county lines, etc. A city map shows streets and major landmarks for that city, such as hospitals and parks. Topographical maps help navigate the wilderness by showing the elevation, mountains, peaks, rivers and trails.

Students work within constraints to construct model trusses and then test them to failure as a way to evaluate the relative strength of different truss configurations and construction styles. Each student group uses Popsicle sticks and hot glue to build a different truss configuration from a provided diagram of truss styles. Within each group, each student builds two exact copies of the team's truss configuration using his/her own construction method, one of which is tested under shear conditions and the other tested under compression conditions. Results are compiled and reviewed as a class to analyze the strength of different types of shapes and construction methods under the two types of loads. Students make and review predictions, and normalize strengths. Teams give brief presentations to recap their decisions, results and analysis.

Students learn about tsunamis, discovering what causes them and what makes them so dangerous. They learn that engineers design detection and warning equipment, as well as structures that that can survive the strong wave forces. In a hands-on activity, students use a table-top-sized tsunami generator to observe the formation and devastation of a tsunami. They see how a tsunami moves across the ocean and what happens when it reaches a coastline. They make villages of model houses to test how different material types are impacted by the huge waves.

There is a 40% chance that the lower ⅓ of the of the Cascadia subduction zone will rupture in the next 50 years, generating a large earthquake and ensuing tsunami. In this project, students will work collaboratively to design and test a model of a vertical evacuation structure. They will evaluate the performance of their models and propose further modifications to improve their design. Students will then make a scale drawing and a model to apply math concepts of scale to designing and creating an ideal model of a vertical evacuation structure. Finally, students will present their findings and proposed final design to their peers and an adult audience. The entire process takes about 2 weeks, and was expanded to include more information and activities with earthquake/tsunami prediction and application of scale. The unit is a great fit for standards within Earth Science (specifically plate tectonics and human mitigation) as well as Engineering and Design standards.

Students are introduced to the concepts of torque, power, friction and gear ratios. Teams modify two robotic LEGO® MINDSTORMS® vehicles by changing their gear ratios, wheel sizes, weight and engine power, while staying within a limit of points to spend on modifications. The robots face each other on a track with a string attaching one to the other. The winning robot, the one with the best adjustments, pulls the other across the line.