Student groups use a "real" 3D coordinate system to plot points in space. Made from balsa wood or wooden dowels, the system has three axes at right angles and a plane (the XY plane) that can slide up and down the Z axis. Students are given several coordinates and asked to find these points in space. Then they find the coordinates of the eight corners of a box/cube with given dimensions.

Using examples from anthropology and sociology alongside classical and contemporary social theory, this course explores the nature of dominant and subordinate relationships, types of legitimate authority, and practices of resistance. The course also examines how we are influenced in subtle ways by the people around us, who makes controlling decisions in the family, how people get ahead at work, and whether democracies, in fact, reflect the “will of the people.”

Students practice human-centered design by imagining, designing and prototyping a product to improve classroom accessibility for the visually impaired. To begin, they wear low-vision simulation goggles (or blindfolds) and walk with canes to navigate through a classroom in order to experience what it feels like to be visually impaired. Student teams follow the steps of the engineering design process to formulate their ideas, draw them by hand and using free, online Tinkercad software, and then 3D-print (or construct with foam core board and hot glue) a 1:20-scale model of the classroom that includes the product idea and selected furniture items. Teams use a morphological chart and an evaluation matrix to quantitatively compare and evaluate possible design solutions, narrowing their ideas into one final solution to pursue. To conclude, teams make posters that summarize their projects.

The Special Theory of Relativity is a theory of classical physics that was developed at the end of the nineteenth century and the beginning of the twentieth century. It changed our understanding of older physical theories such as Newtonian Physics and led to early Quantum Theory and later the Theory of General Relativity. Special Relativity is one of the foundation blocks of physics.

This book will introduce the reader to, perhaps, the most profound discovery of the twentieth century and the modern world: the universe has at least four dimensions.

Playing the role of engineers in collaborations with the marketing and production teams in a chocolate factory, students design a container for a jumbo chocolate bar. The projects constraints mean the container has to be a regular trapezoidal prism. The design has to optimize the material used to construct the container; that is, students have to find the dimensions of the container with the maximum volume possible. After students come up with their design, teams present a final version of the product that includes creative branding and presentation. The problem-solving portion of this project requires students to find a mathematical process to express the multiple variables in the prism’s volume formula as a single variable cubic polynomial function. Students then use technology to determine the value for which this function has a maximum and, with this value, find the prism’s optimal dimensions.

This OLogy activity uses the traditional Japanese art of paper-folding to help kids understand dimensions. The activity begins with a brief introduction to both dimensions and origami. The kids are then given instructions, included as printable PDFs, for morphing 2D paper into 3D models (a simple box and a water bomb).The activity ends with an illustrated look at dimensions, from the zero dimensions of a point to the fourth dimension of time.

Students practice the ability to produce clear, complete, accurate and detailed design drawings through an engineering design challenge. Using only the specified materials, teams are challenged to draw a design for a wind-powered car. Then, they trade engineering drawings with another group and attempt to construct the model cars in order to determine how successfully the original design intentions were communicated through sketches, dimensions and instructions.

Created for a first-year university course, this linear algebra textbook takes an unusual approach: it introduces vector spaces at the outset and deals with linear systems only after a thorough introduction to vector spaces. This approach is based on the authors' experience over the past 25 years that students often need more time to master vector spaces while traditional textbooks relegate the topic to the end of the course. In this way, these new notions at the heart of linear algebra that are often considered abstract and difficult in an introductory course can then be used in the rest of the course as well as in different contexts.

Beavers are generally known as the engineers of the animal world. In fact the beaver is MIT's mascot! But honeybees might be better engineers than beavers! And in this lesson involving geometry in interesting ways, you'll see why! Honeybees, over time, have optimized the design of their beehives. Mathematicians can do no better. In this lesson, students will learn how to find the areas of shapes (triangles, squares, hexagons) in terms of the radius of a circle drawn inside of these shapes. They will also learn to compare those shapes to see which one is the most efficient for beehives. This lesson also discusses the three-dimensional shape of the honeycomb and shows how bees have optimized that in multiple dimensions. During classroom breaks, students will do active learning around the mathematics involved in this engineering expertise of honeybees. Students should be conversant in geometry, and a little calculus and differential equations would help, but not mandatory.