Students analyze their social networks using graph theory. They gather data on their own social relationships, either from Facebook interactions or the interactions they have throughout the course of a day, recording it in Microsoft Excel and using Cytoscape (a free, downloadable application) to generate social network graphs that visually illustrate the key persons (nodes) and connections between them (edges). The nodes in the Cytoscape graphs are color-coded and sized according to the importance of the node (in this activity, nodes are people in students' social networks). After the analysis, the graphs are further examined to see what can be learned from the visual representation. Students gain practice with graph theory vocabulary, including node, edge, betweeness centrality and degree on interaction, and learn about a range of engineering applications of graph theory.

Students are introduced to different ways of displaying visual spectra, including colored "barcode" spectra, like those produced by a diffraction grating, and line plots displaying intensity versus color, or wavelength. Students learn that a diffraction grating acts like a prism, bending light into its component colors.

Students visit second- and fourth-grade classes to measure the heights of older students using large building blocks as a non-standard unit of measure. They also measure adults in the school community. Results are displayed in age-appropriate bar graphs (paper cut-outs of miniature building blocks glued on paper to form bar graphs) enabling a comparison of the heights of different age groups. The activities that comprise this activity help students develop the concepts and vocabulary to describe, in a non-ambiguous way, how heights change as children age. This introduction to graphing provides an important foundation for creating and interpreting graphs in future years.

This activity simulates the extraction of limited, nonrenewable resources from a "mine," so students can experience first-hand how resource extraction becomes more difficult over time. Students gather data and graph their results to determine the peak in resource extraction. They learn about the limitations of nonrenewable resources, and how these resources are currently used.

Engineers create and use new materials, as well as new combinations of existing materials to design innovative new products and technologies—all based upon the chemical and physical properties of given substances. In this activity, students act as materials engineers as they learn about and use chemical and physical properties including tessellated geometric designs and shape to build better smartphone cases. Guided by the steps of the engineering design process, they analyze various materials and substances for their properties, design/test/improve a prototype model, and create a dot plot of their prototype testing results.

In this activity, students will conduct a survey to identify the environmental issues (in their community, their country and the world) for which people are concerned. They will tally and graph the results. Also, students will discuss how surveys are important when engineers make decisions about environmental issues.

Students learn about complex networks and how to use graphs to represent them. They also learn that graph theory is a useful part of mathematics for studying complex networks in diverse applications of science and engineering, including neural networks in the brain, biochemical reaction networks in cells, communication networks, such as the internet, and social networks. Students are also introduced to random processes on networks. An illustrative example shows how a random process can be used to represent the spread of an infectious disease, such as the flu, on a social network of students, and demonstrates how scientists and engineers use mathematics and computers to model and simulate random processes on complex networks for the purposes of learning more about our world and creating solutions to improve our health, happiness and safety.

Students use a LEGO® ball shooter to demonstrate and analyze the motion of a projectile through use of a line graph. This activity involves using a method of data organization and trend observation with respect to dynamic experimentation with a complex machine. Also, the topic of line data graphing is covered. The main objective is to introduce students graphs in terms of observing and demonstrating their usefulness in scientific and engineering inquiries. During the activity, students point out trends in the data and the overall relationship that can be deduced from plotting data derived from test trials with the ball shooter.

The learning of linear functions is pervasive in most algebra classrooms. Linear functions are vital in laying the foundation for understanding the concept of modeling. This unit gives students the opportunity to make use of linear models in order to make predictions based on real-world data, and see how engineers address incredible and important design challenges through the use of linear modeling. Student groups act as engineering teams by conducting experiments to collect data and model the relationship between the wall thickness of the latex tubes and their corresponding strength under pressure (to the point of explosion). Students learn to graph variables with linear relationships and use collected data from their designed experiment to make important decisions regarding the feasibility of hydraulic systems in hybrid vehicles and the necessary tube size to make it viable.

Students use latex tubes and bicycle pumps to conduct experiments to gather data about the relationship between latex strength and air pressure. Then they use this data to extrapolate latex strength to the size of latex tubing that would be needed in modern passenger sedans to serve as hybrid vehicle accelerators, thus answering the engineering design challenge question posed in the first lesson of this unit. Students input data into Excel spreadsheets and generate best fit lines by the selection of two data points from their experimental research data. They discuss the y-intercept and slope as it pertains to the mathematical model they generated. Students use the slope of the line to interpret the data collected. Then they extrapolate with this information to predict the latex dimensions that would be required for a full-size hydraulic accumulator installed in a passenger vehicle.

Students learn about slope, determining slope, distance vs. time graphs through a motion-filled activity. Working in teams with calculators and CBL motion detectors, students attempt to match the provided graphs and equations with the output from the detector displayed on their calculators.

After conducting the associated activity, students are introduced to the material behavior of elastic solids. Engineering stress and strain are defined and their importance in designing devices and systems is explained. How engineers measure, calculate and interpret properties of elastic materials is addressed. Students calculate stress, strain and modulus of elasticity, and learn about the typical engineering stress-strain diagram (graph) of an elastic material.

Learn about position, velocity, and acceleration graphs. Move the little man back and forth with the mouse and plot his motion. Set the position, velocity, or acceleration and let the simulation move the man for you.

Students come to see the exponential trend demonstrated through the changing temperatures measured while heating and cooling a beaker of water. This task is accomplished by first appealing to students' real-life heating and cooling experiences, and by showing an example exponential curve. After reviewing the basic principles of heat transfer, students make predictions about the heating and cooling curves of a beaker of tepid water in different environments. During a simple teacher demonstration/experiment, students gather temperature data while a beaker of tepid water cools in an ice water bath, and while it heats up in a hot water bath. They plot the data to create heating and cooling curves, which are recognized as having exponential trends, verifying Newton's result that the change in a sample's temperature is proportional to the difference between the sample's temperature and the temperature of the environment around it. Students apply and explore how their new knowledge may be applied to real-world engineering applications.

The purpose of this lesson is to teach students about the three dimensional Cartesian coordinate system. It is important for structural engineers to be confident graphing in 3D in order to be able to describe locations in space to fellow engineers.

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.

Students observe four different classroom setups with objects in motion (using toy cars, a ball on an incline, and a dynamics cart). At the first observation of each scenario, students sketch predicted position vs. time and velocity vs. time graphs. Then the classroom scenarios are conducted again with a motion detector and accompanying tools to produce position vs. time and velocity vs. time graphs for each scenario. Students compare their predictions with the graphs generated by technology and discuss their findings. This lesson requires assorted classroom supplies, as well as motion detector technology.

Building on their understanding of graphs, students are introduced to random processes on networks. They walk through an illustrative example to see how a random process can be used to represent the spread of an infectious disease, such as the flu, on a social network of students. This demonstrates how scientists and engineers use mathematics to model and simulate random processes on complex networks. Topics covered include random processes and modeling disease spread, specifically the SIR (susceptible, infectious, resistant) model.

Student teams assign importance factors, called "desirability points," the rock properties found in the previous lesson/activity in order to mathematically determine the overall best rocks for building caverns within. They learn the real-world connections and relationships between the rock and the important engineering properties for designing and building caverns (or tunnels, mines, building foundations, etc.).

Students explore whether rooftop gardens are a viable option for combating the urban heat island effect. Can rooftop gardens reduce the temperature inside and outside houses? Teams each design and construct two model buildings using foam core board, one with a "green roof" and the other with a black tar paper roof. They measure and graph the ambient and inside building temperatures while under heat lamps and fans. Then students analyze the data and determine whether the rooftop gardens are beneficial to the inhabitants.