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.).

Riding at a Constant Speed focuses primarily on application of ratio and rate reasoning to solve problems. The problem presents Lin riding a bike at a constant speed: 20 miles in 150 minutes. The resource uses students' apply their initial understanding of ratios and rates to solve a real-life problem. The task uses friendly numbers so students can easily develop different solution strategies (unit rate, double number line, table, graph) to solve the problem. While the resource does not explicitly mention it, this task has potential to discuss the different representations and have students make connections among them.

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.

Students are introduced to several types of common medical sensor devices, such as ear and forehead thermometers, glucometers and wrist blood pressure monitors; they use the latter to measure their blood pressure and pulse rates. Students also measure their heights and weights in order to calculate their BMIs (body mass index). Then they use the collected data to create and analyze scatterplots of the different variables to determine if any relationships exist between the measured variables. Discussions about the trends observed and possible health concerns conclude the activity.

Students are introduced to the concepts of graywater and water reuse within households. They calculate the amount of used water a family generates in one day and use a model of home plumbing to find out how much graywater is produced in homes every day. They graph their results and discuss energy efficiency implications. Students are then challenged to find ways to reduce water use within the home.

To get a better understanding of complex networks, students create their own, real social network example by interacting with their peers in the classroom and documenting the interactions. They represent the interaction data as a graph, calculate two mathematical quantities associated with the graph—the degree of each node and the degree distribution of the graph—and analyze how these quantities can be used to infer properties of the social network at hand.

This activity is based on an activity from NASA's Solar Math.  This activity has students analyzing sunspot cycle data.  Students find patterns within the data to explore sunspot cycles.

In this lesson, students learn how adaptations, limiting factors, and predator prey relationships all affect the survival of plants and animals. Predator-prey relationships are simulated in two games, where students record their experiences and display data in story and chart/graph form, and explore the adaptations of animals in terrestrial and aquatic habitats. Extension activities include habitat investigations in natural areas.

Students are introduced to the health risks caused by cooking and heating with inefficient cook stoves inside homes, a common practice in rural developing communities. Students simulate the cook stove scenario and use the engineering design process, including iterative trials, to increase warmth inside a building while reducing air quality problems. Students then collect and graph data, and analyze their findings.

Students analyze dramatic works using graph theory. They gather data, record it in Microsoft Excel and use Cytoscape (a free, downloadable application) to generate graphs that visually illustrate the key characters (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 represent characters in the work and their relative importance to the story). After the analysis, the graphs are further examined to see what the visual depiction of the story in the form of a graph tells readers about the inner workings of the dramatic work. 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 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.

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.

This lesson helps student develop a concrete understanding of the connection between a graph and the situation it models.  Students start by graphing a simple case with a chance to check their work, then move on to more complicated cases.  Students must also answer extenstion questions.  Finally, students create their own situation and can try those created by their peers.  The teacher can view student products throughout and after the activity.

Students measure the effectiveness of water filters in purifying contaminated water. They prepare test water by creating different concentrations of bleach (chlorine-contaminated) water. After passing the contaminated water through commercially available Brita® water filters designed to purify drinking water, students determine the chlorine concentration of the purified water using chlorine test strips and measure the adsorption of chlorine onto activated carbon over time. They graph and analyze their results to determine the effectiveness of the filters. The household active carbon filters used are one example of engineer-designed water purification systems.