An interactive applet that allows the user to graphically explore the properties of a linear functions. Specifically, it is designed to foster an intuitive understanding of the effects of changing the two coefficients in the function y=ax+b. The applet shows a large graph of a quadratic (ax + b) and has two slider controls, one each for the coefficients a and b. As the sliders are moved, the graph is redrawn in real time illustrating the effects of these variations. Applet can be enlarged to full screen size for use with a classroom projector. This resource is a component of the Math Open Reference Interactive Geometry textbook project at http://www.mathopenref.com.

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.

This course covers the mathematical techniques necessary for understanding of materials science and engineering topics such as energetics, materials structure and symmetry, materials response to applied fields, mechanics and physics of solids and soft materials. The class uses examples from the materials science and engineering core courses (3.012 and 3.014) to introduce mathematical concepts and materials-related problem solving skills. Topics include linear algebra and orthonormal basis, eigenvalues and eigenvectors, quadratic forms, tensor operations, symmetry operations, calculus of several variables, introduction to complex analysis, ordinary and partial differential equations, theory of distributions, and fourier analysis.
Users may find additional or updated materials at Professor Carter's 3.016 course Web site.

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.

In this activity, learners work in groups to determine the mass and volume of four samples: glass marbles, steel washers or nuts, pieces of pine wood, and pieces of PVC pipe. Learners then plot the data points on a large class graph of mass vs. volume to discover that data points for a particular material form a straight line, the slope of which gives the density of the material.

In this activity, students sort 10 types of fruit by tastiness and ease of eating in order to learn how those attributes can be represented on a coordinate plane, and to determine which fruit truly is "best."

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.

Putting a graph on the floor using painters tape students practice translation, rotation, reflection,dilation, by doing these concepts to themselves while standing in the graph.

An interactive applet that allows the user to graphically explore the properties of a quadratic equation. Specifically, it is designed to foster an intuitive understanding of the effects of changing the three coefficients in the function. The applet shows a large graph of a quadratic (ax^2 + bx +c) and has three slider controls, one each for the coefficients a,b and c. As the sliders are moved, the graph is redrawn in real time illustrating the effects of these variations. The roots of the equation are shown both graphically and numerically, including the case where the roots are imaginary. Applet can be enlarged to full screen size for use with a classroom projector. This resource is a component of the Math Open Reference Interactive Geometry textbook project at http://www.mathopenref.com.

A short Quiz on RI.6, with a text from Peter Ferrara's article, "To the Horror of Global Warming Alarmists, Global Cooling is Here" and an image from the wiki of www.globalwarmingart.com. The text's Dale-Chall difficulty level is 9-10, and the Flesch-Kincaid level is 13.4.

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.).

In this video adapted from the Encyclopedia of Physics Demonstrations, learn how plotting the changes in an object's position on a graph can provide information about the object's motion.

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.