Student groups are challenged to program robots with light sensors to follow a black line. Learning both the logic and skills behind programming robots for this challenge helps students improve their understanding of how robots "think" and widens their appreciation for the complexity involved in programming LEGO® MINDSTORMS® NXT robots to do what appears to be a simple task. They test their ideas for approaches to solve the problem and ultimately learn a (provided) working programming solution. They think of real-world applications for line-follower robots that use sensor input. A PowerPoint® presentation and pre/post quizzes are provided.

An interactive applet and associated web page that demonstrate the definition of a line segment. The applet presents two points and a line that links them. As the points are dragged the line moves accordingly. See also the entries for line and ray. 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.

An interactive applet and associated web page that show the definition of a line segment in coordinate geometry. The applet has two points that the user can drag. The two points define a line segment, one for each endpoint. The grid, axis pointers and coordinates can be turned on and off. The applet can be printed as it appears on the screen to make handouts. The web page has a full definition of a line segment when the coordinates of the points defining it are known, and has links to other pages relating to coordinate geometry. 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 groups act as aerospace engineering teams competing to create linear equations to guide space shuttles safely through obstacles generated by a modeling game in level-based rounds. Each round provides a different configuration of the obstacle, which consists of two "gates." The obstacles are presented as asteroids or comets, and the linear equations as inputs into autopilot on board the shuttle. The winning group is the one that first generates the successful equations for all levels. The game is created via the programming software MATLAB, available as a free 30-day trial. The activity helps students make the connection between graphs and the real world. In this activity, they can see the path of a space shuttle modeled by a linear equation, as if they were looking from above.

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.

An interactive applet and associated web page that demonstrate a bisector of a line segment. The applet shows a fixed line segment and another line that bisects it. The second line's endpoints can be dragged, but the line adjusts itself so that it always bisects the fixed line. 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.

An interactive applet and associated web page that show the definition of a line in coordinate geometry. The applet has two points that the user can drag. The two points define a line, and the user can see how the line changes when the points are moved. The grid, axis pointers and coordinates can be turned on and off. The applet can be printed as it appears on the screen to make handouts. The web page has a full definition of a line when the coordinates of the points defining it are known, and has links to other pages relating to coordinate geometry. 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.

An interactive applet and associated web page that demonstrate how to find the midpoint of a line segment when the coordinates of the endpoints are given. The applet has two points on a Cartesian plane. As the user drags either point it continuously recalculates the midpoint of the line segment defined by them. The midpoint is shown both on the plane and as a continuously changing formula. The grid, axis pointers and coordinates can be turned on and off. The midpoint calculation can be turned off to permit class exercises and then turned back on the verify the answers. The applet can be printed as it appears on the screen to make handouts. The web page has a full description of the method for finding the midpoint, a worked example and has links to other pages relating to coordinate geometry. 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.

This comprehensive site offers art lessons and activities at a wide range of levels:
- PreK-K
- Grades 1-2
- Grades 3-5
- Grades 6-8
- Grades 9-12
- College/University

An interactive applet and associated web page that demonstrate the concept of parallel lines. The applet shows two lines, one of which has draggable endpoints. As the line is changed by dragging them, the other line changes to remain parallel to it. 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.

An interactive applet and associated web page that demonstrate the properties of parallel lines in coordinate geometry. The applet presents two lines, each defined by a pair of draggable points. If they are parallel the slopes are the same and the applet adds the parallel arrow marks to them. The slope of each line is continuously recalculated and the case of vertical lines (with undefined slope) is handled correctly. The is a software 'detent' that snaps the lines to parallel if they are close to it. The grid, axis pointers and coordinates can be turned on and off. The slope calculation can be turned off to permit class exercises and then turned back on the verify the answers. The applet can be printed as it appears on the screen to make handouts. The web page has a full description of the method for determining if lines are parallel, a worked example and has links to other pages relating to coordinate geometry. 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.

An interactive applet and associated web page that demonstrate the concept of 'perpendicular'. The applet presents two intersecting line segments, one initially at right angles to the other. As you drag the end points of the line segments a message and the right-angle mark at the intersection tell if it is currently perpendicular. The goal is to show what a right angle 'looks like'. 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.

An interactive applet and associated web page that demonstrate the perpendicular bisector of a line segment. The applet shows a fixed line and another moveable one that bisects it. As you drag either end of it, it is seen that only when they are perpendicular to each other is the definition valid. 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.

An interactive applet and associated web page that show how to determine of one line is perpendicular to another in coordinate geometry. The principle used is that if two lines a re perpendicular to each other the slope of one is the negative reciprocal of the other. The applet shows to lines that the user can move. The slopes are continuously calculated as you drag them, and if the they are parallel they change color. The calculation is shown on screen updated continuously as you drag. The grid, axis pointers and coordinates can be turned on and off. The calculation display can be turned off to permit class exercises and then turned back on the verify the answers. The applet can be printed as it appears on the screen to make handouts. The web page has a full description of the concept of perpendicularity, a worked example and has links to other pages relating to coordinate geometry. 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.

An interactive applet and associated web page that demonstrate the definition of a ray. The applet presents one point and a line that goes from that point off to infinity. As the point is dragged the line moves but it is never possible to reveal the other line end. See also the entries for line segment and line. 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.

An interactive applet and associated web page that demonstrate the slope (m) of a line. The applet has two points that define a line. As the user drags either point it continuously recalculates the slope. The rise and run are drawn to show the two elements used in the calculation. The grid, axis pointers and coordinates can be turned on and off. The slope calculation can be turned off to permit class exercises and then turned back on the verify the answers. The applet can be printed as it appears on the screen to make handouts. The web page has a full description of the concept of slope, a worked example and has links to other pages relating to coordinate geometry. 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.

An interactive applet and associated web page that demonstrate the transversal, a line that crosses two other (usually parallel) lines. The applet shows two lines that are initially parallel, and a transversal line. All eight angles thus formed are shown. As you drag the transversal end points, you can see that the angles form congruent, supplementary and complementary sets. If you move one of the parallel lines to make it non-parallel, you can see that these angles lose some of their relationship with each other. 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.

An interactive applet and associated web page that show the definition of a vertical line in coordinate geometry. The applet has two points that the user can drag which define a line. The line flagged when it is vertical (slope=undefined). The grid, details and coordinates can be turned on and off. The applet can be printed exactly as it appears on the screen to make handouts. The web page has a discussion on how to test for vertical and has links to other pages relating to coordinate geometry. 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 the value of writing and art in science and engineering. They acquire vocabulary that is appropriate for explaining visual art and learn about visual design principles (contrast, alignment, repetition and proximity) and elements (lines, color, texture, shape, size, value and space) that are helpful when making visual aids. A PowerPoint(TM) presentation heightens students' awareness of the connection between art and engineering in order to improve the presentation of results, findings, concepts, information and prototype designs. Students also learn about the science and engineering research funding process that relies on effective proposal presentations, as well as some thermal conductivity / heat flow basics including the real-world example of a heat sink which prepares them for the associated activity in which they focus on creating diagrams to communicate their own collected experimental data.