An interactive applet and associated web page that demonstrate the optical properties of elliptical mirrors. Rays that pass through one focus of an ellipse always a reflected so they pass through the other focus. The ellipse can be resized by dragging, and light rays change to show that this is always true. The web page also has links to other pages defining the various properties of an ellipse and to some ellipse constructions. 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 use simple materials to design an open spectrograph so they can calculate the angle light is bent when it passes through a holographic diffraction grating. A holographic diffraction grating acts like a prism, showing the visual components of light. After finding the desired angles, students use what they have learned to design their own spectrograph enclosure.

An interactive applet and associated web page that demonstrate the equation of a line in point-slope form. The user can move a slider that controls the slope, and can drag the point that defines the line. The graph changes accordingly and equation for the line is continuously recalculated with every slider and / or point move. The grid, axis pointers and coordinates can be turned on and off. The equation 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 the equation of a line in point - slope form, 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 equation of a line in coordinate geometry. The equation is in the form y=mx+b. The user can move two sliders that control a and b. The graph changes accordingly and equation for the line is continuously recalculated with every slider move. The grid, axis pointers and coordinates can be turned on and off. The equation 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 the equation of a line, 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 equiangular triangles (all interior angles congruent). The applet presents an equiangular triangle where the user can drag any vertex. As the vertex is dragged, the others move automatically to keep the triangle equiangular. The angles and side lengths are updated continuously to show that the all interior angles are always congruent. 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 have the definition and meaning of 'equidistant' as applied to points. The applet shows to points and another that is equidistant from them no matter how you drag them around. User can also turn on the locus of the equidistant point, illustrating the definition of a line 'the locus of all points equidistant from two others' 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 equilateral triangles (all sides the same length). The applet presents an equilateral triangle where the user can drag any vertex. As the vertex is dragged, the others move automatically to keep the triangle equilateral. The angles are also updated continuously to show that the all interior angles are always congruent. 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.

The accuracy and simplicity of this experiment are amazing. A wonderful project for students, which would necessarily involve team work with a different school and most likely a school in a different state or region of the country, would be to try to repeat Eratosthenes' experiment.

An interactive applet and associated web page that describe the Euler line. It shows a triangle whose vertices can be dragged. As you drag them, the centroid, circumcenter and orthocenter move appropriately, showing that they are always collinear, always lying on the Euler line. There are controls to individually turn on the construction lines for each center. This helps visualize the concept since if they are all drawn at once, the diagram would be hopelessly confused. The web page has a full description the Euler line and has links to separate pages which go into each center in depth. Applet can be enlarged to full screen size for use with a classroom projector. Diagram can be printed. This resource is a component of the Math Open Reference Interactive Geometry textbook project at http://www.mathopenref.com.

This virtual field trip embedded within a Nearpod VR lesson uses real-world examples of geometry to help students analyze and design physical spaces.

As with all of the Nearpod VR lessons, this virtual field trip includes a teacher guide and student resources.

An interactive applet and associated web page that demonstrate the exterior angles that are formed where a transversal crosses two lines. The applet shows the two possible pairs of exterior angles in turn when in animation mode. By dragging the three lines, it can be seen that the angles are supplementary only when the lines are parallel. When not in animated mode, there is a button that alternates the two pairs of angles. The text on the page discusses the properties of the angle pairs both in the parallel and non-parallel cases. 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 short video and interactive assessment activity is designed to teach second graders about counting vertices and sides in various shapes.

This short video and interactive assessment activity is designed to teach third graders an overview of flat surfaces of 3d shapes.

Working individually or in groups, students explore the concept of stress (compression) through physical experience and math. They discover why it hurts more to poke themselves with mechanical pencil lead than with an eraser. Then they prove why this is so by using the basic equation for stress and applying the concepts to real engineering problems.

Students develop and solidify their understanding of the concept of "perimeter" as they engage in a portion of the civil engineering task of land surveying. Specifically, they measure and calculate the perimeter of a fenced in area of "farmland," and see that this length is equivalent to the minimum required length of a fence to enclose it. Doing this for variously shaped areas confirms that the perimeter is the minimal length of fence required to enclose those shapes. Then students use the technology of a LEGO MINDSTORMS(TM) NXT robot to automate this task. After measuring the perimeter (and thus required fence length) of the "farmland," students see the NXT robot travel around this length, just as a surveyor might travel around an area during the course of surveying land or measuring for fence materials. While practicing their problem solving and measurement skills, students learn and reinforce their scientific and geometric vocabulary.

The purpose of this task is to have students work on a sequence of area problems that shows the advantage of increasingly abstract strategies in preparation for developing general area formulas for parallelograms and triangles.

The purpose of this task is to give 4th grade students a problem involving an unknown quantity that has a clear visual representation. Students must understand that the four interior angles of a rectangle are all right angles and that right angles have a measure of 90_ and that angle measure is additive.

This tasks examines how to calculate the area of an equilateral triangle using high school geometry.

An interactive applet and associated web page that provide step-by-step instructions on how to find the center of a circle using any right-angled object, such as a piece of paper. The method uses Thales Theorem to draw two diameters, which intersect at the circle center. The animation can be run either continuously like a video, or single stepped to allow classroom discussion and thought between steps. 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 provide step-by-step instructions on how to find the center of a circle using only a compass and straightedge. The method used involves constructing the perpendicular bisectors of two random chords. The bisectors intersect at the center of the circle. The animation can be run either continuously like a video, or single stepped to allow classroom discussion and thought between steps. 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.