An interactive applet and associated web page that demonstrate a right angle (those equal to 90 deg). The applet presents an angle (initially 90 deg) that the user can adjust by dragging the end points of the line segments forming the angle. As it changes it shows the angle measure and a message that indicate which type of angle it is. There a software 'detents' that make it easy capture exact angles such as 90 degrees and 180 degrees The message and angle measures can be turned off to facilitate classroom discussion. The text on the page has links to other pages defining each angle type in depth. 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 experience the engineering design process as they design and build accurate and precise catapults using common materials. They use their catapults to participate in a game in which they launch Ping-Pong balls to attempt to hit various targets.

Students learn various topics associated with the circle through studying a clock. Topics include reading analog time, understanding the concept of rotation (clockwise vs. counter-clockwise), and identifying right angles and straight angles within circles. Many young students have difficulty telling time in analog format, especially with fewer analog clocks in use (compared to digital clocks). This includes the ability to convert time written in words to a number format, for example, making the connection between "quarter of an hour" to 15 minutes. Students also find it difficult to convert "quarter of an hour" to the number of degrees in a circle. This activity incorporates a LEGO® MINDSTORMS® NXT robot to help students distinguish and visualize the differences in clockwise vs. counter-clockwise rotation and right vs. straight angles, while learning how to tell time on an analog clock. To promote team learning and increase engagement, students work in teams to program and control the robot.

Students learn about rotary encoders and discover how they operate through hands-on experimentation. Rotary encoders are applied in tools to determine angle measurements and for translations of angular motion. One common rotary encoder application is in a computer's ball-type mouse—the ball itself is a type of rotary encoder. In this activity, students experiment with two rotary encoders, including one from a computer mouse and one created using a LEGO® MINDSTORMS® NXT kit. They collect data to define and graph the relationship between the motion of the rotary encoder and its output.

Students explore building a pyramid, learning about the simple machine called an inclined plane. They also learn about another simple machine, the screw, and how it is used as a lifting or fastening device. During a hands-on activity, students see how the angle of inclination and pull force can make it easier (or harder) to pull an object up an inclined plane.

Students learn about the daily and annual cycles of solar angles used in power calculations to maximize photovoltaic power generation. They gain an overview of solar tracking systems that improve PV panel efficiency by following the sun through the sky.

Students continue their pyramid building journey, acting as engineers to determine the appropriate wedge tool to best extract rock from a quarry and cut into pyramid blocks. Using sample materials (wax, soap, clay, foam) representing rock types that might be found in a quarry, they test a variety of wedges made from different materials and with different degrees of sharpness to determine which is most effective at cutting each type of material.

Students learn how using spectrographs helps people understand the composition of light sources. Using simple materials including holographic diffraction gratings, students create and customize their own spectrographs just like engineers. They gather data about different light sources, make comparisons between sources and theorize about their compositions. Before building spectrographs, students learn and apply several methods to identify and interpret patterns, specifically different ways of displaying visual spectra. They also use spectral data from the Cassini mission to Saturn and its moon, Titan, to determine the chemical composition of the planet's rings and its moon's atmosphere.

An interactive applet and associated web page that demonstrate supplementary angles (two angles that add to 180 degrees.) The applet shows two angles which, while not adjacent, are drawn to strongly suggest visually that they add to a straight angle. Any point defining the angle scan be dragged, and as you do so, the other angle changes to remain supplementary to the one you change. 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 work as engineers to design and test trebuchets (in this case LEGO® MINDSTORMS® robots) that can launch objects. During the testing stage, they change one variable at a time to study its effect on the outcome of their designs. Specifically, they determine how far objects travel depending on their weights. As students learn about the different components of robot design and the specific function controls, they determine what design features are important for launching objects.

An interactive applet and associated web page that demonstrate the exterior angles of a triangle. The applet shows a triangle where the user can drag any vertex to reshape it. The exterior angles are shown and a running calculation shows that no matter how you change the triangle, the exterior angles always add up to 360 degrees An exterior angle is equal to the sum of the opposite interior angles 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.

These Trigonometry lecture videos coterminal angles, trig functions, quadrantal angles, special acute angles, co-functions, finding theta, reference angles, trig functions, radian measure, arc length, area of a sector, graphing sine and cosine using t-table, amplitude and frequency, phase shift for sine and consine, vertical shift, tangent curve, cotangent transformations, evaluating trig identities, trig expressions, sum and difference for cosine, double and half angle identities, inverse, principal values, solving difficult trig equations, law of cosines, area of a triangle, and vectors and bearing.

Students investigate the relationships between angles and side lengths in right triangles with the help of materials found in the classroom and a mobile device. Using all or part of a meter stick or dowel and text books or other supplies, students build right triangles and measure the angles using a clinometer application on an Android® (phone or tablet) or iOS® device (iPhone® or iPad®). Then they are challenged to create a triangle with a given side length and one angle. The electronic device is used to measure the accuracy of their constructions.

Learn how to add vectors. Drag vectors onto a graph, change their length and angle, and sum them together. The magnitude, angle, and components of each vector can be displayed in several formats.

Students use inclined planes as they recreate the difficult task of raising a monolith of rock to build a pyramid. They compare the push and pull of different-sized blocks up an inclined plane, determine the angle of inclination, and learn the changes that happen when the angle is increased or decreased.