An interactive applet and associated web page that demonstrate the three types of triangle: acute, obtuse and right. The applet shows a triangle that is initially acute (all angles less then 90 degrees) which the user can reshape by dragging any vertex. There is a message changes in real time while the triangle is being dragged that tells if the triangle is an acute, right or obtuse triangle and gives the reason why. By experimenting with the triangle student can develop an intuitive sense of the difference between these three classes of triangle. 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.

Definition of area of triangle, image of triangle on coordinate grid with height constructed. Area of triangle calculated using distance formula.

An interactive applet and associated web page that explain the area of a triangle. The applet shows a triangle that can be reshaped by dragging any vertex. As it changes, the area is continually recalculated using the 'half base times height' method. The triangle has a fixed square grid in its interior that can be used to visually estimate the area for later correlation with the calculated value. The calculation can be hidden while estimation is in progress. The text page has links to a similar page that uses Heron's Formula to compute the area. 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 student interactive, from Illuminations, allows students to explore the conditions that guarantee uniqueness of a triangle, quadrilateral, or pentagon regardless of location or orientation. Each set of conditions results in a new congruence theorem.

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.

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.

In this assessment task students are given a geoboard and rubberband and are asked to make a square, a triangle and a hexagon. Students can be assessed in a small group or whole class. A checklist and rubric are provided.

This resource describes activities using interactive geoboards to help students identify simple geometric shapes, describe their properties, and develop spatial sense. The first part, Making Triangles, focuses attention on the concept of triangle, helping students understand the mathematical meaning of a triangle and the idea of congruence, or sameness, in geometry. In the next part, Creating Polygons, students make and compare a variety of polygons, describing the salient properties of the shapes they create.

In this assessment task students are asked to use pattern blocks to make sailboats that are on a workmat. They are asked to show different ways to fill the same shape for example a student may use one trapezoid and three triangles to create the shape. The teacher will be able to observe whether a student uses flips, slides or turns purposefully. The workmat and rubric are provided.

This resource is from Tools 4 NC Teachers. This document is the About the Cluster document for Cluster 5 created by the authors of the NC2ML Instructional Frameworks. This document should be read prior to teaching Cluster 5.

Proof that the sum of angles of a triangle equals 180 degrees using vertical angles and corresponding angles.

An interactive applet and associated web page that show the relationship between the perimeter and area of a triangle. It shows that a triangle with a constant perimeter does NOT have a constant area. The applet has a triangle with one vertex draggable and a constant perimeter. As you drag the vertex, it is clear that the area varies, even though the perimeter is constant. Optionally, you can see the path traced by the dragged vertex and see that it forms an ellipse. A link takes you to a page where this effect is exploited to construct an ellipse with string and pins. The 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.

Description of cosine function with image, calculation of length of hypotenuse with known angle and adjacent side, calculation of angle with known adjacent and hypotenuse sides. Explanation of inverse cosine. Interactive fill in the blank of main points.

Image of real life project using Pythagorean Theorem. Definition of theorem, directions with images on how to use theorem to square a construction project.

Course presentation showing relationship of sine and cosine of angles in a right triangle

Description of sine function with image, calculation of length of hypotenuse with known angle and opposite side, calculation of angle with known opposite and hypotenuse sides. Explanation of inverse sine. Interactive fill in the blank of main points.

Description of tangent function with image, calculation of length of opposite side with known angle and adjacent side, calculation of angle with known opposite and adjacent sides. Explanation of inverse tangent Interactive fill in the blank of main points.

Trigonometry ratios of right triangle, image of right triangle with hypotenuse, opposite, and adjacent sides labeled with hotspot information. Interactive Drag and drop image of labeling sides of right triangle

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 that math is important in navigation and engineering. They learn about triangles and how they can help determine distances. Ancient land and sea navigators started with the most basic of navigation equations (speed x time = distance). Today, navigational satellites use equations that take into account the relative effects of space and time. However, even these high-tech wonders cannot be built without pure and simple math concepts — basic geometry and trigonometry — that have been used for thousands of years.