An interactive applet and associated web page that show the relationship between …
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.
This task presents students with some creative geometric ways to represent the …
This task presents students with some creative geometric ways to represent the fraction one half. The goal is both to appeal to students' visual intuition while also providing a hands on activity to decide whether or not two areas are equal.
This lesson unit is intended to help teachers assess how well students …
This lesson unit is intended to help teachers assess how well students are able to: recognize and visualize transformations of 2D shapes; and translate, reflect and rotate shapes, and combine these transformations. It also aims to encourage discussion on some common misconceptions about transformations.
This interactive activity adapted from the Wisconsin Online Resource Center challenges you …
This interactive activity adapted from the Wisconsin Online Resource Center challenges you to plan, measure, and calculate the correct amount of roofing material needed to reroof a house.
An interactive applet and associated web page that demonstrate a right angle …
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.
This task provides a good opportunity to use isosceles triangles and their …
This task provides a good opportunity to use isosceles triangles and their properties to show an interesting and important result about triangles inscribed in a circle: the fact that these triangles are always right triangles is often referred to as Thales' theorem. It does not have a lot of formal prerequisites, just the knowledge that the sum of the three angles in a triangle is 180 degrees.
The result here complements the fact, presented in the task ``Right triangles …
The result here complements the fact, presented in the task ``Right triangles inscribed in circles I,'' that any triangle inscribed in a circle with one side being a diameter of the circle is a right triangle. A second common proof of this result rotates the triangle by 180 degrees about M and then shows that the quadrilateral, obtained by taking the union of these two triangles, is a rectangle.
This task uses geometry to find the perimeter of the track. Students …
This task uses geometry to find the perimeter of the track. Students may be surprised when their calculation does not give 400 meters but rather a smaller number.
The goal of this task is to model a familiar object, an …
The goal of this task is to model a familiar object, an Olympic track, using geometric shapes. Calculations of perimeters of these shapes explain the staggered start of runners in a 400 meter race.
Crea un ¡Runrún! con papel y cuerda para simular una centrífuga manual. …
Crea un ¡Runrún! con papel y cuerda para simular una centrífuga manual. Agentes de Colorado Americorp en los condados de Araphahoe, Denver, Garfield, Larimer y Weld. Trabajo apoyado por la Corporación para el Servicio Nacional y Comunitario bajo el número de subvención 18AFHCO0010008 de Americorps. Las opiniones o puntos de vista expresados en esta lección pertenecen a los autores y no representan necesariamente la posición oficial o una posición respaldada por la Corporación o el programa Americorps.
This is the second version of a task asking students to find …
This is the second version of a task asking students to find the areas of triangles that have the same base and height. This presentation is more abstract as students are not using physical models.
This task is an example of applying geometric methods to solve design …
This task is an example of applying geometric methods to solve design problems and satisfy physical constraints. This task models a satellite orbiting the earth in communication with two control stations located miles apart on earthsŐ surface.
Students build scale models of objects of their choice. In class they …
Students build scale models of objects of their choice. In class they measure the original object and pick a scale, deciding either to scale it up or scale it down. Then they create the models at home. Students give two presentations along the way, one after their calculations are done, and another after the models are completed. They learn how engineers use scale models in their designs of structures, products and systems. Two student worksheets as well as rubrics for project and presentation expectations and grading are provided.
Observe what happens to an image when the scale changes. This interactive …
Observe what happens to an image when the scale changes. This interactive exercise focuses on visually comparing multiplicative and additive relationships.
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