The purpose of this series of tasks is to build in a natural way from accessible, concrete problems involving volume to a more abstract understanding of volume. Here, we are given the volume and are asked to find the height.
The purpose of this series of tasks is to build in a natural way from accessible, concrete problems involving volume to a more abstract understanding of volume. This problem is based on ArchimedesŐ Principle that the volume of an immersed object is equivalent to the volume of the displaced water.
In this video segment you’ll discover how using concentric circles can help you determine how much paint is needed to cover the deck of a carousel.
An interactive applet and associated web page that demonstrate the concept of congruent angles. Three angles are shown which always remain congruent as you drag any defining point on any angle. They all change together. This is designed to demonstrate that the angles are considered congruent even if they are in different orientations and the line segments making them up are different lengths. 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 congruence of polygons. The applet presents nine polygons that are in fact congruent, but don't look it because they are reflected and rotated in various ways. If you click on one, it rotates and flips as needed, then slides over the top of another to show it is congruent. The web page describes how to determine if two polygons are 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.
This task is designed to give students insight into the effects of translations, rotations, and reflections on geometric figures in the context of showing that two figures are congruent.
Students' first experience with transformations is likely to be with specific shapes like triangles, quadrilaterals, circles, and figures with symmetry. Exhibiting a sequence of transformations that shows that two generic line segments of the same length are congruent is a good way for students to begin thinking about transformations in greater generality.
An interactive applet and associated web page that demonstrate the concept of congruent triangles. Applets show that triangles a re congruent if the are the same, rotated, or reflected. In each case the user can drag one triangle and see how another triangle changes to remain congruent to it. The web page describes all this and has links to other related pages. 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 has two goals: first to develop student understanding of rigid motions in the context of demonstrating congruence. Secondly, student knowledge of reflections is refined by considering the notion of orientation in part (b).
This 6-minute video lesson looks at 2010 IIT JEE Paper 1 Problem 45 Circle Hyperbola Common Tangent.
This 11-minute video lesson continues to look at 2010 IIT JEE Paper 1 Problem 45 Circle Hyperbola Common Tangent.
This 9-minute video lesson continues to look at 2010 IIT JEE Paper 1 Problem 45 Circle Hyperbola Common Tangent.
This 11-minute video lesson continues to look at 2010 IIT JEE Paper 1 Problem 45 Circle Hyperbola Common Tangent.
This 12-minute video lesson concludes the look at 2010 IIT JEE Paper 1 Problem 45 Circle Hyperbola Common Tangent.
This 13-minute video lesson looks at 2010 IIT JEE Paper 1 Problem 46 Circle Hyperbola Intersection.
This 9-minute video lesson is about identifying conics.
This 6-minute video lesson looks at non-linear systems of equations.
This 7-minute video lesson concludes the look at non-linear systems of equations.
How to construct different angles using a straight edge and a compass.
An interactive applet and associated web page that show how to construct a 30 degrees angle with a compass and straightedge. The animation can be single-stepped or run as a continuous movie. 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.