This 13-minute video lesson looks at 2010 IIT JEE Paper 1 Problem 46 Circle Hyperbola Intersection.

The construction of the perpendicular bisector of a line segment is one of the most common in plane geometry and it is undertaken here. In addition to giving students a chance to work with straightedge and compass, the problem uses triangle congruence both to show that the constructed line is perpendicular to AB and to show that it bisects AB.

This task is for instruction purposes. Part (b) is subtle and the solution presented here uses a "dynamic" view of triangles with two side lengths fixed. This helps pave the way toward what students will see later in trigonometry but some guidance will likely be needed in order to get students started on this path.

This short video and interactive assessment activity is designed to teach first graders about counting rectangles, squares, and triangles in composite figures.

This short video and interactive assessment activity is designed to teach fourth graders about counting right angles in a turn.

This challenging problem and brainteaser gives first graders an opportunity to compose and decompose squares.

This short video and interactive assessment activity is designed to teach third graders about counting vertices and sides in various shapes.

This short video and interactive assessment activity is designed to teach fourth graders about counting the angles in a closed figure.

This short video and interactive assessment activity is designed to teach fifth graders about counting the number of perpendicular lines.

This short video and interactive assessment activity is designed to teach third graders about describing patterns using letters.

This short video and interactive assessment activity is designed to teach fourth graders about describing patterns using letters.

Students learn how to use wind energy to combat gravity and create lift by creating their own tetrahedral kites capable of flying. They explore different tetrahedron kite designs, learning that the geometry of the tetrahedron shape lends itself well to kites and wings because of its advantageous strength-to-weight ratio. Then they design their own kites using drinking straws, string, lightweight paper/plastic and glue/tape. Student teams experience the full engineering design cycle as if they are aeronautical engineers—they determine the project constraints, research the problem, brainstorm ideas, select a promising design and build a prototype; then they test and redesign to achieve a successful flying kite. Pre/post quizzes and a worksheet are provided.

Students learn about the mathematical characteristics and reflective property of ellipses by building their own elliptical-shaped pool tables. After a slide presentation introduction to ellipses, student “engineering teams” follow the steps of the engineering design process to develop prototypes, which they research, plan, sketch, build, test, refine, and then demonstrate, compare and share with the class. Using these tables as models to explore the geometric shape of ellipses, they experience how particles rebound off the curved ellipse sides and what happens if particles travel through the foci. They learn that if a particle travels through one focal point, then it will travel through the second focal point regardless of what direction the particle travels.

This short video and interactive assessment activity is designed to teach third graders about determining unknown angles in parallelograms.

This short video and interactive assessment activity is designed to teach third graders about determining unknown angles in trapezoids.

This short video and interactive assessment activity is designed to teach fourth graders about determining unknown angles in trapezoids.

This short video and interactive assessment activity is designed to teach fifth graders about determining unknown angles within rectangles and squares.