Working individually or in groups, students explore the concept of stress (compression) through physical experience and math. They discover why it hurts more to poke themselves with mechanical pencil lead than with an eraser. Then they prove why this is so by using the basic equation for stress and applying the concepts to real engineering problems.

In this primary grades Illuminations lesson, students identify figures on a football field. They look for both congruent and similar figures, and they consider figures that are the same but that occur in a different orientation because of translation, rotation, or reflection. The lesson includes a student worksheet and discussion questions.

The purpose of this task is to have students work on a sequence of area problems that shows the advantage of increasingly abstract strategies in preparation for developing general area formulas for parallelograms and triangles.

The purpose of this task is to give 4th grade students a problem involving an unknown quantity that has a clear visual representation. Students must understand that the four interior angles of a rectangle are all right angles and that right angles have a measure of 90_ and that angle measure is additive.

This tasks examines how to calculate the area of an equilateral triangle using high school geometry.

This task "Uses facts about supplementary, complementary, vertical, and adjacent angles in a multi-step problem to write and solve simple equations for an unknown angle in a figure (7.G.5)" except that it requires students to know, in addition, something about parallel lines, which students will not see until 8th grade.

The purpose of this task is for students to translate between measurements given in a scale drawing and the corresponding measurements of the object represented by the scale drawing.

The purpose of this task is to give students practice working the formulas for the volume of cylinders, cones and spheres, in an engaging context that provides and opportunity to attach meaning to the answers.

Using this tool, students build these classic fractals: the Koch snowflake, a fractal tree, a reduced square, and the Sierpinksi triangle. As these shapes grow and change using an iterative process, students can observe patterns in the images created and in the table of values as the fractals progress through several stages.

This short video and interactive assessment activity is designed to teach third graders about fraction of a whole.

The goal of this task is to use ideas about linear functions in order to determine when certain angles are right angles. The key piece of knowledge implemented is that two lines (which are not vertical or horizontal) are perpendicular when their slopes are inverse reciprocals of one another.

This question examines the algebraic equations for three different spheres. The intersections of each pair of spheres are then studied, both using the equations and thinking about the geometry of the spheres. For two spheres where one is not contained inside of the other there are three possibilities for how they intersect.

Reflective of the modernness of the technology involved, this is a challenging geometric modelling task in which students discover from scratch the geometric principles underlying the software used by GPS systems.

This task complements ``Seven Circles'' I, II, and III. This is a hands-on activity which students could work on at many different levels and the activity leads to many interesting questions for further investigation.

This task provides an opportunity to model a concrete situation with mathematics. Once a representative picture of the situation described in the problem is drawn (the teacher may provide guidance here as necessary), the solution of the task requires an understanding of the definition of the sine function. When the task is complete, new insight is shed on the ``Seven Circles I'' problem which initiated this investigation as is noted at the end of the solution.

This task is inspired by the derivation of the volume formula for the sphere. If a sphere of radius 1 is enclosed in a cylinder of radius 1 and height 2, then the volume not occupied by the sphere is equal to the volume of a Ňdouble-naped coneÓ with vertex at the center of the sphere and bases equal to the bases of the cylinder.

This course is an intensive introduction to architectural design tools and process, and is taught through a series of short exercises. The conceptual basis of each exercise is in the interrogation of the geometric principles that lie at the core of each skill. Skills covered in this course range from techniques of hand drafting, to generation of 3D computer models, physical model-building, sketching, and diagramming. Weekly lectures and pin-ups address the conventions associated with modes of architectural representation and their capacity to convey ideas. This course is tailored and offered only to first-year M.Arch students.

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 tool allows you to learn about various geometric solids and their properties. You can manipulate each solid, seeing it from every angle. You can also color each shape to explore the number of faces, edges, and vertices. With that information, you are challenged to investigate the following question: For any polyhedron, what is the relationship between the number of faces, vertices, and edges?