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 problem challenges and extends students' spatial awareness with 2D shapes. The students are given three different irregular shapes. The goal is to divide each of them into two parts that are exactly the same shape and size. The Teachers' Notes page offers rationale, suggestions for implementation with a link to Happy Halving (cataloged seperately), discussion questions, and ideas for extension and support.

This real world word problem requires students to figure out the scale ratio and unit rate.

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.

In this undergraduate level seminar series topics vary from year to year. Students present and discuss the subject matter, and are provided with instruction and practice in written and oral communication. Some experience with proofs required. The topic for fall 2008: Computational algebra and algebraic geometry.

This modeling task involves several different types of geometric knowledge and problem-solving: finding areas of sectors of circles (G-C.5), using trigonometric ratios to solve right triangles (G-SRT.8), and decomposing a complicated figure involving multiple circular arcs into parts whose areas can be found (MP.7).

This task is intended to help model a concrete situation with geometry. Placing the seven pennies in a circular pattern is a concrete and fun experiment which leads to a genuine mathematical question: does the physical model with pennies give insight into what happens with seven circles in the plane?

This task provides a concrete geometric setting in which to study rigid transformations of the plane. It is important for students to be able to visualize and execute these transformations and for this purpose it would be beneficial to have manipulatives and it will important that the students be able to label the vertices of the hexagon with which they are working.

In this activity students try to visualize 3-D shapes from given 2-D silhouettes (projections). Students can describe, draw, model or relate their ideas to objects in their environment. With several possible answers for each silhouette, students become more familiar with using the terms and describing the properties of solid figures. The Teachers' Notes page includes suggestions for implementation, discussion questions, ideas for extension and support. A warmup activity called "Skeleton Shapes" is offered (cataloged separately). [Note: "torch" in the UK = "flashlight" in the US.]

In this scavenger hunt games students are given the task of finding and identifying real-world shapes in their environment.

In this "word search" style puzzle students practice identifying sequences of shapes.

This activity gives students practice drawing straight lines with a ruler and looking for and categorizing shapes, for example, by the number of sides in polygons. The Teachers' Notes page includes suggestions for implementation, discussion questions and ideas for extension.

Students should think of different ways the cylindrical containers can be set up in a rectangular box. Through the process, students should realize that although some setups may seem different, they result is a box with the same volume. In addition, students should come to the realization (through discussion and/or questioning) that the thickness of a cardboard box is very thin and will have a negligible effect on the calculations.

This is a foundational geometry task designed to provide a route for students to develop some fundamental geometric properties that may seem rather obvious at first glance. In this case, the fundamental property in question is that the shortest path from a point to a line meets the line at a right angle, which is crucial for many further developments in the subject.

This activity gives students the opportunity to describe motions along paths involving turns of 45 and 90 degrees. Ideas for implementation, extension and support are included along with a printable sheet of the maps.

In this Cyberchase video segment, the CyberSquad learns what happens to the area of a rectangle when the shape enclosed by the perimeter changes.

This activity gives students an opportunity to explore some of the common 3-D shapes and their names and properties. After discussion and an example, it asks students to count the required number of edges and vertices (corners) to build each of 5 given shapes. The Teachers' Notes page includes suggestions for implementation, discussion questions, ideas for extension and support, and a printable recording sheet (pdf).

The purpose of this task is to lead students through an algebraic approach to a well-known result from classical geometry, namely, that a point X is on the circle of diameter AB whenever _AXB is a right angle.

Total solar eclipses are quite rare, so much so that they make the news when they do occur. This task explores some of the reasons why. Solving the problem is a good application of similar triangles