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.

An interactive applet and associated web page that demonstrate the concept of similar triangles. Applets show that triangles are similar if the are the same shape and possibly rotated, or reflected. In each case the user can drag one triangle and see how another triangle changes to remain similar 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.

An interactive applet and associated web page that demonstrate the concept of similar polygons. Applets show that polygons are similar if the are the same shape and possibly rotated, or reflected. In each case the user can drag one polygons and see how another polygons changes to remain similar 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.

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

Students are tasked with designing a special type of hockey stick for a sled hockey team—a sport designed for individuals with physical disabilities to play ice hockey. Using the engineering design process, students act as material engineers to create durable hockey sticks using a variety of materials. The stick designs will contain different interior structures that can hold up during flexure (or bending) tests. Following flexure testing, the students can use their results to iterate upon their design and create a second stick.

An interactive applet and associated web page that demonstrate the slope (m) of a line. The applet has two points that define a line. As the user drags either point it continuously recalculates the slope. The rise and run are drawn to show the two elements used in the calculation. The grid, axis pointers and coordinates can be turned on and off. The slope calculation can be turned off to permit class exercises and then turned back on the verify the answers. The applet can be printed as it appears on the screen to make handouts. The web page has a full description of the concept of slope, a worked example and has links to other pages relating to coordinate geometry. 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.

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

This short video and interactive assessment activity is designed to teach third graders about identifying and naming 3d figures.

This short video and interactive assessment activity is designed to teach second graders about identifying and naming 3d figures.

This lesson unit is intended to help teachers assess how well students are able to identify and use geometrical knowledge to solve a problem. In particular, this unit aims to identify and help students who have difficulty in: making a mathematical model of a geometrical situation; drawing diagrams to help with solving a problem; identifying similar triangles and using their properties to solve problems; and tracking and reviewing strategic decisions when problem-solving.

Civil engineers design structures such as buildings, dams, highways and bridges. Student teams explore the field of engineering by making bridges using spaghetti as their primary building material. Then they test their bridges to see how much weight they can carry before breaking.

A spatial database is the backbone of a successful organization or website that depends upon maintaining and using data pertinent to locations on Earth. In GEOG 868, Spatial Database Management, capabilities specific to Relational Database Management Systems (RDBMS) and Geographic Information Systems (GIS) are combined to teach students to create, maintain, and query spatial databases in both desktop and enterprise environments. Learn the basics of Standard Query Language (SQL) and database design/normalization, the specifics of managing spatial data in an open-source technologies context (Postgres/PostGIS) and in the context of the Esri geodatabase. Along the way, you will become familiar with spatial functions and versioning, the latter in a server environment hosted by Amazon Web Services.

This short video and interactive assessment activity is designed to give fifth graders an overview of squares and rectangles.

To navigate, you must know roughly where you stand relative to your designation, so you can head in the right direction. In locations where landmarks are not available to help navigate (in deserts, on seas), objects in the sky are the only reference points. While celestial objects move fairly predictably, and rough longitude is not too difficult to find, it is not a simple matter to determine latitude and precise positions. In this activity, students investigate the uses and advantages of modern GPS for navigation.

Students learn that math is important in navigation and engineering. They learn about triangles and how they can help determine distances. Ancient land and sea navigators started with the most basic of navigation equations (speed x time = distance). Today, navigational satellites use equations that take into account the relative effects of space and time. However, even these high-tech wonders cannot be built without pure and simple math concepts — basic geometry and trigonometry — that have been used for thousands of years.

An interactive applet and associated web page that demonstrate supplementary angles (two angles that add to 180 degrees.) The applet shows two angles which, while not adjacent, are drawn to strongly suggest visually that they add to a straight angle. Any point defining the angle scan be dragged, and as you do so, the other angle changes to remain supplementary to the one you change. 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.

Surface area is the sum of the areas of all faces (or surfaces) on a 3D shape. A cuboid has 6 rectangular faces. To find the surface area of a cuboid, add the areas of all 6 faces. We can also label the length (l), width (w), and height (h) of the prism and use the formula, SA=2lw+2lh+2hw, to find the surface area.

Seeing that the surface area to volume ratio of cells generally decreases as cells get larger, making the exchange of resources, waster and heat more and more difficult.