The goal of this task is to use geometry study the structure of beehives. Beehives have a tremendous simplicity as they are constructed entirely of small, equally sized walls. In order to as useful as possible for the hive, the goal should be to create the largest possible volume using the least amount of materials. In other words, the ratio of the volume of each cell to its surface area needs to be maximized. This then reduces to maximizing the ratio of the surface area of the cell shape to its perimeter.

An interactive applet and associated web page that show the definition of a horizontal line in coordinate geometry. The applet has two points that the user can drag which define a line. The line flagged when it is horizontal (slope=0) and the equation of the line is shown. The grid, details and coordinates can be turned on and off. The applet can be printed exactly as it appears on the screen to make handouts. The web page has a discussion on how to test for horizontal, the line equation 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 for students to apply the concepts of mass, volume, and density in a real-world context. There are several ways one might approach the problem, e.g., by estimating the volume of a person and dividing by the volume of a cell.

This is a mathematical modeling task aimed at making a reasonable estimate for something which is too large to count accurately, the number of leaves on a tree.

In this problem, the variables a,b,c, and d are introduced to represent important quantities for this esimate: students should all understand where the formula in the solution for the number of leaves comes from. Estimating the values of these variables is much trickier and the teacher should expect and allow a wide range of variation here.

As written, this problem gives students all of the information they need to estimate the thickness of a soda can.

his is a version of ''How thick is a soda can I'' which allows students to work independently and think about how they can determine how thick a soda can is. The teacher should explain clearly that the goal of this task is to come up with an ''indirect'' means of assessing how thick the can is, that is directly measuring its thickness is not allowed.

An interactive applet and associated web page that provide step-by-step animated instructions on how to measure angles using a protractor. Specifically, it uses a protractor to measure two angles that form a vertical pair, verifying they have the same measure. The animation can be run either continuously like a video, or single stepped to allow classroom discussion and thought between steps. 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 provide step-by-step animated instructions on how to use a protractor to draw an angle. The animation can be run either continuously like a video, or single stepped to allow classroom discussion and thought between steps. 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 is an animation of a square rotating in hyperbolic geometry as represented by the Poincaré Disk Model.

This image is a hyperbolic tiling made from alternating two shapes: heptagons and triangles. This image is a hyperbolic tiling made from alternating two shapes: heptagons and triangles. This image is a hyperbolic tiling made from alternating two shapes: heptagons and triangles. This image is a hyperbolic tiling made from alternating two shapes: heptagons and triangles. This image is a hyperbolic tiling made from alternating two shapes: heptagons and triangles.

This rich task is an excellent example of geometric concepts in a modeling situation and is accessible to all students. In this task, students will provide a sketch of a paper ice cream cone wrapper, use the sketch to develop a formula for the surface area of the wrapper, and estimate the maximum number of wrappers that could be cut from a rectangular piece of paper.

This short video and interactive assessment activity is designed to teach third graders an overview of rectangles, squares, circles and triangles.

This short video and interactive assessment activity is designed to teach first graders an overview of rectangles, squares, circles and triangles.

This short video and interactive assessment activity is designed to teach second graders an overview of rectangles, squares, circles and triangles.

This short video and interactive assessment activity is designed to teach second graders an overview of ellipses, trapezoids, rhombi, and polygons.

This short video and interactive assessment activity is designed to teach third graders an overview of ellipses, trapezoids, rhombi, and polygons.

This short video and interactive assessment activity is designed to teach third graders about determining whether lines are perpendicular.

This short video and interactive assessment activity is designed to teach third graders an overview of quadrilaterals.