This problem is part of a very rich tradition of problems looking to maximize the area enclosed by a shape with fixed perimeter. Only three shapes are considered here because the problem is difficult for more irregular shapes.
The purpose of this task is primarily assessment-oriented, asking students to demonstrate knowledge of how to determine the congruency of triangles.
The purpose of this task is to provide students with a multi-step problem involving volume and to give them a chance to discuss the difference between exact calculations and their meaning in a context.
This task asks students to use similarity to solve a problem in a context that will be familiar to many, though most students are accustomed to using intuition rather than geometric reasoning to set up the shot.
The purpose of this task is to help students understand what is meant by a base and its corresponding height in a triangle and to be able to correctly identify all three base-height pairs.
This short video and interactive assessment activity is designed to teach third graders an overview of lines, curves, vertices, and sides of 2d shapes.
This short video and interactive assessment activity is designed to teach second graders an overview of lines, curves, vertices, and sides of 2d shapes.
This short video and interactive assessment activity is designed to teach second graders an overview of simple figure patterns.
This short video and interactive assessment activity is designed to give fourth graders an overview of simple figure patterns.
This short video and interactive assessment activity is designed to teach third graders an overview of simple figure patterns.
This short video and interactive assessment activity is designed to give fifth graders an overview of simple figure patterns.
STEM focused lesson that incorporates hands on and computer based 3D design. Grade specific math concepts such as budgets, percentages, and square footage is applied.
This task provides the most famous construction to bisect a given angle. It applies when the angle is not 180 degrees.
An interactive applet and associated web page that provide step-by-step instructions on how to bisect an angle using only a compass and straightedge. 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.
In this unit students will learn to find the perimeter and area of plane and composite figures, find the circumference and area of circles, Surface Area of Prisms and Cylinders, Volume of Prisms and Cylinders, Volume and Surface Area Applications.
Students find the volume and surface area of a rectangular box (e.g., a cereal box), and then figure out how to convert that box into a new, cubical box having the same volume as the original. As they construct the new, cube-shaped box from the original box material, students discover that the cubical box has less surface area than the original, and thus, a cube is a more efficient way to package things. Students then consider why consumer goods generally aren't packaged in cube-shaped boxes, even though they would require less material to produce and ultimately, less waste to discard. To display their findings, each student designs and constructs a mobile that contains a duplicate of his or her original box, the new cube-shaped box of the same volume, the scraps that are left over from the original box, and pertinent calculations of the volumes and surface areas involved. The activities involved provide valuable experience in problem solving with spatial-visual relationships.
To display the results from the previous activity, each student designs and constructs a mobile that contains a duplicate of his or her original box, the new cube-shaped box of the same volume, the scraps that are left over from the original box, and pertinent calculations of the volumes and surface areas involved. They problem solve and apply their understanding of see-saws and lever systems to create balanced mobiles.
This task applies reflections to a regular hexagon to construct a pattern of six hexagons enclosing a seventh: the focus of the task is on using the properties of reflections to deduce this seven hexagon pattern.
This task applies reflections to a regular octagon to construct a pattern of four octagons enclosing a quadrilateral: the focus of the task is on using the properties of reflections to deduce that the quadrilateral is actually a square.