In this math meets life science lesson, learners measure the circumference of local trees in order to calculate diameters. Learners use this information and a growth rate table to estimate the age of the trees. This lesson guide includes questions for learners, assessment options, extensions, and reflection questions.

This task gives students a chance to explore several issues relating to rigid motions of the plane and triangle congruence. As an instructional task, it can help students build up their understanding of the relationship between rigid motions and congruence.

Students learn about regular polygons and the common characteristics of regular polygons. They relate their mathematical knowledge of these shapes to the presence of these shapes in the human-made structures around us, especially trusses. Through a guided worksheet and teamwork, students explore the idea of dividing regular polygons into triangles, calculating the sums of angles in polygons using triangles, and identifying angles in shapes using protractors. They derive equations 1) for the sum of interior angles in a regular polygon, and 2) to find the measure of each angle in a regular n-gon. This activity extends students’ knowledge to engineering design and truss construction. This activity is the middle step in a series on polygons and trusses, and prepares students for the Polygon and Popsicle Trusses associated activity.

This Java applet provides opportunities for creative problem solving while encouraging young students to estimate length and angle measure. Using the Turtle Pond Applet, students enter a sequence of commands to help the turtle get to the pond. Children can write their own solutions using LOGO commands and input them into the computer. The turtle will then move and leave a trail or path according to the instructions given. (N.B. the applet is an upgrade of one that supported the Lesson "Get the Turtle to the Pond," cataloged separately.)

In this video segment from Cyberchase, Digit must a make a straight line between the two points and then follow the path created.

Jackie and Matt are looking at the same object along two different lines, in this video segment from Cyberchase.

This task combines two skills from domain G-C: making use of the relationship between a tangent segment to a circle and the radius touching that tangent segment (G-C.2), and computing lengths of circular arcs given the radii and central angles (G-C.5). It also requires students to create additional structure within the given problem, producing and solving a right triangle to compute the required central angles (G-SRT.8).

This resourse will aid students in understanding conceptually what the formula of volume means and how to caclulate volume with that understanding.   

This task presents a context that leads students toward discovery of the formula for calculating the volume of a sphere. Students who are given this task must be familiar with the formula for the volume of a cylinder, the formula for the volume of a cone, and CavalieriŐs principle.

This lesson unit is intended to help you assess how well students are able to: recognize and use common 2D representations of 3D objects and identify and use the appropriate formula for finding the circumference of a circle.

This video is meant to be a fun, hands-on session that gets students to think hard about how machines work. It teaches them the connection between the geometry that they study and the kinematics that engineers use -- explaining that kinematics is simply geometry in motion. In this lesson, geometry will be used in a way that students are not used to. Materials necessary for the hands-on activities include two options: pegboard, nails/screws and a small saw; or colored construction paper, thumbtacks and scissors. Some in-class activities for the breaks between the video segments include: exploring the role of geometry in a slider-crank mechanism; determining at which point to locate a joint or bearing in a mechanism; recognizing useful mechanisms in the students' communities that employ the same guided motion they have been studying.

In this Cyberchase video segment, the CyberSquad must locate each other using a map's grid to construct a coordinate system using letters and numbers.

Students will understand what the volume formula conceptually means by usiig cubes to create a prism.  They will then investigate the relationship between a Rectangular Prism and a Triangular Prism is, and the relationship between a prism to a pyramid, and how that affects the formula.  

Challenged with a hypothetical engineering work situation in which they need to figure out the volume and surface area of a nuclear power plant’s cooling tower (a hyperbolic shape), students learn to calculate the volume of complex solids that can be classified as solids of revolution or solids with known cross sections. These objects of complex shape defy standard procedures to compute volumes. Even calculus techniques depend on the ability to perform multiple measurements of the objects or find functional descriptions of their edges. During both guided and independent practice, students use (free GeoGebra) geometry software, a photograph of the object, a known dimension of it, a spreadsheet application and integral calculus techniques to calculate the volume of complex shape solids within a margin of error of less than 5%—an approach that can be used to compute the volumes of big or small objects. This activity is suitable for the end of the second semester of AP Calculus classes, serving as a major grade for the last six-week period, with students’ project results presentation grades used as the second semester final test.

In this activity, learners walk the sides and interior angles of various polygons drawn on the playground. As they do so, learners practice rotating clockwise 180 and 360 degrees. Learners discover there is a pattern to the sum of the interior angles of any polygon.

In this geometry lesson students classify triangles and explore side lengths of triangles to discover the Triangle Inequality Theorem. The resource includes an exploratory activity and student sheet (pdf), class discussion prompts, a small group spinner activity, extension suggestions, and links to two related resources (cataloged separately).

In these two geometry activities students explore the properties of triangles, discover what shapes triangles can form, and investigate what shapes can form triangles. Each activity includes a student recording sheet, extension ideas, and questions for students. Cataloged separateley within this site are the Patch Tool and the related How Many Triangles Can You Construct? activity.

The triangle congruence criteria, SSS, SAS, ASA, all require three pieces of information. It is interesting, however, that not all three pieces of information about sides and angles are sufficient to determine a triangle up to congruence. In this problem, we considered SSA. Also insufficient is AAA, which determines a triangle up to similarity. Unlike SSA, AAS is sufficient because two pairs of congruent angles force the third pair of angles to also be congruent.

In this task students see different ways of partitioning a circle and a rectangle into two or more equal shares.

Learn how and when the Eastern Shoshone came to Wyoming, what are the Shoshone values, and what are the people of the Eastern Shoshone like? In the accompanying lessons plans (found in the Support Materials), students will gain an understanding of the Fort Bridger Treaty of 1868 including its importance to the state of Wyoming and the Eastern Shoshone Tribe in 1868 and today. The American Bison, or Buffalo as preferred by most tribes, has a significant existence among the Native American people. For thousands of years, the great American Buffalo roamed the Great Plains, migrating from north to south, searching for areas on which to thrive. The Shoshone people depended on the buffalo for many things that included food, clothing, and shelter. Every part of the buffalo was used and provided for the people.

LEARNING OBJECTIVES:

Students will study (Highlight, paraphrase and report) the Treaty of 1868 between the Eastern Shoshone Tribe and the United States Government.
Students will learn about the Eastern Shoshone people through the use of research and technology.
Students will understand that the history of the Shoshone people in the Wind River Mountains dates back thousands of years.
Students will understand that the circle of life continues in a perpetual cycle and is passed on through oral tradition. These stories often taught a lesson to young people.
Students will understand the indigenous perspective of interconnectedness. Students will understand how bison populations were devastated by western expansion.
Students will learn how to construct, read, compare and analyze different population graphs.
Students will understand how the diets of the Shoshone people varied depending on the areas in which they lived.
Students will acquire knowledge of the Wind River Reservation communities and be able to identify these locations on a map.
Students will be able to further describe how their culture has shaped them.
Students will be able to define the concept of culture.
Students will be able to explain some of the attributes of culture.