Students analyze the relationship between wheel radius, linear velocity and angular velocity by using LEGO(TM) MINDSTORMS(TM) NXT robots. Given various robots with different wheel sizes and fixed motor speeds, they predict which has the fastest linear velocity. Then student teams collect and graph data to analyze the relationships between wheel size and linear velocity and find the angular velocity of the robot given its motor speed. Students explore other ways to increase linear velocity by changing motor speeds, and discuss and evaluate the optimal wheel size and desired linear velocities on vehicles.

The purpose of this lesson is to learn about the radius and diameter of a circle, as well as how to draw accurate circles using a compass.

Included is a YouTube video to support Grade 7 Blended Learning Math - Unit 4.1: Circles and Area - Investigating Circles.

The purpose of this lesson is to learn how to use the formula to find the area of a circle.

Included is a YouTube video to support Grade 7 Blended Learning Math - Unit 4.5: Circles and Area - Area of a Circle.

The purpose of this lesson is to relate a chord, its perpendicular bisector and the center of a circle. Then, solve problems using these relationships.

Included is a YouTube video to support Grade 9 Blended Learning Math - Unit 8.2: Circle Geometry - Properties of Chords in a Circle.

An interactive applet and associated web page that demonstrate the diameter of a circle. The applet shows a circle and a diameter line, the ends of which can be dragged to show that the diameter passes through the center and has a constant length regardless of where on the circle it is drawn. The web page has the circle-related formulae. 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.

Students learn about the engineering design process and how it is used to engineer products for everyday use. Students individually brainstorm solutions for sorting coins and draw at least two design ideas. They work in small groups to combine ideas and build a coin sorter using common construction materials such as cardboard, tape, straws and fabric. Students test their coin sorters, make revisions and suggest ways to improve their designs. By designing, building, testing and improving coin sorters, students come to understand how the engineering design process is used to engineer products that benefit society.

Select a tree to study and determine its species. Visit the Tree Benefits website (http://www.treebenefits.com) to determine the ecological services that your selected tree provides.

Students drop water from different heights to demonstrate the conversion of water's potential energy to kinetic energy. They see how varying the height from which water is dropped affects the splash size. They follow good experiment protocol, take measurements, calculate averages and graph results. In seeing how falling water can be used to do work, they also learn how this energy transformation figures into the engineering design and construction of hydroelectric power plants, dams and reservoirs.

Working individually or in groups, students explore the concept of stress (compression) through physical experience and math. They discover why it hurts more to poke themselves with mechanical pencil lead than with an eraser. Then they prove why this is so by using the basic equation for stress and applying the concepts to real engineering problems.

Students work as engineers and learn to conduct controlled experiments by changing one experimental variable at a time to study its effect on the experiment outcome. Specifically, they conduct experiments to determine the angular velocity for a gear train with varying gear ratios and lengths. Student groups assemble LEGO MINDSTORMS(TM) NXT robots with variously sized gears in a gear train and then design programs using the NXT software to cause the motor to rotate all the gears in the gear train. They use the LEGO data logging program and light sensors to set up experiments. They run the program with the motor and the light sensor at the same time and analyze the resulting plot in order to determine the angular velocity using the provided physics-based equations. Finally, students manipulate the gear train with different gears and different lengths in order to analyze all these factors and figure out which manipulation has a higher angular velocity. They use the equations for circumference of a circle and angular velocity; and convert units between radians and degrees.

Adam Savage walks through two spectacular examples of profound scientific discoveries that came from simple, creative methods anyone could have followed -- Eratosthenes' calculation of the Earth's circumference around 200 BC and Hippolyte Fizeau's measurement of the speed of light in 1849. A quiz, thought provoking question, and links for further study are provided to create a lesson around the 7-minute video. Educators may use the platform to easily "Flip" or create their own lesson for use with their students of any age or level.

Working as a team, students discover that the value of pi (3.1415926...) is a constant and applies to all different sized circles. The team builds a basic robot and programs it to travel in a circular motion. A marker attached to the robot chassis draws a circle on the ground as the robot travels the programmed circular path. Students measure the circle's circumference and diameter and calculate pi by dividing the circumference by the diameter. They discover the pi and circumference relationship; the circumference of a circle divided by the diameter is the value of pi.

A web page and interactive applet illustrating Thales Theorem (the diameter of a circle always subtends a right angle to any point on the circumference). The applet shows a circle where the user can rotate the diameter and a move a point on the circumference. The applet continuously shows the resulting right triangle, demonstrating that the theorem holds no matter how the points are moved around. Text on the page defines the theorem and relates it to other geometric entities. 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.