Students work as physicists to understand centripetal acceleration concepts. They also learn about a good robot design and the accelerometer sensor. They also learn about the relationship between centripetal acceleration and centripetal force governed by the radius between the motor and accelerometer and the amount of mass at the end of the robot's arm. Students graph and analyze data collected from an accelerometer, and learn to design robots with proper weight distribution across the robot for their robotic arms. Upon using a data logging program, they view their own data collected during the activity. By activity end , students understand how a change in radius or mass can affect the data obtained from the accelerometer through the plots generated from the data logging program. More specifically, students learn about the accuracy and precision of the accelerometer measurements from numerous trials.

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.

An interactive applet and associated web page that show the properties of a circumcircle of a polygon. The applet shows a regular polygon where the user can drag the vertices to reshape it and alter the number of sides. As the polygon is being varied, the circumcircle is shown, passing through all vertices. The text describes two ways to calculate the radius of the circumcircle, depending on what you are given to start. 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 circumference of a circle. The applet shows a circle with a radius line. The radius endpoints are draggable and the circle is resized accordingly. The formula relating radius to circumference is updated continually as you drag. Introduces the idea of Pi. The formula can be hidden for class discussion and estimation. See also the entries for circumference and diameter. See also entries for radius and diameter. 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 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 learn how to interpret circle graphs and use the information shown on circle graphs to solve problems.

Included is a YouTube video to support Grade 7 Blended Learning Math - Unit 4.6: Circles and Area - Interpreting Circle Graphs.

The purpose of this lesson is to learn various methods to find the surface area of a net.

Included is a YouTube video to support Grade 8 Blended Learning Math - Unit 4.7: Measuring Prisms and Cylinders - Surface Area of a Right Cylinder.

The purpose of this lesson is to discover the relationship between a radius and a tangent, then solve related problems.

Included is a YouTube video to support Grade 9 Blended Learning Math - Unit 8.1: Circle Geometry - Properties of Tangents to 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.

Through this lesson and its two associated activities, students are introduced to the use of geometry in engineering design, and conclude by making scale models of objects of their choice. The practice of developing scale models is often used in engineering design to analyze the effectiveness of proposed design solutions. In this lesson, students complete fencing (square) and fire pit (circle) word problems on two worksheets—which involves side and radius dimensions, perimeters, circumferences and areas—guiding them to discover the relationships between the side length of a square and its area, and the radius of a circle and its area. They also think of real-world engineering applications of the geometry concepts.

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.

Students practice their multiplication skills using robots with wheels built from LEGO® MINDSTORMS® NXT kits. They brainstorm distance travelled by the robots without physically measuring distance and then apply their math skills to correctly calculate the distance and compare their guesses with physical measurements. Through this activity, students estimate parameters other than by physically measuring them, practice multiplication, develop measuring skills, and use their creativity to come up with successful solutions.

Students explore in detail how the Romans built aqueducts using arches—and the geometry involved in doing so. Building on what they learned in the associated lesson about how innovative Roman arches enabled the creation of magnificent structures such as aqueducts, students use trigonometry to complete worksheet problem calculations to determine semicircular arch construction details using trapezoidal-shaped and cube-shaped blocks. Then student groups use hot glue and half-inch wooden cube blocks to build model aqueducts, doing all the calculations to design and build the arches necessary to support a water-carrying channel over a three-foot span. They calculate the slope of the small-sized aqueduct based on what was typical for Roman aqueducts at the time, aiming to construct the ideal slope over a specified distance in order to achieve a water flow that is not spilling over or stagnant. They test their model aqueducts with water and then reflect on their performance.

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.

An interactive applet and associated web page that define and describe the radius of a regular polygon. The applet has a polygon where the user can change the umber of sides and alter the radius by dragging a vertex. The radius is shown with it's length changing accordingly. The web page has formulae for the length of the radius given the number of sides and the apothem or side length. 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 radius of a circle. The applet shows a circle with a radius line. The radius endpoints are draggable and the figure changes to ensure the line is always a radius of the circle. Demonstrates the radius is always a constant length for a given circle. See also the entries for circumference and diameter. 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 describe the radius of an arc and how to derive it from the width and height of the segment defined by that arc. A practical use is described for finding the radius of a circular arch given its other dimensions. 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 build scale models of objects of their choice. In class they measure the original object and pick a scale, deciding either to scale it up or scale it down. Then they create the models at home. Students give two presentations along the way, one after their calculations are done, and another after the models are completed. They learn how engineers use scale models in their designs of structures, products and systems. Two student worksheets as well as rubrics for project and presentation expectations and grading are provided.

Students review what they know about the 20 major bones in the human body (names, shapes, functions, locations, as learned in the associated lesson) and the concept of density (mass per unit of volume). Then student pairs calculate the densities for different bones from a disarticulated human skeleton model of fabricated bones, making measurements via triple-beam balance (for mass) and water displacement (for volume). All groups share their results with the class in order to collectively determine the densities for every major bone in the body. This activity prepares students for the next activity, "Can It Support You? No Bones about It," during which they act as biomedical engineers and design artificial bones, which requires them to find materials of suitable density to perform as human body implants.