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**#10235 K-8 Math - Parachuting: Moving Bodies with Constant Mass (Run time 22 min.) DVD** $69.95

This program uses a parachutist to demonstrate the effects of drag on the force of gravity, showing how to make mathematical approximations and how the resultant forces can be equated to the product of mass and acceleration. A first-order differential equation is then used to find the minimum height from which a parachutist can jump without injury. (21 minutes)

**#10236 K-8 Math - Take-off: Moving Bodies with Constant Mass (Run time 26 min.) DVD** $69.95

This program shows that a single mathematical model can describe the take-off of a wide variety of aircraft, running the gamut from a single-engine trainer to the Concorde. Because the search for approximations is somewhat complex, graphical notation is employed to reveal the interaction and variation of the forces involved. (26 minutes)

**#10237 K-8 Math - Bows, Arrows, and Aircraft Carriers: Moving Bodies with Constant Mass (Run time 59 min.) DVD** $69.95

In this program, geometry is combined with approximation to solve relatively complex problems involving shooting an arrow and landing an airplane on the deck of an aircraft carrier. Emphasizing the value of sketching as a visualization tool, the program also explains how the solution of the archery problem, through geometric inversion, can help solve the problem of a plane landing. (59 minutes)

**#10238 K-8 Math - Impulse: Moving Bodies with Variable Mass (Run time 38 min.) DVD** $69.95

Using Newton's second law and a balloon-powered toy car, this program examines how impulse relates to the change in momentum and how the rate of that change equates to the resultant force. In addition, the exhaust velocity of the jet-propelled car is estimated. (39 minutes)

**#10239 K-8 Math - Rockets and Avalanches: Moving Bodies with Variable Mass (Run time 42 min.) DVD** $69.95

In this program, footage of rockets blasting off and avalanches roaring down mountainsides provides two perspectives of the same principle: the rate of change of momentum. Practical calculations of the time it takes for a rocket to lift off and the time a skier has to escape a landslide, plus an experiment with eggs and flour, reinforce the lesson. (42 minutes)

**#10240 K-8 Math - Modeling Vectors (Run time 24 min.) DVD** $69.95

Employing diverse examples such as trains and water slides, this program illustrates the use of vectors to represent forces operating in both two and three dimensions. The algebraic manipulation of vectors in modeling problems is featured. (24 minutes)

**#10241 K-8 Math - Kites: Modeling with Vectors (Run time 28 min.) DVD** $69.95

After defining the basic concepts of vectors, this program uses algebra to determine how the resultant of numerous forces acting on a body can be obtained and then equated to the product of mass and acceleration. Kites are employed to exemplify both equilibrium and non-equilibrium conditions. (28 minutes)

**#10242 K-8 Math - Vectors and Moments (Run time 56 min.) DVD** $69.95

Moving beyond the concept of simple force, this program expands the application of vectors to include velocity, acceleration, and rotational motion. In addition, moments of greater complexity are investigated through vector geometry. Real-world examples are included. (56 minutes)

**#10243 K-8 Math - Doors, Heart Valves, and Flic-Flacs: Moments (Run time 51 min.) DVD** $69.95

After explaining the principle of moments, this program shows how apparently dissimilar physical phenomena are actually mathematically similar through the examples of a synthetic heart valve, a lock gate, and the gymnastic maneuver known as a flic-flac, or back handspring. The need to make careful approximations during the modeling process is stressed. (51 minutes)

**#10244 K-8 Math - Spinning Tops and Ailerons: Moments and Angular Momentum (Run time 43 min.) DVD** $69.95

In this program, animated graphics help to define the concept of angular momentum and to express the relationship between moments and the rate of change of angular momentum. Problems include determining the dimensions needed for an airplane's ailerons and the amount of force required to rotate a toy spaceship. The reasons why a spinning top shows precession are also addressed. (43 minutes)

**#10245 K-8 Math - Sliding and Toppling: Modeling Forces (Run time 33 min.) DVD** $69.95

This program discusses how geometry, gravity, and the coefficient of friction determine whether an object slides or topples. The mathematical models behind these phenomena are presented through examples such as ice hockey and skiing. The relationship between sliding and a body's velocity as an exercise in energy conservation is explored as well. (33 minutes)

**#10246 K-8 Math - Bikes and Cars: Centripetal Acceleration (Run time 36 min.) DVD** $69.95

This program considers the idea that circular motion must imply a force or component of a force toward the center of a circle, as in the Newtonian theory of how the Moon orbits the Earth. The reasons why bicyclists lean during turns, why roads are banked, and why car tires react as they do during a turn are investigated. (36 minutes)

**#10247 K-8 Math - Pendulum: Simple Harmonic Motion (Run time 54 min.) DVD** $69.95

This program introduces the concept of simple harmonic motion through the operation of the pendulum. The findings of Galileo and his contemporaries on the mechanics of the pendulum are presented, along with examples of pendular motion drawn from the modern world. (54 minutes)

**#10248 K-8 Math - Damping: Simple Harmonic Motion (Run time 44 min.) DVD** $69.95

This program investigates how the mathematical model of simple harmonic motion becomes more complex through the introduction of damping. The application of simple modeling techniques to create homogeneous linear second-order differential equations is illustrated. (44 minutes)

**#10249 K-8 Math - Resonance: Simple Harmonic Motion (Run time 50 min.) DVD** $69.95

In this program, resonance is examined. The value of mathematical models is demonstrated through the physics of applying a time-varying force to a body that fundamentally exhibits simple harmonic motion. Solution techniques for general linear second-order differential equations are featured. (50 minutes)

**#10234 K-8 Math - Math in a Box (Run time min.) DVD** $1049.25

Too many students view mathematics as merely a hurdle to be jumped in their race for an education rather than as a fundamental tool for understanding and solving scientific and mechanical problems. Using real-world examples-plus plenty of animation and graphics-this comprehensive 15-part series helps students to visualize the relationship between forces and motion through phenomena that characterize them. Each program is presented by Dr. Timothy David, a mathematician at the University of Leeds' School of Engineering, and consists of two sections: a case study, with a series of questions and a hint as to how to construct the mathematical model, and a detailed explanation of the principles behind the case study, along with the solutions to the equations. 15-part series, 21-58 minutes each.