Patterns, Relations and Functions

40 Years From Now

Predict future sports records based on past statistics.

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Air Coasters

Determine the velocity of a new "frictionless" roller coaster for three possible designs.

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Aquariums Under Pressure

What qualities or characteristics would you look for in the material that is used to make an aquarium?

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Building a Rover

Build a two-dimensional "rover" and analyze its ability to climb over obstacles as you vary the diameter and spacing of its "wheels."

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Cantilevers

Measure and analyze the relationships between deformation, length of beam, and amount of force applied for a cantilever.

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Curve Control

Learn how a set of coordinates can specify the exact shape of a mast.

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Cowbell Concerts

As you know, it’s an important part of our program to get young people interested in music, but it is often difficult to find instruments for them. I would like you to investigate the use of food cans for this purpose.

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Digital Statistics

Measuring their own hands gives students an opportunity to flex their knowledge of statistics.

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Frets

Suppose you are building a guitar where the distance from the bridge to the nut is 1000 millimeters. Use what you have discovered about the ratios of the fret positions to determine the locations of each of the first 12 frets.

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Ingrid's Cross-Country Practice

Analyze an athlete's workout by graphing her heart rate.

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Light Intensity

Study the relationship between light intensity and distance based.

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Maximum Velocity

The maximum velocity that a solar-powered car can achieve (v) is related to number of solar cells on it (n) by this equation.

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New Car Tips

Sports cars are designed to accelerate quickly and go fast around curves. SUV’s are designed to have a large capacity and travel in rough terrain. But why is it, exactly, that a sports car can make a turn at a speed that will cause an SUV to roll over?

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Paint by Number

Use number patterns as the basis for creating artistic designs.

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Peas in a Pod

Is there a relationship between the length of a pea pod and the number of peas it contains?

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Planet Paths

Determine which function represents the relationship between the time duration of a planet's orbit and its average distance from the sun.

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Polygon Necklaces

Make necklaces using a pattern of polygons.

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PowerMills

Analyze power vs. windspeed data and determine the best-fit cubic equation.

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Rice Production

Graph data on the total amount of rice production of the US over a span of many years; look for patterns and predict rice production over the next 10 years.

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Rocks

Graph data provided regarding the number of rocks found in different size ranges on Mars. Look for a pattern, and compare it to data taken from Death Valley, California.

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Saving the Bald Eagle

Develop a plan to recover an endangered species, based on linear and non-linear projections.

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Snail Trails

An algorithm is a sequence of steps that is repeated. When the steps are drawn on a grid, a small difference in algorithms can produce a big difference in the resulting pattern.

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Straightening Out The Bends

Analyze the relationship between how deep a diver goes and how long he or she can stay at that depth before being in danger of "the bends."

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Strap Stress

When force is applied to a material, it will usually cause the material to change shape, even if just a little bit. In such a situation, the force that is applied is called "stress," and the change of shape of the material is called "strain."

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