The task requires the student to use logarithms to solve an exponential equation in the realistic context of carbon dating, important in archaeology and geology, among other places. Students should be guided to recognize the use of the natural logarithm when the exponential function has the given base of e, as in this problem. Note that the purpose of this task is algebraic in nature -- closely related tasks exist which approach similar problems from numerical or graphical stances.

In the task "Carbon 14 Dating'' the amount of Carbon 14 in a preserved plant is studied as time passes after the plant has died. In practice, however, scientists wish to determine when the plant died and, as this task shows, this is not possible with a simple measurement of the amount of Carbon 14 remaining in the preserved plant. The equation for the amount of Carbon 14 remaining in the preserved plant is in many ways simpler here, using 12 as a base.

This problem introduces the method used by scientists to date certain organic material. It is based not on the amount of the Carbon 14 isotope remaining in the sample but rather on the ratio of Carbon 14 to Carbon 12. This ratio decreases, hypothetically, at a constant exponential rate as soon as the organic material has ceased to absorb Carbon 14, that is, as soon as it dies. This problem is intended for instructional purposes only. It provides an interesting and important example of mathematical modeling with an exponential function.

This exploratory task requires the student to use a property of exponential functions in order to estimate how much Carbon 14 remains in a preserved plant after different amounts of time.

This task lets students explore the concept of independence of events. There are two alternative ways of solving the problem.

In this task, students can see that if the price level increases and peopleŐs incomes do not increase, they arenŐt able to purchase as many goods and services; in other words, their purchasing power decreases.

In some cities, especially large cities such as Los Angeles or Mexico City, visible air pollution is a major problem, both for human health and the environment. A variety of sources contribute to air pollution, but personal vehicles account for one of the main sources. Though each car has relatively low emissions when compared to vehicles of the 1970s, there are so many more cars on the road now that their emissions play a large role in overall pollution. In this activity, students think about alternate ways to power a vehicle to reduce emissions. Student teams design an eco-friendly car using the engineering design process, and make a presentation to showcase their product.

This activiy with cartesian divers introduces the gas laws in a high school chemisry class.

Students consider the Earth's major types of landforms such as mountains, rivers, plains, hills, canyons, oceans and plateaus. Student teams build three-dimensional models of landscapes, depicting several of these landforms. Once the models are built, they act as civil and transportation engineers to design and build roads through the landscapes they have created. The worksheet is provided in English and Spanish.

Students learn about power generation using river currents. A white paper is a focused analysis often used to describe how a technology solves a problem. In this literacy activity, students write a simplified version of a white paper on an alternative electrical power generation technology. In the process, they develop their critical thinking skills and become aware of the challenge and promise of technological innovation that engineers help to make possible. This activity is geared towards fifth grade and older students and computer capabilities are required. Some portions of the activity may be appropriate with younger students. CAPTION: Upper Left: Trey Taylor, President of Verdant Power, talks about green power with a New York City sixth-grade class. Lower Left: Verdant Power logo. Center: Verdant Power's turbine evaluation vessel in New York's East River. In the background is a conventional power plant. Upper Right: The propeller-like turbine can be raised and lowered from the platform of the turbine evaluation vessel. Lower Right: Near the East River, Mr. Taylor explains to the class how water currents can generate electric power.

Students observe the relationship between the angle of a catapult (a force measurement) and the flight of a cotton ball. They learn how Newton's second law of motion works by seeing directly that F = ma. When they pull the metal "arm" back further, thus applying a greater force to the cotton ball, it causes the cotton ball to travel faster and farther. Students also learn that objects of greater mass require more force to result in the same distance traveled by a lighter object.

Students learn the importance of the Pythagorean theorem as applied in radar imaging. They use a sensor unit with IRED (infrared emitting diode) to measure triangle distances and the theorem to calculate and verify distances. Student groups calibrate the sensor units to ensure accurate distance measurements. A "pretend" outdoor radar imaging model is provided to groups for sensor unit testing.

Using the story "The Celebrated Jumping Frog of Calaveras County" by Mark Twain, learners simulate a jumping-frog contest and determine the distances "jumped." Learners record the distance of individual jumps in centimeters and determine the total distance jumped (the sum of the three separate jumps) and the official distance (the straight-line distance from the starting line to the end of the frog's third jump). Learners compare the range and median of the total distances with those of the official distances of the group.

This task presents a real-world problem requiring the students to write linear equations to model different cell phone plans. Looking at the graphs of the lines in the context of the cell phone plans allows the students to connect the meaning of the intersection points of two lines with the simultaneous solution of two linear equations.

This simple task assesses whether students can interpret function notation. The four parts of the task provide a logical progression of exercises for advancing understanding of function notation and how to interpret it in terms of a given context.

In this unit, students look at the components of cells and their functions and discover the controversy behind stem cell research. The first lesson focuses on the difference between prokaryotic and eukaryotic cells. In the second lesson, students learn about the basics of cellular respiration. They also learn about the application of cellular respiration to engineering and bioremediation. The third lesson continues students' education on cells in the human body and how (and why) engineers are involved in the research of stem cell behavior.

The purpose of this task is to use geometric and algebraic reasoning to model a real-life scenario. In particular, students are in several places (implicitly or explicitly) to reason as to when making approximations is reasonable and when to round, when to use equalities vs. inequalities, and the choice of units to work with (e.g., mm vs. cm).

This activity is a indoor lab where student gather data about centripital acceleration and write up a lab based on their findings.

Student groups compete to design a process that removes the most iron from fortified cereal. Students experiment with different materials using what they know about iron, magnets and forces to design the best process for removing iron from the cereal samples.

This Java applet activity allows students to explore the various situations described in "The Chairs Around the Table" lesson (cataloged separately). The user can select Exploration mode, in which the number of chairs needed for a particular arrangement of tables is displayed; or Guess, in which the user is able to construct an arrangement and then predict the number of chairs. There are two types of tables to choose from and two different table arrangements. Instructions and exploration question are provide.