The primary purpose of this task is to lead students to a numerical and graphical understanding of the behavior of a rational function near a vertical asymptote, in terms of the expression defining the function. The canoe context focuses attention on the variables as numbers, rather than as abstract symbols.

The purpose of this task is to use finite geometric series to investigate an amazing mathematical object that might inspire students' curiosity. The Cantor Set is an example of a fractal.

Go through powerpoint about the Canvas Business Model and have students complete the template for the Canvas Business Model for their self created business.

This is an activity about classifying planetary characteristics. Learners will analyze the provided information about each planet in order to make graphs and Venn diagrams. Then, using both, learners will identify similarities and differences of the planets in the Solar System. This is Activity C-11 as part of The Universe At Your Fingertips curriculum, available for purchase.

As part of a (hypothetical) challenge to help a city find the most affordable and environmentally friendly way to clean up an oil spill, students design and conduct controlled experiments to quantify capillary action in sand. Like engineers and entrepreneurs, student teams use affordable materials to design and construct models to measure the rate of capillary action in four types of sand: coarse, medium, fine and mixed. After observing and learning from a teacher-conducted capillary tube demonstration, teams are given a selection of possible materials and a budget to work within as they design their own experimental setups. After the construction of their designs, they take measurements to quantify the rate of capillary action, create graphs to analyze the data, and make concluding recommendations. Groups compare data and discuss as a class the pros and cons of their designs. Pre- and post-evaluations and two worksheets are provided.

By investigating primary sources displaying the American flag, we will explore the various ways people use the flag to show characteristics such as pride, loyalty, and unity for the nation.

In this episode, students will engage in careful observation to identify flags and note details of the variety of places in which American flags are used (See).

This PBS video shows how Klaus Lackner, a geophysicist at Columbia University, is trying to tackle the problem of rising atmospheric CO2 levels by using an idea inspired by his daughter's 8th-grade science fair project. The video examines the idea of pulling CO2 out of the atmosphere via a passive chemical process.

In the exploration of ways to use solar energy, students investigate the thermal energy storage capacities of different test materials to determine which to use in passive solar building design.

In this activity, students will determine the environmental effects of existing cars and a fleet consisting of their dream cars. They compute how many tons of heat-trapping gases are produced each year, how much it costs to fuel the cars, and related information. Then, students research and prepare a report about greener transportation choices.

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 activity from NOAA Earth System Research Laboratory introduces students to the scientific understanding of the greenhouse effect and the carbon cycle. The activity leads them through several interactive tasks to investigate recent trends in atmospheric carbon dioxide. Students analyze scientific data and use scientific reasoning to determine the causes responsible for these recent trends. By studying carbon cycle science in a visual and interactive manner, students can learn firsthand about the reasons behind our changing climate.

In this activity, students use a physical model to learn the basics of photosynthesis and respiration within the carbon cycle.

This is an interactive visualization of the Carbon Cycle, through short-term and long-term processes.

Students are introduced to the concept of energy cycles by learning about the carbon cycle. They will learn how carbon atoms travel through the geological (ancient) carbon cycle and the biological/physical carbon cycle. Students will consider how human activities have disturbed the carbon cycle by emitting carbon dioxide into the atmosphere. They will discuss how engineers and scientists are working to reduce carbon dioxide emissions. Lastly, students will consider how they can help the world through simple energy conservation measures.

In this activity, students work in groups, plotting carbon dioxide concentrations over time on overheads and estimating the rate of change over five years. Stacked together, the overheads for the whole class show an increase on carbon dioxide over five years and annual variation driven by photosynthesis. This exercise enables students to practice basic quantitative skills and understand how important sampling intervals can be when studying changes over time. A goal is to see how small sample size may give incomplete picture of data.

In this experiment, students investigate the importance of carbon dioxide to the reproductive growth of a marine microalga, Dunalliela sp. (Note that the directions are for teachers and that students protocol sheets will need to be created by teachers.)

In this experiment, students observe a natural process that removes carbon dioxide (CO2) from Earth's atmosphere. This process is a part of the carbon cycle and results in temperature suitable for life. Students learn that the carbon cycle is a fundamental Earth process. Throughout Earth's history, the balance of carbon has kept the atmosphere's carbon dioxide (CO2) and Earth's temperature within relatively narrow ranges.