In this two year study funded by the California Energy Commission and S.D. Bechtel, a committee of individuals from major energy research institutions in California develops strategies to meet Executive Order S-3-05. Executive Order S-3-05 requires California to reduce greenhouse gas (GHG) emissions to 80% of 1990 levels by 2050. To accomplish this, CO2 levels will need to drop from 13 tons CO2e per capita (2005) to 1.6 tons CO2e per capita (2050) while the population continues to grow and energy use is expected to double. To offer a solution to this challenge, multiple "energy system portraits" are developed with combinations of nuclear, biomass, electricity, and fossil fuels with carbon capturing systems. It's concluded by applying key aggressive strategies and investing in multiple technologies, implementations, research, development, and innovation, California can meet executive order S-3-05.

Students can sometimes have emotional outbursts in school settings. This fact will not surprise many teachers, who have had repeated experience in responding to serious classroom episodes of student agitation. Such outbursts can be attributed in part to the relatively high incidence of mental health issues among children and youth. It is estimated, for example, that at least one in five students in American schools will experience a mental health disorder by adolescence (U.S. Department of Health and Human Services, 1999). But even students not identified as having behavioral or emotional disorders may occasionally have episodes of agitation triggered by situational factors such as peer bullying, frustration over poor academic performance, stressful family relationships, or perceived mistreatment by educators.

This problem involves the meaning of numbers found on labels. When the level of accuracy is not given we need to make assumptions based on how the information is reported. The goal of the task is to stimulate a conversation about rounding and about how to record numbers with an appropriate level of accuracy, tying in directly to the standard N-Q.3. It is therefore better suited for instruction than for assessment purposes.

Spreadsheets Across the Curriculum module. Students build a spreadsheet to find the combination of mini-pizzas and calzones that maximizes revenue given constraints on labor time and baking time.

This activity is a chance for students to apply the diffraction grating equation m*Λ/d = Θ to solve a real life problem: find the wavelength of given source of light. It is also useful for them to apply trigonometry to real life scenarios.

After completing the associated lesson and its first associated activity, students are familiar with the 20 major bones in the human body knowing their locations and relative densities. When those bones break, lose their densities or are destroyed, we look to biomedical engineers to provide replacements. In this activity, student pairs are challenged to choose materials and create prototypes that could replace specific bones. They follow the steps of the engineering design process, researching, brainstorming, prototyping and testing to find bone replacement solutions. Specifically, they focus on identifying substances that when combined into a creative design might provide the same density (and thus strength and support) as their natural counterparts. After iterations to improve their designs, they present their bone alternative solutions to the rest of the class. They refer to the measured and calculated densities for fabricated human bones calculated in the previous activity, and conduct Internet research to learn the densities of given fabrication materials (or measure/calculate those densities if not found online).

Students construct three-dimensional models of water catchment basins using everyday objects to form hills, mountains, valleys and water sources. They experiment to see where rain travels and collects, and survey water pathways to see how they can be altered by natural and human activities. Students discuss how engineers design structures that impact water collection, as well as systems that clean and distribute water.

Students model a water catchment basin and survey water pathways to understand factors that affect water flow.

Students drop marbles into holes cut into shoebox lids and listen carefully to try to determine the materials inside the box that the marbles fall onto, illustrating the importance of surface composition on dolphins' abilities to sense materials, depth and texture using echolocation. This activity builds on what students learned in the associated lesson about bycatching by fisheries and how it affects marine habitats and species, especially dolphins. Students learn how echolocation works, why certain animals use it to determine the size, shape and distance of objects, and how people can take advantage of dolphins' echolocation ability when developing bycatch avoidance methods.

By using the discrepant event of dropping a burning candle in a jar, students will predict, experiment, and discuss why the candle goes out as soon as it is caught.

The purpose of this task is to give students practice constructing functions that represent a quantity of interest in a context, and then interpreting features of the function in the light of that context. It can be used as either an assessment or a teaching task.

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.

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.

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.