The goal of this activity is for students to learn how to tell a story in order to make a complex topic (such as global warming or ozone holes) easier for a reader to grasp. Students realize that the narrative impulse underlies even scientific and technical writing and gain a better understanding of the role of myth as a "science" of imagination that helps us to gain insight into human motivation.

This classroom task gives students the opportunity to prove a surprising fact about quadrilaterals: that if we join the midpoints of an arbitrary quadrilateral to form a new quadrilateral, then the new quadrilateral is a parallelogram, even if the original quadrilateral was not.

This is a reasonably direct task aimed at having students use previously-derived results to learn new facts about parallelograms, as opposed to deriving them from first principles. The solution provided (among other possibilities) uses the SAS trial congruence theorem, and the fact that opposite sides of parallelograms are congruent.

The first two parts of this task ask students to interpret the meaning of signed numbers and reason based on that meaning in a context where the meaning of zero is already given by convention.

In this task students are asked to write two expressions from verbal descriptions and determine if they are equivalent. The expressions involve both percent and fractions. This task is most appropriate for a classroom discussion since the statement of the problem has some ambiguity.

Students explore how different materials (sand, gravel, lava rock) with different water contents on different slopes result in landslides of different severity. They measure the severity by how far the landslide debris extends into model houses placed in the flood plain. This activity is a small-scale model of a debris chute currently being used by engineers and scientists to study landslide characteristics. Much of this activity setup is the same as for the Survive That Tsunami activity in Lesson 5 of the Natural Disasters unit.

The purpose of this task is to emphasize the use of the Remainder Theorem (a discussion of which should obviously be considered as a prerequisite for the task) as a method for determining structure in polynomial in equations, and in this particular instance, as a replacement for division of polynomials.

The purpose of this task is to help students realize there are different ways to add mixed numbers and is most appropriate for use in an instructional setting.

This task assumes students are familiar with mixing problems. This approach brings out different issues than simply asking students to solve a mixing problem, which they can often set up using patterns rather than thinking about the meaning of each part of the equations.

In order to solve this problem, students must assume that if you mix a cubic foot of sand with a cubic foot of cement, you will have 2 cubic feet of mix.

The problem deals with a rational expression which is built up from operations arising naturally in a context: adding the volumes of the fertilizer and the water, and dividing the volume of the fertilizer by the resulting sum. Thus it encourages students to see the expression as having meaning in terms of numbers and operations, rather than as an abstract arrangement of symbols.

Students learn about the separation techniques of sedimentation and centrifugation and investigate whether blood is a homogeneous or a heterogeneous mixture. Working in groups as if they are biomedical researchers, they employ the scientific method and make observations about the known characteristics of urine, milk and blood. They probe further by analyzing research on the properties and fractionation modes of blood. As students learn about certain strange characteristics with the fractionation behavior of blood, they formulate hypotheses on the unique nature of blood. Using provided materials —olive oil, tomato juice and petroleum jelly—they design an experiment and construct a blood model. They test their hypotheses by conducting experiments on the blood model, and then propose theories for the nature of blood as a mixture—arriving at the theory of mixture dualism in blood—that blood is a complex mixture system. An activity-guiding handout and PowerPoint® presentation are provided for this student-directed, project-based activity.

Through three lessons and their four associated activities, students are introduced to concepts related to mixtures and solutions. Students consider how mixtures and solutions and atoms and molecules can influence new technologies developed by engineers. To begin, students explore the fundamentals of atoms and their structures. The building blocks of matter (protons, electrons, neutrons) are covered in detail. The next lesson examines the properties of elements and the periodic table one method of organization for the elements. The concepts of physical and chemical properties are also reviewed. Finally, the last lesson introduces the properties of mixtures and solutions. A comparison of different mixtures and solutions, their properties and their separation qualities are explored.

The application of engineering principles is explored in the creation of mobiles. As students create their own mobiles, they take into consideration the forces of gravity and convection air currents. They learn how an understanding of balancing forces is important in both art and engineering design.

Students learn about the advantages and disadvantages of the greenhouse effect. They construct their own miniature greenhouses and explore how their designs take advantage of heat transfer processes to create controlled environments. They record and graph measurements, comparing the greenhouse indoor and outdoor temperatures over time. Students are also introduced to global issues such as greenhouse gas emissions and their relationship to global warming.

The primary purpose of this task is to elicit common misconceptions that arise when students try to model situations with linear functions. This task, being multiple choice, could also serve as a quick assessment to gauge a class' understanding of modeling with linear functions.

Students investigate the ways in which ancient technologies six types of simple machines and combinations are used to construct modern buildings. As they work together to solve a design problem (designing and building a modern structure), they brainstorm ideas, decide on a design, and submit it to a design review before acquiring materials to create it (in this case, a mural depicting it). Emphasis is placed on cooperative, creative teamwork and the steps of the engineering design process.

Students make Moebius strips and use them to demonstrate the interconnectedness of an environment. They explore the natural cycles water, oxygen/carbon dioxide, carbon, nitrogen that exist within the environment.

This task asks students to solve a problem in a context involving constant speed. This task provides a transition from working with ratios involving whole numbers to ratios involving fractions.

This task is designed to help students focus on the whole that a fraction refers to. It helps students to realize that two different fractions can describe the same situation depending on what you choose to be the whole.