This task gives students word problems with a given a set of a specified size and a specified number of subsets. The questions ask the student to find out the size of each of the subsets.

This task provides an opportunity to work on the Standard for Mathematical Practice 3 Construct Viable Arguments and Critique the Reasoning of Others.

Students act as mining engineers and simulate ore mining production by using chocolate chip cookies. They focus on the cost-benefit analysis of the chocolate ore production throughout the simulation, which helps them understand the cost of production. As students “mine” with tools such as paperclips and toothpicks, they keep records of their costs—land (cookie), equipment used, cookie size before and after production, and time spent. While the goal is to make as much profit as possible, other costs and goals are taken into consideration—as in real-world mining engineering. For example, mining engineers also consider the resulting amount of destruction to the lithosphere when deciding the best method to obtain ore. Thus, a line item for land reclamation cost is included from the beginning. A provided worksheet serves as a profit and loss statement.

Students learn about using renewable energy from the Sun for heating and cooking as they build and compare the performance of four solar cooker designs. They explore the concepts of insulation, reflection, absorption, conduction and convection.

Student groups are given a set of materials: cardboard, insulating materials, aluminum foil and Plexiglas, and challenged to build solar ovens. The ovens must collect and store as much of the sun's energy as possible. Students experiment with heat transfer through conduction by how well the oven is insulated and radiation by how well it absorbs solar radiation. They test the effectiveness of their designs qualitatively by baking something and quantitatively by taking periodic temperature measurements and plotting temperature vs. time graphs. To conclude, students think like engineers and analyze the solar oven's strengths and weaknesses compared to conventional ovens.

While the task as written does not explicitly use the term "unit rate," most of the work students will do amounts to finding unit rates. A recipe context works especially well since there are so many different pair-wise ratios to consider.

Students are given the engineering challenge to design and build doghouses that shelter a (toy) puppy from the heat—and to create them within material, size and cost constraints. This requires them to apply what they know (or research) about light energy and how it does (or does not) travel through various materials, as well as how a material’s color affects its light absorption and reflection properties. They build their doghouse designs and test them by taking thermometer readings under hot lamps, and then think of ways to improve their designs. This is a great project for learning about light and heat: energy transfer, absorption, insulation and material properties, and easily scales up/down for size and materials.

Students learn the meaning of preservation and conservation and identify themselves and others as preservationists or conservationists in relation to specific environmental issues. They use Venn diagrams to clarify the similarities and differences in viewpoints. They see how an environmental point-of-view affects the approach to an engineering problem.

Students learn and apply concepts in thermodynamics and energy—mainly convection, conduction, and radiation— to solve a challenge. This is accomplished by splitting students into teams and having them follow the engineering design process to design and build a small insulated box, with the goal of keeping an ice cube and a Popsicle from melting. Students are given a short traditional lecture to help familiarize them with the basic rules of thermodynamics and an introduction to materials science while they continue to monitor the ice within their team’s box.

This lesson introduces students to the idea of biomimicry or looking to nature for engineering ideas. Biomimicry involves solving human problems by mimicking natural solutions, and it works well because the solutions exist naturally. There are numerous examples of useful applications of biomimicry, and in this lesson we look at a few fun examples.

In this activity, students examine how to grow plants the most efficiently. They imagine that they are designing a biofuels production facility and need to know how to efficiently grow plants to use in this facility. As a means of solving this design problem, they plan a scientific experiment in which they investigate how a given variable (of their choice) affects plant growth. They then make predictions about the outcomes and record their observations after two weeks regarding the condition of the plants' stem, leaves and roots. They use these observations to guide their solution to the engineering design problem. The biological processes of photosynthesis and transpiration are briefly explained to help students make informed decisions about planning and interpreting their investigation and its results.

Students write poems using rhyme and meter as they come to understand the mechanical concept of rhythm, based on the principle of oscillation, in a broader biological and cultural context, as seen in dance and sports, poetry and other literary forms, and communication in general. Note: The literacy activities for the Mechanics unit are based on physical themes that have broad application to our experience in the world — concepts of rhythm, balance, spin, gravity, levity, inertia, momentum, friction, stress and tension.

Students learn about the many types of expenses associated with building a bridge. Working like engineers, they estimate the cost for materials for a bridge member of varying sizes. After making calculations, they graph their results to compare how costs change depending on the use of different materials (steel vs. concrete). They conclude by creating a proposal for a city bridge design based on their findings.

Students design a simple behavioral survey, and learn basic protocol for primary research, survey design and report writing. Note: The literacy activities for the Mechanics unit are based on physical themes that have broad application to our experience in the world — concepts of rhythm, balance, spin, gravity, levity, inertia, momentum, friction, stress and tension.

Students explore the science of microbial fuel cells (MFCs) by using a molecular modeling set to model the processes of photosynthesis and cellular respiration—building on the concept of MFCs that they learned in the associated lesson, “Photosynthesis and Cellular Respiration at the Atomic Level.” Students demonstrate the law of conservation of matter by counting atoms in the molecular modeling set. They also re-engineer a new molecular model from which to further gain an understanding of these concepts.

The students discover the basics of heat transfer in this activity by constructing a constant pressure calorimeter to determine the heat of solution of potassium chloride in water. They first predict the amount of heat consumed by the reaction using analytical techniques. Then they calculate the specific heat of water using tabulated data, and use this information to predict the temperature change. Next, the students will design and build a calorimeter and then determine its specific heat. After determining the predicted heat lost to the device, students will test the heat of solution. The heat given off by the reaction can be calculated from the change in temperature of the water using an equation of heat transfer. They will compare this with the value they predicted with their calculations, and then finish by discussing the error and its sources, and identifying how to improve their design to minimize these errors.

Students practice counting sequences by standing in a circle and counting one by one.

Students who work on this task will benefit in seeing that given a quantity, there is often more than one way to represent it, which is a precursor to understanding the concept of equivalent expressions.