Students act as structural engineers and learn about forces and load distributions as they follow the steps of the engineering design process to design and build small-scale bridges using wooden tongue depressors and glue. Teams brainstorm ideas that meet the size and material design constraints and create prototype bridges of the most promising solutions. They test their bridges to see how much weight they can hold until they break and then determine which have the highest strength-to-weight ratios. They examine the prototype failures to identify future improvements. This activity is part of a unit in which multiple activities are brought together for an all-day school/multi-school concluding “engineering field day” competition.

The purpose of this task is to help solidify students' understanding of signed numbers as points on a number line and to understand the geometric interpretation of adding and subtracting signed numbers.

This task has students experiment with the operations of addition and multiplication, as they relate to the notions of rationality and irrationality.

Using their knowledge of the phases of matter, the scientific method, and polymers, student teams work as if they are chemical engineers to optimize the formula for slime. Hired by the fictional company, Slime Productions, students are challenged to modify the chemical composition of the basic formula for slime to maximize its "bounce factor."

Students work in engineering teams to optimize cleaner energy solutions for cooking and heating in rural China. They choose between various options for heating, cooking, hot water, and lights and other electricity, balancing between the cost and health effects of different energy choices.

Student groups work with manipulatives—pencils and trays—to maximize various quantities of a system. They work through three linear optimization problems, each with different constraints. After arriving at a solution, they construct mathematical arguments for why their solutions are the best ones before attempting to maximize a different quantity. To conclude, students think of real-world and engineering space optimization examples—a frequently encountered situation in which the limitation is the amount of space available. It is suggested that students conduct this activity before the associated lesson, Linear Programming, although either order is acceptable.

In this ordering task each number has at most 3 digits so that students have the opportunity to think about how digit placement affects the size of the number.

In this task students must place 4-digit numbers into order from smallest to greatest and greatest to smallest.

The purpose of this task is to extend students' understanding of fraction comparison.

In this task students compare numbers less than 100 to benchmark numbers and learn to build an understanding of the relative magnitude of numbers.

Students learn about how a device made with dye from a plant, specifically cherries, blackberries, raspberries and/or black currents, can be used to convert light energy into electrical energy. They do this by building their own organic solar cells and measuring the photovoltaic devices' performance based on power output.

The purpose of this task is to present students with a situation in which they need to divide a whole number by a unit fraction in order to find a solution.

For students that have already been introduced to the water cycle this lesson is intended as a logical follow-up. Students will learn about human impacts on the water cycle that create a pathway for pollutants beginning with urban development and joining the natural water cycle as surface runoff. The extent of surface runoff in an area depends on the permeability of the materials in the ground. Permeability is the degree to which water or other liquids are able to flow through a material. Different substances such as soil, gravel, sand, and asphalt have varying levels of permeability. In this lesson, along with the associated activities, students will learn about permeability and compare the permeability of several different materials for the purpose of engineering landscape drainage systems.

The purpose of this lesson is to introduce the students to the Sun. They explore various aspects of the Sun including its composition, its interior workings, and its relationship to the Earth.

This lesson covers the topic of human bones and joints. Students learn about the skeleton, the number of and types of bones in the body, and how outer space affects astronauts' bones. Students also learn how to take care of their bones here on Earth to prevent osteoporosis or weakening of the bones.

Students are introduced to the fabulous planet on which they live. Even though we spend our entire lives on Earth, we still do not always understand how it fits into the rest of the solar system. Students learn about the Earth's position in the solar system and what makes it unique. They learn how engineers study human interactions with the Earth and design technologies and systems to monitor, use and care for our planet's resources wisely to preserve life on Earth.

Students explore the outermost planets of our solar system: Saturn, Uranus and Neptune. They also learn about characteristics of Pluto and its interactions with Neptune. Students learn a little about the history of space travel as well as the different technologies that engineers develop to make space travel and scientific discovery possible.

This lesson goes over the parts of the human respiratory system and the gas exchange process that occurs in the lungs. It also covers changes in the respiratory system that occur during spaceflight, such as decreased lung capacity.

Student teams are challenged to design and build architecturally inspired cardboard furniture, guided by the steps of the engineering design process. They cultivate their industrial engineering and design skills to design furnishings that meet functional, aesthetic and financial requirements. Given constraints that include limited building materials and tools, groups research architectural styles and period furnishings. The teams brainstorm ideas, make small-scale quick prototypes, then make detailed plans and create full-scale prototypes of their best solutions. The full-size prototypes are evaluated by peer critique for aesthetic alignment to the targeted architectural style and tested for functionality. After final refinements, teams present their concepts and display their final prototype furnishings in an exhibition.

This challenging problem and brainteaser gives students an opportunity to compose and decompose polygons to make rectangles.