This task applies reflections to a regular octagon to construct a pattern of four octagons enclosing a quadrilateral: the focus of the task is on using the properties of reflections to deduce that the quadrilateral is actually a square.

Students design and construct electromagnets that must pick up 10 staples. They begin with only minimal guidance, and after the basic concept is understood, are informed of the properties that affect the strength of that magnet. They conclude by designing their own electromagnets to complete the challenge of separating scrap steel from scrap aluminum for recycling, and share it with the class.

This task is intended for instruction and to motivate "Building a general quadratic function.''

An intensive one-week introduction to leadership, teams, and learning communities. Introduction of concepts and use of a variety of experiential exercises to develop individual and team skills and develop supportive relationships within the Fellows class.

What does the brain look like? As engineers, how can we look at neural networks without invasive surgery? In this activity, students design and build neuron models based on observations made while viewing neurons through a microscope. The models are used to explain how each structure of the neuron contributes to the overall function. Students share their models with younger students and explain what a neuron is, its function, and how engineers use their understanding of the neuron to make devices to activate neurons.

Students are introduced to some basic civil engineering concepts in an exciting and interactive manner. Bridges and skyscrapers, the two most visible structures designed by civil engineers, are discussed in depth, including the design principles behind them. To help students visualize in three dimensions, one hands-on activity presents three-dimensional coordinate systems and gives students practice finding and describing points in space. After learning about skyscrapers, tower design principles and how materials absorb different types of forces, students compete to build their own newspaper towers to meet specific design criteria.The unit concludes with student groups using balsa wood and glue to design and build tower structures to withstand vertical and lateral forces.

Students use their knowledge of tornadoes and damage. The students will work in groups to design a structure that will withstand and protect people from tornadoes. Each group will create a poster with the name of their engineering firm and a picture of their structure. Finally, each group will present their posters to the class.

Student pairs are given 10 minutes to create the biggest box possible using one piece of construction paper. Teams use only scissors and tape to each construct a box and determine how much puffed rice it can hold. Then, to meet the challenge, they improve their designs to create bigger boxes. They plot the class data, comparing measured to calculated volumes for each box, seeing the mathematical relationship. They discuss how the concepts of volume and design iteration are important for engineers. Making 3-D shapes also supports the development of spatial visualization skills. This activity and its associated lesson and activity all employ volume and geometry to cultivate seeing patterns and understanding scale models, practices used in engineering design to analyze the effectiveness of proposed design solutions.

In this activity, the students test the shelters they built in Lesson 3, Activity 1 for durability and water resistance.

We are surrounded everyday by circuits that utilize "in parallel" and "in series" circuitry. Complicated circuits designed by engineers are made of many simpler parallel and series circuits. In this hands-on activity, students build parallel circuits, exploring how they function and their unique features.

Everyday we are surrounded by circuits that use "in parallel" and "in series" circuitry. Complicated circuits designed by engineers are composed of many simpler parallel and series circuits. During this activity, students build a simple series circuit and discover the properties associated with series circuits.

Athletes often wear protective gear to keep themselves safe in contact sports. In this spirit, students follow the steps of engineering design process as they design, build and test protective padding for an egg drop. Many of the design considerations surrounding egg drops are similar to sports equipment design. Watching the transformation of energy from potential to kinetic, observing the impact and working under material constraints introduces students to "sports engineering" and gives them a chance to experience some of the challenges engineers face in designing equipment to protect athletes.

In this task students determine the number of hundreds, tens and ones that are necessary to write equations when some digits are provided. Students must, in some cases, decompose hundreds to tens and tens to ones.

When will objects float and when will they sink? Learn how buoyancy works with blocks. Arrows show the applied forces, and you can modify the properties of the blocks and the fluid.

When will objects float and when will they sink? Learn how buoyancy works with blocks. Arrows show the applied forces, and you can modify the properties of the blocks and the fluid.

Students conduct a simple experiment to see how the water level changes in a beaker when a lump of clay sinks in the water and when the same lump of clay is shaped into a bowl that floats in the water. They notice that the floating clay displaces more water than the sinking clay does, perhaps a surprising result. Then they determine the mass of water that is displaced when the clay floats in the water. A comparison of this mass to the mass of the clay itself reveals that they are approximately the same.

This art history video discussion examines Edward Burne-Jones' "King Cophetua and the Beggar Maid", oil on canvas, 1884 (Tate Britain, London).

Sir Edward Coley Burne-Jones, Hope, 1896, 179 x 63.5 cm, oil on canvas (Museum of Fine Arts, Boston)

This art history video discussion examines Sir Edward Coley Burne-Jones' "The Golden Stairs," 1880, oil on canvas 2692 x 1168 mm (Tate Britain, London).

Students bury various pieces of trash in a plotted area of land outside. After two to three months, they uncover the trash to investigate what types of materials biodegrade in soil.