### Water Bottle Rockets Activity

###### Published on January 14, 2017

What makes rockets fly straight? What makes rockets fly far? Why use water to make the rocket fly? Students are challenged to design and build rockets from two-liter plastic soda bottles that travel as far and straight as possible or stay aloft as long as possible. Guided by the steps of the engineering design process, students first watch a video that shows rocket launch failures and then participate in three teacher-led mini-activities with demos to explore key rocket design concepts: center of drag, center of mass, and momentum and impulse. Then the class tests four combinations of propellants (air, water) and center of mass (weight added fore or aft) to see how these variables affect rocket distance and hang time. From what they learn, student pairs create their own rockets from plastic bottles with cardboard fins and their choices of propellant and center of mass placement, which they test and refine before a culminating engineering field day competition. Teams design for maximum distance or hang time; adding a parachute is optional. Students learn that engineering failures during design and testing are just steps along the way to success.

### Wear’s the Technology? Activity

###### Published on December 29, 2016

Students apply their knowledge of scale and geometry to design wearables that would help people in their daily lives, perhaps for medical reasons or convenience. Like engineers, student teams follow the steps of the design process, to research the wearable technology field (watching online videos and conducting online research), brainstorm a need that supports some aspect of human life, imagine their own unique designs, and then sketch prototypes (using Paint®). They compare the drawn prototype size to its intended real-life, manufactured size, determining estimated length and width dimensions, determining the scale factor, and the resulting difference in areas. After considering real-world safety concerns relevant to wearables (news article) and getting preliminary user feedback (peer critique), they adjust their drawn designs for improvement. To conclude, they recap their work in short class presentations.

### Scaling, Go Figure! Lesson

###### Published on December 29, 2016

Students learn how different characteristics of shapes—side lengths, perimeter and area—change when the shapes are scaled, either enlarged or reduced. Student pairs conduct a “scaling investigation” to measure and calculate shape dimensions (rectangle, quarter circle, triangle; lengths, perimeters, areas) from a bedroom floorplan provided at three scales. They analyze their data to notice the mathematical relationships that hold true during the scaling process. They see how this can be useful in real-world situations like when engineers design wearable or implantable biosensors. This prepares students for the associated activity in which they use this knowledge to help them reduce or enlarge their drawings as part of the process of designing their own wearables products. Pre/post-activity quizzes, a worksheet and wrap-up concepts handout are provided.

### Geometry Tools: Angles & Reflections Lesson

###### Published on December 27, 2016

Students learn about common geometry tools and then learn to use protractors (and Miras, if available) to create and measure angles and reflections. The lesson begins with a recap of the history and modern-day use of protractors, compasses and mirrors. After seeing some class practice problems and completing a set of worksheet-prompted problems, students share their methods and work. Through the lesson, students gain an awareness of the pervasive use of angles, and these tools, for design purposes related to engineering and everyday uses. This lesson prepares students to conduct the associated activity in which they “solve the holes” for hole-in-one multiple-banked angle solutions, make their own one-hole mini-golf courses with their own geometry-based problems and solutions, and then compare their “on paper” solutions to real-world results.

### Polygons and Popsicle Trusses Activity

###### Published on December 22, 2016

Students learn about the role engineers play in designing and building truss structures. Simulating a real-world civil engineering challenge, student teams are tasked to create strong and unique truss structures for a local bridge. They design to address project constraints, including the requirement to incorporate three different polygon shapes, and follow the steps of the engineering design process. They use hot glue and Popsicle sticks to create their small-size bridge prototypes. After compressive load tests, they evaluate their results and redesign for improvement. They collect, graph and analyze before/after measurements of interior angles to investigate shape deformation. A PowerPoint® presentation, design worksheet and data collection sheet are provided. This activity is the final step in a series on polygons and trusses.

### Triangles Everywhere: Sum of Angles in Polygons Activity

###### Published on December 22, 2016

Students learn about regular polygons and the common characteristics of regular polygons. They relate their mathematical knowledge of these shapes to the presence of these shapes in the human-made structures around us, especially trusses. Through a guided worksheet and teamwork, students explore the idea of dividing regular polygons into triangles, calculating the sums of angles in polygons using triangles, and identifying angles in shapes using protractors. They derive equations 1) for the sum of interior angles in a regular polygon, and 2) to find the measure of each angle in a regular n-gon. This activity extends students’ knowledge to engineering design and truss construction. This activity is the middle step in a series on polygons and trusses, and prepares students for the Polygon and Popsicle Trusses associated activity.

### Polygons, Angles and Trusses, Oh My! Lesson

###### Published on December 22, 2016

Students take a close look at truss structures, the geometric shapes that compose them, and the many variations seen in bridge designs in use every day. Through a guided worksheet, students draw assorted 2D and 3D polygon shapes and think through their forms and interior angles (mental “testing”) before and after load conditions are applied. They see how engineers add structural members to polygon shapes to support them under compression and tension, and how triangles provide the strongest elemental shape. A PowerPoint® presentation is provided. This lesson prepares students for two associated activities that continue the series on polygons and trusses.

### Let’s Build an Aqueduct! Activity

###### Published on December 22, 2016

Students explore in detail how the Romans built aqueducts using arches—and the geometry involved in doing so. Building on what they learned in the associated lesson about how innovative Roman arches enabled the creation of magnificent structures such as aqueducts, students use trigonometry to complete worksheet problem calculations to determine semicircular arch construction details using trapezoidal-shaped and cube-shaped blocks. Then student groups use hot glue and half-inch wooden cube blocks to build model aqueducts, doing all the calculations to design and build the arches necessary to support a water-carrying channel over a three-foot span. They calculate the slope of the small-sized aqueduct based on what was typical for Roman aqueducts at the time, aiming to construct the ideal slope over a specified distance in order to achieve a water flow that is not spilling over or stagnant. They test their model aqueducts with water and then reflect on their performance.

### History and Geometry of Roman Aqueducts Lesson

###### Published on December 22, 2016

Students see that geometric shapes can be found in all sorts of structures as they explore the history of the Roman Empire with a focus on how engineers 2000 years ago laid the groundwork for many structures seen today. Through a short online video, brief lecture material and their own online research directed by worksheet questions, students discover how the Romans invented a structure known today as the Roman arch that enabled them to build architecture never before seen by humankind, including the amazing aqueducts. Students calculate the slope and its total drop and angle over its entire distance for an example aqueduct. Completing this lesson prepares students for the associated activity in which teams build and test model aqueducts that meet specific constraints. This lesson serves as an introduction to many other geometry—and engineering-related lessons—including statics and trusses, scale modeling, and trigonometry.

### Scale Model Project Activity

###### Published on December 21, 2016

Students build scale models of objects of their choice. In class they measure the original object and pick a scale, deciding either to scale it up or scale it down. Then they create the models at home. Students give two presentations along the way, one after their calculations are done, and another after the models are completed. They learn how engineers use scale models in their designs of structures, products and systems. Two student worksheets as well as rubrics for project and presentation expectations and grading are provided.

### Build the Biggest Box Activity

###### Published on December 21, 2016

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.

### Discovering Relationships between Side Length and Area Lesson

###### Published on December 21, 2016

Through this lesson and its two associated activities, students are introduced to the use of geometry in engineering design, and conclude by making scale models of objects of their choice. The practice of developing scale models is often used in engineering design to analyze the effectiveness of proposed design solutions. In this lesson, students complete fencing (square) and fire pit (circle) word problems on two worksheets—which involves side and radius dimensions, perimeters, circumferences and areas—guiding them to discover the relationships between the side length of a square and its area, and the radius of a circle and its area. They also think of real-world engineering applications of the geometry concepts.

### Designing an Elliptical Pool Table Activity

###### Published on December 21, 2016

Students learn about the mathematical characteristics and reflective property of ellipses by building their own elliptical-shaped pool tables. After a slide presentation introduction to ellipses, student “engineering teams” follow the steps of the engineering design process to develop prototypes, which they research, plan, sketch, build, test, refine, and then demonstrate, compare and share with the class. Using these tables as models to explore the geometric shape of ellipses, they experience how particles rebound off the curved ellipse sides and what happens if particles travel through the foci. They learn that if a particle travels through one focal point, then it will travel through the second focal point regardless of what direction the particle travels.

### All about Linear Programming Lesson

###### Published on December 15, 2016

Students learn about linear programming (also called linear optimization) to solve engineering design problems. As they work through a word problem as a class, they learn about the ideas of constraints, feasibility and optimization related to graphing linear equalities. Then they apply this information to solve two practice engineering design problems related to optimizing materials and cost by graphing inequalities, determining coordinates and equations from their graphs, and solving their equations. It is suggested that students conduct the associated activity, Optimizing Pencils in a Tray, before this lesson, although either order is acceptable.

### Optimizing Pencils in a Tray Activity

###### Published on December 15, 2016

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.

### Preventing Potholes Activity

###### Published on December 7, 2016

Acting as civil engineers hired by the U.S. Department of Transportation to research how to best use piezoelectric materials to detect road damage, student groups are challenged to independently create their own experiment procedures, working with given materials and tools. The general approach is that they set up model roads using rubber mats to simulate asphalt and piezoelectric transducers to simulate the in-ground road sensors. They drop heavy bolts at various locations on the “road,” collecting data and then analyzing the voltage changes across the piezoelectric transducers caused by the vibrations of the bolt hitting the rubber. After making notches in the rubber “road” to simulate cracks and potholes, they collect more data to see if the piezo elements detect the damage. Students write up their research and conclusions as if presenting evidence to USDOT officials about how the voltage changes across the piezo elements can be used to indicate road damage and extrapolated to determine when roads need maintenance service.

### Keeping Our Roads Smooth Lesson

###### Published on December 7, 2016

Students learn how roadways are designed and constructed, and discuss the advantages and limitations of the current roadway construction process. They look at current practices of roadway monitoring, discuss the limitations, and consider ways to further road monitoring research. To conclude, student groups compete to design smooth, cost-efficient and sound model road bases using gravel, sand, water and rubber (representing asphalt). This lesson prepares students for the associated activity in which they act as civil engineers hired by USDOT to research through their own model experimentation how to best use piezoelectric materials to detect road damage by showing how piezoelectric transducers can indicate road damage.

### New Perspectives: Two-Axis Rotations Activity

###### Published on November 21, 2016

Students learn about two-axis rotations, and specifically how to rotate objects both physically and mentally about two axes. A two-axis rotation is a rotation of an object about a combination of x, y or z-axes, as opposed to a single-axis rotation, which is about a single x, y or z-axis. Students practice drawing two-axis rotations through an exercise using simple cube blocks to create shapes, and then drawing on triangle-dot paper the shapes from various x-, y- and z-axis rotation perspectives. They use the right-hand rule to explore the rotations of objects. A worksheet is provided. This activity is part of a multi-activity series towards improving spatial visualization skills. At activity end, students re-take the 12-question quiz they took in the associated lesson (before conducting four associated activities) to measure how their spatial visualizations skills improved.

### Let’s Take a Spin: One-Axis Rotation Activity

###### Published on November 19, 2016

Students learn about one-axis rotations, and specifically how to rotate objects both physically and mentally to understand the concept. They practice drawing one-axis rotations through a group exercise using cube blocks to create shapes and then drawing those shapes from various x-, y- and z-axis rotation perspectives on triangle-dot paper (isometric paper). They learn the right-hand rule to explore rotations of objects. A worksheet is provided. This activity is part of a multi-activity series towards improving spatial visualization skills.

### Seeing All Sides: Orthographic Drawing Activity

###### Published on November 19, 2016

Students learn how to create two-dimensional representations of three-dimensional objects by utilizing orthographic projection techniques. They build shapes using cube blocks and then draw orthographic and isometric views of those shapes—which are the side views, such as top, front, right—with no depth indicated. Then working in pairs, one blindfolded partner describes a shape by feel alone as the other partner draws what is described. A worksheet is provided. This activity is part of a multi-activity series towards improving spatial visualization skills.

### Connect the Dots: Isometric Drawing and Coded Plans Activity

###### Published on November 19, 2016

Students learn about isometric drawings and practice sketching on triangle-dot paper the shapes they make using multiple simple cubes. They also learn how to use coded plans to envision objects and draw them on triangle-dot paper. A PowerPoint® presentation, worksheet and triangle-dot (isometric) paper printout are provided. This activity is part of a multi-activity series towards improving spatial visualization skills.

### Let’s Learn about Spatial Viz! Lesson

###### Published on November 19, 2016

Spatial visualization is the study of two- and three-dimensional objects and the practice of mental manipulation of objects. Spatial visualization skills are important in a range of subjects and activities like mathematics, physics, engineering, art and sports! In this lesson, students are introduced to the concept of spatial visualization and measure their spatial visualization skills by taking the provided 12-question quiz. Following the lesson, students complete the four associated spatial visualization activities and then re-take the quiz to see how much their spatial visualization skills have improved.

### An Assistive Artistic Device Activity

###### Published on October 28, 2016

Students design and develop a useful assistive device for people challenged by fine motor skill development who cannot grasp and control objects. In the process of designing prototype devices, they learn about the engineering design process and how to use it to solve problems. After an introduction about the effects of disabilities and the importance of hand and finger dexterity, student pairs research, brainstorm, plan, budget, compare, select, prototype, test, evaluate and modify their design ideas to create devices that enable a student to hold and use a small paintbrush or crayon. The design challenge includes clearly identified criteria and constraints, to which teams rate their competing design solutions. Prototype testing includes independent evaluations by three classmates, after which students redesign to make improvements. To conclude, teams make one-slide presentations to the class to recap their design projects. This activity incorporates a 3D modeling and 3D printing component as students generate prototypes of their designs. However, if no 3D printer is available, the project can be modified to use traditional and/or simpler fabrication processes and basic materials.

### Build Your Own Arduino Light Sculpture! Part 2 Activity

###### Published on October 28, 2016

In the companion activity, students experimented with Arduino programming to blink a single LED. During this activity, students build on that experience as they learn about breadboards and how to hook up multiple LEDs and control them individually so that they can complete a variety of challenges to create fun patterns! To conclude, students apply the knowledge they have gained to create LED-based light sculptures.

### Build Your Own Arduino Light Sculpture! Part 1 Activity

###### Published on October 28, 2016

Students create projects that introduce them to Arduino—a small device that can be easily programmed to control and monitor a variety of external devices like LEDs and sensors. First they learn a few simple programming structures and commands to blink LEDs. Then they are given three challenges—to modify an LED blinking rate until it cannot be seen, to replicate a heartbeat pattern and to send Morse code messages. This activity prepares students to create more involved multiple-LED patterns in the Part 2 companion activity.

### Volumes of Complex Solids Activity

###### Published on October 28, 2016

Challenged with a hypothetical engineering work situation in which they need to figure out the volume and surface area of a nuclear power plant’s cooling tower (a hyperbolic shape), students learn to calculate the volume of complex solids that can be classified as solids of revolution or solids with known cross sections. These objects of complex shape defy standard procedures to compute volumes. Even calculus techniques depend on the ability to perform multiple measurements of the objects or find functional descriptions of their edges. During both guided and independent practice, students use (free GeoGebra) geometry software, a photograph of the object, a known dimension of it, a spreadsheet application and integral calculus techniques to calculate the volume of complex shape solids within a margin of error of less than 5%—an approach that can be used to compute the volumes of big or small objects. This activity is suitable for the end of the second semester of AP Calculus classes, serving as a major grade for the last six-week period, with students’ project results presentation grades used as the second semester final test.

### Capillary Action in Sand Activity

###### Published on October 19, 2016

As part of a (hypothetical) challenge to help a city find the most affordable and environmentally friendly way to clean up an oil spill, students design and conduct controlled experiments to quantify capillary action in sand. Like engineers and entrepreneurs, student teams use affordable materials to design and construct models to measure the rate of capillary action in four types of sand: coarse, medium, fine and mixed. After observing and learning from a teacher-conducted capillary tube demonstration, teams are given a selection of possible materials and a budget to work within as they design their own experimental setups. After the construction of their designs, they take measurements to quantify the rate of capillary action, create graphs to analyze the data, and make concluding recommendations. Groups compare data and discuss as a class the pros and cons of their designs. Pre- and post-evaluations and two worksheets are provided.

### Using Microcontrollers to Model Homeostasis Activity

###### Published on October 6, 2016

Students learn about homeostasis and create models by constructing simple feedback systems using Arduino boards, temperature sensors, LEDs and Arduino code. Starting with pre-written code, students instruct LEDs to activate in response to the sensor detecting a certain temperature range. They determine appropriate temperature ranges and alter the code accordingly. When the temperature range is exceeded, a fan is engaged in order to achieve a cooling effect. In this way, the principle of homeostasis is demonstrated. To conclude, students write summary paragraphs relating their models to biological homeostasis.

### Does It Cut It? Understanding Wind Turbine Blade Performance Activity

###### Published on September 30, 2016

Students gain an understanding of the factors that affect wind turbine operation. Following the steps of the engineering design process, engineering teams use simple materials (cardboard and wooden dowels) to build and test their own turbine blade prototypes with the objective of maximizing electrical power output for a hypothetical situation—helping scientists power their electrical devices while doing research on a remote island. Teams explore how blade size, shape, weight and rotation interact to achieve maximal performance, and relate the power generated to energy consumed on a scale that is relevant to them in daily life. A PowerPoint® presentation, worksheet and post-activity test are provided.

### Magnetic Fields and Distance Activity

###### Published on September 22, 2016

Students measure the relative intensity of a magnetic field as a function of distance. They place a permanent magnet selected distances from a compass, measure the deflection, and use the gathered data to compute the relative magnetic field strength. Based on their findings, students create mathematical models and use the models to calculate the field strength at the edge of the magnet. They use the periodic table to predict magnetism. Finally, students create posters to communicate the details their findings. This activity guides students to think more deeply about magnetism and the modeling of fields while practicing data collection and analysis. An equations handout and two grading rubrics are provided.