Measuring the dimensions of nano-circuits requires an expensive, high-resolution microscope with integrated video camera and a computer with sophisticated imaging software, but in this activity, students measure nano-circuits using a typical classroom computer and (the free-to-download) GeoGebra geometry software. Inserting (provided) circuit pictures from a high-resolution microscope as backgrounds in GeoGebra's graphing window, students use the application's tools to measure lengths and widths of circuit elements. To simplify the conversion from the on-screen units to the real circuits' units and the manipulation of the pictures, a GeoGebra measuring interface is provided. Students export their data from GeoGebra to Microsoft® Excel® for graphing and analysis. They test the statistical significance of the difference in circuit dimensions, as well as obtain a correlation between average changes in original vs. printed circuits' widths. This activity and its associated lesson are suitable for use during the last six weeks of the AP Statistics course; see the topics and timing note below for details.

In this activity, students construct their own rocket-powered boat called an "aqua-thruster." These aqua-thrusters will be made from a film canister and will use carbon dioxide gas produced from a chemical reaction between an antacid tablet and water to propel it. Students observe the effect that surface area of this simulated solid rocket fuel has on thrust.

The main objective of this lesson is to illustrate an important application of mathematics in practical life -- namely in art. Most of the pictures selected for this lesson are visible on the walls of Al-Hambra – Granada (Spain), which is one of the most important landmarks in the Islamic civilization. There are three educational goals for this lesson: (1) establishing the concept of isometries; (2) giving real-life examples of groups; (3) demonstrating the importance of matrices and their applications. As background for this lesson, students just need some familiarity with the concept of a group and a limited knowledge about matrices and the inverse of a non-singular matrix.

Students are introduced to Pascal's law, Archimedes' principle and Bernoulli's principle. Fundamental definitions, equations, practice problems and engineering applications are supplied. A PowerPoint® presentation, practice problems and grading rubric are provided.

Students explore the interface between architecture and engineering. In the associated hands-on activity, students act as both architects and engineers by designing and building a small parking garage.

Students create four-legged walking robots and measure how far they travel across different types of surfaces. They design and create "shoes" to add to the robots' feet and observe the effect of their modifications on the net distance traveled across the various surface types. This activity illustrates how the specialized locomotive features of different species help them to survive or thrive in their habitat environments. The activity is best as an enrichment tool that follows a lesson that introduces the concept of biological adaptation to students.

Students learn that dams do not last forever. Similar to other human-made structures, such as roads and bridges, dams require regular maintenance and have a finite lifespan. Many dams built during the 1930-70s, an era of intensive dam construction, have an expected life of 50-100 years. Due to inadequate maintenance and/or for environmental reasons, some of these dams will fail or be removed in the next 50 years. The engineers with Splash Engineering have an ethical obligation to remind Thirsty County of the maintenance and lifespan concerns associated with its dam.

This learning video deals with a question of geometrical probability. A key idea presented is the fact that a linear equation in three dimensions produces a plane. The video focuses on random triangles that are defined by their three respective angles. These angles are chosen randomly subject to a constraint that they must sum to 180 degrees. An example of the types of in-class activities for between segments of the video is: Ask six students for numbers and make those numbers the coordinates x,y of three points. Then have the class try to figure out how to decide if the triangle with those corners is acute or obtuse.

The year is 2032 and your class has successfully achieved a manned mission to Mars! After several explorations of the Red Planet, one question is still being debated: "Is there life on Mars?" The class is challenged with the task of establishing criteria to help look for signs of life. Student explorers conduct a scientific experiment in which they evaluate three "Martian" soil samples and determine if any contain life.

This lesson explores the similarities between how a human being moves/walks and how a robot moves. This allows students to see the human body as a system, i.e., from the perspective of an engineer. It shows how movement results from (i) decision making, i.e., deciding to walk and move, and (ii) implementing the decision by conveying the decision to the muscle (human) or motor (robot).

This lesson teaches the engineering method for testing wherein one variable is changed while the others are held constant. Students compare the performance of a single paper airplane design while changing the shape, size and position of flaps on the airplane. Students also learn about control surfaces on the tail and wings of an airplane.

Create your own shapes using colorful blocks and explore the relationship between perimeter and area. Compare the area and perimeter of two shapes side-by-side. Challenge yourself in the game screen to build shapes or find the area of funky figures. Try to collect lots of stars!

Build rectangles of various sizes and relate multiplication to area. Discover new strategies for multiplying algebraic expressions. Use the game screen to test your multiplication and factoring skills!

Remember your multiplication tables? ... me neither. Brush up on your multiplication, division, and factoring skills with this exciting game. No calculators allowed! The students will be given mutiplication and division problems which they must answer. They also have the option of being given a number then stating the factors of how that number was attained using either multiplication or division.

Remember your multiplication tables? ... me neither. Brush up on your multiplication, division, and factoring skills with this exciting game. No calculators allowed!

Brush up on your multiplication, division, and factoring skills with this interactive multiplication chart. Three levels and timed or untimed options are available.

As an introduction to bioengineering, student teams are given the engineering challenge to design and build prototype artificial limbs using a simple syringe system and limited resources. As part of a NASA lunar mission scenario, they determine which substance, water (liquid) or air (gas), makes the appendages more efficient.

Students learn more about how muscles work and how biomedical engineers can help keep the muscular system healthy. Following the engineering design process, they create their own biomedical device to aid in the recovery of a strained bicep. They discover the importance of rest to muscle recovery and that muscles (just like engineers!) work together to achieve a common goal.

Students are presented with a hypothetical scenario in which they are biomedical engineers asked to design artificial hearts. Using the engineering design process as a guide, the challenge is established and students brainstorm to list everything they might need to know about the heart in order to create a complete mechanical replacement (size, how it functions, path of blood etc.). They conduct research to learn the information and organize it through various activities. They research artificial heart models that have already been used and rate their performance in clinical trials. Finally, they analyze the data to identify the artificial heart features and properties they think work best and document their findings in essay form.