The lesson begins with a demonstration introducing students to the force between two current carrying loops, comparing the attraction and repulsion between the loops to that between two magnets. After formal lecture on Ampere's law, students begin to use the concepts to calculate the magnetic field around a loop. This is applied to determine the magnetic field of a toroid, imagining a toroid as a looped solenoid.

Students design, build and test model roller coasters using foam tubing. The design process integrates energy concepts as they test and evaluate designs that address the task as an engineer would. The goal is for students to understand the basics of engineering design associated with kinetic and potential energy to build an optimal roller coaster. The marble starts with potential energy that is converted to kinetic energy as it moves along the track. The diameter of the loops that the marble traverses without falling out depends on the kinetic energy obtained by the marble.

This short activity helps students analyze a political cartoon about U.S. imperialism in the Philippines. To complete the activity, the teacher will need either a map or a globe to show students the relative distance between the United States and Philippines.

In this task, the students are not asked to find an answer, but are asked to analyze word problems and explain their thinking. In the process, they are faced with varying ways of thinking about multiplication.

In this activity, students discover the relationship between an object's mass and the amount of space it takes up (its volume). Students learn about the concept of displacement and how an object can float if it displaces enough water, and the concept of density and its relationship to mass and volume.

Students develop an app for an Android device that utilizes its built-in internal sensors, specifically the accelerometer. The goal of this activity is to teach programming design and skills using MIT's App Inventor software (free to download from the Internet) as the vehicle for learning. The activity should be exciting for students who are interested in applying what they learn to writing other applications for Android devices. Students learn the steps of the engineering design process as they identify the problem, develop solutions, select and implement a possible solution, test the solution and redesign, as needed, to accomplish the design requirements.

Students investigate the motion of a simple pendulum through direct observation and data collection using Android® devices. First, student groups create pendulums that hang from the classroom ceiling, using Android smartphones or tablets as the bobs, taking advantage of their built-in accelerometers. With the Android devices loaded with the (provided) AccelDataCapture app, groups explore the periodic motion of the pendulums, changing variables (amplitude, mass, length) to see what happens, by visual observation and via the app-generated graphs. Then teams conduct formal experiments to alter one variable while keeping all other parameters constant, performing numerous trials, identifying independent/dependent variables, collecting data and using the simple pendulum equation. Through these experiments, students investigate how pendulums move and the changing forces they experience, better understanding the relationship between a pendulum's motion and its amplitude, length and mass. They analyze the data, either on paper or by importing into a spreadsheet application. As an extension, students may also develop their own algorithms in a provided App Inventor framework in order to automatically note the time of each period.

This task provides a construction of the angle bisector of an angle by reducing it to the bisection of an angle to finding the midpoint of a line segment. It is worth observing the symmetry -- for both finding midpoints and bisecting angles, the goal is to cut an object into two equal parts. The conclusion of this task is that they are, in a sense, of exactly equivalent difficulty -- bisecting a segment allows us to bisect and angle (part a) and, conversely, bisecting an angle allows us to bisect a segment (part b). In addition to seeing how these two constructions are related, the task also provides an opportunity for students to use two different triangle congruence criteria: SSS and SAS.

Students analyze the relationship between wheel radius, linear velocity and angular velocity by using LEGO(TM) MINDSTORMS(TM) NXT robots. Given various robots with different wheel sizes and fixed motor speeds, they predict which has the fastest linear velocity. Then student teams collect and graph data to analyze the relationships between wheel size and linear velocity and find the angular velocity of the robot given its motor speed. Students explore other ways to increase linear velocity by changing motor speeds, and discuss and evaluate the optimal wheel size and desired linear velocities on vehicles.

This section contains links to the image files for the animal body parts. Cards feature animals with distinguishing body parts such as an animal with fins: goldfish or an animal with hooves: sheep.

In this task students have to interpret expressions involving two variables in the context of a real world situation. All given expressions can be interpreted as quantities that one might study when looking at two animal populations.

Students are introduced to the classification of animals and animal interactions. Students also learn why engineers need to know about animals and how they use that knowledge to design technologies that help other animals and/or humans. This lesson is part of a series of six lessons in which students use their growing understanding of various environments and the engineering design process, to design and create their own model biodome ecosystems.

In this lesson plan, students will learn about the 12 animals of the Chinese zodiac. In the introductory first lesson, they will see how animals are often used as symbols. In the second lesson, they will hear one of several versions of how the 12 animals were chosen. They will then focus upon a few of the animals in the story and see how they can be used as symbols of certain human characteristics. In the third lesson, they will be introduced to the other animals of the zodiac, and they will be given a chart on which they will assign traits to each animal. Then they will consult a number of websites to find the traits traditionally associated with the animals, which they will add to their list. Then, they will come up with a number of ways to compare and contrast the animals in the list. In the third lesson, they will focus upon the animal associated with the year of their birth, learning about its traits and discussing whether or not these apply to themselves and their peers. Finally, each student will make an acrostic, combining the letters of his or her first name with adjectives that relate to his or her zodiac sign.

In this problem students are comparing a very small quantity with a very large quantity using the metric system. The metric system is especially convenient when comparing measurements using scientific notations since different units within the system are related by powers of ten.

This is a video and accomanying worksheet that students can use to learn about antiseptics and disinfectants at home, how they are classified, and then research a product on their own.

This task requires students to work with very large and small values expressed both in scientific notation and in decimal notation (standard form). In addition, students need to convert units of mass.

Does the real-world application of science depend on mathematics? In this activity, students answer this question as they experience a real-world application of systems of equations. Given a system of linear equations that mathematically models a specific circuit—students start by solving a system of three equations for the currents. After becoming familiar with the parts of a breadboard, groups use a breadboard, resistors and jumper wires to each build the same (physical) electric circuit from the provided circuit diagram. Then they use voltmeters to measure the current flow across each resistor and calculate the current using Ohm’s law. They compare the mathematically derived current values to the measured values, and calculate the percentage difference of their results. This leads students to conclude that real-world applications of science do indeed depend on mathematics! Students make posters to communicate their results and conclusions. A pre/post-activity quiz and student worksheet are provided. Adjustable for math- or science-focused classrooms.

Students explore Hooke's law while working in small groups at their lab benches. They collect displacement data for springs with unknown spring constants, k, by adding various masses of known weight. After exploring Hooke's law and answering a series of application questions, students apply their new understanding to explore a tissue of known surface area. Students then use the necessary relationships to depict a cancerous tumor amidst normal tissue by creating a graph in Microsoft Excel.

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.