Physics is the scientific study of the basic principles of the universe, including matter, energy, motion and force, and their interactions. Major topics include classical mechanics, thermodynamics, light and optics, electromagnetism and relativity.
This 8-minute video lesson uses unit vectors to represent the components of a vector.
This activity is a hands on investigation in which students will construct, and launch a trebuchet.
Students explore the physics utilized by engineers in designing today's roller coasters, including potential and kinetic energy, friction, and gravity. First, students learn that all true roller coasters are completely driven by the force of gravity and that the conversion between potential and kinetic energy is essential to all roller coasters. Second, they also consider the role of friction in slowing down cars in roller coasters. Finally, they examine the acceleration of roller coaster cars as they travel around the track. During the associated activity, the students design, build, and analyze a roller coaster for marbles out of foam tubing.
This instructional guide (PDF) is for the mobile app Pick-a-Path (both iOS and Android platforms). The guide provides professional development by discussing the math in each level of the game, giving suggestions for classroom use, and recommending related resources from Illuminations. The Pick-a-Path app is cataloged separately and listed as a related resource.
In a class demonstration, the teacher places different pill types ("chalk" pill, gel pill, and gel tablet) into separate glass beakers of vinegar, representing human stomach acid. After 20-30 minutes, the pills dissolve. Students observe which dissolve the fastest, and discuss the remnants of the various pills. What they learn contributes to their ongoing objective to answer the challenge question presented in lesson 1 of this unit.
In this activity related to light and perception, learners use a pinhole in an index card as a magnifying glass to help their eye focus on a nearby object. Learners will also discover that because this magnifier limits the amount of light that reaches their eye from the object, the pinhole makes the object appear dimmer. Learners are encouraged to explore using pins and needles with different diameters to make different-sized holes in index cards to see how this affects the image. They can also try forming a pinhole by curling their index finger.
In this three-lesson unit students conduct surveys, create graphs, and explore combinations related to pizza toppings. Each lesson plan contains worksheets in PDF format.
Student groups use a "real" 3D coordinate system to plot points in space. Made from balsa wood or wooden dowels, the system has three axes at right angles and a plane (the XY plane) that can slide up and down the Z axis. Students are given several coordinates and asked to find these points in space. Then they find the coordinates of the eight corners of a box/cube with given dimensions.
After a brief history of plastics, students look more closely as some examples from the abundant types of plastics found in our day-to-day lives. They are introduced to the mechanical properties of plastics, including their stress-strain relationships, which determine their suitability for different industrial and product applications. These physical properties enable plastics to be fabricated into a wide range of products. Students learn about the different roles that plastics play in our lives, Young's modulus, and the effects that plastics have on our environment. Then students act as industrial engineers, conducting tests to compare different plastics and performing a cost-benefit analysis to determine which are the most cost-effective for a given application, based on their costs and measured physical properties.
In this interactive Flash game learners use their knowledge of coordinates on a grid to move Plotter the penguin and avoid trouble. The game includes three levels of difficulty, a story mode, and a choice of five different games to play. Each game provides instruction as well as in-depth help in linked PDF documents.
In this activity, learners explore how polarizing sunglasses can help diminish road glare. By rotating a pair of polarizing sunglass lenses or other polarizing materials, learners will discover that some angles are better at reducing glare than others. Learners observe light from the sky, reflected from a mirror, or reflected from the surface of a pond. Use this activity to introduce learners to principles of light and polarization.
Students investigate the accuracy of sundials and the discrepancy that lies between "real time" and "clock time." They track the position of the sun during the course of a relatively short period of time as they make a shadow plot, a horizontal sundial, and a diptych sundial. (The activity may be abridged to include only one or two of the different sundials, instead of all three.)
In this unit of nine lessons from Illuminations, students use logical thinking to create, identify, extend, and translate patterns. They make patterns with objects, numbers, and shapes and also explore a variety of patterns in mathematics, physical education and music. Pattern cores explored are AB, ABB, AAB, ABC, ABCD and lastly ABA. Instructional plan, questions for the students, assessment options, extensions with links to the US and state flags, and teacher reflections are given for each lesson.
In this online version of the popular card game, students combine five given number cards, using the four arithmetic operations (addition, subtraction, multiplication, division), to arrive at a target number. This version uses the numbers 1–10 only. Users may ask for a hint or view a possible solution, although there are often multiple solutions.
This course surveys a variety of reasoning, optimization and decision making methodologies for creating highly autonomous systems and decision support aids. The focus is on principles, algorithms, and their application, taken from the disciplines of artificial intelligence and operations research. Reasoning paradigms include logic and deduction, heuristic and constraint-based search, model-based reasoning, planning and execution, and machine learning. Optimization paradigms include linear programming, integer programming, and dynamic programming. Decision-making paradigms include decision theoretic planning, and Markov decision processes.
This textbook, an introduction to the principles and abstractions used in the design of computer systems, is an outgrowth of notes written for 6.033 Computer System Engineering over a period of 40-plus years. Individual chapters are also used in other EECS subjects.
This course introduces students to the modeling, quantification, and analysis of uncertainty. The tools of probability theory, and of the related field of statistical inference, are the keys for being able to analyze and make sense of data. These tools underlie important advances in many fields, from the basic sciences to engineering and management.
Students apply what they have learned about the engineering design process to a real-life problem that affects them and/or their school. They chose a problem as a group, and then follow the engineering design process to come up with and test their design solution. This activity teaches students how to use the engineering design process while improving something in the school environment that matters to them. By performing each step of the design process, students can experience what it is like to be an engineer.
Problem solving is the thought processes involved in solving a problem. It is both a means of developing students' knowledge of mathematics and a critical outcome of a good mathematics education. A mathematical problem, as distinct from an exercise, requires the solver to search for a method for solving the problem rather than following a set procedure. Mathematical problem solving, therefore, requires an understanding of relevant concepts, procedures, and strategies. To become good problem solvers, students need many opportunities to formulate questions, model problem situations in a variety of ways, generalize mathematical relationships, and solve problems in both mathematical and everyday contexts.