In this number line task students must treat the interval from 0 to 1 as a whole, partition the whole into the appropriate number of equal sized parts, and then locate the fraction(s).
This task can be implemented in a variety of ways. For a class with previous exposure to the incenter or angle bisectors, part (a) could be a quick exercise in geometric constructions,. Alternatively, this could be part of a full introduction to angle bisectors, culminating in a full proof that the three angle bisectors are concurrent, an essentially complete proof of which is found in the solution below.
In this instructional task students are given two inequalities, one as a formula and one in words, and a set of possible solutions. They have to decide which of the given numbers actually solve the inequalities.
The goal of this task is to have students appreciate how the different constants (P0, K, and r) influence the shape of the graph.
This problem introduces a logistic growth model in the concrete setting of estimating the population of the U.S. The model gives a surprisingly accurate estimate and this should be contrasted with linear and exponential models, studied in ``U.S. Population 1790-1860.'' This task requires students to interpret data presented.
In this activity students compare objects to see which is longer and heavier than the other.
In this task students figure out how to draw the longest line on a map of the United States without hitting a border. They use color and line plots to keep track of their results.
This task builds on studentsŐ prior knowledge and understanding of conditional probability, and introduces the concept of independence of events.
Students work in teams of two to discover the relative positions of the Earth, Sun and Moon that produce the different phases of the Moon. Groups are each given a Styrofoam ball that they attach to a pencil so that it looks like a lollipop. In this acting-out model exercise, this ball on a stick represents the Moon, the students represent the Earth and a hanging lightbulb serves as the Sun. Students move the "Moon" around them to discover the different phases. They fill in the position of the Moon and its corresponding phase in a worksheet.
Students learn about the unique challenges astronauts face while eating in outer space. They explore different food choices and food packaging. Students learn about the engineering design process, and then, as NASA engineering teams, they design and build original model devices to help astronauts eat in a microgravity environment --- their own creative devices for food storage and meal preparation.
The purpose of this task is for students to compare two options for a prize where the value of one is given $2 at a time, giving them an opportunity to "work with equal groups of objects to gain foundations for multiplication." This context also provides students with an introduction to the concept of delayed gratification, or resisting an immediate reward and waiting for a later reward, while working with money.
The Massachusetts Institute of Technology, with funding from the William and Flora Hewlett Foundation, the Andrew W. Mellon Foundation, and MIT, has launched this "large-scale, Web-based electronic publishing initiative." The website posts lecture notes, problem sets, and other materials from courses across the MIT campus. This section highlights MIT's undergraduate and graduate program in Mathematics. Courses are listed by title and include topics such as Differential Analysis, Linear Algebra, and Statistical Inference. The materials serve as valuable resources for educators, students, or anyone interested in learning more about these topics.
This is an instructor's guide for an experiment to measure electrostatic force, using parallel plates made from two washers, insulating perf-board, and aluminum foil. Photos and detailed instructions are provided for experimental setup. SEE RELATED MATERIALS for a Java simulation by the same authors on the topic of capacitance. For an Excel spreadsheet developed specifically to accompany this experiment, see link below: MIT Physics 8.02 Open Courseware: Labs
LearningEdge is a free learning resource for management educators and students provided open and available to the world. Developed by MIT Sloan faculty and students, this collection of teaching case studies and management flight simulations focuses on areas in which Sloan's innovative research and teaching are on the cutting edge, including entrepreneurship, leadership and ethics, operations management, strategy, sustainability, and system dynamics.
LearningEdge was formerly MIT Sloan Teaching Innovation Resources (MSTIR).
In this activity, students gain first-hand experience with the mechanical advantage of pulleys. Students are given the challenge of helping save a whale by moving it from an aquarium back to its natural habitat into the ocean. They set up different pulley systems, compare the theoretical and actual mechanical advantage of each and discuss their recommendations as a class.
In this activity, students reinforce their understanding of compound machines by building a catapult. This compound machine consists of a lever and a wheel-and-axel. Catapults have been designed by engineers for a variety of purposes from lifting boulders into the air for warfare to human beings for entertainment; the projectiles in this activity are grapes for a magic act. Given the building materials, students design and build their catapult to launch a grape a certain distance.
This lesson introduces students to the effects of magnetic fields in matter addressing permanent magnets, diamagnetism, paramagnetism, ferromagnetism, and magnetization. First students must compare the magnetic field of a solenoid to the magnetic field of a permanent magnet. Students then learn the response of diamagnetic, paramagnetic, and ferromagnetic material to a magnetic field. Now aware of the mechanism causing a solid to respond to a field, students learn how to measure the response by looking at the net magnetic moment per unit volume of the material.
Students explore electromagnetism and engineering concepts using optimization techniques to design an efficient magnetic launcher. Groups start by algebraically solving the equations of motion for the velocity at the time when a projectile leaves a launcher. Then they test three different launchers, in which the number of coils used is different, measuring the range and comparing the three designs. Based on these observations, students record similarities and differences and hypothesize on the underling physics. They are introduced to Faraday's law and Lenz's law to explain the physics behind the launcher. Students brainstorm how these principals might be applied to real-world engineering problems.
This lesson ties the preceding lessons together and brings students back to the grand challenge question on MRI safety. During this lesson, students focus on the logistics of magnetic resonance imaging as well as the MRI hardware. Students can then integrate this knowledge with their acquired knowledge on magnetic fields to solve the challenge question.
This subject traces the history of the European novel by studying texts that have been influential in connection with two interrelated ideas. 1) When serious fiction deals with matters of great consequence, it should not deal with the actions of persons of consequence--kings, princes, high elected officials and the like--but rather with the lives of apparently ordinary people and the everyday details of their social ambitions and desires. To use a phrase of Balzac's, serious fiction deals with "what happens everywhere". 2) This idea sometimes goes with another: that the most significant representations of the human condition are those dealing with persons who try to compel society to accept them as its destined agent, despite their absence of high birth or inheritance.