Middle School Portal: Math and Science Pathways (MSP2)
This online activity challenges students to determine which of four different size grape juice cans labeled with the grape juice concentration would have the strongest grape taste. The activity is one of 80 mathematical challenges featured on the Figure This! web site emphasizing real-world uses of mathematics. The Hint suggests forming ratios that are fractions to compare quantities. Two ways of answering the initial question are illustrated with tables. Related questions have students consider
Author(s): National Council of Teachers of Mathematics (NCTM)

Middle School Portal: Math and Science Pathways (MSP2)
In this online activity, students are challenged to reproduce 20 different figures using the seven pieces of the Chinese tangram game. The figure to be reproduced is shown in the upper right corner of the screen. The student points and clicks to rotate and position the tangram pieces to copy the figure. For each figure, the student must use, but not overlap, all seven pieces. Clicking on the hint will put outlines of the tangram pieces on the figure the student is trying to reproduce. Figures in
Author(s): PBS Kids

Middle School Portal: Math and Science Pathways (MSP2)
Given that a square table sits one person per side, this activity challenges students to figure out how many tables would need to be pushed together to seat a party of nineteen. The activity, part of the Figure This! collection of 80 math challenges emphasizing math in the real world, explains how arranging geometric shapes is important to architects, landscapers, and quilters. Students are encouraged to model the problem using squares of paper to represent tables. Related questions ask students
Author(s): National Council of Teachers of Mathematics (NCTM)

Middle School Portal: Math and Science Pathways (MSP2)
This activity challenges students to think about angles as geometric shapes and to find the sizes of the angles between their fingers. It is part of the Figure This! collection of 80 online mathematical challenges emphasizing real world uses of mathematics. For this challenge, the students trace a hand stretched to form an L-shape with the thumb and sketches angles of 90 degrees and 45 degrees between the thumb and index finger. They use the sketches to estimate the angles between their other fi
Author(s): National Action Council for Minorities in Engineer

Middle School Portal: Math and Science Pathways (MSP2)
This web site contains descriptions and links to more than 60 virtual manipulatives, activities designed to function as concept tutorials. The virtual manipulatives, mostly in the form of Java applets, are designed to facilitate grades 6-8 mathematics learning. By encouraging active student exploration with computers, the virtual manipulatives can help students visualize mathematical relationships. They are organized into five categories based on the National Council of Teachers of Mathematics (
Author(s): Utah State University. National Library of Virtual

Middle School Portal: Math and Science Pathways (MSP2)
This activity asks the student to determine the time in Cairo, Egypt, when it is 3:00 p.m. in San Francisco. It includes a map of the world with the time zones marked. The activity, part of the Figure This! collection of 80 math challenges emphasizing math in the real world, explains how to determine the time in different time zones and what the prime meridian and the international date line are. Students see how positive and negative numbers relate to the time zones and are asked to think about
Author(s): National Council of Teachers of Mathematics (NCTM)

Middle School Portal: Math and Science Pathways (MSP2)
This activity opens with a picture that shows two individuals who have each built a patio using different arrangements of the same number of identical concrete tiles. Both patios have the same total area, and students are challenged to figure out the dimensions of a single concrete tile. The activity, part of the Figure This! collection of 80 math challenges emphasizing math in the real world, explains how area is an important concept used by architects, real estate agents, and artists. The Hint
Author(s): National Council of Teachers of Mathematics (NCTM)

Middle School Portal: Math and Science Pathways (MSP2)
This activity challenges students to develop an algorithm to find the day of the week on which they were born. An algorithm is described as a step-by-step routine for solving a problem. The activity, part of the Figure This! collection of 80 math challenges emphasizing math in the real world, notes how algorithms are used by scientists, factory workers, and chefs. The hint shows students that, for any date, the day of the week changes from one year to the next. Students are reminded to consider
Author(s): National Council of Teachers of Mathematics (NCTM)

Middle School Portal: Math and Science Pathways (MSP2)
This activity opens with an animated picture of an access ramp over a three-step staircase, with steps 7 inches high and 10 inches wide. Students are asked to determine how far away the ramp should start in order to go up the steps. The activity, part of the Figure This! collection of 80 math challenges emphasizing math in the real world, explains how slope, or the measurement of steepness, is important to civil engineers, landscapers, and surveyors. The hint states that ramps usually go up 1 ve
Author(s): National Council of Teachers of Mathematics (NCTM)

Middle School Portal: Math and Science Pathways (MSP2)
In this activity, students read graphs and interpret raw data to determine if there is a correlation between drinking soda and the rate of bone fractures in teenage girls. The activity is part of the Figure This! collection of 80 online mathematical challenges emphasizing real world uses of mathematics. Students are encouraged to organize data into tables to look for associations, but are cautioned that additional factors many influence the appearance of cause and effect. In other related math q
Author(s): National Council of Teachers of Mathematics (NCTM)

Middle School Portal: Math and Science Pathways (MSP2)
This challenge from the Figure This! collection of 80 online math challenges explores two questions about images seen in mirrors. The usefulness of knowing about angles, reflections, and lines of sight for designing theaters and for playing both video and sports games is noted. The suggested hands-on exploratory activities should lead students to conclude that (1) an image in a mirror shows twice as much of the person as the length of the mirror and (2) when backing away from a mirror, the image
Author(s): National Action Council for Minorities in Engineer

Middle School Portal: Math and Science Pathways (MSP2)
This challenge asks students to determine possible ways for combining stamps costing 15 and 33 cents to total 1 dollar 77 cents. It notes that this type of problem is similar to a process used for creating security codes. This online student activity is part of the Figure This! collection of 80 mathematical challenges. Students are encouraged to make a chart as they explore possible number combinations. The answer page describes and illustrates four different approaches to finding the solution,
Author(s): National Action Council for Minorities in Engineer

Middle School Portal: Math and Science Pathways (MSP2)
This symmetry exploration challenges the student to find lowercase alphabet letters that appear the same when inverted. Part of the Figure This! collection of 80 math challenges, this exploration contains links to a solution hint, the solution, and other similar investigations. Students are challenged to find sports team names, words, sentences, and digital clock numbers that read the same in reverse. The exploration also has activities for investigating rotational symmetry. The Did You Know fea
Author(s): National Action Council for Minorities in Engineer

Middle School Portal: Math and Science Pathways (MSP2)
This second challenge in the Figure This! set of 80 math challenges asks students to estimate how fast their hearts beat and how long it will take to beat a million and then a billion times. The web page points out the importance of large numbers when determining the distance to Mars or the size of the national debt. The Getting Started link on the top navigation bar leads to a description of how to determine a person's pulse rate. There are also links to a solution hint, the solution itself, an
Author(s): National Action Council for Minorities in Engineer

Middle School Portal: Math and Science Pathways (MSP2)
This first challenge in the Figure This! list of 80 math challenges addresses the question of how long a person would have to wait in a line if holding ticket number 300. The web page points out the relevance of estimating and measuring time for industries including banking and amusement parks. The page features links to a solution hint, the solution, other related math questions, and an online and print resources related to queuing. The Did You Know link offers interesting facts from the Guinne
Author(s): National Action Council for Minorities in Engineer

Middle School Portal: Math and Science Pathways (MSP2)
This web site offers families, teachers, and tutors 80 mathematical challenges helpful for encouraging problem solving with students in grades 6 to 8. The math challenges focus on concepts and objects found in everyday life, such as how fast your heart beats, what shape container holds the most popcorn, and how much of me shows in a mirror. Each challenge contains an initial problem with a solution hint, a complete explanation of the answer, and additional problems related to the same challenge.
Author(s): National Action Council for Minorities in Engineer

Middle School Portal: Math and Science Pathways (MSP2)
At this award-winning website, try out some engineering design challenges: the Slowly Moving Marble, Civil Engineering Camping, Chemical Engineering, Nuclear Engineering, and Door Alarm. Students can draw their designs on the site, submit them, and receive guidance from an engineer.
Author(s): Creator not set

21M.606 Introduction to Stagecraft (MIT)

Author(s):

6.832 Underactuated Robotics (MIT)
Robots today move far too conservatively, using control systems that attempt to maintain full control authority at all times. Humans and animals move much more aggressively by routinely executing motions which involve a loss of instantaneous control authority. Controlling nonlinear systems without complete control authority requires methods that can reason about and exploit the natural dynamics of our machines. This course discusses nonlinear dynamics and control of underactuated mechanical sys
Author(s):

5.069 Crystal Structure Analysis (MIT)
This course covers the following topics: X-ray diffraction: symmetry, space groups, geometry of diffraction, structure factors, phase problem, direct methods, Patterson methods, electron density maps, structure refinement, how to grow good crystals, powder methods, limits of X-ray diffraction methods, and structure data bases.