This interactive Java application helps students understand the partial quotients algorithm of division in the context of dividing food equally. Students select a character and a type of food as well as the quantities of characters (divisor, 1-50) and food (dividend, 1-500) – or have the applet make selections randomly. The applet creates a story problem and leads users through the algorithm one step at a time, using questions related to the meaning of each step, and displays graphics illustrating the steps. Remainders can be expressed as whole numbers or fractions. An online calculator is available to help with calculations.

Studies how randomization can be used to make algorithms simpler and more efficient via random sampling, random selection of witnesses, symmetry breaking, and Markov chains. Models of randomized computation. Data structures: hash tables, and skip lists. Graph algorithms: minimum spanning trees, shortest paths, and minimum cuts. Geometric algorithms: convex hulls, linear programming in fixed or arbitrary dimension. Approximate counting; parallel algorithms; online algorithms; derandomization techniques; and tools for probabilistic analysis of algorithms.

The three tasks in this set are not examples of tasks asking students to compute using the standard algorithms for multiplication and division because most people know what those kinds of problems look like. Instead, these tasks show what kinds of reasoning and estimation strategies students need to develop in order to support their algorithmic computations.

The three tasks (including part 1 and part 3) in this set are not examples of tasks asking students to compute using the standard algorithms for multiplication and division because most people know what those kinds of problems look like. Instead, these tasks show what kinds of reasoning and estimation strategies students need to develop in order to support their algorithmic computations.

In this 5-lesson multi-media unit, students will explore various real-world applications of different forms of measurement, including time and distance. They will make estimations and calculations. Throughout the unit, students will be using online resources to familiarize themselves with coral reefs, the nation of Belize, and to plan a pretend scuba diving trip. Activity sheets (pdf), links to online resources, assessment options and other commentary are provided.

6.780 covers statistical modeling and the control of semiconductor fabrication processes and plants. Topics include design of experiments, response surface modeling, and process optimization; defect and parametric yield modeling; process/device/circuit yield optimization; monitoring, diagnosis, and feedback control of equipment and processes; analysis and scheduling of semiconductor manufacturing operations.

In this data analysis lesson students explore various representations, including bar graphs, steam-and-leaf plots, and box-and-whisker plots, to analyze the frequency of letters in the names of the 50 states. Students are encouraged to use a systematic approach to collect their data and are shown various tools to help them gather and display it. The lesson includes a student worksheet (PDF), links to a Decrypting Text website, Bar Grapher tool, and Box Plotter tool, and suggested questions, extension, and assessment ideas.

Fundamentals of detection and estimation for signal processing, communications, and control. Vector spaces of random variables. Bayesian and Neyman-Pearson hypothesis testing. Bayesian and nonrandom parameter estimation. Minimum-variance unbiased estimators and the Cramer-Rao bounds. Representations for stochastic processes; shaping and whitening filters; Karhunen-Loeve expansions. Detection and estimation from waveform observations. Advanced topics: linear prediction and spectral estimation; Wiener and Kalman filters.

This Java applet provides opportunities for creative problem solving while encouraging young students to estimate length and angle measure. Using the Turtle Pond Applet, students enter a sequence of commands to help the turtle get to the pond. Children can write their own solutions using LOGO commands and input them into the computer. The turtle will then move and leave a trail or path according to the instructions given. (N.B. the applet is an upgrade of one that supported the Lesson "Get the Turtle to the Pond," cataloged separately.)

Students learn about trigonometry, geometry and measurements while participating in a hands-on interaction with LEGO® MINDSTORMS® NXT technology. First they review fundamental geometrical and trigonometric concepts. Then, they estimate the height of various objects by using simple trigonometry. Students measure the height of the objects using the LEGO robot kit, giving them an opportunity to see how sensors and technology can be used to measure things on a larger scale. Students discover that they can use this method to estimate the height of buildings, trees or other tall objects. Finally, students synthesize their knowledge by applying it to solve similar problems. By activity end, students have a better grasp of trigonometry and its everyday applications.