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.

Students are introduced to the structure, function and purpose of locks and dams, which involves an introduction to Pascal's law, water pressure and gravity.

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.

This course begins with an introduction to the theory of computability, then proceeds to a detailed study of its most illustrious result: Kurt GĚŚdel's theorem that, for any system of true arithmetical statements we might propose as an axiomatic basis for proving truths of arithmetic, there will be some arithmetical statements that we can recognize as true even though they don't follow from the system of axioms. In my opinion, which is widely shared, this is the most important single result in the entire history of logic, important not only on its own right but for the many applications of the technique by which it's proved. We'll discuss some of these applications, among them: Church's theorem that there is no algorithm for deciding when a formula is valid in the predicate calculus; Tarski's theorem that the set of true sentence of a language isn't definable within that language; and GĚŚdel's second incompleteness theorem, which says that no consistent system of axioms can prove its own consistency.

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.

Quantitative techniques of operations research with emphasis on applications in transportation systems analysis (urban, air, ocean, highway, and pickup and delivery systems) and in the planning and design of logistically oriented urban service systems (e.g., fire and police departments, emergency medical services, and emergency repair services). Unified study of functions of random variables, geometrical probability, multi-server queuing theory, spatial location theory, network analysis and graph theory, and relevant methods of simulation. Computer exercises and discussions of implementation difficulties.

This course surveys operations research models and techniques developed for a variety of problems arising in logistical planning of multi-echelon systems. There is a focus on planning models for production/inventory/distribution strategies in general multi-echelon multi-item systems. Topics include vehicle routing problems, dynamic lot sizing inventory models, stochastic and deterministic multi-echelon inventory systems, the bullwhip effect, pricing models, and integration problems arising in supply chain management. Probability and linear programming experience required.

This short video and interactive assessment activity is designed to teach fifth graders about multiple rounds of division - long division word problems.

This short video and interactive assessment activity is designed to teach fourth graders about dividing 3 and 4 digit numbers by 2 digit numbers.

This short video and interactive assessment activity is designed to teach fifth graders about dividing 3 and 4 digit numbers by 2 digit numbers.

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 art history video lesson looks at Sir John Everett Millais' "Ophelia", 1851-52, oil on canvas (Tate Britain, London); and Barnett B. Newman's "Vir Heroicus Sublimis", oil on canvas, 1950-51 (MoMA).

This art history video lecture examines Ambrogio Lorenzetti's "Presentation of Jesus in the Temple", 1342, tempera on panel, (Galleria degli Uffizi, Florence).

The Lost in the Amazon curricular unit is a series of minds-on and hands-on engineering activities based on an adventure scenario set in the Amazon rainforest in Brazil. Students imagine themselves to be a team of EnviroTech engineers returning to the U.S. from a conference in Brasilia, Brazil. When their plane crashes deep in the Amazon forest, they work in groups to overcome various obstacles in their quest to survive and reach the nearest city as quickly and safely as possible. Motivated by this adventurous theme, students discover, learn and apply the following: 1) classification of plants and insects; 2) general categorizing skills; 3) process skills: problem solving and critical thinking; 4) scientific testing and experimentation; 5) materials properties.

This art history video discussion examines Lucas Cranach the Elder's "Judith with the Head of Holofernes", c. 1530, oil on panel (Kunsthistorisches Museum, Vienna).

This art history video discussion examines Lucas Cranach the Elder's "Cupid complaining to Venus", c. 1525, oil on wood (The National Gallery, London).

This art history video discussion examines Lucian Freud's "Standing by the Rags" 1988-89, oil on canvas (Tate Britain, London).