The primary purpose of this task is to lead students to a …
The primary purpose of this task is to lead students to a numerical and graphical understanding of the behavior of a rational function near a vertical asymptote, in terms of the expression defining the function. The canoe context focuses attention on the variables as numbers, rather than as abstract symbols.
The purpose of this task is to use finite geometric series to …
The purpose of this task is to use finite geometric series to investigate an amazing mathematical object that might inspire students' curiosity. The Cantor Set is an example of a fractal.
Explore how a capacitor works! Change the size of the plates and …
Explore how a capacitor works! Change the size of the plates and add a dielectric to see how it affects capacitance. Change the voltage and see charges built up on the plates. Shows the electric field in the capacitor. Measure voltage and electric field.
This short video and interactive assessment activity is designed to teach second …
This short video and interactive assessment activity is designed to teach second graders about capacity comparison problems with illustrations - word problems.
This short video and interactive assessment activity is designed to teach fourth …
This short video and interactive assessment activity is designed to teach fourth graders about finding the amount of water with illustrations and calculations (metric units).
Students are presented with a short lesson on the difference between cohesive …
Students are presented with a short lesson on the difference between cohesive forces (the forces that hold water molecules together and create surface tension) and adhesive forces (the forces that causes water to "stick" to solid surfaces. The interaction between cohesive forces and adhesive forces causes the well-known capillary action. Students are also introduced to examples of capillary action found in nature and in our day-to-day lives.
As part of a (hypothetical) challenge to help a city find the …
As part of a (hypothetical) challenge to help a city find the most affordable and environmentally friendly way to clean up an oil spill, students design and conduct controlled experiments to quantify capillary action in sand. Like engineers and entrepreneurs, student teams use affordable materials to design and construct models to measure the rate of capillary action in four types of sand: coarse, medium, fine and mixed. After observing and learning from a teacher-conducted capillary tube demonstration, teams are given a selection of possible materials and a budget to work within as they design their own experimental setups. After the construction of their designs, they take measurements to quantify the rate of capillary action, create graphs to analyze the data, and make concluding recommendations. Groups compare data and discuss as a class the pros and cons of their designs. Pre- and post-evaluations and two worksheets are provided.
Subject addresses the evolution of the modern capitalist economy and evaluates its …
Subject addresses the evolution of the modern capitalist economy and evaluates its current structure and performance. Various paradigms of economics are contrasted and compared (neoclassical, Marxist, socioeconomic, and neocorporate) in order to understand how modern capitalism has been shaped and how it functions in today's economy. Readings include classics in economic thought as well as contemporary analyses. Subject stresses general analytic reasoning and problem formulation rather than specific analytic techniques. May not be used for economics concentration. One economics HASS-D subject may be used as an economics elective for the economics major and minor. This course examines the implications of economic theories for social and political organization in the context of the historical evolution of industrial societies. Among the authors whose theories will be discussed are Ayn Rand, Milton Friedman, Karl Marx, Max Weber, Joseph Schumpeter, and John Kenneth Galbraith. Emphasis will be placed on class discussion of specific texts. Students will be encouraged to ground their views in concrete textual and empirical material and to consider the implications of different arguments for the understanding of personal, political, and economic events today.
In the exploration of ways to use solar energy, students investigate the …
In the exploration of ways to use solar energy, students investigate the thermal energy storage capacities of different test materials to determine which to use in passive solar building design.
This art history video discussion examines Caravaggio's "Calling of St. Matthew," oil …
This art history video discussion examines Caravaggio's "Calling of St. Matthew," oil on canvas, c. 1599-1600 (Contarelli Chapel, San Luigi dei Francesi, Rome).
This art history video discussion examines Caravaggio's "Death of the Virgin," 1605-06, …
This art history video discussion examines Caravaggio's "Death of the Virgin," 1605-06, Oil on canvas, 12 feet, 10 inches x 8 feet (369 x 245 cm) (Musee du Louvre, Paris). Painted for the altar of a family chapel in the church of Santa Maria della Scala del Trastevere, Rome.
The task requires the student to use logarithms to solve an exponential …
The task requires the student to use logarithms to solve an exponential equation in the realistic context of carbon dating, important in archaeology and geology, among other places. Students should be guided to recognize the use of the natural logarithm when the exponential function has the given base of e, as in this problem. Note that the purpose of this task is algebraic in nature -- closely related tasks exist which approach similar problems from numerical or graphical stances.
In the task "Carbon 14 Dating'' the amount of Carbon 14 in …
In the task "Carbon 14 Dating'' the amount of Carbon 14 in a preserved plant is studied as time passes after the plant has died. In practice, however, scientists wish to determine when the plant died and, as this task shows, this is not possible with a simple measurement of the amount of Carbon 14 remaining in the preserved plant. The equation for the amount of Carbon 14 remaining in the preserved plant is in many ways simpler here, using 12 as a base.
This problem introduces the method used by scientists to date certain organic …
This problem introduces the method used by scientists to date certain organic material. It is based not on the amount of the Carbon 14 isotope remaining in the sample but rather on the ratio of Carbon 14 to Carbon 12. This ratio decreases, hypothetically, at a constant exponential rate as soon as the organic material has ceased to absorb Carbon 14, that is, as soon as it dies. This problem is intended for instructional purposes only. It provides an interesting and important example of mathematical modeling with an exponential function.
This exploratory task requires the student to use a property of exponential …
This exploratory task requires the student to use a property of exponential functions in order to estimate how much Carbon 14 remains in a preserved plant after different amounts of time.
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