This short video and interactive assessment activity is designed to give fifth graders an overview of simple figure patterns.
In the master-equation formalism, a set of differential equations describe the time-evolution of the probability distribution of an ensemble of systems. This can be used, for example, to describe the varied mRNA copy numbers found in individual cells in a population.
The stochastic simulation algorithm (SSA, Kinetic Monte Carlo, Gillespie algorithm) produces an example trajectory for a particular member of a probabilistic ensemble by looping over the following steps. The current state of the system is used to determine the likelihood of each possible chemical reaction in relative comparison to the likelihoods for the other possible reactions, as well as to determine when the next reaction is expected. Pseudo-random numbers are drawn to "roll the dice" to determine exactly when the next reaction will proceed, and which kind of reaction it will happen to be.
This task involves a fairly straightforward decaying exponential. Filling out the table and developing the general formula is complicated only by the need to work with a fraction that requires decisions about rounding and precision.
This task describes two linear functions using two different representations. To draw conclusions about the quantities, students have to find a common way of describing them. We have presented three solutions (1) Finding equations for both functions. (2) Using tables of values. (3) Using graphs.
Short Description:
Welcome to the OER companion to Baylor University's Math 1121: The Calculus Supplement Course, an optional, co-requisite course for students enrolled in Calculus 1. This OER was designed to provide 'just in time' support for the algebraic, trigonometric, and geometric relationships undergirding Calculus 1.
Long Description:
Welcome to the OER companion for Baylor University’s Math 1121: The Calculus Supplement Course! Math 1121 is an optional, co-requisite course for students enrolled in Calculus 1. This OER was designed to provide ‘just in time’ support for the algebraic, trigonometric, and geometric relationships undergirding Calculus 1. The topics and content were deliberately sequenced to coincide with the topics and content Calculus 1 students engage as they study limits, derivatives, applications of derivatives, and integration. Therefore, this text first reviews the essential functions from Pre-Calculus that students need to be successful in Calculus 1. Then, it examines the properties and algebraic transformations of those functions and reinforces strategies for analyzing functions. Finally, it bolsters the relationships between algebra and geometry that the Fundamental Theorem of Calculus and integrals bring together for Calculus 1 students. Although this OER was designed to support Calculus 1 students, there is almost no Calculus within these ‘pages.’ Rather, the focus is on everything that happens in a Calculus problem after that first Calculus step. Enjoy!
Word Count: 77096
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A Beautiful Mind won the Academy Award for best picture in 2001 and it chronicles the life of John Nash who is noted for his pioneering work on general equilibrium theory. This scene is a great way to discuss self-interest and contrast it with the social optimum. Nash's work has augmented Adam Smith's "invisible hand" theory by extending how self-interest is modeled. This scene is must viewing even though the scene itself contains flawed economics (explaining why the scene is NOT a Nash equilibrium helps students learn the concept in greater depth).
The PhET project at the University of Colorado creates "fun, interactive, research-based simulations of physical phenomena." This particular one deals with Beer's Law. "The thicker the glass, the darker the brew, the less the light that passes through." Make colorful concentrated and dilute solutions and explore how much light they absorb and transmit using a virtual spectrophotometer! The simulation is also paired with a teachers' guide and related resources from PhET. The simulation is also available in multiple languages.
This short video and interactive assessment activity is designed to teach third graders about before and after problems.
Visually searchable database of Algebra 1 videos. Click on a problem and watch the solution on YouTube. Copy and paste this material into your CMS. Videos accompany the open Elementary Algebra textbook published by Flat World Knowledge.
This activity is a scientific investigation focusing on inquiry after using the Foss Water Kit. The students will pose a question, create a procedure and produce a poster showing their findings.
Students will be introduced to addition, multiplication, and division of the benchmark fractions 1/2, 1/3, and 1/4 with a fun, hands-on experience. Students will layer the dry ingredients for a brownie recipe into a canning jar while having a rich discussion that aides visualizing operations with fractions. This shared experience can be referred to during future instruction.
This activity will allow students to see light bending. The students will be able to calculate the amount of bend or refraction that occurs with various mediums.
In this optics activity, learners discover that when they rotate a special black and white pattern called a Benham's Disk, it produces the illusion of colored rings. Learners experiment with the speed of rotation and direction of rotation to observe varying patterns. Use this activity to explain to learners how our eyes detect color and how different color receptors in the eye respond at different rates.
This task presents a simple but mathematically interesting game whose solution is a challenging exercise in creating and reasoning with algebraic inequalities. The core of the task involves converting a verbal statement into a mathematical inequality in a context in which the inequality is not obviously presented, and then repeatedly using the inequality to deduce information about the structure of the game.
Demonstrate the Bernoulli Principle using simple materials on a small or large scale. This resource includes two activities that allow learners to experience the Bernoulli Principle, in which an object is suspended in air by blowing down on it. Use this activity to explain how atomizers work and why windows are sometimes sucked out of their frames as two trains rush past each other.
Demonstrate Bernoulli's Principle using balloons and and pop cans. Real world concept of lift can be applied to an airplane demonstration.
This article provides a brief discussion of the importance of teaching students to analyze data and representations of data as well as two resources that can help teachers implement these strategies into their instruction.
Bianca visits a bike shop and learns how bicycle gears work in this Cyberchase video segment.
This Cyberchase video segment features Bianca, who must figure out the fastest route to a movie premiere.