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 course is also intended to provide the student with a strong foundation for intermediate algebra and beyond. Upon successful completion of this course, you will be able to: simplify and solve linear equations and expressions including problems with absolute values and applications; solve linear inequalities; find equations of lines; and solve application problems; add, subtract, multiply, and divide various types of polynomials; factor polynomials, and simplify square roots; evaluate, simplify, multiply, divide, add, and subtract rational expressions, and solve basic applications of rational expressions. This free course may be completed online at any time. It has been developed through a partnership with the Washington State Board for Community and Technical Colleges; the Saylor Foundation has modified some WSBCTC materials. (Mathematics 001)

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.

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 popular maths talk gives an introduction to various different kinds of infinity, both countable and uncountable. These concepts are illustrated in a somewhat informal way using the notion of Hilbert's infinite hotel. In this talk, the hotel manager tries to fit various infinite collections of guests into the hotel. The students should learn that many apparently different types of infinity are really the same size. However, there are genuinely "more" real numbers than there are positive integers, as is shown in the more challenging final section, using Cantor's diagonalization argument.

In Bootstrap:Data Science, students form their own questions about the world around them, analyze data using multiple methods, and write a research paper about their findings. The module covers functions, looping and iteration, data visualization, linear regression, and more. Social studies, science, and business teachers can utilize this module to help students make inferences from data. Math teachers can use this module to introduce foundational concepts in statistics, and it is aligned to state and national standards.

Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions. (Grade 4 expectations in this domain are limited to fractions with denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100.)

The CUNY HSE Curriculum Framework provides direction, structure and materials for teaching math, science and social studies (integrated with reading and writing) in the new era of HSE instruction. The complete framework is available for free download.

The framework was written by the CUNY Adult Literacy PD Team to respond to the challenges facing high school equivalency (HSE) teachers and their students. It is a guide for planning your instruction – including topic recommendations, model lessons, guiding questions, readings, and problems. The framework prioritizes depth over breadth. It does not address all of the content that might potentially be included on an HSE exam, but instead models a focused and coherent study of high priority topics within each content area.

As teachers in adult literacy and HSE education, our work has always been demanding. Now that our students face a new and more challenging HSE test, the demands on teachers are even greater. Teaching students to read, write and do math at the HSE level is no longer enough. Students need specific, deep and coherent content knowledge, as well as the capacity to apply this content knowledge to analysis and problem solving.

As the demands on our students and teachers are increasing, it is important that we don’t lose sight of one of our greatest strengths — our practice of starting from where students are and our serious respect for their learning processes. As a student of ours once said, “You can’t make a plant grow by pulling on it, you only make it rootless.”

The Social Studies section integrates reading and writing through a focus on U.S. history, with extensions to civics, economics and geography. This section has a curriculum map, 12 unit descriptions, six model lesson plans and additional resources.

The Science section provides an introduction to matter and basic chemistry with extensions to science/math connections. This section includes a curriculum map with 23 topic descriptions and key questions, and three complete inquiry-based model lesson plans.

The Math section focuses on problem-solving in functions and algebra. It integrates problem-solving strategies, productive struggle, perseverance and mathematical discussion into content learning. This section includes a curriculum map, model lessons, rich engaging math problems, samples of student work, powerful routines for math classrooms, classroom videos, and more.

This lesson focuses on using the properties of rectangles to calculate area. It is designed to aid adult students to successfully master and apply basic geometry knowledge in a professional setting (construction and related) and can also contribute to achieving High School Equivalency (HSE).
Areas to be covered include properties of rectangles and squares; definition of ‘square’; right-angled triangles; calculating areas of rectangles and right-angled triangles; decomposition of area into manageable units; and calculating costs. Students will apply this knowledge to calculating the costs of purchasing building materials.

This lesson focuses on calculating the areas of rectangles. It is designed to enable adult students to successfully master basic geometry knowledge in order to achieve their High School Equivalency (HSE). Areas to be covered include types of polygons, quadrilaterals, rectangles; calculating areas of rectangle and calculating costs. Students will apply this knowledge to practical areas of their lives such as calculating the costs of purchasing carpets or painting of walls

This lesson focuses on calculating the areas of rectangles. It is designed to enable adult students to successfully master basic geometry knowledge in order to achieve their High School Equivalency Diploma (HSED). Areas to be covered include types of polygons, quadrilaterals, rectangles; calculating areas of rectangles and calculating costs. Students can apply this knowledge to practical areas of their lives such as calculating the cost of purchasing carpet or painting walls.

This lesson focuses on calculating the areas of rectangles. It is designed to enable adult students to successfully master basic geometry knowledge in order to achieve their High School Equivalency (HSE). Areas to be covered include types of polygons, quadrilaterals, rectangles; calculating areas of rectangle and calculating costs. Students will apply this knowledge to practical areas of their lives such as calculating the costs of purchasing carpets or painting of walls

Students first discover what they want from their education, then build a plan to get there. This content takes students through the steps to successfully navigate their journey in higher education. Topics include planning for success, choosing a career path, setting and attaining goals, understanding financial management, developing critical thinking skills, making healthy choices, using effective communication, managing time, developing learning strategies, developing meaningful relationships. Content is available in PDF and Open Document formats and is licensed CC BY. Learning Objectives also are provided. Full course offering available at https://www.cengage.com/c/opennow-college-success-1e-opennow-cengage

Students first discover what they want from their education, then build a plan to get there. This content takes students through the steps to successfully navigate their journey in higher education. Topics include planning for success, choosing a career path, setting and attaining goals, understanding financial management, developing critical thinking skills, making healthy choices, using effective communication, managing time, developing learning strategies, developing meaningful relationships. Content is available in PDF and Open Document formats and is licensed CC BY. Learning Objectives also are provided. Full course offering available at https://www.cengage.com/c/opennow-college-success-1e-opennow-cengage

Students first discover what they want from their education, then build a plan to get there. This content takes students through the steps to successfully navigate their journey in higher education. Topics include planning for success, choosing a career path, setting and attaining goals, understanding financial management, developing critical thinking skills, making healthy choices, using effective communication, managing time, developing learning strategies, developing meaningful relationships. Content is available in PDF and Open Document formats and is licensed CC BY. Learning Objectives also are provided.

This lesson reviews how to change an improper fraction to a mixed number.

An introduction and examples of how to use the Chi square test. The test is used when analyzing assocation between two categorical variables and when comparing proportions. The idea behind the test is to compare the observed frequencies with the expected frequencies, if the two variables are unrelated.

This resource shares all of the documents and planning guidance for the Washington Climate Educator Book Club, which is part of the greater ClimeTime community.  The Book Club’s book study is designed to flexibly support teams of interdisciplinary K–12 educators, from schools and districts across Washington, to explore ways climate education can be integrated into all classrooms.