This Flexbook is community contributed through ck12.org. It covers three lessons on the Pythagorean Theorem. 1) Introduction and Determining if the Triangle is a Right Triangle, 2) Finding the Hypotenuse, and 3) Finding a leg. It includes step by step instructions, application problems, and answers (at the end of each lesson). Ck12.org material is downloadable, editable, and accessible offline and online.

This 12-problem worksheet is an assessment tool I created to see how well my adult education students grasped my lesson on the Pythagorean Theorem. There are plug-and-chug questions that require the students to solve for the lengths of missing sides and more complicated problems.

We use eigenvector-eigenvalue analysis to walk through a simple quasispecies model described in Bull, Meyers, and Lachmann, "Quasispecies made simple," PLoS Comp Biol, 1(6):e61 (2005). The dominance of a genotype depends, not merely on its ability to breed quickly (i.e. the rudimentary concept of survival of the fittest), but also on its ability to breed "true."

Students often think additively rather than multiplicatively. For example, if you present the scenario, "One puppy grew from 5 pounds to 10 pound. Another puppy grew from 100 pounds to 108 pounds." and ask, "Which puppy grew more?" someone who is thinking additively will say that the one who now weighs 108 grew more because he gained 8 pounds while the other gained 5 pounds. Someone who is thinking multiplicatively will say that the one that now weighs 10 pounds grew more because he doubled his weight while the other only added a few pounds. While both are correct answers, multiplicative thinking is needed for proportional reasoning. If your students are thinking additively, you can nudge them toward multiplicative thinking with this activity.

Welcome to this Quantitative Reasoning resource in Spanish. This resource can be used as an alternative to a traditional mathematics textbook for a one-semester course. It consists of free resources available to all users such as YouTube, Khan Academy in Spanish and much more. This resource is intended for Spanish-speaking students, but it does contain some resources in English which can be translated by the student as needed, or for videos in English, instructions are provided so students can view subtitles in English. 

Critical Thinking is important in all areas of life. Math is not an exception. I believe that it is important to teach students to think “outside the box” in mathematics.

In this series of lessons:
Students will learn to observe and note details of sequential patterns and then a math problem.

Students will begin to think critically as they approach a math word problem.

Prior Knowledge:
Students should have a knowledge of basic mathematics: fractions through percents.
Students should be familiar with algebraic equations.

This course has been designed to help students focus learning on specific areas of improvement. Unlike a typical college course where you would complete lessons in chronological order, this course allows you to focus on specific skills. Modules include: Arithmetic Review, Percents, Geometric Figures, Measurement, and Statistics

A step-by-step introduction on how to install and use `R` and RStudio for the purposes of certain courses taught at The University of Texas at Austin.

This resource will provide users step by step guidance in using the central features available as part of the SEC Commons. This guide will be updated as new features are added.

If you require further assistance please contact the support team at info@oercommons.org

This template supports STEM teachers and librarians in working collaboratively to create lessons that build science practice and STEM inquiry skills in alignment with state and national science standards, and that address the Common Core literacy shifts around close reading and building textual evidence.

When a derivative of a function appears on one side of an equation and the function appears somewhere on the other side, it is common to employ a series of manipulations of notation that are called separation of variables. This strategy is often presented in a way that makes it seem as though differentials were quantities that could be independently moved around an equation. The purpose of this video is to show that the same end result can be obtained more rigorously using u-substitution, in other words, using a "change of variables."

Khan Academy Video Tutorial. Introduction to basic algebraic equations of the form Ax=B

This is an activity for students to work on in pairs practicing simple interest. It involves real online research and presents an open-ended question. This would be most effective after students have had instruction and some practice.

In a toy model of a cell, protein X is produced according to a translation rate coefficient and eliminated according to a degradation rate coefficient. The protein copy number at which the rates for these processes balance is called the steady-state level, and the time it takes for a cell initially containing zero copies of protein X to accumulate half the steady-state level is called the _ŃŇrise time._ѝ Surprisingly, the "rise time" depends on the degradation rate coefficient only. The classic textbook presentation of this topic is found in Alon, An Introduction to Systems Biology: Design Principles of Biological Circuits, Boca Raton: Chapman & Hall/CRC, 2007 (p. 18-22).

Build coin expressions, then exchange them for variable expressions. Simplify and evaluate expressions until you are ready to test your understanding of equivalent expressions in the game!

How to solve simultaneous equations graphically using a real coordinate plane and ropes.

In the first video segment, we describe the fundamental postulate of statistical mechanics. The direct product notation we introduce in the second segment helps us to discuss the states available to a collection of many parts, which helps us, in turn, to derive the Boltzmann factor in the third segment. The fourth video segment explains how the Boltzmann factor helps us to calculate average properties for systems in thermal contact with large baths and introduces entropy (Greek letter sigma), free energy (F), and the partition function (Z).

Students will encounter the concept of a distribution, along with parameters that describe a distribution's "typical" values (average) and a distribution's spread (variance). To understand simple distributions and uncertainty propagation in the coming sections, it is necessary to be familiar with the concept of statistical independence. When two variables fluctuate independently, their covariance vanishes, and the variance of their sum is the sum of their variances.

Even when we model the dynamics of the abundances of molecules inside biological systems using calculus, it is important to remember that underlying behavior can be apparently random ("stochastic"). Even a deterministic system containing components moving in periodic ways can, at early times, support dynamics that appear disordered. The behavior of systems containing complicated collections of interacting parts can be difficult to predict with accuracy (chaos). Finally, systems can display stochasticity because the outcomes of measurements on quantum systems are indeterminate in a fundamental way. Random processes are modeled using Markov models.