This site teaches Arithmetic with Polynomials and Rational Expressions to High Schoolers through a series of 4333 questions and interactive activities aligned to 26 Common Core mathematics skills.

This site teaches High Schoolers how to create equations through a series of 298 questions and interactive activities aligned to 5 Common Core mathematics skills.

This undergraduate level course follows Algebra I. Topics include group representations, rings, ideals, fields, polynomial rings, modules, factorization, integers in quadratic number fields, field extensions, and Galois theory.

This site teaches Structure in Algebraic Expressions to High Schoolers through a series of 3482 questions and interactive activities aligned to 26 Common Core mathematics skills.

Algebra and Trigonometry provides a comprehensive exploration of algebraic principles and meets scope and sequence requirements for a typical introductory algebra and trigonometry course. The modular approach and the richness of content ensures that the book meets the needs of a variety of courses. Algebra and Trigonometry offers a wealth of examples with detailed, conceptual explanations, building a strong foundation in the material before asking students to apply what they’ve learned.

In this task students have to interpret expressions involving two variables in the context of a real world situation. All given expressions can be interpreted as quantities that one might study when looking at two animal populations.

Build rectangles of various sizes and relate multiplication to area. Discover new strategies for multiplying algebraic expressions. Use the game screen to test your multiplication and factoring skills!

The CyberSquad tries to figure out a table arrangement for 20 workers in this video from Cyberchase.

In this video segment from Cyberchase, Matt tries for a second time to arrange tables and chairs to accommodate 20 workers.

Matt's third table arrangement helps fit all 20 workers at five tables in this video segment from Cyberchase.

The purpose of this learning video is to show students how to think more freely about math and science problems. Sometimes getting an approximate answer in a much shorter period of time is well worth the time saved. This video explores techniques for making quick, back-of-the-envelope approximations that are not only surprisingly accurate, but are also illuminating for building intuition in understanding science. This video touches upon 10th-grade level Algebra I and first-year high school physics, but the concepts covered (velocity, distance, mass, etc) are basic enough that science-oriented younger students would understand. If desired, teachers may bring in pendula of various lengths, weights to hang, and a stopwatch to measure period. Examples of in- class exercises for between the video segments include: asking students to estimate 29 x 31 without a calculator or paper and pencil; and asking students how close they can get to a black hole without getting sucked in.

This real world task requires students to answer questions about equations for calculating compound interest.

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)

In this beginning algebra course, you'll learn about fundamental operations on real numbers, exponents, solving linear equations and inequalities, applications, functions, graphing linear equations, slope, and systems of linear equations. This course was created by Bossier Parish Community College as part of its MOOC series "Open Campus." NOTE: Open Campus courses are non-credit reviews and tutorials and cannot be used to satisfy requirements in any curriculum at BPCC. (Beginning Algebra Course by Bossier Parish Community College is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License. Based on a work at http://bpcc.edu/opencampus/index.html.)

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.

This task provides an exploration of a quadratic equation by descriptive, numerical, graphical, and algebraic techniques. Based on its real-world applicability, teachers could use the task as a way to introduce and motivate algebraic techniques like completing the square, en route to a derivation of the quadratic formula.

This problem introduces children to algebra by looking for a pattern and generalizing with a rule. Students explore in how many different ways can a stick of 6, 7 or 8 different colored interlocking cubes be broken into two parts. The Teachers' Notes page offers rationale, suggestions for implementation, discussion questions, and an idea for support and extension.

This problem promotes logical thinking and introduces learners to the trial and error (guess and check) problem solving strategy, especially with the interactive provided. In this problem children need to understand the difference between having a certain number of brothers and the number of boys in a family to answer the question, "How many children are there in the Brown family?" The Teachers' Notes page offers suggestions for implementation, discussion questions, ideas for extension and support, and a link to a down loadable worksheet for students to table their trials.

This task is for instructional purposes only and builds on ``Building an explicit quadratic function.''