What is Algebra?

Algebra is defined as a branch of mathematics that uses symbols to describe abstract properties and relationships. In algebra, a symbol known as a variable is used to represent an unknown quantity. The mathematical expression or equation is manipulated to figure out the unknown value. The core principle of algebra is balance.

The five branches of Algebra include elementary algebra, advanced algebra, abstract algebra, communicative algebra, and linear algebra. Each branch is connected and overlaps like all branches of mathematics. Algebraic concepts can be traced back to ancient Babylonia. The name Algebra was derived later from al-jabr, which means a reunion of broken parts or completion. The name comes from the published work of a mathematician named Muhammad ibn Musa al-Khwarizmi.

Algebra is a central topic in mathematics beyond arithmetic. A strong understanding of algebra concepts creates entry points to advanced mathematics. Many fundamental concepts in algebra are necessary for geometry, trigonometry, and calculus.

Learning to read, write, and model with algebra is essential to understanding math concepts deeply. Algebra learning is a core part of comprehensive math education. Pre-algebra concepts are typically part of an upper elementary and middle school curriculum. Students develop a foundational understanding of operations with rational numbers, ratios, expressions, and graphing. Most schools in the United States offer Algebra 1 to students beginning in ninth grade, followed by geometry or Algebra 2. Algebra 1 is also offered as an advanced course for eighth-grade students in some schools. Algebra 1 includes a study of functions and writing, solving, and modeling equations.

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Our collection of algebra courses includes essential concepts in pre-algebra, high school algebra, including Algebra 1 and Algebra 2, linear algebra, and boolean algebra. Comprehensive lessons, activities, and supporting videos help students develop computational, reasoning, and problem-solving skills. Study.com's algebra courses save curriculum planning time for teachers and homeschool instructors with a library of standards-aligned questions and activities.

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Algebra Lesson Plans for Teachers

Study.com offers videos, quizzes, tests, and supplemental teaching tools for pre-algebra, Algebra I, and Algebra II. Algebra teachers can access over 170 standards-aligned lesson plans and activities. Study.com's integration with several popular learning management systems provides a simple and streamlined way to assign class work.

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    Our resources allow for self-paced support for students who need reteaching, review, or challenge. Resources include materials lists, step-by-step tutorials, video transcripts, and guiding questions.

Algebra Skills and Practice

Our Algebra Skills and Practice section provides thousands of algebra practice problems. Algebra Skills and Practice is designed to support students in developing algebraic reasoning and problem-solving skills. Resources include step-by-step tutorial videos and practice questions to aid students in reviewing and mastering math concepts. Teachers and students can access the entire library of Study.com's math resources to review concepts from previous grades and preview more advanced concepts for later grades.

In alignment with math standards, the Algebra Skills and Practice section provides in-depth learning on seeing structure in expressions, interpreting data, and analyzing functions. As with all mathematics, students must use reasoning and analytical skills to find solutions. Students apply the standards of mathematical practice in their problem-solving. Real-world situations create a context for students while learning and applying math skills. Models, graphs, and charts are included where applicable to support student learning.

Learners can review vocabulary, view video and text explanations, and complete practice problems at their own pace. Students can receive extra support for any algebra skill. For practice tests, students receive immediate feedback and can track their progress toward their goals. Students are required to review step-by-step clarification on incorrect questions. For assessments, students receive clarification of solutions once the testing window has closed.

Study.com's Algebra Skills and Practice section is structured to save educators time. View sample questions and instructional resources for each standard. Sort the collection by topic or Texas, New York, or Florida math standards. Teachers can select specific questions or assign general questions for a topic. Algebra Skills and Practice resources can be printed or assigned digitally on Study.com. With a few quick clicks, teachers can post assignments seamlessly on Google Classroom, Canvas, or Schoology. Use the teacher dashboard to track student progress, including whether students have started or completed an assignment. Use the student data from the dashboard to decide which students need additional support, which students are ready to dive deeper into a concept, and what topics need to be revisited. Use these resources for daily instruction, to prepare students for tests, assign extra support materials, or assign assessments.

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Algebra Homeschool Curriculum

Study.com's library of Algebra I and Algebra II lessons, assessments, and project ideas are accompanied by resources and parental guidance. Homeschool students have access to a complete high school math curriculum. Our library of homeschool resources offers video lessons, activities, and math strategies to support learners.

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Frequently Asked Questions

  • What are the basics of algebra?

    The basics of algebra include expressions and equations. Expressions can be evaluated by replacing a variable, or unknown, with a value. An equation can be solved by determining what value can be substituted for the variable in an equation to create balance.

  • What are the four basic rules of algebra?

    There are four basic rules of Algebra:

    1. The commutative property of addition and multiplication states for any two numbers, the order in which they are added or multiplied doesn't change the result.
    2. The associative property of addition and multiplication states for any three numbers, regardless of how they are grouped, the result will be the same.
    3. The distributive property of multiplication states the sum of two or more numbers multiplied by another value will give the same result as each number multiplied by the same value.
    4. The identity property of multiplication states that any number multiplied by one will remain the same.
  • What is a simple definition of algebra?

    Simply put, algebra is a branch of mathematics where symbols represent unknown amounts, and mathematical sentences are required to be balanced.