Algebra is a branch of mathematics in which letters and symbols are used to represent numbers and quantities in formulas and equations. It allows us to solve mathematical problems by using variables and operations.

1. **Variables:** In algebra, letters such as x, y, and z are used to represent unknown quantities or values.

2. **Expressions:** An algebraic expression is a combination of variables, constants, and operations (like addition, subtraction, multiplication, and division).

3. **Equations:** An equation is a mathematical statement that shows the equality of two expressions. It typically contains an equal sign (=).

4. **Terms:** In an algebraic expression, terms are the parts separated by the addition or subtraction signs.

5. **Coefficients:** The coefficient of a term is the numerical factor that is multiplied by the variable.

1. **Addition and Subtraction:** In algebra, we add or subtract like terms by combining the coefficients of the same variables.

2. **Multiplication and Division:** We use multiplication and division to simplify algebraic expressions and solve equations.

To understand and excel in algebra, it's important to practice various problems and concepts. Here's a study guide to help you get started:

- Learn the basic vocabulary and concepts of algebra, such as variables, expressions, and equations.
- Practice simplifying algebraic expressions by combining like terms and using the order of operations.
- Understand how to solve simple equations and inequalities.
- Work on word problems involving algebraic expressions and equations.
- Practice using algebra to represent real-life situations and solve problems related to geometry, physics, and more.

Remember, practice is key to mastering algebra. As you become more familiar with the concepts and operations, you'll gain confidence and improve your problem-solving skills.

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Algebra (NCTM)

Represent and analyze mathematical situations and structures using algebraic symbols.

Develop an initial conceptual understanding of different uses of variables.

Use symbolic algebra to represent situations and to solve problems, especially those that involve linear relationships.

Recognize and generate equivalent forms for simple algebraic expressions and solve linear equations

Grade 7 Curriculum Focal Points (NCTM)

Number and Operations and Algebra: Developing an understanding of operations on all rational numbers and solving linear equations

Students extend understandings of addition, subtraction, multiplication, and division, together with their properties, to all rational numbers, including negative integers. By applying properties of arithmetic and considering negative numbers in everyday contexts (e.g., situations of owing money or measuring elevations above and below sea level), students explain why the rules for adding, subtracting, multiplying, and dividing with negative numbers make sense. They use the arithmetic of rational numbers as they formulate and solve linear equations in one variable and use these equations to solve problems. Students make strategic choices of procedures to solve linear equations in one variable and implement them efficiently, understanding that when they use the properties of equality to express an equation in a new way, solutions that they obtain for the new equation also solve the original equation.