An expression in mathematics is a combination of numbers, symbols, and operators (such as +, -, *, /) that represents a value. It can contain variables, constants, and mathematical operations. Expressions are used to represent a mathematical relationship or to perform calculations.

There are several types of expressions in mathematics:

**Numerical Expression:**A numerical expression contains only numbers and mathematical operations. For example, 3 + 4 * 2 is a numerical expression.**Variable Expression:**A variable expression contains variables, constants, and mathematical operations. For example, 2x + 5 is a variable expression.**Algebraic Expression:**An algebraic expression contains variables, constants, and mathematical operations. For example, 3x^2 - 2xy + 7 is an algebraic expression.

An expression is made up of several parts:

**Term:**A term is a single mathematical expression separated by + or - signs. For example, in the expression 3x^2 - 2xy + 7, the terms are 3x^2, -2xy, and 7.**Coefficient:**The coefficient is the numerical factor of a term. For example, in the term 5x, the coefficient is 5.**Variable:**A variable is a symbol that represents a value. Common variables include x, y, and z.**Constant:**A constant is a fixed value that does not change. For example, in the expression 2x + 5, the constant is 5.

To simplify an expression, you perform operations such as combining like terms, distributing, and factoring. Here are some key steps for simplifying expressions:

**Combine Like Terms:**Combine terms with the same variables and exponents. For example, in the expression 3x + 2x - 5x, you can combine 3x and 2x to get 5x.**Distribute:**Use the distributive property to multiply terms inside parentheses. For example, in the expression 2(3x + 4), you can distribute the 2 to get 6x + 8.**Factor:**Factor out common terms or use factoring techniques to simplify the expression. For example, in the expression x^2 - 4x, you can factor it as x(x - 4).

Now that you understand expressions, here are some practice problems to test your knowledge:

- Simplify the expression 5x + 3 - 2x.
- Factor the expression x^2 + 5x + 6.
- Simplify the expression 2(3x - 4) - 5(2x + 1).

Study GuideArea and Circumference of Circles Activity LessonArea of Circles Activity LessonCircumference of Circles Worksheet/Answer key

Area and Circumference of Circles Worksheet/Answer key

Area and Circumference of Circles Worksheet/Answer key

Area and Circumference of Circles Worksheet/Answer key

Area and Circumference of Circles

Geometry (NCTM)

Use visualization, spatial reasoning, and geometric modeling to solve problems.

Use geometric models to represent and explain numerical and algebraic relationships.

Measurement (NCTM)

Apply appropriate techniques, tools, and formulas to determine measurements.

Select and apply techniques and tools to accurately find length, area, volume, and angle measures to appropriate levels of precision.

Develop and use formulas to determine the circumference of circles and the area of triangles, parallelograms, trapezoids, and circles and develop strategies to find the area of more-complex shapes.

Connections to the Grade 6 Focal Points (NCTM)

Measurement and Geometry: Problems that involve areas and volumes, calling on students to find areas or volumes from lengths or to find lengths from volumes or areas and lengths, are especially appropriate. These problems extend the students' work in grade 5 on area and volume and provide a context for applying new work with equations.