Expressions

An expression is a mathematical phrase that can contain numbers, variables, and operations. Expressions are used to represent a value or a set of values. They can be as simple as a single number or variable, or as complex as a combination of multiple terms and operations.

Types of Expressions

Numeric Expressions: These are expressions that consist of numbers and mathematical operations. For example: 5 + 3, 2 * 7, (4 - 2) / 6.
Variable Expressions: These are expressions that contain variables, which are symbols that represent unknown or changing values. For example: 3x + 7, 2y - 5, 4a² - 9b.
Algebraic Expressions: These are expressions that combine numeric values, variables, and operations. For example: 2x + 3y - 5, 4x² - 7x + 10.

Parts of an Expression

Expressions can be broken down into the following parts:

Terms: These are the individual parts of an expression that are separated by addition or subtraction. For example, in the expression 3x + 4y - 2, the terms are 3x, 4y, and -2.
Coefficients: These are the numerical factors of the variables in the terms. For example, in the term 5x, the coefficient is 5.
Constants: These are terms that are just numbers, without any variables. For example, in the expression 2x + 3, the constant is 3.
Variables: These are symbols that represent unknown or changing values. For example, in the expression 4a - 7b, the variables are a and b.
Operations: These are the mathematical operations such as addition, subtraction, multiplication, and division that are used to combine the terms in an expression.

Evaluating Expressions

To evaluate an expression means to find its value when the variables are replaced with specific numbers. For example, to evaluate the expression 3x + 5 when x = 4, you would substitute 4 for x and then perform the operations to get the value of the expression.

Study Guide

To understand expressions better, it's important to practice identifying the different parts of an expression, combining like terms, and evaluating expressions with specific values for the variables. Here are some key points to focus on:

Identify the terms, coefficients, constants, and variables in a given expression.
Combine like terms by performing the operations (addition or subtraction) on the coefficients of the same variables.
Practice evaluating expressions with different values for the variables to find their numerical values.
Work on simplifying complex expressions by applying the order of operations (PEMDAS: Parentheses, Exponents, Multiplication and Division from left to right, Addition and Subtraction from left to right).

Understanding expressions is crucial for solving equations, simplifying algebraic problems, and working with mathematical models in various real-world scenarios. With practice and a clear understanding of the different components of expressions, you'll be able to tackle more advanced mathematical problems with confidence.

◂Math Worksheets and Study Guides Sixth Grade. Formulas

Study Guide

Formulas

Activity Lesson

Equivalent Expressions (Distributive Property)

The resources above cover the following skills:

Algebra (NCTM)

Use mathematical models to represent and understand quantitative relationships.

Model and solve contextualized problems using various representations, such as graphs, tables, and equations.

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.

Grade 6 Curriculum Focal Points (NCTM)

Algebra: Writing, interpreting, and using mathematical expressions and equations

Students write mathematical expressions and equations that correspond to given situations, they evaluate expressions, and they use expressions and formulas to solve problems. They understand that variables represent numbers whose exact values are not yet specified, and they use variables appropriately. Students understand that expressions in different forms can be equivalent, and they can rewrite an expression to represent a quantity in a different way (e.g., to make it more compact or to feature different information). Students know that the solutions of an equation are the values of the variables that make the equation true. They solve simple one-step equations by using number sense, properties of operations, and the idea of maintaining equality on both sides of an equation. They construct and analyze tables (e.g., to show quantities that are in equivalent ratios), and they use equations to describe simple relationships (such as 3x = y) shown in a table.

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.