Expressions
An expression is a combination of numbers, variables, and operations. It can include addition, subtraction, multiplication, division, and exponentiation. Expressions are used to represent mathematical relationships and can be used to calculate values.
Types of Expressions
- Numeric Expressions: These are expressions that contain only numbers and operations. For example, 5 + 3 * 2.
- Variable Expressions: These are expressions that contain variables, numbers, and operations. For example, 2x + 3y.
- Algebraic Expressions: These are expressions that contain variables, numbers, and operations, including exponents. For example, 3x2 - 2x + 5.
Components of Expressions
Expressions are made up of the following components:
- Numbers: These are numerical values such as 1, 2, 3.14, etc.
- Variables: These are symbols that represent unknown or changing values, such as x, y, a, b, etc.
- Operations: These are mathematical operations such as addition (+), subtraction (-), multiplication (*), division (/), and exponentiation (^).
Key Concepts
When working with expressions, it's important to understand the following key concepts:
- Order of Operations: Expressions should be evaluated using the order of operations - parentheses, exponents, multiplication and division (from left to right), and addition and subtraction (from left to right).
- Like Terms: Terms in an expression that have the same variable raised to the same power are called like terms. Like terms can be combined using the properties of addition and subtraction.
Examples
Here are some examples of expressions:
- 3x + 2y - 5
- 4(x + 3) - 2y
- 2a2 - 3a + 7
Study Guide
When studying expressions, it's important to practice simplifying, evaluating, and solving expressions. Here are some steps to follow:
- Identify the components of the expression - numbers, variables, and operations.
- Apply the order of operations to simplify the expression.
- Combine like terms if applicable.
- If the expression includes variables, substitute specific values for the variables and evaluate the expression.
Practice working with different types of expressions and solving problems involving expressions to strengthen your understanding of the topic.
Remember to seek help from your teacher or tutor if you encounter any challenges!
Good luck with your studies!
.◂Math Worksheets and Study Guides Seventh Grade. Measurement, Perimeter, and Circumference
Study Guide
Measurement, Perimeter, and Circumference 
Worksheet/Answer key
Measurement, Perimeter, and Circumference Worksheet/Answer key
Measurement, Perimeter, and Circumference Worksheet/Answer key
Measurement, Perimeter, and Circumference
Worksheet/Answer keyWorksheet/Answer keyWorksheet/Answer keyThe resources above cover the following skills:
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 7 Focal Points (NCTM)
Measurement and Geometry: Students connect their work on proportionality with their work on area and volume by investigating similar objects. They understand that if a scale factor describes how corresponding lengths in two similar objects are related, then the square of the scale factor describes how corresponding areas are related, and the cube of the scale factor describes how corresponding volumes are related. Students apply their work on proportionality to measurement in different contexts, including converting among different units of measurement to solve problems involving rates such as motion at a constant speed. They also apply proportionality when they work with the circumference, radius, and diameter of a circle; when they find the area of a sector of a circle; and when they make scale drawings.