Expressions & Algebra
Free lessons and practice worksheets for expressions & algebra — worked examples, common mistakes, and step-by-step solutions.
- 01Expressions & Algebra3 min read
Advanced Equations
Advanced equations extend beyond simple one-step problems by incorporating multiple operations, variables on both sides, fractions, and parentheses that require systematic solving techniques. These equations, covered in CCSS.7.EE and CCSS.8.EE standards, form the foundation for algebraic reasoning in middle and high school mathematics. The complexity increases from two-step linear equations like 2x + 6 = 26 to multi-variable expressions requiring bracket expansion and fraction manipulation.
- 02Expressions & Algebra3 min read
Algebraic Patterns
Algebraic patterns are sequences of numbers that follow a consistent mathematical rule. Each term in the sequence connects to the next through addition, subtraction, multiplication, or division by the same amount. The pattern 3, 7, 11, 15 follows the rule "add 4" to generate each successive term.
- 03Expressions & Algebra3 min read
Balance Equations
Balance equations represent mathematical equality using the concept of a balanced scale, where both sides must have equal value. The equation 7 + 3 = 10 demonstrates this balance, as the left side (10) equals the right side (10). This visual model helps establish the fundamental principle that equations maintain equality when identical operations are performed on both sides.
- 04Expressions & Algebra3 min read
Equality & Inequality
Equality in mathematics means two expressions have the same value, represented by the equals sign (=). An equation like 5 + 3 = 8 states that the sum on the left equals the number on the right. Understanding equality forms the foundation for solving equations and comparing mathematical expressions.
- 05Expressions & Algebra3 min read
Formulas
A formula is a mathematical equation that expresses a relationship between different variables using letters and symbols. In the formula A = πr², the area of a circle equals π times the radius squared, where A represents area and r represents radius. Formulas appear throughout mathematics and science, from simple area calculations to complex physics equations.
- 06Expressions & Algebra3 min read
Introduction to Equations
An equation is a mathematical statement showing that two expressions are equal, connected by an equals sign. The simplest equations contain one unknown variable (usually x) and require finding its value through inverse operations. For example, the equation x + 6 = 13 asks what number plus 6 equals 13.
- 07Expressions & Algebra3 min read
Introduction to Powers
A power consists of a base number and an exponent that indicates how many times to multiply the base by itself. The expression 2⁵ means 2 × 2 × 2 × 2 × 2, which equals 32. Powers appear throughout mathematics starting in 6th grade with standards like CCSS.6.EE, providing a foundation for algebra, geometry, and scientific notation.
- 08Expressions & Algebra3 min read
Manipulate Expressions
Manipulating expressions involves rewriting mathematical expressions in different but equivalent forms using algebraic properties. This process includes expanding brackets, factoring terms, and isolating variables through inverse operations. The fundamental principle maintains that whatever operation is performed on one side of an equation must also be performed on the other side.
- 09Expressions & Algebra3 min read
Missing Number
Missing number problems present equations with an unknown value represented by a box, blank, or variable. These problems require finding the value that makes the equation true using inverse operations. The fundamental principle relies on the relationship between opposite operations: addition undoes subtraction, and multiplication undoes division.
- 010Expressions & Algebra3 min read
Number Sets
Number sets organize all mathematical numbers into distinct categories based on their properties and characteristics. The natural numbers (ℕ) represent the counting numbers 1, 2, 3, and so forth, while integers (ℤ) expand this to include zero and all negative whole numbers like -5, -1, 0, 7, 15. These foundational sets build upon each other in a hierarchical structure that forms the backbone of mathematical classification.
- 011Expressions & Algebra3 min read
Sequences
A sequence is an ordered list of numbers that follow a specific pattern or rule. Arithmetic sequences increase by a constant difference between consecutive terms, while geometric sequences multiply by a constant ratio. The sequence 2, 5, 8, 11 adds 3 each time, making it arithmetic with a common difference of 3.
- 012Expressions & Algebra3 min read
Simplify Expressions
Simplifying expressions means combining like terms and reducing mathematical expressions to their most compact form. The process involves identifying terms with identical variables and powers, then adding or subtracting their coefficients. For example, 5x + 3x simplifies to 8x by combining the coefficients 5 and 3.