Overview
This review covers key vocabulary and fundamental principles of algebra, including algebraic expressions, evaluating expressions, ordering integers, and solving one- and two-step equations, as well as basic word problems.
Vocabulary & Key Concepts
- Absolute value measures a number’s distance from 0 on a number line.
- An additive inverse is the opposite of a number.
- An algebraic expression contains at least one variable.
- A coefficient multiplies the variable in an algebraic expression.
- A constant is a quantity that does not change.
- To evaluate means to find the value of a numerical or algebraic expression.
- An integer is a whole number or its opposite.
- Inverse operations undo each other.
- A variable is a symbol representing a quantity that can change.
Algebraic Expressions
- Translate word phrases into algebraic expressions by identifying variables, constants, and operations.
- Change algebraic expressions into word phrases by describing the operations and quantities involved.
Substituting & Evaluating
- Substitute given values for variables in algebraic expressions to solve for a numerical result.
Ordering Integers
- List integers from least to greatest by comparing their values on a number line.
Evaluating Expressions
- Apply arithmetic operations (addition, subtraction, multiplication, division) to evaluate expressions given.
Adding and Subtracting Integers
- Combine integers by following the rules for addition and subtraction of positive and negative numbers.
Multiplying and Dividing Integers
- Multiply or divide integers, using the rule that like signs give a positive result and unlike signs give a negative result.
Solving One-Step Equations
- Isolate the variable by applying the inverse operation (addition, subtraction, multiplication, or division) to both sides of the equation.
Solving Two-Step Equations
- Undo addition/subtraction and multiplication/division in order to solve for the variable in equations with two steps.
Story Problems
- Use algebraic reasoning to translate real-world problems into expressions or equations and solve for unknowns.
Key Terms & Definitions
- Absolute value — a number’s distance from 0 on a number line.
- Additive inverse — the opposite of a number.
- Algebraic expression — an expression with at least one variable.
- Coefficient — the number multiplied by the variable.
- Constant — a value that does not change.
- Evaluate — to find the value of an expression.
- Integer — a whole number or its opposite.
- Inverse operation — operations that undo each other.
- Variable — a symbol representing a changeable value.
Action Items / Next Steps
- Review vocabulary definitions and ensure you can match each term.
- Practice translating word phrases to algebraic expressions and vice versa.
- Complete the evaluating, ordering, and solving equations practice problems.
- Solve the story problems, showing your work for each step.