Unit 4 – Exponents, Order of Operations, prime factorization, properties of operations, evaluating expressions, basic algebra vocabulary
Exponent. A little number that tells you how many times you multiply a number by itself.
Ex. 8 = 23
Order of Operations
When evaluating algebraic expressions, we must follow a certain order of operations to obtain the right answer.
“PEMDAS”. (Acronym) It stands for “Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction”
Vocabulary:
Expression. A mathematical sentence built up from constants, variables, and the algebraic operations
Evaluate an expression. Substitute numbers for the variables and follow the operation symbols to find the numerical value of the expression.
Equation. A mathematical sentence that equates one expression to another expression.
Equivalent expressions. Expressions that have the same value but are represented in a different format using the properties of numbers.
Inequality. A sentence that states one expression is greater than or equal to, less than, less than or equal to another expression.
Essential Questions:
- When are exponents used and why are they important?
- How can an equation or inequality be used to represent a given situation?
- What is Order of Operations?
Learning Targets:
-Explain the difference between an expression and an equation.
-Write numerical expressions involving whole-number exponents. -Evaluate numerical expressions involving whole-number exponents.
-Translate words into expressions.
-Read expressions using appropriate mathematical terms.
-Evaluate expressions using the order of operations.
-Use the properties of operations to create equivalent expressions.
-Identify equivalent expressions
Reason about and solve one-variable equations and inequalities
-Explain what an equation and inequality represent.
-Determine whether a given number makes an equation or inequality true.
-Explain what a variable represents.
-Use variables to solve problems involving expressions.
-Write equations to represent real-world problems.
-Solve one-step equations involving positive numbers.
-Explain the differences between an equation and an inequality.
-Write an inequality to represent a real-world problem.
-Identify multiple solutions to an inequality.
-Represent solutions of inequalities on a number line.