SOL Objective(s):
7.13 The student will...
b) evaluate algebraic expressions for given replacement values of the variables.
8.1 The student will...
a) simplify numerical expressions involving positive exponents, using rational numbers, order of operations, and
properties of operations with real numbers;
8.4 The student will...
apply the order of operations to evaluate algebraic expressions for given replacement values of the variables.
b) evaluate algebraic expressions for given replacement values of the variables.
8.1 The student will...
a) simplify numerical expressions involving positive exponents, using rational numbers, order of operations, and
properties of operations with real numbers;
8.4 The student will...
apply the order of operations to evaluate algebraic expressions for given replacement values of the variables.
The Basics and Background Information
• Expression is a word used to designate any symbolic mathematical phrase that may contain numbers and/or variables. Expressions do not contain equal or inequality signs.
• A numerical expression contains only numbers and the operations on those numbers.
• Expressions are simplified using the order of operations and the properties for operations with real numbers, i.e., associative, commutative, and distributive and inverse properties.
• The order of operations, a mathematical convention, is as follows: Complete all operations within grouping symbols*. If there are grouping symbols within other grouping symbols (embedded), do the innermost operation first. Evaluate all exponential expressions. Multiply and/or divide in order from left to right. Add and/or subtract in order from left to right.
*Parentheses ( ), brackets [ ], braces { }, the absolute value , division/fraction bar −, and the square root symbol should be treated as grouping symbols.
• Algebraic expressions use operations with algebraic symbols (variables) and numbers.
• Algebraic expressions are evaluated by substituting numbers for variables and applying the order of operations to simplify the resulting expression.
• To evaluate an algebraic expression, substitute a given replacement value for a variable and apply the order of operations. For example, if a = 3 and b = 2 then 5a + b can be evaluated as: 5(3) + (2) = 15 + (2) = 13.
• Using the order of operations assures only one correct answer for an expression.
• A numerical expression contains only numbers and the operations on those numbers.
• Expressions are simplified using the order of operations and the properties for operations with real numbers, i.e., associative, commutative, and distributive and inverse properties.
• The order of operations, a mathematical convention, is as follows: Complete all operations within grouping symbols*. If there are grouping symbols within other grouping symbols (embedded), do the innermost operation first. Evaluate all exponential expressions. Multiply and/or divide in order from left to right. Add and/or subtract in order from left to right.
*Parentheses ( ), brackets [ ], braces { }, the absolute value , division/fraction bar −, and the square root symbol should be treated as grouping symbols.
• Algebraic expressions use operations with algebraic symbols (variables) and numbers.
• Algebraic expressions are evaluated by substituting numbers for variables and applying the order of operations to simplify the resulting expression.
• To evaluate an algebraic expression, substitute a given replacement value for a variable and apply the order of operations. For example, if a = 3 and b = 2 then 5a + b can be evaluated as: 5(3) + (2) = 15 + (2) = 13.
• Using the order of operations assures only one correct answer for an expression.
Essential Knowledge and Skills
The student will use problem solving, mathematical communication, mathematical reasoning, connections, and representations to...
• The order of operations prescribes the order to use to simplify a numerical expression.
• Simplify numerical expressions containing:
1) exponents (where the base is a rational number and the exponent is a positive whole number);
2) fractions, decimals, integers and square roots of perfect squares; and 3) grouping symbols (no more than 2 embedded grouping symbols).
• Order of operations and properties of operations with real numbers should be used.
• The order of operations prescribes the order to use to simplify a numerical expression.
• Simplify numerical expressions containing:
1) exponents (where the base is a rational number and the exponent is a positive whole number);
2) fractions, decimals, integers and square roots of perfect squares; and 3) grouping symbols (no more than 2 embedded grouping symbols).
• Order of operations and properties of operations with real numbers should be used.
Vocabulary and Things to Know:

Be Able To:

The topic: What is it and what will we learn?
Bottom Line? Apply what you know about computation to simplify expressions.
Order of Operations...even if they do use "PEMDAS" :)

