7.11 - Evaluate Algebraic Expressions

7.11  The student will evaluate algebraic expressions for given replacement values of the variables.

• I can determine the total cost of a family trip to the movies when the number of people and the cost of tickets varies for each age group, and I can figure my total score on a video game where different tasks give different points.
  

• I will always get the same result as everyone else when evaluating an expression by following the set of rules called order of operations.
  

·  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) and simplified using the order of operations to equal 15 + (-2) which equals 13.

·  Expressions are simplified by using the order of operations.

·  The order of operations is a convention that defines the computation order to follow in simplifying an expression. It ensures that there is only one correct value. The order of operations is as follows:

-  First, complete all operations within grouping symbols¹. If there are grouping symbols within other grouping symbols, do the innermost operations first.

-  Second, evaluate all exponential expressions.

-  Third, multiply and /or divide in order from left to right.

-  Fourth, add and /or subtract in order from left to right.

¹ Parentheses ( ), brackets [ ], and the division bar should be treated as grouping symbols.

·  Expressions are simplified using the order of operations and applying the properties of real numbers. Students should use the following properties, where appropriate, to further develop flexibility and fluency in problem solving (limitations may exist for the values of a, b, or c in this standard).

-  Commutative property of addition: .

-  Commutative property of multiplication: .

-  Associative property of addition: .

-  Associative property of multiplication: .

-  Subtraction and division are neither commutative nor associative.

-  Distributive property (over addition/subtraction):
.

-  The additive identity is zero (0) because any number added to zero is the number. The multiplicative identity is one (1) because any number multiplied by one is the number. There are no identity elements for subtraction and division.

-  Identity property of addition (additive identity property): .

-  Identity property of multiplication (multiplicative identity property): .

-  Inverses are numbers that combine with other numbers and result in identity elements
(e.g., 5 + (–5) = 0; · 5 = 1).

-  Inverse property of addition (additive inverse property): .

-  Inverse property of multiplication (multiplicative inverse property): .

-  Zero has no multiplicative inverse.

-  Multiplicative property of zero: .

-  Division by zero is not a possible mathematical operation. It is undefined.

–  Substitution property: If , then b can be substituted for a in any expression, equation, or inequality.

The student will use problem solving, mathematical communication, mathematical reasoning, connections, and representations to

·  7.11₂  Use the order of operations and apply the properties of real numbers to evaluate expressions for given replacement values of the variables. Exponents are limited to 1, 2, 3, or 4 and bases are limited to positive integers. Expressions should not include braces { } but may include brackets [ ] and absolute value | |. Square roots are limited to perfect squares. Limit the number of replacements to no more than three per expression.

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6-8 Math  Strategies

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