# 6.8 and *6.6c - Expressions (No Calc)

6.8    The student will evaluate whole number numerical expressions, using the order of operations. (No Calculator)

6.6  c)  The student will simplify numerical expressions involving integers.*  (with NO CALCULATOR)

Bloom's Level:  Analyze

### BIG IDEAS

• 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.

### UNDERSTANDING THE STANDARD

• The order of operations is a convention that defines the computation order to follow in simplifying an expression.
• The order of operations is as follows:
• First, complete all operations within grouping symbols*.  If there are grouping symbols within other grouping symbols, do the innermost operation 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.
* Parentheses ( ), brackets [ ], braces {}, and the division bar – as in 3+4/5+6  should be treated as grouping symbols.
• The power of a number represents repeated multiplication of the number (e.g., 83 = 8 · 8 · 8). The base is the number that is multiplied, and the exponent represents the number of times the base is used as a factor. In the example, 8 is the base, and 3 is the exponent.
• Any number, except 0, raised to the zero power is 1. Zero to the zero power is undefined.

·  The set of integers is the set of whole numbers and their opposites (e.g., …-3, -2, -1, 0, 1, 2, 3…). Zero has no opposite and is neither positive nor negative.

·  Integers are used in practical situations, such as temperature changes (above/below zero), balance in a checking account (deposits/withdrawals), golf, time lines, football yardage, and changes in altitude (above/below sea level).

·  Concrete experiences in formulating rules for adding, subtracting, multiplying, and dividing integers should be explored by examining patterns using calculators, using a number line, and using manipulatives, such as two-color counters, drawings, or by using algebra tiles.

·  Sums, differences, products and quotients of integers are either positive, negative, undefined or zero. This may be demonstrated through the use of patterns and models.

·  The order of operations is a convention that defines the computation order to follow in simplifying an expression. Having an established convention ensures that there is only one correct result when simplifying an expression.

·  The order of operations is as follows:

–  First, complete all operations within grouping symbols.1 If there are grouping symbols within other grouping symbols, do the innermost operation 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.

1Parentheses , absolute value  (e.g.,   ), and the division bar (e.g.,  ) 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 multiplication:

-  Associative property of multiplication:

-  Subtraction and division are neither commutative nor associative.

-  Distributive property (over addition/subtraction):  and

-  Identity property of multiplication (multiplicative identity property):

-  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.

-  Multiplicative property of zero:

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

·  The power of a number represents repeated multiplication of the number (e.g., 83 = 8 · 8 · 8). The base is the number that is multiplied, and the exponent represents the number of times the base is used as a factor. In the example, 8 is the base, and 3 is the exponent.

·  Any number, except zero, raised to the zero power is 1. Zero to the zero power (is undefined.

### ESSENTIALS

• What is the significance of the order of operations? The order of operations prescribes the order to use to simplify expressions containing more than one operation. It ensures that there is only one correct answer.

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

6.81  Simplify expressions by using the order of (No Calc) operations in a demonstrated step-­by-­step approach. The expressions should be limited to positive values and not include braces or absolute value.

6.82  Find the value of numerical expressions, (No Calc) using order of operations, mental mathematics, and appropriate tools. Exponents are limited to positive values.

·  6.6c1  Use the order of operations and apply the properties of real numbers to simplify numerical expressions involving more than two integers. Expressions should not include braces { } or brackets [ ], but may contain absolute value bars . Simplification will be limited to three operations, which may include simplifying a whole number raised to an exponent of 1, 2 or 3.

### KEY VOCABULARY

evaluate, numerical expression, order of operations, parentheses, brackets, exponential expressions, power, exponent, base, simplify, positive values

Updated: Oct 27, 2017