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AGA1 1-2 Order of Operations and Evaluating Expressions

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1-2 Order of Operations and Evaluating Expressions

How does the locations of numbers, variables, and operation signs in a mathematical expression affect

the value of that expression?

� You can use powers to shorten how you present repeated multiplication.

� You simplify a numerical expression when you replace it with its single numerical value.

� When simplifying an expression, you need to perform operations in the correct order.

• Read pages 10 – 13.

Key Concepts:

A power has two parts, a base and an exponent. The exponent tell you how many times to use the base

as a factor. You read the power 23 as “two to the third power” or “two cubed.” You read 52 as “five to

the second power” or “five squared.”

The Order of Operations are performed in this sequence:

1. Perform any operation(s) insider grouping symbols, such as parentheses () and brackets []. A

fraction bar also acts as a grouping symbol.

2. Simplify powers.

3. Multiply and divide from left to right

4. Add and subtract from left to right.

You evaluate an algebraic expression by replacing each variable with a given number, then you simplify

the expression using order of operations.

Skills:

You will identify the parts of powers (base and exponent) plus simplify powers.

You will perform order of operations in the correct sequence to simplify expressions.

You will evaluate algebraic expressions including creating expressions from real-world sitautions.

Common Core State Standards:

A-SSE.A.1a: Interpret parts of an expression, such as terms, factors, and coefficients.

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AGA1 1-2 Order of Operations and Evaluating Expressions

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Students review vocabulary/key concepts on page 10.

Class discussion will show a power is made up of a base and an exponent. The exponents reports how

many times to multiply the base by itself. 53 is 5x5x5 (known as extending the power). Powers can be

simplified by performing the repeated multiplication (23 is 2*2*2 which simplifies to 8).

Students need to simplify positive integer bases (102), as well as positive decimal base (1.53) and positive

fractional bases [ (��)2 ]. Knowing how to multiply decimals and fractions is necessary.

Multiplying Decimals

1.5

X 1.5

75

150

2.25 (place the decimal in the product to account for the number of decimal places in the factors.)

Multiplying Fractions

�� x

�� multiply the numerators (tops) over multiply the denominators (bottoms) �

��

Simplifying Powers

Remember: the exponent indicates the number of time you use the base as a factor.

(page 10)

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AGA1 1-2 Order of Operations and Evaluating Expressions

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Simplifying Expressions with Order of Operations

When simplifying an expression, you need to perform operations in the correct order.

Order of Operations is often remembered using PEMDAS

P – Parentheses (meaning any grouping symbols, including fraction bars)

E – Exponents (meaning attend to exponents on powers, also include taking roots like square roots)

MD – Multiplication and Division from left to right

AS – Addition and Subtraction from left to right

Remember: when simplifying an expression that contains a fraction, you start by simplifying the

numerator (top) and the denominator (bottom) separately first, then you divide the simplified

numerator by the simplified denominator.

2. What is the simplified form of each expression? Show each operation separately. (page 11)

a. 5 ● 7 – 42 ÷ 2 b. 12 – 25 ÷ 5 c. �����

Students complete the Kuta Order of Operations worksheet.

Name: Date:

AGA1 1-2 Order of Operations and Evaluating Expressions

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Evaluating an Algebraic Expression

You evaluate an algebraic expression by replacing each variable with a given number then you simplify

the expression using order of operations.

To evaluate an algebraic expression, you must be given a value for the variable(s).

The values for x and y are given here.

When you evaluate an algebraic expression, you substitute in the given value(s) for the variable(s) which

changes the expression from algebraic to numerical. The numerical expression can then be simplified.

Note: some algebraic expressions can be simplified before they are evaluated (more on this in a later

unit).

(page 12)

3. What is the value of each expression when a = 3 and b = 4 in parts (a) and (b) below?

Show all the work for each operation.

a. 3b – a2 b. 2b2 – 7a

Students complete the Kuta Evaluate Algebraic Expressions worksheet.

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AGA1 1-2 Order of Operations and Evaluating Expressions

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Evaluating a Real-World Expression

Real-world situations are often expressed in the form of a word problem.

To evaluate a real-world situation, first identify the key relationships (constants and operations), then

define your variables, and finally write the algebraic expression with the constants, operations, and

variables needed to model the situation. You can then evaluate the expression for given values of the

variable(s) used.

4. The shipping cost for an order at an online store is ��� the cost of the items you order.

What is an expression for the total cost of a given order?

What are the total costs for orders of $43, $79, $95, and $103?

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AGA1 1-2 Order of Operations and Evaluating Expressions

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Group Work

Practice with Real-World Algebraic Expressions

Page 14, problem 44

Note: write the algebraic expression then evaluate for the values given.

Page 15, problem 60a

Note: this simply is a problem involving evaluate an algebraic expression with values given.

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AGA1 1-2 Order of Operations and Evaluating Expressions

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Page 15, problem 63, show your work then select a multiple choice option

Page 15, problem 64, show your work then select a multiple choice option

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Lesson Check: page 13, problems 1 – 8

Evaluate each expression for x = 3 and y = 4.

4. x2 + 2(x + y) 5. (xy)3 6. 4x2 – 3xy

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Practice and Problem Solving

Page 13, problems 9 – 16

Simplify each expression.

9. 35 10. 43 11. 24 12. 108

13. �� �

14. �� �

15. (0.4)6 16. 74

Page 13, probems 17 – 24 - extension

Simplify each expression.

17. 20 – 2 ● 32 18. 6 + 4 ÷ 2 + 3 19. (62 – 32) ÷ 2 20. 5 ● 22 ÷ 2 + 8

21. 80 – (4 – 1)3 22. 52 + 82 – 3(4 – 2)3 23. ��÷��� 24.

●����÷�

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Page 13, problems 25 – 27

Evaluate each expression for s = 4 and t = 8.

Page 13, problems 28 – 33 - extension

Evaluate each expression for s = 4 and t = 8.

28. 3st2 ÷ (st) + 6 29. (t – s)5 30. (2s)2t

31. 2st2 – s2 32. 2s2 – t3 ÷ 16 33. (��)�t+t

�

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Page 13, problem 34

Page 13, problem 35 - extension