Eureka Math Module 4 Topic B

Special Notations of Operations6.EE.A.1:Write and evaluate numerical expressions involving whole – number exponents.

6.EE.A.2c: Write, read, and evaluate expressions in which letters stand for numbers.

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Lesson 5 – Exponents

• Objective:

– I can write an expression in exponential form, expanded form, and standard form. I can evaluate a numerical expression.

• Guiding Question: (Write your answer on the lines below.)

– How is the expression, 32 different from 3 × 2?

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• Numerical Expressions – a math expression that includes numbers and symbols

• Exponent – tells how many times to multiply a number itself

• Base – a number being multiplied in an exponential notation

• Power - Exponent

• Squared – a number raised to the second power: 42

• Cubed – a number raised to the third power: 43

• Exponential notation – a number written with an exponent: 32

• Standard notation – a rational number: 9

• Expanded notation - a number written as an expression: 3 × 3

Lesson 5 – Exponents

Exponential

Form

Standard

Form

Expanded

Form

32 9 3 × 3

Examples: Write the expanded form in exponential form.

Write the exponential form in expanded form.

Lesson 5 – Exponents

Examples: Write the expanded form in exponential form.

Write the exponential form in expanded form.

Lesson 5 – Exponents

Examples 7 and

8 written in

fraction form

Examples: Write the expanded form in exponential form.

Write the exponential form in expanded form.

Lesson 5 – Exponents

Complete the table.

Lesson 5 – Exponents

Base Squared Cubed

2 22 = 2 × 2 = 4 23 = 2 × 2 × 2 = 8

3 32 = 3 × 3 = 9

4

5

6

Lesson 5 – Exponents

Lesson 6 – Order of Operations

• Objective:

– I can use order of operations to evaluate numerical expressions.

• Guiding Question: (Write your answer on the lines below.)

– How would your answer be different in solving numerical expressions if you did not follow order of operations?

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When we solve Numerical Expressions we must follow a specific order to arrive at the correct

value of the expression. We follow the “Order of Operations”. This states what order the

operations will be solved in.

1. Parenthesis are always solved first.

2. Exponents are solved next or if there are not parentheses in the expression.

3. Multiplication and Division are solved in order from left to right in the expression (whichever

comes first).

4. Addition and Subtraction are last and also solved from left to right, whichever comes first in

the expression.

To remember the order we use the acronym: PEMDAS or Please Excuse My Dear Aunt Sally.

Lesson 6 – Order of Operations

Example:

2 × (3 + 5) ÷ 23 - 6

2 × 8 ÷ 23 - 6

2 × 8 ÷ 8 - 6

16 ÷ 8 - 6

8 - 6

2

Lesson 6 – Order of Operations

Solve Parentheses First

Solve Exponents

Next

Then multiply or divide, whichever

comes first

Last, add or

subtract

Lesson 6 – Order of Operations

Since there are no

parentheses, we

move to the next

order of operation,

which are

exponents.

Lesson 6 – Order of Operations

Lesson 6 – Order of Operations

Lesson 6 – Order of Operations

Lesson 6 – Order of Operations