GLE 0606.3.3 * Use exponents In order of operations.

SPI 0606.3 *Use order of operations to

simplify expressions and solve problems

EXPONENTS

Richie Rich celebrates his birthday on June 1st. This year his parents have given him his choice of gifts. He can choose ONE of the following options: Option 1: His parents will give him $500,000 on June 1st.

OR Option 2: His parents will deposit $2 in a savings account on June 1st. Each day they will double the amount in that account until the end of the month. On June 30 th Richie can have whatever money that has accumulated in the account.

WHICH GIFT DO YOU WANT?

You will learn what an exponent is and how to write and solve exponents to represent repeated multiplication.

When you leave today, you will be able to say: I can write expressions using exponents.

I can evaluate expressions containing exponents.

** GOAL FOR THE DAY **

FACTORS PRODUCT OF FACTORS

DESCRIPTION

2x2 4 2 is a factor 2 times

2x2x2 8 2 is a factor 3 times

2x2x2x2 16 2 is a factor 4 times

2x2x2x2x2 32 2 is a factor 5 times

2x2x2x2x2x2 64 2 is a factor 6 times

2x2x2x2x2x2x2 128 2 is a factor 7 times

2x2x2x2x2x2x2x2 256 2 is a factor 8 times

TAKE A LOOK AT THIS….

THERE’S GOT TO BE A BETTER WAY!

Instead of writing out those factors SO many times, we can use EXPONENTS! Exponents will save the day and our time!

Writing numbers in EXPONENTIAL NOTATION is an easier way to write a number as a product of many factors

THERE IS A BETTER WAY

An EXPONENT tells how many times a number is used as a factor. This number can also be called a POWER.

EXPONENTS will indicate how many times the base is multiplied by itself.

A BASE is the number that is multiplied by itself.

WHAT IS AN EXPONENT?

WHAT DOES THIS LOOK LIKE?

Exponent- indicate how many times the base is multiplied by itself.

Base - is the number that is multiplied by itself

So the exponent 3 will tell you how many times to multiply the base, 5, by itself. So is the same as 5x5x5.

Write the following expressions using exponents:

1. 6x6x6x6

2. (-8) x (-8) x (-8)

TRY SOME MORE…

WAIT…

When writing an expression in exponential form, how do you know which number to use as the base and which number to use as an exponent?

REFLECTION TIME

 

DISCUSSING FORMS FOR NUMBERS

 

YOUR TURN

LOOK AT THIS FIGURE

How many squares are in this quadrilateral?

How would this look in expanded form?

What about exponential form?

HOW ABOUT THIS FIGURE?

How many squares are in this quadrilateral?

How would this look in expanded form?

What about exponential form?

Rule Example

Any number (except 0) raised to the zero power is equal to 1.

= 1

Any number raised to the first power is always equal to itself.

= 8

If a number is raised to the second power, we say that it is squared.

is read as three squared

If a number is raised to the third power, we say that it is cubed.

is read as four cubed

RULES OF EXPONENTS

EXPLAIN

Calculators can be used to evaluate exponential expressions.

Does anyone know how to insert an exponent into their calculators?

CALCULATOR TIME

Let’s talk about Richie Rich’s options a little more now… Option 1: His parents will give him $500,000 on June 1st.

Option 2: His parents will deposit $2 in a saving account on June 1st. Each day, they will double the amount in that account until the end of the month. On June 30 th, Richie can have whatever money has accumulated in the account.

WHAT SHOULD RICHIE RICH DO?

Have you ever heard of square footage?

What about cubic feet and cubic meters?

All of these are ways that we use exponents on a regular basis.

REAL-LIFE APPLICATION

Answer the following question on a loose piece of paper:

What are exponents and how do we use them to write and solve problems with repeated multiplication?

TICKET OUT THE DOOR