Lesson 12Meaning of Exponents
Learning Goal
Let’s see how exponents show repeated multiplication.
Learning Targets
I can evaluate expressions with exponents and write expressions with exponents that are equal to a given number.
I understand the meaning of an expression with an exponent like
.
Warm Up: Notice and Wonder: Dots and Lines
Problem 1
What do you notice? What do you wonder?
Activity 1: The Genie’s Offer
Problem 1
You find a brass bottle that looks really old. When you rub some dirt off of the bottle, a genie appears! The genie offers you a reward. You must choose one:
$50,000; or a magical $1 coin.
The coin will turn into two coins on the first day. The two coins will turn into four coins on the second day. The four coins will double to 8 coins on the third day. The genie explains the doubling will continue for 28 days.
The number of coins on the third day will be
. Can you write another expression using exponents for the number of coins there will be on the third day? What do
and represent in this situation? Evaluate and without a calculator. How many days would it take for the number of magical coins to exceed $50,000?
Will the value of the magical coins exceed a million dollars within the 28 days? Explain or show your reasoning.
Print Version
You find a brass bottle that looks really old. When you rub some dirt off of the bottle, a genie appears! The genie offers you a reward. You must choose one:
$50,000, or a magical $1 coin.
The coin will turn into two coins on the first day. The two coins will turn into four coins on the second day. The four coins will double to 8 coins on the third day. The genie explains the doubling will continue for 28 days.
The number of coins on the third day will be
. Write an equivalent expression using exponents. What do
and represent in this situation? Evaluate and without a calculator. Pause for discussion. How many days would it take for the number of magical coins to exceed $50,000?
Will the value of the magical coins exceed a million dollars within the 28 days? Explain or show your reasoning.
Are you ready for more?
Problem 1
A scientist is growing a colony of bacteria in a petri dish. She knows that the bacteria are growing and that the number of bacteria doubles every hour.
When she leaves the lab at 5 p.m., there are 100 bacteria in the dish. When she comes back the next morning at 9 a.m., the dish is completely full of bacteria. At what time was the dish half full?
Activity 2: Make 81
Problem 1
Here are some expressions. All but one of them equals 16. Find the one that is not equal to 16 and explain how you know.
Problem 2
Write three expressions containing exponents so that each expression equals 81.
Lesson Summary
When we write an expression like
If
There are different ways to say