Ms. Drake 7th grade Math Number Theory Lesson 1 Exponents

Week by Week Essentials

Number Theory Addition Property of Equality Algebraic Expression Base Coefficient Composite Number Constant Division Property of Equality Equation

Evaluate Exponent Greatest Common Factor (GFC) Inverse Operations Isolate the Variable Least Common Variable (LCM) Like Terms Number Theory

Multiple Multiplication Property of Equality Numerical Expression Order of Operations Power Prime Factorization Prime Number Scientific Notation Solution

Number Theory Solve Standard Form Subtraction Property Of Equality Term Variable Verbal Expression

Evaluating Powers 2 Base Exponent 5

This means 2∙2∙2∙2∙2

Power: A number produced by raising a base to an exponent

Solve by doing the multiplication 2 = 2∙2∙2∙2∙2 = 32 5 Power

Exponential Growth

Any number to the first power is equal to that number 5 = 5 12 = =

Any number to the zero power, except zero is equal to one. 6 = = 1 100,000 =

You can also express whole numbers as Powers Write each number using an exponent and the given base. 25, base 5 25 = 5 ∙ 5 = 5 2

Let’s practice together with a word problem. The cells of the bacteria E. coli can double every 20 minutes. If you begin with a single cell, how many cells can there be after four hours?

4 hours = How many 20 are in each 60? 12 The bacteria doubles 12 times. 2 =

How about this one. Maria had triplets. Each of her children had triplets. If the pattern occurred for two more years how many great, great, grandchildren would Maria have?

Maria

Maria Her children Her grand children Her great grandchildren Her great-great grandchildren

Give two ways to represent these numbers with exponents

729

Until next time, make your own work of art showing the relationships of exponents to bases and powers! And think about this question…

Would you rather be given one million dollars in one month or one penny doubled everyday for one month? The answer may surprise you!