Laws of Exponents Four: Zero and Negative Exponents
Once the students have learned the basics of exponents, (base, exponent, power, factor) and how to multiply two or more powers that have the same base, and how to raise exponents to a power when finding the quotient, now the student will work with exponents of zero and negative exponents.
Common Core State Standards
A.SSE.2: Use the structure of an expression to identify ways to rewrite it.
F.IF.8b: Use the properties of exponents to interpret expressions for exponential functions
Mathematical Practice(s): 2. Reason abstractly and quantitatively.
Learning Target(s)
- I can explain why equivalent expressions are equivalent.
- I can look for and identify clues in the structure of expressions in order to rewrite it another way.
Essential Question(s)
Why structure expressions in different ways?
Vocabulary: monomial, equivalent expressions, base, exponent, power, factor, quotient
Lesson
Notes:
- Review the vocabulary.
- Add to the Foldable.
- Write Zero exponents on the tab below Power of a Quotient and provide a basic example. Ex: x^{0} = 1, 3^{0} = 1
- Now lift up the tab and write on the top portion – Anything to the zero power is 1. If the base is a variable, the base is gone and the answer is just 1. On the bottom portion that says, “Zero Exponent", provide two examples and explain the examples in detail.
- (Continual reminder): if no exponent is written, the exponent is one (1).
- Write Negative Exponent on the tab below Zero Exponent and provide two basic examples. Ex1:5^{-2} = 1 / 5^{2 }OR 1 / 25; Ex 2: 1 / m^{-3} = m^{3} / 1 = m^{3}
- Now lift up the tab and write on the top portion – When the exponent is negative, take the reciprocal of the term. On the bottom portion that says, “Negative Exponent", provide two examples and explain the examples in detail.
- REMINDER: Inform students that the denominator should not equal zero.
- NOTE: As a first step when you have negative exponents, it may be easier to write the problem as multiplying fractions (with 1 in the numerator or denominator) before taking the reciprocal. EX: x^{-2}y^{3} / z^{-4 }= (x^{-2}/1)(y^{3}/1)(1/z ^{-4}) = y^{3}z^{4} / x^{2}
* Now you have the basis of your lesson and you can move on to Guided Practice.
Guided Practice: 3-6 practice problems. You can do 1or 2 problems with the students at the board (Smart Board, Elmo, etc.) and then put them in small groups of no more than 3 to do the rest. These problems can be pulled from any textbook or other resource.
Independent Practice: Approximately 5 problems to be done alone.
Closure/Review: Ask 1-3 questions relating to today’s lesson to be answered by the class as a whole. This will give you a general idea of the class’ understanding of today’s topic.
Exit Ticket: This is to be done the last 3-5 minutes of class and given to you (by hand or in a designated area of your room) as they leave class.
Possible question(s):
- What is your first step in solving this problem? 4^{-3 }
- What is your first step in solving this problem? 4x^{-3}
- Can any connection be made between the two previous problems?
Below is the entire foldable with examples in a Word document. Each day you can add to the foldable and at the end of the lessons/unit, you will have notes for each area in one location. This attachment will be at the end of each lesson for Laws of Exponents.
(Foldables are interactive organizers created by Dinah Zike). This foldable is the Layered-Look Book.