Lesson: Negative Exponents

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Lesson Objective

We will be able to compute using negative exponents.

Lesson Plan

Do Now: (5 minutes)

 
1) Holly spent $13.76 on a birthday present for her mom. She also spent $3.25 on a snack for herself. If she now has $7.74, how much money did she have initially?
 
2) Evaluate 2ab³ if a = 3 and b = -2
 
3) √289

Direct Instruction: (20 minutes)

Ask students to simplify the following problem in their composition book:
 
Ex. 3²
 
If 3² means 3 x 3, what do you think 31 means? 
 
What about 30 ?
 
Any base to the 0 power is equal to 1.
Mathematicians write this rule as  a0 = 1.
 
We can now simplify any exponent problem that has 0 or a whole number as the exponent. Now let’s think about what happens if we a negative number for the exponent.
 
When we learning how to compute with integers we came up with lots of different words that the negative sign could mean. What were some of them? (Have students brainstorm until they get “opposite”. )
 
If I’m facing in one direction and I am told to face the opposite direction, I am going to flip the direction that I am standing in. What is a word that we use to describe a number “flipping”? (Reciprocal).
 
So if “-“ means opposite and opposite means “flip” and when we flip a number we get the reciprocal, what do you think we need to do when we see this?
 
Ex. 8-2
 
Ex. 7-3       

Guided Practice: (10 minutes)
Let's take a look at how mathematicians discovered this rule.  Have students fill out the following tables as a class. (see file labeled 7.NSO-C.16)

Assessment: (10 minutes)
negative exponents work-out



Lesson Resources

7 NSO C 16   Classwork
415
Negative Exponents work out   Assessment
558

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