Exponents

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Objective

SWBAT evaluate numerical expressions with exponents.

Big Idea

Students learn that exponents have a Napoleon complex.

Do Now

10 minutes

As students have learned more math concepts, I want to assess how well they've retained their understanding of past concepts.  The Do Now problems are topics we've previously covered in class.   

Do Now:

1.  Which set contains only prime numbers?

A={2,4,6,8,}  B={1,2,3,5,7}    C= {1,3,5,7,9}  D= {2,3,5,7}

2.    4.562/0.02 =  

3.  Find the LCM of 15 and 20.

After 10 minutes, I will randomly select students to explain their work and answers.

Misconceptions:

Problem #1 - Students may think that 1 is a prime number.

Problem #2 - Students may not move the decimal points over correctly.  Also, they may confuse the divisor and dividend.

Problem #3 - Students may find the GCF, rather than the LCM.

Hook

5 minutes

To motivate students, I will share with students a little fun history of Napoleon.

Does anyone know about Napoleon I of France?

Students may know a few facts, such as Napoleon was an emperor of France.

Napoleon is known to have been a short man.  It has been said that he tried to make up for his lack of height by seeking power and conquest. If you were to compare him to our President, you would definitely see a difference in height. (See Napoleon vs Obama)

 

Mini Lesson

15 minutes

This lesson will focus on exponents.  I will relate exponents to my story of Napoleon.

Exponents are very powerful.  In fact, they are sometimes called powers.  But, like Napoleon, they are small in size.  The exponent tells the base what to do.

Example 1 -  Evaluate 74

7 is the base. 4 is the exponent. The 4 is in control and orders the base around.  

7is 7x 7 x 7 x 7.  Is this the same as 7 x 4?

Example 2 - Evaluate 53

What number is the base?  What number is the exponent?  How do we evaluate 53? Is it the same as 5 x 3?

It's important for students to recognize that when they evaluate numbers with exponents, they should not multiply the base times the exponent.

Next, students should know that there are special numbers for powers of 2 and 3.

Special Names

The square of a number means to apply the exponent 2 to a base.

32 is called 3 to the second power or 3 squared.

Why do you think it is called squared?

I will share that a square is a 2 dimensional shape.

What do you think a base with a power of 3 is called?

Students may make the connection that cubes are 3 dimensional figures.

The cube of a number means to apply the exponent 3 to a base.

53  is called 5 to the third power or 5 cubed

We will complete a few more examples together.  It is important for students to realize that exponents can be applied to decimals and fractions.

Example 3 - Evaluate 3.82

Example 4 - Evaluate (1/2)3

 

Group Work

10 minutes

For this activity, students are heterogeneously grouped in fours.  Each group will receive a set of Exponents Flashcards.  Students will work together to find the equivalent pairs.  For example, 7 x 7 x 7 x 5 x 5 should be matched with  73 x 52

 As students work, I will circulate throughout the groups to monitor their progress.  Students may have difficulty with the geometric representation cards.  I will remind them of the special names certain exponents have.

 After 5 minutes, we will review the matched pairs.  For each pair, I will select a group to explain their reasoning.

Lesson Summary

5 minutes

We will review the concept of exponents and bases.  

What's one thing that you would be able to teach another student about applying exponents?

Students may answer with:

- Exponents have a lot of power

- A power of 2 is called squared

- A power of 3 is called cubed