Introducing Exponents

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Objective

SWBAT demonstrate an initial understanding of exponents

Big Idea

Understanding exponents is important to modeling growth and change!

Curriculum Reinforcer

5 minutes

For the Warm Up activity, I will have my students complete problems that will review standards NS.2, NS.3, Nd RP.3. I want them to practice these standards specifically because these standards, among others, have proven to continue to be a deficit area for many of my students. Reviewing these standards in the warm up provide students an opportunity to clear misconceptions concerning these standards and eventually master them.

Engagement

5 minutes

To get started with today's lesson, we will complete an opening exercise where the students will explore repeated addition versus repeated multiplication. To participate in this exploration, the students will analyze and discuss the differences between 3+3+3+3 versus 3 x 3 x 3 x 3. I will then have my students record their observations on a T-Chart organizer.

  • Observations that my students may come up with for 3+3+3+3 are as follows:
    1. Produces consecutive multiples of 3 when added step by step (i.e. 3, 3+3=6, 3+3+3=9, and 3+3+3+3=12).
    2. Can be written as 3 x 4
    3. It's solution is 12
    4. It's solution is significantly less than the solution fo 3 x 3 x 3 x 3.
    5. It shows a pattern
    6. It shows addition
    7. It shows repeated additions.
  • Observations that my students may come up with for 3 x 3 x 3 x 3 are as follows:
    1. Produces multiples of 3 but not in consecutive order.
    2. Shows a pattern
    3. Can be written as 3 to the 4th power
    4. It's solution is 81
    5. Its solution is significantly greater than 3+3+3+3
    6. It shows multiplication
    7. It shows repeated multiplication

The significance behind having the students create this organizer is to address the common misconception that 3 to the 4th power is equal to 12. Often times, students will multiply the base number and the exponent and therefore arrive at an incorrect solution. I will have my student use this organizer in a manner that will help them to NOT have this misconception.

After providing my students with 2 minutes to write down their observations, we will then discuss and present these observations as a class. I will write down the observations that my students had for each expression. If the list is not to my satisfaction, i will ask probing questions to get students to make the list longer and more informative.

Instruction & Teacher Modeling

10 minutes

To start off the instructional piece, I will explain the significance of the organizer created during the opening. I will show students that the organizer illustrates the difference between 3 x 4 and 3 to the 4th power. I will then use the organizer to highlight those differences.

After highlighting the differences, I will then direct the students to take a closer look at the side of the organizer that deals with repeated multiplication.

 I will use the example 3 x 3 x 3 x 3 to show students the meaning of the following vocabulary words: base, exponent, and power. I will also illustrate the meaning of perfect squares using 3 to the 2nd power, 5 to the 2nd power, and 9 to the 2nd power. I will do this by drawing an array for each of the three expressions to show that their arrays form a perfect square.

After explaining and illustrating the meaning of the vocabulary for this lesson, I will then complete the following examples:

  • Write 6 x 6 x 6 x 6 using an exponent
  • Write 4 X 4 X 4 using an exponent
  • Write 5 to the 2nd pwer as a product
  • Write 1.5 to the 3rd power as a product
  • Write 1/2  to the 3rd power as a product

As I complete these examples, the students should be taking notes.

After going through the part of this lesson that connects to the engagement activity. I will then recap using the PowerPoint attached to this section of this lesson. In this PowerPoint student will get an opportunity to revisit the following:

  • Objective
  • Vocabulary
  • Exponential Format

 

Try It Out

10 minutes

During this section of the lesson, I will have my students complete a couple of examples where they will put expressions in the exponential format as well as solve a few exponential equations. I will also guide my students through a real world scenario involving exponents. The problem that I will present to students is as follows:

A phone tree is used to contact families at Paul's school. The secretary calls 4 families. Then, each family calls four other families and so on. How many families will be notified during the fourth round of calls?

The PowerPoint attached to this section of this lesson contains all the necessary information to complete this section of this lesson.

Independent Exploration

20 minutes

To practice independently, my students will complete the task called, "The Dijinni's Offer." After working on the task independently, I will then have my students partner up and discuss their solutions. They will compare to see if they came to the same conclusion. If not, they will analyze who is correct and who is not and what misconception caused them to make a mistake. They will talk to each other about their method of solving the problem presented in the task. During their discussion time, the students should be writing down misconceptions that they came across. Similarities and differences between how they solved the problem versus how their partner solved the problem as well as any other important topics that arose during the discussion.

Closing Summary

20 minutes

To close out this lesson, partners will be selected to present their solutions and what they learned about this task and this lesson during their discussion.

 

TOTD: I will have my students complete a five question assessment

The assessment is presented on the PowerPoint that is attached to this section of this lesson.