Organizing Rules of Exponents

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SWBAT recognize and apply rules of exponents when multiplying or dividing terms with like bases.

Big Idea

Students need to internalize five basic rules when dealing with exponents. Using a simple foldable and a series of lessons, students are able to articulate and apply each one in context.

Warm Up

8 minutes

For today's Warm Up assignment, I have selected three problems that review three key concepts for my students. Students continue to struggle with adding integers with different signs, so I was intentional about including this problem. We have been using vertical number lines to solve this type of problem, so my hope is students can begin to draw and use them without prompting if needed. The second problem provides practice with math squares. Students must determine the missing number in the square using number sense strategies. The four boxes must add to the number beneath the math square. Students can use a variety of strategies to answer this question, which I will spot light when the timer sounds

Finally, I have included a question that requires students to plot four different points on the coordinate plane. I saw students struggle with the recently on a homework assignment, so I included this to review quadrants and plotting points.

Once the timer sounds, I launch today's lesson of discovering the rules of exponents by asking students to take out their foldable they picked up on the way into class.

Rules Discovery: Multiplying Exponents

6 minutes

Once students have glued their foldables into their journals, I explain that over the next few days, we will be looking at some patterns created by operations with exponents. These patterns are going to help us generalize rules that we can apply to other situations.  I then show the students five examples of like variables with exponents being multiplied and the results (answers) and ask them to think about what pattern they notice.  After 15 seconds, I ask them to discuss what they see with their tablemates.  I then ask them to generalize a rule at their table for multiplying exponents.  After one minute, I select volunteers to share their table's rule.  I record that rule on the SmartBoard.  I then ask for any additions or corrections to the rule until all groups are happy with what has been generated.

Let's Practice!

15 minutes

I launch today's lesson by explaining that we are going to be using our investigative skills to discover the rules used when multiplying and dividing exponents. Before we get started, however, I want students to fold and glue their exponents rules foldable into their journals. (Students had already picked them up when they entered class --a procedure I continue to reinforce).  I model how to fold the paper so the students have a visual cue.  Then they glue the foldable in the notes section of their journals.

Then, I reveal five examples of exponents with the same base being multiplied. I ask students to study the examples and try to figure what is happening. I use a wait time signal (my hand showing 'stop' at a right angle) so that students know not to talk during this thinking time. After 15 seconds, I ask students to talk at their table about what they see. I eavesdrop on conversations so that I can intentionally select students who have done well articulating what they see. I bring students attention to the Smart board by counting down and ask the student to share with the class. I ask students to confirm their agreement or disagreement with the rule with a thumbs up or thumbs down signal. I then show the students why this is the rule by writing a problem in expanded form: x^4 times x^ 5 as four x's next to 5 x's. I ask the students to count how many x's they see altogether.

Once the rule has been generalized, I provide some group practice via problems on the SmartBoard. I don't want students to write the rule in their foldables yet because I want them to apply the rule several times to solidify their understanding. As students work, I circulate through the room watching for the common error of actually multiplying the exponents. 

After completing the first five practice problems, I ask students to write the rule for multiplying exponents in their own words in their foldable on the top half of the multiplying & dividing tab.  I suggest that they write an example, too, since many of the rules may be used and confused as we add them throughout the week.

Next, I ask students to complete five additional problems on their own. I wander the room as the students work to check for any misconceptions or misunderstandings.  I then "pull sticks" (select student volunteers from a cup full of student names on popsicle sticks) and ask students to donate answers.  I ask the rest of the students to agree with a thumbs up or disagree with a thumbs down. This allows me to again check for any misunderstandings.

Rules Discovery: Dividing Exponents

15 minutes

Once we complete the five independent problems that help us practice multiplying exponents, I explain we have another rule to seek out: dividing exponents.  I then follow the same procedures to help the students find and then practice using the rule for dividing exponents.

On Your Way Out

1 minutes

As closure, I ask student to pair up at their table to have a brief conversation about what was learned in class. I tell them to let the tallest person explain the rule multiplying exponents and the shorter partner will explain the one for dividing. For the following day's lesson, I will provide additional review practice so that students can solidify the rules in their minds.