Laws of Exponents - Division with Like Bases

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Objective

Students will be able to conceptually understand exponents to expand division involving exponents with the same base. By expanding the multiplication, students will develop the rule of subtracting exponents by applying simplification of fractions. Any number divided by itself will always simplify to one over one.

Big Idea

Memorization is short term knowledge but understanding endures time. Create the rules for exponents by expanding the bases to understand.

5 minutes

Beginning the Activity + Homework

30 minutes

Clarifying your learning goals before beginning a lesson is very important.  To watch a short video about clarifying learning intentions and criteria for success click on the resource below.

Clarify for students that today is focused on extending their current understanding of exponents to division and looking for faster methods of writing equivalent expressions when division is the operation between the expressions.

Walk students through the first row of  the table, which is already completed for them as an example.  It is essential that students understand what the table is asking them to complete.  Remind students that they should be expanding the given expressions and then rewriting an equivalent expression in the far right column that hopefully uses fewer exponents if possible.   A great question to ask when reviewing this first row is, "Why are the two's crossed out?"   You are looking for a sound answer such as they simplify to one, not that they merely cancel out.  If a number is canceled out where did it go?  You want a more exact answer than just canceling out.  Tell students to be looking for a pattern or short-cut for rewriting these expressions without expansion because the homework page will be much faster to complete if they discover a short-cut through the activity today.  Allow students to work in cooperative groups to complete the table portion of the handout.  As students are working, move about the room providing feedback that moves learning forward.  For a short video on how to provide feedback, click on the resource below.

As you are questioning students and helping them to develop their thinking, also be selecting students or student groups who will present during the lesson wrap up session.  I like to tell each group which part of the lesson (table) they will be presenting to the class and what exact thinking I want them to share with everyone else.  Try to get a variety of thinking presented if students complete the table using different methods.

Once all or most of your groups have completed the table (about 15 minutes) hold a wrap up session lead by your student experts pre-selected by you.  For tips on holding a wrap up session, click on the resource below.

After students present the answers to the table, allow student groups two minutes (I like to use the stopwatch on my iPhone) to complete the short-cut questions just under the table.  Then ask different student groups to read aloud their rule or short-cut for how to multiply when exponents are involved.  Use the scripting strategy to combine all the different rules into one "best" version class room and tell students to write this class rule on their papers as well.  At this point, you can pass out the unit organizer and have students add this class rule to the organizer for division or save the unit organizer for the end of the unit as a wrap up review of all the rules at once.  I have used the organizer both ways and seen success either way.

For a short video on how to script click on the resource below

Exit Slip/Homework Page

Once you have completed the activity portion of the lesson, explain that students are about to take a formative assessment quiz.  The quiz is not for a grade, but will give students and you valuable information about what they have learned so far and what they still need to work on before taking the unit test.  Remind students that this assessment is individual work and should not be discussed in their groups.  Pass out the exist slip and then bring students the homework practice page as they work to complete the quiz.  The practice page can be finished at home.

I sometimes post solutions to homework on my website or in Edmodo.com because I want students to be able to check their homework as they are finishing to ensure they do not complete the entire page incorrectly.  I do not grade homework, it is practice for the unit test, so giving solutions does not affect their grade.  Also, my students have become accustom to using Edmodo.com to ask each other for help at night with homework and it is really exciting to see them reaching out to other students about math work.  I also get on when I can and answer student questions.

Analyzing Exit Slips

The exit slip is quick to grade and I even let students self grade these if time is available because they are not for a final score in the grade book.  I want students to take ownership of their learning and know where they stand in terms of what they know and don't know.  It is a little more time consuming but very informative to create a spreadsheet or extra column in your grade book just for formative assessments.  You can use a number systems of 3(mastery), 2(partial mastery), and 1(limited mastery) to track your student progress on particular concepts.  I use this information to regroup students homogeneously and for review days when I stop to reteach in small groups.

Student Work Sample:

See resource below.

Teaching Strategies Employed

Several teaching strategies are employed throughout this cooperative group time.  Click on any of the following resources to watch a short video explaining each strategy:

1 minutes