Show What You Know: Factors and Multiples + Introduction to Exponents

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Objective

SWBAT: • Show what they know about factors, multiples, GCF, and LCM. • Define exponent and base • Simplify exponents

Big Idea

What do students understand? What gaps do they have in their understanding? What's greater, 2 to the third power or 3 to the second power? Students take a quiz and then work to understand that repeated multiplication is represented with exponents.

Do Now

10 minutes

See my Do Now in my Strategy folder that explains my beginning of class routines.

Often, I create do nows that have problems that connect to the task that students will be working on that day.  Here, I want students to do a brief reflection about what they have learned related to multiples and factors.  As students are working, I walk around and observe connections and questions.  I have 2 students come to the front and share their maps.  I ask students to share out questions.  Based on the questions, I may create a review question for the students.  They can use the next page to show their work.

I do my best to keep the review brief.  It is easy for this review to stretch and take over the period.  I set a timer and hold myself to this.

Quiz

15 minutes

I give students the Quiz.  If students do not finish in the allotted time, they set up a time (preferably that day) to come in and complete it.  I use this data to inform my instruction.   If students struggle with a concept, I will spiral it into do nows and homework assignments.  I may also add a few problems on that topic to the next quiz.

Repeated Operations & Notes

10 minutes

We go through problems 1 and 2 together.  I want students to make the connection between being able to represent repeated addition with multiplication and repeated multiplication with exponents.  It is okay if students don’t make this connection on their own.   If that is the case, I will introduce that 3 to the fourth power is equivalent to 3x3x3x3.  I also use this time to quickly introduce/review the parentheses and dot as additional ways to represent multiplication. 

Students take notes on the vocabulary words on the next pages.  Students may struggle at first that any number to the first power is itself.  If we think about exponents as indicating repeated multiplication, than a number raised to the power of one is just itself.  I ask students what pattern they see when they have a base of 10 (MP8: Look for and express regularity in repeated reasoning).  

A common mistake is that students simply multiply the base by the exponent (3 squared as 3 x 2).  When I see this I stress that exponents indicate repeated multiplication.  Using the 3 squared example, I say that 3 ^2 tells me to multiply 3 by itself, which is not the same thing as multiplying 3 by 2.  Then I draw models to reinforce my point.  I draw a square that is 3 by 3 units and a rectangle that is 3 by 2 units.  The area of these shapes is different.

Show me the money!

15 minutes

To hype up my students I have them do a drum roll as I announce the new game show they are going to participate in.  I have found that most sixth grade students have fun when anything is presented as a game or competition.  I read through the rules and ask for a volunteer to go through the example round with me.  As the volunteer and I go through the example, I record what I expect students to record on the paper.   Even with this easy example, I have my volunteer help me at the end with the calculator. 

For a game like this, I let students pick their own partners.  If there is an odd number of students, there can be one group of three and they can adjust their worksheet.  As students play, I walk around and monitor that students are following the rules (and making and recording a guess in 5 seconds).  I am looking for what students are guessing and how they are changing their choices with the more rounds they go through.

For students who need an extra challenge have them use the 1-10 spinner with a paperclip, instead of the dice.  The other player still uses the calculator to find the end product.

If students finish the game, they can work on the challenge questions.

Closure and Ticket to Go

10 minutes

 For Closure put this on the board: option a)3^4 and option b) 4^3.  I give students 5 seconds to make a decision and then ask them who chooses a) and who chooses b)?  We represent both options as repeated multiplication and then simplify them.  I ask students what they noticed while they played with their partner.  Did anything surprise you?  Some students may share a round where they were surprised once they simplified both options.  Other students may share their experience with rolling a one, and the pattern they noticed when you compare a number raised to the first power vs. one raised to that power.  Students are engaging in MP8: Look for and express regularity in repeated reasoning.

Now that students are familiar with these types of comparisons, I can use this to fill up a couple minutes of down time throughout lessons or the day.  Students understanding and number sense with exponents will continue to improve!

With the last few minutes of class I give a Ticket to Go for students to independently complete.  I am looking to see if students have grasped the connection between exponents and repeated multiplication.

I pass out the HW Introduction to Exponents at the end of class.