Foldable Book of Exponent Rules

I want to share the foldable book of exponent rules we created in Algebra 1 to glue in our interactive notebooks. We made a “poof book” from a single sheet of copy paper.

After playing The Game of Grudge yesterday as a review game to see what we remembered about exponent rules, my students were disappointed that we were taking notes over exponent rules today instead of playing another round of the game. 

Today we took our notes over exponent rules in the form of a poof book. 

I’ve been wanting to make one of these books since I learned about them during a professional development workshop while I was student teaching.  I’ve heard them called magic books and poof books.  

Basically, you take a sheet of letter sized paper and fold it into a cute little book with the help of a pair of scissors and some magic.  Instructions on making the book can be found here.

This is my copy of the book, so it is titled “Ms. Hagan’s Book of Exponent Rules.”  My students titled their books with their own names.

Our first two pages of the book feature some important vocabulary.  I needed to make sure that all of my students knew what we were talking about when we mentioned the exponent, base, or power.

I had never seen exponent rules presented using P->M->A before Mrs. D left a comment back in February on a post I made during my student teaching.

Here’s what she wrote:

I am currently student teaching. This is what I shared with my algebra students. I write P M A down the side of a piece of paper.

Product -> (2^3)^4 = 2^(3*4) = 2^12
(draw an arrow down to multiply) “look down a line to remember what to do with exponents. I see I need to multiply them.”

Multiply -> 2^3 * 2^4 = 2^(3+4) = 2^7
(draw an arrow down to add) “look down a line to remember what to do with exponents. I see I need to add them. Also keep in mind the bases need to be the same!”

Add -> 2^3 + 2^4
(draw an arrow down to… blank space) “look down a line to remember what to do with exponents. Wait, there’s nothing there. I cannot do anything with the exponents.”

Mrs. D

I changed the P to mean Power to a Power.  And, I explained it to my students like this:  The arrow tells us what to do to the exponent rules.  In a power to a power problem, the arrow points to multiply, so we multiply the exponents.  

In a multiplication problem, the arrow points to add, so we add the exponents.  In an addition problem, the arrow points to nothing, so we do nothing to the exponents.

One of the things I am determined that my students will leave my classroom knowing this year is the word “vinculum.”  It’s one of those things that I use on a daily basis that I didn’t know the name for until a year or so ago.  

You know that bar you put above a repeating decimal?  It’s a vinculum.  

You know that bar you put between the numerator and denominator of a fraction?  It’s a vinculum.  

You know that top line of a radical symbol?  It’s a vinculum.  

I’ve emphasized this word so much this year, my eighth graders found it necessary to correct their science teacher for not referring to the vinculum by its proper name when learning about the density equation.  

Is this word critical to my students’ success?  No.  I earned a degree in pure mathematics without knowing what the word meant.  

But, I do think it goes to show my students that they shouldn’t be scared by new vocab words just because they sound scary.

For negative exponents, I use “cross the line and change the sign of the exponent.”  We didn’t have time to explore why this works, but I will cover it more in depth with my students when they reach Algebra 2.  

We also discussed why anything raised to the zero power is equal to 1.

We ended up finishing up our review of exponent rules with an exponent rules card sort and a game of Exponent Rule Karuta.