Rational Exponents Activity – Square Puzzle
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Practice converting between radical form and rational exponent form with this free and fun rational exponents activity that is formatted as a square tarsia matching puzzle.

What math courses is this activity suitable for?
I created this square matching puzzle to give my AP Calculus AB students some much-needed practice converting between expressions written in radical or rational form and expressions written as rational exponents.
While this is considered an Algebra 2 topic in Oklahoma where I teach, the majority of my calculus students have forgotten that the square root of x can be rewritten as x to the 1/2 power. And don’t even get me started on their knowledge of negative exponents which is an 8th grade standard here.
So, I have found that in order for my calculus students to be able to proficiently apply the power rule when taking derivatives of expressions, I have to spend almost an entire class period doing some focused review on this topic.
Even though I created this for my AP Calculus students, it would also be suitable for classrooms such as Algebra 2 or Precalculus where students are learning about converting between radical form and rational exponent form for the first time.
How does the activity work?
In this rational exponents activity, students are given a set of sixteen square cards which feature various algebraic expressions. This is commonly known as a Tarsia puzzle or a square matching puzzle.
Students will grab one of the cards which will feature between two and four expressions on it. They will choose an expression and use their knowledge of exponents, fractions, and radicals to find an equivalent way to write the expression.
This equivalent form will be located on one of the other cards. These two cards may now be placed on the table next to one another.
When all of the expressions are converted and matched correctly, the sixteen pieces will form a 4 x 4 square. My students like to grab individual dry erase boards to work out the problems on while solving the tarsia puzzle.
Printing and Prepping the Puzzle
These puzzle pieces can easily be printed on either letter sized or A4 paper.
The puzzle can be printed with three different sizes of cards. The larger cards are great for students working in groups. The smaller cards are for you if you have students working individually or if you are looking to save paper!
I recommend printing each copy of the puzzle off on a different color of paper and running it through a laminator for extra durability if you plan to use the puzzles with multiple groups of students or save them to use year after year.
MATH = LOVE RECOMMENDS…
A laminator is a MUST-HAVE for me as a math teacher! I spent my first six years as a teacher at a school with a broken laminator, so I had to find a way to laminate things myself.
I’ve had several laminators over the years. I currently use a Scotch laminator at home and a Swingline laminator at school.
I highly recommend splurging a bit on the actual laminator and buying the cheapest laminating pouches you can find!
The different colors of paper allow you to figure out which set a card belongs to when one of the pieces inadvertently shows up on the floor of your classroom a few days later.
If you don’t plan on reusing the sets of cards, you could have students glue their completed square on a sheet of paper to turn in.
Free Download of Rational Exponents Activity – Square Tarsia Puzzle
This square tarsia puzzle for converting between radicals and rational exponents is available to download in PDF format. You can also download a ZIP file containing the original file I used to generate the tarsia puzzle in the free Formulator Tarsia Program if you would like to edit or customize some of the questions.
PDF File
Editable Tarsia File
Puzzle Solutions
Puzzle solutions are available on a password-protected solution page. I do not openly post the puzzle answer keys because one of my goals as a resource creator is to craft learning experiences for students that are non-google-able. I want teachers to be able to use these puzzles in their classrooms without the solutions being found easily on the Internet.
Please email me at sarah@mathequalslove.net for the password to the answer key database featuring all of my printable puzzles and math worksheets. I frequently have students emailing me for the answer key, so please specify in your email what school you teach at and what subjects you teach. If you do not provide these details, I will not be able to send you the password.
Not a teacher? Go ahead and send me an email as well. Just let me know what you are using the puzzles for. I am continually in awe of how many people are using these puzzles with scouting groups, with senior adults battling dementia, or as fun activities in their workplace. Just give me enough details so I know you are not a student looking for answers to the puzzle that was assigned as their homework!