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Rational Exponents Activity – Square Puzzle

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.

rational exponents activity square matching tarsia 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.

students working on rational exponents activity.

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.

partially solved rational exponents activity.

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.

group of students working on rational exponents activity.

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.


drawing of laminator machine with text "laminating recommendations"

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.

Puzzle Solutions

I intentionally do not make answers to the printable math puzzles I share on my blog available online because I strive to provide learning experiences for my students that are non-google-able. I would like other teachers to be able to use these puzzles in their classrooms as well without the solutions being easily found on the Internet.

However, I do recognize that us teachers are busy people and sometimes need to quickly reference an answer key to see if a student has solved a puzzle correctly or to see if they have interpreted the instructions properly.

If you are a teacher who is using these puzzles in your classroom, please send me an email at with information about what you teach and where you teach. I will be happy to forward an answer key to you.