There are so many reasons that I love reading teacher blogs, and that I love being involved in math education in BC. I was reading Carollee Norris’s “Focus on Math” blog the other day, and noticed that she had reposted a game that Richard DeMerchant had created to develop his students’ proficiency with approximating square roots. Since I’m currently teaching radical expressions with my Pre-Calculus 11 students, it got me thinking about how I could use this activity with my class. As it happened, I began to notice that as my students were adding and subtracting radicals, they seemed to struggle most with simplifying radicals into their simplified mixed radical expression (so that they could be added/subtracted).
Here’s my adapted version of Richard’s game for my Pre-Calculus 11 class. Thank you Richard (and Carollee for reposting)!
The Simplifying Radicals Card Game
We started with a deck of cards for each pair of students in my class. (I got these cards for free from the local casino – it’s a great teacher trick, so if you’re looking for free decks of cards, hit up the casino!)
We assigned values to each of the cards in a standard deck (just like in Richard’s game). As a class we chose that an Ace is 1, numbered cards are “as is”, the Jack is 11, the Queen is 12, and the King is 13
In this two player game, each player receives half of a standard deck of cards. Players then flip over one card each to form the radicand of the radical they are meant to simplify. For example, if a “3” and a “2” are flipped over, then the players would race to simplify the square root of 32. If the cards were a Jack and a Queen, the players would race to simplify the square root of 1112.
The player that gives the correct answer first wins both cards. If there is a tie, the cards stay on the table and two more cards are played, with the winner taking all four cards. The player with the most cards wins!
After playing this game with my class, we noticed that most of the card combinations resulted in a radicand that could not be simplified further. For example, if the cards were “2” and “3”, then the sqrt(23) couldn’t be simplified further. However, if the cards were “3” and “2”, then the sqrt(32) could be simplified to 4sqrt(2). I think the next time we play the game, I’ll add a rule that students need to be able to simplify both radicals (to make it a little more interesting).
I really liked watching how my students interacted with each other throughout the game. I found it neat to see that the students who had fairly similar skills were very much about the “racing”, whereas if students were in a pairing where one student was stronger at simplifying radicals than the other it turned into more of a “quizzing” scenario where the stronger student was assisting the student who was developing their skills. It made me super proud of the students I teach, and it was one of those very cool teacher moments where you are reminded how fantastic it is to have a caring classroom community.
I also am wondering about adapting the game for simplifying cubed roots, or fourth roots. I may make a set of cards that could be used for that activity, so that there would be fewer cases where it isn’t possible to simplify the expression.