Hey my TMC17 buddy, @kcnorojo! This post is for you!
As an intro to reducing radicals… I place students into groups of 3 or 4 and we play several rounds of Go Fish! This by the way was not my original idea. I will need to dig some to find the original post. But I have used it multiple times with all attitudes of students and it has been a great concrete introduction.
Just in case you’ve never played. Here are the official rules from hoylegaming.com
Each player gets five cards. If you are dealt a four of a kind, or get four of a kind during game play, those cards are removed from your hand, and you get a point. Moving clockwise, players take turns asking a specific player for a given rank of card.
I actually adjust the rules a bit in each round. And I believe we start with seven cards as well. Game ends when someone runs out of cards OR I call time.
Round 1: Students must have a pair for a match. Only a pair works. I allow them to play for several minutes to get the flow of the game. When the timer goes off, I ask them to count their matches and high five those with the most points.
Round 2: Students must have a group of three for a match. Even IF you have the 4th card in the set, you CANNOT lay it down with the match. Again, when timer goes off, I ask them to count matches and we celebrate the winners.
Round 3: Students must have an entire set of four cards to complete / lay down their match. This round goes on just a bit longer. Timer, count matches, celebrate winners.
Round 4: I ask them to deal out the cards – and this time they must have a set of 5 to make a match. A few usually continue to deal out the cards, but several pause and say – but we can’t! There are only four cards of each type. Yes!
We have a discussion about which round was their favorite to play. Which round was toughest? Which round was their least favorite. Usually – Round 2…with three in a set, because IF you end up with the last card, you can never lay it down, thus never emptying your hand to end the game. Hmmmm.
I literally draw a radical on the board and describe how it “sort of” looks like my hand when I hold a bunch of cards. I make a big deal of the index on the radical – it tells us the rules of the game. The Go Fish! game lends it to this part very well. Though these are not the greatest examples, hopefully they will give you a quick idea of what the notes may look like.
We practice several on whiteboards and write a reflection at the end of the work. Then I have them open their INBs and write out a few examples to complete – notate for future reference / study. Depending on the class, I may offer a few examples if they are unable to create some on their own.
Depending on the remaining time in class, I will then pass out the Radical Rummy cards to the groups. I have gone over how we can type in the problems on our graphing calculators – rational exponents, radicals, etc. I explain that every card will match to form a group of 4.
When a group has gotten their matches complete, I have them create a small poster or use whiteboards to list equivalent expressions. We then begin a notice / wonder. I jot down their ideas, testing some as we go along, but letting them decide if their “rule” for the rational exponents holds true.
I like this task after the Go FISH! and simplifying a few radical expressions because it shows them how the rational exponents are simply asking us to find that amount of the factors. For example, an exponent of 1/3 asks us to find 1/3 of the factors of say 8. Since 8 = 2*2*2 and we have 3 factors, I want 1/3 of them, so 2 if the 1/3 power of 8.
There are also come GREAT discussions that arise about the negative exponents and what mathematical operations they are telling us to do.
I would love to hear how you approached these same skills and how it goes!