Solving radical equations. It’s a dry subject when you look at the Algebra 2 textbook. I’m trying to find new ways to approach teaching without telling. Thanks to the help of fellow Twitter Math Camper, @misscalcul8 , I was able to help kids figure out traditional mathematical steps without doing a traditional lecture. My take varies slightly from hers in that my access to colored paper while at home the night before didn’t allow me to prep it quite the same.
Each student received a copy of her graphic organizer/follow along worksheet. Students were then placed into groups of 4 and each group received one of four “step” pages inside of sheet protectors. I asked students what they noticed about these pages. “Um, what’s going on?” was the first reaction. Then eventually someone pointed out the (*) by one line of equations on the sheet. Eventually someone said, “so you want us to put these in order?” BINGO! I didn’t even have to tell them! They then worked as a group recording down the steps in the correct order as they reasoned through each line determining which line logically came next. I helped groups by swapping out pages of steps so they would have the opportunity to work on all four sets.
As I walked the room, I over heard students actually talking and reasoning about math! YES!! Score one for trying a non-traditional approach! (Well, excluding the group that was watching hockey highlight videos. They were eventually working.)
Once each group was done, I wanted to see if they could apply what they learned. Students spent the remainder of the period working on 9 problems. On the top of the sheet for these problems, students were exposed to the phrase “extraneous solutions”. When asked, no one knew what that meant. I’ve been challenging them to be resourceful Algebra 2 students, so with a prompt about being resourceful, some looked in the textbook and others used Google on their phones. After a conversation about “extraneous solutions,” students got to work.
Except one thing snagged them. They didn’t have to factor in the examples from the step sorting activity. In several of these problems, they did. And they panicked. “You didn’t teach us these ones!” To which I replied, “Well technically I didn’t teach you any of them, you did.” And yet another student stepped up to the plate and said, “It’s just like example 4 in the book. You factor like we did all last chapter.”
I’m so ecstatic that students were resourceful AND worked together! Bonus that they were also able to do the math.