I begin this lesson with a radical equation on the board: √(4x-7)+2=5
My students will generally begin working on the problem even before the bell, trying to find a solution, so while they're working and talking I walk around and observe and listen. This gives me a snapshot of where my students are with radical equations. When the bell rings, I ask for volunteers to share their solutions with the class. I don't say whether or not they're correct, I simply write their answers on the board and let the rest of the class evaluate them. (MP3) Sometimes students say that they found the solution using guess-and-check or their calculator, so I emphasize the need to be able to explain and justify each step in the solution process. Usually when my students finally all agree that the solution is 4, they also understand a reliable method for finding that answer. If there are still those who struggle with this I refer them to my educreations video for further examples.
You will need copies of the Radical Problems handout for this section of the lesson. I tell my students that today they will get to work with their left-shoulder partner to solve a collection of radical problems and remind them to include their work on their papers, with each student writing their own work for later study and review. I distribute the Radical Problems handout and while my students are working, I walk around offering encouragement and redirection as needed. (MP1)
When everyone is finished, I tell my students that they will be checking their own work today while I go over the answers, but remind them that neither I nor the textbook are infallible, so they should be on the lookout for incorrect answers. (MP6) I intentionally read at least one or two obvious mistakes which I explain in my video. If nobody catches one of the "mistakes" I ask for a couple of volunteers to explain the answer at the board, including showing work. Since my students are pretty typical teenagers, they would rather just sit, so they quickly learn to spot incorrect answers to save themselves some board-time.
To close this lesson I ask my students to reflect silently for a minute about the day's lesson. (That's a long time for teenagers to be silent and reflect!) After a minute (or a little less) I tell them to pair-share what they think the most important part of today's lesson was for them. (MP2) This exercise gives my students the opportunity to really stop and think about what they've just spent almost an hour working on, and hopefully reinforces some of the learning that went on today. The key ideas they should take away from this are that solving radical equations may look daunting, but can be accomplished by taking it one step at a time, and that they should always be ready, willing and able to challenge an answer they think is incorrect!