I was determined not to teach student a "trick" for simplifying radicals. I have heard so many cute explanations, like "needing a partner to get out of the house," but after reading "Nix the Tricks," I realized teaching only a trick robs students of the math behind what they are doing. We are down to a single-digit countdown before the EOC, so my lessons are hurried. I taught simplifying radicals, gave students a couple practice problems that we worked out together and then gave them an exit ticket. I was feeling good about my lesson. Then I saw the Exit Tickets. Yikes! I'm not sure if it was no enough time for them to complete the exit ticket (sometimes I misjudge their pace on new content) or the lack of practice, but overall the scores were terrible. With only a few days left until the EOC, I had to make a decision to cut my losses or spend another day on the topic. I decided if they can do anything with radicals, it should be simplify them, so we stopped and reviewed. We completed a Warm Up, and then reviewed the Exit Ticket. I love the all-or-nothing grading system here because if students didn't get it 100% correct, they don't know where they made the mistake, so they have to go back through their work with a fine-tooth comb to find their error. These select-all-that-apply questions have become my favorite way of questioning.
After we revised the exit tickets, I presented my favorite means of practice - a Tarsia Puzzle. Students had to be careful to "attend to precision" because several of the problems and answer choices were similar. This forced students to really focus on their exponents and see the difference between having x^3 inside a radical and x^4. It also meant that students didn't have to keep re-creating a factor tree for each problem. I heard great discussions about what happens when the radical has a coefficient in front of it too.
I made sure students had plenty of time to work on their exit tickets - another select all that apply question. The results were SO much better than the first day! If I could do a back-flip - I would. I saw several 100%s and so much more confidence from my students, which is exactly what I want as we approach testing season.
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I recently discovered Tarsia Puzzles and they are my new favorite go-to activity for practicing math problems. In this lesson, I used them to practicing power to a power, product rule, and quotient rule for exponents. The students had to correctly work out 30 problems to piece the puzzle together and they had way more fun practicing this way than a worksheet. I overheard some great discussions about the rules and misconceptions (which they can self-identify when they don't find the answer they are looking for).