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What is best way to teach conceptual understanding of simplifying radicals?
Hey, I feel like the process of simplifying a radical is often “out-of-nowhere” for students. Like all of sudden, we are factoring and circling and pulling out, but its still multiplying…anyway, I feel like the process is extremely abstract, and I have been looking to introduce and develop the concept perhaps in a visual way that helps students avoid rushing to a series of steps. Ultimately, I want them to see the multiplicative relationships within a radical, but I’m just not sure the best ways to tackle that. Any suggestions would be helpful, thanks!
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6 Replies
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You’re so right re: how random it can be. Let’s be honest – we often just show up one day and … BAM! We toss it up on the board.
Something that could be helpful is to start pre-radical in a visual manner. Simplifying with algebra tiles, etc and slowly work your way there.
For example, doing a couple easier problems involving simplifying without radicals … kids get some confidence and then you toss the “what about this one… what do you notice and wonder now?”
It’s like a challenge you’re tossing their way. Sometimes it can be all in how you lead up to it that can affect whether students are interested to poke a stick at it or not…
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Okay, so I like where that is headed, but what would that look like in terms of what they are simplifying?? For instance, if their is no radical over 32 why would they need to simplify it. I guess I’m not quite picturing the lead up. Could you perhaps give an me an example that you’re thinking of?
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So going off of what Kyle said, you would start with simplifying fractions, something they already know and are confident it. So like 24/40. Then you take a little step and build on that so maybe 2sqrt4/5sqrt4, then build on that so like sqrt40/sqrt20. Finally throw something like 2/sqrt20 at them.
What I have here needs development obviously, but the principle is to start with what they know how to do and are confident with and over a few problems get them working on what you want them to learn. So by the time they see the practice skill. They are feeling like simplification pros and are willing to at least take a stab at simplifying radicals.
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Thanks George, I appreciate you chiming in. I totally get what you’re going with and definitely use that in building this out.
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Would love to see what you come up with!
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So I tried to create a problem string approach that worked with simplifying. I started with fractions and moved to radicals trying to get them to see how since 6/6 is one, I can factor it out, in the same way √5×5 = 5 so I can “factor” it out. However, I didn’t make it explicit enough, and they really didn’t understand it very well at all, and something I decided to spiral back to in a few weeks.
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