I've never really known what to do about teaching radicals in Algebra 1. Oklahoma's Algebra 1 standards currently have students simplify expressions involving radicals in Algebra 1. This is not the same as simplifying radicals - that happens in Algebra 2.
In the past, I've taken several approaches. I either skip radicals altogether and tell students to type them in on their calculators come test time. Or, I go all-out and teach simplifying radicals, adding/subtracting radicals, and multiplying/dividing radicals. This year, I decided to just teach rationalizing and reducing. It's better than just having kiddos type things in their calculators which teaches them nothing and just helps them pass the test. And, I'm not wasting time by teaching things that won't be tested. My Algebra 1 students are already far behind, so time is at a premium. Plus, this is a high-stakes class. They must pass the end-of-instruction exam to be eligible to graduate. We are slowly but surely making progress, though.
If you notice at the top of the page, this is skill 3 for the year. It directly follows order of operations/integer operations and fraction operations. I specifically taught it after fractions because I wanted to rely on the idea of equivalent fractions for teaching rationalizing the denominator instead of teaching kids to memorize the steps for how to rationalize.
In the past, I've been guilty of explaining rationalizing the denominator like this: "If we want to get rid of a square root in the denominator, multiply the numerator and denominator by the square root you are trying to get rid of." The radicals magically disappeared, but I never explained to them how they should know how to do that. Of course, that strategy fell apart when there was a cube root in the denominator...
This year, I decided to take a different approach. I told them that our goal was to get rid of the radical on the bottom. Then, I encouraged them to think of a radical that could be on the bottom that would simplify. Now, what can we multiply the denominator by to make it into that radical?
This worked sooooooooooo much better. If students had a radical five in the denominator, they recognized that if it was a radical twenty-five that the denominator would reduce to five. Thus, they should multiply the numerator and denominator by radical five.
Some students caught on to the shortcut that I used to teach my students. Other students get out their square root chart and think through the process of what to change the denominator to each time. Either way, students are thinking about what they are doing instead of blindly following steps, and that has me so excited. Why has it taken me so long to figure this out???
Download the file for this lesson here.