Rationalizing Radical Monomial Denominator (got that?)

Here are my powerpoint slides on rationalizing a radical monomial denominator. Before telling students what I was getting at, I asked them to think about what you could multiply a radical by to get a non-radical (not the best math terminology there). I gave them a couple of examples that they figured out. They had trouble recognizing that the nth root of something to the nth power is just equal to that something. For example, the square root of x square is just x. I tried to give them problems that would make the pattern obvious, and they got it eventually, but it took much longer than I expected. Then when I moved on to the next slide where there's a fraction with a radical expression in the denominator and I asked them what I could multiply it by to get a rational number (what I referred to in class as "something without a radical or square root), they had no clue. I thought I helped them make the connection, but clearly not. It's still a concept they struggle with, especially when dealing with roots higher than two.

Whiteboard Art

This is what happens when you let students do work on individual whiteboards.

Introducing Roots

For my very first lesson in Algebra II, I created a powerpoint presentation. I don't usually like powerpoint, but I felt like it would organize my thoughts and help me focus on teaching the material rather than what I was supposed to be doing next. I started out with some basic conceptual questions about roots, and then moved to harder ones to get students to really think about roots higher than two. They did a good job answering the questions posed in the presentation but struggled with the last slide that asked them questions to summarize what they learned.

Adding and Subtracting Radicals

Here are my powerpoint slides on adding and subtracting radicals from the perspective of factoring.

It scared me how little students remember how to factor - even basic things - especially when the whole last chapter was on finding zeros which involves lots of factoring.