As you probably know by now, I love inquiry-based lessons.
Here is one of my favorites --- I decided to try a different approach to teaching rational functions.
Instead of outlining the whole procedure for finding the domain, vertical asymptotes, horizontal asymptotes, etc., I twisted the lesson into an investigation.
The kids figure out for themselves what parts of the rational function cause certain features in the graph.
This process helps them understand the different types of asymptotes a lot better, and they remember what causes each one more easily.
Start with just a 5 minute introduction to what an asymptote means and what it looks like. Then, the kids jump into Investigation 1.
Then, the second investigation follows with horizontal and slant asymptotes.
I like to have the kids work in pairs.
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