This problem has received a lot of attention on my blog the past couple of weeks…

Consider the roots of the first 9 Natural Numbers (√1 to √9), how many of them produce Irrational Numbers?

List them. Graph their approximate location on a number line.

Explain how you determined where to place them on the graph.

Is √10 Rational or Irrational? Explain how you know. Where on the number line would you graph it?

Although I do like this problem, I’m going to cut out what I don’t need. I think I am going to go with this:

**Consider the roots of the first 9 Natural Numbers (√1 to √9), what do you notice?**

**Graph them as accurately as you can.**

**Explain how you graphed them.**

**Consider √10 and compare it to your other roots. What do you notice? Where on the number line would you graph it?**

I want the conversation to come up about how √1, √4 and √9 become “numbers” (as I anticipate students to express), and the others are not as familiar. Hopefully we can get to classifications from this conversation. I took away the labeled number line because I also hope to get students thinking about where those numbers lie and how to label the above graph to most accurately display their position on that line. I anticipate a few misconceptions about labeling the interval. Hopefully by the time we get to √10, students will automatically be thinking of Irrational and Rational numbers and where it belongs. They can do all of that, I need to get out of their way.

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