Irrational Approximations on a Number Line

Using the numbers 1 to 9, each only once, label the following number line.

number line.JPG

Graph the roots of the first nine roots (e.g. √1, √2, … √9) on your number line.


What do you notice?  What do you wonder?


(I’m wondering how I can make a good OM problem out of this, should I keep the boundaries of 1 to 9 ?  Have students find a root that lies between each integer?)

Irrational Numbers on the Number Line- Cutting out what you don’t need

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.

Blank Number Line

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.