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?)


Approximating Irrational Numbers- Open Middle Problem

Directions: Using the integers 2 to 8, at most once each time, fill in the boxes to make the graphic true.


Approximating Irrational Numbers.jpg


Are there any places you know certain numbers have to be on the graphic? How do you know?

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.