# Irrational Approximations on a Number Line

Using the numbers 1 to 9, each only once, label the following number line. 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. Are there any places you know certain numbers have to be on the graphic? How do you know?

# Irrational Numbers on the Number Line

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?