# Line of Best Fit- Open Middle Problem

Directions: Using the digits 0 to 7, at most once each time, fill in the blanks to create a scatter plot with line of best fit y= 1/2x + 4.

(___ , ___) (___ , ___) (___ , ___) (___ , ___) # 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?

# Correlations- Open Middle Problem

Directions: Using the numbers 0-9, without repetition for each case, create a set of points that have the following characteristics:

Non-linear Positive Correlation

(__,__) (__,__) (__,__) (__,__) (__,__)

Non-linear Negative Correlation

(__,__) (__,__) (__,__) (__,__) (__,__)

No Correlation

(__,__) (__,__) (__,__) (__,__) (__,__)

(__,__) (__,__) (__,__) (__,__) (__,__)

# 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?

# Functions- Open Middle Problems

Using the Integers 0-9 (and only each Integer once), create a set of ordered pair that represents a Function.

f(x) = (    ,    ),(    ,    ),(    ,    ),(    ,    ),(    ,    )

Graph the Ordered Pairs Using the Rational Numbers 0-9 (and only each once), create a set of ordered pair that does not represents a Function.

(    ,    ),(    ,    ),(    ,    ),(    ,    )

Graph the Ordered Pairs 