Locating Rational Numbers On the Number Line

Winebrenner, William                     Dunbar Vocational
4722 N. Winthrop Av.                     567-5400
Chicago, Il. 60640


Objective:
1:  The learner will use the name RATIONAL NUMBER when referring to 
    locations on the number line. 
2:  The learner will write rational numbers as the ratio of two integers.
3:  The learner will convert each rational number to a mixed number.
4:  The learner will divide any given length into n equal parts.

Apparatus Needed: 
Number line, straight edge, compass, pencil, paper.

Recommended Strategy: 
Once the student is comfortable with the concept that integers, 
positive and negative, can be located on the number line, proceed to 
identifying all rational numbers as a ratio of two integers.  If the 
rational number is an improper fraction, convert it into a mixed 
number.  It will then become obvious between which two integers is 
this rational number.  For fractional parts of the next integer, such 
as divisions of 5ths or 7ths, for example, the problem is how to 
divide the line segment into n equal parts.  This lesson is about how 
to locate the rational number on the number line which is a fractional 
part of the next integer. 

1. Teach the student that to divide any given length into n equal 
   parts write the fractional part in the form a/b where a and b are 
   positive integers (a rational number). 

2. Change improper fractions to mixed numbers so that a/b = k+(m/n) 
   where k is a positive number and the fraction m/n is converted to 
   lowest terms. 

3. Divide the line segment between k and the k+1 position into n equal 
   parts, which can always be done by straight edge and compass 
   construction, by marking off n equal parts on a y-axis and marking 
   off the length of the line segment on the x-axis.  The two axis do 
   not even have to be at right angles to each other.  Connect the 
   last nth position with a straight line to the end of the line 
   segment on the x-axis and proceed to construct n similar 
   triangles.  You will see that the line segment is now divided into 
   n equal parts. 

4 .Physically place this divided line segment on k and k+1 of the 
   number line and count off m divisions.  This is the location of the 
   a/b rational number. 

5. For negative rational numbers teach the same strategy and instruct 
   the student that this rational number is on the left side of the 
   zero number.