```Locating Rational Numbers On the Number LineWinebrenner, William                     Dunbar Vocational                                         567-5400                           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.```
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