Locating Rational Numbers On the Number Line

Winebrenner, William Dunbar Vocational

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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