Introduction to Fractions on the Numberline 

Jones, Claudia R.             Crane High School
                              997-3750
                           

Objectives

Students often have trouble (for any number of reasons) reading 
fractional parts of an inch on a ruler.  They also have difficulty 
dealing meaningfully with the typical numberline because it does not 
readily lend itself to the students being able to recognize fractional 
parts or mixed numbers in correct ordering or sequencing.  Using color-
cued fraction strips in conjunction with color-cued numberlines and 
color-cued denominators, along with other manipulatives, the students 
will be able to use the numberline to: 
     1. Correctly order and sequence fractions;
     2. Compare, add, and subtract fractions;
     3. Change mixed numbers to improper fractions;
     4. Change improper fractions to mixed numbers;
     5. Find a fractional number between any two fractional numbers.
    
Apparatus Needed
                           
Color-cued fraction strips (whole, halves, fourths).  Numberlines, 
color-cued (four different sizes), with color-cued denominators. Above 
items drawn on white posterboard and laminated.  Magnetic tape, 
transparency sheets(4), rulers, overhead projector, projector pens, 
markers and worksheets. 

Recommended Strategy

     The teacher will discuss some of the difficulties students are having 
when working with fractions, such as:  their inability to write or name 
the points correctly on a typical numberline (here teacher shows the 
drawing of a typical numberline). The teacher will also display an example 
of positive and negative rational numbers being used on the numberline, 
using the overhead projector.  Students will be given color-cued 
fraction strips to develop basic fraction concepts and correct 
sequencing. Once they are familiar with the use of the fraction strips, 
they will work with those fraction strips on the numberline, which will 
also be color-cued for an easier transition. For this lesson we will 
use only four segments of fraction strips on the numberline (wholes, 
halves, and fourths).  Students will review the following terms:  
fraction, improper fractions, equivalent fractions, and mixed numbers.  
A worksheet will be given on the use of equivalent fractions to 
reinforce learning. 
     The students will practice again with the color-cued fraction 
strips to further develop basic fraction concepts and correct 
sequencing.  Also, they will use the color-cued fraction strips above 
the numberline which will provide immediate reference to the concrete 
and because of the visual cueing, they will be able to proceed 
comfortably with other work on the numberline. 
     With concrete examples and demonstrations by the teacher of how 
the numberline can be used to find an infinite number of fractional 
numbers, shown on the overhead projector, the students will be able to: 
     1.  Write a coordinate for each dot on a given numberline;
     2   Correctly order and sequence fractions on the numberline;
     3.  Express improper fractions as mixed numbers;
     4.  Change a mixed number to an improper fraction;
     5.  Find fractional numbers between any two fractional numbers 
         where 
                  a + b
                    2 
     Students will be given worksheets that parallel, step-by-step, 
what is being demonstrated by the teacher on the overhead projector and 
the blackboard. 
     Use of the color-cued fraction strips and color-cued numberline 
will help those students who are having problems find answers to some 
of their more difficult problems when using fractions on the number 
line.