Understanding Fractions
This is a lesson for 3rd grade math about the concept of a fraction. Students color parts to illustrate fractions, write fractions from visual models and from number lines, and learn to draw pie models for some common fractions. Lastly they divide shapes into equal parts themselves and show the given fraction.
Fractions are formed when we have a WHOLE that is divided into so many EQUAL parts. 









“three eighths”

The number ABOVE the line tells HOW MANY PARTS The number BELOW the line tells how
many EQUAL parts
After halves, we use
ordinal numbers to name the fractional parts 
1. Color the parts to illustrate the fraction.
a.  b.  c.  d.  e.  f. 
7 8 
6
10 
4 6 
4 5 
2 4 
4 7 
g.  h.  i.  j.  k.  l. 
2 6 
11
12 
5 9 
1 5 
9
10 
2 7 
2. Write the fractions, and read them aloud.
a.  b.  c.  d. 
e.  f.  g.  h. 
i.  j.  k.  l. 
How
many parts is this “whole” divided into? Don't count the little lines. Count the “units” or the parts. One of them is like this: How many of them are colored?

3. Write the fractions, and read them aloud.
a. 
b. 
c. 
d. 
e. 
f. 
How to draw pie models  
Halves: split the circle 
Thirds: draw lines at
12
o'clock,

Fourths: First draw
halves,
then


Fifths: Draw
like a man 


4. Draw the pie models and color the parts to illustrate the fractions.









5. Color in the whole shape = 1 whole. Then write 1 whole as a fraction.





6. Divide the shapes into equal parts, and color some of the parts, to show the fractions.









7.
Divide the shapes into equal parts. Shade ONE part. Write the area of that part
as a fraction
of the whole area.
a. Divide the shape into two equal parts.

b. Divide the shape into three equal parts.


c. Divide the shape into six equal parts.

d. Divide the shape into four equal parts.


e. Divide the shape into three equal parts.

f. Divide the shape into five equal parts.


g. Divide the shape into four equal parts.

h. Divide the shape into four equal parts.

This lesson is taken from Maria Miller's book Math Mammoth Introduction to Fractions, and posted at www.HomeschoolMath.net with permission from the author. Copyright © Maria Miller.
Math Mammoth Introduction to Fractions
A selfteaching worktext for 2nd4th grade that covers fractions and mixed numbers, adding and subtracting like fractions, adding and subtracting mixed numbers, equivalent fractions, comparing fractions, and finding a fractional part using division.
Download ($5.30). Also available as a printed copy.