# 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.

 A whole is divided into two equal parts. ONE part is one half. 1 2
 A whole is divided into five equal parts. ONE part is one fifth. 1 5
 A whole is dividedinto ten equal parts. ONE part is one tenth. 1 10
 Four parts are colored, andthe whole has four equal parts. Four fourths. 4 4
 Three parts are colored. There are seven equal parts. Three sevenths. 3 7
 Two parts are colored, andthe whole has five equal parts. Two fifths. 2 5

 3 8

“three eighths”

The number ABOVE the line tells HOW MANY PARTS
we have (the colored parts).

The number BELOW the line tells how many EQUAL parts
the whole is divided into.

After halves, we use ordinal numbers to name the fractional parts
(thirds, fourths, fifths, sixths, sevenths, and so on).

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?
Count. You should get 8 parts.

Don't count the little lines. Count the “units” or the parts. One of them is like this:

How many of them are colored?

 You should get 3 colored parts out of 8 in total. So, the fraction is 3 8 .

3. Write the fractions, and read them aloud.

 a. b. c. d. e. f.

How to draw pie models

Halves: split the circle
with a straight line.

Thirds: draw lines at 12 o'clock,
4 o'clock, and 8 o'clock.

Fourths: First draw halves, then
split those like a cross pattern.

Fifths: Draw like a man
doing jumping jacks.

 Sixths: First draw thirds, then split those.

 Eighths: First draw fourths, then split those.

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

 a. 2 3
 b. 2 5
 c. 3 6
 d. 6 8
 e. 4 5
 f. 3 8
 g. 1 3
 h. 7 8

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

 a.   1 = 9 9

 b.   1 =

 c.   1 =
 d.   1 =

 e.   1 =

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

 a. 1 2
 b. 2 2
 c. 1 3
 d. 3 4
 e. 3 3
 f. 1 6
 g. 4 5
 h. 3 4

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.

 shaded area = 1 2 of the whole area

b. Divide the shape into three equal parts.

 shaded area = of the whole area

c. Divide the shape into six equal parts.

 shaded area = of the whole area

d. Divide the shape into four equal parts.

 shaded area = of the whole area

e. Divide the shape into three equal parts.

 shaded area = of the whole area

f. Divide the shape into five equal parts.

 shaded area = of the whole area

g. Divide the shape into four equal parts.

 shaded area = of the whole area

h. Divide the shape into four equal parts.

 shaded area = of the whole area

This lesson is taken from my book Math Mammoth Introduction to Fractions.

#### Math Mammoth Introduction to Fractions

A self-teaching worktext for 2nd-4th 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.