Teaching of Rational
Numbers
Fractions, Decimals and Percents
Why are Fractions
Difficult to Learn?
Fractions
&
YOU
Why are Fractions
Difficult to Learn?
“Fractions are difficult to
teach and learn, but they
should not be viewed as
a lost cause”
Why are Fractions
Difficult to Learn?
Learning the various
fraction operations can
be difficult for many
children. It is not the
concept of fractions that
is difficult . . .
Why are Fractions
Difficult to Learn?
. . . It is the various
operations that are done
with fractions!
Why are Fractions
Difficult to Learn?
There are no less than 10
different procedures.
Why are Fractions
Difficult to Learn?
 Add/Subtract Same Denominators
 Add/Subtract Unlike Denominators
 Writing Equivalent Fractions
 Mixed Numbers to a Fractions
 Simplifying Fractions
Why are Fractions
Difficult to Learn?
 Improper Fraction to a Mixed
Number
 Multiplication of Fractions
 Division of Fractions
 Converting Fractions to Decimals
 Converting Decimals to Fractions
Making Sense of Fractions
If children just memorize
these procedures
without understanding
how they were derived,
they will seem like a
meaningless jumble of
rules.
Making Sense of Fractions
Rules/Procedures
Vs
Visualization
Making Sense of Fractions
Before learning how to
subtract or add fractions with
unlike denominators,
students MUST understand
equivalent fractions.
Visualization Example#1
Equivalent Fractions
These two circles are EQUIVALENT
because the pictures show the same
amount.
Visualization Example#1
Equivalent Fractions
In the second circle
each slice has been cut
into two.
Before 1 slice
After 2 slices
Visualization Example#1
Equivalent Fractions
These two circles are EQUIVALENT
because the pictures show the same
amount.
Visualization Example#1
Equivalent Fractions
Each slice has been
cut into two.
Before 3 colored slices
After 6 colored slices
Visualization Example#1
Equivalent Fractions
These two circle are EQUIVALENT
because the pictures show the same
amount.
Visualization Example#1
Equivalent Fractions
Write two equivalent
fractions for the
green sections in
these circles.
Visualization Example#1
Equivalent Fractions
Write two equivalent
fractions for the
green sections in
these circles.
Visualization Example#1
Equivalent Fractions
Write two equivalent
fractions for the green
sections in these circles.
What is the multiplier?
Equivalent Fractions
Practice #1
Write the name of each fraction beside it.
Connect the fractions that show the same
amount.
Equivalent Fractions
Practice #2
Equivalent Fractions
Practice #3
Equivalent Fractions
Practice #4
Fractions Are Difficult to Learn:
Are Decimals Truly Easier?
Many adults and children
do not have a true
understanding of
decimals and percents?
Fractions Are Difficult to Learn:
Are Decimals Truly Easier?
"We are now slightly less than
one-fifth of the world's
population, but we have slightly
more than 20% of the world's
wealth and income. This is not
a matter requiring Einstein to
calculate.”
Bill Clinton,
1997
Fractions Are Difficult to Learn:
Are Decimals Truly Easier?
The most basic idea
about decimals is that,
like fractions, enable us
to describe parts of a
unit quantity.
Fractions Are Difficult to Learn:
Are Decimals Truly Easier?
They do this not by creating
new "sub-units" but by
creating new numbers.
Decimals and fractions are
two solutions to one problem.
Fractions Are Difficult to Learn:
Are Decimals Truly Easier?
Most students ( and even
adults) do not make the
decimal-fraction link
correctly.
Fractions Are Difficult to Learn:
Are Decimals Truly Easier?
The fundamental
understanding of fractions,
such as dealing with
equivalent fractions, is
critical to decimals as well.
Fractions Are Difficult to Learn:
Are Decimals Truly Easier?
The most basic knowledge
about decimals is to
understand that both
decimals and fractions are
designed for the same
purpose.
Fractions Are Difficult to Learn:
Are Decimals Truly Easier?
Kids basically see the
decimal point as a
character separating two
whole numbers.
4.7
Fractions Are Difficult to Learn:
Are Decimals Truly Easier?
Those who have not
completely made the
decimal-fraction link think
two different types of
whole numbers make up a
decimal.
Fractions Are Difficult to Learn:
Are Decimals Truly Easier?
What does the fraction
tell you?
What does this fraction,
written as a decimal (0.4)
tell you?
Examples of Incorrect
Decimal-Fraction Associations
Fractions with a numerator of
1
4.6 is the same as
8.4 is the same as
Fractions Are Difficult to Learn:
Are Decimals Truly Easier?
denominator
indicates
the
To understand
a fraction,
number
of partsand
in the
the numerator
the
whole
object must be
denominator
considered
numerator indicates the
simultaneously.
number of parts being used
Decimal Number
Misconception #1
Longer
is
Larger
Decimal Number
Misconception #2
Whole Number
Thinking
Decimal Number
Misconception #3
Zero
Makes
Small
Decimal Number
Misconception #4
Reverse Thinking
Decimal Number
Misconception #4
Shorter
is
Larger
Decimal Number
Misconception #5
Denominator
Focused