Upper Primary Mathematics Fractions - Commonwealth of Learning

Same number of different sized parts:
3
8
3
and
5
have the same number of
parts, but they are different sizes. The greater the denominator, the smaller
3
the parts. Since
8
has a greater denominator,
3
5
3
>
8
.
More and less than an easy fraction:
1
2 1
2
. Therefore,
3
>
4
.
1
4
1
is less than
2
2
but
3
is greater than
Closer to an easy fraction:
from one.
3
4
4
is one-quarter from one and
5
is one-fifth
1
But
4
1
4
>
5
, therefore
5
3
is closer to one than
4
. Therefore,
4
5
3
>
4
.
Practice Activity 4
Have a “why we know it is more” discussion. Arrange the class in
cooperative groups or pairs of students. Provide them with one or more
models for fractions. Give the class a pair of fractions to compare. The task is
to find as many good explanations for their choice as possible within an
allotted time. Explanations can be written down and then discussed as a full
class.
Reflection
A group of children are invited to share several chocolate bars. Biggie is
offered the choice of one-third or one-half of a chocolate bar. Since he wants
more chocolate, he chooses a half. He is disappointed, though, when he sees
that Irene, who chose one-third, has bigger piece of chocolate.
What assumption did Biggie make when he made his choice?
Biggie assumed that the chocolate bars were all the same size. However, a
piece representing one-third can be bigger than one-half if it is part of a
larger whole, as shown in Figure 1.7.
1
2
Fig. 1.7: “Chocolate Fallacy”
Module 2: Unit 1 8
Common Fractions
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3