Upper Primary Mathematics Fractions - Commonwealth of Learning

Meaning of Common Fractions
To help pupils grasp the concept of common fractions, you should expose
pupils to more than one definition. A common fraction may be looked at as a
part of a whole, as an expression of division, or as a ratio.
Fraction as a part of whole: a unit in the form of a continuous shape or as a
discrete set is partitioned into equal sized parts.
Fraction as an expression of division: if a woman walks 2 km per hour,
5
how many hours will it take to walk 5 km? She takes 5 ÷ 2 or hours.
2
a
A fraction is another way of writing a ÷ b.
b
Fraction as an expression of ratios: ratios are expressions of a relationship
between two quantities. If two out of five pupils are boys, then the ratio of
2
boys to girls can be expressed as 2 to 5 or 2:5 or
5
. The fraction notation of
ratios is found in proportion.
Fraction Models
Besides the numerical interpretation of common fractions, you should use a
variety of models such as area, length, and set models. As you go through
this unit, think of other model presentations.
Area Models
Area models can be used to demonstrate visually that a fraction is part of a
whole. Figure 1.1 illustrates a variety of area models.
Circular "pie" pieces Rectangular regions
Geoboards Drawings on grids or dot paper
Pattern blocks Paper folding
Figure 1.1: Area or region models for fractions
Module 2: Unit 1 4
Common Fractions