Fraction concepts can often be very confusing for students. We use several models for fractions and their relationships to help them understand just what fractions are and how to work with them. In this lesson, an egg-carton model is used.
The most basic concept is the naming of a fraction. For example, how could we show "1/2" in an egg carton? Here are some ideas:
All four of these models have similarities - they all show egg cartons divided into two equal-sized parts, with one of the parts filled in. Each carton also contains six 'eggs'. The numerator, 1, tells how many parts are filled in, and the denominator, 2, tells how many parts the egg carton is divided into. Here are some other egg carton fraction examples:
We aren't limited to filling in just one part of the egg carton. Here are some other examples that show the possibilities. In all, there are 32 fractions we can represent on the egg carton if we fill in whole parts.
Some egg carton fraction models contain the same number of 'eggs', but have different names. These are called equivalent fractions...
As you can see from the above fraction models, it's the way we divide up the egg carton that determines the fraction name. At the same time, the fraction name tells us how the carton is divided up - how many parts there are in all, and how many of those parts are filled in.
These two basic ideas are the foundation of fraction concepts:
In the next page of this lesson, we will look at a couple of fraction concepts that are not so obvious.