Egg Carton Fractions and Basic Operations
Basic operations with fractions aren't hard to understand if we keep the meanings of the basic operations in mind. Since addition is addition no matter what kind of numbers we use, we can use egg carton models to apply these meanings to the realm of fractions.
Suppose we fill 1/3 of one egg carton and 1/4 of another. How much of an egg carton would be filled if we combined them?
When we combine the amounts in the original carton, an new fraction model representing the sum is formed. We subdivide the new egg carton into equal groups that will allow us to name the new fraction. Here's another example using two different sized egg cartons:
1/3 + 1/2
As you can see, the size of the egg carton didn't make any difference, 1/3 + 1/2 = 5/6 no matter how big the unit is. The bigger carton contains more eggs, but the fraction is the same. This is important - a fraction number is a relationship, not a quantity. 5/6 just means that five out of six parts are under consideration - 'filled' in this case.
Here's one last example. Let's model 3/4 + 5/6...
You may have seen that the egg carton model can give us the answers to the problems without having to determine a common denominator. Through repeated use of the models, the idea of a common denominator emerges in a meaningful way, and becomes conceptual knowledge rather than a memorized procedure.
Here's a couple of problem to model. (Be sure to pay attention to the size of the cartons.) Good luck!