Solving Fraction Computations
The models and ideas from the last two lessons can be applied to modeling fraction computation solutions based upon the meanings of the four basic operations. A wide variety of problems and their solution strategies are explored in class, and students create their own level of abstraction in generalizing about fraction operations, which might include symbolic notation used to describe thinking.
One way we get discussion going in class is to begin with a rectangle with fractional dimensions, use segment strips and grids to determine its
The rectangle's dimensions are 3/5 linear unit by 2/3 linear unit.
Now we use the model to answer the questions posed at the beginning of this page. Can you see a way to think about the sum of the sides? The area - is it greater or less than one? What is it exactly? What is the difference between the length and width? How does the model help you see the answers to those questions?
(Here's one way to find the perimeter,
and to determine the area,
and the difference between the two dimensions.)
By exploring situations like these, strategies are developed that could be used to solve problems like the following. Quite often students begin to develop mental computation strategies as they work through modeling the situations and problems:
In the next two lessons' activities, students use linear and area measurement models to explore the relationships between decimal, metric, and fractional measurement, and to develop algorithms for operations in those systems. The basic models for all of that exploration are contained in this lesson, and in earlier lessons on fraction models.