Modeling Dimensions and Area in Base 10
In a previous lesson, we learned about measuring dimension and area in base five units. In this lesson, we apply the same concepts to base ten measurement, which lead to models for the basic operations in base ten. We begin by filling in a rectangular region with base ten pieces, then looking at what multiplication and division equations might be represented by the model:
The measured area of the rectangle depends on the value of the various pieces. If the small square represents one unit, then we can regroup to find the area is 192 square units. If the mat is the unit, then the area of the rectangle is 1.92 units:
Drawing on our experience with base five area and dimension and multiplication and division models, we can see the following multiplication and division equations modeled by the above rectangle area and dimensions:
After some exploration with other rectangles and collections of base ten pieces, the students can build or sketch models of situations like these, and try to find out as much as they can about them:
By working with examples like these, students build concepts about linear and area measurement relationships, and intuitions about multiplying and dividing in base ten. We'll do some more work with these ideas in the next couple of lessons.