When students group the beans into tens and represent the groups on paper, they are beginning to put together notions of place value. Some students will have a deeper understanding and will begin to realize that counting by 10 is a more efficient way to represent their thinking. This is a nice example of differentiation and will require teachers to probe student thinking by asking such questions as, "Why did you group the blocks by tens?"

Grouping by tens makes counting larger quantities more manageable. Recording the groups and connecting the idea of, for example, 12 groups of 10 to the quantity 120 supports and reinforces the meaning of place value in the number system.

Students often think of estimating as making a "wild" guess. By using representations of a quantity as a basis of comparison, students begin to develop a strategy for making reasonable estimates. The more experience students have with this type of activity, the more adept they become with making estimates.

The representations themselves are a form of communication. Students communicate their thinking by writing, drawing pictures, and using models. When students explain their representations, they reinforce their understanding as they communicate with their classmates and teacher.