Estimation

Introduction

You enter my classroom as a second grade student and are asked, "What's the difference between 1, 10 and 100? How much bigger is 100 than 10? Is it a big difference?" You try to answer, but you're not quite sure. Then I ask, "OK, well let's look at the number 11. What digits are in the number 11 and what do they stand for?" Again, you don't understand. "What's a digit?" you think to yourself. This is how most of my students react when we start to learn about place value.

I teach second grade in an unusual school. We are located within a school district that serves mostly underprivileged minority students. However, we are located amongst a fairly white, upper-middle class neighborhood. We have come to operate like a "magnet" school in that we take students from all over the City of Richmond when we have open spaces. There are often open spaces because a majority of the students in the surrounding neighborhood attend local private schools. These spaces are usually filled by students from schools in the district that are seen as "failing" because they are not making adequate yearly progress. The implication of this for my classroom is that I have a large variety of students from different backgrounds, with sometimes vastly different support systems and early childhood experiences. While one student may have a very supportive parent who is able to provide a lot of extra help at home, another may have a parent who works two jobs and isn't able to be as involved. Some of my students are very well off, and others qualify for free lunch. Many of my students did not start at our school in Kindergarten, and may have just joined our school because a slot opened up.

Just as there is a huge range in the personal backgrounds of my students, they are also often at very different levels in their academic developments. I may have a student who has a very deep understanding of place value, has memorized the math facts to 20, can do two-digit addition, and is ready for multiplication and division when he or she walks into my room in September. On the other hand, a different student may not have any fluency with math facts to 10 and does not have any strategies for one digit addition and subtraction. However, year after year, I have noticed that the majority of my students would not be able to answer the questions presented above. It is the goal of this unit to create a scope and sequence that increases awareness of the meaning of decimal notation and enable my students to use this more accurate number sense to help them estimate lengths and quantities in the real world.