Estimation

Overview

This unit is intended to teach second grade students that there is a significant difference in the value of a digit when it is written in different places in decimal notation. Specifically, it seeks to show them that tens are a lot bigger than ones, and hundreds are a lot bigger than tens. It also seeks to further enforce the difference in the "places" using digits other than 1. For example, we'll explore the difference between 5, 50 and 500. These extensions will help solidify the idea that place value is a significant aspect of our numerical notation system. These concepts will be practiced in a small unit on measurement and estimation in the 3 ^rd quarter of the school year.

However, the path I would use to guide the students to this understanding of place value and order of magnitude starts at the beginning of the year and winds through lessons on digits, composing and decomposing numbers to 10, number bonds to 20, expanded form, multiples of 10 and order of magnitude. In order to be able to successfully engage in the estimation activities described in this unit, I will begin to teach them to have a new perspective of our number system starting at the beginning of the year. I believe very strongly that we need to strengthen our students' sense of number and help them gain fluency in breaking apart and combining numbers. They need to readily be able to see a multi-digit number in many different ways and break it into its place value components before we can ask them to compare large quantities and understand the usefulness of rounding larger numbers. A guide for following this path is included in this unit as an appendix.

Nevertheless, I understand that not all math curricula allow as much flexibility as the one I teach with. If you are not able to implement the full three quarters worth of lessons focusing on a structured path toward greater number sense, I believe that you could take the estimation and measurement activities and insert them into your unit however you see them connecting to your current curriculum. While students' skill in estimating is largely based on the strength of their foundation with the concept of ten and order of magnitude, this does not mean that there is a completely linear progression from number sense to estimation. "Mathematics instruction…should promote numeracy by making students more sensitive to order of magnitude, and to the estimation capabilities of place value notation." ¹ Experiences with measurements and quantities that differ by a power of ten will strengthen each student's understanding of place value, order of magnitude and relative size.