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Estimation is an immense topic that unfortunately gets forgotten because, in most classrooms, it is simply merged with rounding. It's not really our fault though; the little curriculum we have on this subject leads us to assume they are basically the same thing. As adults, we use estimation throughout the day without even realizing it. Just think, how many times today have you asked yourself questions like: What time do I need to leave to beat rush-hour traffic? How long will that gallon of milk last? Do I have enough gas in the car to get home? You didn't round anything! Estimation is so important and needs to be emphasized to our students throughout the year.
Because estimation is so broad, I've focused this unit on introductory topics such as the decimal place value system and relative order of magnitude. It uses quantitative aspects of baseball as the underlying inquiry and motivation for students. It will take approximately two weeks and is intended for 5th or 6th grade students. It starts by developing the basic conceptual idea of place values from the thousandths to the billions place. We want to teach more than whether one number is larger than another, we want to teach how much larger it is, or that certain numbers are close to one another. Students should understand the size of a number before operating with it, and they should understand the relative values of the places. They will then explore larger, base ten numbers by expanding each of the places as a digit multiplied by a power of ten. For example, 6345 = 6 X 1000 + 3 X 100 + 4 X 10 + 5 X 1. Students will eventually notice that the leftmost place value is larger than all the rest of the place values combined. Many students have a hard time conceptualizing, lets say, a hundred thousand dollars compared to a million dollars. By breaking down each place value of a given number, students will realize that each order of magnitude (the place just to the left) represents numbers 10 times as large as the given place! The ultimate goal is for students to fully understand the value of these very large numbers, such as the salary of a major league ballplayer. When students are familiar with this idea, they will calculate real-life estimation problems using baseball facts found on the Internet. Next students will explore relative sizes related to attending a typical professional baseball game and make reasonable estimates for each quantitative aspect, such as concession sales per game vs. per season. After estimates are made, they can be checked for accuracy by using the percent difference formula. An answer less than 10% indicates that a reasonable estimate was made. The unit will culminate with an Internet research-based project. This project can be used as an assessment as well. Students will research given topics for two chosen countries. They will apply their skills by making reasonable estimates and formulating an opinion from what their data shows. The goal is for students to decipher whether large numbers such as population density results in a greater human impact on the environment in one country versus the other.
(Developed for Math and Number Sense, grade 5; recommended for Math, Place Value, Estimation, and Number Sense, grades 5-6)