Introduction
Numbers are all around us every day. They are a crucial part of our everyday life. Mathematics is now so critical to understanding modern society that some have labeled it the “new civil right.”(1) We use numbers without really thinking about them. This unit will focus on developing deeper number sense, interpreting place value and order of magnitude, and how all of these support making reasonable estimations.
Here are some questions I thought about as I prepared my unit. Can students really understand the differences between really big numbers, and between really small numbers? How deep is the knowledge required of our students in determining relative size of numbers based upon the position of the digits? Do students grasp the concept that our place value system is based upon the number 10? Do they know what a thousand, ten thousand, hundred thousand, or even a million items would really look like? As John Allen Paulos said in his book Innumeracy, “Knowing that it takes only about eleven and a half days for a million seconds to tick away, whereas almost thirty-two years are required for a billion seconds to pass gives one a better grasp of the relative magnitude of these two common numbers.”(2)
This unit will focus on clarification of place value and order of magnitude, and likewise improving student’s estimation skills. By reviewing what estimation is and how we can create a reasonable guess, my hope is that students become more comfortable working with and manipulating larger numbers such as ten thousand, hundred thousand and continuing into the billions. In keeping with our theme I will use three key texts: Great Estimations and Greater Estimations by Bruce Goldstone and Millions, Billions, and Trillions, Understanding Big Numbers by David Adler. I will also be using a video to introduce and help to visualize the idea of order of magnitude, called The Powers of 10.
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