Estimation

Strategies

Because zero is so important, we as teachers need to get the children to think about the zero all the time and reinforce that without the zero we could not count, tell time, measure, or use money. Much of the daily routine will incorporate the zero which needs to begin with the first day of school and continue throughout the school year. If a child learns it once they will forget but if we as teachers build that neural pathway with constant reinforcement and representation they will have a solid foundation.

This unit needs to be done beginning with day one of school. In order for the children to understand the power of zero the classroom must be constantly reinforced with the topic. A third grade child will need to become familiar with the fact that zero does not mean "nothing", that it has great value in everyday situations. Depending on the prior knowledge of the class the entire unit of lessons could last from a week to several weeks and then reinforcement throughout the year. It could be to your advantage as a teacher to do it every Friday as part of the classroom weekly procedure. The unit comprises seven separate lessons, with some of the lessons having several activities.

The unit will begin with an introduction to the zero in a unique manner so that the children will be intrigued and excited to learn. Some of the other lessons will include a reintroduction to the order of magnitude using money, an odometer to represent the order of magnitude, watching short video clips about the value of zero, creating zero poems, reading literature about estimating and zero, learning about place value with a game called "Flip it", creating order of magnitude with base ten blocks, using order of magnitude through leading digit estimating and front end addition. Having zero as the place holder will be discussed. One of zero's many useful functions is as a 'place-holder'. For example, in the number 600, the zero immediately to the right of 6 informs us that the 'tens' column is empty; the zero to the right of that tells us that the 'units' column is also empty. The only column that has any values in it is the 'hundreds' column. But if we did not somehow indicate that the two right-hand columns were empty we would write '600' as '6', which is not the number that we mean. We will finish the unit with a class-created book about Zero.

The math literature books are very important to the development of the unit and for many of the lessons they are the starting point. The first book in use is The History of Counting. This is a well-researched, intriguing account of how counting has evolved. Schmandt-Besserat recounts how the Paiela, who cultivate orchards in the highlands of Papua New Guinea, "count by pointing to parts of their body. . . . The number 1 is called 'left little finger,' 11 is 'left neck,' 16 is 'right ear,' etc. The Veddas of Sri Lanka count without numbers, collecting pebbles to indicate how many. She also painstakingly charts the long evolution of counting through abstract counting, the use of ten digits, and the advantages of Arabic numerals over the older systems. Her rigorous, scientific approach to the subject ensures that readers will never take the counting system for granted again. The full-color illustrations make history beautifully visual, while a glossary sets forth concrete definitions for readers to peruse. The next book is Zero. Is it Something? Is it Nothing? This book shows clearly that zero can be both "something" and "nothing," depending on its position in a number. Specific examples show some ways in which zero figures in arithmetic computations and its place in all kinds of measurements. Occasionally there are not enough examples of each operation for readers to reason out the rule behind the example. Directions are given for constructing a paper odometer. Historical and anecdotal facts add further to the book's interest. Cheerful watercolors of children of different ethnic groups and animal characters illustrate the text and make the material more appealing to young readers. The final book we will be discussing is Estimation. The reader of this book will learn to make better estimates. He/she may learn to be on time. He/she may learn to stay within his/her allowance. Estimation strategies will be discussed showing the children how easy it is to make a good estimate rather than guessing at the amount or size of an object.

The mathematical goal of this unit is an understanding of leading digit estimation. You might think, why pick that method? Well, that's simple. In my state the third graders are to take the state standardize assessment test (PSSA) for the very first time. In my research I found out that the third grader can not use the calculator at all. If I can give them a strategy to be able to eliminate several of the multiple choice answers I have served them well, and done my job. The few extra points that this gives a child could be the difference between an advanced student and proficient.