100 Commonly Asked Questions in Math Class: Answers that Promote Mathematical Understanding, Grades 6–12
Publication Year: 2013
100 ways to get students hooked on math!
It happens to the best of us: that one question that's got you stumped. Or maybe you have the answer, but it's not all that compelling or convincing. Al Posamentier and his coauthors to the rescue with this handy reference containing fun answers to students' 100 most frequently asked math questions. Even if you already have the answers, Al's explanations are certain to keep kids hooked·and that's what it's all about.
The questions are all organized around the Common Core's math content standards and relate directly to Numbers and Quantity, Functions, Algebra, Geometry, and Statistics and Probability. The big benefits? You'll discover high-interest ways to:
Teach inquiry and process in mathematical thinking; Encourage flexibility in problem solving; Emphasize efficient test-taking ...
- Front Matter
- Subject Index
- Chapter One: General Questions
- Chapter Two: Arithmetic Questions
- Chapter Three: Algebra Questions
- Chapter Four: Geometry Questions
- Chapter Five: Probability Questions
- 90. What is the Fundamental Principle of Counting?
- 91. What does it Mean when the Probability of an Event is 1? Is 0?
- 92. What are Mutually Exclusive Events?
- 93. What is the Probability of Either or Both of Two Events Happening?
- 94. What is the Difference between Combinations and Permutations?
- 95. What is the Difference between Correlation and Causation?
- 96. What is the Pascal Triangle?
- 97. What is Binomial Probability?
- 98. What is the Birthday Problem?
- 99. How can Algebra help us to Understand a Probability Question?
- 100. What Kind of Averages are Batting Averages?
Copyright © 2013 by Corwin
All rights reserved. When forms and sample documents are included, their use is authorized only by educators, local school sites, and/or noncommercial or nonprofit entities that have purchased the book. Except for that usage, no part of this book may be reproduced or utilized in any form or by any means, electronic or mechanical, including photocopying, recording, or by any information storage and retrieval system, without permission in writing from the publisher.
All trade names and trademarks recited, referenced, or reflected herein are the property of their respective owners who retain all rights thereto.
Printed in the United States of America
Library of Congress Cataloging-in-Publication Data
Posamentier, Alfred S.
100 commonly asked questions in math class : answers that promote mathematical understanding, grades 6–12 / Alfred S. Posamentier, William Farber, Terri L. Germain-Williams, Elaine Paris, Bernd Thaller, Ingmar Lehmann.
Includes bibliographical references and index.
ISBN 978-1-4522-4308-5 (acid-free paper)
1. Mathematics—Study and teaching (Middle school)
2. Mathematics—Study and teaching (Secondary)
3. Mathematics—Problems, exercises, etc. I. Title. II. Title: One hundred commonly asked questions in math class.
III. Title: Hundred commonly asked questions in math class.
This book is printed on acid-free paper.
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About the Authors
It is well known that students will pose questions to teachers about a variety of topics. Oftentimes, these topics are related to what is being taught. Yet on occasion, students who hear about things mathematical from family, friends, or the media will not hesitate to ask their math teacher to explain something that may have been confusing to them. Most of the time, teachers can respond to these questions in proper fashion. However, there may be times when the question asked is not at ready reference for the teacher. We hope that this book will provide a resource for teachers who need a quick response to a variety of questions relating to school mathematics.
In general, mathematics education practitioners and researchers agree that teachers need to present mathematics as a motivating subject to their students—one that promotes and fosters thinking, and, at times, flexible and unrestricted inquiry. In fact, when explaining the Process Standard “Reasoning and Proof,” the National Council of Teachers of Mathematics states thus: “The ability to reason systematically and carefully [in mathematics] develops when students are encouraged to make conjectures, are given time to search for evidence to prove or disprove them, and are expected to explain and justify their ideas.” Clearly, this statement indicates a national imperative in mathematics education for teachers to emphasize the importance of process as well as mathematical thinking in their classes.
At the same time, students want—and need—to know the answers to their mathematics questions without the teacher telling them to think through the problem. In other words, although process in solving mathematical problems and conceptual understanding of mathematical topics are both important, students need to learn procedural methods that will help them solve problems efficiently and effectively.
In this book, the authors identify common mathematics content questions that students, almost exclusively at the secondary level, often ask in class. We then follow each question with clear and concise answers that are aligned with the Common Core State Standards. Although the question-answer dyads themselves will span the middle school and high school grade levels, some questions might be introduced in grade levels prior to [Page xiv]middle school. Accordingly, secondary-level students frequently ask questions that appear to be late elementary in terms of content. Because of their seemingly elementary-level nature, teachers often dismiss such questions. Given the emphasis on secondary-school student mathematics questions, our focus is to tailor seemingly elementary-level questions toward secondary mathematics courses.
This book will help to prepare the novice mathematics teacher or serve as enrichment for the more experienced mathematics teacher in anticipating common content-related mathematics questions that students of all ages and grade levels will undoubtedly ask during the school year. In addition, the authors strive to provide efficient answers that encourage flexibility in ways of solving various mathematics problems. The topic of this book is of increasing importance so that teachers of mathematics answer students’ questions effectively and anticipate what students will ask so that the presentation of answers is clear and concise. Of equal importance is the book's emphasis on answers to mathematical questions as they relate to efficient test-taking strategies in different assessments that students will need to take, especially at the secondary level.
Each chapter provides a detailed list of common mathematics questions along with their answers in the most comprehensive way possible. This book focuses on practical application in mathematics and highlights ways that teachers can engage and motivate students. At the same time, the practical nature of the book is supported by research in mathematics education and human development.