Number Sense and Nonsense: Games, Puzzles, and Problems for Building Creative Math Confidence
()
About this ebook
Read more from Claudia Zaslavsky
Math Games & Activities from Around the World Rating: 4 out of 5 stars4/5Number Sense and Nonsense: Building Math Creativity and Confidence Through Number Play Rating: 3 out of 5 stars3/5More Math Games & Activities from Around the World Rating: 0 out of 5 stars0 ratings
Related to Number Sense and Nonsense
Related ebooks
Big Ideas for Small Mathematicians: Kids Discovering the Beauty of Math with 22 Ready-to-Go Activities Rating: 5 out of 5 stars5/5Big Ideas for Growing Mathematicians: Exploring Elementary Math with 20 Ready-to-Go Activities Rating: 4 out of 5 stars4/5Mind-Blowing Math: Mysteries Revealed Rating: 0 out of 5 stars0 ratingsMultiplication & Fractions: Math You Can Play, #3 Rating: 0 out of 5 stars0 ratingsRethinking Math Learning: Teach Your Kids 1 Year of Mathematics in 3 Months Rating: 0 out of 5 stars0 ratingsUsing Stories to Teach Maths Ages 7 to 9 Rating: 5 out of 5 stars5/5Embracing Math: Cultivating a Mindset for Exploring and Learning Rating: 0 out of 5 stars0 ratingsTwo Trains Leave Paris: Number Problems for Word People Rating: 0 out of 5 stars0 ratings70+ Things to Do with a Hundred Chart: Playful Math Singles Rating: 5 out of 5 stars5/5Counting & Number Bonds: Math You Can Play, #1 Rating: 0 out of 5 stars0 ratingsLet's Play Math Rating: 3 out of 5 stars3/5Math Rescue Kit Rating: 0 out of 5 stars0 ratingsWord Problems Student Workbook: Playful Math Singles Rating: 0 out of 5 stars0 ratingsMaking Mathematics Meaningful - for Children Ages 4 to 7: Nurturing Growth Rating: 0 out of 5 stars0 ratingsWhere’s the Math?: Books, Games, and Routines to Spark Children's Thinking Rating: 0 out of 5 stars0 ratingsTeach Your Children Tables Rating: 0 out of 5 stars0 ratingsWord Problems from Literature: Playful Math Singles Rating: 0 out of 5 stars0 ratingsSeob-Ri Math: Everyday Math with Cooking Rating: 0 out of 5 stars0 ratingsIntroducing Little Kids to the Big Ideas of Mathematics: A Rad Makeover for Teaching Math Rating: 0 out of 5 stars0 ratingsSeriously Fun Maths: The complete guide to motivational mathematics Rating: 0 out of 5 stars0 ratingsLet's Play Math Sampler: Playful Math Singles Rating: 0 out of 5 stars0 ratingsMath for Life: Crucial Ideas You Didn't Learn in School Rating: 4 out of 5 stars4/5Beyond Math Anxiety: 99 Insights (and a Calculation's Not One!) Rating: 0 out of 5 stars0 ratingsBrain-Compatible Mathematics Rating: 0 out of 5 stars0 ratingsMaking Mathineers: Transformational Math Experiences That Build Conceptual Thinking for Both the Teacher and the Student Rating: 0 out of 5 stars0 ratingsHow To Get Your Kid To Like Math Rating: 0 out of 5 stars0 ratingsThe Fear of Maths: How to Overcome it: Sum Hope 3 Rating: 5 out of 5 stars5/5Creative Investigations in Early Math Rating: 0 out of 5 stars0 ratingsGuided Math AMPED: Five Steps to Your Best Math Block Rating: 4 out of 5 stars4/5
Children's Games & Activities For You
Incredibly Vulgar Coloring Book for Adults (Printable Version) Rating: 4 out of 5 stars4/5Karen's Riddles For Kids - Trick Questions And Fun Facts For The Young Ones Rating: 5 out of 5 stars5/5The BIG Book of Animal Crossing: New Horizons: Everything you need to know to create your island paradise! Rating: 5 out of 5 stars5/5Road Trip Activity Book for Kids 8-14: 87 Pages of Riddles, Trivia, Would You Rather Questions & Word Games for Hours of Fun Rating: 0 out of 5 stars0 ratingsThe Super, Epic, Mega Joke Book for Kids Rating: 3 out of 5 stars3/5Codes, Ciphers and Secret Writing Rating: 4 out of 5 stars4/5The Everything Kids' First Spanish Puzzle & Activity Book: Make Practicing Espanol Fun And Facil! Rating: 5 out of 5 stars5/5Fortnite For Dummies Rating: 0 out of 5 stars0 ratingsTruth or Poop? Amazing Animal Facts Rating: 3 out of 5 stars3/5Hilarious Jokes for Minecrafters: Mobs, Creepers, Skeletons, and More Rating: 1 out of 5 stars1/5Lots of Jokes for Kids Rating: 4 out of 5 stars4/5Lots of Knock-Knock Jokes for Kids Rating: 5 out of 5 stars5/5Pokemon Go: Guide + 20 Tips and Tricks You Must Read Hints, Tricks, Tips, Secrets, Android, iOS Rating: 5 out of 5 stars5/5Build It! Christmas: Make Supercool Models with Your Favorite LEGO® Parts Rating: 0 out of 5 stars0 ratingsMemory Superpowers!: An Adventurous Guide to Remembering What You Don't Want to Forget Rating: 4 out of 5 stars4/5300 Toughest Riddles and Brain Teasers for Kids Rating: 5 out of 5 stars5/5The World of Pokémon Rating: 4 out of 5 stars4/5An Unofficial Joke Book for Fortniters: Sidesplitting Jokes and Shenanigans from Salty Springs Rating: 1 out of 5 stars1/5History for Kids | Modern & Ancient History Quiz Book for Kids | Children's Questions & Answer Game Books Rating: 5 out of 5 stars5/5Would You Rather For Kids: Would You Rather Rating: 0 out of 5 stars0 ratingsThe Miner’s Traps: 50+ Unofficial Minecraft Traps Exposed! Rating: 5 out of 5 stars5/5The Everything Kids' Giant Book of Jokes, Riddles, and Brain Teasers Rating: 3 out of 5 stars3/5Video Games: Design and Code Your Own Adventure Rating: 0 out of 5 stars0 ratingsMind-Boggling Word Puzzles Rating: 5 out of 5 stars5/5
Reviews for Number Sense and Nonsense
0 ratings0 reviews
Book preview
Number Sense and Nonsense - Claudia Zaslavsky
1992).
Introduction
A Note to the Reader
This book is about numbers, all kinds of numbers. Numbers have different personalities, just like people. Numbers have relationships, just as people do. A person might be a daughter or son, a sister or brother, a cousin, or a friend. Numbers are also related to other numbers in various ways.
Some ways of connecting numbers make good number sense. Others may make no sense at all; they are just nonsense. In this book you will meet young people who are trying to tell the difference between number sense and nonsense. Often they need some common sense to help them decide. I think you will enjoy their discussions and debates. You may want to have such discussions with your classmates, friends, and even grown-ups. These discussions will help you to build up your own number sense. You will develop a good head for numbers, the ability to see patterns in groups of numbers, and an appreciation of how useful numbers are and how much fun you can have with numbers.
Most of the topics in each chapter include ideas for activities that you can carry out either alone or with other people. There are also many questions for you to think about, questions that sometimes have no definite answers. Many of the activities are easy for you to check; you will decide whether they are correct. (See page 101 for the answers to some of the activities, although you probably won’t need to refer to the answer pages very often. It’s much more satisfying to work out the solutions yourself, even if it takes time.)
Some activities are harder than others and may be too difficult for you to complete at present. Try them anyhow. Discuss them with your friends or a grown-up. Your number sense will grow as you work on them, even if you don’t get the final answer correct. And you will feel so proud when you do work out a hard problem. But if you can’t finish some of the activities now, come back to them next year, or the year after next.
You probably already know about odd and even numbers. But did you know that an odd number might be even, and an even number might be odd? Chapter 1 is all about odds and evens.
Chapter 2 introduces other relationships among numbers. You will have a chance to work on an idea, called a conjecture, about even numbers that no one has been able to prove either true or false, although mathematicians have worked on it for over 200 years.
In chapter 3 you will learn why zero is a very special number. For example, we cannot divide a nonzero number by zero. When I try to divide six by zero on my calculator, the display shows the word error. Zero is special in other ways too.
Chapter 4 deals with money, decimal points, and measures. You will learn how the United States lost hundreds of millions of dollars because of a mix-up in units of measurement.
Riddles and puzzles are the subject of chapter 5, although you will also find some riddles and puzzles in other chapters. You will learn clever tricks with numbers that will make people think you are a genius!
How did numbers begin? How have people used numbers in the past? That’s what chapter 6 is all about. You will read about finger-counting, number words in several languages, signs for numbers, and ways of calculating that have been used in different parts of the world over thousands of years.
You may wonder, what about the calculator? Why bother learning about numbers when the calculator can do all the work? Not true! The calculator has no number sense. It takes a human being to tell the calculator what to do. The same is true of a computer. But the calculator can be very useful, as you will find out in chapter 7. You will learn about negative numbers, repeating and terminating decimal fractions, and a lot more.
Chapter 8 is about big numbers. Would you like your allowance to take the form of one cent on the first day of the month, two cents on the second day, four cents on the third day, eight cents on the fourth day, and double the amount every day until the end of the month? Guess how much money you would receive.
Happy reading, thinking, and talking about math!
A Note to Parents and Teachers
This book introduces groups of children having a wonderful time discussing, reflecting on, and arguing about mathematical ideas. These children discover that some ideas make good number sense, while other ideas do not; they are just plain nonsense.
Math is for everyone! Research has shown that every child can learn math. When experienced through challenging activities, math can be a source of great joy and satisfaction to children and to adults. No longer can parents excuse their children by saying, I was poor in math, so I am not surprised that Jennifer has trouble learning the subject.
No longer can teachers justify their students’ failure with the excuse, Those kids can’t learn.
We now know a great deal about how children learn. The British neuropsychologist Brian Butterworth believes that the brain has specialized circuits that he calls the number module.
In his fascinating and comprehensive book What Counts: How Every Brain Is Hardwired for Math (New York: Free Press, 1999) he writes, There is nothing intrinsically dull or hateful about mathematics. It will be, and can be, fun, as long as children understand what they are doing and feel pride of ownership in mathematical ideas.
He advises teachers to use group discussions, encourage different solution strategies, acknowledge pupils’ own intuitions and knowledge to stimulate inventiveness.
Of course, this advice is equally relevant for parents.
According to the Principles and Standards for School Mathematics, published in 2000 by the National Council of Teachers of Mathematics (NCTM), Students learn more and better when they can take control of their learning…. When challenged with appropriately chosen tasks, students become confident in their ability to tackle difficult problems, eager to figure things out on their own, flexible in exploring mathematical ideas and trying alternative solution paths, and willing to persevere.
In other words, children must learn mathematics with understanding.
Unfortunately, much school instruction in mathematics has been based on rote memorization of facts and procedures, rather than on understanding. Memorized procedures are easily forgotten or confused, but the ability to reconstruct methods and arrive at solutions on the basis of a mastery of the underlying concepts remains with a person over the years.
As I write these words, educators and the public are caught in a dilemma. On one side are parents who feel that their children are being shortchanged because many of the current math programs do not call for extensive drills on multiplication tables and addition facts—the so-called basics. On the other side are those who object to the kind of rote learning advanced by the older math programs, still used in many schools, and by teachers who teach as they have been taught, using drill and kill
methods. With the increasing emphasis on standardized test scores, teachers are pressured to spend a great deal of time drilling for tests, in spite of the fact that research shows that when children learn the basics in the course of doing challenging math work, they are far better prepared to cope with new ideas than if they had learned by rote memorization methods.
This book focuses on numbers, their characteristics and relationships, applications of numbers in society, and the history of number systems. As recommended by current experts, readers also make connections to geometry and other branches of mathematics, develop skills in estimation and problem solving, generalize about patterns of numbers, and are encouraged to engage in discussions with peers and adults. This book provides a model for creativity and independence in the learning of mathematics and for the development of a positive attitude toward the subject.
The book is addressed to children in grades three