Oxton House Publishers, LLC

Nimble Numeracy Preface & Contents

Preface

I have taught courses and given workshops on auto- maticity and fluency in reading since the mid-1970s. While talking with students, parents, teachers, and other professionals about developing automatic skills, the problem of automaticity and fluency in arithmetic has often come up. Many (if not most) students who have difficulty becoming fluent at the reading task also have great difficulty memorizing the basic arithmetic facts. Many of them also have trouble becoming fluent with our counting system. This often results in such learning problems as slow learning of arithmetic concepts, slow processing of arithmetic problems, and inaccurate computations even when the algorithms are known.

As we talked about these problems I would describe how I make speed drills for practice on basic arithmetic facts, and I would talk about how extremely important it is to have fluency with the language of our counting system. Teachers often reminded me that their lives are so busy that they don't have time to create these materials themselves, which aren't part of regular arithmetic programs and aren't available for general use. Parents were also clamoring for materials to use. In response to these requests for materials, I have written this book, and also a set of speed drills for arithmetic facts.

This book explains how to teach our counting system, how to work with the base-ten place-value system, how to teach adding and subtracting as related operations, and how to teach multiplying and dividing as related operations. A major emphasis is on developing fluent use of the language needed for working in these areas and for communicating with other people about these skills and concepts.

The activities presented in this book are easy to do with individuals, small groups, or whole classrooms of students. Suggested wording for the teacher is included, but it is not intended to be a script that must be followed. Some teachers use almost the exact wording suggested; others paraphrase extensively. Teachers have said that they like to have suggested wording because it is the clearest explanation of what is to be done and what is expected of the students. Only very basic materials are needed for the activities and, other than ordinary things to count, displays of the required materials are included in the book for photocopying by any teacher, parent, or tutor.

Phyllis E. Fischer

Preface

Chapter 1: First Thoughts

Chapter 2: Counting to 19

Learning the Numbers 11 through 19

11 and 12

13 through 19

Place Value for the -teen Numbers

Chapter 3: Counting from 20 to 29

Working with the Place Value Chart

Chapter 4: From 30 to 39

Working with the Place Value Chart

Chapter 5: From 40 to 99

Reading and Writing the Number Names

Adding the Ones to the Counting Chart and Counting Chant

Working with the Place Value Chart and Counting Sticks

Comparing the -teen Numbers with 31, 41,...81, and 91

Chapter 6: Adding and Subtracting with Regrouping

Explaining the Standard Notation

For Addition

For Subtraction

Chapter 7: From 100 to 109

One Hundred

101 to 109

Chapter 8: From 110 to 199

One Hundred Ten

111 through 199

Regrouping with Numbers to 199

Addition

Subtraction 63

Chapter 9: From 200 On

From 200 to 999

Thousands

Millions, Trillions, etc.

Chapter 10: Skip Counting

The Tens

The Fives

The Twos

Larger Numbers

The Threes and Fours

Using Skip Counting for Multiplying and Dividing

Multiplying by Nines

Step One: The Number of Tens in the Answer

Step Two: Adding the Digits to Get Nine

Putting the Two Steps Together

Chapter 11: Efficient Finger Addition

Chapter 12: Linking Addition and Subtraction

Creating the Addition Statements

Creating the Subtraction Statements

Creating the Missing Addend Statements

Chapter 13: Linking Multiplication and Division

Creating the Division Statements

Creating the Multiplication Statements

Chapter 14: Fractional Parts of Whole Numbers

Working on the Concept

Introducing the Triangles

Practicing the Standard Language for Fractions

Appendix: Extra Problems

Index

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