Learning Mathematics in Elementary and Middle Schools

by: Cathcart, W. George; Pothier, Yvonne; Vance, James; Bezuk, Nadine; Cathcart, W.

ISBN 13:
9780130322746
ISBN 10:
0130322741
Edition: 2nd
Format: Paperback
Copyright: 12/01/2000
Publisher: Prentice Hall
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Note: Not guaranteed to come with supplemental materials (access cards, study guides, lab manuals, CDs, etc.)

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Summary

Text is appropriate for courses in Mathematics for the Elementary School. Built on the foundation of the new 2000 NCTM Principles and Standards, this major new entry for K-8 math methods has impacted the market because of its point-of-use links to the standards and its emphasis on the importance of a child-centered approachcreating a learning environment that informs teachers how to support children as they build understandings of math concepts. Designed to be neither skimpy nor exhaustive, this text presents theory in an accessible manner and models a wealth of practical activities for teaching. Five videos from the Annenberg/CPB TEACHING MATH video series bring real classrooms to life for teachers and are integrated into the text as four/color, resourceful inserts.

Teaching Mathematics: Influences and Directions

(21)

Influences on Mathematics Education

(1)

Physchological Influences

(1)

Professional Influences

(6)

The Framework of the Principles and Standards for School Mathematics

(3)

Content Standards and Expectations in Each Grade Band

(1)

Integrating the Content and Process Standards

(2)

Integrating State and Local Standards with National Math Standards

(1)

Technological Influences

(3)

Calculators

(2)

Computers

(1)

Interactive Multimedia

(1)

Language Influences

(1)

Societal Influences

(1)

State Government

(1)

School Districts

(1)

Lobby Groups

(1)

Bandwagons

(1)

Research Influences

(1)

TIMSS

(1)

NAEP

(1)

Learner Influences

(1)

What Can Teachers Do?

(1)

Teacher Influences

(1)

Directions in Mathematics Education

(1)

Problem Solving

(1)

Communication

(1)

Reasoning and Proof

(1)

Connections

(2)

Integration with Other School Subjects

(1)

Integration with Real-World Settings

(1)

Representation of Mathematical Ideas

(1)

Equity

(1)

Technology

(1)

Computation and Estimation

(1)

Assessment

(1)

Parent Involvement

(1)

Conclusion

(1)

For Your Journal

(1)

For Your Portfolio

(1)

Resources for Teachers

(1)

Links to the Internet

(1)

Learning and Teaching Mathematics

(23)

Learning Styles

(1)

Learning Theories

(1)

The Behaviorist Approach

(1)

The Cognitive/Constructivist Approach

(5)

Cooperative Learning

(1)

Jean Piaget

(2)

Zoltan Dienes

(2)

Basic Principles Reviewed

(1)

Begin With Concrete Representation

(1)

Develop Understandings

(2)

Encourage Communication

(1)

Make Connections

(1)

Take Time to Motivate Children

(1)

Attitudes

(1)

Provide Opportunities for Practice

(2)

Games

(1)

Puzzles and Riddles

(1)

Surprises

(1)

Novel Algorithms

(1)

Novel Formats

(1)

The Calculator as Practice Tool

(1)

Personal Computers

(1)

Thinking About Teaching

(1)

Pre-Teaching Activities

(2)

Pre-Planning Considerations

(2)

Planning

(1)

Process of Teaching

(4)

Models for Teaching Mathematics

(3)

Post-Teaching Activities

(1)

Evaluation of Teaching

(1)

Reflection on Teaching

(1)

Thinking About the Curriculum

(1)

The Mathematics

(1)

The Activities

(1)

Conclusion

(1)

For Your Journal

(1)

For Your Portfolio

(1)

Resources for Teachers

(1)

Links to the Internet

(2)

Developing Mathematical Thinking and Problem-Solving Ability

(20)

Mathematical Considerations

(1)

What Is a Problem?

(1)

Types of Problems

(1)

Process Problems

(1)

Translation Problems

(1)

Application Problems

(1)

Puzzles

(1)

Ask Children to Write Problems

(1)

Posing Problems

(1)

The Problem-Solving Process

(1)

Understanding the Problem

(1)

Devising a Plan to Solve the Problem

(1)

Implementing a Solution Plan

(1)

Reflecting on the Problem

(1)

Problem-Solving Strategies

(2)

Dramatize or Model the Situation and Solution Process

(1)

Draw a Picture or Diagram

(1)

Construct a Table or Chart

(2)

Find a Pattern

(1)

Solve a Simpler Problem

(1)

Guess and Check

(1)

Working Backwards

(1)

Consider All Possibilities

(1)

Logical Reasoning

(1)

Change Your Point of View

(1)

Write an Open Sentence

(1)

Planning for Instruction

(1)

Selecting Appropriate Tasks and Materials

(1)

Problems That Are Motivating and Culturally Relevant

(1)

Problems with Missing, Extraneous, or Contradictory Information

(1)

Problems That Encourage the Use of Calculators, Computers, and Other Technology

(1)

Activities That Require the Use of a Variety of Problem-Solving Strategies

(1)

Activities That Promote Communication About Mathematical Thinking

(1)

Sources of Problems

(1)

The Teacher's Role

(1)

Before Children Begin to Solve the Problem

(1)

While Children Are Solving the Problem

(1)

After Children Solve the Problem

(1)

Organizing and Implementing Instruction

(1)

Classroom Climate

(1)

Grouping Children

(1)

Allocating Time

(1)

Assessing Children's Understanding

(1)

Changing the Difficulty of Problems

(1)

Problem Context

(1)

Problem Structure

(1)

Classroom Implications

(1)

Other Factors Contributing to Children's Difficulties in Problem Solving

(1)

Knowledge Factors

(1)

Beliefs and Affective Factors

(1)

Control

(1)

Sociocultural Factors

(1)

A Case to Consider the Children

(1)

Benefits of Using a Problem-Solving Approach to Mathematics Instruction

(1)

Conclusion

(1)

For Your Journal

(1)

For Your Portfolio

(1)

Resources for Teachers

(1)

Links to the Internet

(1)

Assessing Mathematics Understanding

(13)

The Assessment Standards

(1)

What Is Assessment?

(1)

Purposes of Assessment

(1)

Phases of Assessment

(1)

Assessment Choices

(1)

Achievement Tests

(1)

Standardized Tests

(1)

Teacher-Made Tests

(1)

Diagnostic Tests

(1)

Individualizing Assessment

(8)

Observation

(1)

Conferences and Interviews

(1)

Performance Assessment

(3)

Portfolio Assessment

(3)

Self-Assessment

(1)

Assessing Attitudes Toward Mathematics

(1)

Conclusion

(1)

For Your Journal

(1)

For Your Portfolio

(1)

Resources for Teachers

(1)

Links to the Internet

(1)

Developing Number Concepts

(22)

The Foundations of Number

(1)

Pre-Number Activities

(4)

Classification

(2)

Seriation

(1)

Patterns

(1)

One-to-One Correspondence

(1)

Conservation of Number

(1)

Number Meanings

(1)

Cardinal Use of Numbers

(1)

Ordinal Use of Numbers

(1)

Nominal Use of Numbers

(1)

Counting

(1)

Discrete and Continuous Quantities

(1)

Rote Counting

(1)

Rational Counting

(1)

Counting All, Counting On

(1)

Counting Back

(1)

Skip Counting

(1)

Representing Numbers

(1)

Concrete Models

(1)

Pictorial and Graphic Representation of Numbers

(1)

Symbolic Representation of Numbers

(3)

Numerals

(1)

Number Relationships

(1)

Order Relations

(1)

More Than, Fewer Than

(1)

One Greater Than, One Less Than

(1)

Part-Part-Whole Relationships

(4)

Relationship to Five and Ten

(1)

Using Action Language

(1)

Bidirectional Relationship of an Equation

(1)

Estimation

(1)

Conclusion

(1)

For Your Journal

(1)

For Your Portfolio

(1)

Resources for Teachers

(1)

Links to the Internet

(1)

Developing Understanding of Numeration

(28)

Numeration

100

(1)

Number Systems

100

(1)

Numeration Systems

100

(1)

Hindu-Arabic Numeration System

100

(1)

Base-Ten

100

(1)

Positional or Place Value

101

(1)

Multiplicative Principle

101

(1)

Additive Principle

102

(1)

Zero as a Placeholder

102

(1)

Understanding Place Value

102

(1)

Grouping

102

(2)

Communicating mathematics

104

(1)

Grouping by Tens

104

(1)

Equivalent Representations

104

(1)

Place Value

105

(1)

Developing Two-Digit Numbers

106

(1)

Introducing Base-Ten Blocks

107

(1)

Using Place-Value Mats

108

(1)

Introducing Nonproportional Materials

108

(3)

Using Hundreds Charts

111

(1)

Assessing Place-Value Knowledge

111

(1)

What Research Says About Place-Value Learning

112

(1)

Stages in Place-Value Development

112

(1)

Three-Digit Numbers

113

(1)

Number Meanings: Oral Expressions

114

(1)

Developing Number Relationships

114

(1)

Thinking and Writing About Numbers

115

(1)

Understanding Large Numbers

115

(1)

Number Names

115

(1)

Writing Consecutive Numbers

116

(1)

Number Periods

116

(1)

Magnitude of Numbers

117

(1)

Counting to a Thousand and Beyond

117

(1)

Expanded Notation

118

(1)

Rounding Numbers

118

(2)

Estimating

120

(1)

Consolidating Number Skills

121

(1)

Other Numeration Systems

122

(1)

Babylonian Numeration

123

(1)

Egyptian Numeration

123

(1)

Mayan Numeration

124

(1)

Roman Numeration

124

(1)

Conclusion

125

(1)

For Your Journal

125

(1)

For Your Portfolio

125

(1)

Resources for Teachers

125

(1)

Links to the Internet

126

(1)

Developing Whole-Number Operations: Meaning of Operations

127

(20)

Introduce Operations with Word Problems

128

(1)

A Model for Beginning With Word Problems

128

(1)

Encoding and Decoding Word Problems

129

(1)

Understanding Addition and Subtraction

130

(1)

Types of Addition and Subtraction Word Problems

130

(3)

Examples of Each Problem Type

130

(3)

Using Models to Solve Addition and Subtraction Problems

133

(4)

Direct Modeling

133

(3)

Using Measurement Models

136

(1)

Writing Number Sentences for Addition and Subtraction

137

(1)

Understanding Multiplication and Division

138

(1)

Types of Multiplication and Division Word Problems

138

(4)

Examples of Each Problem Type

138

(2)

A Note on Multiplication and Division Word Problems

140

(2)

Division With Remainders

142

(1)

Using Models to Solve Multiplication and Division Problems

142

(2)

Modeling Equal Groups and Multiplicative Comparison Problems

142

(1)

Modeling Area and Array Problems

143

(1)

Modeling Combination Problems

143

(1)

Other Models for Multiplication

144

(1)

An Instructional Sequence for Modeling Multiplication and Division

144

(1)

Another Word About Notation and Children's Language

144

(2)

Conclusion

146

(1)

For Your Journal

146

(1)

For Your Portfolio

146

(1)

Resources for Teachers

146

(1)

Links to the Internet

146

(1)

Developing Whole Number Operations: Mastering the Basic Facts

147

(16)

What Are Basic Facts?

148

(1)

A Three-Step Approach to Fact Mastery

148

(1)

Step 1: Understanding the Meaning of the Operations

149

(1)

Step 2: Using Thinking Strategies to Retrieve Facts

149

(1)

Step 3: Consolidating Activities for Drill and Practice

149

(1)

Addition and Subtraction Facts

149

(1)

Thinking Strategies for Addition and Subtraction

150

(2)

Counting On

150

(1)

Counting On in Subtraction

150

(1)

Counting Back

151

(1)

One More or One Less Than a Known Fact

151

(1)

Compensation

151

(1)

Using Thinking Strategies to Organize Instruction

152

(1)

Mathematical Properties of Addition and Subtraction

152

(1)

Commutative Property

152

(1)

Associative Property

153

(1)

Addition Property of Zero

153

(1)

Fact Families for Addition and Subtraction

153

(1)

Multiplication and Division Facts

154

(1)

Thinking Strategies for Multiplication and Division

154

(2)

Repeated Addition

154

(1)

Skip Counting

154

(1)

Splitting the Product Into Known Parts

154

(1)

Facts-of-Five

155

(1)

Pattern Strategy

155

(1)

Mathematical Properties of Multiplication

156

(3)

Commutative Property

156

(1)

Associative Property

157

(1)

Distributive Property of Multiplication Over Addition

157

(1)

The Multiplication Property of One

158

(1)

The Role of Zero in Multiplication

158

(1)

A Note on Division by Zero

158

(1)

Fact Families for Multiplication and Division

159

(1)

Consolidating Activities for Drill and Practice

159

(1)

Games

160

(1)

Puzzles and Riddles

161

(1)

Novel Formats

161

(1)

Computer Software

161

(1)

Conclusion

161

(1)

For Your Journal

162

(1)

For Your Portfolio

162

(1)

Resources for Teachers

162

(1)

Links to the Internet

162

(1)

Estimation and Computational Procedures for Whole Numbers

163

(48)

Computational Estimation and Mental Arithmetic

165

(1)

Mental Computation

165

(2)

Strategies for Mental Computation

165

(2)

Estimation

167

(3)

Strategies for Computational Estimation

167

(3)

Paper-and-Pencil Computation

170

(1)

An Instructional Philosophy

170

(1)

Prerequisites

171

(1)

Other Considerations

171

(4)

Extension Facts

172

(1)

Higher-Decade Addition

172

(1)

Column Addition

172

(1)

Types of Models

173

(1)

Language

173

(1)

Role of the Calculator

174

(1)

Error Patterns

174

(1)

Addition

175

(6)

Unstructured Concrete Manipulations

176

(1)

Recording

177

(1)

Symbolic Representation

177

(2)

Other Addition Algorithms

179

(1)

Common Error Patterns in Addition

180

(1)

Subtraction

181

(8)

Unstructured Concrete Manipulations

181

(2)

Recording

183

(1)

Symbolic Representation

183

(1)

Zeroes in the Minuend

184

(1)

Communication

185

(1)

Interpretations of Subtraction and the Algorithms

185

(1)

Other Subtraction Algorithms

186

(2)

Common Error Patterns in Subtraction

188

(1)

Multiplication

189

(7)

One-Digit Multiplier

189

(1)

Two-Digit Multiplier

190

(3)

Three- and More-Digit Multipliers

193

(1)

Zero in the Multiplier

193

(1)

Zero in the Multiplicand

193

(1)

Other Algorithms

193

(2)

Enrichment Extensions

195

(1)

Connections

195

(1)

Common Error Patterns in Multiplication

195

(1)

Division

196

(6)

One-Digit Divisors

197

(1)

Cases with Zero

197

(1)

Not Enough Hundreds to Share

198

(1)

Short Division

198

(1)

Making Sense of Remainders

199

(1)

Two-Digit Divisors

200

(1)

The Measurement Approach

201

(1)

Common Error Patterns in Division

201

(1)

Checking Calculations

202

(3)

Consolidating Skills

205

(1)

Puzzles

205

(1)

Games

205

(1)

Riddles

206

(1)

Computer Software

207

(1)

Other Algorithms

208

(1)

Problem Solving

209

(1)

Conclusion

209

(1)

For Your Journal

209

(1)

For Your Portfolio

209

(1)

Resources for Teachers

210

(1)

Links to the Internet

210

(1)

Developing Fraction Concepts

211

(25)

What Are Fractions?

212

(1)

What Do Children Know About Fractions?

212

(1)

What Should Children Understand About Fractions?

212

(1)

Developing Fraction Concepts and Number Sense

213

(1)

Number Sense With Fractions

213

(1)

Assessing Fraction Number Sense

213

(1)

Developing the Meaning of Half

213

(1)

Fraction Names

214

(2)

Fraction Symbolism

216

(1)

Different Units

216

(1)

Different Interpretations of Fractions

216

(10)

Part-Whole Interpretations

218

(2)

Part-of-a-Set Model

220

(6)

Other Interpretations of Fractions

226

(1)

Developing Comparison and Ordering of Fractions

226

(1)

Comparing and Ordering Fractions

226

(2)

Using a Calculator to Compare Fractions

228

(1)

Relative Size of Fractions

228

(1)

Improper Fractions and Mixed Numbers

228

(2)

Using the Math Explorer Calculator

230

(1)

Understanding Equivalent Fractions

230

(1)

Equivalent Fractions

230

(2)

Renaming and Simplifying Fractions

232

(2)

Renaming and Simplifying Fractions With a Calculator

232

(2)

Conclusion

234

(1)

For Your Journal

234

(1)

For Your Portfolio

234

(1)

Resources for Teachers

234

(1)

Links to the Internet

235

(1)

Developing Fraction Computation

236

(22)

Prerequisites for Fraction Computation

238

(1)

Introducing Computation

238

(1)

Developmental Activities

238

(1)

About Algorithms

238

(1)

Connecting Operations on Whole Numbers With Operations on Fractions

238

(1)

Properties

239

(1)

Addition and Subtraction of Fractions

239

(1)

Developing Addition Procedures

240

(4)

Addition Algorithms

242

(2)

Developing Subtraction Procedures

244

(2)

Early Subtraction Activities

244

(1)

Renaming Fractions

245

(1)

Symbolic Fraction Algorithm

246

(1)

Multiplication and Division of Fractions

246

(1)

General Considerations

246

(1)

Developing Fraction Multiplication

247

(5)

Multiplying a Fraction by a Whole Number

247

(1)

Multiplying a Whole Number by a Fraction

248

(1)

Multiplying a Fraction by a Fraction

249

(1)

Multiplying Mixed Numbers

250

(2)

Other Considerations

252

(1)

Developing Fraction Division

252

(3)

Whole Number Divided by a Fraction: Even Division

252

(1)

Whole Number Divided by a Fraction: Uneven Division

253

(1)

Fraction Divisor and Whole Number Dividend

253

(1)

Fraction Divisor and Dividend

253

(1)

Mixed Number Dividend

253

(1)

Developing a Symbolic Division Algorithm

253

(2)

Computing Fractions With a Calculator

255

(1)

Mental Arithmetic and Estimation

255

(1)

Assessing Fraction Knowledge

255

(1)

Conclusion

256

(1)

For Your Journal

256

(1)

For Your Portfolio

257

(1)

Resources for Teachers

257

(1)

Links to the Internet

257

(1)

Developing Decimal Concepts and Computation

258

(22)

Instructional Considerations

260

(1)

Connections to Familiar Concepts

260

(3)

Whole-Number Connection

260

(3)

Fraction Number Connection

263

(1)

Reading and Writing Decimals

263

(1)

Decimal Point

263

(1)

Decimal Names

263

(1)

Decimal Notation

264

(1)

Developing Decimal Number Sense

264

(1)

Base-Ten Blocks

264

(1)

A ``Tens'' Block as the Unit

264

(1)

A ``Hundreds'' Block as the Unit

265

(1)

A ``Thousands'' Block (Large Cube) as the Unit

265

(1)

Decimal Squares

265

(1)

Measurement Sticks

266

(1)

Graph Paper

266

(2)

Number Line

267

(1)

Money

268

(1)

Other Materials to Model Decimals

268

(1)

Equivalent Decimals

268

(1)

Ordering and Comparing Decimals

268

(1)

Computation

269

(1)

Addition and Subtraction

270

(2)

Multiplication

272

(3)

Division

275

(1)

Estimating With Decimals

276

(1)

Writing Fractions as Decimals

277

(1)

Using the Math Explorer Calculator

277

(1)

Terminating and Repeating Decimals

278

(1)

Writing Decimals as Fractions

278

(1)

Scientific Notation

278

(1)

Conclusion

279

(1)

For Your Journal

279

(1)

For Your Portfolio

279

(1)

Resources for Teachers

279

(1)

Links to the Internet

279

(1)

Understanding Ratio, Proportion, and Percent

280

(13)

Ratio and Rate

281

(1)

Language and Notation

281

(1)

Ratio and Rational Number

282

(1)

Proportion

282

(1)

Proportional Reasoning

282

(1)

Equal Ratios

283

(1)

Comparing Ratios

284

(1)

Cross Products

284

(1)

Scale Drawings

285

(1)

Comparison Shopping

286

(1)

Percent

286

(1)

Meaning and Notation

286

(1)

Number Sense

286

(1)

Fraction and Decimal Equivalents

287

(1)

Decimals as Percents

287

(1)

Fractions as Percents

288

(1)

Percents as Fractions

288

(1)

Finding the Percent of a Number

288

(2)

Finding the Percent

290

(1)

Other Procedures for Solving Percent Problems

290

(1)

The Proportion Method

290

(1)

The Equation Method

290

(1)

Unitary Analysis Method

291

(1)

Assessment and Instruction

291

(1)

Assessing Proportional Reasoning

291

(1)

Everyday Life Problem Settings

291

(1)

Conclusion

292

(1)

For Your Journal

292

(1)

For Your Portfolio

292

(1)

Resources for Teachers

292

(1)

Links to the Internet

292

(1)

Developing Geometric Thinking and Spatial Sense

293

(31)

Development of Geometric Thinking

295

(1)

The van Hiele Levels of Geometric Thought

295

(1)

Comments on the Levels of Thought

296

(1)

Other Instructional Notes

296

(1)

Developing the Language

296

(1)

Method of Instruction

297

(1)

Connecting With the World

297

(1)

Learning About Topology

297

(1)

Things That Change and Things That Do Not Change

297

(1)

Place and Order

298

(1)

Mazes and Networks

298

(1)

Distortion of Figures

298

(1)

Learning About Euclidean Geometry

298

(1)

Three-Dimensional Shapes

298

(4)

Polyhedra

299

(3)

Learning About Three-Dimensional Shapes

302

(1)

Comparing Polyhedra

302

(1)

Constructing 3-D Shapes

302

(2)

Learning About Two-Dimensional Figures

304

(1)

Polygons

304

(6)

Triangles

306

(1)

Quadrilaterals

306

(3)

Circles

309

(1)

Learning About Symmetry, Congruence, and Similarity

310

(1)

Symmetry

310

(2)

Congruence and Similarity

312

(1)

Learning About Transformational Geometry

313

(1)

Rigid Transformations

313

(1)

Learning About Tessellations

314

(1)

Developing Spatial Sense

315

(1)

Tangram Puzzles

316

(2)

Polyominoes

318

(1)

Describing Figures

318

(1)

Dissection Motion Operations

319

(1)

Learning About Coordinate Geometry

320

(1)

Learning About Curve Stitching

321

(1)

Conclusion

322

(1)

For Your Journal

322

(1)

For Your Portfolio

322

(1)

Resources for Teachers

323

(1)

Links to the Internet

323

(1)

Developing Measurement Concepts and Skills

324

(28)

Concepts and Instructional Sequence

326

(1)

What Is Measurement?

326

(1)

Instructional Sequence

326

(4)

Perception and Direct Comparison

326

(1)

Nonstandard Units

327

(1)

Standard Units

328

(1)

Instruments

329

(1)

Formulas

330

(1)

Problem Solving and Applications

330

(1)

Summary of Teaching Sequence

330

(1)

Teaching Strategies and Learning Activities

330

(1)

Length

330

(5)

Length: Perception and Direct Comparison

331

(1)

Length: Nonstandard Units

331

(1)

Length: Standard Units

332

(3)

Area

335

(4)

Perception and Direct Comparison

335

(1)

Nonstandard Units

335

(1)

Standard Units

336

(3)

Volume

339

(2)

Perception and Direct Comparison

339

(1)

Nonstandard Units

339

(1)

Standard Units

340

(1)

Capacity

341

(2)

Perception and Direct Comparison

341

(1)

Nonstandard Units

342

(1)

Standard Units

343

(1)

Mass

343

(2)

Perception and Direct Comparison

344

(1)

Nonstandard Units

344

(1)

Standard Units

344

(1)

Time

345

(2)

Perception and Direct Comparison

345

(1)

Nonstandard Units

345

(1)

Standard Units

346

(1)

Temperature

347

(1)

Perception and Direct Comparison

347

(1)

Standard Units

348

(1)

Angle

348

(3)

Perception and Direct Comparison

348

(1)

Nonstandard Units

349

(1)

Standard Units

349

(2)

Conclusion

351

(1)

For Your Journal

351

(1)

For Your Portfolio

351

(1)

Resources for Teachers

351

(1)

Links to the Internet

351

(1)

Collecting, Organizing, and Interpreting Data

352

(31)

Collecting and Organizing Data

354

(1)

Graphing Data

355

(1)

Early Experiences

356

(6)

Concrete Stage

356

(1)

Concrete-Pictorial Stage

357

(1)

Pictorial-Abstract Stage

358

(2)

Abstract Stage

360

(2)

Coordinate Graphing

362

(1)

Circle or Pie Graphs

363

(3)

Histograms, Line Plots, and Stem-and-Leaf Plots

366

(1)

Histograms and Line Plots

366

(1)

Stem-and-Leaf Plots

366

(1)

Computer-Generated Graphs

367

(1)

Interpreting Data: Statistics

368

(1)

Frequency

368

(1)

Central Tendency

368

(3)

Mode

369

(1)

Median

369

(1)

Mean

370

(1)

Variation

371

(2)

Box-and-Whisker Plots

371

(2)

Interpretation Data: Probability

373

(1)

Overview

373

(1)

General Teaching Considerations

374

(6)

Early Experiences

374

(1)

Upper Elementary

375

(3)

Middle Grades

378

(2)

Technology and Data

380

(1)

Conclusion

381

(1)

For Your Journal

381

(1)

For Your Portfolio

381

(1)

Resources for Teachers

381

(1)

Links to the Internet

382

(1)

Developing Integers and Algebraic Thinking

383

(19)

Integers

385

(1)

Introducing the Integers

385

(1)

Ordering the Integers

385

(1)

Addition

386

(1)

Electric Charges Model

386

(1)

Number Line Model

386

(1)

Subtraction

386

(2)

Number Pattern Approach

386

(1)

Number Line Model

386

(1)

Electric Charges Model

387

(1)

The Rule

387

(1)

Multiplication

388

(1)

Division

388

(1)

Assessment

388

(1)

Practice Settings

388

(1)

Variables

389

(1)

Meanings

389

(1)

Misconceptions

390

(1)

Expressions and Number Sentences

390

(1)

Evaluating Expressions

390

(1)

Order of Operations

391

(2)

Properties of Operations

393

(1)

Formulas

393

(1)

Algebraic Expressions

394

(1)

Solving Equations

394

(1)

Inequalities

395

(1)

Variables and Computer Programs

395

(1)

Functions

396

(1)

What Is a Function?

396

(1)

Patterns and Relationships

397

(1)

Function Machines and Tables

397

(1)

Sequences

397

(1)

Calculator Functions

398

(1)

Graphing

398

(1)

Instruction and Assessment Activities

398

(2)

Conclusion

400

(1)

For Your Journal

401

(1)

For Your Portfolio

401

(1)

Resources for Teachers

401

(1)

Links to the Internet

401

(1)

Appendix: Blackline Masters

402

(17)

References

419

(10)

Index

429

Learning Mathematics in Elementary and Middle Schools

9780130322746

0130322741

Summary

Table of Contents

Write a Review

Learning Mathematics in Elementary and Middle Schools

9780130322746

0130322741

Summary

Table of Contents

Write a Review

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