Learning Mathematics in Elementary and Middle Schools,9780130322746

Learning Mathematics in Elementary and Middle Schools

by ; ; ; ;
Edition: 2nd
ISBN13: 9780130322746
ISBN10: 0130322741
Format: Paperback
Pub. Date: 2000-12-01
Publisher(s): Prentice Hall
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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.

Table of Contents

Teaching Mathematics: Influences and Directions
1(21)
Influences on Mathematics Education
2(1)
Physchological Influences
2(1)
Professional Influences
2(6)
The Framework of the Principles and Standards for School Mathematics
3(3)
Content Standards and Expectations in Each Grade Band
6(1)
Integrating the Content and Process Standards
6(2)
Integrating State and Local Standards with National Math Standards
8(1)
Technological Influences
8(3)
Calculators
8(2)
Computers
10(1)
Interactive Multimedia
11(1)
Language Influences
11(1)
Societal Influences
12(1)
State Government
12(1)
School Districts
12(1)
Lobby Groups
12(1)
Bandwagons
12(1)
Research Influences
12(1)
TIMSS
13(1)
NAEP
13(1)
Learner Influences
13(1)
What Can Teachers Do?
13(1)
Teacher Influences
14(1)
Directions in Mathematics Education
14(1)
Problem Solving
14(1)
Communication
14(1)
Reasoning and Proof
15(1)
Connections
15(2)
Integration with Other School Subjects
15(1)
Integration with Real-World Settings
16(1)
Representation of Mathematical Ideas
17(1)
Equity
17(1)
Technology
17(1)
Computation and Estimation
17(1)
Assessment
18(1)
Parent Involvement
19(1)
Conclusion
19(1)
For Your Journal
19(1)
For Your Portfolio
19(1)
Resources for Teachers
20(1)
Links to the Internet
20(1)
Learning and Teaching Mathematics
21(23)
Learning Styles
22(1)
Learning Theories
22(1)
The Behaviorist Approach
22(1)
The Cognitive/Constructivist Approach
22(5)
Cooperative Learning
23(1)
Jean Piaget
23(2)
Zoltan Dienes
25(2)
Basic Principles Reviewed
27(1)
Begin With Concrete Representation
27(1)
Develop Understandings
28(2)
Encourage Communication
30(1)
Make Connections
31(1)
Take Time to Motivate Children
32(1)
Attitudes
32(1)
Provide Opportunities for Practice
32(2)
Games
33(1)
Puzzles and Riddles
33(1)
Surprises
33(1)
Novel Algorithms
33(1)
Novel Formats
33(1)
The Calculator as Practice Tool
34(1)
Personal Computers
34(1)
Thinking About Teaching
34(1)
Pre-Teaching Activities
34(2)
Pre-Planning Considerations
34(2)
Planning
36(1)
Process of Teaching
36(4)
Models for Teaching Mathematics
37(3)
Post-Teaching Activities
40(1)
Evaluation of Teaching
40(1)
Reflection on Teaching
40(1)
Thinking About the Curriculum
40(1)
The Mathematics
41(1)
The Activities
41(1)
Conclusion
41(1)
For Your Journal
42(1)
For Your Portfolio
42(1)
Resources for Teachers
42(1)
Links to the Internet
42(2)
Developing Mathematical Thinking and Problem-Solving Ability
44(20)
Mathematical Considerations
45(1)
What Is a Problem?
45(1)
Types of Problems
46(1)
Process Problems
46(1)
Translation Problems
46(1)
Application Problems
46(1)
Puzzles
47(1)
Ask Children to Write Problems
47(1)
Posing Problems
48(1)
The Problem-Solving Process
48(1)
Understanding the Problem
48(1)
Devising a Plan to Solve the Problem
49(1)
Implementing a Solution Plan
49(1)
Reflecting on the Problem
49(1)
Problem-Solving Strategies
49(2)
Dramatize or Model the Situation and Solution Process
51(1)
Draw a Picture or Diagram
52(1)
Construct a Table or Chart
52(2)
Find a Pattern
54(1)
Solve a Simpler Problem
54(1)
Guess and Check
55(1)
Working Backwards
56(1)
Consider All Possibilities
56(1)
Logical Reasoning
56(1)
Change Your Point of View
57(1)
Write an Open Sentence
57(1)
Planning for Instruction
58(1)
Selecting Appropriate Tasks and Materials
58(1)
Problems That Are Motivating and Culturally Relevant
58(1)
Problems with Missing, Extraneous, or Contradictory Information
58(1)
Problems That Encourage the Use of Calculators, Computers, and Other Technology
58(1)
Activities That Require the Use of a Variety of Problem-Solving Strategies
58(1)
Activities That Promote Communication About Mathematical Thinking
58(1)
Sources of Problems
59(1)
The Teacher's Role
59(1)
Before Children Begin to Solve the Problem
59(1)
While Children Are Solving the Problem
59(1)
After Children Solve the Problem
59(1)
Organizing and Implementing Instruction
60(1)
Classroom Climate
60(1)
Grouping Children
60(1)
Allocating Time
60(1)
Assessing Children's Understanding
60(1)
Changing the Difficulty of Problems
60(1)
Problem Context
60(1)
Problem Structure
61(1)
Classroom Implications
61(1)
Other Factors Contributing to Children's Difficulties in Problem Solving
61(1)
Knowledge Factors
61(1)
Beliefs and Affective Factors
62(1)
Control
62(1)
Sociocultural Factors
62(1)
A Case to Consider the Children
62(1)
Benefits of Using a Problem-Solving Approach to Mathematics Instruction
62(1)
Conclusion
63(1)
For Your Journal
63(1)
For Your Portfolio
63(1)
Resources for Teachers
63(1)
Links to the Internet
63(1)
Assessing Mathematics Understanding
64(13)
The Assessment Standards
65(1)
What Is Assessment?
65(1)
Purposes of Assessment
66(1)
Phases of Assessment
66(1)
Assessment Choices
66(1)
Achievement Tests
67(1)
Standardized Tests
67(1)
Teacher-Made Tests
67(1)
Diagnostic Tests
67(1)
Individualizing Assessment
67(8)
Observation
67(1)
Conferences and Interviews
68(1)
Performance Assessment
69(3)
Portfolio Assessment
72(3)
Self-Assessment
75(1)
Assessing Attitudes Toward Mathematics
75(1)
Conclusion
76(1)
For Your Journal
76(1)
For Your Portfolio
76(1)
Resources for Teachers
76(1)
Links to the Internet
76(1)
Developing Number Concepts
77(22)
The Foundations of Number
78(1)
Pre-Number Activities
78(4)
Classification
78(2)
Seriation
80(1)
Patterns
81(1)
One-to-One Correspondence
81(1)
Conservation of Number
82(1)
Number Meanings
82(1)
Cardinal Use of Numbers
83(1)
Ordinal Use of Numbers
83(1)
Nominal Use of Numbers
83(1)
Counting
83(1)
Discrete and Continuous Quantities
83(1)
Rote Counting
83(1)
Rational Counting
83(1)
Counting All, Counting On
84(1)
Counting Back
84(1)
Skip Counting
85(1)
Representing Numbers
86(1)
Concrete Models
87(1)
Pictorial and Graphic Representation of Numbers
87(1)
Symbolic Representation of Numbers
87(3)
Numerals
90(1)
Number Relationships
90(1)
Order Relations
90(1)
More Than, Fewer Than
90(1)
One Greater Than, One Less Than
91(1)
Part-Part-Whole Relationships
91(4)
Relationship to Five and Ten
93(1)
Using Action Language
94(1)
Bidirectional Relationship of an Equation
95(1)
Estimation
96(1)
Conclusion
97(1)
For Your Journal
97(1)
For Your Portfolio
97(1)
Resources for Teachers
97(1)
Links to the Internet
98(1)
Developing Understanding of Numeration
99(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

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