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by Joseph Martinez and Nancy C. Martinez

Edition: 07Copyright: 2007

Publisher: Merrill Education/Prentice Hall

Published: 2007

International: No

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Activities for Elementary and Middle School Mathematics: Developing Mathematical Thinking addresses the changing ways in which students learn and teachers teach mathematics. The traditional mathematics class emphasized memorizing procedures and facts and applying standard algorithms. Reformed mathematics instruction is active rather than passive, with an emphasis on inquiry and process. This text encourages multiple pathways to multiple solutions, as well as the development of mathematical thinking as equally important a result of problem solving as correct solutions. The authors believe that a reformed classroom functions as a learning laboratory, with learning tools such as base-10 blocks, tangrams, geoboards, and fraction or algebra tiles playing integral roles.

The mathematical activities collected in this text provide directions, contexts, and goals for the inquiry process. They emphasize hands-on learning and an inductive rather than deductive approach to mathematics. The authors believe that the starting is questions, as opposed to answers. Students are encouraged to build and construct answers for themselves.

**SECTION I. Understanding Numbers**

Finding the Numbers in Your Life

Making Numbers Books

How Tall is My Dino

Counting with Cheerios

Graphing with Candy Hearts, Jellybeans, or Gumdrops

The Revolving Jar

Walking on the Googol Side

Up, Down, All Around--Show Me with Calculators

**SECTION II. Understanding Number Systems and Place Value**

My Math Journal

How Much Money?

How Big Am I? How Big Are You?

Exploring Place Value with Blocks

How Much is That Pet?

Filling-up or Filling-out: How Much Will Fit in Each Place on the Calculator Display?

Quipus

The Circle of Time

What if You Had a Million Dollars?

Discovering Eight World (6-8)

The 250-mile Race

**SECTION III. Working with Whole Numbers: Addition and Subtraction**

Animals, Numbered and On the Town: A Bilingual Lesson in Spanish and English

Change for More/Change for Less

One-handed Fingermath: Part I: Counting All and On to Add Single-Digit Numbers

One-handed Fingermath: Part II: Counting Up and Down to Subtract Single-Digit Numbers

Exploring Multi-unit Concepts with Base-10 Blocks

Adding Multi-unit Numbers with Base-10 Blocks

Subtracting Multi-unit Numbers with Base-10 Blocks

$100 Shopping Spree

Adding and Subtracting with Chinese Stick Math

**SECTION IV. Working with Whole Numbers: Multiplication and Division**

"A Remainder of One"

Two-handed Fingermath

Jumping Critters: Kids, Frogs, and Bugs

Multiplication and Division: Maps of Facts

Writing Mathematics: Telling Tales by the Numbers

Modeling Multiplication

Modeling Division

Calculating with Chinese Stick Math

**SECTION V. Discovering Geometry and Developing Geometric Thinking**

Friendship Quilt

7 "Magic" Pieces: Tangrams

"Buggy" Geometry

Exploring the Many Facets of Geometry

Tangrams and Grandfather Tang's Story

Building Polygons and Polyhedrons with Gumdrops and Toothpicks

Symmetry and Geometric Transformations: Creating a Frieze Pattern

Spinning Polygons

Dimensions: Exploring Flatland

Origami Zoo (4-8)

**SECTION VI. Understanding and Using Measurement Concepts**

How Much Time Does It Take To ______________________?

Exploring Perimeter and Area with Froot Loops

LOGO's Turtle Math

Making Measurement Tools with Nonstandard and Standard Units

Cooking on the Oregon Trail with Nonstandard and Standard Measurements

Estimating Length, Volume, and Weight

Boiling Potato for Inca Time

Sir Cumference

Measuring Pi

Tessellating Polygons

Tangram Conundrum

**SECTION VII. Algebraic Thinking**

More M&M Math

Making and Guessing Patterns

Pictographs

Writing Story Problem

The Pool Problem

Patterns and Functions

Anno's Magic Seeds (3-5)

Playing Algebra with Equate

Equivalence

Golden Rectangle

**SECTION VIII.Working with Data**

Mini Gardens

Collecting Data in Our Worlds

"Pigs Will Be Pigs": Collecting Data and Money

Waste Collection and Graphing

Exploring Data in the Bigger World

Rolling the Dice

A Slice of the Pie: Percents and Pie Charts

Are You Hot? Are You Cold? Finding Mean, Median, and Mode

$10,000 Stock Market Contest

Probability: Coin Tossing

**SECTION IX. Understanding Fractions**

Tortilla Fractions

Hershey Bar Fractions

Writing and Identifying

Fraction Kits

Introduction to Fractions

Learning Fractions with Pictures

M&M Fractions, Data, and Prediction

Pi as a Fraction

The Fractions of Time

Fractions and Space/Distance

Finding Fractions in Your Life

**SECTION X. Exploring Part-Whole Relationships: Decimals and Percents**

Decimals and Percents in the Newspaper

Shopping by the Numbers

Modeling Decimal Numbers with Base-10 Blocks

Connecting Fractions, Decimals, Percents with Virtual Manipulatives

Rounding

Playing Concentration with Parts of Wholes

Finding Decimals and Percents in Your World

Fractions to Decimals and Percents with Fraction Strips

Fractions to Decimals: Repeating Decimals and Rounding

Percents, Decimals, and the Dream Vacation

Do Women and Men Work for Equal Pay in Sports?

Population Percentages

**SECTION XI. Building Bridges**

Real Numbers in the Workplace

Real Numbers at the Zoo

Irrational Numbers, A Pattern Activity

Is Pi Measurable?

The Golden Ratio, Phi and Physical Beauty

Real Numbers, Math Games, and AlphaNumeric Puzzles

Functions and Straight Lines

Functions: Straight Line Graphing Linear Equations using Intercepts

Trailmix Ratios

M&M Count and Crunch, Fractions and Ratios with M&M's

Summary

Activities for Elementary and Middle School Mathematics: Developing Mathematical Thinking addresses the changing ways in which students learn and teachers teach mathematics. The traditional mathematics class emphasized memorizing procedures and facts and applying standard algorithms. Reformed mathematics instruction is active rather than passive, with an emphasis on inquiry and process. This text encourages multiple pathways to multiple solutions, as well as the development of mathematical thinking as equally important a result of problem solving as correct solutions. The authors believe that a reformed classroom functions as a learning laboratory, with learning tools such as base-10 blocks, tangrams, geoboards, and fraction or algebra tiles playing integral roles.

The mathematical activities collected in this text provide directions, contexts, and goals for the inquiry process. They emphasize hands-on learning and an inductive rather than deductive approach to mathematics. The authors believe that the starting is questions, as opposed to answers. Students are encouraged to build and construct answers for themselves.

Table of Contents

**SECTION I. Understanding Numbers**

Finding the Numbers in Your Life

Making Numbers Books

How Tall is My Dino

Counting with Cheerios

Graphing with Candy Hearts, Jellybeans, or Gumdrops

The Revolving Jar

Walking on the Googol Side

Up, Down, All Around--Show Me with Calculators

**SECTION II. Understanding Number Systems and Place Value**

My Math Journal

How Much Money?

How Big Am I? How Big Are You?

Exploring Place Value with Blocks

How Much is That Pet?

Filling-up or Filling-out: How Much Will Fit in Each Place on the Calculator Display?

Quipus

The Circle of Time

What if You Had a Million Dollars?

Discovering Eight World (6-8)

The 250-mile Race

**SECTION III. Working with Whole Numbers: Addition and Subtraction**

Animals, Numbered and On the Town: A Bilingual Lesson in Spanish and English

Change for More/Change for Less

One-handed Fingermath: Part I: Counting All and On to Add Single-Digit Numbers

One-handed Fingermath: Part II: Counting Up and Down to Subtract Single-Digit Numbers

Exploring Multi-unit Concepts with Base-10 Blocks

Adding Multi-unit Numbers with Base-10 Blocks

Subtracting Multi-unit Numbers with Base-10 Blocks

$100 Shopping Spree

Adding and Subtracting with Chinese Stick Math

**SECTION IV. Working with Whole Numbers: Multiplication and Division**

"A Remainder of One"

Two-handed Fingermath

Jumping Critters: Kids, Frogs, and Bugs

Multiplication and Division: Maps of Facts

Writing Mathematics: Telling Tales by the Numbers

Modeling Multiplication

Modeling Division

Calculating with Chinese Stick Math

**SECTION V. Discovering Geometry and Developing Geometric Thinking**

Friendship Quilt

7 "Magic" Pieces: Tangrams

"Buggy" Geometry

Exploring the Many Facets of Geometry

Tangrams and Grandfather Tang's Story

Building Polygons and Polyhedrons with Gumdrops and Toothpicks

Symmetry and Geometric Transformations: Creating a Frieze Pattern

Spinning Polygons

Dimensions: Exploring Flatland

Origami Zoo (4-8)

**SECTION VI. Understanding and Using Measurement Concepts**

How Much Time Does It Take To ______________________?

Exploring Perimeter and Area with Froot Loops

LOGO's Turtle Math

Making Measurement Tools with Nonstandard and Standard Units

Cooking on the Oregon Trail with Nonstandard and Standard Measurements

Estimating Length, Volume, and Weight

Boiling Potato for Inca Time

Sir Cumference

Measuring Pi

Tessellating Polygons

Tangram Conundrum

**SECTION VII. Algebraic Thinking**

More M&M Math

Making and Guessing Patterns

Pictographs

Writing Story Problem

The Pool Problem

Patterns and Functions

Anno's Magic Seeds (3-5)

Playing Algebra with Equate

Equivalence

Golden Rectangle

**SECTION VIII.Working with Data**

Mini Gardens

Collecting Data in Our Worlds

"Pigs Will Be Pigs": Collecting Data and Money

Waste Collection and Graphing

Exploring Data in the Bigger World

Rolling the Dice

A Slice of the Pie: Percents and Pie Charts

Are You Hot? Are You Cold? Finding Mean, Median, and Mode

$10,000 Stock Market Contest

Probability: Coin Tossing

**SECTION IX. Understanding Fractions**

Tortilla Fractions

Hershey Bar Fractions

Writing and Identifying

Fraction Kits

Introduction to Fractions

Learning Fractions with Pictures

M&M Fractions, Data, and Prediction

Pi as a Fraction

The Fractions of Time

Fractions and Space/Distance

Finding Fractions in Your Life

**SECTION X. Exploring Part-Whole Relationships: Decimals and Percents**

Decimals and Percents in the Newspaper

Shopping by the Numbers

Modeling Decimal Numbers with Base-10 Blocks

Connecting Fractions, Decimals, Percents with Virtual Manipulatives

Rounding

Playing Concentration with Parts of Wholes

Finding Decimals and Percents in Your World

Fractions to Decimals and Percents with Fraction Strips

Fractions to Decimals: Repeating Decimals and Rounding

Percents, Decimals, and the Dream Vacation

Do Women and Men Work for Equal Pay in Sports?

Population Percentages

**SECTION XI. Building Bridges**

Real Numbers in the Workplace

Real Numbers at the Zoo

Irrational Numbers, A Pattern Activity

Is Pi Measurable?

The Golden Ratio, Phi and Physical Beauty

Real Numbers, Math Games, and AlphaNumeric Puzzles

Functions and Straight Lines

Functions: Straight Line Graphing Linear Equations using Intercepts

Trailmix Ratios

M&M Count and Crunch, Fractions and Ratios with M&M's

Publisher Info

Publisher: Merrill Education/Prentice Hall

Published: 2007

International: No

Published: 2007

International: No

The mathematical activities collected in this text provide directions, contexts, and goals for the inquiry process. They emphasize hands-on learning and an inductive rather than deductive approach to mathematics. The authors believe that the starting is questions, as opposed to answers. Students are encouraged to build and construct answers for themselves.

**SECTION I. Understanding Numbers**

Finding the Numbers in Your Life

Making Numbers Books

How Tall is My Dino

Counting with Cheerios

Graphing with Candy Hearts, Jellybeans, or Gumdrops

The Revolving Jar

Walking on the Googol Side

Up, Down, All Around--Show Me with Calculators

**SECTION II. Understanding Number Systems and Place Value**

My Math Journal

How Much Money?

How Big Am I? How Big Are You?

Exploring Place Value with Blocks

How Much is That Pet?

Filling-up or Filling-out: How Much Will Fit in Each Place on the Calculator Display?

Quipus

The Circle of Time

What if You Had a Million Dollars?

Discovering Eight World (6-8)

The 250-mile Race

**SECTION III. Working with Whole Numbers: Addition and Subtraction**

Animals, Numbered and On the Town: A Bilingual Lesson in Spanish and English

Change for More/Change for Less

One-handed Fingermath: Part I: Counting All and On to Add Single-Digit Numbers

One-handed Fingermath: Part II: Counting Up and Down to Subtract Single-Digit Numbers

Exploring Multi-unit Concepts with Base-10 Blocks

Adding Multi-unit Numbers with Base-10 Blocks

Subtracting Multi-unit Numbers with Base-10 Blocks

$100 Shopping Spree

Adding and Subtracting with Chinese Stick Math

**SECTION IV. Working with Whole Numbers: Multiplication and Division**

"A Remainder of One"

Two-handed Fingermath

Jumping Critters: Kids, Frogs, and Bugs

Multiplication and Division: Maps of Facts

Writing Mathematics: Telling Tales by the Numbers

Modeling Multiplication

Modeling Division

Calculating with Chinese Stick Math

**SECTION V. Discovering Geometry and Developing Geometric Thinking**

Friendship Quilt

7 "Magic" Pieces: Tangrams

"Buggy" Geometry

Exploring the Many Facets of Geometry

Tangrams and Grandfather Tang's Story

Building Polygons and Polyhedrons with Gumdrops and Toothpicks

Symmetry and Geometric Transformations: Creating a Frieze Pattern

Spinning Polygons

Dimensions: Exploring Flatland

Origami Zoo (4-8)

**SECTION VI. Understanding and Using Measurement Concepts**

How Much Time Does It Take To ______________________?

Exploring Perimeter and Area with Froot Loops

LOGO's Turtle Math

Making Measurement Tools with Nonstandard and Standard Units

Cooking on the Oregon Trail with Nonstandard and Standard Measurements

Estimating Length, Volume, and Weight

Boiling Potato for Inca Time

Sir Cumference

Measuring Pi

Tessellating Polygons

Tangram Conundrum

**SECTION VII. Algebraic Thinking**

More M&M Math

Making and Guessing Patterns

Pictographs

Writing Story Problem

The Pool Problem

Patterns and Functions

Anno's Magic Seeds (3-5)

Playing Algebra with Equate

Equivalence

Golden Rectangle

**SECTION VIII.Working with Data**

Mini Gardens

Collecting Data in Our Worlds

"Pigs Will Be Pigs": Collecting Data and Money

Waste Collection and Graphing

Exploring Data in the Bigger World

Rolling the Dice

A Slice of the Pie: Percents and Pie Charts

Are You Hot? Are You Cold? Finding Mean, Median, and Mode

$10,000 Stock Market Contest

Probability: Coin Tossing

**SECTION IX. Understanding Fractions**

Tortilla Fractions

Hershey Bar Fractions

Writing and Identifying

Fraction Kits

Introduction to Fractions

Learning Fractions with Pictures

M&M Fractions, Data, and Prediction

Pi as a Fraction

The Fractions of Time

Fractions and Space/Distance

Finding Fractions in Your Life

**SECTION X. Exploring Part-Whole Relationships: Decimals and Percents**

Decimals and Percents in the Newspaper

Shopping by the Numbers

Modeling Decimal Numbers with Base-10 Blocks

Connecting Fractions, Decimals, Percents with Virtual Manipulatives

Rounding

Playing Concentration with Parts of Wholes

Finding Decimals and Percents in Your World

Fractions to Decimals and Percents with Fraction Strips

Fractions to Decimals: Repeating Decimals and Rounding

Percents, Decimals, and the Dream Vacation

Do Women and Men Work for Equal Pay in Sports?

Population Percentages

**SECTION XI. Building Bridges**

Real Numbers in the Workplace

Real Numbers at the Zoo

Irrational Numbers, A Pattern Activity

Is Pi Measurable?

The Golden Ratio, Phi and Physical Beauty

Real Numbers, Math Games, and AlphaNumeric Puzzles

Functions and Straight Lines

Functions: Straight Line Graphing Linear Equations using Intercepts

Trailmix Ratios

M&M Count and Crunch, Fractions and Ratios with M&M's