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Mathematics for Elementary Teachers / Edition 3
     

Mathematics for Elementary Teachers / Edition 3

by Sybilla Beckmann
 

See All Formats & Editions

ISBN-10: 0321646940

ISBN-13: 9780321646941

Pub. Date: 03/28/2010

Publisher: Pearson Education

This activities manul includes activities designed to be done in class or outside of class. These activities promote critical thinking and discussion and give students a depth of understanding and perspective on the concepts presented in the text.

Overview

This activities manul includes activities designed to be done in class or outside of class. These activities promote critical thinking and discussion and give students a depth of understanding and perspective on the concepts presented in the text.

Product Details

ISBN-13:
9780321646941
Publisher:
Pearson Education
Publication date:
03/28/2010
Edition description:
Older Edition
Pages:
736
Product dimensions:
8.70(w) x 11.00(h) x 1.90(d)

Table of Contents

Chapter 1: PROBLEM SOLVING

1.1 Solving Problems

� 1A A Clinking Glasses Problem � 1B Problems about Triangular Numbers � 1C What Is a Fair Way to Split  the Cost?

1.2 Explaining Solutions

� 1D Who Says You Can’t Do Rocket Science?

 

Chapter 2:NUMBERS AND THE DECIMAL SYSTEM

2.1 Overview of the Number Systems

2.2 The Decimal System and Place Value

� 2A How Many Are There? � 2B Showing Powers of Ten

2.3 Representing Decimal Numbers

� 2C Representing Decimal Numbers with Bundled Objects � 2D Zooming In and Zooming Out on Number Lines � 2E Representing Decimals as Lengths

2.4 Comparing Decimal Numbers

� 2F Places of Larger Value Count More than Lower Places Combined � 2G Misconceptions in Comparing Decimal Numbers � 2H Finding Smaller and Smaller Decimal Numbers � 2I Finding Decimals between Decimals � 2J Decimals between Decimals on Number Lines � 2K “Greater Than” and “Less Than” with Negative Decimal Numbers

2.5 Rounding Decimal Numbers

� 2L Why Do We Round? � 2M Explaining Rounding � 2N Can We Round This Way? � 2O Can We Round This Way?

 

Chapter 3: FRACTIONS

3.1 The Meaning of Fractions

� 3A Fractions of Objects � 3B The Whole Associated with a Fraction � 3C Is the Meaning of Equal Parts Always Clear? � 3D Improper Fractions

3.2 Fractions as Numbers

� 3E Counting along Number Lines � 3F Fractions on Number Lines, Part 1

3.3 Equivalent Fractions

� 3G Equivalent Fractions � 3HMisconceptions about Fraction Equivalence � 3I Common Denominators � 3J Solving Problems by Changing Denominators � 3K Fractions on Number Lines, Part 2 � 3L Simplifying Fractions � 3M When Can We “Cancel” to Get an Equivalent Fraction?

3.4 Comparing Fractions

� 3N Can We Compare Fractions this Way? � 3O What Is Another Way to Compare these Fractions? � 3P Comparing Fractions by Reasoning � 3Q Can We Reason this Way?

3.5 Percent

� 3R Pictures, Percentages, and Fractions � 3S Calculating Percents of Quantities by Using Benchmark Fractions � 3T Calculating Percentages � 3U Calculating Percentages with Pictures and Percent Diagrams � 3V Calculating Percentages by Going through 1 � 3W Calculating a Quantity from a Percentage of It

 

Chapter 4: ADDITION AND SUBTRACTION

4.1 Interpretations of Addition and Subtraction

� 4A Addition and Subtraction Story Problems � 4B Solving Addition and Subtraction Story Problems � 4C The Shopkeeper’s Method of Making Change � 4D Addition and Subtraction Story Problems with Negative

Numbers

4.2 Why the Common Algorithms for Adding and Subtracting Decimal Numbers Work

� 4E Adding and Subtracting with Ten-Structured Pictures � 4F Understanding the Common Addition Algorithm � 4G Understanding the Common Subtraction Algorithm � 4H Subtracting across Zeros � 4I Regrouping with Dozens and Dozens of Dozens � 4J Regrouping with Seconds, Minutes, and

Hours � 4K A Third Grader’s Method of Subtraction

4.3 Adding and Subtracting Fractions

� 4L Fraction Addition and Subtraction � 4M Mixed Numbers and Improper Fractions � 4N Adding and Subtracting Mixed Numbers � 4O Are These Story Problems for ½ - 1/3  � 4Q What Fraction Is Shaded?

4.4 When Do We Add Percentages?

� 4R Should We Add These Percentages?

4.5 Percent Increase and Percent Decrease

� 4S Calculating Percent Increase and Decrease � 4T Calculating Amounts from a Percent Increase or Decrease � 4U Percent of versus Percent Increase or Decrease � 4V Percent Problem Solving

4.6 The Commutative and Associative Properties of Addition and Mental Math

� 4W Mental Math � 4X Using Properties of Addition in Mental Math � 4Y Using Properties of Addition to Aid Learning of Basic Addition Facts � 4Z Writing Correct Equations � 4AA Writing Equations That Correspond to a Method of Calculation � 4BB Other Ways to Add and Subtract

 

Chapter 5: MULTIPLICATION

5.1 The Meaning of Multiplication and Ways to Show Multiplication

� 5A Showing Multiplicative Structure

5.2 Why Multiplying Decimal Numbers by 10 Is Easy

� 5B Multiplying by 10 � 5C If We Wrote Numbers Differently, Multiplying by 10 Might Not Be So Easy � 5D Multiplying by Powers of 10 Explains the Cycling of Decimal Representations of Fractions

5.3 The Commutative Property of Multiplication and Areas of Rectangles

� 5E Multiplication, Areas of Rectangles, and the Commutative Property � 5F Explaining the Commutative Property of Multiplication � 5G Using the Commutative Property of Multiplication � 5H Using Multiplication to Estimate How Many

5.4 The Associative Property of Multiplication and Volumes of Boxes

� 5I Ways to Describe the Volume of a Box with Multiplication � 5J Explaining the Associative Property � 5K Using the Associative and Commutative Properties of Multiplication � 5L Different Ways to Calculate the Total Number of Objects � 5M How Many Gumdrops?

5.5 The Distributive Property

� 5N Order of Operations � 5O Explaining the Distributive Property � 5P The Distributive Property and FOIL

� 5Q Using the Distributive Property � 5R Why Isn’t 23 × 23 Equal to 20 × 20 + 3 × 3? � 5S Squares and Products Near Squares

5.6 Mental Math, Properties of Arithmetic, and Algebra

� 5T Using Properties of Arithmetic to Aid the Learning of Basic Multiplication Facts � 5U Solving Arithmetic Problems Mentally � 5V Which Properties of Arithmetic Do These Calculations Use? � 5W Writing Equations That Correspond to a Method of Calculation � 5X Showing the Algebra in Mental Math

5.7 Why the Procedure for Multiplying Whole Numbers Works

� 5Y The Standard Versus the Partial-Products Multiplication Algorithm � 5Z Why the Multiplication Algorithms Give Correct Answers, Part 1 � 5AA Why the Multiplication Algorithms Give Correct Answers, Part 2 � 5BB The Standard Multiplication Algorithm Right Side Up and Upside Down

 

Chapter 6: MULTIPLICATION OF FRACTIONIS, DECIMALS, AND NEGATIVE NUMBERS

6.1 Multiplying Fractions

� 6A Writing and Solving Fraction Multiplication Story Problems � 6B Misconceptions with Fraction Multiplication � 6C Explaining Why the Procedure for Multiplying Fractions Gives Correct Answers � 6D When Do We Multiply Fractions? � 6E Multiplying Mixed Numbers � 6F What Fraction Is Shaded?

6.2 Multiplying Decimals

� 6G Multiplying Decimals � 6H Explaining Why We Place the Decimal Point Where We Do When We Multiply Decimals � 6I Decimal Multiplication and Areas of Rectangles

6.3 Multiplying Negative Numbers

� 6J Patterns with Multiplication and Negative Numbers � 6K Explaining Multiplication with Negative Numbers (and 0) � 6L Using Checks and Bills to Interpret Multiplication with Negative Numbers � 6M Does Multiplication Always Make Larger?

6.4 Scientific Notation

� 6N Scientific Notation versus Ordinary Decimal Notation � 6O Multiplying Powers of 10 � 6P How Many Digits Are in a Product of Counting Numbers?� 6Q Explaining the Pattern in the Number of Digits in Products

 

Chapter 7: DIVISION

7.1 The Meaning of Division

� 7A The Two Interpretations of Division � 7B Why Can’t We Divide by Zero? � 7C Division Story Problems � 7D Can We Use Properties of Arithmetic to Divide? � 7E Reasoning about Division � 7F Rounding to Estimate Solutions to Division Problems

7.2 Understanding Long Division

� 7G Dividing without Using a Calculator or Long Division � 7H Understanding the Scaffold Method of Long Division � 7I Using the Scaffold Method � 7J Interpreting Standard Long Division from the “How Many in Each Group?” Viewpoint � 7K Zeros in Long Division � 7L Using Long Division to Calculate Decimal Number Answers to Whole Number Division Problems � 7M Errors in Decimal Answers to Division

Problems

7.3 Fractions and Division

� 7N Relating Fractions and Division � 7O Mixed-Number Answers to Division Problems � 7P Using Division to Calculate Decimal Representations of Fractions

7.4 Dividing Fractions

� 7Q “How Many Groups?” Fraction Division Problems � 7R “How Many in One Group?” Fraction Division Problems � 7S Using “Double Number Lines” to Solve “How Many in One Group?” Division Problems � 7T Explaining “Invert and Multiply” by Relating Division to Multiplication � 7U Are These Division Problems?

7.5 Dividing Decimals

� 7V Quick Tricks for Some Decimal Division Problems � 7W Decimal Division

7.6 Ratio and Proportion

� 7X Comparing Mixtures � 7Y Using Ratio Tables � 7Z Using Strip Diagrams to Solve Ratio Problems � 7AA Using Simple Reasoning to Find Equivalent Ratios and Rates � 7BB Solving Proportions with Multiplication and Division � 7CC Ratios, Fractions, and Division � 7DD Solving Proportions by Cross-

Multiplying Fractions � 7EE Can You Always Use a Proportion? � 7FF The Consumer Price Index

 

Chapter 8: GEOMETRY

8.1 Visualization

� 8A What Shapes Do These Patterns Make? � 8B Parts of a Pyramid � 8C Slicing through a Board � 8D Visualizing Lines and Planes � 8E The Rotation of the Earth and Time Zones � 8F Explaining the Phases of the Moon

8.2 Angles

� 8G Angle Explorers � 8H Angles Formed by Two Lines � 8I Seeing that the Angles in a Triangle Add to 180� � 8J Using the Parallel Postulate to Prove that the Angles in a Triangle Add to 180� � 8K Describing Routes, Using Distances and Angles � 8L Explaining Why the Angles in a Triangle Add to 180� by Walking and Turning � 8M Angles and Shapes Inside Shapes � 8N Angles of Sun Rays � 8O How the Tilt of the Earth

Causes Seasons � 8P How Big Is the Reflection of Your Face in a Mirror? � 8Q Why Do Spoons Reflect Upside Down? � 8R The Special Shape of Satellite Dishes

8.3 Circles and Spheres

� 8S Points That Are a Fixed Distance from a Given Point � 8T Using Circles � 8U The Global Positioning System (GPS) � 8V Circle Curiosities

8.4 Triangles, Quadrilaterals, and Other Polygons

� 8W Using a Compass to Draw Triangles and Quadrilaterals � 8X Making Shapes by Folding Paper � 8Y Constructing Quadrilaterals with Geometer’s Sketchpad � 8Z Relating the Kinds of Quadrilaterals � 8AA Venn Diagrams Relating Quadrilaterals � 8BB Investigating Diagonals of Quadrilaterals with Geometer’s Sketchpad � 8CC Investigating Diagonals of Quadrilaterals (Alternate)

8.5 Constructions with Straightedge and Compass

� 8DD Relating the Constructions to Properties of Rhombuses � 8EE Constructing a Square and an Octagon with Straightedge and Compass

8.6 Polyhedra and Other Solid Shapes

� 8FF Patterns for Prisms, Cylinders, Pyramids, and Cones � 8GG Making Prisms and Pyramids � 8HH Analyzing Prisms and Pyramids � 8II What’s Inside the Magic 8 Ball? � 8JJ Making Platonic Solids with Toothpicks and Marshmallows � 8KK Why Are There No Other Platonic Solids? � 8LL Relating the

Numbers of Faces, Edges, and Vertices of Polyhedra

 

Chapter 9: GEOMETRY OF MOTION AND CHANGE

9.1 Reflections, Translations, and Rotations

� 9A Exploring Rotations � 9B Exploring Reflections � 9C Exploring Reflections with Geometer’s Sketchpad

� 9D Exploring Translations with Geometer’s Sketchpad � 9E Exploring Rotations with Geometer’s Sketchpad � 9F Reflections, Rotations, and Translations in a Coordinate Plane

9.2 Symmetry

� 9G Checking for Symmetry � 9H Frieze Patterns � 9I Traditional Quilt Designs � 9J Creating Symmetrical Designs with Geometer’s Sketchpad � 9K Creating Symmetrical Designs (Alternate) � 9L Creating Escher-Type Designs with Geometer’s Sketchpad (for Fun) � 9M Analyzing Designs

9.3 Congruence

� 9N Triangles and Quadrilaterals of Specified Side Lengths � 9O Describing a Triangle � 9P Triangles with an Angle, a Side, and an Angle Specified � 9Q Using Triangle Congruence Criteria

9.4 Similarity

� 9R A First Look at Solving Scaling Problems � 9S Using the “Scale Factor,” “Relative Sizes,” and “Set up a Proportion” Methods � 9T A Common Misconception about Scaling � 9U Using Scaling to Understand Astronomical Distances � 9V More Scaling Problems � 9W Measuring Distances by “Sighting” � 9X Using Shadows to Determine the Height of a Tree

 

Chapter 10: MEASUREMENT

10.1 Fundamentals of Measurement

� 10A The Biggest Tree in the World � 10B What Do “6 Square Inches” and “6 Cubic Inches” Mean? � 10C Using a Ruler

10.2 Length, Area, Volume, and Dimension

� 10D Dimension and Size

10.3 Calculating Perimeters of Polygons, Areas of Rectangles, and Volumes of Boxes

� 10E Explaining Why We Add to Calculate Perimeters of Polygons � 10F Perimeter Misconceptions � 10G Explaining Why We Multiply to Determine Areas of Rectangles � 10H Explaining Why We Multiply to Determine Volumes of Boxes � 10I Who Can Make the Biggest Box?

10.4 Error and Accuracy in Measurements

� 10J Reporting and Interpreting Measurements

10.5 Converting from One Unit of Measurement to Another

� 10K Conversions: When Do We Multiply? When Do We Divide? � 10L Conversion Problems � 10M Converting Measurements with and without Dimensional Analysis � 10N Areas of Rectangles in Square Yards and Square Feet � 10O Volumes of Boxes in Cubic Yards and Cubic Feet � 10P Area and Volume Conversions: Which Are Correct and Which Are Not?

 

Chapter 11: MORE ABOUT AREA AND VOLUME

11.1 The Moving and Additivity Principles about Area

� 11A Different Shapes with the Same Area � 11B Using the Moving and Additivity Principles � 11C Using the Moving and Additivity Principles to Determine Surface Area

11.2 Using the Moving and Additivity Principles to Prove the Pythagorean Theorem

� 11D Using the Pythagorean Theorem � 11E Can We Prove the Pythagorean Theorem by Checking Examples? � 11F A Proof of the Pythagorean Theorem

11.3 Areas of Triangles

� 11G Choosing the Base and Height of Triangles � 11H Explaining Why the Area Formula for Triangles Is Valid � 11I Determining Areas

11.4 Areas of Parallelograms

� 11J Do Side Lengths Determine the Area of a Parallelogram? � 11K Explaining Why the Area Formula for Parallelograms Is

Valid

11.5 Cavalieri’s Principle about Shearing and Area

� 11L Shearing a Toothpick Rectangle to Make a Parallelogram � 11M Is This Shearing? � 11N Shearing Parallelograms � 11O Shearing Triangles

11.6 Areas of Circles and the Number Pi

� 11P How Big Is the Number π? � 11Q Over- and Underestimates for the Area of a Circle � 11R Why the Area Formula for Circles Makes Sense � 11S Using the Circle Circumference and Area Formulas to Find Areas and Surface Areas

11.7 Approximating Areas of Irregular Shapes

� 11T Determining the Area of an Irregular Shape

11.8 Relating the Perimeter and Area of a Shape

� 11U How Are Perimeter and Area Related? � 11V Can We Determine Area by Measuring Perimeter?

11.9 Principles for Determining Volumes

� 11W Using the Moving and Additivity Principles to Determine Volumes � 11X Determining Volumes by Submersing in Water � 11Y Floating Versus Sinking: Archimedes’s Principle

11.10 Volumes of Prisms, Cylinders, Pyramids, and Cones

� 11Z Why the Volume Formula for Prisms and Cylinders Makes Sense � 11AA Filling Boxes and Jars � 11BB Comparing the Volume of a Pyramid with the Volume of a Rectangular Prism � 11CC The 13

in the Volume Formula for Pyramids and Cones � 11DD Using Volume Formulas with Real Objects

� 11EE Volume and Surface Area Contests � 11FF Volume Problems � 11GG The Volume of a Rhombic Dodecahedron

11.11 Areas, Volumes, and Scaling

� 11HH Areas and Volumes of Similar Boxes � 11II Areas and Volumes of Similar Cylinders � 11JJ Determining Areas and Volumes of Scaled Objects � 11KK A Scaling Proof of the Pythagorean Theorem

 

Chapter 12: NUMBER THEORY

12.1 Factors and Multiples

� 12A Factors, Multiples, and Rectangles � 12B Problems about Factors and Multiples � 12C Finding All Factors � 12D Do Factors Always Come in Pairs?

12.2 Greatest Common Factor and Least Common Multiple

� 12E Finding Commonality � 12F The “Slide Method” � 12G Problems Involving Greatest Common Factors and Least Common Multiples � 12H Flower Designs � 12I Relationships between the GCF and the LCM and Explaining the Flower Designs � 12J Using GCFs and LCMs with Fractions

12.3 Prime Numbers

� 12K The Sieve of Eratosthenes � 12L The Trial Division Method for Determining whether a Number Is Prime

12.4 Even and Odd

� 12M Why Can We Check the Ones Digit to Determine whether a Number Is Even or Odd? � 12N Questions about Even and Odd Numbers � 12O Extending the Definitions of Even and Odd

12.5 Divisibility Tests

� 12P The Divisibility Test for 3

12.6 Rational and Irrational Numbers

� 12Q Decimal Representations of Fractions � 12R Writing Terminating and Repeating Decimals as Fractions � 12S What Is 0.9999 ...? � 12T The Square Root of 2 � 12U Pattern Tiles and the Irrationality of the Square Root of 3

 

Chapter 13: FUNCTIONS AND ALGEBRA

13.1 Mathematical Expressions, Formulas, and Equations

� 13A Writing Expressions and a Formula for a Flower Pattern � 13B Expressions in Geometric Settings � 13C Expressions in 3D Geometric Settings � 13D Equations Arising from Rectangular Designs � 13E Expressions with Fractions � 13F Evaluating Expressions with Fractions Efficiently and Correctly � 13G Expressions for Story Problems � 13H Writing Equations for Story Situations � 13I Writing Story Problems for

Equations

13.2 Solving Equations Using Number Sense, Strip Diagrams, and Algebra

� 13J Solving Equations Using Number Sense � 13K Solving Equations Algebraically and with a Pan Balance � 13L How Many Pencils Were There? � 13M Solving Story Problems with Strip Diagrams and with Equations � 13N Modifying Problems � 13O Solving Story Problems

13.3 Sequences

� 13P Arithmetic Sequences of Numbers Corresponding to Sequences of Figures � 13Q Deriving Formulas for Arithmetic Sequences � 13R Sequences and Formulas � 13S Geometric Sequences � 13T Repeating Patterns � 13U The Fibonacci Sequence in Nature and Art � 13V What’s the Rule?

13.4 Series

� 13W Sums of Counting Numbers � 13X Sums of Odd Numbers � 13Y Sums of Squares � 13Z Sums of Powers of Two � 13AA An Infinite Geometric Series � 13BB Making Payments into an Account

13.5 Functions

� 13CC Interpreting Graphs of Functions � 13DD Are These Graphs Correct?

13.6 Linear Functions

� 13EE A Function Arising from Proportions � 13FF Arithmetic Sequences as Functions � 13GG Analyzing the Way Functions Change � 13HH Story Problems for Linear Functions � 13II Deriving the Formula for Temperature in Degrees Fahrenheit in Terms of Degrees Celsius

 

Chapter 14: STATISTICS

14.1 Formulating Questions, Designing Investigations, and Gathering Data

� 14A Challenges in Formulating Survey Questions � 14B Choosing a Sample � 14C Using Random Samples

� 14D Using Random Samples to Estimate Population Size by Marking (Capture—Recapture) � 14E Which Experiment Is Better?

14.2 Displaying Data and Interpreting Data Displays

� 14F What Do You Learn from the Display? � 14G Display These Data about Pets � 14H What Is Wrong with These Displays? � 14I Three Levels of Questions about Graphs � 14J The Length of a Pendulum and the Time It Takes to Swing � 14K Investigating Small Bags of Candies � 14L Balancing a

Mobile

14.3 The Center of Data: Mean, Median, and Mode

� 14M The Average as “Making Even” or “Leveling Out” � 14N The Average as “Balance Point” � 14O Same Median, Different Average � 14P Can More Than Half Be above Average?

14.4 Percentiles and the Distribution of Data

� 14Q Determining Percentiles � 14R Percentiles versus Percent Correct � 14S Box-and-Whisker Plots � 14T How Percentiles Inform You about the Distribution of Data: The Case of Household Income � 14U  Distributions of Random Samples

 

Chapter 15: PROBABILITY

15.1 Basic Principles and Calculation Methods of Probability

� 15A Comparing Probabilities � 15B Experimental versus Theoretical Probability: Picking Cubes from a Bag � 15C If You Flip 10 Pennies, Should Half Come Up Heads? � 15D Number Cube Rolling Game � 15E Picking Two Marbles from a Bag of 1 Black and 3 Red Marbles � 15F Applying Probability � 15G Some Probability Misconceptions

15.2 Using Fraction Arithmetic to Calculate Probabilities

� 15H Using the Meaning of Fraction Multiplication to Calculate a Probability � 15I Using Fraction Multiplication and Addition to Calculate a Probability

 

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