Ratio and Proportion -- TABLE OF CONTENTS -- CHAPTER 1: INTRODUCTION -- PART ONE: STRUCTURE OF BOOK AND TEACHING MODEL -- CHAPTER 2: STRUCTURE OF BOOK -- DETAILED STRUCTURE OF THE BOOK -- Part One: Structure of Book and Teaching Model -- Part Two: Theoretical Background -- Part Three: Authentic Investigative Activities -- Part Four: Assessment Tools -- Part Five: Annotated Resource and Bibliography -- INCORPORATING MATERIAL INTO THE COURSE -- Incorporating Theoretical Material -- Using the Authentic Investigative Activities -- CHAPTER 3: A MODEL FOR TEACHING RATIO AND PROPORTION USING AUTHENTIC INVESTIGATIVE ACTIVITIES -- BACKGROUND -- THE COMPONENTS OF THE TEACHING MODEL -- CORE OF THE MODEL: AUTHENTIC INVESTIGATIVE ACTIVITIES -- The Five Types of Authentic Investigative Activities -- Choosing the Activities -- PART TWO: THEORETICAL BACKGROUND -- CHAPTER 4: A MATHEMATICAL PERSPECTIVE OF RATIO AND PROPORTION -- THE CONCEPT OF RATIO -- Mathematical Definition of "Ratio" -- Explanations on the Definition of Ratio -- Types of Ratio -- THE CONCEPT OF PROPORTION -- Mathematical Definition of "Proportion" -- Explanations and Comments on the Definition of Proportion -- Further Insights into Direct and Inverse (Indirect) Proportion -- Direct proportion -- Inverse (indirect) proportion -- STRATEGIES USED FOR SOLVING RATIO AND PROPORTION PROBLEMS -- Pre-formal Strategies -- MATHEMATICAL PROPERTIES OF THE CONCEPTS OF RATIO AND PROPORTION -- Adaptation of the Laws of Fractions on Ratios -- The Rules and Properties of Proportion -- Application of the Rules and Properties of Proportion -- CHAPTER 5: PROPORTIONAL REASONING-A PSYCHOLOGICAL-DIDACTICAL VIEW -- THE DEVELOPMENT OF PROPORTIONAL REASONING -- STRATEGIES FOR SOLVING RATIO-AND-PROPORTION PROBLEMS-A BRIEF REVIEW OF THE LITERATURE -- Strategy Quality.

DIFFICULTIES AND THEIR SOURCES IN THE PROCESS OF SOLVING RATIOAND PROPORTION PROBLEMS -- Difficulties Arising from Cognitive Aspects -- Variables That Influence the Performance Process -- Variables Arising From the Teaching-Learning Process and the Uniform Educational System -- CHAPTER 6: RESEARCH AND NEW APPROACHES IN PREAND IN-SERVICE MATHEMATICS TEACHER EDUCATION -- BACKGROUND -- CONCEPTUAL REVOLUTION -- REQUIREMENTS OF TEACHERS' KNOWLEDGE -- Subject Matter Content Knowledge -- Pedagogical Content Knowledge -- Curricular Knowledge -- TEACHING STRATEGIES PROMOTED IN THIS BOOK -- Subject Matter Content Knowledge in Proportional Reasoning -- Pedagogical Content Knowledge in Proportional Reasoning -- Curricular Knowledge of Proportional Reasoning -- OTHER TEACHING MODELS -- SUMMARY -- PART THREE: AUTHENTIC INVESTIGATIVE ACTIVITIES, INCLUDING DIDACTIC COMMENTS AND EXPLANATIONS -- CHAPTER 7: AUTHENTIC INVESTIGATIVE ACTIVITIES- INTRODUCTION -- THE BASICS -- Incorporating the Activities -- Incorporating the Literature -- Examples of How to Combine Research Articles into Authentic Research Activities -- THE ACTIVITIES BY GROUP -- Group 1: Introductory Activities -- Group 2: Rate Activities -- Group 3: Ratio Activities -- Group 4: Stretching and Shrinking (Scaling) Activities -- Group 5: Indirect Proportion Activities -- Group 6: Additional Tasks/Exercises for Practice and Enrichment -- CHAPTER 8: GROUP 1 INTRODUCTORY ACTIVITIES -- Activity 1.1: A Teaching EventWorksheet -- Description -- Tasks -- Activity 1.1: A Teaching EventDidactic Comments and Explanations -- Comments and explanations for tasks -- Activity 1.2: Statements Concerning Ratio and ProportionWorksheet -- Description -- Tasks -- Activity 1.2: Statements Concerning Ratio and ProportionDidactic Comments and Explanations -- Comments and explanations for tasks.

Activity 1.3: How Do We Compare?Worksheet -- Description -- Tasks -- Activity 1.3: How Do We Compare?Didactic Comments and Explanations -- Comments and explanations for tasks -- Comments Regarding Activity 1: The Juice Activity -- CHAPTER 9: GROUP 2 RATE ACTIVITIES -- Activity 2.1: Who's Correct?Worksheet -- Description -- Activity 2.1: Who's Correct?Extended Activity Worksheet -- Tasks -- Activity 2.1: Who's Correct?Basic Activity: Didactic Comments and Explanations -- Comments and explanations for tasks -- Additional points for discussion. -- Activity 2.1: Who's Correct?Extended Activity Worksheet: Didactic Comments and Explanations -- Additional points for discussion. -- Activity 2.2: Which CD is a Better Buy?Worksheet -- Description -- Tasks -- Activity 2.2: Which CD is a Better Buy?: Didactic Comments and Explanations -- Comments and explanations for tasks -- Adapting the activities for the classroom -- Activity 2.3: Beads, Beads, BeadsWorksheet -- Description -- Tasks -- Activity 2.3: Beads, Beads, BeadsExtended Activity Worksheet -- Activity 2.3: Beads, Beads, BeadsWorksheet: Didactic Comments and Explanations -- Comments and explanations for tasks -- Activity 2.3: Beads, Beads, BeadsExtended Activity Worksheet: Didactic Comments and Explanations -- Activity 2.4: At the Dairy and Bianca the CowWorksheet -- Description -- Activity 2.4: At the Dairy and Bianca the CowDidactic Comments and Explanations -- Activity 2.5: How Many Beans in the Bag?Worksheet -- Description -- Activities: -- Activity 2.5: How Many Beans in the Bag?Didactic Comments and Explanations -- Comments and explanations for tasks -- Activity 2.6: Counting a CrowdWorksheet -- Description -- Activity 2.6: Counting a CrowdDidactic Comments and Explanations -- Comments and explanations for tasks -- CHAPTER 10: GROUP 3: RATIO ACTIVITIES -- Activity 3.1: Which Cola is Best?Worksheet.

Description -- Tasks -- Activity 3.1: Which Cola is Best?Didactic Comments and Explanations -- Comments and explanations for tasks -- Activity 3.2: Pizza PartyWorksheet -- Description -- Tasks -- Activity 3.2: Pizza PartyDidactic Comments and Explanations -- Comments and explanations for tasks -- Activity 3.3: Everyone Solves it DifferentlyWorksheet -- Description -- Tasks -- Activity 3.3: Everyone Solves it DifferentlyDidactic Comments and Explanations -- Comments and explanations for tasks -- Activity 3.4: What's in Rust?Worksheet -- Description -- Tasks -- Activity 3.4: What's in Rust?Didactic Comments and Explanations -- Activity 3.5: Dividing Profits between PartnersWorksheet -- Description -- Activity 3.5: Dividing Profits between PartnersDidactic Comments and Explanations -- Comments and explanations for tasks -- CHAPTER 11: GROUP 4: STRETCHING AND SHRINKING: SCALING ACTIVITIES -- Activity 4.1: Wimpy in WonderlandWorksheet -- Activity 4.1: Wimpy in Wonderland -- Description -- Tasks -- Activity 4.1: Wimpy in WonderlandDidactic Comments and Explanations -- Comments and explanations for tasks -- Note -- Activity 4.2: The Beth-Shean TempleWorksheet -- Description -- Tasks -- Activity 4.2: The Beth-Shean TempleExtended Activities -- Tasks -- Activity 4.2: The Beth-Shean TempleDidactic Comments and Explanations -- Comments and explanations for tasks -- Activity 4.2: The Beth-Shean TempleExtended Activities -- Comments and explanations for tasks -- Activity 4.2: The Beth-Shean TempleConducting the Beth-Shean Temple Activity with Pre-service Student Teachers -- Activity 4.3: What's the Real Size?Worksheet -- Description -- Tasks -- Activities in the study -- Activity 4.3: What's the Real Size?Didactic Comments and Explanations -- Comments and explanations for tasks -- Activities in the study -- Activity 4.4: The PuzzleWorksheet -- Description.

Materials -- Tasks -- Activity 4.4: The PuzzleDidactic Comments and Explanations -- Comments and explanations for tasks -- Comments and explanations for worksheet questions -- Activity 4.5: The Thief, the Teacher and How They ConnectWorksheet -- Description -- Activity 4.5: The Thief, the Teacher and How They ConnectDidactic Comments and Explanations -- Comments and explanations for tasks -- Activity 4.6: The Giant SlayerWorksheet -- Description -- Task -- Activity 4.6: The Giant SlayerDidactic Comments and Explanations -- Comments and explanations for tasks -- Task -- Activity 4.7: The Reduction TriangleWorksheet -- Description -- Tasks -- Activity 4.7: The Reduction TriangleDidactic Comments and Explanations -- Comments and explanations for tasks -- CHAPTER 12: GROUP 5: INDIRECT PROPORTION ACTIVITIES -- Activity 5.1: How Heavy is the Meteoroid?Worksheet -- Description -- Tasks -- Activity 5.1: How Heavy is the Meteoroid?Didactic Comments and Explanations -- Comments and explanations for tasks -- Note -- Activity 5.2: Turn-of-the-Century BicycleWorksheet -- Description -- Tasks -- Activity 5.2: Turn-of-the-Century BicycleDidactic Comments and Explanations -- Comments and explanations for tasks -- Activity 5.3: Graduation Honors StageWorksheet -- Description -- Tasks -- Activity 5.3: Graduation Honors StageDidactic Comments and Explanations -- Comments and explanations for tasks -- CHAPTER 13: GROUP 6: ADDITIONAL ACTIVITIES FOR PRACTICE AND ENRICHMENT (ALL TOPICS) -- Additional Activities: Group 6-AFinding Ratio in Situations of Direct Proportion -- An example showing how to determine whether a new unit is generated. -- General description of the activities -- Specific comments and explanations for Group 6-A Activities: Finding Ratioin Situations of Direct Proportion.

Additional Activities: Group 6-BFinding Ratio in Situations of Indirect Proportion.