Lobato, Joanne
Developing essential understanding of ratios, proportions, and proportional reasoning for teaching mathematics in grades 6-8 / Joanne Lobato, San Diego University, San Diego, California, Amy B. Ellis, University of Wisconsin-Madison, Madison, Wisconsin ; Randall I. Charles, volume editor, Carmel, California ; Rose Mary Zbiek, series editor, The Pennsylvania State University, University Park, Pennsylvania. - Fifth printing 2016. - x, 88 pages: illustrations ; 26 cm. - Essential Understanding Series. . - Essential Understanding Series. .
Includes bibliographical references (pages 87-88).
Why Ratios, Proportions, and Proportional Reasoning? -- Understanding Ratios and Proportional Reasoning -- Big Ideas and Essential Understandings -- Benefits for Teaching, Learning, and Assessing. Introduction. Proportional Reasoning Method 1 -- Proportional Reasoning Method 2 -- One Big Idea and Multiple Essential Understandings -- Essential Understandings 1 -- Essential Understandings 2 -- Essential Understandings 3 -- Essential Understandings 4 -- Essential Understandings 5 -- Essential Understandings 6 -- Essential Understandings 7 -- Essential Understandings 8 -- Essential Understandings 9 -- Essential Understandings 10 -- Conclusion. Chapter 1 Ratios, Proportions, and Proportional Reasoning: The Big Idea and Essential Understandings. Using the Essential Understandings to Reason about Linear Functions, Algebraic Equations, and Slope -- Grounding Measurement in Proportional Reasoning -- Grounding Measurement in Proportional Reasoning -- Foundations of Proportional Reasoning in the Elementary Grades. Chapter 2 Connections: Looking Back and Ahead in Learning. Helping Students Make Transitions to Become Proportional Reasoners -- The Role of Informal Assessment -- Conclusion. Chapter 3 Challenges: Learning, Teaching, and Assessing.
How do you refute the erroneous claim that all ratios are fractions? This book goes beyond a simple introduction to ratios, proportions, and proportional reasoning. It will help broaden and deepen your mathematical understanding of one of the most challenging topics for students and teachers to grasp. It will help you engage your students, anticipate their perplexities, help them avoid pitfalls, and dispel misconceptions. You will also learn to develop appropriate tasks, techniques, and tools for assessing your students understanding of the topic.
Essential Understanding Series topics: Number and Numeration for Grades Pre-K 2 Addition and Subtraction for Grades Pre-K 2 Geometry for Grades Pre-K 2 Reasoning and Proof for Grades Pre-K 8 Multiplication and Division for Grades 3 5 Rational Numbers for Grades 3 5 Algebraic Ideas and Readiness for Grades 3 5 Geometric Shapes and Solids for Grades 3 5 Ratio, Proportion, and Proportionality for Grades 6 8 Expressions and Equations for Grades 6 8 Measurement for Grades 6 8 Data Analysis and Statistics for Grades 6 8 Function for Grades 9 12 Geometric Relationships for Grades 9 12 Reasoning and Proof for Grades 9 12 Statistics for Grades 9 12
"synopsis" may belong to another edition of this title.--backover. https://www.abebooks.com/9780873536226/Developing-Essential-Understanding-Ratios-Proportions-0873536223/plp
9780873536226
Mathematics
Mathematics--Study and teaching
Mathematics --Study and teaching (middle school)--Standards --United States
Middle school education
Middle school education --Curricula --Standards --United States
Curriculum planning
Curriculum planning --Standards --United States
QA135.6 / .L63 2016
Developing essential understanding of ratios, proportions, and proportional reasoning for teaching mathematics in grades 6-8 / Joanne Lobato, San Diego University, San Diego, California, Amy B. Ellis, University of Wisconsin-Madison, Madison, Wisconsin ; Randall I. Charles, volume editor, Carmel, California ; Rose Mary Zbiek, series editor, The Pennsylvania State University, University Park, Pennsylvania. - Fifth printing 2016. - x, 88 pages: illustrations ; 26 cm. - Essential Understanding Series. . - Essential Understanding Series. .
Includes bibliographical references (pages 87-88).
Why Ratios, Proportions, and Proportional Reasoning? -- Understanding Ratios and Proportional Reasoning -- Big Ideas and Essential Understandings -- Benefits for Teaching, Learning, and Assessing. Introduction. Proportional Reasoning Method 1 -- Proportional Reasoning Method 2 -- One Big Idea and Multiple Essential Understandings -- Essential Understandings 1 -- Essential Understandings 2 -- Essential Understandings 3 -- Essential Understandings 4 -- Essential Understandings 5 -- Essential Understandings 6 -- Essential Understandings 7 -- Essential Understandings 8 -- Essential Understandings 9 -- Essential Understandings 10 -- Conclusion. Chapter 1 Ratios, Proportions, and Proportional Reasoning: The Big Idea and Essential Understandings. Using the Essential Understandings to Reason about Linear Functions, Algebraic Equations, and Slope -- Grounding Measurement in Proportional Reasoning -- Grounding Measurement in Proportional Reasoning -- Foundations of Proportional Reasoning in the Elementary Grades. Chapter 2 Connections: Looking Back and Ahead in Learning. Helping Students Make Transitions to Become Proportional Reasoners -- The Role of Informal Assessment -- Conclusion. Chapter 3 Challenges: Learning, Teaching, and Assessing.
How do you refute the erroneous claim that all ratios are fractions? This book goes beyond a simple introduction to ratios, proportions, and proportional reasoning. It will help broaden and deepen your mathematical understanding of one of the most challenging topics for students and teachers to grasp. It will help you engage your students, anticipate their perplexities, help them avoid pitfalls, and dispel misconceptions. You will also learn to develop appropriate tasks, techniques, and tools for assessing your students understanding of the topic.
Essential Understanding Series topics: Number and Numeration for Grades Pre-K 2 Addition and Subtraction for Grades Pre-K 2 Geometry for Grades Pre-K 2 Reasoning and Proof for Grades Pre-K 8 Multiplication and Division for Grades 3 5 Rational Numbers for Grades 3 5 Algebraic Ideas and Readiness for Grades 3 5 Geometric Shapes and Solids for Grades 3 5 Ratio, Proportion, and Proportionality for Grades 6 8 Expressions and Equations for Grades 6 8 Measurement for Grades 6 8 Data Analysis and Statistics for Grades 6 8 Function for Grades 9 12 Geometric Relationships for Grades 9 12 Reasoning and Proof for Grades 9 12 Statistics for Grades 9 12
"synopsis" may belong to another edition of this title.--backover. https://www.abebooks.com/9780873536226/Developing-Essential-Understanding-Ratios-Proportions-0873536223/plp
9780873536226
Mathematics
Mathematics--Study and teaching
Mathematics --Study and teaching (middle school)--Standards --United States
Middle school education
Middle school education --Curricula --Standards --United States
Curriculum planning
Curriculum planning --Standards --United States
QA135.6 / .L63 2016