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El. knyga: Mastering Math Manipulatives, Grades K-3: Hands-On and Virtual Activities for Building and Connecting Mathematical Ideas

, (Mathematics Consultant)
  • Formatas: EPUB+DRM
  • Serija: Corwin Mathematics Series
  • Išleidimo metai: 26-Oct-2021
  • Leidėjas: Corwin Press Inc
  • Kalba: eng
  • ISBN-13: 9781071851128
  • Formatas: EPUB+DRM
  • Serija: Corwin Mathematics Series
  • Išleidimo metai: 26-Oct-2021
  • Leidėjas: Corwin Press Inc
  • Kalba: eng
  • ISBN-13: 9781071851128

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Put math manipulatives to work in your classroom and make teaching and learning math both meaningful and productive.

Would you like to bring math learning to life and make it more concrete, relevant, and accessible to your students? Do you wish you could do more with the manipulatives buried in your supply closet? Do you want to more effectively use virtual manipulatives in your distance learning? Whether physical or virtual, commercial or home-made, manipulatives are a powerful learning tool to help students discover and represent mathematical concepts.

Mastering Math Manipulatives includes everything you need to integrate math manipulativesboth concrete and virtualinto math learning. Each chapter of this richly illustrated, easy-to-use guide focuses on a different powerful tool, such as two-color counters, linking cubes, base ten blocks, fraction manipulatives, pattern blocks, tangrams, geometric solids, and others, and includes a set of activities that demonstrate the many ways teachers can leverage manipulatives to model and reinforce math concepts for all learners. It features:





Classroom strategies for introducing math manipulatives, including commercial, virtual, and hand-made manipulatives, into formal math instruction. Step-by-step instructions for 75 activities that work with any curriculum, including four-color photos, printable work mats, and demonstration videos. Handy charts that sort activities by manipulative type, math topic, domains aligned with standards, and grade-level appropriateness.

Its time to dive in and join in the journey toward making manipulatives meaningful so math learning is concrete, profound, and effective for your students! 

 

Recenzijos

"These exceptional books are overflowing with worthwhile activities. Going well beyond sharing ideas, they illuminate how manipulative(s) can be used to support mathematical thinking. A particularly important feature of this book is the ongoing discussion of making connections among representations. With such intentionality and engagement in multiple representations, we can ensure that every child become confident and competent in mathematics." -- Jennifer Bay-Williams "I expected to like this book, but I flat out love it! Whether you are a veteran teacher, a new teacher just starting your journey, or a parent trying to help your child at home, this book is a wonderful and practical resource. While manipulatives are clearly the star here, solid instructional strategies supported by just the right amount of research provide a strong supporting cast. Each chapter features a manipulative and includes ideas for organization, classroom management, distance learning, homemade alternatives, and multiple lessons highlighting the use of the manipulative. This is a book you will use all year long!" -- Donna Boucher "Every math teacher knows that using manipulatives is a good idea. Now, with Mastering Math Manipulatives, every math teacher can now how to use them best. It unpacks how different manipulatives work, provides rich tasks for using them, and teaches how to maximize their effectiveness. It includes virtual manipulatives! This is a must-have for every math teacher!" -- John SanGiovanni "I highly recommend Mastering Math Manipulatives. Manipulatives play a vital role in developing a solid conceptual understanding of the math. Not only do the authors share wonderful ideas of how to use a variety of manipulatives; they also share reasons why that manipulative is effective for the given topic as well as ways to further develop that concept. This resource is great for those who are new to using manipulatives as well as those who are experienced in using them." -- Kevin Dykema "Sara Delano Moore and Kimberly Rimbey have written a robust and immensely helpful guide to using manipulatives for profound student learning. In short, they have done all the deep, hard work laying out for us the intellectual and pedagogical queries we need to examine when considering using particular manipulativesor even in deciding to use manipulatives at all! And they have done so with insight on matters of attitude and mindset, the availability of student support, fair accessibility, the role of the virtual, and more. Practical. Readable. Concrete. This is a winner of a guide." -- James Tanton "Sara Delano Moore and Kimberly Rimbey masterfully show us why something we know works actually worksthat manipulatives are powerful and essential tools to help children learn mathematics. This book serves as a guide to help teachers in their classrooms and in their PLCs effectively make judicious use of manipulatives. Moore and Rimbey empower teachers to use sound learning theories to select the most appropriate manipulative for a particular topic and task. Mathematics educators can use this book to sharpen their mathematical knowledge for teaching and mathematics leaders can use this book as a reference for building curriculum framework documents and engaging in deep collegial coaching conversations. The best part? Students will benefit from a much deeper understanding of why the mathematics works as it does. Every mathematics teacher needs a highly dog-eared version of this book in their professional library!" -- Paul Gray "I thought I was aware of most everything I needed to know about the use of manipulatives in teaching mathematics at the elementary levelbut Sara Delano Moore and Kimberly Rimbey proved me wrong. Mastering Math Manipulatives: Hands-On and Virtual Activities for Building and Connecting Mathematical Ideas makes a significant contribution in several ways: First, it consistently links the various representations in a useful visual that reminds the reader what mental connections students should be making from this experience. The use of multiple representations is critical to support all students particularly those with special needs in mathematics as per the new IES Practice Guide. The book also is practical and full of "I can use this tomorrow" examples across multiple content areas. An important read." -- Karen S. Karp "Its always so gratifying to find a book filled with the answers to the questions we have asked over and over again. There is widespread belief in the power of concrete materials but the questions I hear are "Which manipulatives are best?", "Where and when do I fit them in?", "How do I best use them?", and "Why are there essential tools for learning?" This wonderful book answers each of these questions with clarity and classroom tested examples. Whether you teach, coach, or administrate in Grades 4 to 8, there is no doubt that the ideas and activities found in this book will strengthen the teaching and significantly enhance the learning of mathematics of your students." -- Steve Leinwand "As a mathematics coach and consultant I have visited dozens of math closets, those dusty corners of every school where you can find the tools you need to unlock hands-on, student-centered learning in your classroom. Mastering Math Manipulatives takes you to those places, yes, but it also takes you to the future with connections to virtual manipulatives, exploring the strengths and limitations of each. In this book you will find seasoned, practical advice and the kind of targeted lessons and directions you need to feel confident enough to dust off those tools and put them to good use. As I like to say, "Put your pencils down and get thinking!"" -- Kimberly Morrow-Leong "We educators spend a great deal of time researching, exploring, and consolidating all the elements that combine to support students as they develop and connect mathematical understandings. It is very exciting to have this uniquely comprehensive resource that unites what is critical and necessary for rich and engaging mathematics instruction, explicitly connecting the research base and mathematics concepts and processes with essential math manipulatives. Distinct and detailed visuals and clearly articulated activities are presented in a consistent format that is accessible to new and experienced teachers." -- Kathleen M. Morris "What a tremendous resource for teachers of mathematics! Sara Delano Moore and Kimberly Rimbey provide helpful tips and practical strategies for incorporating hands-on and virtual manipulatives into daily lessons. This book identifies a wealth of versatile manipulatives that can be used across grade levels and math domains, offers tips for planning and management, and shares sample lessons. And it includes critical discussions about making connections between varied representations to deepen students understanding of the math skill or concept. The organization of the book is easy to follow and allows teachers to jump in and out as needed to find just what works for their students. If you are looking for useful tips and effective strategies for incorporating hands-on and virtual manipulatives into your math teaching, this is the book for you!" -- Sue OConnell "Mastering Math Manipulatives is the perfect support to help teachers move beyond using manipulatives for play during recess. This book provides additional ideas and strategies for supporting students who are struggling by helping them learn and grow mathematically. The practical examples included in the book are helpful for preservice teachers as well." -- Cindy Beaman "Hands-on strategies are essential for student learning, and often natural for teachers in other contents. However, when it comes to math, the connection of hands-on tools to content and activity often seems fuzzy at best. There is finally the resource to connect the tool, the task, and the conceptual understanding together! These manipulatives-based activities provide the foundation for understanding that is essential for mathematics to make sense instead of being memorized. This book is a must for every teacher of mathematics!" -- Nanci Smith "This book is a great resource for assisting educators in teaching mathematics for understanding. It offers preservice teachers a foundation for their future teaching by giving them opportunities to learn math concepts more deeply and conceptually by using physical (or virtual) manipulatives. In-service teachers will find this book a valuable resource to enhance their mathematics curriculum. I applaud the authors for addressing issues of access to manipulatives (physical and virtual) as well as providing helping parents and caregivers understand the importance of manipulatives and how they can assist their children at home." -- Shelly M. Jones

Activities (by Topic) xv
Video List (by Activity Number) xix
About the Authors xx
Preface xxii
Acknowledgments xxiv
Introduction: We Know Manipulatives Matter, but ... 1(29)
What Are Manipulatives?
2(1)
Why Are Manipulatives Important for Students?
2(11)
Attributes of Manipulatives
13(5)
Considerations for Distance Learning
18(1)
Preparing to Use Manipulatives Effectively
18(5)
Managing Your Manipulatives
23(2)
Frequently Asked Questions
25(3)
Let's Go!
28(2)
Chapter 1 Two-Color Counters
30(36)
Activity 1.1 One-to-One Correspondence
32(2)
Activity 1.2 Cardinality
34(2)
Activity 1.3 More and Less
36(2)
Activity 1.4 Sorting and Counting
38(2)
Activity 1.5 Decomposing Numbers Into Pairs in More Than One Way
40(4)
Activity 1.6 Make a Ten
44(2)
Activity 1.7 Commutative Property of Addition With Two Colors
46(2)
Activity 1.8 Ten Ones and Some More Ones and One Group of Ten and Some More Ones
48(2)
Activity 1.9 Even and Odd
50(4)
Activity 1.10 Building Equal Groups for Multiplication
54(2)
Activity 1.11 Building Arrays for Multiplication
56(2)
Activity 1.12 Distributive Property of Multiplication Over Addition With Two-Color Counters
58(4)
Activity 1.13 Data Collection and Graphing
62(2)
Closing Reflection
64(2)
Chapter 2 Linking Cubes
66(26)
Activity 2.1 Linking Cubes as Counters
68(2)
Activity 2.2 Comparing Quantities (More and Less)
70(2)
Activity 2.3 Connecting Models to Number Lines Using Addition
72(2)
Activity 2.4 Representing Compare Problems With a Bar Model
74(2)
Activity 2.5 Associative Property of Addition With Three Towers
76(2)
Activity 2.6 "Groups Of" Multiplication
78(2)
Activity 2.7 Commutative Property of Multiplication (3 × 9 vs. 9 × 3)
80(2)
Activity 2.8 Division With Grouping
82(4)
Activity 2.9 Graphing Towers (Include Scaled Bar Graphs)
86(2)
Activity 2.10 Measuring Trains
88(2)
Closing Reflection
90(2)
Chapter 3 Cuisenaire® Rods
92(30)
Activity 3.1 Addend Pairs
94(2)
Activity 3.2 Creating Bar Models for Addition
96(4)
Activity 3.3 Creating Bar Models for Subtraction
100(4)
Activity 3.4 Exploring Multiplication
104(2)
Activity 3.5 Creating Bar Models for Equal Groups Multiplication and Division
106(4)
Activity 3.6 Commutative Property of Multiplication (2 × 3 vs. 3 × 2)
110(2)
Activity 3.7 Associative Property of Multiplication With 2 × 3 × 4
112(4)
Activity 3.8 Reasoning About Fractions
116(2)
Activity 3.9 Unit Fractions (Three One-Fourths Is the Same as Three-Fourths)
118(2)
Closing Reflection
120(2)
Chapter 4 Unit Squares
122(24)
Activity 4.1 Unit Squares as Counters
124(4)
Activity 4.2 Repeated Addition With Unit Squares
128(2)
Activity 4.3 Iterating Unit Squares to Find Area
130(2)
Activity 4.4 Connecting Iterated Unit Squares and Multiplication as Ways to Find Area
132(4)
Activity 4.5 Area Is Additive: Finding Areas of Rectilinear Figures
136(2)
Activity 4.6 Distributive Property of Multiplication Over Addition
138(4)
Activity 4.7 Same Area and Different Perimeters
142(3)
Closing Reflection
145(1)
Chapter 5 Base-Ten Blocks
146(34)
Activity 5.1 "Ten Ones and Some More Ones" vs. "One Ten and Some More Ones"
150(4)
Activity 5.2 Counting and Grouping to One Hundred
154(2)
Activity 5.3 Representing Two- and Three-Digit Numbers
156(2)
Activity 5.4 Representing Numbers as Quick Images
158(4)
Activity 5.5 Comparing Two-Digit Numbers
162(4)
Activity 5.6 Counting Up and Down by One, Ten, or One Hundred
166(4)
Activity 5.7 Adding With Base-Ten Blocks
170(2)
Activity 5.8 Subtracting With Base-Ten Blocks
172(4)
Activity 5.9 Multiplying by Multiples of Ten
176(3)
Closing Reflection
179(1)
Chapter 6 Pattern Blocks
180(20)
Activity 6.1 How Many Ways to Compose a Hexagon?
182(2)
Activity 6.2 Composing and Decomposing Larger Figures With Pattern Blocks
184(2)
Activity 6.3 How Many Ways to Compose a Given Value?
186(4)
Activity 6.4 Finding the Perimeter of Pattern-Block Shapes
190(2)
Activity 6.5 Equivalent Fractions With Pattern Blocks
192(4)
Activity 6.6 Attending to the "Whole" When Comparing Fractions
196(3)
Closing Reflection
199(1)
Chapter 7 Fraction Manipulatives (Towers, Circles, Tiles/Bars, and Squares)
200(34)
Activity 7.1 Whole Numbers as Fractions With Circles and Rectangles
204(4)
Activity 7.2 "One" as a Fraction
208(2)
Activity 7.3 Representing and Counting Unit Fractions
210(4)
Activity 7.4 Iterating Unit Fractions to Make a Whole
214(2)
Activity 7.5 Fraction Equivalence
216(2)
Activity 7.6 Comparing Fractions With Like Numerators
218(4)
Activity 7.7 Comparing Fractions With Like Denominators
222(4)
Activity 7.8 Building a Set of Fraction Bars
226(4)
Activity 7.9 Fractions on the Clock (Quarters and Halves)
230(3)
Closing Reflection
233(1)
Chapter 8 Tangrams and Geoboards
234(26)
Activity 8.1 Composing and Decomposing Shapes With Tangrams
238(2)
Activity 8.2 Examining Geometric Relationships by Building a Tangram Set
240(4)
Activity 8.3 Finding Relative Values of Tangram Pieces
244(2)
Activity 8.4 Finding Halves, Thirds, and Fourths on a Geoboard
246(4)
Activity 8.5 Same-Sized Parts Need Not Be the Same Shape
250(4)
Activity 8.6 Comparing Polygons on the Geoboard
254(2)
Activity 8.7 Finding the Area of a Rectilinear Figure on a Geoboard
256(3)
Closing Reflection
259(1)
Chapter 9 Geometric Solids
260(18)
Activity 9.1 Identifying Faces of Geometric Solids as Two-Dimensional Figures
264(2)
Activity 9.2 Describing Geometric Solids
266(4)
Activity 9.3 Composing Geometric Solids
270(2)
Activity 9.4 Solids With Curved Surfaces
272(2)
Activity 9.5 Attributes of Geometric Solids
274(2)
Closing Reflection
276(2)
Chapter 10 Continuing the Journey
278(4)
Glossary 282(2)
References 284(1)
Index 285
Sara Delano Moore is an independent mathematics education consultant at SDM Learning.  A fourth-generation educator, her work focuses on helping teachers and students understand mathematics as a coherent and connected discipline through the power of deep understanding and multiple representations for learning. Sara has worked as a classroom teacher of mathematics and science in the elementary and middle grades, a mathematics teacher educator, Director of the Center for Middle School Academic Achievement for the Commonwealth of Kentucky, and Director of Mathematics & Science at ETA hand2mind. Her journal articles appear in Mathematics Teaching in the Middle School, Teaching Children Mathematics, Science & Children, and Science Scope.

Kimberly Rimbey is an author, inventor, entrepreneur, speaker, consultant, coach, mentor, advocate, and, proudest of all, a teacher through and through. Kim currently serves as the Chief Learning Officer and CEO at KP® Mathematics and an Official Building Thinking Classrooms Consultant alongside Peter Liljedahl. A life-long teacher and learner, her hearts work centers on equipping teachers and helping them fall in love with teaching and learning over and over again. 

Always a teacher at heart, Kim has held several leadership positions, including Executive Director of Curriculum and Instruction, Chief Learning Officer, and Mathematica Program Area Coordinator. That said, everything Kim has done in her career is based on what she learned during her 18 years as a mathematics coach and classroom teacher. 

Kim is National Board Certified in Early Adolescent Mathematics, and she is a recipient of the Presidential Award for Excellence in Mathematics Teaching. Kim is the co-inventor of KP® Ten-Frame Tiles and has authored and co-authored several publications, including the Mastering Math Manipulatives and Meaningful Small Groups in Math for Corwin, Math Power: Simple Solutions for Mastering Math for the Rodel Foundation of Arizona, and, most recently, The Amazing Ten Frame series for KP Mathematics. 

Kim earned her BA in Elementary Education and Mathematics from Grand Canyon University, her M.Ed. degrees in Early Childhood Education and Educational Leadership from Arizona State University and Northern Arizona University, and her Ph.D. in Curriculum and Instruction from Arizona State University. Kim lives in Phoenix, Arizona, where she continues to inspire teachers and their leaders.