1.
Number Sense Routines: Building Numerical Literacy Every Day in Grades K-3
Just as athletes stretch their muscles before every game and musicians play scales to keep their technique in tune, mathematical thinkers and problem solvers can benefit from daily warm-up exercises. Jessica Shumway has developed a series of routines designed to help young students internalize and deepen their facility with numbers. The daily use of these quick five-, ten-, or fifteen-minute experiences at the beginning of math class will help build students' number sense.
Students with strong number sense understand numbers, ways to represent numbers, relationships among numbers, and number systems. They make reasonable estimates, compute fluently, use reasoning strategies (e.g., relate operations, such as addition and subtraction, to each other), and use visual models based on their number sense to solve problems. Students who never develop strong number sense will struggle with nearly all mathematical strands, from measurement and geometry to data and equations.
In Number Sense Routines, Jessica shows that number sense can be taught to all students. Dozens of classroom examples -- including conversations among students engaging in number sense routines -- illustrate how the routines work, how children's number sense develops, and how to implement responsive routines.
Additionally, teachers will gain a deeper understanding of the underlying math -- the big ideas, skills, and strategies children learn as they develop numerical literacy.
2.
Math Work Stations: Independent Learning You Can Count On, K-2
If you've ever questioned how to make math stations work, you'll find this photo-filled, idea-packed resource invaluable. This book extends Debbie Diller's best-selling work on literacy work stations and classroom design to the field of mathematics. In Math Work Stations you'll find ideas to help children develop conceptual understanding and skills, use math vocabulary as they talk about their mathematical thinking, and connect big ideas to meaningful independent exploration and practice. This book details how to set up, manage, and keep math stations going throughout the year. There's even a chapter devoted solely to organizing and using math manipulatives. Each chapter includes:
- key concepts based on NCTM and state math standards;
- math vocabulary resources and literature links;
- suggested materials to include at each station for the corresponding math content strand;
- ideas for modeling, troubleshooting, differentiating, and assessment; and
- reflection questions for professional development.
Throughout the book, Debbie has included hundreds of color photos showing math work stations in action from a variety of classrooms in which she has worked. Charts, reproducible forms, and math work stations icons are included to provide everything you'll need to get started with stations in your classroom right away.
3.
It Makes Sense! Using the Hundreds Chart to Build Number Sense, Grades K-2
Do you have a hundreds chart in your classroom? Every lesson and game in this resource supports teachers in making the most of the hundreds chart, helping their students develop strategies and build concepts needed for a robust understanding of numbers and place value. Includes connections to the Common Core State Standards for Mathematics.
4.
It Makes Sense!: Using Ten-frames to Build Number Sense, Grades K-2
From Look, Quick! to Mystery Sums, the 20 classroom-tested lessons in this resource provide friendly, meaningful support for using ten-frames. Many state standards require students to solve addition and subtraction problems using models. Ten-frames are one of the most important models that teachers can use to help students anchor to the landmark number ten and develop all aspects of number sense. Additionally, state standards expect that students be fluent and flexible in their ability to compute numbers. Ten-frames help students develop the skills they need to become flexible and fluent problem solvers.
The step-by-step lessons are presented in three categories:
* routines
* games
* problem-solving activities
The lessons are designed to provide students with opportunities to think, reason, and communicate about numbers. The lessons offer a wealth of teacher support, including:
* strategies for differentiating instruction;
* assessment rubrics;
* examples of student thinking;
* technology tips;
* teacher reflections; and
* reproducible ten-frames, ten-frame cards, and computation cards.
The step-by-step lessons are presented in three categories:
* routines
* games
* problem-solving activities
The lessons are designed to provide students with opportunities to think, reason, and communicate about numbers. The lessons offer a wealth of teacher support, including:
* strategies for differentiating instruction;
* assessment rubrics;
* examples of student thinking;
* technology tips;
* teacher reflections; and
* reproducible ten-frames, ten-frame cards, and computation cards.
5.
Critical Thinking Activities in Pattterns, Imagery, Logic: Mathematics, Grades K-3
Too often, thinking skills have been overlooked or considered extra, something above and beyond the basic that must be taught. Teachers need to recognize that thinking skills are basic and critical thinking activities should be considered indispensable to the education of every child.
These books present activities to help students develop their thinking and problem-solving skills using strategies that can help solve non-routine math problems. Students will use more than one strategy to arrive at a solution, and some of these strategies require that students use skills such as thinking visually, recognizing patterns, using logical reasoning, and doing organized counting—all of which are elements of critical thinking in mathematics.
Critical Thinking Activities can be used as a supplement to an existing math curriculum to introduce, reinforce, and elaborate on specific critical thinking skills. The pages are designed to be reproduced for students to use as individual worksheets or problem cards.
6.
Mastering the Basic Math Facts in Addition and Subtraction: Strategies, Activities, and Interventions to Move Students Beyond Memorization
"When math fact instruction is thoughtful and strategic, it results in more than a student's ability to quickly recall a fact; it cultivates reflective students who have a greater understanding of numbers and a flexibility of thinking that allows them to understand connections between mathematical ideas."
-Susan O'Connell and John SanGiovanni
-Susan O'Connell and John SanGiovanni
In today's math classroom, we want children to do more than just memorize math facts. We want them to understand the math facts they are being asked to memorize. Our goal is automaticity and understanding; without both, our children will never build the foundational skills needed to do more complex math. Both the Common Core State Standards and the NCTM Principles and Standards emphasize the importance of understanding the concepts of addition and subtraction. Susan O'Connell and John SanGiovanni provide insights into the teaching of basic math facts, including a multitude of instructional strategies, teacher tips, and classroom activities to help students master their facts while strengthening their understanding of numbers, patterns, and properties.
Designed to be easily integrated into your existing math program, Mastering the Basic Math Facts:
- emphasizes the big ideas that provide a focus for math facts instruction
- broadens your repertoire of instructional strategies
- provides dozens of easy-to-implement activities to support varied levels of learners
- stimulates your reflection related to teaching math facts.
Through investigations, discussions, visual models, children's literature, and hands-on explorations, students develop an understanding of the concepts of addition and subtraction, and through engaging, interactive practice achieve fluency with basic facts.
Whether you're introducing your students to basic math facts, reviewing facts, or providing intervention for struggling students, this book will provide you with insights and activities to simplify this complex, but critical, component of math teaching.
Extensive online resources include customizable activities, templates, recording sheets, and teacher tools (such as multiplication tables, game templates, and assessment options) to simplify your planning and preparation. Over 450 pages of reproducible forms are included in English and Spanish translations.
A study guide for Professional Learning Communities and book clubs is also included.
7.
Well Played, K-2: Building Mathematical Thinking Through Number Games and Puzzles, Grades K-2
Students love math games and puzzles, but how much are they really learning from the experience? Too often, math games are thought of as just a fun activity or enrichment opportunity. Well Played shows you how to make games and puzzles an integral learning component that provides teachers with unique access to student thinking.
The twenty-five games and puzzles in Well Played, which have all been field-tested in diverse classrooms, contain:
explanations of the mathematical importance of each game or puzzle and how it supports student learning;
variations for each game or puzzle to address a range of learning levels and styles;
clear step-by-step directions; and
classroom vignettes that model how best to introduce the featured game or puzzle.
The book also includes a separate chapter with suggestions for how to effectively manage games and puzzles in diverse classrooms; reproducibles that provide directions, game boards, game cards, and puzzles; assessment ideas; and suggestions for online games, puzzles, and apps.
Well Played will help you tap the power of games and puzzles to engage students in sustained and productive mathematical thinking.
8.
Math Exchanges: Guiding Young Mathematicians in Small Group Meetings
Traditionally, small-group math instruction has been used as a format for reaching children who struggle to understand. Math coach Kassia Omohundro Wedekind uses small-group instruction as the centerpiece of her math workshop approach, engaging all students in rigorous math exchanges. The key characteristics of these mathematical conversations are that they are: 1) short, focused sessions that bring all mathematical minds together, 2) responsive to the needs of the specific group of mathematicians, and 3) designed for meaningful, guided reflection.
As in reading and writing workshop, students in Kassia's math workshop are becoming self-directed and independent while participating in a classroom community of learners. Through the math exchanges, students focus on number sense and the big ideas of mathematics. Teachers guide the conversations with small groups of students, mediating talk and thinking as students share problem-solving strategies, discuss how math works, and move toward more effective and efficient approaches and greater mathematical understanding.
Although grounded in theory and research, Math Exchanges is written for practicing teachers and answers such questions as the following: How can I use a math workshop approach and follow a certain textbook or set of standards? How should I form small groups? and How often should I meet with small groups? What should I focus on in small groups? How can I tell if my groups are making progress? What do small-group math exchanges look like, sound like, and feel like?
9.
Differentiated Math Learning Centers: 35 Independent Centers That Keep Kids Learning While You Teach Small Guided Math Groups
In this book, veteran teacher Deborah Wirth shares her teaching and management tips for keeping the rest of the class is engaged in meaningful work while you meet with small guided math groups. The 35 centers she created address one-to-one correspondence, place value, money, patterns, shapes, symmetry, measurement, and more. Each center accommodates a variety of activities, so students can work at the skill level that’s right for them. An invaluable resource for any teacher differentiating math instruction in the primary grades. For use with Grades K-2.
10.
The Double-Decker Bus: Early Addition and Subtraction (Contexts for Learning Mathematics, Grade K-3: Investigating Number Sense, Addition, and Subtraction)
The Double Decker Bus: Early Addition and Subtractionis one of eight units in the Contexts for Learning Mathematics' Investigating Number Sense, Addition, and Subtraction (K-3)
This unit begins with the story of a double-decker bus-a bus that has two decks with ten seats on each. Five seats on each deck are red and five seats are white. The bus goes by quickly and the little girl in the story, sitting at her bedroom window and watching, works out ways to use the colors of the seats to calculate quickly how many people are on the bus. Her father drives a double-decker bus and she helps him figure out a way to know how many empty seats there are on the top deck even though he can't see them.
The unit introduces the arithmetic rack as a powerful model and tool to act out the story. The arithmetic rack is a calculating frame consisting of two rows of ten beads-two sets of five (one red and one white) in each row. (Instructions for creating or buying your own arithmetic racks are included.)
Cognitive psychologists, such as Susan Carey and Stanislas Dehaene (1999), have shown that even toddlers can recognize small amounts, such as two or three, as a unit and that this ability (known as "subitizing") is probably innate. Children can even do addition and subtraction with amounts of this size because they use this innate perceptual ability to see that three is one more than two. Using the arithmetic rack allows kindergarteners and first graders to build on their natural ability and see five as a unit. When five can be subitized as a whole, it can be used to support understanding of 6 as 5 + 1, 8 as 5 + 3, or 4 as 5 - 1. The arithmetic rack also supports the strategies of doubles and near doubles, 6 + 7 = 6 + 6 + 1, and making tens, 9 + 6 = 10 + 5.
In this unit, children move the beads on the arithmetic rack to represent passengers going from one deck on the bus to the other, and sitting in various combinations in the red and white seats. This context supports the development of the understanding that numbers can be named in many ways, for example 10 as 6 + 4, 7 + 3, or 5 + 5. The unit also includes minilessons with quick images, and strings of related addition and subtraction problems solved with the arithmetic rack to help automatize the basic facts.
Several games-Passenger Pairs, Rack Pairs, and Passenger Combos-are also included in this unit. They can be played throughout the year as a way for children to extend composing and decomposing strategies as they establish equivalence-for example, representing 7 as 5 + 2, 3 + 4, or 1 + 6 (Treffers, 1991).
To learn more visit http://www.contextsforlearning.com
11.
Games for Early Number Sense: A Yearlong Resource (Contexts for Learning Mathematics)
Games for Early Number Sense is one of three yearlong resource guides in Contexts for Learning Mathematics' Investigating Number Sense, Addition, and Subtraction (K - 3)
Games for Early Number Sense contains 24 games that you can choose from as you consider the needs of your students. The unit includes notes for each game describing the mathematical landscape - the possibilities and openings for learning that can occur as children play. Sample dialogues are interspersed throughout to help you anticipate what learners might say and do and to provide you with images of teachers and children at work. The games foster the development of early number sense and addition, including the basic facts, and are appropriate for K - 1.
To learn more visit http://www.contextsforlearning.com
12.
Organizing and Collecting: The Number System (Contexts in Learning Mathematics, Grades K-3: Investigating Number Sense, Addition, and Subtraction)
Organizing and Collecting: The Number Systemis one of eight units in the Contexts for Learning Mathematics' Investigating Number Sense, Addition, and Subtraction (K-3)
This unit begins with the story of the Masloppy family-an endearing, large family that finds it difficult to keep track of things. Everyone is forever losing, misplacing, and looking for things. One of the children, Nicholas, decides to sort, organize, and take inventory of things in the house. He counts and bundles materials and labels containers and baskets, and life in the Masloppy household is smoother thereafter.
The idea of taking inventory is brought to the classroom, where children work to count and label baskets of supplies and materials. The discussion focuses on organizing in groups and skip counting, then specifically on groups of ten. The concept of place value is developed as the children pack objects into groups of ten and study patterns in the data. There are opportunities to deepen their understanding by packing in fives and playing games that focus on groups of ten, and there are minilessons that use the ten-frame as a visual model of five and ten. (The structure of the ten-frame is similar to that of the arithmetic rack, which is discussed in The Double-Decker Bus (previous unit).Both units use five and ten as landmark numbers: the arithmetic rack has four groups of five arranged in two rows of ten, the ten frame has two groups of five. The ten-frame is used in this unit because it resembles the context of packing more closely.) In the second week the inventory context is extended to include ordering more classroom supplies as a way to develop and support addition strategies, which include jumping to friendly numbers (multiples of ten) and jumping by ten.
As children pack and count groups of items, they begin to unitize-to count groups and objects at the same time. Children develop an understanding of place value as they construct the idea that the number of packs and loose items is related to the total number of objects and that the numbers change when items are added to make full packs or when a pack of ten is added.
The game Collecting Stamps and its variations are included in this unit. These can be played throughout the year as a way for children to develop place value and addition strategies. The game and its variations extend composing and decomposing strategies while promoting understanding of equivalence-for example, representing 26 + 8 as equal to 26 + 4 + 4.
To learn more visit http://www.contextsforlearning.com
