In this volume, students will learn how to work strategically with ten frames and a Rekenrek in order to:

Subitize within 5, 10, 20, and 100,

Compose & decompose numbers in groups of 1’s and 10’s,

See 6 – 10 as 5 + (something), and 11-20 as 10 + (something), and

Partition numbers (especially 10) into all possible combinations.

This lays the foundation for the next book where students will learn to rearrange numbers into instantly recognizable amounts, so that addition becomes much less about counting and much more about just seeing the answers.

A condensed version is also available for older students who may need a review of or introduction to subitizing, composing and decomposing numbers up to 100, combinations of 10, and place value using ten frames and a Rekenrek.

Before students learn how to think strategically about addition, they usually resort to either memorizing facts or counting to get the answer.

The addition strategies in this book help students move away from counting and into strategies that rely on subitizing skills and empower them to do less work with more understanding. The activities here train them to get to a point where they can instantly SEE the answers.

When students are faced with a litany of facts to memorize or numerous disjointed, isolated strategies, they can easily get overwhelmed, frustrated, or develop Math anxiety.

This book focuses on simplicity and consistency. Students will master addition through the use of just two manipulatives and four core strategies, with two bonus strategies, that help them make sense of numbers and empower them to think flexibly about ways to regroup numbers into instantly recognizable arrangements.

This book aims to build flexible mathematical thinkers who can discover patterns, stretch strategies, build on prior knowledge, and find solutions – confidently, efficiently, and happily.

This book, the 3rd in the Framework Math series, focuses on subtraction but also includes more advanced addition strategies than were covered in Volume 2.

This book continues the Concrete-Pictorial-Abstract (CPA) journey with the use of ten frames and a Rekenrek. For subtraction, two extra tools are added as well: a 120 chart and number lines. These extra tools unlock new strategies and increase students’ ability to flexibly manipulate numbers in ways that make operations easier.

When students learn to see patterns, draw connections, and ask WHY and HOW things work the way they do, they’ll develop a solid foundation in Math.

Without needing to focus on memorization, students will develop confidence in their ability to understand Math. This approach that is grounded in number sense will help them see the overall cohesive, fluid nature of Math; students will see relationships between addition and subtraction as well as see how numbers can be regrouped or adjusted to friendlier numbers in ways that make Math both easier and more meaningful.

It is these connections, not an approach based purely on memorization, that help students retain and own the information and extend their understanding to more complex Mathematical problems.

It is highly recommended that students of all ages use Volume 1 (complete or condensed version) before using this book. If students are struggling with Addition and Subtraction, those books will also be very helpful as a foundation for this book.

Brief summary: Before students learn how to think strategically about multiplication, they usually resort to memorizing facts through “tricks” or invented songs or stories with the hope that this bank of facts can be used in a “plug and play” approach in the standard algorithm for multi-digit multiplication.

This approach might work, if students are good at memorizing facts and procedures.

However, students will miss a very large portion of the “Developing Number Sense” journey if they just focus on instant recall of single-digit facts and then jump straight into the traditional algorithm, working with every digit of each number in isolation as they run the numbers through a gauntlet of mysterious procedures.

This entire book is strategically designed to help students build connections between numbers and operations as well as discover strategies that they can stretch to use with larger numbers. And it's all based on one simple skill: doubling numbers.

Intrigued? Come and See!

This book, the 5th in the Framework Math series, covers the division facts within 100 up through long division. All the skills covered in the first 4 books of this series should be mastered before beginning this book so that students are completely comfortable and confident subitizing, composing, and decomposing numbers up to 100 and have a clear understanding of place value, as well as adding, subtracting, and multiplying whole numbers of all sizes. They should also be very familiar by this point with how to strategically use ten frames and a Rekenrek as tools to accomplish all these goals. In this book, that foundation will serve students well as they develop a deep understanding of, and fluency with, division.

Here students will discover fact family relationships as well as learn division strategies using area models, partial products, benchmark numbers, and the traditional U.S. algorithm. These strategies will help them see numbers as whole units and enable them to think intuitively through the division process, rather than seeing numbers as combinations of individual digits with sets of mysterious rules to follow. This approach that is grounded in number sense will help students retain and own the information and extend their understanding to more complex Mathematical problems, as well as see the overall cohesive, fluid nature of Math.