The SIOP Model for Teaching Mathematics to English Learners

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Enhance your Mathematics content instruction with the SIOP Model and transform the academic English and mathematics skills of your English learners.

Based on the best-selling resource, Making Content Comprehensible for English Learners: The SIOP Model by acclaimed authors Jana Echevarria, MaryEllen Vogt, and Deborah Short; teachers, coaches, and intervention teachers have access to research-based, SIOP-tested techniques for lessons specifically for the mathematics classroom. This highly anticipated book, The SIOP Model for Teaching Mathematics to English Learners addresses the issues faced in teaching math to English learners (ELs) at each grade-level. SIOP techniques and activities organized around the eight SIOP components guide educators in promoting academic language development along with comprehensible mathematics content.

Written for SIOP teachers and those who have learned the SIOP Model, this book includes proven, effective math lessons and comprehensive units designed by SIOP math educators Araceli Avila and Melissa Castillo. In addition, this book provides ideas to adapt the techniques for students at different levels of English proficiency. This book is sure to become an indispensable resource for math educators of English learners.

  • Presents a systematic process for teaching both the academic content of mathematics and its associated academic language to English learners.
  • Offers ideas and activities about teaching mathematics and organizes activities by grade-bands—K-2, 3-5 (or 6), 6-8, and 9-12 and SIOP components.
  • Provides use-tomorrow ideas and activities for implementing the eight components of the SIOP Model in a mathematics classroom.
  • Includes lesson plans and comprehensive units that illustrate how a particular activity can be effective for ALL students, not just English learners.
  • Create the ideal SIOP classroom with other resourcesfrom the SIOP Model Series: 99 Ideas and Activities for Teaching English Learners with the SIOP Model; Implementing the SIOP Model through Effective Coaching and Professional Development; The SIOP Model for Administrators; Making Content Comprehensible for Elementary English Learners; and Making Content Comprehensible for Secondary English Learners ; The SIOP Model for Teaching Math to English Learners; The SIOP Model for Teaching Social Studies to English Learners; and The SIOP Model for Teaching Science to English Learners (all published by Pearson)
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Product Details

  • ISBN-13: 9780205627585
  • Publisher: Pearson
  • Publication date: 10/16/2009
  • Series: SIOP Series
  • Edition description: New Edition
  • Pages: 192
  • Sales rank: 408,650
  • Product dimensions: 8.40 (w) x 10.80 (h) x 0.50 (d)

Meet the Author

Deborah J. Short is a professional development consultant and a senior research associate at the Center for Applied Linguistics in Washington, DC. She co-developed the SIOP® Model for sheltered instruction and has directed national research studies on English language learn-ers funded by the Carnegie Corporation, the Rockefeller Foundation, and the U.S. Dept. of Education. She recently chaired an expert panel on adolescent ELL literacy. As the director of Academic Language Research & Training, Dr. Short provides professional development on sheltered instruction and academic literacy around the U.S. and abroad. She has numerous publications, including the SIOP® book series and five ESL textbook series for National Geographic/Hampton-Brown. She has taught English as a second/foreign language in New York, California, Virginia, and the Democratic Republic of Congo.

Jana Echevarría is a Professor Emerita at California State University, Long Beach. She has taught in elementary, middle, and high schools in general education, special education, ESL, and bilingual programs. She has lived in Taiwan, Spain and Mexico. An internationally known expert on second language learners, Dr. Echevarría is a Fulbright Specialist. Her research and publications focus on effective instruction for English learners, including those with learning disabilities. Currently, she is Co-Principal Investigator with the Center for Research on the Educational Achievement and Teaching of English Language Learners (CREATE) funded by the U.S. Department of Education, Institute of Education Sciences (IES). In 2005, Dr. Echevarría was selected as Outstanding Professor at CSULB.

MaryEllen Vogt, Ed.D., is Professor Emerita of Education at California State University, Long Beach. MaryEllen has been a classroom teacher, reading specialist, special education specialist, curriculum coordinator, and university teacher educator. She received her doctorate from the University of California, Berkeley, and is a co-author of fifteen books, including Reading Specialists and Literacy Coaches in the Real World (3rd ed., 2011) and the SIOP® book series. Her research interests include improving comprehension in the content areas, teacher change and development, and content literacy and language acquisition for English learners. She was inducted into the California Reading Hall of Fame, received her university’s Distinguished Faculty Teaching Award, and served as President of the International Reading Association in 2004–2005.

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Table of Contents



Chapter 1: Introduction and Review of the SIOP MODEL

Chapter 2: The Academic Language of Mathematics

Chapter 3: Activities and Techniques for Planning SIOP Mathematics Lessons

Chapter 4: Lesson and Unit Design for SIOP Mathematics Lessons

Chapter 5: Pulling It All Together

Appendix A: SIOP Model Components and Features


Key Components of the SIOP Model

1. Lesson Preparation

2. Building Background

3. Comprehensible Input

4. Strategies

5. Interaction

6. Practice & Application

7. Lesson Delivery

8. Review & Assessment

Why Is the SIOP Needed Now?

Organization and Purpose of This Book


What is Academic Language?

How Does Academic Language Fit Into the SIOP Model?

How Is Academic Language Manifested in Classroom Discourse?

Why Do English Learners Have Difficulty with Academic Language?

How Can We Effectively Teach Academic Language In Mathematics?

The Role of Discussion and Conversation in Developing Academic Language

What is the Academic Language of Mathematics?

In Summary

Appendix B Academic Math Vocabulary Based on NCTM Content and Process Standards


LESSONS By Araceli Avila and Melissa Castillo


Lesson Plan Format

Math Techniques and Activities

SIOP Math Techniques and Activities: Lesson Preparation

Number 1-3 for Self Assessment of Objectives

SIOP Lesson Plan

BLM 3.1 What Do You Know About Geometric Shapes?

SIOP Math Techniques and Activities: Building Background

4 Corners Vocabulary Chart

KWL Chart

SIOP Lesson Plan

SIOP Math Techniques and Activities: Comprehensible Input

Math Representations Graphic Organizer

BLM 3.2 Math Representations Graphic Organizer

SIOP Lesson Plan

SIOP Math Techniques and Activities: Strategies

You Are the Teacher

SIOP Lesson Plan

BLM 3.3 Let’s Measure

Vocabulary Alive

SIOP Lesson Plan

SIOP Math Techniques and Activities: Interaction

Conga Line

Group Responses with a White Board

SIOP Lesson Plan

Find Your Match

SIOP Math Techniques and Activities: Practice & Application


SIOP Math Techniques and Activities: Review & Assessment

Find Someone Who

SIOP Lesson Plan

BLM 3.4 Colored Triangles

In Summary


By Araceli Avila and Melissa Castillo


Math unit-grades k-2

Overview of the unit

SIOP Planning Flow Chart

SIOP Lesson Plan-Day 1

BLM 1.1 Vocabulary Activity Sheet

SIOP Lesson Plan-Days 2-3

BLM 2.1 Let’s Measure the Length of…

SIOP Lesson Plan-Day 4

BLM 4.1 Measuring Length and Distance

SIOP Lesson Plan-Day 5

Math Unit-Grades 3-5

Overview of the unit

SIOP Planning Flow Chart

SIOP Lesson Plan-Day 1

BLM 1.1 4-Corners Vocabulary Activity Sheet

BLM 1.2 Shape Characteristics

SIOP Lesson Plan-Days 2

BLM 2.1 Colored Triangles

SIOP Lesson Plan-Day 3-4

SIOP Lesson Plan-Day 5

Math Unit-Grades 6-8

Overview of the unit

SIOP Planning Flow Chart

SIOP Lesson Plan-Day 1-2

BLM 1.1 Integer Dollar Cards

BLM 2.1 Lab Sheet

BLM 2.2 Instruction for Who is Colder? Card Game

SIOP Lesson Plan-Days 3

BLM 3.1 Integers Venn Diagram

BLM 3.2 Weather News Transparency

BLM 3.3 Adding Integers Lab Sheet

BLM 3.4 Simultaneous Round Table Activity Sheet

SIOP Lesson Plan-Day 4

BLM 4.1 Subtracting Integers Lab Sheet

BLM 4.2 Fun With Integers Instructions

BLM 4.3 Fun With Integers Recording Sheet

SIOP Lesson Plan-Day 5

BLM 5.1 Where is The Submarine?

BLM 5.2 Applying Integers Lab Sheet

Math Unit-Grades 9-12

Overview of the Unit

SIOP Planning Flow Chart

SIOP Lesson Plan-Days 1-2

BLM 1.1 Math Representations Graph Organizer

SIOP Lesson Plan-Day 3

BLM 3.1 Tiling Squared Pools

BLM 3.2 Fencing Gardens

BLM 3.3 Layers Galore

BLM 3.4 Function Matrix

SIOP Lesson Plan-Day 4

BLM 4.1 Translating Parent Functions Lab Sheet

BLM 4.2 Ordered Pairs for Quadratic Parent Function

BLM 4.3 Ordered Pairs for Linear Parent Function

BLM 4.4 Ordered Pairs for Exponential Parent Function

SIOP Lesson Plan-Day 5

BLM 5.1 Go To Your Corner Cards

BLM 5.2 Multiplying x by -1 < a < 0

BLM 5.3 Multiplying x by 0 < a < 1

BLM 5.4 Multiplying a by > 1

BLM 5.5 Multiplying x by a < -1

BLM 5.6 Multiplying x by -1

BLM 5.7 Combining Transformations



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