enVision Integrated Mathematics Curriculum

enVision® Integrated Mathematics is a high school math program that uses the successful, research-proven lesson organization of the enVision math series to bring problem-based learning and visual learning to an integrated mathematics curriculum. enVision Integrated Mathematics is used by classrooms across the country and around the world. enVision Integrated Mathematics provides students with real world contexts that connect math concepts to their daily experiences, opportunities to build skills for communicating math ideas, and a pedagogy that ensures true conceptual understanding.

enVision Integrated Mathematics’ lesson design is unique and effective. Lessons start with Explore, featuring Problem-Based Learning (PBL), where students must think critically about a real-world math problem, evaluate options, collaborate, and present solutions. This is followed by Understand & Apply which incorporates visually rich examples to highlight the underlying math concepts; then Practice & Problem Solving solidifies student understanding. It’s the best way to help kids better understand math ideas.

The program is made up of the following:

• Teacher’s Edition - Available in digital or print, the Teacher’s Edition includes wrap-around pages that provide direct instruction and teaching suggestion to engage students. The Interactive Teacher’s Edition online features annotation models and downloadable lesson resources.
• Student Edition - Interactive Student Edition - available in digital or print format.
• Student Companion - A write-in student worktext that actively engages students with lessons in the classroom or at home and fosters conceptual understanding with Habits of Mind questions. This workbook helps students solidify their understanding and record their thoughts, strategies, and understanding
• enVision Integrated Mathematics Digital - enVision Integrated Mathematics digital courseware on Savvas Realize™ includes robust digital tools that give teachers flexibility to use a digital, print, or blended format in their classrooms. Teachers can customize the program to rearrange content, upload their own content, add links to online media, and edit resources and assessments. All program resources, including personalized practice remediation, and assessments are available in one location for easy lesson planning and presentation. Students will use technology to interact with text and activities, and they can write directly in their digital Student Edition to make interaction with text more meaningful. Students will engage in activities that will inspire conceptual understanding, classroom discourse, and build their mathematical thinking skills, while learning to formulate and defend their own opinions. The unique integration of Desmos into digital lessons offers an interactive experience designed to bring concepts to life through highly visual interactives.

The learning model in the enVision program–problem-based learning, visual learning, and data-driven differentiated instruction–has been researched and verified as effective. Core instruction used for every lesson has been shown to be effective for developing conceptual understanding.

enVision Integrated Mathematics features comprehensive differentiated instruction and intervention support to allow access for all students. The program’s balanced instructional model provides appropriate scaffolding, differentiation, intervention, and support for a broad range of learners, and is designed to facilitate conceptual understanding of mathematics for students at a range of learning levels.

Comprehensive, built-in differentiation resources support all levels of learners and ELLs, including students with learning disabilities, through personalized, adaptive learning.

The program meets a variety of student needs and provides Response to Intervention (RtI) during each lesson, at the end of each lesson, at the end of each Topic, and any time as indicated in the Teacher’s Edition. A description of RtI tiered instructional resources for the program is included in the Teacher’s Program Overview for each grade. The following are examples of tiered instructional support found online for each lesson.

Tier 1 ongoing Intervention includes the following resources that can be used during the lesson:

• Prevent Misconceptions. During the Visual Learning Example, a remediation strategy is included to address about the lesson concept.
• Error Intervention (If… Then…). During Practice & Problem Solving, error intervention identifies a common error and provides remediation strategy. Reteaching Set. This set is provided before independent practice to develop understanding prior to practice.
• MathXL for School: Practice & Problem Solving, during the lesson, includes personalized practice for the Practice & Problem Solving portion of the lesson, along with Additional Practice, or Enrichment; auto-scored with on-screen help, including Help Me Solve This and View an Example tools, tutorial videos, Math Tools, and one-click animated glossary access.

Tier 2 strategic intervention includes the following resources that can be used at the end of the Lesson:

• Reteach to Build Understanding. This provides reteaching as a follow-up to the intervention activity.

Tier 3 intensive intervention instruction is delivered daily outside of the core math instruction, often in a one-to-one situation. Resources offered within the program on Savvas Realize® are especially helpful.

• Variety of Instructional Strategies
• Personalized Study Plans
• Virtual Nerd Tutorial Videos
• Online Practice with built-in Learning Aids powered by MathXL for School
• Savvy Adaptive Practice

The authorship team is made up of respected educational experts and researchers whose experiences working with students and study of instructional best practices have positively influenced education. Contributing to enVision Integrated Mathematics with a mind to the evolving role of the teacher and with insights on how students learn in a digital age, these authors bring new ideas, innovations, and strategies that transform teaching and learning in today’s competitive and interconnected world.

Explore the enVision Integrated Mathematics authors:

• Eric Milou is a Professor in the Department of Mathematics at Rowan University in Glassboro, NJ. He is an author of Teaching Mathematics to Middle School Students. Recently, his focus has been on approaches to mathematical content and the use of technology in middle grades classrooms.
• Dan Kennedy, Ph.D is a classroom teacher and the Lupton Distinguished Professor of Mathematics at the Baylor School in Chattanooga, Tennessee. A frequent speaker at professional meetings on the subject of mathematics education reform, Dr. Kennedy has conducted more than 50 workshops and institutes for high school teachers.
• Christine D. Thomas, Ph.D is a professor of mathematics education in the Department of Middle and Secondary Education at Georgia State University. Thomas is a former high school Geometry teacher and taught for 14 years. Her research is grounded in developing, enhancing and retaining effective teachers of mathematics in urban high-need schools.
• Rose Mary Zbiek, Ph. D is a Professor of Mathematics Education at The Pennsylvania State University, College Park, PA. She is a former Pennsylvania mathematics and computer science teacher. Recent work includes theory-building research in the area of representation and models of mathematics teachers' incorporation of technology in classroom practice. She is the series editor for the National Council of Teachers of Mathematics Essential Understanding project.

enVision Integrated Mathematics digital courseware on Savvas Realize® includes robust digital tools that give teachers flexibility to use a digital, print, or blended format in their classrooms. Teachers can customize the program to rearrange content, upload their own content, add links to online media, and edit resources and assessments. Program resources, personalized practice, remediation, and assessments are available in one location for easy lesson planning and presentation.

enVision Integrated Mathematics is designed to achieve a coherent progression of mathematical content within each course and across the program, building lesson to lesson. Every lesson includes online practice instructional examples as the progression of topics builds, allowing students additional practice with these skills and to develop a deeper conceptual understanding.

At the beginning of every topic, teachers are provided with support for the focus of the topic, how the topic fits into an overall coherence of the grade and across the grades, the balance of rigor in the topic, and how the practices enrich the mathematics in the topic. Carefully designed learning progressions achieve coherence across grades.

Coherence is supported by common elements across grades, such as Thinking Habits questions for math practices and diagrams for representing quantities in a problem. Coherence across topics within a grade is the result of developing mathematics as a body of interconnected concepts and skills. Across lessons and standards, coherence is achieved when new content is taught as an extension of prior learning–developmentally and mathematically. (For example, Model & Discuss/Explore & Reason/Critique & Explain at the start of lessons engages students in a problem-based learning experience that connects prior knowledge to new ideas and sets them up for the new concepts they will encounter in Step 2 of the lesson: Understand & Apply.

Look Back! and Look Ahead! connections are highlighted in the Coherence part of Topic Overview pages in the Teacher’s Edition.

The Topic Background: Rigor page shows teachers how areas of rigor will be addressed in the topic, and details how conceptual understanding, procedural skill and fluency, and application builds within each topic to provide the rigor required.

On the first page of every lesson, the Lesson Overview includes sections titled Focus, Coherence, and Rigor. The Rigor section highlights the element or elements of rigor emphasized in the lesson, which may be one, two, or all three. Features in every lesson support each element, but the emphasis will vary depending on the standard being developed for conceptual understanding, procedural fluency, and application during both instruction and practice, as described below:

• Explore
  Step 1 Explore supports coherence by helping students connect what they already know to a problem in which new math ideas are embedded. When students make these connections, conceptual understanding emerges. Problem-based learning provides students with opportunities for productive struggle, time to make connections to the mathematical ideas and conceptual understandings. They can choose to represent their thinking and learning in a variety of ways. Online tools and manipulatives are available.
• Understand and Apply
  Step 2 Understand and Apply is designed to connect students’ thinking about the opening activity to the new ideas of the lesson. These concepts are presented through a series of visually rich example types purposefully designed to promote understanding. Conceptual Understanding examples present a key mathematical concept in the lesson to help students develop deep understanding of the mathematical content. Skill examples focus on helping students build fluency with skills. Finally, Application examples show students how mathematics can be used to solve real-world problems.
• Practice and Problem Solving
  Step 3 Practice & Problem Solving offers robust and balanced practice to solidify understanding. Students embark on a series of carefully sequenced and crafted exercises to apply what they just learned and to practice towards mastery. The design of the Practice & Problem Solving section is intentionally sequenced into four parts: Understand, Practice, Apply, and Assessment Practice.
• Assess & Differentiate
  Step 4 Assess & Differentiate features a Lesson Quiz and a comprehensive array of intervention, on-level, and advanced resources for all learners, with the goal that all students have the opportunity for extensive work in the state standards. Leveled practice with scaffolding is included at times. Varied problems are provided and math practices are identified as appropriate. Higher Order Thinking problems offer more challenge. Students have ample opportunity to focus on conceptual understanding and procedural skills and to apply the mathematics they just learned to solve a range of problems.

Exclusive integration of Desmos into Savvas Realize® offers a groundbreaking interactive experience designed to foster conceptual understanding through highly visual interactives that bring mathematical concepts to life. Embedded interactives powered by Desmos and animated examples engage students and deepen conceptual understanding. Allowing students to manipulate data and see an immediate effect on graphs, number lines, etc. clarifies concepts as students are learning new content. Unique to enVision , the Desmos best-in-class graphing calculator and brand new geometry tools are available to middle and high school enVision students anytime, anywhere.

enVision Integrated Mathematics portrays diverse individuals and groups in a variety of settings and backgrounds. The program has been reviewed and approved for unbiased and fair representation.

Our educational materials feature a fair and balanced representation of members of various cultural groups, including racial, ethnic, and religious group; males and females; older people; and people with disabilities. The program integrates social diversity throughout all of its lessons, and includes a balanced representation of cultures and groups in multiple settings, occupations, careers, and lifestyles.

We strive to accurately portray diverse groups within our society as well as diversity within groups. Our programs use language that is appropriate to and respectful of our cultural diversity. We involve members of diverse ethnic and cultural groups in the concept development of our products as well as in the writing, editing, illustration, and design.