enVision A|G|A – Algebra and Geometry

enVision® A|G|A © 2024 is the only high grades math program for Algebra 1, Geometry, and Algebra 2 that combines problem-based learning and visual learning to deepen students’ conceptual understanding. enVision is used by classrooms across the country and around the world.

enVision packs a unique one-two punch. Lessons start with Problem-Based Learning (PBL), where students must think critically about a real-world math problem, evaluate options, collaborate, and present solutions. Visual Learning throughout the lesson helps to solidify the underlying math concepts. It’s the best way to help kids better understand math ideas.

The program is made up of the following program components:

• Teacher’s Edition - Available in digital or print, the Teacher’s Edition includes wrap-around pages that provide direct instruction and teaching suggestions 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 write-in 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 A|G|A Digital - enVision 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.

Take an Interactive Tour of .enVision A|G|A

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 A|G|A 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, including those with learning disabilities and ELLs, 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 Understand & Apply, a remediation strategy is included to address a common misconception 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 guided 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. Skills Review & Practice scaffolded instruction can be used for this purpose, for example. 

• Variety of Instructional Strategies
• Multisensory instruction is provided in online Explore & Reason/Model & Discuss/Critique & Explain activities that include audio and visual learning
• Virtual Nerd videos, interactive MathXL for School: Practice & Problem Solving, Additional Practice, Mixed Review, Reteach to Build Understanding, and Enrichment, online digital math tools, and embedded Desmos interactivities. example.

To learn more about the enVision program, take a look at the Overview Brochure.

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 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 A|G|A 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 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. Click here to sign up for a demo.

enVision A|G|A 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.

To learn more about enVision’s effective pedagogy, see Eric Milou’s white paper entitled, Teaching for Understanding.

enVision A|G|A diagnostic assessments include the course readiness assessment given at the beginning of the year and the topic readiness assessment given at the beginning of a topic. Teachers use the results to develop personalized study plans for each student that are designed to address gaps in prerequisite knowledge. Students use their study plans to catch up so teachers can focus on grade-level material.

Additionally, the program offers Progress Monitoring Assessments-Form A, B, C-for each course in print and digitally.

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 A|G|A 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 groups; 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.