ENVISION+ TEXAS MATHEMATICS 2027 (PRINT + DIGITAL), GRADE 2

Evaluation for 1.1a
Materials include a scope and sequence outlining the TEKS, ELPS, and concepts taught in the course.

The "End Matter" section of the enVision Plus Mathematics Grade 2 Teacher's Edition provides a suggested scope and sequence that outlines the specific order of Texas Essential Knowledge and Skills (TEKS), English Language Proficiency Standards (ELPS), and concepts taught throughout the instructional year. In the grade 2 "Scope and Sequence" document for the 165 instructional day guide, the TEKS, ELPS, and concepts are included for each topic throughout the document. In the grade 2 "Scope and Sequence" document for the 180 instructional day guide, the TEKS, ELPS, and concepts are included for each topic throughout the document. EnVision Plus Mathematics includes a TEKS and ELPS correlation. The ELPS can be found in the Topic Planner for each unit (topic) and the "End Matter" of the Teacher's Edition.

Evaluation for 1.1b
Materials include suggested pacing (pacing guide/calendar) to support effective implementation for various instructional calendars (e.g., varying numbers of instructional days - 165, 180, 210).

In the grade 2 "Pacing Guide," the resource provides a pacing guide for 165, 180, and 210 days. The materials also provide a pacing guide that provides the teachers with day-to-day suggestions for lesson implementation that align with the scope and sequence of 165, 180, and 210. EnVision Plus Mathematics Teacher's Edition includes a suggested pacing guide in the "End Matter" section, which provides lessons and activities for a full year of instruction. For example, the resource provides a 180-day pacing guide for grade 2. The materials include pacing for 2–3 days of each Topic Review and Topic Assessment, as well as 2–3 days per Topic on differentiation activities. Materials include a pacing guide that offers options for adjusting the time spent on units without disrupting the sequence and coherence of content. For example, the order of the units remains the same with 180-day pacing, but each unit is reduced 4–6 instructional days.

Evaluation for 1.1c
Materials include an explanation for the rationale of unit order as well as how concepts to be learned connect throughout the course.

EnVision Plus Mathematics Teacher's Edition includes an explanation for the rationale of unit order in the "Program Overview" section. The rationale includes how the content is grouped to build connections around a key concept, and how the content is sequenced to build connections from prior knowledge to new content. The materials include a separate Grades K–2 Program Overview for that explains the coherence of the curriculum. It describes how students within grade 2 will make connections to prior learning in both grade 1 and grade 2 lessons based on visual cues to help them make connections across topics and lessons, which also leads into grade 3 content. In the grade 2 Teacher's Edition, Topic 7, the resource provides a "Math Background" section, which is the coherence of lessons to be taught in the unit. It also addresses how the lessons connect to students' prior knowledge, and how they will connect as the student moves throughout the current and next grade level.

Evaluation for 1.1d
Materials include protocols with corresponding guidance for unit and lesson internalization.

EnVison Math includes protocols to help teachers understand and prepare to teach a unit using the "Topic Internalization Protocol." Materials are found in the "Internalization Protocols and Observation Tools." The resource provides guidance on identifying relationships between lessons and how they build toward successful TEKS coverage, noting how concepts develop sequentially, considering strategies to ensure learning for all students, and identifying how the topic builds learning through concrete-representational-abstract progression. The resource also includes protocols to guide teachers in reviewing each lesson using the "Lesson Internalization Protocol" found in the "Internalization Protocols and Observation Tools" section. This resource provides guidance on connecting the lesson objective to the TEKS and ELPS, identifying new vocabulary and relating it to that previously taught, completing the student pages from a student perspective, adjusting the pace to meet the needs of the teacher's specific class, identifying formative assessments given, and providing guidance on appropriate supports to differentiate instruction. The materials include internalization protocols for topics, which is the unit for this curriculum. These protocols provide guidance on pacing, preparing to teach and assess the topic, and gathering the materials needed. This one-pager includes sections on scope, sequence, and pacing; preparing to teach and assess the topic; and collecting the materials and supplies needed for the lesson. The materials also include internalization protocols for lessons that provide a structured approach covering lesson goals, transition, pacing of lesson parts, preparing for teaching, and gathering and preparing materials.

Evaluation for 1.1e
Materials include resources and guidance for instructional leaders to support teachers with implementing the materials as designed.

EnVison Math includes resources for instructional leaders to support teachers with implementing the materials. This includes a Classroom Observation and Analysis Tool, Instructional Leader Topic Internalization protocol, and Instructional Leader Lesson Internalization protocol. In grade 2, this document includes a place to document concept development, practice, differentiated instruction, and student reflection. The materials include resources for leaders to support teachers with implementing the materials. This protocol provides a structured approach for analyzing student work to identify patterns of understanding, misconceptions, and areas for instructional focus. EnVision Plus Mathematics includes resources for leaders to support teachers with implementing the materials as designed. This includes a Classroom Observation and Analysis Tool, Instructional Leaders Topic Internalization protocol, and Instructional Leader Lesson Internalization protocol found in the "Internalization Protocols and Observation Tools" section. These tools serve as a resource to enable leaders to record targeted indicators when observing teachers during instruction. This instrument is designed for documentation purposes only, not for teacher evaluation. Materials provide resources for leaders to guide teachers with implementing the materials through a rationale, implementation, and extension using the Instructional Leaders Topic Internalization Protocol found in the "Internalization Protocols and Observation Tools." The Topic Internalization Protocol offers a structured approach to understanding each topic comprehensively and adds explicit guidance to help teachers understand what students will learn, how their progress will be assessed, and the overall learning progression.

Evaluation for 1.2a
Materials include comprehensive unit overviews that provide the background content knowledge and academic vocabulary necessary to effectively teach the concepts in the unit.

EnVision Plus Mathematics Teacher's Edition includes a "Math Background," a coherence document with visuals to show connections between previous learning that serves as preparation for the future learning of the topic. Materials include comprehensive unit overviews found in the "Math Background" section of each topic in the Teacher's Edition, which provide the background content knowledge teachers need to effectively teach each lesson. For example, the "Math Background" includes key concepts taught throughout the unit, coherence of concepts taught in the past and presented in the future, and a balance of conceptual understanding to procedural fluency. In Topic 1, the "Math Background" states "that students use and choose addition strategies to solve word problems by using prior knowledge of strategies for addition within 20." The resource includes comprehensive unit overviews that provide academic vocabulary necessary to effectively teach concepts in the unit. For example, vocabulary is found in the "Review What You Know" section of Topic 1 in the Teacher's Edition. The vocabulary listed for Topic 1 is equation, addends, sum, doubles, near doubles, subtract, difference, and strip diagram. EnVision Plus Mathematics Teacher's Edition provides a "Topic Planning and Overview" document for each topic that provides teacher guidance to support concept development throughout the topic by outlining background knowledge, key concepts, coherence, and strategies for balance in the topic. In Topic 6, the essential understanding explains how the students will build upon the lessons throughout the topic or unit. The materials include prior skills needed, such as skip counting by 5s, 10s, and 1s, and then shows how the skill will be necessary in grade 3 for success in mastering elapsed time.

Evaluation for 1.2b
Materials contain supports for families in both Spanish and English for each unit with suggestions on supporting the progress of their student.

EnVision Plus Mathematics Teacher's Edition provides supports for families in both Spanish and English by providing a QR code to access an overview, standard explanations and examples, topic support, math help at home pages with sample problems, and home activities. Materials contain supports for families in both Spanish and English for each topic, including at-home activities and online videos for parents provided in the "Planning and Overview Family Engagement" section of every topic in the Teacher's Edition. The "Family Engagement" gives a sample activity to use at home, such as classifying objects into categories. The resource contains supports for families in both Spanish and English for each unit with suggestions on supporting the progress of their student in the "Planning and Overview Family Engagement" section in each topic in the Teacher's Edition. The family engagement activities give a description of what the student is learning, such as Topic 7 which states, "your child is learning different ways to measure length." The engagement also gives an opportunity to practice at home, including having the student measure various items around the house using rulers, measuring tape, or yarn.

Evaluation for 1.3a
Materials include comprehensive, structured, detailed lesson plans that include daily objectives, questions, tasks, materials, and instructional assessments required to meet the content and language standards of the lesson (aligned with the TEKS and the ELPS).

EnVision Plus Mathematics Teacher's Edition provides lesson plans that include a list of materials that are needed to support instructional materials for this lesson, such as counting sticks. Materials include comprehensive lesson plans that include daily objectives, questions, tasks, materials, and instructional assessments required to meet the content and language standards of the lesson, aligned with the TEKS and the ELPS. The resource includes lesson plans that provide the necessary information for the effective implementation of grade-level instruction, including both mathematics and language objectives, vocabulary, and instructional materials. The tasks are aligned to the lesson standards and include questions to promote mastery of the objectives. The lesson plans are included in the Topic Planner section in the Teacher's Edition. The lesson plans in the Teacher's Edition include all components for instructional delivery found in the "Lesson Plan Guide" of every unit. This includes daily objectives, check for understanding and language objective questions, tasks to promote mastery, a materials list, and a reference of how mastery is assessed. For example, the Exit Ticket at the end of the lesson ensures mastery of the standard presented.

Evaluation for 1.3b
Materials include a lesson overview listing the teacher and student materials necessary to effectively deliver the lesson, and the suggested timing for each lesson component.

EnVision Plus Mathematics Teacher's Edition includes a lesson overview listing the teacher and student materials necessary to effectively deliver the lesson. In Lessons 2-8, the materials include place value blocks or Teaching Tool 70. The student resources, C6—regrouping in addition and C7—deciding when to regroup in addition, are listed as well and include a QR code in the Teacher Resources. The materials also include a list of teacher and student materials for each lesson investigation, such as manipulatives and activity pages or templates, which are located at the beginning of each lesson. In Lesson 3-3 of Topic 3 in the Teacher's Edition, the student and teacher materials are listed, including place value blocks and Exit Tickets. In the lesson overview, the resource provides a recommended time for each component. In Lesson 2-6 of Topic 2 in the Teacher's Edition, the "Timeline" section includes suggested allotted times of 10-25 minutes for Step 1: Explore and Share, 5-10 minutes for Step 2: Visual Learning, 15-20 minutes for Step 3: Practice and Problem solving, and 10-20 minutes for Step 4: Assess and Differentiate.

Evaluation for 1.3c
Materials include guidance on the effective use of lesson materials for extended practice (e.g., homework, extension, enrichment).

EnVision Plus Mathematics Teacher's Edition includes a digital resources list with strategies to use to extend learning, intervene, and do more guided practice. It also provides guidance for teachers in assigning online lesson activities through a digital learning platform that offers interactive learning activities to extend and enrich the lesson objective unit. Materials include guidance on the effective use of digital resources for both class extension and differentiation, as well as home activities. This Topic 9 review includes an overview that explains the concept of comparing and ordering numbers in parent friendly language, as well as practice examples to use at home. The resource includes enrichment opportunities to deepen mastery of the lesson objectives. In Lesson 9-3, Topic 9 of the Teacher's Edition, the enrichment activity gives the student an opportunity to plan a pizza party and requires them to partition the pizzas for the correct number of guests in attendance.

Evaluation for 2.1a
Materials include a variety of instructional assessments at the unit and lesson level (including diagnostic, formative, and summative) that vary in types of tasks and questions.

In the grade 2 "Assessment Sourcebook," assessments include diagnostic with a readiness assessment, formative with a progress monitor assessment, and a summative assessment for the end of each topic. Each topic provides Exit Tickets, a topic assessment, and a performance task. At the end of Topics 3, 6, 9, and 12, there are Cumulative/Benchmark assessments. Grade 2 materials include a progress monitoring assessment issued at the beginning, middle, and end of the year. The resource also provides online versions of these assessments. Grade 2 enVision Plus Mathematics Teacher's Edition has an "Assessment Resource" section that provides "Types of Assessment Items," which contains a variety of assessment item formats such as selected response, constructed response, and technology-enhanced items such as "drag and drop, hot spot, inline choice, and equation editor." It also includes a Performance Task with scoring rubrics, which provides other "opportunities to assess TEKS mathematical process standards." At the topic level, grade 2 materials include diagnostic and summative assessments found at the beginning and end of each topic. The diagnostic assessment that appears at the beginning of each topic is titled "Review What You Know." For example, in Topic 5, the "Review What You Know" asks students to identify strategies and vocabulary to answer addition and subtraction word problems. This diagnostic assessment offers a variety of tasks and questions that students complete by circling the example of the vocabulary and solving the addition or subtraction word problems. There are also two different summative assessments for each topic requiring students to complete a variety of tasks. For example, in Topic 5 there is a Topic Assessment and a Topic Performance Task that provide multiple question types including multiple choice and open-ended responses. In Topic 8, Lesson 4 there are multiple assessment tasks available for the teacher including Guided Practice, Quick Checks, and Exit Tickets. These tasks allow for a variety of questions including multiple choice and writing or drawing a correct response. The Exit Tickets located at the end of each lesson also allows for students to reflect on their learning by checking and coloring the image that aligns with the math goal. For example, in Topic 8, Lesson 4 the math goal is, "I can draw bar graphs and use them to solve problems." The student then marks the corresponding face on how they feel. The materials did not explicitly state an example of a summative assessment in the lesson level.

Evaluation for 2.1b
Materials include the definition and intended purpose for the types of instructional assessments included.

EnVision Plus Mathematics Teacher's Edition includes definitions for each type of instructional assessment provided in the program. In the "Assessment Sourcebook in the Assessment Guide, Why and When to Assess" section, grade 2 materials provide an intended purpose for the various types of instructional assessments: diagnostic, progress monitoring, formative, and summative. The resource also provides guidance on the appropriate timing for each assessment throughout the instructional cycle. For example, a "Readiness Test," defined as a diagnostic assessment, is given before instruction and used to diagnose the student's readiness for learning by assessing prerequisite content. Formative assessments, such as observational assessment tools, Quick Checks, Guided Practice, and Exit Tickets, monitor students' progress on learning content during daily lessons. EnVision Plus Mathematics defines a summative assessment as a way to "assess students' conceptual understanding and procedural fluency with topic content; students' ability to apply concepts learned and proficiency with TEKS mathematical process standards." Summative assessments include a Topic Assessment, Topic Performance Task, and Cumulative/Benchmark Assessments. Cumulative/Benchmark Assessments assess students' understanding of and proficiency with concepts and skills throughout the school year.

Evaluation for 2.1c
Materials include teacher guidance to ensure consistent and accurate administration of instructional assessments.

EnVision Plus Mathematics Teacher's Edition includes opportunities for teachers to accurately assess students by providing guidance in the "Assessment Sourcebook" under the "How to Assess" section. The materials give explicit directions on how to utilize instructional assessments like the Observational Assessment, Portfolio Assessment, Performance-Based Task, and Program Assessments. For example, on the Observation Assessment notes, the materials guide the teachers to "walk around and observe as students do work in the class and listen as students reply to questions in class." The Assessment Guide also includes guidance for teachers on the location of the assessments and how they are used in the lessons. For example, the Observation Assessment can be used to assess student learning during the Explore and Share, Guided Practice, or Guiding questions found in the Teacher's Edition. The "Assessment Resources" section in the Program Overview outlines suggested timelines for various types of assessments, including diagnostic, formative, and summative. Progress monitoring assessments are recommended at the beginning, middle, and end of the year to track student growth over time. Diagnostic assessments should be given at the start of the school year and/or at the beginning of a new topic to gauge prior knowledge. Formative assessments are intended to be used during instruction and at the end of each lesson to inform teaching. Summative assessments are recommended at the conclusion of a topic or after a group of topics to evaluate overall mastery. The "How to Administer Assessments" section of the Assessment Guide in enVision Plus Mathematics includes specific teacher guidance on preparing and monitoring an assessment. Within the "Prepare for Assessments" section, the materials include guidance for "Understand the assessments, Schedule a time for assessments, and Ensure a proper testing environment." In the "Monitor Assessments" section, the materials include guidance on "Provide directions and Actively monitor during the testing session." For example, the "Provide directions" section provides a script for teachers to use such as, "This test should take you about  . . . minutes to complete. Do not spend too much time on any single question. If you are unsure of a response, provide the best response you can. You can go back and review your responses at any time."

Evaluation for 2.1d
Diagnostic, formative, and summative assessments are aligned to the TEKS and objectives of the course, unit, or lesson.

EnVision Plus Mathematics Teacher's Edition materials provide a scoring guide for each topic assessment. This item analysis chart includes every tested item, depth of knowledge indicator, and TEK that the question is addressing. In the Teacher's Edition Topic 11: "Explore Numbers to 1,200," Review What You Know" section of the lesson, there is an Item Analysis Chart that lists the TEKS. For example, question 3 states, "Tom is having breakfast. The minute hand on the clock shows half past 7 o'clock. Circle the time on the clock," which aligns to 2.5B, "read and write time to the nearest one‐minute increment using analog and digital clocks and distinguish between a.m. and p.m." The question also aligns with the objectives of the unit. For example, in the Topic Planner of the Teacher's Edition, one of the math objectives listed is "read and write time to the nearest one‐minute increment using analog and digital clocks and distinguish between a.m. and p.m." In enVision Plus Mathematics Teacher's Edition, the Exit Tickets in Topic 2, Lessons 2–6 are aligned to the TEKS 2.4B: "Add up to four two-digit numbers using mental strategies and algorithms." The TEKS are listed under the example of the Exit Ticket. The learning objective, "I can break apart addends and combine them in different ways to make numbers that are easy to add mentally," also aligns with questions 1, 2, and 3 in the formative assessment Exit Ticket. It is also in the teacher directions located at the bottom of the page on the Exit Ticket. The Summative assessments located at the end of each topic clearly align to the TEKS listed for that corresponding topic. Materials provide an Item Analysis Chart that lists each question with the corresponding TEKS. For example in Topic 10, all questions are aligned to the following standards 2.8A, 2.8B, 2.8C, 2.8D, and 2.8E. The Topic Planner for Topic 10 lists the objectives for the unit which align with the Topic 10 Topic Assessment. For example, one objective states, "Combine two-dimensional shapes to make new shapes with given attributes," and question 12 on the Topic Assessment has the students identifying the new shape created.

Evaluation for 2.1e
Instructional assessments include TEKS-aligned items at varying levels of complexity.

EnVision Plus Mathematics Teacher's Edition assessment resources come in various formats, each designed to evaluate different aspects of students' learning and skills. These formats include selected and constructed responses, technology-enhanced items, and performance tasks. Selected response items, such as multiple-choice or true/false questions, allow students to choose the correct answer from a set of options and are useful for quickly assessing knowledge and comprehension. Constructed response items require students to generate their own answers, such as in short answers or essays, and are effective for evaluating critical thinking and written communication. Technology-enhanced items use digital tools to create interactive questions, such as drag-and-drop or simulations, which can assess more complex skills in engaging ways. Lastly, performance tasks involve real-world applications, such as projects, presentations, or experiments, allowing students to demonstrate their understanding through hands-on, authentic experiences. Together, these diverse assessment formats provide a comprehensive picture of student learning and progress. The grade 2 materials include an Item Analysis Chart for each instructional assessment provided in the instructional materials. The Item Analysis Chart states the Depth of Knowledge (DOK) level associated for each question in every assessment. Each unit in the grade 2 instructional assessments contains more than two levels of complexity. For example, in Topic 3 the Exit Tickets have a complexity level of one and/or two. In addition, the Performance Task at the end of each topic also has multiple DOK levels of two and three. For example, question 2, "How many fewer stamps with birds does Mary have than stamps with flowers? Use a different strategy to solve. Show your work," is labeled as a DOK 2 question. The grade 2 Topic 9 Assessment in the Teacher's Edition has TEKS-aligned assessment items that assess students at different levels of complexity. The levels include procedural tasks, application of problems that require multiple tasks, and open-ended questions. enVision Plus Mathematics Topic 9 assessment includes multiple choice questions, drawing/writing the answers to the questions, and open-ended response inquiries. For example, question one in Topic 9 states, "Write the number to match each model. Circle the choice that correctly compares the two numbers." For question 2, "Write the numbers in the correct order on the number line; 26, 12, 18."

Evaluation for 2.2a
Instructional assessments and scoring information provide guidance for interpreting student performance.

Scoring information provided in the "Performance Task Scoring Guide and Rubric" in Topic 4 of the Teacher's Edition gives guidance to teachers on how to score the assessments. For example, in the Topic 4 Performance Task, students can earn a total score of 2 points. The student receives the full 2 points if they complete the bar diagram and answer the question correctly; only 1 point is awarded if the student completes the bar diagram or answers the question correctly. This allows for consistent, reliable, and aligned scoring among all teachers. Teacher's Edition includes guidance for interpreting student performance on instructional assessments. For example, in Topic 10: "Geometry" in the Teacher's Edition, after the Exit Ticket is given to students, the teacher guide states, "Use the Exit Ticket results to support students as needed by reminding them that they can combine shapes to make new shapes with given attributes." This allows teachers to analyze the Exit Tickets and use them to drive future instruction.

Evaluation for 2.2b
Materials provide guidance for the use of included tasks and activities to respond to student trends in performance on assessments.

The materials provide guidance to teachers on activities to use in response to student trends on assessments. For example, in Topic 1: "Add and Subtract Within 20" in the Teacher's Edition, Step 4: Assess and Differentiate, teachers are given an intervention activity to address student misconceptions. The intervention activity requires the teacher to draw one butterfly on 20 sticky notes, attach 10 of them to the desk or table, and then, on chart paper, write the following: "10 - __ = __" and "__ + __ = 10." The resource guides the teacher to pose the subtraction story to pairs or groups: "Ten butterflies land on a rosebush. Then, 4 butterflies fly away. How many butterflies are left on the rosebush?" The materials suggest the teacher repeat the subtraction story and then have a volunteer act it out by taking away the correct number of butterflies. Students work on the subtraction fact and the related addition fact. In the "How to Assess" section of the "Assessment Guide," Teacher's Edition provides guidance on how to use information from an observation assessment. The resource guides the teacher to "walk around and observe as students do work in class" during the "Guided Practice" section of the lesson to gauge students' preparedness to move to the "Independent Practice" section of the lesson. For example, in the "Guided Practice" section of Lesson 4-3, question 1 guides the students to "Use any strategy to solve. Show your work. Explain why the strategy works" when answering the question, "Renee has 11 fewer magnets than Jeffrey. Renee has 25 magnets. How many magnets does Jeffrey have?" Teacher's Edition includes an "Error Intervention" for item 1, which states that "If students have difficulty deciding whether to add or subtract, then ask, "Who has more magnets?" Help them label each part of the strip diagram to help them make sense of the numbers and the unknown in the problem."

Evaluation for 2.2c
Materials include tools for teachers to track student progress and growth, and tools for students to track their own progress and growth.

The materials in grade 2 include a "Student Progress and Growth Teacher Tool" within the "Student and Teacher Progress Trackers" that enables teachers to monitor student progress throughout the topic. As concepts build sequentially upon one another, students are expected to gradually develop a deeper understanding, with full proficiency typically achieved by the end of the topic. The teacher tool features a chart listing the TEKS and the corresponding lessons that cover each TEKS. For example, 2.7C: "Represent and solve addition and subtraction word problems where unknowns may be any one of the terms in the problem" is covered in Lessons 3-9, 3-11, and 3-12. The materials guide teachers to note the development of each student before, during, and at the end of the topic, using the following key: "x" for "working on it," "–" for "almost there," and "✓" for "got it/mastered." The teacher tool is designed for all concepts taught throughout the entire curriculum. In grade 2, materials include student progress and growth trackers that help students analyze and reflect on their own learning. These tools, found in both the "Student and Teacher Progress Trackers," prompt students to consider the math goal before, during, and after each topic. For example, in Lesson 8-2, the math goal is "I can draw bar graphs and use them to solve problems." At each reflection point, students choose from three options: "I Can," "With Help," or "Not Yet." They circle the option that best matches their understanding at the time. This ongoing reflection process encourages students to actively monitor their learning.

Evaluation for 3.1a
Materials include teacher guidance for differentiated instruction, activities, and paired (scaffolded) lessons for students who have not yet reached proficiency on grade-level content and skills.

In the K-2 Program Overview, the "Differentiation Resources" chart plays a crucial role in supporting diverse learners by offering a structured approach to intervention and enrichment. This chart outlines tiered intervention strategies: "Intensive, On-Level, and Advanced," ensuring that instruction is tailored to meet students at their individual levels of understanding. For students requiring additional support, the "Reteach to Build Understanding" component provides a scaffolded, step-by-step guidance that helps break down complex concepts into manageable parts. Teacher-Guided Activities are also included, offering targeted assistance through small-group or one-on-one instruction to reinforce key skills. Additionally, the program emphasizes Math Literacy and Reading Support, which aids students in navigating and comprehending mathematical language and content, thereby bridging gaps in both math and reading proficiency. This comprehensive framework ensures that all learners, regardless of their starting point, have access to the tools and support they need to succeed in mathematics. The "Differentiation Instruction" in the Program Overview offers an Intervention System to help teachers provide effective interventions for learners that are on or below grade level. The Intervention Lessons are separated into three sections: "Guided Instruction, Practice, and Check for Understanding," and include Teacher Support, which provides guidance to teachers to conduct a short lesson. The lessons focus on vocabulary, concept development, and practice. One example from the grade 2 Intervention System includes Lesson E3 from Topic 4, Lesson 4-5. Lesson 4-5 focuses on solving two-step word problems. The Intervention Lesson E3 provides guidance and support by asking guiding questions to break apart the thinking and understanding of the word problem. The first set of questions are "What do you know?" and "What do you need to find?" Additionally, the teacher can ask the students, "How can you find how much time is left for games?" The Teacher's Edition in grade 2 includes an Intervention Activity that serves as a scaffolded lesson for students. Based on the results of the Quick Check, teachers can select different activities to support student learning. If a student receives between 0–3 points on the Quick Check, then the materials provide an Intervention Activity or a Reteach to Build Understanding Activity. The Lesson 5-1 Intervention Activity in Topic 5, "Work with Equal Groups" provides instructions for a direct lesson with students. This activity has students working with a partner to connect cubes. One partner builds a tower with an even number of cubes, while the other partner breaks the tower into equal parts to verify the number is even. The activity continues with various numbers up to 40. The students also discuss how the connecting cubes for each number differ. In the grade 2 Teacher's Edition for Lesson 5-6, teachers are guided to use 12 counters and a grouping mat to help students develop an understanding of equal groups and repeated subtraction, which are early foundations of division. The activity begins with a relatable context: "Suppose you have 12 apples. For how many days can you eat 2 apples a day until there are none left?" Students physically model this scenario by grouping counters into sets of two, reinforcing the concept through hands-on learning. This intervention supports students with concrete, visual representations of mathematical ideas they may struggle to grasp abstractly. It also offers opportunities for repeated practice by modifying the daily apple count to three, four, six, and one, allowing students to develop fluency with grouping and counting strategies across multiple contexts. The explicit teacher directions and use of manipulatives ensures that the lesson is accessible and meaningful for all learners. Additionally, the activity is scaffolded, moving from modeling a single grouping problem to adjusting

Evaluation for 3.1b
Materials include pre-teaching or embedded supports for unfamiliar vocabulary and references in text (e.g., figurative language, idioms, academic language).

The materials include regular practice in teaching vocabulary at the beginning of each topic. For example, the Topic Opener of the Teacher's Edition provides a vocabulary activity for teachers to pre-teach the vocabulary needed to understand the concepts in the topic. In Topic 11: "Explore Numbers to 1,200," the vocabulary activity includes teacher guidance on using a graphic organizer—a word web—to help students look at words in different ways to fully understand their meanings. For example, the students work in pairs to write the word "compare" along with a number in the center oval. Then, the students write six different numbers in standard and expanded form around the oval, connecting each number to the number in the center. Teachers encourage students to include examples that show "greater than ( > )," "less than ( < )," and "equals ( = )." In the Teacher's Edition, teachers can access the Academic Vocabulary in the Topic Opener. New academic language will be introduced prior to the lesson and then used throughout the entire topic. The academic language is cross-curricular and utilized throughout the school day and year. Topic 12: "Add and Subtract within 1,000 Using Models and Number Sentences" includes teacher guidance on students defining and utilizing the words: "observe," "relate," and "strategy," while responding to questions as well as through discussions during the lessons. The Teacher's Edition also provides explanations for the students. For example, in reference to the word relate, it is suggested to use the term when discussing solution strategies. "How does using place-value blocks to find the sum of 2-digit numbers relate to using place-value blocks to find the sum of 3-digit numbers?" In grade 2 Teacher's Edition, Lesson 10-1, language support and math talk are thoughtfully embedded to ensure all students can access and engage with the lesson content. This lesson focuses on geometry concepts, such as identifying and describing solid figures, and includes pre-teaching strategies for key academic vocabulary including faces, edges, and vertices. The terms are introduced with visual models and real-world examples to help students connect abstract language to concrete understanding. The lesson plan also incorporates English Language Learner strategies which guide teachers in supporting second language learners through scaffolded instruction, including the use of sentence frames, visual cues, and opportunities for repeated exposure to new terms in context.

Evaluation for 3.1c
Materials include teacher guidance for differentiated instruction, enrichment, and extension activities for students who have demonstrated proficiency in grade-level content and skill.

The materials in grade 2 include guidance for differentiated instruction for students who demonstrate proficiency in the grade-level skills. In the Teacher's Edition, the guidance includes a Quick Check in the "Assess and Differentiate" section of Lesson 4-2 in Topic 4. Based on the results of the Quick Check, if students score 4–5 points, they are assigned an enrichment activity. The big idea of Lesson 6-3 focuses on ways to represent the same amount in coins. The enrichment activity for Lesson 6-3 is provided in the online program and extends learning by having students use a spinner with coins on it to make $1.00. For example, the students spin the paper clip on the spinner to get coin one and then coin two and then uses the coins to make $1.00. Grade 2 Teacher's Edition offers enrichment and extension activities in the Differentiation Library at the beginning of each topic, such as "Pick a Project," "Math and Literacy," "Amazing Contributions," and "Stand Up and Think." Guidance is provided in the Teacher's Edition on when to use these extension activities. In Topic 7: "Measurement," the "Pick a Project" can be used anytime during the topic, whereas "Stand Up and Think Problem 7A" can be used anytime after Lesson 7-6. The "Pick a Project" offers four projects for students to choose from, and each option includes a visual, an action, and a final product. Project 7C has students looking at a visual representation of a Ferris wheel. The students will answer the question, "How tall are Ferris wheels?" and then write a Ferris wheel story. In enVision Mathematics Grade 2 Teacher's Edition, Topic 9, the "Building Understanding," "Sustain Understanding," and "Fluency" sections are thoughtfully designed to deepen students' grasp of place value and numbers up to 1,000, while also promoting strong language development and math communication skills. These sections incorporate a variety of engaging tools such as digital manipulatives, lesson resources, spiral review, hands-on games, digital games, and fluency practice. These activities are not only effective for reinforcing mathematical concepts, but also serve as student-choice enrichment tasks that connect math to real-world scenarios, encouraging students to apply their learning in creative, open-ended ways. Language support is embedded throughout these activities with academic vocabulary routines, visual aids, and sentence frames that help students articulate their mathematical thinking. For example, when using digital manipulatives to build and break apart numbers, students are prompted to describe their actions using precise math language. Teachers are encouraged to facilitate "Math Talk" by asking guiding questions that prompt students to explain their reasoning, compare strategies, and engage in collaborative discussions. These structured conversations help students internalize vocabulary and develop confidence in expressing mathematical ideas. The spiral review and fluency games also reinforce previously learned concepts, providing repeated exposure to key terms and structures in a fun, interactive format. Altogether, these components create a rich, supportive environment where students can build both conceptual understanding and language proficiency through meaningful, real-world math experiences.

Evaluation for 3.2a
Materials include explicit (direct) prompts and guidance to support the teacher in modeling and explaining the concept(s) to be learned.

In Topic 3, Lesson 3-4, the "Visual Learning" section states, "Read the questions aloud. What does the ? mean? Is it easy to subtract 48 from 73? Would it be easier if you broke apart 48 into 4 tens and 8 ones? What numbers do you get? Is 40 easy to subtract? Would 8 be easier if you broke it apart? What are some pairs of numbers that make 8?" These questions explicitly guide the teacher in modeling a mental math strategy using number decomposition and supporting the explanation of how breaking apart numbers can simplify subtraction. The questions provided by the resource scaffold student thinking and promote number sense by encouraging flexible ways to work with numbers. The materials include guidance to support the teacher in both modeling and explaining the concepts to be learned. In grade 2, Lesson 3-5, the Teacher's Edition includes a "Same but Different" "Math Talk" card that presents two models showing different ways to break apart the number 18 into 10 and eight, and into nine and nine. This section provides specific prompts for teachers to use while students work in pairs to compare and contrast the models. Teacher guidance is provided to "have students share what is alike and different," supporting the explanation of the concept through a student discussion. Additionally, the teacher is prompted to ask students when it might be helpful to break apart numbers in these ways, which supports modeling of number flexibility and strategic thinking in problem solving. In the Grade 2 Teacher's Edition, Topic 6, the "Visual Learning" section is designed to help students master subtraction strategies through clear, step-by-step visual models. The Teacher's Edition provides structured guidance for introducing each lesson, including scripted prompts such as, "What do you notice about how the tens and ones are regrouped?" and "How can we use a model to show subtraction with regrouping?" Teachers begin by presenting the "Visual Learning Bridge," which uses animations or illustrated examples to demonstrate subtraction concepts like breaking apart tens or using number lines. During this time, the teacher models the process using base-ten blocks or place-value charts, narrating each step and encouraging students to follow along with manipulatives. Teachers also facilitate "Math Talk" by prompting students to explain their thinking, compare strategies, and justify their answers. This approach ensures that students not only practice subtraction, but also understand the reasoning behind each step, building a strong conceptual foundation for future math learning. The Teacher's Edition includes guidance to support teachers in explaining and modeling key concepts from the lesson. In Topic 7, students are learning to estimate and measure lengths using metric and customary units. In the "Explore and Share" section, sample student work is provided for teachers to analyze and use during instruction to model and explain student thinking, as well as to address misconceptions. For example, in Lesson 7-6, two samples are provided; one from Kerry and one from Louis that allow the teacher to address misconceptions in measurement. The teacher discusses both examples with the whole class. She explains, "Both Kerry and Louis found objects that measured about 3 centimeters and 1 meter. Kerry understood that 1 meter is much longer than 3 centimeters, but Louis thought 3 centimeters was the larger measure."

Evaluation for 3.2b
Materials include teacher guidance and recommendations for effective lesson delivery and facilitation using a variety of instructional approaches.

In the Grade 2 Teacher's Edition, Topic 3: "Subtract Within 100 Using Strategies," includes a hands-on game that exemplifies the program's commitment to providing teachers with explicit guidance for delivering instruction through varied, engaging approaches. The Teacher's Edition outlines clear steps for setting up and facilitating the game, which is designed to reinforce subtraction strategies such as using place value, number lines, and mental math. During the game, the teacher begins by stating the objective, "Today, we are going to play a game that helps us practice subtracting numbers up to 100 using different strategies." The teacher models a sample round, using base-ten blocks or a number line, and narrates the process, "I rolled a 60 and a 25. I will subtract 25 from 60 by first taking away 20, then 5 more. That leaves me with 35." Students then play in pairs or small groups, using game boards and manipulatives provided in the "Differentiation Library" or printed from the digital platform. The teacher circulates, observing strategies and prompting deeper thinking with questions like, "Can you explain how you found your answer?" or "Is there another way to subtract that might be quicker?" This hands-on, interactive format not only reinforces math skills, but also supports the use of academic vocabulary through math talks, peer collaboration, and differentiated instruction, ensuring all learners are engaged and supported. The materials include teacher guidance for effective lesson facilitation using a variety of instructional strategies, such as Exit Tickets, and an explore-and-share approach and math talks, that promote mathematical discourse. In Lesson 11-6 of the Teacher's Edition, students are given a statement and must convince a partner of their thinking. For example, "Do 835 and 8 hundreds, 0 tens, 35 ones represent the same number?" Students are provided time to consider their answers before sharing with a partner or small group. The teacher has the students discuss any similarities and differences they notice between the answers and strategies used. In the Lesson 11-6 Exit Ticket students identify numbers on a number line. The "Explore and Share" section engages students with high-interest problems and allows for multiple approaches to each problem. For example, students use critical thinking skills to respond to the question, "If you had people stand in a line according to their age, how would you determine the position of each person in the line?" Students then look for solutions that correctly estimate the position on the number line. In Topic 12, the Grade 2 Teacher's Edition provides teachers with suggestions for using a variety of instructional approaches, including visual learning, language routines, and practice and problem-solving. Visual learning offers a visual example to formalize the mathematics of the lesson. Lesson 12-10 provides both teachers and students with visuals of place value blocks in a place value chart. Students use the visual to create a conceptual understanding of subtraction regrouping. The language routines help students communicate about math to advance their thinking. The language routine in Lesson 12-10 is "Compare and Connect." In this routine the teacher asks, "How is using models to subtract 3-digit numbers similar to using models to subtract 2-digit numbers?" Then, the "Practice and Problem-Solving" section builds proficiency as students work independently by using place-value blocks or drawings to find the difference in subtraction equations.

Evaluation for 3.2c
Materials support multiple types of practice (e.g., guided, independent, collaborative) and include guidance for teachers and recommended structures (e.g., whole group, small group, individual) to support effective implementation.

The Program Overview offers guidance on the lesson components that facilitate guided, independent, and collaborative practice. For example, the materials incorporate guided practice in the following components of a single lesson: "Math Talks," "Guided Practice," "Stand up and Think," "Review What You Know," and "Topic Review." Teachers are provided with independent practice opportunities for students in "Practice and Problem Solving," "Spiral Review," "Adaptive Practice," "Additional Practice," "Fluency Practice," "Review What You Know," and "Topic Review." The resource supports collaborative practice in "Math Talks," "Guided Practice," "Fluency Practice," "Stand up and Think," "Review What You Know," "Topic Review," and hands-on games. The Program Overview also provides recommendations for various structures, including whole-group, small-group, and individual practice. Each structure is represented with a symbol, which is then placed next to the title of each section in the Teacher's Edition. For example, whole-group is represented by one person standing next to a board, small-group is represented by three people, and individual practice is represented by one person. Some components allow for more than one structure, for example, the "Math Talk" portion of the lesson that can be presented either in a whole-group or small-group setting. In Teacher's Edition grade 2, Topic 8, Lesson 8-2, students deepen their understanding of adding 3-digit numbers using models, with structured opportunities for guided, independent, and collaborative practice. During "Guided Practice," the teacher uses base-ten blocks to model the addition of three digit numbers, helping students visualize place value and regrouping. The Teacher's Edition provides prompts such as, "Use base-ten blocks to show 245 + 326. Ask: What do you do when you have more than 10 ones or tens?" to guide students' thinking and discussion. In the "Independent Practice" section, students solve problems in their workbooks using drawings or place-value charts to represent their thinking, reinforcing their conceptual understanding. For "Collaborative Practice," students work in small groups to play a matching game where they pair number cards with correct sums using base-ten models, encouraging peer discussion and strategy sharing. The resource offers detailed teacher guidance, including differentiation tips like, "Provide place-value mats for students who need help organizing their thinking," and grouping suggestions that recommend whole-group instruction for modeling and small-group settings for hands-on activities. This lesson exemplifies how enVision Plus Mathematics supports effective implementation through varied practice types and embedded instructional support. The materials provide teachers with guidance to effectively implement instructional routines and structures. There are three types of lessons in the enVision Plus Mathematics materials including "Let's Investigate" lessons, "Let's Build" lessons, and "Let's Model in 3 Acts" lessons. The "Let's Build" lessons are broken into four sections that allow for varied instructional approaches from the teacher, beginning with "Explore and Share," where students engage in investigating new content during a task. Then, a step-by-step procedure with visual examples is used in the "Visual Learning" section where students then use that new learning and apply it in "Practice and Problem Solving." Finally, students are assessed, and the teacher can differentiate instruction based on the assessment. Lesson 13-2 begins with students exploring how Naomi saved a different amount of money over four weeks and finding the total she saved. Next, students engage in a visual learning activity where they are shown savings over the course of six months on a graph, with step-by-step procedures on how to show whether Jorge spent or saved money from month to month. Students apply their learning to a new graph where they analyze Kenji's savings ove

Evaluation for 3.3a
Materials include teacher guidance on providing linguistic accommodations for various levels of language proficiency [as defined by the English Language Proficiency Standards (ELPS)], which are designed to engage students in using increasingly more academic language.

The Teacher's Edition provides opportunities for teachers to offer linguistic accommodations for various levels of language proficiency. The "Let's Build and Let's Investigate" section of a lesson includes strategies that scaffold activities aligned with lesson content located in the Targeted English Language Proficiency Standards (ELPS) Support, which includes instructional scaffolding suggestions for the five levels of language proficiency and increase in the use of academic language. In Lesson 5-5, students learn to separate objects into equal groups. The Targeted ELPS Support includes teacher guidance to have "students discuss what they think share means. Ask volunteers to give examples of things they have shared before. Expand the discussion to sharing equally." The materials include teacher guidance with scaffolds for each proficiency level. For example, the teacher guidance for students identified as pre-production is "students display eight counters. The teacher asks the student to separate the counters into two equal groups and to explain how many are in each group." Guidance for students identified as beginning is "students display eight counters. The teacher asks, "If you share the counters with a friend, how many will each person get if you share equally?" As the levels progress, the materials provide teacher guidance such as "the teacher asks, "If there were nine muffins, could you share them equally? Why?" for intermediate students. Then, for high intermediate students, the teacher guidance states, "The students count aloud." Then use the provided sentence frame, "I have _ counters. I counted _." Last, the materials provide guidance for students identified as advanced, which shares that students should discuss how sharing equally and separating into two equal groups mean the same thing. Students then describe how to divide eight muffins into two equal groups. Grade 2 materials include teacher guidance with suggestions for specific items during student practice. While students are working independently or in pairs on the Practice and Problem Solving, the Teacher's Edition provides prompts for supporting emergent bilingual students. In Lesson 7-6, students are asked to "choose an object to measure using metric units by first estimating and then measuring." The prompt allows for linguistic support by suggesting that some students may find multi-step directions hard to follow. The materials also suggest having students work in pairs. For example, the Teacher's Edition states, "You may wish to have students work with partners. Then have partners discuss each step in the measuring process before performing the steps one at a time. Have them discuss how to determine whether their estimate was reasonable before writing a response." In Lesson 10-2 of the enVision Plus Mathematics Teacher's Edition grade 2 curriculum, students are introduced to the concept of equal groups as a foundation for understanding repeated addition and early multiplication. The teacher begins by saying, "Today, we are going to learn how to use equal groups to help us add the same number again and again." Using manipulatives such as counters or linking cubes, the teacher models three equal groups of four and says, "Let's count how many in all—4 plus 4 plus 4 equals 12." The teacher writes the repeated addition sentence on the board and explains, "This shows that we added the same number three times." To support English learners, the teacher uses visuals and gestures while providing sentence stems like, "There are __ groups of __. That equals __." For example, a student might say, "There are 3 groups of 4. That equals 12." Additional sentence frames such as "4 plus 4 plus 4 equals 12" and "I see 3 groups and 4 in each. That makes 12," help students at varying levels of English proficiency articulate their mathematical thinking. These supports reflect the curriculum's alignment with the ELPS, which emphasize vocabulary development, structured language

Evaluation for 3.3b
Materials include implementation guidance to support teachers in effectively using the materials in state-approved bilingual/ESL programs.

The materials include a Language Support Handbook in the Online Resource section. The handbook includes guidance on effectively implementing the materials for bilingual and ESL programs. It offers direction on how the materials support rigorous tasks, productive struggle, multiple modes and representations, academic language, conversations, and strategic scaffolding. For example, the materials provide multiple entry points for accessing rigorous tasks. The resource guides teachers to assign tasks such as maintaining the cognitive challenge, building student agency through rigorous tasks, providing access to mathematical tasks, forming groups of students with different language abilities, allowing students to hear tasks read aloud, and enabling students to act out a problem." The rigorous task, maintaining the cognitive challenge, states, "All students should have opportunities to work on rigorous tasks that challenge them to think mathematically, solve problems, and communicate. Do not simplify tasks for students who need language support, but do amplify key ideas in the tasks." The Teacher's Edition provides linguistic accommodations at the beginning of each topic that include vocabulary support, metalinguistic transfer to Spanish, cognates, academic vocabulary, and ELPS. The Teacher's Edition states, "There are many opportunities to interact with the topic's vocabulary in lessons by using vocabulary cards, a vocabulary review of previously learned words, and a review of vocabulary learned in the topic." For example, in Topic 9, equal parts, halves, whole, fourths, and eighths are listed for topic vocabulary; bar graph, symbol, pictograph, and predict are listed for prior terms; and cone, cube, cylinder, edge, face, flat surface, rectangular prism, sphere, triangular prism, vertex, vertices, quadrilateral, pentagon, hexagons, plane shape, parallelogram, and trapezoid are listed for upcoming terms. Furthermore, the materials list context-setting vocabulary that is included in each lesson that provide teachers with guidance to fully implement effective vocabulary strategies for all learners.

Evaluation for 3.3c
Materials include embedded guidance for teachers to support emergent bilingual students in developing academic vocabulary, increasing comprehension, building background knowledge, and making cross-linguistic connections through oral and written discourse.

The digital resources include language development practice tools to support English Learner (EL) students' literacy and language proficiency. The "Build Mathematical Literacy" section provides opportunities to develop academic language, increase comprehension, build knowledge, and make connections through written discourse. For example, in Lesson 5-1, students read the problem and then follow the steps to help understand it. The problem presented is, "If you add two odd numbers, will the sum be odd or even? Explain. Use numbers, pictures, or words." The first step in the process states, "What question is asked in the problem?" The Targeted ELPS Support section in Lesson 7-2 guides teachers to review the terms length and unit with students, while the "Classroom Conversation" section prompts students to use and discuss measurement terms such as inch, foot, and yard. These oral exchanges support both vocabulary development and comprehension as students explain their thinking using academic language. Students build background knowledge orally as they connect their prior experiences with real-world objects to estimate measurements using paper clips. In the "Explore and Share" and "Talk About Math Ideas" sections, students engage in discussions and think-pair-share activities that deepen understanding through collaborative oral reasoning. The lesson also includes opportunities to make cross-linguistic connections orally, as seen in the "Language Routine: Compare and Connect," where students describe relative sizes of familiar objects, a task that naturally supports linguistic transfer between languages. Written discourse is equally supported. Students draw and label classroom objects, reinforcing vocabulary such as "about 1 paper clip" and linking language to visual representation. These tasks promote comprehension and build background knowledge by having students apply learning to real items in their environment. Additionally, the structured supports in the Targeted ELPS section includes sentence stems for intermediate learners that help students organize their written responses and develop awareness of sentence structure that supports cross-linguistic connections. The materials include embedded guidance for teachers to support emergent bilingual students through the use of Language Routines in the Teacher's Edition. There are eight specific Language Routines explicitly described and used throughout the grade 2 materials: "Stronger and Clearer Each Time," "Collect and Display," "Critique, Correct, and Clarify," "Information Gap," "Co-Craft Questions and Problems," "Three Reads," "Compare and Connect," and "Discussion Supports." These routines allow students to develop academic vocabulary, increase mathematical comprehension, build background knowledge, and make cross-linguistic connections through both oral and written discourse. For example, in Lesson 12-5, Language Routine: Critique, Correct, and Clarify, the teacher asks, "Mark said the sum of 127 and 345 is 418. He added the partial sums 400, 6, and 12 to find the sum. Did Mark find the correct sum? Explain." Grade 2 materials provide lesson-specific instructional activities to promote language development through oral and written discourse. The Teacher's Edition includes Language Support activities located at the beginning of the lesson, along with instructions on when best to implement each activity. For example, in Lesson 1-4, the activity is suggested to be "used at the beginning of the "Explore and Share" section to help students understand how making a 10 can assist them in adding other numbers." The materials prompt the teacher to ask, "How can thinking about 10 help you find 9 + 13?" Additionally, the materials guide the teacher to "record students' ideas about ways they can show and explain this, such as using counters and ten-frames, drawing pictures, or writing numbers and words."

Evaluation for 3.3d
If designed for dual language immersion (DLI) programs, materials include resources that outline opportunities to address metalinguistic transfer from English to the partner language.

This guidance is not applicable to the product.

Evaluation for 4.1a
Practice opportunities over the course of a lesson and/or unit (including instructional assessments) require students to demonstrate depth of understanding aligned to the TEKS.

In grade 2, practice opportunities allow students to develop their understanding by first using prior knowledge, then building mental strategies while using concrete and pictorial models. In Topic 2 in the Teacher's Edition, students develop strategies for adding within 100 through a variety of visual and hands-on methods. In Lesson 2-1, they begin by using a 100s chart, learning to add two-digit numbers by moving down and across the chart to find the sum which helps them visualize how tens and ones interact on a number grid. In Lesson 2-2, students are introduced to decomposing numbers into tens and ones, which supports their understanding of how to navigate the chart more efficiently by breaking numbers apart. By Lesson 2-3, they apply a new strategy using a number line to calculate sums, reinforcing the concept of counting on in steps of tens and ones. In Lesson 2-5, students focus solely on decomposing numbers into tens and ones to add two-digit numbers without the support of a chart or number line. This progression helps students build flexible thinking and a deeper understanding of place value and addition strategies. In enVision Plus Mathematics Teacher's Edition grade 2, Topic 9, students begin exploring the concept of fractions by dividing circles and rectangles into equal parts in Lesson 9-1. This helps them understand that fractions of the same shape must be equal in size to be considered fair shares. As they move to Lesson 9-3, students learn to name these parts using terms like whole, halves, and fourths, building their vocabulary and conceptual understanding of fractions. By Lesson 9-5, students are introduced to the basics of improper fractions and mixed numbers, learning how to convert between the two. This progression supports a deeper understanding of how fractions represent parts of a whole and how they relate to whole numbers, laying the groundwork for more advanced fraction concepts in later grades. EnVision Plus Mathematics Teacher's Edition lessons provide multiple opportunities for students to demonstrate a deep understanding of key concepts. For instance, in Lesson 9-4, students begin by comparing shapes during the "Explore and Share" portion of the lesson. The students divide the shapes into halves and fourths, followed by a "Visual Learning" section, where students engage in a think-pair-share activity to discuss their reasoning for which is a larger slice of pizza, a half or a fourth. The lesson then transitions to "Guided Practice" and "Practice and Problem Solving," where the complexity of the tasks gradually increases. In this example, students first identify and circle the shape with the most equal parts, then analyze which square would have the most, and finally draw their own lines to partition the shapes and reason for their answer—each step deepening their conceptual understanding and application of the content.

Evaluation for 4.1b
Questions and tasks progressively increase in rigor and complexity, leading to grade-level proficiency in the mathematics TEKS.

In Topic 2, Lessons 2-1 and 2-2, students begin by using a number chart to help calculate sums, building a strong foundation in number patterns and addition strategies. As the unit progresses to Lesson 2-4, students are introduced to number lines and ten-frames, which provide visual and hands-on tools to deepen their understanding of addition. By Lesson 2-7, students advance to decomposing numbers into tens and ones, allowing them to break apart and recombine numbers to find sums more efficiently. This method not only strengthens place value understanding, but also prepares students to justify their answers by explaining their reasoning and demonstrating multiple strategies. This progression from concrete tools to abstract thinking supports a well-rounded development of addition skills. The instructional materials include questions and tasks that progressively increase in rigor and complexity, leading to grade-level proficiency in the mathematics TEKS. In Topic 3, Lesson 3-3 of Teacher's Edition, questions are provided to engage students. In "Practice and Problem Solving," Questions 4 and 5 start with a lower difficulty level, as the problems require students to solve 41–24= and 86–54=. Then, the teacher guidance prompts students to more complex problems in the "Additional Practice." One example of a question with an increased level of difficulty is, "A school needs to sell 75 tickets for a school concert. The school sells some tickets. Now there are 29 tickets left. How many tickets did the school sell?" Teacher guidance materials include questions for the teacher to ask students that increase in rigor and complexity aligned to the TEKS in the lesson. For example, in Topic 10, Lesson 10-1 in the Teacher's Edition, Step 1: Investigate has three example question stems for teachers to use directly in the lesson. The first set of questions is "Questions to Ask Students Who Need Help," such as "Which one of these pictures would you like to write a problem about?" The second set of questions is "Questions to Help Students Think More Deeply," such as "Is there another way to solve the problem?" The third set is for "Early Finishers," such as "Draw another picture of a way you would want to save or spend money?" In grade 2 Teacher's Edition, students work with different quantities over time to understand how to read, write, and represent numbers up to 1,200 using place value represented by hundreds, tens, and ones. In Topic 11, the "Math Background: Coherence" section, the text specifies that in Topics 2 and 3 the students learned a variety of strategies that build on place-value understanding such as blocks or drawings when adding and subtracting with regrouping. It then specifies in Topic 12 students will be expected to apply these strategies and use place value to add and subtract within 1000 with regrouping and other strategies. Each task progressively increases complexity towards grade-level proficiency with the grade 2 TEKS.

Evaluation for 4.2a
Materials demonstrate coherence across units by explicitly connecting patterns, big ideas, and relationships between mathematical concepts.

The "Math Background: Coherence" in each topic found in the Teacher's Edition provides guidance to show connections between the concepts taught. These concepts allow for connecting patterns, big ideas, and the relationships among mathematical concepts. For example, in Topic 13: "Personal Financial Literacy," the "Math Background" section relates the concepts being taught in Topic 13 to Topic 2. In this section, students begin to represent and solve addition and subtraction word problems in which unknown factors could be included in the problem. Additionally, in Topic 6, students learned about solving word problems involving money, which connects to financial literacy taught in Topic 13. In the grade 2 "Program Overview," the authors explain the rationale behind the content organization, emphasizing that topics are grouped to build strong connections between concepts. The content is organized around key mathematical ideas that support coherence within and across lessons in each unit. Topics are thoughtfully sequenced to align with mathematics learning progressions, connecting new content to students' prior knowledge. Additionally, the TEKS is revisited in multiple lessons across topics to reinforce understanding and deepen connections throughout the year. For example, Topics 1–5 build on students' previous knowledge of addition and subtraction. Students begin in Topic 1 by adding and subtracting within 20, which is extended in Topic 2 to addition within 100 using strategies. These skills continue to build in Topic 3 with subtraction within 100 using strategies, and in Topic 4 with solving more complex problems using multiple strategies. Finally, in Topic 5, students apply their understanding to work with equations and money, integrating problem-solving with real-world applications. Measurement and data analysis concepts are developed across multiple topics. In Topic 7, students explore measurement, including length and time, applying strategies for using standard units and comparing measurements. This connects to Topic 6, where students work with money and time, learning to represent values in multiple ways and applying equivalence in practical contexts. Topic 8 extends this work as students collect and interpret data, applying mathematical process standards to analyze patterns in graphs. Geometry and fractions are introduced and expanded across several topics. In Topic 9, students develop an understanding of equal parts and fractions, building a foundation for future work with part-whole relationships. In Topic 10, they explore geometry by identifying, composing, and decomposing both two-dimensional and three-dimensional shapes, deepening spatial reasoning skills. Finally, financial literacy is revisited and expanded in Topic 13, where students explore income, saving, spending, and economic decision-making, connecting mathematical knowledge to real-life financial scenarios.

Evaluation for 4.2b
Materials demonstrate coherence across units by connecting the content and language learned in previous courses/grade levels and what will be learned in future courses/grade levels to the content to be learned in the current course/grade level.

In grade 2, Topic 5 builds on students' prior experiences with addition fact strategies developed in earlier grades, including the use of doubles and near doubles, and working with up to three addends. These foundational strategies support the understanding of how numbers can be composed and decomposed, which directly connects to grouping concepts introduced in this topic. Students continue to use familiar mathematical language such as add, subtract, doubles, and groups, while expanding their vocabulary to include terms like equal groups and separating groups. This continuity in mathematical language helps bridge conceptual understanding from prior learning into new applications in Topic 5. Topic 5 lays the groundwork for future concepts in grade 3, where students will begin working with repeated addition and arrays. These are key representations for understanding the relationship between multiplication and division. By introducing the idea of equal groups now, students are better prepared to make the transition to these more advanced operations and concepts. EnVision Plus Mathematics Teacher's Edition focuses on a common theme of partitioning plane figures into equal parts and naming these parts as halves, thirds, or fourths in Topic 9: Equal Parts and Fractions of the Teacher's Edition. This is an extension of both the content and academic language taught in grade 1, where students partitioned circles and rectangles into halves and fourths. Then, in grade 3, students will learn how fraction notation is used to represent one or more equal parts of a region and will also represent fractions on number lines. These concepts will build on the work students did involving dividing shapes into equal parts. In the "Let's Investigate" section of Lesson 12-2 in the Teacher's Edition, the lesson reinforces students' understanding of place value by focusing on ones, tens, and hundreds. This lesson helps students build a strong foundation for adding two-digit and three-digit numbers by breaking down each number into its place value components. Through hands-on activities and visual models, students explore how these values interact when adding numbers, strengthening their ability to solve complex addition problems. Additionally, students expand their math vocabulary, learning essential terms such as sum, place value, digit, and regrouping, which are key to mastering addition strategies. By engaging with these concepts, students gain confidence in working with larger numbers and develop essential problem-solving skills for future math challenges.

Evaluation for 4.2c
Materials demonstrate coherence at the lesson level by connecting students' prior knowledge of concepts and procedures from the current and prior grade level(s) to new mathematical knowledge and skills..

In enVision Plus Mathematics Teacher's Edition, Topic 3–1, grade 2 students review key strategies to strengthen their understanding of subtraction within 100. The lesson encourages them to build on their addition skills by using visual methods like drawing groups of tens and ones, which helps break down numbers into manageable parts. Students also practice using a number line to count forward and backward, reinforcing the relationship between addition and subtraction. Another powerful strategy is decomposing numbers, where students break apart numbers into easier chunks to simplify subtraction. By engaging with these methods, students develop a deeper number sense and confidence in working with larger numbers. This foundation supports their ability to solve problems efficiently and prepares them for more advanced mathematical concepts in the future. In grade 2, students learn how to tell and write time to the nearest minute on both analog and digital clocks. They also learn when to use the abbreviations a.m. and p.m. in Topic 6, Lesson 6-4. Prior to learning to tell time to the minute, students in grade 1 learned to tell and write time to the hour and to the half hour. The concept of telling and writing time to the half hour helped build mathematical thinking, allowing for the new learning of telling time to the minute. The procedural understanding of writing time with the hour first and then the minute transferred from one grade level to the next. In grade 2 Lesson 8-1, students build on current grade-level work by developing their understanding of data representation. They compare and interpret a pictograph and a bar graph that represent the same set of data. This deepens their conceptual understanding of how different graphs can show the same information and prepares them to analyze data to solve problems in upcoming lessons. The materials build on students' prior experiences with measurement and the use of a number line as a tool for both measuring and counting. This foundational understanding helps students make the connection between measuring quantities and representing those quantities in a visual graph format. Lesson 8-1 also develops procedural knowledge by teaching students how to read and interpret the number of symbols or bars in a graph as representing the number of data points in a category. This procedural skill supports their ability to accurately gather information from both pictographs and bar graphs and will be used as they solve problems based on the data in future lessons. The materials in Topic 12 in the Teacher's Edition build connections from previous grade-level concepts to new skills taught. For example, in Lesson 12-1, students use mental math and basic facts to add 10 or 100 to 3-digit numbers. Previously, students added 2-digit numbers and used place-value patterns when working with 3-digit numbers. Students use place-value blocks to reinforce the conceptual understanding that adding 10 makes the tens digit increase by 1, and adding 100 makes the hundreds digit increase by 1. This routine procedure helps lead from conceptual understanding to a more abstract understanding when working with larger numbers.

Evaluation for 4.3a
Materials provide spaced retrieval opportunities with previously learned skills and concepts across lessons and units.

In enVision Plus Mathematics Teacher's Edition grade 2, Topic 2: "Add Within 100 Using Strategies," students develop fluency in adding within 100 using strategies, reinforcing their understanding of place value and number relationships. This topic provides space retrieval opportunities, allowing students to revisit previously learned skills, such as breaking numbers into tens and ones, using number lines, and applying properties of operations to simplify addition. By connecting new strategies to earlier concepts, students strengthen their problem-solving abilities and build confidence in working with larger numbers. Through engaging activities and guided practice, they deepen their comprehension of addition, ensuring coherence across learning pathways and preparing for more advanced mathematical concepts. The materials include an opportunity for students to apply previously learned skills from lessons to a hands-on game activity. In Topic 3, "Subtract Within 100 Using Strategies," found in the "Differentiation Library" of the Teacher's Edition, students can play a game called "Race from 100" where the goal is to be the first player to reach 1. Students choose cards from a pile and subtract the number from 100. They may use a hundred chart or other subtraction strategies to move their piece to the new number. Then, they continue drawing cards and subtracting until a player lands on 1 to win the game which helps to address multiple concepts taught in the unit. For example, Lesson 3-1 covers subtracting tens and ones on a hundred chart, Lesson 3-3 covers strategies for two-digit subtraction, and Lesson 3-6 covers place value and two-digit subtraction. Grade 2 materials include opportunities for students to actively retrieve learned information through the "Spiral Review" provided in every lesson in the materials. Topic 7: Measurement, Lesson 7-1 "Spiral Review" found in the Teacher's Edition requires students to review subtraction strategies using addition facts and number lines, as well as problem-solving using a pictorial representation and an equation. For example, question 1 states, "Ella finds 73 - 59. Which shows the solution and how to check it?" In Teacher's Edition grade 2, Topic 8: "Represent and Interpret Data," students build on previously learned skills through space retrieval, reinforcing key mathematical concepts across multiple learning pathways. This topic helps students recall prior experiences with sorting, categorizing, and comparing objects, which they encountered in earlier grades when they explored basic graphs and number relationships. The materials provide structured opportunities for retrieval by guiding students to collect, organize, and analyze data using tables, bar graphs, and picture graphs. Through hands-on activities and interactive exercises, students revisit foundational skills such as recognizing patterns, making comparisons, and using mathematical reasoning to interpret real-world information. By repeatedly applying these concepts in different contexts, students strengthen their ability to read and analyze data efficiently, preparing them for more complex statistical concepts in future lessons. This progressive approach ensures students develop confidence in data representation while reinforcing connections between number operations, graphing, and problem-solving strategies.

Evaluation for 4.3b
Materials provide interleaved practice opportunities with previously learned skills and concepts across lessons and units.

EnVison Math includes a "Stand Up and Think" activity for students to practice previously learned skills and concepts in a variety of ways. In Topic 5, "Stand Up and Think" from the "Differentiation Library" of the Student Edition, students are presented with two word problems to apply their knowledge of even and odd numbers. In "Lapping the Competition," the materials guide the teacher to have the students determine how many laps they can swim in June, July, and August by organizing the data in a chart. The resource then guides the teacher to have students select a month and state if the number of laps in that month are even or odd. Students then create a representation to show their reasoning. In the second word problem, "Parking Lot Puzzle," the problem states, "A parking lot has 4 rows of parking spaces. Each row can fit the same number of cars. How many cars can fit in the parking lot?" Material guidance includes students solving the word problem by creating a pictorial representation and writing an equation. The enVision Plus Mathematics grade 2 Topic 6 Review provides students with interleaved practice that blends current learning on three-digit numbers with previously taught skills such as place value, comparing numbers, and skip counting. This review is structured to reinforce understanding through a variety of learning pathways, including visual models like base-ten blocks, number lines, and word problems that connect math to real-life situations. By revisiting earlier concepts in new contexts, students strengthen their number sense and develop greater flexibility in problem-solving. This integrated approach supports long-term retention and prepares students for more advanced topics by encouraging them to apply their knowledge in diverse and meaningful ways. The resource provides students with time to practice previously learned concepts in the Topic Review. For example, in Topic 9, "Equal Parts and Fractions," in the Student Edition, students apply the big concept of fractions to the skills of fraction vocabulary, fraction identification, and fraction reasoning. Questions 1–4 require students to fill in the blank with the vocabulary word that makes the statement correct. For example, question 1 states, "_ shows four equal parts." Questions 5–6 have students match the fraction word with its pictorial representation, while question 8 asks students to write about how to show a square with two same-sized equal parts. In the grade 2 Lesson 11-2 in the Teacher's Edition, students are given an interleaved practice opportunity during the "Practice and Problem-Solving" section where the materials suggest students work in pairs to solve a problem using their higher-order thinking skills. They are asked to find the number with several clues such as, "It has an odd number of hundreds less than 8. The digit in the tens place has a value of 60. The number of ones is 2 less than 4." Students must use all previously learned skills to draw a model and solve this problem.

Evaluation for 5.1a
Questions and tasks require students to interpret, analyze, and evaluate models and representations for mathematical concepts and situations.

In enVision Plus Mathematics grade 2, Lesson 3-2, the "Visual Learning" component encourages students to actively engage with mathematical models by interpreting and evaluating visual representations of addition strategies. The materials provide guidance to ask the following questions, "Let's look at this number line together. What do you notice about how the jumps are shown? Can you explain what each jump represents?" Students are then prompted to explore different ways to solve the same problem, such as using a number line, breaking apart numbers, or counting on. The teacher continues, "Who used a different method? Why did you choose that one? Let's compare your strategies and see how the models help us understand the math." This approach fosters student-led inquiry by inviting learners to analyze visual tools, justify their reasoning, and evaluate the effectiveness of various strategies in context. The Teacher's Edition supports teachers with questions that prompt students to think critically and in multiple ways. In Topic 5, Lesson 5-1, students engage in a classroom discussion about making a tower with cubes. They begin by interpreting models and representations and examining the questions, "Can the number 8 be shown in two equal groups of cubes?" and "Can the number 9 be shown in two equal groups of cubes?" Students analyze, "How can you use the ones digit to tell if a number is even or odd?" and continue to evaluate other numbers with cubes to determine if they are even or odd. In grade 2, Lesson 9-3, students deepen their understanding of fractions by identifying and describing parts of a whole using words and numbers. During the "Visual Learning" section of the lesson, students participate in classroom conversations that encourage reasoning and mathematical language. Instructional guidance is given to ask questions such as "What does the fraction two fourths tell you? What part of the square is shaded yellow and which part is not? What fraction describes the part that is shaded?" to compel students to interpret visual models and connect them to fractional concepts. As students engage in these discussions, they explain what fourths and eighths represent, using visual representations to support their thinking. These questions and tasks require students to interpret models and representations of mathematical concepts, analyze the parts and their relationship to the whole, and evaluate the accuracy and completeness of fractional models. In enVision Plus Mathematics grade 2, Lessons 11-12, Act 2: The Model provides students with the opportunity to apply mathematical reasoning to real-world problems using visual and contextual models. These 3-Act tasks are a standout feature of enVision and are specifically designed to engage students in mathematical modeling and critical thinking. In Act 1 of "The Hook," students are introduced to a relatable scenario—such as a child measuring ribbon lengths for a craft project—through a video or image that sparks curiosity and invites questions. In Act 2 of "The Model," students develop and analyze mathematical models to solve the problem, using tools like number lines, bar diagrams, or equations to represent their thinking. For example, they might compare lengths of ribbon by subtracting or adding measurements, justifying their strategies with visual models. In Act 3 of "The Resolution," students revisit the original scenario, compare their solutions to the actual outcome, and reflect on the effectiveness of their approach. This process not only deepens their understanding of measurement and operations but also empowers them to think critically and communicate their reasoning clearly.

Evaluation for 5.1b
Questions and tasks require students to create models to represent mathematical situations.

In grade 2, students are prompted to represent a mathematical situation using an open number line. In Topic 3 of the Student Edition, the "Explore and Share" section presents a situation for students to solve. For example, "Roshan has 56 bug stickers. Some of the bugs on the stickers have wings, and 24 of the bugs do not have wings. How many of the bugs have wings?" The Teacher's Edition guides educators to ask, "Do you think there are more or fewer than 56 stickers of bugs with wings?" In grade 2, Lesson 4-2 materials, the "Guided Practice" section engages students in writing an equation with a "?" for the unknown to model the problem and then solve. One example is "Mary has some balloons. 14 balloons popped, and now she has 17 balloons. How many balloons did Mary have at first?" Teacher guidance includes using a strip diagram to help students who are having difficulty. In grade 2, Lesson 11-1 in the "Explore and Share" section, students are prompted to model mathematical situations using concrete representations. For example, the question "How could you use place-value blocks to show 125?" supports students in connecting real-world contexts to mathematical ideas by having them create a visual place value model. This task encourages students to represent the quantities involved and explain how their model matches the situation. This modeling process deepens conceptual understanding and supports the development of problem-solving strategies.

Evaluation for 5.1c
Questions and tasks provide opportunities for students to apply conceptual understanding to new problem situations and contexts.

In grade 2, Lesson 6-1, students apply their conceptual understanding of place value and counting strategies to determine the value of a collection of coins. By identifying coin values and using strategies such as counting on or skip-counting, students solve real-world problems involving money. This task provides a meaningful context for students to apply their understanding in a new situation, reinforcing their ability to reason flexibly and make sense of numbers in everyday life. In the "Talk About Math Ideas" section, students apply their conceptual understanding of skip counting and coin values by engaging in a Think-Pair-Share activity. Students discuss the similarities between skip counting and finding the total value of a group of coins, such as recognizing patterns when counting by 5s or 10s and how each coin type represents a repeated unit. This structured discussion allows students to connect prior knowledge to a new context, deepening their understanding of counting strategies and their application in solving real-world problems involving money. The grade 2, Topic 9, Student Edition provides students with opportunities to apply conceptual understandings to new problem situations. During Lesson 9-4, students determine if a fractional part is larger or smaller than another fractional part by comparing the number of parts into which each same-sized whole is divided through guided teacher lessons. In the "Practice and Problem Solving" section, students apply their new understanding to different situations. For example, students draw lines to divide the first square into halves, the second square into fourths, and the third square into eighths. Then in question 5, students need to determine which square will have the most equal parts and in question 6 determine which square will have the smallest equal parts. EnVision Plus Mathematics provides materials for students to apply conceptual understanding to new problems. The Teacher's Edition offers guidance for teachers to present new situations to students in the "Math Talk" section of each lesson. For example, in Lesson 12-3, the "Math Talk" uses a Number Strings routine. Students think about the problems and how they would solve them, then discuss the relationships between the problems before solving the following related equations: "155 + 10, 155 + 100, 234 + 10, and 234 + 100."

Evaluation for 5.2a
Materials provide tasks that are designed to build student automaticity and fluency necessary to complete grade-level tasks.

In the grade 2 Teacher's Edition Topic 1: Build Automaticity, the "Find the Match" activity provides students with meaningful practice in addition and subtraction within 20 to build automaticity and fluency. Working with a partner, students take turns solving problems and matching clues to equations from the problem set. The teacher prompts students to think strategically and use addition and subtraction relationships to find matches efficiently and accurately. This repeated and engaging practice strengthens students' ability to recall basic facts quickly, laying a solid foundation for success with grade-level problem solving. The grade 2 Student Edition allows students to develop automaticity with addition facts up to 20 by using the counting-on strategy along with changing the order of addends. Students' proficiency and automaticity with addition facts build as they develop the habit of looking for and thinking about doubles and near doubles. Students' proficiency and automaticity with addition facts build as they develop this "make a 10" strategy. Eventually, most students will be able to perform this strategy in their heads, without the aid of tools. For example, in the "Visual Learning" section of Lesson 1-3, students need to find the answer to the equations "7+8" and "7+9." Students practice using the double fact of "7+7=14" to know that "7+8" is one more than "7+7," and "7+9" is two more than "7+7." Throughout Topic 3 in the Teacher's Edition, students use a variety of subtraction strategies, including adding up, counting back, breaking apart, drawing models of place-value blocks, compensation, and partial differences that foster fluency. In Lesson 3-10, students choose any of these strategies to find the differences of two-digit numbers. For questions 3–8 in the "Practice and Problem Solving" section, students are prompted to "use any strategy to subtract" while showing their work.

Evaluation for 5.2b
Materials provide opportunities for students to practice the application of efficient, flexible, and accurate mathematical procedures within the lesson and/or throughout a unit.

The materials support efficient, flexible, and accurate mathematical procedures throughout grade 2, Topic 1, as students develop and apply a variety of strategies to build fluency with basic addition and subtraction facts within 20. In the early lessons according to the Teacher's Edition "Math Background Coherence" section, students use cubes and counters to visually represent and model addition problems, supporting conceptual understanding and accuracy. As students progress to Lessons 1-5 through 1–8, they explore the relationship between addition and subtraction. Strategies such as counting on and making ten are revisited and extended, allowing students to flexibly apply them to both operations. This connection deepens their understanding of inverse operations and supports procedural efficiency, helping students choose appropriate strategies based on the numbers involved. In grade 2, students use a variety of addition strategies that involve an understanding of place value, properties of operations, the partial-sums method, and mental math. In Lesson 2-10 of the Teacher's Edition, students can choose any of these strategies to find the sums of more than two 2-digit numbers. Students need to achieve proficiency in addition strategies to demonstrate automaticity which lead to flexibility in the various procedural skills. The materials provide opportunities for students in grade 2 to practice place-value understanding and apply it to word problems throughout the course of a unit. In the Student Edition, Lessons 12-1 through 12–3 use place-value models and number lines to show the relationship between place value and addition. In Lessons 12-4 and 12–5, students build on those understandings as they use partial sums to add. Lesson 12-6 provides tasks for students to apply those addition strategies to word problems, such as, question two in the "Practice and Problem Solving" section states, "The first plane to leave the terminal has 240 passengers. The second plane has 312 passengers. The third plane has 159 passengers. How many passengers are on all three planes?" In grade 2, Lesson 12-3, the "Math Talk" section in the Teacher's Edition supports the development of efficient, flexible, and accurate mathematical procedures through number strings. Students are prompted to consider and solve problems such as "155 + 10," "155 + 100," "234 + 10," and "234 + 100," and then discuss the relationships between them which encourages students to recognize and apply place value reasoning to efficiently add tens and hundreds. As they share strategies and compare the problems, students demonstrate flexibility in thinking and reinforce an accurate understanding of how changes in place value affect the sum.

Evaluation for 5.2c
Materials provide opportunities for students to evaluate procedures, processes, and solutions for efficiency, flexibility, and accuracy within the lesson and throughout a unit.

In the grade 2 Teacher's Edition, Topic 2 Review, the "Talk About It" section provides students with multiple opportunities to evaluate and apply efficient, flexible, and accurate addition strategies. Students are asked, "What are strategies for adding numbers to 100?" and are then encouraged to apply and reflect on different methods, such as using a hundred chart, an open number line, breaking apart numbers, and applying compensation strategies. For example, students solve "49 + 32" using an open number line, which promotes flexibility in how they break apart and add numbers in steps. By comparing strategies and discussing their reasoning, students reflect on which methods are most efficient based on the numbers involved and ensure accuracy through visual or structured representation. These tasks, embedded within the Topic 2 Review, reinforce students' ability to select and evaluate strategies that best support their understanding and success with grade-level addition tasks. The materials provide the teacher with sample student work in the Teacher's Edition. The teacher can use the sample student work to anticipate student responses or to project in class to prompt discussions and make connections. In Lesson 3-4, the teacher can project the sample student work of Maureen and Mike. The students were given the following prompt to complete, "Choose any strategy to find 45 - 26. Use pictures, words, or numbers to explain." The class then examines the two samples of work to evaluate the process and solution of each student. Maureen used place-value blocks and broke apart 26 into 20, 5, and 1 to make the subtraction easier. She took away 20 first to get 25, then subtracted 5 to get 20, and finally subtracted 1 to get 19. Mike used an open number line and counted back by 20, 5, and 1 to reach 19. Students can analyze that both samples used different strategies but still arrived at the same solution and can then determine which strategy is more efficient. In grade 2, Teacher's Edition, Lesson 4-5, the "Language Support" section encourages rich student discourse during the "Visual Learning" component, providing opportunities for students to evaluate procedures and solutions for efficiency, flexibility, and accuracy. Students engage in a discussion about the problem "15 + 16 = ?" by exploring multiple strategies such as strip diagrams, compensation, and the break-apart model. This activity prompts students to compare and contrast the methods, explaining how each approach arrives at the same solution but through different processes. As students discuss how these strategies work together yet differently, they reflect on which method is most efficient for them, demonstrate flexibility in choosing appropriate tools, and ensure accuracy through clear reasoning and representation. EnVision Plus Mathematics provides questions for teachers to ask throughout the entire unit to evaluate procedures, processes, and solutions. In Lesson 4-2, the materials provide example questions for the teacher to ask, such as, "Think about the strategies you have learned to solve a missing addend problem. Which strategies can help you solve the problem?" In Lesson 4-7, the question for teacher guidance is, "Can Patty solve the problem using only subtraction? Do you agree with Luis that his solution strategy might not be the same as a real-world model?"

Evaluation for 5.2d
Materials contain embedded supports for teachers to guide students toward increasingly efficient approaches.

The materials contain embedded supports for the teacher to guide students in exploring what they already know and applying it to new learning. The Teacher's Edition provides these supports in the form of questioning and suggestions. In Lesson 2-2, the teacher begins by asking the whole class, "How could you find 21 + 34?" The materials guide the teacher to observe as students work to solve the equation. A suggestion is provided to assist the teacher in their observation by stating, "How do students move on the hundred chart to add tens?" This is followed by what the teacher may anticipate the students might do, such as, "Students might move right to add tens, rather than up." While observing, teachers select solutions for students to present the most efficient ways to find the number of marbles for the two children. In grade 2 Teacher's Edition, Lesson 5-1, the "Visual Learning" section includes embedded teacher supports designed to guide students toward increasingly efficient ways of determining whether numbers are even or odd. In the "Classroom Conversations" section of the lesson, teachers are prompted to have students build cube towers and match them into two equal groups, providing a hands-on, visual approach to develop foundational understanding. To move students toward more efficient reasoning, teachers are encouraged to ask guiding questions such as, "Can the number eight be shown in two equal groups of cubes?" and "How can you use the ones digit to tell if a number is even or odd?" These prompts help transition students from concrete models to recognizing patterns in the ones digit, a more efficient mental strategy. Sample student responses are provided to support teacher facilitation and reinforce accurate reasoning as students build fluency with identifying even and odd numbers.

Evaluation for 5.3a
Materials explicitly state how the conceptual and procedural emphasis of the TEKS are addressed.

The materials provided in the Teacher's Edition offer an overview of understanding even and odd numbers and equal groups that connect the conceptual and procedural foundations of multiplication and division for grade 2. Topic 5 begins with using linking cubes and separating them into equal groups to determine if they are even or odd. This conceptual understanding of equal groups relates to double facts that lead to the procedural understanding of repeated addition and equal groups. The conceptual understanding of separating equal groups leads to the procedural understanding of skip counting and repeated subtraction later in Topic 10. The grade 2 Teacher's Edition materials explicitly state how both the conceptual and procedural emphases of the TEKS are addressed. In Topic 6, the "Math Background: Balance" section reinforces that "a balanced curriculum emphasizes conceptual understanding, procedural skill, and fluency applications." For conceptual understanding, Topic 6 connects telling time and counting money to mental math strategies, emphasizing their relationship to skip counting by fives and tens. Counting money also reinforces key place value concepts, as students group coins and relate their values to tens and ones. For procedural skill, students practice finding the value of a set of coins by sorting and applying counting strategies. They also learn to tell time to the nearest minute by counting by fives and ones using the numbers on the clock face, strengthening fluency with these real-world skills. Grade 2 includes materials which progress from conceptual understanding to procedural understanding of place value up to 1,200. At the beginning of Topic 11 in the Teacher's Edition, students start by understanding the place value system using base-ten blocks to represent numbers through composing and decomposing. Students then transition from concrete to pictorial representations of the blocks and move to procedural understanding by learning how to compose and decompose numbers. The transition from concrete to procedural understanding using base-ten blocks also helps students recognize the patterns of place value when finding 10 or 100 more or less than a given number.

Evaluation for 5.3b
Questions and tasks include the use of concrete models and manipulatives, pictorial representations (figures/drawings), and abstract representations, as required by the TEKS.

EnVision Plus Mathematics provides questions and tasks that allow students to progress from using concrete models, to pictorial representations, to abstract concepts when learning to find area. Lesson 7-11 has students using square tiles to find the area of a given shape. Students use the tiles to cover the space of various rectangles and then count the tiles used to determine the area. Lesson 7-12 progresses to using pictorial representations with grid paper to create shapes with the given area. Students then solve word problems to find the area. For example, in Lesson 7-12, question 4 of the "Practice and Problem Solving" section states, "Lisa bakes focaccia, a type of bread from Italy that has toppings like herbs or cheese. She cuts it into equal square pieces. How many equal squares do you see? Write two equations to show the total number of square pieces." In grade 2, Teacher's Edition, Lesson 10-6, the instructional materials provide strong alignment to the TEKS through the use of concrete models, pictorial representations, and abstract representations. Concrete representations are encouraged as students physically draw plane shapes, measure side lengths, and count vertices to sort and describe polygons. The hands-on drawing process in the "Explore and Share" section such as Tara's and Dominick's work helps students explore the structure of shapes by actively creating them. Pictorial representations are found in both student examples and the "Visual Learning" section, which displays a variety of clearly labeled polygons such as "hexagon," "triangle," and "octagon" in columns sorted by the number of sides and vertices. Students are guided to circle and compare shapes, supporting visual understanding of geometric properties. Abstract representations are built through vocabulary and language development, including terms like hexagon, nonagon, and decagon, along with their prefixes. The "Targeted ELPS Support" and "Language Routine: Compare and Connect" reinforce this abstract language by prompting students to identify, name, and compare shapes using academic terms and sentence frames. This integrated approach ensures that students develop geometric understanding through multiple, connected forms of representation. The resource tasks students with using concrete models and manipulatives to create pictorial and abstract representations. In Topic 12, students use models and number strategies to add and subtract. Lesson 12-1 begins with students using place-value blocks to add 10 or 100 to 3-digit numbers and Lesson 12-3 progresses to using open number lines to add 3-digit numbers. Lesson 12-6 then allows students to use drawings, models, and equations to solve multi-step problems. For example, question 3 from the practice and problem-solving section of Lesson 12-6 states, "There are 328 nonfiction books at a small library. There are 129 fewer fiction books than nonfiction books. There are 162 fewer magazines than fiction books. How many fiction books and magazines are in the library?"

Evaluation for 5.3c
Materials include supports for students in connecting, creating, defining, and explaining concrete and representational models to abstract (symbolic/numeric/algorithmic) concepts, as required by the TEKS.

Grade 2 materials provide opportunities for students to create concrete and representational models and relate them to abstract concepts. In the "Brainingcamp" section of the online resources, tasks allow students to create concrete and pictorial models for the abstract concept of finding the unknown in a problem. In the task "Take From Problem, Change Unknown," students use linking cubes and a number line to model and solve a "take from, change unknown" situation. For example, the problem on the task card states, "There were 24 slices of pizza. A class of students ate some slices. Now, there are 5 slices of pizza. How many slices did the students eat?" In the "Visual Learning Animation" section from Lesson 2-6, students learn ways to use compensation to make numbers easier to add. The video connects counters and ten frames to the concept of compensation and allows students to visually see the strategy of taking from one addend and adding it to the other addend to create an easier number to add. An example in the "Visual Learning" section is the equation 18+15=?. By taking 2 from 15 and giving it to 18, we can make it 20+13. In grade 2, Teacher's Edition, Lesson 7-2, the materials provide multiple embedded supports for students to connect, create, and explain both concrete and representational models to abstract concepts, as required by the TEKS. Concrete models are introduced as students use real-world objects like paper clips to estimate and measure the length of classroom items. In the "Explore and Share" section, students measure and compare physical items such as erasers and blocks using paper clips, which builds a hands-on understanding of length. The student work sample from Christine and Joseph demonstrates how concrete measurement experiences are recorded and used to reason about object lengths. The lesson also provides support for connecting concrete models to abstract concepts by guiding students to compare estimated and measured lengths and encouraging numeric recording of measurements such as "1 paper clip" and "2 paper clips." Representational models are supported in the "Visual Learning" section, where students view images of rulers and various objects with labeled measurements in inches and yards. These visual tools help students generalize from real experiences to symbolic representations. The materials further support creating representational models through activities where students draw and label measurements or compare estimated and actual lengths, helping them move toward numeric reasoning. Additionally, the materials help students define and explain both concrete and representational models. The "Classroom Conversation" and "Talk About Math Ideas" sections include prompts such as "What does it mean that one eraser is about 2 paper clips long?" and "How do you know?" which support students in articulating the relationship between the physical models and their abstract measurements. The "Language Routine: Compare and Connect" section also encourages students to make comparisons using both model-based and numeric reasoning, ensuring they understand and can communicate the meaning behind standard and nonstandard units of measurement.

Evaluation for 5.4a
Materials provide opportunities for students to develop academic mathematical language using visuals, manipulatives, and other language development strategies.

In grade 2, Lesson 13-3 of "Let's Build: Deposits and Withdrawals," students are introduced to foundational financial literacy concepts while developing academic mathematical language through structured teacher guidance and hands-on learning. The lesson begins with a real-world connection as the teacher asks, "Have you ever been to a bank? Where do you keep the money that you earn?" This opening discussion activates prior knowledge and introduces key vocabulary such as deposit and withdrawal. During the "Explore and Share" section, students analyze a scenario involving a character named Jada, who had $136 and now has $142. The teacher prompts students with the question, "What did Jada do at the bank?" This encourages students to reason mathematically and use precise vocabulary to explain that Jada made a deposit. Students are guided to use sentence frames such as, "Jada deposited ___ dollars, so now she has ___ dollars," which supports both their conceptual understanding and language development. Teachers are provided with embedded guidance in the Teacher's Edition to scaffold vocabulary use, including prompts such as "What happens to the balance when you deposit money?" and "How can we show a withdrawal using a number sentence?" These strategies help students internalize the meaning of financial terms in mathematical contexts. In the "Practice and Problem Solving" section, students solve word problems that require them to apply the terms deposit and withdrawal accurately. For example, a problem might ask, "If you had $150 and withdrew $20, what is your new balance?" Students are encouraged to explain their thinking using academic language, reinforcing their understanding through both oral and written expression. In Lesson 7-2, "Let's Build: Using Models for Customary Units," grade 2 students explore how the size of a measurement unit affects the number of units needed to measure an object. This lesson provides rich opportunities for students to develop academic mathematical language through the use of visuals, manipulatives, and structured language supports. The lesson begins with the teacher prompting discussion with questions such as, "What are some things you might measure in inches? In feet? In yards?" introducing the key concept that shorter units require more repetitions to measure the same length. Students engage in hands-on exploration using snap cubes, paper clips, and inch rulers to measure classroom objects, then compare and discuss their results. Teachers model and reinforce vocabulary such as inch, foot, yard, and unit of measure, while guiding students to use sentence frames such as "It took ___ paper clips but only ___ inches to measure the same object." During the Step 3: "Practice and Problem Solving" section, students are encouraged to explain their reasoning in problems seven and 10, using precise mathematical language to articulate their understanding. The lesson also incorporates opportunities for students to record and compare measurements in a chart, supporting both data organization and vocabulary application. Through a combination of manipulatives, visual models, and structured discussion, this lesson effectively builds students' conceptual understanding of measurement and strengthens their use of academic mathematical language.

Evaluation for 5.4b
Materials include embedded teacher guidance to scaffold and support students' development and use of academic mathematical vocabulary in context.

The grade 2, Academic Vocabulary Teacher's Guide provides strong evidence that the materials include embedded guidance to scaffold and support students' development and use of academic mathematical vocabulary in context. The materials include a printable one-pager to guide the teacher, as well as assignable online activities for each vocabulary word, which include the word's pronunciation, a student-friendly definition, a brief contextual task, and an opportunity for students to use the word in a sentence. These components promote active engagement with academic language and support vocabulary acquisition in a structured way. In addition, the guide offers teaching suggestions for each word, such as how to introduce it, examples of related tasks, sentence stems, and engaging activities, along with related words and synonyms. In the grade 2, Lesson 11-3 "Let's Build" section, students deepen their understanding of place value by learning to name, read, and write numbers up to 1,200 in standard form, expanded form, and word form. The teacher begins by writing the number 842 on the board and asks, "How can we show this number in different ways?" Students respond by breaking it into hundreds, tens, and ones, saying, "Eight hundred forty-two is 800 + 40 + 2," which is its expanded form. The teacher reinforces vocabulary by modeling sentence stems such as, "The standard form is ___," "The expanded form is ___," and "The word form is ___." Students then practice writing numbers in all three forms using place value blocks and number cards. During the guided discussion, the teacher asks, "Why is it helpful to write numbers in expanded form?" prompting students to explain how it shows the value of each digit. Visual aids, such as anchor charts and labeled examples, support students in connecting the vocabulary to the number representations. Through repeated use and discussion, students build confidence in using expanded form, standard form, and word form to describe and understand numbers up to 1,200.

Evaluation for 5.4c
Materials include embedded teacher guidance to support the application of appropriate mathematical language to include vocabulary, syntax, and discourse to include guidance to support mathematical conversations that provide opportunities for students to hear, refine, and use math language with peers and develop their math language toolkit over time as well as guide teachers to support student responses using exemplar responses to questions and tasks.

The Teacher's Edition provides guidance to support student responses with sample student work. The sample student work exhibits the thinking of two students. One of the samples includes misconceptions and teacher guidance to correct the student's error. The resource provides guidance to use the student samples to anticipate student responses or projected in class to prompt discussions and make connections. There are specific questions in the Teacher's Edition that the teacher can ask individual students, along with desired student responses to listen for. For example, in Lesson 4-1, "Orion used partial sums," the guidance provided states, "You might ask Orion: 'What place value do you start with?'" and the desired student response to listen for, "You can start with either place value, tens or ones. I started with tens." The grade 2 Teacher's Edition, Topic 11 materials include embedded teacher guidance to support the application of appropriate mathematical language, including vocabulary, syntax, and discourse. The Vocabulary Activity provides teacher guidance to have the students use the graphic organizer, Word Web, to explore vocabulary such as compare, greater than, less than, and equals, encouraging students to use precise mathematical terms in context. By recording numbers in different forms such as standard and expanded and making comparisons, students engage in meaningful conversations using correct vocabulary and comparative language structures. The "Academic Vocabulary" section further supports syntax and discourse development by providing sentence stems, "The value of the digit in the hundreds place is _____," and guiding questions such as "How can you extend the number pattern?" while encouraging students to articulate mathematical reasoning using words like develop, extend, and value. These structured supports enable students to effectively communicate mathematical ideas, justify reasoning, and engage in academic discourse using appropriate vocabulary and grammar. In grade 2, Lesson 13-5 "Let's Build: Producers and Consumers," students engage in academic conversations that support the development of content-specific vocabulary and structured reasoning within a social studies context. While this lesson shifts from mathematics to economics, the instructional design still emphasizes the use of academic language through vocabulary, syntax, and discourse. Students explore the roles of producers and consumers in a community, using sentence stems and guided discussions to articulate their understanding. For example, a student might begin by saying, "A farmer makes food," and the teacher prompts them to expand using the question, "Can you say that using our vocabulary?" The student refines their response to, "A farmer is a producer because they grow food for others to buy," demonstrating the use of precise vocabulary and improved syntax. Another student might say, "I go to the store and get stuff," and the teacher models a more academic response, "Let's say, 'I am a consumer because I buy goods from producers.'" The student repeats, "I am a consumer because I buy things," showing growth in using economic terms. These exchanges reflect how the lesson materials provide opportunities for students to hear, refine, and use academic language with peers, while also guiding teachers with exemplar responses to scaffold student thinking. Through structured conversations and vocabulary-rich tasks, students build their understanding of economic roles and strengthen their ability to communicate clearly and confidently in academic settings.

Evaluation for 5.5a
TEKS process standards are integrated appropriately into the materials.

The grade 2 materials integrate the TEKS Mathematical Process Standards in an appropriate and intentional manner, as evidenced by the inclusion of the Problem-Solving Model provided in the Problem-Solving Handbook. This model supports students in engaging with multiple process standards by guiding them through structured thinking steps: analyzing given information, formulating a plan, determining a solution, justifying their reasoning, and evaluating the overall process. Each section includes student-friendly questions that align with the TEKS Process Standards such as 1A: "applying mathematics to solve everyday problems," 1B: "using problem-solving models," 1D: "communicating mathematical ideas," and 1F: "analyzing mathematical relationships." This tool not only reinforces critical thinking and reflection, but also encourages consistent use of academic math language. By embedding this model into lessons and tasks, the materials ensure that students are regularly practicing essential problem-solving skills and that the TEKS Process Standards are authentically woven into instruction across the grade 2 curriculum. In grade 2 Topic 6: Work with Money and Time, the TEKS Process Standards are thoughtfully integrated into each lesson through real-world problem solving, hands-on tools, and mathematical reasoning. In Lesson 6-1: Solving Problems about Money, students apply skip counting, addition, and subtraction to determine the value of a group of coins, aligning with TEKS 2.1C, 2.1E, and 2.1G, which emphasize selecting tools, using strategies, and justifying solutions. Teachers prompt students with questions such as, "How can you count these coins efficiently?" while students explain their strategies aloud or in writing. In Lesson 6-2, students use real or plastic coins and number cubes to solve coin value problems, reinforcing the idea that coin value is not related to size. This supports TEKS 2.1D and 2.1E, encouraging students to use mathematical tools and communicate their thinking.

Evaluation for 5.5b
Materials include a description of how TEKS process standards are incorporated and connected throughout the course.

The Program Overview includes clear descriptions of how the TEKS process standards are incorporated and connected throughout the course. Each topic's "Connections" section highlights how students apply process skills such as problem solving, reasoning, representing, and communicating. They apply strategies to solve addition and subtraction problems in Topics 1–5, represent equivalent values of money and time in Topics 6–7, and analyze and interpret data in Topic 8. Concepts of equal parts and fractions in Topic 9, geometry in Topic 10, and place value relationships to 1,200 in Topics 11–12 further develop students' mathematical thinking. Topic 13 applies these skills to real-world financial literacy. The process standards are clearly connected and revisited throughout the year. The materials include opportunities for students to connect the process standards to their content learning. The enVision program is developed with three types of lessons: Let's Build, Let's Investigate, and Let's Model. Every topic in the course has at least one Let's Model lesson that incorporates the process standards in a real-world situation with recently learned content. The "Let's Model" section consists of three acts: Act 1: The Hook, Act 2: The Model, and Act 3: The Solution. The Teacher's Edition provides a description of how the three acts connect the TEKS to process standards, which states, "Mathematical modeling is practiced as students: pose a mathematical question about a situation, identify information needed to solve a problem, develop a model that represents the situation, use the model to propose a solution, and test the appropriateness of the math model." For example, in Lesson 7-13, "Students are tasked with determining the difference in lengths between two toy vehicles given their lengths."

Evaluation for 5.5c
Materials include a description for each unit of how TEKS process standards are incorporated and connected throughout the unit.

The Teacher's Edition provides a description of how the process standards are connected throughout the unit. Each topic in the enVision program incorporates the process standards within the units while also explicitly focusing on how to connect two process standards throughout the unit. Topic 2 places greater emphasis on grade 2 students creating and using representations to organize, record, and communicate mathematical ideas, as well as to display, explain, and justify mathematical concepts and arguments. The description includes characteristics of proficient students for these two process standards, as well as how the process standards relate to the TEKS. For example, it states, "provide opportunities for students to reflect on these mathematical process standards as they progress from using a hundred chart and developing strategies to add two-digit numbers mentally to adding on a number line and using place-value models." In the "Mathematical Process Standards" section in the Teacher's Edition, the process standards for Topic 13 are listed. This topic addresses personal financial literacy and focuses on developing proficiency with standards 2.1B: "The student is expected to use a problem-solving model that incorporates analyzing given information, formulating a plan or strategy, determining a solution, justifying the solution, and evaluating the problem-solving process and reasonableness of the solution" and 2.1F: "The student is expected to analyze mathematical relationships to connect and communicate mathematical ideas." Students are consistently engaged in problem-solving activities that require them to analyze information, determine relevance, develop strategies, and justify their reasoning. The materials also emphasize the connection between mathematical relationships and real-world financial concepts, such as saving, spending, borrowing, and the roles of producers and consumers. Instructional guidance, lesson tasks, and reflection questions are designed to help students make meaningful connections between the process standards and financial decision-making. This intentional integration ensures students deepen their mathematical thinking and understanding of personal finance across the unit.

Evaluation for 5.5d
Materials include an overview of the TEKS process standards incorporated into each lesson.

In grade 2, Topic 10, Lesson 10-2, "Let's Build: Solid Figures," students explore and describe three-dimensional shapes through hands-on activities and structured problem-solving that align with the TEKS Process Standards. The lesson begins with an "Explore and Share" activity where students are asked to find and describe three solid figures in their classroom, such as a box (cube), a can (cylinder), or a ball (sphere). This encourages observation, classification, and real-world connections. The "Visual Learning" section supports conceptual understanding with prompts like, "How can you describe each shape?" and "What are some examples of these shapes?" Students then move into Practice and Problem Solving, where they name figures, count flat surfaces or faces, and identify vertices. For example, students complete sentences such as, "A cylinder has __ flat surfaces or faces," and, "A cone has __ flat surface(s)." Higher-order thinking tasks ask students to draw a rectangular prism with specific dimensions and compare solid figures to everyday objects. The lesson concludes with Step 4: Assess and Differentiate, which includes a Quick Check, Additional Practice, a Video Tutorial, and an Intervention Activity. In the grade 2 Teacher's Edition materials for Lesson 12-2, "Add Using Math Models and Place Value," include a clear and detailed overview of the TEKS mathematical process standards incorporated into the lesson. In the "Texas Essential Knowledge and Skills (TEKS)" section, the lesson identifies process standards 2.1C, 2.1D, and 2.1E. These standards support students in selecting appropriate tools and techniques, communicating reasoning using multiple representations, and organizing and recording mathematical ideas. The lesson objectives and activities align with these standards by having students model three-digit number addition using place-value blocks and explain their thinking both orally and in writing. The integration of these standards into the conceptual understanding and procedural focus of the lesson ensures students are actively engaging with the mathematical process standards throughout their learning.

Evaluation for 6.1a
Materials provide opportunities for students to think mathematically, persevere through solving problems, and to make sense of mathematics.

In the "Math Walk" section of Topic 6, students are introduced to the topic's essential question, "How can you solve problems about counting money or telling time to the nearest minute?" Students then watch a short video to generate excitement about clocks. As students watch the video, they try to think mathematically about questions such as, "What time is it?" Then the teacher poses questions such as, "What did you notice?" "What did you see in the video that would help you answer the question?" "What math do you already know that can help you answer the question?" and "What math questions do you have about what you saw in the video?" The resource guides the teacher to have students discuss the questions with a partner and then in a whole-class discussion. After completing Lesson 6-5, the materials guide the teacher to revisit the video and then ask, "What math did you learn that could help you answer the question or find the answer in a different way?" In the "Visual Learning" section of Lesson 8-4, the materials guide the teacher to begin the lesson with a classroom conversation using questions such as, "What does the information in the table show? What do the numbers at the bottom of the graph show? What does each graph show? Which graph makes it easier to see quickly who sold the most/least?" They are asked to reason about which graph makes it easier to interpret the data and why, helping them make sense of mathematical representations. The Prevent Misconceptions note addresses common errors such as ignoring the key or scale, prompting teachers to reinforce careful attention to graph features. In enVision Math, students solve a real-world problem involving ways to earn money in Lesson 10-10. Students are asked the question, "What will the design look like?," make a prediction, and then the teacher is guided to survey the students' predictions. The teacher guides the students to analyze their predictions by asking, "Why do you think your prediction is the answer to the main question?" "Who has a similar prediction?" and "Who has a different prediction?" Students think about what information they need to solve the problem before the teacher reveals the information to them. Students develop a math model to the problem and share strategies with the class and update their predictions based on the new information learned. The answer is revealed to the class, and students reflect on their thinking. Then, the teacher encourages deeper understanding by asking questions such as, "Explain how you used math to represent the situation. How did doing that help you answer the main question?" "How do pattern blocks help you create a design? What made pattern blocks an especially helpful tool for brainstorming design ideas?" "How might you analyze and evaluate the efficiency of the approach you chose to solve the problem?" and then students create their own problems.

Evaluation for 6.1b
Materials support students in understanding, explaining, and justifying that there can be multiple ways to represent and solve problems and complete tasks.

The Let's Investigate Lesson in the Student Edition supports students in building understanding and explaining key concepts in the lesson. The Step 2: "Connect" section provides questions for students to represent and solve problems and tasks in multiple ways. For example, in Lesson 2-1 of Topic 2, the directions state, "What patterns do you see in the hundred chart that help you add by tens and by ones? If you spin a nine, is there another way to go nine more without counting one square at a time? You land on 45. How can you use what you know about skip counting to add 25?" In addition, students are asked, "Is there more than one way to add 45 + 25? Why might it be helpful to know different ways to add?" EnVision Plus Mathematics encourages students to discuss possible sources of error involved in using math to model a real-world situation which allows students to justify their thinking and compare it to incorrect responses or misconceptions. For example, the Teacher's Edition in Topic 4 prompts the teacher to ask students, "How useful was your model at predicting the answer? Would you change your model after watching the video? How would you change it?" Teachers can also test students' understanding of the real-world problem by asking, "What real-world variables can impact this answer to the Main Question?" In grade 2, Lesson 12-5, the "Language Support" section guides students in understanding, explaining, and justifying that there are multiple ways to represent and solve problems. The activity encourages students to use partial sums charts as they work through addition problems, helping them make connections between solving with and without the chart. By comparing representations and discussing partial sums for different place values, students recognize flexibility in how problems can be broken down and solved.

Evaluation for 6.1c
Materials are designed to require students to make sense of mathematics through multiple opportunities for students to do, write about, and discuss math with peers and teachers.

EnVision Plus Mathematics provides opportunities for students to make sense of mathematics throughout Lesson 3-4 in the Student Edition. Students begin by choosing a strategy to find 45−26 and then explain their reasoning using pictures, words, or numbers. Students continue to learn the key concepts of subtraction during a think-pair-share activity when they "use mental math to explain how you can break apart 36 to find 62−36 with a partner" and then finish the lesson by solving a problem and explaining in writing the most efficient way to solve it. For example, question 7 states, "Ramona finds 82−39 by breaking apart 39. Then she uses the number line. Find 82−39. Do you think this is an efficient way to solve it? Explain." The "Language Support" section in Lesson 5-7 provides opportunities for students to complete a Frayer model for the term equal groups. The teacher asks the students to write the word in the center of the graphic organizer and complete the outer sections of the model, including definition, characteristics, examples, and non-examples. Students then share their ideas with a partner and add more to their own graphic organizer and then the teacher facilitates a whole class discussion of the graphic organizers. In grade 2 Teacher's Edition Lesson 6-5, the "Math Talk" section titled "Quick Look" promotes meaningful mathematical discourse as students explore concepts in geometry and measurement. The teacher is guided to display an image of an analog clock for about five seconds, and then in a small group, have students describe and discuss what they observed. Guiding questions such as, "At what number was the longer hand pointing?" and "What does that mean?" encourage students to analyze the position of the clock hands and interpret their meaning. Students also discuss where the shorter hand was pointing, and what that reveals about the time shown and are invited to share their thinking with a partner and then reflect as a class when the image is displayed again.

Evaluation for 6.2a
Materials support teachers in guiding students to share and reflect on their problem-solving approaches, including explanations, arguments, and justifications.

In grade 2, students reflect on their problem-solving approaches by describing the picture of the ten-frame that contains seven red counters and three yellow counters in Topic 1. The materials in the Teacher's Edition then prompt the teacher to ask the students to reason about the ten-frame and the facts by stating, "What is represented by the addition facts written above the ten-frame?" Students then justify their approach when the teacher asks, "What strategy would you use to find 7 + 3 = 10?" and "How can you use 7 + 3 = 10 to find 3 + 7 = 10?" In Lesson 7-8, students share their knowledge of finding length during a classroom conversation. The materials provide prompts for teachers to guide students in sharing their thinking with questions such as, "Why do you need to think about both parts of the path when you estimate and measure? Why do you need to measure the two parts of the blue and red paths? Which path is longer? How do you know?" The grade 2 Teacher's Edition, Lesson 12-6 in the "Explore and Share" section supports teachers in guiding students to share and reflect on their problem-solving approaches through explanations, arguments, and justifications. Students solve a two-step word problem involving three-digit numbers and are encouraged to use drawings, models, or equations. The teacher guidance prompts discussion on the strategies students choose, such as using partial products or equations, and encourages students to explain how they reached their answer. Sample student work from Aimee and Devin provides contrasting methods, prompting conversations around accuracy and reasoning. Teachers are encouraged to select both correct and incorrect solutions for discussion, helping students justify their thinking and reflect on number sense. The "Connect" section reinforces this by having students compare strategies and explain their choices, promoting meaningful reflection and mathematical argumentation.

Evaluation for 6.2b
Materials include prompts and guidance to support teachers in providing explanatory feedback based on student responses and anticipated misconceptions.

EnVision Plus Mathematics provides sample student work that describes what the student did and shows a sample of the student's work. One student work sample includes a misconception for the teacher and students to analyze as a class. Specific questions are provided for the teacher to ask individual students, along with responses for which the teacher should listen. For example, in Lesson 8-1, the materials include two samples for the following problem: "Compare a pictograph and a bar graph that correctly represent the results of a survey about pet adoptions. Explain how the pictograph and bar graph are alike and how they are different." One of the student responses includes, "Jared stated that both graphs list the same animals and the same title." The suggested feedback for Jared is, "How do the graphs show the votes in different ways?" Jared noticed what was alike in the graphs but not different, so the teacher guidance helps the student understand the depth of the problem. The "Prevent Misconceptions" section in Lesson 9-1 includes teacher guidance that helps address a common misunderstanding about partitioning shapes—that the whole is made up of all the equal parts. It prompts teachers to encourage students to explicitly state the number of equal parts and count them to recognize that all parts together make up the whole. This support can be incorporated into classroom conversations by asking students to reflect on their diagrams and explain how they know the shape is divided equally. For instance, during discussions about dividing rectangles or circles into fourths, teachers can use this prompt to redirect students who mistakenly believe that fewer parts can still represent the whole or who confuse the number of lines drawn with the number of parts created. The reminder to point out that all parts are needed to make the whole reinforces foundational understanding of fractions and equal partitioning. In the "Guided Practice" section of Lesson 11-6, students are tasked with locating whole numbers on an open number line. The materials prompt the teacher by stating, "If students connect 242 and 295 to the wrong locations, then have students count aloud by 10s from 200 to 250 and then from 250 to 300 to listen for 240 and 290. Encourage them to use place values to compare the numbers." The materials continue to offer feedback: "Explain to students that you can count by 10s to determine the middle number, which is the number that is halfway between the two numbers on the open number line." Within the same lesson, the teacher provides feedback to the student "reminding them you can locate a whole number on an open number line."