ENVISION+ TEXAS MATHEMATICS 2027 (PRINT + DIGITAL), GRADE 1

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

In the "End Matter" section of the Teacher's Edition, enVision Plus Mathematics provides a suggested scope and sequence that outlines the specific order of math Texas Essential Knowledge and Skills (TEKS), English Language Proficiency Standards (ELPS), and concepts taught throughout the instructional year. In the Grade 1 Scope and Sequence document for the 165- and 210-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 and in the "End Matter" in 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).

The resource provides a pacing guide for 165, 180, and 210 days. The materials also provide a pacing guide with a day-to-day suggestion for lesson implementation that aligns with the scope and sequence of 165, 180, and 210 days. EnVision Plus Mathematics includes a suggested pacing guide in the "End Matter" section of the Teacher's Edition, which provides lessons and activities for a full year of instruction. For example, the resource provides a 180-day pacing guide for grade 1. The materials include pacing for two–three days of each Topic Review and Topic Assessment, as well as two–three days per topic on differentiation activities. The materials include a pacing guide that offers options for adjusting the time spent on units without disrupting the sequence and coherence of the content. For example, the order of the units remains the same with 180-day pacing, but each unit is reduced to four–six 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 includes an explanation for the rationale of unit order in the "Program Overview" found within the Teacher's Edition. 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 over the course of a year. The resource includes a Grades K–2 Program Overview that explains the coherence of the curriculum and describes how students within grade 1 will make connections to prior learning in both grade K and previous grade 1 lessons. Topic 9 in the Grade 1 Teacher's Edition provides a "Math Background Section," which is the coherence of lessons to be taught in the unit, as well as how they connect to student's prior knowledge, and how they will connect as the student moves throughout the grade level.

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

EnVision Plus Mathematics includes protocols for teachers to thoroughly understand and prepare to teach a unit, using the "Topic Internalization Protocol." The 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 includes protocols to guide teachers to thoroughly review 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 and relating new and previously taught vocabulary, completing the student pages from a student perspective, adjusting pacing to meet the needs of the teacher's specific class, identifying formative assessments given, and providing appropriate supports to differentiate instruction. The materials include internalization protocols for topics in this curriculum. These protocols include 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 a section to help gather the materials and supplies needed for the lesson. The materials include internalization protocols for lessons that offer a structured approach including lesson goals, transition and pacing of lesson components, preparation to teach the lesson, and the gathering and preparing of materials.

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

EnVision Plus Mathematics includes resources for instructional leaders to support teachers with implementing the materials designed. This includes a Classroom Observation and Analysis Tool, Instructional Leader Topic Internalization protocol, and an Instructional Leader Lesson Internalization protocol. In grade 1, this document includes a place to document concept development, practice, differentiated instruction, and student reflection. The materials include resources for instructional 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 instructional leaders to support teachers with implementing the materials provided. This includes a classroom observation and analysis tool, instructional leader topic internalization protocol, and an instructional leader lesson internalization protocol found in the "Internalization Protocols and Observation Tools" section. The tools serve as a resource to enable instructional leaders to record targeted indicators when observing teachers instruct students. This instrument is designed for documentation purposes only, not for teacher evaluation. The materials provide resources for instructional leaders to guide teachers with implementing the materials provided through rationale, implementation, and extension using the Instructional Leaders Topic Internalization Protocol. This is 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 includes 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 previously taught along with those in upcoming instruction, and a balance of conceptual understanding to procedural fluency. In Topic 1, the "Math Background" states, "that students use different patterns to recognize how many from numbers one to 10, and observe that the number of objects in some patterned arrangement can be recognized without counting." The resource includes comprehensive unit overviews that provide academic vocabulary necessary to effectively teach concepts in the unit. For example, in "Review What You Know" in Topic 1, the academic vocabulary includes parts, whole, equation, equal sign, equals, subtract, minus, difference, more, compare, fewer, addend, sum, plus, and add. The materials provide 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 3, the materials show the sequence between beginning addition and subtraction to 10 in kindergarten, and how this topic connects to future learning of fact fluency with facts up to 20 in both addition and subtraction.

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 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 that include sample problems, and home activities. The materials contain supports for families in both Spanish and English for each topic (unit), 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. One example activity includes 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 the caregiver a description of what the student is learning. For example, in Topic 4, the resource states, "your child is using different strategies to solve subtraction facts to 20." Then it shares activities to do with the student at home, including creating a game with a ten-frame and subtracting numbers.

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 provides lesson plans that include a list of materials that are necessary to support instructional materials for this lesson. In Lesson 3-1: "Use Counting On," counting sticks are listed under the Materials Section. The 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. The resource includes lesson plans that provide the necessary information for the effective implementation of grade-level instruction. The lesson plans include both mathematics objectives and language objectives, vocabulary, and instructional materials to meet all grade-level objectives. 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 enVision Plus Mathematics include all components for instructional delivery found in the "Lesson Plan Guide" in the Teacher's Edition of every unit. This includes daily objectives, check-for-understanding questions, 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 being taught.

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 includes a list of teacher and student materials in each lesson, such as manipulatives, and activity pages or templates, at the beginning of each lesson. In Lesson 10-2 of Topic 10 in the Teacher's Edition, the student and teacher materials are listed, such as measuring tools and 2-D shapes. In the lesson overview, the resource provides a recommended time for each component. In Lesson 2-4 of Topic 2 in the Teacher's Edition, the "Timeline" section includes an allotted time for Step 1: Explore and Share is suggested for 10–15 minutes, Step 2: Visual Learning is suggested for 5–10 minutes, Step 3: Practice and Problem solving is suggested for 15–20 minutes, and Step 4: Assess and Differentiate is suggested for 10–20 minutes. The materials include a lesson overview listing the teacher and student materials necessary to effectively deliver the lesson. In Lesson 5, the materials include connecting cubes, teaching tool 72, two-colored counters, and teaching tool 77. The student resources, B13-adding in any order and B20-adding doubles, are listed and available in the Teacher Resources section with a QR code.

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

The materials include a digital resources list with strategies to use to extend learning, intervene, and do more guided practice. The resource also supports teachers in assigning online lesson activities through a digital learning platform that offers interactive learning activities to extend and enrich the lesson objective unit. EnVision Plus Mathematics includes guidance on the effective use of lesson materials. One example is in the Topic 5 Building Automaticity review and includes an "extra challenge" that encourages students to work in partners to identify which numbers can be subtracted to make 10. The resource includes enrichment opportunities to deepen mastery of the lesson objectives. In Lesson 12-1, Topic 12 of the Teacher's Edition, the enrichment activity gives the student an opportunity to explain their reasoning on which one is the shorter path and why.

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 1 Assessment Sourcebook, assessments include diagnostic, formative, 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 1 materials include a progress monitoring assessment issued at the beginning of the year, middle of the year, and end of the year. The resource also provides online versions of these assessments. The Grade 1 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 1 materials include diagnostic and summative assessments found at the beginning and end of each topic. The diagnostic assessment appears at the beginning of each topic labeled "Review What You Know." For example, in Topic 3, the "Review What You Know" guides the students to identify strategies and vocabulary, as well as answer addition and subtraction word problems. This diagnostic assessment offers a variety of tasks and questions by having the students complete the task by choosing one of three answer choices or writing the correct response. There are also two different summative assessments for each topic, allowing for a variety of tasks. In Topic 3, there is a "Topic Assessment" and a "Topic Performance Task." Both assessments provide multiple question types including multiple choice and open ended responses. In the Grade 1 Teacher's Edition, at the end of each topic there is an assessment with varied types of questions going from recall of information such as "Look at the pattern of cubes, what is the total number?" to more rigorous questions such as, "A team starts practice with 7 balls, they lose 4 of them, how many are left?" There is also a Topic 1 performance task that includes space for the students to read, draw, and write to answer. They must also explain their thinking, which includes the higher-level thinking skills required to explain why their answer is right. In Topic 6, Lesson 2 in the Teacher's Edition, there are multiple assessment tasks available in the lesson 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 6, Lesson 2 the math goal is "I can collect information and organize it using a picture graph." The students then mark the corresponding face on how they feel. In the grade 1 Lesson 8-6, there is a quick check to do a formative review of a specific skill for that lesson. One example of a quick check is "Count the tens and ones. Give two ways to break apart 41 and enter your answers in the boxes." There is also an Exit Ticket that includes other types of questions for the specific skills in Lesson 8-6, where it asks the student if they do not agree and why.

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

EnVision Plus Mathematics 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 1 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 used to diagnose the student's readiness for learning by assessing prerequisite content. The assessment is given before instruction. 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 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 assess instructional assessments like the "Observational Assessment," "Portfolio Assessment," "Performance-Based Task," and "Program Assessments." For example, in the "Observation Assessment," 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 where the assessments can be found and 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," which can be 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 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." In the online version for each assessment, which is available for all assessments, directions are prerecorded for each question and all students have it read aloud to them. The students can press the "play" button as many times as necessary to have the question/directions read to them. This helps ensure consistent administration of assessments and that all students receive the same instructions and testing environment, leading to more reliable and comparable results.

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

Diagnostic assessments are clearly aligned to the TEKS and objectives of each course. For example, in the "Review What You Know" found in Topic 7: "Numbers to 120," there is an "Item Analysis Chart" that lists the TEKS and each question aligned with the standards. In Topic 7: "Numbers to 120," the "Review What You Know" section, questions 1, 2, 4, and 5 are aligned with 1.5D, and questions 3 and 6 are aligned with 1.5F. Question 4 states, "Margie finds 7 rocks. Kara finds 6 rocks. How many rocks did they find all," which aligns to 1.5D, which represents word problems involving addition and subtraction of whole numbers up to 20 using concrete and pictorial models and number sentences. The questions also align with the objectives of the unit. For example, in the "Topic Planner" of the Teacher's Edition, one of the math objectives listed includes "solve a real world problem involving counting groups." Questions 4 and 5 students are solving real word problems. Formative assessments identify alignment of the TEKS and objectives of each lesson. The Exit Tickets in Topic 2, Lessons 2–3 are aligned to the TEKS 1.3D: Apply basic fact strategies to add and subtract within 20. The TEKS are listed under the example of the Exit Ticket found in the Teacher's Edition. The learning objective of "use doubles and near doubles facts to solve problems" aligns with questions 1 and 2. The Summative assessments located at the end of each topic clearly align to the TEKS listed for that corresponding topic. The materials provide an "Item Analysis Chart" that lists each question with the corresponding TEKS. For example, in Topic 6, questions 1, 2, 3, 5, and 6 are aligned with 1.8C, question 4 is aligned with 1.8A, and questions 7 and 8 are aligned with 1.8B. The "Topic Planner" for Topic 6 lists the objectives for the unit; these objectives align with the Topic 6 Topic Assessment. For example, one objective states "Interpret data and draw conclusions from picture graphs," and question 3 on the Topic Assessment has the students using the picture graph to identify which of the following statements are true. The enVision grade 1 Topics 1–3 Cumulative/Benchmark Assessment Item Analysis Chart is designed to align with the TEKS standards, ensuring that each tested item corresponds to a specific learning objective. This chart provides educators with a detailed breakdown of student performance, linking each question to its respective TEKS objective and Depth of Knowledge (DOK) level. By categorizing items based on cognitive demand—ranging from recall and basic application to strategic thinking—teachers can assess students' mastery of foundational math concepts and adjust instruction accordingly.

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

EnVision assessment resources come in various formats, each designed to evaluate different aspects of students' learning and skills. These formats include selected responses, 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, like 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. Grade 1 materials include an Item Analysis Chart for each instructional assessment provided in the Topic Assessment located in the online resources. The Item Analysis Chart states the DOK level associated for each assessment and correlating question number. Each unit in the grade 1 instructional assessments contains more than two levels of complexity. For example, in Topic 3 the Exit Tickets have a complexity level of 1 and/or 2. In addition, the Performance Task at the end of each topic also has multiple DOK levels of 2 and 3. For example, question 1 "Roger read 4 more books in July than he did in January. How many books did he read in July? Draw a picture to solve. Then write an equation to match," is labeled as a DOK 2 question. Topics 1–6 Cumulative/Benchmark Assessment includes a variety of questions aligned to the TEKS. The assessment includes a variety of questions with different levels of complexity. For example, "Which color was chosen most? Use the data in the tally chart to complete the bar graph. Which number is missing? Explain how you know your answer is correct. Which equations show how to make 10 to solve 13 – 7?" Topics 1–6 Cumulative/Benchmark Assessment question 2 says "Which addition fact can help you solve the subtraction problem? 17–9 = ?" For question 4, "Which doubles fact will help you find 5 + 6?"

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 9 of the Teacher's Edition gives guidance to teachers on how to score the assessments. For example, on the Topic 9 Performance Task, item 2 is based on two points. The student earns the full two points if they correctly identify the number of Pat's door as well as the possible colors of Ming's door. Only one point is earned if the student correctly identifies the number of Pat's door or the possible colors of Ming's door. This allows for consistent, reliable, and aligned scoring among all teachers. The materials include guidance for interpreting student performance on instructional assessments. For example, in Topic 2: "Add and Subtract Within 10," in the Teacher Edition guides teachers to give the Exit Ticket to students and then "[u]se the Exit Ticket results to support students as needed by reminding them that a ten-frame can be used to solve addition facts with numbers up to 10." 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.

Grade 1 materials include guidance for teachers to use intervention activities based on student performance on tasks. For example, in Topic 5, Step 4, "Assess and Differentiate" in the Teacher's Edition, teachers are provided with an intervention activity that relates to the skill and concept taught in the lesson. First, the teacher writes the following expression frames on the board: " _ + and - __." Then, the teacher asks students to work individually using the given images of two-color counters to write two equal expressions based on the equation frames. The teacher allows for pictorial and concrete representations. Students then explain their expressions to a partner. Teachers are provided with guidance on ways to respond to student trends on assessments. For example, in Topic 8: "Represent and Add Greater Numbers," Lesson 8-2 in the Teacher's Edition, if students make a mistake on question 5, "Karl fills 2 ten-frames with counters," the student is then guided to put 5 counters in another ten-frame and circle the ways that show the number of counters Karl uses. The materials suggest that "If students are confused with tens and ones and choose 52 or 5 tens and 2 ones as their answer, have them build a concrete model that shows how Karl fills the ten-frames with counters and ask them to count the counters aloud to determine the correct answer." In the "How to Assess" section of the "Assessment Guide," enVision Plus Mathematics 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 5-4, the directions guide the teacher to, "Check student's work," as students write the missing number to make the equations true on question 1, "10 + ? = 5 + 7," and question 2, "9 - 5 = 6- ?" and use counters as needed for support. Teacher guidance includes an "Error Intervention" for item 2," which states, "If students have difficulty with the first step, then remind them that they should first solve the side that shows both numbers." For example in question number 2, the students would first solve the equation, "9–5."

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 1 include a Student Progress and Growth Teacher Tool within the Student and Teacher Progress Trackers. This tool 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, 1.2A: "Recognize instantly the quantity of structured arrangements" is covered in Lessons 2-4 and 2-6. 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 1, materials include student progress and growth trackers that support students in analyzing their own learning. These tools, available in both the "Student and Teacher Progress Trackers," guide students in reflecting on the math goal before, during, and after each topic. For example, in Lesson 4-1, the math goal is "I can subtract using a number line." At each stage, students choose one of three reflection options: "I Can," "With Help," or "Not Yet." They circle the option that best represents their current level of understanding. This structured reflection process encourages students to monitor their progress and take ownership of 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 enVision 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 scaffolded, step-by-step guidance that helps break down complex concepts into manageable parts. Teacher-Guided Activities are also included, offering students 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 grade 1 materials include intervention activities that provide clear teacher guidance, hands-on support, and scaffolded instruction for students who have not yet reached proficiency on grade-level content and skills. In Lesson 1-4 Intervention Activity in the Teacher's Edition, teachers are guided to use simple, familiar objects such as pencils or markers to help students visualize and act out subtraction scenarios. The activity begins with a relatable story problem: "8 students are on the bus; 2 get off. How many students are still on the bus?" Teachers guide students to physically represent the problem using manipulatives and then retell the story, modeling the thinking and reasoning behind the subtraction. This concrete approach supports differentiated instruction by allowing students to engage kinesthetically and visually with math concepts they may struggle to understand in the abstract form. The activity also includes opportunities for repeated practice with similar stories, reinforcing understanding through multiple exposures. Additionally, the structure of the activity shows clear scaffolding—from acting out a single scenario to telling and solving new subtraction stories independently. These features demonstrate that the materials not only provide instructional support, but also offer engaging, developmentally appropriate intervention activities for students needing additional practice with foundational subtraction concepts. The materials provide teacher guidance for differentiated instruction, activities, and paired lessons to support a range of student needs. For example, the "Differentiated Instruction" section in the Program Overview outlines an Intervention System designed to help teachers deliver effective support for students performing at or below grade level. Each Intervention Lesson includes guided instruction followed by targeted practice activities. Teacher Support notes offer clear guidance for conducting short lessons that emphasize vocabulary development, conceptual understanding, and skill practice. For a grade 1 example, the Intervention System includes Intervention Lesson B2 and B6 which reinforce subtraction skills and finding differences. These lessons pair with Lesson 1-6. All lessons include specific teacher directions and student activity pages that reinforce foundational number skills. The Grade 1 Teacher's Edition includes an Intervention Activity which 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 Intervention Activity in Lesson 4-8 provides instructions for a direct lesson with students. Teacher directions require that stud

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).

In enVision Plus Mathematics Grade 1, Lesson 1-1, language support and math talk are intentionally integrated to help students build both conceptual understanding and academic language proficiency. The lesson introduces foundational concepts in addition, counting, and includes pre-teaching of key vocabulary such as add, in all, and altogether, which are essential for understanding the mathematical context. These terms are supported with visual aids, gestures, and contextual examples to ensure clarity for all learners. The materials also embed language development strategies directly into instruction, utilizing sentence frames and guided math discussions that encourage students to articulate their thinking using precise mathematical language. Additionally, the lesson avoids figurative language and idioms that might confuse early learners, instead focusing on clear, literal language that supports comprehension. Through "Math Talk" prompts, students are encouraged to explain their reasoning, listen to peers, and use academic vocabulary in meaningful ways. These structured conversations not only reinforce math concepts but also promote language development by modeling and practicing the use of math-specific terms in context. The materials include regular practice in teaching vocabulary at the beginning of each topic. For example, in the Teacher's Edition, the Topic Opener provides a vocabulary activity for teachers to pre-teach the vocabulary needed to understand the concepts in the topic. In Topic 9: "Comparing and Ordering Numbers," the vocabulary activity guides teachers to write the words greater and greatest on the board. Then, the teachers acknowledge that the words follow the spelling rule about adding a suffix at the end of a word without changing the spelling of the word. The teacher asks students which letter is silent when they say these words. Teachers have students say a sentence that uses greater and another sentence that uses greatest. Finally, the students show the teacher how they decided which word to use: "Use 'greater' when comparing two things and 'greatest' when comparing more than two things." The materials include an "Academic Vocabulary" section in the Topic Opener of the Teacher's Edition. EnVision Plus Mathematics guides the teacher to introduce academic language prior to the lesson and then use the vocabulary throughout the entire topic. The academic language is cross-curricular and utilized throughout the school day and year. Topic 10 "Geometry" instructs the teacher to facilitate student learning of the following words: define, explore, make sense, and observe. In the Teacher's Edition, the resource provides explanations for the teacher to reference. For example, for the phrase make sense, it is suggested to encourage students to ask themselves, "Will my answer make sense to someone else?" Teachers are also encouraged to use pictures to help communicate their ideas.

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.

In enVision Plus Mathematics Grade 1, Topic 2, the Building Understanding, Sustain Understanding, and Fluency sections offer a rich blend of activities that support both mathematical thinking and language development. These sections include digital manipulative activities, lesson resources, spiral review, hands-on games, digital games, and fluency practice, all designed to reinforce key concepts such as addition strategies and number relationships. These tools are not only engaging but also serve as platforms for language-rich instruction, helping students develop the vocabulary and communication skills needed to express mathematical ideas. Each activity is embedded with language supports such as visual models, vocabulary cards, sentence frames, and guided prompts that help students articulate their reasoning. For example, digital manipulatives allow students to explore math concepts interactively while using structured language to describe their actions. Teachers are encouraged to facilitate math talks by prompting students to explain their thinking, compare strategies, and use precise academic language in discussions. The spiral review and fluency games include previously taught concepts, reinforcing both math skills and language in a fun, low-stakes environment. These sections not only deepen conceptual understanding but also build students' confidence in using math vocabulary in real-world and collaborative contexts. The materials in grade 1 include guidance for differentiated instruction for students who demonstrate proficiency in grade-level skills. In the Teacher's Edition, the guidance provides a Quick Check in the "Assess and Differentiate" section of Lesson 5-5 in Topic 5. Based on the results of the Quick Check, if students score 4–5 points, they will be assigned an enrichment activity. The big idea of Lesson 5-5 focuses on solving word problems with three addends. The enrichment activity for Lesson 5-5 is provided in the online program and extends learning by having students use a chart of shells collected from a beach to write equations to find the total number of shells collected. For example, question one states, "Rayven collected _ shells. Kai collected _ shells. _ collected 5 shells. How many shells did they collect in all? + _ + = __." enVision Plus Mathematics Grade 1 offers enrichment and extension activities in the Differentiation Library at the beginning of each topic in the Teacher's Edition, such as "Pick a Project," "Math and Literacy," "Amazing Contributions," and "Stand Up and Think." Guidance is provided in the Teacher Guide on when to use these extension activities. In Topic 6: "Represent and Interpret Data," the "Pick a Project" can be used anytime during the topic, whereas the "Stand Up and Think Problem 6A" can be used anytime after Lesson 6-1. The "Pick a Project" offers four projects from which the students can choose. For Topic 6, each project includes a visual, an action, and a final product. Project 6B has students looking at a visual of six dogs. The students answer the question, "Which dog is your favorite?" and create a pet data display as the activity.

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.

The materials include guidance to support the teacher in both modeling and the explanation of concepts to be learned. In the Grade 1 Teacher's Edition Lesson 2-4, the "Language Support" section provides a scaffolded activity to connect to students' experiences using ten-frames. The teacher is guided to show or draw a ten-frame and ask, "Why do you think this is called a ten-frame?" with a sample student response provided, "Because it has a frame around 10 boxes." This question helps the teacher model the concept of a ten-frame and its structure. The guidance continues with an explanation that a ten-frame can be used to solve math problems with sums up to 10, supporting the teacher in explaining how and why ten-frames are useful. Students are then encouraged to apply the concept independently, reinforcing understanding through practice. An additional online activity for "Thinking Aloud with Guided Practice" offers extended support for both modeling and explanation. The Teacher's Edition includes guidance to support teachers in explaining and modeling key concepts from the lesson. In Topic 4, students are learning strategies for subtraction within 20. 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 4-4, two student samples, one from Barry and one from Maya, are presented. The teacher discusses both examples with the whole class. The teacher explains, "Both Barry and Maya were able to correctly identify the whole and the parts; however, only Barry demonstrated the relationship between addition and subtraction by correctly placing the whole and parts in the facts." The teacher reinforces that addition and subtraction have inverse relationships and can be demonstrated through part-whole relationships. In grade 1, Topic 9-5, the Teacher's Edition provides questions in the "Visual Learning" section to guide instruction, such as, "What do you notice about the number line? How does 45 on the number line help you decide how the number should be placed? How do you decide where to place 47 on the number line?" These questions explicitly support the teacher in modeling how to analyze and use a number line, while also guiding the explanation of place value and number relationships to determine number placement and rounding.

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

In the enVision Plus Mathematics Grade 1 Digital Teacher Resources, the lesson "Showing a Number as Groups of Ten" exemplifies how the program supports teachers with explicit guidance for delivering instruction through multiple approaches. When implementing the lesson in Topic 10, the teacher begins by introducing the concept using bundles of ten sticks or ten-frames. The Teacher's Edition provides clear prompts such as, "Let's count how many groups of ten we have," and "How many tens make 30?" The teacher models grouping by physically bundling ten objects and writing the corresponding numeral, saying, "Here are three groups of ten. That's 30. We can write it as three tens or 30." Students are then encouraged to use their own manipulatives to create groups of ten and represent them with numbers. The teacher circulates, asking guiding questions, such as, "Can you show me how many tens are in 40?" or "What happens if we add one more group of ten?" For students needing support, the teacher may use visual aids or simpler numbers, while advanced learners might be challenged to represent numbers in multiple ways. The lesson also includes "Math Talk" opportunities, where students explain their thinking and compare strategies with peers, reinforcing understanding through discussion and hands-on practice. The materials include teacher guidance for effective lesson facilitation using a variety of instructional strategies, such as math talks, Exit Tickets, and an explore-and-share approach. The math talks promote mathematical discourse. In Lesson 9-3 of the Teacher's Edition of Topic 9, students are shown graphs, one at a time. Students share what they notice and wonder as each graph is shown. As more information is revealed, students refine their interpretations and discuss what data is being presented. The Lesson 9-3 Exit Ticket has students examine pictorial representations of base ten blocks and identify which comparison symbol is correct. Students are then given a problem situation in which they have to determine which bag of apples is greater, less, or equal. The teacher can use this information to drive further instruction based on misconceptions from the assessment. The "Explore and Share" section engages students with high-interest problems and allows for multiple approaches to the problem. Lesson 9-3 "Explore and Share" requires students to write different two-digit numbers. They compare the numbers to complete the sentence and explain how they know. The materials for Topic 10 in the Teacher's Edition provide teachers with suggestions for using a variety of instructional approaches, including visual learning, language routines, and practice problem-solving. Visual learning offers a visual example to formalize the mathematics of the lesson. Lesson 10-5 provides both teachers and students with visualizations of two-dimensional shapes. The visuals of the shapes are used to compose and create a new shape. Students continue to use pattern blocks to compose new shapes. Language routines help students communicate about math to advance their thinking. The Language Routine in Lesson 10-5 is "Compare and Connect." In this routine, students demonstrate how to make the shape from Box B using only a blue rhombus block and green triangle blocks. The teacher asks, "How is the large shape made of blue blocks, or rhombuses, similar to the large shape made of green blocks, or triangles? How are they different?" Practice and problem-solving build proficiency as students work independently. In the same lesson, students apply their new knowledge by practicing composing shapes, such as in question 5, which asks, "Two of which shape can be used to make (picture of hexagon)?"

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, a 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 can be presented either in a whole-group setting or a small-group setting. In enVision Plus Mathematics Grade 1, Topic 4, Lesson 4-3, students explore the concept of arrays and repeated addition through a variety of structured learning experiences. During Guided Practice, the teacher uses counters and ten-frames to model how to organize objects into equal rows and columns, helping students visualize and understand the structure of arrays. The Teacher's Edition provides guidance to teachers with prompts such as, "Use counters to build an array with two rows of three. Ask: How many counters are there in all? How do you know?" This encourages students to connect visual models to addition sentences. In the "Independent Practice" portion, students complete workbook problems where they draw arrays and write corresponding addition equations, reinforcing their understanding through individual application. For "Collaborative Practice," students work in small groups to play a matching game using number cards and counters, where they build arrays and match them to the correct total, promoting discussion and peer learning. The Teacher's Edition provides detailed teacher guidance, including differentiation tips such as, "Provide grid paper for students who need help organizing their arrays," 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 Grade 1 supports multiple types of practice with embedded teacher support to ensure effective implementation. The grade 1 curriculum, Lesson 6-1: Organize Data in Three Categories, includes a "Math Talk." The lesson begins with whole-group instruction, where the teacher introduces a data set using a visual like a picture graph or tally chart. The Teacher's Edition provides explicit prompts such as, "What do you notice about the categories?" and "Which category has the most?" These questions guide students to observe and interpret data while encouraging discussion. During Guided Practice, the teacher works through examples with the class, modeling how to organize and compare data using real-life contexts like favorite fruits or pets. Students move into independent practice, where they complete problems that require them to sort and count data into three categories. For collaborative learning, the teacher is encouraged to pair students to discuss their findings and explain their reasoning, using prompts like, "Tell your partner how you figured out which category had the fewest." For students needing additional support, the teacher uses small-group instruction with simplified data sets and visual aids, ensuring

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 ELPS Support, which includes instructional scaffolding suggestions for the five levels of language proficiency and increase in the use of academic language. In Lesson 2-3, students are learning strategies to add within 10, including doubles and near doubles. The Targeted ELPS Support guides the teacher to have students work together to decode terms by associating sounds with letters and blending sounds together. The materials then include teacher guidance with scaffolds for each proficiency level. For example, the teacher guidance for students identified as pre-production is "Students work in pairs to decode and say aloud the term 'doubles fact' and point to a picture of the doubles fact, then repeat for the near doubles fact." Guidance for students identified as beginning is, "Students work in pairs to say, identify, and copy a picture of a doubles fact and a related near doubles fact." As the levels progress, the materials provide teacher guidance such as "Students work in pairs and discuss why 4+5 is a near doubles fact" for intermediate students. Then, for high intermediate students, the teacher guidance states, "Students talk in groups to compare 4+5 and 4+4, and then 4+6 and 4+4." "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 to work in groups and "in their own words describe doubles facts and near doubles facts, and then provide their own examples of each." Grade 1 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 (EB) students. In Lesson 4-4, students are asked to "write a fact family to match the picture of the tall robots and the short robots." This prompt allows for linguistic support by having students underline the word "robots" and think about its meaning. The materials also provide explicit teacher questioning. For example, the Teacher's Edition states, "How can you find out how many yellow robots are in the picture? How can you find out how many green robots are in the picture?"

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, "Maintain the cognitive challenge, Build student agency through rigorous tasks, Provide access to mathematical tasks, Form groups of students with different language abilities, Allow students to hear tasks read aloud, and Enable 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. The accommodations 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 8, break apart, standard form, and expanded form are listed for topic vocabulary; less is listed for prior terms, and compare, greater than, less than, closest ten, least, greatest, and order are listed for upcoming terms. Furthermore, the materials list context-setting vocabulary that is included in each lesson. These opportunities 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.

Lesson 1-10 includes written discourse in the "Targeted ELPS Support" section of the lesson. The resource offers tiered guidance across language proficiency levels, encouraging students to interact with the bar model and explain their thinking in writing. Beginning and intermediate students focus on identifying numbers and labeling diagrams, while more advanced students are supported in writing full equations and responses. Academic vocabulary is reinforced through the use of labeled student drawings and sample responses that show how to represent and solve part-unknown problems using both addition and subtraction. Comprehension and background knowledge are further developed as students write and draw to explain how they use the bar model to find the missing part, supported by the teacher's prompts and scaffolds. The digital resources include language development practice tools to support EB 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 3-5, students draw counters to make ten and solve the following problem, "Carlos sees seven yellow birds. Then he sees six white birds. How many birds are there in all?" Students then answer four more questions to help them understand the problem, including question one: "What tools will you use to show how to make ten?" The materials include embedded guidance for teachers to support EB students through the use of Language Routines in the Teacher's Edition. EnVision Plus Mathematics Grade 1 provides eight specific Language Routines explicitly described and used throughout the lesson: "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 11-9, Language Routine: Stronger and Clearer Each Time, students first think about how to identify the hour and minute hands on a clock. Then, in structured pairs, each partner has the opportunity to explain how they know which hand is which, listening to and clarifying each other's ideas about telling time before sharing with the whole group. Grade 1 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 and instructions on when best to implement the activities. For example, in Lesson 13-2, the activity is suggested to "use with the Visual Learning activity to help students activate prior knowledge about using money to buy things they want and need." The materials prompt the teacher to ask, "Can you think of a time you used money to buy something you wanted?" and "Can you think of a time you used money to buy something you needed?" The materials further guide "students to work with partners to brainstorm in writing more examples."

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 Topic 8 in the Teacher's Edition, students explore the concept of comparing numbers by identifying 10 more or 10 less. Early in the topic, they use a number chart to visually understand how numbers increase or decrease by ten, helping them recognize patterns in place value. As the lessons progress, students begin using base-10 blocks to model and physically demonstrate what it means to add or subtract ten from a number. By Lessons 8–10, students are not only adding 10 to a given number but also decomposing numbers into tens and ones to find the sum more efficiently. This hands-on and visual approach deepens their understanding of place value and prepares them to justify their thinking using multiple strategies. The instructional assessments in Topic 9 of the Teacher's Edition allow multiple opportunities for students to show depth of understanding aligned to the TEKS. The Lesson 9-3 Exit Ticket has students practice comparing numbers, first using pictorial representations, then moving to numerical representations. The Exit Ticket also aligns with using real world problems, such as comparing the number of apples in different bags. The progression in the assessment allows for depth of understanding by assessing in concrete to pictorial to more abstract (numerical) thinking. In Topic 11, students are introduced to the concept of money through a structured learning process that builds understanding step by step. In Lesson 11-1, they begin by learning about the penny, nickel, and dime, focusing on the fact that each coin has a unique value, regardless of its size. This helps students understand that size does not determine worth. In Lesson 11-2, the quarter is introduced, and students learn to identify it and recognize its value in relation to the other coins. By Lesson 11-3, students apply their knowledge by counting sets of coins, combining different denominations to find total amounts. This progression helps students develop both coin recognition and the foundational skills needed for real-world money use, such as making purchases and giving change.

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

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 3, Lesson 3-1 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, "How did you get your answer?" 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, "If you already have 6 points, then how many more would you need to win?" In Topic 4, the "Guided Practice" section of Lesson 4-4 in the Teacher's Edition directs students to write the fact family for each model of sets of counters in questions 1 and 2. Then in question 6, the materials show a more complex problem: "Tanya has 8 stickers. Miguel gives her 5 more. How many stickers does Tanya have in all? Write an equation to solve the problem. Complete the fact family." In enVision Plus Mathematics Grade 1, students work with different quantities over time to add and subtract within 20 using models and strategies, as well as compare numbers and apply their understanding of equality in equations. In Topic 5 the Math Background: Coherence section in the Teacher's Edition, the resource provides guidance on content learned in Topics 1 and 2; the students first learned to add and subtract by making 10 and using doubles and near doubles. As quantities increase, students represent numbers with a group of 10 and some ones, as well as add and subtract by decomposing numbers. It then specifies in Topic 9 students will be expected to compare numbers using <, >, or = within 120. Each task progressively increases complexity towards grade-level proficiency with the grade 1 TEKS.

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

In the Grade 1 Teacher's Edition, Topic 3, Math Background: Coherence, the focus on understanding and applying strategies for addition and subtraction builds on prior learning from kindergarten, where students explored decomposing and composing numbers in different ways. It also connects to earlier grade 1 instruction, where students were introduced to strategies like counting on, counting back, using doubles, and near doubles. This topic lays the foundation for later grade 1 work involving adding and subtracting to represent and interpret data, as well as understanding place value using tens and ones to describe numbers. Looking ahead to grade 2, students will build on this understanding to develop fluency with addition and subtraction within 20 and begin adding and subtracting within 1,000. In the grade 1 "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 are revisited in multiple lessons across topics to reinforce understanding and deepen connections throughout the year. For example, Topics 1–5 develop students' understanding of addition and subtraction, starting with foundational concepts and progressing to more complex problem-solving strategies. In Topic 1, students build an understanding of addition and subtraction, which is expanded in Topic 2 to adding and subtracting within 10. This learning progresses in Topic 3 to addition facts to 20 using strategies, and in Topic 4 to subtraction facts to 20. Finally, Topic 5 has students apply their understanding through work with addition and subtraction equations. This strong foundation in operations supports students in Topic 7, where they extend their understanding of patterns and relationships to numbers up to 120, further reinforcing counting, place value, and number sense. That understanding prepares students for Topics 8 and 9, where they apply their knowledge to representing and working with two-digit numbers, representing greater numbers, and comparing and ordering multi-digit numbers. Measurement and geometry concepts are also intentionally sequenced. In Topic 6, students explore data collection and representation, using graphs to answer questions based on their prior work in addition and subtraction. In Topic 10, students deepen their understanding of geometry by identifying, classifying, and composing two- and three-dimensional shapes. Financial literacy is also included, building on students' understanding of numbers and value. Then in Topic 13, students explore income, spending, saving, and charitable giving, connecting mathematical concepts to real-world financial decisions.

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 the Grade 1 Teacher's Edition, Topic 3 builds directly on foundational concepts from kindergarten, where students practiced decomposing and composing numbers. This prior knowledge supports students' understanding of addition and subtraction strategies introduced in grade 1, such as counting on, counting back, and using doubles and near doubles. Mathematical language from kindergarten, including terms like more, less, add, and subtract, is reinforced and expanded in Topic 3. Students now apply this language to describe and justify their use of specific strategies like "counting on" and "near doubles," ensuring continuity in mathematical vocabulary and reasoning. The strategies taught in Topic 3 set the stage for upcoming grade 1 work in interpreting data and understanding place value using tens and ones. These skills are essential as students transition into grade 2, where they will build fluency with addition and subtraction within 20 and begin working with numbers up to 1,000 through place value understanding and more complex operations. In grade 1, students develop an understanding of the definition of the equal sign as "the same value as" to interpret a variety of addition and subtraction equations in Topic 5 of the Teacher's Edition. Students use prior knowledge from kindergarten, where they began to develop the understanding of equality by determining whether two groups of objects were equal. Then, the students will use that language in grade 2, where they interpret, write, and complete equations as they develop fluency with addition and subtraction. EnVision Plus Mathematics demonstrates a coherent use of content across prior, current, and future grade levels. For example, in Topic 10: "Geometry" in the Teacher's Edition, students examine defining and non-defining attributes of two- and three-dimensional shapes. Students build on previous learning from kindergarten, where they distinguished between two- and three-dimensional shapes and described them as flat or solid. Students also learned to identify, name, and describe circles, triangles, squares, rectangles, hexagons, cubes, cones, cylinders, and spheres. Grade 1 students can take their current and previous learning to apply it to future learning, where they will need to identify and draw triangles, quadrilaterals, pentagons, hexagons, and other polygons based on defining attributes.

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 grade 1, Lesson 4-1 in the Teacher's Edition, students build on current grade-level work by extending their understanding of subtraction. The lesson supports procedural development by teaching students how to use a number line to solve subtraction facts within 20. Students practice counting back on the number line, reinforcing their procedural fluency with subtraction and providing a visual model to support accuracy. They deepen their conceptual understanding by using both counting on and counting back strategies to solve subtraction problems. This helps solidify the relationship between addition and subtraction and prepares students for more advanced subtraction strategies in future lessons. The materials build on students' prior knowledge from earlier grades where they practiced counting to 10 and counting on from a given number. In this lesson, students apply their prior knowledge to learn how to count back as a strategy for subtraction. This connection helps students transfer familiar counting skills to new subtraction situations. In Lesson 9-1, Teacher's Edition on "Coherence," students deepen their understanding of comparing numbers by connecting past learning, engaging with new concepts, and preparing for future mathematical reasoning. In the "Look Back" section, students revisit their prior experiences with counting and recognizing numbers, reinforcing their ability to compare quantities using visual models and objects. This lesson introduces the concept of greater than, guiding students to compare two numbers and determine which is larger using symbols like ">" and mathematical language. Through hands-on activities and number-based exercises, students practice identifying greater numbers within real-world scenarios, strengthening their ability to use comparative reasoning. In the "Look Ahead" section, students build on their understanding by exploring related concepts such as less than, equal to, and ordering numbers, which prepare them for more advanced problem-solving in later grades. This structured learning approach ensures students develop confidence in numerical comparison, supporting their ability to analyze and work with numbers effectively. In Topic 9: "Comparing and Ordering Numbers," in the Teacher's Edition, the resource provides teachers with guidance on how concepts and procedures relate to new mathematical skills being taught at the lesson level. For example, in Lesson 9-4, students use a number-line model to help them determine which numbers are greater than or less than a given number. Previously, in Topic 8, the materials provided teacher guidance to have students use models to compare two two-digit numbers. They used the terms greater than and less than, as well as the symbols (>, =,) and (<) which builds on student learning in Topic 9.

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

In Lesson 5-2, students strengthen their understanding of addition and subtraction equations through structured opportunities for space retrieval, reinforcing previously learned concepts across multiple learning pathways. Lesson 5-2 builds on foundational skills, helping students recall prior knowledge of basic number relationships, counting strategies, and fact families to develop fluency in solving equations. The materials provide activities that integrate visual models, number bonds, and hands-on problem-solving, allowing students to actively retrieve and apply concepts they have encountered earlier in the curriculum. By revisiting familiar strategies such as using a part-part-whole approach, recognizing inverse operations, and solving for missing numbers, students reinforce their ability to see connections between addition and subtraction. Through repeated exposure and carefully sequenced practice, learners develop stronger mathematical recall, enabling them to approach equations with confidence and efficiency. This structured retrieval process ensures that students deepen their problem-solving skills while preparing for more advanced mathematical concepts in future lessons. In the Grade 1 Teacher's Edition Topic 4 Opener, the lesson begins with exploring subtraction facts to 20 during a "Math Walk" video. The information and learning are then addressed again in Lesson 4-7 when the video is shown again, and the materials guide the teacher to ask the students, "What have learned that could help them answer the question in a different way with their new knowledge?" In the "Review What You Know" section of the Topic 4 Opener, the materials provide problem-solving opportunities that include several skills that were previously learned. For example, students will need to know how to make a tally chart, how to write numbers representing a set, and how to compare numbers using more and less. EnVision Plus Mathematics Grade 1 includes opportunities for students to revisit skills and concepts taught throughout the lesson after the skill has been first introduced. In the Topic 7 "Differentiation Library," students are given practice opportunities to review skills related to numbers up to 120. Students use problem-solving skills to apply the concept of adding numbers to find the total number of runners in the race. Additionally, there are scaffolded questions for the teacher to ask, such as, "Can you use ten frames or a number line to find out how many runners there are in total?" The "Stand Up and Think" activities help to address multiple concepts taught in the unit. For example, Lesson 7-1 covers counting by 10s to 120, Lesson 7-4 covers counting on a Hundred Chart, and Lesson 7-6 covers skip counting to 120.

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

The grade 1 Topic 5 Review offers students meaningful interleaved practice by combining current learning on addition and subtraction strategies with previously taught concepts, such as counting on, making ten, and understanding number relationships. This review is thoughtfully designed to reinforce fluency and deepen comprehension by presenting problems in varied formats across multiple learning pathways, including visual models, number lines, and word problems. By revisiting earlier skills in new contexts, students strengthen their ability to apply mathematical thinking flexibly and confidently. This integrated approach supports long-term retention and prepares learners for more complex problem-solving in future topics. The materials include a hands-on game that provides opportunities for students to practice learned concepts and apply skills using the strategies taught. In Topic 2: "Add and Subtract Within 10" in the Student Edition, students have a hands-on game that includes a 100-chart game board with playing cards. The goal is to be the first player to create a path with their counters from 1 to 100. The path must be connected with flat sides, so players may not move diagonally. A player flips an equation card and solves it; then they are allowed to add that many counters to continue the path to 100. If it is a subtraction equation, the player is allowed to remove the opponent's counters. This game allows students to practice skills in a fun way. In Grade 1, Lesson B25: Thinking Addition to 12 to Subtract in the "Teacher Resource Tool," enVision Plus Mathematics Grade 1 deliberately sequences learning through the Concrete–Representational–Abstract (CRA) model to build a strong foundation in subtraction. The lesson begins with concrete experiences, where students use physical objects like counters or cubes to model addition facts and see how they relate to subtraction. This hands-on exploration helps students visualize the part-whole relationship in number sentences. Next, students transition to the representational stage, using drawings, number lines, and fact family diagrams to represent their thinking visually. Finally, they move to the abstract stage, solving subtraction problems using equations and mental math strategies based on their understanding of addition. This progression ensures that students develop conceptual understanding before relying on abstract symbols, supporting all learners in mastering subtraction through addition.

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

In grade 1, Lesson 3-2, students extend their understanding of addition by using the counting on strategy to add within 20. During the Explore and Share section, students are presented with the problem: "Abby has 4 cubes. Salina gives her 7 more cubes. How many cubes does Abby have now? Show your thinking." Students are encouraged to use a variety of tools, such as counters, number lines, and connecting cubes, to model their thinking. The task requires students to count on to find the total and represent their strategy visually or physically. The Teacher's Edition supports teachers with guiding questions to deepen students' reasoning and foster meaningful discussion, such as: "Can you count on to find the sum? Do you have to start counting with the first cube?" and "Show and explain to a partner how you would count on to add 14 and 5." These questions prompt students to interpret and analyze models, communicate their thinking, and explore different approaches to addition. In grade 1, students interpret, analyze, and evaluate models and representations during the "Explore and Share" section of Lesson 4-2. In Topic 4, Subtraction Facts to 20: Use Strategies located in the Teacher's Edition, there are opportunities for students to make sense of problems by answering such questions as, "Have you ever been asked to share with a friend or sibling? How do you know what you have left after you have given something away?" Students then analyze the problem by exploring different ways to make 10 on a ten-frame and determining how many are left over. Finally, they evaluate their models by explaining their thinking using objects or drawings. In grade 1, Teacher's Edition, Lesson 11-5, students divide shapes into two or four equal shares and begin to reason about the parts that make up a whole. During the Visual Learning activity, students engage in classroom conversations using questions such as: "How could you describe the yellow share of the shape? What about the orange share? What could you do to check if the two shares of the triangle are equal?" Students also compare shapes by observing and discussing questions like: "What do you notice about the green shares of the rectangle and the one in box two? How are they alike and different?" These types of questions and tasks require students to interpret models and representations of mathematical concepts and situations. Students are also expected to analyze these models and representations as they compare equal shares and determine how parts relate to the whole. Furthermore, they evaluate models and representations by checking for equal parts and justifying their reasoning through discussion.

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

In grade 1, Topic 1 of the Student Edition in the "Guided Practice" section, two practice problems involving an image of bats and a cave are presented. Students are prompted to use tools and write equations to show how many bats could be inside and outside of the cave. The teacher reads the statements aloud, and the students use tools to represent the situation. Students write an equation to illustrate their representation. For example, question 1 states, "5 bats in all. Some inside. Some outside." Students then use tools to create their problem-solving graphic. In the grade 1 materials, Lesson 5-3, the "Guided Practice" section engages students to use counters to model the equation and decide if it is true or false. For example, question 2 displays the problem, "7= 8–1." The students answer the question by circling true or false. As the lesson progresses, the students are given guidance to draw a model or use counters as a strategy to help determine if the equation is true or false. The objective of this lesson is for students to understand that an equation is true only if both sides of the equals sign are the same. In the grade 1 materials, Lesson 8-1 of the "Visual Learning" section, students are prompted to model mathematical situations using concrete representations. For example, the question states, "How could you use a hundreds chart to find a number that is 10 more than 86?" This question supports students in connecting real-world contexts to mathematical ideas by having them create a visual model with cubes in the number chart. This task encourages students to represent the quantities involved using manipulatives and number charts 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 1, Lesson 5-4, the "Math Talk" section supports students in applying their conceptual understanding of the equals sign as meaning "the same as" or "is equal to." Students are presented with three different equations and asked to find the missing number that makes each equation true. To do so, the students must draw on their prior knowledge of number relationships and operations. Working in pairs or small groups, students identify, describe, and extend patterns to reason through each equation. This activity challenges students to apply their understanding in new ways, deepening their grasp of equality and the structure of equations. Topic 7 in the Student Edition provides students with opportunities to apply conceptual understandings to new problem situations. During Lesson 7-1, students investigate counting by 10s up to 120 through guided teacher lessons in Explore and Share and Visual Learning. In the "Practice and Problem Solving" section, students apply their new understanding to solve new situations. For example, in question 5, students draw counters in the ten-frames to solve each problem. They write the numbers and the number words. Question 5 states, "Jose has three boxes. There are 10 books in each box. How many books does Jose have in all?" EnVision Plus Mathematics provides materials for students to apply conceptual understanding to new problems. The Teacher's Edition offers guidance for teachers on presenting new situations to students in the "Connect" section of the "Investigate" lessons. For example, in Lesson 8-2, the "Connect" section has students applying their new learning to solve word problems. In question 2, students are asked to solve the problem, "How could you wake up Robot 46 using different ways to show 46? Show two different ways to make 46. Draw your different ways. Then tell a partner about your different ways to wake up Robot 46."

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

Topic 1 in the Teacher's Edition has students using different patterns to recognize quantities from numbers one to ten. Students observe that the number of objects in some patterned arrangements can be recognized without counting, which helps build students' fluency for more complex tasks. For example, in the "Guided Practice" section of Lesson 1-1, students are given images of dot patterns to quickly recognize the total number of dots. In question 1, students recognize 5 dots on one side and 4 on the other, leading to a total of 9 dots. In grade 1 Teacher's Edition, Topic 3, the "Build Automaticity" section includes a Point and Tally partner activity that supports students in developing addition fluency and automaticity. Students take turns adding the numbers on their assigned shapes, either a circle or a square, and record tally marks on their pages based on the sums they find. This engaging practice encourages students to apply their knowledge of addition strategies to quickly and accurately find sums that match the numbers on their shapes. As students play the game, the teacher reinforces the use of strategies such as counting on, using doubles, or making a 10, and encourages partners to compare and discuss their methods, promoting both efficiency and flexible thinking in solving addition problems. In enVision Plus Mathematics Grade 1, Lesson 4-4, titled "Make a Ten to Add," the lesson begins with a Problem-Based Learning (PBL) activity where students explore different ways to make 10 using counters or number lines. This is followed by the "Visual Learning Bridge," which models the strategy step-by-step. A guiding prompt from the lesson, "How can you break apart the second number to make a 10 with the first number?" encourages students to think flexibly and apply number sense. Fluency is reinforced through "Number and Operations Routines," which are short, daily exercises embedded in the curriculum to build automaticity with addition facts. Students also engage with the "Interactive Practice Buddy" on the Savvas Realize platform, which provides adaptive digital practice and immediate feedback. These components ensure that students not only understand the strategy but also develop the automatic recall needed for efficient problem-solving.

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 1, Topic 2, as students explore and apply a variety of addition and subtraction strategies. In the grade 1 Teacher's Edition, Topic 2, Math Background: Coherence Section, the topic begins with counting on using a number line, helping students build efficiency by starting with the larger addend. As students progress, they are introduced to near doubles and adding with five, allowing them to recognize and apply patterns in numbers. Visual tools like ten-frames support accuracy and reinforce number relationships with five and 10. In Lesson 2-5, students learn the Commutative Property of Addition, deepening their understanding of number order and flexibility in solving. The topic concludes with subtraction strategies, including counting back and thinking addition to subtract, reinforcing accuracy through strategic reasoning and flexible thinking. This progression encourages students to select and apply strategies that are both efficient and conceptually grounded. In enVision Plus Mathematics Grade 1, Lesson 4-6: "Use Addition to Subtract," students develop procedural flexibility by using concrete models such as counters, cubes, and ten-frames to explore different strategies for solving subtraction problems. This hands-on approach allows students to visualize subtraction as an unknown addend problem, reinforcing the relationship between addition and subtraction. For example, when solving "9 – 6," students might use counters to find what number added to six equals nine. The "Visual Learning Bridge" then transitions students from these concrete experiences to symbolic representations, helping them connect their models to equations like "6 + ___ = 9." The lesson encourages students to choose strategies based on efficiency, prompting them with questions such as, "How can you use what you know about addition to help you subtract?" and "Is there another way to solve it?" These prompts support students in explaining their thinking and comparing strategies with peers, which builds a deeper understanding and flexibility in their mathematical reasoning. This structured approach ensures that students not only solve problems accurately but also learn to think strategically and communicate their reasoning effectively. In grade 1, Teacher's Edition, Lesson 9-4, the "Math Talk" section supports the development of efficient, flexible, and accurate mathematical procedures. Students are presented with a card containing number sentences with missing numbers, such as, "17 < ?," "14 > ?," and "12 = ?," and are asked to determine what each missing number could be. The structure of these number strings allows for multiple correct answers, promoting flexible thinking as students justify their reasoning and consider various possibilities. Through discussion and sharing of strategies, students reinforce accurate understanding of relational symbols and develop efficient mental math approaches for comparing numbers.

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 Lesson 3-2: "Add in Any Order," students explore the commutative property of addition, which allows them to add numbers in any order and still arrive at the same sum. This lesson provides a strong foundation for evaluating the efficiency and flexibility of different addition strategies. Students begin by solving problems like "3 + 5" and "5 + 3" using cubes, drawings, and number sentences. The "Visual Learning Bridge" models both equations and prompts students to consider, "Did changing the order help you solve it faster?" and "Which way was easier for you?" These reflective questions guide students to assess which method is more intuitive or efficient for them. During guided practice, students are encouraged to try both orders and circle the one they preferred, while the PBL task invites them to apply this strategy in a real-world context, such as combining groups of objects in different sequences. The Teacher's Edition reinforces this evaluative thinking by stating, "Ask students to explain why they chose a particular order and whether it made solving the problem easier." This lesson supports the development of strategic decision-making by helping students recognize that while the sum remains the same, the process they choose can impact how quickly and accurately they solve a problem. In grade 1, 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 5-2, the teacher can project the sample student work of Darnell and Lucy. The students were given the following prompt to complete, "Find the missing number in this equation: 7 + __ = 13. Explain how you found the missing number." The class then examines the two samples of work to evaluate the process and solution of each student. Darnell used counters and the count-on strategy. He started with seven counters and then numbered the counters that he added to have a total of 13 counts. He wrote six more to show that from seven, he counted six to get 13. Lucy used her understanding that addition and subtraction are inverse operations. She knew that "13 - 7 = 6," so she said that "7 + 6 = 13." Students can analyze that both samples used different strategies but still came to the same solution. In the grade 1, Topic 7 Review, students are provided with multiple opportunities to evaluate and apply counting strategies for efficiency, flexibility, and accuracy. Through reflective questions such as, "How can you use what you know about counting to count past 100?" "How can you count by 10s when you have a lot of objects?" and "How can you use a number chart to count forwards and backwards by 1s?" students are encouraged to explore various methods of counting and representing numbers. They are also asked to show three different ways to write the number 100, which promotes flexible thinking in number representation. Using tools such as the number chart, students practice moving efficiently through numbers and justifying their strategies. These activities help students develop an understanding of counting patterns, select appropriate tools and strategies for different tasks, and ensure accuracy in their number work as they extend their understanding beyond 100. In grade 1, Lesson 9-4, the "Visual Learning" guides students in analyzing the position of numbers in relation to 55, prompting discussion with questions like, "How does the location on the number line show that these numbers are less than 55?" Students then use the less than sign to compare additional numbers to 55. The activity extends to numbers greater than 55, with students describing their position on the number line. This comparison work helps students accurately identify numerical relationships, develop flexible thinking about number magnitude, and build efficient strategies for using tools like number lines to support comparison.

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

Lesson 3-2: "Make a Ten to Add" includes embedded supports that help teachers guide students toward more efficient addition strategies by introducing the concept of making a ten. The lesson begins with a PBL activity where students use counters or ten-frames to solve problems like "8 + 5." Teachers are prompted to ask, "How can you make 10 first?" and "What do you add to 8 to make 10?" encouraging students to decompose numbers and use known facts to simplify addition. The "Visual Learning Bridge" models this strategy step-by-step, showing how to break apart five into two and three, then add "8 + 2 = 10" and "10 + 3 = 13." Students are guided with sentence frames such as, "I made 10 by adding ___, then I added ___ more." This helps them articulate their thinking and internalize the strategy. The "Practice Buddy" digital tool reinforces the concept with interactive visuals and hints like, "Try making 10 first to help you add." In order to support all learners, the lesson includes English Language Learning scaffolds, vocabulary cards, and differentiated instruction options such as reteach activities and enrichment tasks. These embedded supports ensure that students not only understand the strategy but begin to apply it fluently in various contexts. The Teacher's Edition provides supports for teachers in the form of questions and suggestions. In Lesson 8-1, the teacher begins by asking the whole class, "What do you know about the number of Sarah's marbles? What do you know about Chris's and Lucia's marbles? What are you asked to find?" The Teacher's Edition guides teachers to observe as students work to find how many marbles Chris and Lucia have. A suggestion is given to assist the teacher in their observation by stating, "How do students find the number of Chris's and Lucia's marbles?" This is followed by what the teacher may anticipate the students doing, such as, "Students might show Sarah's marbles with cubes, then add 1 and 10 more blocks." While observing, teachers select solutions for students to present the most efficient ways to find the number of marbles for the two children.

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 addition and subtraction that connects conceptual and procedural foundations for grade 1. Topic 2 begins with counting on using a number line and moves on to near doubles and adding with four. Students use ten-frames to help conceptualize adding with ten. They progress to procedural understanding of the Commutative Property of Addition, which allows for procedural efficiency in solving addition problems with more than two addends. Topic 2 concludes with solving subtraction problems based on the conceptual understanding of counting back, followed by applying the procedural understanding of how addition and subtraction are related and using strategies for word problems. Grade 1 includes materials that progress from conceptual understanding to procedural understanding when organizing, representing, and interpreting data. In the Teacher's Edition at the beginning of Topic 6, students begin by using tally marks and tally charts to organize data. Students then use the collected data to represent their own data. Progress toward procedural understanding occurs when students analyze and interpret data; for example, they learn to identify which category has the most or least, or to compare one category to another. The Grade 1 Teacher's Edition materials explicitly state how both the conceptual and procedural emphases of the TEKS are addressed. In Topic 8, the Math Background: Balance page reinforces that "a balanced curriculum emphasizes conceptual understanding, procedural skill, and fluency applications." For conceptual understanding, Topic 8 focuses on place value with two-digit and three-digit numbers. Students decompose numbers into tens and ones to build a strong foundation in place value. They then apply this understanding to add numbers by grouping tens and ones, reinforcing the structure of our base-ten number system. For procedural skill, Topic 8 provides the foundation for computation strategies involving one more, one less, ten more, and ten less. These skills are taught through the lens of place value, helping students internalize efficient strategies for mental math and number manipulation.

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.

In the Grade 1 Teacher's Edition, Lessons 5–6, the materials provide clear evidence of incorporating concrete models, pictorial representations, and abstract representations, as required by the TEKS. Students use concrete manipulatives such as two-color counters and connecting cubes to explore and solve problems involving the addition of three addends. In the "Explore and Share" section, students manipulate these tools to build understanding, as seen in the sample student work from Nick and Alexis, where cubes are grouped to make 10 and assist in solving the problem. Pictorial representations are used throughout the lesson, especially in the "Visual Learning" section, which includes images of cubes and labeled diagrams that help students visualize combinations that make 10 and identify strategies like using doubles or counting on. Abstract representations are clearly present as students write and solve number sentences such as "6 + 4 + 6 = 1," using numerals and symbols to express their thinking. This combination of representations ensures students develop a strong conceptual foundation while building fluency in addition strategies. enVision Plus Mathematics Grade 1 provides questions and tasks that allow students to progress from using concrete models to pictorial representations to abstract concepts when learning to count and use patterns for numbers up to 120. Lessons 7-2 and 7-3 in Topic 7 have students using place-value blocks to count and write numbers up to 120. Lessons 7-4 and 7-5 continue with the use of the hundred chart and the 120 chart to practice counting to 120. Lesson 7-7 then progresses to using abstract thinking with flexible counting skills to count to 120 by "10s and 1s" to help determine the number of objects in a group. Additional questions are provided in the Teacher's Edition to facilitate classroom conversations such as "What do you think is the best way to count the stickers?" In the Grade 1 Teacher's Edition, Lesson 9-5, the instructional materials include a range of representations that align with the TEKS expectations for developing numerical understanding. Concrete models are supported through the use of hundreds charts and open number lines as physical tools for students to manipulate and visualize number placement. In the "Explore and Share" section, students are prompted to draw and label numbers like 23 on a number line using such tools as seen in sample student work from Arleth and Osvaldo. Pictorial representations are prominently featured in both the student examples and the "Visual Learning" section, where number lines are illustrated to show the placement of numbers like 42, 45, and 47, with arrows, labels, and spacing that guide conceptual understanding. Students analyze number placement based on tens and ones digits, further developing visual reasoning. Abstract representations are incorporated through the use of numerical labels, equations (identifying numbers greater than or less than others), and written number comparisons that require students to apply place value knowledge in symbolic form. This layered approach supports learners in building a deep understanding of number order and value on a number line.

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.

The materials include supports for students in connecting concrete models and representational models to abstract concepts in the online resources. In Visual Learning Animation from Lesson 4-2, students learn to make 10 to subtract. The video connects counters and ten frames to the concept of making 10 to subtract. This allows students to visually see the strategy and apply it in more complex situations. The Teacher's Edition provides support for students to define and explain the use of concrete and representational models to understand abstract concepts through the Math Talk in the "Let's Build" section of the lesson. In Lesson 5-4, the Math Talk uses the routine "What's the Pattern?" to have students describe and explain the pattern. The materials state, "to have students share their answers with a small group and work together to identify, describe, and extend the pattern." In the Teacher's Edition, Lesson 9-7, concrete models are embedded through the use of hundred charts, which students interact with physically or visually to locate and compare numbers. In both the "Explore and Share" section and "Visual Learning" section, students use models to identify numbers greater than and less than a target number, such as 53 or 60. This hands-on tool serves as a bridge between counting strategies and more abstract number comparisons. Representational models appear through annotated number charts and highlighted paths, as shown in the "Visual Learning" section. These visuals help students analyze tens and ones digits and understand numerical relationships. Sample student work from Eric and Diamond demonstrates how students mark and interpret number positions to write correct comparative statements such as "34 is less than 35" and "37 is greater than 35." The lesson also supports students in creating abstract representations by prompting them to generate and write comparison sentences using appropriate math symbols ">," and "<." Students move from manipulating and interpreting models to expressing their thinking numerically. Additionally, the materials provide guidance for defining and explaining the reasoning behind comparisons, such as how digits in the tens and ones places affect a number's position. The "Language Routine: Compare and Connect" and the "Classroom Conversation" prompts guide students to articulate why a number is greater or less, strengthening the connection between model-based reasoning and symbolic understanding.

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

In Lesson 6-3: Interpret Data, grade 1 students deepen their understanding of data by analyzing picture graphs and bar graphs. The lesson begins with a visual learning bridge, where the teacher displays a bar graph showing favorite fruits and asks, "What does this graph tell us?" This encourages students to observe and describe data using mathematical language. Manipulatives such as linking cubes or counters are used to build physical representations of the graphs, helping students connect abstract data to concrete experiences. The teacher guides students through interpreting the graphs by asking questions such as, "Which fruit has the most votes?" and "How many more students chose apples than bananas?" These prompts support the use of comparative vocabulary such as more, fewer, and equal. Students are encouraged to use sentence frames like "There are ___ more ___ than ___" to explain their thinking. During the "Convince Me" portion of the lesson, teachers prompt students to justify their answers, saying, "Tell me how you know that." This fosters mathematical discourse and reasoning. By integrating visuals, hands-on tools, and structured language supports, this lesson effectively builds both data literacy and academic vocabulary in young learners. In Lesson 11-3 of the grade 1 curriculum, students deepen their understanding of coin values by solving real-world word problems, while simultaneously developing academic mathematical language. The lesson begins with the teacher presenting a scenario such as, "Write the value of each coin—penny, nickel, and dime. How can you make 25 cents using the fewest coins?" Using a visual display of coins, the teacher models how to count and combine values. Students then engage with manipulatives by drawing coins in piggy banks and calculating totals, reinforcing their understanding of different denominations. Throughout the lesson, teachers scaffold language development by asking guiding questions like, "What coin should we count first?" and "How do you know this is 25 cents?" These prompts encourage students to use precise vocabulary such as value, total, and cents. Sentence frames like "I added ___ and ___ to get ___ cents" support students in articulating their mathematical thinking. In the "Convince Me!" section of the lesson, students justify their answers and explore alternative strategies, responding to prompts such as, "Can you show another way to make the same amount?" This promotes flexible thinking, verbal reasoning, and collaborative discussion. By integrating visuals, hands-on tools, and intentional language supports, the lesson effectively builds both financial literacy and academic mathematical language for all learners.

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

In Lesson 9-1, students begin to explore how to compare numbers using the terms greater than and less than. The teacher introduces two sets of counters and asks, "Which group has more? Which has fewer?" prompting students to describe what they see. As students investigate, the teacher models how to use comparison language by saying, "Let us compare the two numbers. Seven is greater than five because it has more counters." Students are encouraged to use sentence stems such as "___ is greater than" and "is less than ___" to explain their thinking. During partner activities, students use number cards and counters to build and compare sets, discussing their results using the academic vocabulary. The teacher scaffolds understanding by drawing number lines and using visual cues like arrows pointing to the larger number. To reinforce vocabulary, the teacher asks guiding questions such as, "How do you know which number is greater?" and "What does it mean when a number is less?" These strategies help students develop confidence in using "compare," "greater than," and "less than" in mathematical conversations. In Lesson 12-2, students explore how to measure and compare objects using nonstandard units, focusing on the concepts of length and height. The teacher begins by showing two classroom objects, such as a pencil and a glue stick, and asks, "Which one is longer? Which one is taller?" prompting students to use precise vocabulary. During guided practice, students use connecting cubes to measure the length of a book and the height of a water bottle, recording their findings. The teacher scaffolds vocabulary by modeling sentence stems such as "The length of the ___ is ___ cubes" and "The height of the ___ is ___ cubes." To deepen understanding, the teacher facilitates a discussion by asking "Why do we use the word length when measuring across and height when measuring up and down?" Students respond using academic language such as "The pencil is longer because it goes sideways," or "The bottle is taller because it goes up." Visual supports, such as anchor charts and labeled diagrams, reinforce vocabulary in context. Embedded guidance encourages teachers to revisit these terms throughout the lesson, ensuring students confidently use length and height to describe and compare objects in their environment.

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. For example, in Lesson 7-4, the materials state, "Leonora used the bottom-up hundred chart to solve the problem but made a mistake." The materials state, "You might ask Leonora: 'What happens to the numbers as you move down or up across a column?'" The desired student response to listen for, "As I move down across a column, the numbers also go down by 10s. That means I should have moved up, instead of down, to find the next three numbers by 10s. It is also correct to move one space up when counting by ones from 50." In grade 1, Lesson 8-5, "Let's Build: Make Numbers in Different Ways," students engage in mathematical conversations that deepen their understanding of number composition while developing academic language. The lesson encourages students to explore multiple combinations that make a given number, such as nine or 10, using manipulatives like counters or connecting cubes. For example, a student might begin by saying, "I used 5 and 4 to make 9," and the teacher, using embedded guidance, prompts the student to expand their explanation with a sentence stem: "Can you say that using our math sentence?" The student then refines their response to, "I can make 9 by adding 5 and 4," demonstrating improved syntax and vocabulary. Another student might say, "I made 9 with 6 and 3 because I saw it on the ten-frame," and the teacher models a more precise response: "Great! Let's say, 'I decomposed 9 into 6 and 3 using a ten-frame.'" The student repeats, "I decomposed 9 into 6 and 3," reinforcing the academic term decompose. These structured exchanges support the development of vocabulary such as "decompose," "addends," and "make," and syntax using sentence frames such as "I can make ___ by adding ___ and ___. Then, discourse through peer sharing and teacher-facilitated refinement. The materials guide teachers with exemplar responses and prompts that help students transition from informal to formal mathematical language, building their confidence and fluency over time. In the "Math Talk" section in Lesson 10-4, the activity focuses on geometry and measurement. Students are shown an image briefly and asked to discuss the shapes and their attributes with a partner. This structured partner talk allows students to hear and use precise math language in a collaborative setting, helping them develop and refine their vocabulary and syntax. Teachers are guided to display the image again and provide students with the opportunity to revise or enhance their descriptions before engaging in a whole-class discussion. This process encourages students to reflect on and articulate their thinking, supporting the development of flexible reasoning and deeper understanding of geometric concepts through meaningful discourse.

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

enVision Plus Mathematics Grade 1 integrates the TEKS Mathematical Process Standards in a developmentally 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 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 one curriculum. In grade 1, Topic 11: "Money, Equal Parts, and Time," the TEKS Process Standards are thoroughly integrated into the lesson structure, ensuring students engage in meaningful mathematical thinking. For example, in Lesson 11-1: Value of Penny, Nickel, and Dime, students are introduced to the concept that "specific coins have a known value" and that "one coin does not indicate its value." This aligns with TEKS 1.1A and 1.1B, which emphasize applying mathematics to real-life situations and using a problem-solving model. The teacher's actions include identifying and naming coins and their values, while students are expected to identify pennies and name the coin, promoting active engagement and vocabulary development. Materials such as real or plastic coins are used to support hands-on learning. In Lesson 11-4: Equal Parts in Shapes, students explore partitioning shapes into equal parts, with the teacher guiding them to recognize and describe halves and fourths supporting TEKS 1.1C: "selecting tools and techniques to solve problems." These lessons consistently include sections such as "Let's Build" and "Let's Investigate," which prompt inquiry and reasoning, ensuring that process standards are not only present but meaningfully embedded in both instruction and student activity.

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. Students use various strategies to build understanding of addition and subtraction in Topics 1–5, interpret data in Topic 6, and explore number patterns to 120 in Topic 7. They develop place value concepts with two-digit numbers in Topics 8–9, classify and combine shapes in Topic 10, and use measurement and financial literacy to apply math in real-world contexts in Topics 11–13. These connections reflect a coherent progression of process skills across the year. The materials include opportunities for students to connect the process standards to their content learning. EnVision Plus Mathematics Grade 1 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 6-7, "Students are tasked with determining how many gummies of each flavor or color are in each bag and the number of gummies of each color or flavor in each bag."

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 enVision Plus Mathematics Grade 1 incorporates the process standards within the units while also explicitly focusing on how to connect two process standards throughout the unit. Topic 1 places greater emphasis on grade 1 students selecting tools to solve problems and communicating mathematical ideas, reasoning, and implications. The description includes characteristics of how students implement 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 select tools to solve addition and subtraction problems and communicate their mathematical ideas." In the Mathematical Process Standards section in the Teacher's Edition, the process standards for Topic 5 are listed. The TEKS mathematical process standards are both incorporated and connected throughout the unit. The topic begins with a clear explanation of how process standards 1.1D: "The student is expected to communicate mathematical ideas, reasoning, and their implications using multiple representations, including symbols, diagrams, graphs, and language as appropriate," and 1.1G: "The student is expected to display, examine, and justify mathematical ideas and arguments using precise mathematical language in written or oral communication" are embedded within addition and subtraction equation lessons. These standards are integrated through instructional tasks that engage students in using pictures, diagrams, and symbols to identify missing numbers, determine if two expressions have the same value, and justify their mathematical thinking. The materials also make intentional connections between the process standards and lesson activities by emphasizing how students can represent and explain their reasoning using mathematical language, compare strategies, and solve word problems. The provided teacher guidance and questioning strategies reinforce these connections, ensuring students engage with the process standards in meaningful and developmentally appropriate ways across the unit.

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

In grade 1, Topic 6, Lesson 6-5: "Let's Build: Interpret Data from Picture Graphs," students develop essential data analysis skills by interpreting visual information in picture graphs. This lesson is closely aligned with the TEKS Process Standards, particularly those that emphasize analyzing information, communicating mathematical ideas, and using logical reasoning. For example, students are guided through activities that ask them to observe and interpret data using prompts such as, "How do you know?" encouraging them to explain their thinking and justify their answers. In the "Explore and Share" section, students examine a picture graph showing pets such as cats, dogs, and fish and engage in tasks such as counting and comparing quantities, as demonstrated in Kelly's and Kevin's sample work. The "Visual Learning" section builds on this by presenting a bar graph of favorite fruits and asking questions like, "How many more apples than bananas?" and "Which fruit is liked the most?" These activities not only reinforce data interpretation but also connect classroom learning to real-world contexts, fulfilling the "Connect: Realize Student Learning" objective. This integration of the TEKS-aligned process standards ensures students are not just learning to read graphs, but also to think critically and communicate their understanding effectively. In the Grade 1 Teacher's Edition, materials for Lesson 11-10, "Tell and Write Time to the Hour," include an overview of the TEKS process standards that are incorporated into the lesson. In the "Texas Essential Knowledge and Skills (TEKS)" section at the bottom, process standards 1.1B, 1.1C, and 1.1D are identified and described. These standards support students in problem-solving, selecting appropriate tools such as analog and digital clocks, and communicating mathematical understanding using multiple representations. The lesson structure and objectives reinforce these standards through conceptual understanding and skill-building, ensuring that students apply, represent, and explain time-telling concepts using both visual and numerical formats.

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 3, students are introduced to the topic's essential question, "What strategies can you use for adding to 20?" Students then watch a short video to generate excitement about planning a picnic. As students watch the video, they try to think mathematically about the question, "How many picnic tables are there?" 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. Anytime after completing Lesson 3-2, 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 Lesson 9-6, the "Explore and Share" section provides students with opportunities to develop their number sense by comparing and ordering two-digit numbers. Students analyze the digits in the tens and ones places to determine which number is greatest and which is least by answering questions such as, "How should you begin to order the numbers?" "Why do you compare the hundreds first?" and "Why do you compare the ones after the tens?" Teachers are guided to observe whether students use the correct place value strategy, looking at the tens digit first, then the ones when needed, in order to make comparisons. Grade 1 students use attributes of two-dimensional figures to solve a real-world problem in the "Let's Model" section of Lesson 11-7. After being given information about the shapes and format of the design element, students are posed with the question, "What will the design look like?" Students then make a prediction, and the teacher is guided to survey the students' predictions. The teacher guides 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 the tiles help you create a design? What made tiles 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?" Students then create their own problem.

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" section of the Student Edition supports students in building understanding and explaining key concepts in the lesson. In the "Step 2: Connect" section, questions are provided for students to represent and solve problems and tasks in multiple ways. For example, in Lesson 1-2, the directions state, "Think about Alex's small blocks and big blocks. How was addition used in this problem? Use objects or drawings to show your own addition problem. Share with a classmate to solve." In addition, students are asked, "Are there different ways to think about addition? Tell what you think." enVision Plus Mathematics Grade 1 encourages students to discuss possible sources of error involved in using math to model a real-world situation. For example, the Teacher's Edition in Topic 8 prompts teachers 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, "Would the answer be the same if all the toy vehicles were trucks?" In grade 1, Lesson 9-2 of the Teacher's Edition, the "Language Support" section provides structured guidance to help students understand, explain, and justify that there are multiple ways to represent and solve problems using place-value blocks. By building the numbers 113 and 115 with hundreds flats, tens rods, and ones units, students engage in hands-on representation of numbers. The teacher is guided to prompt comparison and reasoning through guided questions such as, "How many hundreds does each number have?" and "The hundreds are the same, so compare the tens. How many tens does each number have?" This questioning encourages students to break apart and analyze the value of each digit. This activity supports flexible thinking by showing how numbers can be decomposed and compared in different ways and fosters mathematical justification through student discussion and reasoning.

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.

In Lesson 2-3, students begin by writing addition facts on sticky notes and discussing how the facts are alike and different. The teacher asks, "How can you sort these facts into two groups?" Students continue to learn about key concepts of addition facts during a think-pair-share activity "to explain why some addition facts are called double facts." Students then finish the lesson by solving a problem and explaining their reasoning by drawing double facts and writing an equation to match. In the "Language Support" section of Lesson 5-3: True or False Equations, the teacher is guided to "have students write one sentence telling why they chose each of their answers." The teacher then provides the following stems for students, "One of my answers is _____________. I chose it because _________. My other answer is ____________. I chose it because ___________." Teacher guidance includes having the students read their answers aloud and explain why their equations are true. EnVision Plus Mathematics Grade 1 allows students to make sense of mathematics by doing math, writing about math, and discussing it with peers and teachers. The "Language Support" section in Lesson 10-8 provides opportunities for students to complete a table about the attributes of 3-D solids. Students work together in pairs to discuss and complete the table. The teacher initiates a classroom conversation and asks questions about the solid figures such as, "How are these shapes alike or different?" and "What is the name for a shape that has six faces, eight vertices, and twelve edges?"

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 1, students reflect on their problem-solving approaches by describing a model of a strip diagram. In the "Practice and Problem" section of Lesson 4-8, the materials include a reflection which prompts the teacher to ask students to reason by asking questions such as, "What information is unknown?," "What could be the question?," and "Which are the parts and which is the whole in this model?" Students continue to reason by stating the unknown and known parts. They then justify their approach when the teacher asks, "How does the model help you solve the problem?" The Teacher's Edition provides materials that support teachers in guiding students to share their problem-solving approaches through explaining, arguing, and justifying. In Lesson 7-7, during a classroom conversation, students share their knowledge of writing and show how many objects are in a group. The materials provide prompts for teachers to guide students in sharing through questions such as, "How are the stickers arranged? What do you think is the best way to count the stickers? What do the numbers on the stickers show? How are the stickers being counted? Why does the number in the tens digit go up by 1 while the number in the ones digit stays at 0?" In the "Visual Learning" section of Lesson 9-7, the Classroom Conversation provides structured opportunities for students to explain how the digits change as numbers increase or decrease on a hundred chart with questions such as, "How does the ones digit change from 53 to 52? Why?" Students are asked to justify their reasoning using mathematical language related to place value and sequencing. Next, students are guided to explain how to determine which number is greater or less based on digit patterns, encouraging analytical thinking. Students are then guided to analyze by answering the question, "What happens to the digits when you move from 60 to the number just before it? Why?"

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 Grade 1 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 5-1, the materials include four samples from a math memory game where students match four pairs of game cards that show equal expressions. The student response containing a misconception states, "Daniela matched expressions that show exactly the same numbers, with the misconception of Daniela not considering the operation symbols." The suggested feedback for Daniela is, "What number is equal to 3 + 9? How about 9 - 3? Based on your answers, do you think 3 + 9 and 9 - 3 are equal?" This allows the teacher to address the student's misconception effectively. In the "Visual Learning" section of Lesson 7-6, the Classroom Conversation prompts are strategically designed to guide student thinking and reinforce understanding of skip counting. Students are first asked to apply math skills by identifying which number patterns are easiest to skip count. Then, they analyze digit changes when counting from 100 to 120 by fives, focusing on the patterns in the tens and ones places. Finally, they connect the concept by comparing skip counting by 10s from 100 to 120 with counting by five from 100 to 110, emphasizing that both progress by adding two to the tens digit. The Prevent Misconceptions note provides essential teacher guidance to address a common error such as students counting by ones when asked to skip count. Teachers are reminded to clarify that skip counting involves intentionally not saying every number. Grade 1 materials offer prompts and guidance for teachers based on student responses and misconceptions. For example, in the "Guided Practice" section in Lesson 12-2, students are tasked with measuring length. The materials prompt the teacher by sharing, "If students are confused about how to measure height, show how to use the cubes to measure vertically." The materials continue to provide feedback such as, "Remind students not to leave any gaps when measuring the items with cubes and to ensure that the cubes form a line." Within the same lesson, the teacher provides feedback to the student, "reminding them that when measuring length the same units must be used, the units cannot overlap, and there cannot be any space between the units."