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

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

The "End Matter" of the Teacher's Edition 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 for grades K–5. In the "Kindergarten Scope and Sequence" for the 165 instructional day guide, the TEKS, ELPS, and concepts are included for each topic throughout the document. In the "Kindergarten Scope and Sequence" for the 180 instructional day guide, the TEKS, ELPS, and concepts are included for each topic throughout the document. EnVision Plus Mathematics Grade K includes TEKS and ELPS correlation. The TEKS can be found in the "Pacing Guide" and the "Texas Essential Knowledge and Skills (TEKS) Correlation" section in the End Matter. The ELPS can be found in the Teacher's Edition in both the "Topic Planner" for each topic and the "English Language Proficiency Standards Correlation" section in the "End Matter."

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 materials provide pacing guides for 165, 180, and 210 days that provides teachers with a day-to-day suggestion for lesson implementation that aligns with the scope and sequence. EnVision Plus Mathematics Grade K includes a suggested pacing guide in the "End Matter" 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 K. The materials include pacing for 2–3 days of each Topic Review and Topic Assessment, as well as 2–3 days per Topic on Differentiation activities. Materials include a pacing guide that offers options for adjusting the time spent on units without disrupting the sequence and coherence of content. For example, the order of the units remains the same with 180-day pacing, but each unit is reduced 4–6 instructional days.

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

EnVision Plus Mathematics Grade K 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 "Program Overview" for grades K–2 that explains the coherence of the curriculum and describes how students within the kinder level will make connections based on visual cues to help them make connections across topics and lessons, which will also lead into grade 1 content. In the Grade K Teacher's Edition, Topic 12 includes 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 Grade K includes protocols for teachers to thoroughly understand and prepare to teach a unit, using the "Topic Internalization Protocol." Materials are found in the "Internalization Protocols and Observation Tools." The resource provides guidance on: identifying relationships between lessons and how they build toward successful TEKS coverage, noting how concepts develop sequentially, considering strategies to ensure learning for all students, and identifying how the topic builds learning through concrete-representational-abstract progression. The resource 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 new vocabulary and relating it to 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 guidance on appropriate supports to differentiate instruction. The materials include internalization protocols for topics, which is the unit for this curriculum. These protocols include guidance on pacing, preparing to teach the topic, assessing the topic, and gathering the materials needed. This one-pager includes a section on scope, sequence, and pacing; preparing to teach the topic; assessing the topic; and how to 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 parts, preparing to teach the lesson, and gathering and preparing materials.

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

EnVision Plus Mathematics Grade K includes resources for instructional leaders to support teachers. Materials include a "Classroom Observation and Analysis Tool," an "Instructional Leader Topic Internalization" protocol, and an" Instructional Leader Lesson Internalization" protocol. In grade K, 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 Grade K 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 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. Materials provide resources for instructional leaders to guide teachers with implementing the materials 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 Grade K includes comprehensive unit overviews found in the "Math Background" section of each topic in the Teacher's Edition. It provides the background content knowledge teachers need to effectively teach each lesson. For example, the "Math Background" section includes key concepts taught throughout the unit, coherence of concepts previously taught and to be taught, and balance of conceptual understanding to procedural fluency. In Topic 1, the "Math Background" states, "students use the standard list of counting words in order (one, two, three); they also learn to count a set of objects by pairing each object with one and only one number." In the "Linguistic Accommodations" section of the Teacher's Edition, the resource includes comprehensive unit overviews that provide academic vocabulary necessary to effectively teach concepts in the unit. For example, the academic vocabulary found under "Linguistic Accommodations" states and defines the vocabulary for the unit. In Topic 1, "the word is given (match), the math meaning is given (making pairs; pair one of each group to the other), and other meanings are given (a sport event)." The materials provide teacher guidance to support concept development with an outline of background knowledge and the vocabulary teachers need to effectively teach this lesson. In Topic 5, the Planning and Overview document provides information including the following vocabulary: left, separate, subtraction sentence, take away, difference, subtract, minus sign (–). EnVision Plus Mathematics Grade K includes a math background coherence document with visuals to show connections between previous learning as well as prep for the future learning in the topic.

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 Grade K provides supports for families in both Spanish and English by providing a QR code to access an overview, standard explanations and examples, topic support, and math help at home pages, which include sample problems and home activities. Materials contain supports for families in both Spanish and English for each 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, such as classifying objects into categories. The resource contains supports for families in both Spanish and English for each unit with suggestions on supporting the progress of their student in the "Planning and Overview Family Engagement" section in each Topic in the Teacher's Edition. The family engagement activities give the family a description of what the student is learning. For example, in Topic 2, "your child is learning about writing, counting, and comparing numbers from 6 to 10." Then, the activity gives the family an activity to do with the student at home. For example, "give your child a number and ask them to draw the appropriate number of simple objects."

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 Grade K provides lesson plans that include a list of materials that are necessary to support instructional materials for this lesson. In this lesson plan, counting sticks are needed. Materials include 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 that are 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. 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 Grade K 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 each 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 Grade K includes a list of teacher and student materials for each lesson (such as manipulatives and activity pages or templates) at the beginning of each lesson. In the Teacher's Edition, Topic 5, Lesson 5-1, the student and teacher materials are listed, including connecting cubes and the Exit Ticket. The materials include a lesson overview listing the teacher and student materials necessary to effectively deliver the lesson. In Lesson 5-7, the materials include number cards 0–11 or Teaching Tool 84. The student resources B2 Subtraction and B6 Finding Differences are also listed and can be found in the Teacher Resources with a QR code. In the lesson overview, the resource provides a recommended time for each component. In the Teacher's Edition, Topic 2, Lesson 2–2, the "Timeline" suggests the following: Step 1: "Explore and Share"—10–15 minutes, Step 2: "Visual Learning"—5–10 minutes, Step 3: "Practice and Problem Solving"—15–20 minutes, and Step 4: "Assess and Differentiate"—10–20 minutes.

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

EnVision Plus Mathematics Grade K provides guidance to teachers in assigning online lesson activities through a digital learning platform that offers interactive learning activities to extend and enrich the lesson objective unit. Materials include enrichment opportunities to deepen mastery of the lesson objectives. In the Teacher's Edition, Topic 4, Lesson 4-1, the enrichment activity gives the student an opportunity to show different ways to represent the number six. The resource includes guidance on the effective use of activities for extension, extra practice, etc., in the topic review and building automaticity. There are several activities listed, as well as an extra challenge to use for fast finishers. The Topic 12 Review is a writing activity to build vocabulary by writing with math academic language. This review encourages students to work together to build another set of clues to the automaticity number challenge.

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 Kindergarten Assessment Sourcebook, assessments include diagnostic with a readiness assessment, formative with a progress monitor assessment, and a summative assessment for the end of each topic. Each topic provides an Exit Ticket, a topic assessment, and a performance task. At the end of Topics 3, 6, 9, and 12, there are Cumulative/Benchmark assessments. Grade K 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. EnVision Plus Mathematics Grade K 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 K materials include diagnostic and summative assessments found at the beginning and end of each topic. The diagnostic assessment that appears at the beginning is titled "Review What You Know." For example, in Topic 2, the "Review What You Know" assessment has four questions for students to identify which set of objects is either greater or less. This diagnostic assessment offers a variety of tasks and questions by having the students complete the task by circling, writing, or drawing the correct answer. There are also two different summative assessments for each topic, allowing for a variety of tasks. For example, in Topic 2, there is a Topic Assessment and a Topic Performance Task. Both assessments provide multiple question types including multiple choice, draw or color, and write to identify the correct answers. In the Teacher's Edition, Lesson 1-2, Exit Ticket 2 asks the students to "Count the dots. Which shows how many dots there are?" For Exit Ticket 3 it states, "I can count groups of 1, 2 and 3 objects shown in different ways." Topic 1 Assessment guides teachers to have the students mark the best answer. Examples of assessment questions include, number 1, "Which shows 3 suns?" and number 2, "How many stars are there?" In the Teacher's Edition, Topic 4, Lesson 6, there are multiple assessment tasks available for the teacher including Guided Practice, Quick Checks, and Exit Tickets. These tasks allow for a variety of questions including multiple choice and writing or drawing a correct response. The Exit Tickets located at the end of each lesson also allow students to reflect on their learning by checking and coloring the image that aligns with the math goal. For example, in Topic 4, Lesson 6, the math goal is "I can use reasoning to solve addition problems." The student then marks the corresponding face on how they feel. In the Teacher's Edition, Topic 5, the assessment questions start from multiple choice representation of a story problem to a number sentence. The expectations then progress to writing the numbers into the spaces to create the number sentence. In the Topic 5 "Performance Task," the materials guide the students to write the numbers and generate their own equations. This assesses in a multi-part format and has the students move to the higher-level thinking skills.

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

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

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

EnVision Plus Mathematics Grade K materials provide a scoring guide for each topic assessment. This item analysis chart includes every tested item, depth of knowledge indicator, and TEK that the question is monitoring. In the Teacher's Edition, Topic 9, "Measurement, Review What You Know" section of the lesson, there is an Item Analysis Chart that lists the questions and the TEKS aligned to each question. For example, question two has the student circle the solid figure that can roll, matching TEKS K.6E "to classify and sort a variety of regular and irregular two- and three-dimensional figures regardless of orientation or size." The question also aligns with the objectives of the unit. For example, in the Topic Planner of the Teacher's Edition, one of the math objectives listed include "use measurable attributes to describe and compare different objects." In the Teacher's Edition, Topic 5, Lesson 5-2, Exit Ticket, the items are aligned to TEKS K.3A: "Model the action of joining to represent addition and the action of subtracting to represent subtraction." The TEKS are listed under the example of the Exit Ticket. The learning objective "I can take apart a number and tell the parts" also aligns to the formative assessment Exit Ticket. It is also in the teacher directions located at the bottom of the page on the Exit Ticket. The summative assessments located at the end of each topic clearly align to the TEKS listed for that corresponding topic. Materials provide an Item Analysis Chart that lists each question with the corresponding TEKS. For example, in Topic 6, questions 1, 2, 11, and 12 are aligned with K.2i; questions 3, 4, 6, 7, and 10 are aligned with K.3C; and questions 5, 8, and 9 are aligned with K.3A. 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 "Find number partners for 10," and on the Topic Assessment has the students looking at a ten frame with 7 counters one color and 3 counters another color.

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 K 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 Depth of Knowledge (DOK) level associated for each assessment and correlating question number. Each unit in the grade K instructional assessments contains more than two levels of complexity. For example, in Topic 1 the Exit Tickets have a complexity level of one and/or two. The Performance Task at the end of each topic also has multiple DOK levels of 2 and 3. For example question 3, "Terrence's sister, Lisa, likes jewelry. She wants to make a new bracelet. She keeps beads in a jewelry box. Have students use the following clues to draw how many of each kind of bead she could have in her jewelry box, and then write the numbers to tell how many. Say: Lisa has four round beads. She has a group of square beads that is equal in number to the group of round beads. The number of long beads Lisa has is less than her group of square beads," is labeled as a DOK 3 question. The grade K Topic 9 assessment in the Teacher's Edition has the TEKS-aligned assessment items that assess students at different levels of complexity. The levels include procedural tasks, application of problems that require multiple tasks, and open-ended questions. EnVision Plus Mathematics Grade K Topic 9 assessment includes questions ranging from multiple choice, to drawing/writing the answers to the questions, along with an open-ended response. For example, question one in Topic 9 says, "Write the number to match each model. Circle the choice that correctly compares the two numbers." For question two, "Write the numbers in the correct order on the number line; 26, 12, 18."

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

Scoring information provided in the "Performance Task Scoring Guide and Rubric" in Topic 3 of the Teacher's Edition gives guidance to teachers on how to score the assessments. For example, item 2 in the Topic 3 Performance Task, students can earn a total score of two points. The student receives the full two points if they correctly identify the number of each type of paintbrush and correctly indicate which group has fewer. Only one point is earned if the student correctly identifies the number of each type of paintbrush or correctly indicates which group has fewer. This allows for consistent, reliable, and aligned scoring among all teachers. EnVision Plus Mathematics Grade K includes guidance for interpreting student performance on instructional assessments. For example, in the Teacher's Edition, Topic 12: "Personal Financial Literacy," Lesson 12-1, teachers are guided to give the Exit Ticket to students and then "[u]se the Exit Ticket results to support students as needed by reminding them that the amounts 1¢ and 10¢ mean 1 cent and 10 cents. The cent symbol tells you that it represents a money amount." This allows teachers to analyze the Exit Ticket and use the data 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 K materials provide an "Item Analysis Chart for all Topic Assessments." For example, the "Item Analysis Chart" found in the Teacher's Edition for the Topic 1 assessment contains a chart that provides guidance on the intervention activity to use with students who miss a question from the topic assessment. If students incorrectly answer questions 1–10, the chart guides teachers to use Intervention Lesson A1. If students miss questions 11–13, the chart suggests using Intervention Lesson A2. If students are unable to recognize how many of an object there are and find the corresponding picture, Intervention Lesson A1 gives them extra practice in object number identification. 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 theLesson 5-6 "Guided Practice," question 1 provides a series of subtraction problems: "4–0=, 4–1=, 4–2=, and 4–3=" and guides the teacher to have students solve the problems and determine the pattern. Teacher guidance includes an "Error Intervention" for item 1, which states that "if students are unable to see a pattern, then have them look at how each of the numbers change starting with the equations on the left and then going to those on the right."

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.

EnVision Plus Mathematics Grade K includes 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 each topic. The teacher tool features a list of the TEKS and the corresponding lessons that cover the TEKS in a chart. For example, K.2A: "count forward and backward to at least 20 with and without objects" is covered in Lessons 1-1, -8, -9, and -10. The materials guide teachers to note the development of each student before the topic, during the topic, 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. The grade K materials include student progress and growth trackers designed to help students analyze their own learning. These tools, found in both the "Student and Teacher Progress Trackers," support student reflection on math goals before, during, and after each topic. For example, in Lesson 7-2, the math goal is "I can name shapes as flat or solid." At each stage, students select one of three reflection options: "I Can," "With Help," or "Not Yet." They circle the option that best reflects their understanding of the math goal at that point in time. This ongoing reflection process encourages students to actively monitor their learning. In grade K, the progress tracker is read aloud collaboratively by the teacher and student, ensuring that students are only responsible for reflecting on their learning, not for reading the text independently.

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 a 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 Differentiation Instruction in the "Program Overview" offers an Intervention System to help teachers provide effective interventions for learners that are on or below grade level. The Intervention Lessons are separated into three sections: "Guided Instruction, Practice, and Check for Understanding" and include Teacher Support, which provides guidance to teachers to conduct a short lesson. The lessons focus on vocabulary, concept development, and practice. An example from the "Grade K Intervention System" includes Lesson A3 from Topic 2, Lesson 2-6: Read, Make, Write 10. Intervention Lesson A3 provides guidance on reading, making, and writing numbers from six to ten and includes teacher instructions that accompany the activity page for students. The Grade K Teacher's Edition includes an Intervention Activity that serves as a scaffolded lesson for students. Based on the results of the Quick Check, teachers can select different activities to support student learning. If a student receives between 0–3 points on the Quick Check, then the materials provide an Intervention Activity or a Reteach to Build Understanding Activity. The Intervention Activity in Lesson 3-2 provides step-by-step instructions for reteaching foundational math concepts using hands-on manipulatives such as colored cubes and a part-part mat. Teachers are guided to engage students in sorting activities based on color attributes: "blue vs. not blue, yellow vs. not yellow, etc." The teacher prompts students to explain their thinking, reinforcing conceptual understanding through discussion. These activities offer students concrete, visual experiences to support comprehension and retention. Furthermore, the lesson is scaffolded in a way that gradually increases in complexity—from sorting by a single attribute to exploring combinations and abstract reasoning: "identifying a purple group made of red and blue cubes and explaining why no cubes fit that category." This structured approach not only reinforces prior learning but also builds the skills necessary for mastery, demonstrating how the materials include both targeted intervention activities and scaffolded lesson components to meet the needs of struggling learners. In the Grade K Teacher's Edition, Lesson 11-1: "Count Greater Numbers," enVision Plus Mathematics provides an intervention activity for students who earned a 0–3 on the lesson's Quick Check. The lesson guides the teacher to use a 100 chart as a teaching tool and provide each student with a copy of a hundred chart showing the numbers 1–30. The resource prompts the teacher to say, "We will practice counting to 30." The students work in pairs and begin the lesson by counting to 30 together while using their hundred chart as a visual support. Next, each student takes turns counting to 30. "As one student counts, the other student can point to each number on th

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, Lesson 2-1, language support and math talk are thoughtfully embedded to help young learners access and engage with mathematical content. The lesson materials include pre-teaching strategies for academic vocabulary, ensuring that students are introduced to key terms before they encounter them in context. This proactive approach helps build familiarity and confidence. Additionally, the lesson integrates embedded supports for unfamiliar vocabulary, including visual aids, simplified definitions, and contextual examples that clarify meaning during instruction. Teachers are guided to address academic language, as well as figurative language and idiomatic expressions, which can often be barriers for early learners and English language learners. These supports are woven into the lesson through Math Talk prompts, which encourage students to use precise language, explain their thinking, and engage in structured discussions. This dual focus on language and content development ensures that all students, regardless of language proficiency, can participate meaningfully in mathematical conversations and deepen their conceptual understanding. EnVision Plus Mathematics Grade K includes 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 7: "Shapes and Solids," the vocabulary activity guides the teacher to create a two-column vocabulary chart on the board labeled "New Word" and "What It Means." The teacher then writes three new vocabulary words in the first column and asks students to share everyday or mathematical definitions and records the students' responses in the second column. For example, the teacher writes the word vertex in the "New Word" column and records a student derived meaning, such as corner in the "What it Means" column. The students are given guidance to copy the chart into their notes, and the materials guide the teacher to inform the students that they will explore these words further in the lesson. Grade K materials include embedded supports for unfamiliar references in the topic. In the Teacher's Edition, teachers can access the Academic Vocabulary in the Topic Opener. New academic language is introduced prior to the lesson and then used throughout the entire topic. The academic language is cross-curricular and used throughout the school day and year. Topic 8: "Work with Shapes and Solids" has the teacher highlight the following words: attention, discover, and suggestion in the lesson. In the Teacher's Edition, the resource provides definitions for the teacher to reference. For example, for the word attention, the materials suggest that the teacher explain to students that they will look closely at, or pay attention to, the different attributes of shapes as they compare them.

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 K, Topic 2, the "Building Understanding," "Sustain Understanding," and "Fluency" sections are enriched with a variety of engaging tools and activities that support both language development and math talk. These sections include digital manipulatives, lesson resources, spiral review, hands-on games, digital games, and fluency practice, all designed to reinforce key concepts such as comparing numbers zero to five in fun, interactive ways. Each activity is structured to include academic vocabulary, visual cues, and sentence frames that help students articulate their thinking. For example, digital manipulatives allow students to explore math concepts visually and kinesthetically while using guided prompts to describe their actions. Math Talks are embedded throughout the materials, encouraging students to explain their reasoning, ask questions, and engage in peer discussions using precise mathematical language. The spiral review and fluency games revisit previously learned concepts, reinforcing both content and vocabulary in a low-pressure, engaging format. These components collectively create a rich, supportive environment where students can build confidence in both math and language through meaningful, real-world connections. The grade K materials include guidance for differentiated instruction for students who demonstrate proficiency in the grade-level skills. In the Teacher's Edition, the guidance includes a Quick Check in the "Assess and Differentiate" section of Lesson 4-2. 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 4-2 is focused on representing addition as "adding to." The enrichment activity for Lesson 4-2 is provided through the online program, which extends the learning by requiring students to count and circle each set of objects in order to find how many there are in all and write that number. In addition, students complete the number sentences in the box. Grade K materials offer 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." There is guidance in the Teacher Guide on when to use these extension activities. In Topic 5: "Understand Subtraction," the "Pick a Project" can be used anytime during the topic, whereas the "Stand Up and Think Problem 5A" can be used anytime after Lesson 5-2. The "Pick a Project" offers four projects for students to choose from. For Topic 5, each project includes a visual, an action, and a final product. Project 5A has students looking at a visual of a girl in a bookstore. The students are to create their own math observations about all the math they see in the real world using that image.

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

In the "Language Support" section of Lesson 4-3, the materials provide clarity on possible challenges students may encounter in the lesson by providing an "Anticipating Struggles" activity. This guidance helps teachers address potential difficulties students may face when distinguishing between colors of objects or connecting representations such as green tomatoes to yellow counters. To support modeling, teachers are advised to adapt the task using easily identifiable differentiators, such as big tomatoes and small tomatoes. For example, using the phrases "big tomatoes" and "small tomatoes," the materials guide teachers to adjust their vocal register by using a deeper, louder voice when saying "big tomatoes" and a softer, higher voice when saying "small tomatoes" to reinforce conceptual understanding. For explaining the concept, the materials suggest using manipulatives, like big and small connecting cubes, to represent different quantities, helping students visualize the comparison. An example problem is provided, "Kai sees two tomato plants. One has two small tomatoes. The other has three big tomatoes. Use big cubes and small cubes to show the tomatoes on each plant. How many tomatoes are there in all?" This structured support helps teachers explain and model both the mathematical concept of combining groups and the language used to describe quantity and size. In Lesson 7-1, the teacher introduces the concept of addition by guiding students through a hands-on modeling activity. The teacher begins by stating, "Today, we are going to learn about addition, which means putting groups together to find out how many we have in all." Using two-color counters, the teacher places two red counters on the left side of a mat and three yellow counters on the right side. The teacher prompts the class, "Let's count how many counters we have altogether," and leads them in counting aloud, "One, two, three, four, five." The teacher explains, "We had two red counters and added three yellow counters. Now we have five counters in all. That is what addition means—putting things together." To connect the hands-on activity to symbolic representation, the teacher writes the number sentence "2 + 3 = 5" on the board and says, "This is how we show it in math. The plus sign means we are adding, and the equal sign tells us the total." The teacher continues with a think-aloud strategy, "I see two counters. I am adding three more. I will count them all to find the total. One, two, three, four, five. So, two plus three equals five." To reinforce the concept, the teacher invites a student to model a new combination, such as four red and one yellow counter, and together they write the number sentence. The lesson concludes with guided practice, where students use their own counters to model and explain addition problems, following the teacher's example. In Lesson 9-3, the "Visual Learning" section provides a detailed teacher script in the "Classroom Conversation." The materials prompt the teacher to ask the Essential Question, "What does it mean to compare the capacity of objects?" The script guides the teachers to say, "There are two glasses. Are the glasses full or empty? Which glass holds more? How do you know?" This script directly supports the teacher in modeling the comparison of capacity by guiding students to observe and discuss the attributes of the glasses. The script also includes exemplar answers for each question to support the teacher with modeling and explaining the concept. Additionally, the prompts help the teacher explain the concept by encouraging students to use reasoning related to size and volume, reinforcing an understanding of capacity through guided questioning. The enVision Plus Mathematics Grade K curriculum Lesson 11-1: "Count Using Patterns to 30," includes explicit prompts and guidance to support the teacher in modeling and explaining the concept. In Lesson 11-1, the teacher introduces the concept of counting using patterns to 30 b

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 K Digital Teacher Resources, the lesson "Equal Groups of Popsicles?" is a great example of how the program supports teachers with explicit guidance for delivering instruction using a variety of approaches. When launching the lesson in Topic 2, the teacher begins by gathering students in a whole-group setting and presenting a visual or real-life scenario involving groups of popsicles. The lesson plan provides questions such as, "Do these groups have the same number of popsicles?" and "How can we check if the groups are equal?" to activate students' thinking about whether or not the groups of popsicles are equal. The teacher models the concept by physically grouping counters or drawing popsicles on the board while narrating each step, "Let's count the popsicles in this group—1, 2, 3. Now let's count the next group—1, 2, 3. Are they equal?" Students are encouraged to use their own counters or drawings to explore the concept hands-on. The teacher facilitates Math Talk, asking students to explain their thinking and compare their groups with a partner. For students needing extra support, the teacher may use the "Differentiation Library" to provide visual aids or simpler groupings, while advanced learners might be challenged to create their own equal and unequal groups. This lesson structure ensures that all students are actively engaged and supported through modeling, questioning, hands-on practice, and peer discussion. 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 the Teacher's Edition, Topic 6, Lesson 6-1, students work in pairs to share the methods they used to determine the quantity of each animal in the "Let's Count" numeracy routine. The Lesson 6-1 Exit Ticket has students examining pictures and choosing the correct equation that matches. 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 entries to the problem. For example, students are prompted to begin thinking about planted flowers, "Some are yellow, and some are red." Students explore the concept of addition using counters to show how to break apart a group of five daisies. The grade K materials in the Teacher's Edition of Topic 8 provide teachers with suggestions for using a multitude of instructional approaches, including visual learning, language routines, and practice and problem-solving. The "Visual Learning" section provides a visual example to formalize the mathematics of the lesson. Lesson 8-2 provides the teacher and students with visualizations of two-dimensional shapes. The visuals are used to understand the attributes of squares and how the square is a special kind of rectangle. Language routines help students communicate about math to advance their thinking. The language routine in Lesson 8-2 is "Critique, Correct, and Clarify." In this routine, the teacher states, "Determine if each statement is always true, sometimes true, or never true" for the following statements, "A rectangle is a rectangle," "A rectangle is a square," and "A triangle is a square." Then, in the "Practice and Problem-Solving component of the lesson, students build proficiency as they work independently.

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 K, Topic 3, Lesson 3-2, students engage in a variety of structured learning experiences that support conceptual understanding of grouping numbers, six and seven. During Guided Practice, the teacher uses counters and ten-frames to model how to make and count groups of six and seven, with students actively participating by using their own manipulatives to mirror the teacher's actions. The Teacher's Edition provides clear instructions, stating, "Use two-color counters and a ten-frame to model six. Ask: How many counters are there? How do you know?" This type of questioning encourages students to verbalize their thinking and reinforces number sense. In the "Independent Practice" section, students complete workbook problems that prompt them to draw or use objects to represent groups of six and seven, applying what they learned during the guided portion. For Collaborative Practice, the lesson suggests a small-group matching game using number cards and counters, where students work together to match quantities with numerals, promoting peer interaction and mathematical discourse. The Teacher's Edition supports implementation with differentiation tips such as, "For students who need support, use real objects to build understanding before moving to drawings," and offers grouping suggestions, recommending whole-group instruction for modeling and small-group settings for games and reinforcement. This lesson exemplifies how enVision Plus Mathematics Grade K structures instruction to include multiple types of practice with embedded teacher support. Lesson 11-5 includes various types of student practice to support learning. The "Explore and Share" section provides a collaborative and guided practice opportunity, where students work in small groups to count numbers on a hundred chart with teacher guidance and prompting questions. Teachers observe and ask probing questions to monitor understanding. In the "Visual Learning" section, students engage in independent and paired practice, such as pointing to numbers, counting with arrows, and discussing counting patterns. This section includes partner conversations and Think-Pair-Share in the "Talk About Math Ideas" section, supporting collaborative practice. Additional practice is built into the Early Finishers tasks, encouraging independent learning through extended number work such as "Color the box with 2 yellow. Color the box with 11 yellow. What numbers do you count when you count forward from 2–11?" In the "Monitor, Select, and Sequence" section, teachers are given specific questions to check for conceptual understan

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" sections 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 1-1, students are learning to count to one, two, and three. The Targeted ELPS Support guides the teacher to model counting three counters with students and then use a sentence frame. The materials include teacher guidance with scaffolds for each proficiency level. For example, the teacher guidance for students identified as pre-production is "The students point to each counter as you count aloud." Guidance for beginning is, "The students point to each counter as they count aloud." As the levels progress, the materials provide teacher guidance such as, "The students count aloud. Then use the provided sentence frame, 'I have _ counters,'" for intermediate students. Then, for high intermediate the teacher guidance states, "The students count aloud." Then use the provided sentence frame, "I have _ counters. I counted _." Last, the materials provide guidance for students identified as advanced, "The students work with a partner and ask their partner to count their counters and tell them the number they have, then demonstrate how they counted their counters." The grade K materials include teacher guidance and suggestions for specific items during student practice. While students work independently or in pairs on Practice and Problem Solving, the Teacher's Edition provides prompts for supporting emergent bilingual students. In Lesson 3-2, students are asked to describe how the animals are classified by drawing another animal that belongs in the same category. The prompt allows for linguistic support by enabling students to verbally describe their thoughts with prompts before drawing. For example, the Teacher's Edition states, "Encourage students to describe the animals in the top box to help them discover what is similar about the animals." In Lesson 10-5: "Count On" from the enVision Plus Mathematics Grade K curriculum, students develop fluency in counting forward from any number up to 20 by identifying number patterns and using visual tools. The lesson begins with the teacher displaying a large number chart and saying, "Today, we are going to count numbers and look for patterns that help us know what comes next." Students count aloud together, moving left to right across the chart. The teacher emphasizes structure by pointing out, "Look, after 10 comes 11, and it's right under 1. That's a pattern!" To support English learners, the curriculum integrates Targeted ELPS Support strategies. Teachers use color-coded number rows, sentence stems like, "The next number is ___ because ___," and structured routines such as Three Reads to help students comprehend and explain their thinking. For example, a student might say, "The next number is 12 because it comes after 11." These supports align with the ELPS, ensuring all students can access and express mathematical ideas. Students engage in hands-on activities such as counting balloons, shading number charts, and using connecting cubes or drawings to represent numbers. In the "Practice and Problem Solving" section, students solve problems like identifying the total number of balloons shown with numbers 9, 7, and 8. They are encouraged to reflect on their strategies and explain patterns they notice, such as, "I see 7, and one more is 8." The lesson also includes a Quick Check and Item Analysis to assess understanding. Teachers can differentiate instruction using the Differentiation Library, which offers intervention activities, visual models, and video tutorials. For example, students who need more support might use a number line to count

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. It 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 6, operation is listed for topic vocabulary; there are no prior terms listed while flat, solid, circle, triangle, side, vertex, vertices, rectangle, and square 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.

In enVision Plus Mathematics Grade K, Topic 4, Lesson 3: "Compare Numbers," the curriculum provides targeted support for emergent bilingual students to develop academic vocabulary and deepen comprehension through structured oral and written discourse. The lesson incorporates sentence frames such as "___ is more than" and "is less than ___," which guide students in using precise mathematical language while comparing quantities. Partner talk activities encourage students to engage in meaningful conversations, allowing them to practice new vocabulary in context and build confidence in expressing mathematical ideas. Additionally, the bilingual glossary and audio support offer cross-linguistic connections by reinforcing key terms in both English and Spanish, helping students relate new concepts to their home language. These embedded supports collectively foster background knowledge, enhance understanding, and promote active participation in math discussions. In enVision Plus Mathematics Grade K, Topic 8, Lesson 1: "Identify Shapes," the curriculum thoughtfully supports emergent bilingual students by integrating language development with mathematical understanding. The lesson introduces shape vocabulary such as circle, square, and triangle through real-life examples, helping students connect abstract concepts to familiar objects in their environment. To strengthen cross-linguistic connections, the curriculum highlights cognates like círculo and circle, enabling students to draw on their home language as a bridge to English. Interactive games and center activities provide hands-on opportunities for students to use new vocabulary in context, promoting both oral and written discourse. Additionally, the bilingual glossary and audio support ensure that students can access and practice key terms in both languages, reinforcing comprehension and encouraging active participation in classroom discussions. The digital resources include language development practice tools to support Emergent Bilingual (EB) students' literacy and language proficiency. The "Build Mathematical Literacy" found in the Digital Resources provides opportunities to develop academic language, increase comprehension, build knowledge, and make connections through oral discourse. For example, in Lesson 9-2, students are shown images of a leaf and a branch. The resource guides the teacher to say, "What objects do you see? You need to draw a circle around the longer object or underline the objects if they are the same length. What does 'longer' mean? Is one object longer than the other, or are they the same length? How can you decide which object is longer?" 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 K 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 10-1, the Language Routine: Collect and Display guides the teacher to have the students pair up and then "prompt each student to convince their partner why these were all ways to show 11, and ask students to present reasons why they are all 11."

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 enVision Plus Mathematics, the materials provide multiple opportunities for students to demonstrate their understanding throughout the unit, all aligned with the TEKS standards. For instance, in Topic 1: "Count and Compare Numbers 0 to 5," students begin by focusing on numbers one through three in the first three lessons, as outlined in the Topic Planner in the Teacher's Edition. They expand their learning to include numbers four and five in the following three lessons, along with a dedicated lesson on the number zero. The remaining seven lessons in the topic offer continued practice and review of numbers zero through five. These lessons are designed to support the grade K standard K.2B, which involves reading, writing, and representing numbers from 0 to 20 using objects or pictures. The instructional sequence helps students first recognize and read numbers, then move on to making and writing them. This foundational understanding is further developed in later topics, such as ": Count and Compare Numbers 0 to 10" and Topic 10: "Count and Compare Numbers 0 to 20," allowing students to build toward full mastery of the standard. In enVision Plus Mathematics Grade K, Topic 4, students begin learning the concept of adding numbers through a gradual and developmentally appropriate progression. In Lesson 4-1, they start by connecting pictures to numbers, counting the total of two groups of objects without using any number sentence words or mathematical symbols. This helps the students build a concrete understanding of combining quantities. In Lesson 4-2, students are introduced to the words "and" and "is" to begin forming simple number sentences using language. By Lesson 4-5, they learn that "and" represents the plus sign (+) and "is" represents the equals sign (=), and they begin to see these symbols placed above and below the corresponding words to reinforce the connection. Finally, in Lesson 4-6, students progress to writing addition number sentences using only symbols, without the support of the words "and" or "is." This sequence helps young learners transition from concrete to symbolic understanding of addition in a clear and supportive way. The lessons in the Teacher's Edition provide multiple opportunities for students to demonstrate a deep understanding of key concepts. For instance, in Lesson 7-2, students begin by sorting 2D and 3D shapes during the "Explore and Share" portion of the lesson. This is followed by a "Visual Learning" section, where students engage in a think-pair-share activity to discuss their reasoning for sorting the shapes in specific ways. The lesson then transitions to "Guided Practice" and "Practice and Problem Solving," where the complexity of the tasks gradually increases. In this example, students identify 2D shapes, then sort them into categories, and finally draw their own shapes—each step deepening their conceptual understanding and application of the content.

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

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, Topic 4, Lesson 4-1, 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 many wheels would there be if there was one bicycle and one tricycle?" The second set of questions address "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, "Can you show a third combination of two vehicles that Jada and Roshan could add to the parade?" The instructional materials include tasks that progress in rigor and complexity across the unit in the lessons. In Teacher's Edition, Topic 7, students are required to first explore, name, identify, describe, and finally solve real-world problems involving shapes. These tasks progress to meet proficiency of the mathematics standards. In enVision Plus Mathematics Grade K, students work with different quantities over time to understand how to read, write, and represent numbers up to 20, and fluently count by 10s and 1s to 120. In the Topic 10 "Math Background: Coherence" document, the text specifies that in Topics 1 and 2 the students first learned to read, write, and represent numbers one to 10 and move to greater quantities, building complexity of representation, such as including comparing quantities. As quantities increase, students represent numbers with a group of 10 and some ones. It then specifies in Topic 11 students will be expected to sequence and count by ones and tens using a hundreds chart. Each task progressively increases complexity towards grade-level proficiency with the grade K TEKS.

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

The Teacher's Edition, Topic 1, "Math Background: Coherence," highlights how early counting and number comparison (0–5) build upon students' previous experiences, such as using fingers to count, reciting numbers up to 10, and making simple comparisons like big versus small or tall versus short. These foundational skills are crucial for later learning in grade K, where students begin working with numbers up to 20 and developing a stronger understanding of mathematical relationships. In the Grades K-2 Program Overview, the authors explain the rationale behind the content organization, emphasizing that topics are grouped to build strong connections between concepts. The content is organized around key mathematical ideas that support coherence within and across lessons in each unit. Topics are thoughtfully sequenced to align with mathematics learning progressions, connecting new content to students' prior knowledge. Additionally, the TEKS are revisited in multiple lessons across topics to reinforce understanding and deepen connections throughout the year. For example, Topics 1 and 2 introduce counting and comparing numbers from 0 to 5 and then extend to 0 to 10, building students' foundational understanding of number sense and quantity. This foundation supports Topics 4–6, where students apply counting skills to understand addition and subtraction by joining and separating quantities in real-world contexts. Later, in Topic 10, students extend counting skills to numbers up to 20, and in Topic 11, they work with counting to 100, further building on their earlier experiences with smaller number sets. The program also revisits measurement and data throughout the year. In Topic 3, students begin by collecting and categorizing data, laying the groundwork for representing data in graphs. This understanding of categorizing and comparing objects prepares students for Topic 9, where they explore measurement by comparing measurable attributes such as length, capacity, and weight. Finally, the inclusion of Topic 12: "Personal Financial Literacy" builds on students' understanding of quantity and value, introducing basic financial concepts such as earning, spending, and distinguishing between wants and needs.

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 Teacher's Edition, Topic 3: "Data," the materials guide the teacher to have students use data to create graphs with real objects, as well as picture graphs, by using knowledge learned before entering school to classify and sort objects by finding similarities and differences. Students then use their new learning from grade K in grade 1 to organize data into three categories and use data to create a typical tally chart and picture graph representation. The materials demonstrate consistent use of academic language learned in previous grade levels, as well as in future ones. In Topic 4: "Understand Addition," in the Teacher's Edition, grade K students learn about the meaning of addition and progress from using addition sentences to equations to describing addition situations. The addition sentence initially serves as a bridge to help connect the meaning of the equation. Prior to grade K, children begin to develop an understanding of the concept of addition by grasping the idea of "more" as it relates to addition. Then, students use their new learning in grade 1 to build strategies and fluency in addition. In enVision Plus Mathematics Grade K, Lesson 9-1, "Let's Investigate" begins with an activity where students compare the size of two dogs. This introduction helps young learners build a foundational understanding of comparing objects based on different attributes, such as size, color, and shape. As the lesson progresses, students transition to comparing numbers, focusing on single-digit values. By exploring these early comparison concepts, they develop essential math skills that will support their ability to analyze and differentiate objects and numbers in later lessons. For example, in Lesson 9-5, students will describe and compare objects by measurable 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 Lesson 3-1, the "Math Background: Coherence" section helps students develop foundational skills in collecting and classifying written numbers by connecting previous learning, engaging with the current lesson, and preparing for future number sense concepts. In the "Look Back" section, students revisit earlier lessons where they explored basic number recognition, practiced counting small groups of objects, and identified numbers in various contexts, helping them understand that numbers represent quantities. This lesson introduces students to collecting and organizing numbers, guiding them to recognize, sort, and classify written numerals based on specific attributes such as order, sequence, and visual patterns. Through hands-on activities, they practice grouping numbers that share common characteristics, reinforcing their ability to identify and structure numerical information. In the "Look Ahead" section, students build upon these classification skills as they progress to comparing numbers, ordering them from least to greatest, and eventually applying their understanding to solve simple problems related to number relationships. This structured progression ensures that students gain confidence in working with numbers, setting a strong foundation for future mathematical learning. In the Teacher's Edition, lessons in Topic 7: "Shapes and Solids" provide guidance on how the lesson concepts and procedures are connected to new mathematical learning. For example, starting in Lessons 7-1 and 7-2, students are introduced to the concepts of flat and solid shapes. This lays a foundation for further classifying flat shapes in Lessons 7-3 and 7-4, and then classifying solid shapes in Lesson 7-5. Additionally, the materials include opportunities for language routines to be used as a procedure throughout multiple lessons. The "Three Reads Language Routine" helps build new learning by asking questions such as, "Can you predict the number and shapes of the prints by looking at the block?" or "How can you describe the flat shapes your block makes?" In enVision Plus Mathematics Grade K, Topic 9, Lesson 9-1, students use different strategies to compare the length, height, capacity, and weight of objects. For example, in the "Connect" section of the lesson, students are asked to look at the pictures, and asked to "Tell what words you can use to describe the comparisons of each object." In prior learning before grade K, students compared the number of objects in two groups. Learning the cardinal number of a group of objects is a discrete attribute that leads to new learning in Topic 9 about continuous attributes, since they can always be subdivided into smaller units. The "more than" and "less than" procedures allow for coherent learning from earlier experiences into grade K.

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

The materials allow students to revisit content repeatedly over days and weeks to help strengthen memory of the skills and concepts. For example, in the Topic 2 review in the Student Edition, students are expected to retrieve information from the unit's lessons to demonstrate mastery of the standards K.2A: "Count forward and backward to at least 20 with and without objects," K.2B: "Read, write, and represent whole numbers from 0 to at least 20 with and without objects or pictures," and K.2: "Count a set of objects up to at least 20 and demonstrate that the last number said tells the number of objects in the set regardless of their arrangement or order." The Topic Review includes the following questions related to the standards: "Count the number of objects and then write the number that tells how many," "Draw 7 counters in a row and then write the number that tells how many," and "Count the fruit in each group, write the numbers that tell how many, and draw a line from each piece of fruit in the top group to a piece of fruit in the bottom group." The "Topic Review" covers all concepts taught in the unit. For example, Lesson 2-1 covers building numbers 6 and 7, and Lesson 2-2 covers reading, making, and writing numbers 6 and 7. In enVision Plus Mathematics Grade K, Topic 8: "Work with Shapes and Solids," students strengthen their understanding of geometry through space retrieval, reinforcing previously learned skills across multiple learning pathways. This topic builds on earlier experiences with identifying and sorting shapes, helping students recall prior knowledge of basic two-dimensional and three-dimensional shapes like circles, squares, spheres, and cubes. The materials provide structured opportunities for retrieval by encouraging students to recognize, compare, and describe shapes based on attributes such as sides, corners, and faces. Through hands-on activities using pattern blocks, real-world objects, and visual models, students refine their ability to distinguish between flat and solid shapes while making connections to their everyday surroundings. The lesson also integrates spatial reasoning by guiding students to analyze shapes in different orientations and use positional words to describe their locations. By revisiting and applying these concepts repeatedly in different contexts, students develop stronger retention and problem-solving skills, preparing them for more complex geometric reasoning in future grades. This progressive learning approach ensures students build confidence in working with shapes, laying a strong foundation for measurement, symmetry, and spatial awareness in mathematics. EnVision Plus Mathematics Grade K includes spaced practice opportunities that allow students to retrieve prior learning of skills and concepts from previous lessons and units. For example, the Math Talk in Lesson 11-2, has students taking turns counting to 14 with a partner. The students then discuss which numbers come before and after a given number. Furthermore, the students discuss and identify how many tens and ones are in 13 with their partner.

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

EnVision Plus Mathematics Grade K provides students with opportunities to represent a learned skill in multiple ways. In Topic 2: "Count and Compare Numbers 0 to 10," in the Student Edition, students are asked to circle a group of objects that is either greater or less than another group. Then, the students have to count to determine how many are greater or less, as well as draw objects to equal the image shown. For example, question 1 illustrates two shovel images above three shovel images. Then, students are asked to circle the group that is greater. The materials include practice opportunities for students to apply previously learned skills and concepts across lessons and units. For example, in Topic 6: "More Addition and Subtraction," Lesson 6-1, students are given an interleaved practice opportunity during the "Practice and Problem Solving" section. Teacher guidance provides students with a card from 1–5 or the symbol card for + or =. Students are then put into groups and work together to find another way to break apart 5= _ +_. In the "Spiral Review" from Lesson 6-1, students apply the skill of comparing numbers to pictorial and numerical representations. In question 2, students are presented with an image of three teddy bears; they must circle the group of teddy bears that is fewer in number than the group of teddy bears in the box. In enVision Plus Mathematics Grade K Topic 6 Review, students are given an opportunity to use all of the skills acquired throughout the topic to solve problems using these skills. For example, in Topic 6 Review, students must solve problems in more than one way with addition and subtraction. Some of the strategies include: making 10, counting on, counting back, and decomposing numbers in more than one way. This blends current learning about numbers to 10 with previously introduced skills such as counting, comparing, and recognizing patterns. This intentional design ensures that students not only review Topic 6 content but also deepen their grasp of earlier math ideas in meaningful, connected ways.

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

The Teacher's Edition supports teachers with questions that prompt students to think critically and in multiple ways. In Topic 1, Lesson 1-1, "Classroom Conversation," students engage in a classroom discussion about worms. They begin by interpreting models and representations and move to examining a visual of worms to determine how many are shown. Students then use counters to represent the same quantity. Next, they explain how the image corresponds to the three counters. Finally, they make additional connections, such as identifying how the numeral 3 represents the number of worms in both the picture and their model. In enVision Plus Mathematics Grade K, students interpret, analyze, and evaluate models and representations during the "Explore and Share" section of Lesson 2-1. In Topic 2: "Count and Compare Numbers 0 to 10," the Teacher's Edition offers opportunities for students to make sense of problems, such as identifying "What are some different types of balls used for sports?" Students then analyze the problem by exploring different ways to represent the balls. Finally, they evaluate their models by determining whether they can use counters to effectively represent their thinking. In enVision Plus Mathematics Grade K, Lesson 3-5, the 3-Act Math Modeling Lesson "Create a Problem," showcases how young learners can engage deeply with mathematical thinking through real-world contexts. These lessons are a standout feature of enVision Plus Mathematics and are specifically designed to foster curiosity, critical thinking, and problem-solving. In Act 1: "The Hook," students watch a short video showing a child setting up a snack table with different numbers of plates and cups, prompting a question such as, "How many more cups are needed?" In Act 2: "The Model," students use drawings, counters, or number sentences to represent and solve the problem they created based on the scenario. For example, a student might include a drawing of five plates and three cups, with a number sentence like 5 – 3 = 2 to show how many more cups are needed. In Act 3: "The Resolution," students compare their solutions to the actual outcome shown in the video and reflect on their reasoning. This structure not only supports mathematical modeling but also encourages students to interpret visual information, construct their own problems, and evaluate the effectiveness of their strategies. In the "Visual Learning" section of Lesson 8-2: "Analyze and Compare Shapes," students utilize their background knowledge and visual models to explore and describe 2D shapes. They interpret visual representations by identifying familiar shapes and naming their attributes. Students analyze shapes by examining the number of sides and vertices, and by identifying whether the edges are straight or curved. Finally, they evaluate models as they sort shapes in different ways based on shared attributes, determining which criteria best represent the relationships among the shapes.

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

The materials in enVision Plus Mathematics Grade K offer opportunities for students to create models that represent mathematical situations. In Topic 4, Lesson 4-2 of the Student Edition, the "Guided Practice" section engages students in using connecting cubes to model a scenario where more boats join a group. Students write an addition sentence to represent the total number of boats. The Teacher's Edition provides instructional guidance by prompting teachers to guide students in selecting effective strategies; for example, teachers are encouraged to remind students that they can count the boats in one group and then count on from that number to find the total. In the Lesson 5-3 "Visual Learning" section, students are prompted to model mathematical situations using concrete representations. For example, the resource guides the teacher to ask the question, "How do the counters model the story problem?" This supports students in connecting real-world contexts to mathematical ideas by having them create a visual model with counters. This task also encourages students to interpret the story problem, represent the quantities involved using manipulatives, and explain how their model matches the situation. This modeling process deepens conceptual understanding and supports the development of problem-solving strategies. In grade K students are prompted to represent the number 12 in two different, easily countable ways using counters. In Topic 10 of the Student Edition, the "Explore and Share" section presents an image of 12 toy cars as a visual reference. The Teacher's Edition then guides educators to ask, "How can you tell if you have the same number of counters? Can you match the counters to the toy cars to confirm they are equal in number?"

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

In Lesson 4-5, the "Talk About Math Ideas" section provides students with the opportunity to apply their conceptual understanding of the plus sign as a symbol that joins two groups and the equals sign as a symbol that shows the total amount. During a Think-Pair-Share, students describe how and why these symbols are used in an addition equation. This discussion helps students connect their understanding of combining groups to the written symbols, allowing them to make sense of addition in both visual and symbolic forms and apply that understanding in new contexts. Topic 5 in the Student Edition provides students with opportunities to apply conceptual understandings to new problem situations. In Lesson 5-1, students investigate the meaning of subtraction through guided teacher lessons. In the "Practice and Problem Solving" section, students apply their new understanding to different situations. For example, in question 2, students are guided to use their fingers or objects to solve the problem and then write how many are left for each subtraction situation. The problem states, "Marta tosses 6 blue cubes. 5 land inside the circle. How many are left outside the circle?" In the grade K, Topic 11 Pick a Project, students are provided with multiple opportunities to apply conceptual understanding to new problem situations and contexts. These open-ended, student-driven projects encourage young learners to apply what they have learned in creative and meaningful ways. For example, "Create a Numbers Dance" is a project option in the Topic 11 Pick a Project. Teacher guidance instructs the students to work with a partner. The students select one row on a hundreds chart, create a dance move for each number, and are encouraged to say the number as they perform the dance move. The task promotes discussion and reasoning as students share their models, compare ideas, and reflect on their strategies. By engaging with visual models and familiar contexts, students deepen their understanding of numbers, counting, and problem-solving while building confidence in their ability to communicate mathematical ideas.

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

EnVision Plus Mathematics Grade K provides tasks that allow students to begin to develop fluency with addition within five by finding patterns in addition facts. Finding patterns will help students add fluently. For example, students may recognize that numbers can be added in any order or that if zero is added to a number, the sum is that number. Seeing addition facts for a number organized in a list helps students notice other patterns. For example, students may notice that if one of the two addends increases and the other addend decreases by the same amount, the sum remains unchanged. In the Math Talk section in Lesson 4-7, students are shown each set of connecting cubes one at a time. The students decide how many cubes are taken away and what addition equation could be used to represent each set of cubes. The teacher asks the students to "describe the pattern to a partner." The teacher models how to write and say the equation for each representation. In Lesson 5-1: "Count to 100 by Ones and Tens," the lesson begins with a Problem-Based Learning (PBL) activity where students use number charts and manipulatives to explore counting patterns. Through guided instruction and visual models, students learn to recognize the structure of the number system, particularly how numbers increase by ones and tens. A prompt from the lesson, "Point to each number as you count. What do you notice about the numbers in each row?" encourages students to observe and articulate patterns in the number chart. Fluency is reinforced through daily counting routines, interactive games, and digital tools available on the Savvas platform, such as the "Practice Buddy," which provides adaptive practice and immediate feedback. These components ensure that students not only practice counting but also develop the automaticity needed to recall number sequences quickly and accurately. In Lesson 5-6, students begin to develop automaticity with subtraction within five by finding patterns. Understanding the part-whole relationship and identifying patterns such as the fact that if zero is subtracted from a number, the difference is that number, will help students develop automaticity with subtraction facts up to five. Viewing subtraction facts in an organized list helps students notice other patterns, such as the fact that the difference decreases when the number being subtracted increases. For example, in the "Visual Learning" section of the lesson, students see five red counters, with zero marked out. The next row of five red counters has one marked out, leaving four counters remaining. The pattern continues to the last row, where all five counters are marked out, resulting in zero remaining.

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.

In enVision Plus Mathematics Grade K, Lesson 6-3: "Add with Objects," the "Practice & Problem Solving" section is thoughtfully designed to support the development of procedural fluency through scaffolded practice. The section begins with guided problems where students use counters and visual models to count and combine groups of objects. For example, students might be shown two sets of apples and asked, "How many apples are there in all?" which prompts the students to physically count and combine the groups. As students gain confidence, the lesson transitions to independent problems where students are asked to write addition equations that match visual representations, such as ten-frames or picture sets. This gradual release of responsibility from supported exploration to independent application helps students apply mathematical procedures efficiently, flexibly, and accurately. By first building understanding with concrete tools and teacher guidance, then moving to symbolic representation and independent problem-solving, students strengthen their ability to solve addition problems with confidence and precision. The materials promote efficient, flexible, and accurate mathematical procedures within and across lessons in Topic 6. In the Teacher's Edition, Topic 6, "Math Background: Coherence" section, Lessons 6-1 through 6-3 focus on developing automaticity with addition and subtraction within five. Students engage with a variety of problem types, including word problems with both addends unknown, encouraging them to think flexibly about number combinations. They also begin to see the relationship between addition and subtraction, building accuracy and understanding of inverse operations. As students progress to Lessons 6-4 and 6-5, the complexity increases with addends and totals up to nine, requiring more efficient strategies. By the end of the topic, students are solving problems with sums of 10 using tools such as cubes and ten-frames to support accuracy and fluency. This progression ensures students build procedural skill and conceptual understanding simultaneously. The grade K materials provide guidance to prompt students to use number charts to help them see and hear patterns as they count. The students carry over and extend this learning to count to 50 in Lesson 11-3, and then to 100 in Lessons 11-4 through 11-7. These opportunities allow for efficient and flexible counting strategies. For students to become proficient with counting, they need to understand the patterns in the counting sequence. The hundred chart allows for the patterns to become visual, such as how the decade numbers are made up of tens and the other two-digit numbers are made up of tens and ones.

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.

EnVision Plus Mathematics Grade K provides teachers with sample student work in the Teacher's Edition. The teacher can use the sample student work to anticipate student responses or to prompt discussions and make connections. In Lesson 4-2, the teacher can project the sample student work of Abby and Latrice. The students were given the following prompt to complete, "Kai sees two boats on the water. Then two more boats go out on the water. How many boats are there in all? Think about the problem. Use your cubes or draw a picture to show how you know." The class then examines the two samples of work to evaluate the process and solutions of each student. Abby drew a picture to show how she knew the answer. The teacher asks the class, "What does Abby's picture show?" Students can respond that it shows the boats Kai saw, with four boats in all. Then Latrice's work is shown. The teacher asks, "What did Latrice do wrong? Why might she have done this?" Latrice used two red cubes together and two blue cubes together and wrote, "2 boats in all." Students can evaluate Latrice's work to find the misconception and develop their own accurate response. In the Teacher's Edition, Lesson 5-5, the "Language Support" section provides opportunities for students to develop and explain accurate mathematical understanding using flexible strategies. Students listen to a word problem and focus on the numbers, as well as what is happening. The problem was "7 beavers are on a log in the water. 4 beavers swim away. How many beavers are left on the log?" After students solve the problem, they are asked to reflect with guiding questions, "How did you model the problem?" and "How does your model match your subtraction?" Students then discuss with a partner how they each represented the problem using drawings, counters, or equations and check whether they used the same or different strategies and arrived at the same equation. This activity supports flexible thinking as students compare representations, reinforces accurate modeling, and helps them build efficient problem-solving approaches through peer dialogue. In Lesson 8-3: "Compare Numbers to 10," students are introduced to multiple strategies for comparing quantities, such as using counters, ten-frames, and number lines. The lesson is designed to help students not only understand the concept of comparing numbers but also to evaluate which method is most effective for them. During the "Visual Learning Bridge," students observe modeled examples and are prompted with reflective questions such as, "Which way helped you decide faster?" and "Was it easier to see the answer with the ten-frame or the number line?" These prompts encourage students to think critically about the efficiency and accuracy of each method. In guided and independent practice, students are asked to solve comparison problems using different tools and then choose the one they found most helpful, fostering flexibility in their problem-solving approach. The Teacher's Edition reinforces this by stating, "Encourage students to try more than one method and talk about which one helped them decide more quickly or clearly." This lesson exemplifies how enVision Plus Mathematics embeds opportunities for students to reflect on and evaluate their mathematical thinking, supporting the development of strategic and independent learners.

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

The materials contain embedded supports for the teacher to guide students in exploring what they already know and applying it to new learning. The Teacher's Edition provides support for teachers in the form of questioning and suggestions. In Lesson 2-1, the teacher begins by asking the whole class, "What are some different types of balls used for sports?" The resource guides teachers to observe as students work to find the number of balls from their student page. A suggestion is provided to support the teacher in their observation by stating, "They might touch each ball as they count, draw a picture, or place a counter as they count each one." While observing, teachers select solutions for students to present the most efficient ways to count the number of balls. EnVision Plus Mathematics Grade K provides scaffolded questioning in the Targeted ELPS to support teachers in guiding students. In Lesson 10-4, the teacher shows students 18 objects and then draws 18 circles in a double ten-frame on the board. The guide prompts the teacher to differentiate based on the five ELPS levels, scaffolding their learning according to the students' proficiency. In Pre-Production, students repeat after the teacher when counting each object. The prompts scaffold all the way to Advanced, where the teacher distributes 20 counters to students and asks them to repeat with 19 and 20, asking them how many objects and circles there are, and to explain how they know.

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

EnVision Plus Mathematics Grade K provides an overview of understanding addition that connects conceptual and procedural foundations for grade K in the Teacher's Edition. Topic 4 begins with adding using objects, fingers, claps, mental images, and drawings. Students progress to using number sentences and equations. By the end of the topic, students will be able to explain their thinking by using different representations through real-world problems. In Teacher's Edition, Topic 7 includes a "Math Background: Balance" section that states, "A balanced curriculum emphasizes conceptual understanding, procedural skill and fluency applications." For conceptual understanding, Topic 7 focuses on students distinguishing between two and three-dimensional shapes. It introduces key concepts such as shape names being based on attributes and clarifies that size and orientation are not defining attributes. The procedural focus in Topic 7 outlines foundational skills that support fluency in identifying and understanding shapes, which prepares students to work with shapes and solids in Topic 8. Additionally, the topic includes a real-world application problem where students identify objects by name and then by their geometric shape, reinforcing procedural knowledge through practical use. EnVision Plus Mathematics Grade K provides materials that progress from conceptual understanding to procedural understanding when counting and comparing numbers up to 20. In Teacher's Edition at the beginning of Topic 10, students are provided with visual representations of quantities to help them build mental representations of the same quantity. Visual representations include counters, ten-frames, and linking cubes. Students develop conceptual understanding by viewing quantities in different arrangements, recognizing that the number remains the same. This understanding then transitions to the procedural understanding of successive numbers, knowing that 13 follows 12 and that 13 is one more than 12.

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

EnVision Plus Mathematics Grade K provides questions and tasks that allow students to progress from using concrete models to pictorial representations to abstract concepts when learning to count from zero to ten. Lessons 2-1 through 2-6 in Topic 2 incorporate the use of counters, five-frames, and ten-frames to count numbers six through ten. In Lesson 2-7, the task shifts to students using pictorial representations to show the numbers six through ten. Finally, in Lesson 2-8, the materials guide the teacher to have students use patterns to represent numbers. For example, a student is shown eight yellow counters; then, one is turned over and made red, resulting in seven yellow and one red. Another red counter is turned over, making it six yellow and two red. The pattern continues until there are eight red counters. This final activity bridges the pictorial to abstract representations of numbers. Additional questions are provided in the Teacher's Edition to facilitate classroom conversations, such as, "Does the pattern change the total number of counters in each row?" The materials provided in the Teacher's Edition task students with using concrete models and manipulatives to create pictorial representations and abstract representations. In Topic 5, students are learning to understand subtraction. Lesson 5-1 begins with students using counters and pictures to show subtraction. Lesson 5-3 continues by introducing subtraction sentences, such as, "___ take away is ___." Lesson 5-4 bridges the sentence to a subtraction equation. Finally, in Lesson 5-6, students use patterns to help them subtract. Additional questions are provided for the teacher to ask the students directly, as well as questions for the teacher to consider while observing the students working. For example, the teacher can ask students, "Can you tell/show what you did?" or reflect, "Are students using one-to-one correspondence to count the cubes?" In the Teacher's Edition, Lesson 6-3, the materials provide multiple forms of mathematical representation aligned with the TEKS expectations. Students engage with concrete models and manipulatives using two-color counters to physically represent and solve addition and subtraction equations within 5. This hands-on work is shown in the "Explore and Share" section and in sample student work from "Eli and Maddie," where students used counters and number paths to build and solve problems. The lesson also includes pictorial representations, particularly in the "Visual Learning" section, where pictures are used to model subtraction equations with crossed-out circles to show taking away. Students also interpret and create visual models of number sentences using images and diagrams. Lastly, abstract representations are incorporated as students write and solve symbolic equations such as "1 + 2 = 3" and "3 – 1 = 2" using numerals and operation signs. This progression from concrete to pictorial to abstract helps build foundational understanding of operations and equation structure in developmentally appropriate ways.

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 the Visual Learning Animation from Lesson 1-5, students recognize 4 and 5 in different arrangements. The video connects counters and visuals of bees representing 4 and 5 in various arrangements to the automaticity of knowing the exact amount regardless of the arrangement. Grade K materials provide opportunities for students to create concrete and representational models and relate them to abstract concepts. In the "Brainingcamp" section of the online resources, the tasks allow students to create concrete and pictorial models for the abstract concept of understanding which is greater or less. In the task "Which Group Has More?" students use five-frames and counters to compare two groups of objects to determine which group has a greater number. 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 3-3, the Math Talk includes the routine "Convince Me" to have students explain how they would sort the plants pictured. The materials state, "Once students have shared their sorting categories, provide opportunities for them to respectfully critique, defend, and clarify their categories." In the Teacher's Edition, Lesson 10-2, includes strong supports for students to connect, create, and explain both concrete and representational models to abstract (symbolic/numeric) concepts, as required by the TEKS. Students begin by using concrete models, such as counters and visual representations of the American flag's stripes, to count to 13. In the "Explore and Share" section, students place counters in ten-frames to model quantities, as seen in Charlie and Sunny's work, with both students physically building quantities using tangible objects. Representational models are incorporated through ten-frame diagrams, drawings of counters, and images of leaves or boxes used to show the number 13. These visuals help students internalize the structure of numbers and bridge their understanding to symbolic forms. In the "Visual Learning" section, students see the number 13 represented with objects, counters in a ten-frame, a written numeral, and the word "thirteen," promoting a deeper connection to abstract concepts. The lesson also supports students in creating concrete and representational models by asking them to draw, build, or manipulate objects to represent 13. Defining and explaining is supported through targeted questioning and the ELPS guidance, which encourages students to explain their representations and reasoning with questions such as "Why do you think this number will be 13 if you trace it?" The "Language Routine: Compare and Connect" and "Talk About Math Ideas" sections prompt students to articulate how different models show the same number in multiple forms, solidifying their conceptual understanding.

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

In grade K, Lesson 3-2, students engage in classifying and counting data, which provides a rich context for developing academic mathematical language. The lesson incorporates visuals such as images of animals or everyday objects that students sort into categories, helping them visually distinguish and compare groups. Manipulatives such as real or illustrated items such as bugs, birds, and frogs are used to physically group and count, reinforcing one-to-one correspondence and quantity recognition. To support language development, the lesson includes sentence frames such as, "There are ___ in this group," encouraging students to articulate their observations using complete mathematical sentences. Additionally, vocabulary terms like more, less, and equal are explicitly taught and used in context. Students also participate in activities like drawing and labeling posters to explain their sorting choices, which further promotes the use of precise mathematical language in both spoken and written forms. This integrated approach ensures that students build a strong foundation in both mathematical understanding and communication. In Lesson 12-1: "Pennies and Dimes," students begin developing academic mathematical language through a combination of real-world connections, visual models, and hands-on activities. The lesson opens with the teacher asking, "Have you ever used money to buy something?" a question designed to activate prior knowledge and introduce key vocabulary such as coins, cent, cent sign (¢), dime, value, penny, and dimes. During the "Explore and Share" section, students are invited to draw their responses to the opening question, helping them connect personal experiences to mathematical concepts. The teacher then introduces a scenario involving coins and models how to identify and count them using a visual display. For example, the materials guide the teacher to say, "This is a penny. It is worth one cent. This is a dime. It is worth ten cents. Let us count how much money we have." As students observe and participate, they are encouraged to use manipulatives such as plastic coins or coin cutouts to build combinations of pennies and dimes. Teachers are provided with embedded guidance to scaffold vocabulary development. They model the use of academic terms in context and prompt students with questions such as "How many cents is this coin worth?" and "Can you show me a dime and tell me its value?" Sentence frames such as "This is a ___, and it is worth ___ cents" help students articulate their understanding using precise mathematical language. In the "Guided Practice" section, students solve problems that involve identifying coins and determining their total value. For example, students are asked to count a group of coins and write the total using the cent sign. Teachers support this process by encouraging students to explain their thinking aloud, reinforcing vocabulary and promoting verbal reasoning.

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

The Academic Vocabulary Teacher's Guide includes embedded teacher guidance to support and scaffold students' development and use of the academic mathematical vocabulary word, "represent," through a structured routine. In the "Develop Word Meaning" section, the materials guide the teacher to display the word, say the word, and then have students say the word. Next, the materials guide the teacher to read the definition and use the word in a sentence such as, "Sharon wrote her initials to represent her name." The guide prompts students to think critically about how symbols, drawings, or words can be used in place of actual objects, reinforcing the concept of representation in math such as, "What does the + represent?" In the "Continue to Build Word Power" section, enVision Plus Mathematics includes the activities Sensible or Silly, Related Words, and Synonyms. The activity, Sensible Silly, prompts the teacher to read sentences and have students say, "sensible" or "silly" based on the accuracy of the sentence using the word "represent." In grade K, Lesson 9-2, the development of academic mathematical language is purposefully embedded through structured teacher guidance and student-centered activities designed for all learners. The lesson begins with a Problem-Based Learning (PBL) activity where students are prompted to compare the lengths of objects using precise vocabulary such as "longer" and "shorter." Teachers are guided to model this language explicitly, using sentence frames like, "This object is longer than that one because . . ." to scaffold student responses. The "Visual Learning" section reinforces vocabulary through animations and visual models, helping students connect terms to real-world contexts. The Teacher's Edition includes "Prevent Misconceptions" notes and "Error Intervention" strategies such as, "If a student says both objects are long, then ask them to point to the longer one and explain why," which supports vocabulary clarification during instruction. The lesson features a Language Objective that applies to all students such as, "Students will use the terms 'longer' and 'shorter' to describe and compare lengths." These integrated supports ensure that all students engage with and use academic mathematical language in meaningful, contextualized ways.

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.

EnVision Plus Mathematics Grade K, Topic 5 includes embedded teacher guidance to support the application of appropriate mathematical language, including vocabulary, syntax, and discourse to support mathematical conversations. The "Vocabulary Activity" section instructs teachers to use the Frayer Model to help students explore and internalize key terms such as subtract, difference, and minus sign. This structured activity prompts students to define vocabulary words, identify characteristics, and provide examples and non-examples, which encourages them to use precise mathematical language. Teachers are also guided to have students work in groups and incorporate both words and pictures, promoting collaborative mathematical discourse. By discussing and justifying their understanding of vocabulary in multiple ways, students practice the syntax and structure needed for mathematical conversations. These strategies provide meaningful opportunities for students to apply and communicate mathematical thinking using appropriate academic language. The Math Talk section of Lesson 10-2 encourages students to observe and interpret a series of images, sharing what they notice, and what they wonder with their peers. As additional images are revealed, students are guided to refine their thinking and adjust their interpretations, which supports the development of precise and flexible mathematical language over time. This progression allows students to hear math language in context, practice using it collaboratively, and deepen their understanding through peer discussion. The activity also promotes flexibility in thinking, encouraging students to consider multiple perspectives and revise their ideas as new information is introduced. Teachers are supported in facilitating these discussions to help students clearly articulate their reasoning and engage in rich mathematical discourse. 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 11-1, "Madeline placed seeds below the number chart. She marked off a number each time she touched and counted a seed." The guidance provided states, "You might ask Madeline: 'Is there any number you can start counting from so you would not have to always start at 1?'" and the desired student response to listen for "I could start counting on from 10 because I know the first row has 10 seeds."

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

The grade K materials integrate 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 the TEKS Process Standards such as 1A: "applying mathematics to solve everyday problems," 1B: "using problem-solving models," 1D: "communicating mathematical ideas," and 1F: "analyzing mathematical relationships." This tool not only reinforces critical thinking and reflection but also encourages consistent use of academic math language. By embedding this model into lessons and tasks, the materials ensure that students are regularly practicing essential problem-solving skills and that the TEKS Process Standards are authentically woven into instruction across the grade K curriculum. In grade K, Topic 12: "Personal Financial Literacy," the TEKS Process Standards are meaningfully embedded through real-world scenarios and interactive learning. One standout lesson focuses on distinguishing needs versus wants, where students engage in a teacher-guided game using picture cards of items like food, toys, and clothing. The teacher asks, "Is this something you need to live, or something you want?" prompting students to sort items into two categories. This supports TEKS K.9A, which emphasizes identifying basic human needs and wants. Materials include visual cards, anchor charts, and cut-and-paste worksheets that allow students to physically manipulate and categorize items. In another lesson, students listen to the story "Those Shoes" by Maribeth Boelts, followed by a class discussion about making smart spending choices. The teacher facilitates reflection with questions like, "Why did Jeremy decide to give the shoes away?" encouraging students to connect emotions with financial decisions, aligning with TEKS K.9B. Additionally, students participate in a role-play activity called "Fast Food Fun," where they use pretend money to buy items from a classroom menu. One student acts as the cashier, while others calculate totals and determine if they have enough money supporting TEKS K.9C and K.1C (problem solving and reasoning). These lessons use storybooks, manipulatives, and real-life simulations to build foundational financial literacy while reinforcing communication, reasoning, and decision-making skills.

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. For example, students count, compare, and represent quantities in Topics 1–2, collect and analyze data using graphs in Topic 3, and solve addition and subtraction problems using various strategies in Topics 4–6. They also explore and describe shapes in Topics 7–8, compare measurable attributes in Topic 9, extend counting to 100 in Topics 10–11, and apply mathematical reasoning to personal financial literacy in Topic 12. These connections build coherently across topics, reinforcing the TEKS process standards throughout the year. The materials include opportunities for students to connect the process standards to their content learning. The enVision Plus Mathematics program is developed with three types of lessons: Let's Build, Let's Investigate, and Let's Model. Every topic in the course has at least one Let's Model lesson that incorporates the process standards in a real-world situation with recently learned content. The "Let's Model" section consists of three acts: Act 1: "The Hook," Act 2: "The Model," and Act 3: "The Solution." The Teacher's Edition provides a description of how the three acts connect the TEKS to process standards, which states, "Mathematical modeling is practiced as students: pose a mathematical question about a situation, identify information needed to solve a problem, develop a model that represents the situation, use the model to propose a solution, and test the appropriateness of the math model." For example, in Lesson 5-7, "Students are tasked with determining how many apple slices are in a bowl given the number at the start, the number consumed, and the number added."

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

In the "Mathematical Process Standards" section in the Teacher's Edition, the process standards for Topic 9 are listed. The topic begins with a clear explanation of how process standards K.1B: "The student is expected to use a problem-solving model that incorporates analyzing given information, formulating a plan or strategy, determining a solution, justifying the solution, and evaluating the problem-solving process and reasonableness of the solution," and K.1C: "The student is expected to select tools, including real objects, manipulatives, paper and pencil, and technology as appropriate, and techniques, including mental math, estimation, and number sense as appropriate, to solve problems," are embedded within measurement lessons. These standards are integrated through instructional tasks that engage students in analyzing, comparing, selecting appropriate tools, and justifying their reasoning. The materials also make intentional connections between the process standards and lesson activities by highlighting how students can apply problem-solving strategies and use tools to compare measurable attributes such as length, height, weight, and capacity. The provided teacher guidance and questioning strategies reinforce these connections, ensuring students repeatedly engage with the standards in meaningful ways across the unit. The Teacher's Edition provides a description of how the process standards are connected throughout the unit. Each topic in the enVision Plus Mathematics program incorporates the process standards within the units while also explicitly focuses on how to connect two process standards throughout the unit. Topic 12 places greater emphasis on students in grade K selecting tools to solve problems and displaying, explaining, and justifying mathematical ideas and arguments. The description includes characteristics of proficient students for those two process standards, as well as how the process standards are connected to the TEKS. For example, it states, "provide opportunities for students to reflect on these mathematical process standards as they solve problems involving financial literacy, and as they progress from a basic understanding of coins and their values to a deeper understanding of how money is earned and used."

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

In Topic 8, Lesson 8-2: "Analyze and Compare 2-D Shapes," the instructional design integrates the TEKS Process Standards to support students in developing foundational geometry skills. This lesson encourages students to explore and compare two-dimensional shapes by building and analyzing them, fostering critical thinking and problem-solving aligned with TEKS K.6A and K.6B. The Process Standards Connections are evident as students are guided to "describe shapes in the environment using informal language" and "analyze and compare two-dimensional shapes using attributes such as number of sides and vertices." For example, the lesson might prompt students to "build a triangle and a square using sticks and compare how many sides and corners each has," helping them engage in mathematical reasoning. In the Teacher's Edition, the materials for Lesson 12-1: "Pennies and Dimes," include a clear overview of the TEKS process standards that are incorporated into the lesson. In the "Texas Essential Knowledge and Skills (TEKS)" section at the bottom, the document identifies relevant standards such as K.1A, K.1C, and K.1E. These process standards guide students to apply mathematical ideas in real-world contexts, select and use appropriate tools such as coins, and communicate mathematical ideas effectively. The "Lesson Objectives," "Conceptual Understanding," and "Procedural Skill" sections reflect these standards by helping students recognize and compare coin values, understand their purpose in monetary transactions, and communicate their understanding orally. This alignment ensures that the TEKS process standards are purposefully embedded throughout the lesson.

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

In the "Visual Learning" section of Lesson 6-8, the materials guide the teacher to begin the lesson with a classroom conversation using questions such as, "What do you see in the picture? What does the number three represent in the equation? What does the 10 represent? Which color cubes were hidden? What is happening to the picture?" This prompts students to analyze a missing part to make 10, encouraging them to connect the image with the equation, reason through hidden quantities, and explain their thinking. The "Prevent Misconceptions" note supports persistence by addressing common challenges. Additionally, the "Talk About Math Ideas" and "Revisit the Essential Question" sections guide students in reflecting on strategies and making connections, further supporting their mathematical reasoning and problem-solving stamina. In the "Math Walk" section of Topic 9, students are introduced to the topic's essential question, "How can objects be compared by length, height, capacity, and weight?" Students then watch a short video to generate excitement about comparing pumpkins. As students watch the video, they try to think mathematically about questions such as, "Which has more height? And which has less weight?" 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 engage in a whole-class discussion. The materials guide the teacher to revisit the video any time after completing Lesson 9-4 and ask, "What math did you learn that could help you answer the question or find the answer in a different way?" In enVision Plus Mathematics, students solve a real-world problem involving ways to earn money in Lesson 12-7. Students are asked the question, "How many quarters are in the jar?" Students first make a prediction, and then the teacher is guided to survey the students' predictions. The teacher guides students to understand estimation and reasonableness by asking the question, "What is a number too small to be the number of quarters in the jar?" 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 does drawing pictures help you solve the problem? 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 in the Student Edition supports students in building understanding and explaining key concepts in the lesson. The Step 2: "Connect" section provides questions for students to represent and solve problems and tasks in multiple ways. For example, in Lesson 4-1, the directions state, "Tell students each problem shows Jada and Roshan's wheels for the parade. How is each way different? How are they alike? Could we use other ways? Have students write how many wheels for each and how many in all." In addition, students are asked, "How can we find how many in all in different ways?" EnVision Plus Mathematics Grade K encourages students to discuss possible sources of error involved in using math to model a real-world situation. This allows students to justify their thinking and compare it to incorrect responses or misconceptions. For example, the Teacher's Edition in Topic 5 prompts the teacher to ask students, "How useful was your model at predicting the answer? Would you change your model after watching the video? How would you change it?" Teachers can also test students' understanding of the real-world problem by asking, "If the boy had eaten one more apple slice before the man added some slices, how many slices would be in the bowl?" In Lesson 11-3, the "Language Support" section provides guidance in the "Visual Learning" section that helps students understand, explain, and justify that there are multiple ways to represent and solve problems. The activity encourages students to act out the thinking of Marta and Kai by connecting their strategies represented in the number chart and thought bubbles. The resource guides the teacher to have students work with a partner and cover up the numbers on the bottom five rows of a hundred chart, and then discuss how their choices align or differ from Marta and Kai's.

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

EnVision Plus Mathematics provides opportunities for students to make sense of mathematics throughout. In the Student Edition, Lesson 2-2. Students begin by using counters to create a pattern with the number six. Then, students are prompted to ask a partner to tell how many they see. Students continue to learn about key concepts of reading, writing, and making six and seven during a think-pair-share activity to compare the different ways to show six with objects, counters, and by writing the number. Students finish the lesson by representing the numbers six and seven first with counters and then by drawing circles to represent them. In Lesson 5-6, the Math Talk: "Same but Different" provides meaningful opportunities for students to make sense of mathematics by engaging with peers and teachers. The activity prompts students to analyze two sets of counters and consider the subtraction problems they represent. Students are guided to work with a partner to discuss and compare what is the same and what is different about the counters. This promotes mathematical discussion and collaboration with peers. The teacher then calls on student volunteers to share their thinking with the class, allowing students to articulate their reasoning and deepen understanding through classroom discourse. These tasks foster critical thinking and provide structured opportunities for students to do, write, and talk about math in meaningful ways. The "Language Support" section in Lesson 11-2 provides opportunities for students to write about the patterns they see or hear when the teacher counts to 30 using the numbers on the reverse hundred chart. The teacher will then show the written work of one of the students and ask the other students to describe the pattern that they think is represented. The student whose work is being discussed will then indicate whether they agree. Other students can then add any additional descriptions to the pattern.

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 Lesson 3-1, students reflect on their problem-solving approaches by describing an image of a phone and eight blocks. The materials then prompt the teacher to ask students to reason about, "What objects do they see?" Students continue to explain what the numbers on the phone represent, as well as what the number below the blocks represent. Students then justify their approach when the teacher asks, "Why do some numbers not tell how many?" 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 8-3, during a classroom conversation, students share their knowledge of the attributes and characteristics of three-dimensional shapes. The materials provide prompts for teachers to guide students in sharing through questions such as, "Which solid figure has two or more vertices? Which solid figures have flat surfaces?" "What movement is each figure doing? What does an object have to look like to roll?" "Can these 3-D solid figures be stacked?" and "Which can stack, slide, and roll?" In Lesson 10-12 the "Explore and Share" section supports teachers in guiding students to share and reflect on their problem-solving approaches through explanations, arguments, and justifications. As students investigate ways to show one more and one less than a number using double ten-frames and counters, the teacher is prompted to observe and discuss the strategies students use, such as efficient modeling or mental math. Students are encouraged to explain how they arrived at their answers, for example, "I count one up from 12 to get 13," or "I count one back from 12 to get 11." These explanations offered by the students, foster mathematical justification and reasoning. Sample student work is used to compare approaches and support whole-class discussion with teachers prompting students to analyze how strategies differ and why they work. The "Connect" section reinforces these ideas by linking student strategies to mental math methods and emphasizing the value of explaining one's thinking.

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

The Teacher's Edition for Lesson 5-2 demonstrates how the instructional materials guide teachers in providing explanatory feedback based on anticipated misconceptions. Specifically, the Prevent Misconceptions prompt helps teachers identify and address a common misunderstanding such as, "students not recognizing that a group of 7 can be broken into subgroups, such as 2 and 5." The resource includes teacher guidance on addressing the misunderstanding, "Display a group of 7 counters all on the red side, turn two of them over to show the yellow side. Point out there are still seven counters, but they are in two groups." EnVision Plus Mathematics Grade K 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 needs to listen. For example, in Lesson 10-5, the materials include four samples for the problem, "Find how many total coupons Naomi and Kai give away if they each give away 8 coupons or if they each give away 9 coupons." One of the student responses states, "To find the total of 8 and 8, Ethan drew coupons and counted on from 8 by ones. He wrote an 8 above one of Naomi's coupons and a number above each of Kai's coupons." The suggested feedback for Ethan is, "Why did you write these numbers above the coupons?" Ethan knew Naomi had eight, so he used the counted-on strategy to find the total. In the "Guided Practice" section of Lesson 11-6, students are tasked with recognizing the numerals four and five in different arrangements. Materials provide guidance to the teacher including, "If students have difficulty writing the numbers 4 and 5, they can practice by using a finger to trace over the numbers 4 and 5 on number cards." The resource also prompts the teacher to "Ask students to explain how they knew their written number matched the drawing." Within the same lesson, the teacher provides feedback to the student "reminding students that they can point to each object while counting aloud, the last number said tells the total number of objects, and a unique symbol goes with each number word."