Renaissance Math Texas, Grade 2

Evaluation for 1.1a
Materials include an alignment guide outlining the TEKS, ELPS, and concepts covered, with a rationale for learning paths across grade levels (vertical alignment) and within the same grade level (horizontal alignment) as designed in the materials.

The materials include a content alignment chart that outlines the Texas Essential Knowledge and Skills (TEKS)–aligned domains covered at each grade level, including Number Sense and Operations, Fractions, Place Value, Multiplication and Division, Algebraic Thinking, and Financial Literacy. The chart identifies the concepts that the program covers across all grade levels.

The Renaissance Math Solution Guide outlines vertical alignment across grade levels and demonstrates how concepts build in complexity from foundational to advanced skills. For example, Number Sense and Operations concepts progressively build computational sophistication while maintaining connections to place value understanding. Fraction concepts advance from foundational number line understanding to fraction operations and rational number reasoning. However, the materials do not include an alignment guide that outlines the ELPS or a rationale for learning paths within the same grade level.

Evaluation for 1.1b
Materials include an implementation guide with usage recommendations and strategies for effective educator use in various contexts, such as just-in-time supports, advanced learning, or as a course.

The Renaissance Math Solution Guide serves as an implementation guide, providing educators with usage recommendations and strategies for effective use across multiple instructional contexts. The guide outlines how the Nearpod and Freckle platforms can be used for tier 1 whole-class instruction, tier 2 small-group reteach, and tier 3 targeted intervention, providing clear guidance for adapting materials to meet student needs across settings. Both platforms include multilingual student support, including Spanish platform navigation and language settings.

The Renaissance Math Solution Guide also provides usage recommendations and strategies for effective use by educators across multiple instructional contexts. For just-in-time support, educators use Nearpod’s real-time dashboard to identify misconceptions immediately and adjust groupings accordingly, and Freckle’s adaptive practice addresses prerequisite skills in grade-level contexts. For advanced learning, educators provide access to above-grade-level challenges for students demonstrating mastery, and the materials can be used as a course through Freckle’s adaptive learning pathways, which continuously adjust according to student performance.

Evaluation for 1.1c
Materials include a TEKS correlation guide with recommended skill entry points based on diagnostic assessment results.

The Renaissance Math TEKS Correlation Guide outlines prerequisite, grade-level, and extension skills for each TEKS standard and maps the TEKS to corresponding lessons. Educators can use the guide to identify key prerequisites and forthcoming lessons for each TEKS standard, pinpoint appropriate entry points, and plan personalized instruction based on students’ current skill levels.

The materials include a diagnostic assessment through the Freckle platform that educators can assign to determine appropriate skill entry points. The adaptive assessment evaluates students’ current understanding and provides TEKS-aligned skill entry points, allowing educators to personalize instruction and target specific skills based on individual student performance.

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

The Renaissance Math Internalization Protocols guide educators through a structured lesson internalization process that includes reviewing lesson objectives, analyzing instructional phases, anticipating student misconceptions, preparing language and accessibility supports, and planning for closure and next steps using real-time data.

The materials include a lesson internalization protocol designed to be completed before daily instruction and guide educators through lesson objectives, instructional phases, and preparation of differentiation supports. However, the materials do not include a unit internalization protocol to guide educators in previewing the unit, understanding the learning progression, or considering the diverse needs of students across the full unit of instruction.

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

The Renaissance Math Leader Guide provides instructional leaders with resources and guidance to support educators in implementing the program. Key resources include the Lesson Library, Usage and Engagement Reports, and Professional Learning Resources. The guide also includes a “Monitoring and Sustaining Implementation” section that provides guidance to help educators maintain consistent, effective use of the program.

The Renaissance Math Leader Guide outlines key steps for successful implementation and provides guidance for instructional leaders about supporting educators and coaches. “Step 1, Instructional Leader’s Role” guides leaders in setting clear expectations for lessons and routines and in providing feedback and coaching to strengthen lesson delivery. In “Step 2, Supporting Teachers with Lesson and Unit Implementation,” leaders receive guidance about helping educators plan with the materials and determine which components to use. For example, leaders can direct educators to leverage the Freckle Adaptive Pathway for pre-teaching or skill reinforcement based on class needs. Nearpod Academy further supports implementation through modules and on-demand or live professional development webinars.

Evaluation for 1.2a
If designed to be static, materials include detailed lesson plans with learning objectives, teacher and student materials, lesson components with suggested timeframes, and assessment resources aligned with the TEKS and ELPS.

The materials include detailed lesson plans with learning objectives, lesson components with suggested time frames, and assessment resources aligned to the TEKS. Nearpod lessons include TEKS-aligned learning objectives and suggested time allotments for each lesson component, including pre-assessment, authentic connection, explicit instruction, and post-assessment, and Freckle skill pages provide educators a student objective, connection to prior learning, skill summary, connection to future learning, guiding questions, common misconceptions, skill limitations, and vocabulary. However, the materials do not include ELPS alignment, and the Freckle skill pages do not include student-facing materials.

The materials include educator materials to support effective lesson delivery across multiple instructional approaches. For example, in the Concrete-Representational-Abstract (CRA) approach, students spend 20 minutes in the concrete phase, 20 minutes in the representational phase, and 15 minutes in the abstract phase, and there is guidance for adjusting pacing based on student performance. However, the materials do not include educator materials, student materials, or assessment resources aligned with the ELPS.

Evaluation for 1.2b
If designed to be adaptive, materials include responsive learning objectives, lesson components with suggested timeframes, and assessment resources aligned with the TEKS and ELPS.

In the Freckle platform, the materials provide educators with learning objectives aligned with the TEKS. The materials include lesson components for educators and students, with suggested timeframes, such as targeted practice, differentiated practice, skills and prerequisites, instructional videos, and academic vocabulary. However, the materials do not include detailed overviews with learning objectives or assessment resources aligned to the ELPS.

The materials include lesson components with suggested timeframes. The Math Usage Recommendations document outlines key lesson components of the Freckle platform and suggested usage times. For example, for grades K–2, the document recommends 10 minutes of use per day across all lesson components—adaptive math pathway, targeted math practice, and focus skills practice—at least two times a week.

Evaluation for 1.2c
Materials contain support for families in Spanish and English for each unit, with suggestions on supporting the progress of their student(s).

The materials include family letters in both English and Spanish that inform families about the objectives of the current unit by providing a skills overview explaining what students are learning and why it matters mathematically. The letters also describe how learning will take place in the classroom by outlining the methods of instruction, visual models, and strategies that will be used, enabling families to reinforce the same approaches at home.

The family letters provide families with practical, topic-specific home support suggestions in both English and Spanish for each unit. These suggestions include grade-appropriate activities that extend learning beyond the classroom and give families concrete strategies to reinforce current mathematical concepts, creating a partnership between school and home that supports consistent student learning.

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

The materials include a Renaissance Math Solution Guide that provides a table outlining the definition and instructional purpose of each assessment type. Under the “Instructional Purpose” column, the Solution Guide states that diagnostic placement assessments are used “to find each student’s starting point before/start of instruction.” This information clarifies for educators both the intended use of this assessment type and the appropriate timing for administration.

The Renaissance Math Solution Guide includes a section titled “Assessment Types in Renaissance Math.” This section outlines the instructional purpose for diagnostic/placement, formative, interim/benchmark, and summative assessments. The guide also identifies where each assessment type appears in the Freckle and Nearpod platforms.

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

In the Freckle Teacher Home Guide, there is a section titled “How Can I Assign Assessments to My Students?” In this section, the materials direct educators to have students log in to the Freckle platform using their class code, select Assignments from the dashboard, choose the assigned assessment, complete the assessment, and return to the dashboard to continue working on other assigned activities.

The Freckle Teacher Home Guide includes a section titled “How Can I Assign Assessments to My Students?” This section directs educators to have students complete the assessment, which the guide notes “will take anywhere from 10 to 30 to 60 minutes or more.”

Evaluation for 2.1c
Digital assessments include printable versions and accommodations, including text-to-speech, content and language supports, and calculators, that educators can enable or disable to support individual students.

The Freckle platform includes printable versions of digital assessments, such as diagnostic, targeted practice, and benchmark assessments. The printables allow educators to generate assessments as adaptive math pathways or targeted math practice, giving educators the flexibility to focus on student-leveled material or standard-specific content.

The Freckle and Nearpod platforms provide accommodations that educators can enable or disable to support individual students. Within Freckle’s settings, educators can use the “Edit Student” tab to enable or disable text-to-speech and calculator access for students. In Nearpod, educators can enable Immersive Reader to activate text-to-speech and additional content and language supports, giving students access to a picture dictionary, preferred language selection, color-coding for parts of speech, and syllable-by-syllable word reading.

Evaluation for 2.1d
Materials include diagnostic assessments with TEKS-aligned tasks or questions, including interactive item types with varying complexity levels.

The materials include diagnostic assessments on the Freckle platform with TEKS-aligned questions and tasks. Within the diagnostic assessments, questions include two levels of complexity: basic recall and application and skill/concept. For example, the diagnostic assessment includes computation questions for basic recall and word problems for application and skill/concept. The materials do not include questions with more than two levels of complexity.

The materials include diagnostic assessments with TEKS-aligned questions that, through adaptive assessment functionality, demonstrate at most two levels of complexity. The materials also include interactive assessment items with varying response types, including multiple-choice, multiple-answer, and type-in. For example, in the Nearpod platform, educators can use multiple-choice preassessment questions to gauge students’ prior knowledge.

Evaluation for 2.1e
Materials include a variety of formative assessments with TEKS-aligned tasks or questions, including interactive item types with varying complexity levels.

The materials include a variety of formative assessments with TEKS-aligned questions and tasks, including adaptive practice, targeted practice, and benchmark assessments, that feature more than two levels of complexity ranging from basic recall to application, reasoning, and higher-order thinking. The formative assessments also include more than two unique interactive item types, such as multiple-choice, multiple-answer, type-in, drag-and-drop, graphs, and complete-the-table, providing students with diverse question formats aligned to the TEKS.

The Freckle Depth of Knowledge (DOK) Challenges provide formative assessment opportunities with varying levels of complexity by including three to four related questions that scale from DOK 1 through DOK 3 within a single session. Each challenge includes a real-world introduction, multiple question formats, and audio and Spanish support, and reporting tools allow educators to monitor student performance on advanced mathematical thinking tasks aligned to the TEKS.

Evaluation for 2.2a
Instructional assessments include scoring information and guidance for interpreting student performance, including rationale for each correct and incorrect response.

The Renaissance Math Solution Guide includes a section titled “Interpreting Student Performance” that provides educators with guidance on monitoring and adjusting instruction. For example, the guide directs educators to review student progress, identify question-level patterns, and use postsession reports to plan next-day instruction. This section provides a broad overview of how to interpret student performance.

The materials provide teacher resources for each lesson, including a full lesson answer key. The key provides preassessment and postassessment questions and answers with rationales for incorrect answers. However, the materials do not include rationales for correct answers.

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

The materials provide adaptive pathways based on student performance on assessments. The materials recommend a pathway of tasks and activities that adjusts based on preassessment performance. All students begin with a pretest in each domain that determines their starting levels. As students work in each domain, the Freckle platform continuously adjusts to their performance. The platform provides remediation problems when students struggle and advances them to more-challenging concepts when they perform well.

In the platform, the “Performance by Topic” report allows educators to view how students progress on a particular standard across all math topics. The system groups students by accuracy level—below 50 percent as struggling, 50–80 percent as approaching, and above 80 percent as proficient—and educators can assign targeted activities to individual students or entire groups based on identified needs.

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

The materials include a Report Card feature that enables educators to monitor both individual student performance and overall class data. Educators can access an overview of assignment types or topics, the number of questions completed, and student accuracy percentages.

The materials include a Student Goal Setting feature that allows students in all grades to set a goal and work toward achieving it throughout the week. Students can set a goal to answer questions correctly or to meet a minimum accuracy threshold across a set number of sessions. Once students reach their goal, the platform immediately notifies students and allows them to set a new goal. Visual progress bars and badges celebrate milestones and encourage student engagement.

Evaluation for 2.2d
If designed to be static, materials provide prompts and guidance to support educators in conducting frequent checks for understanding at key points throughout each lesson or activity.

The Renaissance Math Solution Guide provides guidance to help educators conduct frequent checks for understanding. The guide includes a checklist that educators can use to make checks for understanding consistent, fast, and instructionally useful. For example, the guide provides educators with guidance on what to do before, during, and after each check for understanding, including suggestions for in-the-moment moves and determining whether a reteach, reinforce, or extend activity is necessary.

In the Nearpod platform, educators receive a slide deck that includes a preassessment, quizzes, and a Time to Climb assessment to check for understanding at key points in the lesson. Educators can view student answers in real time and address misconceptions at predetermined points in the lesson as needed.

Evaluation for 2.2e
If designed to be adaptive, materials provide frequent checks for understanding at key points throughout each lesson or activity.

The materials include a “Checklist for Successful Checks for Understanding” that prompts and guides educators to check student understanding. The checklist provides guidance before, during, and after, directing educators through the steps for consistent, accurate results and next steps for groups of students based on the results. While students work, the guidance instructs educators to identify which students are struggling and on which item, step, or representation. The materials also offer suggestions for next steps, such as providing in-the-moment feedback, pulling a small group, or delivering a quick reteach.

The program provides frequent checks for understanding at key points during an activity. As students work through the program, the materials provide checks for understanding through the Teach Me feature, which reinforces a key skill before a subsequent check. Additionally, students receive immediate feedback that guides them to correct misunderstandings after answering a question.

The Freckle Adaptive Pathway provides continuous feedback to students and adjusts task difficulty as they progress. Adaptive assessments embedded in each lesson generate real-time data on student understanding. Based on student responses, the pathway adjusts lesson pacing and complexity and provides differentiated practice problems to reinforce skills.

Evaluation for 3.1a
Materials include explicit educator guidance for lessons or activities scaffolded for students who have not yet reached proficiency in prerequisite or grade-level concepts and skills.

The Implementation Guide’s Assignments report feature provides educators with guidance for supporting students who have not yet demonstrated grade-level proficiency. Using the reports, educators can assign additional resources targeting specific concepts or skills before students progress to grade-level content. The materials also provide options for reassigning the current skill, assigning prerequisite skills, and generating supplemental worksheets to support remediation and skill development.

The program includes built-in adaptive algorithms that provide students with practice problems based on their current levels of understanding. The program automatically adjusts exercise and question difficulty based on each student’s past performance. The program also provides recommendations for differentiating prerequisite skills in a selected standard through Targeted Practice assignments.

Evaluation for 3.1b
Materials include explicit educator guidance for language supports, including pre-teaching and embedded supports for developing academic vocabulary and unfamiliar references in text.

The materials include embedded supports for developing academic vocabulary. Within the Freckle platform, students can select underlined academic vocabulary terms to view or hear their definitions, along with guided questions and prompts. The “Freckle Help” section also provides video examples that explain target words with visuals and introduce their use in context.

The materials include embedded supports for unfamiliar references in text. Within the Nearpod platform, ESL lessons include an Academic Vocabulary Teacher Guide that provides embedded guidance to support students’ understanding of unfamiliar references during instruction, including strategies such as explaining words orally, providing student-friendly definitions, and structuring oral practice opportunities. However, the materials do not include pre-teaching supports for developing academic vocabulary or for unfamiliar references in the text.

Evaluation for 3.1c
Materials include explicit educator guidance for enrichment and extension activities for students who have demonstrated proficiency in grade-level and above grade-level content and skills.

The materials include explicit educator guidance for enrichment and extension activities for students who have demonstrated proficiency in grade-level and above-grade-level content and skills. In the Freckle platform, the program provides educators with recommended activities for students who are ready for a challenge, defined as students who have scored above 79 percent on skills. The materials direct educators to assign DOK activities where students apply their skills to real-world challenges. Within the Inquiry-Based Lessons (IBLs) on the Freckle platform, students explore math standards and build critical thinking skills through real-world challenges.

The materials include guidance to help educators identify students ready for enrichment or extension activities using assignment data. The “Class Grouping” report in Freckle identifies students who have demonstrated proficiency in grade-level and above-grade-level content. The materials also provide educators with guidance on assigning activities to these students, and that guidance is organized into same-level, grade-level, and above-grade-level content.

Evaluation for 3.1d
Digital materials include accommodations, including text-to-speech, content and language supports, and calculators that educators can enable or disable to support individual students.

The materials outline how educators can enable or disable student supports in the “Roster” page. By selecting the Edit Student feature, educators can access the “Support Settings” tab and activate features, such as the calculator. Educators can apply these supports to an individual student or to all students, depending on instructional need.

The digital materials include text-to-speech accommodations that educators can enable or disable to support individual students. On the “Roster” page, educators can use the Edit Student feature to access student support settings and enable or disable audio settings to read aloud to individual students. However, the materials do not include content and language supports that educators can enable or disable to support individual students.

Evaluation for 3.1e
Materials include educator guidance on offering options and supports for students to demonstrate understanding of mathematical concepts in various ways, such as perform, express, and represent.

The “Multiple Representations in Renaissance Math” document provides educators guidance to support student understanding through activities that allow students to perform, express, and represent their mathematical reasoning and ideas. The materials include implementation guidance and suggested activities that educators can use to accommodate different learning styles and strengths and deepen student understanding. For example, the guidance suggests using audio responses and open-ended responses to allow students to express and communicate mathematical reasoning in different formats. The materials also provide examples of models, diagrams, and digital tools that support students in representing mathematical thinking. Additionally, the guidance includes multimodal activities and interactive tools, such as virtual manipulatives and peer-to-peer activities, that allow students to perform mathematical tasks.

The materials include IBLs that provide students multiple opportunities to engage in and demonstrate mathematical thinking. The Inquiry Sheets included in these lessons encourage a variety of problem-solving approaches, such as drawing models, creating tables or charts, and applying logical reasoning. The materials provide educators student-facing Inquiry Sheets that support students in organizing their thinking and representing mathematical concepts. The IBL educator slide decks promote diverse problem-solving strategies by encouraging students to ask clarifying questions, reflect on and revise their solutions after testing them, and collaborate with partners or in small groups to deepen their understanding.

Evaluation for 3.2a
Materials include explicit (direct) prompts and guidance for educators to build knowledge by activating prior knowledge, anchoring big ideas, and highlighting and connecting key patterns, features, and relationships through multiple means of representation.

The materials provide prompts and guidance in lesson plans to help educators build knowledge. The lesson plans ground educators in student objectives aligned with the TEKS and activate prior knowledge through a “Connection to Prior Learning” section that ties what students already know to what they will learn by the end of the lesson. Additionally, the lesson plans include a “Connection to Future Learning” section. The materials also provide a “Skill Summary” section that connects key patterns, features, and relationships through multiple means of representation.

On the Nearpod platform, materials provide questions designed to help educators elicit what students already know about a topic before introducing new information. These questions are embedded in the slides as a preassessment quiz to support the activation of prior knowledge. In the “Think About It” slide, the materials provide educators with questions that prompt students to make connections to related skills and to identify key patterns, features, and relationships.

Evaluation for 3.2b
If designed to be static, materials include educator guidance for effective lesson delivery and facilitation using various instructional approaches.

The materials include guidance that supports effective instructional grouping and flexible classroom arrangements. The Renaissance Math Solution Guide describes how educators can organize students for whole-class instruction using educator-led Nearpod lessons, for small-group instruction through Nearpod preteach and reteach lessons, and for differentiated learning stations that incorporate Freckle independent practice and Nearpod center activities. The guide also outlines structures for independent learning through differentiated Freckle assignments and supports collaborative learning through interactive Nearpod activities. Inquiry-based learning is further reinforced through the IBLs available in Freckle. These structures equip educators with clear, practical guidance for grouping students and facilitating learning across varied instructional formats.

The Renaissance Math Solution Guide includes educator guidance for effective lesson delivery and facilitation using various instructional approaches. The guide offers eight different instructional approaches that educators can use to meet the diverse needs of all students. For example, when educators use a small-group approach, the guide instructs them to “break the class into small groups and provide pre-teach or re-teach lessons using Nearpod and practice in Freckle for students that need more support.” Another instructional approach that the guide provides is inquiry-based learning. The guide provides guidance for educators on using an inquiry-based approach when they want to move “beyond procedural understanding and encourage students to explore concepts.”

Evaluation for 3.2c
Materials include multi-tiered intervention methods for various types of practice and structures and educator guidance to support effective implementation.

The materials include multi-tiered intervention methods and effective implementation guidance. In the Renaissance Math Solution Guide, the section titled “Strategies for Utilizing Renaissance Math Resources in Daily Instruction” gives educators guidance on how to use small-group instruction with preteach or reteach lessons in Nearpod, differentiated learning stations including independent practice in Freckle, one small-group lesson from Nearpod and another using Nearpod center activities, and independent practice in which students complete differentiated Freckle assignments. The section titled “Differentiating with Renaissance Math” guides educators on how to use Nearpod and Freckle lessons for tier 1 core instruction, for tiers 2 and 3 small-group and individual support, and for multilingual learners.

The Renaissance Math Solution Guide includes educator guidance for effective lesson delivery and facilitation using various instructional approaches. The guide offers eight different instructional approaches that educators can use to meet the diverse needs of all learners. For example, the small-group approach instructs educators to divide the class into small groups and provide pre- or reteach lessons using Nearpod, with practice in Freckle for students who need additional support. The guide also provides guidance on an inquiry-based learning approach, directing educators to use it when moving beyond procedural understanding to encourage students to explore concepts.

Evaluation for 3.2d
Materials include enrichment and extension methods that support various forms of engagement, and guidance to support educators in effective implementation.

The materials include enrichment and extension activities that support multiple forms of engagement for students who have demonstrated proficiency in grade-level and above-grade-level content. Within the Freckle “Assignment” report, educators can expand an assignment to view each student’s performance and identify learners who are ready for a challenge. The platform then provides direct links to aligned enrichment options, such as DOK lessons and IBLs. Educators can navigate directly to the DOK level aligned to the standard and assign these activities to individual students or groups. IBLs ask students to collaborate in small groups to create representations of their mathematical thinking, while DOK lessons require students to apply mathematical concepts to real-world scenarios.

The materials provide guidance to support educators in the effective implementation of enrichment and extension methods. In the Freckle platform, educators can sort content by targeted skills and domains, building basics, extending thinking, and assessments. For extending thinking, educators can assign DOK activities—a set of higher-level thinking questions for a specific standard—to help students master concepts. Students apply mathematical concepts to real-world scenarios to demonstrate their understanding. Educators can also assign IBLs, which allow students to explore math standards and build critical-thinking skills through real-world challenges. Students work with peers to create representations that demonstrate their mathematical thinking.

Evaluation for 3.2e
Materials include prompts and guidance to support educators in providing timely feedback during lesson delivery.

The “Providing Feedback” article provides educators guidance for delivering timely feedback during instruction. The materials explain that effective feedback should be timely, specific, actionable, and asset-based, and provide guidance for multiple feedback contexts, including in-the-moment feedback, feedback for learning, and feedback after practice. For example, when providing in-the-moment feedback, educators can use short, repeatable prompts while circulating or reviewing student responses, such as “What in the problem told you that?” to press for reasoning and “What is that step in your equation?” to connect student thinking to representations. While the materials provide guidance to help educators deliver timely feedback during instruction, the prompts are general rather than lesson-specific.

The materials include a Live Teacher Feedback option that provides educators with guidance on delivering feedback during instruction. In the Nearpod platform, educators can use the Live Teacher Feedback feature in the educator dashboard to provide timely feedback to students as they work through lesson activities. Educators can view student responses in real time and provide feedback by directly annotating student work or leaving written comments. Students can immediately view the feedback and make adjustments to their work accordingly.

Evaluation for 3.3a
If designed to be static, materials include educator guidance on providing and incorporating linguistic accommodations for all 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 materials include generic guidance on supporting language development. For example, the materials suggest using visuals for beginning-level students, sentence stems for intermediate-level students, academic vocabulary for advanced-level students, and open-ended items for advanced high-level students during instruction. However, these proficiency level descriptions do not align with the ELPS, which identify proficiency levels as pre-production, beginning, intermediate, high intermediate, and advanced. Additionally, the linguistic supports the materials provide are generic rather than differentiated. For example, the same sentence stems appear across units and lessons regardless of student proficiency level.

The “Immersive Reader” article provides educators with guidance on supporting students with linguistic accommodations in Nearpod lessons through the Immersive Reader feature. Educators can use this feature to provide support, such as text-to-speech, parts-of-speech identification, syllable and grammar options, picture dictionaries, and translation in more than 60 languages. However, the materials do not reference the proficiency levels identified by the ELPS, and the accommodations are generic rather than differentiated by language proficiency level.

Evaluation for 3.3b
If designed to be adaptive, materials include embedded linguistic accommodations for all 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 adaptive materials provide several features to support multilingual learners, including English and Spanish language options, vocabulary supports, hints, and audio and read-aloud functionality. These features provide access supports that help students engage with mathematical content. The materials acknowledge that language development may affect student progress in the adaptive program. However, these accommodations are generic and are not differentiated by language proficiency level.

The materials provide embedded linguistic accommodations, including Spanish navigation and audio support, hints, and academic vocabulary supports, that help multilingual students access mathematical content. The materials also include proficiency descriptions for emergent bilingual students. However, these descriptions use such levels as beginner, intermediate, advanced, and advanced high rather than the ELPS proficiency levels of pre-production, beginning, intermediate, high intermediate, and advanced. Additionally, the accommodations are not differentiated by proficiency level.

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

The Renaissance Math Solution Guide includes guidance for implementing the program in bilingual settings, such as dual language, transitional bilingual, and alternating language models. However, this guidance does not constitute implementation guidance for state-approved bilingual or ESL programs because the it does not align with or address the specific requirements of state-approved program models.

While the Solution Guide references bilingual instructional routines, vocabulary supports, and language allocation plans, these resources do not provide guidance specific to state-approved bilingual or ESL program models as defined by Texas.

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

The Nearpod Academic Vocabulary lessons introduce prerequisite vocabulary connected to each lesson by providing definitions, parts of speech, and structured opportunities for oral discourse. A “Real-World Connection” component builds background knowledge by connecting vocabulary to relevant contexts. Students then respond to discussion questions and participate in think-pair-share activities that develop academic vocabulary, increase comprehension, and build background knowledge through oral discourse. However, the materials do not include embedded guidance to support emergent bilingual students in making cross-linguistic connections through oral discourse.

The Nearpod Academic Vocabulary lessons pre-teach new vocabulary through an explicit instructional routine that includes modeling pronunciation, defining terms in student-friendly language, using visual representations, and checking for understanding. For example, in the Centimeter Academic Vocabulary lesson, students view real-world visual contexts and participate in think-pair-share discussions using the target vocabulary. However, the materials do not include embedded guidance to support emergent bilingual students through written discourse. While the materials provide fill-in-the-blank sentence stems, students insert only the target vocabulary word and are not required to demonstrate understanding in extended written responses. The materials do not address developing academic vocabulary, increasing comprehension, making cross-linguistic connections, or building background knowledge through written discourse.

Evaluation for 3.3e
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 because the program is not designed for dual language immersion (DLI) programs.

This guidance is not applicable to the program.

Evaluation for 4.1a
Practice opportunities throughout learning pathways (including instructional assessments) require students to demonstrate depth of understanding aligned to the TEKS.

The materials provide practice opportunities and instructional assessments throughout the learning pathways, requiring students to demonstrate depth of understanding aligned to the TEKS. In the Create & Interpret Number Lines Nearpod lesson, instruction begins with a four-question “Show What You Know” preassessment that identifies what students already know about creating number lines and representing whole numbers within 100, including identifying missing numbers on partially labeled number lines. The lesson anchors instruction in a real-world context in which students analyze a number line that Willow created to help volunteers place items on a park trail and determine how the placement can be improved. Students then learn to define a number line and its properties—such as numbers in order, equally spaced, and the same distance between tick marks—through writing activities in which they identify and explain three errors in an incorrectly constructed number line and draw their own number line from 20 to 30. A drag-and-drop activity extends this understanding by asking students to identify sequencing errors on community garden plant markers and to place them in the correct numerical order. Students also practice determining interval size to label tick marks on partially labeled number lines and plot given whole numbers, such as 37, 62, and 23, on a number line from 20 to 60. The lesson concludes with a gamified postassessment—including questions that ask students to identify the location of a point on a labeled number line—that mirrors the preassessment but has slightly different questions to measure student growth. Answers, explanations, and additional resources are available in the Handouts feature.

The DOK Challenges in the Freckle platform provide assessment opportunities for students to demonstrate depth of understanding aligned to the TEKS. The DOK Challenges allow educators to assign a set of higher-level thinking questions for a specific standard to help students master concepts. In these challenges, students solve problems in real-world contexts and justify their responses by selecting the best evidence to support their reasoning. Additionally, the challenges require students to engage in critical thinking by identifying errors in mathematical work, evaluating and selecting appropriate problem-solving strategies, and determining the next step in the solution process.

Evaluation for 4.1b
Questions and tasks, including enrichment and extension materials, increase in rigor and complexity, leading to grade-level and above grade-level proficiency in the mathematics TEKS.

The materials include IBLs that provide enrichment and extension opportunities to deepen students’ understanding of the TEKS through real-world, problem-based scenarios. In the Importing and Exporting Goods IBL, which addresses TEKS 2.4.B, students add up to four two-digit numbers and find missing addends as they explore how countries trade with one another. On day one, students help a local car dealership determine how many vehicles to import from Japan by finding the sum of three two-digit numbers. On day two, students help a U.S. airplane manufacturer export planes to Japan by determining missing addends when given the sum and remaining addends. The lesson culminates on day three with a classified project for the U.S. government, in which students apply both skills—determining the sum of up to four two-digit numbers and finding missing addends—to make decisions about trade. Each day includes an instructional video, an Inquiry Sheet for student work, and a solution guide. This progression across three days—from foundational addition to missing-addend reasoning to a multi-skill synthesis task—creates multiple entry points for learners, supports conceptual development, and extends students toward grade-level and above-grade-level proficiency.

The Freckle platform provides questions and tasks that increase in rigor and complexity, supporting students in progressing toward grade-level and above-grade-level proficiency. In the adaptive learning pathways, students who demonstrate a strong understanding are automatically advanced to more challenging content, including above-grade-level questions when appropriate. The adaptive system continually adjusts based on student performance, offering remediation through scaffolded supports such as step-by-step instructional videos, hints, and a Show Me feature when students struggle, and extending learning when students show readiness. Students can also see their current performance level, including when they are working above their grade level, which promotes transparency and ownership of learning. As students answer questions correctly, the program increases the depth and complexity of tasks, ensuring that students are consistently challenged and supported according to their individual progress.

Evaluation for 4.2a
Materials demonstrate coherence across concepts horizontally within the grade level by connecting patterns, big ideas, and relationships.

The materials demonstrate horizontal coherence by connecting related mathematical concepts in each grade level. The program organizes instruction around major mathematical domains and intentionally sequences lessons so that students build on previously learned concepts and make connections among patterns, big ideas, and mathematical relationships. The lessons use concrete, visual, and abstract representations to help students connect related concepts rather than learn isolated procedures. IBLs further strengthen these connections by requiring students to apply multiple mathematical ideas in authentic problem-solving contexts and by reinforcing conceptual understanding across the grade-level curriculum.

The materials demonstrate horizontal coherence by connecting patterns, big ideas, and relationships in grade 2. The Renaissance Math Teacher Guide clearly articulates the conceptual purpose of each skill and explains how it supports future learning. In the Create & Interpret Number Lines lesson, instruction begins with a concrete foundation—students measure length by laying equal-sized units end to end without gaps or overlaps—before transitioning to the number line as a visual representation of that same concept. Students first create number lines and identify that tick marks must be equally spaced, then label partially labeled number lines to determine interval size, and finally progress to plotting given whole numbers and estimating locations between tick marks. This intentional sequence connects measurement concepts, number relationships, and place value reasoning in the grade level and helps students develop a deeper, more-coherent understanding of how numbers and distance relate to one another.

Evaluation for 4.2b
Materials demonstrate coherence vertically across concepts and grade bands, including connections from grade K–6, by connecting patterns, big ideas, and relationships.

The materials demonstrate vertical alignment across grade levels by building mathematical concepts and skills in a coherent, developmentally appropriate progression. The Renaissance Math Solution Guide outlines how the grade 2 program connects base-ten understanding, addition and subtraction, and measurement as integrated content strands that reinforce one another at the grade level while simultaneously building toward future concepts. In the Number Sense & Operations progression, grade 2 builds on students’ work with addition and subtraction within 20 from grade 1 to include multidigit operations within 1,000, preparing students for multiplication and division concepts in grade 3. Place value serves as a unifying thread across this progression. In grade 2, students develop the conceptual understanding of tens and ones that anchors grade 3 work with thousands and grades 4–5 work in multidigit contexts. The Solution Guide also identifies grade 2 as the entry point for fraction reasoning, in which students begin to understand units with unit fractions on a number line—a concept that advances to equivalent comparison in grade 4, fraction operations in grade 5, and rational number reasoning in grade 6. This vertical coherence ensures that each stage of learning prepares students for the next and reinforces patterns, big ideas, and relationships from one grade to the next.

In the Freckle platform, the materials demonstrate vertical coherence by connecting mathematical concepts across grade bands and adjusting instruction based on each student’s prior learning. When students struggle with a concept, the program automatically assigns prerequisite skills from earlier grade levels and continues to provide targeted support until mastery is reached. As students demonstrate proficiency with grade-level content, the program advances them to connected above-grade-level concepts in the same domain. After completing a diagnostic assessment, students are placed on a personalized learning pathway that reflects their current levels of understanding. If they perform above grade level, the adaptive system immediately provides more advanced tasks to extend their learning. This structure ensures that students receive remediation, on-level practice, or enrichment aligned with their individual progress, reinforcing coherent learning trajectories across grade bands.

Evaluation for 4.2c
Materials demonstrate coherence across lessons or activities by connecting students’ prior knowledge of concepts and procedures to the mathematical concepts to be learned in the current grade level and future grade levels.

The materials demonstrate coherence across lessons or activities by connecting students’ prior knowledge of concepts and procedures to be learned in current and future grade levels. In the Fluently Add and Subtract Within 20 Nearpod lesson, the Teacher Resource informs educators of prior learning connections, such as developing addition and subtraction fluency within 10, using various strategies. The Teacher Resource further explains that students will use these prior concepts and procedures to develop mental math strategies by counting on, counting back, decomposing numbers to make 10, and using relationships between addition and subtraction to recognize numerical patterns. Additionally, the Teacher Resource states that these same procedures will be used in the future to address the concepts of fluently adding and subtracting within 100, using place value and the properties of operations.

The materials include a Renaissance Math TEKS Alignment Guide that allows educators to view the vertical alignment for each lesson. The guide lists the current grade-level TEKS or skills with hyperlinks to the corresponding assignments. The guide then identifies the aligned lesson from the previous grade and the aligned lesson from the upcoming grade. This structure allows educators to see how learning progresses across grade levels and also provides options for assigning extension lessons when students need enrichment. For example, the grade 2 alignment guide maps 2.2(A) composing and decomposing numbers to 1,200 to the prerequisite lessons 1.2(B) Understand the Composition of Numbers Up to 100 and 1.2(C) Write Expanded & Word Form of Numbers Up to 100 and to the forthcoming lesson 3.2(A) Decompose 3-Digit Numbers. Similarly, 2.4(B) adding up to four two-digit numbers and subtracting two-digit numbers using place value strategies connects to the prior grade lessons 1.3(A) Add Multiples of 10 & 1-Digit Numbers and 1.3(B) Solve Add To/Take From Problems Within 20 and prepares students for the forthcoming lessons 3.4(A) Add Within 1,000 Using Algorithms and 3.4(A) Subtract Within 1,000 Using Algorithms.

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

In the Freckle Adaptive Pathway, the program continuously revisits previously learned skills and concepts as students progress through learning pathways or domains. Students begin each domain with a diagnostic pretest. As they work through a selected domain, Freckle’s adaptive algorithm adjusts the difficulty according to ongoing performance and returns students to earlier skills when gaps are detected. This structure creates built-in spaced retrieval opportunities by reactivating prior skills before students advance to more complex content. Students may move between below-, on-, and above-grade-level content within the same domain and encounter previously learned skills in new contexts throughout the learning pathway.

The Determine If Numbers to 20 Are Odd or Even Nearpod lesson provides spaced retrieval opportunities for previously learned skills and concepts. The lesson reactivates prior knowledge of grouping and counting objects from grade 1, including the How Many Do You See lesson. Students apply this understanding to identify equal pairs and represent even and odd numbers using arrays and equations. By completing these tasks, students retrieve and apply previously learned concepts of addition and grouping to build an understanding of even and odd numbers in new contexts.

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

The Freckle Adaptive Pathway provides interleaved practice with previously learned skills and concepts across learning pathways. In each domain, students encounter problems that require the simultaneous application of multiple previously learned skills rather than isolated practice of a single skill. As students progress through a domain, the adaptive system presents mixed-skill problems that require them to select and apply prior knowledge in combination, including movement across below-, on-, and above-grade-level content. This design ensures that students regularly revisit and integrate earlier skills and engage with new mathematical content across the learning pathway.

The Create Picture & Bar Graphs Nearpod lesson provides interleaved practice by requiring students to apply counting, comparing, organizing, and data interpretation skills in a single task. Students draw on prior knowledge of tally charts and counting strategies to create and analyze picture and bar graphs, interpret category totals, and compare data across representations. By working across multiple representations of the same dataset, students continuously revisit and integrate previously learned concepts while extending their understanding of data analysis and mathematical communication.

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

The materials provide questions and tasks that require students to interpret, analyze, and evaluate mathematical models. In the Add and Subtract 3- and 2-Digit Numbers lesson, students interpret color-coded base ten blocks to solve 256 + 7 by circling a group of ten ones to regroup. Students then analyze models as they build two additional equations with base-ten blocks, determining whether regrouping is needed, and finding the sum. The lesson extends this work by asking students to evaluate whether regrouping in the tens place is necessary, requiring them to assess the model’s accuracy. Students continue to interpret, analyze, and evaluate representations in the Time to Climb activity as they apply these skills to new problems.

The materials provide an IBL that guides students through solving a real-world problem involving the sum of two three-digit numbers. Students analyze imports and exports from different countries and respond to guiding questions, such as “What information does the factory in Japan need in order to complete the sale?” and “How many total cars is the local dealership trying to purchase?” These prompts require students to reason through the addition process and apply their understanding of place value in a meaningful scenario, which supports their analysis of mathematical situations through inquiry and real-world application.

Evaluation for 5.1b
Questions and tasks provide opportunities for students to create concrete models and pictorial representations to represent mathematical situations.

A lesson on reading and writing whole numbers to 1,000 provides tasks that require students to interpret, analyze, and evaluate mathematical information across standard, word, and expanded forms. Students analyze a base-ten pictorial model to determine the standard form of a number, using place-value understanding to identify that a model showing four hundreds and eight ones represents 408. Students interpret information from a real-world visual—a check—and use image details to answer related questions, connecting visual models and real-world representations to numerical concepts. Students also evaluate their interpretations to determine whether they accurately match the numerical forms presented.

On the Freckle platform, educators can assign Targeted Practice that prompts students to build concrete models with digital base-ten blocks to match or represent pictorial models. In the 2.2(D) Compare and Order to 1,200 lesson, students create models with base-ten blocks to compare numbers, use a number line as demonstrated in the instructional video, generate pictorial representations of place-value relationships, and construct their own models rather than relying on prebuilt representations.

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

In the Solve Problems Involving Money lesson, students begin with a contextual scenario involving the price of a fidget spinner and a collection of coins and use their understanding of coin values, skip counting, and equivalent amounts to determine how much money remains after a purchase. Students then transfer this understanding to a new context, which states, “Sammy has 45 cents. Matty has 1 dime, 2 nickels, 1 quarter, and 1 penny. Who has more money?” To solve the problem, students convert mixed collections of coins to their total values, compare the amounts, and justify their reasoning, applying their conceptual understanding of money and place value in a different situation.

The IBL structure further provides opportunities for students to apply conceptual understanding to novel problem situations. Each lesson begins with an authentic scenario that prompts students to activate prior knowledge and make sense of the problem before any solution method is introduced. As students collaborate to solve each day’s task, they apply mathematical concepts and reasoning to new contexts, evaluate possible solution strategies, and adapt their thinking to the problem. The lesson concludes with student presentations in which students justify and defend their mathematical reasoning, which demonstrates flexible application of conceptual understanding across real-world situations.

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

Students repeatedly connect target numbers to related addition and subtraction expressions, strengthening students’ ability to recall fact families and verify relationships between operations. Through repeated identification of sums and differences, students build accuracy, efficiency, and automatic recall of basic facts needed for later problem-solving and multistep computation.

A drag-and-drop activity builds students’ automaticity and fluency with addition and subtraction facts by providing repeated opportunities to determine unknown values in equations. As students place numbered balloons to complete equations with sums and minuends of 20, they apply their understanding of number relationships, fact families, and inverse operations to efficiently identify missing values. The task encourages students to recognize and use mathematical structure, such as rewriting an addition equation as a related subtraction equation, to solve more strategically, which strengthens rapid fact recall and develops the flexibility and efficiency needed to complete grade-level mathematical tasks.

Evaluation for 5.2b
Materials provide opportunities for students to practice the application of efficient, flexible, and accurate mathematical procedures throughout learning pathways.

The Importing and Exporting Goods IBL on the Freckle platform provides multiple opportunities for students to apply efficient, flexible, and accurate mathematical procedures across a two-day learning pathway. On day one, students work collaboratively to determine the total number of vehicles needed to order from Japan using addition and subtraction of two-digit numbers. Reflection prompts, such as “Explain your strategy for adding 3 numbers together” and “If you could start over, what would you do differently?” guide students to evaluate the efficiency of their chosen strategies and consider alternative approaches. On day two, students solve a related task involving the number of planes to send to a destination, with directions encouraging them to “draw pictures or use any other strategies,” promoting flexibility as they select and adapt procedures that fit the context. Working in small groups allows students to check one another’s reasoning and refine accuracy as they compute and justify their solutions.

The materials provide opportunities for students to apply efficient, flexible, and accurate mathematical procedures throughout the Add and Subtract Within 100 Using Number Lines lesson. Students are introduced to multiple ways of using a number line, including number lines with preplotted values, open number lines, and several methods for structuring jumps—adding tens and then ones, jumping to the next multiple of ten and adjusting backward, or decomposing numbers into tens and ones to add by place value. These options promote flexibility as students choose among valid strategies. Prompts, such as “Do you think it matters which number we start with when we use this strategy? Why or why not?” guide students to evaluate the efficiency of different approaches, while repeated practice plotting and calculating on number lines supports accuracy because students refine their procedures and verify their results.

Evaluation for 5.2c
Materials provide opportunities for students to evaluate mathematical representations, models, strategies, and solutions for efficiency, flexibility, and accuracy throughout learning pathways.

In the Add and Subtract Within 100 Using Number Lines Nearpod lesson, students engage with multiple approaches for solving addition and subtraction problems using both structured and open number lines, including adding tens and ones separately, counting to the next multiple of ten and adjusting, and decomposing two-digit numbers by place value. The Teacher Guide prompts educators to “allow students the opportunity to compare the different strategies used by their peers to solve the same problems” and to “encourage students to analyze the efficiency and logic of each approach,” supporting students in reflecting on accuracy, efficiency, and flexibility across strategies.

The IBLs provide opportunities for students to evaluate mathematical representations, models, and solutions for efficiency, flexibility, and accuracy. After presenting their daily findings, educators lead students through a class discussion using the following prompts: “I agree with _____ because _____,” “I solved it differently than _____ because _____,” and “The way that _____ explained the solution caused me to change my thinking because _____.”

Evaluation for 5.2d
Materials contain guidance to support students in selecting increasingly efficient approaches to solve mathematics problems.

In the Freckle Adaptive Pathway, students receive scaffolded support when encountering review questions. The Teach Me feature provides step-by-step worked examples, and hints offer visual and conceptual guidance to help students reengage with the problem and refine their approach.

The Importing and Exporting Goods IBL on the Freckle platform provides students increasingly efficient approaches to solve mathematics problems. Students work in collaborative groups to solve a real-world problem involving the addition and subtraction of two-digit numbers, and the Teacher Guide provides daily tasks and reflection questions. Prompts, such as “I solved it differently than _____ because _____” and “The way that _____ explained the solution caused me to change my thinking because _____,” support students in comparing approaches and selecting more-efficient methods for solving problems.

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

The materials provide a “Design a Balanced Instructional Approach” document that explains how the program integrates conceptual understanding, procedural fluency, and application. Nearpod’s models, manipulatives, and exploratory activities support conceptual understanding. Educators can assign targeted Freckle practice aligned to daily lessons to support procedural fluency. Educators can incorporate Freckle’s IBLs and real-world challenges to reinforce application.

The Fluently Add & Subtract Nearpod lesson guides students through a progression of strategies that explicitly address both the conceptual and procedural emphasis of the TEKS. Students build conceptual understanding by using a variety of methods, such as counting on, decomposing numbers into tens and ones with ten-frames, and adding or subtracting on a number line. The lesson then transitions to procedural application, in which students use these strategies to solve a word problem by creating an equation to find the sum.

Evaluation for 5.3b
Questions and tasks provide opportunities for students to use concrete models, pictorial representations, and abstract models as required by the TEKS.

The Freckle Targeted Practice assignments provide opportunities for students to progress from concrete and pictorial representations to abstract mathematical reasoning. Students interpret pictorial models and connect them to abstract numerical representations, supporting the development of mathematical understanding as they transition from visual models to symbolic reasoning.

The materials provide opportunities for students to use pictorial and abstract models in the Write Equations to Solve One-Step Problems Nearpod lesson. Students begin with pictorial representations of apples to complete the Start-Change-Result model by visualizing the structure of the problem. Students then draw their own pictorial model for a new word problem, which reinforces how quantities relate in the scenario. The lesson concludes with an abstract model by asking students to write and solve an equation that represents the situation.

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.

In the Add and Subtract 1- and 2-Digit Numbers Nearpod lesson, students use base ten blocks to create concrete models and connect them to abstract representations, such as recognizing that “35 + 7 is adding 3 tens and 12 ones.” As the lesson progresses, students use place value charts and drag-and-drop base ten pictorial models to solve problems, such as 72 + 7 = and 89 − 7 = . Guiding questions, such as “How many ones should we draw?” support students in explaining the process of addition and subtraction using models, and sentence frames provide additional support for articulating connections between models and abstract concepts.

The Freckle DOK 2.9F activity further supports students in connecting representational models to abstract concepts. Students determine the number of square tiles needed to cover a rectangle, construct and interpret area models, and explain their reasoning using visual representations. Students then extend their understanding by applying these models to solve problems involving multiple dimensions, connecting area representations to abstract calculations and formulas.

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

In the Even and Odd Numbers: Disagree or Debate activity, students review even and odd numbers by circling pairs of objects, such as boots, gloves, and mittens, and by using the crayon tool to determine whether each quantity is even or odd. Students then use the highlighter tool to complete declarative statements that show whether they agree or disagree with a friend’s claim, such as “17 is (even/odd). Every boot (has/does not have) a pair,” by selecting the words that make each statement true. These multimodal tasks connect visual-manipulative reasoning with structured academic language, including vocabulary for even and odd numbers and declarative sentence structures for agreeing or disagreeing.

In the Three Dimensional Shape Sort lesson, students receive an anchor chart introducing key geometric vocabulary, including surface, face, curved, straight, edge, and vertex, and each vocabulary term is paired with a definition, a visual representation, and an example sentence demonstrating accurate mathematical usage. Students then apply this vocabulary during a sorting activity by using the terms to describe and classify pictorial representations of three-dimensional figures.

Evaluation for 5.4b
Materials include embedded educator guidance to scaffold, support, and extend students’ use of academic mathematical vocabulary in context when communicating with peers and educators.

In the Even or Odd Numbers: Disagree or Debate activity, the materials provide students with academic vocabulary and sentence starters that model how the terms may be used. However, these supports are entirely student-facing. The materials do not give educators guidance on how to prompt, model, or facilitate vocabulary use during peer or educator-student communication.

Freckle’s Academic Vocabulary feature highlights key terms in practice items and allows students to click for a definition, but the platform does not provide educators with embedded guidance on building on, applying, or deepening students’ vocabulary use during conversations with peers or educators. Freckle’s Peer-to-Peer Math Supports do not include sentence stems, prompts, or other scaffolds to help students use mathematical vocabulary terms when communicating with peers and educators.

Evaluation for 5.4c
Materials include embedded guidance to support student application of appropriate mathematical language and academic vocabulary in discourse.

The Renaissance Math Solution Guide includes sample sentence frames, such as “I used _____” and “I know my answer is right because _____,” along with guidance encouraging educators to use interactive checks and require structured talk to support students’ application of academic mathematical language during discourse. These prompts provide educators with a consistent structure for encouraging students to communicate their reasoning using academic vocabulary across lessons.

In a lesson on arrays, students construct an array through a drag-and-drop activity and complete the embedded sentence frame “My array has _____ rows and _____ columns” to describe their model. This embedded sentence frame scaffolds students’ use of academic vocabulary, such as array, rows, and columns, as they communicate their mathematical thinking to peers and the educator.

Evaluation for 5.4d
Materials include embedded guidance to facilitate mathematical conversations allowing students to hear, refine, and use math language with peers.

The Renaissance Math Solution Guide lesson template requires structured talk, directing educators to have students “partner rehearse and share out” during instruction. Its “Structured Partner Talk” routine gives students sentence stems, such as “I chose _____ because _____” and “My strategy was _____,” to use in that exchange. This structure gives students the chance to hear a partner’s reasoning, rehearse and refine their own explanation, and use academic vocabulary before sharing out with the class.

Freckle’s Peer-to-Peer Math Supports identify classmates who have mastered the standard being practiced, providing an opportunity for students to seek peer support during independent work. When combined with the “Structured Partner Talk” routine in the Solution Guide and sentence stems such as “I used _____” and “I know my answer is right because _____,” students have supports to organize and communicate their mathematical thinking during peer exchanges.

Evaluation for 5.4e
Materials include embedded guidance to anticipate a variety of student answers including exemplar responses to questions and tasks, including guidance to support and/or redirect inaccurate student responses.

In the Teacher Guide of the Nearpod lessons, the materials include answer keys for activities, such as multiple-choice questions, draw it, matching pairs, and drag-and-drop tasks. However, the answer keys show only the correct response and do not show exemplar work or a variety of anticipated student answers. Nearpod skill resources include a “Common Misconceptions” section in the Teacher Resource. However, this section is separate from the answer key and identifies only one general misconception rather than providing redirection questions or alternative strategies at the point when educators check student work.

In the IBLs on the Freckle platform, the materials include answer keys for activities, such as daily reviews and the daily inquiry task. However, these answer keys show only one equation or expression used to reach the correct answer and do not include exemplar responses or a variety of anticipated student work. The “Providing Feedback” section outlines redirect scripts and next-step actions for common error types, but this guidance is not embedded in the IBL answer key, so educators receive no anticipated-response or redirection support at the point of grading.

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

Each IBL on the Freckle platform structures students’ daily work around TEKS 2.1B, guiding them through a problem-solving model that involves analyzing given information, forming a plan, reaching a solution, and evaluating the reasonableness of that solution. On each day of the IBL, students take the given information, form a plan, and work toward a solution. At the end of the lesson, students present their findings to the class, applying TEKS 2.1A by using this problem-solving model to address a real-world task.

In the Make Groups to Find Even and Odd Numbers Nearpod lesson, students apply TEKS process standard 2.1A, which asks students to “apply mathematics to problems arising in everyday life, society, and the workplace,” through a real-world cooking-class scenario. Each of four characters holds a bag of cookies labeled with a specific number, and students first complete a drag-and-drop activity matching each bag to its correct cookie image before working with that character’s total. Students then use pictorial representations of the cookies to split each character’s total evenly between two cookie jars, placing any leftover cookies on a plate in front of the jars. By modeling this real-world sharing task with a hands-on, split-the-total action, students determine whether each character’s total number of cookies is even, when no cookies remain on the plate, or odd, when one cookie is left over.

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

The Renaissance Math Solution Guide lists and explains how process standards are included in the materials. However, this explanation is limited to a single general description rather than describing how the TEKS process standards are incorporated and connected throughout the program’s learning pathways. For example, the materials state that “In Renaissance Math, each skill area includes two activities intentionally designed to address specific process standards. Each activity is accompanied by a teacher resource that clearly outlines the learning goals and the targeted process standard. These resources are crafted to help students connect mathematical content with the ways they engage in and make sense of mathematics.” Although the materials reference how the process standards are included, they do not describe where those standards are incorporated throughout the learning pathways.

The Solution Guide’s scope table and “Alignment Across and Within Grades” section address how content skills are incorporated and connected across grade levels. However, neither resource extends this same treatment to the TEKS process standards. The scope table charts only content skills, such as place value, fractions, and measurement, and resource titles by grade level by marking which domains appear at which grades. The “Alignment Across and Within Grades” section goes further for content, offering a narrative description of how strands, such as number sense and operations, fractions and decimals, and place value, build in sophistication from grade to grade. However, this narrative description is limited to content domains and does not reference how the TEKS process standards are incorporated or connected across those same learning pathways. As a result, an educator using the Solution Guide can see which content skills appear at each grade level and how those skills progress over time, but the materials do not provide a comparable description showing how the TEKS process standards are incorporated and connected throughout the program’s learning pathways.

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

The Renaissance Math Solution Guide includes a list of the TEKS process standards and states that “in Renaissance Math, each skill area includes two activities intentionally designed to address specific process standards” and that “each activity is accompanied by a teacher resource that clearly outlines the learning goals and the targeted process standard.” However, this description appears only in the ”General Overview” section of the Solution Guide, and the guide does not indicate which process standard applies to any individual lesson.

The Teacher Resource template used for individual Nearpod skills, such as Create & Interpret Number Lines, does not include a TEKS process-standard reference in the lesson document. Nearpod’s standard Teacher Resource template instead includes a “Mathematical Practice Application” section that labels each skill’s activities with a Common Core Standard for Mathematical Practice but does not include an overview of which TEKS process standards apply to that lesson’s activities.

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

The Sea Turtle Hatchlings lesson engages students in mathematical thinking, perseverance, and sense-making through a real-world scenario requiring addition and subtraction within 100 to analyze sea turtle habitats. Questions, such as “If 98 eggs were laid in the nest, how many eggs have yet to hatch?” prompt students to think mathematically and make sense of mathematics by identifying known and unknown quantities and selecting appropriate operations. On the final day, students determine which beach provides a better habitat for the sea turtles, persevering through problem-solving by analyzing hatchling data from each beach and using their findings to write a report for a nature magazine. This extended task requires students to revisit information, synthesize data, and justify their conclusions.

The DOK Challenges enrich and extend student learning by presenting scaled question sets that move from foundational recall (DOK 1) to application and strategic thinking (DOK 2–3). This structure ensures that students progress beyond procedural fluency toward the deeper conceptual reasoning required for on-grade-level and above-grade-level proficiency. The program’s adaptive design personalizes this progression by unlocking DOK Challenges only after a student demonstrates mastery at their current adaptive level, ensuring that enrichment is both timely and appropriately targeted. Grounded in real-world contexts and available in English and Spanish, these challenges increase rigor and complexity in a meaningful, structured way and push students to analyze, justify, and apply mathematical thinking at the level demanded by state assessments and beyond.

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

In the Sea Turtle Hatchlings lesson, students engage with a series of videos and tasks requiring them to analyze the number of turtles hatched across different habitats. Class discussions around prompts, such as “What information from the video was important or interesting?” help students recognize that multiple observations and approaches can inform a solution. At the end of each day, student groups present how they arrived at their solution, explain their reasoning, and hear alternative approaches from peers, which exposes students to multiple valid ways to solve the same problem. On the final day, students determine which beach is a better habitat for sea turtles and justify their conclusions by defending their method and explaining why their approach leads to a valid recommendation. This culminating task reinforces the idea that different strategies can be mathematically sound when supported by evidence.

The materials include lessons that guide students to understand, explain, and justify that problems and tasks can be solved in more than one way. Students are shown two different ways to make $32—three tens and two ones, and two tens and 12 ones—and evaluate why both representations are equal by labeling the tens and ones and identifying the value each model shows, which supports understanding that different combinations can represent the same number. Students then explain why the two representations show the same value, even though the bills and groupings differ, using place value reasoning to account for the equivalence. Finally, students justify that both solution paths are valid by explaining how each representation computes $32, reinforcing that multiple approaches can accurately solve the same problem.

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/or educators.

The Starting a Lemonade Stand IBL engages students in doing mathematics, writing about mathematics, and discussing mathematics with peers and educators as they make sense of mathematics. Throughout the three-day Starting a Lemonade Stand investigation, students do mathematics by comparing one- and two-digit numbers, analyzing sales scenarios, and applying comparison symbols (>, <, =) to make pricing and business decisions for both the lemonade stand and a friend’s snack shack. Students write about mathematics by recording comparisons, mathematical representations, and written justifications on the Inquiry Sheets, describing how students used place value and comparison symbols to support their decisions across the investigation. Students discuss mathematics with peers and educators as they compare solution strategies, explain how they determined which numbers were greater than, less than, or equal to, and justify the business decisions made during the culminating project.

In the Life as an Animal Scientist IBL, students build their understanding of how to organize data in graphs through hands-on work, written reflection, and peer conversation across a three-day investigation. Students work through the mathematics hands-on when they interpret two unlabeled graphs to determine what data each represents, represent the lifespan of four animals using both a bar graph and a picture graph, and then build their own picture graph and bar graph from data they collect. Students put their thinking in writing on each day’s inquiry sheet through the “Developing the Question” prompt, framing the question they are trying to answer or the task they are completing before beginning their work, and recording their graphs and representations directly on the inquiry sheet. On day three, students engage in mathematical conversation with peers by posing a data question to classmates, collecting and tallying responses, and using the shared data to build graphs together.

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

The program equips educators to guide students in sharing and reflecting on their problem-solving approaches, including their explanations, arguments, and justifications. On the Nearpod platform, educators can add a Collaborate Board to any lesson. A Collaborate Board “allows students to post text and images to a shared class board. It’s a great way to spark class discussion, brainstorm, or check in on how students are feeling.” In a Collaborate Board, educators can add word problems aligned with the lesson and pose questions that require students to share how they solve problems by explaining, justifying, reflecting on, and evaluating their own problem-solving approaches as well as others’.

The Starting a Lemonade Stand IBL equips educators to guide students in sharing and reflecting on their problem-solving approaches when they compare one- and two-digit numbers in business scenarios. During a three-day investigation, students determine lemonade prices, identify the most successful sales location, and apply their understanding to help a friend’s snack shack. When comparing numbers with >, <, and =, students explain how they determined which numbers were greater than, less than, or equal to, recording their reasoning on daily inquiry sheets. Students share arguments by discussing why one pricing option or sales location is the better choice and defending how their comparisons support each decision. Students share justifications by citing place value, comparison symbols, and numerical relationships as evidence. As problems progress from a one-digit vs. two-digit comparison on day one to two two-digit numbers and a culminating project on day three, students reflect by revisiting and refining their reasoning.

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

The Targeted Practice and Adaptive Practice assignments in the Freckle platform give educators tools to deliver explanatory feedback tied to students’ responses and anticipated misconceptions. As students work through Targeted Practice assignments, the program provides hints, explanatory videos, and a Show Me feature when a student enters an incorrect response, and the assignments allow students to reattempt the problem after working through these supports.

The Teacher Resource document accompanying a Nearpod lesson provides educators information related to student misconceptions but does not provide guidance on how to turn that information into feedback for students. A ”Common Misconceptions” section identifies the errors students are likely to make on the lesson’s content, and an item analysis for the pre/post assessment explains, for each answer choice, why the response is correct or incorrect, supported by an answer key for the lesson’s activities. However, none of these resources direct educators on how to respond to an individual student’s specific answer or misconception with explanatory feedback. The materials only identify and explain errors and do not provide prompts to support educators in providing feedback.