Renaissance Math Texas, Grade 3

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 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 progress 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 reteaching, and tier 3 targeted intervention, and provides clear guidance on adapting materials to meet student needs across settings. Both platforms include multilingual learner support, including Spanish platform navigation and language settings.

The Renaissance Math Solution Guide provides usage recommendations and strategies for effective use by educators across multiple instructional contexts. For just-in-time support, educators use the Nearpod platform’s real-time dashboard to identify misconceptions immediately and adjust groupings accordingly, while the Freckle Adaptive Pathway practice addresses prerequisite skills within 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 based on 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 skills, grade-level skills, and extension skills for each TEKS. The guide maps these skills to corresponding Renaissance Math lessons. Educators can use the guide to identify key prerequisites and forthcoming lessons for each TEKS, pinpoint appropriate entry points, and plan personalized instruction based on students’ current skill levels.

The materials include a diagnostic assessment through the Freckle Adaptive Pathway 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, guiding 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 Renaissance Math. 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 and effective use of the program.

The Renaissance Math Leader Guide outlines key steps for successful implementation and provides guidance to instructional leaders on supporting teachers and coaches. In “Step 1, Instructional Leader’s Role,” leaders are guided to set clear expectations for lessons and routines and provide feedback and coaching to strengthen lesson delivery. In “Step 2, Supporting Teachers with Lesson and Unit Implementation,” leaders receive guidance on helping teachers plan with the materials and determine which components to use. For example, leaders can direct teachers to leverage the Freckle Adaptive Pathway for pre-teaching or skill reinforcement based on class needs. The Nearpod platform 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 platform lessons include TEKS-aligned learning objectives and suggested time allotments for each lesson component, including preassessment, authentic connection, explicit instruction, and postassessment. Freckle platform skill pages provide educators with a student objective, a connection to prior learning, a skill summary, a connection to future learning, guiding questions, common misconceptions, skill limitations, and vocabulary. However, the materials do not include ELPS alignment, and the Freckle platform skill pages do not include student-facing materials.

The materials include teacher 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, with guidance for adjusting pacing based on student performance. However, the materials do not include teacher materials, student materials, or assessment resources aligned to 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 Adaptive Pathway, the materials provide educators with learning objectives aligned to the TEKS. The materials include lesson components for teachers and students with suggested time frames. Examples include 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 time frames. The Math Usage Recommendations document outlines key lesson components of the Freckle platform along with suggested usage times. For example, for grades 3–12, the document recommends 20 minutes of use per day across all lesson components, at least twice per week. These lesson components include adaptive math pathway, targeted math practice, and focus skills practice.

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 these 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 solution guide that provides a table outlining the definition and instructional purpose of each assessment type. Under the Instructional Purpose column, the Renaissance Math 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 purposes of the “Diagnostic/Placement,” “Formative,” “Interim/Benchmark,” and “Summative” assessments. The guide also identifies where each assessment type appears within 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 into 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, including Diagnostic
Assessments, Targeted Practice, and Benchmark Assessments. 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 the Freckle platform settings, teachers can use the “Edit Student” tab to enable or disable text-to-speech and calculator access for students. In the Nearpod platform, teachers can enable an Immersive Reader tool to activate text-to-speech, additional content, and language supports. These tools give 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 in 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, such as multiple-choice, multiple-answer, and type-in. For example, in the Nearpod platform, teachers can use multiple-choice pre-assessment 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. These include Adaptive Practice, Targeted Practice, and Benchmark Assessments, which 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 platform 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. Reporting tools allow teachers 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.” This section provides teachers with guidance on monitoring and adjusting instruction. For example, the guide directs teachers to review student progress, identify question-level patterns, and use post-session reports to plan next-day instruction. This section provides a broad overview of how to interpret student performance.

The materials provide teacher resources within the lesson, including a full lesson answer key. The key provides pre- and postassessment questions, along with answers and 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 level. 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.

Within the platform, the “Performance by Topic” report allows teachers 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. Teachers 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 teachers to monitor both individual student performance and overall class data. Teachers 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 them 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.

Within the Nearpod platform, educators receive a slide deck that includes a pre-assessment, quizzes, and a “Time to Climb” assessment to check for understanding at key points in the lesson. Teachers 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 steps for consistent, accurate results and outlining next steps for groups of students based on those results. While students work, the guidance instructs teachers 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 Freckle Adaptive Pathway 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 within 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. Through the report, 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 level of understanding. The program automatically adjusts the difficulty of exercises and questions based on each student’s past performance. The program also provides recommendations for differentiating prerequisite skills within a selected standard in Targeted Practice.

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

The materials provide embedded supports for unfamiliar references in text. Within the Nearpod platform, emergent bilingual (EB) lessons include an Academic Vocabulary Teacher Guide that provides embedded guidance to support students’ understanding of unfamiliar references during instruction. The guide includes strategies such as explaining words aloud, providing student-friendly definitions, and structuring opportunities for oral practice. However, the materials do not include pre-teaching supports to develop academic vocabulary or address 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. On the Freckle platform, the program provides educators with recommended activities for students who are ready for a challenge. The program defines this as students who have scored above 79 percent on skills. The materials direct educators to assign DOK activities in which students apply their skills to real-world challenges. Within the Inquiry-Based Lessons on the Freckle platform, students explore math standards and build critical thinking skills through real-world challenges.

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

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 within the Roster page. By selecting the Edit Student feature, educators can access the Support Settings tab and activate features such as the calculator. Teachers 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 with guidance to support student understanding throughout 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 while deepening student understanding. For example, the guidance suggests using audio and open-ended responses to allow students to express their 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 Inquiry-Based Learning (IBL) lessons that provide students with 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 teachers with student-facing Inquiry Sheets to help students organize their thinking and represent mathematical concepts. The IBL teacher 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 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 educators with prompts and guidance to build knowledge through lesson plans. Lesson plans ground educators in a student objective tied to the TEKS. Additionally, lesson plans activate prior knowledge through the “Connection to Prior Learning” and “Connection to Future Learning” sections, which tie what students already know to what they will learn by the end of the lesson. The materials also provide a “Skill Summary” section that connects key patterns, features, and relationships through multiple means of representation.

On the Nearpod platform, the materials provide questions designed to help educators elicit what students already know about a topic before introducing new information. These questions are embedded into the slides as a preassessment quiz to activate prior knowledge. Within the Think About It slide, the materials provide teachers 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 provide guidance that supports effective instructional grouping and flexible classroom arrangements. The Renaissance Math Solution Guide describes how teachers can organize students for whole-class instruction using teacher-led Nearpod platform lessons and for small-group instruction through Nearpod platform pre-teach and reteach lessons. Additionally, the guide describes how teachers can organize students into differentiated learning stations that incorporate independent practice on the Freckle platform and center activities on the Nearpod platform. The guide also outlines structures for independent learning through differentiated assignments on the Freckle platform and supports collaborative learning through interactive activities on the Nearpod platform. Inquiry-based learning is further reinforced through the Inquiry-Based Lessons (IBLs) available within the Freckle platform. These structures equip educators with clear, practical guidance for grouping students and facilitating learning across varied instructional formats.

The Renaissance Math Solution Guide includes guidance for educators on 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, when using a small-group approach, the guide instructs educators 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 educators with guidance on using an inquiry-based approach 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 “Strategies for Utilizing Renaissance Math Resources in Daily Instruction” section provides guidance on using small-group instruction with pre-teach or reteach lessons on the Nearpod platform. It also gives educators differentiated learning stations, including independent practice on the Freckle platform. Additionally, the section includes one small-group lesson from the Nearpod platform and another using Nearpod platform center activities. Finally, the section includes independent practice where students complete differentiated Freckle assignments. The “Differentiating with Renaissance Math” section includes educator guidance on how to use Nearpod and Freckle platform lessons for multilingual learners, tier-one core instruction, and tier-two and tier-three small-group and individual support.

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-teaching or reteaching using the Nearpod platform, with practice in the Freckle platform 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 platform Assignment Report, teachers can expand an assignment to view each student’s performance and identify learners who are ready for a challenge. Students ready for a challenge are those who score above 79 percent in targeted skills. The platform then provides direct links to aligned enrichment options, such as Depth of Knowledge (DOK) lessons and Inquiry-Based Lessons (IBLs). Educators can navigate directly to the DOK level aligned to the standard and assign these activities to individual students or groups. IBLs have students 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. On the Freckle platform, educators can sort content by targeted skills and domains, building basics, extending thinking, and assessments. DOK activities are a set of higher-level thinking questions for a specific standard. In “Extend Thinking,” educators can assign DOK activities to help students master concepts. Students apply mathematical concepts to real-world scenarios to demonstrate their understanding. Educators can also assign Inquiry-Based Lessons, 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 offers educators guidance on 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. Some of these prompts include “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. Within the Nearpod platform, educators can use the Live Teacher Feedback feature in the teacher 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 during instruction 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. However, these proficiency level descriptions do not align with the ELPS. The ELPS identify proficiency levels as pre-production, beginning, intermediate, high intermediate, and advanced. Additionally, the linguistic supports provided by the materials 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 a Nearpod platform lesson 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 current ELPS, and the accommodations provided 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 within 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 learners access mathematical content. The materials also include proficiency descriptions for emergent bilingual students. However, these descriptions use levels such as beginner, intermediate, advanced, and advanced high rather than the current 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 within bilingual settings, such as dual language, transitional bilingual, and alternating language models. However, this guidance does not constitute implementation guidance for state-approved bilingual/ESL programs, as it does not align with or address the specific requirements of state-approved program models.

The materials do not include implementation guidance to support educators in effectively using the materials in state-approved bilingual/ESL programs. While the Renaissance Math Solution Guide references bilingual instructional routines, vocabulary supports, and language allocation plans, these resources do not provide guidance specific to state-approved bilingual/ESL program models as defined by TEKS.

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 platform’s “Academic Vocabulary” lessons introduce the prerequisite vocabulary for 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 platform “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.

In the grade 3 “Add & Subtract to Solve Word Problems Within 1,000” Nearpod platform lesson, students develop depth of understanding through a structured instructional progression that builds from conceptual understanding to multi-step application. The lesson introduces the Start, Change, Result (SCR) framework using color-coded models to help students identify each component of a word problem. Then the lesson engages students in collaborative activities in which they determine whether the start, change, or result is the unknown quantity. During writing activities, students represent unknowns with a question mark, write equations, and use related facts to rewrite equations so the unknown appears at the end before solving. The lesson extends to two-step word problems, in which students must identify two distinct changes and apply two operations to find the solution. Drag-and-drop practice reinforces students’ ability to categorize word problem components and select the correct equation structure, requiring them to apply the SCR framework rather than solve by rote.

The DOK Challenges within 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. Within 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 Inquiry-Based Lessons that provide enrichment and extension opportunities to deepen students’ understanding of the TEKS through real-world, problem-based scenarios. In the Designing a City Zoo IBL, which addresses TEKS 3.4.J and 3.4.H, students interpret whole-number quotients of whole numbers by taking on the role of a city zoo designer. Students separate animals into sections and habitats, help a veterinarian determine the daily diet of each reptile to calculate appropriate medicine amounts, and assist a zoo rescue team in placing animals at zoos across the nation. Each task requires students to apply division concepts in a new context. The lesson is structured across multiple days, with each day including an instructional video, an Inquiry Sheet for student work, and a solution guide. As students move through the tasks, they explain their reasoning, present solutions, and engage in collaborative problem-solving, progressing from visual representations to more complex applications without support. This progression in rigor and complexity creates multiple entry points for learners and supports students in reaching grade-level and above-grade-level proficiency.

The Freckle Adaptive Pathway online math program provides questions and tasks that increase in rigor and complexity. The program supports students’ progress toward grade-level and above-grade-level proficiency. Within the adaptive learning pathways, students who demonstrate 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. The system offers remediation through scaffolded supports such as step-by-step instructional videos, hints, 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 learners 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.

Renaissance Math is a TEKS-aligned supplemental program that demonstrates horizontal coherence by connecting related mathematical concepts within each grade level. The program organizes instruction around major mathematical domains and intentionally sequences lessons so students build on previously learned concepts while making connections among patterns, big ideas, and mathematical relationships. Lessons use concrete, visual, and abstract representations to help students connect related concepts rather than learn isolated procedures. Inquiry-Based Lessons further strengthen these connections by requiring students to apply multiple mathematical ideas within authentic problem-solving contexts, reinforcing conceptual understanding across the grade-level curriculum.

The materials demonstrate horizontal coherence by connecting patterns, big ideas, and relationships within grade 3. The Academic Vocabulary Teacher Guide clearly articulates how multiplication, division, and fractions work together through coordinated units, helping students see these concepts as interconnected rather than isolated. Instruction begins with concrete tools such as base-ten blocks, fraction strips, and arrays to build conceptual understanding. Then, instruction transitions to visual representations such as number lines, tape diagrams, and area models, and ultimately to abstract numerical methods. Throughout grade 3 lessons, students explore how mathematical ideas relate to one another. For example, students explore how understanding equal groups supports both multiplication and division, and how placing unit fractions on a number line connects the meaning of fractions to prior number-sense work. This intentional progression helps students make meaningful connections across skills and develop a deeper, more coherent understanding of mathematics within the grade level.

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 coherence across grade levels by building mathematical concepts and skills in a coherent, developmentally appropriate progression. The Academic Vocabulary Teacher Guide includes explicit “Connection to Prior Learning” and “Connection to Future Learning” sections that explain how each lesson fits within the broader K–6 learning progression. For example, in the grade 3 lesson “Add & Subtract to Solve Word Problems Within 1,000,” the Academic Vocabulary Teacher Guide notes that students previously solved one- and two-step word problems within 100 using drawings and equations with unknowns in grade 2. During the lesson, students extend these concepts by using tape diagrams and place value strategies to solve problems within 1,000. The guide also explains that this learning prepares students for solving multi-step problems involving all four operations and equations with variables in later grades. By explicitly connecting prior knowledge, current learning, and future mathematical concepts, the materials reinforce the progression of operations, mathematical modeling, and algebraic reasoning across grade bands.

In the Freckle Adaptive Pathway, 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 within the same domain. After completing a diagnostic assessment, students are placed on a personalized learning pathway that reflects their current level of understanding. If they perform above grade level, the adaptive system immediately provides more advanced tasks that extend their learning. This structure ensures that students receive remediation, on-level practice, or enrichment aligned to 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 grade 3 “Fluently Multiply Within 100” Nearpod platform lesson, the “Teacher Resource” document informs educators of prior learning connections. For example, using place value understanding to skip count by 2s, 5s, and 10s while connecting repeated addition to multiplication. The procedures for decomposing expressions, skip counting, and relating facts to known repeated-addition skills provide coherence across lessons. The materials inform educators how students will connect lessons to future learning by stating, “Students will extend their work with this skill to multiply multi-digit numbers using various strategies such as partial products, the area model, and the standard algorithm for multiplication.”

The materials include a TEKS Alignment Guide that allows educators to view the vertical alignment for each grade 3 lesson. The guide lists the current grade-level TEKS with a hyperlink to the corresponding Renaissance Math lesson, identifies the aligned prerequisite lesson from a prior grade, and identifies forthcoming lessons from the next grade. For example, grade 3 TEKS 3.4(D), which addresses interpreting multiplication using arrays, links back to grade 2 lessons on solving add-to and take-from problems within 100. Then, it looks forward to grade 4 lessons on fluently adding and subtracting multi-digit whole numbers and solving multi-step problems. Similarly, grade 3 TEKS 3.3(A), which addresses representing fractions using objects, pictorial models, and number lines with denominators 2, 3, 4, 6, and 8, connects back to grade 2 work partitioning circles and rectangles into equal parts. Then, it looks forward to grade 4 lessons on decomposing fractions into sums of fractions and expressing fractions as tenths and hundredths. This structure allows educators to see how grade 3 learning fits within the broader vertical progression and provides options for assigning prerequisite or extension lessons based on student need.

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, also known as domains. Students begin each domain with a diagnostic pretest. As they work through a selected domain, Freckle’s adaptive algorithm adjusts the difficulty based on ongoing performance, returning students to earlier skills when gaps are detected. This creates built-in spaced retrieval opportunities as prior skills are reactivated before students advance to more complex content. Students may move between below-grade-level, on-grade-level, and above-grade-level content within the same domain, encountering previously learned skills in new contexts across the learning pathway.

The grade 3 “Solve Problems to Find Elapsed Time” Nearpod platform lesson provides spaced retrieval opportunities for previously learned skills and concepts. The lesson reactivates prior knowledge of open number line tools from grade 2. Throughout the lesson, the questions and tasks reinforce mathematical tools and concepts, requiring students to retrieve previously learned skills and concepts. For example, students apply their prior understanding of number lines to reason about elapsed time.

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. Within each domain, students encounter problems that draw on multiple previously learned skills rather than practicing one skill in isolation. As the adaptive algorithm advances students through a domain, it introduces problems of increasing complexity that require applying and selecting among prior skills in combination. Students who perform well on one skill are not simply given more of the same type of problem. Instead, they are moved into content where previously learned concepts intersect with new material, requiring them to integrate skills from across the learning pathway. Additionally, because the adaptive practice spans below-grade, on-grade, and above-grade content within the same domain, students regularly encounter problems that interleave earlier foundational skills with grade-level and above-grade-level applications.

The materials provide interleaved practice opportunities with previously learned skills by requiring students to apply addition, subtraction, multiplication, division, estimation, and equation-writing skills within the context of two-step problem solving. For example, in the grade 3 “Represent & Solve 2-Step Word Problems” Nearpod platform lesson, students draw upon prior experiences with representing unknown quantities, using mathematical models, solving equations, and evaluating the reasonableness of solutions as they work through increasingly complex problem situations. The materials also provide interleaved practice opportunities with previously learned concepts across learning pathways by connecting numeric operations, algebraic reasoning, mathematical modeling, and problem-solving strategies. Students use representations such as tape diagrams and equations with unknowns to make sense of real-world situations, reinforcing conceptual understanding developed in earlier grades. The progression from single-operation problems to multi-step problems requiring multiple operations encourages students to integrate previously learned concepts while extending their understanding of mathematical relationships. Additionally, the introduction of parentheses as a structure for organizing operations supports connections between arithmetic reasoning and future algebraic thinking.

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 include tasks that require students to interpret, analyze, and evaluate fraction models. In “Show Fraction Equivalence Using Models,” students interpret pizza models to determine whether Matty or Zain ate more by comparing the shaded portions. They analyze two fraction strips, one shaded and one unshaded, to determine whether the fractions shown are equivalent. In the Check for Understanding activity, students evaluate whether one half is equivalent to one third by shading each model and using drag-and-drop tools to justify their answer. Number lines are then introduced as another representation, giving students additional opportunities to interpret placement, analyze intervals, and evaluate fraction equivalence across models.

The materials provide an inquiry-based lesson that guides students through solving real-world problems involving addition and subtraction within 1,000. In this lesson, students apply these skills to determine how to help pass littering legislation, requiring them to analyze information in a meaningful context. After completing the mathematical tasks, students use the Reflection Question slide to explain their thinking. Students respond to prompts such as “Explain how you add multi-digit numbers together” and “What is the sum of 187, 212, and 436?” These questions require students to evaluate their process and justify their reasoning.

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

The materials provide opportunities for students to create concrete and pictorial representations of mathematical situations. In a grade 3 addition lesson, students use base-ten blocks to model addition with regrouping, creating concrete representations to solve multi-digit addition problems. Students then represent a contextual problem involving a 1,025-piece safari animal puzzle by connecting the concrete model to a pictorial or written representation that supports their solution.

The materials provide multiple opportunities for students to create concrete and pictorial representations of fractional situations. Using the Shape Tool, students draw their own shapes with equal and unequal shares to create pictorial models of fractions rather than relying on pre-made representations. Students then evaluate whether their drawings accurately represent fair shares. The lesson concludes with students using the Build a Fraction tool to construct fractions by selecting and manipulating digital pieces, providing a virtual concrete model that supports understanding of fractional relationships.

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

The materials include tasks that require students to apply their conceptual understanding to new problem situations and real-world contexts. In a grade 3 lesson on measurement and multiplication, students read and analyze a contextualized word problem involving area, identify the relevant measurements, and determine how to use the area formula to solve the situation. They then complete a written statement explaining their answer and label the solution using appropriate square units, requiring them to interpret mathematical information, transfer their understanding of area to a novel scenario, and communicate their reasoning using precise mathematical language.

The materials provide an IBL in which students apply their conceptual understanding of fractions to new, real-world problem situations as they take on the role of managing a pizzeria. Students use their prior knowledge of fractional parts to compare and reason about pizza orders, requiring them to transfer their understanding of fraction size and equivalence to an authentic scenario. Through inquiry, students create their own equivalent fractions while designing pizzas. They use prompts such as “The first pizza is cut into 8 slices, the second is cut into 12 slices, and the third is split into 16 slices.” This task requires students to apply their conceptual understanding of fractional relationships in a novel context, make sense of varying denominators, and generate equivalent representations to meet the pizzeria’s needs.

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

The materials include an activity designed to build students’ automaticity and fluency with the addition and subtraction facts needed to complete grade-level mathematical tasks. Students repeatedly connect each target number to a corresponding addition expression and a subtraction expression, requiring them to efficiently recall fact relationships and verify the accuracy of their solutions. Through ongoing identification of sums and differences and by making connections between related operations, students strengthen fact fluency and develop greater accuracy and efficiency in computation.

The materials include an activity designed to build students’ automaticity and fluency with division facts. The activity requires students to solve as many division problems as possible within a designated time frame. The activity encourages students to use their most efficient strategy, promoting rapid recall of division facts and related multiplication relationships. The timed structure provides repeated opportunities for students to apply known fact families and computation strategies with increasing speed and accuracy. As students repeatedly solve division equations, they strengthen automaticity by reducing reliance on counting or labor-intensive procedures and developing more efficient retrieval of facts.

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

The Passing a Bill into Law IBL on the Freckle platform provides multiple opportunities for students to apply efficient, flexible, and accurate mathematical procedures across a two-day learning arc. On day one, students collaborate to determine how many votes were recorded for their bill, using multi-digit addition and subtraction. Reflection prompts guide students to evaluate the efficiency of their chosen strategies and consider alternative approaches. These prompts include, “Explain how you add multi-digit numbers together” and “If you could start over, what would you do differently?” On day two, students solve a related task involving how to secure additional votes. Directions encourage them to “draw pictures or use any other strategies,” promoting flexibility as they select and adapt procedures that make sense for 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 to determine the perimeters of polygons and solve for unknown side lengths. In a grade 3 perimeter lesson, students build efficiency by repeatedly calculating perimeter through systematic addition of side lengths and by using known perimeter relationships to determine missing measurements. The lesson promotes flexibility by engaging students in multiple contexts involving perimeter. For example, these contexts include finding the total perimeter, solving for unknown side lengths, and applying perimeter concepts in real-world situations. Students strengthen their accuracy as they measure, compute, and verify side lengths and perimeters using mathematical reasoning and appropriate units.

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.

The materials include opportunities for students to evaluate mathematical representations, models, strategies, and solutions for efficiency, flexibility, and accuracy throughout learning pathways. In the grade 3 “Add & Subtract 3-Digit Numbers to Solve Word Problems” Nearpod platform lesson, students engage with multiple approaches for solving addition and subtraction word problems. The lesson presents several strategies, including using bar models and writing equations to solve one- and two-step word problems. The lesson prompts students to use both strategies while reflecting on how to identify where the unknown is in the problem. The Teacher Guide also prompts educators to allow “students to select the most efficient and appropriate strategy to solve the equation,” supporting students in reflecting on accuracy, efficiency, and flexibility as they determine which approaches are most efficient.

The materials provide inquiry-based lessons that give students opportunities 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 ______. 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.

The materials provide guidance to help students select increasingly efficient approaches to solving mathematics problems. In the Freckle Adaptive Pathway, students receive scaffolded instructional support as they solve review questions. When students select the Teach Me icon, the platform provides a step-by-step model of a similar problem, demonstrating an efficient method for solving. Students may also use the Hint feature, which provides an alternative visual model and guidance to support understanding of the problem structure, helping students move toward more efficient problem-solving approaches.

The materials also provide guidance on evaluating and refining strategies to support increasingly efficient problem-solving. In the grade 3 Passing a Bill Into Law IBL, students collaborate to solve real-world addition and subtraction problems and reflect on their solution methods. Teacher prompts guide students to compare strategies and consider how their approach could be improved. These questions include “I solved it differently than ____ because _____” and “The way that ____ explained the solution caused me to change my thinking because _____.” These reflections help students identify and adopt more efficient approaches over time.

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” that explains how Renaissance Math integrates conceptual understanding, procedural fluency, and application within the program. Conceptual understanding is supported through the Nearpod platform’s models, manipulatives, and exploratory activities. Procedural fluency is supported when teachers assign targeted Freckle platform practice aligned to daily lessons. Application is reinforced when teachers incorporate the Freckle platform’s Inquiry-Based Lessons and real-world challenges.

In the grade 3 “Fluently Multiply within 100” Nearpod lesson, the materials explicitly address the conceptual and procedural emphasis of the TEKS by first building conceptual understanding through skip counting by 6s and 7s and identifying patterns within multiplication sequences. This conceptual understanding transitions into procedural fluency as repeated practice strengthens students’ ability to recall multiplication facts and apply increasingly efficient strategies.

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 platform Targeted Practice activities provide opportunities for students to progress from pictorial representations to abstract mathematical reasoning. Throughout Freckle platform lessons, students interpret pictorial models and connect them to abstract numerical representations.

The materials provide opportunities for students to use concrete, pictorial, and abstract models as required by the TEKS. In the grade 3 “Determine the Number in Each Group” Nearpod platform lesson, students begin with concrete models by sorting jellybeans and gummy worms into equal and unequal groups, building conceptual understanding of fair shares. The lesson then progresses to pictorial representations as students create visual models of equal shares. Finally, the lesson connects these ideas to abstract representations of division, helping students generalize the concept of equal groups.

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 contain supports for students to connect, create, and explain concrete and representational models to abstract models as required by the TEKS. In the grade 3 “Multiply Teen and 1-Digit Numbers” Nearpod platform lesson, students use base-ten blocks to connect and create concrete models to abstract models, connecting “3 x 12 by counting 3 groups of 1 ten and 3 groups of 2 ones.” Students relate concrete models to abstract models of the distributive property and explain how the two are related. As the lesson progresses, the lesson introduces ways to decompose teen numbers, both pictorially and abstractly. Some methods include base-ten models, number bonds, and expressions. The materials explain the connection between the pictorial representation and the abstract model of the distributive property, and students respond to the question “How are they similar and different from the base ten models we created?” when comparing area models and base-ten models.

The materials provide opportunities for students to connect concrete and pictorial models to abstract representations as required by the TEKS. In the grade 3 Freckle platform DOK 3.4C activity, students determine the value of collections of money, identify combinations that represent equivalent amounts, and calculate change from a $20 purchase. Students interpret concrete and pictorial representations of money and connect visual models to abstract numerical reasoning.

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

In the grade 3 “Academic Vocabulary” lesson for the term group, students complete listening and writing tasks using visuals and contextual examples. For example, students examine the sentence, “The fruits are arranged in groups.” Students then apply the vocabulary during a “Real World Connection” activity that presents a visual of a group of tigers at a Scottish zoo, paired with related discussion questions. A think-air-share routine gives students further practice using the term in conversation, and afterward they complete a writing or drawing task to represent the meaning of “group”. Together, these activities build academic mathematical language through speaking, listening, writing, and visual representation.

In the grade 3 “How, What, Why Questions: Division Interpretation” activity, students develop academic mathematical language by reviewing vocabulary such as dividend, divisor, and quotient through a labeled equation model (dividend ÷ divisor = quotient) connected to real-world division scenarios. Students then analyze classmates’ written arguments explaining their reasoning and use word-bank phrase fragments to construct questions that demonstrate understanding of division vocabulary. Students answer questions such as, “Why did you divide the dividend by 3?” and, “What is the dividend that we are dividing equally?” Students read their completed questions aloud, using academic mathematical language in both written and oral contexts.

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 grade 3 “Add & Subtract to Solve Word Problems Within 1,000” teacher resource, the Guiding Questions prompt teachers to foster comprehension of the problem-solving process. For example, the materials include questions such as, “What do the quantities represent in the problem?” and, “Will you need to do more than one step to solve this problem?” However, these questions do not direct teachers to model or elicit the lesson’s academic vocabulary, such as expression, equation, sum, and difference, during student discourse. The Vocabulary section defines these terms for teacher reference. However, it is separate from the Guiding Questions and does not provide educators with guidance for prompting students to apply this vocabulary when explaining their reasoning to peers or the teacher.

The Teacher Resource for “Divide Within 100 Using Base Ten” lists academic terms such as dividend, divisor, and quotient with definitions only. While students encounter these terms within the slide deck, the resource does not direct teachers on how to model, prompt, or facilitate students’ use of this vocabulary in peer or teacher discourse.

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 general sample sentence frames, such as “I used ___” and “I know my answer is right because ___.” The guide also encourages teachers to “use interactive checks” and “require structured talk,” supporting students’ use of academic mathematical language during discourse. These prompts provide teachers a consistent structure for prompting students to communicate their reasoning using academic vocabulary across lessons.

In a Renaissance Math lesson on arrays, students construct an array through a drag-and-drop activity and then use fill-in-the-blank sentence frames to describe the number of rows and columns in their model. These embedded stems scaffold students’ use of academic mathematical vocabulary, including the terms array, rows, and columns, while supporting them in communicating their mathematical thinking with peers and the teacher. Pairing hands-on modeling with structured language supports helps students accurately describe mathematical representations and communicate their mathematical thinking.

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

In the grade 3 materials, the Renaissance Math Solution Guide requires structured partner talk. The guide directs students to rehearse with a partner and share out using sentence stems such as “My strategy was ___ because ___” and “I checked my work by ___” to justify their reasoning. Requiring consistent use of these stems during partner talk reinforces a productive discourse routine that supports students in communicating their mathematical thinking.

In the grade 3 Freckle platform IBLs, students work together to solve a problem, discuss their reasoning as a group, and select a spokesperson to share the team’s thinking with the class. This gives students the opportunity to hear math language from peers. The lessons also include sentence frames that help students structure explanations, use precise mathematical vocabulary, and refine their language as they respond to classmates and build on one another’s ideas. Together, these supports let students hear, refine, and use mathematical language during peer discourse.

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.

Within 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 only show the correct response, not examples of exemplary work or a variety of anticipated student answers. Nearpod platform skill resources include a “Common Misconceptions” section in the “Teacher Resource” document. However, it is separate from the answer key and identifies only one general misconception, rather than providing redirection questions or alternative strategies for teachers to use when checking student work.

Within 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 only show one equation or expression used to reach the correct answer, without exemplar responses or a variety of anticipated student work. The Providing Feedback guide outlines redirect scripts and next-step actions for common error types, but this guidance is not embedded within the IBL answer key itself, so teachers get 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 Inquiry-Based Lesson on the Freckle platform structures students’ daily work around TEKS 3.1B. The lessons guide them through a problem-solving model that involves analyzing the given information, forming a plan, arriving at a solution, and evaluating the reasonableness of that solution. 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 3.1A by using this problem-solving model to address a real-world task.

In the “Solve Addition and Subtraction Word Problems” Nearpod platform lesson, students work through a problem-solving process that reflects components of TEKS process standard 3.1B. They use the Highlighter tool to identify important information in each word problem, write an equation to represent it, and solve it using a strategy of their choosing before dragging the matching robot onto the box with the correct answer. The lesson also applies process standard 3.1A by situating these problems in a real-world workplace scenario—a robot factory tracking daily packaging totals—which provides students with an authentic context for applying addition and subtraction.

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, “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.” While the materials reference how the process standards are included, they do not describe where those standards are incorporated throughout the learning pathways.

The Renaissance Math 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 only charts content skills, such as place value, fractions, and measurement. Additionally, the guide charts resource titles by grade level, indicating which domains appear at each grade. The “Alignment Across and Within Grades” section goes further in 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, that 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, a teacher using the Renaissance Math 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 TEKS process standards. The guide 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 Renaissance Math Solution Guide’s general overview section, and the guide does not show which process standard applies to any individual lesson.

The Teacher Resource template used for individual Nearpod platform skills, such as “Add & Subtract to Solve Word Problems Within 1,000,” does not include a TEKS process standard reference in the lesson document. Instead, its “Mathematical Practice Application” section labels each activity with a Common Core Standard for Mathematical Practice. For example, MP1: make sense of problems and persevere in solving them for the draw-it activity, and MP2: reason abstractly and quantitatively for the drag-and-drop activity. These give no 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 grade 3 “At the Box Office” lesson engages students in mathematical thinking, perseverance, and sense-making. The lesson provides a real-world scenario in which students compare fractions to prepare for an opening weekend at the theater. Questions such as “Can you compare the popularity of the theaters by looking at the fraction of seats filled?” prompt students to think mathematically and make sense of mathematics. The questions lead students to interpret fractional quantities and explain the rationale behind their comparisons. On the final day of the lesson, students create a display poster advertising the top three movies, persevering through problem solving by analyzing fractional data, revisiting earlier comparisons, and justifying which theaters had the highest attendance. This extended application requires students to synthesize information and communicate their mathematical reasoning.

In the Renaissance Math lesson “Decompose Up to 4-Digit Numbers,” students engage in mathematical thinking and make sense of mathematics. The lesson opens with a real-world inquiry: “What are some ways we can represent the number 1,025?” This prompt requires students to interpret the quantity, identify its structure, and consider multiple valid representations. The materials explicitly teach that ten hundreds compose 1,000. Students apply this understanding by determining which base-ten block sets accurately represent 1,000, reinforcing conceptual place-value relationships. Throughout the lesson, students identify numbers shown in place value, standard form, and expanded form, supporting their ability to interpret and compare multiple representations of the same number.

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

The Inquiry-Based Lesson “Giuseppe’s Pizzeria” guides students to understand, explain, and justify multiple solution paths through the context of managing a pizzeria. Across four days, students compare fractions, generate equivalent fractions using visual models, and represent whole numbers as fractions to solve authentic pizzeria problems involving orders, promotions, website issues, and planning for Pizza Palooza. Working through scenarios such as determining whether a principal’s order qualifies for the Super Splitz promotion, students recognize that fraction relationships can be solved using different models and strategies. Using the Inquiry Sheets, students explain how they determined equivalence and how their visual models support their conclusions. In the culminating Pizza Palooza project, students analyze tasting-event data and recommend which specialty pizzas to add to the menu, justifying their conclusions with fraction models and demonstrating that different approaches can lead to valid solutions.

In the lesson “Decompose Up to 4-Digit Numbers,” students learn to understand, explain, and justify multiple solution paths. Students begin with the inquiry “What are some ways we can represent the number 1,025?” which prompts them to recognize that a single quantity can be represented in multiple valid ways. This supports students’ understanding that different approaches can lead to the same result. The materials teach that ten hundreds compose 1,000, and students explain this idea by identifying which base-ten block sets correctly represent 1,000, articulating why different groupings still show the same value as they compare models. Throughout the lesson, students justify that multiple solution paths are valid by explaining numbers shown in different forms, including place-value charts, standard form, expanded form, and other representations, and describing how each representation accurately models 1,025.

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.

In the Nearpod lesson “Represent and Solve Multiplication Word Problems,” students do math, write about math, and discuss math with peers and educators through structured Think, Practice, Write, and Collaborate slides. Students do math on Think slides. For example, students solve problems such as “Will Pao have enough room on her music player to download all 8 songs?” and work through the multiplication needed to answer the problem, sharing their thinking with a peer or educator. Students write about math on Write slides, recording their answers, completing models, and representing their reasoning in written form. Students discuss math on Collaborate slides, which return to the original problem and ask students to write and solve an equation using a chosen strategy, sharing their reasoning and comparing approaches with peers.

In the grade 3 Nearpod lesson “Add Within 1,000 Using Algorithms,” the materials state, “as we complete each step…,” which signals that students are expected to do math collaboratively. Students do math collaboratively by building the equation, analyzing each step, and completing the work alongside peers or the educator, actively engaging in the problem-solving process rather than passively observing. The lesson also provides opportunities for students to discuss math on a Think About It slide. This slide opens with a discussion prompt structured to initiate mathematical conversation as students share their initial reasoning. Students write about math by recording the sum for each set of base-ten blocks, giving them a structured opportunity to represent their mathematical thinking in writing. Later in the lesson, students further engage in writing and doing math by writing the number, finding the sum, and adding to determine the answer, reinforcing mathematical sense-making through both written and hands-on work.

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

Renaissance Math equips educators to guide students in sharing and reflecting on their problem-solving approaches, including their explanations, arguments, and justifications. Within the Nearpod platform, educators can build a Collaborate Board into 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.” Within a Collaborate Board, educators can add word problems aligned to the lesson and pose questions that require students to share how to solve problems by explaining, justifying, reflecting, and evaluating their own problem-solving approaches as well as others’.

The “Giuseppe’s Pizzeria” IBLs equip educators to guide students in sharing and reflecting on their problem-solving approaches as they develop an understanding of equivalent fractions through real-world situations. Over four days, students compare fractions, generate equivalent fractions, and represent whole numbers as fractions while running a pizzeria project. They explain their thinking, discuss ideas, and justify conclusions with fraction representations. Students explain how they determined equivalence, such as by checking whether a principal’s order qualifies for the Super Splitz deal and recording their reasoning on daily inquiry sheets. They argue for their solutions by comparing strategies and defending decisions about orders, website issues, and menu selections, and justify their conclusions with mathematical evidence. For example, in the Pizza Palooza project, students use tasting-event data to recommend specialty pizzas. As tasks build from comparing fractions to a culminating real-world project, students reflect by revisiting and refining their strategies.

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 programs within the Freckle Adaptive Pathway 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, then allows the student to reattempt the problem after working through these supports.

The Teacher Resource document accompanying a Nearpod lesson provides teachers with information about student misconceptions but does not offer guidance on translating that information into student feedback. A “Common Misconceptions” section identifies the errors students are likely to make on the lesson’s content. Additionally, an item analysis for the pre/post-assessment explains why the response is correct or incorrect for each answer choice and is supported by an answer key for the lesson’s activities. None of these resources, however, direct teachers on how to respond to an individual student’s specific answer or misconception with explanatory feedback. The materials only identify and explain errors, without offering prompts to support educators in giving feedback.