HMH Into Math Texas, Grade 3

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

The materials include multiple scope and sequence resources that clearly outline the Texas Essential Knowledge and Skills (TEKS), English Language Proficiency Standards (ELPS), and concepts taught throughout the course. The materials include yearlong scope and sequence information in the Program Overview and the Implementation Guide.


The scope and sequence charts include the TEKS and ELPS alignments for each module and lesson and identify the concepts taught throughout the instructional year. Additional materials further support this alignment through TEKS and ELPS correlations and “Correlations by Lesson” documents that break down concepts taught by module. In the “Discover” tab, the scope and sequence also outlines the TEKS, ELPS, and lesson concepts to support instructional planning and pacing.

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

The materials provide a “Scope and Sequence with Yearly Pacing” for 165-day and 210-day instructional calendars. The guidance provided in the calendar “moves step by step through each module and shows how each module covers the instructional sequence and standards, and then lists each Module Review and Module Test.” These options support effective implementation to remain aligned with the TEKS, ELPS, and course concepts.

The materials provide guidance on extending the 165-day pacing calendar to 180 days by adding “one extra day to each lesson where a Readiness Standard is first taught.” Educators can use the extra day to provide targeted reinforcement, practice, or challenges using formative assessments, quick checks, and observations.

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

The materials include clear explanations of the unit rationale and lesson order and explain how concepts connect throughout the course. The Teacher’s Guide includes a “Module Order Rationale” that outlines the sequence of modules and describes how the organization reflects natural mathematical progressions and students’ cognitive development.

The materials explain how concepts build across modules and lessons to develop deeper mathematical understanding. For example, students represent and compare whole numbers using place-value concepts before progressing to representing and comparing fractions. The materials also explain how addition and subtraction concepts progress from fluently solving problems within 1,000 to applying place-value strategies, estimating sums and differences, and using flexible problem-solving strategies.

Additionally, multiplication instruction progresses from counting equal-size groups and relating addition to multiplication to representing multiplication with arrays, number lines, and strip diagrams before applying multiplication properties and solving word problems. The materials further explain how fraction concepts develop from comparing fractions using objects and pictorial models to reasoning about equivalent fractions and applying problem-solving strategies.

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

The materials include guidance that supports educators with unit and lesson internalization through comprehensive planning supports, structured instructional routines, and embedded educator guidance. The Teacher’s Guide provides planning support that reviews the standards, outlines what students will learn in each module, explains the module flow, identifies the TEKS and ELPS, and includes background information to support instructional preparation and lesson internalization.

The materials also include resources that help educators understand the sequence of learning in each module and prepare for daily instruction. The “Before You Teach” sections outline the mathematical understanding needed for each lesson and explain what students will learn. Planning tools such as the “Editable Lesson Plan,” pacing guidance, module flow charts, and lesson sequencing explanations support educator preparation.

Additionally, the “Step Through a Module” section of the Implementation Guide provides guidance for internalizing module and lesson components, and the “Teacher Background” sections include mathematical rationale, examples, summaries, and explanations of the importance of concepts to deepen educator understanding before instruction. The materials also include a “Module Internalization Tool” and “Lesson Internalization Tool” that provide protocols to support module and lesson internalization through guiding questions such as “What concepts, strategies, or procedures will students learn?” and “What do the lesson and language objectives expect from students?” Educators can use the tools individually or collaboratively as note-taking or discussion guides in preparing for and internalizing upcoming modules and lessons.

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

The materials include resources and guidance documents for instructional leaders to support educators with implementing the program as designed. The materials provide implementation supports through resources such as the Professional Learning and Coaching Guide, which includes instructional support, implementation guidance, pacing recommendations, and professional learning resources to assist leaders in supporting effective program use.

The materials also include tools that support classroom observations, reflection, and coaching conversations. For example, the Look-Fors and Reflection Guide provides classroom observation indicators, implementation expectations, reflection questions, and suggested discussion topics to help instructional leaders monitor instruction and support educator planning.

Additionally, the materials include look-for checklists designed for the first 30 days of instruction and reflection tools and guiding questions to support classroom visits, targeted feedback, and ongoing instructional implementation conversations with educators.

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

The materials include comprehensive unit overviews that provide the background content knowledge and academic vocabulary necessary to effectively teach mathematical concepts. The materials include educator guidance that supports concept development by outlining prior learning connections, strategy examples, instructional explanations, and academic vocabulary at the beginning of each unit.

The materials provide educator background information, examples, summaries, and explanations of mathematical concepts to support understanding and procedural fluency. For example, they offer guidance for teaching addition and subtraction within 1,000 through place value, expanded notation, estimation, regrouping, and modeling with equations and drawings. The materials also support multiplication instruction through explanations of equal groups, arrays, multiplication facts, properties of operations, comparisons, and problem-solving.

Additionally, the fraction modules include prior learning connections, vocabulary, and educator guidance to support understanding of fraction models, equivalent fractions, and comparison strategies. The materials further support educator understanding through a “Teacher’s Glossary” section that includes academic vocabulary introduced in each module and mathematical definitions to support instructional delivery and mathematical understanding.

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

The materials include supports for families through “Family Letters” in both English and Spanish for each module. The materials support communication and family engagement by explaining unit learning goals, introducing key academic vocabulary, and providing guidance for supporting student learning at home.

The “Family Letters” include lesson-specific online resources, home activities, and suggestions for reinforcing mathematical concepts through real-world applications and mathematical discussions. For example, the materials provide activities that support concepts such as multiplication and perimeter through hands-on practice and real-world objects. Additionally, the materials include guidance for families on how to support student progress using online resources such as “Practice Plus” and activities that reinforce in-class learning outside school.

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

The materials include comprehensive, structured, and detailed lesson plans that provide daily objectives, instructional tasks, required materials, guiding questions, and instructional assessments aligned with the TEKS and ELPS. Each lesson includes learning and language objectives, instructional routines, discussion opportunities, practice tasks, and assessment opportunities aligned with the lesson goal. Additionally, the “Before You Teach” section at the beginning of each lesson supports educator planning through TEKS and ELPS correlations, lesson objectives, questions, tasks, and assessments designed to support student mastery.

The materials also include hands-on instructional supports and embedded opportunities for student discourse and formative assessment. For example, lessons identify manipulatives and materials such as foam counters, color tiles, hundred charts, fraction circles, fraction tiles, counters, and digital fraction bars to support conceptual understanding. Lessons such as “Count Equally-Sized Groups” and “Decompose Fractions into Sums” include clearly defined learning objectives focused on mathematical reasoning and problem-solving using concrete and pictorial models.

The materials also incorporate routines such as “Spark Your Learning,” “Learn,” “Assess,” “Three Reads,” “Collect and Display,” “Compare and Connect,” “Turn and Talk,” and “Quick Checks” to support student engagement, mathematical discussions, and ongoing assessment of understanding and integrate the TEKS mathematical process standards and ELPS expectations for communication, reasoning, speaking, and writing.

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

The materials include lesson overviews that identify the educator and student materials necessary for effective lesson implementation and provide suggested timing for instruction. The overviews and “Before You Teach” sections outline the manipulatives, resources, and instructional materials needed for each lesson and instructional group.

The materials include clear instructional routines, hands-on supports, and embedded opportunities for student discourse and formative assessment. For example, the lessons identify manipulatives and materials such as foam counters, color tiles, hundred charts, fraction circles, fraction tiles, counters, and digital fraction bars to support conceptual understanding.

The materials also provide suggested time allocations for lesson components, including approximately 45 minutes for Essential Sessions and additional time for “Differentiation and Practice” opportunities. The “Step Through the Module” and “Before You Teach” sections outline timing expectations for lesson routines such as “Learning Goals,” “Spark Your Learning,” guided instruction, and assessment activities. Additionally, the lessons include instructional structures and routines such as “Learn” and “Assess” to support pacing, lesson delivery, and student engagement throughout instruction.

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

The materials include guidance for effective extended practice through differentiated activities, independent practice opportunities, homework, and enrichment resources connected to each lesson. Each lesson provides a clear overview of the instructional components, including lesson objectives, academic vocabulary, required materials, and resources needed to support effective lesson implementation.

The materials also include ”Differentiation and Practice” sections that guide educators in selecting appropriate next steps based on student needs. For example, the “Program Activity Report” provides guidance for selecting resources aligned with student performance, including opportunities for review, additional practice, or extensions. The “Differentiation and Practice” sections included after lessons guide educators through instructional decisions and questioning strategies to support students who require intervention, reinforcement, or enrichment.

Additionally, independent practice rotations, “Project-Based Learning” opportunities, and digital supports provide continued reinforcement and extended learning beyond the core lessons.

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

The materials include a variety of instructional assessments at both the lesson and unit levels, including diagnostic, formative, summative, and performance-based assessments. The assessment system includes “Benchmark Assessments,” “Prerequisite Checks,” “Quick Checks,” Module Reviews, Module Tests, and Module Projects that provide multiple opportunities to monitor student progress and measure mastery of grade-level content.

The materials include varied task types and questioning structures to assess student understanding in multiple ways. For example, “Prerequisite Checks” assess readiness before each module, “Quick Checks” provide formative assessment opportunities during and after instruction, and Module Tests measure mastery of skills taught in each module through a variety of item types, including multiple-choice, open-ended, drag-and-drop, and fill-in-the-blank questions.

Additionally, Module Projects engage students in Depth of Knowledge (DOK) Level 4 tasks that require the application and extension of mathematical understanding. The lessons also include opportunities for students to demonstrate learning through problem-solving activities, estimation tasks, written explanations, equations, models, arrays, strip diagrams, repeated addition, and real-world applications, which allows students to communicate their understanding using multiple representations.

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

The materials include clear definitions and explanations of the intended purposes for the various assessment types used throughout the program. The Implementation Guide and Program Assessments at a Glance resources identify the formative and summative assessments and provide information regarding their purpose, benefits, administration, access, and recommended timing throughout the school year.

The materials explain how each assessment supports instruction and monitors student progress. For example, “Prerequisite Checks” assess previously learned concepts and help determine student readiness for a module, and “Quick Checks” provide formative data after instruction to identify students who need support, additional practice, or enrichment. Module Projects are performance-based assessments that engage students in DOK Level 4 tasks that apply and extend mathematical understanding.

Additionally, Module Tests are summative assessments that measure student understanding of the TEKS and mathematical process standards taught in a module and monitor mastery of content and mathematical practices. The materials also include “Data-Driven Support” tables that help educators analyze prerequisite understanding, determine readiness for instruction, and make decisions regarding reteaching and reassessment based on student performance data.

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

The materials include educator guidance that supports the consistent and accurate administration of instructional assessments. The assessment resources provide clear information regarding the purpose, timing, format, duration, and administration of assessments to promote consistent implementation across classrooms.

The materials include guidance for administering both formative and summative assessments. For example, the Program Assessments at a Glance resource identifies when educators should administer assessments: before each module by using “Prerequisite Checks,” after instructional tasks by using “Quick Checks,” and at the end of each module by using Module Tests. The materials also provide suggested administration times and identify assessment formats, including digital assessments, editable files, and PDFs.

The Module Test guidance includes information on the purpose, administration procedures, and recommended duration (approximately 45 minutes) and also includes sections such as “What Should I Do?” “What More Can I Do?” and “What Can I Aspire to Do?” to assist educators with implementation. The “Quick Checks” and “Learning Goal” resources provide educator guidance for collecting formative assessment data, monitoring mastery of lesson objectives, and determining appropriate instructional next steps based on student performance.

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

The materials include formative and summative assessments that align with the TEKS and instructional objectives of the lessons and modules. Assessment resources include item guides, answer keys, and assessment documentation that identify TEKS alignment, DOK levels, lesson connections, and scoring guidance to ensure that assessments measure the intended learning outcomes.

The materials demonstrate alignment among assessment tasks, lesson objectives, and the TEKS throughout the program. For example, the module 4 assessments, including the “Prerequisite Check,” Module Review, Module Test, and Module Project, align with the TEKS and objectives focused on solving and estimating addition and subtraction problems within 1,000. Similarly, the module 6 assessments align with the TEKS that address multiplication concepts and problem-solving. The formative assessments, such as “Quick Checks” and “Practice on Your Own” tasks, directly connect to lesson learning goals and TEKS-based instructional objectives.

Assessment item guides identify the TEKS assessed, DOK levels, and aligned instructional tasks, and Module Test answer keys identify the correct response for each item, provide the TEKS correlations, include point values and scoring rationales, and support accurate interpretation of student performance. Additionally, the diagnostic “Benchmark Assessments” include answer keys with a TEKS correlation table that aligns each assessment item with the corresponding TEKS and specific lessons and provides evidence of alignment among the assessments, course standards, and instructional content.

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

The materials include TEKS-aligned assessment items at varying levels of complexity across lessons and modules. Assessment resources incorporate multiple DOK levels and provide opportunities for students to demonstrate understanding through modeling, explaining, solving, justifying, and applying mathematical concepts.

The materials include formative and summative assessments that progress from foundational skills to more complex reasoning and problem-solving. For example, assessment tasks include one-step and two-step addition and subtraction problems, estimation and reasonableness tasks, equal groups, repeated addition, arrays, strip diagrams, number lines, and multistep problem-solving activities aligned with the grade-level TEKS. Lesson assessments include DOK Levels 1–3 questions that support increasingly complex thinking, and Module Test answer keys identify the DOK level and TEKS alignment for assessment items.

Additionally, Module Projects provide opportunities for students to engage in DOK Level 4 tasks that extend mathematical application, reasoning, and problem-solving. Assessment answer keys also include the TEKS correlations for each item, which ensures alignment between assessment tasks and the content taught in the module.

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

The materials include instructional assessments and scoring information that provide guidance for interpreting student performance and using assessment data to inform instruction. The assessment system includes diagnostic, formative, and summative measures such as “Prerequisite Checks,” “Quick Checks,” Module Reviews, Module Tests, and Module Projects, which provide multiple opportunities to monitor student understanding and mastery of the grade-level TEKS and lesson objectives.

The materials support educators in analyzing assessment results and determining appropriate instructional next steps. For example, Module Reviews identify key vocabulary, concepts, and skills for students to review prior to the Module Test, and the accompanying “Data-Driven Support” tables connect assessment results to the specific TEKS, content areas, and recommended reteaching resources or lessons. Assessment answer keys provide correct responses, scoring guidance, explanations of student responses, and rubrics for open-ended items to support accurate interpretation of student performance.

Additionally, Module Projects include scoring rubrics that evaluate mathematical understanding, reasoning, and completeness across multiple proficiency levels. When assessments are administered digitally, educators can access class and student performance data to identify trends, determine mastery levels, and select targeted intervention, on-level support, or enrichment activities to address student needs.

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

The materials provide guidance for using instructional tasks and activities to respond to student trends in assessment performance through differentiated support and data-driven instructional planning. The materials include “Data-Driven Support” tables, “Differentiation and Practice” guidance, assessment reports, and targeted instructional recommendations that help educators address student learning needs.

The materials guide educators in analyzing assessment results and selecting appropriate instructional responses based on student performance. Guidance directs educators to review “Program Activity Reports” and assessment data to determine student mastery and identify students who will benefit from small-group instruction, reteaching, additional practice, or enrichment. The “Differentiation and Practice” resources provide a structured process for grouping students and assigning targeted supports, including “Almost There” reteach activities, “On Track” practice activities, “Ready for More” or “Extension” activities, “Practice Plus” homework, and personalized adaptive practice through Waggle.

Additionally, “Data-Driven Support” tables connect assessment results to specific reteaching resources, lessons, and activities that are available in digital and printable formats. Assessment guidance also includes performance thresholds that help educators determine appropriate instructional pathways and respond to patterns in student understanding, misconceptions, and learning gaps.

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 educator-facing and student-facing tools that support monitoring student progress and growth throughout the school year. These tools provide educators resources such as the “Whole-Class Proficiency and Growth Tracker,” “Program Activity Reports,” “Assessment Reports,” “Standards Reports,” “Growth Reports,” and TEKS proficiency reports available through “Ed” to monitor student performance, identify trends, and inform instructional decisions.

The materials also include tools to support student goal-setting, self-assessment, and reflection. Students use “Learning Goal” routines during lessons to assess their understanding of lesson objectives and reflect on their progress toward goals. At the beginning of each lesson, students preview an “I Can” statement and revisit it at the end of the lesson to evaluate their understanding.

Additionally, the “Student Learning Tracker” allows students to establish goals; reflect on growth at the beginning, middle, and end of the year; track Module Test scores; and compare assessment results to personal goals. These resources provide ongoing opportunities for both educators and students to monitor growth, celebrate progress, and make informed decisions about future learning.

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

The materials include educator guidance for differentiated instruction and scaffolded support for students who have not yet reached proficiency in grade-level content and skills. Each lesson includes differentiated learning opportunities, targeted small-group instruction, and reteaching resources to address learning gaps and support access to grade-level content.

The materials provide structured supports through “15+ minutes of suggested Differentiation and Practice opportunities,” educator-led small-group activities, intervention resources, collaborative learning experiences, games, and independent practice. The “Data-Driven Support” tables guide educators in using assessment data to determine instructional responses and select targeted supports for students who need additional assistance. The “Almost There” small-group activities provide explicit educator guidance, questioning strategies, manipulatives, visual models, and step-by-step instruction to build conceptual understanding before students apply grade-level concepts independently. The materials include multiple representations to support understanding, including fraction circles, strip diagrams, number representations, arrays, number lines, and base 10 manipulatives.

The lessons provide additional supports through “Mathematical Language Routines,” vocabulary instruction, “Turn and Talk” opportunities, guided practice, and intervention activities that promote student learning and participation.

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

The materials include embedded supports for unfamiliar vocabulary, academic language, and references to support student access to and communication of mathematical concepts. The lessons incorporate content-specific vocabulary instruction, student-friendly definitions, visual representations, structured discussion opportunities, and educator guidance to support language development and comprehension of grade-level content.

The materials provide dedicated vocabulary supports through routines such as “Words to Learn,” “Mathematical Language Routines,” and ELPS Teaching Strategies. Educators receive guidance for introducing, discussing, and reinforcing academic vocabulary before and during instruction. Support for mathematical terms such as unit square, break apart, and congruent includes definitions, visual models, word banks, sentence stems, and guided discussions. “Mathematical Language Routines” such as “Three Reads,” “Compare and Connect,” and “Stronger and Clearer Each Time” support the development of mathematical language and the explanation of mathematical reasoning.

Educator guidance supports connections between unfamiliar concepts and real-world experiences, such as relating unit squares to painting walls, tiling floors, paving roads, and filling gardens with soil. Embedded ELPS Teaching Strategies support comprehension through context clues, structured conversations, and scaffolded responses to help students understand unfamiliar references, figurative language, and academic concepts.

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

The materials include educator guidance for differentiated instruction, enrichment, and extension activities for students who have demonstrated proficiency in grade-level content and skills. Each lesson includes differentiated learning opportunities and small-group activities to extend learning, deepen conceptual understanding, and provide additional challenges for students who are ready for advanced work.

A range of research-based instructional routines and scaffolds support effective instruction. Guidance prompts educators to use routines such as “Three Reads,” “Turn and Talk,” “Collect and Display,” “Defend,” and “Process Standards” to support student understanding and mathematical discourse. The materials incorporate whole-group instruction, partner discussions, hands-on exploration, and independent practice throughout lessons and guide transitions between instructional formats. Supports include Universal Design for Learning (UDL), guidance for addressing common errors, emergent bilingual supports, and connections to prior learning to address diverse student needs. Features such as representation strategies, sentence frames, word banks, visual models, and questioning techniques support student engagement and understanding of mathematical concepts. The instruction incorporates manipulatives and models such as fraction tiles, fraction circles, number lines, arrays, and digital tools, and DOK questions promote reasoning, justification, and complex thinking.

Each Module Project provides a DOK Level 4 learning experience that synthesizes concepts and applies understanding in authentic, real-world contexts. Projects such as “Millions of Apples” require students to analyze information, make conjectures, justify decisions, and solve complex real-world problems using grade-level mathematics. The materials do not include explicit guidance identifying separate instructional pathways specifically designed for students who have already demonstrated proficiency.

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

The materials include explicit prompts and educator guidance that support the modeling and explanation of mathematical concepts throughout instruction. Guidance for educators includes explanations of mathematical concepts, worked examples, summaries of key understandings, learning objectives, recommended manipulatives, and instructional routines to support the clear modeling of concepts and mathematical reasoning.

The lessons provide direct instructional prompts and questioning strategies to guide the explanation of concepts and facilitation of mathematical discourse. The materials include questions such as “How do you know how many equal groups there are?” “How can you represent equal groups?” “What does each factor represent in the multiplication equation?” and “How can you use the equal groups to determine the total?” to support connections between equal groups, repeated addition, and multiplication. The materials also provide possible student responses, visual models, worked examples, and guidance for addressing misconceptions.

The materials include instructional routines such as “Three Reads,” “Turn and Talk,” “Discussion Supports,” and “Words to Learn” to support the modeling of mathematical thinking and development of student understanding. Step-by-step guidance in the Teacher’s Guide supports lesson facilitation, analysis of student thinking, and opportunities for students to compare solution strategies and explain their reasoning. The program embeds consistent support for modeling, explaining, and reinforcing mathematical concepts and skills throughout the modules.

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

The materials include educator guidance and recommendations for effective lesson delivery and facilitation using a variety of instructional approaches. Instructional supports include routines and strategies to support student engagement through multiple methods of representation, discussion, exploration, and problem-solving.

The materials support effective instruction through a range of research-based instructional routines and scaffolds. Educator guidance explains the use of routines such as “Three Reads,” “Turn and Talk,” “Collect and Display,” “Defend,” and “Process Standards” to support student understanding and mathematical discourse. The materials incorporate whole-group instruction, partner discussions, hands-on exploration, and independent practice throughout lessons and provide guidance for transitions between instructional formats. Universal Design for Learning (UDL) materials include support for addressing common errors, guidance for addressing diverse student needs, and connections to prior learning. The guidance includes representation strategies, sentence frames, word banks, visual models, and questioning techniques to support student engagement and understanding of mathematical concepts. The lessons incorporate manipulatives and models such as fraction tiles, fraction circles, number lines, arrays, and digital tools throughout instruction, and DOK questions promote reasoning, justification, and complex thinking.

Assessment resources such as “Quick Checks” provide guidance for evaluating both content and language objectives and include recommendations for instructional next steps. The materials embed multiple instructional approaches to support meaningful learning experiences and student success.

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

The materials support multiple types of practice and provide educator guidance and instructional structures to support implementation. The lessons incorporate guided, collaborative, and independent practice opportunities, allowing students to explore mathematical concepts through a variety of instructional formats and learning experiences.

Structured opportunities for practice include whole-group instruction, educator-led small groups, collaborative partner work, and independent practice. The lessons include Essential Sessions, “Mathematical Language Routines,” “Turn and Talk” discussions, problem-solving activities, games, and “Differentiation and Practice” opportunities. Step-by-step guidance explains instructional routines such as “Learning Goals,” “Three Reads,” and “Turn and Talk,” and the materials include recommendations for facilitating mathematical discourse and student collaboration. Small-group activities include materials lists, grouping recommendations, implementation procedures, and expectations for student interaction. Differentiated practice options include “Almost There,” “On Track,” “Challenge” or extension activities, and independent “Practice Plus” assignments.

The “Lesson Pacing Guidance” provides recommended instructional frameworks that balance whole-class instruction with collaborative groups, independent practice, and educator-led small-group instruction. The lessons provide multiple opportunities for students to practice, apply, discuss, and extend their learning through a variety of instructional structures.

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

The materials guide educators to support students at varying levels of English language proficiency and promote the use of academic language. The lessons embed dedicated emergent bilingual supports aligned with the ELPS, instructional routines, vocabulary-development opportunities, and language scaffolds to support student participation in mathematical discourse.

The “Emergent Bilinguals” and “Supporting All Language Learners” sections provide differentiated linguistic accommodations that are appropriate for multiple proficiency levels, including pre-production/beginning, intermediate, and high intermediate/advanced. Concrete models, pictures, gestures, and simple words support beginning-level students in communicating mathematical thinking. The materials give intermediate students simple sentences and visual references to explain reasoning, and they guide advanced students toward the use of abstract representations, written equations, and increasingly sophisticated oral and written explanations. Response scaffolds, sentence frames, word banks, vocabulary routines, and “Mathematical Language Routines” such as “Three Reads”, “Compare and Connect”, and “Stronger and Clearer Each Time” help students use increasingly precise academic language.

Structured opportunities for speaking, listening, reading, and writing about mathematics include partner discussions, collaborative learning experiences, and mathematical discourse activities. These embedded supports help educators implement appropriate linguistic accommodations and foster academic language development across proficiency levels.

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

The materials include implementation guidance for educators using the materials with emergent bilingual students in bilingual and English as a Second Language (ESL) instructional settings. The instruction integrates language development through lesson-level language objectives, ELPS-aligned supports, vocabulary-development routines, and instructional strategies designed to promote both mathematical understanding and academic language growth.

Resources such as the “Language Growth for All Learners” and Language Development Resource Guide provide guidance on embedded language supports across lessons and instructional routines. Educators get support from observable and measurable language objectives, ELPS connections, visual vocabulary supports, formative language assessment tools, and scaffolds for varying levels of language proficiency. Supports such as the “Words to Learn” routine, vocabulary cards, sentence stems, word banks, “Mathematical Language Routines,” and discussion protocols promote mathematical communication and academic discourse.

The Language Development Resource Guide highlights language supports embedded throughout Essential Sessions, “Spark Your Learning” activities, instructional tasks, formative assessments, and ELPS-specific teaching strategies. Resources such as the 4Ls routine (“Look, Lean, Lower, and Listen”) provide explicit guidance for supporting student participation and collaborative conversations. The lessons provide ELPS supports that allow teachers to plan and implement targeted language development opportunities and maintain access to grade-level mathematics content. The materials include comprehensive guidance for integrating language supports in bilingual and ESL instructional settings.

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

The materials include embedded guidance for educators 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 lessons embed ELPS-aligned supports, vocabulary routines, discussion protocols, sentence stems, word banks, and “Mathematical Language Routines” to promote both language development and mathematical understanding.

The materials support academic vocabulary development through routines such as “Words to Learn,” visual vocabulary supports, sentence frames, and structured opportunities for students to use content-specific language in speaking and writing. The materials strengthen comprehension and background knowledge through routines such as “Three Reads,” educator questioning, “Discussion Supports,” and collaborative discourse activities that help students understand mathematical situations and connect new learning to prior knowledge. Questions focus on understanding the context of a problem, identifying important quantities, and explaining mathematical reasoning, and the instruction incorporates opportunities for “Turn and Talk” discussions and written responses using academic vocabulary.

Explicit support for cross-linguistic connections helps educators teach cognates such as decomposition/descomposición, value/valor, and digit/dígito, and the materials encourage students to use their home-language knowledge to support their comprehension of mathematical concepts. The materials prompt educators to pair students who share the same home language, provide opportunities for students to discuss ideas orally before writing, and use sentence stems and word banks to support both oral and written discourse. Meaningful opportunities for mathematical communication support academic vocabulary, comprehension, background knowledge, and cross-linguistic connections

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

This guidance is not applicable because the program is not designed for dual language immersion (DLI) programs.

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

The materials provide practice opportunities and formative assessments that require depth of understanding aligned with the TEKS. The lessons and modules embed conceptual exploration, mathematical discourse, problem-solving activities, performance-based tasks, and instructional assessments to support students’ application of mathematical concepts using multiple strategies and representations.

Practice opportunities require students to represent, explain, justify, and apply concepts through real-world contexts and multiple mathematical models. For example, module 6, lesson 2 demonstrates the understanding of multiplication as repeated addition through equal-group situations, multiplication equations, and contextual problem-solving. The lesson activities reinforce learning, and the “Quick Checks” assess connections among repeated addition, multiplication equations, and real-world situations. The assessments require students to represent situations using repeated addition, write multiplication equations, solve problems, and demonstrate mastery aligned with the TEKS. The “Quick Checks” and lesson learning goals also provide opportunities for self-assessment, and student performance data helps inform instructional decisions and targeted support.

Additional opportunities for demonstrating depth of understanding include “Prerequisite Checks,” Module Reviews, Module Tests, “Challenge” activities, and “Project-Based Learning” tasks. Module Projects, which are designated as DOK Level 4 tasks, require students to apply mathematical concepts in authentic contexts through reasoning, problem-solving, and decision-making. The “Challenge” activity “Multiply with 1 and 0” requires students to apply multiplication concepts in a real-world game scenario and demonstrate conceptual understanding beyond procedural fluency. End-of-module assessments such as the “Compare and Represent Fractions” Module Test require students to use multiple representations and strategies, including strip diagrams, pictorial models, number lines, comparative symbols, and written explanations, to demonstrate understanding aligned with the TEKS.

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

The materials include questions and tasks that progressively increase in rigor and complexity to support grade-level proficiency in the mathematics TEKS. The materials develop conceptual understanding through a progression of learning experiences that move from concrete models and foundational skills to strategic thinking, justification, problem-solving, and real-world application.

The materials sequence questions and tasks to build understanding and increase cognitive demand throughout lessons and modules. In module 3, lesson 4, “Use Reasoning Strategies to Compare Fractions,” instruction begins with a simple comparison task in “Spark Your Learning” and progresses to tasks that require solution planning, strategy selection, justification of reasoning, and evidence to support mathematical arguments. The lesson provides opportunities for students to engage in fraction comparison through visual models, identify missing fractional parts, use comparison symbols, and do real-world problem-solving. The lesson culminates in a “Practice on Your Own” activity that helps educators evaluate students’ mastery of the TEKS. Similarly, in module 3, lesson 5, “Represent Equivalent Fractions with Smaller Parts,” learning progresses from identifying correct representations of equivalent fractions to representing, comparing, and justifying equivalent fractions using fraction tiles, area models, number lines, objects, and pictorial models.

Instructional frameworks support the gradual increase of rigor, moving students from concrete to pictorial and abstract representations. For example, module 5, lesson 5 explores three-digit addition through concrete models, number lines, and equations before students engage with DOK questions requiring recall, application of skills and concepts, and strategic reasoning. The “Teacher Background” section further explains how the modules intentionally sequence concepts to build understanding over time. In module 1, place-value concepts progress from composing and decomposing numbers to representing numbers on number lines, comparing numbers using multiple strategies, applying problem-solving processes, and justifying mathematical thinking. Additional opportunities for deeper application include “Project-Based Learning” tasks designated as DOK Level 4 experiences, in which students apply concepts in authentic contexts that require analysis, reasoning, and problem-solving.

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

The materials demonstrate coherence across units by explicitly connecting patterns, big ideas, and relationships between mathematical concepts. The materials connect previously learned skills to new learning so that students develop mathematical understanding across lessons and modules.

Instructional routines, discussion prompts, and opportunities create connections between concepts to help students apply prior learning to new situations. Module 6 connects multiplication concepts to prior understanding of repeated addition, extending the concepts through equal groups, arrays, expressions, and problem-solving applications. In module 8, lesson 1, a “Turn and Talk” prompt asks, “Does multiplying a number and 0 have the same effect as adding 0 to a number?” The lesson connects prior learning related to adding 0 from earlier modules to the zero property of multiplication, which helps students recognize relationships between operations. Similarly, the lessons about fractions connect prior understanding of unit fractions and partitioning to new learning about naming and representing fractions of wholes. Questions such as “How does your understanding of unit fractions help you name fractions of wholes when partitioning?” and “How does the denominator tell you how to partition the whole in a strip diagram?” prompt connections between previously learned concepts and current learning.

The materials support coherence across concepts by providing opportunities for students to connect strategies across modules. For example, module 7, lesson 4 asks students, “How else could you have solved the problem?” to encourage students to apply multiplication strategies they learned in earlier modules, such as breaking apart factors and using known multiplication facts. The Teacher’s Guide explains how concepts build across grade-level expectations by connecting place-value understanding, addition and subtraction strategies, multiplication concepts, estimation, computation, reasoning, and problem-solving throughout the modules. These connections reinforce relationships among mathematical ideas and extend student understanding over time.

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

The materials demonstrate coherence across grade levels by connecting content and mathematical language from previous grades to current learning and preparing students for future mathematical understanding. Educator resources identify prior learning, current grade-level expectations, and future learning so students’ vocabulary and understanding of mathematical concepts build progressively across grades.

The “Teacher Background” and “Before You Teach” sections connect previously learned concepts to current instruction and explain how current learning prepares students for future grade-level content. The materials identify prior learning through concepts such as comparing whole numbers using the symbols >, =, and <; representing fractions on number lines; partitioning figures; solving one- and two-step addition and subtraction problems; representing multiplication through skip counting and arrays; and using mathematical vocabulary such as sum and difference. Current lessons extend these understandings through concepts such as fraction comparison, rounding, multiplication, and problem-solving and introduce new mathematical language, including numerator, denominator, equivalent fractions, and reasoning strategies.

The materials also prepare students for future learning by explicitly identifying concepts and vocabulary that will be developed in later grades. Future connections include comparing and ordering fractions using benchmarks, adding and subtracting fractions with like denominators, generating equivalent fractions with common denominators, rounding to larger place values, solving multistep multiplication and division problems, and developing algebraic reasoning. The “Why This Is Important” sections further explain how current learning supports future mathematical understanding by connecting concepts across grade levels and reinforcing the progression of mathematical ideas and academic language.

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

The materials demonstrate coherence at the lesson level by connecting students’ prior knowledge of concepts and procedures to new mathematical learning. Lessons activate previously learned skills through “Prerequisite Checks,” “Spark Your Learning” activities, educator questioning, and “Data-Driven Support” tables before introducing new mathematical concepts and procedures.

The materials connect prior knowledge to new learning through instructional routines, scaffolded questions, and multiple representations. “Prerequisite Checks” and “Data-Driven Support” tables help educators identify unfinished learning and provide targeted intervention before new instruction begins. In the lessons about fractions, “Spark Your Learning” activities engage students with concrete and pictorial models before students reason about fraction size, and educator questioning bridges previous learning to new understanding. Module 6, lesson 6 extends prior knowledge of equal groups, arrays, and repeated addition to develop the commutative property of multiplication. Students compare four rows of six and six rows of four, connect multiplication to repeated addition, write multiplication expressions, solve contextual problems using arrays and properties of operations, and explain how to use the commutative property of multiplication to write related equations. These instructional supports help educators connect prior knowledge to new learning and develop conceptual understanding throughout each lesson.

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

The materials provide spaced retrieval opportunities for previously learned skills and concepts across lessons and units. Lesson routines, cumulative practice, formative assessments, module assessments, and performance tasks revisit previously taught content, reinforcing learning over time.

The materials incorporate “Prerequisite Checks,” “Practice Plus,” “Train Your Memory,” Module Reviews, Module Tests, and “Project-Based Learning” experiences to reinforce previously learned concepts and introduce new content. “Practice Plus” and the “Train Your Memory” section provide ongoing opportunities to revisit multiplication, fractions, place value, computation, and fluency skills from earlier lessons and modules. Students review concepts through activities such as writing multiplication sentences for arrays, solving fraction-sharing problems, using place value to subtract, and completing addition and subtraction fluency practice. Cumulative assessments also revisit foundational concepts. For example, the Module Test for module 8 requires students to apply previously learned concepts involving repeated addition, arrays, and number patterns and assesses current grade-level expectations.

Module Projects incorporate additional spaced retrieval opportunities by requiring students to apply previously learned skills and concepts as well as current learning in DOK Level 4 tasks. These cumulative opportunities reinforce mathematical understanding across lessons and units and give educators ongoing evidence of student learning to inform instructional decisions.

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

The materials provide interleaved practice opportunities with previously learned skills and concepts across lessons and units. New learning integrates previously taught content so that students apply multiple concepts and strategies in the same lesson, practice activity, and assessment.

The materials incorporate interleaved practice through lesson activities, “Practice Plus,” and the “Train Your Memory” section. The lessons integrate previously learned concepts, including such as place value, properties of addition, expanded form, skip counting, equal groups, arrays, repeated addition, and multiplication, with new grade-level content. For example, in module 6, lesson 2, students connect equal groups, repeated addition, and multiplication equations to represent and solve multiplication problems. They continue to apply these representations in later lessons through arrays, strip diagrams, number lines, and the commutative property of multiplication. Similarly, in module 4, students apply previously learned addition and subtraction strategies across multiple lessons before using those strategies to solve word problems by selecting an appropriate solution method.

“Practice Plus” and the “Train Your Memory” section incorporate additional interleaved practice by combining concepts from multiple lessons and units in the same set of practice problems. Students engage with multiplication, division, related facts, equal groups, place value, expanded form, fractions, and fluency in a single activity, which requires students to select and apply different concepts and procedures across tasks. For example, students solve missing-factor multiplication and division problems while also decomposing numbers into expanded form and completing fraction and fluency tasks. These opportunities reinforce previously learned skills and concepts across lessons and units and strengthen flexible mathematical thinking.

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

The materials provide questions and tasks that require students to interpret, analyze, and evaluate models and representations for mathematical concepts and situations. Students interpret mathematical situations using visual models, analyze the relationships among multiple representations, and evaluate how those representations support mathematical reasoning and problem-solving.

The materials engage students in interpreting, analyzing, and evaluating mathematical models across a variety of lessons. In module 6, lesson 1, students represent equal groups with concrete objects and visual models; interpret how the models represent multiplication, analyze relationships among equal groups, arrays, and equations; and evaluate whether their representations accurately model the situation. In module 6, lesson 4, the “Quick Check” requires students to interpret a four-by-five array, analyze the corresponding multiplication equation, and explain how equal-group models connect to the array representation. Similarly, in module 7, lesson 5, students interpret a real-world area problem, analyze an area model by decomposing a factor with the distributive property, and evaluate how both the model and equations support their solution.

Additional opportunities require students to interpret real-world situations, analyze mathematical relationships, and evaluate the effectiveness of representations. For example, students identify the total number of plants and equal rows, construct an array model to determine the number of plants in each row, connect the representation to both multiplication and division equations, and explain the relationship between the operations. These tasks require students to interpret, analyze, and evaluate mathematical models and justify how the representations accurately describe mathematical situations.

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

The materials provide questions and tasks that require students to create models to represent mathematical situations. Students construct concrete, pictorial, and visual models to represent mathematical concepts, solve problems, and explain their reasoning.

The materials engage students in creating mathematical models across a variety of lessons. In module 6, lesson 4, students use objects to model equal groups, draw a matching array, label the rows and columns, and write a corresponding multiplication equation. During “Practice on Your Own,” students continue creating models by using objects to represent multiplication situations, drawing arrays to solve real-world problems, and applying a five-part problem-solving process to justify their solutions. Similarly, in module 2, lesson 2, students use objects to model fractional parts of a watermelon shared among friends, identify the numerator and denominator, and create an additional representation to model the same fraction.

Additional tasks require students to create models that represent mathematical situations using multiple representations. For example, students use fraction circles or other tools to model fractions before drawing pictorial representations; create equal-group models, arrays, and equations to represent multiplication situations; and explain how their models accurately represent real-world contexts. These opportunities require students to construct mathematical models that support problem-solving, conceptual understanding, and mathematical communication.

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

The materials’ questions and tasks give students opportunities to apply conceptual understanding to new problem situations and contexts. Students apply mathematical concepts in unfamiliar situations by using models, representations, equations, and reasoning to solve real-world problems rather than by simply performing procedures.

The materials engage students in applying conceptual understanding across a variety of lessons. In module 6, lesson 1, students develop an understanding of multiplication through equal groups before applying that understanding to solve new multiplication situations using arrays, strip diagrams, and equations. In module 10, lesson 3, students apply their understanding of the relationship between multiplication and division by explaining how to use multiplication to determine an unknown quotient. Students also solve real-world division problems by representing ribbon lengths on a number line, writing division equations, explaining the relationship between multiplication and division, and extending their thinking to related situations.

Additional opportunities require students to apply conceptual understanding in new mathematical contexts. For example, the “Ready for More” small-group activity has students create original addition and subtraction problems for a partner to solve within specified parameters, which requires students to transfer conceptual understanding to new situations. Students also apply multiplication concepts by drawing arrays to represent real-world situations and using repeated subtraction to solve application problems. These opportunities require students to extend conceptual understanding to unfamiliar contexts while explaining and justifying their mathematical thinking.

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

The materials provide tasks designed to build student automaticity and fluency necessary to complete grade-level tasks. Students engage in repeated practice with mathematical facts and procedures while applying those skills in increasingly complex problem-solving situations that promote both efficiency and conceptual understanding.

The materials develop automaticity by providing students repeated opportunities to practice multiplication and division facts, related fact families, unknown factors, and place-value concepts. In module 6, lesson 1, students repeatedly represent equal groups, connect repeated addition to multiplication, write multiplication equations, and solve similar multiplication situations using arrays and visual models. “Practice on Your Own” continues this progression by asking students to apply multiplication and division facts, identify unknown factors, and determine when to use multiplication or division in a variety of contexts. “Fluency Practice” reinforces these skills through basic computation, multiplication, division, and related fact practice in multiple formats to strengthen efficient fact recall.

Additional opportunities strengthen fluency by requiring students to apply automaticity in grade-level tasks. “Practice Plus” reinforces place-value concepts by asking students to compose numbers in multiple forms, and later lessons require students to solve unknown-factor problems, complete multiplication and division word problems, and explain their reasoning. These repeated practice opportunities build automaticity with foundational skills and develop the fluency students need to solve grade-level mathematical tasks accurately, efficiently, and strategically.

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

The materials provide opportunities for students to practice applying efficient, flexible, and accurate mathematical procedures in lessons and throughout each module. Students solve problems using multiple strategies, compare solution methods, justify their reasoning, and select procedures that best fit the mathematical situation.

The materials develop procedural fluency by engaging students in multiple representations and solution strategies throughout instruction. In module 6, students solve multiplication situations using equal groups, repeated addition, arrays, strip diagrams, equations, and the commutative property before applying these strategies to increasingly complex problems. In module 8, lesson 7, students use place-value strategies and pictorial models to multiply by multiples of 10, represent quantities with tens, model multiplication situations, and connect place-value reasoning to multiplication equations. Students practice selecting efficient strategies, comparing representations, and explaining how each procedure supports an accurate solution.

Additional opportunities strengthen flexibility and accuracy through independent practice, small-group instruction, and cumulative review. Students solve two-step multiplication problems, represent solutions with equations and models, verify answers using multiple strategies, and justify the reasonableness of their solutions. The “Almost There” small-group activity reinforces multiplication through arrays, manipulatives, doubles facts, and real-world problem-solving and encourages students to select efficient procedures. These varied opportunities help students develop efficient, flexible, and accurate mathematical procedures that transfer across grade-level tasks and problem-solving situations.

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

The materials provide opportunities for students to evaluate procedures, processes, and solutions for efficiency, flexibility, and accuracy in lessons and throughout each module. Students compare multiple strategies, analyze mathematical representations, justify their reasoning, and reflect on the effectiveness of different solution methods.

The materials engage students in evaluating mathematical procedures through discussion routines, reflection prompts, and problem-solving tasks. In module 6, lesson 6, students compare equal groups, repeated addition, arrays, and the commutative property to determine whether each strategy produces the same product and which representation most effectively communicates the solution. Students explain why multiple procedures lead to the same answer and evaluate the efficiency and flexibility of each approach. Students also compare equivalent fractions using fraction rectangles and number lines, determine whether fractions are equivalent, explain how the models support their conclusions, and reflect on whether a different strategy would be more effective in future situations.

Additional opportunities encourage students to evaluate both their processes and solutions in real-world contexts. Students select appropriate measurement tools, compare liquid volumes, determine whether mathematical claims are reasonable, and justify their conclusions with evidence. Reflection prompts ask students to explain the process they used, evaluate how well their plan worked, and identify strategies they can use to solve similar problems in the future. These opportunities require students to evaluate the efficiency, flexibility, and accuracy of mathematical procedures and develop deeper mathematical reasoning and problem-solving skills.

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

The materials contain embedded supports for educators to guide students toward increasingly efficient mathematical approaches. Educator guidance includes questioning routines, discussion prompts, scaffolds, and instructional supports that help students compare strategies, justify their reasoning, and refine their mathematical thinking throughout instruction.

The Teacher’s Guide embeds instructional supports that move students from concrete models to increasingly efficient representations and solution strategies. In module 6, lesson 1, students progress from representing multiplication with equal groups to using arrays and multiplication equations, and educator prompts encourage discussion about which representations are most efficient. Throughout the lesson, routines such as “Three Reads,” “Compare and Connect,” and UDL supports guide students in comparing concrete models, strip diagrams, equations, and other representations to determine the most effective strategy. Educator prompts ask students to explain their thinking, justify why one approach is more efficient than another, and use precise mathematical language to describe their reasoning.

Additional embedded supports help educators refine student thinking throughout instruction. Educator notes include suggested responses, intervention questions, and prompts that address misconceptions; encourage students to compare multiple solution methods; and build on initial strategies rather than simply provide answers. Students also select from multiple solution strategies, justify why a chosen approach is most efficient, and reflect on how different representations support problem-solving. These embedded supports consistently guide students toward increasingly efficient mathematical approaches and maintain conceptual understanding.

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

The materials explicitly state how they address the conceptual and procedural emphasis of the TEKS. The Teacher’s Guide explains that students first develop conceptual understanding through models, visual representations, and mathematical reasoning before they apply increasingly efficient procedures and algorithms. Module overviews and “Teacher Background” sections consistently describe how conceptual understanding serves as the foundation for procedural fluency.

The materials make these connections explicit across multiple modules. In module 4, the planning guide, module overview, and “Teacher Background” section explain that students develop conceptual understanding of addition and subtraction through place-value models, base 10 blocks, and visual representations before progressing to efficient computational strategies using place value and properties of operations. Likewise, module 6 explains that instruction begins with concrete equal-group models and visual representations before progressing to arrays, repeated addition, multiplication equations, and properties of operations. Throughout these lessons, students connect conceptual models to increasingly efficient procedures and explain how the representations support their computations.

The Teacher’s Guide further reinforces this progression through module overviews and introductory guidance. In Module 13, the section titled “How does the module support the conceptual and procedural emphasis of the TEKS?” explains that students first develop a conceptual understanding of area by relating addition and multiplication to counting unit squares before using repeated addition, multiplication, and area formulas to find the area of rectangles and composite figures. The “Grade Three Focus Areas” section also explains that the instructional sequence intentionally builds procedural fluency on a foundation of conceptual understanding, ensuring that students strengthen mathematical connections and prepare for future learning.

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

The materials include questions and tasks that require students to use concrete models and manipulatives, pictorial representations, and abstract representations, as required by the TEKS. Throughout the lessons, students progress from using hands-on materials to visual models and symbolic equations, which helps students connect multiple representations and develop conceptual understanding and procedural fluency.

The materials consistently incorporate this progression across multiple modules. In module 4, students use base 10 blocks to model addition and subtraction, create place-value drawings, connect those representations to equations, and explain how each model represents the same mathematical situation. Similarly, in module 6, students develop multiplication concepts as they use counters or connecting cubes to model equal groups, organize the groups into arrays and drawings, write repeated addition and multiplication equations, and connect concrete, pictorial, and abstract representations.

The materials also provide lesson-level opportunities for students to move among concrete, pictorial, and abstract representations. In module 6, lesson 4, task 1, students solve a multiplication problem by first using objects, then drawing an array, and finally writing a multiplication equation. In module 7, lesson 3, task 1, students use hands-on materials to solve a multiplication problem before writing a matching multiplication equation. Another lesson asks students to represent 652 with base 10 blocks, draw a quick picture to show regrouping, and connect the models to a symbolic subtraction equation, which reinforces the progression from manipulatives to abstract reasoning.

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

The materials include supports for students in connecting, creating, defining, and explaining concrete and representational models to abstract (symbolic, numeric, and algorithmic) concepts, as required by the TEKS. Educator guidance and embedded questioning intentionally help students make connections among manipulatives, visual representations, and symbolic notation and explain the mathematical relationships represented by each model.

For example, module 4 guides students to represent addition and subtraction with base 10 blocks, create place-value drawings, and connect both representations to symbolic equations. Educator prompts ask students to explain how regrouping is represented in the concrete model, how the drawings match the manipulatives, and how both models connect to the written algorithm. Similarly, in module 6, students build equal-group models with manipulatives, draw arrays, connect these representations to repeated addition and multiplication equations, and define the relationships among the factors and product. Students also strengthen place-value understanding by connecting digits to place value, word form, and expanded notation and explaining how each representation describes the same number.

Additional lessons about fractions require students to create concrete models, label numerators and denominators, record symbolic fractions, and explain how the models relate to abstract fraction notation. These supports consistently help students transition from concrete and pictorial models to abstract concepts by connecting, creating, defining, and explaining mathematical representations.

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

The materials provide opportunities for students to develop academic mathematical language through the intentional use of visuals, manipulatives, and embedded language supports aligned with mathematical concepts. Throughout the materials, students engage with concrete models, visual representations, and structured discourse routines that encourage them to communicate mathematical ideas using precise vocabulary and academic language.

The materials embed these supports across multiple modules. In module 4, students use base 10 units, rods, flats, digital base 10 blocks, and number lines to model addition and subtraction strategies, discuss place-value concepts, and explain their reasoning using mathematical language. Similarly, in module 6, students use linking cubes, two-color counters, number-line mats, and digital number lines to represent multiplication and describe relationships among equal groups, repeated addition, factors, and products by using increasingly precise mathematical vocabulary.

The materials also provide explicit language-development opportunities through visuals and structured routines. In module 12, lesson 3, students use a photograph of a garden sign and geometric illustrations to define and apply terms such as quadrilateral, parallel, and trapezoid and explain and correct misconceptions using precise mathematical language. Additionally, vocabulary cards include labeled visuals, definitions, and routines such as “Say It,” “Define It,” “Discuss It,” “Use It,” and “Your Turn” that require students to pronounce vocabulary, complete sentence frames, and apply mathematical language in context. The “Peer Coach” videos further support academic language development by modeling productive mathematical discussions when students use visual representations such as drawings and labeled rectangles to explain their thinking.

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

The materials include embedded educator guidance that supports students’ development and use of academic mathematical vocabulary in the context of instruction. The materials provide routines, discussion prompts, and visual supports that guide educators to help students develop and apply precise mathematical language when engaging in meaningful mathematical tasks and discussions.

The materials embed these supports across multiple modules. In module 4, educators model addition and subtraction using base 10 blocks, number lines, and multiple representations; facilitate discussions aligned with TEKS process standard 3.1.G; and encourage students to explain and justify their reasoning using precise mathematical vocabulary. Similarly, in module 6, educators use linking cubes, counters, and number lines to model multiplication concepts and support students in discussing equal groups, repeated addition, factors, and products using content-specific language during classroom discussions and problem-solving.

The materials also provide explicit educator guidance for vocabulary development through embedded instructional routines. In one lesson, students use the terms polygon, heptagon, and nonagon when graphing points, constructing polygons, and discussing attributes during a “Turn and Talk.” Another lesson directs educators to use “Discussion Supports” to reinforce students’ use of terms such as closed figure, plane figure, and line segment and includes an “Emergent Bilingual” strategy that has students rehearse responses in their home language before using mathematical terms in English. Additional supports, including the Language Development Resource Guide, “High-Utility Word Routine,” “Quick-Teach Routine,” and “UDL Support: Representation,” provide educators strategies such as vocabulary checklists and visual displays that help students connect mathematical vocabulary to representations and use academic language accurately in speaking and writing.

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

The materials include embedded educator guidance to support the application of appropriate mathematical language through vocabulary, syntax, and mathematical discourse. Sentence frames, discussion routines, exemplar responses, and questioning strategies guide educators to encourage students to explain and justify their reasoning using precise mathematical language during collaborative conversations and written responses.

The materials embed these supports across multiple modules. In module 4, educators facilitate mathematical discussions using visual models, sentence frames, and “Turn and Talk” opportunities that encourage students to explain and justify addition and subtraction strategies using place-value vocabulary. Similarly, in module 6, educators use mathematical language routines, discussion prompts, and response scaffolds to support students in describing equal groups, repeated addition, factors, and products and refining explanations during partner and whole-group discussions. The educator materials include sample prompts and exemplar responses that help educators extend student thinking and strengthen mathematical communication.

The materials also provide explicit guidance for supporting mathematical discourse and academic language development. In module 8, lesson 2, the “Words to Learn” routine introduces the term distributive property and provides possible responses that model accurate vocabulary and complete mathematical explanations. Students participate in the “Stronger and Clearer Each Time” routine, in which they explain their reasoning, ask questions, hear peers’ ideas, and revise their responses using increasingly precise language. Additional supports include sentence stems such as “Before I thought . . . Now I think . . .” in module 9, lesson 4, task 2, as well as “Compare and Connect” routines that prompt students to question one another about their strategies and refine their explanations. Embedded exemplar responses, vocabulary cards, and discussion prompts consistently support students in developing a stronger mathematical language toolkit and communicating their reasoning with increasing precision.

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

The materials appropriately integrate the TEKS process standards throughout instruction by embedding problem-solving, mathematical communication, multiple representations, and justification in lesson activities. Students routinely analyze problems, select appropriate tools, represent mathematical ideas in multiple ways, evaluate the reasonableness of solutions, and explain their thinking during partner and whole-group discussions. The instruction, practice activities, and assessments all embed these opportunities.

The materials consistently integrate the TEKS process standards across multiple modules. In module 4, students solve one- and two-step addition and subtraction problems using concrete and pictorial models, communicate mathematical ideas using equations and precise mathematical language, and justify their reasoning through classroom discussions. Similarly, in module 6, students analyze multiplication situations; create visual representations using equal groups, arrays, and number lines; compare repeated addition and multiplication equations; explain mathematical relationships; and evaluate the reasonableness of their solutions.

The materials also provide lesson-level opportunities that intentionally integrate the process standards. In module 2, lesson 4, item 3 of the “Practice on Your Own,” students use a problem-solving model to determine the fraction located halfway between 6/8 and 8/8 and explain their reasoning, which requires them to represent, justify, and communicate their thinking. In module 1, lesson 5, task 2, students compare and order whole numbers using comparison symbols and defend their choice of mathematical tools such as number lines and place-value charts. Additionally, the Teacher’s Guide explicitly explains how the process standards are embedded throughout each module and lesson and notes that students learn the steps of the problem-solving model and then apply all the steps together to solve increasingly complex mathematical tasks.

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

The materials describe how the course incorporates and connects the TEKS process standards by embedding them in the instructional design, lesson sequence, and assessment structure. The materials identify the applicable process standards and explain that students repeatedly engage in problem-solving, reasoning, communication, justification, and multiple representations as they progress through lessons, module assessments, and “Project-Based Learning” experiences. The materials guide educators to reinforce these standards through consistent instructional routines, mathematical discussions, and problem-solving experiences throughout the year.

The materials provide a comprehensive, course-level description of how the program integrates the TEKS process standards across mathematical domains. The “Correlations by Standard” documents map each process standard to multiple lessons throughout the year and demonstrate that students repeatedly engage in problem-solving, reasoning, communication, and representation as they develop new mathematical concepts. The Implementation Guide further supports this coherence by organizing the standards by the TEKS, providing the text of each process standard, and identifying every lesson in which the standard is addressed, helping educators understand where process standards are introduced, reinforced, and applied.

The materials also include resources that explicitly connect mathematical content and process standards across modules. In the “Mathematical Connections” section of the Teacher’s Guide, the materials explain how mathematical connections, supported by the TEKS mathematical process standards, deepen understanding, promote transfer of learning, and strengthen problem-solving and reasoning across topics.

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

The materials include a unit-level description of how each unit incorporates and connects the TEKS process standards throughout each module. In the Teacher’s Guide, the section titled “How are the Process Standards (PS) connected to the content in this module?” explicitly identifies the lessons in which students apply specific process standards and explains how those standards support the mathematical content. For example, students apply mathematics to real-world problems (PS 1.A), use a problem-solving model (PS 1.B), select appropriate tools and techniques (PS 1.C), and use representations (PS 1.E) as they develop an understanding of addition, subtraction, multiplication, and fractions. This guidance helps educators understand how the materials intentionally embed and reinforce the process standards throughout the module.

The materials clearly describe how the lessons integrate the TEKS process standards and connect the process standards to the progression of mathematical content. Module overviews identify where students apply the problem-solving model, choose tools, share ideas, use representations, analyze relationships, and communicate using precise mathematical language as they learn new concepts. The overviews explain how students first develop these process skills and then revisit and apply them in subsequent lessons to solve problems, analyze patterns, and justify their reasoning. By embedding and revisiting the process standards throughout the unit, the materials provide a coherent framework for strengthening students’ mathematical reasoning and problem-solving skills over time.

Throughout the modules, the materials explicitly state how lessons incorporate specific process standards, such as using representations to show fractions in different ways and applying a problem-solving model when multiplying by factors. By outlining the process standards alongside the mathematical content, the materials support intentional planning and provide clear guidance for integrating and reinforcing the process standards throughout instruction.

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

The materials include an overview of how each lesson incorporates the TEKS process standards, identifying the applicable standards and connecting them to lesson objectives and instructional activities. Each lesson highlights the mathematical processes students will use, such as problem-solving, selecting appropriate tools, creating representations, communicating mathematical reasoning, and justifying solutions. For example, lesson overviews identify opportunities for students to use a problem-solving model, communicate mathematical ideas using multiple representations, and explain solutions using precise mathematical language as they engage in grade-level mathematical tasks.

The “Correlations by Lesson” documents provide a lesson-by-lesson overview of the TEKS process standards associated with each lesson. Rather than listing only the content TEKS, the guide explicitly cross-references the process standards with every lesson, including applying mathematics, problem-solving, selecting tools, communicating mathematical ideas, analyzing relationships, and using precise mathematical language. This lesson-level correlation helps educators identify the mathematical practices students are expected to use. The documents demonstrate that daily instruction intentionally embeds the process standards instead of teaching them in isolation.

Additionally, sections such as “What will students learn in this lesson?” explain how students will apply specific process standards, such as creating and using representations (3.1E) and displaying, explaining, and justifying mathematical ideas (3.1G), when learning new content. These resources provide educators clear guidance for intentionally integrating the TEKS process standards into every lesson.

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

The materials provide opportunities for students to think mathematically, persevere in solving problems, and make sense of mathematics through open-ended problem-solving, multiple representations, and increasingly complex learning tasks. The materials encourage students to analyze problems, select appropriate strategies and tools, represent mathematical ideas in multiple ways, justify their reasoning, and evaluate the reasonableness of their solutions. Instructional routines and problem-solving tasks promote productive struggle and provide opportunities for students to refine their thinking, explain their ideas, and make meaningful connections among mathematical concepts.

Throughout grade 3, students engage in structured problem-solving experiences that require them to analyze information, develop plans, solve problems using multiple representations, justify their reasoning, and evaluate the effectiveness of their strategies. Lessons prompt students to use strip diagrams, arrays, equations, number lines, repeated addition, and related division situations to solve increasingly complex tasks and refine their thinking through collaboration and reflection. Students explain how equations match models, compare fractions on number lines, solve multiplication and division situations, determine whether solutions are reasonable, and discuss how they might approach problems differently. These opportunities encourage students to make sense of mathematical situations, revise strategies when necessary, and persevere through challenging tasks.

Each lesson includes a problem-solving process that encourages students to take time to understand problems before calculating, select and adjust strategies based on context, and determine whether solutions are reasonable. Grade-level mathematical word problems require students to read and interpret information, identify important details, represent situations in multiple ways, and justify their solutions using mathematical evidence. Through routines such as “Turn and Talk,” “Review Spark Your Learning,” and reflective questions that ask students to explain why their answers make sense, students regularly engage in mathematical thinking, perseverance, and sense-making and develop confidence in solving increasingly complex problems.

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

The materials support students in understanding, explaining, and justifying that they can represent and solve problems in multiple ways. The materials encourage students to use a variety of representations and strategies, compare different approaches, and explain why multiple methods can lead to the same solution. Instructional routines and mathematical discussions provide opportunities for students to communicate their reasoning, justify their choices, and develop flexibility in mathematical thinking.

Throughout grade 3, students demonstrate understanding that they can represent and solve mathematical situations in multiple ways by using arrays, strip diagrams, equations, number lines, place-value models, counters, and pictorial representations. Students model multiplication and division situations with different representations, solve addition problems using various place-value strategies, and represent multistep problems in more than one way. Lessons regularly prompt students to explain how different representations are related, compare strategies, and discuss how changes in quantities affect their models. Students also justify why their solutions make sense and explain how different methods can represent the same mathematical relationships and produce equivalent solutions.

The materials consistently provide opportunities for students to explain and justify multiple approaches through routines such as “Show Another Way,” “Turn and Talk,” and “Compare and Connect.” Grade-level word problems encourage students to solve problems using multiple representations, verify solutions using inverse operations, create additional models, and communicate their reasoning using academic vocabulary and sentence stems. These experiences promote conceptual understanding and mathematical discourse and help students recognize that they can flexibly represent and solve problems through different yet equally valid approaches.

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

The materials require students to make sense of mathematics through multiple opportunities to do mathematics, write about their reasoning, and discuss ideas with peers and educators. Throughout the materials, students solve problems, create mathematical representations, write to explain their thinking, and participate in collaborative discussions. Instructional routines and opportunities for mathematical discourse encourage students to clarify their reasoning, ask questions, and refine their understanding through meaningful interactions with peers and educators.

Throughout grade 3, students use arrays, equations, fraction strips, number lines, and pictorial models to solve problems and communicate mathematical thinking. Lessons prompt students to compare fractions, explain how representations support their solutions, analyze mathematical relationships, and connect models to equations and mathematical properties. Students write explanations using academic vocabulary, describe how arrays and equations represent contexts, explain how their representations support regrouped equations, and identify and correct errors with a partner. These opportunities allow students to do mathematics and communicate their reasoning through both written and oral explanations.

The materials consistently embed opportunities for mathematical discussion through routines such as “Turn and Talk,” “Spark Your Learning,” “Collect and Display,” “Stronger and Clearer Each Time,” and “Mathematical Language Routines.” Students compare and contrast strategies, ask clarifying questions, discuss how to avoid errors, and refine their explanations based on feedback from peers and educators. By solving problems, writing about their mathematical thinking, and engaging in collaborative conversations, students develop conceptual understanding, mathematical reasoning, and the ability to communicate mathematical ideas effectively.

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

The materials support educators in guiding students to share and reflect on their problem-solving approaches through explanations, arguments, and justifications. Questioning strategies, discussion routines, and collaborative structures encourage students to explain their thinking, compare solution methods, justify conclusions, and reflect on the effectiveness of their strategies. These opportunities promote meaningful mathematical discourse and support students in refining their reasoning through peer and educator interactions.

Throughout grade 3, students explain and justify their mathematical thinking using place-value models, arrays, multiplication strategies, and visual representations. Lessons require students to discuss why strategies work, explain how they verified solutions, compare different methods, and revise their explanations based on feedback from peers. Project-based tasks and lesson activities also ask students to defend decisions, determine fairness, justify classifications using mathematical evidence, and explain relationships among numbers and operations. These experiences encourage students to support their reasoning with models, equations, and precise mathematical language.

The materials consistently embed routines such as “Turn and Talk,” “Three Reads,” “Compare and Connect,” “Collect and Display,” “Critique, Correct, and Clarify,” and “Stronger and Clearer Each Time” to guide students in sharing and reflecting on their problem-solving approaches. Prompts encourage students to analyze misconceptions, ask clarifying questions, defend their conclusions, and evaluate others’ reasoning. Through these structured opportunities for explanation, argumentation, and reflection, students develop deeper conceptual understanding and strengthen their ability to communicate and justify mathematical ideas.

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

The materials include prompts and guidance that support educators in providing explanatory feedback based on student responses and anticipated misconceptions. Scripted questions, sample responses, and instructional supports help educators identify misconceptions, build on student thinking, and guide students toward conceptual understanding. The embedded guidance encourages educators to use student errors as opportunities for discussion, reflection, and deeper mathematical reasoning rather than simply correct incorrect answers.

Throughout grade 3, the materials anticipate common misconceptions related to place value, multiplication, division, estimation, and rounding. Educator guidance includes “Spark Discussions,” “Addressing Common Errors,” and “Common Error” supports that identify likely mistakes, explain why students may make those mistakes, and provide targeted questions and concrete examples to address misunderstandings. Students revise models, recompute solutions, explain why strategies work, and connect mathematical concepts through feedback that emphasizes reasoning and conceptual understanding. The materials also provide possible student responses and follow-up prompts that help educators extend learning and encourage students to explain and compare their thinking.

The materials consistently support educators in facilitating meaningful mathematical discussions through reflective questioning, corrective instructional strategies, and evidence-based reasoning routines. The materials guide educators to ask students to defend their thinking, analyze incorrect reasoning, explain relationships among mathematical concepts, and develop generalizations from their observations. By anticipating misconceptions and providing purposeful explanatory feedback, the materials equip educators with ways to address student misunderstandings in real time and strengthen students’ mathematical reasoning, communication, and conceptual understanding.