Program Information
- ISBN
- 9798898864231
- Technical Specifications: Checklist
- Tech Specs: Checklist (pdf 240.86 KB)
- Technical Specifications: Professional Development
- Tech Specs: Professional Development (pdf 204.27 KB)
TX ClearMath 1e, Grade 3
Math (English) Grade 3
IMRA 2026
Publisher: Carnegie Learning, Inc.
Copyright: 2027
Series includes:
Rubric: Mathematics K–12 (English) | 2025 (Download Not Available)
* Some programs submit evidence for only part of a standard, while others submit all sections. A 100% score means this program met all the expectations it submitted.
Quality Review
Standards Alignment
Rubric Section
| Grade | TEKS % | ELPS % |
|---|---|---|
| Grade 3 | 100% | 100% |
Criteria for Quality
Rubric Section 1
Intentional Instructional Design
Materials support educators in effective implementation through intentional course, unit, and lesson-level design.
Total
100% (24 out of 24 points)
Evaluation for 1.1a
In the Texas ClearMath Grade 3 Scope and Sequence (165), module 1, topic 1, lessons 1–13 identify the grade 3 instructional progression and connect grade-level concepts to the Texas Essential Knowledge and Skills (TEKS) and English Language Proficiency Standards (ELPS). This scope and sequence provides educators with a yearlong course map that outlines the TEKS, ELPS, and concepts taught throughout the instructional year.
In the Texas ClearMath Grade 3 Scope and Sequence (180), module 1, topic 1, lessons 1–13 identify the instructional progression for the 180-day instructional calendar and connect grade-level concepts to the TEKS and ELPS. This additional scope and sequence provides educators with another course-level map that outlines the TEKS, ELPS, and concepts taught in the course.
Evaluation for 1.1b
The Scope and Sequence (165) organizes the course by module and topic and provides pacing guidance for implementation across the school year. This pacing guide/calendar resource supports effective implementation by helping educators plan instruction while maintaining the intended sequence of the materials.
The materials also include suggested pacing to support effective implementation for a different instructional calendar. The Scope and Sequence (180) organizes the course by module and topic and provides pacing guidance for a 180-day instructional calendar. Together, the 165-day and 180-day pacing guide/calendar resources support effective implementation for various instructional calendars.
Evaluation for 1.1c
The Texas ClearMath Grade 3 Mathematical Progressions and Connections describes mathematical progressions and connections across modules and topics. This resource explains how concepts build within the course, allowing educators to see how earlier learning supports later topics and how concepts to be learned connect throughout the year.
In the Texas ClearMath Grade 3 Teacher’s Implementation Guide Overview, the “Course Sequence” section identifies the course sequence and shows how modules and topics build across the instructional year. This overview supports educators in understanding the rationale of unit order and how concepts to be learned connect throughout the grade 3 course.
Evaluation for 1.1d
The Texas ClearMath K–5 Teacher Topic Internalization Protocol provides a structured protocol for topic-level internalization by guiding educators to identify key concepts, instructional goals, and planning considerations before teaching. This protocol provides corresponding guidance for internalizing the materials so educators can prepare for implementation as designed.
The Texas ClearMath K–5 Teacher Lesson Internalization Protocol provides a structured process for lesson internalization by guiding educators to examine lesson goals, instructional moves, materials, and anticipated student thinking before instruction. Together, the topic and lesson internalization protocols provide corresponding guidance for unit and lesson internalization.
Evaluation for 1.1e
The Texas ClearMath K–5 Coach Topic Internalization Protocol provides a coach-facing protocol for supporting educators as they internalize topic-level content and prepare to implement the materials. This resource gives instructional leaders guidance for coaching conversations focused on implementing the materials as designed.
The Texas ClearMath K–5 Coach Re-Engagement Protocol provides coach-facing guidance for supporting educators through re-engagement planning and implementation. This resource supports instructional leaders by providing a structure for coaching conversations and implementation that is aligned with the design of the materials.
Evaluation for 1.2a
In the Teacher’s Implementation Guide, module 1, topic 1, the “Topic Summaries” section includes “Key Ideas” and “Key Terms” sections for the topic. The “Key Ideas” section provides background content knowledge for the unit concepts, and the “Key Terms” section identifies academic vocabulary necessary to effectively teach the concepts in the unit.
In the Teacher’s Implementation Guide, module 3, topic 7, lesson 7 provides educator-facing instructional guidance, questions, tasks, materials, and content-specific information connected to the topic. This lesson-level guidance within the unit supports educators in understanding the background content knowledge and academic vocabulary necessary to effectively teach the concepts in the unit.
Evaluation for 1.2b
In the Texas ClearMath Grade 3 Student Practice Book, module 1, topic 1, the “Family Guide” section provides families with information about the mathematical concepts students will encounter in the topic and suggestions for supporting student progress. It also provides unit-level family supports connected to the learning students complete in the materials.
In the Student Practice Book, module 1, topic 1, the “Spanish Family Guide” section provides families with information about the mathematical concepts students will encounter and suggestions for supporting student progress at home. Together, the English and Spanish “Family Guides” provide supports for families with suggestions on supporting the progress of their students.
Evaluation for 1.3a
In the Teacher’s Implementation Guide, module 3, topic 7, lesson 7 provides educator-facing instructional guidance, questions, tasks, lesson materials, and checks for understanding. Together, these lesson components support the content and language standards of the lesson and provide the structure needed for educators to deliver the lesson as designed.
In the Teacher’s Implementation Guide, module 3, topic 7, lesson 8 provides educator-facing instructional guidance, questions, tasks, lesson materials, and opportunities for instructional assessment. These lesson components further demonstrate how the materials provide detailed lesson plans aligned with the TEKS and ELPS.
Evaluation for 1.3b
In the Teacher’s Implementation Guide, module 2, topic 5, lesson 9, the “Lesson Structure and Pacing Guide” section identifies the sequence of instructional activities and suggested timing for lesson components. This lesson overview helps educators prepare the materials and timing necessary to effectively deliver the lesson.
In the Teacher’s Implementation Guide, module 1, topic 1, lesson 5, the “Lesson Structure and Pacing Guide” section identifies the sequence of instructional activities and suggested timing for lesson components. This second lesson overview confirms that the materials consistently provide lesson structure, materials, and timing guidance for effective lesson delivery.
Evaluation for 1.3c
In the Teacher’s Implementation Guide, the “Monitoring Student Progress” section explains how educators can use the Student Practice Book to monitor student progress and support continued practice. This guidance supports the effective use of lesson materials for additional practice and reinforcement beyond the core lesson.
In the Teacher’s Implementation Guide, the “Understanding the Teaching Cadence: Explore Centers” section explains how “Explore Centers” are used as part of the teaching cadence to provide continued practice and reinforcement beyond the core lesson. Together, the Student Practice Book guidance and “Explore Centers” guidance provide structures for additional practice, reinforcement, and extension.
1.1 Course-Level Design
1.1a
Materials include a scope and sequence outlining the TEKS, ELPS, and concepts taught in the course.
Materials include a scope and sequence outlining the TEKS, ELPS, and concepts taught in the course.
3 out of 3 points
Evaluation for 1.1a
Evaluation for 1.1a
Materials include a scope and sequence outlining the TEKS, ELPS, and concepts taught in the course.
3 out of 3 points
In the Texas ClearMath Grade 3 Scope and Sequence (180), module 1, topic 1, lessons 1–13 identify the instructional progression for the 180-day instructional calendar and connect grade-level concepts to the TEKS and ELPS. This additional scope and sequence provides educators with another course-level map that outlines the TEKS, ELPS, and concepts taught in the course.
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).
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).
2 out of 2 points
Evaluation for 1.1b
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).
2 out of 2 points
The materials also include suggested pacing to support effective implementation for a different instructional calendar. The Scope and Sequence (180) organizes the course by module and topic and provides pacing guidance for a 180-day instructional calendar. Together, the 165-day and 180-day pacing guide/calendar resources support effective implementation for various instructional calendars.
1.1c
Materials include an explanation for the rationale of unit order as well as how concepts to be learned connect throughout the course.
Materials include an explanation for the rationale of unit order as well as how concepts to be learned connect throughout the course.
2 out of 2 points
Evaluation for 1.1c
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.
2 out of 2 points
In the Texas ClearMath Grade 3 Teacher’s Implementation Guide Overview, the “Course Sequence” section identifies the course sequence and shows how modules and topics build across the instructional year. This overview supports educators in understanding the rationale of unit order and how concepts to be learned connect throughout the grade 3 course.
1.1d
Materials include protocols with corresponding guidance for unit and lesson internalization.
Materials include protocols with corresponding guidance for unit and lesson internalization.
2 out of 2 points
Evaluation for 1.1d
Evaluation for 1.1d
Materials include protocols with corresponding guidance for unit and lesson internalization.
2 out of 2 points
The Texas ClearMath K–5 Teacher Lesson Internalization Protocol provides a structured process for lesson internalization by guiding educators to examine lesson goals, instructional moves, materials, and anticipated student thinking before instruction. Together, the topic and lesson internalization protocols provide corresponding guidance for unit and lesson internalization.
1.1e
Materials include resources and guidance for instructional leaders to support teachers with implementing the materials as designed.
Materials include resources and guidance for instructional leaders to support teachers with implementing the materials as designed.
2 out of 2 points
Evaluation for 1.1e
Evaluation for 1.1e
Materials include resources and guidance for instructional leaders to support teachers with implementing the materials as designed.
2 out of 2 points
The Texas ClearMath K–5 Coach Re-Engagement Protocol provides coach-facing guidance for supporting educators through re-engagement planning and implementation. This resource supports instructional leaders by providing a structure for coaching conversations and implementation that is aligned with the design of the materials.
1.2 Unit-Level Design
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.
Materials include comprehensive unit overviews that provide the background content knowledge and academic vocabulary necessary to effectively teach the concepts in the unit.
2 out of 2 points
Evaluation for 1.2a
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.
2 out of 2 points
In the Teacher’s Implementation Guide, module 3, topic 7, lesson 7 provides educator-facing instructional guidance, questions, tasks, materials, and content-specific information connected to the topic. This lesson-level guidance within the unit supports educators in understanding the background content knowledge and academic vocabulary necessary to effectively teach the concepts in the unit.
1.2b
Materials contain supports for families in both Spanish and English for each unit with suggestions on supporting the progress of their student.
Materials contain supports for families in both Spanish and English for each unit with suggestions on supporting the progress of their student.
2 out of 2 points
Evaluation for 1.2b
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.
2 out of 2 points
In the Student Practice Book, module 1, topic 1, the “Spanish Family Guide” section provides families with information about the mathematical concepts students will encounter and suggestions for supporting student progress at home. Together, the English and Spanish “Family Guides” provide supports for families with suggestions on supporting the progress of their students.
1.3 Lesson-Level Design
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).
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).
5 out of 5 points
Evaluation for 1.3a
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).
5 out of 5 points
In the Teacher’s Implementation Guide, module 3, topic 7, lesson 8 provides educator-facing instructional guidance, questions, tasks, lesson materials, and opportunities for instructional assessment. These lesson components further demonstrate how the materials provide detailed lesson plans aligned with the TEKS and ELPS.
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.
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.
3 out of 3 points
Evaluation for 1.3b
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.
3 out of 3 points
In the Teacher’s Implementation Guide, module 1, topic 1, lesson 5, the “Lesson Structure and Pacing Guide” section identifies the sequence of instructional activities and suggested timing for lesson components. This second lesson overview confirms that the materials consistently provide lesson structure, materials, and timing guidance for effective lesson delivery.
1.3c
Materials include guidance on the effective use of lesson materials for extended practice (e.g., homework, extension, enrichment).
Materials include guidance on the effective use of lesson materials for extended practice (e.g., homework, extension, enrichment).
1 out of 1 points
Evaluation for 1.3c
Evaluation for 1.3c
Materials include guidance on the effective use of lesson materials for extended practice (e.g., homework, extension, enrichment).
1 out of 1 points
In the Teacher’s Implementation Guide, the “Understanding the Teaching Cadence: Explore Centers” section explains how “Explore Centers” are used as part of the teaching cadence to provide continued practice and reinforcement beyond the core lesson. Together, the Student Practice Book guidance and “Explore Centers” guidance provide structures for additional practice, reinforcement, and extension.
Rubric Section 2
Progress Monitoring
Materials support educators in effective implementation through frequent, strategic opportunities to monitor and respond to student progress.
Total
100% (18 out of 18 points)
Evaluation for 2.1a
In the Texas ClearMath Grade 3 Assessment Suite, module 2, topic 4, the “ReadyCheck Assessments” identify prerequisite skills and misconceptions before instruction, the “Snapshot Assessments” provide formative checks of understanding during instruction, and the “End-of-Topic Assessments” and “Performance Tasks” measure student mastery of topic concepts and skills after instruction.
In the Assessment Suite, module 2, topic 4 assessments include multiple-choice questions, written responses, mathematical models, and performance-based tasks that allow students to demonstrate understanding in different ways. Additionally, in the Teacher’s Implementation Guide, module 1, topic 2, lesson 2 includes ongoing assessment opportunities that help educators monitor student understanding and provide “Just-in-Time Supports” or “Challenge Opportunities” strategies during instruction.
Evaluation for 2.1b
In the Teacher’s Implementation Guide Overview, the “Comprehensive Assessment and Data-Driven Instruction” section describes assessment of learning, assessment for learning, and assessment as learning. The overview explains how each assessment approach supports monitoring student progress and informing instructional decisions.
In the Teacher’s Implementation Guide Overview, the “Comprehensive Assessment and Data-Driven Instruction” section explains the use of “Beginning-,” “Middle-,” and “End-of-Year Assessments” as well as “ReadyCheck Assessments,” “Snapshot Assessments,” “End-of-Topic Assessments,” and “Performance Tasks.” This guidance explains how educators use assessment results to identify student needs and plan instruction.
Evaluation for 2.1c
The Texas ClearMath Grade 3 Year-at-a-Glance (165) identifies when educators administer assessments throughout the instructional year, including “ReadyCheck Assessments,” “Topic Assessments,” and dedicated assessment days. This guidance helps educators implement assessments consistently within the intended instructional sequence.
In the Year-at-a-Glance (165), pacing recommendations outline the number of instructional and assessment days within each module and topic. The document explains when educators use “ReadyCheck Assessments” and when students complete summative assessments, supporting accurate and consistent assessment administration.
Evaluation for 2.1d
In the Texas ClearMath Grade 3 Assessment Guide, the “Assessment Blueprints” section identifies the TEKS, item types, and Depth of Knowledge (DOK) levels for “ReadyCheck Assessments,” “Snapshot Assessments,” and “End-of-Topic Assessments.” The Assessment Guide also connects assessment items to the lessons that address each TEKS standard, supporting alignment between instruction and assessment.
In the Assessment Guide, each topic includes a lesson-by-lesson alignment of the TEKS addressed during instruction and ongoing assessments embedded throughout the lessons. The guide links assessment items to corresponding lessons and learning goals, demonstrating alignment between diagnostic, formative, and summative assessments and the objectives of the course, unit, and lesson.
Evaluation for 2.1e
In the Assessment Guide, the “Assessment Blueprints” section identifies the TEKS alignment and DOK level for each assessment item. The blueprints show a range of DOK levels across assessment questions, supporting evaluation of student learning at multiple levels of cognitive demand.
In the Assessment Guide, the “Assessment Blueprints” section identifies item formats such as multiple-choice, multiple-select, short-answer, and constructed-response questions. The guide includes descriptions of item types and DOK levels, demonstrating that assessments measure student understanding through multiple formats and levels of complexity.
Evaluation for 2.2a
In the Assessment Suite, each “Performance Task” section includes a rubric that identifies scoring criteria and performance expectations. The rubric supports consistent scoring of student responses across assessment tasks.
In the Assessment Suite, the “Performance Task” section includes facilitation notes and scoring rubrics to help educators analyze student responses and evaluate levels of understanding. These tools support instructional decision-making based on assessment results.
Evaluation for 2.2b
In the Teacher’s Implementation Guide Overview, the “Unpacking a Re-Engagement Lesson” section explains how educators use assessment evidence and student work to plan targeted instruction. This guidance supports educators in addressing misconceptions, strengthening understanding, and extending learning based on student needs.
In the Teacher’s Implementation Guide Overview, the “Preparing to Re-Engage” recording sheet helps educators analyze student responses from “Reflection” activities and identify trends in performance. The accompanying guidance supports educators in selecting instructional supports and activities to address identified learning needs.
Evaluation for 2.2c
In the digital platform, educators access assessment reports that monitor student performance on assessments, games, and standards-based measures. These reports support ongoing monitoring of student growth and instructional planning.
In the Teacher’s Implementation Guide Overview, the “Using Data to Monitor and Celebrate Success” section describes reflection tools that help students evaluate their learning and identify areas for growth. Students use “Self-Reflection” activities to monitor progress toward learning goals and set goals for continued improvement.
2.1 Instructional Assessments
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.
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.
3 out of 3 points
Evaluation for 2.1a
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.
3 out of 3 points
In the Assessment Suite, module 2, topic 4 assessments include multiple-choice questions, written responses, mathematical models, and performance-based tasks that allow students to demonstrate understanding in different ways. Additionally, in the Teacher’s Implementation Guide, module 1, topic 2, lesson 2 includes ongoing assessment opportunities that help educators monitor student understanding and provide “Just-in-Time Supports” or “Challenge Opportunities” strategies during instruction.
2.1b
Materials include the definition and intended purpose for the types of instructional assessments included.
Materials include the definition and intended purpose for the types of instructional assessments included.
1 out of 1 points
Evaluation for 2.1b
Evaluation for 2.1b
Materials include the definition and intended purpose for the types of instructional assessments included.
1 out of 1 points
In the Teacher’s Implementation Guide Overview, the “Comprehensive Assessment and Data-Driven Instruction” section explains the use of “Beginning-,” “Middle-,” and “End-of-Year Assessments” as well as “ReadyCheck Assessments,” “Snapshot Assessments,” “End-of-Topic Assessments,” and “Performance Tasks.” This guidance explains how educators use assessment results to identify student needs and plan instruction.
2.1c
Materials include teacher guidance to ensure consistent and accurate administration of instructional assessments.
Materials include teacher guidance to ensure consistent and accurate administration of instructional assessments.
1 out of 1 points
Evaluation for 2.1c
Evaluation for 2.1c
Materials include teacher guidance to ensure consistent and accurate administration of instructional assessments.
1 out of 1 points
In the Year-at-a-Glance (165), pacing recommendations outline the number of instructional and assessment days within each module and topic. The document explains when educators use “ReadyCheck Assessments” and when students complete summative assessments, supporting accurate and consistent assessment administration.
2.1d
Diagnostic, formative, and summative assessments are aligned to the TEKS and objectives of the course, unit, or lesson.
Diagnostic, formative, and summative assessments are aligned to the TEKS and objectives of the course, unit, or lesson.
6 out of 6 points
Evaluation for 2.1d
Evaluation for 2.1d
Diagnostic, formative, and summative assessments are aligned to the TEKS and objectives of the course, unit, or lesson.
6 out of 6 points
In the Assessment Guide, each topic includes a lesson-by-lesson alignment of the TEKS addressed during instruction and ongoing assessments embedded throughout the lessons. The guide links assessment items to corresponding lessons and learning goals, demonstrating alignment between diagnostic, formative, and summative assessments and the objectives of the course, unit, and lesson.
2.1e
Instructional assessments include TEKS-aligned items at varying levels of complexity.
Instructional assessments include TEKS-aligned items at varying levels of complexity.
2 out of 2 points
Evaluation for 2.1e
Evaluation for 2.1e
Instructional assessments include TEKS-aligned items at varying levels of complexity.
2 out of 2 points
In the Assessment Guide, the “Assessment Blueprints” section identifies item formats such as multiple-choice, multiple-select, short-answer, and constructed-response questions. The guide includes descriptions of item types and DOK levels, demonstrating that assessments measure student understanding through multiple formats and levels of complexity.
2.2 Data Analysis and Progress Monitoring
2.2a
Instructional assessments and scoring information provide guidance for interpreting student performance.
Instructional assessments and scoring information provide guidance for interpreting student performance.
2 out of 2 points
Evaluation for 2.2a
Evaluation for 2.2a
Instructional assessments and scoring information provide guidance for interpreting student performance.
2 out of 2 points
In the Assessment Suite, the “Performance Task” section includes facilitation notes and scoring rubrics to help educators analyze student responses and evaluate levels of understanding. These tools support instructional decision-making based on assessment results.
2.2b
Materials provide guidance for the use of included tasks and activities to respond to student trends in performance on assessments.
Materials provide guidance for the use of included tasks and activities to respond to student trends in performance on assessments.
1 out of 1 points
Evaluation for 2.2b
Evaluation for 2.2b
Materials provide guidance for the use of included tasks and activities to respond to student trends in performance on assessments.
1 out of 1 points
In the Teacher’s Implementation Guide Overview, the “Preparing to Re-Engage” recording sheet helps educators analyze student responses from “Reflection” activities and identify trends in performance. The accompanying guidance supports educators in selecting instructional supports and activities to address identified learning needs.
2.2c
Materials include tools for teachers to track student progress and growth, and tools for students to track their own progress and growth.
Materials include tools for teachers to track student progress and growth, and tools for students to track their own progress and growth.
2 out of 2 points
Evaluation for 2.2c
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.
2 out of 2 points
In the Teacher’s Implementation Guide Overview, the “Using Data to Monitor and Celebrate Success” section describes reflection tools that help students evaluate their learning and identify areas for growth. Students use “Self-Reflection” activities to monitor progress toward learning goals and set goals for continued improvement.
Rubric Section 3
Supports for All Learners
Materials support educators in reaching all learners through design focused on engagement, representation, and action/expression for learner variability.
Total
100% (20 out of 20 points)
Evaluation for 3.1a
In the Teacher’s Implementation Guide, module 1, topic 1, lesson 5, the “Re-Engagement Lesson” provides opportunities for students to revisit area and array models through targeted reteaching activities. The lesson supports educators in addressing unfinished learning and strengthening conceptual understanding.
In the Teacher’s Implementation Guide, module 1, topic 1, lesson 4, the “Assistance for All” and “Just-in-Time Supports” sections provide strategies for responding to student needs during instruction. These supports help educators scaffold learning and adjust instruction based on student understanding.
Evaluation for 3.1b
In the Teacher’s Implementation Guide, module 1, topic 2, lesson 13 includes a “Language Link: Developing Contextual Language” section that guides educators in reviewing terms such as temperature, thermometer, and degree. These supports help students develop the vocabulary needed to engage with lesson content.
In the Teacher’s Implementation Guide, “Topic Overview” sections include everyday connections, sentence stems, and “About the Math” sections that help educators introduce academic language and connect mathematical concepts to familiar experiences. These supports help students build vocabulary and access grade-level content.
Evaluation for 3.1c
In the Teacher’s Implementation Guide, “Stretch Centers” provide opportunities for students to extend their mathematical thinking through challenging problem-solving activities. For example, module 2, topic 4, lesson 5 includes the “Creating Statements with Pattern Blocks Stretch Center,” which encourages students to apply and extend their understanding beyond the core lesson.
The materials also provide extension opportunities through differentiated center activities embedded within “Re-Engagement Lessons.” In the Teacher’s Implementation Guide, “Stretch Centers” encourage students to deepen conceptual understanding, explore multiple solution strategies, and engage in higher-level mathematical reasoning while working with grade-level concepts.
Evaluation for 3.2a
In the Teacher’s Implementation Guide, “Concept Lessons” and “Re-Engagement Lessons” include purposeful questions, anticipated student responses, and facilitation notes that guide educators in explaining concepts, modeling mathematical thinking, and supporting student understanding during instruction.
In the Teacher’s Implementation Guide, lesson facilitation notes include sample explanations, discussion prompts, and instructional recommendations that help educators model strategies, address misconceptions, and deepen student understanding of mathematical concepts.
Evaluation for 3.2b
In the Teacher’s Implementation Guide, purposeful questions embedded throughout “Concept Lessons” and “Re-Engagement Lessons” prompt students to explain their thinking, justify solutions, and make connections among mathematical ideas. These questions support discussion-based instruction and help educators assess student understanding during instruction.
In the Teacher’s Implementation Guide, educator facilitation notes include discussion prompts, anticipated student responses, and follow-up questions that help educators extend conversations, address misconceptions, and deepen conceptual understanding. These supports guide educators in facilitating whole-group, small-group, and student-centered learning experiences.
Evaluation for 3.2c
In the Teacher’s Implementation Guide, the “Lesson Structure and Pacing Guide” section includes opportunities for guided practice, paired practice, collaborative problem-solving, and independent work. Activities such as Think-Pair-Share and Guided Play support student learning through multiple modes of engagement and interaction.
In the Teacher’s Implementation Guide, facilitation notes and lesson structures identify when students work collaboratively, engage in mathematical discussions, solve problems with partners, and complete independent practice. These structures support effective implementation and provide students with multiple opportunities to apply learning.
Evaluation for 3.3a
The Texas ClearMath Grade 3 Emergent Bilingual Student Support Handbook includes ELPS-aligned supports for Pre-Production/Beginning, Intermediate/High Intermediate, and High Intermediate/Advanced learners. These supports include sentence stems, word banks, visual supports, and modeling strategies that help students engage with mathematical content and academic language.
The Emergent Bilingual Student Support Handbook provides lesson-level guidance for scaffolded speaking, listening, reading, and writing supports aligned to the ELPS. These supports help students participate in mathematical discussions and develop increasingly sophisticated academic language.
Evaluation for 3.3b
In the Teacher’s Implementation Guide, the “Embedding Language Development into Instruction: Empowering Emergent Bilingual Students” section provides guidance for integrating language development supports and instructional routines throughout mathematics instruction.
In the Teacher’s Implementation Guide and Emergent Bilingual Student Support Handbook, educators receive recommendations for using language routines, scaffolds, and instructional supports that help emergent bilingual (EB) students access mathematical content while developing academic language.
Evaluation for 3.3c
In the Teacher’s Implementation Guide, EB student support activities encourage students to discuss observations in their home language before using sentence frames to communicate ideas in English. These activities help students connect prior knowledge to new learning while strengthening academic language.
In the Teacher’s Implementation Guide, students use visuals, gestures, repetitive language, and structured discussion routines to build vocabulary and deepen comprehension. These supports help students engage with mathematical concepts while developing proficiency in academic language.
Evaluation for 3.3d
This guidance is not applicable because the program is not designed for dual language immersion (DLI) programs.
3.1 Differentiation and Scaffolds
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.
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.
1 out of 1 points
Evaluation for 3.1a
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.
1 out of 1 points
In the Teacher’s Implementation Guide, module 1, topic 1, lesson 4, the “Assistance for All” and “Just-in-Time Supports” sections provide strategies for responding to student needs during instruction. These supports help educators scaffold learning and adjust instruction based on student understanding.
3.1b
Materials include pre-teaching or embedded supports for unfamiliar vocabulary and references in text (e.g., figurative language, idioms, academic language).
Materials include pre-teaching or embedded supports for unfamiliar vocabulary and references in text (e.g., figurative language, idioms, academic language).
2 out of 2 points
Evaluation for 3.1b
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).
2 out of 2 points
In the Teacher’s Implementation Guide, “Topic Overview” sections include everyday connections, sentence stems, and “About the Math” sections that help educators introduce academic language and connect mathematical concepts to familiar experiences. These supports help students build vocabulary and access grade-level content.
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.
Materials include teacher guidance for differentiated instruction, enrichment, and extension activities for students who have demonstrated proficiency in grade-level content and skill.
1 out of 1 points
Evaluation for 3.1c
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.
1 out of 1 points
The materials also provide extension opportunities through differentiated center activities embedded within “Re-Engagement Lessons.” In the Teacher’s Implementation Guide, “Stretch Centers” encourage students to deepen conceptual understanding, explore multiple solution strategies, and engage in higher-level mathematical reasoning while working with grade-level concepts.
3.2 Instructional Methods
3.2a
Materials include explicit (direct) prompts and guidance to support the teacher in modeling and explaining the concept(s) to be learned.
Materials include explicit (direct) prompts and guidance to support the teacher in modeling and explaining the concept(s) to be learned.
2 out of 2 points
Evaluation for 3.2a
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.
2 out of 2 points
In the Teacher’s Implementation Guide, lesson facilitation notes include sample explanations, discussion prompts, and instructional recommendations that help educators model strategies, address misconceptions, and deepen student understanding of mathematical concepts.
3.2b
Materials include teacher guidance and recommendations for effective lesson delivery and facilitation using a variety of instructional approaches.
Materials include teacher guidance and recommendations for effective lesson delivery and facilitation using a variety of instructional approaches.
1 out of 1 points
Evaluation for 3.2b
Evaluation for 3.2b
Materials include teacher guidance and recommendations for effective lesson delivery and facilitation using a variety of instructional approaches.
1 out of 1 points
In the Teacher’s Implementation Guide, educator facilitation notes include discussion prompts, anticipated student responses, and follow-up questions that help educators extend conversations, address misconceptions, and deepen conceptual understanding. These supports guide educators in facilitating whole-group, small-group, and student-centered learning experiences.
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.
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.
2 out of 2 points
Evaluation for 3.2c
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.
2 out of 2 points
In the Teacher’s Implementation Guide, facilitation notes and lesson structures identify when students work collaboratively, engage in mathematical discussions, solve problems with partners, and complete independent practice. These structures support effective implementation and provide students with multiple opportunities to apply learning.
3.3 Support for Emergent Bilingual Students
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.
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.
2 out of 2 points
Evaluation for 3.3a
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.
2 out of 2 points
The Emergent Bilingual Student Support Handbook provides lesson-level guidance for scaffolded speaking, listening, reading, and writing supports aligned to the ELPS. These supports help students participate in mathematical discussions and develop increasingly sophisticated academic language.
3.3b
Materials include implementation guidance to support teachers in effectively using the materials in state-approved bilingual/ESL programs.
Materials include implementation guidance to support teachers in effectively using the materials in state-approved bilingual/ESL programs.
1 out of 1 points
Evaluation for 3.3b
Evaluation for 3.3b
Materials include implementation guidance to support teachers in effectively using the materials in state-approved bilingual/ESL programs.
1 out of 1 points
In the Teacher’s Implementation Guide and Emergent Bilingual Student Support Handbook, educators receive recommendations for using language routines, scaffolds, and instructional supports that help emergent bilingual (EB) students access mathematical content while developing academic language.
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.
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.
8 out of 8 points
Evaluation for 3.3c
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.
8 out of 8 points
In the Teacher’s Implementation Guide, students use visuals, gestures, repetitive language, and structured discussion routines to build vocabulary and deepen comprehension. These supports help students engage with mathematical concepts while developing proficiency in academic language.
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.
If designed for dual language immersion (DLI) programs, materials include resources that outline opportunities to address metalinguistic transfer from English to the partner language.
Not applicable.
Evaluation for 3.3d
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.
Not applicable.
Rubric Section 4
Depth and Coherence of Key Concepts
Materials are designed to meet the rigor of the standards while connecting concepts within and across grade levels/courses.
Total
100% (19 out of 19 points)
Evaluation for 4.1a
In the Student Practice Book, module 1, topic 1, students demonstrate depth of understanding by representing multiplication and area with equal groups, arrays, repeated addition, and equations. In lesson 1, students count dots arranged in equal groups, draw images to explain their thinking, and solve problems involving equal groups. In lesson 2, students determine rows, columns, square units, and addition expressions for rectangular arrays. Later in the topic, students connect arrays and area, determine areas of rectangles, and write equations to represent the models. These practice opportunities require students to connect concrete and pictorial representations to multiplication and area concepts rather than only recall facts.
In the Assessment Suite, module 1, the “End-of-Module Assessment” requires students to demonstrate depth of understanding across multiple TEKS-aligned concepts. Students create and interpret scaled pictographs and bar graphs and solve comparison questions using data displays. Students shade a grid to show a rectangle with an area of 12 square units, write a multiplication equation to represent the rectangle, and identify an expression represented by an array. Then, they evaluate whether an estimate is reasonable; solve addition and subtraction problems using strategies; write an equation with a letter for an unknown in a multistep word problem; and draw an area model, array, or equal groups to represent 4 × 7. These assessment tasks require students to apply concepts through representations, equations, reasoning, and problem-solving.
Evaluation for 4.1b
In the Teacher’s Implementation Guide, module 1, topic 1, questions and tasks progressively increase in rigor and complexity as students move from counting equal groups to using multiplication representations. In lesson 1, students organize manipulatives into equal groups, count by equal groups, and determine totals. In lesson 2, students connect rows and columns to arrays and square tiles. In lesson 6, students identify equal groups, use anchor charts, and connect multiplication to the number of groups and numbers in each group. This progression moves students from counting and organizing objects to representing multiplication more abstractly.
The progression continues in module 1, topic 1, lessons 7 and 8 as students apply multiplication concepts in more complex ways. In lesson 7, students determine the number of toothbrushes and field goals in real-world contexts, identify factors, and write multiplication word problems. In lesson 8, students use choral counting, skip counting, and games to identify factor and multiple relationships. This sequence moves students from visual and concrete models to real-world multiplication situations, factor language, multiples, patterns, and mathematical justification.
Evaluation for 4.2a
In the Teacher’s Implementation Guide, the module 1 overview demonstrates coherence across units by connecting patterns, big ideas, and relationships among mathematical concepts. The module overview explains that students use equal groups, arrays, area models, and data displays to develop strategies for operations and data. The “Mathematical Progressions Across Modules” chart shows how module 1 connects to later work in module 2, “Measuring with Units,” module 3, “Bridging Space and Number,” and module 4, “Introducing Division and Fraction Relationships.” This shows how multiplication, area, data, measurement, division, and fractions are connected across the grade 3 course.
In the Teacher’s Implementation Guide, module 3, topic 8 explicitly connects area and perimeter concepts across topics and modules. The “Topic Overview” section explains that students connect counting tiles in an array to multiplication to determine the area of rectangles and then apply this understanding to determine the area of composite shapes. The “Connection to Prior Learning” section connects to topic 1, where students explored models of rectangular arrays and used repeated addition to determine the total number of square tiles. This connects prior multiplication and array work to current learning with area and composite figures.
Evaluation for 4.2b
In the Teacher’s Implementation Guide, module 1, topic 1 connects content and language from previous grade levels to current grade 3 learning. The “Connection to Prior Learning” section explains that in grade 2, students modeled and described multiplication and division through repeated addition and equal groups and worked with rows and columns through rectangular arrays. The current topic extends that learning as students use equal groups, arrays, and area models to make sense of multiplication and the area of rectangles.
The module 3, topic 8 overview also connects current learning to future grade-level content. The “Connection to Future Learning” section explains that in topic 9 students will create area models to represent multiplication and use those models to make sense of the commutative, associative, and distributive properties. This vertical connection shows how students’ grade 3 work with rectangular arrays, area, and composite figures prepares them for more advanced multiplication strategies and properties.
Evaluation for 4.2c
In the Teacher’s Implementation Guide, module 3, topic 8, lesson 6, students build on their prior work with rectangular arrays, area, and composite figures. The lesson begins with the “Take the L or the T?” activity, where students determine whether an L-shaped or T-shaped figure is larger and explain how they know. Students use their understanding of partitioning composite shapes into rectangles and finding area to justify their reasoning.
In the same lesson, students continue applying prior area concepts in the “Clarify Centers,” “Solidify Centers,” and “Stretch Centers.” In center 1, students determine missing side lengths in L-shaped and T-shaped figures before calculating area. In center 2, students determine areas of composite shapes made of rectangles. In center 3, students determine the area of each room in tiny floor plans. These tasks connect prior knowledge of arrays, multiplication, side lengths, and rectangular area to more complex work with composite shapes.
Evaluation for 4.3a
The Teacher’s Implementation Guide provides spaced retrieval opportunities through “Re-Engagement Lessons.” In module 3, topic 8, lesson 6, students revisit previously learned concepts after the initial instruction. The lesson includes a “Planning to Re-Engage” section after lesson 5, which directs educators to use the “Reflect” activity to assess students’ level of understanding of determining unknown side lengths in composite shapes. Lesson 6 then uses that information to reengage students with area, side lengths, and composite shapes.
The same “Re-Engagement Lesson” includes a “Spaced Review” component that directs educators to download and print spaced review for students. This gives students an additional opportunity to retrieve previously learned skills while they are also reengaging with the current topic. The “Re-Engagement Lesson” structure, combined with the “Clarify Centers,” “Stretch Centers,” and “Solidify Centers,” supports retrieval of prior learning over time rather than only practicing a skill immediately after the initial instruction.
Evaluation for 4.3b
The Student Practice Book provides interleaved practice opportunities by mixing previously learned skills with current lesson content. Module 1, topic 1, lesson 1 identifies interleaved practice that reviews modeling equivalent sets while students determine the number of dots in arrays and images of equal groups. This requires students to apply prior counting and grouping concepts while working in a new multiplication context.
In lesson 6, the Student Practice Book identifies interleaved practice that reviews drawing equal groups while students define multiplication and connect equal groups to multiplication expressions. In lesson 7, the Student Practice Book identifies interleaved practice that reviews solving word problems involving multiplication by drawing a model. These tasks mix current multiplication learning with previously learned modeling, counting, equal-group, and problem-solving skills across the topic.
4.1 Depth of Key Concepts
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.
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.
2 out of 2 points
Evaluation for 4.1a
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.
2 out of 2 points
In the Assessment Suite, module 1, the “End-of-Module Assessment” requires students to demonstrate depth of understanding across multiple TEKS-aligned concepts. Students create and interpret scaled pictographs and bar graphs and solve comparison questions using data displays. Students shade a grid to show a rectangle with an area of 12 square units, write a multiplication equation to represent the rectangle, and identify an expression represented by an array. Then, they evaluate whether an estimate is reasonable; solve addition and subtraction problems using strategies; write an equation with a letter for an unknown in a multistep word problem; and draw an area model, array, or equal groups to represent 4 × 7. These assessment tasks require students to apply concepts through representations, equations, reasoning, and problem-solving.
4.1b
Questions and tasks progressively increase in rigor and complexity, leading to grade-level proficiency in the mathematics TEKS.
Questions and tasks progressively increase in rigor and complexity, leading to grade-level proficiency in the mathematics TEKS.
1 out of 1 points
Evaluation for 4.1b
Evaluation for 4.1b
Questions and tasks progressively increase in rigor and complexity, leading to grade-level proficiency in the mathematics TEKS.
1 out of 1 points
The progression continues in module 1, topic 1, lessons 7 and 8 as students apply multiplication concepts in more complex ways. In lesson 7, students determine the number of toothbrushes and field goals in real-world contexts, identify factors, and write multiplication word problems. In lesson 8, students use choral counting, skip counting, and games to identify factor and multiple relationships. This sequence moves students from visual and concrete models to real-world multiplication situations, factor language, multiples, patterns, and mathematical justification.
4.2 Coherence of Key Concepts
4.2a
Materials demonstrate coherence across units by explicitly connecting patterns, big ideas, and relationships between mathematical concepts.
Materials demonstrate coherence across units by explicitly connecting patterns, big ideas, and relationships between mathematical concepts.
1 out of 1 points
Evaluation for 4.2a
Evaluation for 4.2a
Materials demonstrate coherence across units by explicitly connecting patterns, big ideas, and relationships between mathematical concepts.
1 out of 1 points
In the Teacher’s Implementation Guide, module 3, topic 8 explicitly connects area and perimeter concepts across topics and modules. The “Topic Overview” section explains that students connect counting tiles in an array to multiplication to determine the area of rectangles and then apply this understanding to determine the area of composite shapes. The “Connection to Prior Learning” section connects to topic 1, where students explored models of rectangular arrays and used repeated addition to determine the total number of square tiles. This connects prior multiplication and array work to current learning with area and composite figures.
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.
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.
3 out of 3 points
Evaluation for 4.2b
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.
3 out of 3 points
The module 3, topic 8 overview also connects current learning to future grade-level content. The “Connection to Future Learning” section explains that in topic 9 students will create area models to represent multiplication and use those models to make sense of the commutative, associative, and distributive properties. This vertical connection shows how students’ grade 3 work with rectangular arrays, area, and composite figures prepares them for more advanced multiplication strategies and properties.
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..
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..
4 out of 4 points
Evaluation for 4.2c
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..
4 out of 4 points
In the same lesson, students continue applying prior area concepts in the “Clarify Centers,” “Solidify Centers,” and “Stretch Centers.” In center 1, students determine missing side lengths in L-shaped and T-shaped figures before calculating area. In center 2, students determine areas of composite shapes made of rectangles. In center 3, students determine the area of each room in tiny floor plans. These tasks connect prior knowledge of arrays, multiplication, side lengths, and rectangular area to more complex work with composite shapes.
4.3 Spaced and Interleaved Practice
4.3a
Materials provide spaced retrieval opportunities with previously learned skills and concepts across lessons and units.
Materials provide spaced retrieval opportunities with previously learned skills and concepts across lessons and units.
4 out of 4 points
Evaluation for 4.3a
Evaluation for 4.3a
Materials provide spaced retrieval opportunities with previously learned skills and concepts across lessons and units.
4 out of 4 points
The same “Re-Engagement Lesson” includes a “Spaced Review” component that directs educators to download and print spaced review for students. This gives students an additional opportunity to retrieve previously learned skills while they are also reengaging with the current topic. The “Re-Engagement Lesson” structure, combined with the “Clarify Centers,” “Stretch Centers,” and “Solidify Centers,” supports retrieval of prior learning over time rather than only practicing a skill immediately after the initial instruction.
4.3b
Materials provide interleaved practice opportunities with previously learned skills and concepts across lessons and units.
Materials provide interleaved practice opportunities with previously learned skills and concepts across lessons and units.
4 out of 4 points
Evaluation for 4.3b
Evaluation for 4.3b
Materials provide interleaved practice opportunities with previously learned skills and concepts across lessons and units.
4 out of 4 points
In lesson 6, the Student Practice Book identifies interleaved practice that reviews drawing equal groups while students define multiplication and connect equal groups to multiplication expressions. In lesson 7, the Student Practice Book identifies interleaved practice that reviews solving word problems involving multiplication by drawing a model. These tasks mix current multiplication learning with previously learned modeling, counting, equal-group, and problem-solving skills across the topic.
Rubric Section 5
Balance of Conceptual and Procedural Understanding
Materials are designed to balance conceptual understanding, procedural skills, and fluency.
Total
100% (41 out of 41 points)
Evaluation for 5.1a
In the Teacher’s Implementation Guide, module 1, topic 1, lesson 2, “Arrays of Square Tiles,” students interpret and analyze arrays as mathematical models for multiplication and area. In “Counting Square Tiles,” students connect arrays to unit squares in a rectangle, determine the number of rows and columns, and write repeated-addition expressions that match the array. Educator prompts ask students to explain how the rows, columns, and total number of tiles are represented in the array, requiring students to analyze how the visual model represents the mathematical relationship.
In the same lesson, students continue analyzing representations in “Describing the Array.” Students use square tiles to build arrays, compare arrays with a partner, and use mathematical language such as row, column, and total number of square tiles to describe each model. Students explain how different arrays represent different arrangements and how the arrangement connects to a repeated-addition expression. These lesson tasks require students to interpret and analyze concrete and visual models for multiplication and area concepts.
Evaluation for 5.1b
In the Teacher’s Implementation Guide, module 2, topic 6, lesson 3 “Bunny Goes for a Run,” students create mathematical models to represent a real-world fractional situation. In “The Race Begins!,” students use colored rods to build a number line for a three-mile race with refueling stations every one-half mile. Students label whole-number and fractional benchmarks, show Bunny’s progress along the race, and explain how the number line represents the distance Bunny has traveled. These tasks require students to create a model that represents a mathematical situation involving fractional units.
In module 2, topic 4, lesson 4, “Pattern Blocks,” students create models to represent equal-sharing and fraction situations. In “Make It Equal,” students draw models to solve equal-sharing problems involving quesadillas and then explain how much each student receives. Later in the lesson, students use pattern blocks to model parts and wholes and then connect each block to a fraction based on the whole. These tasks require students to create concrete and visual models that represent mathematical situations involving fractional parts.
Evaluation for 5.1c
In the Teacher’s Implementation Guide, module 1, topic 2, lesson 13, students apply conceptual understanding to new problem situations and contexts. Students use the Problem-Solving Model to solve two-step word problems about temperature changes. Students identify what the problem is asking, determine how temperature changes throughout the day, write an equation, and solve for the unknown temperature. These tasks require students to apply addition and subtraction reasoning in an authentic measurement context.
The same lesson extends conceptual understanding through the “Changing Temperatures” section. Students use a thermometer and equations to solve two-step word problems about temperature changes. Educator prompts ask students to explain how the thermometer helps make sense of the problem, how the equation represents the situation, and how each step supports the final answer. These tasks require students to transfer addition and subtraction concepts to a new real-world context and justify their reasoning.
Evaluation for 5.2a
In the Teacher’s Implementation Guide, module 1, topic 1, lesson 8, students build automaticity and fluency through repeated skip counting and pattern recognition. During the “Choral Counting” activity, students count by twos, fives, and tens and then discuss the patterns they notice. This repeated practice supports fluency with multiplication-related number patterns and helps students develop automaticity with multiples.
In the same lesson, the “Carousel Counting” activity provides additional fluency practice with factors and multiples. Students work with multiplication charts to record multiples, identify the relationship between factors and multiples, and analyze patterns in the chart. Educator prompts ask students to explain how skip counting supports multiplication and how the listed numbers are related. These activities build fluency with multiplication facts, multiples, and number relationships needed for grade-level tasks.
Evaluation for 5.2b
In the Teacher’s Implementation Guide, module 3, topic 9, lesson 8, students practice efficient, flexible, and accurate mathematical procedures. In the “Multiplying Using Related Facts” section, students complete related multiplication equations using the distributive property. Students break apart factors, use known facts to determine unknown facts, and explain how related facts help them multiply efficiently. These tasks give students opportunities to practice flexible multiplication procedures while maintaining accuracy.
In the same lesson, the “Comparing Partial Products and the Standard Algorithm” section gives students opportunities to compare and practice multiple multiplication procedures. Students analyze partial products and the standard algorithm, explain how each method represents the same multiplication problem, and discuss why one procedure may be more efficient in certain situations. These lesson tasks support procedural fluency by helping students apply accurate strategies and compare the efficiency of different approaches.
Evaluation for 5.2c
In the Teacher’s Implementation Guide, module 1, topic 2, lesson 2, students evaluate procedures, processes, and solutions for efficiency, flexibility, and accuracy. In the “Decomposing Numbers to Add” section, students solve addition equations by decomposing numbers and using place-value strategies. Educator prompts ask students to explain how they broke apart numbers, whether they used an efficient strategy, and whether their sum is reasonable. Students evaluate the strategy they used and justify the accuracy of their solution.
The same lesson provides additional opportunities for students to compare procedures through “Expanded Form” and “Reflection” tasks. Students represent numbers in expanded form, solve addition problems, and discuss how expanded form helps them add accurately. In the “Reflection” task, students solve addition equations within a real-world situation and explain what strategy they used. Students evaluate how different procedures support efficient and accurate addition.
Evaluation for 5.2d
In the Teacher’s Implementation Guide, module 3, topic 8, lesson 2, the “About the Math” section explains that students begin by partitioning shapes on a grid into smaller rectangles and then use the grid to determine side lengths. The guidance then explains that students transition to determining side lengths without a grid. This progression supports educators in moving students from visual models toward more efficient procedures for finding area.
In the same lesson, the “Areas of Composite Shapes Made of Rectangles” section provides embedded educator guidance for helping students determine the area of composite figures. Students partition composite shapes into smaller rectangles, write multiplication equations for each part, and add the smaller areas to find the total area. “Ongoing Assessment” prompts guide educators to observe whether students partition correctly, determine side lengths, and connect the visual model to multiplication and addition equations. These supports help educators guide students toward increasingly efficient area strategies.
Evaluation for 5.3a
In the Teacher’s Implementation Guide Overview, the “Emphasizing Focus, Coherence, and Balance” section explicitly states how conceptual understanding is developed. The “Building Conceptual Understanding” section explains that students use models, manipulatives, and visual representations to develop understanding before moving to abstract procedures. Grade 3 examples include students using square tiles, arrays, and area models to connect rows, columns, and total square units to multiplication. This guidance explicitly describes how the conceptual emphasis of the TEKS is addressed.
The same “Emphasizing Focus, Coherence, and Balance” overview explicitly describes how procedural fluency is developed alongside conceptual understanding. The materials explain that students use strategies, patterns, and repeated practice to develop efficient and accurate procedures. The grade 3 multiplication examples connect visual models and contextual tasks to equations and multiplication procedures, showing how conceptual understanding supports procedural fluency rather than treating procedures as isolated steps.
Evaluation for 5.3b
In the Teacher’s Implementation Guide, module 2, topic 6, lesson 3, “Bunny Goes for a Run,” students use concrete models, pictorial representations, and abstract representations as required by the TEKS. Students use colored rods as concrete models to build a fractional number line, label benchmark distances, and connect the model to fraction language such as halves and fourths. Students then use the number line representation to answer questions about Bunny’s distance in the race.
In module 3, topic 8, lesson 2, students also use concrete and pictorial models connected to abstract representations. Students use grid models of L-shaped and T-shaped polygons, partition the shapes into rectangles, determine side lengths, and write multiplication and addition equations to find total area. These tasks connect visual area models, drawings of composite figures, and symbolic calculations.
Evaluation for 5.3c
In the Teacher’s Implementation Guide, module 2, topic 4, lesson 4 includes supports for students in connecting, creating, defining, and explaining concrete and representational models to abstract fraction concepts. Students create models with pattern blocks to represent parts of a whole and determine the unit fraction represented by each block. Educator prompts guide students to define the whole, identify the fractional part, and explain why the same pattern block can represent different fractional values depending on the whole. Students connect concrete pattern blocks and visual models to abstract fraction notation and fraction language.
In Teacher’s Implementation Guide, module 3, topic 8, lesson 2 includes supports for students in connecting, creating, defining, and explaining concrete and representational models to abstract area concepts and procedures. Students create and analyze grid models of composite polygons, partition the figures into rectangles, define side lengths and partial areas, and explain how each smaller rectangle contributes to the total area. Educator prompts guide students to connect the visual partitions to multiplication equations and addition of partial areas. Students move from concrete and representational area models to abstract symbolic procedures for finding the area of composite figures.
Evaluation for 5.4a
In the Teacher’s Implementation Guide, module 1, topic 1, lesson 2, students develop academic mathematical language using visuals, manipulatives, and structured language supports. Students use dot array cards to identify rows, columns, and the total number of dots. Students describe the arrays using mathematical vocabulary such as row, column, horizontal, vertical, and total. Educator guidance includes labeled array illustrations, visual representations, and purposeful questions that encourage students to use academic mathematical language as they explain observations and justify reasoning.
In the Teacher’s Implementation Guide, module 2, topic 4, lesson 4, students develop academic mathematical language through concrete models and educator-facilitated discourse. Students use pattern blocks to identify fractional parts of a whole and describe relationships among the shapes using terms such as whole, part, equal parts, and fraction. Educator prompts guide students to explain how each pattern block represents a fractional part of the whole while using visual models to support mathematical discussions.
Evaluation for 5.4b
In the Teacher’s Implementation Guide, module 1, topic 1, lesson 12 includes embedded educator guidance to scaffold students’ development and use of academic mathematical vocabulary in context. In the “Language Link: Developing Mathematical Language,” section students solve equal-group multiplication problems by completing tables that show the number of legs for groups of animals. The “Language Link” defines and reinforces vocabulary such as equal groups and multiplication, while educator prompts guide students to apply these terms as they explain their strategies and discuss multiplication situations. Additional differentiation guidance encourages educators to revisit the class anchor chart and support students as they progress from drawing pictures to representing multiplication with models and equations.
In the Teacher’s Implementation Guide, module 4, topic 10, lesson 3 includes embedded support for using academic vocabulary in context. The “Teacher Story” supports students as they determine unknown factors and describe the strategies they use to solve multiplication problems. Educator guidance connects students’ prior understanding of inverse operations to multiplication and division while modeling the use of precise mathematical vocabulary during instruction.
Evaluation for 5.4c
In the Teacher’s Implementation Guide, module 4, topic 11, lesson 6 includes embedded educator guidance to support mathematical conversations through vocabulary, syntax, and discourse. Students compare fractions represented on a number line and explain which fraction is greater using mathematical vocabulary. During a Think-Pair-Share, students discuss whether each fraction is closer to 0 or 1 and justify their reasoning. Educator guidance includes facilitation notes, sample responses, and differentiation strategies that support students in communicating mathematical ideas clearly while refining their use of academic mathematical language.
In the Teacher’s Implementation Guide, module 2, topic 4, lesson 7, students apply mathematical language through concrete models and guided discussion. Students use colored rods to model fractions, explain how the rods represent equal parts of a whole, compare models, describe fractional relationships, and connect their concrete models to fraction notation. Educator questioning encourages students to communicate their reasoning using precise mathematical language, giving students opportunities to hear, refine, and use mathematical vocabulary during discussion.
Evaluation for 5.5a
In the Teacher’s Implementation Guide, module 1, topic 2, lesson 6, the TEKS mathematical process standards are integrated appropriately into the materials. During the “Reflect: Reflect and Summarize” activity, students compare multiple subtraction strategies, explain which strategy they selected, and justify why it is effective for solving the problem. “Reflect” prompts ask students to describe similarities and differences among strategies and explain how each method leads to the correct solution. Educator guidance encourages students to discuss their reasoning and evaluate solution methods using precise mathematical language.
In the Teacher’s Implementation Guide, module 3, “Mindset Reflection” activity, the TEKS mathematical process standards are integrated as students reflect on how they approached challenging mathematical tasks. Students identify strategies that helped them persevere when solving problems, discuss their thinking, recognize productive learning behaviors, and connect their experiences to future mathematical learning. These structured reflection opportunities promote students’ awareness of their mathematical reasoning and learning process.
Evaluation for 5.5b
In the Teacher’s Implementation Guide Overview, the “Foundations for Effective Math Instruction: Attending to the Mathematical Process Standards” describes how the TEKS mathematical process standards are incorporated and connected throughout the course. The overview explains that “Topic Overview” sections identify the process standards emphasized within each topic and that Student Look-Fors help educators recognize evidence of students demonstrating the process standards during instruction. These embedded supports help educators intentionally plan for and monitor students’ engagement with the TEKS mathematical process standards.
The same “Foundations for Effective Math Instruction: Attending to the Mathematical Process Standards” section explains that “Reflect” activities and “Mindset Reflections” in “Re-Engagement Lessons” provide structured opportunities for students to consider how they applied the TEKS mathematical process standards while solving problems. Educator guidance encourages students to reflect on mathematical reasoning and productive learning behaviors, reinforcing continued use of the process standards throughout the course.
Evaluation for 5.5c
In the Teacher’s Implementation Guide Overview, the “Foundations for Effective Math Instruction: Attending to the Mathematical Process Standards” section describes how process standards are incorporated and connected throughout instruction. The overview explains that Student Look-Fors identify observable behaviors that demonstrate students’ use of the TEKS mathematical process standards as they solve problems, communicate mathematical ideas, justify reasoning, and make connections among mathematical concepts. These supports help educators recognize and reinforce students’ application of the process standards across lessons within a topic.
The same overview describes how “Reflect” activities and “Mindset Reflections” provide structured opportunities for students to evaluate how they used the TEKS mathematical process standards during learning. Educator guidance encourages students to discuss their reasoning, reflect on productive mathematical behaviors, and consider how their thinking supports future problem-solving. These reflection opportunities reinforce students’ ongoing use of the TEKS mathematical process standards across the unit or topic.
Evaluation for 5.5d
In the Teacher’s Implementation Guide Overview, the “Foundations for Effective Math Instruction: Attending to the Mathematical Process Standards” section provides an overview of how the TEKS mathematical process standards are incorporated into instruction. The “Topic Overview” sections identify the TEKS mathematical process standards emphasized within each topic and describe how those standards are intentionally incorporated into the lesson sequence. This guidance helps educators recognize where students will engage in reasoning, problem-solving, mathematical communication, and making connections throughout instruction.
The same overview explains that Student Look-Fors identify observable evidence educators can use to monitor students’ application of the TEKS mathematical process standards during instruction. The materials describe how educators observe students communicating mathematical ideas, selecting solution strategies, justifying their reasoning, and making mathematical connections throughout lessons. These embedded supports help educators intentionally monitor and reinforce students’ use of the TEKS mathematical process standards during daily instruction.
5.1 Development of Conceptual Understanding
5.1a
Questions and tasks require students to interpret, analyze, and evaluate models and representations for mathematical concepts and situations.
Questions and tasks require students to interpret, analyze, and evaluate models and representations for mathematical concepts and situations.
3 out of 3 points
Evaluation for 5.1a
Evaluation for 5.1a
Questions and tasks require students to interpret, analyze, and evaluate models and representations for mathematical concepts and situations.
3 out of 3 points
In the same lesson, students continue analyzing representations in “Describing the Array.” Students use square tiles to build arrays, compare arrays with a partner, and use mathematical language such as row, column, and total number of square tiles to describe each model. Students explain how different arrays represent different arrangements and how the arrangement connects to a repeated-addition expression. These lesson tasks require students to interpret and analyze concrete and visual models for multiplication and area concepts.
5.1b
Questions and tasks require students to create models to represent mathematical situations.
Questions and tasks require students to create models to represent mathematical situations.
1 out of 1 points
Evaluation for 5.1b
Evaluation for 5.1b
Questions and tasks require students to create models to represent mathematical situations.
1 out of 1 points
In module 2, topic 4, lesson 4, “Pattern Blocks,” students create models to represent equal-sharing and fraction situations. In “Make It Equal,” students draw models to solve equal-sharing problems involving quesadillas and then explain how much each student receives. Later in the lesson, students use pattern blocks to model parts and wholes and then connect each block to a fraction based on the whole. These tasks require students to create concrete and visual models that represent mathematical situations involving fractional parts.
5.1c
Questions and tasks provide opportunities for students to apply conceptual understanding to new problem situations and contexts.
Questions and tasks provide opportunities for students to apply conceptual understanding to new problem situations and contexts.
1 out of 1 points
Evaluation for 5.1c
Evaluation for 5.1c
Questions and tasks provide opportunities for students to apply conceptual understanding to new problem situations and contexts.
1 out of 1 points
The same lesson extends conceptual understanding through the “Changing Temperatures” section. Students use a thermometer and equations to solve two-step word problems about temperature changes. Educator prompts ask students to explain how the thermometer helps make sense of the problem, how the equation represents the situation, and how each step supports the final answer. These tasks require students to transfer addition and subtraction concepts to a new real-world context and justify their reasoning.
5.2 Development of Fluency
5.2a
Materials provide tasks that are designed to build student automaticity and fluency necessary to complete grade-level tasks.
Materials provide tasks that are designed to build student automaticity and fluency necessary to complete grade-level tasks.
2 out of 2 points
Evaluation for 5.2a
Evaluation for 5.2a
Materials provide tasks that are designed to build student automaticity and fluency necessary to complete grade-level tasks.
2 out of 2 points
In the same lesson, the “Carousel Counting” activity provides additional fluency practice with factors and multiples. Students work with multiplication charts to record multiples, identify the relationship between factors and multiples, and analyze patterns in the chart. Educator prompts ask students to explain how skip counting supports multiplication and how the listed numbers are related. These activities build fluency with multiplication facts, multiples, and number relationships needed for grade-level tasks.
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.
Materials provide opportunities for students to practice the application of efficient, flexible, and accurate mathematical procedures within the lesson and/or throughout a unit.
3 out of 3 points
Evaluation for 5.2b
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.
3 out of 3 points
In the same lesson, the “Comparing Partial Products and the Standard Algorithm” section gives students opportunities to compare and practice multiple multiplication procedures. Students analyze partial products and the standard algorithm, explain how each method represents the same multiplication problem, and discuss why one procedure may be more efficient in certain situations. These lesson tasks support procedural fluency by helping students apply accurate strategies and compare the efficiency of different approaches.
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.
Materials provide opportunities for students to evaluate procedures, processes, and solutions for efficiency, flexibility, and accuracy within the lesson and throughout a unit.
3 out of 3 points
Evaluation for 5.2c
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.
3 out of 3 points
The same lesson provides additional opportunities for students to compare procedures through “Expanded Form” and “Reflection” tasks. Students represent numbers in expanded form, solve addition problems, and discuss how expanded form helps them add accurately. In the “Reflection” task, students solve addition equations within a real-world situation and explain what strategy they used. Students evaluate how different procedures support efficient and accurate addition.
5.2d
Materials contain embedded supports for teachers to guide students toward increasingly efficient approaches.
Materials contain embedded supports for teachers to guide students toward increasingly efficient approaches.
1 out of 1 points
Evaluation for 5.2d
Evaluation for 5.2d
Materials contain embedded supports for teachers to guide students toward increasingly efficient approaches.
1 out of 1 points
In the same lesson, the “Areas of Composite Shapes Made of Rectangles” section provides embedded educator guidance for helping students determine the area of composite figures. Students partition composite shapes into smaller rectangles, write multiplication equations for each part, and add the smaller areas to find the total area. “Ongoing Assessment” prompts guide educators to observe whether students partition correctly, determine side lengths, and connect the visual model to multiplication and addition equations. These supports help educators guide students toward increasingly efficient area strategies.
5.3 Balance of Conceptual Understanding and Procedural Fluency
5.3a
Materials explicitly state how the conceptual and procedural emphasis of the TEKS are addressed.
Materials explicitly state how the conceptual and procedural emphasis of the TEKS are addressed.
2 out of 2 points
Evaluation for 5.3a
Evaluation for 5.3a
Materials explicitly state how the conceptual and procedural emphasis of the TEKS are addressed.
2 out of 2 points
The same “Emphasizing Focus, Coherence, and Balance” overview explicitly describes how procedural fluency is developed alongside conceptual understanding. The materials explain that students use strategies, patterns, and repeated practice to develop efficient and accurate procedures. The grade 3 multiplication examples connect visual models and contextual tasks to equations and multiplication procedures, showing how conceptual understanding supports procedural fluency rather than treating procedures as isolated steps.
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.
Questions and tasks include the use of concrete models and manipulatives, pictorial representations (figures/drawings), and abstract representations, as required by the TEKS.
3 out of 3 points
Evaluation for 5.3b
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.
3 out of 3 points
In module 3, topic 8, lesson 2, students also use concrete and pictorial models connected to abstract representations. Students use grid models of L-shaped and T-shaped polygons, partition the shapes into rectangles, determine side lengths, and write multiplication and addition equations to find total area. These tasks connect visual area models, drawings of composite figures, and symbolic calculations.
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.
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.
6 out of 6 points
Evaluation for 5.3c
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.
6 out of 6 points
In Teacher’s Implementation Guide, module 3, topic 8, lesson 2 includes supports for students in connecting, creating, defining, and explaining concrete and representational models to abstract area concepts and procedures. Students create and analyze grid models of composite polygons, partition the figures into rectangles, define side lengths and partial areas, and explain how each smaller rectangle contributes to the total area. Educator prompts guide students to connect the visual partitions to multiplication equations and addition of partial areas. Students move from concrete and representational area models to abstract symbolic procedures for finding the area of composite figures.
5.4 Development of Academic Mathematical Language
5.4a
Materials provide opportunities for students to develop academic mathematical language using visuals, manipulatives, and other language development strategies.
Materials provide opportunities for students to develop academic mathematical language using visuals, manipulatives, and other language development strategies.
3 out of 3 points
Evaluation for 5.4a
Evaluation for 5.4a
Materials provide opportunities for students to develop academic mathematical language using visuals, manipulatives, and other language development strategies.
3 out of 3 points
In the Teacher’s Implementation Guide, module 2, topic 4, lesson 4, students develop academic mathematical language through concrete models and educator-facilitated discourse. Students use pattern blocks to identify fractional parts of a whole and describe relationships among the shapes using terms such as whole, part, equal parts, and fraction. Educator prompts guide students to explain how each pattern block represents a fractional part of the whole while using visual models to support mathematical discussions.
5.4b
Materials include embedded teacher guidance to scaffold and support students' development and use of academic mathematical vocabulary in context.
Materials include embedded teacher guidance to scaffold and support students' development and use of academic mathematical vocabulary in context.
1 out of 1 points
Evaluation for 5.4b
Evaluation for 5.4b
Materials include embedded teacher guidance to scaffold and support students' development and use of academic mathematical vocabulary in context.
1 out of 1 points
In the Teacher’s Implementation Guide, module 4, topic 10, lesson 3 includes embedded support for using academic vocabulary in context. The “Teacher Story” supports students as they determine unknown factors and describe the strategies they use to solve multiplication problems. Educator guidance connects students’ prior understanding of inverse operations to multiplication and division while modeling the use of precise mathematical vocabulary during instruction.
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.
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.
6 out of 6 points
Evaluation for 5.4c
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.
6 out of 6 points
In the Teacher’s Implementation Guide, module 2, topic 4, lesson 7, students apply mathematical language through concrete models and guided discussion. Students use colored rods to model fractions, explain how the rods represent equal parts of a whole, compare models, describe fractional relationships, and connect their concrete models to fraction notation. Educator questioning encourages students to communicate their reasoning using precise mathematical language, giving students opportunities to hear, refine, and use mathematical vocabulary during discussion.
5.5 Process Standards Connections
5.5a
TEKS process standards are integrated appropriately into the materials.
TEKS process standards are integrated appropriately into the materials.
1 out of 1 points
Evaluation for 5.5a
Evaluation for 5.5a
TEKS process standards are integrated appropriately into the materials.
1 out of 1 points
In the Teacher’s Implementation Guide, module 3, “Mindset Reflection” activity, the TEKS mathematical process standards are integrated as students reflect on how they approached challenging mathematical tasks. Students identify strategies that helped them persevere when solving problems, discuss their thinking, recognize productive learning behaviors, and connect their experiences to future mathematical learning. These structured reflection opportunities promote students’ awareness of their mathematical reasoning and learning process.
5.5b
Materials include a description of how TEKS process standards are incorporated and connected throughout the course.
Materials include a description of how TEKS process standards are incorporated and connected throughout the course.
2 out of 2 points
Evaluation for 5.5b
Evaluation for 5.5b
Materials include a description of how TEKS process standards are incorporated and connected throughout the course.
2 out of 2 points
The same “Foundations for Effective Math Instruction: Attending to the Mathematical Process Standards” section explains that “Reflect” activities and “Mindset Reflections” in “Re-Engagement Lessons” provide structured opportunities for students to consider how they applied the TEKS mathematical process standards while solving problems. Educator guidance encourages students to reflect on mathematical reasoning and productive learning behaviors, reinforcing continued use of the process standards throughout the course.
5.5c
Materials include a description for each unit of how TEKS process standards are incorporated and connected throughout the unit.
Materials include a description for each unit of how TEKS process standards are incorporated and connected throughout the unit.
2 out of 2 points
Evaluation for 5.5c
Evaluation for 5.5c
Materials include a description for each unit of how TEKS process standards are incorporated and connected throughout the unit.
2 out of 2 points
The same overview describes how “Reflect” activities and “Mindset Reflections” provide structured opportunities for students to evaluate how they used the TEKS mathematical process standards during learning. Educator guidance encourages students to discuss their reasoning, reflect on productive mathematical behaviors, and consider how their thinking supports future problem-solving. These reflection opportunities reinforce students’ ongoing use of the TEKS mathematical process standards across the unit or topic.
5.5d
Materials include an overview of the TEKS process standards incorporated into each lesson.
Materials include an overview of the TEKS process standards incorporated into each lesson.
1 out of 1 points
Evaluation for 5.5d
Evaluation for 5.5d
Materials include an overview of the TEKS process standards incorporated into each lesson.
1 out of 1 points
The same overview explains that Student Look-Fors identify observable evidence educators can use to monitor students’ application of the TEKS mathematical process standards during instruction. The materials describe how educators observe students communicating mathematical ideas, selecting solution strategies, justifying their reasoning, and making mathematical connections throughout lessons. These embedded supports help educators intentionally monitor and reinforce students’ use of the TEKS mathematical process standards during daily instruction.
Rubric Section 6
Productive Struggle
Materials support students in applying disciplinary practices to productive problem-solving, including explaining and revising their thinking.
Total
100% (22 out of 22 points)
Evaluation for 6.1a
In the Teacher’s Implementation Guide, module 1, topic 1, lesson 12, “Explore 1: Animal Problem Solving” activity, students solve multiplication word problems by representing equal groups with drawings, models, and multiplication equations. Students use the Problem-Solving Model to determine a solution, explain how they selected their strategy, and justify their mathematical reasoning. Educator guidance includes purposeful questions, differentiation supports, and “Ongoing Assessment” prompts that encourage students to persevere, explain their thinking, and refine their problem-solving strategies.
In the same lesson, the “Reflect: Reflect and Summarize” activity reinforces students’ ability to make sense of mathematics by analyzing and explaining their problem-solving process. Students explain how they determined unknown quantities, identify the mathematical tools they used (including tables, equal-group drawings, arrays, and multiplication equations), and describe why a variable represents an unknown value. Educator guidance facilitates discussion that prompts students to reflect on their solution strategies and communicate their mathematical thinking.
Evaluation for 6.1b
In the Teacher’s Implementation Guide, module 1, topic 1, lesson 12, students understand, explain, and justify that there can be multiple ways to represent and solve problems. In “Explore 1: Animal Problem Solving,” students represent multiplication situations using drawings, models, addition sentences, and multiplication equations. Educator prompts guide students to explain the strategies they selected, compare their representations, and describe how each representation models the same mathematical situation.
In the same lesson, “Explore 3: Problem Solving with Equal Groups” and “Reflect: Reflect and Summarize” provide additional opportunities for students to justify multiple representations and solution strategies. Students solve classmates’ multiplication problems using words, numbers, pictures, equal-group models, arrays, and multiplication equations. Students explain how they determined each equation, identify the mathematical tools they used, and justify how their chosen representation supported their solution. Educator guidance facilitates discussion that encourages students to compare strategies and explain why different representations can produce valid solutions.
Evaluation for 6.1c
In the Teacher’s Implementation Guide, module 1, topic 2, lesson 13, students make sense of mathematics through opportunities to do, write about, and discuss mathematics with peers and educators. In “Explore 2: Reasonable and Unreasonable Answers,” students work with a partner to solve temperature problems and determine whether proposed solutions are reasonable or unreasonable. Students explain their reasoning, compare solutions, and justify why a solution is valid based on the context of the problem. Educator guidance includes facilitation prompts that encourage students to discuss their thinking, question one another’s reasoning, and support conclusions with mathematical evidence.
In the same lesson, the “Explore 3: Solving Temperature Problems” activity gives students additional opportunities to make sense of mathematics through problem-solving and explanation. Students apply the Problem-Solving Model to real-world temperature situations and explain how they determined the unknown quantity. Educator prompts guide students to describe the strategy they selected, defend why it was appropriate, and verify that their solution is reasonable. These activities reinforce students’ ability to justify mathematical reasoning while solving contextual problems.
Evaluation for 6.2a
In the Teacher’s Implementation Guide, module 1, topic 2, lesson 13 provides educators with guidance to support students in sharing and reflecting on problem-solving approaches through explanations, arguments, and justifications. In “Explore 3: Solving Temperature Problems,” students use the Problem-Solving Model to analyze temperature situations, develop a solution plan, and explain how they determined the unknown quantity. Educator guidance includes purposeful questions prompting students to describe the problem is asking, how they selected a strategy, and how they know their solution is reasonable. “Ongoing Assessment” guidance supports educators in monitoring students’ explanations and mathematical reasoning throughout the problem-solving process.
In the same lesson, the “Reflect: Reflect and Summarize” activity provides additional support for students to share and evaluate their problem-solving approaches. Students explain the strategies they used to solve temperature problems and discuss how the Problem-Solving Model supported their thinking. Educator guidance facilitates mathematical discussions that encourage students to reflect on their reasoning and communicate how they determined their solutions.
Evaluation for 6.2b
In the Teacher’s Implementation Guide, module 5, topic 12, lesson 4 provides educators with prompts and guidance to support explanatory feedback based on student responses and anticipated misconceptions. In “Activate: Understanding Quantities Beyond 1,000,” the “Common Misconception” support identifies a likely misunderstanding that students may believe two digits can occupy the same place-value position. Educator guidance explains the misconception and provides instructional prompts that help educators question students about their reasoning, clarify misunderstandings, and reinforce accurate place-value concepts using base 10 blocks and place-value representations.
In the same lesson, the “Explore 1: Building Numbers Beyond 1,000” section provides additional prompts and guidance for explanatory feedback. Students use base 10 blocks to model numbers greater than 1,000 and explain how each digit represents a specific place value. Educator guidance includes “Ongoing Assessment” prompts that encourage educators to monitor students’ explanations, identify misconceptions, and provide feedback that builds conceptual understanding of place value. These instructional supports help educators respond to student thinking with timely explanatory feedback.
6.1 Student Self-Efficacy
6.1a
Materials provide opportunities for students to think mathematically, persevere through solving problems, and to make sense of mathematics.
Materials provide opportunities for students to think mathematically, persevere through solving problems, and to make sense of mathematics.
3 out of 3 points
Evaluation for 6.1a
Evaluation for 6.1a
Materials provide opportunities for students to think mathematically, persevere through solving problems, and to make sense of mathematics.
3 out of 3 points
In the same lesson, the “Reflect: Reflect and Summarize” activity reinforces students’ ability to make sense of mathematics by analyzing and explaining their problem-solving process. Students explain how they determined unknown quantities, identify the mathematical tools they used (including tables, equal-group drawings, arrays, and multiplication equations), and describe why a variable represents an unknown value. Educator guidance facilitates discussion that prompts students to reflect on their solution strategies and communicate their mathematical thinking.
6.1b
Materials support students in understanding, explaining, and justifying that there can be multiple ways to represent and solve problems and complete tasks.
Materials support students in understanding, explaining, and justifying that there can be multiple ways to represent and solve problems and complete tasks.
6 out of 6 points
Evaluation for 6.1b
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.
6 out of 6 points
In the same lesson, “Explore 3: Problem Solving with Equal Groups” and “Reflect: Reflect and Summarize” provide additional opportunities for students to justify multiple representations and solution strategies. Students solve classmates’ multiplication problems using words, numbers, pictures, equal-group models, arrays, and multiplication equations. Students explain how they determined each equation, identify the mathematical tools they used, and justify how their chosen representation supported their solution. Educator guidance facilitates discussion that encourages students to compare strategies and explain why different representations can produce valid solutions.
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.
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.
3 out of 3 points
Evaluation for 6.1c
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.
3 out of 3 points
In the same lesson, the “Explore 3: Solving Temperature Problems” activity gives students additional opportunities to make sense of mathematics through problem-solving and explanation. Students apply the Problem-Solving Model to real-world temperature situations and explain how they determined the unknown quantity. Educator prompts guide students to describe the strategy they selected, defend why it was appropriate, and verify that their solution is reasonable. These activities reinforce students’ ability to justify mathematical reasoning while solving contextual problems.
6.2 Facilitating Productive Struggle
6.2a
Materials support teachers in guiding students to share and reflect on their problem-solving approaches, including explanations, arguments, and justifications.
Materials support teachers in guiding students to share and reflect on their problem-solving approaches, including explanations, arguments, and justifications.
6 out of 6 points
Evaluation for 6.2a
Evaluation for 6.2a
Materials support teachers in guiding students to share and reflect on their problem-solving approaches, including explanations, arguments, and justifications.
6 out of 6 points
In the same lesson, the “Reflect: Reflect and Summarize” activity provides additional support for students to share and evaluate their problem-solving approaches. Students explain the strategies they used to solve temperature problems and discuss how the Problem-Solving Model supported their thinking. Educator guidance facilitates mathematical discussions that encourage students to reflect on their reasoning and communicate how they determined their solutions.
6.2b
Materials include prompts and guidance to support teachers in providing explanatory feedback based on student responses and anticipated misconceptions.
Materials include prompts and guidance to support teachers in providing explanatory feedback based on student responses and anticipated misconceptions.
4 out of 4 points
Evaluation for 6.2b
Evaluation for 6.2b
Materials include prompts and guidance to support teachers in providing explanatory feedback based on student responses and anticipated misconceptions.
4 out of 4 points
In the same lesson, the “Explore 1: Building Numbers Beyond 1,000” section provides additional prompts and guidance for explanatory feedback. Students use base 10 blocks to model numbers greater than 1,000 and explain how each digit represents a specific place value. Educator guidance includes “Ongoing Assessment” prompts that encourage educators to monitor students’ explanations, identify misconceptions, and provide feedback that builds conceptual understanding of place value. These instructional supports help educators respond to student thinking with timely explanatory feedback.