Program Information
- ISBN
- 9798898864255
- 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 5
Math (English) Grade 5
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 5 | 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 5 Scope and Sequence (165), module 1, topic 1, lessons 1–10 identify the grade 5 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 5 Scope and Sequence (180), module 1, topic 1, lessons 1–9 organize grade 5 instruction by module and topic and identify the TEKS, ELPS, and mathematical concepts taught throughout the year. This course map helps educators see the standards, concepts, and pacing expectations for implementation.
Evaluation for 1.1b
The Scope and Sequence (165) provides pacing guidance for a 165-day instructional calendar. In module 1, topic 1, lessons 1–9, the scope and sequence identifies the grade 5 instructional progression, including the TEKS, ELPS, and mathematical concepts addressed throughout the course. This helps educators plan instruction while maintaining the intended sequence of the materials.
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 and calendar resources support effective implementation for various instructional calendars.
Evaluation for 1.1c
The Texas ClearMath Grade 5 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 the concepts connect throughout the year.
In the Texas ClearMath Grade 5 Teacher’s Implementation Guide Overview, the “Course Sequence” section identifies the course sequence and shows how modules and topics build across the instructional year.
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 also provides guidance for internalizing the materials so educators can prepare to implement them 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 topic 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 reengagement planning and implementation. This resource supports instructional leaders by providing a structure for coaching conversations and implementation support aligned with the design of the materials.
Evaluation for 1.2a
In the Teacher’s Implementation Guide, module 1, topic 1, the “About the Math,” “Connections to Prior and Future Learning,” and “Mathematical Progressions Across Topics” sections provide educators with background content knowledge, mathematical progressions, and instructional context for the concepts covered in the topic.
The Texas ClearMath Grade 5 Topic Summaries include academic vocabulary for each topic. In module 1, topic 1, the “Key Ideas” and “Key Terms” sections identify important vocabulary and provide descriptions and visual supports connected to the mathematics of the topic. These resources support educators in preparing students to use the academic vocabulary needed for instruction.
Evaluation for 1.2b
In the Texas ClearMath Grade 5 Student Practice Book, module 1, topic 1, the “Family Guide” section explains the mathematical concepts students are learning and includes key terms, conversation starters, practice opportunities, and a “Family Fun” activity. These resources provide families with guidance and activities that support student learning at home.
In the Student Practice Book, module 1, topic 1, the “Spanish Family Guide” section explains the mathematical concepts students are learning and includes key terms, conversation starters, and activities families can use to support student progress. These resources provide Spanish-speaking families with suggestions to reinforce learning outside the classroom.
Evaluation for 1.3a
In the Teacher’s Implementation Guide, module 2, topic 4, lesson 1 includes learning goals, TEKS, ELPS, and a sequence of “Activate,” “Explore,” and “Reflect” activities. These components provide lesson objectives, standards alignment, and instructional tasks that support content and language expectations.
In the Teacher’s Implementation Guide, module 2, topic 4, lesson 1, the “Ongoing Assessment” section prompts educators to monitor student understanding throughout instruction and to use student responses to inform instructional decisions. These embedded questions and assessments help educators measure student progress toward the lesson goals.
Evaluation for 1.3b
In the Teacher’s Implementation Guide, module 1, topic 1, lesson 1, the “Lesson Structure and Pacing Guide” section identifies the resources needed for instruction, including student book resources, digital downloads, kit materials, and other materials.
In the Teacher’s Implementation Guide, module 1, topic 1, lesson 1, the “Lesson Structure and Pacing Guide” section recommends time allocations for the “Activate,” “Explore,” and “Reflect” sections. This pacing guidance helps educators plan and deliver each lesson component.
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 use of lesson materials for 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 within 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 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 5 Scope and Sequence (180), module 1, topic 1, lessons 1–9 organize grade 5 instruction by module and topic and identify the TEKS, ELPS, and mathematical concepts taught throughout the year. This course map helps educators see the standards, concepts, and pacing expectations for implementation.
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 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 and 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 5 Teacher’s Implementation Guide Overview, the “Course Sequence” section identifies the course sequence and shows how modules and topics build across the instructional year.
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 topic 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 reengagement planning and implementation. This resource supports instructional leaders by providing a structure for coaching conversations and implementation support 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
The Texas ClearMath Grade 5 Topic Summaries include academic vocabulary for each topic. In module 1, topic 1, the “Key Ideas” and “Key Terms” sections identify important vocabulary and provide descriptions and visual supports connected to the mathematics of the topic. These resources support educators in preparing students to use the academic vocabulary needed for instruction.
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 explains the mathematical concepts students are learning and includes key terms, conversation starters, and activities families can use to support student progress. These resources provide Spanish-speaking families with suggestions to reinforce learning outside the classroom.
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 2, topic 4, lesson 1, the “Ongoing Assessment” section prompts educators to monitor student understanding throughout instruction and to use student responses to inform instructional decisions. These embedded questions and assessments help educators measure student progress toward the lesson goals.
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 1, the “Lesson Structure and Pacing Guide” section recommends time allocations for the “Activate,” “Explore,” and “Reflect” sections. This pacing guidance helps educators plan and deliver each lesson component.
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 within 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 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 5 Assessment Suite, 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, assessments include multiple-choice questions, written responses, mathematical models, and performance-based tasks that allow students to demonstrate understanding in different ways. Additionally, Teacher’s Implementation Guide includes ongoing assessment opportunities within lessons to help educators monitor student understanding and provide targeted support 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 5 Year-at-a-Glance (165) outlines when educators should 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 5 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, topic, 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, “Performance Task” sections include a rubric with scoring criteria and educator facilitation notes that support consistent scoring of student responses. The rubric provides clear expectations for evaluating student work and interpreting performance levels.
The Assessment Guide offers scoring guidance and assessment rubrics to support the evaluation of “End-of-Topic Assessments” and “Performance Tasks.” The guide also includes recommendations for using assessment results to inform instructional decisions.
Evaluation for 2.2b
In the Teacher’s Implementation Guide Overview, the “Unpacking a Re-Engagement Lesson” section explains how educators analyze student responses and use assessment evidence to plan targeted instruction. The guidance helps educators clarify, strengthen, and extend student understanding.
In the Assessment Guide, “Targeted Instruction Recommendations by TEKS” and “Suggestions for Using the Performance Task as an Assessment for Learning” offer guidance on responding to student performance and supporting continued growth.
Evaluation for 2.2c
In the Teacher’s Implementation Guide Overview, the “Using Data to Monitor and Celebrate Success” section describes assessment reports and recording tools that support monitoring student performance and informing instructional decisions. Interactive course-level assessment recording sheets also support ongoing tracking of student growth across modules.
In the Texas ClearMath Grade 5 Student Resource Book, “Topic Self-Reflection” activities provide student-friendly I Can statements that help students monitor their understanding of concepts and skills. These reflection tools encourage students to identify strengths, set goals, and track their progress over time.
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, assessments include multiple-choice questions, written responses, mathematical models, and performance-based tasks that allow students to demonstrate understanding in different ways. Additionally, Teacher’s Implementation Guide includes ongoing assessment opportunities within lessons to help educators monitor student understanding and provide targeted support 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, topic, 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
The Assessment Guide offers scoring guidance and assessment rubrics to support the evaluation of “End-of-Topic Assessments” and “Performance Tasks.” The guide also includes recommendations for using assessment results to inform instructional decisions.
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 Assessment Guide, “Targeted Instruction Recommendations by TEKS” and “Suggestions for Using the Performance Task as an Assessment for Learning” offer guidance on responding to student performance and supporting continued growth.
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 Texas ClearMath Grade 5 Student Resource Book, “Topic Self-Reflection” activities provide student-friendly I Can statements that help students monitor their understanding of concepts and skills. These reflection tools encourage students to identify strengths, set goals, and track their progress over time.
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 4, the “Re-Engagement Lesson” gives students opportunities to revisit building rectangular prisms through targeted reteaching activities. The lesson helps educators address unfinished learning and strengthen conceptual understanding.
In the Teacher’s Implementation Guide, module 1, topic 2, lesson 3, “Just-In-Time Supports” and “Assistance for All” sections help educators respond to students’ needs during instruction. These supports provide scaffolded opportunities for students to deepen their understanding and engage with grade-level content.
Evaluation for 3.1b
In the Teacher’s Implementation Guide, module 2, topic 5, lesson 4, a “Language Link: Developing Contextual Language” section introduces the term apiary and guides educators in building background knowledge before students engage in lesson tasks. These supports help students understand unfamiliar language and access mathematical content.
In the Teacher’s Implementation Guide, “Topic Overview” sections include language development supports, real-world connections, and contextual learning opportunities that help educators introduce unfamiliar terms and strengthen student comprehension.
Evaluation for 3.1c
In the Teacher’s Implementation Guide, “Stretch Centers” offer students opportunities to extend their mathematical thinking through complex problem-solving activities. For example, in module 1, topic 1, lesson 9, the “Shrinking Prisms Stretch Center” challenges students to apply volume concepts and engage in deeper mathematical reasoning.
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 investigate mathematical relationships, apply concepts in new contexts, and deepen their understanding through advanced reasoning and problem-solving tasks.
Evaluation for 3.2a
In the Teacher’s Implementation Guide, facilitation notes include purposeful questions, anticipated student responses, and educator prompts that guide explanations, support mathematical discussions, and help educators build students’ understanding of key concepts.
In the Teacher’s Implementation Guide, “Concept Lessons” and “Re-Engagement Lessons” include instructional recommendations, discussion prompts, and sample explanations that help educators model mathematical thinking, address misconceptions, and support student learning.
Evaluation for 3.2b
In the Teacher’s Implementation Guide, purposeful questions embedded throughout the lessons prompt students to explain strategies, justify solutions, and engage in mathematical discourse that deepens conceptual understanding. These questions promote active participation and ongoing assessment of student learning.
In the Teacher’s Implementation Guide, educator facilitation notes include anticipated student responses, discussion prompts, and follow-up questions to help educators extend student thinking, address misconceptions, and strengthen conceptual understanding.
Evaluation for 3.2c
In the Teacher’s Implementation Guide, the “Lesson Structure and Pacing Guides” section includes guided practice, paired practice, collaborative problem-solving, games, cumulative review activities, and independent work. These structures provide students with multiple opportunities to practice and apply mathematical concepts.
In the Teacher’s Implementation Guide, lesson facilitation notes identify when students participate in collaborative discussions, partner activities, games, and independent practice. These recommended structures support effective lesson implementation and encourage students to engage with content through a variety of learning experiences.
Evaluation for 3.3a
The Texas ClearMath Grade 5 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 discourse and learn complex academic language.
Evaluation for 3.3b
In the Emergent Bilingual Student Support Handbook, topic-level resources provide instructional guidance for implementing language supports through modeling, real-world connections, structured discourse, and language-rich learning experiences.
The materials provide additional guidance to help educators implement language supports during daily instruction. In the Teacher’s Implementation Guide and the Emergent Bilingual Student Support Handbook, educators receive recommendations for using language-development routines, scaffolded supports, and instructional strategies that help emergent bilingual (EB) students engage with mathematical content and build academic language proficiency.
Evaluation for 3.3c
In the Teacher’s Implementation Guide, EB support activities guide students in learning and applying academic terms, such as x-axis and y-axis, through vocabulary-matching activities and visual representations. These supports help students access mathematical concepts while strengthening academic language.
In the Teacher’s Implementation Guide, students create visual displays, explain mathematical ideas, and engage in structured language-development activities that reinforce vocabulary and deepen conceptual understanding. These supports help students communicate mathematical thinking using precise academic language.
Evaluation for 3.3d
This guidance does not apply 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 2, lesson 3, “Just-In-Time Supports” and “Assistance for All” sections help educators respond to students’ needs during instruction. These supports provide scaffolded opportunities for students to deepen their understanding and engage with grade-level content.
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 language development supports, real-world connections, and contextual learning opportunities that help educators introduce unfamiliar terms and strengthen student comprehension.
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 investigate mathematical relationships, apply concepts in new contexts, and deepen their understanding through advanced reasoning and problem-solving tasks.
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, “Concept Lessons” and “Re-Engagement Lessons” include instructional recommendations, discussion prompts, and sample explanations that help educators model mathematical thinking, address misconceptions, and support student learning.
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 anticipated student responses, discussion prompts, and follow-up questions to help educators extend student thinking, address misconceptions, and strengthen conceptual understanding.
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, lesson facilitation notes identify when students participate in collaborative discussions, partner activities, games, and independent practice. These recommended structures support effective lesson implementation and encourage students to engage with content through a variety of learning experiences.
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 discourse and learn complex 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
The materials provide additional guidance to help educators implement language supports during daily instruction. In the Teacher’s Implementation Guide and the Emergent Bilingual Student Support Handbook, educators receive recommendations for using language-development routines, scaffolded supports, and instructional strategies that help emergent bilingual (EB) students engage with mathematical content and build academic language proficiency.
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 create visual displays, explain mathematical ideas, and engage in structured language-development activities that reinforce vocabulary and deepen conceptual understanding. These supports help students communicate mathematical thinking using precise 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 modeling and calculating volume using unit cubes, rectangular prisms, layers, and formulas. Students determine the area of the base and the volume of rectangular prisms, calculate volume using given dimensions, and connect area of the base to total volume. These practice opportunities require students to connect visual models, dimensions, area, volume, and formulas rather than simply substituting values into an equation.
In the Student Practice Book, module 1, topic 1, lesson 8, students propose sets of dimensions for boxes with specified volumes, determine the volume of a cube, compare the volume of two toy boxes with different dimensions, and explain which box has the greater volume. These tasks require students to apply volume concepts, reason about dimensions, compare quantities, and explain their mathematical thinking in problem contexts.
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 develop understanding of volume. The topic overview explains that students explore volume with unit cubes, identify attributes of rectangular prisms, use the size of layers to understand how to multiply the area of the base by the height, and relate volume to formulas such as (V = B \times h) and (V = l \times w \times h). This progression moves students from concrete unit-cube models to abstract formulas.
In the Teacher’s Implementation Guide, the student practice sequence in module 1, topic 1 shows increasing rigor across lessons. Students first identify dimensions and volumes of three-dimensional figures, then calculate the area of the base and volume of rectangular prisms, and later connect volume and area. In lesson 7, students determine the area of the base and volume of rectangular prisms with different dimensions and then analyze how doubling or halving one dimension affects the volume. This progression moves students from calculating volume to reasoning about relationships among dimensions, area, and volume.
Evaluation for 4.2a
In the Teacher’s Implementation Guide, the module 1 overview demonstrates coherence across units by connecting volume, expressions, order of operations, multiplication, division, and numerical relationships. The module overview identifies key concepts, including identifying attributes for calculating the volume of rectangular prisms, determining structure, representing calculations with numeric expressions, and using place value to develop fluency. This connects geometric measurement with numerical reasoning and expression writing.
In the Teacher’s Implementation Guide, module 1, the “Mathematical Progressions Across Modules” section focuses on constructing volume and expressions, while later modules build toward extending fraction concepts, multiplying and dividing fractions, solving problems with rational numbers, and analyzing classification and shapes. The “Connections to Future Learning” section explains that students will later use order of operations to evaluate numerical expressions, use all four operations with fractions and decimals, interpret expressions, and solve problems involving two- and three-dimensional figures. This shows how volume, operations, expressions, and problem-solving develop coherently across the course.
Evaluation for 4.2b
In the Teacher’s Implementation Guide, module 1, topic 1 overview connects prior grade-level learning to current grade 5 content. The “Connection to Prior Learning” section explains that in grade 2, students used an additive approach with square tiles to find area, and in grade 3, they developed a multiplicative approach using tiling and the formula for area. In grade 5, students extend that learning from area to volume by packing rectangular prisms with unit cubes and using layers to develop volume formulas.
In the Teacher’s Implementation Guide, module 1, topic 1 overview, the “Connection to Future Learning” section explains that in grade 6, students will solve problems involving the area of triangles, trapezoids, and parallelograms and will further explore solids and define the surface area of a solid figure. This shows a vertical progression from earlier area work, to grade 5 volume of rectangular prisms, to future work with more complex area concepts and surface area.
Evaluation for 4.2c
In the Teacher’s Implementation Guide, module 1, topic 1, students build on their prior understanding of area to develop volume. The topic overview explains that students explored area in earlier grades using additive and multiplicative approaches and now extend that understanding to rectangular prisms by counting unit cubes and using layers. Students learn that the area of the base can be multiplied by the height to determine the volume of a rectangular prism.
In the Student Practice Book, module 1, topic 1, lesson 6, students determine the area of the base and the volume of rectangular prisms. In lesson 7, they also determine the area of the base and volume and then analyze how changing a dimension affects volume. These tasks connect prior work with area and multiplication to new learning about volume, rectangular prisms, and volume formulas.
Evaluation for 4.3a
The Teacher’s Implementation Guide provides spaced retrieval opportunities through “Re-Engagement Lessons.” In module 1, topic 1, lesson 9, students revisit volume concepts after initial instruction. The Student Practice Book has students use images of bases and given heights to build prisms and record volumes, giving them an opportunity to apply previous learning about area of the base, height, and volume.
In the Teacher’s Implementation Guide, module 1, topic 2, lesson 4 includes a “Spaced Review” component that prompts students to revisit numeric expressions, order of operations, and all four operations. This structure provides repeated opportunities to retrieve previously learned skills while engaging with current grade-level content.
Evaluation for 4.3b
In the Student Practice Book, module 1, topic 1, lesson 1 includes interleaved practice that reviews how to determine the perimeter of a rectangle while students identify the dimensions and volumes of three-dimensional figures. This requires students to apply prior measurement understanding while developing new volume concepts.
In the Student Practice Book, module 1, topic 2, lesson 3 includes interleaved practice that reviews how to describe a multiplication expression as a comparison while students evaluate numeric expressions using all four operations. In module 1, topic 2, lesson 4 students practice evaluating expressions involving addition, subtraction, multiplication, and division using the order of operations. These tasks blend current work with expressions and operations with previously learned multiplication-comparison and computation skills.
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 Student Practice Book, module 1, topic 1, lesson 8, students propose sets of dimensions for boxes with specified volumes, determine the volume of a cube, compare the volume of two toy boxes with different dimensions, and explain which box has the greater volume. These tasks require students to apply volume concepts, reason about dimensions, compare quantities, and explain their mathematical thinking in problem contexts.
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
In the Teacher’s Implementation Guide, the student practice sequence in module 1, topic 1 shows increasing rigor across lessons. Students first identify dimensions and volumes of three-dimensional figures, then calculate the area of the base and volume of rectangular prisms, and later connect volume and area. In lesson 7, students determine the area of the base and volume of rectangular prisms with different dimensions and then analyze how doubling or halving one dimension affects the volume. This progression moves students from calculating volume to reasoning about relationships among dimensions, area, and volume.
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 1, the “Mathematical Progressions Across Modules” section focuses on constructing volume and expressions, while later modules build toward extending fraction concepts, multiplying and dividing fractions, solving problems with rational numbers, and analyzing classification and shapes. The “Connections to Future Learning” section explains that students will later use order of operations to evaluate numerical expressions, use all four operations with fractions and decimals, interpret expressions, and solve problems involving two- and three-dimensional figures. This shows how volume, operations, expressions, and problem-solving develop coherently across the course.
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
In the Teacher’s Implementation Guide, module 1, topic 1 overview, the “Connection to Future Learning” section explains that in grade 6, students will solve problems involving the area of triangles, trapezoids, and parallelograms and will further explore solids and define the surface area of a solid figure. This shows a vertical progression from earlier area work, to grade 5 volume of rectangular prisms, to future work with more complex area concepts and surface area.
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 Student Practice Book, module 1, topic 1, lesson 6, students determine the area of the base and the volume of rectangular prisms. In lesson 7, they also determine the area of the base and volume and then analyze how changing a dimension affects volume. These tasks connect prior work with area and multiplication to new learning about volume, rectangular prisms, and volume formulas.
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
In the Teacher’s Implementation Guide, module 1, topic 2, lesson 4 includes a “Spaced Review” component that prompts students to revisit numeric expressions, order of operations, and all four operations. This structure provides repeated opportunities to retrieve previously learned skills while engaging with current grade-level content.
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 the Student Practice Book, module 1, topic 2, lesson 3 includes interleaved practice that reviews how to describe a multiplication expression as a comparison while students evaluate numeric expressions using all four operations. In module 1, topic 2, lesson 4 students practice evaluating expressions involving addition, subtraction, multiplication, and division using the order of operations. These tasks blend current work with expressions and operations with previously learned multiplication-comparison and computation skills.
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 2, topic 5, lesson 2, students interpret, analyze, and evaluate models and representations for decimal multiplication. In the “Explore 1” activity, students use area models to represent decimal multiplication, analyze how each factor and product appears within the model, and connect the visual representation to multiplication expressions. Educator questions prompt students to explain how the model represents the computation, compare the decimal model to whole-number multiplication, and justify the relationships they observe.
In the Student Practice Book, module 2, topic 5, students continue analyzing decimal multiplication using area models and symbolic equations. They use visual representations to model decimal products, connect these models to multiplication expressions, and explain how the representations support the solution. These practice tasks require students to interpret mathematical models, analyze the relationship between factors and products, and communicate mathematical reasoning.
Evaluation for 5.1b
In the Teacher’s Implementation Guide, module 3, topic 8, lesson 1, students create models to represent fraction-division situations. In the “Explore 1” activity, students use pattern blocks to model division involving unit fractions and whole numbers. Students select a manipulative to represent the whole, identify the unit fraction, partition it into equal parts, determine the quotient, and connect the concrete model to a symbolic division expression.
In the Teacher’s Implementation Guide, module 3, topic 8, lesson 1, students continue creating models in the “Explore 2” activity by using colored rods to represent quotients of unit fractions and whole numbers. Students compare multiple representations, explain how each model supports the quotient, and discuss why identifying the whole is necessary before determining the value of each fractional piece. These tasks require students to create, interpret, and explain mathematical models that represent fraction-division situations.
Evaluation for 5.1c
In the Teacher’s Implementation Guide, module 1, topic 1, lesson 8, students apply conceptual understanding to a new real-world problem situation. In “Explore 1,” students design an outdoor storage space by determining dimensions, calculating volume, and evaluating whether each design meets the stated requirements. They compare possible solutions, explain how their calculations support their decisions, and justify why their final design satisfies the constraints.
In the Assessment Suite, module 1, “Performance Task,” students apply volume concepts and mathematical reasoning to solve a real-world design challenge. They analyze the task, determine appropriate calculations, represent their mathematical thinking, and justify conclusions using models, equations, and written explanations. These “Performance Tasks” require students to transfer their conceptual understanding of volume to an authentic problem-solving context.
Evaluation for 5.2a
In the Teacher’s Implementation Guide, module 3, topic 9, lesson 11, students build fluency with rational number operations. They solve problems involving addition and subtraction of positive rational numbers expressed as fractions, mixed numbers, and decimals. Students estimate solutions, complete repeated computations, compare strategies, and explain how they determined accurate answers. These repeated tasks strengthen procedural fluency with grade-level rational number operations.
In the Student Practice Book, module 3, topic 9, students complete additional practice in adding and subtracting fractions, mixed numbers, and decimals across a variety of problem formats. Students repeatedly apply computation strategies, verify the reasonableness of their solutions, and explain their mathematical thinking. These practice activities reinforce procedural fluency and support accurate, efficient computation.
Evaluation for 5.2b
In the Teacher’s Implementation Guide, module 2, topic 5, lesson 8, students practice efficient, flexible, and accurate mathematical procedures. In the “Explore 1” activity, students analyze a worked example, compare the standard algorithm with place-value strategies, and apply the algorithm to divide decimal dividends by whole-number divisors. They solve multiple problems, explain how regrouping connects across strategies, and justify the accuracy of their solutions.
In the Teacher’s Implementation Guide, module 1, topic 2, lesson 10, students revisit numeric expressions through learning centers designed to clarify, strengthen, or extend understanding. Students interpret, model, write, and evaluate numeric expressions; create expressions during games; and write expressions to reach target values. These reengagement activities provide opportunities for students to refine efficient, flexible, and accurate procedures for working with expressions and operations.
Evaluation for 5.2c
In the Teacher’s Implementation Guide, module 2, topic 5, lesson 1, students evaluate procedures, processes, and solutions for efficiency, flexibility, and accuracy. In the “Explore 1” activity, students estimate decimal products, model multiplication with base 10 blocks, analyze the relationship between decimal products and related whole-number products, and describe patterns they observe in the models. Educators ask students to compare strategies and determine when base-ten blocks may no longer be the most efficient approach for larger factors or more complex decimal values.
In the Teacher’s Implementation Guide, module 4, topic 10, lesson 4, students evaluate the accuracy of mathematical procedures and solutions. In center 1, students analyze completed coordinate grids, determine whether ordered pairs were plotted correctly, identify mistakes in the work of fictional students, and explain how to correct the errors. These tasks require students to evaluate accuracy and justify their reasoning.
Evaluation for 5.2d
Teacher’s Implementation Guide includes embedded supports to help educators guide students toward increasingly efficient approaches. In module 2, topic 5, lesson 7, the “About the Math” section explains that students previously used a (10 x 10) grid as an area model to determine decimal quotients. The guidance explains that although the area model establishes relationships among the dividend, divisor, and quotient, it is not always practical for every division expression.
In the Teacher’s Implementation Guide, module 2, topic 5, lesson 7, the “About the Math” section introduces additional strategies that build on students’ prior experience with area models and prepare them to solve a broader range of decimal division problems efficiently. These embedded supports help educators guide students from conceptual grid models to more efficient decimal division strategies while maintaining understanding of the relationships among the dividend, divisor, and quotient.
Evaluation for 5.3a
In the Teacher’s Implementation Guide Overview, the “Emphasizing Focus, Coherence, and Balance” section explicitly states how conceptual understanding is addressed. The “Building Conceptual Understanding” section explains that students use colored rods and strip diagrams to represent fraction addition before extending those representations to addition and subtraction with unlike denominators. This guidance explains how students build conceptual understanding through concrete and pictorial models before developing procedural fluency.
In the Teacher’s Implementation Guide Overview, the “Developing Procedural Fluency” section describes how students apply procedures for fraction operations after establishing conceptual understanding through models and representations. This guidance shows an intentional progression from conceptual understanding to efficient, accurate procedures.
Evaluation for 5.3b
In the Teacher’s Implementation Guide, module 2, topic 5, lesson 1, students use concrete models and pictorial and abstract representations as required by the TEKS. In the “Explore 1” activity, students use base 10 blocks to model decimal multiplication, represent the products using grid models, and connect these models to symbolic multiplication expressions. Students explain how the representations show the same mathematical relationship and justify their reasoning.
In the Teacher’s Implementation Guide, module 1, topic 3, lesson 8, students connect visual representations to symbolic division procedures. In the “Field Trip” activity, students model division situations with visual representations before connecting those models to partial quotients and symbolic procedures. Students compare representations and explain how each supports determining the quotient.
Evaluation for 5.3c
In the Teacher’s Implementation Guide, module 3, topic 8, lesson 6 provides supports that help students connect, create, define, and explain concrete and representational models for abstract fraction-division concepts. Students use pattern blocks and colored rods to model division expressions involving whole numbers and unit fractions. They identify and define the whole, determine the unit fraction, connect the manipulatives to symbolic division expressions, and explain how the quotient is represented. Educators guide students to justify their models and explain the mathematical relationship between the concrete model and the symbolic expression.
In the Teacher’s Implementation Guide, module 3, topic 8, lesson 6, students connect, create, define, and explain models by comparing multiple manipulative representations of the same division expression. Students explain how each model supports the symbolic quotient, describe how the value of each fractional piece depends on the whole, and justify why the quotient changes with the selected representation. These supports help students move from concrete pattern blocks and colored rods to representational reasoning and then to abstract symbolic fraction division concepts.
Evaluation for 5.4a
In the Teacher’s Implementation Guide, module 1, topic 1, lesson 1, students develop academic mathematical language through manipulatives, visual representations, and educator-facilitated discussion. In the “Explore 1” activity, students use connecting cubes to build rectangular prisms and describe their models using academic vocabulary such as unit cube, dimensions, rectangular prism, and cube. Educators prompt students to explain the dimensions of their models, determine whether each prism is a cube, and communicate their thinking using the visual models.
In the Teacher’s Implementation Guide, module 3, topic 8, lesson 6, students develop academic mathematical language through concrete models and structured mathematical conversations. In the “Explore” activity, students use pattern blocks and colored rods to model division involving whole numbers and unit fractions and describe their work using vocabulary such as whole, unit fraction, quotient, and partition. Educators encourage students to explain how the manipulatives represent the division expression and to justify their reasoning with precise mathematical language.
Evaluation for 5.4b
In the Teacher’s Implementation Guide, module 1, topic 3, lesson 2, the “Language Link: Developing Mathematical Language” section defines factor and product, compares these terms to addend and sum, and provides guidance for educators to help students identify this vocabulary in multiplication equations. Students compare area models and explain which representation does not belong, using academic vocabulary. The “Emergent Bilingual Student Support” section includes sentence stems that encourage students to communicate their mathematical reasoning with precise mathematical language.
In the Teacher’s Implementation Guide, module 1, topic 2, lesson 11, the “Emergent Bilingual Student Support” section provides embedded guidance to help students investigate factor pairs while describing numerical relationships and explaining their reasoning. Educator guidance connects mathematical vocabulary to familiar real-world examples, provides examples of words associated with factor pairs, and supports students as they communicate their mathematical thinking with precise academic language.
Evaluation for 5.4c
In the Teacher’s Implementation Guide, module 1, topic 3, lesson 1 includes embedded educator guidance that supports mathematical conversations through vocabulary, syntax, and discourse. In “Activate: Zeroing In,” students analyze multiplication patterns, describe the relationships they observe, and explain how place-value concepts influence the products. “Teacher Stories,” facilitation notes, and sample responses support mathematical discussions by encouraging students to justify their observations and communicate their reasoning using precise mathematical language. These supports give students opportunities to hear, refine, and use mathematical language during structured classroom discussions.
In the Teacher’s Implementation Guide, module 2, topic 5, lesson 1, students apply mathematical language through concrete models, visual representations, symbolic notation, and guided discussion. In the “Explore 1” activity, students use base 10 blocks to model decimal multiplication and explain how the models represent the multiplication expression. Students compare concrete models, visual representations, and symbolic notation. Educator guidance includes questions that prompt students to justify their reasoning and connect the representations. These activities strengthen mathematical communication by encouraging students to explain and defend their thinking using multiple representations.
Evaluation for 5.5a
In the Teacher’s Implementation Guide, module 2, topic 5, lesson 8, appropriately integrates the TEKS mathematical process standards. In the “Reflect: Reflect and Summarize” activity, students compare strategies for dividing decimals, explain how place-value understanding supports the standard algorithm, and justify their choice of solution method. Reflection prompts ask students to evaluate the efficiency of different approaches and to communicate their mathematical reasoning. Educator guidance facilitates classroom discussions by encouraging students to explain and defend their thinking with mathematical evidence.
In the Teacher’s Implementation Guide, module 2, the “Mindset Reflection,” appropriately integrates the TEKS process standards as students reflect on the strategies they used to solve mathematical problems. Students identify how they overcame challenges and describe how their thinking changed throughout the learning process. Educator guidance provides structured prompts that encourage students to evaluate their reasoning, discuss productive learning behaviors, and connect these experiences to future mathematical tasks.
Evaluation for 5.5b
In the Teacher’s Implementation Guide Overview, the “Foundations for Effective Math Instruction: Attending to the Mathematical Process Standards” section describes how the course incorporates and connects the TEKS mathematical process standards throughout. The “Topic Overview” sections identify the process standards addressed in each topic and that Student Look-Fors help educators observe students’ demonstration of the process standards during instruction. These embedded supports help educators intentionally incorporate and monitor the TEKS mathematical process standards across lessons.
In the Teacher’s Implementation Guide Overview, the “Foundations for Effective Math Instruction: Attending to the Mathematical Process Standards” section explains that “Reflect” activities and “Mindset Reflections” provide structured opportunities for students to examine how they applied the TEKS mathematical process standards while solving problems. Educator guidance encourages students to reflect on their mathematical reasoning, evaluate productive learning behaviors, and connect those experiences to future problem-solving situations. These supports reinforce the ongoing use of the TEKS mathematical process standards throughout the course.
Evaluation for 5.5c
In the Teacher’s Implementation Guide Overview, “Foundations for Effective Math Instruction: Attending to the Mathematical Process Standards,” it describes how process standards are incorporated and connected throughout instruction. The overview explains that “Student Look-Fors” help educators identify observable evidence that students are applying the Mathematical Process Standards, including communicating mathematical reasoning, evaluating solution strategies, making mathematical connections, and justifying conclusions. These supports help educators intentionally recognize and reinforce students’ use of the TEKS mathematical process standards across lessons within a topic.
The Teacher’s Implementation Guide Overview explains that “Reflect” activities and “Mindset Reflections” provide structured opportunities for students to examine how they applied the TEKS mathematical process standards while solving mathematical tasks. Educator guidance encourages students to evaluate their reasoning, discuss productive mathematical behaviors, and connect those experiences to future learning. These reflection opportunities reinforce students’ continued application of the TEKS mathematical process standards across the curriculum.
Evaluation for 5.5d
In the Teacher’s Implementation Guide Overview, the “Foundations for Effective Math Instruction: Attending to the Mathematical Process Standards” section explains how TEKS process standards are incorporated into instruction. “Topic Overviews” identify the TEKS mathematical process standards emphasized within each topic and support educators in intentionally incorporating those standards into instruction. This guidance describes where students engage in mathematical reasoning, representation, communication, and problem-solving throughout the lesson sequence.
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 reasoning, evaluating solution strategies, making mathematical connections, and justifying conclusions during lesson activities. These embedded supports help educators intentionally monitor and reinforce students’ use of the TEKS mathematical process standards throughout the curriculum.
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 Student Practice Book, module 2, topic 5, students continue analyzing decimal multiplication using area models and symbolic equations. They use visual representations to model decimal products, connect these models to multiplication expressions, and explain how the representations support the solution. These practice tasks require students to interpret mathematical models, analyze the relationship between factors and products, and communicate mathematical reasoning.
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 the Teacher’s Implementation Guide, module 3, topic 8, lesson 1, students continue creating models in the “Explore 2” activity by using colored rods to represent quotients of unit fractions and whole numbers. Students compare multiple representations, explain how each model supports the quotient, and discuss why identifying the whole is necessary before determining the value of each fractional piece. These tasks require students to create, interpret, and explain mathematical models that represent fraction-division situations.
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
In the Assessment Suite, module 1, “Performance Task,” students apply volume concepts and mathematical reasoning to solve a real-world design challenge. They analyze the task, determine appropriate calculations, represent their mathematical thinking, and justify conclusions using models, equations, and written explanations. These “Performance Tasks” require students to transfer their conceptual understanding of volume to an authentic problem-solving context.
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 Student Practice Book, module 3, topic 9, students complete additional practice in adding and subtracting fractions, mixed numbers, and decimals across a variety of problem formats. Students repeatedly apply computation strategies, verify the reasonableness of their solutions, and explain their mathematical thinking. These practice activities reinforce procedural fluency and support accurate, efficient computation.
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 Teacher’s Implementation Guide, module 1, topic 2, lesson 10, students revisit numeric expressions through learning centers designed to clarify, strengthen, or extend understanding. Students interpret, model, write, and evaluate numeric expressions; create expressions during games; and write expressions to reach target values. These reengagement activities provide opportunities for students to refine efficient, flexible, and accurate procedures for working with expressions and operations.
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
In the Teacher’s Implementation Guide, module 4, topic 10, lesson 4, students evaluate the accuracy of mathematical procedures and solutions. In center 1, students analyze completed coordinate grids, determine whether ordered pairs were plotted correctly, identify mistakes in the work of fictional students, and explain how to correct the errors. These tasks require students to evaluate accuracy and justify their reasoning.
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 Teacher’s Implementation Guide, module 2, topic 5, lesson 7, the “About the Math” section introduces additional strategies that build on students’ prior experience with area models and prepare them to solve a broader range of decimal division problems efficiently. These embedded supports help educators guide students from conceptual grid models to more efficient decimal division strategies while maintaining understanding of the relationships among the dividend, divisor, and quotient.
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
In the Teacher’s Implementation Guide Overview, the “Developing Procedural Fluency” section describes how students apply procedures for fraction operations after establishing conceptual understanding through models and representations. This guidance shows an intentional progression from conceptual understanding to efficient, accurate procedures.
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 the Teacher’s Implementation Guide, module 1, topic 3, lesson 8, students connect visual representations to symbolic division procedures. In the “Field Trip” activity, students model division situations with visual representations before connecting those models to partial quotients and symbolic procedures. Students compare representations and explain how each supports determining the quotient.
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 the Teacher’s Implementation Guide, module 3, topic 8, lesson 6, students connect, create, define, and explain models by comparing multiple manipulative representations of the same division expression. Students explain how each model supports the symbolic quotient, describe how the value of each fractional piece depends on the whole, and justify why the quotient changes with the selected representation. These supports help students move from concrete pattern blocks and colored rods to representational reasoning and then to abstract symbolic fraction division concepts.
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 3, topic 8, lesson 6, students develop academic mathematical language through concrete models and structured mathematical conversations. In the “Explore” activity, students use pattern blocks and colored rods to model division involving whole numbers and unit fractions and describe their work using vocabulary such as whole, unit fraction, quotient, and partition. Educators encourage students to explain how the manipulatives represent the division expression and to justify their reasoning with precise mathematical language.
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 1, topic 2, lesson 11, the “Emergent Bilingual Student Support” section provides embedded guidance to help students investigate factor pairs while describing numerical relationships and explaining their reasoning. Educator guidance connects mathematical vocabulary to familiar real-world examples, provides examples of words associated with factor pairs, and supports students as they communicate their mathematical thinking with precise academic language.
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 5, lesson 1, students apply mathematical language through concrete models, visual representations, symbolic notation, and guided discussion. In the “Explore 1” activity, students use base 10 blocks to model decimal multiplication and explain how the models represent the multiplication expression. Students compare concrete models, visual representations, and symbolic notation. Educator guidance includes questions that prompt students to justify their reasoning and connect the representations. These activities strengthen mathematical communication by encouraging students to explain and defend their thinking using multiple representations.
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 2, the “Mindset Reflection,” appropriately integrates the TEKS process standards as students reflect on the strategies they used to solve mathematical problems. Students identify how they overcame challenges and describe how their thinking changed throughout the learning process. Educator guidance provides structured prompts that encourage students to evaluate their reasoning, discuss productive learning behaviors, and connect these experiences to future mathematical tasks.
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
In the Teacher’s Implementation Guide Overview, the “Foundations for Effective Math Instruction: Attending to the Mathematical Process Standards” section explains that “Reflect” activities and “Mindset Reflections” provide structured opportunities for students to examine how they applied the TEKS mathematical process standards while solving problems. Educator guidance encourages students to reflect on their mathematical reasoning, evaluate productive learning behaviors, and connect those experiences to future problem-solving situations. These supports reinforce the ongoing use of the TEKS mathematical 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 Teacher’s Implementation Guide Overview explains that “Reflect” activities and “Mindset Reflections” provide structured opportunities for students to examine how they applied the TEKS mathematical process standards while solving mathematical tasks. Educator guidance encourages students to evaluate their reasoning, discuss productive mathematical behaviors, and connect those experiences to future learning. These reflection opportunities reinforce students’ continued application of the TEKS mathematical process standards across the curriculum.
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 reasoning, evaluating solution strategies, making mathematical connections, and justifying conclusions during lesson activities. These embedded supports help educators intentionally monitor and reinforce students’ use of the TEKS mathematical process standards throughout the curriculum.
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 3, topic 9, lesson 12, “Explore 1: Ocean Trails” activity, students solve a real-world problem involving positive rational numbers by determining distances between landmarks that meet multiple design criteria. Students use the Problem-Solving Model to develop a solution, verify that all conditions are met, and explain how they determined their answers. Educator guidance includes purposeful questions, ongoing assessment prompts, and differentiation supports that encourage students to persevere, evaluate their reasoning, and justify their mathematical decisions.
In the Teacher’s Implementation Guide, module 3, topic 9, lesson 12, the “Closing Discussion” section reinforces students’ ability to make sense of mathematics through explanation, reflection, and justification. Students explain the strategies they used to determine distances between landmarks, compare solution approaches, and verify that their design met the investor’s requirements. Educator guidance facilitates mathematical discussions that encourage students to reflect on their reasoning and evaluate the effectiveness of different solution strategies.
Evaluation for 6.1b
In the Teacher’s Implementation Guide, module 3, topic 9, lesson 7, students understand, explain, and justify that there can be multiple ways to solve mathematical problems. In the “Explore 2: Mixing Mixed Numbers” activity, students create multiple number-line models to represent addition and subtraction of mixed numbers. Educator guidance prompts students to partition number lines in different ways, explain how each representation models the same mathematical situation, and compare their strategies with classmates.
In the Teacher’s Implementation Guide, module 3, topic 9, lesson 7, the “Closing” and “Reflect: Patchwork Blanket” sections provide additional opportunities for students to justify multiple representations and solution strategies. Students compare number-line models, explain how their strategies differ from their classmates’ strategies, and justify why multiple representations produce the same solution. Educator guidance encourages students to defend their reasoning and evaluate different approaches to solving the problem.
Evaluation for 6.1c
In the Teacher’s Implementation Guide, module 1, topic 2, lesson 13, explore 1, students develop a savings plan by analyzing financial information, selecting an appropriate strategy, and connecting the situation to the order of operations. Students explain their decisions, justify why their plan meets the stated goals, and revise their thinking as needed. Educator guidance includes facilitation prompts that encourage students to defend their reasoning with mathematical evidence.
In the Teacher’s Implementation Guide, module 1, topic 2, lesson 13, the “Reflect: Reflect and Summarize” activity reinforces students’ ability to justify their mathematical reasoning and decision-making. Students evaluate their completed financial plans, explain how they determined their solutions, and justify why their approach meets the task requirements. Educator guidance encourages students to communicate their reasoning, compare approaches, and support their conclusions with mathematical evidence.
Evaluation for 6.2a
In the Teacher’s Implementation Guide, module 1, topic 1, lesson 8, educators support students in sharing their problem-solving approaches through explanations, arguments, and justifications. In explore 1, students use the Problem-Solving Model to analyze a real-world design task, develop a solution, and explain the mathematical reasoning behind their decisions. Educator guidance includes questions that prompt students to describe their strategy and how they determined their solution. Ongoing assessment guidance helps educators monitor students’ explanations and mathematical reasoning throughout the activity.
In the Teacher’s Implementation Guide, module 1, topic 1, lesson 8, the “Reflect: Reflect and Summarize” activity provides support for students to share and evaluate their problem-solving approaches. Students explain how they solved the design problem and the reasoning behind their decisions and then evaluate the effectiveness of their strategy. Educator guidance encourages students to discuss their mathematical thinking, respond to classmates’ ideas, and reflect on the problem-solving process.
Evaluation for 6.2b
In the Teacher’s Implementation Guide, module 1, topic 3, lesson 7 includes prompts and guidance to help educators provide explanatory feedback based on student responses and anticipated misconceptions. The “Common Misconception” support identifies likely misunderstandings students may have when interpreting area models for division. Educator guidance explains the misconception and provides instructional prompts to question students about their reasoning, address incorrect interpretations, and reinforce accurate mathematical concepts.
In the Teacher’s Implementation Guide, module 1, topic 3, lesson 7, students use area models to solve division problems and explain how each section of the model represents the mathematical situation. Ongoing assessment guidance prompts educators to monitor students’ reasoning, identify misconceptions, and provide explanatory feedback to help students refine their understanding of division with visual models. These instructional supports help educators respond to student thinking with meaningful feedback that advances conceptual understanding.
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 Teacher’s Implementation Guide, module 3, topic 9, lesson 12, the “Closing Discussion” section reinforces students’ ability to make sense of mathematics through explanation, reflection, and justification. Students explain the strategies they used to determine distances between landmarks, compare solution approaches, and verify that their design met the investor’s requirements. Educator guidance facilitates mathematical discussions that encourage students to reflect on their reasoning and evaluate the effectiveness of different solution strategies.
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 Teacher’s Implementation Guide, module 3, topic 9, lesson 7, the “Closing” and “Reflect: Patchwork Blanket” sections provide additional opportunities for students to justify multiple representations and solution strategies. Students compare number-line models, explain how their strategies differ from their classmates’ strategies, and justify why multiple representations produce the same solution. Educator guidance encourages students to defend their reasoning and evaluate different approaches to solving the problem.
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 Teacher’s Implementation Guide, module 1, topic 2, lesson 13, the “Reflect: Reflect and Summarize” activity reinforces students’ ability to justify their mathematical reasoning and decision-making. Students evaluate their completed financial plans, explain how they determined their solutions, and justify why their approach meets the task requirements. Educator guidance encourages students to communicate their reasoning, compare approaches, and support their conclusions with mathematical evidence.
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 Teacher’s Implementation Guide, module 1, topic 1, lesson 8, the “Reflect: Reflect and Summarize” activity provides support for students to share and evaluate their problem-solving approaches. Students explain how they solved the design problem and the reasoning behind their decisions and then evaluate the effectiveness of their strategy. Educator guidance encourages students to discuss their mathematical thinking, respond to classmates’ ideas, and reflect on the problem-solving process.
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 Teacher’s Implementation Guide, module 1, topic 3, lesson 7, students use area models to solve division problems and explain how each section of the model represents the mathematical situation. Ongoing assessment guidance prompts educators to monitor students’ reasoning, identify misconceptions, and provide explanatory feedback to help students refine their understanding of division with visual models. These instructional supports help educators respond to student thinking with meaningful feedback that advances conceptual understanding.