Program Information
- ISBN
- 9798898864224
- 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 2
Math (English) Grade 2
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 2 | 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 2 Scope and Sequence (165), module 1, topic 1, lessons 1–14 identify the grade 2 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 2 Scope and Sequence (180), module 1, topic 1, lessons 1–14 identify the instructional progression for the 180-day instructional calendar and connect grade-level concepts to the TEKS and ELPS. This additional scope and sequence provides educators with another course-level map that outlines the TEKS, ELPS, and concepts taught in the course.
Evaluation for 1.1b
The Scope and Sequence (165) organizes the course by module and topic and provides pacing guidance for implementation across the school year. This pacing guide/calendar resource supports effective implementation by helping educators plan instruction while maintaining the intended sequence of the materials.
The materials also include suggested pacing to support effective implementation for a different instructional calendar. The Scope and Sequence (180) organizes the course by module and topic and provides pacing guidance for a 180-day instructional calendar. Together, the 165-day and 180-day pacing guide/calendar resources support effective implementation for various instructional calendars.
Evaluation for 1.1c
The Texas ClearMath Grade 2 Mathematical Progressions and Connections describes mathematical progressions and connections across modules and topics. This resource explains how concepts build within the course, allowing educators to see how earlier learning supports later topics and how concepts to be learned connect throughout the year.
In the Texas ClearMath Grade 2 Teacher’s Implementation Guide Overview, the “Course Sequence” section identifies the course sequence and shows how modules and topics build across the instructional year. This overview supports educators in understanding the rationale of topic order and how concepts to be learned connect throughout the grade 2 course.
Evaluation for 1.1d
The Texas ClearMath K–5 Teacher Topic Internalization Protocol provides a structured protocol for topic-level internalization by guiding educators to identify key concepts, instructional goals, and planning considerations before teaching. This protocol provides corresponding guidance for internalizing the materials so educators can prepare for implementation as designed.
The Texas ClearMath K–5 Teacher Lesson Internalization Protocol provides a structured process for lesson internalization by guiding educators to examine lesson goals, instructional moves, materials, and anticipated student thinking before instruction. Together, the topic and lesson internalization protocols provide corresponding guidance for 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.
TheTexas 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 to the design of the materials.
Evaluation for 1.2a
In the Teacher’s Implementation Guide, module 1, topic 1, the “Topic Summaries” section includes “Key Ideas” and “Key Terms” sections for the topic. The “Key Ideas” section provides background content knowledge for the topic concepts, and the “Key Terms” section identifies academic vocabulary necessary to effectively teach the concepts in the topic.
In the Teacher’s Implementation Guide, module 1, topic 3, lesson 3 provides educator-facing instructional guidance, questions, tasks, materials, and content-specific information connected to the topic. This lesson-level guidance within the unit supports educators in understanding the background content knowledge and academic vocabulary necessary to effectively teach the concepts in the topic.
Evaluation for 1.2b
In the Texas ClearMath Grade 2 Student Practice Book, module 2, topic 6, the “Family Guide” section provides families with information about the mathematical concepts students will encounter in the topic and suggestions for supporting student progress. It also provides topic-level family supports connected to the learning students complete in the materials.
In the Student Practice Book, module 2, topic 6, the “Spanish Family Guide” section provides families with information about the mathematical concepts students will encounter and suggestions for supporting student progress at home. Together, the English and Spanish “Family Guides” provide supports for families with suggestions on supporting the progress of their students.
Evaluation for 1.3a
In the Teacher’s Implementation Guide, module 1, topic 3, lesson 3 provides educator-facing instructional guidance, questions, tasks, lesson materials, and checks for understanding. Together, these lesson components support the content and language standards of the lesson and provide the structure needed for educators to deliver the lesson as designed.
In the Teacher’s Implementation Guide, module 1, topic 3, lesson 4 provides educator-facing instructional guidance, questions, tasks, lesson materials, and opportunities for instructional assessment. These lesson components further demonstrate how the materials provide detailed lesson plans aligned to the TEKS and ELPS.
Evaluation for 1.3b
In the Teacher’s Implementation Guide, module 1, topic 2, lesson 6, the “Lesson Structure and Pacing Guide” section identifies the sequence of instructional activities and suggested timing for lesson components. This lesson overview helps educators prepare the materials and timing necessary to effectively deliver the lesson.
In the Teacher’s Implementation Guide, module 2, topic 4, lesson 13, the “Lesson Structure and Pacing Guide” section identifies the sequence of instructional activities and suggested timing for lesson components. This second lesson overview confirms that the materials consistently provide lesson structure, materials, and timing guidance for effective lesson delivery.
Evaluation for 1.3c
In the Teacher’s Implementation Guide, the “Monitoring Student Progress” section explains how educators can use the Student Practice Book to monitor student progress and support continued practice. This guidance supports the effective use of lesson materials for additional practice and reinforcement beyond the core lesson.
In the Teacher’s Implementation Guide, the “Understanding the Teaching Cadence: Explore Centers” section explains how “Explore Centers” are used as part of the teaching cadence to provide continued practice and reinforcement beyond the core lesson. Together, the Student Practice Book guidance and “Explore Centers” guidance provide structures for additional practice, reinforcement, and extension.
1.1 Course-Level Design
1.1a
Materials include a scope and sequence outlining the TEKS, ELPS, and concepts taught in the course.
Materials include a scope and sequence outlining the TEKS, ELPS, and concepts taught in the course.
3 out of 3 points
Evaluation for 1.1a
Evaluation for 1.1a
Materials include a scope and sequence outlining the TEKS, ELPS, and concepts taught in the course.
3 out of 3 points
In the Texas ClearMath Grade 2 Scope and Sequence (180), module 1, topic 1, lessons 1–14 identify the instructional progression for the 180-day instructional calendar and connect grade-level concepts to the TEKS and ELPS. This additional scope and sequence provides educators with another course-level map that outlines the TEKS, ELPS, and concepts taught in the course.
1.1b
Materials include suggested pacing (pacing guide/calendar) to support effective implementation for various instructional calendars (e.g., varying numbers of instructional days - 165, 180, 210).
Materials include suggested pacing (pacing guide/calendar) to support effective implementation for various instructional calendars (e.g., varying numbers of instructional days - 165, 180, 210).
2 out of 2 points
Evaluation for 1.1b
Evaluation for 1.1b
Materials include suggested pacing (pacing guide/calendar) to support effective implementation for various instructional calendars (e.g., varying numbers of instructional days - 165, 180, 210).
2 out of 2 points
The materials also include suggested pacing to support effective implementation for a different instructional calendar. The Scope and Sequence (180) organizes the course by module and topic and provides pacing guidance for a 180-day instructional calendar. Together, the 165-day and 180-day pacing guide/calendar resources support effective implementation for various instructional calendars.
1.1c
Materials include an explanation for the rationale of unit order as well as how concepts to be learned connect throughout the course.
Materials include an explanation for the rationale of unit order as well as how concepts to be learned connect throughout the course.
2 out of 2 points
Evaluation for 1.1c
Evaluation for 1.1c
Materials include an explanation for the rationale of unit order as well as how concepts to be learned connect throughout the course.
2 out of 2 points
In the Texas ClearMath Grade 2 Teacher’s Implementation Guide Overview, the “Course Sequence” section identifies the course sequence and shows how modules and topics build across the instructional year. This overview supports educators in understanding the rationale of topic order and how concepts to be learned connect throughout the grade 2 course.
1.1d
Materials include protocols with corresponding guidance for unit and lesson internalization.
Materials include protocols with corresponding guidance for unit and lesson internalization.
2 out of 2 points
Evaluation for 1.1d
Evaluation for 1.1d
Materials include protocols with corresponding guidance for unit and lesson internalization.
2 out of 2 points
The Texas ClearMath K–5 Teacher Lesson Internalization Protocol provides a structured process for lesson internalization by guiding educators to examine lesson goals, instructional moves, materials, and anticipated student thinking before instruction. Together, the topic and lesson internalization protocols provide corresponding guidance for 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
TheTexas 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 to the design of the materials.
1.2 Unit-Level Design
1.2a
Materials include comprehensive unit overviews that provide the background content knowledge and academic vocabulary necessary to effectively teach the concepts in the unit.
Materials include comprehensive unit overviews that provide the background content knowledge and academic vocabulary necessary to effectively teach the concepts in the unit.
2 out of 2 points
Evaluation for 1.2a
Evaluation for 1.2a
Materials include comprehensive unit overviews that provide the background content knowledge and academic vocabulary necessary to effectively teach the concepts in the unit.
2 out of 2 points
In the Teacher’s Implementation Guide, module 1, topic 3, lesson 3 provides educator-facing instructional guidance, questions, tasks, materials, and content-specific information connected to the topic. This lesson-level guidance within the unit supports educators in understanding the background content knowledge and academic vocabulary necessary to effectively teach the concepts in the topic.
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 2, topic 6, the “Spanish Family Guide” section provides families with information about the mathematical concepts students will encounter and suggestions for supporting student progress at home. Together, the English and Spanish “Family Guides” provide supports for families with suggestions on supporting the progress of their students.
1.3 Lesson-Level Design
1.3a
Materials include comprehensive, structured, detailed lesson plans that include daily objectives, questions, tasks, materials, and instructional assessments required to meet the content and language standards of the lesson (aligned with the TEKS and the ELPS).
Materials include comprehensive, structured, detailed lesson plans that include daily objectives, questions, tasks, materials, and instructional assessments required to meet the content and language standards of the lesson (aligned with the TEKS and the ELPS).
5 out of 5 points
Evaluation for 1.3a
Evaluation for 1.3a
Materials include comprehensive, structured, detailed lesson plans that include daily objectives, questions, tasks, materials, and instructional assessments required to meet the content and language standards of the lesson (aligned with the TEKS and the ELPS).
5 out of 5 points
In the Teacher’s Implementation Guide, module 1, topic 3, lesson 4 provides educator-facing instructional guidance, questions, tasks, lesson materials, and opportunities for instructional assessment. These lesson components further demonstrate how the materials provide detailed lesson plans aligned to the TEKS and ELPS.
1.3b
Materials include a lesson overview listing the teacher and student materials necessary to effectively deliver the lesson, and the suggested timing for each lesson component.
Materials include a lesson overview listing the teacher and student materials necessary to effectively deliver the lesson, and the suggested timing for each lesson component.
3 out of 3 points
Evaluation for 1.3b
Evaluation for 1.3b
Materials include a lesson overview listing the teacher and student materials necessary to effectively deliver the lesson, and the suggested timing for each lesson component.
3 out of 3 points
In the Teacher’s Implementation Guide, module 2, topic 4, lesson 13, the “Lesson Structure and Pacing Guide” section identifies the sequence of instructional activities and suggested timing for lesson components. This second lesson overview confirms that the materials consistently provide lesson structure, materials, and timing guidance for effective lesson delivery.
1.3c
Materials include guidance on the effective use of lesson materials for extended practice (e.g., homework, extension, enrichment).
Materials include guidance on the effective use of lesson materials for extended practice (e.g., homework, extension, enrichment).
1 out of 1 points
Evaluation for 1.3c
Evaluation for 1.3c
Materials include guidance on the effective use of lesson materials for extended practice (e.g., homework, extension, enrichment).
1 out of 1 points
In the Teacher’s Implementation Guide, the “Understanding the Teaching Cadence: Explore Centers” section explains how “Explore Centers” are used as part of the teaching cadence to provide continued practice and reinforcement beyond the core lesson. Together, the Student Practice Book guidance and “Explore Centers” guidance provide structures for additional practice, reinforcement, and extension.
Rubric Section 2
Progress Monitoring
Materials support educators in effective implementation through frequent, strategic opportunities to monitor and respond to student progress.
Total
100% (18 out of 18 points)
Evaluation for 2.1a
In the Texas ClearMath Grade 2 Assessment Suite, module 1, topic 1, the “ReadyCheck Assessment,” “Snapshot Assessment,” “End-of-Topic Assessment,” and “Performance Tasks” include matching, drawing, multiple-choice, and fill-in-the-blank items. Together, the assessment resources support educators in monitoring student progress and measuring mastery of mathematical concepts and skills throughout instruction.
In the Assessment Suite, topics with 10 or more lessons include “Snapshot Assessments,” which serve as formative mid-topic checks of understanding. “End-of-Topic Assessments” and “Performance Tasks” function as summative assessments that measure mastery of the skills and concepts taught within the topic. “Performance Tasks” also allow students to demonstrate application and reasoning in open-ended contexts.
Evaluation for 2.1b
In the Teacher’s Implementation Guide Overview, the “Comprehensive Assessment and Data-Driven Instruction” section explains the purpose and use of the Assessment Suite, including diagnostic, formative, and summative assessments. This guidance supports educators in interpreting results and making instructional decisions based on student data.
In the Texas ClearMath Grade 2 Assessment Guide, the “Assessment Types” section describes course-level, module-level, topic-level, and lesson-level assessments and explains the purpose of each assessment type. The guide also identifies what each assessment measures, how educators collect assessment data, and how they use student results to determine next steps for instruction.
Evaluation for 2.1c
The Texas ClearMath Grade 2 Year-at-a-Glance organizes the course by module and identifies the number of instructional days, review days, and assessment days within each module. This pacing structure helps educators administer assessments within a consistent instructional timeframe.
In the Year-at-a-Glance, the course overview identifies lessons, assessments, and targeted instruction within each module. This structure helps ensure students receive similar instructional experiences and opportunities for practice before assessment, allowing assessment data to more accurately reflect student understanding of the taught concepts and skills.
Evaluation for 2.1d
In the Assessment Guide, module 4, topic 11, the “Assessment Blueprints” section identifies the TEKS and learning goals connected to assessment items. The “ReadyCheck Assessment Blueprint” also identifies the TEKS and objectives assessed. This alignment supports consistency between instruction and assessment and helps educators monitor student progress toward grade-level expectations.
The materials also include module-level and topic-level “ReadyCheck Assessments” administered before instruction to assess student readiness. In the Assessment Guide, the module and topic assessment guidance identifies the TEKS and topic objectives measured by each assessment. This information helps educators use diagnostic assessment results to plan instruction aligned to grade-level expectations and lesson objectives.
Evaluation for 2.1e
In the Assessment Guide, module 2, topic 4, the “End-of-Topic Assessment Blueprint” section includes a chart that identifies the TEKS aligned to each assessment item and the corresponding Depth of Knowledge (DOK) level. The blueprint includes items ranging from DOK 1 to DOK 3 and uses multiple item formats, including multiple-select, drawing, short-answer, and matching questions.
The materials also include “Beginning-,” “Middle-,” and “End-of-Year Assessments” with TEKS-aligned items that evaluate student understanding through varied item types and levels of complexity. These assessments include multiple-choice, short-answer, and fill-in-the-blank items that require students to demonstrate procedural understanding, apply concepts, and explain mathematical thinking. Together, these assessment components allow students to demonstrate understanding across a range of TEKS-aligned skills.
Evaluation for 2.2a
In module 5, topic 12, the “Performance Task: Partitioning in the Playground” section includes a scoring rubric with two criteria and descriptors for scores ranging from zero to two points for each criterion. These descriptors support accurate scoring by clearly defining performance expectations and levels of proficiency.
In module 5, topic 12, the “Performance Task: Partitioning in the Playground” section includes a scoring rubric, sample student responses, and Student Look-Fors that identify evidence of understanding. These supports help educators identify student strengths, misconceptions, and areas for continued growth.
Evaluation for 2.2b
In the Assessment Guide, module 1, topic 1, the “Assessment Blueprints” and “Targeted Instruction Recommendations” sections align each assessment item to the TEKS and identify instructional supports connected to each skill. The “Targeted Instruction by TEKS” section gives educators suggested tasks and activities to address specific areas of need based on assessment results.
In the Assessment Guide, the “Targeted Instruction Recommendations by TEKS” section helps educators analyze student performance by standard and identify next steps. For example, after the topic 1 “End-of-Topic Assessment,” students who need additional practice with TEKS 2.4A participate in a small-group activity during which they take turns drawing addition and subtraction fact cards within 20 and solving each problem quickly.
Evaluation for 2.2c
The Assessment Guide directs educators to “Assessment Reports” that are available in the Clear Learning Center. These reports include customizable progress-monitoring charts that allow educators to track individual student and whole-class performance over time. The reports also provide instructional actions based on assessment results, supporting data-driven instructional decisions.
In the Teacher’s Implementation Guide, the topic 8 overview includes a “Topic Self-Reflection” section with a student-friendly data tracker after each “Topic Assessment.” Students color a circle for each I Can statement to show their progress toward mastery of topic objectives. This tool supports student reflection, goal-setting, and ownership of learning by helping students identify strengths and areas for continued growth.
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, topics with 10 or more lessons include “Snapshot Assessments,” which serve as formative mid-topic checks of understanding. “End-of-Topic Assessments” and “Performance Tasks” function as summative assessments that measure mastery of the skills and concepts taught within the topic. “Performance Tasks” also allow students to demonstrate application and reasoning in open-ended contexts.
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 Texas ClearMath Grade 2 Assessment Guide, the “Assessment Types” section describes course-level, module-level, topic-level, and lesson-level assessments and explains the purpose of each assessment type. The guide also identifies what each assessment measures, how educators collect assessment data, and how they use student results to determine next steps for 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, the course overview identifies lessons, assessments, and targeted instruction within each module. This structure helps ensure students receive similar instructional experiences and opportunities for practice before assessment, allowing assessment data to more accurately reflect student understanding of the taught concepts and skills.
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
The materials also include module-level and topic-level “ReadyCheck Assessments” administered before instruction to assess student readiness. In the Assessment Guide, the module and topic assessment guidance identifies the TEKS and topic objectives measured by each assessment. This information helps educators use diagnostic assessment results to plan instruction aligned to grade-level expectations and lesson objectives.
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
The materials also include “Beginning-,” “Middle-,” and “End-of-Year Assessments” with TEKS-aligned items that evaluate student understanding through varied item types and levels of complexity. These assessments include multiple-choice, short-answer, and fill-in-the-blank items that require students to demonstrate procedural understanding, apply concepts, and explain mathematical thinking. Together, these assessment components allow students to demonstrate understanding across a range of TEKS-aligned skills.
2.2 Data Analysis and Progress Monitoring
2.2a
Instructional assessments and scoring information provide guidance for interpreting student performance.
Instructional assessments and scoring information provide guidance for interpreting student performance.
2 out of 2 points
Evaluation for 2.2a
Evaluation for 2.2a
Instructional assessments and scoring information provide guidance for interpreting student performance.
2 out of 2 points
In module 5, topic 12, the “Performance Task: Partitioning in the Playground” section includes a scoring rubric, sample student responses, and Student Look-Fors that identify evidence of understanding. These supports help educators identify student strengths, misconceptions, and areas for continued growth.
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, the “Targeted Instruction Recommendations by TEKS” section helps educators analyze student performance by standard and identify next steps. For example, after the topic 1 “End-of-Topic Assessment,” students who need additional practice with TEKS 2.4A participate in a small-group activity during which they take turns drawing addition and subtraction fact cards within 20 and solving each problem quickly.
2.2c
Materials include tools for teachers to track student progress and growth, and tools for students to track their own progress and growth.
Materials include tools for teachers to track student progress and growth, and tools for students to track their own progress and growth.
2 out of 2 points
Evaluation for 2.2c
Evaluation for 2.2c
Materials include tools for teachers to track student progress and growth, and tools for students to track their own progress and growth.
2 out of 2 points
In the Teacher’s Implementation Guide, the topic 8 overview includes a “Topic Self-Reflection” section with a student-friendly data tracker after each “Topic Assessment.” Students color a circle for each I Can statement to show their progress toward mastery of topic objectives. This tool supports student reflection, goal-setting, and ownership of learning by helping students identify strengths and areas for continued growth.
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 3 includes educator guidance for differentiated instruction, activities, and scaffolded lessons for students who have not yet reached proficiency on grade-level content and skills. The “Lesson Structure and Pacing Guide” section includes differentiation supports through “Assistance for All” and “Just-in-Time Supports” strategies that provide targeted reteaching opportunities during instruction. These supports include explicit educator guidance, instructional prompts, and strategies designed to address misconceptions and build student understanding of the lesson concepts.
The Teacher’s Implementation Guide provides “Clarify Centers” within “Re-Engagement Lessons” that enable targeted, educator-facilitated support for students who need additional instruction by offering structured opportunities to revisit and strengthen their understanding of key concepts. For example, in module 1, topic 2, after lessons 3 and 4 regarding composing and decomposing two-dimensional shapes, lesson 5 provides a “Clarify Center” activity in which the educator gives directions for students to create polygons on a geoboard and asks questions about each polygon’s attributes.
Evaluation for 3.1b
In the Teacher’s Implementation Guide, module 4, topic 10, lesson 8 includes a “Language Link: Developing Contextual Language” section that has pre-teaching supports for unfamiliar vocabulary and references in text. This section provides guidance for addressing unfamiliar references that may interfere with students’ understanding of mathematical situations. For example, educators are guided to explain contextual references, such as understanding what it means to be responsible and irresponsible, before students engage with the task. These language supports help students develop understanding of unfamiliar references that are essential for accessing grade-level content.
The Teacher’s Implementation Guide includes a “Language Links: Developing Mathematical Language” section that provides guidance for developing mathematical language, including strategies for using precise vocabulary and discussing mathematical reasoning. In module 1, topic 2, lesson 8, this section reminds the educator that students will use the term base to describe one face of a 3-D solid and they will more formally define and use that term in grade 5.
Evaluation for 3.1c
In the Teacher’s Implementation Guide, the “Differentiation Strategy” section includes “Challenge Opportunity” tasks that provide enrichment activities designed to extend student thinking beyond grade-level expectations. These activities engage proficient students in deeper application of mathematical concepts through more complex problems and tasks that promote reasoning and conceptual understanding.
The Assessment Guide includes rubrics for various evaluations, including performance tasks. The “Recommendations for Future Topics” section provides educator guidance for differentiated instruction, including grouping strategies and suggestions for extension opportunities for students who have demonstrated proficiency in grade-level content and skills. These recommendations support educators in appropriately challenging proficient students by offering opportunities for deeper engagement and continued application of mathematical concepts beyond the core task. These supports ensure that students who demonstrate mastery are provided with meaningful extension experiences that promote higher-level thinking and sustained academic growth.
Evaluation for 3.2a
The Teacher’s Implementation Guide includes explicit prompts and guidance to support educators in modeling and explaining the concepts to be learned. Each task includes step-by-step instructional guidance in bullet-point format that outlines how educators should model and explain the concept. In addition, speech-bubble icons provide explicit educator prompts that can be used during instruction to support clear explanations and facilitate student understanding. Together, these supports guide educators in effectively modeling concepts and using consistent language to support student learning.
Facilitation notes also include Common Misconception embedded supports that identify likely student misunderstandings and provide guidance for addressing them during instruction. For example, the Teacher’s Implementation Guide, module 1, topic 1, lesson 4 reminds educators that students may incorrectly think that zero is neither even nor odd and to guide students to define zero as even using the definition.
Evaluation for 3.2b
The Texas ClearMath Instructional Strategies Handbook provides educators with a range of instructional strategies organized into categories such as Authentic Problem-Solving, Explaining Their Thinking, Guided Interactions, Math Talks, and Multiple Representations. Each strategy includes descriptions, examples, implementation guidance, and tips for strengthening instructional delivery over time. Together, these supports provide educators with multiple approaches for delivering instruction, engaging students in mathematical discourse, and facilitating learning through varied instructional methods.
Each lesson in the Teacher’s Implementation Guide includes a “Lesson Structure and Pacing Guide” section that highlights the specific strategy associated with each activity, illustrating a range of instructional approaches within a single lesson. This guidance supports educators in selecting and implementing appropriate strategies for individual lessons.
Evaluation for 3.2c
The Teacher’s Implementation Guide volume 2 incorporates multiple forms of practice, including guided, collaborative, and independent learning opportunities that reinforce key concepts and skills. Clear educator guidance and recommended instructional structures, such as whole-group, small-group, partner, and individual activities, support effective implementation. These varied practice formats help students build understanding, apply learning, and develop confidence through meaningful engagement with the content.
The Teacher’s Implementation Guide volume 1 provides a variety of practice opportunities, including guided, collaborative, and independent tasks that strengthen student understanding of key concepts and skills. Embedded educator guidance outlines effective implementation through whole-group, small-group, partner, and individual learning structures. These diverse practice experiences support skill development, encourage active engagement, and help students apply their learning with increasing independence and confidence.
Evaluation for 3.3a
The Texas ClearMath Grade 2 Emergent Bilingual Student Support Handbook includes educator guidance for each lesson on providing linguistic accommodations for multiple levels of language proficiency. The “Emergent Bilingual Student Support” section provides connected ELPS-aligned scaffolds and supports for Pre-Production/Beginning, Intermediate/High Intermediate, and High Intermediate/Advanced learners. These supports include leveled sentence stems, reminders, and structured prompts that guide student discussion and participation in mathematical discourse. Across proficiency levels, the materials progressively increase expectations for students to use more complex and academic language, supporting students in developing and applying increasingly sophisticated language structures as they engage with grade-level content.
The Emergent Bilingual Student Support Handbook provides guidance for implementing linguistic accommodations that support students at varying levels of English language proficiency in alignment with the ELPS. Embedded supports—including sentence stems, visual representations, structured discussion opportunities—and targeted academic vocabulary instruction, help students access grade-level content while developing language skills. These scaffolds encourage students to progressively strengthen their use of academic language across listening, speaking, reading, and writing tasks.
Evaluation for 3.3b
The Teacher’s Implementation Guide includes implementation guidance to support educators in effectively using the materials in state-approved bilingual and English as a second language (ESL) programs. The “Empowering Emergent Bilingual Students” section in both the Teacher’s Implementation Guide and Emergent Bilingual Student Support Handbook provide educators with structured strategies to support multilingual learners during instruction. This includes embedded ELPS-aligned guidance, sentence frames for verbalizing mathematical thinking, word banks to support academic vocabulary development, and language goals that define expected language use within each topic. Together, these supports provide clear implementation guidance for adapting instruction to meet the linguistic and academic needs of emergent bilingual students while maintaining access to grade-level content.
The Emergent Bilingual Student Support Handbook provides clear guidance for implementing instruction within state-approved bilingual and ESL programs. Embedded supports include language development strategies, ELPS-aligned instructional recommendations, and opportunities for students to build both academic content knowledge and language proficiency. These resources help educators effectively support multilingual learners while ensuring access to rigorous, grade-level instruction.
Evaluation for 3.3c
The Emergent Bilingual Student Support Handbook offers comprehensive topic-level resources that effectively address the needs of emergent bilingual students. In topic 12, instructional supports build background knowledge and comprehension through concrete demonstrations and visual references, while opportunities for home-language use encourage meaningful cross-linguistic connections. Additional scaffolds, including sentence frames and word banks, provide targeted support for developing academic vocabulary.
The educator facilitation notes in the Teacher’s Implementation Guide include guidance for supporting emergent bilingual students. In module 5, topic 12, lesson 13, the “Emergent Bilingual Student Support” section suggests that educators partner emergent bilingual students with native English speakers to assist in building background knowledge and supporting vocabulary and comprehension as students utilize academic vocabulary in their written story problems.
Evaluation for 3.3d
This guidance is not applicable because the program is not designed for dual language immersion (DLI) programs.
3.1 Differentiation and Scaffolds
3.1a
Materials include teacher guidance for differentiated instruction, activities, and paired (scaffolded) lessons for students who have not yet reached proficiency on grade-level content and skills.
Materials include teacher guidance for differentiated instruction, activities, and paired (scaffolded) lessons for students who have not yet reached proficiency on grade-level content and skills.
1 out of 1 points
Evaluation for 3.1a
Evaluation for 3.1a
Materials include teacher guidance for differentiated instruction, activities, and paired (scaffolded) lessons for students who have not yet reached proficiency on grade-level content and skills.
1 out of 1 points
The Teacher’s Implementation Guide provides “Clarify Centers” within “Re-Engagement Lessons” that enable targeted, educator-facilitated support for students who need additional instruction by offering structured opportunities to revisit and strengthen their understanding of key concepts. For example, in module 1, topic 2, after lessons 3 and 4 regarding composing and decomposing two-dimensional shapes, lesson 5 provides a “Clarify Center” activity in which the educator gives directions for students to create polygons on a geoboard and asks questions about each polygon’s attributes.
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
The Teacher’s Implementation Guide includes a “Language Links: Developing Mathematical Language” section that provides guidance for developing mathematical language, including strategies for using precise vocabulary and discussing mathematical reasoning. In module 1, topic 2, lesson 8, this section reminds the educator that students will use the term base to describe one face of a 3-D solid and they will more formally define and use that term in grade 5.
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 Assessment Guide includes rubrics for various evaluations, including performance tasks. The “Recommendations for Future Topics” section provides educator guidance for differentiated instruction, including grouping strategies and suggestions for extension opportunities for students who have demonstrated proficiency in grade-level content and skills. These recommendations support educators in appropriately challenging proficient students by offering opportunities for deeper engagement and continued application of mathematical concepts beyond the core task. These supports ensure that students who demonstrate mastery are provided with meaningful extension experiences that promote higher-level thinking and sustained academic growth.
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
Facilitation notes also include Common Misconception embedded supports that identify likely student misunderstandings and provide guidance for addressing them during instruction. For example, the Teacher’s Implementation Guide, module 1, topic 1, lesson 4 reminds educators that students may incorrectly think that zero is neither even nor odd and to guide students to define zero as even using the definition.
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
Each lesson in the Teacher’s Implementation Guide includes a “Lesson Structure and Pacing Guide” section that highlights the specific strategy associated with each activity, illustrating a range of instructional approaches within a single lesson. This guidance supports educators in selecting and implementing appropriate strategies for individual lessons.
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
The Teacher’s Implementation Guide volume 1 provides a variety of practice opportunities, including guided, collaborative, and independent tasks that strengthen student understanding of key concepts and skills. Embedded educator guidance outlines effective implementation through whole-group, small-group, partner, and individual learning structures. These diverse practice experiences support skill development, encourage active engagement, and help students apply their learning with increasing independence and confidence.
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 guidance for implementing linguistic accommodations that support students at varying levels of English language proficiency in alignment with the ELPS. Embedded supports—including sentence stems, visual representations, structured discussion opportunities—and targeted academic vocabulary instruction, help students access grade-level content while developing language skills. These scaffolds encourage students to progressively strengthen their use of academic language across listening, speaking, reading, and writing tasks.
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 Emergent Bilingual Student Support Handbook provides clear guidance for implementing instruction within state-approved bilingual and ESL programs. Embedded supports include language development strategies, ELPS-aligned instructional recommendations, and opportunities for students to build both academic content knowledge and language proficiency. These resources help educators effectively support multilingual learners while ensuring access to rigorous, grade-level instruction.
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
The educator facilitation notes in the Teacher’s Implementation Guide include guidance for supporting emergent bilingual students. In module 5, topic 12, lesson 13, the “Emergent Bilingual Student Support” section suggests that educators partner emergent bilingual students with native English speakers to assist in building background knowledge and supporting vocabulary and comprehension as students utilize academic vocabulary in their written story problems.
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 Teacher’s Implementation Guide, module 2, topic 6, students demonstrate depth of understanding by representing subtraction with open number lines, equations, and strategy explanations. In lesson 1, students write subtraction equations based on open number line models, label number lines to subtract, and use take-away jumps to solve subtraction situations. Students also explain why jumps on a number line can be labeled in different ways and still represent the same difference. These tasks require students to connect visual models, equations, and subtraction reasoning within 100.
The Student Practice Book provides practice opportunities that require students to demonstrate depth of understanding with addition and subtraction strategies. In module 2, topic 6, lesson 7, students compare expressions and match story problems to equations. In module 4, topic 11, lesson 9, students determine sums and explain how addition strategies work. These practice opportunities require students to represent relationships, compare expressions, connect story situations to equations, and explain mathematical thinking rather than simply compute answers.
Evaluation for 4.1b
In the Teacher’s Implementation Guide, module 2, topic 6, questions and tasks progressively increase in rigor and complexity as students develop subtraction strategies within 100. In lesson 1, students label open number lines and use take-away jumps to subtract. In lesson 2, students use open number lines and addition strategies to determine the difference between two numbers. In lesson 4, students compare subtraction strategies and determine whether to use take-away subtraction or addition to subtract.
The progression continues in module 2, topic 6, lessons 5–7 as students move toward more complex reasoning and application. In lesson 5, students use reasoning to compare expressions with unknowns and determine whether comparison statements are true. In lesson 6, students sort word problems, create questions, write equations, and match answers to subtraction story contexts. In lesson 7, students compare expressions and match story problems to equations. This sequence moves students from modeling subtraction to comparing strategies, reasoning with unknowns, and applying addition and subtraction in story problem contexts.
Evaluation for 4.2a
In the Teacher’s Implementation Guide, the module 2 overview demonstrates coherence across topics by connecting addition and subtraction strategies to place-value understanding. The module overview explains that students apply place-value concepts, number relationships, and strategies to add and subtract within 100. The “Connection to Prior Learning” section connects this work to module 1, in which students composed and decomposed numbers, represented three-digit numbers, and compared numbers using place-value relationships.
The “Mathematical Progressions Across Modules” chart in module 2 shows how addition and subtraction strategies develop across the grade 2 course. Module 1 focuses on comparing and decomposing numbers, while module 2 extends that work to using strategies to add and subtract. The chart also shows later connections to module 3, module 4, and module 5. This progression connects place value, number relationships, addition and subtraction, measurement, money, and partitioning across the course.
Evaluation for 4.2b
In the Teacher’s Implementation Guide, the module 1 overview connects previous learning to current grade-level content. The module overview explains that students build on grade 1 experiences with place value, number bonds, addition and subtraction story problems, and representing numbers in multiple forms. In grade 2, students use those understandings to compose and decompose numbers, represent three-digit numbers, compare numbers, and apply addition and subtraction strategies within 20.
The same module overview connects current grade 2 learning to future mathematical work. The “Connection to Future Learning” section explains that students will use their understanding of place value and number relationships in module 2 when they apply base 10 blocks, open number lines, and strategies for adding and subtracting two-digit numbers. This shows a coherent progression from grade 1 number relationships and story problems to grade 2 place-value reasoning and later addition and subtraction within 100.
Evaluation for 4.2c
In the Teacher’s Implementation Guide, module 2, topic 6, lesson 1, students build on prior work with number lines and take-away subtraction strategies. The lesson guides students to write subtraction equations based on open number line models, label number lines, and use jumps to represent subtraction. Students connect the starting number, jumps, and ending number on the number line to the corresponding subtraction equation.
In the Teacher’s Implementation Guide, module 4, topic 11, lesson 9, students extend earlier subtraction strategies to larger numbers. The lesson overview explains that students are already familiar with using addition to subtract and will now apply that strategy to three-digit numbers. Students use open number lines to represent the difference between numbers, determine whether to count up or subtract, and explain which strategy is more efficient. This connects prior learning from topic 6 to new learning with subtraction within 1,000.
Evaluation for 4.3a
The Teacher’s Implementation Guide provides spaced retrieval opportunities through “Re-Engagement Lessons.” In module 1, topic 1, lesson 5, students revisit addition and subtraction relationships after initial instruction. The lesson includes “Clarify Centers,” “Solidify Centers,” and “Stretch Centers” that have students play number cube games to create fact families, complete addition puzzles, and arrange counters in boxes to create equations. These centers require students to retrieve prior learning about sums, differences, fact families, and number relationships.
The materials also provide spaced retrieval through Spaced Review components in the lessons. In module 1, topic 1, lesson 5, educators are directed to download and print spaced review for students after they complete the centers. Module 2, topic 6, lesson 7 includes a “Spaced Review” component while students revisit adding and subtracting within 100. These structures give students repeated opportunities to retrieve previously learned concepts over time.
Evaluation for 4.3b
The Student Practice Book provides interleaved practice by mixing previously learned skills with current lesson content. In module 2, topic 6, lesson 1, the Student Practice Book identifies interleaved practice that reviews applying basic fact strategies to add and subtract within 20 while students use number lines to subtract within 100. This requires students to apply prior fact fluency while working in a new subtraction strategy context.
In module 4, topic 11, lesson 9, the Student Practice Book identifies interleaved practice that reviews determining the number represented by an addition or subtraction equation while students work on using addition to subtract three-digit numbers. This mixes current work with three-digit subtraction strategies and prior equation interpretation, helping students connect previously learned skills to new problem contexts.
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
The Student Practice Book provides practice opportunities that require students to demonstrate depth of understanding with addition and subtraction strategies. In module 2, topic 6, lesson 7, students compare expressions and match story problems to equations. In module 4, topic 11, lesson 9, students determine sums and explain how addition strategies work. These practice opportunities require students to represent relationships, compare expressions, connect story situations to equations, and explain mathematical thinking rather than simply compute answers.
4.1b
Questions and tasks progressively increase in rigor and complexity, leading to grade-level proficiency in the mathematics TEKS.
Questions and tasks progressively increase in rigor and complexity, leading to grade-level proficiency in the mathematics TEKS.
1 out of 1 points
Evaluation for 4.1b
Evaluation for 4.1b
Questions and tasks progressively increase in rigor and complexity, leading to grade-level proficiency in the mathematics TEKS.
1 out of 1 points
The progression continues in module 2, topic 6, lessons 5–7 as students move toward more complex reasoning and application. In lesson 5, students use reasoning to compare expressions with unknowns and determine whether comparison statements are true. In lesson 6, students sort word problems, create questions, write equations, and match answers to subtraction story contexts. In lesson 7, students compare expressions and match story problems to equations. This sequence moves students from modeling subtraction to comparing strategies, reasoning with unknowns, and applying addition and subtraction in story problem contexts.
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
The “Mathematical Progressions Across Modules” chart in module 2 shows how addition and subtraction strategies develop across the grade 2 course. Module 1 focuses on comparing and decomposing numbers, while module 2 extends that work to using strategies to add and subtract. The chart also shows later connections to module 3, module 4, and module 5. This progression connects place value, number relationships, addition and subtraction, measurement, money, and partitioning 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
The same module overview connects current grade 2 learning to future mathematical work. The “Connection to Future Learning” section explains that students will use their understanding of place value and number relationships in module 2 when they apply base 10 blocks, open number lines, and strategies for adding and subtracting two-digit numbers. This shows a coherent progression from grade 1 number relationships and story problems to grade 2 place-value reasoning and later addition and subtraction within 100.
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 Teacher’s Implementation Guide, module 4, topic 11, lesson 9, students extend earlier subtraction strategies to larger numbers. The lesson overview explains that students are already familiar with using addition to subtract and will now apply that strategy to three-digit numbers. Students use open number lines to represent the difference between numbers, determine whether to count up or subtract, and explain which strategy is more efficient. This connects prior learning from topic 6 to new learning with subtraction within 1,000.
4.3 Spaced and Interleaved Practice
4.3a
Materials provide spaced retrieval opportunities with previously learned skills and concepts across lessons and units.
Materials provide spaced retrieval opportunities with previously learned skills and concepts across lessons and units.
4 out of 4 points
Evaluation for 4.3a
Evaluation for 4.3a
Materials provide spaced retrieval opportunities with previously learned skills and concepts across lessons and units.
4 out of 4 points
The materials also provide spaced retrieval through Spaced Review components in the lessons. In module 1, topic 1, lesson 5, educators are directed to download and print spaced review for students after they complete the centers. Module 2, topic 6, lesson 7 includes a “Spaced Review” component while students revisit adding and subtracting within 100. These structures give students repeated opportunities to retrieve previously learned concepts over time.
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 module 4, topic 11, lesson 9, the Student Practice Book identifies interleaved practice that reviews determining the number represented by an addition or subtraction equation while students work on using addition to subtract three-digit numbers. This mixes current work with three-digit subtraction strategies and prior equation interpretation, helping students connect previously learned skills to new problem contexts.
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 7, students interpret, analyze, and evaluate models and representations for addition strategies. In the “Select Your Strategy” section, students solve an addition expression by choosing from strategy stations such as base 10 blocks, a number line, mental math, or a strategy of their choice. Students explain why they selected a particular representation, compare their strategy with classmates’ strategies, and discuss how they can use different models or procedures to determine the same sum. These tasks require students to interpret representations, analyze strategy choices, and evaluate whether a selected approach is efficient and accurate.
In the same lesson, students use connecting cubes and decomposed addends to explore related sums, such as combinations that make 100 or 50. Educator prompts ask students to explain what they notice about the combinations, how the decomposed parts relate to the total, and why different decompositions can represent the same value. These tasks require students to analyze and evaluate mathematical models and representations for addition relationships.
Evaluation for 5.1b
In the Teacher’s Implementation Guide, module 3, topic 12, lesson 9, students create models to represent mathematical situations. During the “How Many Squares?” activity, students estimate the number of rows, columns, and unit squares in rectangles and then cover the rectangles with square tiles to determine the number of unit squares. Students use the tiles to create area models, record their results, and compare their estimates to the actual area.
In the same lesson, students continue creating mathematical models during the “Tiling to Determine Areas” activity. Students use one square tile to trace and complete rectangles and then count the unit squares to determine the area of each rectangle. These tasks require students to create concrete and pictorial area models that represent measurement situations and support their understanding of area as the number of square units that cover a rectangle.
Evaluation for 5.1c
In the Teacher’s Implementation Guide, module 1, topic 1, lesson 13, students apply conceptual understanding to new problem situations and contexts. During the “Solve the Story” activity, students use the Problem-Solving Model to solve addition and subtraction word problems. Students identify what is known and unknown, determine whether the story involves joining or separating, choose an appropriate operation, and explain the strategy they used to solve the problem.
In the same lesson, students extend their conceptual understanding by writing and explaining equations that match action word problems. Students read story contexts, act out or model what happens, write equations using addition or subtraction symbols, and explain how the equation represents the situation. These opportunities require students to apply conceptual understanding of addition, subtraction, and unknown quantities in new story contexts rather than simply solve isolated computation problems.
Evaluation for 5.2a
In the Teacher’s Implementation Guide, module 1, topic 1, lesson 7, students build automaticity and fluency through the “Combinations of 5 and Some More” activity. Students use the five-fingers strategy to add one-digit numbers greater than five. For example, students model 8 + 8 with their hands and then raise one additional finger to represent 9 + 8 and recognize that the sum increases from 16 to 17. Students use the same strategy with additional sums, such as 7 + 7 and 7 + 8, and explain the patterns they notice.
The Teacher’s Implementation Guide also builds fluency through “Daily Math Routines” activities. The “Daily Math Routines” connected to module 1, topic 1 include “Mental Math” opportunities such as counting by 1s and 2s to 20, skip-counting by 2s to 50, skip-counting by 5s and 10s to 100, and skip-counting by 10s across 100. These repeated routines support the automaticity with number patterns, skip counting, and foundational fact fluency needed for grade-level tasks.
Evaluation for 5.2b
In the Teacher’s Implementation Guide, module 4, topic 11, lesson 7, students practice efficient, flexible, and accurate mathematical procedures. Students analyze addends and choose a strategy to solve addition problems, such as decomposing 48 + 2 to make 50 or using place-value reasoning to solve 463 + 104. Students compare strategies, explain why their chosen approach is efficient, and verify that their method accurately determines the sum.
In the same lesson, students continue practicing efficient and flexible procedures through the “Target 999” activity. Students create and add three-digit numbers to get closest to 999. They record their numbers, add by place value, and compare results with a partner. This activity gives students opportunities to apply addition strategies flexibly, reason about place value, and monitor the accuracy of their calculations while working toward a specific target.
Evaluation for 5.2c
In the Teacher’s Implementation Guide, module 2, topic 5, lesson 7, students evaluate procedures, processes, and solutions for efficiency, flexibility, and accuracy. Students also choose whether to use base 10 blocks, a number line, mental math, or another strategy to solve the same addition expression. Students then explain why they selected their strategy, compare their approach with classmates’ approaches, and discuss how different strategies can produce the same correct sum.
In the same lesson, students evaluate addition strategies, use decomposing strategies to calculate sums, and discuss why one strategy may be more efficient than another. Educator prompts ask students to share how they solved the problem, compare strategies, and explain whether a different strategy would have been more efficient. These tasks require students to evaluate mathematical procedures and solutions for efficiency, flexibility, and accuracy.
Evaluation for 5.2d
In the Assessment Guide, topic 11 includes embedded supports for educators to guide students toward increasingly efficient approaches. The “Coach’s Playbook” section directs educators to emphasize place-value reasoning as the foundation for addition and subtraction strategies. It also guides educators to encourage students to compose and decompose numbers in multiple ways and connect expanded form to their written and mental strategies.
The “Coach’s Playbook” section also gives educators specific support for developing strategic flexibility before focusing on efficiency. The guidance explains that students should explore open number lines, expanded form, and place-value strategies before transitioning to more streamlined algorithms. It also prompts educators to monitor whether students use appropriate benchmarks, such as multiples of 10, and whether they understand the structure of the situation without relying on key words. These embedded supports help educators guide students toward increasingly efficient mathematical approaches.
Evaluation for 5.3a
The Texas ClearMath Teacher’s Implementation Guide explicitly states how the “Foundations for Effective Math Instruction” addresses the conceptual and procedural emphasis of the TEKS. The overview identifies rigor as a three-legged stool made up of conceptual understanding, procedural fluency, and real-world application. It explains that students develop conceptual understanding through concrete models, visual representations, and opportunities to make sense of mathematical relationships before moving toward abstract reasoning.
The same “Foundations for Effective Math Instruction” section explains how students develop procedural fluency alongside conceptual understanding. The overview describes students building procedural fluency by exploring and applying strategies, using different representations, playing games that reinforce relationships, and practicing procedures in meaningful contexts. This guidance explicitly identifies how the materials balance conceptual understanding, procedural fluency, and application in grade-level mathematics instruction.
Evaluation for 5.3b
In the Teacher’s Implementation Guide, module 2, topic 4, lesson 1, students use concrete models, pictorial representations, and abstract representations as required by the TEKS. Students use base 10 blocks and 10 frames as concrete and visual models to represent numbers as 10 and some more. Students then connect those models to numerals and equations, using symbolic representations to show the value of each number.
In the Teacher’s Implementation Guide, module 3, topic 12, lesson 9, students use concrete and pictorial models to support area understanding. Students use square tiles as concrete manipulatives to cover rectangles, trace or draw square units as pictorial representations, and record the area using numbers and units. These tasks intentionally connect concrete tiles, visual area models, and numeric representations of area.
Evaluation for 5.3c
In the Texas ClearMath Grade 2 Teacher’s Implementation Guide, module 5, topic 13, lesson 1, students connect, create, define, and explain concrete models to abstract place-value concepts. Students use base 10 blocks and the Wonder Wheel Factory context to represent how ones are grouped into tens, tens are grouped into hundreds, and hundreds are grouped into thousands. Students create concrete models with base 10 blocks, record the corresponding numerals, define the value represented by each place, and explain how the blocks show the composition of larger numbers. These supports help students connect concrete models to abstract numeric and place-value representations.
In the Teacher’s Implementation Guide, module 1, topic 1, lesson 4, students connect, create, define, and explain representational models to abstract even-and-odd concepts. Students draw trains of connecting cubes to represent addition situations and determine whether sums are even or odd. They define evenness by explaining whether each cube has a partner or whether one cube is left unpaired and then connect the drawing to the abstract classification of a number as even or odd. These supports help students create and explain representational models and connect them to symbolic and numeric mathematical ideas.
Evaluation for 5.4a
In the Teacher’s Implementation Guide, module 1, topic 2, lesson 2, students develop academic mathematical language through visuals, manipulatives, and intentional language-development strategies. Students examine a visual of four quadrilaterals and discuss their similarities and differences using mathematical vocabulary such as quadrilateral, rectangle, square, trapezoid, sides, and vertices. During the Think-Pair-Share discussion, students compare attributes, explain why each figure is or is not a quadrilateral, and justify their thinking using precise mathematical language. The “Emergent Bilingual Student Support” section extends vocabulary development by connecting the word part quad to quadrilateral and encouraging discussion of the term’s meaning. Later, students use polygon cards to match polygon names to corresponding shapes, reinforcing mathematical language through hands-on practice.
In the Teacher’s Implementation Guide, module 1, topic 2, lesson 6, students develop academic mathematical language through visuals, manipulatives, and targeted language-development strategies. Students use geoblocks to observe and discuss three-dimensional solids and then read formal definitions for face, edge, and vertex in the “Solid Gold” activity. Students use diagrams to visually identify each attribute; return to the physical manipulatives to count the faces, edges, and vertices; and describe the shapes of the faces. The “Language Link” supports students in distinguishing between two-dimensional and three-dimensional figures and defining a face, helping them connect vocabulary to concrete models and visual representations.
Evaluation for 5.4b
In the Teacher’s Implementation Guide, module 1, topic 2, lesson 1 guides educators to scaffold and support students’ development and use of academic mathematical vocabulary in context. In the “Language Link: Developing Mathematical Language” section, educators allow students to participate in the polygon-sorting activity without requiring academic vocabulary before students are ready to use it. As students develop vocabulary, educators encourage classmates to explain mathematical terms to one another, rephrase responses, and discuss the attributes used to sort polygons. This embedded educator guidance supports students in developing and applying academic mathematical vocabulary within a meaningful geometry context.
In the Teacher’s Implementation Guide, module 1, topic 2, lesson 2 guides educators to scaffold students’ development and use of academic mathematical vocabulary. During the “Language Link” activity, educators encourage students to discuss the similarities and differences among four-sided shapes using their own mathematical language while noticing shared attributes. Educator guidance acknowledges that students may use informal terms, such as diamond for rhombus, and guides discussions that emphasize geometric reasoning before introducing formal mathematical vocabulary such as trapezoid. This embedded guidance supports students in developing and applying academic vocabulary while describing and comparing shapes.
Evaluation for 5.4c
In the Teacher’s Implementation Guide, module 1, topic 1, lesson 11 guides educators to support mathematical conversations through vocabulary, syntax, and discourse. Students determine the difference in a subtraction equation before participating in a Think-Pair-Share routine to explain and justify the subtraction strategy they used. Educator questions prompt students to describe their reasoning using mathematical language, while partner discussions provide opportunities for students to hear, refine, and apply mathematical language through conversation. Exemplar responses model complete mathematical explanations and support educators in facilitating and monitoring student discussions.
In the Teacher’s Implementation Guide, module 1, topic 1, lesson 2 offers educators guidance in supporting mathematical conversations through vocabulary, syntax, and discourse. Students use counters to solve addition puzzles with unknown quantities before sharing and comparing their solution strategies with a partner. Educator questions prompt students to explain how they determined the missing quantities and justify the strategies they used during the whole-group discussion. Partner and class discussions give students opportunities to hear, refine, and apply mathematical language while communicating their thinking, and exemplar responses model complete mathematical explanations.
Evaluation for 5.5a
In the Teacher’s Implementation Guide, module 1, topic 1, lesson 13, the TEKS mathematical process standards are identified in the blue “Mathematical Process Standards” section and integrated throughout the lesson. TEKS 2.1B guides students in using a problem-solving model to solve addition and subtraction word problems. Students use the Problem-Solving Model resource to identify known and unknown information, determine what the question is asking, develop a plan, and solve the problem. Educator questions prompt students to identify relevant information, explain their reasoning, and apply each step of the problem-solving model as they solve word problems.
In the Teacher’s Implementation Guide, module 1, topic 1, lesson 14, the TEKS mathematical process standards are identified in the blue “Mathematical Process Standards” section and integrated throughout the lesson. TEKS 2.1G guides students in identifying, explaining, and communicating mathematical ideas using multiple representations. Students compare sums within 20 and differences within 10, identify the strategies they used to solve each expression, and explain why their strategies produce the correct solution. Educator questions prompt students to justify their reasoning and communicate their mathematical thinking using precise mathematical language.
Evaluation for 5.5b
In the Assessment Guide, the “Mathematical Process Standards” section describes how TEKS mathematical process standards are incorporated and connected throughout the course. The “TEKS Correlation Chart” identifies where each mathematical process standard is addressed across topics, demonstrating that the process standards are intentionally incorporated throughout the curriculum. The “Mathematical Process Standards” section also identifies the specific process standards emphasized within each “Re-Engagement Lesson,” showing how students revisit and apply the mathematical process standards across topics and lessons over time.
In the Teacher’s Implementation Guide, module 1, topic 1 overview, the “Mathematical Process Standards” section describes how TEKS mathematical process standards are incorporated and connected throughout the topic. The “Mathematical Process Standards” section identifies the process standards emphasized throughout topic 1 and includes Student Look-Fors that describe how students demonstrate each process standard during instruction. These supports show how the TEKS process standards are intentionally incorporated and connected throughout the topic.
Evaluation for 5.5c
In the Teacher’s Implementation Guide, module 1, topic 1 overview, the “Mathematical Process Standards” section describes how TEKS mathematical process standards are incorporated and connected throughout the topic. The “Mathematical Process Standards” table identifies the process standards emphasized within the topic and includes Student Look-Fors that describe how students demonstrate each process standard during instruction. These Student Look-Fors provide consistent expectations for applying the mathematical process standards across lessons within the topic.
In the Teacher’s Implementation Guide, module 1, topic 2, lesson 10 describes how TEKS mathematical process standards are incorporated and connected throughout the topic. During the “Mindset Reflection,” students reflect on the learning goals and mathematical process standards emphasized throughout the topic and evaluate their own progress by selecting an emoji that represents their understanding. This reflection reinforces the mathematical process standards developed throughout the topic and provides a consistent opportunity for students to connect their mathematical thinking across lessons.
Evaluation for 5.5d
In the Teacher’s Implementation Guide, module 1, topic 1, lesson 1, the lesson overview identifies the TEKS mathematical process standards incorporated into the lesson. The “Texas TEKS” box identifies the mathematical process standards alongside the content TEKS and ELPS, providing educators with an overview of the standards addressed during instruction. This lesson overview appears at the beginning of each lesson throughout the curriculum, giving educators consistent access to the TEKS process standards before instruction begins.
In the Teacher’s Implementation Guide, module 1, topic 1, lesson 1, the “Mathematical Process Standards” section provides an overview of the TEKS mathematical process standards incorporated into the activity. The box identifies the specific mathematical process standards addressed during the lesson, giving educators immediate access to the process standards integrated into instruction. This embedded overview reinforces the mathematical process standards as students engage in the lesson activities.
5.1 Development of Conceptual Understanding
5.1a
Questions and tasks require students to interpret, analyze, and evaluate models and representations for mathematical concepts and situations.
Questions and tasks require students to interpret, analyze, and evaluate models and representations for mathematical concepts and situations.
3 out of 3 points
Evaluation for 5.1a
Evaluation for 5.1a
Questions and tasks require students to interpret, analyze, and evaluate models and representations for mathematical concepts and situations.
3 out of 3 points
In the same lesson, students use connecting cubes and decomposed addends to explore related sums, such as combinations that make 100 or 50. Educator prompts ask students to explain what they notice about the combinations, how the decomposed parts relate to the total, and why different decompositions can represent the same value. These tasks require students to analyze and evaluate mathematical models and representations for addition relationships.
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 same lesson, students continue creating mathematical models during the “Tiling to Determine Areas” activity. Students use one square tile to trace and complete rectangles and then count the unit squares to determine the area of each rectangle. These tasks require students to create concrete and pictorial area models that represent measurement situations and support their understanding of area as the number of square units that cover a rectangle.
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 same lesson, students extend their conceptual understanding by writing and explaining equations that match action word problems. Students read story contexts, act out or model what happens, write equations using addition or subtraction symbols, and explain how the equation represents the situation. These opportunities require students to apply conceptual understanding of addition, subtraction, and unknown quantities in new story contexts rather than simply solve isolated computation problems.
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
The Teacher’s Implementation Guide also builds fluency through “Daily Math Routines” activities. The “Daily Math Routines” connected to module 1, topic 1 include “Mental Math” opportunities such as counting by 1s and 2s to 20, skip-counting by 2s to 50, skip-counting by 5s and 10s to 100, and skip-counting by 10s across 100. These repeated routines support the automaticity with number patterns, skip counting, and foundational fact fluency needed for grade-level tasks.
5.2b
Materials provide opportunities for students to practice the application of efficient, flexible, and accurate mathematical procedures within the lesson and/or throughout a unit.
Materials provide opportunities for students to practice the application of efficient, flexible, and accurate mathematical procedures within the lesson and/or throughout a unit.
3 out of 3 points
Evaluation for 5.2b
Evaluation for 5.2b
Materials provide opportunities for students to practice the application of efficient, flexible, and accurate mathematical procedures within the lesson and/or throughout a unit.
3 out of 3 points
In the same lesson, students continue practicing efficient and flexible procedures through the “Target 999” activity. Students create and add three-digit numbers to get closest to 999. They record their numbers, add by place value, and compare results with a partner. This activity gives students opportunities to apply addition strategies flexibly, reason about place value, and monitor the accuracy of their calculations while working toward a specific target.
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 same lesson, students evaluate addition strategies, use decomposing strategies to calculate sums, and discuss why one strategy may be more efficient than another. Educator prompts ask students to share how they solved the problem, compare strategies, and explain whether a different strategy would have been more efficient. These tasks require students to evaluate mathematical procedures and solutions for efficiency, flexibility, and accuracy.
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
The “Coach’s Playbook” section also gives educators specific support for developing strategic flexibility before focusing on efficiency. The guidance explains that students should explore open number lines, expanded form, and place-value strategies before transitioning to more streamlined algorithms. It also prompts educators to monitor whether students use appropriate benchmarks, such as multiples of 10, and whether they understand the structure of the situation without relying on key words. These embedded supports help educators guide students toward increasingly efficient mathematical approaches.
5.3 Balance of Conceptual Understanding and Procedural Fluency
5.3a
Materials explicitly state how the conceptual and procedural emphasis of the TEKS are addressed.
Materials explicitly state how the conceptual and procedural emphasis of the TEKS are addressed.
2 out of 2 points
Evaluation for 5.3a
Evaluation for 5.3a
Materials explicitly state how the conceptual and procedural emphasis of the TEKS are addressed.
2 out of 2 points
The same “Foundations for Effective Math Instruction” section explains how students develop procedural fluency alongside conceptual understanding. The overview describes students building procedural fluency by exploring and applying strategies, using different representations, playing games that reinforce relationships, and practicing procedures in meaningful contexts. This guidance explicitly identifies how the materials balance conceptual understanding, procedural fluency, and application in grade-level mathematics instruction.
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 3, topic 12, lesson 9, students use concrete and pictorial models to support area understanding. Students use square tiles as concrete manipulatives to cover rectangles, trace or draw square units as pictorial representations, and record the area using numbers and units. These tasks intentionally connect concrete tiles, visual area models, and numeric representations of area.
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 1, topic 1, lesson 4, students connect, create, define, and explain representational models to abstract even-and-odd concepts. Students draw trains of connecting cubes to represent addition situations and determine whether sums are even or odd. They define evenness by explaining whether each cube has a partner or whether one cube is left unpaired and then connect the drawing to the abstract classification of a number as even or odd. These supports help students create and explain representational models and connect them to symbolic and numeric mathematical ideas.
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 1, topic 2, lesson 6, students develop academic mathematical language through visuals, manipulatives, and targeted language-development strategies. Students use geoblocks to observe and discuss three-dimensional solids and then read formal definitions for face, edge, and vertex in the “Solid Gold” activity. Students use diagrams to visually identify each attribute; return to the physical manipulatives to count the faces, edges, and vertices; and describe the shapes of the faces. The “Language Link” supports students in distinguishing between two-dimensional and three-dimensional figures and defining a face, helping them connect vocabulary to concrete models and visual representations.
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 2 guides educators to scaffold students’ development and use of academic mathematical vocabulary. During the “Language Link” activity, educators encourage students to discuss the similarities and differences among four-sided shapes using their own mathematical language while noticing shared attributes. Educator guidance acknowledges that students may use informal terms, such as diamond for rhombus, and guides discussions that emphasize geometric reasoning before introducing formal mathematical vocabulary such as trapezoid. This embedded guidance supports students in developing and applying academic vocabulary while describing and comparing shapes.
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 1, topic 1, lesson 2 offers educators guidance in supporting mathematical conversations through vocabulary, syntax, and discourse. Students use counters to solve addition puzzles with unknown quantities before sharing and comparing their solution strategies with a partner. Educator questions prompt students to explain how they determined the missing quantities and justify the strategies they used during the whole-group discussion. Partner and class discussions give students opportunities to hear, refine, and apply mathematical language while communicating their thinking, and exemplar responses model complete mathematical explanations.
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 1, topic 1, lesson 14, the TEKS mathematical process standards are identified in the blue “Mathematical Process Standards” section and integrated throughout the lesson. TEKS 2.1G guides students in identifying, explaining, and communicating mathematical ideas using multiple representations. Students compare sums within 20 and differences within 10, identify the strategies they used to solve each expression, and explain why their strategies produce the correct solution. Educator questions prompt students to justify their reasoning and communicate their mathematical thinking using precise mathematical language.
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, module 1, topic 1 overview, the “Mathematical Process Standards” section describes how TEKS mathematical process standards are incorporated and connected throughout the topic. The “Mathematical Process Standards” section identifies the process standards emphasized throughout topic 1 and includes Student Look-Fors that describe how students demonstrate each process standard during instruction. These supports show how the TEKS process standards are intentionally incorporated and connected throughout the topic.
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
In the Teacher’s Implementation Guide, module 1, topic 2, lesson 10 describes how TEKS mathematical process standards are incorporated and connected throughout the topic. During the “Mindset Reflection,” students reflect on the learning goals and mathematical process standards emphasized throughout the topic and evaluate their own progress by selecting an emoji that represents their understanding. This reflection reinforces the mathematical process standards developed throughout the topic and provides a consistent opportunity for students to connect their mathematical thinking across lessons.
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
In the Teacher’s Implementation Guide, module 1, topic 1, lesson 1, the “Mathematical Process Standards” section provides an overview of the TEKS mathematical process standards incorporated into the activity. The box identifies the specific mathematical process standards addressed during the lesson, giving educators immediate access to the process standards integrated into instruction. This embedded overview reinforces the mathematical process standards as students engage in the lesson activities.
Rubric Section 6
Productive Struggle
Materials support students in applying disciplinary practices to productive problem-solving, including explaining and revising their thinking.
Total
100% (22 out of 22 points)
Evaluation for 6.1a
In the Teacher’s Implementation Guide, module 1, topic 2, lesson 9, students think mathematically, persevere through solving problems, and make sense of mathematics as they design a three-dimensional structure and create two-dimensional top and side views of their model. Students exchange drawings with another pair and use the representations to re-create the original structure, comparing the model to the drawings and revising their work as needed. Educator questions prompt students to explain how they determined the top and side views, evaluate whether the representations accurately match the model, and describe the strategies they used to complete the task. Ongoing assessment guidance directs educators to monitor students’ ability to connect two-dimensional and three-dimensional representations and accurately re-create the models.
In the Teacher’s Implementation Guide, module 1, topic 2, lesson 10, students think mathematically, persevere through problem-solving, and make sense of mathematics as they identify three-dimensional solids by analyzing descriptive attributes. Students listen to geometric clues, determine the corresponding solid, and explain the attributes that support their reasoning. Students then create three or four descriptive clues about a three-dimensional solid for a partner to identify, requiring them to apply their understanding of geometric attributes and communicate precise mathematical language. Educator questions prompt students to justify their reasoning and explain how they identified each solid.
Evaluation for 6.1b
In the Teacher’s Implementation Guide, module 2, topic 5, lesson 13, students develop an understanding that there can be multiple ways to represent and solve mathematical problems. Students model two-digit addition using a tool of their choice, such as base 10 blocks, an open number line, or a 100s chart, and compare their results with classmates. Educator questions prompt students to explain the strategy they selected, justify why they chose that strategy, and discuss how different representations and strategies can determine the same sum. During the closing discussion, students compare the efficiency of different addition strategies and explain which strategies they prefer and why.
In the Teacher’s Implementation Guide, module 2, topic 4, lesson 11, Explore 2, students understand, explain, and justify that subtraction problems can be represented and solved in multiple ways. Students work with a partner to use base 10 blocks to model subtraction equations, draw their representations, and regroup flats and rods as needed to determine the difference. Students share their representations with another pair and compare the different strategies they used to solve the problem. During the closing discussion, educator questions prompt students to explain and justify the strategies they used to determine the difference, reinforcing that subtraction problems can be represented and solved in more than one way.
Evaluation for 6.1c
In the Teacher’s Implementation Guide, module 3, topic 3, lesson 13, students make sense of mathematics through opportunities to do, write about, and discuss mathematics with peers and educators. Students work with a partner to use base 10 blocks to determine multiple ways to bundle 256 wheels, record different combinations, and complete additional combinations after discussing their ideas during a Think-Pair-Share routine. Educator questions and whole-group discussions prompt students to compare similarities and differences among the combinations, explain their reasoning, and justify how different combinations can represent the same quantity.
In the Teacher’s Implementation Guide, module 2, topic 4, lesson 12, students make sense of mathematics through opportunities to do, write about, and discuss mathematics with peers and educators. Students work with a partner to count two groups of pattern blocks, combine the groups, and determine the total number of shapes. Students represent their first example by drawing and recording the groups in the “How Many of Each Shape?” activity. During an educator-facilitated discussion, students explain how they determined the total and describe the number of shapes in each group and in the combined set.
Evaluation for 6.2a
In the Teacher’s Implementation Guide, module 1, topic 1, lesson 13, “Explore 2: Solve the Story” and “Reflect: Sharing Snacks” give educators guidance to support students in sharing and reflecting on their problem-solving approaches through explanations, arguments, and justifications. Students use the Problem-Solving Model to identify what the problem is asking, explain what the numbers represent, determine a solution plan, and complete the problem with a partner. Educator questions prompt students to explain how the equation represents the word problem, justify their solution, and discuss how different equations within the same fact family can solve the problem. During the “Reflect” activity, students explain how the Three Reads strategy supported their understanding of the problem and reflect on how explaining their thinking helps them identify errors and check their work.
In the Teacher’s Implementation Guide, module 1, topic 1, lesson 11, students share and reflect on their problem-solving approaches through explanations, arguments, and justifications. While the educator models the game “Attention!” educator questions prompt students to explain how they determined possible addends for a given sum, justify why a card could represent a particular number, and support their reasoning with mathematical evidence. Students then play the game in groups of three, explaining and discussing their strategies as they determine unknown addends. During the closing discussion, students share the strategies they used and reflect on their problem-solving approaches by explaining and justifying their mathematical thinking.
Evaluation for 6.2b
In the Teacher’s Implementation Guide, module 1, topic 1, lesson 13 guides educators in giving explanatory feedback based on student responses and anticipated misconceptions. The “Common Misconception” section anticipates that students may interpret the equal sign as an instruction to perform an action rather than as a symbol representing equality. Educator guidance reinforces the meaning of the equal sign as students determine whether a story represents addition or subtraction, identify known and unknown quantities, and write an equation to match the word problem.
In the Teacher’s Implementation Guide, module 1, topic 2, lesson 2 provides prompts and guidance that supports educators in providing explanatory feedback based on student responses and anticipated misconceptions. As students work with a partner to identify and count polygons in a picture, educator questions prompt students to explain the attributes of a polygon and justify why a star is a polygon while a moon is not. The “Common Misconception” section prepares educators to address students who recognize only prototypical shapes and do not identify valid variations in orientation or proportions. This section directs educators to draw shapes in different orientations, emphasize defining attributes rather than appearance, and provide explanatory feedback that reinforces students’ understanding of polygons.
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 1, topic 2, lesson 10, students think mathematically, persevere through problem-solving, and make sense of mathematics as they identify three-dimensional solids by analyzing descriptive attributes. Students listen to geometric clues, determine the corresponding solid, and explain the attributes that support their reasoning. Students then create three or four descriptive clues about a three-dimensional solid for a partner to identify, requiring them to apply their understanding of geometric attributes and communicate precise mathematical language. Educator questions prompt students to justify their reasoning and explain how they identified each solid.
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 2, topic 4, lesson 11, Explore 2, students understand, explain, and justify that subtraction problems can be represented and solved in multiple ways. Students work with a partner to use base 10 blocks to model subtraction equations, draw their representations, and regroup flats and rods as needed to determine the difference. Students share their representations with another pair and compare the different strategies they used to solve the problem. During the closing discussion, educator questions prompt students to explain and justify the strategies they used to determine the difference, reinforcing that subtraction problems can be represented and solved in more than one way.
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 2, topic 4, lesson 12, students make sense of mathematics through opportunities to do, write about, and discuss mathematics with peers and educators. Students work with a partner to count two groups of pattern blocks, combine the groups, and determine the total number of shapes. Students represent their first example by drawing and recording the groups in the “How Many of Each Shape?” activity. During an educator-facilitated discussion, students explain how they determined the total and describe the number of shapes in each group and in the combined set.
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 11, students share and reflect on their problem-solving approaches through explanations, arguments, and justifications. While the educator models the game “Attention!” educator questions prompt students to explain how they determined possible addends for a given sum, justify why a card could represent a particular number, and support their reasoning with mathematical evidence. Students then play the game in groups of three, explaining and discussing their strategies as they determine unknown addends. During the closing discussion, students share the strategies they used and reflect on their problem-solving approaches by explaining and justifying their mathematical thinking.
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 2, lesson 2 provides prompts and guidance that supports educators in providing explanatory feedback based on student responses and anticipated misconceptions. As students work with a partner to identify and count polygons in a picture, educator questions prompt students to explain the attributes of a polygon and justify why a star is a polygon while a moon is not. The “Common Misconception” section prepares educators to address students who recognize only prototypical shapes and do not identify valid variations in orientation or proportions. This section directs educators to draw shapes in different orientations, emphasize defining attributes rather than appearance, and provide explanatory feedback that reinforces students’ understanding of polygons.