Program Information
- ISBN
- 9781970651591
- Technical Specifications: Checklist
- Tech Specs: Checklist (pdf 884.25 KB)
- Technical Specifications: Professional Development
- Tech Specs: Professional Development (pdf 181.54 KB)
Step Up to the TEKS 6th Math Practice
Supplemental Math (English) Grade 6
IMRA 2026
Publisher: GF Educators, Inc.
Copyright: 2022
Series includes:
Rubric: Supplemental Mathematics 6–12 (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 6 | 100% | N/A |
Criteria for Quality
Rubric Section 1
Intentional Instructional Design
Materials support educators in effective implementation through intentional course, unit, and lesson-level design.
Total
78% (18 out of 23 points)
Evaluation for 1.1a
The materials include an alignment guide that outlines the Texas Essential Knowledge and Skills (TEKS), the English Language Proficiency Standards (ELPS), and concepts covered. The materials are organized by TEKS and grouped into coherent domains with the Table of Contents of the Practice Book and Appendix A of the Implementation Guide connecting lessons to the TEKS, while ELPS are reflected in the Teacher Education (TE) front matter. This organization supports educators in understanding the progression of mathematical concepts across grade 6 standards.
The materials include a rationale for learning paths across grade levels for vertical alignment. For example, the organization of the materials into coherent domains reflects a logical progression of mathematical concepts and supports educators’ understanding of how learning develops across the grade level.
The materials do not include a rationale for learning paths within the same grade level, horizontal alignment, as designed in the materials. The material does not identify guidance that explains how concepts connect, align, or build across units or domains within grade 6.
Evaluation for 1.1b
The materials include an implementation guide with usage recommendations and strategies for effective educator use in various contexts. For example, an Implementation Guide is located in the digital bookcase and includes sections designed to support schools with implementation of the materials, including a section for differentiation. The guide also includes recommendations for adapting instruction to meet student needs in various instructional contexts.
The materials include strategies for effective educator practices across a variety of instructional contexts. For example, the grade 6 Math Implementation Guide outlines two instructional pathways, “Practice Book” and “TEKS-tivity,” with tables describing time allotments and suggested groupings for each activity. The Lesson-at-a-Glance for lesson 2, “Multi-Step Unit Conversions,” includes whole class, small group, and individual groupings throughout the pathway, supporting implementation in multiple instructional settings.
Evaluation for 1.1c
The materials include a TEKS correlation guide. For example, in the Table of Contents and the “Program Overview” section of the Implementation Guide, it provides direct connections between grade 6 topics, TEKS, and supplemental practice focus areas.
The Item map page included in the Unit Overview contains entry points based on diagnostic results. Recommended Responses and TEKS-Level Decision Rules are also included.
Evaluation for 1.1d
Materials include protocols with corresponding guidance for unit internalization. The materials include processes for educators to thoroughly understand and prepare to teach lessons. The Unit Overview includes Unit Rationale, Big Ideas, Background Knowledge, Instructional Notes to support all learners, and required materials. An Internalization protocol to guide educators when preparing for each lesson is also provided.
The Lesson Overview contains the TEKS Statement, student objective, conceptual goal, procedural goal, lesson overview with grouping recommendations, process standards connections, academic vocabulary and mathematical discourse support and emergent bilingual oral and written discourse supports. A sample unit with the lessons for the unit is provided.
Evaluation for 1.1e
Materials include resources for instructional leaders to support educators with implementing the materials as designed. For example, the materials include implementation guidance and instructional recommendations to support educators in using the supplemental resource as designed. The “Program Overview” and “Instructional Design” sections describe intended instructional uses, including Tier 1 reinforcement, intervention, small-group instruction, independent practice, and review cycles. Additionally, the TEKS Checklist, Grade 6 provides a thorough breakdown of each standard presented in the lessons and is available to educators as well as instructional leaders.
Resources and guidance for administrators are in the “Unit Level Internalization” materials in the Implementation Guides. Additionally, the “Leadership Lens” section sample for unit 1 provides further implementation guidance for administrators.
Evaluation for 1.2a
Materials include detailed lesson plans with learning objectives aligned with the TEKS and ELPS, as well as educator and student materials with lesson components and suggested time frames. For example, lessons include learning objectives, conceptual learning goals, vertical alignment connections, educator guidance, student materials, and structured lesson components with suggested instructional timeframes.
Materials include structured lesson components and educator-facing supports to support instructional planning and implementation. For example, the educator pages for each lesson provide relevant information for preparation of the lesson. The TEKS information, vertical alignment, ELPS, Conceptual Goal, and lesson information along with timing information are all provided for each TEKS lesson. The materials also include “facilitating questions,” “Important Concepts,” “Extension Opportunity,” and “Misconceptions” to support lesson delivery and preparation.
The materials do not include assessment resources aligned with the TEKS or assessment resources aligned with the ELPS. It is not clear where the ELPS are connected throughout the lesson/assessment; they are listed at the beginning of the lesson.
Evaluation for 1.2b
This guidance is not applicable because the program is not designed to be adaptive.
This guidance is not applicable to the program.
Evaluation for 1.2c
Materials do not contain support for families in Spanish and English for each unit, with suggestions on supporting the progress of their student(s). For example, the materials do not include family-facing guidance, home support suggestions, communication tools, or resources specifically designed to support family involvement in monitoring student progress or reinforcing learning at home.
The materials include supports such as academic vocabulary, visual models, and structured discussion opportunities that can be leveraged for educators to support communication with families and reinforce student learning outside the classroom; however, the materials do not contain resources to support families.
1.1 Course-Level Design
1.1a
Materials include an alignment guide outlining the TEKS, ELPS, and concepts covered, with a rationale for learning paths across grade levels (vertical alignment) and within the same grade level (horizontal alignment) as designed in the materials.
Materials include an alignment guide outlining the TEKS, ELPS, and concepts covered, with a rationale for learning paths across grade levels (vertical alignment) and within the same grade level (horizontal alignment) as designed in the materials.
4 out of 5 points
Evaluation for 1.1a
Evaluation for 1.1a
Materials include an alignment guide outlining the TEKS, ELPS, and concepts covered, with a rationale for learning paths across grade levels (vertical alignment) and within the same grade level (horizontal alignment) as designed in the materials.
4 out of 5 points
The materials include a rationale for learning paths across grade levels for vertical alignment. For example, the organization of the materials into coherent domains reflects a logical progression of mathematical concepts and supports educators’ understanding of how learning develops across the grade level.
The materials do not include a rationale for learning paths within the same grade level, horizontal alignment, as designed in the materials. The material does not identify guidance that explains how concepts connect, align, or build across units or domains within grade 6.
1.1b
Materials include an implementation guide with usage recommendations and strategies for effective educator use, such as just-in-time supports, advanced learning, or as a course.
Materials include an implementation guide with usage recommendations and strategies for effective educator use, such as just-in-time supports, advanced learning, or as a course.
3 out of 3 points
Evaluation for 1.1b
Evaluation for 1.1b
Materials include an implementation guide with usage recommendations and strategies for effective educator use, such as just-in-time supports, advanced learning, or as a course.
3 out of 3 points
The materials include strategies for effective educator practices across a variety of instructional contexts. For example, the grade 6 Math Implementation Guide outlines two instructional pathways, “Practice Book” and “TEKS-tivity,” with tables describing time allotments and suggested groupings for each activity. The Lesson-at-a-Glance for lesson 2, “Multi-Step Unit Conversions,” includes whole class, small group, and individual groupings throughout the pathway, supporting implementation in multiple instructional settings.
1.1c
Materials include a TEKS correlation guide with recommended skill entry points based on diagnostic assessment results.
Materials include a TEKS correlation guide with recommended skill entry points based on diagnostic assessment results.
2 out of 2 points
Evaluation for 1.1c
Evaluation for 1.1c
Materials include a TEKS correlation guide with recommended skill entry points based on diagnostic assessment results.
2 out of 2 points
The Item map page included in the Unit Overview contains entry points based on diagnostic results. Recommended Responses and TEKS-Level Decision Rules are also included.
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 Lesson Overview contains the TEKS Statement, student objective, conceptual goal, procedural goal, lesson overview with grouping recommendations, process standards connections, academic vocabulary and mathematical discourse support and emergent bilingual oral and written discourse supports. A sample unit with the lessons for the unit is provided.
1.1e
Materials include resources and guidance for instructional leaders to support educators with implementing the materials as designed.
Materials include resources and guidance for instructional leaders to support educators 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 educators with implementing the materials as designed.
2 out of 2 points
Resources and guidance for administrators are in the “Unit Level Internalization” materials in the Implementation Guides. Additionally, the “Leadership Lens” section sample for unit 1 provides further implementation guidance for administrators.
1.2 Lesson-Level Design
1.2a
If designed to be static, materials include detailed lesson plans with learning objectives, teacher and student materials, lesson components with suggested timeframes, and assessment resources aligned with the TEKS and ELPS.
If designed to be static, materials include detailed lesson plans with learning objectives, teacher and student materials, lesson components with suggested timeframes, and assessment resources aligned with the TEKS and ELPS.
5 out of 7 points
Evaluation for 1.2a
Evaluation for 1.2a
If designed to be static, materials include detailed lesson plans with learning objectives, teacher and student materials, lesson components with suggested timeframes, and assessment resources aligned with the TEKS and ELPS.
5 out of 7 points
Materials include structured lesson components and educator-facing supports to support instructional planning and implementation. For example, the educator pages for each lesson provide relevant information for preparation of the lesson. The TEKS information, vertical alignment, ELPS, Conceptual Goal, and lesson information along with timing information are all provided for each TEKS lesson. The materials also include “facilitating questions,” “Important Concepts,” “Extension Opportunity,” and “Misconceptions” to support lesson delivery and preparation.
The materials do not include assessment resources aligned with the TEKS or assessment resources aligned with the ELPS. It is not clear where the ELPS are connected throughout the lesson/assessment; they are listed at the beginning of the lesson.
1.2b
If designed to be adaptive, materials include detailed lesson overviews with learning objectives, lesson components with suggested timeframes, and assessment resources aligned with the TEKS and ELPS.
If designed to be adaptive, materials include detailed lesson overviews with learning objectives, lesson components with suggested timeframes, and assessment resources aligned with the TEKS and ELPS.
Not applicable.
Evaluation for 1.2b
Evaluation for 1.2b
If designed to be adaptive, materials include detailed lesson overviews with learning objectives, lesson components with suggested timeframes, and assessment resources aligned with the TEKS and ELPS.
Not applicable.
This guidance is not applicable to the program.
1.2c
Materials contain support for families in Spanish and English for each unit, with suggestions on supporting the progress of their student(s).
Materials contain support for families in Spanish and English for each unit, with suggestions on supporting the progress of their student(s).
0 out of 2 points
Evaluation for 1.2c
Evaluation for 1.2c
Materials contain support for families in Spanish and English for each unit, with suggestions on supporting the progress of their student(s).
0 out of 2 points
The materials include supports such as academic vocabulary, visual models, and structured discussion opportunities that can be leveraged for educators to support communication with families and reinforce student learning outside the classroom; however, the materials do not contain resources to support families.
Rubric Section 2
Progress Monitoring
Materials support educators in effective implementation through frequent, strategic opportunities to monitor and respond to student progress.
Total
75% (15 out of 20 points)
Evaluation for 2.1a
The materials include the definition and intended purpose for the types of instructional assessments. For example, the Teacher Guide Practice Book Overview lists each component of the book along with the intended use within the program, including Guided Practices, Partner Practices, Independent Practices, and Engaging Activities. The Unit Assessment Overview provides the “Definition and Purpose,” “Primary Instrument,” and “How Teachers Use the Evidence” for each of the different assessment types.
The “To the Teacher” introduction offers directions for using the program’s assessments. The Unit Assessment Overview includes guidance in the “How Teachers Use the Evidence” section depending on the primary instrument used.
Evaluation for 2.1b
The educator edition front matter includes guidance in the “To the Teacher” section explaining how the assessment components are intended to be used and identifies them as formative assessments. While the materials provide embedded administration guidance within the lessons, they offer limited front matter guidance on broader expectations or procedures for administering instructional assessments consistently across settings.
Partner Practice and Independent Practice include separate educator directions that support implementation of each assessment activity. The guidance addresses instructional facilitation, such as grouping and delivery, while the embedded directions and facilitating questions within each activity support administration.
Evaluation for 2.1c
The digital assessment materials correspond to printable versions available in the Practice Student Edition. For example, the assessments available on the digital platform mirror those included in the printable Practice SE. However, educators cannot print the assessments directly from the digital platform and must instead access the printable Practice SE.
The digital platform includes assessment accommodations that educators can configure to support individual student needs. For example, the accommodations settings page allows educators to enable or disable features such as a basic calculator, text-to-speech, translation (English only), and content and language supports for assessment activities. However, content and language supports are available only for assessment items and are not available for practice activities.
Evaluation for 2.1d
The materials include diagnostic assessments with TEKS-aligned tasks or questions, and include interactive types with varying complexity levels. The Item Map in the Implementation Guide provides the associated level (EP/Bridge/GL) along with the target TEKS and Diagnostic Look-Fors. Many questions are lower-level to provide a baseline, but several higher level items are included along with several item types. For example, the diagnostic assessments contain multiple item types including text entry, drag and drop, selection table, and multiple choice.
The Scoring and Instructional Response provides strategies for responding to the results of the diagnostic assessments for students at various levels. The “How Teachers Use the Evidence” in the Unit Assessment Overview on the opposite page also provides ways to respond to students who have not yet reached proficiency.
Evaluation for 2.1e
The Guided Practice and Partner Practice formative assessments contain multiple item types including multiple choice and text entry. For example, the Engaging Activity for TEKS 6.12D has different assessment items than those in the Guided Practice and Partner Practice.
Materials include a variety of formative assessments with TEKS-aligned tasks or questions or interactive item types with varying levels of complexity. For example, within the digital platform, TEKSnology.com, Reporting Category 1 has TEKS-aligned questions with more than two unique interactive item types. This assessment is TEKS-aligned, with item types including multiple-choice, inline-choice, drag-and-drop, and text entry.
Evaluation for 2.2a
The materials do not include a rationale for either correct or incorrect responses. For example, the educator pages for each Independent Practice contain the answers shown on the student edition inset. The concept assessed by each question is noted in the sidebar callouts. In the bottom callout, Important Concepts and Misconceptions are provided. Additional notes are also provided to give the educator information to make actionable decisions based on the results of the assessment. These Independent Practices are not instructional assessments.
Instructional assessments do not include scoring information or guidance for interpreting student performance. For example, TEKSnology.com provides multiple ways for educators to keep track of their students’ performance. Educators can view individual assignments with the results in the Gradebook under “Assignments - Graded.” They can also look at various reports, including Course and Standards Reports, which show results by Assignment or TEKS and can be filtered down to the individual student. The materials do not provide a rationale for correct or incorrect answers.
Evaluation for 2.2b
The materials do not provide guidance for the use of included tasks and activities to respond to student trends in performance on assessments. For example, the “Implementation Guidance” section of the Implementation Guide provides various methods for implementation of the materials within the Practice Book.
The “Using the Practice Book for Small Groups and Intervention” segment discusses the different options for targeted use of the materials with various levels of students. The materials do not give explicit guidance for educators on how to respond to student trends in performance on assessments.
Evaluation for 2.2c
The materials include tools for educators to track student progress and growth through TEKSnology.com reporting features. Educators can look at various reports, including “Course” and “Standards Reports,” that show results by assignment or TEKS and can be filtered down to the individual student level. Educators can then print and review these reports with individual students.
However, the materials do not include tools for students to track their own progress and growth. The printable reports are available for educators to give to students, but the materials do not provide a tool for students to access this same information on their own, or allow students to track progress over time, observe trends, or compare their progress with the class.
Evaluation for 2.2d
The materials provide prompts and guidance to support educators in conducting frequent checks for understanding at key points throughout each lesson or activity. For example, TEKS lessons contain instructions for educators walking them through the lesson, along with key points and strategies. It also gives insight into what should be looked for during the lesson/discussions.
The Guided Practices and Partner Practices contain directions on implementing this part of the lesson, but also contain facilitating questions to help the educator better monitor the students’ progress and ability to grasp the concept.
Evaluation for 2.2e
This guidance is not applicable because the program is not designed to be adaptive.
This guidance is not applicable to the program.
2.1 Instructional Assessments
2.1a
Materials include the definition and intended purpose for the types of instructional assessments.
Materials include the definition and intended purpose for the types of instructional assessments.
1 out of 1 points
Evaluation for 2.1a
Evaluation for 2.1a
Materials include the definition and intended purpose for the types of instructional assessments.
1 out of 1 points
The “To the Teacher” introduction offers directions for using the program’s assessments. The Unit Assessment Overview includes guidance in the “How Teachers Use the Evidence” section depending on the primary instrument used.
2.1b
Materials include guidance to ensure consistent and accurate administration of instructional assessments.
Materials include guidance to ensure consistent and accurate administration of instructional assessments.
1 out of 1 points
Evaluation for 2.1b
Evaluation for 2.1b
Materials include guidance to ensure consistent and accurate administration of instructional assessments.
1 out of 1 points
Partner Practice and Independent Practice include separate educator directions that support implementation of each assessment activity. The guidance addresses instructional facilitation, such as grouping and delivery, while the embedded directions and facilitating questions within each activity support administration.
2.1c
Digital assessments include printable versions and accommodations, including text-to-speech, content and language supports, and calculators, that educators can enable or disable to support individual students.
Digital assessments include printable versions and accommodations, including text-to-speech, content and language supports, and calculators, that educators can enable or disable to support individual students.
2 out of 2 points
Evaluation for 2.1c
Evaluation for 2.1c
Digital assessments include printable versions and accommodations, including text-to-speech, content and language supports, and calculators, that educators can enable or disable to support individual students.
2 out of 2 points
The digital platform includes assessment accommodations that educators can configure to support individual student needs. For example, the accommodations settings page allows educators to enable or disable features such as a basic calculator, text-to-speech, translation (English only), and content and language supports for assessment activities. However, content and language supports are available only for assessment items and are not available for practice activities.
2.1d
Materials include diagnostic assessments with TEKS-aligned tasks or questions, including interactive item types with varying complexity levels.
Materials include diagnostic assessments with TEKS-aligned tasks or questions, including interactive item types with varying complexity levels.
4 out of 4 points
Evaluation for 2.1d
Evaluation for 2.1d
Materials include diagnostic assessments with TEKS-aligned tasks or questions, including interactive item types with varying complexity levels.
4 out of 4 points
The Scoring and Instructional Response provides strategies for responding to the results of the diagnostic assessments for students at various levels. The “How Teachers Use the Evidence” in the Unit Assessment Overview on the opposite page also provides ways to respond to students who have not yet reached proficiency.
2.1e
Materials include a variety of formative assessments with TEKS-aligned tasks or questions, including interactive item types with varying complexity levels.
Materials include a variety of formative assessments with TEKS-aligned tasks or questions, including interactive item types with varying complexity levels.
4 out of 4 points
Evaluation for 2.1e
Evaluation for 2.1e
Materials include a variety of formative assessments with TEKS-aligned tasks or questions, including interactive item types with varying complexity levels.
4 out of 4 points
Materials include a variety of formative assessments with TEKS-aligned tasks or questions or interactive item types with varying levels of complexity. For example, within the digital platform, TEKSnology.com, Reporting Category 1 has TEKS-aligned questions with more than two unique interactive item types. This assessment is TEKS-aligned, with item types including multiple-choice, inline-choice, drag-and-drop, and text entry.
2.2 Data Analysis and Progress Monitoring
2.2a
Instructional assessments include scoring information and guidance for interpreting student performance, including rationale for each correct and incorrect response.
Instructional assessments include scoring information and guidance for interpreting student performance, including rationale for each correct and incorrect response.
0 out of 3 points
Evaluation for 2.2a
Evaluation for 2.2a
Instructional assessments include scoring information and guidance for interpreting student performance, including rationale for each correct and incorrect response.
0 out of 3 points
Instructional assessments do not include scoring information or guidance for interpreting student performance. For example, TEKSnology.com provides multiple ways for educators to keep track of their students’ performance. Educators can view individual assignments with the results in the Gradebook under “Assignments - Graded.” They can also look at various reports, including Course and Standards Reports, which show results by Assignment or TEKS and can be filtered down to the individual student. The materials do not provide a rationale for correct or incorrect answers.
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.
0 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.
0 out of 1 points
The “Using the Practice Book for Small Groups and Intervention” segment discusses the different options for targeted use of the materials with various levels of students. The materials do not give explicit guidance for educators on how to respond to student trends in performance on assessments.
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.
1 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.
1 out of 2 points
However, the materials do not include tools for students to track their own progress and growth. The printable reports are available for educators to give to students, but the materials do not provide a tool for students to access this same information on their own, or allow students to track progress over time, observe trends, or compare their progress with the class.
2.2d
If designed to be static, materials provide prompts and guidance to support educators in conducting frequent checks for understanding at key points throughout each lesson or activity.
If designed to be static, materials provide prompts and guidance to support educators in conducting frequent checks for understanding at key points throughout each lesson or activity.
2 out of 2 points
Evaluation for 2.2d
Evaluation for 2.2d
If designed to be static, materials provide prompts and guidance to support educators in conducting frequent checks for understanding at key points throughout each lesson or activity.
2 out of 2 points
The Guided Practices and Partner Practices contain directions on implementing this part of the lesson, but also contain facilitating questions to help the educator better monitor the students’ progress and ability to grasp the concept.
2.2e
If designed to be adaptive, materials provide frequent checks for understanding at key points throughout each lesson or activity.
If designed to be adaptive, materials provide frequent checks for understanding at key points throughout each lesson or activity.
Not applicable.
Evaluation for 2.2e
Evaluation for 2.2e
If designed to be adaptive, materials provide frequent checks for understanding at key points throughout each lesson or activity.
Not applicable.
This guidance is not applicable to the program.
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
90% (35 out of 39 points)
Evaluation for 3.1a
The materials include explicit educator guidance for lessons or activities scaffolded for students who have not yet reached proficiency in prerequisite or grade-level concepts and skills. Each lesson is provided with guidance for misconceptions as well as the rationale behind each question.
The Scoring and Instructional Response provides strategies for responding to the results of the diagnostic assessments for students at various levels. The “How Teachers Use the Evidence” in the Unit Assessment Overview on the opposite page also provides ways to respond to students who have not yet reached proficiency.
Evaluation for 3.1b
The grade 6 materials include pre-teaching supports for developing academic vocabulary through unit vocabulary lists, word banks, vocabulary activities, and blackline masters aligned to the TEKS concepts for each unit. The vocabulary activities also include embedded supports within the instructional materials and reinforce academic language throughout the lesson sequence, supporting ongoing vocabulary development.
The materials do not include explicit educator guidance for language supports, including pre-teaching and embedded supports for unfamiliar references in text. For example, while the Teacher Edition contains blackline masters of vocabulary activities to include as part of the lessons, the materials do not include pre-teaching and embedded supports for educators to help develop academic vocabulary and decoding unfamiliar references in text.
Evaluation for 3.1c
The materials include explicit educator guidance for enrichment and extension activities for students who have demonstrated proficiency in grade-level and above grade-level content and skills. For example, the “Extension Learning Opportunity” sections are included with every Independent Practice to provide ways to extend the lesson for those who need extended practice.
For students demonstrating proficiency, enrichment and extension activities have students explain multiple strategies, create mathematical problems, apply concepts to real-world scenarios, and compare solution methods. Materials also include educator guidance for implementation by identifying extension opportunities within the Implementation Guide and recommending use as extension activities for advanced learners.
Evaluation for 3.1d
The digital materials include a basic calculator as an accommodation, which educators can enable or disable for individual students. For example, within assignments and assessments, students can access and use the basic calculator tool. The calculator can be used once students click on the corresponding calculator image.
The materials include text-to-speech and a few content and language supports that educators can enable or disable to support individual students. For example, text-to-speech is functional when users first highlight the desired text before selecting the speak option. The materials also include some content and language supports, such as a dictionary that appears when a word is highlighted and visual supports. However, the materials do not include additional embedded language supports, such as rollovers or hover-over explanations of vocabulary or symbols. Although a translation icon is present, the only available language option is English.
Evaluation for 3.1e
The materials include educator guidance on offering options and supports for students to demonstrate understanding of mathematical concepts in various ways, such as performing, expressing, and representing. Opportunities for students to demonstrate their understanding of mathematical concepts in various ways exist throughout the book. For example, in the TEKS lessons, students must create a representation, solve a problem, show their work, and solve a problem and then explain how they solved the problem.
The materials include multiple problem-solving options and support online. For example, the digital materials include interactive exercises, video explanations, and real-world applications.
Evaluation for 3.2a
The materials include explicit, direct prompts and guidance for educators to build knowledge by activating prior knowledge, anchoring big ideas, and highlighting and connecting key patterns and relationships through multiple means of representation. The materials activate prior knowledge through facilitating questions that ask students to connect new learning to previously learned additive and multiplicative situations and prior representations. Materials also anchor big ideas through the “Important Concepts” section, which explicitly identifies the defining characteristics of additive and multiplicative relationships. Key patterns are highlighted and connected through multiple representations, including tables, equations, verbal descriptions, contextual situations, and graphs. Key relationships are also emphasized by comparing additive versus multiplicative relationships across representations and identifying how dependent and independent variables change.
The materials include educator prompts that connect mathematical ideas across multiple representations within individual TEKS lessons. For example, the TEKS lesson for 6.2C guides educators in connecting graphing inequalities with writing inequalities using symbols by relating the number line representation to the symbolic notation. Similarly, the TEKS lesson for 6.4C connects ratio representations from diagrams to verbal and symbolic forms, and the TEKS lesson for 6.4F incorporates strip diagrams, 10 × 10 grids, and number lines to represent benchmark fractions.
Evaluation for 3.2b
The materials include educator guidance for effective lesson delivery and facilitation using various instructional approaches. For example, the materials incorporate TEKS lessons for direct instruction and concept development, Guided Practice for educator-supported instruction, Partner Practice for collaborative learning, Independent Practice for individual application, and Engaging Activities for conceptual exploration and extension.
The lesson guidance further supports facilitation through modeling with manipulatives, discussion prompts, questioning, visual representations, and hands-on activities. For example, in the Implementation Guide, there is a flow chart that describes the lesson delivery, which uses the Gradual Release of Responsibility Model.
Evaluation for 3.2c
The materials include multi-tiered intervention methods for various types of practice and structures. The Practice Books contain multiple instructional approaches, including a TEKS lesson, a Guided Practice, a Partner Practice, and an Engaging Activity. These parts are modular and can be used in multi-tiered interventions. Along with the Practice Book, TEKSnology.com extends these parts of the lesson by using videos for the TEKS lesson and the Guided Practice.
The materials do not include educator guidance to support effective implementation. For example, while there are guided practices, partner practices, and independent practices, all students are provided with the same materials and tasks, and the materials do not provide criteria for forming groups, specific activities to use, or guidance on what skills to work on with these groups.
Evaluation for 3.2d
The materials include enrichment and extension methods that support various forms of engagement. However, the materials do not include guidance to support educators in effective implementation. For example, in TEKS lesson 6.8B, the extension task suggests using digital geometry tools to decompose trapezoids into triangles and rectangles. There is no educator guidance to support the student through the process.
In TEKS lesson 6.8A, the Extension Learning Opportunity activity supports various forms of engagement. In the activity, students use straws of various lengths to test out side-angle relationships of triangles. This extension activity allows students to explore using manipulatives to solidify their understanding of side-angle relationships. There is no educator guidance to support the student through the process.
Evaluation for 3.2e
The materials include prompts and guidance to support educators in providing timely feedback during lesson delivery through discussion questions, observation prompts, misconception guidance, and educator directions asking students to explain reasoning, share strategies, and discuss solutions. For example, the TEKS lesson explicitly directs educators to listen to student discussions, observe strategies before formal instruction, facilitate class sharing, and monitor understanding through discussion. Materials also include guidance for feedback through the “Misconceptions” section, which identifies likely student errors and instructional responses, and through lesson directions describing how educators should conceptualize and check student understanding before progressing.
The “Guided Practice” and “Partner Practice” sections include directions for how to implement this part of the lesson, along with questions educators can use to monitor students’ progress and understanding. The guidance provides specific details about how long students should work, how to follow up on the activity, and what misconceptions to watch for. These supports help educators better guide students and respond to their learning needs during the lesson.
Evaluation for 3.3a
The materials include educator guidance on providing and incorporating linguistic accommodations for one level of language proficiency (as defined by the ELPS), which are designed to engage students in using increasingly more academic language. For example, the materials provide “Strategies for Teacher Vocabulary” to use with the vocabulary found in Appendix C.
Within the “Academic Vocabulary” section of the lesson guide used for internalization is the section for “The Emergent Bilingual Oral and Written Discourse Support” which provides connection examples, embedded oral discourse guidance, embedded written discourse guidance, and the ELPS sentence stems.
Evaluation for 3.3b
This guidance is not applicable to the program because it is not designed to be adaptive.
Evaluation for 3.3c
The materials include implementation guidance to support educators in effectively using the materials in state-approved bilingual/ESL programs. For example, the Supplemental Math Implementation Guide includes a section titled “Supporting Emergent Bilingual Students.” The guide states that the materials support emergent bilingual students through explicit academic vocabulary instruction, visual models and diagrams, structured partner discussions, opportunities for oral and written explanations, and connections to the English Language Proficiency Standards (ELPS).
Within the “Academic Vocabulary” section of the lesson guide used for internalization is the section for “The Emergent Bilingual Oral and Written Discourse Support” which provides connection examples, embedded oral discourse guidance, embedded written discourse guidance, and ELPS sentence stems.
Evaluation for 3.3d
The materials include embedded guidance to support emergent bilingual students in developing academic vocabulary, increasing comprehension, building background knowledge, and making cross-linguistic connections through oral and written discourse. For example, in the grade 6 materials, the “Strategies for Teaching Vocabulary” section recommends interactive word walls, vocabulary journals, graphic organizers, collaborative learning, real-world examples, and educator modeling of mathematical language. Students engage in written discourse through vocabulary journals and vocabulary activities that require them to define and apply academic vocabulary. Students engage in oral discourse through collaborative discussions and opportunities to explain mathematical concepts to develop academic vocabulary. The materials also increase comprehension by connecting mathematics vocabulary to real-world contexts, such as fractions and multiplication.
In the Teacher Edition, the materials include blackline masters of vocabulary activities to use in lessons. This embedded support covers the academic vocabulary for each unit of instruction, helping students develop vocabulary and increase comprehension. The “Strategies for Teaching Vocabulary” include oral and written discourse.
Evaluation for 3.3e
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 explicit educator guidance for lessons or activities scaffolded for students who have not yet reached proficiency in prerequisite or grade-level concepts and skills.
Materials include explicit educator guidance for lessons or activities scaffolded for students who have not yet reached proficiency in prerequisite or grade-level concepts and skills.
1 out of 1 points
Evaluation for 3.1a
Evaluation for 3.1a
Materials include explicit educator guidance for lessons or activities scaffolded for students who have not yet reached proficiency in prerequisite or grade-level concepts and skills.
1 out of 1 points
The Scoring and Instructional Response provides strategies for responding to the results of the diagnostic assessments for students at various levels. The “How Teachers Use the Evidence” in the Unit Assessment Overview on the opposite page also provides ways to respond to students who have not yet reached proficiency.
3.1b
Materials include explicit educator guidance for language supports, including pre-teaching and embedded supports for developing academic vocabulary and unfamiliar references in text.
Materials include explicit educator guidance for language supports, including pre-teaching and embedded supports for developing academic vocabulary and unfamiliar references in text.
2 out of 4 points
Evaluation for 3.1b
Evaluation for 3.1b
Materials include explicit educator guidance for language supports, including pre-teaching and embedded supports for developing academic vocabulary and unfamiliar references in text.
2 out of 4 points
The materials do not include explicit educator guidance for language supports, including pre-teaching and embedded supports for unfamiliar references in text. For example, while the Teacher Edition contains blackline masters of vocabulary activities to include as part of the lessons, the materials do not include pre-teaching and embedded supports for educators to help develop academic vocabulary and decoding unfamiliar references in text.
3.1c
Materials include explicit educator guidance for enrichment and extension activities for students who have demonstrated proficiency in grade-level and above grade-level content and skills.
Materials include explicit educator guidance for enrichment and extension activities for students who have demonstrated proficiency in grade-level and above grade-level content and skills.
2 out of 2 points
Evaluation for 3.1c
Evaluation for 3.1c
Materials include explicit educator guidance for enrichment and extension activities for students who have demonstrated proficiency in grade-level and above grade-level content and skills.
2 out of 2 points
For students demonstrating proficiency, enrichment and extension activities have students explain multiple strategies, create mathematical problems, apply concepts to real-world scenarios, and compare solution methods. Materials also include educator guidance for implementation by identifying extension opportunities within the Implementation Guide and recommending use as extension activities for advanced learners.
3.1d
Digital materials include accommodations, including text-to-speech, content and language supports, and calculators that educators can enable or disable to support individual students.
Digital materials include accommodations, including text-to-speech, content and language supports, and calculators that educators can enable or disable to support individual students.
3 out of 3 points
Evaluation for 3.1d
Evaluation for 3.1d
Digital materials include accommodations, including text-to-speech, content and language supports, and calculators that educators can enable or disable to support individual students.
3 out of 3 points
The materials include text-to-speech and a few content and language supports that educators can enable or disable to support individual students. For example, text-to-speech is functional when users first highlight the desired text before selecting the speak option. The materials also include some content and language supports, such as a dictionary that appears when a word is highlighted and visual supports. However, the materials do not include additional embedded language supports, such as rollovers or hover-over explanations of vocabulary or symbols. Although a translation icon is present, the only available language option is English.
3.1e
Materials include educator guidance on offering options and supports for students to demonstrate understanding of mathematical concepts in various ways, such as perform, express, and represent.
Materials include educator guidance on offering options and supports for students to demonstrate understanding of mathematical concepts in various ways, such as perform, express, and represent.
2 out of 2 points
Evaluation for 3.1e
Evaluation for 3.1e
Materials include educator guidance on offering options and supports for students to demonstrate understanding of mathematical concepts in various ways, such as perform, express, and represent.
2 out of 2 points
The materials include multiple problem-solving options and support online. For example, the digital materials include interactive exercises, video explanations, and real-world applications.
3.2 Instructional Methods
3.2a
Materials include explicit (direct) prompts and guidance for educators to build knowledge by activating prior knowledge, anchoring big ideas, and highlighting and connecting key patterns, features, and relationships through multiple means of representation.
Materials include explicit (direct) prompts and guidance for educators to build knowledge by activating prior knowledge, anchoring big ideas, and highlighting and connecting key patterns, features, and relationships through multiple means of representation.
5 out of 5 points
Evaluation for 3.2a
Evaluation for 3.2a
Materials include explicit (direct) prompts and guidance for educators to build knowledge by activating prior knowledge, anchoring big ideas, and highlighting and connecting key patterns, features, and relationships through multiple means of representation.
5 out of 5 points
The materials include educator prompts that connect mathematical ideas across multiple representations within individual TEKS lessons. For example, the TEKS lesson for 6.2C guides educators in connecting graphing inequalities with writing inequalities using symbols by relating the number line representation to the symbolic notation. Similarly, the TEKS lesson for 6.4C connects ratio representations from diagrams to verbal and symbolic forms, and the TEKS lesson for 6.4F incorporates strip diagrams, 10 × 10 grids, and number lines to represent benchmark fractions.
3.2b
If designed to be static, materials include educator guidance for effective lesson delivery and facilitation using various instructional approaches.
If designed to be static, materials include educator guidance for effective lesson delivery and facilitation using various instructional approaches.
2 out of 2 points
Evaluation for 3.2b
Evaluation for 3.2b
If designed to be static, materials include educator guidance for effective lesson delivery and facilitation using various instructional approaches.
2 out of 2 points
The lesson guidance further supports facilitation through modeling with manipulatives, discussion prompts, questioning, visual representations, and hands-on activities. For example, in the Implementation Guide, there is a flow chart that describes the lesson delivery, which uses the Gradual Release of Responsibility Model.
3.2c
Materials include multi-tiered intervention methods for various types of practice and structures and educator guidance to support effective implementation.
Materials include multi-tiered intervention methods for various types of practice and structures and educator guidance to support effective implementation.
2 out of 3 points
Evaluation for 3.2c
Evaluation for 3.2c
Materials include multi-tiered intervention methods for various types of practice and structures and educator guidance to support effective implementation.
2 out of 3 points
The materials do not include educator guidance to support effective implementation. For example, while there are guided practices, partner practices, and independent practices, all students are provided with the same materials and tasks, and the materials do not provide criteria for forming groups, specific activities to use, or guidance on what skills to work on with these groups.
3.2d
Materials include enrichment and extension methods that support various forms of engagement, and guidance to support educators in effective implementation.
Materials include enrichment and extension methods that support various forms of engagement, and guidance to support educators in effective implementation.
1 out of 2 points
Evaluation for 3.2d
Evaluation for 3.2d
Materials include enrichment and extension methods that support various forms of engagement, and guidance to support educators in effective implementation.
1 out of 2 points
In TEKS lesson 6.8A, the Extension Learning Opportunity activity supports various forms of engagement. In the activity, students use straws of various lengths to test out side-angle relationships of triangles. This extension activity allows students to explore using manipulatives to solidify their understanding of side-angle relationships. There is no educator guidance to support the student through the process.
3.2e
Materials include prompts and guidance to support educators in providing timely feedback during lesson delivery.
Materials include prompts and guidance to support educators in providing timely feedback during lesson delivery.
2 out of 2 points
Evaluation for 3.2e
Evaluation for 3.2e
Materials include prompts and guidance to support educators in providing timely feedback during lesson delivery.
2 out of 2 points
The “Guided Practice” and “Partner Practice” sections include directions for how to implement this part of the lesson, along with questions educators can use to monitor students’ progress and understanding. The guidance provides specific details about how long students should work, how to follow up on the activity, and what misconceptions to watch for. These supports help educators better guide students and respond to their learning needs during the lesson.
3.3 Support for Emergent Bilingual Students
3.3a
If designed to be static, materials include educator guidance on providing and incorporating linguistic accommodations for all levels of language proficiency [as defined by the English Language Proficiency Standards (ELPS)], which are designed to engage students in using increasingly more academic language.
If designed to be static, materials include educator guidance on providing and incorporating linguistic accommodations for all levels of language proficiency [as defined by the English Language Proficiency Standards (ELPS)], which are designed to engage students in using increasingly more academic language.
4 out of 4 points
Evaluation for 3.3a
Evaluation for 3.3a
If designed to be static, materials include educator guidance on providing and incorporating linguistic accommodations for all levels of language proficiency [as defined by the English Language Proficiency Standards (ELPS)], which are designed to engage students in using increasingly more academic language.
4 out of 4 points
Within the “Academic Vocabulary” section of the lesson guide used for internalization is the section for “The Emergent Bilingual Oral and Written Discourse Support” which provides connection examples, embedded oral discourse guidance, embedded written discourse guidance, and the ELPS sentence stems.
3.3b
If designed to be adaptive, materials include embedded linguistic accommodations for all levels of language proficiency [as defined by the English Language Proficiency Standards (ELPS)], which are designed to engage students in using increasingly more academic language.
If designed to be adaptive, materials include embedded linguistic accommodations for all levels of language proficiency [as defined by the English Language Proficiency Standards (ELPS)], which are designed to engage students in using increasingly more academic language.
Not applicable.
Evaluation for 3.3b
Evaluation for 3.3b
If designed to be adaptive, materials include embedded linguistic accommodations for all levels of language proficiency [as defined by the English Language Proficiency Standards (ELPS)], which are designed to engage students in using increasingly more academic language.
Not applicable.
3.3c
Materials include implementation guidance to support educators in effectively using the materials in state-approved bilingual/ESL programs.
Materials include implementation guidance to support educators in effectively using the materials in state-approved bilingual/ESL programs.
1 out of 1 points
Evaluation for 3.3c
Evaluation for 3.3c
Materials include implementation guidance to support educators in effectively using the materials in state-approved bilingual/ESL programs.
1 out of 1 points
Within the “Academic Vocabulary” section of the lesson guide used for internalization is the section for “The Emergent Bilingual Oral and Written Discourse Support” which provides connection examples, embedded oral discourse guidance, embedded written discourse guidance, and ELPS sentence stems.
3.3d
Materials include embedded guidance to support emergent bilingual students in developing academic vocabulary, increasing comprehension, building background knowledge, and making cross-linguistic connections through oral and written discourse.
Materials include embedded guidance to support emergent bilingual students in developing academic vocabulary, increasing comprehension, building background knowledge, and making cross-linguistic connections through oral and written discourse.
8 out of 8 points
Evaluation for 3.3d
Evaluation for 3.3d
Materials include embedded guidance to support emergent bilingual students in developing academic vocabulary, increasing comprehension, building background knowledge, and making cross-linguistic connections through oral and written discourse.
8 out of 8 points
In the Teacher Edition, the materials include blackline masters of vocabulary activities to use in lessons. This embedded support covers the academic vocabulary for each unit of instruction, helping students develop vocabulary and increase comprehension. The “Strategies for Teaching Vocabulary” include oral and written discourse.
3.3e
If designed for dual language immersion (DLI) programs, materials include resources that outline opportunities to address metalinguistic transfer from English to the partner language.
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 3.3e
Evaluation for 3.3e
If designed for dual language immersion (DLI) programs, materials include resources that outline opportunities to address metalinguistic transfer from English to the partner language.
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
50% (8 out of 16 points)
Evaluation for 4.1a
The materials include practice opportunities throughout the learning pathway that require students to demonstrate the depth of understanding aligned to the TEKS. For example, the TEKS lesson and Engaging Activity for TEKS 6.2D requires students to apply rational numbers in both mathematical and real-world contexts. Across the learning pathway, students engage with the verb, concept, and implementation aspects of the TEKS through progressively applied practice.
The instructional assessments within the learning pathways require students to demonstrate depth of understanding aligned to the TEKS. For example, Guided Practice and Partner Practice provide opportunities for educators to gather evidence of student understanding during instruction, while Independent Practice allows students to independently demonstrate mastery of the lesson’s TEKS through tasks that reflect the depth, rigor, and complexity of the standard.
Evaluation for 4.1b
The materials include questions, tasks, enrichment, and extension activities that progressively increase in rigor and complexity, leading students to grade-level proficiency in the mathematics TEKS. For example, lessons progress from prerequisite knowledge and supported practice using concrete models and visual representations to independent application of grade-level concepts. In grade 6, students move from representing integers with counters and number lines to fluently performing integer operations and analyzing rational numbers through multiple representations, including contextual problems. Throughout the learning pathway, the increasing complexity of the tasks supports students in demonstrating grade-level mastery of the TEKS.
The materials do not include questions, tasks, enrichment, or extension activities that increase in rigor and complexity to lead students to above-grade-level proficiency in the mathematics TEKS. The instructional progression builds from prerequisite knowledge to independent mastery of grade-level concepts, but the enrichment and extension activities continue to reinforce the current grade-level standards rather than providing opportunities for mathematical reasoning or content beyond grade-level expectations.
Evaluation for 4.2a
The materials connect mathematical ideas within the grade level to help students build understanding across related concepts. For example, in the grade 6 Math Practice SE, student guidance called “Why do I need to know this?” is located at the beginning of each lesson. In lesson TEKS 6.7D, this section states, “You will need to understand the math properties that can be used in both addition and multiplication to recognize and generate equivalent expressions. This knowledge will later be applied to solving equations and inequalities.” The materials provide coherence across concepts horizontally by connecting relationships within the grade level.
The materials reinforce mathematical connections by encouraging students to apply multiple related concepts within a single task. For example, the grade 6 Math Practice TE includes a sidebar for TEKS 6.3A that states, “This standard helps prepare students for the readiness standard 6.3E. They will learn several processes at that time for dividing fractions. The understanding of this standard should be a clear understanding of why the ‘keep, change, flip’ algorithm is a valid process.” Additionally, students analyze a table by identifying the independent and dependent quantities, determining the operation that relates x to y, connecting that operation to the concept of a factor, and writing an equation that represents the relationship.
Evaluation for 4.2b
The materials connect mathematical understanding across grade levels by building on previously developed concepts and supporting progression within the TEKS. For example, in the grade 6 Math Practice TE, an educator guidance sidebar for TEKS 6.4C states, “Previous experience with equivalent fractions from grades 4 and 5 will serve as a foundation for the students’ comprehension of equivalent ratios.” This guidance explicitly links learning from grades 4 and 5 to grade 6 by showing how students apply prior understanding of equivalent fractions to develop the concept of equivalent ratios.
In the digital TEKS lesson for TEKS 6.11A Graphing Ordered Pairs, the introductory video reminds students that they previously graphed points in the first quadrant during grade 4 before introducing graphing in all four quadrants with integers and negative rational numbers. This progression helps students extend prior knowledge to more advanced graphing concepts while reinforcing relationships between earlier and current grade-level expectations.
Evaluation for 4.2c
The materials demonstrate coherence across lessons and activities by connecting students’ prior conceptual and procedural knowledge to the mathematical concepts learned in the current grade level. For example, the “Why do I need to know this?” sections and TEKS lessons connect prior learning to new grade-level concepts by prompting educators to review prerequisite knowledge, such as ratios before multiplicative comparisons, order of operations before simplifying expressions, and grade 5 concepts before introducing reciprocals. These connections help students build on previously learned concepts and procedures as they engage with current grade-level mathematics.
The materials do not demonstrate coherence across lessons and activities by connecting students’ prior conceptual and procedural knowledge to the mathematical concepts to be learned in future grade levels. While the “Why do I need to know this?” sections occasionally reference future mathematics courses or concepts, the materials do not provide explicit educator guidance explaining how current learning develops into future grade-level mathematical concepts or procedures. References to future learning identify where concepts may be encountered later but do not support educators in making instructional connections that build mathematical understanding across grade levels.
Evaluation for 4.3a
The materials do not provide spaced retrieval opportunities with previously learned skills and concepts across learning pathways. The materials are designed to target specific, focused TEKS and provide many opportunities for students to practice these skills in isolation through Independent Practice, Guided Practice, and Partner Practice. However, they are not designed to include spaced retrieval opportunities and do not provide tasks or assessments that use this best practice. For example, the Guided and Partner Practice do not provide spaced retrieval opportunities through procedural memory, instead simply providing a succession of practice problems with no increasing intervals of time to prove retention.
The grade 6 Math Practice TE frequently references prior knowledge, highlights patterns and relationships across lessons, and identifies connections to future grade-level concepts. In TEKS lesson 6.8D, the educator guidance provides vertical alignment to other grade levels and connects the lesson to simplifying expressions and solving equations; however, the lesson does not include opportunities for students to revisit and practice previously learned content before engaging with the new standard.
Evaluation for 4.3b
The materials do not provide interleaved practice opportunities with previously learned skills and concepts across learning pathways. The materials use Guided Practice, Partner Practice, and Independent Practice to provide focused opportunities for individual TEKS concepts in a nonspiraling approach, rather than revisiting and connecting concepts across learning pathways over time. For example, although different solution types are evident in the problems on pages 2–3 of the Student Edition, interleaving of different and related concepts does not occur.
In the grade 6 Math Practice SE, lessons are taught as individual concepts focusing on one TEKS at a time. Even though there is mention of other concepts and skills within some lessons, none of the lessons intentionally bundle multiple standards to improve retention of skills. For example, TEKS 6.3E, which focuses on operations with rational numbers, could be partnered with TEKS 6.8D, which focuses on finding area and volume.
4.1 Depth of Key Concepts
4.1a
Practice opportunities throughout learning pathways (including instructional assessments) require students to demonstrate depth of understanding aligned to the TEKS.
Practice opportunities throughout learning pathways (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 throughout learning pathways (including instructional assessments) require students to demonstrate depth of understanding aligned to the TEKS.
2 out of 2 points
The instructional assessments within the learning pathways require students to demonstrate depth of understanding aligned to the TEKS. For example, Guided Practice and Partner Practice provide opportunities for educators to gather evidence of student understanding during instruction, while Independent Practice allows students to independently demonstrate mastery of the lesson’s TEKS through tasks that reflect the depth, rigor, and complexity of the standard.
4.1b
Questions and tasks, including enrichment and extension materials, increase in rigor and complexity, leading to grade-level and above grade-level proficiency in the mathematics TEKS.
Questions and tasks, including enrichment and extension materials, increase in rigor and complexity, leading to grade-level and above grade-level proficiency in the mathematics TEKS.
2 out of 4 points
Evaluation for 4.1b
Evaluation for 4.1b
Questions and tasks, including enrichment and extension materials, increase in rigor and complexity, leading to grade-level and above grade-level proficiency in the mathematics TEKS.
2 out of 4 points
The materials do not include questions, tasks, enrichment, or extension activities that increase in rigor and complexity to lead students to above-grade-level proficiency in the mathematics TEKS. The instructional progression builds from prerequisite knowledge to independent mastery of grade-level concepts, but the enrichment and extension activities continue to reinforce the current grade-level standards rather than providing opportunities for mathematical reasoning or content beyond grade-level expectations.
4.2 Coherence of Key Concepts
4.2a
Materials demonstrate coherence across concepts horizontally within the grade level by connecting patterns, big ideas, and relationships.
Materials demonstrate coherence across concepts horizontally within the grade level by connecting patterns, big ideas, and relationships.
1 out of 1 points
Evaluation for 4.2a
Evaluation for 4.2a
Materials demonstrate coherence across concepts horizontally within the grade level by connecting patterns, big ideas, and relationships.
1 out of 1 points
The materials reinforce mathematical connections by encouraging students to apply multiple related concepts within a single task. For example, the grade 6 Math Practice TE includes a sidebar for TEKS 6.3A that states, “This standard helps prepare students for the readiness standard 6.3E. They will learn several processes at that time for dividing fractions. The understanding of this standard should be a clear understanding of why the ‘keep, change, flip’ algorithm is a valid process.” Additionally, students analyze a table by identifying the independent and dependent quantities, determining the operation that relates x to y, connecting that operation to the concept of a factor, and writing an equation that represents the relationship.
4.2b
Materials demonstrate coherence vertically across concepts and grade bands, including connections from grades 3–12, by connecting patterns, big ideas, and relationships.
Materials demonstrate coherence vertically across concepts and grade bands, including connections from grades 3–12, by connecting patterns, big ideas, and relationships.
1 out of 1 points
Evaluation for 4.2b
Evaluation for 4.2b
Materials demonstrate coherence vertically across concepts and grade bands, including connections from grades 3–12, by connecting patterns, big ideas, and relationships.
1 out of 1 points
In the digital TEKS lesson for TEKS 6.11A Graphing Ordered Pairs, the introductory video reminds students that they previously graphed points in the first quadrant during grade 4 before introducing graphing in all four quadrants with integers and negative rational numbers. This progression helps students extend prior knowledge to more advanced graphing concepts while reinforcing relationships between earlier and current grade-level expectations.
4.2c
Materials demonstrate coherence across lessons or activities by connecting students’ prior knowledge of concepts and procedures to the mathematical concepts to be learned in the current grade level and future grade levels.
Materials demonstrate coherence across lessons or activities by connecting students’ prior knowledge of concepts and procedures to the mathematical concepts to be learned in the current grade level and future grade levels.
2 out of 4 points
Evaluation for 4.2c
Evaluation for 4.2c
Materials demonstrate coherence across lessons or activities by connecting students’ prior knowledge of concepts and procedures to the mathematical concepts to be learned in the current grade level and future grade levels.
2 out of 4 points
The materials do not demonstrate coherence across lessons and activities by connecting students’ prior conceptual and procedural knowledge to the mathematical concepts to be learned in future grade levels. While the “Why do I need to know this?” sections occasionally reference future mathematics courses or concepts, the materials do not provide explicit educator guidance explaining how current learning develops into future grade-level mathematical concepts or procedures. References to future learning identify where concepts may be encountered later but do not support educators in making instructional connections that build mathematical understanding across grade levels.
4.3 Coherence and Variety of Practice
4.3a
Materials provide spaced retrieval opportunities with previously learned skills and concepts across learning pathways.
Materials provide spaced retrieval opportunities with previously learned skills and concepts across learning pathways.
0 out of 2 points
Evaluation for 4.3a
Evaluation for 4.3a
Materials provide spaced retrieval opportunities with previously learned skills and concepts across learning pathways.
0 out of 2 points
The grade 6 Math Practice TE frequently references prior knowledge, highlights patterns and relationships across lessons, and identifies connections to future grade-level concepts. In TEKS lesson 6.8D, the educator guidance provides vertical alignment to other grade levels and connects the lesson to simplifying expressions and solving equations; however, the lesson does not include opportunities for students to revisit and practice previously learned content before engaging with the new standard.
4.3b
Materials provide interleaved practice opportunities with previously learned skills and concepts across learning pathways.
Materials provide interleaved practice opportunities with previously learned skills and concepts across learning pathways.
0 out of 2 points
Evaluation for 4.3b
Evaluation for 4.3b
Materials provide interleaved practice opportunities with previously learned skills and concepts across learning pathways.
0 out of 2 points
In the grade 6 Math Practice SE, lessons are taught as individual concepts focusing on one TEKS at a time. Even though there is mention of other concepts and skills within some lessons, none of the lessons intentionally bundle multiple standards to improve retention of skills. For example, TEKS 6.3E, which focuses on operations with rational numbers, could be partnered with TEKS 6.8D, which focuses on finding area and volume.
Rubric Section 5
Balance of Conceptual and Procedural Understanding
Materials are designed to balance conceptual understanding, procedural skills, and fluency.
Total
92% (35 out of 38 points)
Evaluation for 5.1a
The questions and tasks provide opportunities for students to interpret, analyze, and evaluate models and representations for mathematical concepts and situations. For example, the grade 6 Teacher’s Edition provides students with opportunities to interpret, analyze, and evaluate problems involving comparing and ordering rational numbers. The Introductory activity has students place integers on a number line and then asks them to write an inequality to compare them. It moves into explaining what they know about the placement of a rational number on the number line and continues with Partner Practice problems that are real-world.
Questions and tasks require students to evaluate mathematical concepts and complex, real-world situations. For example, in the grade 6 Math Practice SE, there are tasks that require students to evaluate complex, real-world situations. Question #2 of the Guided and Partner Practice has students check the completed work in a real-world situation for errors. In these problems, there is a table and number line representing rational numbers. The student is required to evaluate the work and determine where the error occurs.
Evaluation for 5.1b
The materials provide opportunities for students to create concrete models and representations of mathematical situations. For example, students construct number line models by graphing numbers and their opposites, representing absolute value as distance from zero, and modeling real-world situations involving gains, losses, debt, temperature, and depth. These activities require students to generate mathematical models rather than merely interpret educator-provided representations. Students also create representations that connect contextual situations to mathematical concepts through the use of number lines and signed numbers.
The TEKS lesson overview guides educators to use two-color counters to reinforce the outcomes of integer operations. The students move from concrete to representative pictorial models with number lines and mathematical and symbolic representations. The final Independent Practice questions use thermometers and gift card scenarios, and the students work with real-world situations. The educator’s guidance in the wrap-around notes asks the educator to have students create these models. The Extension Learning Opportunity also asks students to be creators, asking them to write the matching expressions that correspond with their concrete integer models.
Evaluation for 5.1c
The questions and tasks provide opportunities for students to apply conceptual understanding to new problem situations and contexts. For example, in the grade 6 Math Practice SE, the TEKS lesson “Reciprocals” provides students with a scenario to figure out using conceptual understanding of fractions. In the scenario, students are asked to determine the number of friends who could receive a half-size of three cakes. The student must use the concept of fractions and models to determine the solution, even though the lesson is using the algorithm of dividing with fractions.
The materials provide opportunities for students to apply conceptual understanding to new problem situations and contexts. Students transfer their understanding of rational numbers, ordering, comparison, and proportional reasoning to a variety of real-world scenarios, including plant growth data, voter turnout statistics, assessment results, recipes, sports teams, classroom survey data, and ratio relationships. Tasks require students to apply mathematical concepts across multiple contexts rather than simply perform isolated procedures. Students use conceptual understanding to interpret information, compare quantities, order values represented in different forms, and reason about proportional relationships in unfamiliar situations. The materials demonstrate opportunities for students to apply conceptual understanding to new situations and contexts.
Evaluation for 5.2a
The materials provide tasks that are designed to build student automaticity and fluency necessary to complete grade-level mathematical tasks. For example, in the grade 6 Math Practice SE, in the TEKS lesson “Data from Graphical Representations,” students are introduced to the lesson using graphs learned in previous grades, dot plots, and histograms (similar to bar graphs). Students are asked general questions designed to build automaticity and fluency in analyzing graphs, such as describing the information given in the graphs and finding percents, a skill taught earlier in the year.
Students analyze and compare rational numbers in real-world contexts, requiring them to interpret values, evaluate relationships, and justify conclusions. Tasks go beyond computation and require reasoning and decision-making. Students compare and order numbers across multiple representations (fractions, decimals, percents), requiring analysis and synthesis of information. This promotes higher-order thinking and conceptual understanding.
Evaluation for 5.2b
The materials provide opportunities for students to practice the application of efficient mathematical procedures throughout learning pathways. For example, in the grade 6 Math Practice TE, there are opportunities for students to practice finding the probability using either pictures, diagrams, formulas, or reasoning within the Engaging Activity for TEKS lesson “Simulations.” The students decide which method to use to display their data, then explain which is the better method.
The materials provide opportunities for students to practice the application of efficient mathematical procedures throughout learning pathways. Located in the grade 6 Math Practice TE, educator guidance provided for the TEKS lesson “Multiple Representations” states that after students have found the equation from the graph in question 12 of the Independent Practice, ask them to explain the process they used. This question provides opportunities for students to determine the most efficient mathematical procedures for this type of task.
Evaluation for 5.2c
The materials do not provide opportunities for students to classify numbers, represent values using Venn diagrams and number lines, or explain mathematical reasoning. Students engage with multiple representations and apply classification procedures across guided, partner, and independent practice activities. However, students do not compare procedures, determine which strategy is most efficient, analyze alternative representations, evaluate the accuracy of completed solutions, or identify and correct errors in mathematical work. As a result, the materials do not demonstrate opportunities for students to evaluate efficiency, flexibility, or accuracy throughout learning pathways.
The materials provide educators with guidance in many areas. However, they do not encourage educators to ask students about efficient or flexible solution methods. For example, wrap-around notes in the Teacher’s Edition remind educators that “Students need to convert numbers to the same form to order the numbers,” but materials do not prompt discussion about which method might be most efficient, what alternative forms the numbers could be written in, or why one representation might be preferred over another in a given situation.
Evaluation for 5.2d
The materials do not contain guidance to support students in selecting increasingly efficient approaches to solve mathematics problems. The materials do provide instruction and practice opportunities related to classifying numbers, identifying opposites and absolute values, and comparing and ordering rational numbers. Students use representations such as Venn diagrams and number lines and progress through guided, partner, and independent practice activities. However, while students apply mathematical procedures and representations, the materials do not prompt students to compare strategies, determine which approach is more efficient, or justify why one representation or method may be preferred over another. As a result, evidence of guidance supporting the selection of increasingly efficient approaches is not demonstrated.
The Teacher’s Edition provides guidance in many areas. However, the materials do not include guidance for supporting students in selecting increasingly efficient approaches to solving mathematical problems. For example, in the TEKS lesson “Integer Operations,” the “Why do I need to know this?” tells students that modeling will help them become fluent in using algorithms to compute signed numbers. However, nowhere in this lesson does it ask a student about selecting an efficient method. Independent Practice Q4 uses a number line to model a relationship with larger numbers, but never prompts the student to generalize so that they can solve this more efficiently. The TEKS lesson “Operations with Integers” does not bridge this knowledge either. Rather, the generalizations are made for students in the form of a table, and then students are expected to calculate signed operations using these rules. There is no guidance to support students in using more efficient methods once they understand the generalization.
Evaluation for 5.3a
The materials explicitly state how the conceptual and procedural emphasis of the TEKS is addressed. For example, in the grade 6 Practice TE, there is an educator guidance that correlates with the given TEKS of the lesson called “Conceptual Learning Goal.” In this section of the lesson, educators are provided with explicit descriptions of how the TEKS will be addressed both conceptually and procedurally.
In the TEKS lesson “Multiplying Polynomials,” the Conceptual Learning Goal for TEKS A.10B states, “Students learn how the distributive property and area models can be used to multiply binomials and other polynomials of degree one and two.” The area model represents the conceptual understanding of the TEKS, leading to students being able to apply procedural skills. The materials include explicit connections under the Conceptual Learning Goal. Students use hands-on models with two-color counters to connect the integer operation algorithms.
Evaluation for 5.3b
The questions and tasks provide opportunities for students to use concrete models, pictorial representations, and abstract models as required by the TEKS. For example, in the grade 6 Math Practice TE, lesson 6.3C “Integer Operations” provides students with opportunities to use counters, numberlines, and numeric expressions to represent integer operations such as adding and multiplying.
The Teacher Edition provides opportunities for students to use concrete models, pictorial representations, and abstract models as required by the TEKS. Students engage with concrete models through activities such as creating Venn diagrams with number cards and constructing large floor number lines using tape to physically represent mathematical relationships. The materials also incorporate pictorial representations, including Venn diagrams and number lines, to support classification, comparison, and reasoning about numbers. In addition, students use abstract models by classifying numbers symbolically, comparing and ordering rational numbers, working with opposites and absolute values, and reasoning about numerical relationships using mathematical notation. The materials integrate these representations throughout instruction and practice, supporting students’ progression from concrete and visual experiences to abstract reasoning.
Evaluation for 5.3c
The 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. For example, in the grade 6 Math Practice TE, lesson 6.3C “Integer Operations” provides evidence of students connecting concrete models (counters) to representational models (number lines) to abstract concepts (numeric expressions).
In the TEKS lesson “Integer Operations,” students use two-color counters and number lines to create and connect to the symbolic. The Facilitating Questions ask students to explain how the algorithms are connected to the models, and the Extension Learning opportunity allows students to create, connect, and explain how the model matches the algorithm.
Evaluation for 5.4a
The materials provide opportunities for students to develop their academic mathematical language using visuals, manipulatives, or other language development strategies. For example, in the grade 6 Math Practice TE, the TEKS lesson “Classifying Numbers” provides educator guidance that prompts students to discuss the Venn diagram and the terms used to label each part of the diagram. The guidance states, “Allow students to discuss in groups how the diagram should be labeled, and call on groups to share out by adding labels to a projected diagram.” Students also generate more examples of each category. This activity provides an opportunity for students to develop the terms: natural number, whole number, integer, and rational number. The ability to generate examples also provides an opportunity for students to practice with the vocabulary.
The materials provide opportunities for students to develop academic mathematical language through visual representations and language development strategies. For example, in the Student Edition, students compare and order rational numbers using number lines and real-world contexts, requiring them to interpret and communicate mathematical relationships among fractions, decimals, and integers while connecting visual models to mathematical vocabulary. In the Teacher Edition, the Engaging Activity extends this work by having students order rational numbers using multiple representations and contextual situations, reinforcing mathematical language through educator-facilitated discussion and representation-based reasoning.
Evaluation for 5.4b
The Teacher Edition includes embedded educator guidance that scaffolds students’ use of academic mathematical vocabulary during instruction. The lesson directions encourage educators to discuss mathematical concepts using number lines, while the Guided Practice facilitation questions prompt students to explain mathematical relationships using appropriate terminology. The materials also identify important concepts and common misconceptions to support educators in reinforcing precise vocabulary throughout the lesson.
Each Lesson Guide used for internalization contains an “Academic Vocabulary” and “Mathematical Discourse Support” section. Within this section are communication targets, key vocabulary, sentence frames, precise language and peer conversation guidance, and anticipated responses with examples and redirection. These are available for every lesson and embedded in the Lesson Guide for internalization.
Evaluation for 5.4c
The materials include embedded guidance to support student application of appropriate mathematical language and academic vocabulary in discourse. Each Lesson Guide used for internalization contains Academic Vocabulary and Mathematical Discourse Support. In the sections “Embedded Oral Discourse Guidance” and “Embedded Written Discourse Guidance,” educators are provided with appropriate vocabulary support for students to use during written and oral discourse. This section also supports comprehension, background building, and cross-linguistic connections. These are available for every lesson embedded in the Lesson Guide for internalization.
The materials guide educators to model precise academic language and help students replace vague words with specific mathematical terms. For example, the materials include guidance on asking students to restate their thinking using more accurate language without changing the meaning.
Evaluation for 5.4d
The materials include embedded guidance to facilitate mathematical conversations, allowing students to hear math language with peers. For example, in the grade 6 Math Practice TE, there are many opportunities for educators to facilitate conversations so that students can hear math language with their peers. An example found in the TEKS lesson “Representing Rules” shows that conversations are prompted, such as the instruction for educators that states, “Have students turn to a partner and discuss how an equation using variables might be written.”
In the Academic Vocabulary and Mathematical Discourse Support, the “Precise Language and Peer Conversation” section provides embedded guidance to facilitate mathematical conversations. The section provides “precision guidance” for an educator to understand what to listen for in the lesson, provides a “Hear-refine-use routine” for students to use with their peers, and “educator prompts” to facilitate the conversations.
Evaluation for 5.4e
The materials include embedded guidance that helps educators anticipate student thinking through Important Concepts, Misconceptions, Teacher Notes, and Facilitating Questions. These supports identify common misconceptions, provide exemplar responses, and prepare educators for likely student thinking during instruction. For example, the “Guided Practice” sections in TEKS 6.9B, TEKS 6.10A, and TEKS lesson 6.11A include educator prompts that guide discussions around important mathematical vocabulary and anticipated student responses. Collectively, these embedded supports help educators anticipate common student answers and misconceptions during instruction.
The Academic Vocabulary and Mathematical Discourse Support has a section titled “Anticipated Responses, Exemplar, and Redirection.” This section includes embedded guidance to anticipate correct responses, partial responses, or inaccurate responses. It also provides an example of what the likely inaccuracy is that a student makes. The support/redirect also provides guidance for how educators can respond with next steps.
Evaluation for 5.5a
The materials integrate the TEKS process standards. For example, students independently classify rational numbers without scaffolds, requiring them to apply learned concepts and demonstrate mastery. Tasks ensure students can perform skills and explain reasoning independently. Students also independently solve multi-step problems involving the comparison and ordering of rational numbers. These tasks require the application of multiple concepts and reinforce mastery through independent reasoning.
The materials integrate the TEKS process standards through activities that promote mathematical communication and multiple representations. For example, in the Engaging Activity, Graphing Ordered Pairs, students plot their initials on a coordinate plane using all four quadrants, record the ordered pairs, exchange their coordinate lists with a partner, and graph each other’s design. This activity requires students to communicate mathematical ideas, interpret coordinate pairs, and use mathematical representations while applying the grade-level content.
Evaluation for 5.5b
The materials include a description of how process standards are incorporated throughout the learning pathways, but not how they are connected. For example, in the grade 6 Math Practice TE, there is a section at the beginning of the materials titled “Process Standard”. This section provides educators with the process standards used for each TEKS covered in the materials. Although the alignment and incorporation is provided, there is no description of how the process standards are connected throughout learning pathways.
The materials do not describe how the process standards connect to instruction throughout the learning pathways. For example, the “Incorporation and Connection Through the Learning Pathway” section of each lesson in the Implementation Guide is the same and only states the process standards as they relate to the sections “Guided Practice,” “Partner Practice,” and “Independent Practice,” but not how the standards serve the specific skills and learning objective of the lesson.
Evaluation for 5.5c
The materials include an overview of the TEKS process standards incorporated into each lesson. For example, in the grade 6 Math Practice Teacher Edition, each lesson identifies the TEKS content standard, includes vertical alignment information across grade levels, lists the applicable ELPS, and describes the conceptual understanding for the lesson.
The lesson components provide opportunities for students to engage in mathematical processes throughout instruction, and the materials include a “Unit Rationale” that provides a generic statement of how students will apply the process standards in the lessons for the unit.
5.1 Development of Conceptual Understanding
5.1a
Questions and tasks provide opportunities for students to interpret, analyze, and evaluate mathematical concepts and complex, real-world situations.
Questions and tasks provide opportunities for students to interpret, analyze, and evaluate mathematical concepts and complex, real-world situations.
3 out of 3 points
Evaluation for 5.1a
Evaluation for 5.1a
Questions and tasks provide opportunities for students to interpret, analyze, and evaluate mathematical concepts and complex, real-world situations.
3 out of 3 points
Questions and tasks require students to evaluate mathematical concepts and complex, real-world situations. For example, in the grade 6 Math Practice SE, there are tasks that require students to evaluate complex, real-world situations. Question #2 of the Guided and Partner Practice has students check the completed work in a real-world situation for errors. In these problems, there is a table and number line representing rational numbers. The student is required to evaluate the work and determine where the error occurs.
5.1b
Questions and tasks provide opportunities for students to create concrete models and representations of mathematical situations.
Questions and tasks provide opportunities for students to create concrete models and representations of mathematical situations.
2 out of 2 points
Evaluation for 5.1b
Evaluation for 5.1b
Questions and tasks provide opportunities for students to create concrete models and representations of mathematical situations.
2 out of 2 points
The TEKS lesson overview guides educators to use two-color counters to reinforce the outcomes of integer operations. The students move from concrete to representative pictorial models with number lines and mathematical and symbolic representations. The final Independent Practice questions use thermometers and gift card scenarios, and the students work with real-world situations. The educator’s guidance in the wrap-around notes asks the educator to have students create these models. The Extension Learning Opportunity also asks students to be creators, asking them to write the matching expressions that correspond with their concrete integer models.
5.1c
Questions and tasks provide opportunities for students to apply conceptual understanding to new problem situations and contexts.
Questions and tasks provide opportunities for students to apply conceptual understanding to new problem situations and contexts.
1 out of 1 points
Evaluation for 5.1c
Evaluation for 5.1c
Questions and tasks provide opportunities for students to apply conceptual understanding to new problem situations and contexts.
1 out of 1 points
The materials provide opportunities for students to apply conceptual understanding to new problem situations and contexts. Students transfer their understanding of rational numbers, ordering, comparison, and proportional reasoning to a variety of real-world scenarios, including plant growth data, voter turnout statistics, assessment results, recipes, sports teams, classroom survey data, and ratio relationships. Tasks require students to apply mathematical concepts across multiple contexts rather than simply perform isolated procedures. Students use conceptual understanding to interpret information, compare quantities, order values represented in different forms, and reason about proportional relationships in unfamiliar situations. The materials demonstrate opportunities for students to apply conceptual understanding to new situations and contexts.
5.2 Development of Fluency
5.2a
Materials provide tasks that are designed to build student automaticity and fluency necessary to complete grade-level mathematical tasks.
Materials provide tasks that are designed to build student automaticity and fluency necessary to complete grade-level mathematical 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 mathematical tasks.
2 out of 2 points
Students analyze and compare rational numbers in real-world contexts, requiring them to interpret values, evaluate relationships, and justify conclusions. Tasks go beyond computation and require reasoning and decision-making. Students compare and order numbers across multiple representations (fractions, decimals, percents), requiring analysis and synthesis of information. This promotes higher-order thinking and conceptual understanding.
5.2b
Materials provide opportunities for students to practice the application of efficient, flexible, and accurate mathematical procedures throughout learning pathways.
Materials provide opportunities for students to practice the application of efficient, flexible, and accurate mathematical procedures throughout learning pathways.
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 throughout learning pathways.
3 out of 3 points
The materials provide opportunities for students to practice the application of efficient mathematical procedures throughout learning pathways. Located in the grade 6 Math Practice TE, educator guidance provided for the TEKS lesson “Multiple Representations” states that after students have found the equation from the graph in question 12 of the Independent Practice, ask them to explain the process they used. This question provides opportunities for students to determine the most efficient mathematical procedures for this type of task.
5.2c
Materials provide opportunities for students to evaluate mathematical representations, models, strategies, and solutions for efficiency, flexibility, and accuracy throughout learning pathways.
Materials provide opportunities for students to evaluate mathematical representations, models, strategies, and solutions for efficiency, flexibility, and accuracy throughout learning pathways.
2 out of 3 points
Evaluation for 5.2c
Evaluation for 5.2c
Materials provide opportunities for students to evaluate mathematical representations, models, strategies, and solutions for efficiency, flexibility, and accuracy throughout learning pathways.
2 out of 3 points
The materials provide educators with guidance in many areas. However, they do not encourage educators to ask students about efficient or flexible solution methods. For example, wrap-around notes in the Teacher’s Edition remind educators that “Students need to convert numbers to the same form to order the numbers,” but materials do not prompt discussion about which method might be most efficient, what alternative forms the numbers could be written in, or why one representation might be preferred over another in a given situation.
5.2d
Materials contain guidance to support students in selecting the most efficient approaches when solving mathematics problems.
Materials contain guidance to support students in selecting the most efficient approaches when solving mathematics problems.
0 out of 1 points
Evaluation for 5.2d
Evaluation for 5.2d
Materials contain guidance to support students in selecting the most efficient approaches when solving mathematics problems.
0 out of 1 points
The Teacher’s Edition provides guidance in many areas. However, the materials do not include guidance for supporting students in selecting increasingly efficient approaches to solving mathematical problems. For example, in the TEKS lesson “Integer Operations,” the “Why do I need to know this?” tells students that modeling will help them become fluent in using algorithms to compute signed numbers. However, nowhere in this lesson does it ask a student about selecting an efficient method. Independent Practice Q4 uses a number line to model a relationship with larger numbers, but never prompts the student to generalize so that they can solve this more efficiently. The TEKS lesson “Operations with Integers” does not bridge this knowledge either. Rather, the generalizations are made for students in the form of a table, and then students are expected to calculate signed operations using these rules. There is no guidance to support students in using more efficient methods once they understand the generalization.
5.3 Balance of Conceptual Understanding and Procedural Fluency
5.3a
Materials explicitly state how the conceptual and procedural emphasis of the TEKS are addressed.
Materials explicitly state how the conceptual and procedural emphasis of the TEKS are addressed.
2 out of 2 points
Evaluation for 5.3a
Evaluation for 5.3a
Materials explicitly state how the conceptual and procedural emphasis of the TEKS are addressed.
2 out of 2 points
In the TEKS lesson “Multiplying Polynomials,” the Conceptual Learning Goal for TEKS A.10B states, “Students learn how the distributive property and area models can be used to multiply binomials and other polynomials of degree one and two.” The area model represents the conceptual understanding of the TEKS, leading to students being able to apply procedural skills. The materials include explicit connections under the Conceptual Learning Goal. Students use hands-on models with two-color counters to connect the integer operation algorithms.
5.3b
Questions and tasks provide opportunities for students to use concrete models, pictorial representations, and abstract models as required by the TEKS.
Questions and tasks provide opportunities for students to use concrete models, pictorial representations, and abstract models as required by the TEKS.
3 out of 3 points
Evaluation for 5.3b
Evaluation for 5.3b
Questions and tasks provide opportunities for students to use concrete models, pictorial representations, and abstract models as required by the TEKS.
3 out of 3 points
The Teacher Edition provides opportunities for students to use concrete models, pictorial representations, and abstract models as required by the TEKS. Students engage with concrete models through activities such as creating Venn diagrams with number cards and constructing large floor number lines using tape to physically represent mathematical relationships. The materials also incorporate pictorial representations, including Venn diagrams and number lines, to support classification, comparison, and reasoning about numbers. In addition, students use abstract models by classifying numbers symbolically, comparing and ordering rational numbers, working with opposites and absolute values, and reasoning about numerical relationships using mathematical notation. The materials integrate these representations throughout instruction and practice, supporting students’ progression from concrete and visual experiences to abstract reasoning.
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 TEKS lesson “Integer Operations,” students use two-color counters and number lines to create and connect to the symbolic. The Facilitating Questions ask students to explain how the algorithms are connected to the models, and the Extension Learning opportunity allows students to create, connect, and explain how the model matches the algorithm.
5.4 Development of Academic Mathematical Language
5.4a
Materials provide opportunities for students to develop academic mathematical language using visuals, manipulatives, or other language development strategies.
Materials provide opportunities for students to develop academic mathematical language using visuals, manipulatives, or other language development strategies.
1 out of 1 points
Evaluation for 5.4a
Evaluation for 5.4a
Materials provide opportunities for students to develop academic mathematical language using visuals, manipulatives, or other language development strategies.
1 out of 1 points
The materials provide opportunities for students to develop academic mathematical language through visual representations and language development strategies. For example, in the Student Edition, students compare and order rational numbers using number lines and real-world contexts, requiring them to interpret and communicate mathematical relationships among fractions, decimals, and integers while connecting visual models to mathematical vocabulary. In the Teacher Edition, the Engaging Activity extends this work by having students order rational numbers using multiple representations and contextual situations, reinforcing mathematical language through educator-facilitated discussion and representation-based reasoning.
5.4b
Materials include embedded educator guidance to scaffold, support, and extend students’ use of academic mathematical vocabulary in context when communicating with peers and educators.
Materials include embedded educator guidance to scaffold, support, and extend students’ use of academic mathematical vocabulary in context when communicating with peers and educators.
2 out of 2 points
Evaluation for 5.4b
Evaluation for 5.4b
Materials include embedded educator guidance to scaffold, support, and extend students’ use of academic mathematical vocabulary in context when communicating with peers and educators.
2 out of 2 points
Each Lesson Guide used for internalization contains an “Academic Vocabulary” and “Mathematical Discourse Support” section. Within this section are communication targets, key vocabulary, sentence frames, precise language and peer conversation guidance, and anticipated responses with examples and redirection. These are available for every lesson and embedded in the Lesson Guide for internalization.
5.4c
Materials include embedded guidance to support student application of appropriate mathematical language and academic vocabulary in discourse.
Materials include embedded guidance to support student application of appropriate mathematical language and academic vocabulary in discourse.
1 out of 1 points
Evaluation for 5.4c
Evaluation for 5.4c
Materials include embedded guidance to support student application of appropriate mathematical language and academic vocabulary in discourse.
1 out of 1 points
The materials guide educators to model precise academic language and help students replace vague words with specific mathematical terms. For example, the materials include guidance on asking students to restate their thinking using more accurate language without changing the meaning.
5.4d
Materials include embedded guidance to facilitate mathematical conversations allowing students to hear, refine, and use math language with peers.
Materials include embedded guidance to facilitate mathematical conversations allowing students to hear, refine, and use math language with peers.
2 out of 2 points
Evaluation for 5.4d
Evaluation for 5.4d
Materials include embedded guidance to facilitate mathematical conversations allowing students to hear, refine, and use math language with peers.
2 out of 2 points
In the Academic Vocabulary and Mathematical Discourse Support, the “Precise Language and Peer Conversation” section provides embedded guidance to facilitate mathematical conversations. The section provides “precision guidance” for an educator to understand what to listen for in the lesson, provides a “Hear-refine-use routine” for students to use with their peers, and “educator prompts” to facilitate the conversations.
5.4e
Materials include embedded guidance to anticipate a variety of student answers including exemplar responses to questions and tasks, including guidance to support and/or redirect inaccurate student responses.
Materials include embedded guidance to anticipate a variety of student answers including exemplar responses to questions and tasks, including guidance to support and/or redirect inaccurate student responses.
2 out of 2 points
Evaluation for 5.4e
Evaluation for 5.4e
Materials include embedded guidance to anticipate a variety of student answers including exemplar responses to questions and tasks, including guidance to support and/or redirect inaccurate student responses.
2 out of 2 points
The Academic Vocabulary and Mathematical Discourse Support has a section titled “Anticipated Responses, Exemplar, and Redirection.” This section includes embedded guidance to anticipate correct responses, partial responses, or inaccurate responses. It also provides an example of what the likely inaccuracy is that a student makes. The support/redirect also provides guidance for how educators can respond with next steps.
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
The materials integrate the TEKS process standards through activities that promote mathematical communication and multiple representations. For example, in the Engaging Activity, Graphing Ordered Pairs, students plot their initials on a coordinate plane using all four quadrants, record the ordered pairs, exchange their coordinate lists with a partner, and graph each other’s design. This activity requires students to communicate mathematical ideas, interpret coordinate pairs, and use mathematical representations while applying the grade-level content.
5.5b
Materials include a description of how process standards are incorporated and connected throughout the learning pathways.
Materials include a description of how process standards are incorporated and connected throughout the learning pathways.
1 out of 2 points
Evaluation for 5.5b
Evaluation for 5.5b
Materials include a description of how process standards are incorporated and connected throughout the learning pathways.
1 out of 2 points
The materials do not describe how the process standards connect to instruction throughout the learning pathways. For example, the “Incorporation and Connection Through the Learning Pathway” section of each lesson in the Implementation Guide is the same and only states the process standards as they relate to the sections “Guided Practice,” “Partner Practice,” and “Independent Practice,” but not how the standards serve the specific skills and learning objective of the lesson.
5.5c
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 5.5c
Evaluation for 5.5c
Materials include an overview of the TEKS process standards incorporated into each lesson.
1 out of 1 points
The lesson components provide opportunities for students to engage in mathematical processes throughout instruction, and the materials include a “Unit Rationale” that provides a generic statement of how students will apply the process standards in the lessons for the unit.
Rubric Section 6
Productive Struggle
Materials support students in applying disciplinary practices to productive problem-solving, including explaining and revising their thinking.
Total
71% (15 out of 21 points)
Evaluation for 6.1a
The materials provide opportunities for students to think mathematically, persevere through solving problems, and make sense of mathematics. For example, in the grade 6 Math Practice Teacher Edition, each lesson contains educator guidance called Facilitating Questions. Educators ask these questions during the Guided and Partner Practice portions of the lesson, where students collaboratively determine solutions to problems. The problems provide students with opportunities to think mathematically. The educator’s guidance encourages students to persevere through problem-solving.
In the TEKS lesson “Multiplying by a Fraction”, students reason about how multiplying by a fraction affects a quantity, determine whether quantities increase or decrease, compare situations, and explain their thinking using contextual examples. Students justify whether statements are true, interpret number line representations, and explain real-world scenarios involving fractional quantities. These tasks require students to analyze relationships, make sense of mathematical concepts in context, and engage in sustained problem solving.
Evaluation for 6.1b
The materials support students in understanding, explaining, and justifying that there can be multiple ways to solve problems and complete tasks. For example, in the TEKS lesson “Reciprocals”, students determine equivalent expressions for division by fractions, identify alternative expressions that produce the same result, and consider other methods that could be used to solve contextual problems. Students recognize that dividing by a fraction and multiplying by its reciprocal produce equivalent values and reason about why these approaches are mathematically equivalent. These opportunities allow students to explore multiple solution paths, explain their reasoning, and justify the validity of different strategies, promoting flexibility in mathematical thinking and a deeper conceptual understanding of operations with rational numbers.
The materials support students in explaining and justifying that there can be multiple ways to solve problems and complete tasks. For example, the grade 6 Math Practice TE contains student supports through guidance in the TEKS lesson “Equivalent Forms.” In the lesson, educator guidance for question 15 states, “This question asks students to find the percentage of the whole. This is a problem that can be solved in a variety of ways. Ask students to explain how they determined their answer.” Students discuss their strategies for solving the problem, illustrating supports in the material.
Evaluation for 6.1c
The materials require students to make sense of mathematics through multiple opportunities for students to do, write about, and discuss math with peers and/or educators. For example, in the grade 6 Math Practice TE, the TEKS lesson “Percents” provides educator guidance for introducing the lesson, in which educators instruct students to discuss example problems on percents. This task requires students to use proportions to solve for missing information in percent problems. Students then discuss with their peers the strategies they should use, as well as the calculations needed to find the solution. The educator’s guidance also states, “Ask volunteers from each group to share ideas with the class on how they solved their problem. Everyone should take notes on the problems being discussed.”
In the Engaging Activity “Triangles”, the materials allow students to measure and record the side lengths of three triangles. They analyze patterns in their measurements to draw conclusions and use those conclusions to determine whether the given sets of side lengths can form a triangle. The students have multiple opportunities to record and explain their findings.
Evaluation for 6.2a
The materials support educators in guiding students to share their problem-solving approaches, particularly through explanations and justifications. For example, the grade 6 Supplemental Math Teacher Guide includes a section labeled “Step 4: Review and Reflect within Polya’s Four-Step Problem-Solving Process” that prompts students to determine whether their solution is correct, check their work, and reflect on the strategies they used. This process encourages students to explain their reasoning and justify their approaches. Additionally, the grade 6 Supplemental Math Implementation Guide describes how educators can monitor student progress by reviewing student work, identifying misconceptions, and adjusting instruction, providing structures for facilitating reflection on students’ problem-solving processes. However, the materials do not include specific mathematical tasks, discussion prompts, or examples that demonstrate students constructing arguments about solution methods or engaging with problems through multiple entry points.
The materials do not include supports for educators to facilitate student reflection on mathematical reasoning and solution strategies. For example, in the TEKS lesson “Operations with Integers”, the wrap-around educator note on the left suggests that some students may use models to help solve the problems and prompts them to explain how they determined their answers. This note helps educators guide students in accessing the content through multiple entry points, but it does not ask for students to share or reflect on these different strategies.
Evaluation for 6.2b
The materials provide guidance for educators in monitoring student thinking and making instructional adjustments, but they do not include prompts for explanatory feedback based on student responses or anticipated misconceptions. For example, the grade 6 Supplemental Math Implementation Guide describes monitoring student progress, including reviewing student work, identifying misconceptions, and adjusting instruction. Similarly, the grade 6 Supplemental Math Teacher Guide includes a lesson flow in which educators review student work and make extend/enrich or reteach/intervention decisions based on student performance. These structures guide educators in recognizing misconceptions and responding instructionally. However, the materials do not provide explicit educator prompts, sample feedback statements, or anticipated incorrect responses, illustrating how educators should deliver explanatory feedback in response to student thinking.
The materials do not include prompts to support educators in providing explanatory feedback based on anticipated misconceptions and student responses. For example, in the TEKS lesson Representation of Ratios and Rates, the educator guidance states, “Listen to conversations and pull the group together if misconceptions arise regarding scale factor or the related proportion. Ask for a volunteer to share the meaning of the scale factor in their own words.” Although this guidance helps educators address misconceptions, it does not include specific student responses during the collaborative task. This pattern continues throughout the materials, with guidance for misconceptions but no reference to prompts for possible student responses or strategies for addressing those responses.
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 TEKS lesson “Multiplying by a Fraction”, students reason about how multiplying by a fraction affects a quantity, determine whether quantities increase or decrease, compare situations, and explain their thinking using contextual examples. Students justify whether statements are true, interpret number line representations, and explain real-world scenarios involving fractional quantities. These tasks require students to analyze relationships, make sense of mathematical concepts in context, and engage in sustained problem solving.
6.1b
Materials support students in understanding, explaining, and justifying that there can be multiple ways to solve problems and complete tasks.
Materials support students in understanding, explaining, and justifying that there can be multiple ways to solve problems and complete tasks.
3 out of 3 points
Evaluation for 6.1b
Evaluation for 6.1b
Materials support students in understanding, explaining, and justifying that there can be multiple ways to solve problems and complete tasks.
3 out of 3 points
The materials support students in explaining and justifying that there can be multiple ways to solve problems and complete tasks. For example, the grade 6 Math Practice TE contains student supports through guidance in the TEKS lesson “Equivalent Forms.” In the lesson, educator guidance for question 15 states, “This question asks students to find the percentage of the whole. This is a problem that can be solved in a variety of ways. Ask students to explain how they determined their answer.” Students discuss their strategies for solving the problem, illustrating supports in the material.
6.1c
Materials are designed to require students to make sense of mathematics through multiple opportunities for students to do, write about, and discuss math with peers and/or educators.
Materials are designed to require students to make sense of mathematics through multiple opportunities for students to do, write about, and discuss math with peers and/or educators.
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/or educators.
3 out of 3 points
In the Engaging Activity “Triangles”, the materials allow students to measure and record the side lengths of three triangles. They analyze patterns in their measurements to draw conclusions and use those conclusions to determine whether the given sets of side lengths can form a triangle. The students have multiple opportunities to record and explain their findings.
6.2 Facilitating Productive Struggle
6.2a
Materials support educators in guiding students to share and reflect on their problem-solving approaches, including explanations, arguments, justifications, and multiple points of entry.
Materials support educators in guiding students to share and reflect on their problem-solving approaches, including explanations, arguments, justifications, and multiple points of entry.
4 out of 8 points
Evaluation for 6.2a
Evaluation for 6.2a
Materials support educators in guiding students to share and reflect on their problem-solving approaches, including explanations, arguments, justifications, and multiple points of entry.
4 out of 8 points
The materials do not include supports for educators to facilitate student reflection on mathematical reasoning and solution strategies. For example, in the TEKS lesson “Operations with Integers”, the wrap-around educator note on the left suggests that some students may use models to help solve the problems and prompts them to explain how they determined their answers. This note helps educators guide students in accessing the content through multiple entry points, but it does not ask for students to share or reflect on these different strategies.
6.2b
Materials include prompts and guidance to support educators in providing explanatory feedback based on student responses and anticipated misconceptions.
Materials include prompts and guidance to support educators in providing explanatory feedback based on student responses and anticipated misconceptions.
2 out of 4 points
Evaluation for 6.2b
Evaluation for 6.2b
Materials include prompts and guidance to support educators in providing explanatory feedback based on student responses and anticipated misconceptions.
2 out of 4 points
The materials do not include prompts to support educators in providing explanatory feedback based on anticipated misconceptions and student responses. For example, in the TEKS lesson Representation of Ratios and Rates, the educator guidance states, “Listen to conversations and pull the group together if misconceptions arise regarding scale factor or the related proportion. Ask for a volunteer to share the meaning of the scale factor in their own words.” Although this guidance helps educators address misconceptions, it does not include specific student responses during the collaborative task. This pattern continues throughout the materials, with guidance for misconceptions but no reference to prompts for possible student responses or strategies for addressing those responses.