Program Information
- ISBN
- 9781970651577
- 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 4th Math Practice
Supplemental Math (English) Grade 4
IMRA 2026
Publisher: GF Educators, Inc.
Copyright: 2022
Series includes:
Rubric: Supplemental Mathematics K–5 (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 4 | 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
74% (17 out of 23 points)
Evaluation for 1.1a
The materials do not include a rationale for learning paths within the same grade level (horizontal alignment) as designed in the materials. For example, the “Unit Rationale” explains how the unit’s math concepts are connected to future topics. However, the “Unit Rationale” provides generic topics rather than specific skills, the units or lessons they are connected to, or how they are sequenced to be interconnected.
The materials include an alignment guide that outlines Texas Essential Knowledge and Skills (TEKS), lessons, and English Language Proficiency Standards (ELPS). For example, the educator edition page for each lesson provides TEKS information, vertical alignment, ELPS, and a conceptual learning goal in the page sidebar.
Evaluation for 1.1b
The materials include an implementation guide with usage recommendations and strategies for effective educator use in various contexts, such as just-in-time supports, advanced learning, or as a course. For example, the 4th Grade Math Implementation Guide in the digital bookcase includes a sample “Implementation Guidance” with suggested time-by-minute pacing.
The materials include an implementation guide with usage recommendations and strategies for effective educator use in various contexts. For example, the 4th Grade Math Implementation Guide includes a “Differentiation” section. The materials also include explicit intervention strategies for students needing support (guided practice first, visual representations, break multistep problems, guided questioning, revisit prerequisite skills) and enrichment strategies for advanced learners (multiple solution strategies, create own problems, real-world application, compare methods). The student group table also distinguishes support by level (needing support, on-level, or advanced).
Evaluation for 1.1c
The materials include a TEKS correlation guide. For example, within the scope and sequence, educators can view the TEKS and focus skills for each unit of study.
The materials include a TEKS correlation guide with recommended skill entry points based on diagnostic assessment results. For example, the “Item Map” section lists the TEKS from the diagnostic assessment, entry points if students did not master that standard, and a diagnostic look-for.
Evaluation for 1.1d
The materials include a protocol with corresponding guidance for lesson internalization. For example, within the 4th Grade Math Implementation Guide, each lesson has an “Internalize the Lesson” section for educators to thoroughly understand and prepare to teach lessons.
The materials do not include a protocol with corresponding guidance for unit internalization. For example, the 4th Grade Math Implementation Guide includes a rationale, Big IDeas for the unit, and some instructional notes, but the materials do not provide clear steps or expectations for how educators should internalize units.
Evaluation for 1.1e
The materials include resources for instructional leaders to support educators with implementing the materials as designed. For example, resources such as the “Program Overview” and “Instructional Design” outline how the program should be used in the classroom, which can be valuable for instructional leaders.
The materials include guidance for instructional leaders to support educators with implementing the materials as designed. For example, the “Leadership Lens” section includes guidance for priorities, classroom look-fors, coaching, and evidence review.
Evaluation for 1.2a
In the materials, the educator pages for each lesson provide relevant information for preparation of the lesson. The TEKS information, vertical alignment, ELPS, conceptual learning goal, and lesson information along with timing information are all provided for each TEKS lesson. The “Guided Practice” and “Partner Practice” sections also contain facilitating questions, and the “Independent Practice” section contains “Important Concepts,” “Extension Opportunities,” and “Misconceptions” sections in order to help teachers best prepare for the lesson.
The materials include digital books for educators, paper workbooks for students, and an online platform. For example, the digital books include the 4th Grade Math Teacher Guide, the 4th Grade Math Implementation Guide, the 4th Grade Math TEKS Checklist, the 4th Grade Math Practice Book Student Edition, and the 4th Grade Math Practice Book Teacher Edition.
The materials do not indicate to educators that “Partner Practice” and “Independent Practice” portions of the lesson can also be utilized as formative assessments. When considered as assessment resources, the questions found in the “Partner Practice” and “Independent Practice” sections are aligned to the TEKS and the ELPS as indicated at the beginning of each lesson.
Evaluation for 1.2b
This guidance is not applicable because the program is not designed to be adaptive.
Evaluation for 1.2c
The materials do not include English support for families with suggestions on supporting the progress of their students. The educator-facing materials are in English and include real-world problem contexts and accessible representations that can connect to learning outside of the classroom.
The materials do not include Spanish support for families with suggestions on supporting the progress of their students. The educator-facing and student-facing materials are all in English.
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 an alignment guide that outlines Texas Essential Knowledge and Skills (TEKS), lessons, and English Language Proficiency Standards (ELPS). For example, the educator edition page for each lesson provides TEKS information, vertical alignment, ELPS, and a conceptual learning goal in the page sidebar.
1.1b
Materials include an implementation guide with usage recommendations and strategies for effective educator use in various contexts, 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 in various contexts, 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 in various contexts, such as just-in-time supports, advanced learning, or as a course.
3 out of 3 points
The materials include an implementation guide with usage recommendations and strategies for effective educator use in various contexts. For example, the 4th Grade Math Implementation Guide includes a “Differentiation” section. The materials also include explicit intervention strategies for students needing support (guided practice first, visual representations, break multistep problems, guided questioning, revisit prerequisite skills) and enrichment strategies for advanced learners (multiple solution strategies, create own problems, real-world application, compare methods). The student group table also distinguishes support by level (needing support, on-level, or advanced).
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 materials include a TEKS correlation guide with recommended skill entry points based on diagnostic assessment results. For example, the “Item Map” section lists the TEKS from the diagnostic assessment, entry points if students did not master that standard, and a diagnostic look-for.
1.1d
Materials include protocols with corresponding guidance for unit and lesson internalization.
Materials include protocols with corresponding guidance for unit and lesson internalization.
1 out of 2 points
Evaluation for 1.1d
Evaluation for 1.1d
Materials include protocols with corresponding guidance for unit and lesson internalization.
1 out of 2 points
The materials do not include a protocol with corresponding guidance for unit internalization. For example, the 4th Grade Math Implementation Guide includes a rationale, Big IDeas for the unit, and some instructional notes, but the materials do not provide clear steps or expectations for how educators should internalize units.
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
The materials include guidance for instructional leaders to support educators with implementing the materials as designed. For example, the “Leadership Lens” section includes guidance for priorities, classroom look-fors, coaching, and evidence review.
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
The materials include digital books for educators, paper workbooks for students, and an online platform. For example, the digital books include the 4th Grade Math Teacher Guide, the 4th Grade Math Implementation Guide, the 4th Grade Math TEKS Checklist, the 4th Grade Math Practice Book Student Edition, and the 4th Grade Math Practice Book Teacher Edition.
The materials do not indicate to educators that “Partner Practice” and “Independent Practice” portions of the lesson can also be utilized as formative assessments. When considered as assessment resources, the questions found in the “Partner Practice” and “Independent Practice” sections are aligned to the TEKS and the ELPS as indicated at the beginning of each lesson.
1.2b
If designed to be adaptive, materials include responsive learning objectives, lesson components with suggested timeframes, and assessment resources aligned with the TEKS and ELPS.
If designed to be adaptive, materials include responsive 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 responsive learning objectives, lesson components with suggested timeframes, and assessment resources aligned with the TEKS and ELPS.
Not applicable.
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 do not include Spanish support for families with suggestions on supporting the progress of their students. The educator-facing and student-facing materials are all in English.
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 materials provide administration guidance for embedded formative assessments through the 4th Grade Math Assessment Teacher Edition’s lesson organization. For example, the “Suggested Daily Implementation” section identifies the instructional sequence, including warm-up, core instruction, guided practice, partner practice, supplemental practice, and discussion/reflection, and provides recommended pacing and educator actions to support consistent delivery of lesson activities and formative assessment opportunities.
The 4th Grade Math Practice Book Teacher Edition includes embedded directions and facilitating questions for guided practice and partner practice, providing educators with lesson-specific guidance for administering the formative assessments. These directions and facilitation prompts support consistent implementation by guiding educators through each assessment activity and helping them prepare for instructional delivery.
Evaluation for 2.1c
The digital assessment materials correspond to printable versions available in the 4th Grade Math Practice Book Student Edition. For example, the assessments available on the digital platform mirror those included in the printable 4th Grade Math Practice Book Student Edition. However, educators cannot print the assessments directly from the digital platform and must instead access the printable 4th Grade Math Practice Book Student Edition.
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 featuring TEKS-aligned tasks or questions at varying levels of complexity. For example, each unit includes an assessment, such as “Diagnostic Unit 2: Fractions,” that addresses the specific supporting and readiness TEKS covered in the unit, and educators can use the “Item Map” section to identify next steps based on the TEKS.
The materials include diagnostic assessments with TEKS-aligned tasks and questions using various interactive item types. For example, the assessments include multiselect, drag-and-drop, inline choice, hot-spot, and text-entry item types.
Evaluation for 2.1e
The materials include an “Independent Practice” section within each lesson that is aligned to the lesson’s TEKS. For example, the 4th Grade Math Practice Book Teacher Edition gives educators suggestions for the independent practice, such as, “Make sure the students understand the meaning of place value.”
The materials include embedded formative assessment opportunities with varying complexity levels throughout each lesson. For example, TEKS lesson 4.3B begins with the facilitating question, “What kinds of models are helpful to represent different ways to decompose fractions?” Then, guided practice and partner practice progress from knowledge-level questions to application and higher-level reasoning tasks that require students to provide verbal explanations and complete representations. These formative assessments incorporate multiple item types, including multiple-choice, free-response, and table-completion tasks.
Evaluation for 2.2a
The materials include scoring information and guidance for interpreting student performance within lessons. The educator pages include answer keys within the student inset, important concepts, misconceptions, and additional notes intended to support instructional decisions.
The materials include rationales for incorrect responses through the “Misconceptions” section with “Independent Practice” pages, helping identify likely student errors and instructional next steps. The materials do not include instructional assessments that contain scoring information and guidance for interpreting student performance, including a rationale for each correct and incorrect response.
The digital platform provides correctness feedback only by indicating whether responses are right or wrong, and the materials do not provide explanations for incorrect answers for lesson assignments. The test builder includes assessment functionality. However, additional items cannot be generated, preventing further verification of scoring guidance and response rationales.
Evaluation for 2.2b
The materials include tasks and activities for responding to performance trends but do not include guidance on their use. For example, the materials include the “How Teachers Use the Evidence” section for diagnostic, formative, and summative assessments. However, the materials do not contain activities based on the specific unit in which those formative and summative assessments are administered for specific skills.
The materials do not provide guidance for the use of included tasks and activities to respond to student trends in performance on all assessments. For example, the materials include a “Scoring and Instructional Response” section specifically for diagnostic assessments but not for formative and summative 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 reports 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, nor do they allow students to track progress over time, observe trends, or compare their progress with the class.
Evaluation for 2.2d
The TEKS lessons provided within the materials include instructional guidance that educators use throughout each lesson, highlighting key points and instructional strategies. The materials also provide insight into what educators should monitor and look for during lessons and discussions. For example, the “Misconceptions” section of the TEKS 4.4E lesson states, “Students may not understand how to use a model to represent a division problem. Ask students to model a multiplication problem using base tens and record the division problem that is also being represented. This helps them relate the area of the model to the quotient.”
The materials include prompts within the “Guided Practice” and “Partner Practice” sections that contain facilitating questions to help educators monitor student progress and students’ ability to grasp concepts. In the “Independent Practice” portion of each lesson, “Important Concepts” and the “Extension Opportunities” sections are included to help focus the learning in the direction of the stated goals of the standard.
Evaluation for 2.2e
This guidance is not applicable because the program is not designed to be adaptive.
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
The 4th Grade Math Practice Book Teacher Edition includes embedded directions and facilitating questions for guided practice and partner practice, providing educators with lesson-specific guidance for administering the formative assessments. These directions and facilitation prompts support consistent implementation by guiding educators through each assessment activity and helping them prepare for instructional delivery.
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 materials include diagnostic assessments with TEKS-aligned tasks and questions using various interactive item types. For example, the assessments include multiselect, drag-and-drop, inline choice, hot-spot, and text-entry item types.
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
The materials include embedded formative assessment opportunities with varying complexity levels throughout each lesson. For example, TEKS lesson 4.3B begins with the facilitating question, “What kinds of models are helpful to represent different ways to decompose fractions?” Then, guided practice and partner practice progress from knowledge-level questions to application and higher-level reasoning tasks that require students to provide verbal explanations and complete representations. These formative assessments incorporate multiple item types, including multiple-choice, free-response, and table-completion tasks.
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
The materials include rationales for incorrect responses through the “Misconceptions” section with “Independent Practice” pages, helping identify likely student errors and instructional next steps. The materials do not include instructional assessments that contain scoring information and guidance for interpreting student performance, including a rationale for each correct and incorrect response.
The digital platform provides correctness feedback only by indicating whether responses are right or wrong, and the materials do not provide explanations for incorrect answers for lesson assignments. The test builder includes assessment functionality. However, additional items cannot be generated, preventing further verification of scoring guidance and response rationales.
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 materials do not provide guidance for the use of included tasks and activities to respond to student trends in performance on all assessments. For example, the materials include a “Scoring and Instructional Response” section specifically for diagnostic assessments but not for formative and summative 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, nor do they 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 materials include prompts within the “Guided Practice” and “Partner Practice” sections that contain facilitating questions to help educators monitor student progress and students’ ability to grasp concepts. In the “Independent Practice” portion of each lesson, “Important Concepts” and the “Extension Opportunities” sections are included to help focus the learning in the direction of the stated goals of the standard.
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.
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
79% (31 out of 39 points)
Evaluation for 3.1a
The materials include a “Scoring and Instructional Response” section specifically for the diagnostic assessment with some quick strategies to incorporate.
The “Item Map” includes entry points and look-fors based on the addressed TEKS.
Evaluation for 3.1b
The materials include “Strategies for Teacher Vocabulary,” which provides explicit strategies for preteaching and developing academic vocabulary. For example, “Role Play: Encourage students to act out the meaning of terms, such as drawing a line and labeling it ‘line segment’ to reinforce understanding through movement and kinesthetic learning.”
Each unit includes a vocabulary list and either a matching or fill-in-the-blank activity. For example, in unit 1, lessons 4.2A, 4.2B, and 4.3C include a list of vocabulary words and a fill-in-the-blank activity.
The materials do not include preteaching or embedded supports for unfamiliar references in text. For example, in the 4.4F lesson, words or phrases found in word problems (such as commercial fishing boat and charity organization) are not pretaught, and there are no embedded supports to help students define the terms.
Evaluation for 3.1c
The materials include “Extension Learning Opportunity” sections with every independent practice to provide ways to extend the lesson for those who need additional practice. These activities encourage higher levels of thinking through problem-solving, real-world applications, and opportunities for students to create, design, or explain mathematical ideas. Because the extension tasks are embedded within each lesson and identified, the materials provide practical educator guidance for challenging students who have already mastered the lesson objectives, but the materials do not include this guidance for students who are above grade level.
The materials include a “Working with Diverse Learners” section that aligns the TEKS lesson page vertically and notes that this feature supports advanced learners. The materials direct educators to “introduce future grade-level concepts for extended learners.” The materials do not include explicit educator guidance for enrichment and extension activities for students who have demonstrated proficiency in content and skills above grade level.
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 works properly and 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 provide opportunities for students to demonstrate their understanding of mathematical concepts in various ways throughout the program. In the TEKS lessons, students must create a representation, solve a problem (and show their work), and then explain how they solved the problem. For example, during the TEKS 4.3C lesson, students demonstrate learning by representing equivalent fractions using models and number lines.
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
To anchor on Big Ideas and connect patterns and relationships, the materials include facilitating questions that ask students to explain their strategies for solving problems. The facilitating questions serve as explicit guidance for the educator to listen for answers, including using objects and pictorial models (such as arrays and area models). For example, in a lesson, students are asked about how a strip model is used to represent word problems with unknown values.
The materials activate prior knowledge within the “Teacher Notes” section of the lessons. For example, in a grade 4 lesson about products, the educator reminds students of their work with arrays. The lesson demonstrates how different strategies with representations can be used to solve the same multiplication problem. Students also connect the models and discuss which they prefer and why.
Evaluation for 3.2b
The materials provide clear guidance for multiple instructional approaches within every lesson. The lesson cycle includes direct instruction, guided practice, partner collaboration, independent practice, and hands-on activities, with descriptions of how each component should be implemented. Additional guidance highlights the role of collaborative learning and hands-on experiences in helping students practice new skills, apply concepts, and demonstrate understanding. This structure ensures that educators have clear direction for using a variety of instructional methods throughout instruction.
The individual lessons provide detailed guidance for a variety of instructional approaches. The guidance directs educators to use strategies such as small-group learning, whole-class discussions, partner collaboration, hands-on exploration with manipulatives, and think-alouds to model student thinking. Lessons also include step-by-step directions for facilitating transitions between instructional formats, along with suggested questions, timing, and expected student responses. This guidance helps educators effectively engage students through multiple instructional methods throughout the lesson.
Evaluation for 3.2c
All students are provided with the same materials and tasks with no differentiation or tiers of support based on need. For example, all students receive support through the “TEKS Lesson” and “Guided Practice” sections, collaborate with peers during the “Partner Practice,” and engage with tasks independently through the “Independent Practice” section. However, these are part of the lesson design, not an intervention. The materials do not include guidance for educators on implementing multi-tiered intervention methods.
The “Flexible Use” section states that the materials are supplemental practice materials that can be implemented across multiple instructional settings, including intervention blocks. This section states that this flexibility allows educators to adapt the materials to meet their students’ needs and classroom schedules. However, the grade 4 materials do not include multi-tiered intervention methods for various types of practice or structures.
The “Guided Practice,” “Partner Practice,” and “Independent Practice” sections do not provide multi-tiered interventions based on student need. The materials provide different ways for students to engage with the same 4th Grade Math Practice Book Student Edition components, such as educator-led activities, partner practice, independent practice, and engaging activities, but do not provide differentiated interventions within these structures. All students engage with the same materials and tasks without targeted or intensive supports based on identified needs. Although the 4th Grade Math Implementation Guide suggests using the materials for small-group instruction or intervention, it does not provide criteria for determining which students need additional support, guidance for forming groups based on student data, specific intervention activities, or direction for selecting and targeting identified skill deficits. The flexibility to use the same materials across different instructional groupings does not demonstrate a multi-tiered system of increasingly targeted intervention supports.
Evaluation for 3.2d
The materials include extension activities but do not include various forms of engagement. For example, in lesson 4.5A, while studying multistep problems, students are asked to write their own multistep story problem, but the lesson does not use any form of engagement, such as virtual simulations, reports, or manipulatives.
The materials do not provide guidance to support educators in effectively implementing extension methods. For example, the 4th Grade Math Implementation Guide includes a “Differentiation” section that lists scaffolding strategies such as using concrete models and providing sentence stems. However, these are not incorporated into lessons with guidance for the educator to follow.
Evaluation for 3.2e
The materials include prompting for educators to check for understanding and provide feedback. For example, the “Guided Practice” and “Partner Practice” sections include facilitating questions to help the educator better monitor students’ progress and ability to grasp the concept.
The materials include an online tool for educators to record and provide feedback to students on the Teacher Notepad during the “TEKS Lesson” and “Guided Practice” sections of lessons. The materials do not include guidance on when or how to use these features.
Evaluation for 3.3a
The materials include educator guidance on providing and incorporating linguistic accommodations for all levels of language proficiency. For example, within the “Emergent Bilingual Oral and Written Discourse Support” section, educators are given ELPS sentence stems based on students’ level and discourse guidance.
The materials include ELPS sentence stems that target students at the pre-production, beginning, intermediate, high-intermediate, and advanced levels. For example, a student at the intermediate level may have a sentence stem, “I used __ to explain how a digit’s place value changes with its place because __.”
Evaluation for 3.3b
This guidance is not applicable to the program because it is not designed to be adaptive.
Evaluation for 3.3c
A cross-linguistic recommendation for emergent bilingual (EB) discourse is to display and discuss place-value vocabulary cognates and compare their sounds, spellings, and meanings. This strategy helps educators adapt to students’ linguistic and academic needs while staying aligned to the target TEKS.
Each lesson includes a cross-linguistic section for guidance on oral and written discourse.
Evaluation for 3.3d
The 4th Grade Math Practice Book Teacher Edition includes 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” section includes oral and written discourse.
Before introducing a new math concept, the online program materials present key terms and related vocabulary with visual aids and context in the “TEKS Lesson” video. For example, in grade 4, before discussing perimeter and area, a lesson reviews the terms and includes the units and formulas for perimeter and area with visuals.
The materials include building background knowledge and making cross-linguistic connections through oral and written discourse. For example, the “Embedded Oral Discourse Guidance” and the “Embedded Written Discourse Guidance” sections provide educators with guidance on activating background knowledge and strategies for cross-linguistic connections.
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 “Item Map” includes entry points and look-fors based on the addressed TEKS.
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
Each unit includes a vocabulary list and either a matching or fill-in-the-blank activity. For example, in unit 1, lessons 4.2A, 4.2B, and 4.3C include a list of vocabulary words and a fill-in-the-blank activity.
The materials do not include preteaching or embedded supports for unfamiliar references in text. For example, in the 4.4F lesson, words or phrases found in word problems (such as commercial fishing boat and charity organization) are not pretaught, and there are no embedded supports to help students define the terms.
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.
1 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.
1 out of 2 points
The materials include a “Working with Diverse Learners” section that aligns the TEKS lesson page vertically and notes that this feature supports advanced learners. The materials direct educators to “introduce future grade-level concepts for extended learners.” The materials do not include explicit educator guidance for enrichment and extension activities for students who have demonstrated proficiency in content and skills above grade level.
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 activate prior knowledge within the “Teacher Notes” section of the lessons. For example, in a grade 4 lesson about products, the educator reminds students of their work with arrays. The lesson demonstrates how different strategies with representations can be used to solve the same multiplication problem. Students also connect the models and discuss which they prefer and why.
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 individual lessons provide detailed guidance for a variety of instructional approaches. The guidance directs educators to use strategies such as small-group learning, whole-class discussions, partner collaboration, hands-on exploration with manipulatives, and think-alouds to model student thinking. Lessons also include step-by-step directions for facilitating transitions between instructional formats, along with suggested questions, timing, and expected student responses. This guidance helps educators effectively engage students through multiple instructional methods throughout the lesson.
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.
0 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.
0 out of 3 points
The “Flexible Use” section states that the materials are supplemental practice materials that can be implemented across multiple instructional settings, including intervention blocks. This section states that this flexibility allows educators to adapt the materials to meet their students’ needs and classroom schedules. However, the grade 4 materials do not include multi-tiered intervention methods for various types of practice or structures.
The “Guided Practice,” “Partner Practice,” and “Independent Practice” sections do not provide multi-tiered interventions based on student need. The materials provide different ways for students to engage with the same 4th Grade Math Practice Book Student Edition components, such as educator-led activities, partner practice, independent practice, and engaging activities, but do not provide differentiated interventions within these structures. All students engage with the same materials and tasks without targeted or intensive supports based on identified needs. Although the 4th Grade Math Implementation Guide suggests using the materials for small-group instruction or intervention, it does not provide criteria for determining which students need additional support, guidance for forming groups based on student data, specific intervention activities, or direction for selecting and targeting identified skill deficits. The flexibility to use the same materials across different instructional groupings does not demonstrate a multi-tiered system of increasingly targeted intervention supports.
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.
0 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.
0 out of 2 points
The materials do not provide guidance to support educators in effectively implementing extension methods. For example, the 4th Grade Math Implementation Guide includes a “Differentiation” section that lists scaffolding strategies such as using concrete models and providing sentence stems. However, these are not incorporated into lessons with guidance for the educator to follow.
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 materials include an online tool for educators to record and provide feedback to students on the Teacher Notepad during the “TEKS Lesson” and “Guided Practice” sections of lessons. The materials do not include guidance on when or how to use these features.
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
The materials include ELPS sentence stems that target students at the pre-production, beginning, intermediate, high-intermediate, and advanced levels. For example, a student at the intermediate level may have a sentence stem, “I used __ to explain how a digit’s place value changes with its place because __.”
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
Each lesson includes a cross-linguistic section for guidance on oral and written discourse.
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
Before introducing a new math concept, the online program materials present key terms and related vocabulary with visual aids and context in the “TEKS Lesson” video. For example, in grade 4, before discussing perimeter and area, a lesson reviews the terms and includes the units and formulas for perimeter and area with visuals.
The materials include building background knowledge and making cross-linguistic connections through oral and written discourse. For example, the “Embedded Oral Discourse Guidance” and the “Embedded Written Discourse Guidance” sections provide educators with guidance on activating background knowledge and strategies for cross-linguistic connections.
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
63% (10 out of 16 points)
Evaluation for 4.1a
The materials include lessons that provide practice opportunities throughout learning pathways that require students to demonstrate depth of understanding aligned to the TEKS. For example, in the 4.5A lesson, students begin with a breakdown of problem-solving steps and then later determine solutions to multistep problems with only equations or strip diagrams to show the corresponding steps. This includes writing the equation to match a word problem and filling in parts of strip diagrams to match the given word problem.
The materials include instructional assessments throughout learning pathways and provide a variety of practice opportunities within each lesson, including guided, collaborative, and independent tasks. This structure allows students to engage with content through multiple instructional formats, supporting skill development and conceptual understanding.
Evaluation for 4.1b
The materials include questions and tasks that increase in rigor and complexity, leading to grade-level proficiency in the mathematics TEKS. For example, in the “Representing Products” lesson, students represent two-digit by two-digit multiplication using arrays, area models, and equations. In the “Multiplying Using Various Methods” lesson, students advance to mental math using the properties of operations, partial products, and the standard algorithm. Students then analyze a partial-products area model for 23 × 44, determine a missing partial product, and connect the model to the standard algorithm, requiring students to apply multiplication at the rigor of the grade-level TEKS.
The materials include extension materials that increase in rigor and complexity, leading to grade-level proficiency in the mathematics TEKS. For example, in an extension focused on division, students use square tiles or graph paper to model real-world division problems (e.g., arranging chairs into rows) and then represent their solutions using equations and area models.
The materials do not include questions, tasks, enrichment, or extension activities that lead to above-grade-level proficiency. The lessons scaffold learning through progressively more rigorous tasks that remain aligned to grade-level expectations. For example, the lessons in the 4th Grade Math Practice Book Teacher Edition are based on the current grade-level TEKS, including the “Extension Learning Opportunity” section, but do not challenge students beyond grade-level proficiency.
Evaluation for 4.2a
The materials demonstrate coherence across concepts horizontally within the grade level by connecting patterns and relationships. For example, the “Relating Decimals to Fractions” lesson connects decimals, fractions, and the base 10 place-value system. Students use a place-value chart to relate a decimal such as 2.43 to the fraction 2 and 43/100, and the lesson establishes that decimal numbers are another way to represent fractional amounts and that students should connect these quantities to the base 10 notation system, connecting these concepts within the grade level.
The materials demonstrate coherence across concepts horizontally within the grade level by connecting Big Ideas. For example, in the 4th Grade Math Practice Book Student Edition, each lesson begins with a “TEKS Lesson” section to review a focus question, define previously learned vocabulary, and connect any patterns and ends with a “Why Do I Need to Know This?” section that ties to the Big Idea of the lesson.
Evaluation for 4.2b
In the lesson on representing multistep problems, the educator guidance states that using strip diagrams and equations lays a foundation for algebra, connecting to grade 6 and beyond.
The “Interpreting Base-Ten” lesson guides educators to connect to prior grade-level learning and show how that learning extends. The guidance notes that expanded notation is a review from grade 3. However, at this level, expanded notation extends to the one-billion place, as well as to the tenths and hundredths decimal places, which connects the grade 3 place-value concept to its grade 4 extension.
Evaluation for 4.2c
In the materials, students continue learning about place value to the hundredths place, using charts and connecting to base 10. This learning connects to grade 5 and beyond when students understand the value of digits past the billions or hundredths places.
The materials demonstrate coherence across lessons or activities by connecting students’ prior knowledge of procedures to the mathematical concepts to be learned in the current grade level and future grade levels. For example, a grade 4 lesson about finding products directs the educator to remind students of their work with arrays. The lesson demonstrates how different strategies using representations can be used to solve the same multiplication problem. In future learning, students will multiply two- and three-digit numbers using these strategies.
Evaluation for 4.3a
The materials do not review previously learned skills or concepts across learning pathways. Lessons focus only on current learning, are designed to target a specific TEKS standard for a single lesson, and do not include spaced-retrieval opportunities. For example, the 4.9A lesson includes “Guided Practice,” “Partner Practice,” and “Independent Practice” sections focused on representing data, but this skill is not covered again after this lesson.
The materials do not provide spaced retrieval opportunities with previously learned concepts across learning pathways. For example, the “Mathematics Appendix A: Additional Activities” section includes an engagement activity for only the specific TEKS lesson. The materials do not include spiraled activities, assessments, or retrieval opportunities.
Evaluation for 4.3b
The materials do not provide interleaved practice opportunities with previously learned skills across learning pathways. Students are not required to review different skills or mixed problem types within a single lesson or learning pathway. For example, the 4.5A lesson includes “Guided Practice,” “Partner Practice,” and “Independent Practice” sections focused on representing multistep problems, but the lesson focuses on a single skill and doesn’t mix in any other TEKS.
The materials do not provide interleaved practice opportunities with previously learned concepts across learning pathways. Students are not required to review multiple concepts within a single lesson or learning pathway. For example, the “Data Analysis and Personal Financial Literacy” lesson addresses only the current TEKS for these concepts and does not engage students in any additional practice or review of previously learned concepts.
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 materials include instructional assessments throughout learning pathways and provide a variety of practice opportunities within each lesson, including guided, collaborative, and independent tasks. This structure allows students to engage with content through multiple instructional formats, supporting skill development and conceptual understanding.
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 include extension materials that increase in rigor and complexity, leading to grade-level proficiency in the mathematics TEKS. For example, in an extension focused on division, students use square tiles or graph paper to model real-world division problems (e.g., arranging chairs into rows) and then represent their solutions using equations and area models.
The materials do not include questions, tasks, enrichment, or extension activities that lead to above-grade-level proficiency. The lessons scaffold learning through progressively more rigorous tasks that remain aligned to grade-level expectations. For example, the lessons in the 4th Grade Math Practice Book Teacher Edition are based on the current grade-level TEKS, including the “Extension Learning Opportunity” section, but do not challenge students beyond grade-level proficiency.
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 demonstrate coherence across concepts horizontally within the grade level by connecting Big Ideas. For example, in the 4th Grade Math Practice Book Student Edition, each lesson begins with a “TEKS Lesson” section to review a focus question, define previously learned vocabulary, and connect any patterns and ends with a “Why Do I Need to Know This?” section that ties to the Big Idea of the lesson.
4.2b
Materials demonstrate coherence vertically across concepts and grade bands, including connections from grade K–6, by connecting patterns, big ideas, and relationships.
Materials demonstrate coherence vertically across concepts and grade bands, including connections from grade K–6, 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 grade K–6, by connecting patterns, big ideas, and relationships.
1 out of 1 points
The “Interpreting Base-Ten” lesson guides educators to connect to prior grade-level learning and show how that learning extends. The guidance notes that expanded notation is a review from grade 3. However, at this level, expanded notation extends to the one-billion place, as well as to the tenths and hundredths decimal places, which connects the grade 3 place-value concept to its grade 4 extension.
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.
4 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.
4 out of 4 points
The materials demonstrate coherence across lessons or activities by connecting students’ prior knowledge of procedures to the mathematical concepts to be learned in the current grade level and future grade levels. For example, a grade 4 lesson about finding products directs the educator to remind students of their work with arrays. The lesson demonstrates how different strategies using representations can be used to solve the same multiplication problem. In future learning, students will multiply two- and three-digit numbers using these strategies.
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 materials do not provide spaced retrieval opportunities with previously learned concepts across learning pathways. For example, the “Mathematics Appendix A: Additional Activities” section includes an engagement activity for only the specific TEKS lesson. The materials do not include spiraled activities, assessments, or retrieval opportunities.
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
The materials do not provide interleaved practice opportunities with previously learned concepts across learning pathways. Students are not required to review multiple concepts within a single lesson or learning pathway. For example, the “Data Analysis and Personal Financial Literacy” lesson addresses only the current TEKS for these concepts and does not engage students in any additional practice or review of previously learned concepts.
Rubric Section 5
Balance of Conceptual and Procedural Understanding
Materials are designed to balance conceptual understanding, procedural skills, and fluency.
Total
87% (33 out of 38 points)
Evaluation for 5.1a
The materials include multistep problem-solving tasks that require students to apply mathematical concepts in real-world contexts. For example, students analyze given information, determine appropriate operations, and solve problems involving multiplication and division. These tasks promote the application of skills and support the development of problem-solving strategies. The materials include real-world data analysis tasks that require students to interpret, organize, and analyze information to solve problems. For example, students engage with data sets, create representations, and answer questions that require application of mathematical reasoning in authentic contexts.
The materials include questions and tasks that provide opportunities for students to evaluate models and representations. For example, when adding and subtracting mixed numbers, students have access to fraction strips and complete an “Engaging Activity” that has them first evaluate the reasonableness of their equation. For example, “1 7/8 plus 2 5/8, the sum will be: more than 4 or less than 4?” Then, students use “think” questions to explain their answers.
Evaluation for 5.1b
In the “Models for Perimeter and Area” lesson, students create concrete models where they use centimeter cubes to build a rectangle with an area of 18 square centimeters and a non-square rectangle with an area of 36 square centimeters. In a lesson about decimals, students create pictorial representations where they shade a 10 × 10 grid with the correct amount and then write the decimal the model shows.
The materials include questions and tasks that provide opportunities for students to create concrete models of mathematical situations. For example, students use paper strips divided into ninths for their activity on decomposing fractions.
Evaluation for 5.1c
Students apply their skills in multiplication and time to real-world situations. For example, “Felipe finished his math homework at school at 5:30 PM. He worked six division problems in all and spent five minutes on each problem. What time did Felipe start his homework?” In another lesson about perimeter and area, during the “Engaging Activity,” students apply the concepts of perimeter and area to open tasks with multiple valid solutions. Students accomplish this by using a 20 centimeter string to create a non-square rectangle and a square, determining the dimensions, and generating various figures.
In the “Engaging Activity” for determining quotients, students practice looking at shaded base 10 models to represent fractions out of 100, and the “TEKS Lesson” then focuses on prior learning about the value of numbers and a place-value chart to represent decimals as fractional amounts.
Evaluation for 5.2a
The materials provide tasks designed to build student fluency necessary to complete grade-level mathematical tasks. For example, some of the “Engaging Activity” pages include completing a table for 10 times a number and 1/10 of a number and practice of rounding whole numbers greater than 100,000. In the 4.4A lesson, students develop flexible reasoning by solving a variety of problems, such as analyzing rainfall tables, calculating track-and-field distances, and determining profits. This lesson ensures that students find a strategy for each problem rather than just the same algorithm, further building their fluency.
The materials do not provide tasks designed to build student automaticity necessary to complete grade-level mathematical tasks. For example, the materials do not support automatic recall of multiplication and division facts, quick multiplication of powers of 10, or mental math tasks. All lessons begin with a “TEKS Lesson” component and end with word problems during “Independent Practice.”
Evaluation for 5.2b
The materials provide opportunities for students to practice the application of efficient and flexible mathematical procedures throughout learning pathways. For example, in the “Multiplying Using Various Methods” lesson, students apply efficient procedures including mental math, partial products, and the standard algorithm, and they practice flexibility by comparing two students’ mental strategies for 20 × 18 (decomposing versus doubling and halving) and responding to the prompt “Can you think of another way to solve 20 × 18 mentally?”
The materials do not provide opportunities for students to practice the application of accurate mathematical procedures throughout learning pathways. For example, “Independent Practice” and “Engaging Activity” opportunities emphasize correct answers rather than the process used to obtain them or the efficiency of the selected method, and “Engaging Activity” pages include answer keys for educator use only. The materials present “Misconceptions,” “Important Concepts,” and “Extension Suggestions” sections for educators but do not prompt students to evaluate or refine the accuracy or efficiency of their own procedures. Additionally, the materials do not provide opportunities for students to independently verify the accuracy of their procedures beyond educator feedback.
Evaluation for 5.2c
The materials provide opportunities for students to evaluate mathematical representations, models, strategies, and solutions for efficiency and accuracy throughout learning pathways. For example, in “Engaging Activity: Solving with Fluency,” students solve two related problems and respond to “How does your answer from Problem 1 help you solve Problem 2?” This prompts students to consider how a previous solution can support a more efficient approach to a related problem. Students also respond to, “Can eight students equally share 46 oranges? Why or why not?” This requires them to evaluate the accuracy of a solution and explain their reasoning.
The materials do not provide opportunities for students to evaluate mathematical representations, models, strategies, and solutions for flexibility throughout learning pathways. “Engaging Activity: Solving with Fluency” asks students to consider how one answer can help solve a related problem and explain “Why or why not?” However, these prompts focus on using prior reasoning efficiently and determining an accurate solution. Other prompts ask students to identify, “What is known?”, “What is unknown?”, “What do you need to find?”, and “What is the solution?” The materials do not prompt students to compare strategies based on their usefulness across different contexts, determine when one approach might work better than another, or evaluate how a strategy could adapt to different problems.
Evaluation for 5.2d
Questions within the “Guided Practice,” “Partner Practice,” and “Independent Practice” sections follow similar formats and use similar question types, which do not encourage the use of various approaches. For example, in the lesson on decimals, students learn how to locate decimals on a number line, and educators provide procedural steps for labeling tenths and hundredths, but the lesson does not guide students toward selecting increasingly efficient strategies for determining decimal locations. The lesson does not include prompts to compare methods, move from less efficient to more efficient approaches, or reflect on which strategy is fastest or most effective. Educator guidance focuses on accuracy and task completion rather than on supporting students in developing or choosing more efficient strategies.
4th Grade Math Practice Book Teacher Edition does not include differentiation or scaffolding strategies specific to the lesson to expose students to more efficient approaches to the skill or to provide explanations of those approaches.
Evaluation for 5.3a
The materials explicitly state how the conceptual emphasis of the TEKS is addressed. For example, under the listed TEKS, the “Conceptual Learning Goal” section emphasizes understanding of mathematical ideas, relationships, and reasoning. For example, in lesson 4.3E, this section states that students need to understand how to combine and separate fractions with like denominators through concrete, visual, and symbolic representations.
The materials do not explicitly state how the procedural emphasis of the TEKS is addressed. For example, each lesson lists the TEKS and the conceptual learning goal. For example, “Students develop a conceptual understanding of multiplication as area by modeling two-digit products with arrays and area models.” However, the educator must infer how specifically the procedural emphasis is being addressed. The materials do not explicitly state how the procedural emphasis of the TEKS is addressed.
Evaluation for 5.3b
The materials include questions and tasks that provide opportunities for students to use concrete models and pictorial representations as required by the TEKS. For example, students use paper strips divided into ninths for their activity on decomposing fractions. Students also draw pictorial models of angles using protractors and rays and use base 10 blocks to model decimals.
The materials include questions and tasks that provide opportunities for students to use abstract models as required by the TEKS. For example, students estimate sums and differences using benchmark fractions such as one whole or one half. Students also use numeric expressions and formulas to calculate area and perimeter.
Evaluation for 5.3c
The materials include supports for students in defining and explaining concrete and representational models in relation to abstract concepts. For example, in a fractions lesson, students use a number line to explain whether a peer’s claim that 1/2 + 1/4 = 2/6 is correct. In a place-value lesson, students explain how each digit contributes to the total when writing a number in expanded form using base 10 models.
The materials include supports for students in connecting concrete and representational models to abstract (symbolic/numeric/algorithmic) concepts, as required by the TEKS. For example, students use fraction circle models to label fractions and discuss questions with their group.
The materials include supports for students in creating concrete and representational models to abstract (symbolic/numeric/algorithmic) concepts, as required by the TEKS. For example, students use paper strips divided into ninths for their activity on decomposing fractions.
Evaluation for 5.4a
The materials include engaging problem-solving tasks that require students to apply mathematical concepts in meaningful, real-world contexts. Students solve problems involving money, quantities, and real-life scenarios, increasing relevance and engagement.
The materials provide opportunities for students to develop academic mathematical language using visuals, manipulatives, or other language development strategies. For example, “Appendix C” contains a “Strategies for Teaching Vocabulary” section that explains strategies such as using pictures and diagrams and includes fill-in-the-blank pages based on sets of TEKS.
Evaluation for 5.4b
The materials connect mathematics to real-world situations such as shopping, budgeting, and grouping objects. These contexts help students understand the practical application of mathematical concepts in everyday life.
The materials include embedded educator guidance to scaffold and support students’ use of academic mathematical vocabulary in context when communicating with peers and educators. For example, “Appendix C” contains a “Strategies for Teaching Vocabulary” section that explains strategies such as using pictures and diagrams; using spiral review; providing active engagement opportunities such as role-play or vocabulary games; and using formative feedback, educator modeling, and think-alouds.
The materials include embedded guidance to scaffold, support, and extend the use of academic math vocabulary, including communication targets, key vocabulary, sentence frames, precise language, peer conversation guidance, and anticipated responses with exemplars and redirection.
Evaluation for 5.4c
The materials include embedded guidance to support student application of appropriate mathematical language and academic vocabulary in discourse. For example, the 4th Grade Math Implementation Guide includes a “Precise Language and Peer Conversation” section that has guidance on recasting words and educator prompts.
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 promote active student participation through structured partner work and guided practice. Students engage in discussions, complete tasks collaboratively, and actively construct understanding through interaction. This allows students to hear math language with peers.
The materials include embedded guidance to facilitate mathematical conversations, allowing students to refine and use math language with peers within the “Academic Vocabulary and Mathematical Discourse Support” section using the “Hear-Refine-Use” routine For example, a student is given a sentence stem, such as “What evidence shows __?” Their partner has to revise the statement with precise mathematical language.
Evaluation for 5.4e
The materials include embedded guidance to anticipate a variety of student answers, including exemplar responses to questions and tasks. For example, the 4th Grade Math Practice Book Teacher Edition includes a “Misconceptions” section within each lesson. In the 4.4A lesson, this section states that students may not understand how adding and subtracting decimals relate to adding and subtracting whole numbers. The section guides educators to have students use a T-chart that shows how adding and subtracting decimals demonstrate similarities to and differences from adding whole numbers. This enables educators to quickly assess understanding and facilitate effective discussions.
The materials include embedded guidance to support and/or redirect inaccurate student responses. For example, the 4th Grade Math Implementation Guide has a section called “Anticipated Responses, Exemplar, and Redirection” that is specific to student lessons and problems, guiding the educator in quickly assessing understanding or strategies to support struggling students and in targeting instruction.
Evaluation for 5.5a
In the lesson on perimeter and area, students solve real-world problems involving wrapping ribbon around a box and planning a garden. Students analyze mathematical relationships and connect arrays and other representations to the formulas for perimeter and area as they justify their solutions.
The materials align instruction with the TEKS process standards. For example, the 4th Grade Math Practice Book Teacher Edition includes a “Process Standards” table that indicates which standards the TEKS lesson covers. For example, 4.2A includes 4.1A, 4.1B, 4.1F, and 4.1G.
Evaluation for 5.5b
The materials include a description of how process standards are incorporated throughout the learning pathways. In the beginning of the “Incorporation and Connection Through the Learning Pathway” section of each lesson, there is a specific statement about how the process standards are incorporated into the skill practice. For example, “Through base-ten blocks, place-value charts, standard form, expanded form, word form, and equations, students build a shared conceptual model, communicate ideas in more than one form, and analyze the relationships that define the content (3.C, 3.D, 3.E, 3.F, 3.G).”
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 4th Grade Math Implementation Guide is the same and only states the process standards as they relate to the sections “Guided Practice,” “Partner Practice,” and “Independent Practice.” However, it does not state how the standards serve the specific skills and learning objective of the lesson.
Evaluation for 5.5c
The materials include a description of how process standards are incorporated throughout the learning pathways. In the beginning of the “Incorporation and Connection Through the Learning Pathway” section of each lesson, there is a specific statement about how the process standards are incorporated into the skill practice. For example, “Through base-ten blocks, place-value charts, standard form, expanded form, word form, and equations, students build a shared conceptual model, communicate ideas in more than one form, and analyze the relationships that define the content (3.C, 3.D, 3.E, 3.F, 3.G).”
The materials include a “Unit Rationale” section that provides a generic statement of how students will apply the process standards. For example, one unit states, “Throughout the unit, students apply the mathematical process standards by analyzing relationships, representing problems with models and equations, and communicating mathematical reasoning.”
5.1 Development of Conceptual Understanding
5.1a
Questions and tasks provide opportunities for students to interpret, analyze, and evaluate models and representations for mathematical concepts and situations.
Questions and tasks provide opportunities for students to interpret, analyze, and evaluate models and representations for mathematical concepts and situations.
3 out of 3 points
Evaluation for 5.1a
Evaluation for 5.1a
Questions and tasks provide opportunities for students to interpret, analyze, and evaluate models and representations for mathematical concepts and situations.
3 out of 3 points
The materials include questions and tasks that provide opportunities for students to evaluate models and representations. For example, when adding and subtracting mixed numbers, students have access to fraction strips and complete an “Engaging Activity” that has them first evaluate the reasonableness of their equation. For example, “1 7/8 plus 2 5/8, the sum will be: more than 4 or less than 4?” Then, students use “think” questions to explain their answers.
5.1b
Questions and tasks provide opportunities for students to create concrete models and pictorial representations to represent mathematical situations.
Questions and tasks provide opportunities for students to create concrete models and pictorial representations to represent 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 pictorial representations to represent mathematical situations.
2 out of 2 points
The materials include questions and tasks that provide opportunities for students to create concrete models of mathematical situations. For example, students use paper strips divided into ninths for their activity on decomposing fractions.
5.1c
Questions and tasks provide opportunities for students to apply conceptual understanding to new problem situations and contexts.
Questions and tasks provide opportunities for students to apply conceptual understanding to new problem situations and contexts.
1 out of 1 points
Evaluation for 5.1c
Evaluation for 5.1c
Questions and tasks provide opportunities for students to apply conceptual understanding to new problem situations and contexts.
1 out of 1 points
In the “Engaging Activity” for determining quotients, students practice looking at shaded base 10 models to represent fractions out of 100, and the “TEKS Lesson” then focuses on prior learning about the value of numbers and a place-value chart to represent decimals as fractional amounts.
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.
1 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.
1 out of 2 points
The materials do not provide tasks designed to build student automaticity necessary to complete grade-level mathematical tasks. For example, the materials do not support automatic recall of multiplication and division facts, quick multiplication of powers of 10, or mental math tasks. All lessons begin with a “TEKS Lesson” component and end with word problems during “Independent Practice.”
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.
2 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.
2 out of 3 points
The materials do not provide opportunities for students to practice the application of accurate mathematical procedures throughout learning pathways. For example, “Independent Practice” and “Engaging Activity” opportunities emphasize correct answers rather than the process used to obtain them or the efficiency of the selected method, and “Engaging Activity” pages include answer keys for educator use only. The materials present “Misconceptions,” “Important Concepts,” and “Extension Suggestions” sections for educators but do not prompt students to evaluate or refine the accuracy or efficiency of their own procedures. Additionally, the materials do not provide opportunities for students to independently verify the accuracy of their procedures beyond educator feedback.
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.
3 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.
3 out of 3 points
The materials do not provide opportunities for students to evaluate mathematical representations, models, strategies, and solutions for flexibility throughout learning pathways. “Engaging Activity: Solving with Fluency” asks students to consider how one answer can help solve a related problem and explain “Why or why not?” However, these prompts focus on using prior reasoning efficiently and determining an accurate solution. Other prompts ask students to identify, “What is known?”, “What is unknown?”, “What do you need to find?”, and “What is the solution?” The materials do not prompt students to compare strategies based on their usefulness across different contexts, determine when one approach might work better than another, or evaluate how a strategy could adapt to different problems.
5.2d
Materials contain guidance to support students in selecting increasingly efficient approaches to solve mathematics problems.
Materials contain guidance to support students in selecting increasingly efficient approaches to solve mathematics problems.
0 out of 1 points
Evaluation for 5.2d
Evaluation for 5.2d
Materials contain guidance to support students in selecting increasingly efficient approaches to solve mathematics problems.
0 out of 1 points
4th Grade Math Practice Book Teacher Edition does not include differentiation or scaffolding strategies specific to the lesson to expose students to more efficient approaches to the skill or to provide explanations of those approaches.
5.3 Balance of Conceptual Understanding and Procedural Fluency
5.3a
Materials explicitly state how the conceptual and procedural emphasis of the TEKS are addressed.
Materials explicitly state how the conceptual and procedural emphasis of the TEKS are addressed.
1 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.
1 out of 2 points
The materials do not explicitly state how the procedural emphasis of the TEKS is addressed. For example, each lesson lists the TEKS and the conceptual learning goal. For example, “Students develop a conceptual understanding of multiplication as area by modeling two-digit products with arrays and area models.” However, the educator must infer how specifically the procedural emphasis is being addressed. The materials do not explicitly state how the procedural emphasis of the TEKS is addressed.
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 materials include questions and tasks that provide opportunities for students to use abstract models as required by the TEKS. For example, students estimate sums and differences using benchmark fractions such as one whole or one half. Students also use numeric expressions and formulas to calculate area and perimeter.
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
The materials include supports for students in connecting concrete and representational models to abstract (symbolic/numeric/algorithmic) concepts, as required by the TEKS. For example, students use fraction circle models to label fractions and discuss questions with their group.
The materials include supports for students in creating concrete and representational models to abstract (symbolic/numeric/algorithmic) concepts, as required by the TEKS. For example, students use paper strips divided into ninths for their activity on decomposing fractions.
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 using visuals, manipulatives, or other language development strategies. For example, “Appendix C” contains a “Strategies for Teaching Vocabulary” section that explains strategies such as using pictures and diagrams and includes fill-in-the-blank pages based on sets of TEKS.
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
The materials include embedded educator guidance to scaffold and support students’ use of academic mathematical vocabulary in context when communicating with peers and educators. For example, “Appendix C” contains a “Strategies for Teaching Vocabulary” section that explains strategies such as using pictures and diagrams; using spiral review; providing active engagement opportunities such as role-play or vocabulary games; and using formative feedback, educator modeling, and think-alouds.
The materials include embedded guidance to scaffold, support, and extend the use of academic math vocabulary, including communication targets, key vocabulary, sentence frames, precise language, peer conversation guidance, and anticipated responses with exemplars and redirection.
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
The materials include embedded guidance to facilitate mathematical conversations, allowing students to refine and use math language with peers within the “Academic Vocabulary and Mathematical Discourse Support” section using the “Hear-Refine-Use” routine For example, a student is given a sentence stem, such as “What evidence shows __?” Their partner has to revise the statement with precise mathematical language.
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 materials include embedded guidance to support and/or redirect inaccurate student responses. For example, the 4th Grade Math Implementation Guide has a section called “Anticipated Responses, Exemplar, and Redirection” that is specific to student lessons and problems, guiding the educator in quickly assessing understanding or strategies to support struggling students and in targeting instruction.
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 align instruction with the TEKS process standards. For example, the 4th Grade Math Practice Book Teacher Edition includes a “Process Standards” table that indicates which standards the TEKS lesson covers. For example, 4.2A includes 4.1A, 4.1B, 4.1F, and 4.1G.
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 4th Grade Math Implementation Guide is the same and only states the process standards as they relate to the sections “Guided Practice,” “Partner Practice,” and “Independent Practice.” However, it does not state 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 materials include a “Unit Rationale” section that provides a generic statement of how students will apply the process standards. For example, one unit states, “Throughout the unit, students apply the mathematical process standards by analyzing relationships, representing problems with models and equations, and communicating mathematical reasoning.”
Rubric Section 6
Productive Struggle
Materials support students in applying disciplinary practices to productive problem-solving, including explaining and revising their thinking.
Total
79% (15 out of 19 points)
Evaluation for 6.1a
The materials provide opportunities for students to think mathematically and to make sense of mathematics. Lessons include visual supports to help students organize their thinking and ask questions that require reasoning, as well as opportunities for students to review their work. For example, in a lesson about rounding, students use information from a table to label the ten thousands and one thousands on given number lines and then explain using, “What patterns do you notice?” before rounding the number 658,319. They also discuss with peers and explain their thinking, while the educator is guided to create an anchor chart for the class.
The materials do not provide opportunities for students to persevere through solving problems. For example, in a lesson about multiplication, a problem is shown using the strategies of mental math, partial products within an area model, and the standard algorithm given as fill-in-the-blanks. However, students do not have to show and use their own choice of strategy to engage in productive struggle.
Evaluation for 6.1b
The materials support students in understanding and explaining that there can be multiple ways to solve problems and complete tasks. The materials provide problem-solving processes and questions that prompt students to make connections between strategies and explain their mathematical thinking. For example, in “Engaging Activity: Solving with Fluency,” students solve related problems and respond to the question, “How does your answer from Problem 1 help you solve Problem 2?” Students also answer, “Why or why not?” after determining whether eight students can equally share 46 oranges. These prompts require students to explain their thinking and make connections between problems and solution processes.
The materials do not support students in justifying that there can be multiple ways to solve problems and complete tasks. The materials include prompts such as “How does your answer from Problem 1 help you solve Problem 2?” and “Why or why not?” These questions ask students to explain their reasoning for a particular problem or solution. They do not ask students to justify the validity of multiple approaches, defend why different strategies can correctly solve the same problem, or support why one strategy may be appropriate compared with another.
Evaluation for 6.1c
The materials provide structured practice opportunities for students to do math with peers and educators to make sense of mathematics. Educators use guided practice to check for understanding and determine readiness before transitioning students to independent work.
The materials require students to make sense of mathematics through multiple opportunities for students to do and discuss math with peers and/or educators. All students engage in “Partner Practice” to work through math problems with a peer. “Facilitating Questions” and other prompts within the “TEKS Lesson” ensure that students discuss the lesson’s focus skill. For example, in the 4.4D lesson, students work in small groups to write the factors of a multiplication problem, discuss as a whole class how the numbers could be arranged for easier mental calculation, and then work with a partner to find a missing partial product and share answers with the group.
The materials require students to make sense of mathematics through multiple opportunities for students to write about math with peers and/or educators. For example, in a lesson on financial literacy, students write a response to the question: “Explain your answer to question 1, listing the advantages and disadvantages of each choice.”
Evaluation for 6.2a
The materials support educators in guiding students to share their problem-solving approaches, including explanations and arguments. For example, in lesson 4.4D, students discuss with a partner how to find the missing partial products and share their answers with the whole group. Students also work in pairs to examine the examples for Cami’s problem and respond to questions.
The materials do not support educators in guiding students to reflect on their problem-solving approaches, including justifications. For example, in a lesson about division strategies, students examine partial quotients, properties, and mental math fill-in-the-blank strategies, and then they solve a problem as a group. Volunteers share their fill-in-the-blank answers and thinking, but students do not think critically about their own reasoning, even though reflection involves evaluating, revising, or considering their math thinking.
The materials do not support educators in guiding students to share their problem-solving approaches through justifications. For example, the 4.4D facilitating question asks, “What are some strategies for multiplying a 2-digit number by a 2-digit number, or a 4-digit number by a 1-digit number?” However, it does not require students to provide reasoning for why a strategy is valid.
Evaluation for 6.2b
The materials include prompts to support educators in providing explanatory feedback based on student responses. The “Facilitating Questions” section of every lesson includes questions and exemplar answers that students should respond to. However, the materials do not include prompts to support educators in providing feedback based on anticipated misconceptions. For example, one lesson includes the prompt “What is the relationship between multiplying by 10 and 100 in our number system?” Then, the exemplar student response is “Our number system is based on 10, so when you multiply by 10 or 100, you are changing the place value of the number.”
The materials do not include guidance to support educators in providing explanatory feedback based on anticipated misconceptions. For example, every lesson includes a “Misconceptions” section with guidance for educators on anticipating misconceptions related to the lesson’s skill focus. The 4.4E lesson “Misconceptions” section states, “Students may not understand how to use a model to represent a division problem . . . model a multiplication problem using base tens and record the division problem that is also being represented . . . relate the area of the model to the quotient.”
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.
2 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.
2 out of 3 points
The materials do not provide opportunities for students to persevere through solving problems. For example, in a lesson about multiplication, a problem is shown using the strategies of mental math, partial products within an area model, and the standard algorithm given as fill-in-the-blanks. However, students do not have to show and use their own choice of strategy to engage in productive struggle.
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.
2 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.
2 out of 3 points
The materials do not support students in justifying that there can be multiple ways to solve problems and complete tasks. The materials include prompts such as “How does your answer from Problem 1 help you solve Problem 2?” and “Why or why not?” These questions ask students to explain their reasoning for a particular problem or solution. They do not ask students to justify the validity of multiple approaches, defend why different strategies can correctly solve the same problem, or support why one strategy may be appropriate compared with another.
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
The materials require students to make sense of mathematics through multiple opportunities for students to do and discuss math with peers and/or educators. All students engage in “Partner Practice” to work through math problems with a peer. “Facilitating Questions” and other prompts within the “TEKS Lesson” ensure that students discuss the lesson’s focus skill. For example, in the 4.4D lesson, students work in small groups to write the factors of a multiplication problem, discuss as a whole class how the numbers could be arranged for easier mental calculation, and then work with a partner to find a missing partial product and share answers with the group.
The materials require students to make sense of mathematics through multiple opportunities for students to write about math with peers and/or educators. For example, in a lesson on financial literacy, students write a response to the question: “Explain your answer to question 1, listing the advantages and disadvantages of each choice.”
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, and justifications.
Materials support educators in guiding students to share and reflect on their problem-solving approaches, including explanations, arguments, and justifications.
4 out of 6 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, and justifications.
4 out of 6 points
The materials do not support educators in guiding students to reflect on their problem-solving approaches, including justifications. For example, in a lesson about division strategies, students examine partial quotients, properties, and mental math fill-in-the-blank strategies, and then they solve a problem as a group. Volunteers share their fill-in-the-blank answers and thinking, but students do not think critically about their own reasoning, even though reflection involves evaluating, revising, or considering their math thinking.
The materials do not support educators in guiding students to share their problem-solving approaches through justifications. For example, the 4.4D facilitating question asks, “What are some strategies for multiplying a 2-digit number by a 2-digit number, or a 4-digit number by a 1-digit number?” However, it does not require students to provide reasoning for why a strategy is valid.
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.
4 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.
4 out of 4 points
The materials do not include guidance to support educators in providing explanatory feedback based on anticipated misconceptions. For example, every lesson includes a “Misconceptions” section with guidance for educators on anticipating misconceptions related to the lesson’s skill focus. The 4.4E lesson “Misconceptions” section states, “Students may not understand how to use a model to represent a division problem . . . model a multiplication problem using base tens and record the division problem that is also being represented . . . relate the area of the model to the quotient.”