Step Up to the TEKS Algebra I Practice

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.

The materials are organized by the Texas Essential Knowledge and Skills (TEKS) requirements and grouped into coherent domains, with the table of contents in the Practice Book and Appendix A of the Implementation Guide connecting lessons to the TEKS, while the English Language Proficiency Standards (ELPS) are reflected in the Teacher Edition (TE) front matter. This organizational structure helps educators understand the progression of mathematical concepts to make vertical connections between prerequisite learning and Algebra II.

The materials include a Rationale for Learning Paths across grade levels for vertical alignment. For example, the Algebra I Implementation Guide identifies connections between prior learning and Algebra II, supporting an understanding of how mathematical concepts develop vertically through connections between prerequisite learning, Algebra I content, and subsequent mathematics learning

The materials do not include a Rationale for Learning Paths within the same grade level (horizontal alignment) as designed in the materials. The materials provide structures to support instructional planning, monitoring, and implementation, including diagnostic guidance, instructional responses, lesson-planning procedures, and leadership supports. While these features support continuity across grade levels and implementation of the Algebra I curriculum, the materials do not establish horizontal alignment across the Algebra I standards.

Evaluation for 1.1b
Materials include an implementation guide with usage recommendations and strategies for effective educator use, such as just-in-time supports, advanced learning, or as a course.

The materials include an Implementation Guide with Usage Recommendations and effective strategies for educators to use in various contexts, such as “just-in-time” supports, to support advanced learning or throughout the course. For example, the lesson structure includes the TEKS Instruction, guided practice, partner practice, independent practice, and activity components. Each component includes suggested instructional time ranges for each section.

The materials provide Usage Recommendations for adapting the materials to meet student needs in various instructional contexts and include strategies for effective educator practices across multiple settings. For example, the Algebra I Implementation Guide breaks each lesson into two pathways: the Practice Book and the TEKS-tivity. Each lesson includes a table that describes each pathway and details the time for each component or activity. These components also include a suggested grouping type that varies throughout the pathway.

Evaluation for 1.1c
Materials include a TEKS correlation guide with recommended skill entry points based on diagnostic assessment results.

The materials include a TEKS Correlation Guide. For example, the table of contents and the Program Overview section of the Implementation Guide provide direct connections between Algebra I topics, the TEKS, and supplemental practice focus areas. Additionally, the Instructional Design section outlines a flexible lesson structure that includes guided practice, partner practice, independent practice, engaging activities, intervention, and extension opportunities. Educators can select specific lesson components for targeted reteaching, small-group instruction, review, or additional independent practice.

The materials provide additional guidance for instructional planning and differentiation through the Algebra 1 Math Practice Teacher Edition and Implementation Guide. Teacher lesson pages identify the relevant TEKS, vertical alignment, and lesson-specific instructional information. Guided Practice and Partner Practice include facilitating questions, while Independent Practice identifies important concepts, extension opportunities, and potential misconceptions to support teachers in planning responsive instruction. Additionally, the Item Map included in the unit overview identifies skill entry points based on diagnostic assessment results and provides recommended responses and TEKS-level decision rules.

Evaluation for 1.1d
Materials include protocols with corresponding guidance for unit and lesson internalization.

The materials include protocols with corresponding guidance for unit internalization. The materials provide processes to help educators understand and prepare to teach lessons thoroughly. The unit overview includes a unit rationale, big ideas, background knowledge, and instructional notes to support all learners, along with other required materials. The unit overview also includes an internalization protocol to guide educators as they prepare each lesson.

The lesson overview includes the TEKS statement, student objective, conceptual goal, procedural goal, lesson overview with grouping recommendations, process standards connections, academic vocabulary and mathematical discourse support, and oral and written discourse supports for emergent bilingual students. Additionally, the overview provides a sample unit with the lessons.

Evaluation for 1.1e
Materials include resources and guidance for instructional leaders to support educators with implementing the materials as designed.

The materials include implementation and instructional guidance and recommendations to help educators use the supplemental resource as designed. The Program Overview and Instructional Design sections describe the intended instructional uses, including tier 1 reinforcement, intervention, small-group instruction, independent practice, and review cycles. Additionally, the Algebra I TEKS Checklist provides a thorough breakdown of each standard presented in the lessons and is available to educators and instructional leaders.

The unit-level internalization materials, found in the Implementation Guide, include resources and guidance for administrators. Additionally, the “Leadership Lens” section sample for unit 1 provides further implementation guidance for administrators.

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.

The materials include detailed lesson plans with learning objectives aligned with the TEKS and ELPS, along with materials for educators and students, lesson components, and suggested time frames. For example, lessons include learning objectives, conceptual learning goals, and vertical alignment connections. Additionally, the lessons provide educator guidance, student materials, and structured lesson components with suggested instructional timeframes.

The materials include structured lesson components and educator-facing supports to assist in instructional planning and implementation. For example, each lesson’s educator pages provide relevant information to help educators prepare. Each TEKS lesson includes the TEKS information, vertical alignment, and ELPS. The lesson also provides lesson information, including the conceptual goal, along with timing information. The materials also include facilitating questions, important concepts, extension opportunities, and misconceptions to support lesson preparation and delivery.

The materials do not include assessment resources aligned with the TEKS or assessment resources aligned with the ELPS. The beginning of each lesson includes a list of the ELPS; however, it is unclear how the ELPS connect throughout the lesson or assessments.

Evaluation for 1.2b
If designed to be adaptive, materials include detailed lesson overviews with learning objectives, lesson components with suggested timeframes, and assessment resources aligned with the TEKS and ELPS.

This guidance is not applicable because the program is not designed to be adaptive.

This guidance is not applicable to the program.

Evaluation for 1.2c
Materials contain support for families in Spanish and English for each unit, with suggestions on supporting the progress of their student(s).

The materials do not include Spanish and English support for families for each unit, with suggestions for supporting their student(s) ‘ progress. The materials do not include family-facing guidance, home support suggestions, communication tools, or resources specifically designed to support family involvement in monitoring student progress or reinforcing learning at home.

The materials include supports educators can use to strengthen communication with families, such as academic vocabulary, visual models, and structured discussion opportunities. These supports reinforce student learning outside the classroom. However, the materials do not contain resources to support families.

Evaluation for 2.1a
Materials include the definition and intended purpose for the types of instructional assessments.

The Teacher Guide Practice Book overview lists each component of the book along with its intended use within the program. This includes guided practices, partner practices, independent practices, and engaging activities. The unit Assessment Overview defines the materials and their purpose, identifies the primary instructional instrument, and includes a “How Teachers Use the Evidence” section for each assessment type.

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
Materials include guidance to ensure consistent and accurate administration of instructional assessments.

The Teacher Edition introductory pages include guidance in the “To the Teacher” section explaining the intended use of the assessment components and identifying them as formative assessments. While the materials provide embedded administration guidance within the lessons, they offer limited front-matter guidance on broader expectations or procedures for administering instructional assessments consistently across settings.

The partner practice and independent practice sections include separate directions for the educator that support the implementation of each assessment activity. The guidance addresses instructional facilitation, such as grouping and delivery, while the embedded directions and facilitating questions within each activity support the administration.

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.

The digital assessment materials correspond to the printable versions available in the Practice Student Edition (SE). For example, the assessments available on the digital platform mirror those included in the printable Practice Student Edition. However, educators cannot print the assessments directly from the digital platform and must access the printable Practice SE instead.

The digital platform includes assessment accommodations for educators to 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 assistive technology, translation accommodation (English only), and content and language supports for assessment activities. However, the content and language supports are available only for the assessment items and are not available for practice activities.

Evaluation for 2.1d
Materials include diagnostic assessments with TEKS-aligned tasks or questions, including interactive item types with varying complexity levels.

The materials include interactive assessments with varying complexity levels. The Item Map in the Implementation Guide provides the associated level (extended practice/bridge/grade level) along with the target TEKS and diagnostic look-fors. Many questions are lower-level to establish a baseline, but the assessment includes several higher-level options and multiple question types. For example, the diagnostic assessment includes text entry, drag-and-drop, selection table, and multiple-choice questions.

The “Scoring and Instructional Response” section provides educators with strategies for responding to diagnostic assessment results for students at various levels. The “How Teachers Use the Evidence” section on the opposite page in the unit Assessment Overview also provides ways to respond to students who have not yet reached proficiency.

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.

The materials include formative assessments with interactive question types incorporating varying complexity levels. For example, within TEKSnology.com, Reporting Category 2 has TEKS-aligned questions with more than two unique interactive item types. This assessment is TEKS-aligned with multiple interactive question types, including multiple choice, text entry, multiselect, inline choice, and match table grid.

The materials include guided and partner practices, listed as formative assessments with TEKS-aligned tasks, questions, or interactive item types with varying levels of complexity. Within the digital platform, TEKSnology.com, Reporting Category 1 has TEKS-aligned questions with more than two unique interactive item types. This assessment is TEKS-aligned with non-interactive item types such as multiple choice, inline choice, and text entry.

Evaluation for 2.2a
Instructional assessments include scoring information and guidance for interpreting student performance, including rationale for each correct and incorrect response.

The instructional assessments do not provide scoring information, guidance for interpreting student performance, or rationales for incorrect responses. For example, the educator pages for each independent practice include answers displayed on the student edition inset. Sidebar callouts identify the key concepts addressed by each question. These independent practice activities reinforce skills rather than serve as formal instructional assessments.

TEKSnology.com provides multiple ways for educators to track students’ performance. Educators view individual assignments with the results in the Gradebook under “Assignments—Graded.” The materials provide various reports, including course and standards reports, that show results by assignment or TEKS and filter down to the individual student. Educators navigate to assignments with feedback included, along with class averages compared with individual students. Educators access information about each question by hovering over individual student scores. However, the materials do not provide a rationale for correct or incorrect answers.

Evaluation for 2.2b
Materials provide guidance for the use of included tasks and activities to respond to student trends in performance on assessments.

The materials do not provide guidance for the use of included tasks and activities to respond to student trends in performance on assessments. For example, the “Implementation Guidance” section of the Implementation Guide provides various methods for implementation of the materials within the “Practice Book.”

The Using the Practice Book for Small Groups and Intervention segment discusses the different options available to educators for targeted use of the materials with students at various levels. The materials do not provide explicit guidance for educators on how to respond to trends in student assessment performance.

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.

The materials include tools that help educators track student progress and growth through TEKSnology.com reporting features. Educators can access Course and Standards Reports that display student results by assignment or TEKS and filter the data to review individual student performance. Educators can also print and share these reports with students to communicate assessment results and support discussions about academic progress.

While TEKSnology.com provides educators with reports to monitor student performance, the materials do not include student-facing tools that allow students to independently track their own progress and growth. Students cannot directly access the reporting features to monitor performance over time, identify trends, or compare results across assessments. Instead, students rely on educators to share and explain their performance data through printed reports.

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.

The materials do provide prompts and guidance to support educators in conducting frequent checks for understanding at key points throughout each lesson or activity. For example, the TEKS lessons include instructions that walk educators through the lesson, along with key points and strategies. They also provide insight into what educators should look for during lessons and discussions.

The guided and partner practices include directions for implementing this part of the lesson. They also include facilitating questions to help the educator better monitor students’ progress and their ability to grasp the concept.

Evaluation for 2.2e
If designed to be adaptive, materials provide frequent checks for understanding at key points throughout each lesson or activity.

This guidance is not applicable because the program is not designed to be adaptive.

This guidance is not applicable to the program.

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.

The materials include explicit guidance for educators on lessons or activities scaffolded for students who have not yet reached proficiency in the prerequisite or grade-level concepts and skills. Each lesson provides guidance for misconceptions as well as the rationale behind each question. The Scoring and Instructional Response provides strategies for responding to the results of the diagnostic assessments for students at various levels. The “How Teachers Use the Evidence” section in the Unit Assessment Overview on the opposite page also provides ways to respond to students who have not yet reached proficiency.

The Scoring and Instructional Response provides strategies for responding to the results of the diagnostic assessments for students at various levels of proficiency. The “How Teachers Use the Evidence” section in the unit Assessment Overview on the opposite page also provides ways to respond to students who have not yet reached proficiency.

Evaluation for 3.1b
Materials include explicit educator guidance for language supports, including pre-teaching and embedded supports for developing academic vocabulary and unfamiliar references in text.

The materials include pre-teaching supports for developing academic vocabulary through unit vocabulary lists, word banks, vocabulary activities, and blackline masters aligned to the TEKS concepts for each unit. The vocabulary activities also include embedded supports within the instructional materials for developing academic vocabulary. The activities support ongoing vocabulary development and reinforce academic language throughout the lesson sequence.

The materials do not include explicit educator guidance for language supports, including pre-teaching and embedded supports for unfamiliar references in the text. For example, while the Teacher Edition includes blackline masters of vocabulary activities to use as part of the lessons, the materials do not include pre-teaching and embedded supports to help educators decode unfamiliar references in the text.

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.

Every independent practice activity includes an “Extension Learning Opportunity” section with opportunities to extend the lesson for those who need extended practice.

For students demonstrating proficiency, the enrichment and extension activities give them opportunities to explain multiple strategies, create mathematical problems, apply concepts to real-world scenarios, and compare solution methods. The materials also include educator guidance for implementation, including identifying extension opportunities in the Implementation Guide and recommending extension activities for advanced learners.

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.

Students can access and use the basic calculator tool by clicking the corresponding calculator image.

The materials include text-to-speech and other content and language supports that educators can enable or disable to support individual students. For example, the text-to-speech tool becomes functional when users first highlight the desired text. Users then select the “speak” option. The materials also include other content and language supports, such as a dictionary that appears when a word is highlighted, along with additional 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
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.

The Implementation Guide supports educators within the dedicated extension settings.

The materials include multiple problem-solving options and online support. For example, the digital materials include interactive exercises, video explanations, and real-world applications.

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.

The materials include explicit, direct prompts and guidance for educators to build knowledge by activating prior knowledge, anchoring big ideas, and highlighting and connecting key patterns and relationships through multiple representations. For example, the materials activate prior knowledge through TEKS lesson discussions, review of coordinate plane vocabulary, and previously learned concepts such as quadrants, ordered pairs, the x-axis, and the y-axis. The materials anchor big ideas through “Conceptual Learning Goals” and “Why do I need to know this?” sections. Key patterns and relationships are highlighted through repeated use of coordinate plane models, ordered pairs, signs, and quadrant structure, and by connecting ordered pairs, quadrant location, sign conventions, and movement on the coordinate plane across verbal and graphical representations.

The materials include educator prompts that connect mathematical concepts across multiple representations within the individual TEKS lessons. For example, the TEKS lesson for A.4C guides educators in connecting tables, graphs, and equations to illustrate linear relationships. The TEKS lesson for A.2C connects the slope represented in graphs and equations and suggests using a calculator and table to reinforce those relationships. Similarly, the TEKS lesson for A.8B guides educators in connecting data displayed in a table to a regression equation as another way to represent data.

Evaluation for 3.2b
If designed to be static, materials include educator guidance for effective lesson delivery and facilitation using various instructional approaches.

The materials include guidance for educators to deliver lessons effectively using various instructional approaches. For example, the materials incorporate the TEKS lessons for direct instruction and concept development. Guided Practice sections provide educator-supported instruction, and Partner Practice activities provide opportunities for collaborative learning. Additionally, there are Independent Practice sections, which provide opportunities for individual application and further engaging activities for conceptual exploration and extension.

The lesson guidance further supports facilitation through modeling with manipulatives, discussion prompts, questioning, visual representations, and hands-on activities. For example, the Implementation Guide includes a flow chart that describes lesson delivery using the Gradual Release of Responsibility Model.

Evaluation for 3.2c
Materials include multi-tiered intervention methods for various types of practice and structures and educator guidance to support effective implementation.

The materials include multiple practice structures and instructional groupings that support flexible implementation. The Practice Books include the TEKS lessons, guided practice, partner practice, engaging activities, and further technology-based practice opportunities. The Implementation Guide also describes instructional structures for each phase of the lesson, including individual, partner, educator-led small-group, and whole-group instruction.

The materials do not include educator guidance for implementing instructional supports based on student need. The Implementation Guide describes how to use the Practice Books flexibly across instructional settings and includes TEKS Lessons, Guided Practice, Partner Practice, Independent Practice, Engaging Activities, and technology-based practice. However, the materials do not provide guidance for selecting or adapting these components for targeted instruction. For example, the materials do not include criteria for forming instructional groups, identifying the skills students should address within groups, or selecting specific activities based on student performance. Most educator guidance focuses on lesson facilitation through prompts such as “Ask students” or “Lead a discussion” rather than providing guidance for implementing targeted instructional supports.

Evaluation for 3.2d
Materials include enrichment and extension methods that support various forms of engagement, and guidance to support educators in effective implementation.

The materials do not include enrichment and extension methods that support various forms of engagement or guidance for effective implementation. Although each lesson includes an Extension Learning Opportunity with an additional task for students, the materials do not provide educators with specific instructional strategies or guidance for implementing the activity to support different forms of student engagement.

The materials include general guidance for Enriching Opportunities, suggesting educators explain their understanding using multiple strategies or create their own math problem; however, they do not offer varied ways to engage with the individual lesson content or specific guidance for the educator. For example, in Lesson TEKS A.3E, students use graphing technology or manipulatives to explore transformations of parent functions; however, nothing else helps the educator guide students through the process.

Evaluation for 3.2e
Materials include prompts and guidance to support educators in providing timely feedback during lesson delivery.

The materials support educators in guiding students through discussion questions, observation prompts, and guidance on misconceptions. Additionally, the materials provide educator prompts to direct students to explain reasoning, share strategies, and discuss solutions. For example, the TEKS lessons clearly direct educators to listen to student discussions and observe strategies before engaging in formal instruction. Educators should facilitate class sharing and monitor understanding through discussion. Materials also include feedback guidance through the “Misconceptions” section, which identifies likely student errors and provides instructional responses. The guidance additionally provides lesson directions that describe how educators should conceptualize and check student understanding before progressing.

The Guided Practice and Partner Practice include implementation guidance and questions to help educators monitor students’ progress and understanding. The guidance provides specific details on how long the activities should take, how to follow up, and what misconceptions to watch for. These supports help educators to better guide students and respond to their learning needs during the lesson.

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.

The materials include guidance for educators on providing and incorporating linguistic accommodations for one level of language proficiency (as defined by the ELPS). This guidance encourages students to use increasingly more academic language. For example, the materials provide “Strategies for Teacher Vocabulary” to use with the vocabulary found in Appendix C.

The lesson guide includes a segment titled “The Emergent Bilingual Oral and Written Discourse Support” within the Academic Vocabulary section. This segment provides connection examples, embedded oral discourse guidance, embedded written discourse guidance, and ELPS-sentence stems.

The Algebra I materials provide educator guidance and instructional support during a lesson on graphing ordered pairs. For example, the instructional directions guide educators to review coordinate plane vocabulary, discuss quadrants, and facilitate questions about ordered pairs and graphing. The materials also suggest that students trace clockwise through the quadrants using a finger to reinforce understanding. However, the materials do not include educator guidance for linguistic accommodations aligned to multiple ELPS proficiency levels, such as differentiated sentence stems, word banks, or language supports for emergent bilingual students.

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.

This guidance is not applicable to the program because it is not designed to be adaptive.

Evaluation for 3.3c
Materials include implementation guidance to support educators in effectively using the materials in state-approved bilingual/ESL programs.

The materials include implementation guidance to help educators use the materials effectively in state-approved bilingual/ESL programs. For example, the Supplemental Math Implementation Guide includes a section titled “Supporting Emergent Bilingual Students.” The guide states that the materials support emergent bilingual students through explicit academic vocabulary instruction, visual models and diagrams, structured partner discussions, and opportunities for oral and written explanations. The materials also connect to the Texas ELPS.


The Academic Vocabulary section of the lesson guide used for internalization includes The Emergent Bilingual Oral and Written Discourse Support, which provides connection examples, embedded oral discourse guidance, embedded written discourse guidance, and ELPS sentence stems.

Evaluation for 3.3d
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.

In the Algebra I materials, Strategies for Teaching Vocabulary recommends that students use a variety of tools, including educators modeling mathematical language and using interactive word walls and graphic organizers. Students engage in written discourse through vocabulary journals and vocabulary activities that require them to define and apply academic vocabulary. Students engage in oral discourse through collaborative discussions and opportunities to explain mathematical concepts to develop academic vocabulary. The materials also increase comprehension by connecting mathematics vocabulary to real-world contexts, such as fractions and multiplication.

The Teacher Edition materials include blackline masters for vocabulary activities to use in lessons. This embedded support includes the academic vocabulary for each unit of instruction, helping students build vocabulary and improve comprehension. Strategies for Teaching Vocabulary includes oral and written discourse.

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.

This guidance is not applicable because the program is not designed for dual language immersion (DLI) programs.

Evaluation for 4.1a
Practice opportunities throughout learning pathways (including instructional assessments) require students to demonstrate depth of understanding aligned to the TEKS.

The materials include practice opportunities throughout the learning pathway that require students to demonstrate the depth of understanding aligned to the TEKS. For example, the Practice Book’s quadratic function graphing lessons require students to analyze key features and geometric attributes, apply algebraic constraints across multiple representations, and solve real-world problems. Students use tables, graphs, and contextual situations to extend their understanding beyond identifying key attributes, demonstrating the depth of understanding expected by the TEKS.

The instructional assessments within the learning pathways require students to demonstrate the depth of understanding aligned to the TEKS. For example, Guided Practice and Partner Practice activities give educators opportunities to gather evidence of student understanding during instruction, while Independent Practice tasks allow students to independently demonstrate mastery of the lesson’s TEKS through tasks that reflect the standard’s depth, rigor, and complexity.

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.

The materials include questions, tasks, enrichment, and extension activities that progressively increase in rigor and complexity, leading students to grade-level proficiency in the mathematics TEKS. For example, in the quadratic function and linear inequality lessons, students progress from identifying key features and graphing using multiple representations to analyzing contextual situations and explaining mathematical relationships. Throughout the learning pathway, students move from introductory concepts in the TEKS lesson to increasingly complex applications in practice tasks. The Extension Learning Opportunities activities reinforce grade-level concepts by engaging students in contextual problem solving, such as interpreting quadratic models and applying systems of inequalities to real-world scenarios, supporting mastery of the current grade-level TEKS.

The materials do not include questions, tasks, enrichment, or extension activities that increase in rigor and complexity to lead students to above-grade-level proficiency in the mathematics TEKS. The instructional progression builds from prerequisite knowledge to independent mastery of the grade-level concepts. However, the enrichment and extension activities continue to reinforce the current grade-level standards rather than providing opportunities for mathematical reasoning or content beyond grade-level expectations.

Evaluation for 4.2a
Materials demonstrate coherence across concepts horizontally within the grade level by connecting patterns, big ideas, and relationships.

The materials connect related Algebra I concepts by highlighting mathematical relationships within the course. For example, the TEKS lesson A.12D in the Algebra I Math Practice Student Edition includes a section titled “Why do I need to know this?” that references other Algebra I lessons connected to the current content. The section states, “We use formulas in geometry to find area, volume, etc. We can also use formulas to explain the rule for sequences. Arithmetic sequences are similar to linear equations with a constant rate of change.” The Teacher Edition also includes a Vertical Alignment section for the TEKS A.12D that identifies related Algebra I standards.

The materials build understanding across related Algebra I concepts by connecting patterns to multiple mathematical representations. For example, in the Writing a Formula for a Sequence lesson, students use groups of tennis balls to model the first five terms of an arithmetic sequence, identify the patterns from one step to the next, and write an expression that represents the relationship. The task connects the concrete model to algebraic expressions through the patterns observed in the sequence.

Evaluation for 4.2b
Materials demonstrate coherence vertically across concepts and grade bands, including connections from grades 3–12, by connecting patterns, big ideas, and relationships.

The materials demonstrate clear vertical coherence across concepts and grade bands, including connections from grades K–6, by linking patterns, big ideas, and relationships.

For example, in the Algebra I Math Practice Teacher Edition, the TEKS lesson A.12E includes a section called “Why do I need to know this?” In this section, the materials connect the patterns involved in solving equations. It states, “You started solving equations in 6th grade. You will solve many more in algebra. You learned to solve equations by doing inverse operations, and you will continue to solve equations using the same process. When you solve literal equations, the process is the same, except that most of the values in the equations are variables. Just remember the process is the same.”

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.

The materials demonstrate coherence across lessons or activities by connecting students’ prior knowledge of concepts and procedures to the mathematical concepts they will learn in the current grade level. For example, the Algebra I Practice Book Teacher Edition provides a Facilitating Questions resource to help educators guide lessons to target the individual TEKS. In the Lesson for A.10C, the Facilitating Questions section asks, “How is dividing polynomials similar to long division of real numbers?” This asks students to activate their prior knowledge of division and apply it to the new concept of polynomials at this grade level. However, the materials fail to build on current ideas and concepts for future grade levels.

The materials do not demonstrate coherence across lessons or activities by connecting students’ prior knowledge of concepts and procedures to the mathematical concepts they will learn in future grade levels. For example, in the Algebra I Math Practice Teacher Edition, there is a Vertical Alignment section for each lesson. In the TEKS lesson A.3C, the vertical alignment references the TEKS 7.4B, 8.4C, and 2A.2A, which apply to a future grade level in Algebra 2. However, the materials provide no specific connection between the skills and concepts in the Algebra 2 lesson. The materials do not connect current concepts and procedures to those in future grade levels.

Evaluation for 4.3a
Materials provide spaced retrieval opportunities with previously learned skills and concepts across learning pathways.

The materials do not provide spaced retrieval opportunities with previously learned skills and concepts across learning pathways. As designed, the materials target specific, focused TEKS and provide many opportunities for students to practice these skills in isolation through independent practice, guided practice, and partner practice activities. However, they are not designed to include spaced retrieval opportunities and do not provide tasks or assessments that use this best practice.

In the TEKS A.10A, students engage in various practice opportunities involving addition and subtraction of polynomials. However, the tasks focus exclusively on the current standard. In the Independent Practice task, question 5 requires students to find the sum and difference of two polynomial profit expressions. However, the task does not require students to revisit or retrieve previously learned skills or concepts from earlier learning pathways. While the materials include real-world contexts, they serve only as applications of the current learning rather than opportunities for spaced review. The materials do not provide opportunities for the intentional retrieval of previously learned skills or concepts across learning pathways.

Evaluation for 4.3b
Materials provide interleaved practice opportunities with previously learned skills and concepts across learning pathways.

The materials do not provide interleaved practice opportunities with previously learned skills and concepts across learning pathways. The materials use guided practice, partner practice, and independent practice to provide focused opportunities for the individual TEKS concepts in a nonspiraling approach, rather than revisiting and connecting concepts across learning pathways over time.

The Algebra I Practice Book SE TEKS A.11B lesson introduces exponent rules, provides a reference chart of exponent properties, and then asks students to repeatedly apply those same exponent rules in guided practice, partner practice, and independent practice. Students simplify the expressions, identify equivalent expressions, and solve area problems using exponent operations. However, all the tasks remain focused on the current TEKS. The materials do not ask students to draw upon previously learned concepts from other learning pathways, nor are they required to select from among multiple previously learned strategies or concepts while solving problems.

Evaluation for 5.1a
Questions and tasks provide opportunities for students to interpret, analyze, and evaluate mathematical concepts and complex, real-world situations.

The materials provide questions and other tasks within both real-world and mathematical contexts. For example, students interpret perimeter and area situations represented by polynomial expressions. They analyze mathematical relationships and break down solutions into step-by-step processes. Additionally, they evaluate the validity of the mathematical claims by determining whether the solutions are correct and then justifying their reasoning. The tasks require students to explain why an answer is correct, identify errors, and defend their conclusions. These activities move beyond procedural computation and require students to make mathematical judgments based on evidence.

Students develop a conceptual understanding of polynomial multiplication using area models and real-world contexts. The tasks require students to connect algebraic expressions to geometric representations and analyze how changes in dimensions affect area. Students build a conceptual understanding of functions by analyzing tables, graphs, and ordered pairs to determine whether relationships meet the definition of a function. The tasks involving structure and relationships emphasize students’ ability to reason rather than memorize.

Evaluation for 5.1b
Questions and tasks provide opportunities for students to create concrete models and representations of mathematical situations.

The Teacher Edition materials direct students to use algebra tiles and area models to model polynomial operations, including multiplication, factoring, and the distributive property. Students also create mathematical representations by writing polynomial expressions, equations, and area models to represent real-world situations involving perimeter and area. Students then construct their own models and representations, rather than simply interpreting the examples in the materials.

The questions and tasks give students opportunities to create concrete models and representations of mathematical situations. For example, in the Algebra I Practice Teacher Edition, there is a Difference of Squares activity in Appendix A. In this activity, students create an area model using algebra tiles to represent the polynomials and their factors.

Evaluation for 5.1c
Questions and tasks provide opportunities for students to apply conceptual understanding to new problem situations and contexts.

Students extend their understanding of polynomial operations beyond procedural practice by applying concepts to real-world scenarios involving perimeter, area, playground dimensions, and geometric models. Students also use algebra tiles, area models, and polynomial reasoning to solve unfamiliar tasks and justify solutions, requiring them to transfer their conceptual understanding to new contexts rather than simply repeat previously demonstrated procedures.

In the Algebra I Practice Teacher Edition, the guidance for the TEKS lesson “Adding and Subtracting Polynomials” gives students opportunities to apply conceptual understanding to a new problem situation. The educator guidance provided for the lesson prompts the educator to ask the students how they would usually find the perimeter of the shape if the side lengths were whole numbers. Students then discuss how they would apply that process to the current problem using polynomials. This progression lets students apply conceptual understanding and build on prior knowledge.

Evaluation for 5.2a
Materials provide tasks that are designed to build student automaticity and fluency necessary to complete grade-level mathematical tasks.

Students engage in multiple opportunities that require repeated application of polynomial functions and the distributive property. These structured practice opportunities help students develop efficiency and accuracy while also promoting the flexible use of mathematical procedures and concepts across multiple problem types and representations.

In the Algebra I Practice Teacher Edition, the TEKS Factoring Trinomials lesson builds fluency by giving the educator prompts to review a number’s factors. The “Important Concepts” section provides additional review and highlights how it may affect students’ ability to master the grade-level task.

Evaluation for 5.2b
Materials provide opportunities for students to practice the application of efficient, flexible, and accurate mathematical procedures throughout learning pathways.

Students solve polynomial operations using multiple methods and representations, including symbolic procedures, area models, and algebra tiles. This framework promotes flexibility in problem solving. A variety of practice activities provide repeated opportunities to develop efficiency. Additionally, guided educator materials, including facilitating questions and misconception supports, help students refine procedures and improve their accuracy.

In the Algebra I Practice Teacher Edition, the TEKS Factoring Trinomials lesson guides educators on different strategies for factoring trinomials. This list includes “guess and check,” “the box method,” “split the middle term,” and algebra tiles. Throughout the lesson, the educator does not provide specific guidance requiring students to use a particular method. Instead, students can practice whatever they deem most efficient, flexible, or accurate.

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.

The materials provide students with opportunities to justify their reasoning, identify errors, and determine whether solutions are accurate. For example, in the Guided Practice for TEKS A.2.B, Facilitating Question 2 asks, “How can you determine if a point is a solution to a function?” The sample response explains checking by substitution or by graphing the point and line. This explicitly asks students how to verify a solution’s accuracy.

The materials provide students with opportunities to practice flexibility through learning pathways. For example, in the activity "Solving Quadratic Functions,” the material asks students to sort quadratic equations according to their likely solution method—completing the square, square roots, factoring, or the quadratic formula—and then directs them to “Choose one equation that could reasonably be placed in two categories. Compare the methods and defend your preferred method.” This explicitly requires students to evaluate alternative strategies for the same equation and justify their selection, supporting flexibility in problem-solving approaches.

The materials provide students with opportunities to practice efficiency through learning pathways. For example, in the Engaging Activity "Definition of a Function", question 4 states “Which representation makes it easiest to determine whether a relation is a function? Explain.” After using ordered pairs, tables, graphs, and verbal representations, students must evaluate which representation makes the task easiest and justify their choice. This directly supports evaluating representations for efficiency.

Evaluation for 5.2d
Materials contain guidance to support students in selecting the most efficient approaches when solving mathematics problems.

The Teacher Edition provides educators with guidance in many areas. However, it does not include guidance for supporting students in selecting more efficient approaches to solving mathematical problems. In the TEKS Factoring Trinomials lesson, the “Misconceptions” section suggests that students need multiple strategies for factoring, but they do not provide guidance for fostering this type of thinking. They also do not include questions that prompt students to analyze a problem and determine the most efficient factoring strategy.

The materials provide guidance for educators, practice opportunities for students, and support for developing procedural understanding. However, the materials do not guide students to select more efficient approaches for solving mathematical problems. While the materials include facilitating questions, important concepts, and misconception supports, they do not explicitly direct students to compare strategies or evaluate and select more efficient solution methods throughout the learning pathway.

Evaluation for 5.3a
Materials explicitly state how the conceptual and procedural emphasis of the TEKS are addressed.

The materials explicitly address and state both the conceptual and procedural emphasis of the TEKS. Each lesson identifies the TEKS and includes an “Important Concept” section. That section explains the underlying learning objectives, such as combining like terms, polynomial operations, or the structure of polynomial expressions. The lessons also provide students with step-by-step instruction through various practice activities. These encourage students to develop the procedures necessary to perform the required polynomial operations.

The wrap-around lesson overview in the TEKS Factoring Trinomials lesson suggests that educators should discuss the factors of a familiar number to build students’ conceptual understanding of factoring. This foundational understanding then extends to factoring polynomials and eventually progresses to special cases, such as perfect square trinomials, as stated in the Conceptual Learning Goal. Facilitating Questions also asks students how algebra tile models connect to polynomials, further emphasizing the conceptual and procedural connections.

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.

The educator guidance in the Algebra I Practice TE correlates with the specific TEKS of each lesson, listed in the Conceptual Learning Goal. Here, educators clearly state how the lesson will address the TEKS, both conceptually and procedurally. For example, in the TEKS Multiplying Polynomials lesson, the Conceptual Learning Goal for TEKS A.10B states, “Students learn how the distributive property and area models can be used to multiply binomials and other polynomials of degree one and two.” The area model supports conceptual understanding of the TEKS and helps students apply procedural skills.

Students use multiple building blocks and methods of representation to model and analyze mathematical relationships. These include tables, graphs, coordinate sets, algebraic expressions, and equations. The tasks require students to connect visual and symbolic representations to develop an understanding of functions and polynomial concepts.

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.

In the Teacher Edition, the materials require students to connect algebra tiles and area models to symbolic polynomial operations. This helps them to bridge concrete and representational models with abstract expressions and algorithms. Students create models using algebra tiles and area representations and then translate those models into symbolic polynomial expressions and solutions. Tasks also require students to explain their reasoning and justify how the models represent polynomial operations. This supports students in learning how to define and explain both concrete and representational models in relation to abstract mathematical concepts.

In the Algebra I Practice Teacher Edition, the Transformations of the Parent Function engaging activity allows students to connect changes in the graph to the corresponding equations. Then, students must explain what they noticed about the parent graph when other terms are applied.

Evaluation for 5.4a
Materials provide opportunities for students to develop academic mathematical language using visuals, manipulatives, or other language development strategies.

The Algebra I Practice Teacher Edition provides multiple opportunities for students to develop mathematical language. In the TEKS Multiplying Polynomials lesson, students apply their previous knowledge of area to related concepts. Students use visuals of known shapes like rectangles and triangles to represent the area formula. During the lesson, students practice the new concept of multiplying polynomials. The lesson introduction provides a rectangle to demonstrate area models and develops academic language. Students participate in a discussion regarding the methods used.

In the Algebra I Practice Teacher Edition, the TEKS Factoring Trinomials lesson requires students to use algebra tiles and area models to represent trinomials and determine each model’s dimensions. As students connect the visual representation to symbolic expressions, they develop and apply academic vocabulary such as trinomial, factor, product, and area model while explaining relationships among the representations. The combination of manipulatives, visual models, and mathematical discussion supports students’ development of precise mathematical language in meaningful contexts.

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.

The Teacher Edition includes embedded educator guidance that scaffolds students’ use of academic mathematical vocabulary during instruction. The lesson directions encourage educators to discuss mathematical concepts using number lines, while the Guided Practice facilitation questions prompt students to explain mathematical relationships using the appropriate terminology. The materials also identify key concepts and common misconceptions to help educators reinforce precise vocabulary throughout the lesson.

Each lesson internalization guide includes sections to support academic vocabulary and mathematical discourse. These provide communication targets, key vocabulary, sentence frames, and precise language supports. Additionally, they provide peer conversation guidance and anticipated responses with exemplars and redirection. These are available for every lesson and embedded in the lesson guide for internalization.

Evaluation for 5.4c
Materials include embedded guidance to support student application of appropriate mathematical language and academic vocabulary in discourse.

The materials include embedded guidance to help students apply appropriate mathematical language and academic vocabulary in discourse. Each Lesson Guide used for internalization contains Academic Vocabulary and Mathematical Discourse Support. Embedded Oral Discourse Guidance and Embedded Written Discourse Guidance provide educators with appropriate vocabulary support for students to use in written and oral discourse. This section also supports comprehension, background building, and cross-linguistic connections. These are available for every lesson embedded in the Lesson Guide for internalization.

The materials guide educators to model precise academic language and help students replace vague words with specific mathematical terms. For example, the materials include guidance on asking students to restate their thinking using more accurate language without changing the meaning.

Evaluation for 5.4d
Materials include embedded guidance to facilitate mathematical conversations allowing students to hear, refine, and use math language with peers.

The materials include embedded guidance to facilitate mathematical conversations, allowing students to hear math language with their peers. For example, the introduction of the Teacher Edition, titled “To the Teacher,” provides partner practice opportunities that direct educators to invite the students to work in pairs to complete the activity. This activity allows students to hear and use math language with their peers.

In the Academic Vocabulary and Mathematical Discourse Support, Precise Language and Peer Conversation section, embedded guidance supports mathematical conversations. The section provides precision guidance for educators on what to listen for in the lesson, a hear-refine-use routine for students to use with their peers, and educator prompts to facilitate conversations.

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.

The materials include embedded guidance that helps educators anticipate student thinking. The guidance includes important concepts, common misconceptions, educator notes, and facilitating questions. These supports identify common misconceptions, provide exemplar responses, and provide educators the opportunity to predict likely student thinking during instruction. For example, TEKS A.10E includes educator guidance to prompt discussion about why a student’s solution is partially correct, while the embedded notes highlight key concepts and anticipated misconceptions.

The “Anticipated Responses, Exemplar, and Redirection” section in Academic Vocabulary and Mathematical Discourse Support includes embedded guidance to anticipate correct, partial, or inaccurate responses. It also provides an exemplar and an example of a likely student inaccuracy. The support/redirect also provides guidance for how educators can respond with next steps.

Evaluation for 5.5a
TEKS process standards are integrated appropriately into the materials.

The materials integrate the TEKS process standards by engaging students in problem-solving, representation, and reasoning tasks. For example, in the TEKS Multiplying Polynomials lesson, students demonstrate the mathematical construct of area. Students use algebraic expressions, determine products, and justify whether their conclusions about changes in area are reasonable. In the TEKS Writing Linear Equations from Multiple Representations lesson, students interpret graphs, tables, and equations to identify linear relationships and connect multiple representations. These activities embed the process standards within the content instruction by requiring students to represent mathematical ideas, analyze relationships, and communicate mathematical reasoning in meaningful contexts.

The materials integrate the TEKS process standards through engaging activities that require students to apply mathematical reasoning, representation, and communication in authentic contexts. For example, in the Exponential Growth and Decay engaging activity, students create exponential functions on coordinate planes. Students use specified attributes and represent the relationships graphically. During the activity, students organize and record mathematical information, interpret representations, and communicate their reasoning while applying grade-level algebraic concepts. The TEKS process standards are embedded throughout the learning experience.

Evaluation for 5.5b
Materials include a description of how process standards are incorporated and connected throughout the learning pathways.

The materials describe how the learning pathways fully incorporate the process standards, but not how they connect. For example, in the grade 6 Math Practice Teacher Edition, there is a section at the beginning of the materials titled “Process Standard.” This section provides educators with the process standards used for each of the TEKS covered in the materials. Although it describes the alignment and incorporation, it does not explain how the process standards connect throughout the learning pathways.

The materials do not describe how the process standards connect to the instruction throughout the learning pathways. For example, the “Incorporation and Connection Through the Learning Pathway” section of each lesson in the Implementation Guide also states the process standards only as they relate to the Guided Practice, Partner Practice, and Independent Practice sections, not how the standards support the lesson’s specific skills and learning objective.

Evaluation for 5.5c
Materials include an overview of the TEKS process standards incorporated into each lesson.

The materials include an overview of the TEKS process standards incorporated into each unit rationale. For example, in the TEKS Adding and Subtracting Polynomials lesson, students apply polynomial operations within contextual situations and communicate solutions using mathematical representations. In the TEKS Laws of Exponents lesson, students apply exponent properties to simplify expressions, interpret geometric contexts, and justify solutions.

The lesson components give students opportunities to engage in mathematical processes throughout instruction. The materials include a unit rationale with a generic statement describing how students will apply the process standards in the unit’s lessons. For example, in the Algebra I Practice Teacher Edition, each lesson includes educator guidance describing the standard covered in the lesson as well as the vertical alignment standards from various grades. Each lesson lists the covered ELPS and describes the conceptual understanding that takes place during the lesson.

Evaluation for 6.1a
Materials provide opportunities for students to think mathematically, persevere through solving problems, and to make sense of mathematics.

The Algebra I Practice Teacher Edition includes guidance for educators in a section titled Facilitating Questions within every lesson. Educators use these questions during guided and partner practice as students collaborate to solve problems. The questions promote mathematical thinking and perseverance by encouraging students to explain their reasoning, analyze mathematical relationships, and make sense of problem-solving strategies. For example, in the Adding and Subtracting Polynomials lesson, students analyze changes in the area of a playground, determine the difference between two expressions, and justify their solutions through error analysis. This task requires students to make sense of the mathematical concepts, evaluate the accuracy of their reasoning, and persevere through multiple steps to reach a solution.

In the TEKS Determining Slope lesson, students analyze equations, tables, graphs, and contextual situations to determine rates of change and interpret slope in meaningful contexts. In the TEKS Parallel Lines and Perpendicular Lines lesson, students investigate relationships between equations, graphs, and geometric properties. This requires them to apply prior knowledge to unfamiliar situations and justify conclusions. Finally, in the TEKS Writing Systems of Linear Equations lesson, students translate verbal descriptions into equations, interpret graphical solutions, and solve real-world application problems involving systems. These varied representations and application tasks help students connect mathematical ideas while building perseverance through increasingly complex problem-solving.

Evaluation for 6.1b
Materials support students in understanding, explaining, and justifying that there can be multiple ways to solve problems and complete tasks.

In the Algebra I Practice Teacher Edition, the TEKS Simplifying Radicals lesson guides educators in modeling two methods for simplifying radical expressions. The guidance prompts educators to “Lead a discussion on which methods the students are more comfortable with. Have them justify their answers.” This guidance supports students in understanding, explaining, and justifying that multiple methods can simplify radical expressions.

In the TEKS Writing Linear Equations from Multiple Representations lesson, students analyze linear relationships presented through graphs, tables, and equations. They then determine which linear function best represents a given situation. Students interpret and connect multiple representations of the same mathematical relationship. This promotes understanding that mathematical ideas can be represented and solved in different ways. The Teacher Guide further emphasizes a gradual release model that includes guided practice, independent application, engaging activities, and extension opportunities. These activities support students in discussing strategies and developing conceptual understanding through multiple approaches. Additionally, the opportunities encourage flexibility in mathematical thinking and support students in explaining and justifying various methods for solving problems.

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.

The materials provide opportunities for students to make sense of mathematics by actively engaging in mathematical tasks. In the Algebra 1 Math Practice Teacher Edition, each lesson includes Guided Practice and Partner Practice sections that encourage students to apply mathematical concepts and solve problems collaboratively. For example, in the Solving Linear Equations in One Variable lesson, students work together to determine and write the sequence of steps needed to solve a linear equation. These activities require students to apply mathematical reasoning, evaluate problem-solving strategies, and demonstrate their understanding through active participation.

The materials provide opportunities for students to make sense of mathematics by writing about mathematical concepts, reasoning, and conclusions. For example, in the Algebra 1 Practice Teacher Edition, the Engaging Activity on Domain and Range of Exponential Functions prompts students to graph functions and write a statement explaining their observations about the domain and range. Additionally, in the Algebra 1 Practice Book Teacher Edition (p. 302), the Engaging Activity on Association and Causation asks students to identify a flaw in a conclusion and explain their reasoning in a written response. The activity provides 10 lines for students to communicate their thinking.

The materials provide opportunities for students to make sense of mathematics through discussions with peers and educators. The Algebra 1 Math Practice Teacher Edition includes Guided Practice and Partner Practice sections that encourage students to collaborate, explain their reasoning, and discuss mathematical concepts. For example, in the Multiplying Polynomials lesson, teacher guidance recommends facilitating class discussions about polynomial multiplication, evaluating the accuracy of solutions, and identifying common errors. Students analyze an incorrect solution and explain how the error may have occurred. These opportunities encourage students to communicate mathematical reasoning, evaluate different approaches, and deepen their understanding through collaborative discussions.

Evaluation for 6.2a
Materials support educators in guiding students to share and reflect on their problem-solving approaches, including explanations, arguments, justifications, and multiple points of entry.

The materials support educators in guiding students to explain their mathematical thinking and communicate problem-solving strategies. For example, in the Algebra 1 Practice Teacher Edition, the TEKS Graphing Quadratic Functions lesson includes facilitating questions that prompt students to explain how to determine x-intercepts, identify minimum and maximum values, and describe how the vertex relates to the characteristics of a quadratic function. Additionally, the TEKS Transformations of the Quadratic Parent Function lesson includes discussion questions that encourage students to explain reflections, stretches, compressions, and translations. These opportunities support students in communicating their mathematical reasoning and explaining their approaches to solving problems.

The materials provide educators with guidance to facilitate mathematical discussions in which students share their solutions and justify their reasoning. For example, in the Algebra 1 Practice Teacher Edition, the TEKS Solving Linear Equations in One Variable lesson directs educators to ask students to complete the first step of a problem, share their answers, and participate in a discussion justifying their responses. Additionally, the Extension Learning Opportunity in the Transformations of the Quadratic Parent Function lesson asks students to create transformed functions and describe the transformations in words. In this activity, students communicate their approaches, provide mathematical justifications, and demonstrate understanding through explanations and discussion.

The materials do not provide explicit guidance for educators to facilitate structured student reflection on problem-solving approaches involving multiple points of entry. Although the Implementation Guide incorporates mathematical discourse, reasoning, and reflection into the instructional framework, the lessons do not consistently include specific reflection prompts or activities that require students to evaluate the effectiveness of their strategies, compare alternative approaches, or reconsider their reasoning after completing a task. While students have opportunities to explain and justify their solutions, the materials do not have instructional guidance for helping students reflect on and evaluate different problem-solving approaches.

Evaluation for 6.2b
Materials include prompts and guidance to support educators in providing explanatory feedback based on student responses and anticipated misconceptions.

The materials include prompts to support educators in providing explanatory feedback based on student responses. For example, in the Algebra 1 Practice Book Teacher Edition, the TEKS lesson “Writing Linear Equations from Multiple Representations” includes instructional prompts that guide educators in asking students to determine slope, identify the y-intercept, and write linear equations. The “Misconceptions” section provides specific suggestions for responding to student errors, including asking students to compare equations written using different points and explain their reasoning. Additionally, the TEKS lesson “Graphing Systems of Linear Functions” includes discussion prompts that ask students to explain why a point represents a solution and evaluate whether points on a line satisfy a system of equations.

The materials include guidance to support educators in providing explanatory feedback based on anticipated student misconceptions. For example, the materials recommend having students use different points to write equations, compare their results, and explain their processes to address these misunderstandings. Additionally, the “Transformations of the Parent Function” lesson identifies anticipated misconceptions involving vertical shifts, horizontal shifts, stretches, and compressions. Teacher notes recommend discussing the similarities between vertical stretches and compressions to clarify these concepts.