Aprendizaje Bluebonnet Matemáticas de Secundaria Grado 6

Evaluation for 1.1a
Materials include a scope and sequence outlining the TEKS, ELPS, and concepts taught in the course.

The materials include a detailed scope and sequence table under "Alcance y secuencia de matemáticas de secundaria grado 6" that breaks down each module. This table highlights how the Texas Essential Knowledge and Skills (TEKS) are introduced in each module and throughout the year. The materials include two scope and sequence tables: one for 150 instructional days and another for 165 instructional days. Each table presents the title of the lesson, a summary of the lesson, the essential ideas, the corresponding TEKS, and the number of instructional days allocated for each lesson. These tables provide a structured overview that supports effective pacing and ensures alignment with the TEKS. The materials include a "Guía de ritmo por temas de matemáticas de secundaria, grado 6 (150 días)" document. This document outlines the scope and sequence and details the TEKS and concepts. The document is organized by module and includes a table that provides the lecture title, a brief summary of daily concepts, the number of instructional days, and short teacher guidance for each day.

Evaluation for 1.1b
Materials include suggested pacing (pacing guide/calendar) to support effective implementation for various instructional calendars (e.g., varying numbers of instructional days - 165, 180, 210).

The materials offer flexible pacing guides and calendars to accommodate various instructional calendars. The "Guía de ritmo por temas de matemáticas de secundaria, grado 6 (150 días)" document presents an alternative 150-day suggested curriculum pacing option. Additionally, the materials provide a 165-day "Year-at-a-Glance (YAG)" scope and sequence as a recommended pacing tool. This tool is outlined in the Guía de programa e implementación de matemáticas de secundaria. Both the 150-day and 165-day pacing guides include detailed scope and sequence tables. These tables list each lesson title, a summary, essential concepts aligned to the TEKS, and the number of instructional days allocated per lesson. Together, these resources offer structured, adaptable pacing options that support effective implementation across a range of school calendars while maintaining alignment with the TEKS standards.

Evaluation for 1.1c
Materials include an explanation for the rationale of unit order as well as how concepts to be learned connect throughout the course.

The "Organización del contenido de matemáticas de secundaria" resource includes a "La justificación y los beneficios de la secuencia" section. This section explains the rationale for the unit order and how concepts are thoughtfully organized. The section offers a brief overview of each module, highlighting how the modules progress and connect. Such information helps teachers understand what to expect and how the content builds across the five modules.

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

The materials provide teachers with a four-step process for understanding each module and topic. The steps include planning instruction, key terms, and information on the overall learning progression protocols with corresponding guidance for the unit. The "Preparación" section of the "Protocolo de internalización de módulos y temas de matemáticas de secundaria para maestros" details these steps.

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

The materials provide instructional resources in a step-by-step process for instructional leaders. The "Preparación del maestro, Pasos 1–4" section of the "Protocolo de internalización de módulos y temas de matemáticas de secundaria para líderes de instrucción y administradores" includes planning instruction for identifying key terms. The section also details the overall learning progression protocols with corresponding guidance for the unit. The "Recursos para Instrucción y administradores" include a "Recursos por nivel del programa" section, which outlines three key components that provide detailed supports educators can use before teaching each module. Additionally, implementation guidance encourages collaborative planning. For example, in Step 1 of such guidance, the materials direct instructional leaders to facilitate discussions as teachers review lesson content, objectives, and the TEKS, highlighting key ideas to ensure instructional alignment and a shared understanding.

Evaluation for 1.2a
Materials include comprehensive unit overviews that provide the background content knowledge and academic vocabulary necessary to effectively teach the concepts in the unit.

The Versión del maestro de matemáticas de secundaria, grado 6 includes a "Contenido general Módulo 1" section, which explains what students will learn. This information includes the academic vocabulary and background knowledge that students need. For example, the "Componer y descomponer" lesson within the module explains why it appears at the start of grade 6: the module lays the foundation for the year by strengthening students' understanding of numbers and shapes, helping students recognize structures and make connections across mathematical concepts.

Evaluation for 1.2b
Materials contain supports for families in both Spanish and English for each unit with suggestions on supporting the progress of their student.

The grade 6 instructional materials in the Guía de matemáticas de secundaria para la familia, grado 6 - inglés y español include a "Family Guide" document, which is designed to help families support their students at home in English and Spanish. The guide is organized by module and provides an overview of what students are currently learning and what they will be working on next. The guide also includes suggested questions that parents can ask and key vocabulary for each unit.

Evaluation for 1.3a
Materials include comprehensive, structured, detailed lesson plans that include daily objectives, questions, tasks, materials, and instructional assessments required to meet the content and language standards of the lesson (aligned with the TEKS and the ELPS).

In grade 6, Volume 1 of the Versión del maestro de matemáticas de secundaria, the materials offer structured and comprehensive lesson plans with objectives, key terms, and preparation tools such as summaries, side notes, and material lists. The lesson plans include linguistic accommodations, sample responses, interactive tasks, and exit tickets to support instruction and assess understanding. In grade 6, Volume 2 of the Versión del maestro de matemáticas de secundaria, the materials provide structured lesson plans that guide classroom instruction. Each lesson begins with objectives, an introductory question, new terms, and activities. The materials support teachers with clear summaries, planning notes, material lists, and interactive tasks that foster student-teacher dialogue.

Evaluation for 1.3b
Materials include a lesson overview listing the teacher and student materials necessary to effectively deliver the lesson, and the suggested timing for each lesson component.

At the beginning of each lesson, the materials outline all the materials students will need during the lesson. For example, in grade 6, Volume 2, Module 4, Topic 3, Lesson 1 of the Versión del maestro de matemáticas de secundaria, the materials include a blue "Materiales" box. This box notes that students will need scissors, tape or glue, and "situation cards," which can be found at the end of the lesson. Volumes 1–2 of the grade 6 Versión del maestro de matemáticas de secundaria begin with an "Estructura y ritmo de la lección" section, which includes suggested instructional timing information. For example, Module 4, Topic 3, Lesson 1's "Activar" section is 10–15 minutes, while the "Desarrollar" section is 30–35 minutes.

Evaluation for 1.3c
Materials include guidance on the effective use of lesson materials for extended practice (e.g., homework, extension, enrichment).

The materials in the Guía de programa e implementación de matemáticas de secundaria guide extended practice through the "Diferenciación y apoyo" section, which includes strategies for access, support, and enrichment. This section includes specific examples that can be used for homework, reteaching, or extension, supporting all learners beyond the core lesson. In the Versión del maestro de matemáticas de secundaria, grado 6, the "Práctica de destrezas" resource includes a "Mejores prácticas para la aplicación de practica de destrezas" section. This section includes "Días de aprendizaje individual" materials that guide extended practice. These materials recommend the flexible use of problem sets, grouping strategies, and targeted support to reinforce or extend learning. This information is useful for homework, reteaching, and enrichment.

Evaluation for 2.1a
Materials include a variety of instructional assessments at the unit and lesson level (including diagnostic, formative, and summative) that vary in types of tasks and questions.

The materials provide the definitions and intended purposes of the types of formative assessments that the modules include. For example, in grade 6, the "Evaluaciones" section of the Versión del maestro explains how the different types of evaluations are part of the ongoing lesson cycle. This section also explains how such evaluations support the entire learning experience by including the definition and intended purpose of summative evaluations. The materials include diagnostic, formative, and summative assessments, which appear across the instructional sequence. The Guía de programa e implementación explains that diagnostic tools (such as the "Prepárate" section) and spaced retrieval tasks help activate students' prior knowledge and assess readiness for upcoming content. Formative assessments such as "Demuestra lo que sabes," "Pulgar arriba/pulgar abajo," and "¿Quién tiene la razón?" check for understanding, uncover misconceptions, and guide in-the-moment instruction. Summative assessments appear at the end of each unit, allowing teachers to evaluate student mastery of the TEKS and make informed instructional decisions. The materials include unit-level diagnostic and summative assessments that vary in task and question types. Mid-module evaluations serve as diagnostic tools. In grade 6, the "Evaluaciones" section of the Versión del maestro de matemáticas de secundaria states the following: "la evaluación de la mitad del módulo incluye preguntas que varían en formato, incluyendo opción múltiple, respuesta abierta y representaciones visuales." End-of-module evaluations assess multistep problem solving, graph analysis, and reasoning justification.

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

The Guía de programa e implementación defines each assessment type used in instruction. The guide describes exit tickets as brief, daily formative assessments that help teachers identify misconceptions and adjust instruction. The guide identifies other formative tools such as "Demuestra lo que sabes" and "Prepárate," which check real-time understanding, revisit prior knowledge, or promote reflection. The guide defines end-of-module assessments as summative tools that evaluate overall mastery of module content. In grade 6, the "Evaluaciones" section of the Versión del maestro de matemáticas de secundaria explains that mid-module assessments serve a diagnostic purpose: these assessments check student understanding of the first half of the module and uncover misconceptions. The materials state that end-of-module assessments serve a summative purpose, requiring students to demonstrate mastery through multistep problems, graphical analysis, and written justifications.

Evaluation for 2.1c
Materials include teacher guidance to ensure consistent and accurate administration of instructional assessments.

The "Evaluaciones" section of the Guía de programa e implementación provides procedures to help teachers administer instructional assessments consistently. The "Orientación de administración" table instructs teachers to use the print or digital end-of-topic evaluation, allocate 45 minutes per assessment, and follow calculator-use rules, such as "No se permite el uso de calculadora" for grades 6–7. The Guía de programa e implementación provides a scoring guide and annotated student responses. The Guía de puntuación de la evaluación defines scoring criteria for each level, while the "Respuesta al desempeño del estudiante" resource shows sample responses that illustrate how to apply the rubric. These tools help educators score assessments accurately, interpret student answers consistently, and make data-informed decisions.

Evaluation for 2.1d
Diagnostic, formative, and summative assessments are aligned to the TEKS and objectives of the course, unit, or lesson.

In grade 6, the "Evaluaciones" section of the Versión del maestro de matemáticas de secundaria aligns mid-module assessments to the TEKS and the specific objectives of each unit, classifying the assessments as diagnostic. The "Evaluación de la mitad del módulo" section states the following: "Las preguntas abordan los estándares enseñados en la primera mitad del módulo." This information demonstrates direct alignment with the TEKS and the content covered thus far. The "Mid-Module 3 Assessment" includes questions that require students to graph and interpret ratios, directly addressing TEKS 6.4B and 6.4D, which are the unit's focus. The Guía de programa e implementación de matemáticas de secundaria includes formative assessments in each lesson, such as "Prepárate" and "Demuestra lo que sabes." In Unidad 2, for example, the "Prepárate" activity prompts students to review unit rates and part-to-whole relationships, which align with TEKS 6.4D and 6.5B and support the unit's focus.

Evaluation for 2.1e
Instructional assessments include TEKS-aligned items at varying levels of complexity.

In grade 6, the "Evaluaciones" section of the Versión del maestro includes TEKS-aligned items that assess more than two levels of complexity. For example, in the "Evaluación final del tema" for Module 3, Topic 1, students perform procedural calculations with data, apply conceptual understanding to interpret graphs, and demonstrate strategic reasoning by justifying conclusions based on real-world scenarios. In grade 6, the "Evaluaciones" section of the Versión del maestro includes an "Evaluación final del tema" for Module 5, Topic 2. This evaluation asks students to analyze a random sample of 15 players' scores to estimate typical point values in a math game. Students interpret the data, calculate statistical measures, and draw conclusions about the larger group, showing more than two levels of complexity. In grade 6, Topic 1, the "Evaluación de final del tema" summative assessment reflects varying levels of complexity and directly aligns with the TEKS. In Topic 2, titled "Porcentajes," students answer multiple-choice questions using shaded models. Students then complete tables with missing values representing equivalent fractions, decimals, and percentages. This progression demonstrates an increase in rigor.

Evaluation for 2.2a
Instructional assessments and scoring information provide guidance for interpreting student performance.

In grade 6, the "Evaluaciones" section of the Versión del maestro includes the Guía de análisis de la evaluación. This resource provides clear guidance for interpreting student performance through multiple components. Each end-of-topic assessment includes a Guía de puntuación that outlines the TEKS assessed, the number of points per item, and the specific criteria used to determine if students earned full, partial, or no credit. Additionally, the "Respuesta al desempeño del estudiante" section offers recommendations based on student outcomes, including reteaching strategies and targeted practice sets. These components help teachers analyze student work and plan next steps for instruction. The Guías de puntuación provide scoring information for each assessment in the "Evaluaciones" section of the grade 6 Versión del maestro. These guides include the TEKS aligned with each question, each item's point value, and specific scoring criteria that distinguish between full, partial, and incorrect responses. This information allows teachers to apply consistent scoring practices and understand what student responses indicate about students' mastery.

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

In grade 6, the "Evaluaciones" section of the Versión del maestro includes a Guía y análisis de la evaluación. This resource explains that each assessment provides a "Respuesta al desempeño del estudiante" section, which includes explicit guidance on how to respond to student trends. This section recommends reteaching strategies, extension tasks, and specific practice sets based on question-level performance. In grade 6, the "Evaluaciones" section of the Versión del maestro includes a "Sugerencias de aplicación para las evaluaciones de final del tema" section. This section instructs teachers to use data from both formative and summative assessments to determine where to place días de aprendizaje individual within a unit to provide targeted instruction based on students' needs. The materials encourage teachers to revisit previous lesson assignments and provide targeted skill practice based on student performance trends. These review days allow flexible scheduling, enabling teachers to respond to the evolving needs of individuals and groups.

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.

In grade 6, the Recopilación de datos de los estudiantes book includes a tracker that allows teachers to monitor student mastery of content and language standards, record assessment results, and collect student self-reflections that are aligned to each topic. The tracker also provides space for teachers to document real-time observations and trends to monitor student progress and growth. In grade 6, the "Evaluaciones" section of the Versión del maestro includes a "Reflexión sobre la evaluación" form that students complete after assessments. This form prompts students to compare their performance to their previous self-assessments, identify effective learning behaviors, and plan for improvements. The form encourages student ownership of learning and helps students track their growth over time.

Evaluation for 3.1a
Materials include teacher guidance for differentiated instruction, activities, and paired (scaffolded) lessons for students who have not yet reached proficiency on grade-level content and skills.

The materials provide consistent teacher guidance for differentiated instruction, which targets students who have not mastered the grade-level TEKS. For each assessed standard, the "Evaluaciones" section of the Versión del maestro outlines specific skill gaps such as ordering rational numbers and multiplying fractions, guiding teachers to targeted practice sets in "Prácticas de destrezas VI.A, IV.D." The scaffolded lesson practice includes items by number under the "Respuesta al desempeño del estudiante" section. This section includes specific guidance for activities that are responsive to student performance on grade-level content and skills. The "Evaluaciones" section of the Versión del maestro includes differentiated activity recommendations for struggling students, such as assigning specific questions from prior lessons. For example, in Module 1, Topic 1, the Guía de puntuación de la evaluación gives teachers the following guidance: "Repase las preguntas 1 a 8 de la sección 'Práctica de la asignación' de la Lección 5." The guide directs students to focused skill-building resources. These guided activities help scaffold learning and are responsive to student data by TEKS.

Evaluation for 3.1b
Materials include pre-teaching or embedded supports for unfamiliar vocabulary and references in text (e.g., figurative language, idioms, academic language).

The materials include support for unfamiliar academic vocabulary through a student-accessible glossary, which is located at the end of grade 6, Volume 1 of the Versión del estudiante. This 23-page section, titled "Glosario de matemáticas," defines key mathematical terms using student-friendly language and visual representations. Diagrams and contextual examples accompany terms such as algoritmo, base, and modelo de barras, supporting student understanding. The materials embed language development support for academic and mathematical vocabulary. The "Apoyo lingüístico" sections of the grade 6 Versión del maestro guide teachers to differentiate between similar-sounding or conceptually dense terms such as intervalo versus escala, parte, porcentaje, and entero. Supports include visual representations, structured formulas, and color-coding to reinforce meaning. The materials embed these supports throughout the lessons to help students interpret unfamiliar academic language in context.

Evaluation for 3.1c
Materials include teacher guidance for differentiated instruction, enrichment, and extension activities for students who have demonstrated proficiency in grade-level content and skill.

In grade 6, the "Evaluaciones" section of the Versión del maestro provides teacher guidance for enrichment and extension activities, which are designed for students who have demonstrated proficiency in grade-level skills. For multiple TEKS across different Guías de puntuación de la evaluación, the materials include a dedicated "Para desafiar a los estudiantes" section that directs teachers to targeted extension practice sets. These activities allow proficient students to deepen their understanding and engage with more complex applications of the content. In grade 6, the "Evaluaciones" section of the Versión del maestro includes "Oportunidad de desafío" sections, which offer differentiated tasks for students who have mastered core content. For example, students calculate total surface area and cost based on equivalent ratios, interpret proportional relationships in real-world contexts (such as pizza data and voting models), and design and analyze histograms based on scenario-based variables.

Evaluation for 3.2a
Materials include explicit (direct) prompts and guidance to support the teacher in modeling and explaining the concept(s) to be learned.

The materials in grade 6, Volume 1 of the Versión del maestro provide explicit prompts to guide the teacher in modeling mathematical concepts. For example, in Module 1, Topic 1, Lesson 1, the materials prompt the teacher to do the following: "Demuestre cómo puede ayudar la propiedad distributiva con los cálculos mentales expresando un factor como la suma de los valores de las decenas y las unidades." This prompt directs teachers to show students how to solve using the distributive property. These supports help teachers scaffold mathematical concepts and promote accurate, meaningful modeling for a range of learners. The materials include direct prompts for teachers to explain key mathematical concepts. For example, Module 1, Topic 1, Lesson 1 directs teachers to "explique que en esta actividad se utiliza el símbolo del punto de multiplicación." The module also directs teachers to guide conceptual understanding with questions and prompts such as "¿Qué significa distribuir algo?" and "Explica qué quiere decir multiplicación sobre suma." These supports are embedded throughout the instructional materials and provide scaffolds for teachers to make mathematical ideas explicit to students.

Evaluation for 3.2b
Materials include teacher guidance and recommendations for effective lesson delivery and facilitation using a variety of instructional approaches.

The Guía del curso e implementación de grado 6 includes clear teacher guidance to implement at least two distinct instructional approaches: "Aprender juntos," addressing collaborative or whole-group instruction, and "Aprender individualmente," addressing independent practice. The "Preparación para facilitar el aprendizaje" section guides teachers to facilitate collaborative discourse, use structured lesson parts, and implement differentiated group configurations. For independent learning, teachers plan skill practice and interpret student strengths or misconceptions. In grade 6, Volume 1 of the Versión del maestro, the "Notas de facilitación" section of each lesson provides teacher guidance for multiple instructional strategies. These strategies include hands-on modeling, discussion-based questioning, error analysis, and student-led exploration and justification. The materials embed these strategies throughout teacher-facing notes, lesson structures, and differentiation supports, demonstrating the use of more than two instructional approaches.

Evaluation for 3.2c
Materials support multiple types of practice (e.g., guided, independent, collaborative) and include guidance for teachers and recommended structures (e.g., whole group, small group, individual) to support effective implementation.

Grade 6, Volume 1 of the Versión del maestro supports multiple forms of student practice. For example, Module 1, Topic 1, Lesson 1 incorporates collaborative activities such as group and partner tasks, independent problem-solving, and structured discourse through teacher-guided questions and modeling prompts. The materials apply these approaches consistently across lessons. Moreover, the planning guide in "Aprender juntos y aprender individualmente" reinforces the approaches. The materials provide teacher guidance throughout each lesson in grade 6, Volumes 1–2 of the Versión del maestro in the form of facilitation notes, specific teacher prompts, differentiation strategies, and misconception alerts. For example, Module 1, Topic 1, Lesson 1 instructs teachers to discuss specific mathematical symbols and structures through directions such as the following: "explique que en esta actividad se utiliza el símbolo del punto de multiplicación." The materials support teachers in observing common errors such as misusing rectangular models. The materials provide recommended structures that support effective implementation through whole group, small group, and individual configurations. The "Preparación para facilitar el aprendizaje" section, part of the Guía del curso e implementación, provides explicit guidance for teachers to structure instruction during días de aprender juntos. Teachers use whole-group practices such as setting mathematical objectives, facilitating collaborative discourse, and guiding reflection. The section also recommends organizing the classroom into stations or small groups to promote peer collaboration, differentiated support, and ongoing formative assessment. For individual learning, the guide outlines how to use skill practice intentionally, analyze student work to address misconceptions, and support students in developing independence.

Evaluation for 3.3a
Materials include teacher guidance on providing linguistic accommodations for various levels of language proficiency [as defined by the English Language Proficiency Standards (ELPS)], which are designed to engage students in using increasingly more academic language.

This guidance is not applicable because the Spanish program does not require guidance on providing linguistic accommodations.

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

In grade 6, Volume 2 of the Versión del maestro, the materials include a "Facilitar el aprendizaje de los estudiantes" section. This section includes "Apoyo lingüístico" strategies that support teachers in differentiating instruction for emergent bilingual students across various English proficiency levels. These strategies include prompts to guide academic conversations, sentence frames, vocabulary support, and tasks that build conceptual understanding while reinforcing language development. These supports help teachers meet the linguistic and academic needs of students in bilingual/ESL classrooms. In grade 6, Volume 2 of the Versión del maestro, the materials include "Glosario académico," "Glosario de matemáticas," and "Estudiantes bilingües emergentes" sections. These sections provide teachers with bilingual glossaries that include definitions, visual representations, and sample questions to promote academic language acquisition. In addition, the materials offer guidance on using cognates, bilingual journals, and digital word walls to foster cross-linguistic connections and deepen students' conceptual and linguistic understanding.

Evaluation for 3.3c
Materials include embedded guidance for teachers to support emergent bilingual students in developing academic vocabulary, increasing comprehension, building background knowledge, and making cross-linguistic connections through oral and written discourse.

The materials include embedded guidance to support oral discourse for emergent bilingual students. In grade 6, Volume 2 of the Versión del maestro, the "Facilitar el aprendizaje de los estudiantes" section includes "Sella el aprendizaje" notes. These notes help students articulate concepts using academic language, reinforcing students' vocabulary development through structured talk. The "Glosario académico" section provides explicit prompts and sample questions that encourage students to express mathematical reasoning verbally, such as "¿Por qué sí o por qué no?" Such prompts directly support students' vocabulary use and comprehension. The "Estudiantes bilingües emergentes" section offers explicit strategies for bilingual discussion and the oral use of cognates, such as journaling reflections aloud or in shared word walls. These strategies promote cross-linguistic connections during discourse. In grade 6, Volume 2 of the Versión del maestro, the materials support vocabulary development and comprehension by embedding structured writing tasks across multiple sections. In the "Facilitar el aprendizaje de los estudiantes" section, "Apoyo lingüístico" boxes guide teachers to prompt students to write reflections using key academic terms. For example, the materials direct teachers to do the following: "Pida a los estudiantes que escriban una o dos oraciones que acompañen a sus representaciones visuales y matemáticas." To develop written discourse, the "Apoyo lingüístico" boxes encourage students to "practiquen el uso de palabras conectoras escribiendo sobre lo que aprendieron en esta lección." Additionally, the "Estudiantes bilingües emergentes" section equips teachers with guidance to strengthen cross-linguistic written expression. For example, this section includes the following prompt: "Anime a los estudiantes a llevar un diario bilingüe de matemáticas en el que anoten sus reflexiones y conocimientos previos sobre los temas nuevos, ya sea en formato escrito u oral, añadiendo elementos visuales para mayor claridad. Incorpore extractos del diario a un muro de palabras compartido o a un glosario bilingüe digital, haciendo énfasis en los cognados." This prompt supports academic vocabulary development, cross-linguistic connections, and written discourse.

Evaluation for 3.3d
If designed for dual language immersion (DLI) programs, materials include resources that outline opportunities to address metalinguistic transfer from English to the partner language.

The materials include multiple resources that promote metalinguistic transfer from English to the partner language by explicitly guiding students to build connections between the two languages. Students develop a bilingual glossary using targeted vocabulary words. This activity offers opportunities to recognize and analyze cognates and false cognates while incorporating visuals to reinforce meaning. A student-facing "KWHL" chart further supports this process, which stands for "Know," "Want to Know," "How Can I Learn," and "What Did I Learn." Learners first write in their primary language to activate their prior knowledge. They then reflect on how these ideas connect to the partner language. Such activities encourage students to draw direct links between languages, enhancing their comprehension and language development. The materials also provide resources for instructional strategies that strengthen students' oral proficiency in the partner language through structured practice. For example, teachers use choral response activities in which students repeat vocabulary words in their primary language and then practice them in the partner language. Lessons consistently integrate opportunities for metalinguistic transfer in "Engage," "Develop," and "Demonstrate" sections, where students read, engage in discourse, and apply vocabulary in both languages. The Program and Implementation Guide explicitly prompts educators to "encourage students to solve math problems in the language of their choice, while making explicit connections to the strategies, vocabulary, or reasoning they've used in the partner language." This guidance fosters metalinguistic awareness and supports students in transferring conceptual understanding across languages.

Evaluation for 4.1a
Practice opportunities over the course of a lesson and/or unit (including instructional assessments) require students to demonstrate depth of understanding aligned to the TEKS.

The grade 6 student materials include practice tasks that require students to apply mathematical reasoning in varied and complex contexts. These practice tasks are aligned to the TEKS. For example, in grade 6, Volume 1, Module 1, Topic 3, Lesson 3 of the Versión del maestro, students must represent and solve multistep ratio problems using a tape diagram and double number line. These tasks prompt students to make connections between representations and real-world contexts, requiring them to explain their thinking, justify strategies, and build conceptual understanding. The grade 6 materials align all assessments to the TEKS by labeling each item with standards such as "6.3D" or "6.5A." The materials also include a correlation table that aligns each standard to specific assessment items. Tasks require students to justify their reasoning, solve multistep problems, and apply concepts in varied contexts. In grade 6, Module 1, Topic 3 of the Versión del maestro, the "Evaluación del final del tema" asks students to solve complex ratio problems using models. Students explain their thinking in the end-of-unit assessment.

Evaluation for 4.1b
Questions and tasks progressively increase in rigor and complexity, leading to grade-level proficiency in the mathematics TEKS.

Grade 6, Volume 1 of the Versión del estudiante de matemáticas de secundaria progressively builds rigor and complexity across lessons. In Module 1, Topic 3, Lesson 3, students first use visual models of equivalent ratios. Students then progress to solving multistep, real-world problems with written justifications. The "Explora, conecta, demuestra lo que sabes" structure increases cognitive demand and supports mastery of the grade-level TEKS. In grade 6, Volume 1 of the Versión del estudiante de matemáticas de secundaria, the materials build rigor through the "Explora, conecta, demuestra lo que sabes" sequence. In Module 1, Lesson 10, students first model ratios with tape diagrams. Students then write and solve ratio equations. Last, students solve multistep, real-world problems with written justifications. This progression actively develops students' TEKS-aligned proficiency and provides scaffolds for students, supporting their transition from the concrete to the representational to the abstract.

Evaluation for 4.2a
Materials demonstrate coherence across units by explicitly connecting patterns, big ideas, and relationships between mathematical concepts.

The materials demonstrate coherence across units by connecting big ideas throughout the course. At the beginning of each module, the "Contenido general del módulo" section provides an overview of how the materials connect big patterns and ideas across units. For example, in Module 1, the section states that composing and decomposing help students deepen their understanding of numbers and shapes by better grasping their structure. In Topic 3, titled "Decimales," students apply the same composing and decomposing reasoning to decimal multiplication. The materials demonstrate coherence by building on the concept of numeric operations and models to develop algebraic thinking. In grade 6, Volume 2, Module 4, Topic 1 of the Versión del maestro, de "Contenido general" section states that "los estudiantes se basan en su conocimiento actual de cómo realizar operaciones con números y medidas geométricas para desarrollar su conocimiento de las expresiones algebraicas y variables." This statement demonstrates the connection across concepts. The module later explains that students "utilizan una variedad de números racionales para evaluar expresiones y crear expresiones equivalentes," reinforcing connections between numeric and algebraic reasoning.

Evaluation for 4.2b
Materials demonstrate coherence across units by connecting the content and language learned in previous courses/grade levels and what will be learned in future courses/grade levels to the content to be learned in the current course/grade level.

The materials connect current instruction to prior learning by referencing content and language students have already developed. Module 1's "Contenido general" section includes the following question: "¿Cómo se relaciona componer y descomponer con lo aprendido anteriormente?" This question prompts students to retrieve their prior knowledge from a previous unit and relate it to their current learning. The "Contenido general" section also states that students "empiezan este curso con experiencias con números y operaciones de base diez" and have previously used "modelos de área para representar la propiedad distributiva." The materials thus demonstrate horizontal alignment between earlier learning and current grade-level content across the grade-level units. The materials describe how current learning prepares students for future grade-level content. Module 1's "Contenido general" section includes the following question: "¿En qué momento utilizarán los estudiantes el conocimiento de componer y descomponer en el aprendizaje futuro?" This question demonstrates that students continue to use the same strategies in "figuras geométricas, porcentajes, expresiones, ecuaciones, gráficas y estadística." The "Contenido general" section also notes that students will revisit "el área, el volumen y el área de la superficie" when solving problems using one-step equations, establishing a connection between current and future math topics.

Evaluation for 4.2c
Materials demonstrate coherence at the lesson level by connecting students' prior knowledge of concepts and procedures from the current and prior grade level(s) to new mathematical knowledge and skills..

The materials demonstrate coherence within the grade level by connecting earlier concepts to new learning. For example, in Topic 3, titled "Decimales," students apply place value understanding to develop and use algorithms for decimal operations. The overview states: "Los estudiantes razonan sobre la colocación del punto decimal...y resuelven problemas del mundo real utilizando los algoritmos normales." This work builds on prior lessons from Topics 1 and 2 involving whole numbers and fractions, moving from visual models to standard procedures. In grade 6, Volume 1 of the Versión del maestro, the materials connect prior grade-level learning to current content. For example, the materials pose the following question: "¿Cómo se relaciona componer y descomponer con lo aprendido anteriormente?" This question highlights the integration of prior knowledge. Students previously "utilizaron modelos de área para representar la propiedad distributiva" and practiced "multiplicar y dividir fracciones entre fracciones unitarias." The materials demonstrate coherence at the lesson level by connecting students' prior knowledge to new concepts. For example, in grade 6 of the Versión del maestro de matemáticas de secundaria, instructional materials link activities through a "Preguntas para respaldar la conversación" table, which includes the following question: "En la actividad anterior, ¿importaba si empezabas con los dos lados o creando un tercer lado?" This question prompts students to recall a previously learned procedure. This approach helps students use their prior knowledge as a scaffold for new learning, reinforcing their understanding and encouraging the application of familiar concepts to new contexts.

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

The materials provide opportunities for the spaced retrieval of previously learned skills, embedding structured review into new lessons through the "Inicio" section. In Module 3, Topic 1, Lesson 4's "Inicio" section, students "utilizan su conocimiento previo del primer cuadrante del plano de coordenadas y de la recta numérica de números racionales para extenderse de un cuadrante a cuatro cuadrantes." This work demonstrates how the materials apply a previously learned concept to the current lesson. Students practice skills in Actividad 4.1, titled "Plano de coordenadas humano," by physically marking, identifying, and labeling ordered pairs across all four quadrants, revisiting graphing and placement skills from earlier grade levels and previous lessons. In grade 6, Volume 2, Module 4, Topic 2, Lesson 5 of the Versión del maestro, the "Ecuaciones en comparación con desigualdades" section requires students to revisit the conceptual difference between solution sets for equations and inequalities. Students respond to prompts such as "¿Por qué las desigualdades tienen más soluciones que las ecuaciones?" and "¿Por qué es útil utilizar una recta numérica para demostrar la solución de una desigualdad?" The materials support the retrieval of previously learned concepts by prompting students to compare and reason about equations and inequalities using number lines and mathematical language that they previously learned.

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

In the Guía de programa e implementación de matemáticas de secundaria, the materials support interleaved practice with previously learned skills across lessons and units. The "Guiar el desarrollo matemático de los estudiantes" instructional framework encourages the use of "recuperación espaciada…mediante la práctica estratégicamente espaciada," guiding teachers to optimize long-term retention through strategically placed mixed and spiraled reviews. Such a design for the materials ensures that students revisit and apply prior skills through diverse problem types over time. The materials emphasize concept connections across lessons by encouraging a pedagogical method called the "Tres fases del método pedagógico." This method appears within each of the activities in the materials and includes "activar, desarrollar, and demostrar." The materials prompt teachers to "aproveche los conocimientos previos y las experiencias del mundo real de los estudiantes," providing purposeful opportunities for connections. The materials provide structures that allow students to make "conexiones a lo largo de la lección," improving students' retention and understanding throughout the learning pathway.

Evaluation for 5.1a
Questions and tasks require students to interpret, analyze, and evaluate models and representations for mathematical concepts and situations.

In the grade 6 Versión del estudiante, the "Práctica de destrezas" section requires students to interpret and analyze mathematical representations in meaningful contexts. For example, Module 2, Topic 2's "Práctica de destrezas" activity asks students to convert Olympic medal counts into fractions, decimals, and percentages, allowing students to demonstrate their ability to interpret equivalent values across multiple forms. Students then analyze those representations to rank countries from greatest to least based on medal type. Students note patterns in the data. The materials require students to evaluate models and representations. For example, in grade 6, Module 4, Topic 2's "Práctica de destrezas," students analyze a series of balance scales to determine the relationship between multiple unknown quantities. Students use reasoning and structural relationships to determine a correct solution. Similarly, in Module 2, Topic 1 and Module 5, Topic 1, students evaluate sets of visual ratio models (such as apples to oranges or forks to spoons). Students identify which representations show equivalent ratios.

Evaluation for 5.1b
Questions and tasks require students to create models to represent mathematical situations.

The materials guide students to create models to represent mathematical situations. For example, the graphic organizer in the grade 6 "Organizador gráfico del modelo de resolución de problemas" document and embedded reflection questions offer opportunities to model thinking at each stage of solving real-world and mathematical problems. Such reflection questions include "¿Mostré mi trabajo utilizando múltiples representaciones?" and "¿Utilicé múltiples representaciones para representar mis matemáticas?" The materials guide students to create models to represent mathematical situations. Throughout the problem-solving process, the materials prompt students to use multiple representations—such as visual models, numerical expressions, and written explanations—to organize, analyze, and communicate their reasoning. For example, in grade 6, Volume 1, Module 1, Topic 1, Lesson 1 of the Versión del estudiante, the "Demuestra lo que sabes" task asks students to draw a diagram of a gym floor and apply the distributive property to divide the floor's area according to various activities. Students must represent their thinking through labeled visuals and explain how to apply the distributive property.

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

The materials require students to apply their understanding of mathematical concepts to new real-world contexts. For example, in grade 6, Volume 1, Module 1, Topic 1, Lesson 1 of the Versión del estudiante, the "Demuestra lo que sabes" section requires students to divide the area of a gym floor by creating a diagram and explaining how to apply the distributive property. This task pushes students to apply a mathematical concept to a practical planning scenario, deepening students' conceptual understanding through modeling and justification. In grade 6, Volume 1 of the Versión del estudiante, the materials ask students to apply their conceptual knowledge of mathematics to new numerical contexts through different activities. For example, in Module 1, Topic 2, Lesson 4, students use volume formulas to calculate the space inside rectangular prisms with rational numbers, extending their prior understanding of whole-number dimensions to unfamiliar fractional values. This lesson challenges students to apply their conceptual understanding to more complex, non-routine problems.

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

The materials in grade 6, Volume 1 of the Versión del maestro include repeated, structured tasks that promote student fluency with the distributive property, supporting students' automaticity with mathematical concepts. For example, Module 1, Topic 1, Lesson 1's "Asignación" section provides students with multiple visual models. Students must decompose rectangles into partial products, such as "3(100 + 22) = 300 + 66" and "6(120 + 2) = 720 + 12." These problems require students to apply the distributive property efficiently and repeatedly, reinforcing the mental math strategies necessary for grade-level computation. The materials provide scaffolded fluency tasks that help students internalize numerical relationships and efficient strategies for solving problems. In Actividad 1.1, students repeatedly break apart factors in multiplication expressions to explore equivalent forms using area models. Such opportunities promote students' operational fluency with multi-digit multiplication and reinforce the flexible thinking strategies necessary for grade-level mastery.

Evaluation for 5.2b
Materials provide opportunities for students to practice the application of efficient, flexible, and accurate mathematical procedures within the lesson and/or throughout a unit.

The materials provide repeated opportunities for students to find and apply efficient mathematical strategies across models and contexts, such as the distributive property. For example, in Module 1, Topic 1, Lesson 1's "Demuestra lo que sabes" section, students divide a gym's length into parts and use the distributive property to calculate the area: "50(40 + 34 + 10) = 2000 + 1700 + 500 = 4200." The materials promote flexibility by guiding students to represent the same numerical expression in multiple ways using area models, mental math, and symbolic equations. For example, Actividad 1.1 asks students how they might rewrite "5 × 27" by decomposing "27" into different addends. Prompts such as "¿En qué otras formas podrías descomponer uno de los factores?" support flexible thinking and the application of the distributive property with varied number combinations. Such prompts encourage students to explore more than one valid method. The materials include structured exercises for students to verify the correctness of procedures and correct errors. In Question 5, students identify whether distributive expressions such as "3(2 + 4) = 3 × 2 + 4" are true or false. The materials ask students to rewrite inaccurate expressions to make them mathematically correct. This direct practice with feedback enables the precise application of mathematical procedures.

Evaluation for 5.2c
Materials provide opportunities for students to evaluate procedures, processes, and solutions for efficiency, flexibility, and accuracy within the lesson and throughout a unit.

The materials provide multiple structured opportunities for students to evaluate procedures, processes, and solutions for efficiency across lessons. For example, in Module 1, Topic 1, Lesson 6, Actividad 6.4, titled "Diferentes estrategias para dividir números," students solve division problems and "elegir la estrategia más eficiente." Similarly, in Module 2, Topic 2, Lesson 3, students compare five distinct solution methods to determine which is most efficient under varying percentage scenarios. In grade 6, Volumes 1–2 of the Versión del maestro, the materials prompt students to evaluate and compare multiple strategies to solve problems, supporting flexible mathematical thinking. In Module 1, Topic 3, Lesson 2, students respond to questions such as "¿Cuál es otra estrategia para resolver este problema?" and "¿Cuál es la estrategia más eficiente? ¿Por qué?" These questions require students to analyze and justify different approaches, reinforcing the idea that students can apply and evaluate multiple strategies based on the problem context. The materials consistently prompt students to verify the accuracy of their procedures and solutions. In Module 1, Topic 3, Lesson 2, students estimate and calculate the product of decimals, then determine whether a decimal point is placed correctly by comparing their estimate to the computed result. In Topic 3, Lesson 1, students identify whether a peer's decimal comparisons are correct or incorrect. Students then explain how to revise inaccurate reasoning using their understanding of place value.

Evaluation for 5.2d
Materials contain embedded supports for teachers to guide students toward increasingly efficient approaches.

The materials in Module 1, Topic 3, Lesson 2 include an "Ejemplo práctico" that demonstrates how to estimate the product of decimals by rounding one or both factors before solving (e.g., "32.75 × 7.5" becomes "30 × 8"). The teacher notes explicitly direct educators to guide students in estimating first and then strategically placing the decimal, promoting a more efficient problem-solving process. These supports help teachers model estimation strategies that lead to quicker, more accurate computations. In Module 1, Topic 3, Lesson 1, teacher guidance for Question 8 addresses common misconceptions when comparing decimal numbers. The materials prompt teachers to use visual tools such as place value charts and hundredths grids to steer students away from digit-by-digit comparisons and instead develop conceptual understanding. These supports enable teachers to lead students toward more efficient, reasoning-based comparison strategies that align with grade-level expectations.

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

The materials state how they address the conceptual intent of the TEKS. For example, the materials outline lesson purposes and learning objectives that focus on promoting understanding through representations and context. In the "Facilitar el aprendizaje de los estudiantes" section, the materials explicitly detail their emphasis on conceptual reasoning: "El propósito de esta actividad es que los estudiantes representen el cociente de dos fracciones como un número que da sentido a una situación." The "Notas de facilitación" section states the following: "En esta actividad, los estudiantes convierten fracciones en decimales utilizando diagramas de tiras e interpretando el significado de la barra de fracción como división." In the "Resumen" section, the materials state: "Puedes usar los algoritmos normales para la división de números enteros y decimales para resolver problemas del mundo real." These examples describe how students engage in conceptual learning as defined by the TEKS. The materials detail how they address the procedural intent of the TEKS by outlining how instruction progresses from conceptual representations to symbolic procedures. In the "Optimizar el aprendizaje" section, the materials include prompts such as the following: "Esta actividad ayuda a decodificar el texto, la notación matemática y los símbolos." The "Objetivo de la lección" section specifies that students will use equations and numerical procedures after developing conceptual understanding. For example, the section specifies that students will "utilizan modelos de diagramas de tiras y rectas numéricas para investigar la división de fracciones entre fracciones. Los estudiantes utilizan estos modelos para desarrollar un algoritmo para reescribir oraciones de división como operaciones de multiplicación." In the "Resumen" section, the materials reinforce procedural fluency by stating the following: "Los algoritmos son el método más eficiente para sumar, restar, multiplicar y dividir enteros." Overall, these sections describe how the materials address the procedural expectations outlined in the TEKS.

Evaluation for 5.3b
Questions and tasks include the use of concrete models and manipulatives, pictorial representations (figures/drawings), and abstract representations, as required by the TEKS.

The materials provide opportunities for students to use concrete models and manipulatives to explore mathematical concepts. For example, in Module 1, Topic 1, Lesson 5 and Module 2, Topic 1, Lesson 2, students use tarjetas de tasas and mosaicos to model fractional areas and equivalent ratios. The teacher guides students to construct physical models using items such as cuadros transparentes and tijeras, allowing them to manipulate and compare fractional quantities. The materials embed the use of manipulatives in the core lesson cycle, supporting concept development before transitioning to pictorial and abstract strategies. The materials provide opportunities for students to use pictorial representations to develop mathematical understanding. In Module 2, Topic 1, Lessons 1–2, students engage with diagramas de tiras and representaciones visuales to compare and order ratios, represent fractions, and connect part-to-part and part-to-whole relationships. Students create and interpret these drawings during tasks such as "Comparar cantidades" and "Ordenar las tasas," promoting the use of visual models aligned with the TEKS. The materials include abstract representations aligned to the grade-level TEKS, such as equations with variables and symbolic expressions. In Module 4, Topic 2, Lesson 1, students determine whether number sentences and algebraic expressions are always, sometimes, or never true, prompting students to reason abstractly about mathematical relationships. The lesson also engages students in analyzing and writing multiple equivalent expressions, such as "x + 4 = 19" and "3x = 45," reinforcing students' symbolic fluency and understanding of abstract representations.

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.

The materials integrate precise mathematical vocabulary in both teacher guidance and student-facing content. In Module 2, Topic 1, Lesson 1, the materials clearly define and reinforce terms such as razón, tasa, and comparación through sentence frames, anchor charts, word problems, and classroom discourse. The teacher materials prompt educators to model correct usage (e.g., "Una razón compara…"), while students apply vocabulary through structured talk and writing activities that require academic precision. The materials define and use mathematical terms with accuracy and consistency across teacher guidance and student tasks. In Module 2, Topic 1, Lesson 1, the materials define the term razón as a comparison between two quantities with the same or different units. This definition appears in teacher instructional notes and student materials, ensuring alignment. The term reinforces guided questions, visual models, and real-world contexts, avoiding conflicting or informal interpretations. The materials provide structured opportunities for students to define and explain how concrete and representational models connect to abstract mathematical concepts. In Module 1, Topic 1, Lesson 6, the teacher guide states that "Los estudiantes basan su algoritmo en los modelos de diagramas de tiras y rectas numéricas," connecting representational models to abstract concepts as emphasized in the TEKS. Additionally, prompts in the teacher notes elicit explicit explanation, such as "Explica cómo representa tu modelo la situación." This guidance ensures students not only create the model but also articulate how the parts of the diagram correspond to components of the symbolic expression.

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

The materials offer multiple opportunities for students to use visuals and manipulatives to develop mathematical language and conceptual understanding. In grade 6, Volume 1, Module 1, Topic 1, Lesson 3 of the Versión del maestro de matemáticas de secundaria, the materials list diagramas de tiras and tijeras as required materials. Students use these manipulatives and visuals to construct and compare equivalent fractions with different denominators. The "Ideas esenciales" section explains that students manipulate these diagrams to represent fractional relationships and observe equivalencies. This hands-on visual modeling supports the use of academic vocabulary such as fracción unitaria, numerador, and denominador in context. In grade 6, Volume 1, Module 2, Topic 1, Lesson 1 of the Versión del maestro de matemáticas de secundaria, the materials include a "Notas de facilitación" section. This section includes prompts such as "¿Cuáles son las cuatro razones para esta situación?" and "Comparen sus respuestas con un grupo." These prompts guide structured peer conversations using mathematical language. The materials incorporate language routines in which students explain their reasoning verbally, use comparison statements, and apply math vocabulary in complete sentences.

Evaluation for 5.4b
Materials include embedded teacher guidance to scaffold and support students' development and use of academic mathematical vocabulary in context.

In grade 6, Volume 1, Module 1, Topic 1, Lesson 5 of the Versión del maestro de matemáticas de secundaria, the materials embed vocabulary instruction in the "Notas de facilitación" section. Teachers prompt students to use terms such as productos, números mixtos, mínimos múltiplos comunes, and denominadores during problem solving. The "Resumen de la actividad" and "Concepto erróneo común" sections integrate terms in context and clarify how students apply these terms during mathematical tasks. This guidance supports teachers in introducing, reinforcing, and reviewing academic vocabulary as students reason through algorithms and solutions with peers and educators. The materials provide embedded teacher guidance to explicitly scaffold the development of mathematical vocabulary in context. In grade 6, Volume 2, Module 4, Topic 1, Lesson 2 of the Versión del maestro, the "Notas de facilitación" section directs teachers to define and model the use of academic terms such as variable, expresión algebraica, coeficiente, and término. Teachers engage students in discussions that clarify meanings, encourage rephrasing in their own words, and incorporate vocabulary in written and oral mathematical reasoning. The "Sella el aprendizaje" boxes and linguistic support strategies guide educators to integrate vocabulary instruction meaningfully within problem-solving activities.

Evaluation for 5.4c
Materials include embedded teacher guidance to support the application of appropriate mathematical language to include vocabulary, syntax, and discourse to include guidance to support mathematical conversations that provide opportunities for students to hear, refine, and use math language with peers and develop their math language toolkit over time as well as guide teachers to support student responses using exemplar responses to questions and tasks.

In grade 6, Volume 1, Module 2, Topic 1, Lessons 1–5 of the Versión del maestro de matemáticas de secundaria, the materials include sentence frames and conversation guides that are labeled "Reunir," "Ver la estructura," and "Sondear." These resources support students in using precise vocabulary, expressing ideas in complete sentences, and justifying mathematical reasoning. For example, students answer questions such as "¿Cómo puedes usar la razón en palabras?" and "¿Qué significa el mínimo número de vueltas?" The materials coach teachers to facilitate structured discourse and reinforce mathematical grammar and logic through repeated student talk opportunities. The materials embed consistent teacher guidance to support students in applying mathematical language through structured conversation and collaboration. In Module 4, Topic 1, Lesson 2, the materials include facilitation notes that repeatedly instruct teachers to organize students into pairs or groups to respond to guided discussion questions using academic terms in context. Question sets labeled "Preguntas para respaldar la conversación" prompt students to engage in peer conversations that build and refine their math language. These questions include the following: "¿Cuál es la diferencia entre una expresión algebraica y una expresión numérica?"

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

The "Alcance y secuencia de matemáticas de secundaria, grado 6 (165 días)" document integrates the TEKS process standards explicitly across multiple units. For example, in Module 1, Topic 3, titled "Decimales," the materials list the standards 6.1A, 6.1B, 6.1C, 6.1D, 6.1F, and 6.1G at the top of the module. Lesson summaries describe how students estimate, justify, and represent mathematical operations, such as using models to multiply decimals and reasoning through estimation. The materials thus demonstrate clear alignment with the process standards related to problem-solving, representation, and communication. The "Guía de ritmo por temas de matemáticas de secundaria, grado 6 (150 días)" document integrates the TEKS process standards within daily lesson tasks. For example, in Module 1, Topic 3, titled "Decimales," students "razonan sobre los resultados estimados antes de utilizar algoritmos" and "explican y representan el producto de un número decimal por otro número decimal menor que uno mediante un modelo." These tasks align with TEKS 6.1A (problem-solving), 6.1C (representation), and 6.1F (communication). The materials thus meaningfully integrate process standards into student learning experiences and instructional design.

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

The "Resumen anual de matemáticas de secundaria, grado 6 (165 días)" document shows that the materials embed the TEKS process standards 6.1A–6.1G throughout the entire course. The one-page table that summarizes each of the five modules explicitly notes that these standards are "integrados en cada módulo." This consistent labeling across all units confirms that the materials systematically incorporate process standards across the course structure. The "Resumen anual de matemáticas de secundaria, grado 6 (165 días)" states that "Los TEKS de proceso (6.1A–6.1G) se aplican a lo largo de todos los temas del curso e incluyen estrategias como modelar, estimar, justificar y comunicar razonamientos." This course-level description confirms that the materials intentionally connect process standards across all topics in grade 6. Rather than offer isolated objectives, the materials thread these standards throughout the entire curriculum to support coherence, transfer, and cumulative skill development.

Evaluation for 5.5c
Materials include a description for each unit of how TEKS process standards are incorporated and connected throughout the unit.

The "Alcance y secuencia de matemáticas de secundaria, grado 6 (165 días)" document and the "Guía de ritmo por temas de matemáticas de secundaria, grado 6 (150 días)" document provide unit-level descriptions of how the materials incorporate process standards. For example, in Module 1, Topic 1, titled "Factores y múltiplos," the introductory lesson states the following: "Los estudiantes reflexionan sobre su aprendizaje del modelo de resolución de problemas y repasan los estándares de procesos matemáticos de TEKS." Each subsequent lesson connects process skills to student tasks, such as using diagrams, justifying factorization strategies, and engaging in collaborative problem-solving. These details illustrate how the materials intentionally integrate process standards at the unit level. In the "Guía de ritmo por temas de matemáticas de secundaria, grado 6 (150 días)" document, each unit description describes the process standard connections across lessons. For example, in Module 5, Topic 1, Lesson 2, titled "Analizar las representaciones de datos numéricos," students "interpretan los datos, justifican sus observaciones y utilizan representaciones gráficas para explicar tendencias." These activities demonstrate the continuous reinforcement of TEKS 6.1C, 6.1F, and 6.1G across the unit, connecting process skills such as representation, justification, and communication from one lesson to the next.

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

In grade 6, Volume 1, Module 1, Topic 1, Lesson 1 of the Versión del maestro de matemáticas de secundaria, the materials include a dedicated section titled "Estándares de procesos matemáticos" in the lesson's front matter. This section lists the TEKS process standards 6.1A, 6.1C, and 6.1D. The section also describes how the materials expect students to apply math in real-world contexts, select appropriate tools and strategies, and communicate ideas using mathematical representations. This overview consistently appears at the beginning of the lesson, giving teachers a clear understanding of the process standards that the instructional sequence addresses. In grade 6, Volume 1 of the Versión del maestro de matemáticas de secundaria, the materials embed the TEKS process standards directly into lessons through margin notes. For example, the Module 1, Topic 1, Lesson 1 notes instruct the teacher to model the TEKS process standards 6.1A and 6.1D during instructional activities. The teacher prompts students to relate area models to real-life scenarios, such as measuring flooring for a hallway. Students explain their thinking using visual models and mathematical language. These annotations connect specific student tasks to the targeted process standards, reinforcing their application throughout 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 materials prompt students to think mathematically, requiring students to "enfrentarse a problemas del mundo real, clasificación de actividades, ejemplos prácticos y los análisis de los compañeros en un entorno en donde la colaboración, las conversaciones y el cuestionamiento sean prácticas de rutina." This routine, which can be found in the "Tres fases del método pedagógico" section of the Guía de programa e implementación de matemáticas de secundaria, fosters student-led reasoning and a deep engagement with mathematical ideas. The materials thus challenge students to think and make sense of mathematics. The materials support students in persevering through problem solving by encouraging them to "tomar un breve descanso y volver a intentarlo," "pedir ayuda a compañeros o maestros," and express effort-based statements such as "Lo intentaré de otra manera." Teacher guidance emphasizes productive struggle by advising teachers to "mostrar paciencia," "hacer preguntas," and "dar retroalimentación relacionada con el esfuerzo" to help students persevere through problem-solving. The materials guide students to make sense of mathematics by progressing from "la comprensión con objetos o movimientos concretos" to "la representación visual de los conceptos." Students last move to "la abstracción mediante el modelado con símbolos." This concrete-to-representational-to-abstract approach helps students connect conceptual understanding to procedural fluency.

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

The materials support students in understanding multiple ways to represent and solve problems by guiding them through a concrete, representational, and abstract progression. Students begin with manipulatives ("objetos o movimientos concretos"), then transition to visual models such as number lines ("representación visual"), and finally apply symbolic notation ("modelado con símbolos"). The materials support students in explaining different representations and solutions by including teacher prompts, which can be found in the "Facilitar el esfuerzo productivo" chart in the Guía de programa e implementación de matemáticas de secundaria. These prompts ask students to articulate and reflect on their thinking. They include the following: "¿Usaste el modelo de resolución de problemas?"; "Explica tu razonamiento"; and "¿Cómo lo sabes?" These prompts reinforce that multiple methods are valid and worth verbalizing. The materials support students in justifying their approaches through embedded reflection opportunities in which students must "explicar su razonamiento matemático" and share it with others. The materials promote such reflection through structured phases of the "Resolución de problemas" model as well as self-evaluation tasks after each topic.

Evaluation for 6.1c
Materials are designed to require students to make sense of mathematics through multiple opportunities for students to do, write about, and discuss math with peers and teachers.

The Guía de programa e implementación de matemáticas de secundaria includes a "Diseño y método pedagógico" section. This section explains that the materials engage students in collaborative math learning by including activities where students "se enfrenten a problemas del mundo real…en un entorno en donde la colaboración, las conversaciones y el cuestionamiento sean prácticas de rutina." Additionally, the "Aprender juntos" section promotes peer interaction by encouraging students to "compartir ideas, escucharse unos a otros y aprender juntos." Students make sense of mathematics through writing by engaging in structured reflection tasks. Such tasks prompt students to evaluate their progress and respond to essential questions. For example, the "Reflexión" section of the Guía de programa e implementación de matemáticas de secundaria directs teachers to do the following: "Pida a los estudiantes que evalúen sus progresos…de la lección mientras reflexionan y responden a la pregunta esencial." This task allows students to reflect on their procedures to write about math. The materials provide opportunities for students to engage in mathematical discussion through embedded teacher prompts and partner dialogue routines. Such routines can be found in the "Facilitar el esfuerzo productivo" section of the Guía de programa e implementación de matemáticas de secundaria. Students say things such as "Lo intentaré de otra manera" and "¿No hicimos algo parecido ayer? ¿Quizá eso ayude?" Teachers ask questions such as "¿Tu pareja está de acuerdo?" and "¿Cómo lo sabes?" These prompts and routines promote meaningful peer-to-peer and student-teacher mathematical conversations.

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

The materials include teacher prompts such as "Explica tu razonamiento" and "¿Tu pareja está de acuerdo?" These prompts guide students in articulating their thinking and mathematical arguments. The prompts can be found in the "Facilitar el esfuerzo productivo" teacher guidance sections of the Guía de programa e implementación de matemáticas de secundaria. Teacher guidance in the materials encourages student reflection through structured activities. These activities include the "Reflexión sobre la evaluación" activity, in which students evaluate their own understanding and strategies and create a plan for improvement. Such reflection supports students' development of metacognitive skills and their justification of problem-solving approaches.

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

The materials provide embedded prompts such as "¿Cómo lo sabes?" and "Explícalo otra vez." Such prompts reinforce responsive instruction, helping teachers give explanatory feedback that builds on student responses. These prompts appear in the "Facilitar el esfuerzo productivo" teacher support sections. The Guía de programa e implementación de matemáticas de secundaria includes guidance that supports the use of student responses to adjust instruction and provide targeted feedback. For example, the "Evaluación formativa" section instructs teachers to use reflection documents and student answers to deepen understanding. This section also recommends using scaffolded questioning to address gaps or misconceptions. The materials include prompts and guidance to support teachers in providing explanatory feedback based on student responses and anticipated misconceptions. For example, in Module 1, Topic 1, Lesson 5, "Demuestra lo que sabes," the materials support the teacher with a "Concepto erróneo común" section. In this section, the materials state common misconceptions, such as how students often generalize and think that they will obtain a larger number when multiplying two numbers. The materials guide teachers to provide explanatory feedback based on student responses. For example, the materials provide the following guidance: "Pídales que editen su declaración para especificar para qué tipos de números es verdadera la declaración." Teachers ask students to reflect on their responses to specify what types of numbers make their statements true.