Aprendizaje Bluebonnet Matemáticas K-5 Grado 4

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

The materials include a comprehensive scope and sequence table under "Alcance y secuencia de grado 4" that breaks down each module. This scope and sequence highlights how the Texas Essential Knowledge and Skills (TEKS) are introduced in each module and throughout the year. This evidence can also be located in the Matemáticas K–5 guía de programa e implementación. The materials include two scope and sequence tables under "Alcance y secuencia de grado 4." One is a 150-day instructional table, and another is a 165-day instructional table. 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 an overview that supports effective pacing and ensures alignment with the TEKS.

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 "Grade-level matematicas K–5" section of the Versión del maestro includes a suggested pacing calendar at the start of each module. The Guía de programa e implementación includes a section called "Additional Days School Year." This section explains the modules that provide additional flexible-use days, which can serve as a supplement to the core curriculum. The materials include suggested pacing to support effective implementation. For example, the materials provide 30 additional instructional days that include 25 extra lessons, a pre-evaluation, a post-evaluation, and three flexible days. The "Matemáticas grado 4, días adicionales del año escolar (ADSY)" resource in the Versión del maestro outlines this information.

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 materials provide an explanation for the rationale of unit order. The "Contenido general" section of the Versión del maestro explains how each topic builds on students' prior knowledge in each of the modules. For example, in Módulo 1, "Valor de posición, redondeo, y algoritmos para la suma y la resta," the Versión del maestro describes how students first strengthen their understanding of place value, then apply such knowledge to comparing and rounding numbers. Students later use this knowledge in addition, subtraction, and multistep problems. Each stage increases in complexity.

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

The "Protocolo de internalización de módulos para el maestro" section in the Matemáticas K–5 guía de programa e implementación provides unit internalization guidance. This section offers a step-by-step process that supports teachers in understanding each module before instruction begins. The protocols help teachers understand the concept objective, the structure of the module, the lesson progression, and the organization of resources. The Versión del maestro includes a grade-level "Matemáticas K–5 aprender" section. At the beginning of the module, the materials offer an overview of the content that the teacher will deliver to students. The "Contenido general" section includes a table with common misconceptions, along with ways to address these misconceptions. The table also includes focus standards, fundamental standards, process TEKS, information on the general content of modules, lesson objectives, and a vocabulary preview.

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

The Guía de programa e implementación includes an "Observation Tool" table, which serves as a resource for coaches to document observations of teachers' instruction and their implementation of the materials. This tool includes sections that identify activities the coach should look for before, during, and after the classroom visit. The table also includes checkboxes to indicate the presence or absence of observed evidence.

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 for grade 4 provides a detailed explanation of each module's general content. This explanation also includes background knowledge that students will apply and strategies that the teacher can implement during instruction.

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 materials include strategies and activities for families in English and Spanish. The Guía del curso includes a "Tips for Families" section for each of the seven grade 4 modules. This section features key terminology, visuals, and clearly defined objectives for families that outline the content students will review throughout the module. This information helps families support the progress of their child at home. The "Recursos por nivel de programa" provide letters to families in both English and Spanish. These letters explain the vision of the materials and outline the resources they offer.

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 4, Modules 1–7 of the Versión del maestro, the materials include detailed and comprehensive lesson plans with clear, consistent structure. For example, each lesson begins with a specific objective and incorporates fluency practice, application problems, concept development, and a student debrief. Each lesson includes a suggested timing for instructional pacing. In Modules 1–7 of the Versión del maestro, the materials provide teachers with summaries, planning notes, and material lists to support preparation. The materials also include interactive activities to encourage student discussion and exit tickets to help assess understanding and guide instruction. The "Evaluaciones" section of the Versión del maestro de matemáticas K–5 includes formative and summative assessments. These instructional assessments are aligned with the TEKS.

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.

Module 6 of the Versión del maestro includes the "Lista de materiales del Module 6: Descripción general de la lección." This resource provides a lesson overview that lists the specific materials needed for the lesson. The materials include all necessary teacher and student resources to deliver each lesson. For example, Module 1, Lesson 1 includes a "Desarrollo del concepto" section. This section labels materials with an "(M)" for maestro and an "(E)" for estudiante to clearly indicate which materials belong to each group according to the needs of the lesson.

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

In the Matemáticas K–5 guía de programa e implementación, the "Lesson Structure" resource includes a "Homework" section. This section provides teachers with the goal for the assignment and guidance on how to effectively implement homework. The Versión del maestro offers extensions to lessons, including a homework sheet after each lesson. Students use this sheet to independently apply what they learned on a particular day.

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.

In the grade 4 Versión del maestro, the materials include an evaluation and rubric at the end of every unit. For example, the "Contenido general de la evaluación de grado 4" includes a summative evaluation for each module, which is composed of the specific TEKS that were covered in the module. The materials include a mid-module evaluation and rubric. These resources allow educators to utilize some of the questions as a diagnostic practice assessment for the TEKS that will be covered again in the module's summative evaluation. The "Evaluación de la mitad del módulo" within each module includes progress-monitoring tools for teachers. The evaluations include various types of questions, such as multiple-choice, multiple-selection, and constructed-response questions. The "Grado 4 evaluaciones" section of the Versión del maestro identifies mid-module assessments as diagnostic and end-of-module assessments as summative. The assessments use various formats—multiple-choice, fill-in-the-blank, and open-ended questions—to support instructional decisions and reveal misconceptions. For example, the "Evaluación de la mitad del Módulo 1" asks students to organize numbers, draw number lines to round, and identify a number that is ten times another. The grade 4 materials include formative and summative lesson-level assessments with varied tasks and question types. Problem sets engage students in modeling, using unit form, and solving real-world problems through open-ended responses and visuals. Each lesson ends with a student debrief and exit ticket. The "Grado 4 evaluaciones" section of the Versión del maestro states the following: "Los grupos de problemas también pueden servir como evaluaciones formativas que brinda otra oportunidad para monitorear el aprendizaje de los estudiantes." The section also states that "Boletos de salida son evaluaciones formativas breves, diarias." The materials thus include a variety of instructional assessments.

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

The Matematicas K–5 guia de programa e implementacion includes an "Enfoque de las evaluaciones" section, which defines the purpose of each assessment type embedded in instruction. Exit tickets function as brief, daily formative assessments that uncover misconceptions and guide next-day instruction. Problem sets act as formative checks that help teachers monitor student progress in real time. For instance, problem sets are meant to move from simple to complex problems, and exit tickets are formative assessments that are meant to be brief. As the Versión del maestro explains in the "Contenido general de las evaluaciones de grado 4" section, the mid-module assessments serve a diagnostic purpose—they check understanding of the first half of the module and reveal misconceptions. End-of-module assessments serve a summative purpose and measure mastery of the module's TEKS. Mid-module and end-of-module assessments provide learning evidence that teachers use to adjust instruction or measure content mastery.

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

The "Enfoque de las evaluaciones" section of the Matemáticas K–5 guía de programa e implementación offers guidance on administering assessment materials consistently. For example, the materials state the following: "These mid-module and end-of-module tasks are designed to be used in conjunction with instructionally embedded tasks and other formative assessment strategies to realize the full benefits of data-driven instruction." The "Enfoque de las evaluaciones" section of the Matemáticas K–5 guía de programa e implementación explains how to administer tests accurately. For example, the materials state the following: "Mid-module assessment tasks are designed to be completed independently by students within one class period. These tasks should also be new to the students and not preceded by analogous problems." The materials guide consistent administration of exit tickets in grade 4, Modules 1–7. The materials inform teachers when exit tickets should be administered and how exit ticket data should be tracked and used. The materials inform teachers that oral administration is permitted. The materials include a section titled "Sugerencias para la implementación," which guides teachers on the implementation of instructional assessments, including time frame expectations.

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

The materials include diagnostic and summative assessments aligned to the TEKS and the objectives of the course, unit, and lesson. In the "Grado 4 evaluaciones" section of the Versión del maestro, teachers can reference the "Evaluación y estándares evaluados" chart, which lists the specific TEKS and learning objectives that the materials assess. The chart further supports alignment by identifying the TEKS addressed in each question for both mid-module and end-of-module assessments, helping teachers track which standards students have or have not mastered. The materials include formative assessments aligned to the TEKS and lesson objectives at the end of each lesson in the form of an exit ticket. For example, in Module 2, Lesson 2 of the Versión del maestro, the lesson objective describes using addition and subtraction to solve multistep problems involving length, mass, and capacity. The corresponding exit ticket asks students to solve a two-part word problem involving mass and length, directly assessing the stated objective.

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

The "Evaluación del final del Módulo 5" in the "Matemáticas grado 4 evaluaciones" section of the Versión del maestro includes tasks that reflect more than two levels of complexity. For example, students calculate, analyze diagrams, and design figures with written justifications. These tasks build in rigor and require students to apply, explain, and justify their mathematical understanding in varied ways. The "Matemáticas grado 4 evaluaciones" section of the Versión del maestro demonstrates more than two levels of complexity in the "Evaluación del final del Módulo 3." This assessment includes tasks in which students measure side lengths with a ruler, explain why a figure is or is not a quadrilateral, and create a new shape with specific attributes. These items require students to apply measurement skills, analyze geometric properties, and construct justifications using mathematical reasoning.

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

The instructional assessments in the "Grado 4 evaluaciones" section of the Versión del maestro provide clear guidance for interpreting student performance through a progress rubric. This rubric describes how students demonstrate increasing levels of conceptual understanding and mathematical reasoning across four categories, which range from "Poca evidencia" to "Evidencia de razonamiento sólido." The materials guide teachers to use this tool diagnostically to identify misconceptions and strengths, enabling targeted instruction and reflection on student needs. The materials' scoring information in the "Grado 4 evaluaciones" section of the Versión del maestro includes detailed rubrics that guide educators in evaluating student work. The materials include a four-tier performance rubric aligned to the TEKS, which is titled "Progreso hacia el dominio." This rubric includes specific descriptors that distinguish levels of reasoning and accuracy. These tools support teachers' interpretation of student performance through proficiency levels that help them determine students' strengths and weaknesses. The materials thus personalize instruction to meet student needs concerning intervention and enrichment.

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 grade 4 materials include clear guidance on using specific tasks to address student trends in performance. For example, the "Contenido general" section includes a dedicated table in the "Solución colaborativa de problemas de conceptos erróneos de los estudiantes" resource in each of the modules. This table identifies common misconceptions aligned to the TEKS and suggests concrete instructional responses to correct these errors. The materials offer structured activity guidance to address student misconceptions that teachers have identified through student assessment performance. For example, to respond to observed errors concerning regrouping while subtracting across place values (TEKS 4.4A), the program recommends using a value chart and base-ten models to represent the regrouping process visually and concretely.

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 Guía del curso del grado 4 in the Versión del maestro includes a structured "Herramienta de reflexión sobre la evaluación" that prompts teachers to guide student reflection before and after assessments. This tool provides scripted teacher language to initiate reflective discussion, prompts to analyze assessment trends, and guidance for tracking specific student misconceptions and student confidence levels. The "Reflexión sobre la evaluación" worksheet explicitly supports students in tracking their thinking. The worksheet prompts students to identify which questions were confusing, reflect on what they know, and determine what they will do differently next time. Asking students to track their progress supports their engagement in error analysis. This process allows students to write about their reflection and determine action steps, building student agency.

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 include clear teacher guidance for differentiated instruction and activities for students who have not reached proficiency on grade-level content and skills. The Matemáticas K–5 guía de programa e implementación in the Versión del maestro includes a section titled "Diferenciación y soportes." This section outlines how to use the margin notes embedded throughout the lessons to address the needs of emergent bilinguals, students with disabilities, and students requiring additional practice. Teachers receive scaffolded activities such as breaking tasks into smaller parts, using graphic organizers, offering sentence stems, and providing real-world connections. Modules 1–7 of the Version del maestro include teacher guidance for differentiated, scaffolded instruction through a structured routine designed to address student misconceptions. The "Solución colaborativa de problemas de conceptos erróneos de los estudiantes" section provides a three-step process that stimulates students' thinking, validates students' ideas, and guides students toward deeper understanding. Teachers receive targeted strategies, visual aids, and sample prompts to scaffold learning based on specific student needs, supporting small group and paired instruction for students who have not yet reached proficiency.

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 "Contenido general del módulo" resource includes a "Terminología" section, which appears in Modules 1–7 of the Versión del maestro. This section includes pre-teaching supports for unfamiliar academic vocabulary. The section clearly defines newly introduced mathematical terms, uses cognates when applicable, and provides visual representations as embedded supports. Modules 1–7 of the Versión del maestro embed supports throughout the "Notas sobre las diferentes formas de representación" for teachers, which clarify unfamiliar references for students through multilingual scaffolds, visual examples, and academic language support. The materials thus provide guidance for helping students access and understand academic terms 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.

The materials include teacher guidance for differentiated instruction for students who have demonstrated proficiency in content and skills. In the "Diseño de materiales de instrucción" section of the Matemáticas K–5 guía de programa e implementación in the Versión del maestro, the program encourages teachers to create daily opportunities for advanced learners to reflect, justify, and choose from various problem-solving approaches. This lesson structure fosters conceptual depth and transfer by supporting metacognition, discourse, and mathematical connections throughout the module activities. The materials provide teachers with embedded guidance for enrichment and extension activities for students who demonstrate proficiency. In the "Diseño de materiales de instrucción" section of the Matemáticas K–5 guía de programa e implementación in the Versión del maestro, the program recommends offering more complex materials, encouraging flexible solution paths, and deepening conceptual understanding through strategic prompts and reflections. The notes on participation and representation suggest specific ways teachers can challenge students and extend their learning beyond grade-level expectations.

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 4, Module 2 of the Versión del maestro include explicit, scripted prompts for the teacher to model and explain key concepts related to metric conversions and mixed units. For example, in Lesson 1, "Desarrollo del concepto," a script directs teachers to provide the problem "M: Muestre horizontal: 5 m + 2,500 mm." The materials then provide follow-up dialogue for explaining strategies such as the following: "Podemos convertir los metros en milímetros antes de sumar." These step-by-step modeling cues, which include prompts for regrouping and converting units, ensure teachers clearly and accurately demonstrate mathematical concepts to students. The materials include teacher guidance for modeling concepts by providing concrete examples, sentence stems, and recommended visual representations. In Lesson 1, "Notas Sobre las siferentes formas de representación," the notes on the side of the lesson guide teachers to connect the regrouping strategy to earlier fluency work. The notes suggest language such as the following: "No podemos sumar unidades diferentes. Si necesito convertir cinco metros a milímetros…Ahora, puedo sumar 5,000 milímetros y 2,500 milímetros." This language allows teachers to explain the concept using explicit procedural thinking steps.

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

In grade 4, Module 6, Lesson 1, "Desarrollo del concepto," the Versión del maestro provides teacher guidance for effective lesson delivery through a variety of instructional approaches, including hands-on manipulation, visual representation, mathematical dialogue, and number line modeling. For example, the lesson engages students in using physical objects such as bolsas de arroz, reglas de metro, and balanzas digitales to represent decimals concretely. The lesson then transitions to pictorial representations such as diagrams and number lines. Finally, the lesson connects to abstract notation through equations and place value charts. Embedded teacher prompts support each approach and recommend facilitating whole-class discussions, partner tasks, and tactile activities, ensuring that educators teach concepts through multiple modalities. The materials provide teacher guidance for effective lesson facilitation using more than two instructional approaches. For example, in grade 4, Module 6, Lesson 12, "Desarrollo del concepto," the Versión del maestro integrates visual models, procedural fluency, and conceptual discussions. The materials prompt teachers to pose questions, anticipate misconceptions, and lead conversations that compare strategies.

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.

The Matemáticas K–5 guía de programa e implementación in the Versión del maestro includes more than two practice types to support effective implementation. For instance, the "Estructura de la lección" section outlines guided practice through teacher-student dialogue and the use of manipulatives. Students then engage in independent practice during the "Grupo de problemas" section, in which students apply conceptual understanding on their own. The materials embed collaborative learning through structured peer discussions such as "Expliquen a su compañero." These discussions appear daily during the "Reflexión" portion of the lesson. The materials provide teacher guidance to support effective implementation through step-by-step instructional dialogue, questioning, and anticipated student responses for whole-group instruction across all seven modules. The Matemáticas K–5 guía de programa e implementación in the Versión del maestro outlines detailed prompts. These prompts can be found in the "Desarrollo del concepto" section. The prompts provide teacher cues that are labeled with "M," such as "¿Qué ven, y qué debemos hacer?" Additionally, the materials include instructional tips that emphasize aligning mathematical strategies. The materials label student responses with an "E."

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.

The Matemáticas K–5 guía de programa e implementación in the Versión del maestro includes linguistic scaffolds to support emergent bilingual students with vocabulary development, including a structured routine called "Rutina lingüística reunir y mostrar" in the "Apoyo para estudiantes bilingües emergentes" section. This routine guides teachers to capture student language during discussions and map this language to academic terms using visual aids, diagrams, and real-life objects. According to the materials, this practice explicitly connects everyday language to mathematical terminology, enhancing metacognitive processing and comprehension in bilingual classrooms. The Matemáticas K–5 guía de programa e implementación in the Versión del maestro embeds bilingual instructional strategies throughout its four-part lesson model. The "Apoyos lingüísticos para que los estudiantes EB desarrollen comprensión y conocimiento" section provides specific guidance that activates prior knowledge ("Fluidez") and encourages academic discourse using visual aids and sentence stems ("Desarrollo del concepto" and "Reflexión"). This practice promotes students' structured oral language in their first language. The materials prompt teachers to strategically group students by language or math proficiency levels. The materials use translanguaging to reduce students' cognitive load and support effective implementation in bilingual/ESL settings.

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 for teachers to support emergent bilingual students across all lessons in all seven modules. This guidance fosters students' development of academic vocabulary, comprehension, background knowledge, and cross-linguistic connections through oral discourse. For example, grade 4, Module 1, Lesson 1 in the Version del maestro includes structured student-teacher dialogue, sentence stems, and opportunities for peer discussion that promote students' use of academic language, such as "uno decena es 10 veces más que uno unidad." The teacher prompts guide students to explain their thinking aloud, compare quantities, and articulate multiplication patterns. These actions reinforce students' conceptual understanding. Margin notes within the lessons encourage the use of visual models and oral repetition to support meaning-making. These notes also recommend strategies such as using sentence stems and allowing oral rehearsal in each student's primary language to promote linguistic transfer. The materials state the following: "Algunos estudiantes que necesitan más apoyo lingüístico pueden beneficiarse de la oportunidad de practicar simultáneamente hablando y mostrando unidades (por ejemplo, decenas)." The materials thus incorporate teacher guidance to help students make language connections. The materials provide embedded supports for emergent bilingual students through structured writing opportunities and teacher guidance across all lessons in the seven modules. For example, the materials use sentence stems such as "___ decena es ___ veces más que ___ unidad" consistently throughout Module 1, Lesson 1 of the Version del maestro to build students' academic vocabulary and support their oral and written discourse. Debriefing questions prompt students to explain their reasoning using math terms, drawings, and complete sentences, deepening students' comprehension. In addition, teacher guidance in the "Margin Notes" section activates prior knowledge from earlier grade-level content (e.g., area and perimeter from grade 3) to support background understanding during written problem-solving tasks. The materials include embedded guidance to support emergent bilingual students in developing academic vocabulary through written discourse. The materials prompt students to write equations and use precise mathematical terms such as ángulo llano, ángulo recto, and ángulos suplementarios during the "Reflexión" and "Boleto de salida" sections of Module 4, Lesson 10. Students increase their comprehension through written responses to questions such as "¿Por qué es importante ser preciso al medir los ángulos?" Students justify their reasoning using academic language. To support cross-linguistic connections, teacher guidance in the "Notas sobre las diferentes formas de representación" and "Notas sobre las diferentes formas de participación" across all modules encourage the use of visual glossaries and illustrated word lists. This guidance also encourages attention to terms with bilingual relevance, such as rayo, línea, and cuarto. Module 4 uses these terms to help emergent bilinguals make connections between Spanish and English vocabulary.

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, offering them 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 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 sections such as "Fluency," "Application Problems," and "Concept Development." In these sections, students read, engage in discourse, and apply vocabulary in both languages. In the K–5 Math Program and Implementation Guide, the materials explicitly prompt 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 have 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.

In grade 4, Modules 1–7 of the Versión del maestro, the materials provide daily practice that fosters a deeper understanding of TEKS-aligned content. Each lesson begins with a "Practica de fluidez" task, transitions into a "Problema de aplicación" task to revisit or extend prior learning, and progresses to "Desarrollo del concepto" tasks that increase in rigor. Students apply concepts through problem solving and conclude with "Boleto de salida" and "Reflexión" tasks that reinforce and extend learning. Modules 1–7 of the Version del maestro include daily and unit-level assessments that are aligned to the TEKS. Lessons incorporate exit tickets that check for understanding through targeted, standards-based questions. Mid-module and end-of-module assessments feature varied formats and levels of challenge, requiring students to apply concepts, justify their reasoning, and demonstrate mastery across multiple standards.

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

The materials include tasks and assessments in modules that provide students with scaffolding as support. The materials demonstrate a progression of rigor and complexity, integrating grade-appropriate question sets that lead to grade-level proficiency. In grade 4, Module 3, Leccion 5 of the Version del maestro, the "Grupo de problemas" section includes tasks that increase in complexity. Students begin by calculating perimeter and area, then solve multi-step problems using those formulas. Finally, students determine unknown dimensions based on a given area. This progression supports students' mastery of the grade-level TEKS in application. In grade 4, Module 5 of the Version del maestro, Leccion 16 introduces tasks in increasing order of complexity. This lesson begins with fluency practice, then moves to tasks involving adding and subtracting fractions with visual models. The lesson concludes with decomposition and benchmark fraction tasks. A student debrief at the end of the lesson reinforces the day's objective and aligns the lesson with grade-level TEKS expectations.

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

In the grade 4 Guia del curso, the materials demonstrate coherence across units by connecting geometry and operations through shared conceptual models. As Module 3 states, "La medición del perímetro y el área proveen la base concreta detrás de la propiedad distributiva en el algoritmo de multiplicación." The materials use area measurement to support students' understanding of the distributive property and multiplication, reinforcing conceptual relationships across concept progression. In the grade 4 Guia del curso, the materials demonstrate coherence across units by connecting relationships and patterns in fractions and decimals through consistent representation and fluency practice. Module 6 explains the following: "Las actividades de fluidez a lo largo del módulo continúan enfatizando la conexión entre decimales y fracciones...los estudiantes aprenden a relacionar 3/10 = 0.3 = 3 décimos." The materials thus support students' conceptual understanding of rational numbers and reinforce patterns across number systems.

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.

Modules 1–5 of the Version del maestro includes a "Contenido general" section, which clearly defines how content knowledge is built and connected to what students have learned or are learning. For example, Module 5, titled "Equivalencia de fracciones, orden y operaciones," states the following: "En este módulo de 35 días, los estudiantes extienden su trabajo de 3er grado sobre el uso de objetos concretos y modelos pictóricos para consolidar su comprensión de las fracciones como números. Los estudiantes ahora exploran la equivalencia de fracciones y extienden esta comprensión a los números mixtos. Esto lleva a la comparación de fracciones y números mixtos y a la representación de ambos en una variedad de modelos." This example demonstrates a connection between students' knowledge from a previous grade and the current lesson. Students' learning extends from concrete fraction models to equivalent fractions to mixed numbers. The materials consistently connect students' prior knowledge by building on the language of mixed units that was introduced in earlier grades. For example, in Module 2, students expand their understanding of composition and decomposition from representations such as "2 centenas y 5 decenas" in grade 2 to more complex mixed units such as "2 h. y 5 min.," "$2.50 y $5.00," and "2 km. y 5 m." This work reinforces consistent mathematical language and conceptual continuity across grade levels. The materials explicitly prepare students for future grade-level expectations by connecting their current learning to upcoming content. For example, in grade 4, Module 2, the materials state the following: "Los estudiantes amplían sus conocimientos de 3er grado, en el que representan relaciones de la vida diaria utilizando pares de números en tablas y describen los patrones mediante descripciones verbales (TEKS 3.5E) y se preparan para el 5to grado, en el que los estudiantes generarán patrones numéricos cuando se les den reglas en los formatos de y = ax o y = x + a y graficarán estos puntos en planos de coordenadas (TEKS 5.4C)." This example connects what students are currently learning to what they will be learning in the future, making purposeful connections to the TEKS.

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 at the lesson level by explicitly building on students' prior knowledge from grade 3, including their knowledge of multiplication, division, and foundational measurement concepts. In grade 4, Module 7, Topic C, students revisit and expand on grade 3 skills such as partitioning measurement tools and understanding unit conversions. Students engage in hands-on experiences that connect fractions and measurement. The materials state the following: "Coherencia se desprende de G3–M1: Propiedades de la multiplicación y la división...y G3–M2: Valor de posición y solución de problemas con unidades de medición." The materials thus connect students' prior knowledge in grade 3 to new concepts in grade 4. The materials demonstrate coherence within the current grade by integrating prior grade 4 learning on place value and operations into new contexts involving mixed number conversions. Module 7, Topic C states the following: "Los estudiantes utilizan su conocimiento de las tablas de conversión con esta nueva comprensión para convertir unidades numéricas mixtas en unidades más pequeñas…aplicando unidades numéricas mixtas para resolver problemas de varios pasos." This statement explains how students make connections between previously learned concepts (such as conversion tables) to new on-grade-level learning, as students apply the concept to solve multi-step problems.

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

Grado 4, Módulo 7, Leccion 9 of the Versión del maestro explicitly includes a 12-minute fluency practice section that revisits previously learned skills from earlier lessons and modules. For example, students complete tasks from TEKS 4.4A (resolving problems with multiplication and division), TEKS 4.8A (unit conversions), and TEKS 4.3A (fractional units). These fluency activities are intentionally designed to reinforce computation and measurement strategies and skills developed across prior units. The materials thus revisit and strengthen procedural fluency through repeated, distributed practice. Grado 4, Módulo 7, Leccion 9 of the Versión del maestro revisits concepts from earlier grades and modules, such as part-to-whole reasoning, unit conversions, and fraction equivalence. For example, activities involving rulers and diagrams of strips require students to apply their understanding of fractional parts of a whole, which students developed in earlier modules and grades. Students now apply such knowledge to explore the relationships between feet, inches, and other measurement units (e.g., 1/4 yard = 1 foot; 1/12 foot = 1 inch).

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

The materials offer interleaved practice by intentionally revisiting and requiring students to apply previously learned skills in the context of measurement conversions, such as multiplication, fractions, and area models. For example, Module 7 states that "utilizan sus habilidades de multiplicación adquiridas en el Módulo 3 para completar las tablas y logran identificar y explicar las conexiones." This explanation demonstrates how the materials allow students to practice previously learned skills in the context of new learning. Throughout the module, students revisit and apply key conceptual understandings from earlier content throughout the units. For example, in the "Contenido general" section of grade 4, Module 7 in the Versión del maestro, the materials state the following: "Este trabajo es directamente análogo al trabajo anterior con la equivalencia de fracciones utilizando el diagrama de tiras, el modelo de área y la recta numérica en los Topics A, B, y D del Módulo 5." This statement explains how students will use strip diagrams, area models, and number lines to practice previously learned concepts and make connections to measurement conversions and fractions.

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

In grade 4, Module 3 of the Versión del estudiante, titled "Aprender multiplicación y división de varios dígitos," students interpret area models in Lecciones 11–12 to understand expressions such as 425 × 4. Students connect each component to its numerical representation. Students regularly engage with area models, strip diagrams, and equations that visually represent multi-digit multiplication and division. The Versión del estudiante's seven modules (Modules 1–7) consistently require students to interpret visual models. All seven modules (Modules 1–7) of the Versión del estudiante include embedded opportunities to analyze models. For example, in grade 4, Module 3, "Aprender multiplicación y división de varios dígitos," Leccion 11 of the Versión del estudiante requires students to decompose numbers within strip diagrams and partial product models, examining how these structures represent place value and operations. Tasks prompt students to break down and analyze visual models to identify relationships between parts. Students then justify their reasoning.

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

The questions and tasks in the materials require students to consistently create visual models (such as area models, strip diagrams, and labeled drawings) to solve real-world problems. For example, grade 4, Module 3, Lesson 2 of the Versión del estudiante asks students to do the following: "Dibuja un modelo de área y, luego, resuélvelo utilizando el algoritmo normal." This task prompts students to create an area model to represent multiplication. The materials consistently guide students to construct their representations to make sense of and solve mathematical problems. Across Modules 1–7 of the Versión del estudiante, the materials include problems that explicitly instruct students to model their thinking using drawings, numbers, or words. For example, grade 4, Module 3, Lesson 3 of the Versión del estudiante includes a "Grupo de problemas" section, which requires students to do the following: "Resuelve los siguientes problemas. Utiliza dibujos, números, o palabras para mostrar tu trabajo." This task requires students to create and show mathematical situations with pictorial representations.

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

Modules 1–7 of the grade 4 Versión del maestro include "Problema de aplicación" sections, which consistently prompt students to apply their conceptual understanding in new contexts. For example, Module 7, Lesson 7 includes the following question: "La cantidad total de la compra de un cliente es de $73.55. ¿Cuánto gastó el cliente?" This problem challenges students to extend their understanding of numerical patterns. Students use inverse reasoning to apply a known mathematical rule in a real-world scenario. Tasks within the "Desarrollo del concepto," "Grupo de problemas," and "Reflexión" sections across Modules 1–7 of the grade 4 Versión del maestro enable students to apply conceptual understanding in complex and unfamiliar situations. For example, in Module 7, Lesson 7, students must solve problems such as "3 días, 12 horas + 9 días, 20 horas" and "¿En qué se parece resolver 25 min 8 s – 12 min 46 s a 8/60 – 46/60?" These problems foster opportunities for students to apply concepts and skills to solve a problem.

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

The Matemáticas K–5 guía de programa e Implementación in the Versión del maestro emphasizes that materials build student automaticity through a balanced, repetitive, gradual release model. The guide states that precision and fluency help students apply learned procedures and concepts to new mathematical problems, enabling students to work independently in increasingly complex situations. The materials state the following: "Aunque los materiales de instrucción de matemáticas K–5 no siguen el modelo convencional de 'yo hago, nosotros hacemos, ustedes hacen,' es necesario contar con soportes receptivos y una liberación gradual de responsabilidad para que los estudiantes participen en un proceso de esfuerzo adecuado." This statement shows that the materials are designed to build automaticity, which is conducive to students' productive struggle to access grade-level tasks. The Matemáticas K–5 guía de programa e implementación in the Versión del maestro outlines the importance of fluency for mathematical success. The guide states that with adequate teacher support, students can develop "la fluidez procedimental y la comprensión conceptual" and then "transferir su aprendizaje a situaciones nuevas y más complejas que no han visto antes." Such tasks build fluency by helping students internalize foundational concepts and apply them flexibly in unfamiliar contexts in later lessons.

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 frequent opportunities for students to apply efficient mathematical procedures throughout lessons and across the program. For example, the Matemáticas K–5 guía de programa e implementación in the Versión del maestro explains that fluency routines are purposefully designed to prepare students "con la base de cálculo para resolver problemas de manera flexible, eficiente, y precisa." This design reflects a deliberate effort to build and reinforce students' ability to use efficient methods when solving mathematical problems. The materials provide opportunities for students to apply flexible mathematical procedures during fluency routines, application problems, and student discourse. The Guía de programa e implementación affirms that "los problemas de cada práctica veloz se seleccionan y secuencian cuidadosamente para ayudar a los estudiantes a reconocer patrones y estructuras," encouraging the flexible use of strategies. Problem-solving tasks support razonamiento flexible, and instructional planning promotes grouping students in ways that support strategic and flexible thinking. The Matemáticas K–5 guía de programa e implementación in the Versión del maestro explains that boletos de salida serve as daily formative checks of student understanding and accuracy, allowing teachers to identify and address misconceptions.

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 prompt students to compare multiple strategies to determine which is more efficient. The "Desarrollo de la autoeficacia—representaciones múltiples" section of the Matemáticas K–5 guía de programa e implementación encourages students to revise and compare their reasoning, which encourages student reflection on the efficiency of solution paths. The materials include phrases such as "los estudiantes pueden tener diferentes soluciones" and "se anima a los estudiantes a revisar su razonamiento y sus estrategias." These phrases build opportunities into the lesson structure for students to evaluate the effectiveness and speed of approaches. The materials emphasize flexibility by showing that students can solve problems in different ways and learn from their peers. The "Desarrollo de la autoeficacia—rutinas de resolución de problemas" section of the Matemáticas K–5 guía de programa e implementación states that the materials reference the lee-dibuja-escribe strategy across all modules, helping students internalize various approaches and representations. This routine fosters flexibility by having students ask themselves the following: "¿Qué puedo dibujar?...¿Qué me muestra mi dibujo?" Such questions encourage students to select strategies that work best for them. The materials support accuracy through the use of reflection and partner discussions. The "Estructura de la lección" section of the Matemáticas K–5 guía de programa e implementación states that during the "Reflexión" and "Boleto de salida" routines, the materials prompt students to explain how they solve problems, evaluate their choices, and revisit strategies.

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

The materials include embedded lesson structure and margin notes that help teachers guide students toward more efficient strategies. For example, in the "Práctica de fluidez" routine, students engage in short, targeted routines such as "Carrera de varios números" and "Muéstrame tus dedos para contar." These routines are explicitly designed to promote automaticity and efficient calculation. The materials state that fluency routines prepare students to "resolver problemas de manera flexible, eficiente y precisa," which guides students toward efficient and accurate approaches. The materials contain embedded supports that guide teachers in helping students refine their approaches. Teacher guidance states that "los maestros pueden enfatizar pasos específicos que los estudiantes necesitan dominar o ampliar...para los estudiantes que desean un desafío." Teacher guidance also encourages the use of "soportes y extensiones recomendados en las notas al margen." These supports enable teachers to strategically adjust instruction to help students adopt more efficient, targeted strategies based on their readiness.

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

The materials explicitly state how the conceptual emphasis of the TEKS is addressed. For example, grade 4, Module 1 of the Version del maestro guides students to build number sense through the exploration of place value and estimation strategies. Lesson 1 includes a "Notas para el maestro" section, which emphasizes conceptual development by stating the following: "En este módulo, los estudiantes amplían su comprensión del valor de posición al trabajar con números más grandes, lo que les permite realizar estimaciones razonables y explicar sus estrategias de suma y resta." Lessons emphasize understanding number relationships before introducing algorithms, aligning with the conceptual intent of the TEKS. Module 1 of the grade 4 Versión del maestro explicitly states how the procedural emphasis of the TEKS is addressed. Module 1 provides direct instruction and practice using the standard algorithm for multi-digit addition and subtraction. Lesson 13's "Notas para el maestro" section states the following: "En esta lección, los estudiantes aplican el algoritmo estándar para la resta con números de hasta 1,000,000, consolidando la comprensión desarrollada en lecciones anteriores." This guidance ensures that students have opportunities to apply precise steps for solving problems. It also ensures that students develop procedural fluency following conceptual instruction.

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 include the use of concrete models and manipulatives throughout Modules 1–7 of the Version del maestro. For example, in Module 1, Lesson 1, students use bloques multibase to build numbers and physically represent place value quantities. The "Vocabulario visual" resource provides labeled images of each block, and students are directed to "utiliza bloques multibase para representar 1,000, 100, 10, y uno." The materials thus require students to use hands-on tools to model multi-digit numbers and operations. The materials use pictorial representations throughout all modules, such as place value disks and number lines. For example, in Module 1, Lesson 5, students draw disks to represent regrouping during subtraction. The materials prompt students to "dibujar discos de valor posicional para representar la resta de cuatro cifras." The materials include questions and tasks that require the use of abstract representations (such as numerals and algorithms) throughout lessons. In Module 1, Lesson 13, the student problem set presents equations using the standard algorithm without visual models. The materials direct students to solve subtraction problems with statements such as "algoritmo estándar sin dibujos ni modelos" to show abstract representation. The materials thus move from concrete and visual models to abstract ones as required by the TEKS.

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 support students in connecting concrete and representational models to abstract concepts. In Module 1, Lesson 13, students explain how their drawn disks represent the regrouping process. The teacher prompts students with questions such as the following: "¿Cómo los ayuda el diagrama de tiras a determinar qué operación utilizar para encontrar la respuesta?" Such tasks bridge the relationship between physical or visual models and abstract numeric methods. The materials include supports for students to create their own concrete and representational models to demonstrate understanding of abstract mathematical concepts. In Module 1, Lesson 14, students are instructed to do the following: "Con su compañero, dibujen un diagrama de tiras para representar el entero, la parte conocida y la parte desconocida." This task allows students to construct their representations, reinforcing the TEKS requirement for students to produce models that reflect symbolic reasoning. The materials include prompts for students to define and explain how their concrete or representational models relate to abstract concepts. In Module 1, Lesson 15, teacher guidance includes questions such as the following: "¿Cómo los ayuda el diagrama de tiras a determinar qué operación utilizar para encontrar la respuesta?" Such questions encourage metacognitive reflection, helping students verbalize the mathematical ideas behind their models. The materials thus align with the TEKS expectation for explanation and justification.

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

Modules 1–7 of the Version del maestro provide multiple opportunities for students to develop academic mathematical language. In Module 2 of the Version del maestro, students develop academic mathematical language through the use of visuals as a strategy. Students use visuals to represent academic vocabulary, such as number bonds, labeled strip diagrams, mixed metrics, and horizontal models to represent part-to-whole relationships. Students engage with concrete manipulatives, including paper clips, rulers, meter sticks, coins, and familiar classroom objects, to measure and compare lengths in millimeters, centimeters, and meters. Throughout the lessons, structured partner talk, teacher questioning, and prompts (e.g., "Hablen durante un minuto con su compañero…" and "¿Cómo lo resolviste?") support students' oral language development and reasoning. Module 6 of the Version del maestro provides opportunities for students to develop academic mathematical language. Students develop academic mathematical language using visuals such as strip diagrams, place value charts, and number bonds to represent relationships between tenths and hundredths, such as "2/10 = 20/100 = 0.2 = 0.20." Students explore and explain these equivalencies by shading paper strip diagrams and converting figures between fractional and decimal forms. The lesson integrates manipulatives such as one-meter strips, which are divided into tenths and hundredths. The lesson includes templates for students to visually model parts of a meter. Additionally, the materials incorporate language development strategies such as student-to-student discussion, written reflection, and teacher questioning (e.g., "¿Cómo se representa 3/100 en forma decimal?"). The materials also provide vocabulary scaffolds, which focus on key academic terms such as décimo and centésimo to support students' academic language development.

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

The materials embed teacher-facing guidance that supports the development of academic mathematical vocabulary such as centímetro, décimo, centésimo, fracción, and their decimal equivalents. The materials prompt teachers to ask students the following questions: "¿Qué fracción de metro es uno centímetro? ¿Cómo se representa 3/100 metro en forma decimal? ¿Cuál es la relación entre uno décimo y uno centésimo?" Students communicate their answers with their peers and teacher. The materials progressively introduce and reinforce vocabulary with teacher questioning and repeated visual and verbal modeling. Notes on the side of the lesson emphasize the correct pronunciation and meaning of mathematical terms such as centésimos versus centenar. These notes recommend scaffolds such as slowing down one's speech, using visuals such as place value charts, and explicitly adding decimal columns for clarity. Students are asked to explain terms in their own words, such as "Explica por qué 25 centésimos es 0.25." Students also participate in structured discussions that apply vocabulary in context. The materials intentionally develop academic vocabulary through teacher questioning, structured prompts, and embedded guidance. In grade 4, Module 2, Lesson 1 of the Versión del maestro, teachers prompt students to use terms such as metro, centímetro, unidad mixta, and renombrar in context through questions like "¿Qué fracción de un metro es uno centímetro?" and "¿Van a utilizar el algoritmo o una estrategia de simplificación?" The lesson reinforces vocabulary through number bonds, strip diagrams, and decimal conversions. Students justify their reasoning using mathematical language. Margin notes labeled "Notas sobre las diferentes formas de representación" further support students' language development by encouraging teachers to model pronunciation and connect new terms to concrete objects.

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.

The materials embed structured teacher guidance that supports the use of mathematical language, including vocabulary, syntax, and discourse. In grade 4, Module 2, Lesson 1 of the Versión del maestro, scripted prompts model how to elicit student responses using precise academic vocabulary such as centímetros, milímetros, and unidades mixtas. Students respond to fill-in-the-blank prompts such as the following: "M: (Muestre 1 km 300 m = ___ m)." The materials facilitate discourse by prompting students to explain their reasoning and compare strategies aloud. These prompts include the following: "¿Por qué?"; "¿Cómo lo saben?"; and "Coméntenlo con un compañero." This guidance is consistently present across fluency skill problems, concept development, and problem-solving activities, supporting students' language development throughout the lesson. The "Desarrollo del concepto" section of all lessons prompt teachers to guide students through structured peer discussion and vocabulary development using sentence stems. For example, in grade 4, Module 6, Lesson 4 of the Versión del maestro, the materials provide statements for teachers to use. These statements include "Hablen con su compañero y escriban sus pensamientos…" and "Expliquen a su compañero por qué es cierto," which support students' ability to listen to and refine math language in context. Teachers model precise academic language such as centésimos and décimos in decimal and fraction form, while also prompting students to explain numeric relationships using that language in partner tasks and class discussions. Teachers also model exemplary responses by guiding students through their own process of thinking out loud throughout the lesson, promoting mathematical conversations over time.

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

The materials integrate the TEKS process standards throughout instruction, using a collaborative problem-solving approach to address student misconceptions. For example, the Guía del curso outlines a three-step routine that requires teachers to "estimular el pensamiento, validar lo correcto, y crear un puente." This routine guides students to explain their reasoning, revise errors, and deepen their understanding. Students use visual models and teacher questioning to make connections. These strategies support the application of process skills such as using representations (4.1C), communicating mathematical ideas (4.1D), and analyzing relationships (4.1E). The materials integrate TEKS process standards throughout instruction using teacher prompts, student tasks, and visual models. In the "Solución colaborativa de problemas de conceptos erróneos de los estudiantes" section, the teacher asks the following: "¿Cuál fue tu razonamiento? ¿Puedes mostrarlo en el diagrama de tiras?" These questions prompt students to use representations and explain their thinking (TEKS 4.1C, 4.1E). The teacher then says, "Dime por qué tu nueva respuesta tiene sentido," encouraging students to evaluate the reasonableness of their solution (TEKS 4.1G). In the "Resumen del año" section, students solve "problemas escritos de múltiples pasos que involucran suma y resta representadas con diagramas de tiras," reinforcing the consistent use of modeling and problem-solving strategies. These examples demonstrate that the materials intentionally integrate process standards across instructional components.

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

The Guía del curso in the Versión del maestro describes how the materials embed TEKS process standards across the course. For example, the "Secuencia de módulos de grado 4 alineados con los TEKS" section explains how students use visual models, tape diagrams, and numerical relationships to solve multistep problems. The sequence of modules includes a progression that integrates process skills with content. For example, Module 1 uses place value patterns to support problem solving, while Module 4 uses tape diagrams to provide such support. The materials describe how TEKS process standards are connected across the course through the repeated use of representations, reasoning, and problem-solving strategies. The "Secuencia de módulos de grado 4 alineados con los TEKS" section of the Guía del curso states the following: "Los estudiantes extienden sus conocimientos de 3er grado para usar tablas de entrada-salida y expresiones numéricas para representar patrones numéricos y la relación entre la posición de un número en un patrón…." This evidence reflects an early application of representational reasoning and aligns with process standards such as 4.1C and 4.1E. The "Alcance y secuencia de grado 4" table shows that these same process skills are vertically embedded across later modules. For example, students "representa[n] problemas escritos usando un diagrama de tiras y una recta numéric." Furthermore, students "usa[n] representaciones para justificar sus respuestas" in previous modules, which demonstrates an alignment throughout the course. These repeated references demonstrate that process standards are not isolated; rather, the materials intentionally connect and revisit standards throughout the course in multiple contexts.

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 grado 4" table provides unit-by-unit details on how the materials incorporate process standards. For example, in Module 1, students are expected to represent "problemas escritos usando un diagrama de tiras y una letra para representar una cantidad desconocida…." The materials list process standards 4.1B, 4.1D, 4.1E, and 4.1G as the central TEKS for the module. The materials embed these skills in lesson activities rather than treat them as isolated standards. Each module connects multiple process standards across its sequence of lessons. The "Estándares de grado 4 por lección" table, located in the Guía del curso in the Versión del maestro, shows that each lesson integrates several process TEKS. For instance, Module 3 incorporates 4.1C in Lecciones 11 and 18, 4.1D in Lecciones 4–8, 10, 14–17, 20–24, 29, 33, and 34, and 4.1E in Lessons 1, 19, 25, and 30–32. The materials thus revisit multiple TEKS process standards, which the materials connect across the same module.

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

The Guía del curso in the Version del maestro includes a comprehensive chart titled "Estándares de procesos matemáticos de grado 4 por lección de cada módulo." This chart maps each TEKS process standard to specific lessons across all modules. The chart provides teachers with an at-a-glance reference to identify where and how each process standard is addressed, ensuring alignment with the TEKS framework. The "Contenido general del módulo" section in Modules 1–7 of the Versión del maestro includes references to the TEKS process standards that the materials integrate within each module lesson. The module overview explicitly cites how students engage with standards such as 4.1B, 4.1C, 4.1D, 4.1F, and 4.1G, describing how students select tools, communicate ideas, justify their reasoning, and use models and strategies to solve problems. This alignment provides teachers with a lesson and module-level overview of how the materials weave process standards into instruction.

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

The materials promote mathematical thinking by including daily routines and tasks that push students to reason independently, develop conceptual models, and engage in reflection. For example, the "Una cultura de aprendizaje" table of the K–5 guía de programa e implementación and accompanying narrative emphasize that students "seguir explorando hasta alcanzar una mejor comprensión conceptual." These resources encourage students to think critically through "Reflexión" and "Problema de aplicación" routines. The materials include embedded supports and guidance that encourage productive struggle and persistence. The "Apoyo a las intenciones de los maestros de mantener altos estándares para todos los estudiantes" section explains that the materials expect students to "persistir en elaborar matemáticas desafiantes para convertirse en solucionadores de problemas independientes." The materials frame effort and difficulty as part of the learning process and provide routines to help students manage and learn from challenging tasks. The materials help students make sense of mathematics through collaborative problem-solving routines that reframe errors as opportunities for understanding. The "Solución colaborativa de problemas" strategy in the K–5 guía de programa e implementación guides students to reflect, explain their reasoning, and build new understanding through steps such as "crear un puente a una mejor comprensión." The "Language Guidance" table encourages students to connect ideas and articulate their thinking in a way that deepens their conceptual understanding.

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 promote student understanding of multiple ways to represent and solve problems, fostering una cultura de aprendizaje that values exploration, persistence, and conceptual thinking. The materials encourage students to "seguir explorando hasta alcanzar una mejor comprensión conceptual" and support students through collaborative problem-solving routines that prompt them to reapproach problems using different representations. The materials include the following teacher prompt: "¿Podrías mostrarme lo que ya has intentado para que pueda entender tu razonamiento?" Such prompts appear in the "Cómo resolver problemas de manera colaborativa" section of the K–5 guía de programa e implementación. The prompts reinforce that multiple solution paths exist, helping students build confidence in trying alternate strategies. The materials include embedded "Reflexión" and "Boleto de salida" instructional routines, which prompt students to explain their thinking and articulate different ways of approaching a task. Teacher guidance encourages the use of open-ended prompts, which appear in the "Importancia de una comunicación clara" section of the K–5 guía de programa e implementación. These prompts support metacognitive reflection and include "¿Por dónde empezaste?" and "¿Qué hiciste después?" In addition, collaborative problem-solving and error analyses offer students repeated opportunities to describe and explain their unique strategies for representing and solving problems. The materials include intentional teacher language that validates student effort and highlights strategic thinking. For example, prompts such as "Nota que estás usando una estrategia que aprendimos antes" help students recognize the value in their process, not just the final answer. The materials include opportunities for students to revisit and refine their thinking through everyday lessons, especially in the context of collaborative routines. Such opportunities allow students to defend their approaches and justify alternative ways of solving or representing 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 teachers.

The materials include collaborative structures that require students to do mathematics with peers and teachers. In the "Solución colaborativa de problemas" routine, students analyze errors, explain their reasoning, and work alongside the teacher to refine their understanding. Lesson guidance includes prompts that invite students to revisit strategies and solve problems jointly, approaching math as a shared experience. The materials include written components such as "Boletos de salida" and "Problemas de aplicación" that require students to write about their mathematical thinking. These opportunities appear across lessons and provide space for students to document understanding, describe their strategies, and connect ideas through written reflection. The materials provide multiple opportunities for students to discuss mathematics with peers and teachers. For example, the materials include sentence stems such as "¿Qué puedes decirme sobre tu pensamiento en este problema?" The materials also include "Rutinas de gira y habla," which appear in the "Solución colaborativa de problemas" section. Such routines guide structured mathematical conversations. The K–5 guía de programa e implementación includes instructional supports that prompt students to explain, question, and build ideas aloud throughout the lesson.

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-facing prompts and structures that guide students to explain and justify their problem-solving approaches. The "Discurso y elaboración" section of the K–5 guía de programa e implementación instructs teachers to use prompts such as "Comenten con sus compañeros, ¿Qué acaba de ocurrir?" and "Explícale a tu compañero los pasos que tomaste para resolverlo." These prompts encourage student-generated explanations and mathematical arguments during class discussions. The materials provide multiple embedded opportunities for students to reflect on their reasoning and strategy selection. The "Reflexión" section outlines how teachers guide students to connect their choices to prior problems, lesson goals, and mathematical models. Sample teacher questions include the following: "¿Cómo nos ayudaron nuestras actividades de fluidez…con nuestro trabajo de redondeo hoy?" Such questions support structured reflection in which students provide explanations and justifications for their 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 include scripted feedback prompts within the "Rutinas de resolución de problemas" section. Such prompts help teachers respond to student misconceptions in real time. For example, the materials prompt teachers to say the following: "Veo cómo empezaste con un enfoque y cuando eso no funcionó, en vez de rendirte, intentaste una estrategia diferente." Another prompt reads: "¿Qué es lo que ya sabes? ¿Qué es lo que pregunta el problema?" These prompts explicitly acknowledge student thinking, productively redirect such thinking, and model how to affirm effort while guiding students toward conceptual clarity. The materials include multiple forms of teacher-facing guidance for responding to student reasoning. Margin notes labeled "Notas sobre diferentes formas de representación" and "Participación" offer suggestions for adjusting instruction based on observed student responses. For example, one prompt reads as follows: "Resalte la palabra por y el signo x con otro color." Such prompts help teachers reinforce meaning when students misinterpret symbols. The materials also highlight ways to extend feedback through metacognitive prompts that include the following: "¿Cómo muestra tu dibujo la manera en que resolviste el problema?"