Aprendizaje Bluebonnet Matemáticas K-5 Grado 2

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

The materials include a scope and sequence document in Guía del curso del grado, under "Documentos del nivel del curso." The materials include a year-long scope and sequence, "Vistazo del año de grado 2," organized as a table to include the title of the module and the aligned TEKS taught for the corresponding Modules 1–8. The year-at-a-glance, "Vistazo del año de grado 2," includes suggested days as pacing for each module. For example, the year at a glance for Module 1 recommends a nine-day pacing focusing on TEKS 2.4A, 2.4B, 2.4C, and 2.7C. The materials include a table in section "Alcance y secuencia de grado 2," in the Guía del curso del grado. The table provides an overview of the concepts taught by Módulos, Temas y días de enseñanza, and Estándares. For example, in "Módulo 4: Suma y resta hasta el 200 con problemas escritos hasta el 100," the TEKS mainly focus on 2.4B, 2.4C, 2.4D, 2.7B, and 2.7C. In the "Estándares de grado 2 por lección," in the Guía del curso del grado, TEKS are provided in a table as an overview for each Module 1–8. The table provides the TEKS de grado 2 por lección de cada módulo taught in each lesson for Modules 1–8, to include grade 2 mathematics TEKS. In the Guía del curso del grado, the "Desarrollo de la fluidez en grado 2" section lists the fluency-related specific TEKS addressed in each module throughout the year. The fluency-related TEKS are organized in a table by module with the corresponding lesson. For example, the table for Números y Operaciones in Module 4 addresses TEKS 2.2A in lessons 1–2, 4–7, 13, 15, 18, 22, and 25.

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 in Guía del curso del grado, under "Documentos del nivel del curso," include a section "Alcance y secuencia de grado 2." The material in "Alcance y Secuencia de grado 2" provides information organized as a table with the module number, topics and days of instruction, concepts and skills, and the TEKS. The pacing for instructional days varies from Module 1 to Module 8, for a total of 165 calendar days. For example, in Module 1, the total number of instructional days is nine, including evaluation days. In Module 4, the pacing is 30 days for instruction, including evaluation days. In the Guía del curso del grado, the materials include a document, "Vistazo del año de grado 2," which is a year-at-a-glance that has a clear overview of the content standards addressed in a calendar year of 165 days. The "Vistazo del año de grado 2" document provides a pacing guide, including the specific number of days allocated to each concept. The materials include a document, "Progresión de conceptos matemáticos," under the Guía del curso del grado, providing a table as a visual support at-a-glance outlining the vertical alignment in grades K through grade 5. The document includes the concept for each module, the number of suggested instructional days, and alignment across grade levels by three trimesters or four trimesters. In "Dias adicionales del año escolar (ADSY), Versión del maestro," the materials include 30 additional instructional days in addition to the 165 days that may be implemented during the regular school calendar year or during summer session. The module consists of 25 lessons, a pre-assessment, and a post-evaluation component.

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 include a document, "Progresión de conceptos matemáticos," under the Guía del curso del grado. This document provides a table as visual support, outlining at a glance the vertical alignment for learning progression in K through grade 5. The document includes the concept for each module, the number of suggested instructional days, and alignment across grade levels, organized by one, two, three, or four trimesters. In the Guía del curso del grado, under "Documentos del Nivel de Curso," the materials include Secuencia de Módulos de grado 2 alineados con los TEKS, providing a rationale for the order of the Modules 1–8. The materials include a sequence guide for each module and describe how the TEKS connect throughout the course. It provides a clear explanation of the logic behind each module and how it connects with future learning. For example, the rationale of Module 2 states that students will use their learning with metric units to support upcoming work with place value in Module 3. In Module 1, the goal is for students to achieve automaticity with addition and subtraction facts up to 20 early in the year and to work toward fluency with numbers up to 100 by the end of grade 2 during "Module 4: Suma y resta hasta el 200 con problemas escritos hasta el 100."

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

The "Recursos para maestros" section includes two separate general protocols under Matemáticas K–5 guia del programa e implementación to provide guidance for module and lesson internalization. In this section, the materials provide a protocol to support teachers in internalizing modules and lessons using a four-step process. The "Protocolo de internalización de módulos para el maestro" document under "Recursos para maestros," provides the purpose for the internalization of the modules and pre-work components. The four-step process is described as follows: Step 1: Understand the big picture. Step 2: Know your destination. Step 3: Examine the arch of learning. Step 4: Organize your resources. Each step provides guidance and includes debrief questions. For example, Step 1 requires teachers to revisit the module overview, noting the pacing days for instruction and assessment and reflecting on why the module is important and how it connects to prior modules. The "Protocolo de internalización de lecciones para el maestro" document under "Recursos para maestros" provides the purpose for the internalization of the lessons and prework components. The four-step process is described as follows: Step 1: Understand the lesson purpose and objectives. Step 2: Understand the sequence and pacing of activities. Step 3: Prepare to teach each activity with an activity deep dive. Step 4: Organize your resources. Each step provides guidance on what to use or create for the lesson. For example, Step 4 asks teachers to locate the manipulatives or materials listed and identify additional supplies needed to support groups of students. In each module's Versión del maestro, the materials include a general overview of the concepts at the beginning of each module and include the learning progression explanation for the specific standards in the lessons. The materials provide teachers with the background information for the concept to support internalization of the lesson, including examples as diagrams. In the "Contenido general del módulo" section, the materials provide detailed descriptions of each module’s TEKS, objectives, lesson sequences, and progression, explaining how concepts build across modules and grade levels (e.g., Module 1 connects to Modules 3 and 5). In each Module 1–8, under Versión del maestro, the materials include a "Terminología" section to support lesson internalization. This section provides terminology that may be a cognate and used throughout the module, including a visual diagram for math strategies. The document includes Términos nuevos o recién presentados and Términos y símbolos conocidos. These two documents include vocabulary that students use throughout the module, or vocabulary used as spiraling from previous grade levels or modules. The materials in Modules 1–8, Versión del maestro, include Topics (A-F), which vary by module. The materials in each Topic (A–F) is organized in a table highlighting the Topic, TEKS, Concepto erróneo del estudiante, and Como llegar a una mejor comprensión. This table serves as an overview for each topic in the module to support lesson internalization. For example, Module 1 contains Tema A: Fundamentos para la fluidez con sumas y diferencias hasta el 100 and Tema B: Iniciar la fluidez con sumas y restas hasta el 100. Module 4 contains Topics A through D for adding and subtracting up to 1,000.

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

In Matemáticas K–5 guía del programa e implementación, the materials provide a protocol to support module internalization using a four-step process. The Protocolo de internalización de módulos para el líder de instrucción describes four different steps: Step 1: Understand the big picture by using the module and topic overview, terminology, scope and sequence, and reflecting component. Step 2: Know your destination by reviewing the topics in the module, the objective, and the assessments. Step 3: Establish the arc of learning by reviewing connections between the topics and assessments, and think about how all learners will be supported. Step 4: Identify all materials needed for a successful module implementation. The Protocolo de internalización de módulos para el líder de instrucción, under Recursos para líderes, includes a recommended time that varies for each step in the process, starting at five minutes to twenty minutes. The materials guide the instructional leader in helping teachers explore previous instruction, its purpose, implementation, and a deep level of reflection for future instruction. In Matemáticas K–5 guía del programa e implementación, the materials include a protocol to support lesson internalization using a four-step process. The materials include a Protocolo de internalización de lecciones para lider de instrucción, under Recursos para lideres to be used as a guide to support teachers with lesson internalization. The four-step process is described as follows: Step 1: Understand the lesson purpose and objectives. Step 2: Understand the sequence and pacing of activities. Step 3: Prepare to teach each activity with an activity deep dive. Step 4: Organize your resources. The protocol includes a recommended time frame for each step in the process. In Matemáticas K–5 guía del programa e implementación, the materials include an Observation Tool to use as a resource before, during, and after classroom observations to support the implementation of high-quality instructional materials. In Guía del curso del grado, Versión del maestro, the "Documentos del nivel del curso" section includes a Lista de manipulativos y materiales that contains a comprehensive list of materials that will be needed throughout the year. This list can be a resource for administrators to support teachers with the materials needed for implementation.

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.

In the Versión del maestro for Modules 1 to 8, the materials include a general overview of the concepts, "Contenido general del módulo," at the beginning of each module, which provides examples of visuals aligned to the TEKS. In the "Contenido general del módulo" section, the materials provide detailed descriptions of each module’s TEKS, objectives, lesson sequences, and progression, explaining how concepts are built across modules and grade levels. The section also provides teachers with the background content knowledge necessary to effectively teach the concept. For example, Module 1 notes students are expected to have knowledge of the following TEKS: K.2E, K.2F, K,2I, 1.2A, 1.2B, 1.3A, 1.3D, 1.3E, 1.3F, 1.5C, and 1.5G from previous grade levels. In the "Terminologia" section, under the Versión del maestro for each Modules 1–8, the material includes a detailed explanation of the vocabulary, with a pictorial diagram of the strategies or math representations being used in the lesson. The materials include a "Notas" section that explains how these terms are used across grades K–5 and provides various synonyms to support understanding. In each Module 1–8, under Versión del maestro, the materials include a "Terminologia" section with vocabulary terms that will be used throughout the module or lesson and highlighted in bold letters. The document includes "Términos nuevos o recién presentados" and "Términos y símbolos conocidos." These two sections include vocabulary that students will be using throughout the module, or vocabulary spiraling from previous grade levels or modules. The materials provide terminology that may be a cognate and used throughout the module to include a pictorial diagram for math strategies and representations. In Module 1, Versión del maestro, for example, the "Terminologia" section includes mathematical terms within the lesson context, and terms with English cognates are listed to connect to word-meaning words, such as the following: Expresión (Expression): una oración numérica sin el símbolo igual. In Module 4, for example, componer and descomponer are listed as new vocabulary, and diferencia and posición de las centenas are listed as known terms and symbols.

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.

In the Guía del curso del grado, under the "Documentos del nivel del curso" section "Consejo para las familias," the materials provide a general content information page for families in both English and Spanish, per module. This section gives guardians general information on key concepts the student is learning in the module, and recommendations on additional ways to support the child at home. The document includes the terminology used and pictorial math representations as examples of those terms. For example, in Module 5, families are encouraged to prompt students to use place value language to explain their thinking: "When I have a group of 10 ones, I can make a group of 1 ten. When I have a group of 10 tens, I can make a group of 1 hundred." In Modules 1–8, Versión del maestro, the "Tarea" section, the material includes practice problems assigned as homework after each lesson is taught, and is not recommended for the introduction of new concepts. In "Triunfar," under Version del estudiante, Modules 1– 8, the materials include additional practice problems that students can complete at home, supported by a step-by-step visual guide under "Ayuda para la tarea." For example, in Module 1, Topic A, Lesson 2: Ayuda para la tarea, the support text appears in bubble diagrams with phrases like "Esta es una parte," "Esta es la otra parte," and "Este es el entero," to support making sense of part-part–whole relationships.

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).

The materials in Modules 1–8 include a table, Contenido general de los temas del módulo y objetivos de la lección, organized as an overview indicating the focused TEKS, topics, and objectives for each lesson, including the number of days for each Topic (A–F), daily exit tickets as formative assessments, and evaluation at the end of each module. The materials at the beginning of each lesson include a section on "Materiales de instrucción de matemáticas," which provides teachers with information outlining the focus TEKS, days of instruction, and detailed background knowledge of the concepts. For example, in Module 3, Lesson 3, the material provides teachers with the objective, suggested structure of the lesson, materials needed, a debrief component, and an exit ticket as a formative assessment. Lesson structures include daily objectives along with suggested timing to guide the pacing of instructional components such as fluency practice, application problems, and concept development. Embedded throughout each component is additional guidance for TEKS alignment, language supports, mastery activities, and a variety of questions. Margin notes are also included to provide teachers with guidance on how to support emergent bilingual (EB) students by connecting key vocabulary to visual representations, cues, or gestures. Materials are also embedded within each lesson and activity. For example, in Module 3, Lesson 1, a cinta métrica (plantilla de fluidez) is listed as the material needed during the activity Practica de Fluidez (20 min).

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.

The materials for each lesson in the Versión del maestro include a suggested time allotment for each lesson component under Estructura sugerida para la lección. The materials include a suggested structure for each lesson. They are listed using a color-coded key next to a pie graph displaying the four components: Fluency Practice, an Application Problem, Concept Development, and a Student Debrief. Lessons are designed for a suggested time allotment of 60 minutes for grades 1–5 and 50 minutes for Kindergarten. For example, Module 1, Lesson 5 outlines the following: Práctica de fluidez (15 min.), Desarrollo del concepto (20 min.), Problema de aplicación (15 min.), and Reflexión (10 min.) with a total of 60 minutes of instruction. In the Guía del curso del grado, the materials include a table identified as Listas de manipulativos y materiales, which lists the items needed for the entire school year, organized by the number of items and a description of the material. For example, 240 barras de base diez are needed for every 10 students. In the Versión del maestro, the materials in Modules 1–8 include a general list of materials needed for each lesson. The "Lista de materiales del módulo—descripción general de la lección" section includes a table organized by lesson number, materials for teachers, and materials needed for each student. In every lesson, under Modules 1–8, the materials are described for each component of the lesson. They are listed, indicating what teacher and student materials will be needed, and they are differentiated by the symbol (M) for maestro and (E) for estudiante. For example, in the Versión del maestro, Lista de materiales del módulo 3, in leccion 1, the teacher materials are listed as 24-inch ribbon (M) and 1200 sticks (M). The student materials are a 24-inch measuring tape (E).

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

In "Triunfar," under Version del estudiante, Modules 1–8, the materials include additional practice problems as extended practice to be completed at home, supported by a step-by-step Homework Helper as a visual guide under Ayuda para la tarea. For example, in Module 1, Topic B in Lesson 6 within Ayuda para la tarea, the strategy for Quita de 10 includes a diagram, pictorial math representations, and a text surrounded by a dialogue frame. It includes phrases like "Puedo dibujar 20 y demostrar cómo quitaré 9 de una decena" to support the concept of regrouping under the Quita de 10 strategy. In Matemáticas K–5 Guía del Programa e implementación, the materials include an overview of various options available for students to practice concepts or skills in the classroom as extended practice or at home. For example, students may complete fluency problems, application problems, or both. The materials support teachers assigning either fluency or word problems in the form of Lee, Dibuja y Escribe (LDE), based on the needs of the student in the implementation guide and Aprender, versión del estudiante.

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 Modules 1–8, the materials include diagnostic assessments that vary in types of tasks and questions, such as fluency practice or Mid-Module assessments. For example, in Module 3, Lesson 2, the students are asked to subtract, measure, count forward, and count backward by using different tools and strategies. The material requires teachers to use the assessment from previous modules as a foundation for the following module. For example, the knowledge gained in Module 2, Sumas y restas de unidades de medida hasta 100, will serve as a key connection for Module 3, Valor de posición, conteo y comparación de números hasta 1200. The materials include a diagnostic assessment, mitad del módulo, under Evaluaciones, and Versión del maestro to evaluate the TEKS that will be tested at the end of the module. In Modules 1–8, the materials include formative assessments that vary in task type and are embedded throughout daily instruction. In each lesson, formative assessments are incorporated in various task types and questions, such as Problemas de aplicación, Grupo de problemas, and Boletos de salida. For example, in Module 2, Lesson 5, the exit ticket has a variety of question types that include multiple choice, estimated number response, and a short constructed response. In Module 8, Lesson 5, the Exit Ticket prompts students to label and justify answer by "completa los espacios en blanco para etiquetar las características del prisma rectangular y explica por qué un cilindro no es un prisma." In G2 Evaluaciones, versión del maestro, the materials include summative assessments as mid-module and end-of-module assessments with a variety of task types, including multiple-choice questions, number sentences, short constructed responses, and illustrations aligned to the TEKS covered in instruction. The materials include a rubric to score the short constructed responses embedded in mid-module and end-of-module assessments.

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

In Evaluaciones, versión del maestro, the materials include a brief explanation and purpose for the types of instructional assessments, such as "Evaluación mitad del módulo" and "Evaluación final del módulo." For example, "Evaluación de la mitad del módulo es una Evaluación de la mitad del módulo se provee en la mayoría de los módulos, junto con información de criterios de calificación." The mid-module assessment task is provided with scoring information as a rubric. It is specifically tailored to address approximately the first half and the entirety of the student learning outcomes for each module, respectively. In Evaluaciones, versión del maestro, the materials for the Evaluación final del módulo task include a brief explanation of the purpose of the assessment and the rubric for Modules 1–8. These tasks provide an overall performance of the student's understanding of the complete content at each module. In Matemáticas K–5 guía del programa e implementación, within the "Enfoque de las evaluaciones" section, there is a brief definition and intended purpose for the types of instructional assessments, such as diagnostic, formative, and summative assessments. For example, exit tickets are a brief, three-minute daily formative assessment containing one or two problems to provide teachers with a snapshot of a student's understanding of the lesson or misconceptions that need to be addressed. Problem Sets provide insight into student understanding and may be used as formative assessments that provide another opportunity for teachers to monitor student learning.

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

In Modules 1–8, the materials include formative assessments and guidance to ensure accurate administration of assessments. Materials provide teachers with instructions on the time allotted for students to complete assessments and implementation directions. For example, in Module 2, Lesson 3, the "Boleto de salida" section provides instructions for teachers to allow three minutes for students to complete the assessment, and questions may be read aloud to the students. Within the same lesson, the "Reflexión" section provides guidance for teachers to invite students to think and process problem-solving in the lesson. In Evaluaciones, versión del maestro, the materials include the "Contenido general de la evaluación de grado 2" section explaining the importance of testing fidelity with new activities and tasks. Teachers are also informed that the assessment can be formative or summative, depending on their needs. The materials explain how teachers can use the Progression Toward Proficiency rubric to score student responses, which are used alongside each mid-module and end-of-module assessment task. These rubrics help teachers consistently evaluate student performance on TEKS-aligned tasks. In Matemáticas K–5 guía del programa e implementación, the materials include the "Enfoque de las evaluaciones" section, providing an explanation of the focus of each evaluation component to ensure consistent and accurate administration of instructional assessments. The materials include a visual table as an example to demonstrate when teachers may administer the assessments. For example, the Boletos de salida assessments are administered daily at the end of each lesson, the "Evaluación de mitad de módulo" is administered in the middle of the module, and the "Evaluación final del módulo" is administered at the end of the module. Materials include instructions for tasks to be completed independently by students within one class period, including information on how the tasks should be new to the students and not preceded by analogous problems.

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

In Modules 1–8, the material includes diagnostic, formative, and summative assessments aligned to the TEKS and objectives for each lesson. The materials include an information page with the TEKS tested and an explanation of each standard and what the student is expected to master. The materials identify alignment in diagnostic assessment with the TEKS for the course, such as listing aligned TEKS within rubrics. For example, in Module 3, the mid-unit assessment evaluates the following TEKS: 2.2B, 2.2A, and 2.2E. These TEKS align with the course objective on place value, counting, and comparing numbers up to 1,200. In the Evaluaciones resource, the materials include the "Contenido general de la evaluación en grado 2" section explaining how the assessments, mid-module, and end-of-module tasks are aligned directly to the TEKS and provide a table "Progreso hacia el dominio" with the TEKS and rubric for each evidence. For example, in Module 6, "Evaluación de la mitad del módulo," TEKS 2.6A is tested using multiple ways of showing multiplication or adding multiple numbers. In Matemáticas K–5 guía del programa e implementación, the materials include an "Evaluaciones" section with information regarding the evaluations that provide students with opportunities to demonstrate their level of proficiency on the TEKS within each module. In the "Aprender and Triunfar" resource, the materials include group problems, exit tickets, homework, and tools for debriefing.

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

In Modules 1–8, the material includes instructional assessments aligned to TEKS items at varying levels of complexity. For example, in Module 3, for TEKS 2.2D in Lesson 15, students compare numbers by using symbols (<, >, =) and place value disks. In Module 3, Lesson 16, students compare using symbols and written comparative language. Lesson 17, students order numbers in various forms, such as placing digits in various places using place value, then ordering the numbers from least to greatest or greatest to least. In "Boleto de salida," the material provides more than two levels of complexity of the TEKS 2.2D learned in Lessons 15–17. In Module 6, Lesson 3 in "Problema de aplicación," real-world problems vary in levels of complexity. For example, the task builds complexity by allowing students to apply repeated addition or multiplication concepts for the following word problem: "Las flores estan floreciendo en el jardin de Maria. Hay 3 rosas, 3 ranúnculos, 3 girasoles, 3 margaritas, y 3 tulipanes. ¿Cuántas flores hay en total?." The students use chips and strip diagrams to represent repeated addition, complete a sentence stem, and write an equation to represent 3 + 3 + 3 + 3 + 3 = 15, demonstrating varying levels of complexity. In the Evaluaciones resource, the materials include assessments with varying levels of complexity, such as "Evaluación de la mitad del módulo" and "Evaluación final del módulo," using various ways for students to demonstrate learning using multiple-choice, text-entry, and open-response items aligned to the TEKS. The materials include diagnostic assessments with multiple-choice, text-entry, and open-response items aligned to the TEKS. For example, Module 5, "Evaluación de mitad del módulo," shows that problems 1, 3, and 4 test TEKS 2.4B in various ways, including the algorithm and mental math using place value. In "Evaluación del final del módulo," TEKS 2.4B is assessed in problems 1, 3, 4, and 5 using different problem-solving strategies (e.g., using strip diagrams, mental math by place value, standard algorithm, and arrows are used in the assessment to solve equations).

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

The Evaluaciones resource includes mid-module and end-of-module instructional assessments and scoring information guidance for teachers to interpret student performance. Each mid-module and end-of-module assessment includes a rubric table, Progreso hacia el dominio. This rubric guides teachers to analyze assessment data to identify students’ strengths, misconceptions, and areas of understanding that need instructional support. The Progreso hacia el dominio rubric, within the Evaluaciones resource, is structured from left to right, representing the growth toward mastery based on four different descriptors for student responses. The table is divided into columns, providing the standard assessed and describing each piece of evidence of solid reasoning for student responses toward mastery, such as little evidence of reasoning with no response to evidence of solid reasoning, or a correct response. In the Evaluaciones resources, within the "Evaluación de resultados de los estudiantes" section, the materials include a table as a guide for teachers to use, indicating the question type (multiple-choice, multi-select, or short constructed response), a description, total points, and a breakdown of the points to use for interpreting student performance of each item.

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 Evaluaciones, versión del maestro, the materials include guidance for using the included tasks and activities to respond to student trends in assessment performance. For example, the Progreso hacia el dominio rubric can be used in conjunction with Alcance y la secuencia, TEKS, and fluency information in the Guía del curso del grado to locate lessons and activities for students needing additional support. The Alcance y secuencia document within the Guía del curso del grado includes a table providing teachers with information on the skills and knowledge for each module aligned with the standards assessed at the middle or end of the module. Desarrollo de la fluidez within Guía del curso del grado resources are various tables displaying the location of each TEKS within each module and lesson to use to find tasks or activities to respond to student trends in performance on assessments. In Matemáticas K–5 guía del programa e implementación, the materials include the "Responding to Trends in Student Performance" section, providing teachers with an overview and guidance to use the "Solución colaborativa de problemas de conceptos erróneos de los estudiantes" section, which is included at the beginning of each module, to understand trends in student performance. The document guides teachers with suggestions on how to obtain student performance based on the rubric Progreso hacia el dominio and how to locate objects based on each topic within the modules.

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 Guía del curso, Versión del maestro, within the "Herramienta de reflexión sobre la evaluación" section, the materials include a table that teachers can use as a conversation guide before or after an assessment. The materials include a template for students to answer questions reflecting before and after the evaluation assessment is implemented; for example, teachers ask debrief questions and have students analyze errors by inviting them to choose one or two questions to focus on to track their own progress and growth. In the "Consejos para las familias" section within Guía del curso, Versión del maestro, the materials provide families and students with a checklist to track progress and growth for the concepts learned in each module aligned to TEKS and a focus on deepening comprehension of the concepts learned. The student work analysis protocol teacher guide within Matemáticas K–5 guía del programa e implementación, the materials include a tool to analyze student work samples to understand and track student progress and growth. The tool includes five steps with essential questions as teachers analyze student work; for example, the steps include: Step 1: Discuss the task, related text, and standards; Step 2: Determine the success criteria; Step 3: Analyze and sort student work; Step 4: Discuss and analyze; Step 5: Determine action steps for whole and sub-groups.

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.

In Módulos 1 al 8, Versión del maestro, the materials include margin note sections paired with scaffolded lessons to guide teachers for differentiated instruction and activities for students who have not yet reached proficiency on grade-level content and skills. For example, in Module 1, Lesson 2, within the lesson for Parte 2: Conteo Feliz, the materials guide teachers to practice fluency by sharing the number sentence for a two-digit number in tens and ones. The teacher says, "2 tens 8," students respond, "20 + 8 = 28." The margin note provides additional guidance for this lesson to return to the activity by adding a ten and some ones, using drawing or manipulatives. In Module 1, Lesson 3, the margin note guides teachers to invite students who would benefit from a visual model to draw quick tens to represent the problems with the lesson on adding and subtracting like units, tens to solve problems within 100. The note also encourages them to visualize the quick tens in their minds for reinforcement of the concept. In Module 3, Lesson 2, the margin note guides teachers to instruct students to use sticks as they count, starting with 100. The teacher gradually releases the responsibility to the students, counting by 100s as they listen to each other. In addition, the note provides suggestions to instruct a small group of students who struggle with counting and encourages students through the use of prompts. In Module 3, Lesson 5, the margin note guides teachers to allow the students who need more opportunities to practice to use concrete objects, such as base ten blocks or bundles of sticks to represent numbers, and then asks students to hide the material and solve using abstract or written formats. In Module 5, Lesson 8, within the "Desarrollo del concepto" section, students learn the concept of addition and subtraction problems using the standard algorithm and strip diagrams. The margin note provides teacher guidance to use step-by-step directions and prompts to help students who have not yet reached proficiency in solving word problems: "Ahora, dibujen los centavos de M.J. ¿Quién tiene más monedas de un centavo? ¿Cómo saben?" In Module 5, Lesson 15, the margin note provides teacher guidance on letting students who have not yet reached proficiency use numbers that require one step toward decomposing instead of two steps and to increase the numbers as students become proficient in decomposing concepts. In Module 8, Lesson 9, the materials provide a margin note guiding teachers to differentiate for students needing additional language support by pointing to specific shapes (e.g., rombo, hexágono, trapecio) and using sentence stems or structured prompts during partner conversations aligning to the concepts of identifying two-dimensional shapes.

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).

In Modules 1–8, the materials include preteaching or embedded support for unfamiliar vocabulary and references in texts. For example, in Module 2, Lesson 2, within the "Desarrollo del concepto" section, the materials include unfamiliar vocabulary in bold, such as se encimen, as teachers model the use of the word while explaining how to use a measurement strategy of making a mark at the beginning of a cube and making a mark at the end of the cube without overlapping or se encimen. In Module 2, Lesson 3, the materials include margin note guidance for teachers to illustrate unfamiliar vocabulary, such as marcas, using real objects or by showing images while speaking. In Module 3, Lesson 6, the materials include embedded support for unfamiliar in-text vocabulary and references in the margin note within the "Desarrollo del concepto" section. The note guides teachers in pairing the new vocabulary word componer with hand gestures that represent the significance of the term and previous terminology for grouping. In addition, the guidance provides a pictorial of the hand gestures to use while students learn the concept of grouping with the use of place value discs. In Module 6, Lesson 9, the margin note suggests supporting the term vagon de tren with a picture of a train and multiple train cars. In Modules 1–8, the materials include a "Terminologia" section at the beginning of each module with a list of new and previously used vocabulary terms in two separate sections: "Términos nuevos o recién presentados" and "Términos y símbolos conocidos." The list of vocabulary terms includes the definition, a pictorial image as an example, and the Spanish-English cognates (e.g., octágono–octagon) where applicable. This section provides guidance on ways to pre-teach unfamiliar vocabulary. For example, in Module 6, the "Terminologia" section includes the new vocabulary term: teselación. Then, Lesson 15 guides teachers to prompt students to create tessellations with various concrete objects. Afterward, teachers explain what they have created using the new term and ask students to repeat the term.

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 Modules 1–8, the materials provide teacher guidance for differentiating instruction, enrichment, and extension activities for students who have demonstrated proficiency in grade-level content and skills. For example, in Module 2, Lesson 8, within the "Reflexión" section, the margin note includes guiding prompts to encourage students to demonstrate different methods they can use to obtain the same solution: "¿Alguien llegó a la misma solución, pero de forma diferente? ¿Pueden explicar como lo resolvieron?" In Module 2, Lesson 4, the materials include teacher guidance by providing proficient students with complex, open-ended problems that require applying grade-level math concepts to real-world scenarios. For example, students are given a real-world task to measure their science books and figure out the measurement for a book stand. Then, students work with a partner to locate a place in the room in which the book stand would fit based on the measurements. In Module 5, Lesson 10, the teacher guidance in the margin note encourages students to add numbers by breaking them apart by place value and to use pencil and paper when writing and decomposing numbers. The guidance asks students to make columns for each place value, use color coding for each place value, and draw dots to represent the number of hundreds, tens, and ones. The guidance also emphasizes mathematical precision in maintaining vertical alignment by using the standard algorithm. In Module 8, Lesson 7, the margin note guides teachers to create flexible grouping based on math proficiency, including creating enrichment groups for those who perform above grade level. For example, the margin note states: "Desafíe a los estudiantes que hayan demostrado su dominio…," inviting those who have already mastered the content to extend their learning by reconstructing the original square using all seven tangram pieces or to form a new large rectangle.

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.

In Modules 1–8, the materials include explicit prompts and guidance to support teachers in modeling and explaining the concepts learned. For example, in the "Desarrollo del concepto" section, within Module 1, Lesson 3, teachers model and explain the idea of adding and subtracting to solve problems by decomposing numbers while asking explicit prompts. The guidance directs teachers to draw five circles and two X symbols, then write 5 + 2 = 7 and 7 - 2 = 5, which corresponds to the image. Then, the guidance directs teachers to ask the students to add 40 tens to the five ones to make it 45. Finally, the guidance directs teachers to model how the strategy makes it easier to add 45 + 2 by decomposing 40 + 5, then adding two ones to make a sum of 47. The guidance provides explicit prompts for teachers to use while students continue to use the strategy for additional problems (e.g., "¿Qué problema más sencillo utilizaron para sumar y restar?"). In the "Desarrollo del concepto" section, in Module 3, Lesson 20, the materials include explicit prompts and guidance to support teachers in modeling and explaining. The guidance assists teachers in creating numbers that are more or less than a given number in a direct instruction portion of the lesson. For example, during the concrete lesson, teachers model 266 using place value disks and ask students, "¿Cuales serían los siguientes números del patrón?" as students add in the hundreds place to make 366, 466, 566, and so forth. In the "Problema de aplicación" section of Module 8, Lesson 10, the materials provide teachers with explicit questions to ask students as they work independently or in pairs to solve problems, such as "¿Cuánto dinero más necesitan recaudar para alcanzar su objetivo?" and "¿Cuánto dinero extra tendrán?" In the "Práctica de fluidez" section, in Module 8, Lesson 23, the material provides explicit prompts for teachers to guide student interaction, such as "¿Cuál es el título de nuestra gráfica?" and "¿Qué animal es nuestra mascota menos favorita?" The materials also include examples of expected student responses (e.g., perro and hámster) to help teachers anticipate and model accurate interpretations of the graph.

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

In Modules 1–8, the materials include teacher guidance and recommendations for effective lesson delivery and facilitation, utilizing a variety of instructional approaches. For example, in the "Desarrollo del concepto" section, in Module 1, Lesson 3, the materials include teacher guidance to facilitate using a think-pair-share instructional approach as students explore the concepts using manipulatives and explain their reasoning as the lesson develops. Then, teachers ask students to measure an object and compare their responses with a partner, using sentence stems for students who may need extra support. In the "Desarrollo del Concepto" section, within Module 3, Lesson 20, the materials include teacher guidance and recommendations for using pictorials and the Lee-Dibuje-Escribe (LDE) process to help students solve word problems. For example, the guidance directs teachers to support students in discussing word problems with their partners and using different methods to solve them (e.g., drawing pictorials by grouping numbers into tens, using a place value chart with place value disks, or counting on by tens). In the "Desarrollo del Concepto" section, within Module 5, Lesson 5, the Problem 1 guidance directs teachers to use tools to facilitate and deliver an effective lesson by using a whiteboard, a place value template, and place value disks to solve 570 - 110. For example, teachers are directed to use arrows to demonstrate that 570 - 100 = 470 and draw arrows to show 470 - 10 is 460. Then, teachers direct the students to add the numbers that have been used, such as 100 + 10 = 110. Finally, the materials guide teachers to have students discuss with their partner the steps to subtract 110 from 570.

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.

In Modules 1–8, the materials include teacher guidance and recommendations for using multiple types of practice and structures to support effective implementation. In the margin note within Module 1, Lesson 2, the note guides teachers to create opportunities for students to participate at any moment using various structures (e.g., oral responses, partner talk, whiteboards, place value cards) and to allow sufficient wait time for responses. The margin note in Module 3, Lesson 7, guides teachers to support multiple types of practices, such as students working with partners. The teacher guides students to simultaneously talk and write expanded notations of the value of a given number using dollar bills and cents—for example, Partner A places five dollar bills in a horizontal line. Then, Partner B uses the sentence stem, "El valor de ____ billets de un dólar es __" to identify the value of the money displayed and writes the value with symbols. In Modules 1–8, the materials provide opportunities for independent practice and teacher-recommended structure for individual responses through the "Grupo de problemas," "Boleto de Salida," and "Reflexión" sections within the lessons. These sections allow students to demonstrate their understanding through written responses for each lesson. For example, in the "Grupo de problemas" section, within Module 8, Lesson 10, students work independently in the problem sets to identify fractions based on the shaded portion. In the "Reflexión" section, students divide circles and rectangles into equal parts as they reflect on their work during the problem set practice. After the debrief, students complete an Exit Ticket by shading equal parts on the given figures.

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 materials in the K–5 Implementation Guide include a summary of the approach to Spanish transadaptation, but do not align with the 3.3d indicator guidance. The materials do not include resources that outline opportunities to address metalinguistic transfer from English to the parent language or strategies that enhance the cross-linguistic connections that guide the teacher for explicit instruction. In the Matemáticas K–5 guía de programa e implementación, the materials include a "Support for Emergent Bilingual (EB)" students section that describes how the embedded instructional best practices support EB students. This section explicitly outlines instructional best practices, such as modeling, metacognitive strategies, turn-and-talk opportunities, and use of visuals and gestures as linguistic accommodation supports. In the Matemáticas K–5 guía de programa e implementación, the materials include margin notes and embedded scaffolds throughout to provide just-in-time linguistic and academic support. The design of these scaffolds supports a range of learners, including students in bilingual programs. Supports include sentence stems, language visuals, home-language connections, and suggested grouping strategies. In the Matemáticas K–5 guía de programa e implementación, the materials include an "Approach to Spanish Transadaptation" section that describes the guidance embedded in the materials. This guidance supports teachers using the materials in state-approved bilingual/ESL programs. For example, the material informs teachers that the program has meaningful opportunities to engage in rich language-based conversations with peers and in real-world problem-solving experiences.

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.

In Modules 1–8, the materials include embedded guidance for teachers to support EB students in developing academic vocabulary and building background knowledge while increasing comprehension. The modules consistently use the Lee-Dibuja-Escribe (LDE) strategy when solving problems: students read the problem, draw and label, write a numerical sentence, and write debrief sentences for their solution as they develop vocabulary and build background knowledge. In Module 2, Lesson 4, the materials include guidance for teachers to support EB students in building background knowledge and making cross-linguistic connections through oral and written discourse by sharing strategies with their peers. For example, teachers direct students to turn and talk with their partners to discuss their solutions and the strategies they use to solve problems, building background knowledge on various ways to solve problems. In Module 4, Lesson 11, the material includes embedded guidance for teachers to support EB students in developing vocabulary and building background knowledge through oral and written discourse by using sentence stems when sharing and writing mathematical solutions. For example, teachers guide students during the fluency practice in order to build background knowledge: "La práctica de la suma y la resta de múltiplos de 10 prepara a los estudiantes para la lección." This practice also supports academic vocabulary with words, such as "decenas, ___ es ____mas que." The lesson guides teachers to make connections between concrete and mathematical models to support students who struggle with language acquisition. During the debrief of the lesson, the guidance gives teachers questions to support student discourse by asking questions (e.g., "¿Cómo les ayudó la descomposición de una decena a resolver el problema?").

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.

In Matemáticas K–5 guía de programa e implementación, the materials provide an overview of the "Cross-Linguistic Connections" section on how the materials support students' learning concepts in Spanish, including linguistic approaches for students who are native to the Spanish language and those who are learning Spanish, such as a dual language immersion program. The materials include instructional strategies and sample activities for teachers to provide opportunities for metalinguistic transfer that may be embedded into any lesson across the modules. The instructional strategies include tips on fluency, application problems, concept development, and student debrief opportunities in oral and written language development.

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 materials in Modules 1–8 include practice opportunities over the course of the lesson in each module that require students to demonstrate depth of understanding aligned to the TEKS. Each module includes a varied number of topics, or Temas. In each topic, the lessons provide practice opportunities across various sections, such as "Práctica de fluidez," "Problema de aplicación," "Desarrollo del concepto," "Reflexión," and "Boleto de salida." For example, in Module 4 within the Practicar, versión del estudiante resource, the students practice relationships of 1 more, 1 less, 10 more, or 10 less with addition and subtraction in the "Práctica de fluidez" section for 10 minutes. In the "Aprender" resource for Module 4, in "Problema de aplicación" and "Grupo de problemas," students use strip diagrams to solve a word problem of adding 10 more. In the "Boleto de salida" section within Module 4, the students find patterns to continue with numbers provided and create their own patterns applying the concept of 1 more, 1 less, 10 more, or 10 less, using addition and/or subtraction. In Module 8, Lesson 1, the materials provide practice opportunities and/or instructional assessment within the lesson to apply geometric vocabulary and develop classification skills that align with TEKS 2.8A and 2.8C. For example, in the "Grupo de problemas" section, the guidance directs students with the following: "Identifica el número de lados, ángulos y vértices de cada figura" to apply geometric vocabulary aligned with the TEKS. The "Triunfar" resource for Module 8 includes practice opportunities and a "Tarea" section for each lesson with guidance on how to use strategies to complete homework.

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

In Modules 1–8, the materials include questions and tasks that progressively increase in rigor and complexity, leading students to grade-level proficiency. For example, in Module 8, Lesson 12, students identify the time on an analog clock and write the time, which aligns to TEKS 2.9G. By Lesson 16, students solve multi-step word problems involving elapsed time, requiring them to calculate start or end times. In Module 8, Lesson 4, the "Grupo de problemas" section directs students to name and describe basic two-dimensional shapes by identifying sides and angles. By Lesson 8, the "desarrollo del concepto" section instructs students to explore composite shapes and identify how many smaller shapes are needed to make the whole. In Modules 1–8, the material includes an explanation of how each topic progresses in rigor according to the targeted TEKS within "Contenido General." For example, in Topic A within Module 3, the students work on making groups by ones, tens, and hundreds to 1200. In Topic B, the students understand the value of the position, and in Topic D, students will represent numbers to 1200 using a money ($) symbol.

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

In Guía del curso del grado, Versión del maestro, in the "Secuencia de módulos de grado 2 alineados con los TEKS" section, the materials include an explicit description of how each Module 1–8 connects to patterns, big ideas, and relationships between mathematical concepts. For example, in Module 1, the students learn addition and subtraction up to 100. Then, in Module 5, students make connections of addition and subtraction up to 1,000 with written problems up to 1,000. In the "Contenido General" section within each Module 1–8, the materials provide an overview describing the focused concepts in the current module for each lesson and the connections to future learning in other modules, connecting big ideas between mathematical concepts. For example, Module 1, Lesson 1 lays the foundation for students to master addition and subtraction up to 20. Then, students apply these skills to fluently add one- and two-digit numbers to 100, using their understanding of place value, the properties of operations, and the relationship between addition and subtraction. In Module 8, Lesson 6, students draw different quadrilaterals, like rectangles and rhombuses. This practice connects to concepts in Lessons 2 and 3, where they learned to name and sort shapes by their number of sides, equal lengths, and right angles. In Module 8, Lesson 8, students identify and describe equal parts of shapes as halves, thirds, or fourths, making connections to Lessons 1–4, where the students previously learned to name and describe 2D shapes by counting sides, angles, and equal lengths.

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 "Progresión de conceptos matemáticos" section, within the Guía del curso del grado, provides a table displayed as a vertical alignment document from K through grade 5 to demonstrate the connecting content learned in previous, current, and future grade levels. For example, in grade 1, the concept is reading and writing numbers up to 120 and identifying equal parts of shapes. In grade 2, these same concepts connect to reading and writing numbers up to 1,200, using number lines, and partitioning shapes into halves, thirds, and fourths. In Módulos 1 al 8, Versión del maestro, the "Tema" (or Topic) section within each module includes a table and a description of how content and language connect to previous grade levels and future grade levels to the content learned in the current course. For example, in Module 1, Topic A, students recognize the combinations of numbers that can be added to make a sum of ten in Kindergarten (TEKS K.2I) to recognizing numbers from 11 to 19 as 10 + n in grade 1 (TEKS 1.2AB), and use the foundation concepts to connect to current learning of adding and subtracting up to 20 in grade 2 (TEKS 2.4A). In Módulos 1 al 8, Versión del maestro, the materials include a "Terminologia" section across modules to demonstrate the connection between language learned in previous grade levels and the current grade level. The materials include vocabulary words that will be introduced in the module and previously learned terminology. For example, in Module 3, the word agrupar is marked as términos conocidos, or known terms. In Module 6, the word matrix is introduced.

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..

In "Contenido General," within Módulos 1 al 8, Versión del maestro, the materials include a list of current grade level standards and a list of fundamental standards of previous grade levels to demonstrate coherence across lessons for each module. In Módulos 1 al 8, Versión del maestro, the materials demonstrate coherence at the lesson level by connecting students’ prior knowledge of concepts from the prior grade level to new mathematical knowledge and skills. For example, in Module 3, students use previous knowledge of place value to compare whole numbers up to 120 using comparative language (TEKS 1.2E) to connect to new learning in Lesson 15 to compare numbers up to 1,200 using symbols (TEKS 2.2CD). In Module 6, students previously learned to understand the relationships of the equal sign in expressions and how the value on each side of the symbol has an equal value (TEKS 1.5E) in grade 1. The lessons demonstrate coherence throughout Module 6 so that students can make connections to new mathematical knowledge of multiplication and division concepts (TEKS 2.6AB; 2.7A). In Module 8, Lesson 8, students connect previous learning in grade 1 on separating 2D shapes into two and four equal parts (TEKS 1.6G) to new knowledge of interpreting equal parts of composed figures with halves, thirds, or fourths (TEKS 2.8DE).

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

In Guía del curso del grado, Versión del maestro, the materials include a table within the "Estándares de grado 2 por lección por módulo" section. The table provides an overview of the standards for each lesson and module to locate spaced retrieval opportunities with previously learned skills and concepts. The materials include various tables within Desarrollo de la fluidez en grado 2 to provide information on the standards for spaced retrieval opportunities within each module. In Modules 1–8, the materials provide spaced retrieval opportunities with previously learned concepts across lessons. For example, in Module 2, Topic D, the students relate addition and subtraction to length by applying their conceptual understanding, choosing appropriate tools and strategies, such as using a ruler as a number line, benchmarks for estimation, and strip diagrams for comparison to solve written problems (TEKS 2.9E). In Modules 1–8, the "Practica de Fluidez" section provides opportunities for students to activate their prior knowledge through various lessons across modules. For example, in Module 3, Lesson 1, students engage in a 10–15-minute fluency practice targeting basic skills needed for a successful lesson. Lesson 1 asks the students to practice counting by 5 forward and backward and use two other counting strategies.

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

In Modules 1–8, the material provides interleaved practice opportunities with previously learned skills and concepts across lessons and units. For example, in Module 3, Topic A, students count and group ones, tens, and hundreds to 1200. In Topic D, students implement the skill learned to represent the value of $1, $10, and $100 to $1200 bills. In Module 2, Topic D, students connect addition and subtraction to length measurement. They use tools like rulers as number lines, estimation benchmarks, and strip diagrams to solve word problems. These problems progress from concrete tasks—such as measuring objects and using rulers to add or subtract lengths—to more abstract tasks, like representing lengths with strip diagrams to solve problems involving unknown starting points or multiple steps. Module 6, Lesson 4, shows students that a matrix is made up of rows and columns and that organizing concrete objects into rows and columns makes it easier to count. They are given the opportunities to practice counting in multiple ways, including making ten strategies, the associative property, and skip counting. In Module 8, Lesson 1, students sort and name shapes by their attributes, then use that to talk about equal parts and fractions. In Module 8, Lesson 7, students place clocks along a number line to show how time passes. This activity connects to skip counting and number line work from Module 2, and the concept of time.

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

In Modules 1–8, the materials include questions and tasks that require students to analyze and evaluate models and representations of mathematical concepts and situations. For example, in Module 2, Lesson 7, a math problem contains a student-created model representation of measurements using quarters and pennies. The problem asks students to analyze the student model and evaluate why the student is incorrect in thinking that both lines have the exact measurement. A homework problem within Module 2 requires students to analyze the table and answer: "What is the difference between the longest measurement and the shortest?" In Module 3, Lesson 7, the questions and tasks require students to interpret, analyze, and evaluate models across the lessons. For example, students compare two amounts, $190 and $109, using different combinations of bills. A student explains that $190 includes a $100 bill and nine $10 bills, while $109 only uses $10 bills. Students must interpret the structure of each amount, analyze how value changes with different combinations, and evaluate which set of bills holds more value. Module 8, Lesson 8, Boleto de Salida requires students to interpret diagrams of shapes that are divided and shaded, analyze the diagrams to identify the fraction as halves or fourths, and then evaluate the diagrams to provide the correct fraction that corresponds to the shaded shapes. In Module 6, Lesson 11 of Aprender, versión del estudiante, the lesson requires students to decompose 2D shapes into equal parts to interpret and solve word problems. For example, the application problem asks students to break apart a brownie tray into three rows and three columns. Students must draw a model and write a number sentence. As an extension, the problem asks students to reinterpret their image and analyze how they would decompose the same tray of brownies (one whole) to feed 12, 16, and 20 people with equal portions. In Module 8, Lesson 2, the lesson provides students with 2D shapes (tangrams) divided into parts, asks them to build new shapes using different triangle pieces, and poses questions about the number of equal parts and halves within the larger figures they create.

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

In Modules 1–8, the materials include questions and tasks that require students to create models to represent mathematical situations. For example, in Module 2, Lesson 6, within the "Grupo de problemas" section, a problem set includes a task that asks students to draw a rectangle and label its sides, representing the mathematical situation, to find the total length of the perimeter. In Module 2, Lesson 9, within the "Grupo de problemas" section, a problem set asks students to draw a strip diagram to compare their estimate with the actual length of the path. In Module 8, Lesson 3 of the Aprender, versión del estudiante, the questions and tasks ask students to use a ruler to draw different polygons with specific attributes, such as a triangle with three angles, a quadrilateral with four sides, or a hexagon with six vertices. These drawings help students represent and understand the structure of each shape. Lesson 6 asks students to build 3D shapes using given attributes, such as a shape with six equal faces and eight vertices, or a shape with two circular faces and one curved surface. The lesson asks students to use physical components or draw their models to represent these solids, then write the corresponding names for each shape. Aprender, versión del estudiante, and Triunfar, versión del estudiante, include questions and tasks that allow students to create models representing math situations. Module 6, Lesson 7 within Aprender, versión del estudiante requires students to develop models to decompose matrices when solving word problems. Lesson 10 within Triunfar, versión del estudiante requires students to create matrices to represent the area using a given number of rows and columns, then write a linear equation representing the model.

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

In Modules 1–8, the materials include questions and tasks that provide opportunities for students to apply their conceptual understanding to new problem situations and contexts. For example, in Module 1, Lesson 5, within "Desarrollo del concepto," students use their knowledge of breaking apart numbers to make 10 for new addition situations. Students add 49 + 5 by breaking apart 5 into 1 and 4. Then, they mentally add a 1 to 49 to make 50 + 4 = 54. In addition, the materials provide teachers with questions to ask students to support their application of conceptual understanding: "How much more do you need to make a 10? Where could we get one more? What should we take away from the other example? And how does your numerical bond match your quick tens drawing?" In Module 3, Lesson 7, Part C of the "Desarrollo del concepto" section provides opportunities for students to apply their conceptual understanding to new problems. The teacher asks students to use a one-dollar, a ten-dollar, and a hundred-dollar bill to demonstrate the value of a number. For example, teachers ask, "Muéstrenme $64?" Students work in pairs to show $64 using bills. The teacher follows up, asking student A to change two bills to $10 and two bills to $100 to make a new value: "¿Cuál es el nuevo valor?" The lesson expects the student to answer with $240. Module 8, Lesson 7 within Aprender, versión del estudiante, asks students to build new shapes using triangles, such as a square or a parallelogram, and reason about how many equal parts or halves make up each figure. This task requires students to transfer their understanding of shape composition and fraction concepts into new configurations. Lesson 14 asks students to show the clocks to determine the given time. Students must reason through what part of the hour or half-hour has passed using their understanding of fractions and angles.

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

In Modules 1–8, the modules include a "Practica de fluidez" section at the start of each lesson. These tasks work to build student automaticity and fluency necessary to complete grade-level tasks. For example, in Module 1, Lesson 2, the students review how to represent numbers with two digits by identifying the displayed pictorial representation. The students then use the Rekenrek abacus and place value cards to display the number given into tens and ones. Next, students decompose numbers to add by making tens. Finally, the students complete 30 problems independently and work with a partner to check each other’s work. In Module 5, Lesson 4, the "Practica de fluidez" section provides teacher-guided tasks for students to subtract multiples of hundreds and tens in order to prepare them for the lesson. For example, students review for fluency on how to subtract multiples of tens and hundreds (e.g., 130 minus two tens, which equals 110). Then, students use the Practicar, versión del estudiante, resource to complete the "Practica Veloz" section corresponding to Module 5, Lesson 4. The Triunfar, version del estudiante materials in grade 2 include the LDE strategy. This strategy helps students build fluency with multi-step problem solving. By following repeated steps—reading, drawing, writing an equation, and writing a sentence—students practice solving problems consistently. The repetition builds automaticity and confidence.

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.

In Modules 1–8, the materials provide opportunities for students to practice applying efficient, flexible, and accurate mathematical procedures. For example, in Module 1, Lesson 6, the Application Problem asks students to solve a word problem using the decomposing method or strip diagrams as an efficient, flexible, and accurate mathematical procedure. Students first decompose 30 into 20 and 10, then subtract 7 to find the difference of 23. Students use a part-part-whole visual to indicate 30 as the total, 7 as a part, and the missing addend. Students close with writing the numerical sentences (i.e., 30 - 7 = 23 and 7 + 23 = 30) in order to find the solution to the word problem. In the "Desarrollo del Concepto" section, in Module 1, Lesson 6, the materials include opportunities for students to apply efficient mathematical procedures. Students subtract numbers of one digit using pictorials. For example, students use efficient strategies to subtract 40 - 9 by decomposing 40 into 30 and 10, then subtracting 9 from 10. Finally, the students add 30 + 1 to obtain a sum of 31. The teacher informs students that knowing pairs of 10 makes solving problems more efficient. In the Aprender, versión del estudiante resource, the materials provide students with opportunities to practice using flexible, efficient, and accurate mathematical procedures. For example, the activities use the LDE strategy when solving problems. The LDE process requires students to read the problem, draw and label, write a numerical sentence, and write a word sentence. Module 6, Lesson 7, asks students to read the word problem, then draw a matrix with labels to represent the multiplication process for each problem. The last step of the process asks students to write a numeral sentence and a word sentence representing each word problem.

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 in Modules 1–8 provide opportunities for students to evaluate procedures, processes, and solutions for efficiency, flexibility, and accuracy. For example, in the debrief section of Module 2, Lesson 1, students compare their solutions for the problem set with a partner to evaluate procedures and processes. The teacher asks, "¿Alguien descubrió, al compartir su trabajo, que tenían una medida diferente a la de su compañero?," as students share with a partner and discover differences in methods of measuring objects. In the "Problema de aplicación" section, within Module 3, Lesson 4, the material provides an opportunity for students to evaluate procedures for efficiency, flexibility, and accuracy in finding solutions. For example, students draw dollar bills, counting by tens to make a total of $250. Then, students remove six $10 bills to demonstrate the subtraction problem to arrive at a total of $190. The margin note within the lesson guide enables teachers to invite students to analyze different strategies to find solutions and to select student work to share with the whole class. In the "Desarrollo del Concepto" section, within Module 5, Lesson 14, the materials provide opportunities for students to evaluate solutions for efficiency, flexibility, and accuracy throughout the lesson. The teacher asks students to explain why 147 + 437 helps them to consider 584 - 147. Students use place value disks to demonstrate regrouping strategies and evaluate solutions by explaining how 147 and 437 represent 500 + 80 + 4, resulting in a sum of 584.

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

In Modules 1–8, the lessons contain embedded supports to guide teachers in helping students develop increasingly efficient approaches to learning. The embedded supports provide examples of pictorials or visuals within lessons to support teachers. For example, in Module 1, Lesson 1, students practice making tens and adding up to 10 using number bonds. The teacher draws a number bond diagram, writes the number 10, and draws a connecting circle with the number 5. The teacher guides the students to identify the number that is missing next to number 5 to make 10. The materials include embedded supports as direct prompts for teachers to guide students toward increasingly efficient approaches. For example, in Module 4, Lesson 5, students use strip diagrams to solve word problems. Teachers use questions to guide them through solving the word problems: "¿Qué operación eligieron para resolver el Problema 2? ¿Por qué? ¿Cómo le ayudó a resolver el dibujo de un diagrama de tiras? ¿Por qué eligieron esa estrategia? ¿Podrían haber resuelto este problema de otra manera?." In Modules 1–8, the lessons include sidenotes as embedded supports to guide teachers in supporting students toward increasingly efficient approaches. For example, in the margin note within Module 8, Lesson 2, teachers guide students to evaluate a diagram of a pentagon as a puzzle to identify the shapes within and write a number in each triangle or shade each part of the triangle as they count all the triangles inside the pentagon.

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

In Modules 1–8, the materials explicitly state how the conceptual and procedural emphasis of the TEKS is addressed. In the "Contenido General" section for each module, the materials include an overview of the progression from conceptual to procedural learning by decomposing numbers to practice and apply basic operations. For example, in Module 1, within the "Contenido General" section, the students explore various ways to decompose numbers and strengthen their numeracy skills through conceptual understanding. Students use this basic understanding to compose and decompose numbers up to 20 (TEKS 2.4A) to apply when adding and subtracting one to two-digit numbers up to 100 (TEKS 2.4B) during procedural understanding when using place value strategies. Then, students use these strategies to regroup when subtracting two digits by one digit. In Module 4, "Contenido General" section, the material explicitly states how the conceptual and procedural emphasis of the TEKS is addressed. For example, the materials provide an overview of how Module 4 is based on three areas of work. Students develop conceptual understanding as they recognize place value and the properties of operations to add and subtract two digits up to 100 (TEKS 2.4B). The material provides students opportunities for procedural understanding by using number lines to solve one- and two-step word problems up to 100 (TEKS 2.4C, 2.7C). Then, students learn the conceptual understanding to add and subtract with various digits up to 200 (TEKS 2.4C, 2.4D) as a foundation for addition and subtraction up to 1,000 in Module 5 while using number lines or strip diagrams. In Module 8, Lesson 1, the materials explicitly state how students describe two-dimensional shapes based on their attributes, classify shapes, and use concrete objects to build two-dimensional figures. The teacher guides students to a conceptual understanding of figures through exploring characteristics like the number of sides and angles. Students use this conceptual understanding to draw and classify shapes by attributes, such as vertices and side lengths of two-dimensional figures (TEKS 2.8A, 2.8C). In Lesson 2, students use raw spaghetti to build and analyze polygons with increasing numbers of sides, then classify and label them using the correct names (TEKS 2.8A, 2.8C).

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.

In Modules 1–8, the materials include questions and tasks that include the use of concrete models and manipulatives, pictorial representations (figures/drawings), and abstract representations, as required by the TEKS. In Module 1, Lesson 1, the materials direct teachers to guide students through questions and tasks using the Rekenrek to model creating tens. For example, teachers show ten beads moving one by one while students count by ones. Then, teachers guide students to count by tens as the beads are moved in the Rekenrek, and finally, students count backwards by tens. In Lesson 5, the materials guide teachers to direct students to draw pictorial representations based on their foundational knowledge of counting by ones and tens. For example, teachers model a pictorial representation of 39 + 4 by using pictorials in the place value template. The teacher draws vertical lines to represent the tens, dots or circles used to represent the ones. The teacher draws three lines and nine dots to represent 39 and four dots to represent the number four. Teachers ask students to show their method of regrouping to find the sum of 39 + 4. In Module 4, Lesson 8, in the "Desarrollo del Concepto" section, the material questions and tasks include the use of concrete models and manipulatives, pictorial representations, and abstract representations, as required by the TEKS. For example, students use a strip diagram to show how to solve multi-step word problems for addition or subtraction. Then, students use place value disks to group quantities to solve the problem. Finally, students write an equation using vertical algorithms (TEKS 2.4B, 2.4C). In Module 5, Lesson 11, the materials include questions and tasks within the "Problema de aplicación" section to use concrete manipulatives, pictorial representations, and abstract representations to solve word problems. For example, students use place value disks to represent 55 + 37. Then, students draw a strip diagram as a pictorial model to represent 37 + 55. Finally, students use a vertical algorithm procedure to add 37 + 55 and compare it to the place value disks to verify the accuracy of their solutions.

Evaluation for 5.3c
Materials include supports for students in connecting, creating, defining, and explaining concrete and representational models to abstract (symbolic/numeric/algorithmic) concepts, as required by the TEKS.

In Modules 1–8, the materials include support for students in connecting, creating, defining, and explaining concrete representational models to abstract (symbolic/numeric/algorithmic) concepts, as required by the TEKS. In the "Practica de Fluidez" section within Module 1, Lesson 2, the materials support students by directing them to use place value cards and the Rekenrek to connect to abstract concepts. For example, the students are asked to display the number 15 using the place value cards, then separate the cards to represent 10 and 5. Finally, students use the Rekenrek to display 15 while they count by tens and write the number in expanded form. In the "Desarrollo del Concepto" section within Module 3, Lesson 6, the material includes support for students in connecting, creating, defining, and explaining concrete and representational models to abstract concepts, as required by the TEKS. For example, students use base-ten blocks to manipulate and create given numbers with a partner. Partner A creates the number 12 by using units and tens. Partner B creates the number 12 using tens and hundreds. Then students compare both numbers by mentioning the value of each number (one ten, two units) or (one hundred, two tens). Students organize their models in place value charts for visual support and write the number in standard form numerals. At the end, the lesson prompts the students to explain what each part represents, reinforcing the link between manipulatives, visuals, and numerical structure. In the "Desarrollo del Concepto" section in Module 4, Lesson 18, the material includes support for students in creating and explaining concrete and representational models to abstract concepts, as required by the TEKS. For example, students write an addition problem using a vertical algorithm (e.g., 76 + 27) and create a representation using the place value disks to show seven tens and six ones plus two tens and seven ones. The teachers prompt students to explain how elements of the drawing connect to each part of the addition, explicitly guiding the transition from model to abstract concepts of regrouping when solving addition problems.

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

In Modules 1–8, the materials provide opportunities for students to develop academic mathematical language by using concrete and pictorial representations while answering questions or completing tasks. In the "Practica de fluidez" section within Module 1, Lesson 2, the materials include opportunities for students to use visuals and manipulatives to develop academic mathematical language. The materials direct teachers to use place value cards for the number 12 by separating the cards to demonstrate ten and two. The teacher prompts students to say the number in standard form and then to use the word decenas to indicate the digit in the tens place. For example, the students respond "4 decenas 7" for the number 47 to develop academic mathematical language corresponding with the visual. Then, teachers use the Rekenrek as students count by tens using the word decenas. For example, teachers move the beads and students count "decena 5, decena 6, decena 7, decena 8, y decena 9" as an additional opportunity to develop academic mathematical language using manipulatives. In the "Desarrollo del concepto" section, in Module 4, Lesson 10, the materials provide opportunities for students to develop academic mathematical language using manipulatives. The materials direct teachers to use place value disks to guide students to subtract and use the academic mathematical vocabulary descomponer. For example, the materials direct teachers to display number 35, placing the disks of three tens and five ones in the place value chart. The teacher prompts students with questions such as "¿Cuántas decenas ves? ¿Cuántas unidades? ¿Cuántas estoy restando?" The students respond using academic vocabulary such as tres decenas and cinco unidades. The teacher introduces the term descomponer, and students work with a partner to describe the process of subtraction using place value disks and academic mathematical language such as decenas, unidades, descomponer, and restar. In the "Problema de aplicación" section in Module 8, Lesson 1, the materials provide opportunities for students to develop academic mathematical language using concrete tools, such as geoboards, while communicating with educators. For example, the materials direct teachers to draw a figure of a triangle and ask students to describe the figure without naming it, "¿Cómo describirían esta figura sin utilizar su nombre?" Students develop their academic mathematical language by describing the figure as "Tiene tres lados," "Tiene tres esquinas," and "Los lados tienen diferentes longitudes." Then, students use geoboards and rubber bands to create two-dimensional figures that are similar to a triangle with three sides, but with different lengths for the sides. The students describe their triangles using academic mathematical language such as vértices, ángulo, lados, parece diferente, or ángulo concavo.

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

In Modules 1–8, the materials include embedded guidance for teachers to scaffold, support, and extend students’ use of academic mathematical vocabulary in context when communicating with peers and educators. In the "Desarrollo del concepto" section within Module 2, Lesson 2, the materials include embedded guidance for teachers to use prompts as students communicate with peers. For example, the materials direct teachers to model a strategy for measuring a line drawn on the board using centimeter cubes. The teacher makes a mark at the end of the centimeter cube, then moves it forward without overlapping or leaving any space. The guidance prompts teachers to use the academic mathematical vocabulary se encimen or aproximadamente when communicating with students. The students work with a partner to measure a crayon using the terms aproximadamente, centímetros, and longitud in context when communicating. In the "Desarrollo del concepto" section within Module 2, Lesson 3, the materials include embedded supports for teachers to guide students to apply their previous learning using academic mathematical vocabulary in context to create a centimeter ruler. For example, teachers model using a centimeter cube to measure the length of different objects, then use the centimeter cube to measure and make marks for each centimeter to create a ruler. The students extend the use of the academic mathematical vocabulary by communicating with their peers how they used their ruler to measure their math book using terminology, such as marcas, reglas, cubos, and centímetros. In Module 8, Lesson 1, the materials include embedded supports for teachers in margin notes to scaffold, support, and extend students’ use of academic mathematical vocabulary in context. The margin notes direct teachers to write key math terms (e.g., ángulo, lado vértice/vértices, atributo) on the word wall as they are introduced in context. Students revisit the terms throughout the lesson to build understanding and support precise mathematical language when describing the characteristics or attributes of shapes. For example, teachers prompt students with "¿Cómo describirían un ángulo?" The students respond with answers such as, "Un ángulo son dos lados de una figura. Un ángulo tiene dos lados y un vértice." These responses use academic mathematical vocabulary in context when communicating with educators.

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 Modules 1–8, the materials include embedded teacher guidance to support the application of appropriate mathematical language. In the "Desarrollo del concepto" section, in Module 1, Lesson 6, the materials include embedded supports as margin notes to guide teachers to provide opportunities for students to hear, refine, and use math language with peers and develop their mathematical toolkit over time. The margin notes guide teachers to provide opportunities for students to first share their solutions with peers, then with the whole class, fostering the use of clear and precise mathematical language. For example, students explain to a partner the relationships between two number sentences, 10 - 9 = 1 and 10 + 1 = 11. The students respond by applying appropriate mathematical language such as, "El 10 menos el 9 muestra cómo tomamos de diez" and "Descomponemos 20 en 10 y 10, para poder tomar 9 de los diez. Luego sumamos lo que quedaba." In the "Desarrollo del concepto" section within Module 3, Lesson 16, the materials include embedded teacher guidance to support the application of appropriate mathematical language. The materials provide teachers guidance by directing them to use questions and exemplar sentence stems to scaffold academic responses "__ es mayor que __ porque…" Students listen to each other and revise explanations built in through guided partner work. The guidance directs teachers to guide students to compare numbers using the symbols >, <, and = by using place value charts and applying mathematical language (e.g., mayor que, menor que, igual a, centena, decena, and unidad). In the "Desarrollo del concepto" section within Module 4, Lesson 5, the materials include embedded teacher guidance to support the application of appropriate mathematical language to include vocabulary, syntax, and discourse. In the Problem Set, students solve two-step word problems using strip diagrams and explain their reasoning to their peers using terms such as total, parte conocida, parte desconocida, operación, and diagrama de tiras. The materials include scaffolded sentence frames for teachers to help students express multi-step reasoning with clarity. For example, students communicate with their peers to explain how they interpreted and solved each step by answering questions, "¿Cuántos estudiantes hay en el autobús rojo? ¿Cuántos estudiantes hay en ambos autobuses juntos?" The teacher models responses, encourages students to clarify their thinking, and revisits key terms during debrief.

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

In Modules 1–8, the materials integrate the TEKS process standards appropriately into the materials. The "Desarrollo del concepto" section in Module 1, Lesson 6, integrates the TEKS process standard 2.1F. The lesson asks students to analyze mathematical relationships to connect and communicate mathematical ideas. For example, the materials direct teachers to ask students to subtract using pictorial representations, such as 10 - 9 or 20 - 9. Students use number bonds to analyze mathematical relationships by decomposing the number 20 into 10 and 10, and communicate mathematical ideas with a peer, explaining the process of decomposing to find a solution. In the "Reflexión" section in Module 2, Lesson 3 integrates TEKS process standard 2.1G. The lesson asks students to demonstrate, explain, and justify their mathematical ideas using precise mathematical language. The materials direct teachers to ask questions and guide students to reflect and explain mathematical ideas with a peer. For example, teachers guide students with directions and questions such as, "Gírense hacia su compañero y comparen sus medidas en los Problemas 1–3. ¿Qué hicieron para medir con precisión con su regla en centímetros? Gírese hacia su compañero y comparen sus medidas en los Problemas 1–3. ¿Qué hicieron para medir con precisión con su regla en centímetros?" Students review the solutions of their independent work and compare solving strategies with a peer. In the "Desarrollo del concepto" section, within Module 3, Lesson 10 integrates process standards 2.1C, 2.1D, and 2.1G. The materials direct teachers to guide the students in selecting tools to solve problems. Students use base ten blocks, place value disks, and the base ten table to solve problems. Students communicate mathematical ideas by explaining how the models represent the same quantity when adding two-step word problems, justifying their thinking, and using precise mathematical vocabulary, such as decena and centena, to support mathematical language use.

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

In Modules 1–8, the Matemáticas K–5 guía de programa e implementación resource includes a description of how TEKS process standards are incorporated throughout the course. The "Diseño de materiales de instrucción" section emphasizes how TEKS process standards are carefully built into the modules to create a clear and connected math progression. It explains how reasoning, representation, and application are practiced throughout the course, with key ideas like place value, fractions, and area introduced, repeated, and strengthened through a consistent teaching approach. In the "Estandares de procesos matemáticos de TEKS" section, within Matemáticas K–5 guía de programa e implementación, the materials include a description of how the process standards are integrated throughout the course. The materials provide examples of how the TEKS function within the materials. For example, the materials state, "a purposeful integration of a variety of problem types that range in complexity naturally invites students to analyze given data, constraints, relationships, and goals." The process standards are integrated by providing opportunities to use models, drawings, numerical representations, and precise language to enable others to understand students' learning and reasoning. During the debrief section, teachers lead students to discuss their independent work by analyzing and explaining to their peers while comparing strategies used to solve problems.

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

In Modules 1–8, the materials include a description for each TEKS process standard incorporated and connected throughout each module. In the "Contenido general" section within Module 4, the materials include a description of how students engage with mathematical representations, reasoning, justification, and communication of ideas, to include information of the TEKS process standards used in the module. For example, "A lo largo del módulo, los manipulativos y los dibujos matemáticos permiten a los estudiantes ver los números en términos de unidades de valor de posición; A lo largo del módulo, se anima a los estudiantes a ser reflexivos en su pensamiento y a utilizar múltiples estrategias en la resolución de problemas" (TEKS 2.1D, 2.1G). In the "Contenido General" section within Module 6, the materials include a description of how the TEKS process standards are incorporated and connected throughout the module. For example, the students participate in communicating mathematical ideas, reasoning, and implications while using multiple representations, such as strip diagrams, matrices, repeated addition, and repeated subtraction (TEKS 2.1D). In Topics A and B, students use precise mathematical language to describe and distinguish between groups and the number in each group (TEKS 2.1G). Finally, students communicate their reasoning by explaining if a number is even or uneven using a representation as a matrix (TEKS 2.1D). In the "Contenido General" section within Module 8, the materials provide clear descriptions and an overview of the integration of TEKS process standards throughout each module. This stress on the integration of TEKS process standards makes educators feel the comprehensive nature of the materials. For example, the materials describe how students apply math to real-life contexts (TEKS 2.1A) while solving problems involving time and shape. Students organize and communicate their thinking using number lines and models (TEKS 2.1E) and justify their conclusions using precise language when building and analyzing composite shapes (TEKS 2.1G). These practices are woven throughout the module, demonstrating how to implement reasoning, justification, and representation.

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

In Modules 1–8, the Guía del curso del grado 2 resource includes the "Estándares de procesos matemáticos TEKS de grado 2 por lección por módulo" section. This section provides a table overview that notes each TEKS process standard (e.g., 2.1A–2.1G) within the specific modules and lessons. For example, Module 2, Lesson 1, and Module 5, Lessons 2 and 10 incorporate the TEKS process standard 2.1C. In the "Contenido General" section within each module, the materials provide an overview of the TEKS process standards and the integration into each lesson in an organized, topic structure. The materials include a specific overview of how the TEKS process standards are incorporated into the module. This overview extends into the lesson materials with the "Contenido general de los temas del módulo y objetivos de la leccion" section overview. This overview lists the process TEKS and the location of the TEKS in each topic or lesson.

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

In the "Desarrollo del Concepto" section, within Module 2, Lesson 5, the materials provide opportunities for students to think mathematically, persevere through solving problems, and make sense of mathematics using tools such as centimeter rulers and meter sticks to measure objects. For example, students are instructed to use nonstandard units of measurement, such as their small finger, to make an estimate of the lengths of an eraser, a desk, a pencil, and a whiteboard. Students persevere through solving problems by estimating and using centimeter rulers and meter sticks to obtain an accurate measurement. In the "Desarrollo del concepto" section within Module 6, Lesson 5, the students think mathematically and persevere through solving problems using beans to make sense of the mathematical concept of repeated addition. During the lesson, students build an array using beans to represent four groups of five. The students write the number 5 next to each separate row of four beans and write the expression of repeated addition 5 + 5 + 5 + 5. Students are provided additional opportunities to persevere through solving problems of repeated addition by creating additional arrays to represent 5 x 4 and 6 x 3 and communicating to their partners how many columns and rows are represented in the model. In Module 8, Lesson 7, the materials provide students with opportunities to think mathematically, persevere, and make sense of math by exploring and creating new shapes using tangrams. For example, the materials guide students to create shapes by cutting a tangram and identifying the attributes or characteristics of the shapes. Students flip, slide, and rotate pieces to form composite figures. They also work with peers to build larger shapes and identify attributes with their peers, such as the number of angles, vertices, and sides. Then, students combine a square and two triangles to make a larger square to make sense of mathematical concepts.

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.

In Module 4, Lesson 13, in the "Homework" section, the materials support students in understanding, explaining, and justifying that there can be multiple ways to represent and solve problems and complete subtraction tasks. In Problem 3, the students analyze two different visuals to represent the solution for 166 - 48. The first visual displays the vertical algorithm for 166 - 48. The second visual uses place value disks to represent regrouping to find the difference between 166 - 48. The students complete the task by analyzing and interpreting each visual to find out if it represents an accurate solution to a subtraction problem. Then, students explain and justify whether they agree or disagree with the representations and what could be changed to make an accurate representation to solve 166 - 48. In the "Grupo de Problemas" section within Module 6, Lesson 4, the materials support students in understanding that there are multiple ways to represent and solve a variety of problems by composing matrices with columns and rows to represent groups. Students draw a circle to compose two groups with four triangles in each. The students create an array with two rows and four columns to represent the two equal groups. Then, students create three rows or three columns of happy face images to represent three rows with two happy faces in each. Finally, students create matrices with a given number, such as 15, to create three rows with five triangles in each row. In Module 8, Lesson 10, the materials support students in understanding that there are multiple ways to represent and solve a variety of problems or complete a task. During the "Concept development" lesson, the students use a blank sheet of paper and fold the paper in different ways to represent one-half. The students label and share their halves and compare with their peers to describe what is different and what is the same about their shapes. Students explain to their peers the shape they created and justify that it has two equal parts, which, when placed together, make a whole.

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.

In Modules 1–8, the 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. In Module 2, Lesson 1, the materials require students to make sense of mathematics to practice the concept of measuring using tools. For example, students work with a partner to estimate the length of a set of used colored pencils. Students turn to a partner and estimate how many one-centimeter cubes they think they will need for each crayon in the bag. They share their estimate with their partner and use centimeter cubes to obtain an accurate measurement. In the "Desarrollo del concepto" section within Module 3, Lesson 4, the materials are designed to require students to make sense of mathematics through multiple opportunities to do, write about, and discuss math. Students use base ten number cards to create numbers, then manipulate them to form the greatest number, writing it in standard form. For example, the teacher directs students to count four ones, three tens, and two hundreds. The students count by ones, such as "1 unidad, 2 unidades, 3 unidades, 4 unidades, 1 decena, 2 decenas, 3 decenas, 1 centana, 2 centenas" to make the number 234. The students make 234 using the place value cards, and the teachers model the representation of the number in standard and written form. Students work with a partner to demonstrate 234 using the place value cards by composing and decomposing the cards, reading the number in standard form and written form. In the "Desarrollo del concepto" section within Module 8, Lesson 2, the materials provide students with multiple ways to make sense of math by doing, writing, and discussing. For example, in the triangle puzzle activity, students actively search for triangles of different sizes and orientations within a larger figure. They can write numbers inside the triangles they find or lightly shade them, helping them keep track of their thinking. The activity also encourages students to share strategies and compare findings with peers, giving them chances to talk about their reasoning and learn from each other.

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

In Module 2, Lesson 3, the materials include support for teachers in guiding students to reflect on their problem-solving approaches, including explanations, arguments, and justifications. For example, in the debrief section, the teachers ask students to compare 24 + 5 with 24 + 50 with their partner. Students work with a partner and share their results by explaining the problem-solving approaches. Students explain the differences in their approach, justify their solution, and decide if they would be able to teach what they have learned to another peer. In the "Desarrollo del Concepto" section within Module 3, Lesson 12, the material provides support for teachers to guide students in sharing and reflecting on their problem-solving approaches. The materials direct teachers to prompt students with questions such as, "¿Cuál es el valor total de este nuevo número? Escríbanlo en sus pizarras individuales. Muéstrenme el valor cuando dé la señal," for students to share their strategies and reasoning. For example, students construct equations, name quantities, and justify their answers using tools like place value disks and visual models. This activity fosters student explanations like "Podemos ver las unidades," arguments based on structure like "hay marcos de diez," and justifications for how they determined the value or constructed a number. The materials in Module 8's "Reflexión" section encourage teachers to guide students in sharing and reflecting on their thinking. They also direct teachers to guide students in sharing and reflecting on their problem-solving approaches. For example, students are invited to "revisar el trabajo comparando las respuestas con un compañero" and to explain how they solved their "Grupo de Problemas" section tasks. Teachers prompt students to reflect and justify their solutions with their peers with questions such as, "¿Cómo le explicarían su error?" and "Expliquen a su compañero por qué hay que prestar atención a algo más que el aspecto al agrupar las figuras."

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

In the "Desarrollo del concepto" section in Module 2, Lesson 3, the materials support teachers by providing explanatory feedback based on student responses. During the lesson, the students create a ruler using a one-centimeter cube and cardboard. The materials guide the teachers to anticipate errors and prompt students to notice that there are many ways to make mistakes with all this counting. For example, "What could I do to keep track next time I use my ruler?" Students respond, "You can label the marks with numbers." Materials guide teachers to respond, "That’s a good idea to label the marks with numbers. I can keep track more effectively, and next time I will not have to count again." In the "Desarrollo del concepto" section, within Module 3, Lesson 2, the materials include prompts and guidance to support teachers in providing explanatory feedback based on student responses and anticipated misconceptions. The materials recommend that teachers encourage students to verbalize and reflect on their thinking, allowing the teacher to listen for misconceptions or partial understandings, validating multiple strategies, and inviting students to revise or expand their work based on peer explanations. "Expliquen a sus compañeros cómo sus dibujos les ayudan a contestar a la pregunta." "¿A quién le gustaría compartir lo que pensó?" "¡Todas esas son estrategias muy inteligentes para resolver este problema! Si alguien desea añadir alguna de estas estrategias a su documento, por favor, hágalo ahora." In Modules 1–8, the "Contenido General" section within "Solución colaborativa de problemas erroneos" for each module includes guidance to support teachers in providing explanatory feedback based on student responses and anticipated misconceptions. The materials also provide guidance for teachers to address student misunderstandings. It outlines three steps: "(1) estimular el pensamiento en los estudiantes; (2) validar lo que el estudiante hizo bien; y (3) crear un puente a una mejor comprensión." This guidance explicitly helps teachers give explanatory feedback based on common errors, supporting students in refining their understanding and correcting misconceptions.