Aprendizaje Bluebonnet Matemáticas K-5 Grado 3

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 de grado under "Documentos del nivel del curso." The materials include a year-long scope and sequence, "Vistazo del año de grado 3," organized as a table to include the title of the module and the aligned Texas Essential Knowledge and Skills (TEKS) taught for the corresponding Modules 1 through 7. The year at a glance, "Vistazo del año de grado 3," includes suggested days as pacing for each module. For example, the year at a glance for Module 1 is recommended for a 22-day pacing focusing on TEKS 3.4D, 3.4E, 3.4F, 3.4H, 3.4J, 3.4K, 3.5A, 3.5B, and 3.5D. The materials include a table in the section "Alcance y Secuencia de grado 3" 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, Module 5, "Fracciones como números en la recta numérica," mainly focuses on TEKS 3.3A–H, 3.6E, and 3.7A. In the "Estándares de grado 3 por lección" in the Guía del curso del grado, the TEKS are organized in a table as an overview for Module 1 through 7. The table provides the "TEKS de grado 3 por lección de cada módulo" taught in each lesson for Modules 1–7, including grade 3 mathematics TEKS. In the Guía del curso grado, the "Desarrollo de la fluidez en Grado 3" 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 Module 3, "Números y operaciones," addresses TEKS 3.2B in lesson 9, 15–22, and 26.

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 grado, under "Documentos del nivel del curso," include the section "Alcance y secuencia de grado 3." The materials in this section provide information organized as a table with the module number, topics and days of instruction, concepts and skills, and TEKS. The pacing for instructional days varies from Module 1 to Module 7 for a total of 165 calendar days. For example, in Module 1, the total number of instructional days is twenty-two, including evaluation days. In Module 4, the pacing is ten days for instruction, including days of evaluation. In the Guía del curso del grado, the materials include a document, "Vistazo del año de grado 3," as a year-at-a glance outline that offers a clear overview of the content standards addressed in a calendar year of 165 days. The "Vistazo del año de grado 3" 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 grado, providing a table as an at-a-glance visual support outlining the vertical alignment in kindergarten through grade 5. The document includes the concept for each module, the number of suggested instructional days, and alignment across grade levels organized by three trimesters or four trimesters. In Días adicionales del año escolar (ADSY), versión del maestro, the materials include thirty 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 includes twenty-five 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 grado, providing a table as an at-a-glance visual support outlining the vertical alignment in kindergarten 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 3 alineados con los TEKS," providing a rationale for the order of Modules 1 through 7. The materials include a sequence guide for each module explaining how the TEKS are connected throughout the course. This guide provides a clear explanation of the rationale behind each module and how it connects with future learning. For example, in Module 1, students begin by building on concepts introduced in grade 2: "El primer módulo se basa en la base del pensamiento multiplicativo con unidades que comenzaron en el 2do grado." The materials include the learning progression described in Module 2, "Valor de posición y resolución de problemas con unidades de medida," as a foundation for concepts in Module 5, "Fracciones como números en la recta numérica."

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 the Matemáticas K–5 guía de programa e implementación to provide guidance for module and lesson internalization. In this section, the materials provide a protocol to support the teacher in internalizing modules and lessons using a four-step process. The "Protocolo de internalización de módulos para el maestro" document in "Recursos para maestros" explains 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, note the pacing days for instruction and assessment, and reflect on why the module is important as well as how it connects to prior modules. Each step also provides guidance on what to use or create for the lesson. For example, Step 4 asks teachers to locate manipulatives or materials listed and identify additional supplies needed to support groups of students. In Modules 1 through 7, 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 lesson internalization, including examples presented as diagrams. The "Contenido general del módulo" section provides 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 concepts in module 5). In Modules 1–7, under versión del maestro, the materials include a "Terminología" section to support lesson internalization. This section provides terminology and relevant cognates used throughout the module, as well as 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 will be using throughout the module or vocabulary used to spiral from previous grade levels or modules. The materials in Modules 1–7, versión del maestro include Topics (A–F), which vary by module. The materials in Topic (A–F) are 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. Topics vary for each module. For example, Module 1 Topics A–F with total of nineteen lessons, and Module 6 contains "Tema A: Comprensión de finanzas," "Tema B: Generar y analizar datos categóricos," and "Tema C: Representar pares numéricos en una tabla" with a total of fifteen lessons.

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 de 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, objective, and assessments. Step 3: Establish the arc of learning by reviewing connections between the topics and assessments and think 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" document in "Recursos para líderes" includes a recommended time, varying for each step in the process from five minutes to twenty minutes. The materials guide the instructional leader to help teachers explore previous instruction, purpose, implementation, and a deep level of reflection for future instruction. In Matemáticas K–5 guía de 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 lecciónes para lider de instrucción" in "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 de 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 contains a "Lista de manipulativos y materiale" that contains a comprehensive list of materials that will be needed throughout the year, and 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 Módulos 1 al 7, versión del maestro, the materials include a general overview of the concepts, "Contenido general del módulo," at the beginning of each module, providing examples as visuals aligned to the TEKS. The "Contenido General del módulo" section provides 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 the teacher with the background content knowledge necessary to effectively teach the concept. For example, Module 1 notes that students are expected to have knowledge of TEKS 2.6A as the foundation for repeated addition from the previous grade level to connect to the new learning. In the "Terminología" section in the versión del maestro for each Module 1 through 7, the material includes a detailed explanation of the vocabulary with explicit explanations of the meaning of each word and 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 Modules 1 through 7, in the versión del maestro, the materials include a "Terminología" 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 used to spiral from previous grade levels or modules. The materials provide terms that may be cognates and are used throughout the module, as well as a pictorial diagram for math strategies and representations. In Módulo 1, versión del maestro, for example, in the "Terminología" section, the mathematical terms within context of the lesson and terms with English cognates are listed to connect words to their meanings, such as "Producto (Product): el resultado cuando dos o más números se multiplican." In Module 6, for example, credito and deudor are listed as new vocabulary, and encuesta, gráfica de barras, and datos 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 de grado, the "Documentos del nivel del curso" section includes a "Consejo para las familias" section that provides a general content information page for families in both English and Spanish for each module. The "Consejo para familias" informs parents of the general content for key concepts the student is learning in the module, with recommendations on additional ways to support their child at home. The document includes the terminology used and pictorial math representations as examples of those terms. For example, in Module 4, families are encouraged to have students cut out a rectangle from a piece of graph paper or use floor tiles as the students learn about area as an attribute of two-dimensional figures. In Módulos 1 through 7, versión del maestro, in the "Tarea" section, the material includes practice problems assigned as homework after each lesson is taught, not recommended to be used for the introduction of new concepts. In Triunfar, versión del estudiante Módulos 1 al 7, 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 in 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 through 7 include a table, "Contenido general de los temas del módulo y objetivos de la lección," organized as an overview indicating the focus TEKS, topics, and objectives for each lesson, including the number of days for Topics (A–F), daily "exit tickets" as formative assessments, and an evaluation at the end of each module. The materials at the beginning of each lesson include "Materiales de instrucción de matemáticas," providing teachers with information outlining the focus TEKS, days of instruction, and detailed background knowledge of the concepts. For example, in Module 2, Lesson 1, 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. In Module 2, versión del maestro, Lesson 1, the materials provide tasks and activities for students to engage in critical thinking and opportunities for practice and discussion. 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. Throughout each component, TEKS alignment, language supports, mastery activities, and a variety of questions are embedded. The margin notes include support for emergent bilingual (EB) students by connecting key vocabulary to visual representations, cues, or gestures. The lessons also embed materials within each lesson and activity to support understanding. For example, in Module 2, Lesson 1, the teacher will need an analog clock, stopwatch, and class clock. Students will need an individual whiteboard and a stopwatch.

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 Lección 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 and are listed using a color-coded key next to a pie graph displaying the following 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, in Module 7, Lesson 1 includes a "Práctica de fluidez" (15 min), "Desarrollo del concepto" (35 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, "Listas de manipulativos y materiales," listing the items needed for the entire school year organized by the number of items and a description of the material, for example, 25 discos de valor de posición de números enteros per group and one set for the teacher. In the versión del maestro, the Modules 1 through 7 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 the teacher, and materials needed for each student. In every lesson under Modules 1 through 7, the materials are described for each component of the lesson and are listed using the symbol (M) for teacher materials and and (E) for student materials. For example, in the versión del maestro, "Lista de materiales del Módulo 2" in Lección 5, the teacher materials include a digital balance (M), and the student materials needed for this lesson are a balance (E), whiteboard (E), counters (E), and popcorn kernels (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, versión del estudiante Módulos 1 al 7, 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 2, Topic B in Lesson 5, "Ayuda para la tarea," includes pictorial math representations and text surrounded by a dialogue frame. It includes phrases to support the concept of measuring weight, such as, "El cubo C pesa 14 lb y el cubo B pesa 7 lb. Se que 14 – 7 = 7, así que el cubo C pesa 7 lb más." In Matemáticas K–5 guía de 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 the fluency practice, the application problems, or both. The materials support the teacher assigning either fluency or word problems in the form of Leer–Dibujar–Escribir 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 1–7, the materials include diagnostic assessments that vary in types of tasks and questions, such as fluency practice or mid-module assessments. The materials include a diagnostic assessment, "Mitad del módulo" in Evaluaciones, versión del maestro to evaluate the same TEKS that will be tested at the end of the module. For example, in the "Evaluación de la mitad del Módulo 7," for TEKS 3.6B, students identify quadrilaterals, then draw two-dimensional figures, in question 2: "¿Cuáles de las tres figuras son cuadriláteros? Explica cómo lo sabes?" and question 5: "Dibuja una figura de cuatro lados sin ángulos rectos ni lados iguales. Usa medidas para etiquetar las longitudes de los lados." In Modules 1–7, 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 2, the exit ticket instructions instruct students to draw their answer in the diagram, explain, and show their reasoning on a number line. In Grado 3 Evaluaciones, versión del maestro, the materials include summative 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. For example, as per "Contenido general de los temas del módulo y objetivos de la lección" in Module 7, teachers administer a mid-module assessment after Topics A–C and a final module assessment after Topic E.

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 de la 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 and end-of-module assessment tasks include scoring information as a rubric to use as formative or summative assessment. In Evaluaciones, versión del maestro, the materials for the Evaluación final del módulo task includes a brief explanation of the purpose for the assessment and the rubric included for each Module 1 through 7. These tasks assess the overall performance of the student's understanding of the complete content at each module. Matemáticas K–5 guía de programa e implementación, within the "Enfoque de las evaluaciones" section, includes 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 are intended for practice that 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 through 7, the materials include formative assessments and guidance to ensure accurate administration of assessments. Materials provide teachers with guidance on the time allotted for students to complete assessments and implementation directions. For example, in Module 5, Lesson 4, the "Boleto de salida" section provides instructions for teachers to allow three minutes for students to complete the assessment. Within the same lesson, the "Reflexión" section provides guidance for teachers to invite students to think and process the concepts learned in the lesson. In Evaluaciones, versión del maestro, the materials include the "Contenido general de la evaluación de Grado 3" section, which explains the importance of testing fidelity with new activities and tasks. In addition, teachers are informed that the assessment can be formative or summative, depending on teacher needs. The materials explain how teachers can use the Progression Toward Proficiency rubric to score student responses and how it can be 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 de programa e implementación, the materials include an "Enfoque de las evaluaciones" section providing an explanation on the focus of each evaluation component to ensure consistency and accurate administration of instructional assessments to be completed by the student during the instructional day. The materials include a visual table as an example to demonstrate when teachers may administer the assessments. For example, the Boletos de salida are administered daily at the end of each lesson, the Evaluación de la mitad de módulo is administered in the middle of the module, and Evaluación final del módulo is administered at the end of the module.

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 through 7, the material includes diagnostic, formative, and summative assessments that align to the TEKS and objectives of each lesson. The materials include an information page with the TEKS tested as well as 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. In Module 7, Lesson 1, the materials include formative assessments such as Grupo de problemas and Boletos de salida aligned to TEKS 3.4K, 3.5A, and 3.5B. The Boleto de salida instructs students to solve a two-step real-world problem involving multiplication and addition for the following example: "Samuel guarda su colección de pegatinas en 7 álbumes... ¿Cuántas pegatinas en total tiene Samuel en su colección?" In the Evaluaciones resource, the materials include the "Contenido general de la evaluación en grado 3" section, which explains how the Mid-Module and End-of-Module Assessment Tasks are aligned directly to the TEKS and provide a table titled "Progreso hacia el dominio" with the TEKS and rubric for each evidence. For example, in Module 1 the Evaluación de la mitad del módulo assessment evaluates the following TEKS: 3.4D, 3.4E, 3.4H, 3.4K, and 3.5D, which align with the course objective on properties of multiplication and division and problem solving with units of two to five and ten. In Matemáticas K–5 guía de 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 resources, the materials include group problems, exit tickets, homework, and tools for reflection.

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

The materials for Modules 1 through 7 include instructional assessments at varying levels of complexity that align with the TEKS. For example, in Module 4, Lesson 1, the students decompose figures by using inch tiles to form rectangles. In Module 4, Lesson 2, the students compare the length of sides of a rectangle and demonstrate their relationship with area. In Module 4, Lesson 3, students draw the rows and columns to represent measurement of area. In Module 7, Lesson 1, within Grupo de problemas, the materials include real-world problems that vary in levels of complexity and move from simple to complex. For example, in Module 7, Lesson 1, the task is a multi-step word problem that states, "Samuel guarda su colección de pegatinas en 7 álbumes. Cada álbum tiene 8 pegatinas. Empieza un nuevo álbum con 9 pegatinas. ¿Cuántas pegatinas en total tiene Samuel en su colección?" This task increases in complexity by requiring students to apply both multiplication and addition to solve the word problem. 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 through the use of multiple-choice, text-entry, and open-response items aligned with the TEKS. For example, In the Module 5 Evaluación de la mitad del módulo, TEKS 3.C assesses unit fractions through labeling each fraction using strip diagrams. Then, in the Evaluación final del módulo, TEKS 3.C, students answer questions aligned to a pie chart by stating if the statement is true or false.

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

In the Evaluaciones resource, the materials include Mid-Module and End-of-Module Instructional Assessment Tasks and scoring information guidance for teachers to interpret student performance. These mid-module and end-of-module assessments include 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. In the "Progreso hacia el dominio rubric," the document is structured from left to right, representing growth toward mastery in four different evidence guidances. The table is divided in columns stating the standard assessed and describing evidence of solid reasoning toward mastery, ranging from little evidence of reasoning with no response to evidence of solid reasoning with 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 for 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 the use of included tasks and activities to respond to student trends in performance on assessments, such as using the "Progreso hacia el dominio" rubric in conjunction with "Alcance y secuencia," TEKS, and fluency information in the Guía del curso to locate lessons and activities for students needing additional support. The "Alcance y secuencia" document within the Guía del curso 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 the Guía del curso resources provides various tables displaying the location of each TEKS within each module and lesson to help teachers find tasks or activities to respond to student trends in performance on assessments. In Matemáticas K–5 guía de programa e implementación, the materials include a "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 to obtain student performance based on the rubric "Progreso hacia el dominio" and 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 "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 reflection questions before and after the evaluation assessment is implemented. For example, the teacher will 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 parents and students with a checklist to track progress and growth for the concepts learned in each module aligned with the TEKS with a focus on deepening the comprehension of the concepts learned. The "Student Work Analysis Protocol Teacher Guide" within Matemáticas K–5 guía de programa e implementación provides 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 analysis; Step 5: Determine action steps for whole and subgroups.

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

The lessons within Modules 1 to 7, the "Desarrollo del concepto" section includes margin notes to guide teachers in implementing differentiated instruction, activities, and paired (scaffolded) lessons for students who need additional support. Module 2, Lesson 2 guides teachers in encouraging students to solve addition and subtraction problems with time intervals using an analog clock. In addition, the margin notes guide teachers to read the problems aloud for students who need support with comprehension and provide opportunities to ask clarifying questions. In Module 1, Lesson 10, the margin notes include guidance for teachers to use concrete objects for pictorial representations with students who need extra academic support, such as connecting cubes to show how to distribute the rows of six for the problem 3 × 6. In Module 4, Lesson 2 within the "Desarrollo del concepto" section, the margin notes guide teachers to simplify and clarify words, offering questions to scaffold the lesson as students are learning about the concept of area using one-inch tiles, from "¿Qué información sabemos" to "¿Cuántas filas de cuadros de pulgadas tenemos? ¿Cómo lo saben?" In Module 6, Lesson 1, the margin notes guide teachers to use real or plastic coin manipulatives with students who need support counting money and grouping to make a dollar. The guidance in Module 7, Lesson 14 provides targeted support for students who need additional help, including those struggling with academic language. In the margin notes advise teachers to offer a sentence stem ("encontrar el perímetro, necesitamos saber...") and a word bank with terms like longitud, ancho, área, rectángulo, diferente, and perímetro. These supports help students explain their reasoning and participate meaningfully in problem solving, even if they are not yet proficient with the content or vocabulary.

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 through 7, the teacher materials provide pre-teaching or embedded support for unfamiliar vocabulary and references in the text. For example, in Module 1, Lesson 2 within the "Desarrollo del concepto" section, the margin notes guide teachers to color code the word por in one color and use a different color for es igual a as students learn the concept of multiplication using written forms of 6 × 2 (seis por dos es igual a). Module 2, Lesson 3 includes embedded support to guide teachers when teaching the new vocabulary word tonelada for the concept of weight. The guidance provides teachers with questions to guide students: "¿Donde han oído la palabra tonelada antes? ¿Qué creen que significa la palabra 'tonelada'?" The margin notes in Module 2, Lesson 6, "Notas sobre las diferentes formas de acción y expresión" provide teacher guidance to assist students with differentiating between the new terms capacidad and volumen líquido using images that illustrate the distinction. Module 4, Lesson 3 within "Desarrollo del concepto" provides embedded teacher guidance to help students develop an understanding for the new vocabulary words in bold (cuadros unitarios). The guidance models drawing unit squares with rows and columns inside a rectangle to determine the area. In Modules 1 through 7, the materials include a "Terminología" 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 include the definition, a pictorial image as an example, and Spanish–English cognates (e.g., diagonal–diagonal). For example, the "Terminología" section in Module 7 includes the new vocabulary term perímetro. In addition, Lesson 19 provides teacher guidance to use questions as embedded supports to teach new vocabulary: "¿Qué significa perímetro? ¿Cómo encontramos el perímetro? ¿Qué unidades se utilizan para medir el perímetro de este rectángulo?"

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 through 7, the materials provide guidance for different instruction, enrichment, and extension activities for students who have demonstrated proficiency in grade-level content and skill. For example, the margin notes in Module 3, Lesson 2 guide teachers to allow opportunities for students to write their own problem using real-life situations as an enrichment activity. The task includes differentiation, asking students to share with a partner in order to resolve each other's word problems with the use of academic vocabulary and flexible application of problem solving strategies. The margin notes in Lesson 7 include guidance to increase the level of complexity within a problem as an extension activity. The lesson asks students to estimate menos de la mitad or mas de la mitad using several examples: 225 mL, 50 mL, 675 mL, and 790 mL. The teacher guidance in Module 6, Lesson 3 provides proficient students with complex, open-ended problems that require applying grade-level math concepts to real-world scenarios. For example, the enrichment and extension activity suggests that the teacher relates human capital and income to professions and salaries of interest for the students. The students extend their learning by creating a table with the name of the profession, the years of education required, and the average salary (TEKS 3.9A). The margin notes in Module 7, Lesson 8, "Notas sobre las diferentes formas de participación," provides teacher guidance 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, "Considere la posibilidad de invitar a los estudiantes que estén preparados para una extensión…," which encourages teachers to have advanced students draw and compare the perimeter of individual figures and their combined shape.

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 through 7, the materials include explicit (direct) prompts and guidance to support the teacher in modeling and explaining the concept(s) learned. For example, in "Desarrollo del concepto" within Module 1, Lesson 1, the teacher selects ten students to come to the front of the classroom to model the lesson by counting the total number of arms. The teacher asks the students, "How many arms does each person have?" Students respond with two arms. Then, the materials guide the teacher to explain that since each person represents a group of two arms, we count our volunteers by twos to find the total number of arms. Then the teacher writes "2 + 2 + 2 + 2 + 2 + 2 + 2 + 2 + 2 + 2 = 20," followed by "ten groups of two equals twenty." In the "Problema de aplicación" section in Module 5, Lesson 11, the materials include explicit prompts and guidance to support the teacher in modeling a division problem by drawing equal parts. For example, the teacher draws four lemons in a bowl and then asks, "Cuantos limones recibirá cada persona?" to demonstrate four lemons will be divided for each of the four people in the group. Then, the teacher models the similar process with eight lemons divided into four people. In the "Desarrollo del Concepto" section within Module 6, Lesson 8, the materials include explicit prompts and guidance to support the teacher in modeling and explaining how to rotate a strip diagram vertically to represent a set of data with units of two, comparing it to a pictograph. For example, the teacher asks, "¿En qué se diferencian los diagramas de tiras verticales de las pictografías?" The teachers draw strip diagrams with units of four and write multiplication number sentences corresponding to their set of data while modeling and explaining the process. In the "Reflexión" section of Module 7, Lesson 11, the materials provide the teacher with multiple explicit questions to guide student discussion and help them compare strategies with a partner on how to identify the perimeter of shapes. For example, students share their solutions with their partners while the teacher guides them with direct prompts (e.g., "Han sumado y multiplicado para encontrar los perímetros? ¿Por qué? ¿Qué estrategia han utilizado para sumar las longitudes de los lados en el Problema 4? Expliquen su elección de estrategia con su compañero").

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 through 7, the materials include teacher guidance and recommendations for effective lesson delivery and facilitation utilizing a variety of instructional approaches. In the "Desarrollo del Concepto" section within Module 1, Lesson 2, the materials include teacher guidance and recommendations to use pictorials and the Lee–Dibuje–Escribe (LDE) process to guide students in solving word problems. This process prompts students to read the problem, draw and label it, write an equation, and write a sentence using words. For example, students use the LDE process to solve a real-world problem: "Camila has three plates. On each plate, there are five cookies. How many cookies does Camila have in total?" The materials guide the teacher to ask students to discuss with a partner the question "How can we draw an array from our multiplication expression, 3 × 5?" and use the LDE process to solve. In the "Desarrollo del concepto" section of Module 5, Lesson 24, the materials include teacher guidance and recommendations to use pictorials for effective lesson delivery and facilitation. For example, the teacher guidance directs the teacher to use fraction strips from the previous day and find the equivalent fraction of one half. Students name the fraction three sixths as the equivalent fraction of one half using the fraction strips. Teachers guide students to work with a partner and find evidence of other fractions that are equivalent by asking, "Hablen con su compañero. ¿Notan alguna relación entre los números de estas fracciones?" In Module 6, Lesson 2, students determine the value of a group of bills and coins. In the "Desarollo del concepto" section, The guidance in Part 1 directs teachers and students to engage in a dialogue while collaborating using plastic coins to practice multiple ways to make $1.00. The guidance directs the teacher to ask questions about the students’ combinations: "How did you decide which combinations work? Which combinations are most helpful, and how can making a dollar be helpful in counting money?" The guidance in Part 2 expands, providing teachers with examples of direct modeling (e.g., how to count a quantity of $14.36) and continuing direct questioning on the different strategies the students used to count the amount.

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 through 7, the materials include teacher guidance and recommendations for using multiple types of practice and structures to support effective implementation. The materials include recommendations for instructional routines with clear headings and descriptions to help the teacher effectively implement recommended structures for whole-group, small-group, and individual instruction throughout each lesson. For example, in Module 1, Lesson 5, during the whole-group instruction, students are invited to participate by answering questions throughout the lesson. Then, students apply conceptual knowledge as they complete the Grupo de problemas independently. The materials direct teachers to engage students in a "Reflexión" section to review their solutions with a partner and compare strategies used to solve problems. In Module 3, Lesson 21, in the Problema de aplicación, the material provides support for multiple types of practice. It includes guidance for teachers and recommended structures to support effective implementation, as outlined in the margin notes. For example, students draw and use a part–part–whole strategy to solve a subtraction problem, preparing them for the lesson, where they will draw models to represent multiplication using two-digit numbers. The margin note recommends teachers guide students to write the number first before drawing the place value disks in the place value table. During the lesson, the materials include guidance for teachers to use place value disks to represent 2 × 24. Then, students draw circles as models to represent the place value disks, using the place value table to solve 3 × 44. In Module 6, Lesson 1, on determining the value of a set of coins and bills, the "Desarrollo del concepto" section provides teachers with guided steps to facilitate and introduce the lesson. For example, the teacher projects a $5 bill, two $ bills, one quarter, three dimes, and five pennies. The teacher guides students to work with a partner to find the value of the money projected. The teacher models how to solve Problem 1 and then assigns Problem 2 to the partners. After modeling Problem 2, the students work independently to complete a group of problems. The students return to the whole group to answer debrief questions and compare their solutions with those of other students, demonstrating alternative approaches to problem solving.

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 describing how 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. These scaffolds are designed for 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 describing the guidance embedded in the materials to support teachers using the materials in state-approved bilingual/English as a second language (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 through 7, the materials include embedded guidance for teachers to support emergent bilingual students in developing academic vocabulary while increasing comprehension by using the Lee–Dibuja–Escribe (LDE) strategy when solving problems. The 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 2, the materials include guidance for teachers to support emergent bilingual students in building background knowledge and making cross-linguistic connections through oral discourse as students share their solutions with a partner. For example, the teacher directs students to turn and talk with their partner during the debrief of the lesson to discuss their solutions and the strategies they used to solve problems. The teacher asks the following questions: "Comenten con un compañero su estrategia para resolver el Problema 6. ¿Qué otras estrategias de conteo podrían utilizar con el reloj para obtener la misma respuesta?" In Module 4, Lesson 8, the material includes embedded guidance for teachers to support emergent bilingual students in developing vocabulary and building background knowledge through conversation by formulating their own questions with a partner. For example, the materials direct the teacher to use cognates such as rectangle/rectángulo, area/área, sum/suma. The students participate in oral and written discourse using the academic vocabulary introduced. The materials include guidance for the teacher to provide opportunities for students to generate their own questions by including teacher directions such as "Ofrézcales más tiempo para que formulen sus ideas y conversen con sus compañeros" and asking questions such as "¿Qué pasos han tenido que seguir para resolver el Problema 2? ¿Cómo han podido encontrar el área del rectángulo más pequeño?"

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 "Cross-Linguistic Connections" section of how the materials support students in learning concepts in Spanish, including linguistic approaches for both students who are native to the Spanish language and those who are learning Spanish, such as in 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 in fluency, application problems, concept development, student debrief, and opportunities for 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 through 7 include practice opportunities over the course of the lesson in each module that requires students to demonstrate depth of understanding aligned to the TEKS. Each module varies in the number of topics, or Temas. Within each topic, the number of lessons varies, providing practice opportunities such as Práctica de fluidez, Problema de aplicación, Desarrollo del concepto, Reflexión, Tarea, and Boleto de salida. For example, in Module 1, Lesson 5, within the Practicar resource, the students count two by twos, then three by threes in order to relate this practice to division for an unknown number. In the Aprender resource for Module 7, Lesson 1, the materials provide a Grupo de problemas for students to practice solving word problems using multiplication and division. Students apply the Lee–Dibuja–Escribe (LDE) process, promoting problem-solving fluency aligned with TEKS 3.4K and 3.5D, which focuses on applying and reasoning multiplication–division relationships and solving for unknowns. In Module 7, Lesson 10, the materials provide practice opportunities and instructional assessments within the lesson for TEKS 3.7B in Topics C–E, focusing on the concept of developing an understanding of perimeter and measurement strategies. Within Topic C, Lesson 10 includes a fluency activity titled "Encontrar el perímetro," which focuses on reinforcement of this concept. In the Triunfar resource for Module 7, the materials include practice opportunities with a "Tarea" section for each lesson and 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 through 7, the materials include questions and tasks that progressively increase in rigor and complexity, leading students to grade-level proficiency. For example, in Module 5, the materials include questions aligned to TEKS 3.3C, which asks students to apply their learning about fractions. In Lesson 7, students use pictorial models to shade parts of a shape and label unit fractions such as one fourth or one third. In Lesson 17, students use open number lines between zero and one to identify and label unit fractions. This progression across lessons leads to grade-level proficiency. In Module 7, Lesson 9, the Grupo de problemas focuses on the concrete task of measuring and labeling the sides of given figures to find the perimeter. By Lesson 13 in Module 7, the Problema de aplicación prompts students to calculate the perimeter of a composite figure by first determining the missing side length, which increases the use of abstract reasoning. In the "Contenido general" sections within Modules 1 through 7, the material includes an explanation of how each topic progresses in rigor according to the targeted TEKS. For example in Module 3, Topic A, the students use repeated addition to find the total in a group of equal numbers. In Module 3, Topic C, the students count on matrix models to comprehend multiplication concepts. In Module 3, Topic D, students represent, write, and solve world problems involving division by skip counting.

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

In Guía del curso, versión del maestro, in the "Secuencia de módulos de Grado 3 alineados con los TEKS" section, the materials include an explicit description of how Modules 1 through 7 connect to patterns, big ideas, and relationships between mathematical concepts. For example, in Module 1, students learn properties of multiplication and division and resolve problems with units of two through five and ten. In Module 4, students make connections with properties of multiplication when solving for area. In the "Contenido General" sections with Modules 1 through 7, the materials provide an overview describing the main 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, in Module 1, Lesson 1, the students find relationships between multiplication and array models. In Lesson 9, students represent the distributive property by making connections to the array models to decompose units when multiplying. In Module 7, Lesson 1, students solve two-step word problems that use multiplication and measurement, connecting Module 4 and 5 concepts of how to multiply and solve problems about length. In Module 7, Lesson 6, students classify quadrilaterals by comparing their sides and angles. This connects to concepts in Lesson 3, reviewing basic shape attributes. These connections help students sort and name shapes using more precise math language.

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 "Progresion de conceptos matemáticos" section within the Guía del curso provides a table displayed as a vertical alignment document from kindergarten through grade 5 to demonstrate the connecting content learned in previous, current, and future grade levels. For example, the concept of two-dimensional figures is introduced in kindergarten, and in grade 2, students identify, compose, and divide figures. In Módulos 1 al 7, versión del maestro, the materials within each topic include a table and a description of how content and language learned in the current course connect to previous grade levels and future grade levels. For example, for Module 4, Topic A, students in grade 2 determined the length of objects using concrete models with standard units of length (TEKS 2.9A). In Grade 3, students will make connections from previous content to determine the area of rectangles (TEKS 3.6C) and prepare them for Grade 4, when they will explore measurement using multiplication and data (4.8C). In Módulos 1 al 7, versión del maestro, the materials include a "Terminología" section across modules to demonstrate connections between language learned in previous grade levels and in the current grade level. The materials include vocabulary words that will be introduced in the module and previously learned terminology. For example, in Module 4, the word área is marked as "términos conocidos" or "known terms." In Module 6, the words crédito and deudor are new terms 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 the "Contenido general" sections within Módulos 1 al 7, versión del maestro, the materials include a list of current grade-level standards and a list of fundamental standards for previous grade levels to demonstrate coherence across lessons for each module. In Módulos 1 al 7, the materials demonstrate coherence at the lesson level by connecting students’ prior knowledge of concepts from the prior grade level(s) to new mathematical knowledge and skills. For example, in Module 2, students connect previous learning of determining the length of an object using concrete models with standard units of measurement (TEKS 2.9A) to connect to the new skills in Lesson 20 of using algorithms when adding measurements with two or three digits (3.4A). In Module 4, Lesson 5, students determine the area of a rectangle utilizing multiplication related to the number of lines by the number of units in each row (TEKS 3.6CD), connecting to previous knowledge of representing and describing situations of multiplication in context (TEKS 2.6A). In Module 6, students connect the previous skill of determining the value of a collection of coins up to a dollar (TEKS 2.15A) to new learning of identifying the costs and benefits of making or not making a spending plan (TEKS 3.9C).

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

In Guía de curso, versión del maestro, the materials include a table within the "Estándares de Grado 3 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 the "Desarrollo de la fluidez en Grado 3" section that provide information on the standards for spaced retrieval opportunities within each module. In Modules 1 through 7, the materials provide spaced retrieval opportunities with previously learned concepts across lessons. For example, in Module 2, in Topic F, students apply the multiplication and division strategies they have used for mixed practice with all the factors included in Module 1 (3.4K). Students represent the relationships between the factors, analyzing the arithmetic patterns that arise to compose and decompose numbers, as they continue exploring the relationship between multiplication and division (3.4J). In Modules 1 through 7, the "Práctica de fluidez" section provides opportunities for students to activate their prior knowledge through various lessons across modules. For example, in Module 4, Lesson 3, students will engage in a 10–15-minute fluency practice targeting basic skills needed on a daily basis.

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

In Modules 1 through 7, the materials provide interleaved practice opportunities with previously learned concepts across lessons. For example, in Module 1, Topic E, students learn to analyze the relationship between multiplication and division. Then, students combine both operations in units of four and make connections between them (TEKS 3.4J). In Module 2, Lesson 3, students solve problems with time intervals. Students measure intervals in minutes and then add and subtract those intervals to solve problems. In Module 4, Topic A, students learn about the concepts of measurements for area. In Topic B, the students implement the concepts learned to analyze and find the area of rectangles, or they decompose shapes to form rectangles. In Module 7, Lesson 5, students find the perimeter of shapes using repeated addition and multiplication, connecting previous skills in earlier modules when students worked on multiplication and area. In Module 7, Lesson 7, students solve word problems using bar graphs and choose operations like addition or multiplication.

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

In Modules 1–7, the materials include questions and tasks that require students to interpret, analyze, and evaluate models and representations for mathematical concepts and situations. For example, the Module 1, Lesson 1 margin note guides teachers to use models of number bonds to explore the relationship between the factors of multiplication by prompting students as they complete tasks. Students interpret a visual and a multiplication expression by analyzing how to use repeated addition to solve the problem. Then, students are asked to evaluate the problem by discussing with a partner if they agree or disagree with the solution. In Module 6, Lesson 11, students interpret and analyze information on a table and think of other ways that the information may be presented, such as in a bar graph or frequency table. Then, students create a line plot diagram based on the information in the table while evaluating the information based on teacher guided questions: "¿Qué cantidad de estudiantes de las familias de 3er grado tiene más puntos? ¿Tiene sentido decir que 2 estudiantes es la cantidad preferida de estudiantes de las familias de los estudiantes de 3er grado? ¿Cuál es el número de estudiantes menos frecuente?" Triunfar, versión del estudiante includes questions and tasks for students to interpret, analyze, and evaluate. For example, Module 7, Lesson 14 asks students to draw as many rectangles as possible with an area of eighteen square centimeters and then shade the rectangles on grid paper and calculate the perimeter of each. This activity requires students to generate multiple valid models for a fixed area and reason through how side lengths affect perimeter. Lesson 15 gives students cut-out square units and asks them to use manipulatives to build as many rectangles as possible for a given area (e.g., six, seven, eight, nine units). Students record the width and length of each rectangle in a table and then create a dot plot to show how many different rectangles they made for each area.

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

In Modules 1–7, the materials include questions and tasks that require students to create models to represent mathematical situations. For example, in Module 1, Lesson 1 within the "Boleto de salida" section, a problem set asks students to make a drawing to show 3 + 3 + 3 = 9 and write a multiplication sentence to represent the mathematical situation. In Lesson 2 within the "Grupo de problemas" section, a problem set asks students to write a multiplication expression and draw a matrix representing the multiplication expression to determine the total for the following: "Emma collects stones. She arranges them in 4 rows of 3." In Module 2, Lesson 7, the "Grupo de problemas" section asks students to draw models representing math situations. For example, the lesson asks students to draw a triangle with one right angle for a problem. Then, students draw a quadrilateral with four right angles measuring two inches for another problem. Finally, students draw, analyze, and interpret a problem situation and explain why the problem is incorrect in another problem. In Aprender, versión del estudiante and Triunfar, versión del estudiante, the materials include questions and tasks for students to create models representing math situations. For example, in Module 5, Lesson 7 within Triunfar, versión del estudiante, students create shapes representing fractional parts to complete a table. In Lesson 14 within Aprender, versión del estudiante, students draw fractions representing two different whole numbers using different colors and labeling their models.

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

In Modules 1–7, the materials include questions and tasks providing opportunities for students to apply conceptual understanding to new problem situations and contexts. For example, Module 1, Lesson 1 within the "Desarrollo del concepto" section includes questions for teachers to guide students to think about a more efficient way to add equal groups. Students use their understanding between repeated addition and counting unit groups to apply conceptual understanding to new multiplication situations. The teacher writes 2 + 2 + 2 + 2 + 2 + 2 = 12 and explains how six twos and six groups of two equals twelve. Then, students talk with a partner explaining how they think 6 × 2 = 12 is related to the other number sentences and create a new number sentence. Module 2, Lesson 7, within the "Desarrollo del concepto" section, the students apply their previous learning of using a number line to create a vertical line with intervals of 100 mL when learning the concept of volume. The students draw a vertical line on the outside of an empty one-liter bottle and label the measurements in 100 mL intervals. The teacher asks questions to guide the students as they work through the tasks: "There is 1,000 mL in 1 liter of water. Measure 100 mL each time. Think about yesterday, how many times will you have to measure and mark to make 1 liter?" Aprender, versión del estudiante includes the Read, Draw, and Write strategy to solve mathematical word problems as students apply conceptual understandings. For example, Module 5, Lesson 12 asks students to apply their conceptual understanding of fractions to solve a word problem by dividing their model in equal parts and explaining what fraction would be remaining. In Lesson 22, the "Boleto de salida" section asks students to divide each drawing into thirds, shade two equal parts, and explain if the parts are equivalent as they apply conceptual understandings to new problem situations.

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

In Modules 1–7, the materials include a "Práctica de fluidez" section at the start of each lesson, designed as tasks to build the student automaticity and fluency necessary to complete grade-level tasks. For example, in Module 1, Lesson 4, the fluency lesson is recommended to last twelve minutes and includes a variety of tasks designed to build automaticity and fluency. Students review adding and subtracting numbers up to two. This activity supports grouping and counting skills, which are fundamental for interpreting multiplication as repeated addition in future lessons. In Module 1, Lesson 3, in the Práctica de fluidez, students count forward and backward up to twenty by skip counting in intervals of twos. Then, the tasks require students to skip count by threes up to twenty to build fluency when using repeated addition to solve multiplication problems. In Module 4, Lesson 5, the "Práctica de fluidez" section provides tasks guided by the teacher for students to multiply by six. The teacher guides students to count by six to solve 7 × 6. Then, students multiply the sequence of 9 × 6, 6 × 6, and 8 × 6. Finally, the students count forward and backward using repeated addition for tasks such as "De cuatro en cuatro hasta el 40," "De siete en siete hasta el 70," and "De ocho en ocho hasta el 90" to build automaticity and fluency to complete grade-level tasks. The Triunfar, versión del estudiante materials for grade 3 include the Lee–Dibuja–Escribe (LDE) strategy, which 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 in a consistent way, supporting 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 through 7, the materials provide opportunities for students to practice applying efficient, flexible, and accurate mathematical procedures within the lesson and throughout the modules. For example, in the Grupo de problemas within Module 1, Lesson 1, students solve problems independently by using pictorials, counting by fives, or using repeated addition. Then, students reflect on their solutions by discussing with a partner the efficient, flexible, and accurate strategy each used to solve the problems. In Module 2, Lesson 1, the "Desarrollo del Concepto" section includes opportunities for students to practice efficient and accurate mathematical procedures. For example, students use a chronometer to practice applying the concept of time to solve a real-life word problem. The teachers guide the students to let the chronometer count the seconds to know how many seconds it takes for Ms. Bower to tie her shoelaces. Then, students take turns with their partner to use the chronometer to time different tasks such as "Contar de cinco en cinco hasta el 60 y dibujar una matriz de 6 por 10." Finally, students complete the Grupo de problemas independently, applying the concept of time by using chronometers to measure different tasks. In the Aprender, versión del estudiante resource, the materials provide students with opportunities to practice using flexible, efficient, and accurate mathematical procedures such as the Leer–Dibujar–Escribir (LDE) strategy when solving problems. The LDE process requires students to read the problem, draw and label it, write a numerical sentence, and write a corresponding word sentence. For example, in Module 5, Lesson 3, in the Grupo de problemas, the students read the word problem, draw a rectangle, and divide it into two, three, and four equal parts. Finally, students explain what they observed in the two given rectangles and how they would divide them into twenty equal parts.

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.

In Modules 1 through 7, the materials provide opportunities for students to evaluate procedures, processes, and solutions for efficiency, flexibility, and accuracy. For example, in the debrief section within Module 2, Lesson 1, students compare their solutions for the problem set with a partner to evaluate procedures and processes. The teacher asks, "¿En qué se diferencian los Problemas 1 y 2? ¿Cómo afectó eso la forma en que resolvieron cada problema? ¿Qué intervalos usaron para etiquetar las rectas numéricas? Comenten con un compañero su estrategia para resolver el Problema 6. ¿Qué otras estrategias de conteo podrían utilizar con el reloj para obtener la misma respuesta?" In the "Problema de aplicación" section within Module 2, Lesson 9, the material provides an opportunity for students to evaluate procedures in terms of efficiency, flexibility, and accuracy. For example, as students work on using the distributive property with arrays to break apart units as a strategy for multiplication, they are asked to reflect on this strategy. The teacher asks the following question: "In problems 1 and 2, why might dividing an array into two parts to multiply, add, and then solve be easier than simply multiplying the total number of groups by their size?" Students reflect on and explain why a particular strategy is more efficient. In "Desarrollo del concepto" within Module 6, Lesson 14, the materials provide opportunities for students to evaluate solutions for efficiency, flexibility, and accuracy throughout the lesson. The teacher uses the previous information on skip counting, understanding multiples and divisors, and reviewing how to read a bar graph, which leads students to evaluate the process of interpreting data using dot plots. The students evaluate their solutions by answering questions such as, "¿Cuántas familias tienen menos de 2 estudiantes? ¿Cuántas familias tienen más de 2 estudiantes? ¿Cuántas tienen menos de 3 estudiantes?"

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

In Modules 1 through 7, the materials contain embedded supports to guide teachers in helping students develop increasingly efficient approaches to learning. The materials provide examples of pictorials or real pictures within lessons to support teachers. For example, in Module 4, Lesson 6, the teacher models how to cut the centimeter graphing paper to have two equal rectangles. Then, the teacher directs students to count the length and width of the rectangles using the centimeter squares to find the area. Then, students learn a more efficient approach by placing two rectangles together to find the area of the new rectangle created. The materials include embedded supports as direct prompts for teachers to guide students toward increasingly efficient approaches. For example, in Module 4, Lesson 8, students use a separation strategy based on the shaded part of the figure displayed. The teachers ask, "¿Podrían haberse invertido las estrategias para estos dos problemas? ¿Qué pasos han tenido que seguir para resolver el Problema 2? ¿Cómo han podido encontrar el área del rectángulo más pequeño?" In Modules 1 through 7, the materials include embedded supports, such as sidenotes, to support teachers in guiding students toward increasingly efficient approaches. For example, in the margin notes within Module 7, Lesson 3, the teacher guides students to work with a partner and explain their reasoning for the strategy they choose when solving multiplication problems with two digits. Students use strip diagrams, decompose numbers, or use an algorithm to find solutions while the teacher guides them toward efficient approaches.

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

In Modules 1 through 7, the materials explicitly state how the conceptual and procedural emphasis of the TEKS are 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 create equal groups, arrays, and number lines to represent repeated addition for multiplication problems (TEKS 3.4H, 3.4J, 3.5D). Then, students develop a conceptual understanding of division as an unknown-factor problem and analyze mathematical relationships to connect multiplication and division (3.1F). Students use strategies such as skip counting and array models to make connections between multiplication and division for procedural understanding. In Module 5, Lesson 11, the materials include the "Desarrollo del concepto" section explicitly stating how the conceptual and procedural emphasis of the TEKS are addressed. For example, the materials guide the teacher to draw four oranges and label each as one fourth. Then, they guide students to develop a conceptual understanding of the similarities between four equal parts and a rectangle with one fourth. The students apply the understanding of equal parts making a whole by drawing and labeling pictorials to solve word problems (TEKS 3.3E) through procedural understanding. In Module 7, Lesson 4, the materials within the "Desarrollo del concepto" section help students develop conceptual understanding by using diagrams to classify and compare quadrilaterals and analyze properties such as angles and parallel sides. This lesson helps students conceptually distinguish between types of quadrilaterals while procedurally practicing how to classify them by given attributes (TEKS 3.6B).

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 through 7, the materials include questions and tasks, including the use of concrete models and manipulatives, pictorial representations (figures/drawings), and abstract representations, as required by the TEKS. In the "Desarrollo del concepto" section within Module 1, Lesson 1, the materials direct the teacher to guide students through questions and tasks using counting chips to solve problems. For example, the students use twelve counting chips to create two equal groups. The teacher asks "¿Cuántas fichas para contar colocarán en cada grupo?" Students use the chips to represent six groups of two, then write the number sentence 2 + 2 + 2 + 2 + 2 + 2 = 12. Finally, students draw a pictorial to represent six groups of two. In the "Problema de aplicación" section within Module 4, Lesson 6, the materials include questions and tasks for the use of pictorial representations and abstract representations, as required by the TEKS. For example, students are tasked with solving a two-step problem by first drawing an area model and labeling it to represent eight by six inches. Then, students draw a strip diagram to show 48 – 42 = 6 and explain how they found a solution. Finally, students write the number sentences "8 × 6 = 48" and "48 – 42 = 6" as a process to solve a two-step word problem using pictorials and abstract representations. In the "Desarrollo del concepto" section in Module 7, Lesson 15, the materials include concrete models, pictorial representations, and abstract representations, as required by the TEKS. For example, students use unit square tiles to build rectangles with specified areas and record combinations of length and width in tables. Then, they create dot plots to visualize the number of rectangle configurations, integrating concrete manipulatives with pictorial data representation.

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 through 7, the materials include support for students in connecting, creating, defining, and explaining concrete representational models of abstract (symbolic/numeric/algorithms) concepts, as required by the TEKS. In the "Problema de aplicación" section in Module 3, Lesson 13, the materials include connecting and explaining concrete and representational models of abstract concepts. For example, students create a strip diagram to represent 8 × 9. Then, students decompose the number eight to (5 + 3) × 9. Students connect the strip diagram to abstract concepts by using the distributive property to multiply (5 × 9) + (3 × 9) and explain the process of decomposing and multiplying to solve two-step word problems. The "Práctica de fluidez" section within Module 4, Lesson 8 includes support for students in connecting, creating, defining, and explaining concrete and representational models of abstract concepts, as required by the TEKS. For example, students use grid paper to represent the area of 6 × 8. Then, the students count by six to shade a different area model for 6 × 9. The students continue counting by six and explaining the patterns observed, writing sentences such as "8 unidades cuadradas + 6 unidades cuadradas = 48 unidades." In Module 5, Lesson 1, the "Desarrollo del concepto" section includes support for students in creating and explaining concrete and representational models of abstract concepts. For example, the materials include guidance for students to fill a cup with water up to one fourth and draw a small line indicating the top of the liquid. Then, students pour the liquid into another cup and draw a small line. The students repeat the process four times to have two cups with marks indicating the level of the water. Students make connections, create, and define the parts labeled as fractions. Finally students explain the concrete models for abstract concepts by writing the fractions for each cup as one fourth and one half.

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

In Modules 1–7, the materials provide opportunities for students to develop academic mathematical language using measuring tools while communicating with peers. In Module 2, Lesson 2, the "Problema de aplicación" section guides teachers to use a chronometer as a tool for measuring time in segundos. For example, students estimate how many seconds it takes to walk from the carpet area to their seats. Then, the students use a chronometer to time themselves walking up to their seats. The teacher encourages students to use the following sentence stem "Tardamos ___ segundos" and asks students to share the comparison between their estimations and the actual time in seconds with a partner. In Module 3, Lesson 4, the "Desarrollo del concepto" section provides opportunities for students to develop academic mathematical language using visuals and manipulatives. The margin notes "Notas sobre las diferentes formas de representación" provide guidance for teachers to encourage students to use sentence stems in order to develop academic mathematical language. For example, students use strip diagrams to identify the underlined number for 77,777 by describing, "podemos dibujar un diagrama de tiras que tenga 10 partes de 700 cada una." Students engage in partner talk using the sentence frame "1_decena___ es __10___veces mas que 1 __unidad__." In the Triunfar, versión del estudiante resource, the materials include opportunities for students to develop academic mathematical language using visuals. In Module 7, Lesson 2, the students use the Lee–Dibuja–Escribe strategy to solve two-step word problems. For example, students read the problem and use strip diagrams, comparison bars, and bubble maps to represent and organize the known and unknown numbers. Then, students label their diagrams, write an equation, and write an explanation using academic mathematical language such as diferencia, altura total, and mas alta que for their solution to the word problem.

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 through 7, the materials include embedded teacher guidance 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 6, the embedded materials guide teachers to provide opportunities for students to explore the relationships between vocabulary terms un litro and mililitros. For example, the materials guide the teacher to use ten empty cups and label each cup as 100 millimeters. The teacher explains that they will decompose one liter into equal parts by pouring 100 millimeters into the ten empty cups labeled A–J. The teacher asks scaffolding questions: "¿Cuántos mililitros de agua hay en 1 litro?" Students communicate with the educator by responding "1,000 mililitros." Then, the materials direct teachers to guide students to communicate with their peers to explain the expression 1,000 mL ÷ 10 = 100 mL using academic mathematical vocabulary. In the "Desarrollo del concepto" section within Module 3, Lesson 5, the materials include embedded teacher guidance to scaffold and support students' development and use of academic mathematical vocabulary in context. Students create array models to represent multiplication and explain their thinking to peers in response to questions: "¿Cómo se relacionan las oraciones de multiplicación? ¿Qué nos dice esta propiedad sobre el producto y sus factores? ¿Cuántas filas tiene esta matriz? ¿Cuántas columnas?" The embedded guidance directs teachers to prompt students to respond to the previous questions using academic mathematical vocabulary like matriz, fila, columna, producto, and factores. In the "Reflexión" section within Module 7, Lesson 4, the materials include embedded supports as prompts for teachers to scaffold, support, and extend students’ use of academic mathematical vocabulary in context. The materials direct the teachers to ask questions such as "¿Cómo nos ayuda la agrupación de cuadriláteros por atributos…?" when communicating with peers. For example, students review the solutions to their independent work and compare the results with a partner by using academic terms to communicate (e.g., atributos, polígonos, paralelos, cuadrilátero, trapecio, paralelogramo, rombo, ángulo recto, and diagonal).

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 Module 2, Lesson 4, the "Desarrollo del concepto" section includes embedded teacher guidance to support the application of appropriate mathematical language to mathematical conversations that provide opportunities for students to hear math language with peers and develop their math language toolkit over time. For example, students determine the weights of objects by using the appropriate units and tools. Then, students communicate with peers using appropriate mathematical comparative language such as, "menos que, más que o casi lo mismo que." In Module 4, Lesson 7, the "Desarrollo del concepto" section includes embedded teacher guidance to support the application of appropriate mathematical language, including vocabulary, syntax, and discourse, with guidance to provide opportunities for discourse. The materials provide guidance for the teachers to direct students to explain their reasoning to their peers by using sentence stems such as, "Área de A + Área de B: __________ unidades cuadradas +__________ unidades cuadradas = __________ unidades cuadradas" to answer questions such as,"¿Cómo podríamos utilizar una estrategia como esa para encontrar el área de la figura sombreada? Conversen con su compañero: ¿Cómo podemos encontrar el área sombreada utilizando el cuadrado sin sombrear?" Across the modules, the materials include embedded teacher guidance to support the application of appropriate mathematical language and help students develop their math language toolkit over time, as well as guiding teachers to support student responses using exemplary responses to questions and tasks. For example, the teacher displays a number line with fractions five eighths, six eighths, and seven eighths and then asks, "Quien corrio mas, Teresa o Debora?" The students use comparative appropriate mathematical language to complete the sentence stem, "______ es mayor que _____" or "____ es menor que ___." Exemplars included in the materials support teachers in guiding students' responses.

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

In Modules 1 through 7, the materials integrate the TEKS process standards appropriately. In Module 1, Lesson 1, the "Desarrollo del concepto" section integrates TEKS process standard 3.1F. The lesson directs students to analyze mathematical relationships to connect and communicate mathematical ideas. For example, the materials direct the teacher to provide opportunities for students to explain their understanding of the relationship between repeated addition, equal groups, and multiplication. Students explain their reasoning to peers during the debrief part of the lesson. In Module 3, Lesson 5, the "Desarrollo del concepto" section integrates TEKS process standards 3.1D and 3.1G. The lesson asks students to use representations to organize and communicate mathematical ideas. For example, the students use visual models or arrays to represent multiplication (TEKS 3.1D) and then explain and justify the meaning of each component (TEKS 3.1G) using precise mathematical language such as fila, columna, and producto.

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

In Modules 1–7, 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. The "Estandares de procesos matemáticos de TEKS" section within Matemáticas K–5 guía de programa e implementación includes 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, "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 through 7, the materials include a description for each TEKS process standard incorporated and connected throughout each module. In the "Contenido general" section within Module 3, the materials include a description of how students evaluate procedures, processes, and solutions for efficiency throughout the module. For example, "Durante el Módulo 3, los estudiantes se involucran con los estándares de procesos matemáticos de TEKS analizando las relaciones multiplicativas entre cantidades. Usan el lenguaje de la comparación para comunicar la relación multiplicativa entre cantidades y unidades de valor de posición" (TEKS 3.1E–F). In the "Contenido general" section in Module 6, the materials include a description of how TEKS process standards are incorporated and connected throughout the module. For example, in Module 6, students make connections with previous learning to determine the value of a collection of bills and coins (TEKS 3.1F). Students use data standards and determine appropriate mathematical tools to create and analyze data tables (TEKS 3.1C). In the last topic for the module, students create and use tables to organize, record, and communicate relationships between real-world and numerical pairs (TEKS 3.1E). In "Contenido general" in Module 7, the material provides clear descriptions and an overview of the integration of TEKS process standards throughout each module. For example, in Module 8, the materials describe how students apply a problem-solving model (TEKS 3.1B) to analyze information, formulate strategies, and evaluate the reasonableness of their solutions. Later in the module, students use precise mathematical language to explain and justify how they classify and organize geometric figures (TEKS 3.1G). These descriptions reflect the progressive development of reasoning, justification, and communication across lessons.

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

In Modules 1–7, the Guía del curso del grado resource includes the "Estándares de procesos matemáticos TEKS de Grado 3 por lección por módulo" section, which provides a table as an overview for each TEKS process standard (3.1A–3.1G) addressed by the specific lessons in each module. For example, in one module, the table indicates standard 3.1B is taught in Lessons 2 and 18, while standard 3.1G is incorporated in Lessons 4 and 7–10. In the "Contenido general" section within each Module 1–8, the materials provide an overview of how the TEKS process standards are integrated into each lesson and are embedded across lessons in an organized, thematic structure. The materials include an overview with specific content 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 lección" 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 10, the materials provide opportunities for students to think mathematically, persevere through solving problems, and make sense of mathematics by using place value disks for addition. Students use the place value disks to represent six tens and seven tens. Students think mathematically by regrouping the sum of thirteen to make ten tens and create 1,000. Then, students persevere through solving problems when directed to combine two thousands and eleven tens. Students regroup to make 3,100 using place value disks, making sense of mathematics concepts. In the "Problema de aplicación" section in Module 4, Lesson 8, the materials provide opportunities for students to persevere through solving problems and to make sense of mathematics to solve for areas of a square with shaded and unshaded portions. The students persevere through solving problems when directed to divide a shaded figure into two rectangles and identify the area for each. The students draw one rectangle with an area of three by four to equal twelve square centimeters. Then, they draw another rectangle with an area of two by two, equal to four square centimeters, for a total area of sixteen square centimeters. The students make sense of the mathematics by subtracting the area of the unshaded portion with the shaded portion of the figure (20 – 4 = 16) to verify their accurate measurement. In the "Desarrollo del concepto" section within Module 7, Lesson 6, the materials include opportunities for students to think mathematically and persevere through solving problems by playing a game of identifying shapes and their attributes. Students work with a partner and are directed to group solid figures into three categories that "tengan sentido para ti," encouraging them to think mathematically about the attributes of each shape. Then, students describe how they organized their groups, explaining their reasoning (for example, "se puede rodar" or "hecho con triángulos") to make sense of mathematics.

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 the "Desarrollo del concepto" section within Module 3, Lesson 5, the materials support students in understanding, explaining, and justifying that there can be multiple ways to represent and solve problems and complete tasks. Students are supported in understanding a single concept, multiplication, and that it can be represented through multiple models: number lines, arrays, area models, and number bonds. Students practice and complete problems using all these representations. "¿Cuáles son algunas de las formas en que representamos la multiplicación aparte de mostrar saltos iguales en una recta numérica? Hablen con su compañero y hagan una lista." Students are regularly asked to explain their reasoning about how different model areas, number lines, and arrays show the same relationships. Teachers prompt students to talk with a partner, discuss similarities and differences between strategies, and express their understanding orally and visually. In Module 4, Lesson 1, the materials support students in understanding, explaining, and justifying that there can be multiple ways to represent and solve problems and complete tasks. Students are supported in understanding when they are asked to construct models using tiles of different units and configurations. Students also explore areas with manipulatives, draw diagrams, and apply counting strategies. "Utilicen los mosaicos para formar una matriz de 3 por 5. Indique a los estudiantes que cambien los mosaicos de pulgadas cuadradas por mosaicos de centímetros cuadrados." Students are given structured opportunities to verbalize their thinking, both with partners and in whole-group discussion. Students also use their own words and reasoning to explain why their models work: "Dibujen el rectángulo en su pizarra blanca individual. Después, retiren los mosaicos y etiqueten las longitudes de los lados. Ahora, escriban el área dentro del rectángulo." Then, students are directed to analyze the impact of gaps or overlaps and how they affect the area. Students will compare rectangle A and B and must defend their understanding using logic and mathematical language. In the "Desarrollo del concepto" section within Module 7, Lesson 2, the materials provide students opportunities to understand, explain, and justify that there are multiple ways to solve problems. For example, in the "Parte 1" section, students work with a partner to solve the same problem using two different models: one with arrays (matrices) and one with strip diagrams (diagramas de tiras). They compare their models by discussing how the rows and numbers are represented in each and explain why both give the same result. The teacher asks questions like "¿Cómo representaron el hecho de dar a 3 compañeros el mismo número de flores?" and "¿Cómo los ayudó su modelo a saber qué operaciones utilizar?" This helps students understand, explain, and justify that there are multiple valid ways to represent and solve the same mathematical problem.

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 through 7, the materials are designed to require students to make sense of mathematics through multiple opportunities for students to do, write about, and discuss with peers and teachers. In the "Reflexión" section within Module 2, Lesson 11, the students are tasked to work with a peer to compare the solutions for their Grupo de problemas 1 and 2. Students write 87,063 in the place value template. Then, they write the number in standard, written, and expanded form. Students compare their solutions and discuss how the zero was represented in their solutions and the difference in value. Students discuss how the numbers in written form may be confusing with other numbers in written form. In the "Desarrollo del concepto" section within Module 3, Lesson 1, the materials are designed to require students to make sense of mathematics through multiple opportunities to write about, and discuss math with peers and teachers. During the lesson, the students use differently colored paper strips as manipulatives to represent lengths and solve four different word problems using the paper strips. For example, students use the blue paper strip measuring one inch to determine the length of the yellow strip, which measures three times the blue strip. Students determine that three blue paper strips is the length of the yellow strip. Then, the teacher asks students to write an equation to represent the length of the yellow strip compared to the blue strip. Students write 1 × 3 = 3 as the equation to represent their solution. In the "Desarrollo del concepto" section in Module 5, Lesson 12, the materials are designed to require students to make sense of mathematics through multiple opportunities to write about and discuss math with peers. The teachers direct students to use fractions strips (halves, thirds, fourths, sixths, and eighths) and whiteboards. The students organize their fraction strips from greatest to least by halves, thirds, fourths, sixths, and eighths. The teachers direct students to discuss their observations with partners. The students discuss how the eighths fraction pieces are the smallest even though the digit is the greatest to make sense of mathematics. In Module 7, Lesson 7, the materials provide opportunities for students to write about and discuss math with peers. During the concept development of the lesson, the students explore three-dimensional solids by identifying, naming, and comparing their attributes, such as faces, edges, and vertices. The teachers direct students to work with a peer and share observations. Students share, "Las latas de sopa son cilindros" and explain how shapes are similar or different: "Es el único sólido que tenemos que tiene algunos triángulos por caras." Students make sense of mathematical concepts by discussing why certain solids, like cylinders, do not have edges.

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 1, Lesson 2, the materials include support for teachers in guiding students to reflect on their problem-solving approaches, including explanations, arguments, and justifications. The teacher directs students to discuss with a partner why two images of two groups of four are the same. Students discuss how the two groups have the same size of gray circles with the same shape. Then, students write the repeated sum and a number sentence to represent the pictorial. Students write 4 + 4 = 8 and 2 × 4 = 8 to justify their discussion with their peers. In Module 4, Lesson 2, in the "Reflexión" section, the material provides support to the teacher to guide students to share and reflect on their problem-solving approaches. Teachers are directed to guide students in sharing different solution paths and comparing how each student approached the tasks for the Grupo de problemas. For example, the materials provide teachers with directives such as, "Los estudiantes pueden tener soluciones diferentes para el Problema 3. Invítelos a compartir y comparar sus trabajos." Students are guided to explain their strategies using multiple representations like words, numbers, and images and justify with a peer the strategies used with questions such as, "¿Qué estrategia utilizaron para encontrar la longitud desconocida del lado?" and "Utiliza palabras, imágenes y números para apoyar tu respuesta." Students share and reflect on their problem-solving approaches. In the "Desarrollo del concepto" section within Module 3, Lesson 4, the material provides support for the teacher to guide students to share and reflect on their problem-solving approaches using explanations, arguments, and justifications by exploring the relationships between underlined digits. For example, students demonstrate the relationship of the underlined digits for the number 54,294. The materials direct the teachers to ask, "¿Cuál es el valor del primer 4?" Students share the number of 4,000 because the number is in the thousands. The teacher directs students to reflect on the relationship between two digits. The students justify their problem-solving approach by describing that 4,000 is 1,000 times more than four because 4 × 1,000 = 4,000 and the thousands is three places to the left of the ones place, which is 10 × 10 × 10 = 1,000.

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

In Modules 1–7, the 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 3, Lesson 6, the materials include prompts to support teachers in providing explanatory feedback based on student responses. For example, students create an array for 1 × 3 and a different one for 3 × 3. The teachers prompt students to share if another group had a different solution using questions such as, "¿Algún otro grupo encontró una respuesta diferente? ¿Qué notan en los dos productos? ¿Qué par de tablas les parece más sencillo?" Based on student responses, the teachers guide students by directing them to work with a partner to find different ways to divide 6 × 8 in two arrays using the same size of rectangle. In the "Reflexión" section within Module 3, Lesson 6, the materials include prompts and guidance to support teachers in providing explanatory feedback based on student responses. The materials direct teachers to guide students to check their work by comparing solutions with a partner and resolving misconceptions or concept errors. Students discuss the strategy they used to resolve the group of problems to find the area of rectangles with a partner. The materials include prompts to support teachers in providing explanatory feedback based on student responses: "¿Alguien utilizó la estrategia de separar y distribuir para resolver el problema? Expliquen lo que separaron. ¿Por qué tomaron esa decisión?" In Modules 1–7, the "Contenido general" section within the "Solución colaborativa de problemas erroneos" section for each module includes guidance to support teachers in providing explanatory feedback based on student responses and anticipated misconceptions. The materials 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;" and "(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.