Aprendizaje Bluebonnet Matemáticas K-5 Grado K

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

The kindergarten mathematics materials include a structured scope and sequence that outlines the TEKS and key concepts taught throughout the instructional year. Multiple documents support this, including "Vistazo del año de kindergarten," "Alcance y secuencia de kindergarten," and Guía del curso: Matemáticas K–5 grado K. These resources provide a suggested sequence of modules aligned to the TEKS and are organized by instructional topics, concepts, and standards. Each module lists the focus TEKS, student expectations, and mathematical processing skills, along with the number of instructional days and assessment timelines. For example, Module 1 focuses on "números hasta el 10," with specific TEKS and concepts detailed, such as counting, classifying, and understanding the concept of zero. Standards are consistently presented in charts by module and lesson, ensuring clear alignment and progression of content across the year. The materials offer a comprehensive and coherent instructional plan that supports both vertical alignment and instructional pacing.

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 kindergarten mathematics materials include a defined pacing guide that supports effective implementation across various instructional calendars, including standard and extended-year schedules. The pacing is broken down by module, with suggested instructional and evaluation days provided (e.g., Module 1: 41 days). Materials are organized into trimesters and offer teacher flexibility through tools such as the "Progresión de conceptos matemáticos," which outlines pacing within a 165-day calendar and highlights the progression of concepts across grade levels. To accommodate extended calendars, the materials include the Matematicas grado K días adicionales del año escolar (ADSY) resource, which offers up to 30 additional instructional days. This includes a pretest, a posttest, and three flexible instructional days to tailor learning to classroom needs. The ADSY guide provides an option for schools operating on extended-year models, with recommendations and planning support for integrating these days effectively. The structured yet adaptable pacing tools ensure the materials can be implemented with fidelity across diverse instructional settings.

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 kindergarten mathematics materials include a rationale for the order of units, grounded in both cognitive development and the logical progression of mathematical understanding. The curriculum is intentionally sequenced to build foundational skills before introducing more complex concepts, following a learning trajectory that supports student readiness and long-term retention. For example, early modules focus on number fluency and manipulation up to 10, which lays the groundwork for addition and subtraction introduced in Module 4. Similarly, the final lessons of earlier modules prepare students for the next module by progressively expanding their understanding, for instance, moving from numbers up to five to numbers up to 10, which is essential for grasping place value concepts in later modules. The Guía del curso outlines the instructional philosophy, emphasizing the development of number sense, operations with whole numbers, and spatial reasoning. "Module Overviews" further support this with summaries of learning progression, common misconceptions, key terminology, and connections to future learning both within the grade and across grade levels. Additionally, the "Estructura del módulo" section explains how individual topics within each module contribute to a cohesive and comprehensive mathematical journey. Overall, the materials organize content to "tell the story of math" throughout the year, making intentional and developmentally appropriate connections between concepts that build on one another to ensure a coherent and connected learning experience.

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

The kindergarten mathematics materials provide structured and comprehensive protocols with corresponding guidance to support both unit and lesson internalization. They equip teachers with tools and resources that promote a deep understanding of the instructional content and flow of each unit. The "Contenido general del módulo" section within the Versión del maestro outlines background knowledge, TEKS alignment, key learning goals, vocabulary, common misconceptions, differentiation strategies, and necessary materials. These components help teachers internalize the purpose and structure of each module before instruction begins. In addition, the materials include specific internalization protocols for both units and lessons through dedicated resources such as the "Protocolo de internalización de módulos para el líder de instrucción" and the "Protocolo de internalización de lecciones para el líder de instrucción." Each protocol breaks down the internalization process into four steps, with time-related guidance and clear explanations for each step’s purpose, ensuring that instructional leaders and teachers can approach preparation in a consistent and intentional way.

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

The kindergarten mathematics materials offer comprehensive support for instructional leaders to guide effective implementation. Key tools include the "Herramienta de observación," which helps leaders conduct focused classroom observations and deliver constructive feedback aligned with the intended instructional practices. Leaders are also equipped to collaborate with teachers in analyzing student learning through the Guía del protocolo de análisis del trabajo del estudiante para el líder de instrucción, which provides structured guidance for reviewing student work and tracking progress. The K–5 Math Program and Implementation Guide contains detailed "Module and Lesson Internalization Protocols," each organized into four clear steps with suggested timing and purpose. These protocols support leaders in facilitating efficient planning sessions and ensuring teachers internalize lesson goals, pacing, instructional activities, and materials effectively. Additional guidance is found in the "Recursos para líderes" section of the Guía del programa e implementación, which outlines how leaders can coach teachers using program tools. The "Classroom Culture and Learning Pyramid" further supports this by emphasizing instructional components that promote productive struggle and equitable learning opportunities. Lesson summaries, debrief structures, and margin notes are highlighted as tools to help teachers manage student misconceptions and reduce math-related anxiety.

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

The kindergarten materials provide comprehensive unit overviews that include essential background content and academic vocabulary needed for effective instruction. Each module in the Versión del maestro begins with a "Contenido general" section, which includes foundational content knowledge, common student misconceptions, and instructional strategies. For example, Module 1 explains early numeracy development and offers guidance on teaching numbers one to ten effectively. The materials clearly outline conceptual progression. For instance, the materials scaffold from counting sticks in groups of 10 to composing and decomposing numbers, helping teachers understand the developmental flow of mathematical concepts. The materials explicitly identify academic vocabulary and tie it to lesson objectives, with examples and visuals to support instruction. Vocabulary terms are often presented in bold and paired with visual representations, enhancing teacher understanding and making instruction accessible for all students, including emergent bilinguals. The materials clearly organize TEKS-aligned objectives and terminology by module and lesson and include sample student responses, illustrated definitions, and suggested examples for how to introduce and reinforce these terms during instruction. These overviews help teachers feel well prepared to teach by giving them a clear understanding of the key vocabulary, how the content builds over time, and helpful tips for teaching each unit.

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

The kindergarten materials include bilingual family supports in both Spanish and English for each unit, ensuring equitable access to learning strategies for all families. These supports are specifically designed to enhance home-to-school connections and reinforce students’ progress. The materials offer unit-level newsletters and guides in both languages, such as the "Guía para la familia" and "Tips for Families." These resources highlight key concepts, unit objectives, and vocabulary in student-friendly terms, providing families with a clear understanding of what their child is learning. Suggestions for home support include concrete activities and games aligned to unit concepts. For instance, in one example, families are encouraged to motivate their child to count objects up to 10 or to practice counting forward and backward using a game like "Sunrise, Sunset Counting." The Matemáticas K–5 guía de programa e implementación and the "Family Guide" provide sample problems, illustrated terminology, and simple strategies in both English and Spanish to reinforce understanding and support practice outside of school. These materials are not only translated but also mirrored in content and structure, ensuring that all families, regardless of language preference, receive equitable and aligned support for helping their students at home.

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 kindergarten materials offer thorough and well-structured lesson plans that align with the TEKS. Each lesson includes the necessary components to support content and language development. Lessons are structured consistently across modules, featuring sections such as "Práctica de fluidez," "Problema de aplicación," "Desarrollo del concepto," and "Reflexión." The materials include all required materials for teachers and students, such as tarjetas grandes and pizarra blanca individual, clearly listed in each lesson. The materials clearly state daily objectives and align them to specific TEKS. For example, Lesson 1 includes the objective "Modelar la composición y descomposición de números hasta 5 utilizando acciones, objetos y dibujos" and aligns with TEKS K.2I and K.3A. Similarly, in Module 1, Lesson 4, the objective "Comparar la longitud de barras de cubos conectables con la de una barra de 5" aligns with TEKS K.7B. Instructional questions guide student discourse and support conceptual understanding, especially during debrief. For example, in Module 2, Lesson 1, teachers are given prompts like, "¿Cómo se relaciona el Problema de aplicación con la lección de hoy?" The concept development phase features tasks and activities embedded throughout. For instance, Module 3, Lesson 4 includes comparing the length of objects using unifix cubes and includes checks for understanding. The end of each lesson consistently offers instructional assessments such as "exit tickets" to evaluate student understanding and progress.

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 kindergarten materials provide detailed and clear lesson overviews that list both teacher and student materials. Materials are outlined in charts by module and lesson, such as in Module 3, where materials are organized in a table format in the Versión del maestro and tied to each lesson’s topic and objectives. Materials include comprehensive materials lists by lesson, specifying both teacher and student needs. For example, Module 4, Lesson 3 specifies that teachers need one moneda de un centavo and one moneda de cinco centavos, while students need five cubos conectables, a vínculo numérico (P), and a pizarra blanca individual. Lessons also specify whether items are individual or shared, such as tarjetas grandes de marcos de 5 and hula hoops in Lesson 1. The materials break lesson components down by time, consistently totaling 50 minutes. For instance, Module 2, Lesson 1 includes the following breakdown: "Práctica de fluidez"—17 minutes; "Desarrollo del concepto"—25 minutes; and "Reflexión"—8 minutes.

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

The kindergarten materials provide consistent guidance for extended practice through homework, enrichment tasks, and scaffolded support aligned to daily instruction. Triunfar, Versión del estudiante includes an "Ayuda para la tarea" section that supports students with clear, accessible explanations. For example, in Module 5, the homework includes speech bubbles, drawings, and plain language to reinforce the day's learning independently at home. Enrichment is embedded in the "Grupo de problemas" section, where students apply skills using the "Lee–Dibuja–Escribe" ("Read–Draw–Write") strategy, fostering independent problem solving and deeper thinking. A "Reflexión" section that encourages metacognition follows these tasks. The materials also recognize that homework may not be standard for all kindergarten classrooms. For example, Module 1, Lesson 1 suggests that fluency exercises can serve as optional homework or alternative extended practice. Homework tasks directly align with lesson objectives. For instance, in Module 1, Lesson 2, students complete a comparison activity with the sentence frame that reinforces the skill of comparing similar objects: "Estos son iguales, pero este ___ y este otro ___." The Matemáticas K–5 guía de navegación de componentes confirms that Triunfar problems are designed to align with each lesson and may be used as homework or for additional practice. The materials offer a range of developmentally appropriate and linguistically accessible tools to reinforce student learning beyond the classroom and to accommodate varied school policies and home support environments.

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

The materials include a range of diagnostic, formative, and summative assessments at both the unit and lesson level, offering varied task types and question formats aligned to kindergarten TEKS. At the unit level, each module begins with an "Evaluación inicial" and ends with an "Evaluación final" found in the teacher guides (e.g., Module 4). For example, in Module 4, the initial assessments prompt students to identify number pairs using visual models, while final assessments include word problems, number bonds, and numeric expressions that assess procedural fluency and conceptual understanding. Within lessons, the materials provide embedded formative assessment sections such as "Problema de aplicación" and "Grupo de problemas" in Lessons 1–5 of both the Aprender and Triunfar student materials. These tasks require students to respond using multiple modes—drawing, hands-on tools, writing number sentences, or verbal explanations. The daily "Boletos de salida" and fluency practice also function as quick, informal checks on understanding, as outlined in the Matemáticas K–5 guía del programa e implementación under the "Enfoque de las evaluaciones" section. The materials also include formative assessments in the form of observational rubrics and TEKS-aligned skills checklists. For example, in Module 1, the checklist connects each topic with specific TEKS. For example, Topic B connects with TEKS K.2A, K.2C, K.2D, and K.8A and includes detailed skills like classifying objects into categories or counting to find totals. These tools allow teachers to document student performance and adjust instruction accordingly. Mid-module assessments serve both formative and diagnostic purposes. In Module 4, Topics E–H, the "Evaluación de la mitad del módulo" includes a rubric and reporting sheets that prompt teachers to record what students say and do during assessment tasks. This provides insight into student reasoning and understanding. Similarly, the Grado K evaluaciones book and the Guía de navegación de componentes: Evaluaciones describe mid-module assessments and application problems as tools that can be used diagnostically, since the same TEKS are reassessed in the final evaluation.

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

The materials define various types of instructional assessments and clearly describe their intended purposes across program components. In the Matemáticas K–5 guía del programa e implementación, the "Enfoque de las evaluaciones" section explains that application problems, exit tickets, and observational assessments serve as formative tools to monitor student understanding and guide instruction. Mid-module assessments are presented as both formative and diagnostic, while end-of-module assessments are defined as summative and used to evaluate overall mastery. The "Guía de navegación de componentes" further clarifies that fluency practice and early application problems can serve diagnostic purposes by identifying learning gaps and readiness. Formative tools, such as the “Reflexión” activity section, help students consolidate learning and allow teachers to make instructional adjustments. In the teacher guides, rubrics describe mid- and end-of-module evaluations as intentionally designed to measure progress toward the TEKS. Mid-module assessments support ongoing instruction, whereas final assessments provide a comprehensive check of student understanding at the end of each module. The Libro de evaluaciones outlines the use of TEKS-aligned checklists and reporting tools, emphasizing that assessments are used both to measure learning and to inform next steps in instruction. Across materials, assessments are positioned as essential to a continuous instructional cycle that supports responsive teaching and student growth.

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

The materials include clear, structured guidance to support teachers in consistently and accurately administering instructional assessments. The materials provide teachers with detailed protocols to prepare for assessments, including directions for reviewing lesson plans, completing model responses, and identifying mastery expectations before evaluating student work. For example, teachers are instructed to compare responses with the model provided or to create their own example if none is available, ensuring consistent evaluation across classrooms (Guía del maestro). Daily formative assessments such as exit tickets and observational tools include administration notes and are embedded into instruction with guidance on how to collect and use data for instructional decision-making. The Guía del programa e implementación describes how teachers should regularly check for understanding and adjust instruction based on student responses, promoting real-time instructional responsiveness. Assessment rubrics, found in each module by topic, include behavior-based performance descriptors across four proficiency levels (i.e., Non-proficient to Proficient). These rubrics describe expected student reasoning and provide explicit examples of performance, helping teachers identify misconceptions and determine appropriate next steps for support. For instance, in Topic A, a proficient response includes correctly identifying two objects and explaining differences using accurate mathematical language. The Evaluaciones del grado K guide offers specific scoring guidance, including rubrics and instructions to consider local policies when interpreting results. It reinforces that progress should be evaluated as a continuum, moving from developing to solid mathematical reasoning. Additionally, teachers are directed to use pacing tools, such as the "Guía de ritmo," and observation checklists to ensure assessments are implemented consistently and aligned with the intended learning goals. These lists specify the skills and concepts to observe, supporting systematic and equitable evaluation practices across all students.

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

The materials clearly align diagnostic, formative, and summative assessments with the kindergarten TEKS and the objectives of each lesson and module. Each lesson lists its associated TEKS in the Módulo: Versión del maestro under the "Contenido general de los temas del módulo y objetivos de la lección" section. Assessment alignment is also documented in tools like the "Estándares de TEKS de Grado K por lección de cada módulo" chart and the "Un progreso hacia el dominio" table, which appear in both mid- and end-of-module assessments and specify the TEKS being evaluated. For example, Module 3, Topic A (Lessons 1–3) assesses TEKS K.7A and K.7B, as shown in the "Lista de verificación del estudiante." Rubrics provided for each Topic list the specific TEKS assessed (e.g., the Module 1 mid-module rubric covers TEKS K.2B, K.2C, K.2D, K.2I, and K.8A) and offer guidance on analyzing student progress. Though the term diagnostic may not always appear, assessments such as mid-module evaluations and application problems function diagnostically by informing instruction based on student understanding of targeted TEKS.

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

The materials include TEKS-aligned assessment items that range in complexity, from simple procedural tasks to more complex, open-ended questions. For example, in Módulo 6, "Evaluación final del módulo," students complete tasks such as constructing a square with sticks (procedural) and then describing it using academic language like lados and esquinas (conceptual). Assessments are intentionally sequenced to grow in complexity across lessons and modules. In Module 5, the Lesson 1 "Boleto de salida" section asks students to count groups of ten, while Lesson 27 tasks students with applying understanding in more abstract ways, such as distinguishing between necesidades and deseos. The "Evaluación de la mitad del módulo" for Module 3 includes performance-based and comparative tasks, such as estimating capacity using different containers and explaining reasoning using prompts like más que. Rubrics, checklists, and one-on-one observational assessments further support varied assessment methods and capture student thinking across multiple levels of understanding.

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

The kindergarten materials provide clear, structured guidance for interpreting student performance through observational tools. The observational tools include whole-class and individual checklists aligned to key skills across lessons and topics, allowing teachers to track student progress and identify patterns in understanding. The kindergarten materials also provide clear, structured guidance for interpreting student performance through module-based assessments. Module assessments come with rubrics that define three levels of mastery—2 = dominio, 1 = en proceso, 0 = no evidente—and link student responses to common misconceptions. These rubrics help teachers determine whether a student is meeting expectations and inform next steps in instruction. The Guía del curso supports teachers in using the assessments as formative and summative assessments. This resource includes debrief prompts noted as pretest and posttest prompts, and it offers explicit guidance for addressing misconceptions through a three-step process: stimulate student thinking, acknowledge correct reasoning, and bridge toward improved understanding. The Guía del programa e implementación emphasizes that assessment data serves as evidence of learning and guides instructional adjustments and programmatic decisions. Additionally, scoring rubrics present student progress from left to right and are aligned to specific standards, often including annotated examples of student work to help teachers interpret varying levels of mastery. The Evaluaciones del grado K section titled "Evaluando los resultados de los estudiantes" offers further clarity on how to score responses and adjust instruction while also encouraging alignment with local district guidelines for student support.

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

The materials offer structured guidance to help teachers respond to student performance trends using embedded tools and routines. For example, each module includes a "Solución colaborativa de problemas de conceptos erróneos" table, which organizes common misconceptions by TEKS and offers suggested questions and instructional strategies for correcting misunderstandings. These tables serve as an immediate-response tool following assessments, helping teachers plan targeted instruction based on specific student needs. Scoring rubrics, such as the "Progreso hacia el dominio" rubric included with mid- and end-of-module assessments, help teachers analyze trends across class data. The rubrics display scores from left to right and help teachers quickly identify where students fall on the mastery continuum as well as analyze class-wide trends. This structured format assists teachers in determining which students need additional support and in what areas. In the Guía del programa e implementación, teachers are further supported through the "Guía del protocolo de análisis del trabajo del estudiante-5," a collaborative protocol for analyzing student work. This tool supports teachers in identifying student reasoning, monitoring progress toward proficiency, and pinpointing conceptual gaps. It also provides a framework for administrators and coaches to assist teachers in planning next steps for instruction. In addition, the materials encourage student involvement in the assessment process. For example, the Guía del curso del grado includes debrief tools that prompt students to evaluate their own understanding before and after assessments, promoting metacognitive awareness. These structured discussions help reinforce learning goals and deepen conceptual understanding, ensuring students are active participants in their learning progress.

Evaluation for 2.2c
Materials include tools for teachers to track student progress and growth, and tools for students to track their own progress and growth.

The materials provide multiple teacher-facing tools for monitoring student progress across time. For example, in Matemáticas K–5 evaluaciones del grado K, teachers are provided with individual and class-wide checklists organized by module, topic, TEKS, and lesson. These checklists support observational evaluations of key concepts and skills and allow teachers to document student mastery and growth across multiple domains. The "Evaluando los resultados de los estudiantes" section includes a detailed form that helps teachers systematically track progress during one-on-one conferences or classroom observation. Teachers can share rubrics from mid- and end-of-module assessments with students to promote goal setting and self-monitoring. These rubrics outline the standards being assessed and include examples of student responses to demonstrate varying levels of mastery. Located in the Grado K: Evaluaciones manual, these rubrics can be used diagnostically to guide both instruction and student reflection. For example, teachers might use these rubrics to group students by need and also invite students to mark their own level of understanding on a copy of the rubric. Student-facing tools are also embedded throughout the materials to encourage self-reflection and promote metacognition, even at the kindergarten level. In the Guía del curso del grado, under the section titled "Herramientas de reflexión antes de la evaluación y después de la evaluación," students use visual prompts to express their confidence or understanding before and after assessments (e.g., circling an image that represents how they feel about a skill). This process supports ownership of learning and helps students recognize areas of growth and strength.

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

The materials include teacher guidance for delivering differentiated instruction through scaffolded activities and explicit supports embedded in daily lessons. For example, Module 4, Lesson 11 within the "Desarrollo del concepto" section features a support box instructing teachers to create a list of number pairs that add up to six, seven, and eight. Students then use connecting cubes to model combinations like "8 is 7 and 1," reinforcing understanding through hands-on learning. Similarly, Module 4, Lesson 22 advises teachers to break down subtraction steps (e.g., "Draw your 6 cubes. Now, cross out 2.") to support learners who need more guided practice before working independently. The lessons provide differentiation support through specific margin notes, which appear throughout the teacher lesson materials. For instance, the teacher guidance in Module 6, Lesson 4 recommends modeling complex tasks and providing visual station examples to support access for all students. Module 4, Lesson 16 encourages teachers to chunk tasks step by step for students who benefit from reduced cognitive load. These embedded notes provide consistent support for adjusting instruction in real time. The Guía del curso del grado offers additional tools for addressing learning gaps through the "Solución colaborativa de problemas de conceptos erróneos de los estudiantes" tables. These tables outline common misconceptions by TEKS and recommend targeted instructional strategies, such as guiding questions and collaborative routines. For example, the Module 5 materials direct teachers to use the "Say Ten" method paired with manipulatives to build number sense and reinforce place value understanding for students requiring foundational support.

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

The materials provide consistent, embedded support to help students access and understand unfamiliar academic vocabulary. Each module includes a "Terminología" section that introduces key terms with developmentally appropriate definitions, visual cues, and cognates (when applicable). For example, Module 3 highlights the terms height and balance scale and defines the terms with simple explanations supported by visuals in order to help students connect new words to hands-on learning experiences. The lesson revisits these terms through guided activities using visual and tactile tools (e.g., comparing objects and describing one is heavier than or the same as the other). Vocabulary instruction follows a clear progression as explained in the K–5 Math Program and Implementation Guide. Students first encounter concepts through concrete materials and informal language before being introduced to discipline-specific vocabulary. For instance, Module 2, Lesson 1 provides teachers with guidance in the form of a script to gradually introduce the term vertices by first referring to corners. Then, the guidance models the academic term in context, for example "The pointed parts of the shape are called corners or vertices." Additional scaffolds are embedded in the teacher materials to reinforce vocabulary throughout instruction. Module 6, Lesson 3 within "Notas sobre las diferentes formas de participación" encourages teachers to support vocabulary development by prompting students to point to real objects shaped like cubes or spheres. Similarly, Module 3, Lesson 2 within "Notas sobre las diferentes formas de representación" highlights critical terms like más alto que and más bajo que. This prompting ensures students understand comparative language through visuals and gestures.

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

The materials provide consistent teacher guidance for extending learning beyond grade-level expectations through enrichment and extension activities. Each module includes margin notes that offer guidance to teachers on how to challenge students who have demonstrated mastery. For example, Module 4, Lesson 2 encourages teachers to have advanced students help write all possible decompositions of the numbers 2–5. Lesson 5 encourages teachers to ask students to explain, verbally or in writing, how they determined the total number of triangles in a number bond, which extends the learning with mathematical reasoning and justification. The lessons also guide teachers to facilitate peer discussion and deeper conceptual exploration. The extensions in Module 3, Lesson 4 provide prompts for teachers to ask students who show mastery to help them defend their comparison of connecting cubes, supporting the development of mathematical language and argumentation skills. The extension activity in Module 4, Lesson 35 encourages students to determine all the ways to separate nine pennies in an application problem, reinforcing part–whole relationships and flexibility with numbers. Some modules offer content that stretches into concepts from the next grade level as a form of enrichment. For example, Module 5, Topic D includes grade 1 standard 1.2C, supporting students in extending counting to 100. Additionally, students engage with real-world applications of math through financial literacy lessons where they explore income, needs vs. wants, and ways to earn money, promoting higher-order thinking and cross-curricular connections.

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

The materials include consistent, explicit prompts to support teachers in modeling and explaining key mathematical concepts. Lessons provide explicit teacher language and embedded actions to guide instruction. For example, in Module 3, teachers act out comparisons using phrases such as "¿Quieren decir que es más grande?" and "Este libro es más pesado que esta cinta" to help students connect descriptive language with observable size attributes. The explicit guidance continues as teachers introduce new concepts: "Hoy vamos a comparar pensando en más largo que, más alto que o más bajo que." Instructional guidance is consistently supported with clear modeling routines and dialogue that make abstract concepts accessible. In Module 1, Lesson 7, teachers model sorting cubes by color and counting them using a color-coded set of manipulatives and number cards. Similarly, in Module 2, Lesson 2, the explicit guidance prepares teachers to introduce triangles through student-led observations, gradually reinforcing geometric vocabulary and shape recognition. Prompts in the teacher guide reinforce direct modeling through "think-alouds" and visual aids. In Module 5, Lesson 5, teachers use hand gestures and the "Say Ten" method to demonstrate how to count and bundle by tens: "Voy a enseñar números con las manos . . . Díganme el número y luego díganmelo usando Decir Diez." Module 4, Lesson 13 similarly supports number bond instruction. The guidance prompts teachers to ask, "¿De qué nos habla este 5?" as students represent decompositions using equations and visuals. The lessons embed additional teacher modeling along with hands-on activities. In Module 3, Lessons 14 and 15, the guidance explicitly directs teachers to use physical actions—such as scooping rice with a spoon or comparing volumes of containers—to demonstrate capacity. Prompts support real-time modeling and reinforce vocabulary through action (e.g., "¿Cuántas cucharadas creen que se necesitarán para llenar esto?").

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

The program materials include teacher guidance and recommendations for effective lesson delivery and facilitation using a variety of instructional approaches, such as gestures, real-world comparisons, and hands-on activities. For example, in Module 3, teachers use tools such as balance scales and cups of rice to model comparison concepts, combining verbal questioning, visuals, and physical interaction to reinforce understanding. The "Solución colaborativa de problemas de conceptos erróneos de los estudiantes" section outlines specific instructional responses to common misconceptions, such as reformulation, the use of anchoring tools, and guided questioning. The K–5 Math Program and Implementation Guide and Grado K guía del curso provide overarching guidance that supports effective lesson delivery and facilitation. In the module sequence overview, the guide explains how students build conceptual understanding of numbers 0–10through various strategies, including fingers, cubes, drawings, groups of five, and the rekenrek. These instructional tools help students relate numbers to five, creating a foundation for number sense and decomposing strategies. The Program and Implementation Guide also outlines core routines such as turn-and-talk, sprints, exit tickets, and student error analysis that foster a classroom culture centered on exploration and problem-solving rather than compliance. Instructional guidance is supported by visual frameworks and lesson breakdowns that help teachers implement lessons effectively. For example, the "Pyramid of Culture and Learning in the Classroom" in the K–5 Math Program and Implementation Guide compares traditional lesson formats to the program’s structure. The framework aligns daily components such as fluency practice ("bell ringer"), concept development ("I do"), class discussion ("We do"), and independent application ("You do"). Lessons like Module 3, Lesson 4 reflect these components as teachers use unifix cubes to lead a guided task and assess understanding through an exit ticket. Embedded prompts and debrief questions help teachers facilitate lessons effectively. In Module 3, Lesson 15, the debrief includes embedded prompts and debrief questions to encourage student discussion: "¿Qué recipiente tenía más capacidad? ¿Cómo lo supieron?"

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

The materials support a variety of practice types, including guided, independent, and collaborative, and provide teachers with clear guidance and structures to support effective implementation. Lessons regularly incorporate teacher modeling and guided practice (e.g., shared counting, direct questioning), partner activities (e.g., "por pareja" routines with shared manipulatives), and independent tasks (e.g., drawing findings or completing the "hoja de registro"). Each module embeds guidance for these types of practice and structures to help teachers organize student learning through multiple approaches. The K–5 Math Program and Implementation Guide offers detailed recommendations for structuring different modes of practice. In the "Suggested Methods of Instructional Delivery" section, teachers are guided to implement fluency routines and the Read–Draw–Write process using a progression from modeling to guided practice to independent work. Additionally, the section on "Structuring Student Groupings" outlines the benefits of whole-group, small-group, and individual instruction to meet the diverse needs of learners. Instructional routines are framed within a consistent lesson structure, as outlined in the "Pyramid of Culture and Learning in the Classroom" found in the K–5 Program and Implementation Guide. The framework aligns conventional lesson components to the program’s daily structure: fluency practice ("bell ringer"), teacher modeling through "Problema de aplicación" and "Desarrollo del concepto" ("Yo hago"), collaborative debrief ("Nosotros hacemos"), and independent application through the "Boleto de salida" section ("Ustedes hacen"). Embedded lesson components provide opportunities for students to engage in varied practice formats. For example, in Module 4, Lesson 27, students work in pairs to explore number bonds using counters and share observations: "Hablen sobre los grupos de cuentas asociadas que encontraron escondidos en el 10." In the same lesson, the "Grupo de problemas" transitions students into independent practice by prompting them to complete application problems within a set time: "Los estudiantes deberán hacer su mejor esfuerzo para completar el Grupo de problemas en los 10 minutos asignados."

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.

According to the evidence guide for this indicator, materials should include resources that provide interactive, student-facing opportunities for cross-linguistic comparison (e.g., bilingual glossaries, comparing sentence structure across languages, or solving math problems in both English and Spanish). While the product includes some activities, it does not provide the structured resources outlined in the indicator guidance. As a result, teachers themselves become the resource, creating glossaries or additional supports that should have been embedded or provided as ready-to-use templates. The supports that are present focus mainly on vocabulary and Spanish content access, but they do not rise to the level of structured, intentional metalinguistic transfer expected in dual language immersion (DLI) designed materials. Across modules (e.g., Modules 2 and 5), the "Contenido general del módulo" section includes a "Terminología list that sometimes pairs Spanish terms with English cognates (e.g., capacidad/capacity, círculo/circle). While helpful, this falls short of the side-by-side, "grab-and-go" design expected of DLI instructional materials, where resources should be consistently available for students to analyze, compare, and discuss both languages. There are no embedded tasks, prompts, or student-facing activities that guide this level of comparison. The Matemáticas K–5 guía de programa e implementación includes an "Apoyo para estudiantes bilingües emergentes" section with strategies such as pre-teaching vocabulary, visuals, and cognates, as well as an approach to transadaptation that preserves Spanish grammar and syntax. While these supports reflect sensitivity to Spanish-speaking learners, they do not include explicit resources or guidance for fostering metalinguistic transfer. Without those built-in resources, the materials do not meet the criteria for this indicator. The materials incorporate linguistic accommodations throughout lesson components to support vocabulary development and comprehension. For example, the routine "Reunir y mostrar" guides teachers to collect student responses and connect them visually to precise academic vocabulary. This routine reinforces word meaning in context and fosters oral language development by prompting structured student discourse in both English and Spanish. Margin notes and teacher prompts provide additional bilingual scaffolds that align with elements of the Sheltered Instruction Observation Protocol (SIOP). In lessons such as Module 5, Lesson 12, margin notes recommend reviewing key terms, offering extra wait time, and providing targeted vocabulary support—practices that build language access and comprehension for emergent bilingual students. The Program and Implementation Guide and lesson materials promote a language-rich environment by embedding research-based routines that support oral rehearsal and academic discussion. Sentence stems, structured partner activities, and flexible grouping strategies appear throughout the materials and help teachers meet the varied needs of students in bilingual and ESL programs.

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

The materials embed consistent guidance to help teachers support emergent bilingual students in developing academic vocabulary and building comprehension through oral discourse. For example, in Module 4, Lesson 1, teachers introduce the term vínculo numérico through concrete experiences such as stepping into hula hoops and drawing representations. The guidance then transitions students toward abstract representations and oral storytelling, reinforcing background knowledge and vocabulary through visual, kinesthetic, and verbal learning. The lessons provide embedded prompts that support oral and written communication as tools for language development and concept reinforcement. In Module 3, Lesson 1, teacher instructions direct students to compare height and length using real-life classroom objects and structured partner talk. The teacher guidance emphasizes vocabulary use (e.g., más alto que, más corto que) and encourages students to draw and circle responses, ensuring access for students at different proficiency levels. The Matemáticas K–5 guía de programa e implementación, under "Apoyo para estudiantes bilingües emergentes," includes embedded strategies that help teachers activate prior knowledge, incorporate home language connections, and guide structured discussions. Teachers receive tools like sentence stems, visual supports, and multimodal tasks that prompt students to read, speak, draw, and write—supporting comprehension and cross-linguistic transfer. Modules begin with a "Terminología" section that explicitly supports vocabulary development through cognates and visuals. In Module 1, for example, teacher guidance introduces the term columnas alongside its English cognate and a visual of two columns of bears. Teachers are prompted to preview these terms with students to build linguistic connections. Debrief prompts within the module also include recently introduced terms and sentence frames to reinforce vocabulary and promote accurate oral language use (e.g., "¿Son sus zapatos exactamente iguales?").

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 learning concepts in Spanish to include linguistic approaches for both students who are native to the Spanish language and those who are learning Spanish, such as a dual language immersion program. The materials include instructional strategies and sample activities for teachers to provide opportunities for metalinguistic transfer that may be embedded into any lesson across the modules. The instructional strategies include tips in fluency, application problems, concept development, student debrief opportunities in oral language 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 provide varied, TEKS-aligned practice opportunities that promote deep conceptual understanding throughout each lesson and unit. Lessons progress from concrete to representational to abstract, enabling students to build number sense, compose and decompose numbers, and explore patterns and relationships. For example, in Module 6, students construct two-dimensional figures with craft sticks and clay, describe their constructions using ordinal numbers, and analyze how changes in side length affect the figures (TEKS K.6F, K.1D). Students engage in hands-on fluency activities like "Enséñame los dedos hasta 5" (Module 1, Lesson 14) and writing numbers on whiteboards (Lesson 16), reinforcing number composition up to 10. Practice includes problem sets, exit tickets, and multi-day integrated projects such as the Math Olympics, which require applying skills across domains and reflecting on learning. This range of tasks encourages reasoning, explanation, and application, supporting students in demonstrating a depth of understanding aligned with kindergarten TEKS.

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

The materials show a clear, intentional progression in rigor and complexity aligned with the kindergarten TEKS. Lessons move from concrete to abstract learning, helping students build from foundational skills like comparing physical attributes or counting with manipulatives to more complex tasks such as interpreting data from graphs or analyzing three-dimensional shapes. Tasks and assessments, including problem sets, exit tickets, and fluency activities, gradually increase in cognitive demand. For example, students begin fluency routines with numbers up to three in early lessons and progress to counting and comparing numbers up to 20 by Module 5. Similarly, students move from informally identifying shapes to formally classifying them and exploring their properties. This structured progression ensures students have accessible entry points and are supported in achieving grade-level proficiency over time.

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

The kindergarten materials demonstrate strong coherence across units by explicitly connecting mathematical patterns, big ideas, and concept relationships. For example, Modules 2 and 3 focus on building fluency with counting and manipulating numbers up to 10, which lays the foundation for addition and subtraction introduced in Module 4. Similarly, the final lessons of Module 4 prepare students for understanding the structure of teen numbers in Module 5 by recognizing 10 as a unit. Geometry concepts are also carefully sequenced—students begin with informal exploration of two-dimensional shapes in Module 2 and progress to formal classification and three-dimensional figures in Module 3. In Module 6, students apply prior knowledge of shape attributes learned earlier to construct and classify shapes, reinforcing concept continuity. The inclusion of integrated activities like the Math Olympics highlights the interconnectedness of domains such as numbers, operations, measurement, and geometry, promoting a unified and logical progression of mathematical understanding.

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 kindergarten materials demonstrate coherence across grade levels by intentionally connecting content and language from Pre-K through future grades. For example, Module 3 builds on prekindergarten standards (PK4.V.D.1–3) by deepening measurement concepts using academic vocabulary to compare length, weight, and capacity and also introduces foundational ideas like unit equivalence ("4 tazas de arroz es lo mismo que 1 tazón"), which support grade 1 TEKS: 1.2A and 1.2B related to place value and units. In Modules 1 and 2, students begin decomposing numbers and using number bonds to show part–whole relationships, preparing them for formal addition and subtraction work in grades 1 and 2. This is reinforced in Module 5, where students express numbers 11–19 as 10 ones and additional ones (e.g., 13 = 10 + 3), laying groundwork for expanded form and place value in later grades. Academic language is introduced progressively—for example, terms like grupo de 5 and historia numérica appear early in Module 1—to ensure students build the vocabulary they will need in future mathematical learning.

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

The kindergarten materials demonstrate lesson-level coherence by consistently connecting students’ prior knowledge from earlier lessons and grade levels to new mathematical learning. For example, in Module 6, Lesson 1, students draw on shape attribute knowledge from Module 2 to construct and describe two-dimensional figures using ordinal numbers, reinforcing earlier concepts while extending spatial reasoning. In Module 1, foundational prekindergarten standards such as PK4.V.A.1 (counting to 30) and PK4.V.A.4 (subitizing) are explicitly referenced in the Contenido General del módulo, supporting the development of skills like number recognition and comparison in later lessons. The curriculum progression chart in the Guía del curso del grado outlines how each lesson builds logically from prior concepts—such as using number bonds in Module 1, Topic A to understand part–whole relationships, which prepares students for addition and subtraction introduced in Topic C and Topic D. This intentional sequencing ensures students activate and build upon earlier understandings as they encounter new skills.

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

The kindergarten materials demonstrate intentional use of spaced retrieval by revisiting previously taught skills and concepts across lessons and units to support long-term retention and deeper understanding. For example, in Module 6, Lesson 1, students engage in a shape construction task using sticks and clay that extends their earlier exploration of two- and three-dimensional figures from Module 2, as noted in the teacher guidance: "En este último módulo de kindergarten, los estudiantes extienden y profundizan su aprendizaje sobre las figuras de dos dimensiones y de tres dimensiones del Módulo 2." Similarly, fluency routines throughout Topics A–C provide recurring practice with number combinations that total six, seven, and eight, reinforcing content initially introduced and ensuring it remains active in students' memory. The materials also spiral key TEKS such as K.2E across Modules 1, 3, and 5, giving students multiple opportunities to generate sums using concrete and pictorial models in a variety of contexts. Finally, the Math Olympics activity in Module 6 serves as a culminating event that revisits and integrates major concepts from earlier modules, such as numbers to 10, measurement, and operations, offering a comprehensive review that connects learning across the year.

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

The kindergarten materials provide interleaved practice by strategically mixing previously learned skills and concepts across lessons and domains, ensuring students continually apply and reinforce prior learning in new contexts. In Module 6, Lesson 1, for example, the "Práctica de fluidez" section rotates between reading picture graphs (TEKS K.8C), identifying shapes (TEKS K.6A), and counting skills (K.2), giving students exposure to multiple strands in a single session. Throughout the program, fluency routines—such as pairing number bonds from Module 1 in later lessons of Module 4—integrate foundational number strategies like making 10 or decomposing numbers, as seen in Lesson 7 and Lesson 15. Materials include interleaved practice of previously learned skills across lessons as seen in Module 4, lesson 26, where students practice gaining automaticity in counting forward and backward to at least 20 with and without objects. Through revisiting the "Practica de fluidez," students reconnect to the "Ola rekenrek" practice from Lesson 25. The culmination of interleaved learning occurs in the Math Olympics in Module 6, where stations combine concepts from geometry (Modules 2 and 6), measurement (Module 3), and number operations (Module 4), reinforcing students' ability to transfer and apply skills across domains.

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

The materials consistently include questions and tasks that require students to engage with and analyze mathematical models and representations. For example, Module 4, Lesson 1 asks students to use number bond models to compose and decompose numbers. Teachers guide students to explain how parts and wholes relate, asking the students to interpret the model and reason through verbal prompts (e.g., "Has the story changed? What do you observe?"). The lesson asks students to apply the model to real-life contexts, such as counting birds at the beach or students at a party. The guidance directs teachers to encourage students to validate and explain their thinking. Throughout the modules, the "Problemas de aplicación" section prompts students to use visual representations to interpret and evaluate mathematical scenarios. Module 5, Lesson 1 asks students to solve a problem about sharing raisins, representing their thinking with drawings. The teacher guidance notes multiple correct answers, supporting students in analyzing the modeling flexibly. Similarly, Module 3, Lesson 1 asks students to compare building sizes using visual models and academic vocabulary (e.g., más grande and más pesada) to describe their observations and connect to real-world objects like books or measuring tapes. Lessons ask students to interpret data representations in order to answer analytical questions. Module 3, Lessons 4 and 13 include class-created tables and graphs within the "Práctica de fluidez" section. The lessons ask students to respond to questions to evaluate data visually (e.g., "¿Hay menos estudiantes que prefieren el rojo o el azul? ¿Qué clase especial ha tenido más votos?") in order to support their reasoning and comparison skills within a mathematical context.

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

The materials regularly require students to create concrete, pictorial, or symbolic models to represent mathematical situations. Module 6, Lesson 1 asks students to use clay and sticks to construct two-dimensional shapes. The lesson asks students to explain their process as they build using ordinal numbers (e.g., "First, I cut four sticks of the same length. Second, I made a square . . ."), combining physical modeling with verbal reasoning. Module 4, Lessons 3–6 ask students to draw number bonds to model the composition and decomposition of numbers. These representations are directly tied to math stories and support students in visualizing part–whole relationships. Later in Module 4, Lesson 7 asks students to create two number bonds to represent the gifts shown in an image, and Lesson 9 asks students to draw dots to complete decompositions of the number eight, reinforcing understanding through modeling. The "Problemas de aplicación" section prompts students to model real-world scenarios. For example, Module 5, Lesson 1 asks students to figure out how to share 10 raisins between two hands, then draw pictures to show different combinations. The activity encourages multiple solutions and supports reasoning through student-created models. In Module 3, Lesson 1, students compare buildings by size, using visuals as models to explore terms like más grande and ocupa más espacio. The lesson also asks students to relate those representations to real-world references such as a book or measuring tape.

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

The materials consistently offer tasks that require students to apply their conceptual understanding to real-world and new situations. For example, Module 2 asks students to explore how geometric shapes appear in familiar contexts, such as recognizing a wheel as a circle or a traffic cone as a cone. Connecting abstract geometric terms to everyday objects supports students with conceptual transfer. Module 3, Lesson 20 asks students to collect real class data by graphing the number of letters in their names, then creating a second graph to show how many names contain the letter E. Students analyze the graphs by answering questions (e.g., "Which group has more names?"). This application task helps students use conceptual understanding of data and quantity in meaningful, student-centered ways. The "Grupo de problemas" sections across multiple modules provide opportunities for students to demonstrate understanding in new contexts. For example, Module 3, Lesson 1 asks students to draw a flower that is "más alta que el jarrón" and a tree that is taller than a pictured house. Module 3, Lesson 3 asks students to distinguish rectangles from other shapes by coloring specific figures and marking others with an X, which asks students to apply shape knowledge in hands-on visual tasks. Module 4, Lesson 1 asks students to apply their understanding of decomposition by completing number bonds based on real-life scenarios. One task asks them to separate a group of cats to show different combinations that make five. Similarly, Module 1 asks students to act out and draw number bonds using hula hoops and tape to physically demonstrate part–whole relationships with numbers like three, four, and five—translating conceptual understanding into physical and pictorial models.

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

The materials include fluency activities that are intentionally designed to help students develop the automaticity needed to access and complete grade-level tasks. Each module features daily "Práctica de fluidez" segments that provide repeated, engaging opportunities for students to strengthen their number sense and practice foundational math skills. For example, in Module 1, Lesson 1, students participate in counting activities such as "Contar frijoles y dedos hasta 3" to build fluency with small quantities. Module 1, Lesson 12 introduces "Hacer combinaciones de tres dedos" to support automaticity with number combinations that make three. Fluency practice is purposefully embedded in lessons to reinforce previously taught content and prepare students for new learning. In Module 2, although the primary focus is on geometry, fluency practice includes activities targeting numerical fluency. Activities such as "draw to make 5" and "hands in groups of 5" help students maintain and build number flexibility alongside the module’s shape content. Similarly, in Module 5, Lesson 6, students engage in fluency routines. Activities such as "¿Cuántos más para llegar a 10?" and "Decir Diez" help students build efficient strategies for adding and subtracting within 10. The Matemáticas K–5 guía de programa e implementación outlines the role of fluency in developing procedural skills and conceptual understanding. This guide emphasizes how the design of fluency activities supports both automatic recall and flexible problem solving. The guide explains that automaticity is critical because it allows students to solve problems accurately and efficiently. The guide describes fluency work as a bridge between foundational knowledge and the demands of future grade-level content. The instructional design of this program ensures students revisit key skills frequently to support meaningful practice and long-term retention. For instance, in Módulo 1: Versión del maestro, the "Contenido general" section presents tasks that focus on counting, representing numbers, and understanding number relationships up to 10. Consistent routines reinforce these skills daily, helping students develop confidence and fluency in foundational math concepts.

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

The materials provide embedded opportunities for students to practice applying efficient, flexible, and accurate mathematical procedures throughout lessons and across units. The design intentionally builds procedural fluency through varied strategies and representations. For example, in Module 4, Lesson 25, students use coins to model different combinations of nine bears, some in caves and some looking for honey, allowing them to flexibly compose and decompose numbers in multiple ways. This supports numerical fluency while promoting strategic problem solving. Hands-on experiences throughout the program encourage students to reason about math concepts using efficient and developmentally appropriate methods. In Module 3, Lessons 13–15, students compare container capacities using rice and spoons. As they explore measurement through direct comparison and conservation of volume, the materials prompt students to think flexibly about measurement: "¿Me pregunto cuántas cucharaditas cabrán en la taza?" These opportunities deepen conceptual understanding while reinforcing accurate use of measurement procedures. Daily fluency routines also support procedural accuracy and flexibility. In Module 1, Lesson 12, "Esconderse y ver" helps students compose and decompose the number three. In Lesson 20, "Muéstrame frijoles" encourages them to model combinations using two colors of beans. These practices foster flexible thinking and efficient strategies for understanding part–part–whole relationships. The materials encourage students to make sense of problems and apply different strategies with confidence. For instance, in Module 4, Lesson 19, students use objects or drawings to determine how many items are left in a given scenario. Teachers prompt with "¿Cuántas pelotas le quedan?" to guide student reasoning, accuracy, and flexible use of subtraction strategies. Additionally, Module 6 includes a Math Olympics event that engages students in a variety of tasks across five stations—making 10, measuring relative mass, counting by fives, composing shapes, and generating number sentences. These tasks invite students to demonstrate accurate and efficient problem-solving skills while transferring their conceptual understanding across multiple formats.

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

The materials provide regular opportunities for students to evaluate mathematical procedures and reflect on their problem-solving approaches within lessons and across units. Debrief questions embedded in daily instruction prompt students to consider the accuracy and efficiency of their strategies. For example, in Module 1, Lesson 26, students reflect on number combinations within nine and compare their methods with a partner: "¿Cómo coloreaste los 5 cuadros?" and "¿Tu compañero los coloreó igual?" These types of prompts help students assess different ways to represent numbers and consider the flexibility of their own thinking. Lessons consistently include guided discussions that encourage students to explain their reasoning and evaluate their solutions. In Module 3, Lesson 10, students are asked to reflect on weight measurement and estimation with questions (e.g., "¿Cómo sabías cuándo dejar de añadir monedas a la balanza?" and "¿Te sorprendió algo en la actividad de hoy?"). These open-ended questions help students analyze the efficiency and accuracy of their strategies while building metacognitive awareness. Partner comparison tasks also support the development of flexible thinking. For instance, in Module 2, Lesson 7, students compare their drawings with a partner’s and discuss whether they represent the same objects. This example not only reinforces key concepts but also provides a natural context for students to evaluate the clarity and precision of their own mathematical representations. Debrief components across modules deepen student understanding by connecting the day’s learning to broader mathematical ideas. In Module 4, Lesson 9, the lesson prompts students to consider how the "Problema de aplicación" relates to the core lesson objective: "¿Cómo se relaciona el Problema de aplicación con la lección de hoy?" This guides students to evaluate the purpose and relevance of different strategies. Additionally, the teacher materials support the development of evaluative habits through prompting observation and debrief over time. The program’s fluency guidance uses "Quick Practice" routines to build automaticity and help students track and evaluate their progress across multiple attempts: "Cada estudiante hace lo mejor que puede . . . para medir cuánto ha mejorado . . ." Teachers are encouraged to look for patterns in student responses to inform next steps, further reinforcing a classroom culture of reflection and refinement.

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

The materials contain embedded supports that help teachers guide students toward more efficient and developmentally appropriate strategies for problem solving. Teacher notes and prompts throughout the lessons encourage modeling, questioning, and gesture-based support to scaffold student thinking. For example, in Module 3, Lesson 9, a note within the "Aplicación del problema" guides teachers to pair physical gestures with comparative language: I am lighter (slow upward motion) and I am heavier (quick downward motion). This multimodal approach reinforces conceptual understanding while encouraging students to internalize more efficient ways to compare weight. Materials emphasize fluency development as an opportunity for efficiency. In Module 5, Lesson 10, teacher guidance encourages the use of "Say Ten" language to help students count backward on a rekenrek. The guidance prompts the use of more structured language before transitioning to traditional counting. This scaffolded progression supports conceptual understanding of number patterns and promotes flexible and efficient counting strategies. The guidance also helps teachers address common misconceptions and recognize partially correct strategies as opportunities for growth. For example, in Module 2 under the "Solución colaborativa de problemas de conceptos erróneos de los estudiantes" section, the guidance explains how to help students understand that the name of a shape remains the same even when rotated: "Sigue siendo un cuadrado aunque esté girando." This guidance supports conceptual clarity and encourages efficient reasoning about geometric properties. Prompts within the "Desarrollo del concepto" sections often encourage students to reflect on and refine their approaches. In Module 5, Lesson 9, the guidance prompts teachers to ask: "¿Cómo agruparon los dieciséis?" This question prompts students to shift from rote counting to grouping by tens and ones. Similarly, in Lesson 8, the guidance prompts teachers to model efficient strategies using the "Say Ten" structure to represent teen numbers: "¿Cómo lo dirían usando de Decir Diez?" These examples promote a smooth transition from concrete to more abstract reasoning. Across modules, the program frames teachers as facilitators and coaches who observe closely, celebrate growth, and personalize fluency routines to help each student develop increasingly efficient, flexible, and accurate approaches. This guidance fosters a classroom culture that values progress and mathematical reasoning.

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

The materials explicitly outline how they address the conceptual and procedural focus of the kindergarten TEKS. Each module includes overviews and lesson objectives that connect instruction to specific standards. For example, in Module 1, under the "Contenido general" section, teachers receive clear explanations for how classification activities support TEKS K.8A. Students begin by observing, comparing, and describing objects (e.g., "Estos globos son exactamente iguales"), and then they transition into using cardinal numbers as a lens for categorization. Lessons integrate conceptual development and procedural practice through a clearly sequenced structure that includes "Práctica de fluidez," application problems, "Desarrollo del concepto," and exit tickets. For example, in Module 3, Lesson 4, aligned with TEKS K.7B, students begin by practicing fluency routines with cube trains before comparing their lengths to a benchmark. The application problem prompts real-world reasoning, which transitions into "Desarrollo del concepto," where students use hands-on tasks and guided teacher questioning to explore length. The lesson concludes with a problem set and exit ticket that require students to apply their understanding symbolically, supporting procedural fluency. This intentional structure appears throughout the program and is reinforced by the explicitly stated routines in each lesson that move students from concrete experiences to abstract representation, as seen in Module 4, Lesson 16 with addition equations, or Module 1, Lessons 13–17, where students progress from counting groups to decomposing and writing number sentences (TEKS K.3C). The program overview and topic-level summaries provide teachers with rationale and instructional pathways that clarify instruction for the TEKS-aligned content. In Module 2, the Topic A overview explains that students first explore two-dimensional shapes using informal language and then refine their understanding through classification, composition, and graphing tasks. The materials intentionally sequence these activities to build both vocabulary and procedural fluency aligned with TEKS K.6A and K.8B. Teacher guidance consistently highlights the link between concept and procedure. For example, in Module 1, Topic D, the overview describes how students move from recognizing the number three as a quantity to decomposing it into 2 + 1 and finally writing number sentences such as 3 = 2 + 1. These shifts in representation and structure directly support the development of conceptual understanding and mathematical notation aligned with TEKS K.3C.

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

The materials consistently integrate concrete models, pictorial representations, and abstract representations to support TEKS-aligned instruction. In Module 1, Lesson 32, students build number towers using connecting cubes and then draw the towers to match a given quantity. The problem set guides students to complete drawings and write the corresponding numerals, reinforcing the connection between hands-on modeling, visuals, and abstract symbols. Lessons embed concrete tools and visual aids to develop conceptual understanding before transitioning to symbolic reasoning. For example, in Module 4, Lesson 4, students use number cubes to model the parts of a story problem involving red and green apples. Students then create number bonds on the board or their desks and record numerals to show their thinking. Pictorial tasks and number sentences in the problem set support further practice with abstract representation. The guidance prompts teachers to use manipulatives such as linking cubes, clay, and number mats to anchor early concepts in tangible experiences. In Module 4, Lesson 33, students act out subtraction problems by physically removing cubes that represent ants from a picnic blanket. Similarly, in Lesson 2, the "Números ocultos" activity uses a mat with fish drawings to visually support subtraction strategies like crossing out. Visuals and diagrams are consistently paired with teacher questioning to promote accurate interpretation and mathematical reasoning. In Module 1, Lesson 11, students respond to questions such as "¿Cuántos hay?" by recognizing and circling quantities shown in organized pictorial sets. These supports help bridge the gap between visual input and written output while building fluency with numbers.

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

The materials include embedded supports that guide students in building connections from concrete and pictorial models to abstract mathematical concepts. In Module 3, Lesson 21, students use connecting cubes and clay to create one-to-one correspondences. The students then draw what they built and write numerals to match their models. As part of the debrief, students describe their thinking using academic language, supporting both comprehension and verbal reasoning. Lessons introduce key ideas through hands-on exploration before transitioning to abstract representations. For example, in Module 4, Lesson 2, students begin by composing and decomposing numbers using connecting cubes, and then they record the part–whole relationship using number bond diagrams on their whiteboards. Teachers use prompts such as "¿De qué nos habla este 5?" to help students interpret quantities symbolically. The instructional sequence supports students in defining and explaining math concepts across representations. In Module 4, Lesson 13, students use number bonds and drawings to represent addition stories and then write equations such as 5 = 3 + 2. This progression strengthens understanding of how visual and numeric representations relate. The materials also address common misconceptions when transitioning from concrete to symbolic representations. In Module 4, under the "Solución colaborativa de problemas de conceptos erróneos de los estudiantes" section, the teacher notes guide students through the correct interpretation of number bonds. Teachers prompt students to manipulate physical models, reflect on part–whole relationships, and explain why certain combinations work or do not work (e.g., "No puedo separar 2 en 3 y 5").

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

The materials provide frequent and varied opportunities for students to develop academic mathematical language using visuals and structured language development strategies. In Module 6, Lesson 3, the margin notes guide teachers to build vocabulary by prompting students to identify real-world objects shaped like cubes or spheres. In the same module, students construct figuras planas using palitos and arcilla, and describe their creations with complete sentences such as, "Primero, corté cuatro palitos . . .," while naming attributes like lados and vértices. In Module 5, students compose and decompose numbers from 11–19 using tarjetas de valor de posición, drawings, and the routine "Decir Diez," helping them express quantities using academic math language. Similarly, in Module 4: Versión del maestro Lesson 26, the "Desarrollo del concepto" guides teachers to prompt students with specific vocabulary questions while modeling decompositions with *cubos contables* (e.g., "¿Cuántos cubos hay en su barra?" and "¿Todavía tienen 9 cubos en total?"). The materials also support academic math language through visual tools such as five-frames. In Module 4, Lesson 1, the fluency routine "Marco de 5: Contar puntos y espacios" helps students visualize decompositions while learning and using terms like puntos, espacios vacíos, and descomposición. Teachers also receive embedded scripts, such as that in Lesson 32, that model how to reinforce academic vocabulary like parte, total, and oración numérica through repeated, structured language. In Module 1, Lesson 18, students count objects placed in different configurations and pair them with digit cards, reinforcing number–word associations through verbal responses. In Module 2, Lesson 2, students analyze shape visuals to classify triangles based on their attributes. They use a simple graphic organizer and discuss their reasoning during the mini-lesson and debrief, connecting experiential learning to formal geometry language.

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

The materials embed consistent educator guidance to scaffold, support, and extend students’ use of academic mathematical vocabulary in meaningful contexts. Lessons introduce both formal and informal terms through structured instruction and real-world application. For example, in Module 6, teachers introduce vocabulary such as vértice and arista and support language development using tools like "geoplanos" and pictorial models to describe figuras planas and sólidas. In Lesson 4, under the margin notes, teachers model complex language and display visual examples at activity stations to reinforce geometric terminology. Throughout the modules, the materials guide teachers to embed vocabulary instruction into problem-solving routines and concept development. The "Solución colaborativa de problemas" routine includes specific questioning strategies to address misconceptions and reinforce academic terms during peer discussions. Module 5, Lesson 4 uses prompts such as "¿Y la forma normal?" to help students make connections between structured forms like "diez 1" and conventional terms like once, supporting accurate and fluent use of number language. Early modules provide foundational language support using clear modeling and visual scaffolds. In Module 1, Lesson 1, the "Desarrollo del concepto" guidance includes questions and phrases that highlight key vocabulary such as exactamente iguales and no exactamente iguales. Similarly, in Module 3, Topic A, students compare length, weight, and space using familiar objects while teachers use explicit guidance language to explain how alignment affects comparison (e.g., "Jan remains shorter than Pat even if her head is higher while standing on a ladder"). The materials also extend vocabulary instruction through classroom visuals and sentence frames. In Module 4, Lesson 1, teachers use hula hoops to introduce oraciones numéricas and receive guidance to add visuals to the math word wall for continued reference. In Lesson 13 of the same module, the margin notes include sentence frames to support students who may need help using precise language when solving application problems.

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

The materials include embedded teacher guidance to support the application of appropriate mathematical language, including vocabulary, syntax, and discourse, throughout instruction. Lessons provide structured opportunities for students to hear, refine, and use math language with peers while building their math language toolkit over time. For example, in Module 1, Lesson 2, the "Desarrollo del concepto" section provides scripted guidance to support partner conversations using sentence frames such as "Estos son iguales, pero este es _____, y este es _____," which supports the development of comparative language and mathematical syntax. In Lesson 10, the "Reflexión" section encourages discourse through story creation and vocabulary practice, offering questions such as "Tengo 3 bolas de chicle. 2 chicles son blancos y 1 chicle es _________." The materials guide teachers to model and prompt mathematical conversations throughout instruction. In Module 4, Lesson 1, the teacher uses hula hoops and visuals of ducks and chickens to introduce addition and number bonds. Students compare different representations and create their own word problems using everyday objects, promoting mathematical discourse and reasoning. Similarly, in Lesson 12, guidance prompts teachers to model accurate math language using phrases like "Escribámoslo también en un vínculo numérico . . . También podemos escribirlo así: 5 + 2 = 7," guiding students to explain their reasoning and use mathematical syntax precisely. The materials embed sentence stems and debrief prompts that help students articulate their thinking and respond to peer ideas using mathematical vocabulary. For example, in Module 5, Lesson 1, during the "Reflexión" section, teachers prompt students to use sentence frames such as "I circled the ______ because I counted 10" or "I did not circle ______ because I counted ___ of those." Students then discuss and compare representations (e.g., stacks of 10 sticks versus baggies of 10 items), deepening their understanding of quantity and grouping through language. Across modules, the materials continue to reinforce academic language through structured activities. In Module 5, students explain compositions like "10 + ___ = 13" using drawings and manipulatives, paired with sentence frames that scaffold their responses. In Module 6, students narrate construction processes using ordinal terms and sentence structures, responding to teacher prompts that guide them in refining and clarifying their mathematical explanations. Additionally, the materials support teachers in guiding student responses by providing exemplar responses. For example, in Module 4, Lesson 1, teachers model solving a problem involving birds using number bonds and guide students through comparing group representations. The teacher models language and expected answers that students then use as a reference for creating their own stories and representations. These embedded examples help clarify what high-quality student responses look like and support teacher facilitation of academic language development.

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

The materials integrate the TEKS process standards consistently and appropriately across modules and lessons. Students engage in mathematical thinking by selecting tools (TEKS K.1C), generating representations (TEKS K.1E), and communicating reasoning (TEKS K.1D) through core instructional routines such as "Problemas de aplicación," "Grupo de problemas," and lesson debriefs. For example, in Module 3, students use balanzas to analyze weight, compare objects, and discuss findings with peers, applying TEKS K.1C, K.1D, and K.1F during hands-on activities and discourse. Lessons support the application of math in real-world contexts, as seen in Module 1, Lesson 32. The lesson prompts students to solve a problem involving washed off uniform numbers on jerseys and to draw the correct number sequence to help the team. This activity supports TEKS K.1B and K.1F by connecting math to everyday scenarios and encouraging students to represent solutions with visuals. Lessons ask students to analyze relationships and patterns in relation to math concepts. For example, Module 1, Lesson 35 supports TEKS process standards K.1D and K.1E. The "Reflexión" section invites students to analyze relationships and patterns as they count stairs and prompts them to respond to questions like "¿Notaron algún patrón al contar las escaleras?" The program also provides explicit guidance for integrating process standards in its Guía de programa e implementación. This guide explains how lessons embed a structured problem-solving model, such as the Lee–Dibuja–Escribe (LDE) approach. In this component, students tackle written problems using the LDE model, reinforcing strategic thinking aligned with TEKS K.1A and K.1G. Across modules, students consistently engage in structured discourse and tool selection. For example, in Module 1, Lesson 1, students use manipulatives to compare items and participate in guided partner discussions that emphasize how items are alike or different, which addresses TEKS K.1D and K.1E. In Module 3, Lesson 14, students choose appropriate tools to compare liquid capacity and discuss their reasoning with a partner, integrating both TEKS K.1C and K.1D in context.

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

The materials include clear descriptions of how the TEKS process standards are incorporated and connected throughout the course. The Guía del curso de kindergarten explains that the process standards guide students in making sense of mathematics and persisting through challenges by engaging in routines. The Guía de programa e implementación expands on this by describing how these standards promote a "cultural de aprendizaje" where students engage in discussion, modeling, and productive struggle. Throughout the course materials, the TEKS process standards are systematically woven into instruction and lesson design. For instance, in the Matemáticas K–5 guía de programa e implementación, the "Estándares de procesos matemáticos de TEKS" section explicitly states that these standards are embedded across the program. It highlights how varied problem types invite students to analyze givens, constraints, relationships, and goals—modeling the kinds of behaviors outlined in the standards. In addition, each module overview lists the relevant process standards alongside the focus TEKS, helping teachers see how these practices are integrated into instruction. The lesson debriefs consistently support this integration by prompting students to reflect on their learning, explain their reasoning, and make connections between concepts. In the Guía del curso del grado: Kindergarten, the "Alcance y secuencia" section provides a table that connects each module’s topics and number of instructional days with corresponding "Conocimientos y destrezas" and standards. This layout shows how both content and process standards build across the year. Teachers also find guidance in how visual models, numeric representations, and precise language are used to help students articulate their thinking, supporting the development of mathematical reasoning and communication throughout the course.

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

The materials include a description for each unit of how the TEKS mathematical process standards (MPS) are incorporated and connected throughout instruction. Each Versión del maestro includes a "Contenido general del módulo" section with a table that clearly outlines the lesson objectives, aligned TEKS, and number of instructional days. These descriptions show how the process standards are integrated into daily lessons. For example, in Module 5, the overview explains that students use manipulatives and visual models to decompose teen numbers and justify their strategies, aligning with TEKS K.1D, K.1E, and K.1G. The module also describes how students select tools such as vínculos numéricos or an ábaco rekenrek to represent their thinking and solve problems (TEKS K.1C). Module 6 includes descriptions of how students apply process standards while constructing figures from clay or sticks. The unit summary describes how students formulate a plan and apply problem-solving strategies (K.1B), communicate the steps of their constructions using ordinal language (K.1D), and use mathematical thinking to solve real-life problems by classifying and grouping three-dimensional shapes (K.1A). The module concludes with a Math Olympics in which students apply a wide range of process skills—such as organizing, recording, and communicating ideas—while solving problems involving number, measurement, operations, and geometry (TEKS K.1E). The materials also include descriptions of how the TEKS process standards are embedded in early units. In Module 1, for instance, students are described as matching, sorting, and classifying objects while explaining how they are alike or different, demonstrating the use of precise language and justification of thinking (K.1D, K.1E, K.1G). They also use manipulatives and verbal expressions to show part–part–whole relationships (K.1C, K.1F), supporting communication of mathematical ideas. In addition to individual module descriptions, the Matemáticas K–5 guía de programa e implementación explicitly states that the TEKS process standards are intentionally embedded into lessons to promote reasoning and communication. The Aprendizaje Bluebonnet Matemáticas K–5: Alcance y secuencia de kindergarten provides a table that describes how the process standards are addressed in each unit. For example, the overview for Module 1 notes that the unit emphasizes TEKS MPS 3–7, with descriptions that explain how students will classify and count objects, compare quantities, and justify their strategies. For Module 2, the table shows alignment with TEKS MPS 1, 2, 5, and 7 and includes a note that students will "encuentre y describa triángulos, cuadrados, rectángulos y círculos planos en el mundo real," showing how students will apply mathematical process skills in familiar contexts.

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

The materials include a clear overview of the TEKS process standards incorporated into each lesson. Each module contains a section titled "Contenido general de los temas del módulo y objetivos de la lección," which lists the relevant process standards alongside the content standards for every lesson. For example, Module 4 aligns TEKS K.1C, K.1D, K.1F, and K.1A with lessons that focus on problem solving and fluency using vínculos numéricos and story contexts. The Versión del maestro also presents lesson-level overviews of the TEKS process standards. In Module 2, the Topic A overview describes how students engage with TEKS process standards by using informal language to describe plane figures (Lesson 1), connecting these descriptions to mathematical vocabulary and concepts (Lesson 2), and classifying shapes based on their attributes (Lesson 3). In Lesson 4, students organize their thinking using simple graphs and make inferences based on the data—activities that support mathematical communication and reasoning. The materials include an overview of how the TEKS process standards are incorporated into each lesson. Individual lesson objectives consistently reference both content and process standards, clearly connecting instruction to the TEKS. For example, the overview of Module 3, Lesson 4 describes how students compare the length of connecting cube bars, directly addressing TEKS K.7B while incorporating process standards related to communication and justification of thinking (TEKS K.1D, K.1G). In Module 5, Lesson 9, the "Práctica de fluidez" section notes that the fluency activity builds on previously learned patterns and promotes visualization strategies, reinforcing mathematical reasoning in alignment between the concept TEKS K.2D and K.2F, and the TEKS process standard K.1E. Additionally, the materials include a reference table titled "Estándares de procesos matemáticos de grado K por lección de cada módulo," which maps out the specific lessons where each of the seven TEKS MPS are addressed. For example, the table shows that students are introduced to strategies for making and following a plan (TEKS MPS 1) in Module 2, Lesson 1, and revisit these strategies in several lessons throughout Module 4 and again in Module 6. Similarly, opportunities to recognize and use patterns (TEKS MPS 2) are woven into lessons in Module 2, Module 4, and Module 6.

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

The materials consistently provide students with meaningful opportunities to think mathematically, persevere through solving problems, and make sense of mathematical concepts through guided tasks, discourse, and hands-on activities. For example, in Module 5, students use vínculos numéricos and number sentences to decompose numbers 11–19, applying flexible thinking strategies like composing 10 and some ones. Sentence stems such as "10 pennies equal 1 dime" support students in expressing their reasoning clearly and with precision. Across modules, students engage with real-world tools and concrete models to build a sense of mathematics and understanding. In Module 3, students compare lengths using barras de cubos conectables and balanzas, articulating comparisons like "10 es más que 7" or "el lápiz es más largo que el crayón." Lesson 5 includes a partner game where students select and compare bars, then participate in a class discussion to reflect on strategies, fostering perseverance and mathematical discourse. The program modules encourage mathematical thinking. For example, Module 4 asks students to model decompositions of seven using story problems and complete tasks like "Cuenta una historia sobre las figuras" and "Colorea cubos para que coincida con el vínculo numérico." Similarly, Module 6 asks students to construct geometric shapes with varying side lengths and record their work through drawings. Materials also include embedded debrief opportunities. In Module 5, Lesson 7, students analyze patterns in number bonds and use the "Say Ten" strategy to strengthen understanding of place value. In Lesson 9, they identify and explain errors in mathematical thinking and reasoning using 10-frames, prompting metacognition and justification of their thinking. These tasks, paired with scaffolded teacher guidance, ensure students consistently engage in meaningful, rigorous math learning that develops perseverance and deep understanding over time.

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

The materials consistently support students in understanding, explaining, and justifying that there can be multiple ways to represent and solve problems and complete tasks. Students engage in hands-on learning, visual modeling, and structured debrief that emphasize flexible problem solving and encourage exploration of various solution paths. For example, in Module 5, students solve problems with numbers 11–19 using concrete manipulatives, drawings, and equations such as "10 + ___ = 13" and "13 = ___ + 3." These varied representations allow students to see multiple valid strategies for composing and decomposing numbers. In Lesson 3, debrief questions such as "¿Fueron correctas ambas respuestas? ¿Por qué?" prompt students to justify whether different solutions are valid and explain how their partner represented 10 units, reinforcing that more than one method can lead to the correct answer. Across modules, the materials promote flexible thinking by encouraging students to choose tools and strategies that make sense to them. In Module 3, students compare measurable attributes like length, weight, and quantity using connecting cubes and balance scales. They determine which attribute to focus on and justify their reasoning using comparative language such as más largo que and más pesado que. These open-ended comparisons highlight that students can approach a single task in different ways depending on the attribute they select and the tools they use. Teacher guidance throughout the materials reinforces this idea by supporting multiple representations and solution methods. In Module 4, students explore number bonds for numbers two through five, identifying all possible combinations—including those that include zero—and sharing different ways to represent the same total. This encourages students to see number relationships as flexible and to justify their thinking using visual models and equations. Similarly, in Module 6, students use clay and sticks to build shapes and then create new figures with the same attributes. These activities show that geometric tasks can be completed in various ways while still meeting the same criteria. Throughout the materials, students are regularly prompted to compare their approaches, justify their thinking, and reflect on the validity of different strategies. Prompts such as "¿Qué hiciste tú diferente?" and "¿Cómo supiste que era correcto?" appear throughout lessons to support metacognition and emphasize that multiple solution paths are not only acceptable but expected. These consistent opportunities help students build confidence, deepen understanding, and develop the ability to explain their reasoning clearly.

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

The design of the materials requires students to make sense of mathematics through multiple opportunities to do, write about, and discuss math with peers and teachers. Students engage in hands-on problem solving to build conceptual understanding. For example, in Module 6, students construct two-dimensional shapes using clay and sticks. As they describe their figures using shape attributes and vocabulary, they reason about geometry collaboratively with teachers and peers. These tasks provide meaningful opportunities to engage physically with mathematical concepts while reinforcing academic language. Writing is embedded throughout the materials to support students in making sense of math through debrief and explanation. In Module 5, Lesson 24, students represent quantities with number bonds and equations during homework tasks and then explain their thinking in writing. This written debrief supports the transfer of learning and helps deepen understanding by requiring students to express their reasoning. To promote mathematical discourse, the materials provide consistent opportunities for students to talk about their thinking with peers and teachers. In Module 3, students compare object weights through estimation and direct measurement using a balanza, and then they use comparative language such as más pesado que and más ligero que to describe their findings. Graphic organizers and structured prompts support peer conversations and help students justify their thinking. In Lesson 25 of the same module, the Leer–Dibujar–Escribir strategy prompts students to explain their reasoning with a partner and connect their representations to real-world contexts. Across the materials, students also develop understanding through drawing, modeling, and using mathematical tools. In Module 5, they build and justify number sentences with 10-frames and discuss their visual models with a partner. Teacher prompts such as "Expliquen por qué su dibujo muestra diez 8." and "¿Qué número es mayor: el entero o una parte?" encourage students to reflect on their representations and use precise mathematical language in conversation.

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

The materials consistently support teachers in guiding students to share and reflect on their problem-solving approaches, including explanations, arguments, and justifications, through structured discussions, targeted questions, and sentence stems embedded throughout lessons. These supports help students articulate their reasoning, compare approaches, and justify their mathematical thinking in both oral and written formats. For example, in Module 1, Lesson 19, teachers prompt students to reflect on their counting strategies by asking, "Who did it the same way? Who did it differently?" This guided discussion supports students in sharing and comparing their problem-solving approaches while explaining their reasoning. Similarly, in Module 2, students describe the attributes of shapes to partners without using formal names. This activity strengthens their ability to justify their observations using precise mathematical language and visual reasoning. In the Versión del maestro, lessons consistently include structured prompts to help teachers guide students toward explaining and justifying their strategies. For instance, in Module 1, Lesson 32, teachers are directed to ask, "¿Hay alguna forma de saber cuántos escalones hay en la escalera que falta sin contar desde 1?"—a question designed to elicit part–whole reasoning and encourage students to support their answers with logical justification. Likewise, in Module 3, Lesson 16, students explain how they knew they had enough pennies, reinforcing the habit of backing up their solutions with evidence-based reasoning. To further support debrief and mathematical discourse, the materials include debrief questions such as "¿Qué ocurre en esta historia?" and "¿Qué signo podemos utilizar para mostrar lo que está ocurriendo?" These questions help students express their thinking clearly and connect it to mathematical representations and operations while giving teachers tools to facilitate purposeful conversations that deepen understanding.

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

The materials include prompts and guidance to support teachers in providing explanatory feedback based on student responses and anticipated misconceptions. Across modules, teacher-facing resources offer targeted prompts, scripted language, and visual aids that help clarify misunderstandings and reinforce accurate mathematical thinking. For example, in Module 1 and Module 2, teacher guidance includes tables listing anticipated misconceptions, explanations for why they may occur, and the related TEKS. These tables also provide specific feedback strategies to address student errors and guide them toward conceptual clarity. In one instance from Module 2, teachers are supported in explaining that rotating a square does not change its identity, using student-friendly language and hand gestures to reinforce geometric understanding. In Module 5, an error analysis chart helps teachers identify common student mistakes, such as confusing "trece" with "treinta y uno." The materials suggest corrective strategies, including the use of place value cards and structured counting methods like "Decir Diez," to build stronger number sense and support accurate mathematical reasoning. The materials also anticipate real-time classroom misunderstandings and include sample teacher language to address them. For example, in Module 3, the "Concept Development" section prompts teachers to say, "Tienes razón. Los extremos de los lápices tienen que estar en el mismo lugar para que podamos comparar de forma justa," offering direct feedback on comparison errors during measurement activities. Similarly, in Module 4, guidance is provided for supporting students who misplace numbers or objects in number bonds, helping teachers respond effectively to student thinking.