Aprendizaje Bluebonnet Matemáticas K-5 Grado 1

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

The grade 1 mathematics materials provide a comprehensive scope and sequence that outlines the Texas Essential Knowledge and Skills (TEKS), English Language Proficiency Standards (ELPS), and key concepts taught throughout the instructional year. This structure ensures that educators can easily navigate the curriculum and plan effectively for instruction. The Guía del curso del grado 1 and "Vistazo del año de grado 1" section offer a module-by-module breakdown of the year, presenting suggested instructional sequences, the number of instructional days, and the specific TEKS addressed in each module. The "Alcance y secuencia de grado 1" chart further supports such resources by organizing instructional topics and identifying the focus TEKS for each unit. For example, Module 1, "Sumas y restas hasta el 10," includes components such as hidden numbers, addition strategies, and fluency development that align with bolded focus standards such as TEKS 1.2A, 1.3B, and 1.5D. The Course Guide: Mathematics K–5 Grade 1 expands on this foundation by categorizing standards into mathematical processing skills and student expectations, aligning them to the instructional topics and learning goals of each module. As the "Contenido general del módulo" section of the Versión del maestro explains, each module includes the TEKS, lesson objectives, and suggested pacing, providing an understanding of how knowledge and skills progress throughout the year.

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

The grade 1 mathematics materials provide comprehensive pacing guidance designed to accommodate varying instructional calendars, including traditional (165–180 days) and extended (up to 210 days) school years. Overall, the materials offer adaptable pacing support for a range of academic schedules, ensuring instructional coverage and continuity regardless of calendar structure. The materials include a suggested pacing guide, which is organized by trimester and outlines the recommended number of instructional days per module. This structure ensures that educators can effectively manage instructional time during the year. The "Progression of Mathematical Concepts" table offers a detailed overview of the instructional days allocated per module within a 165-day academic calendar. The table illustrates how concepts build across the year and from grade to grade. This overview supports thoughtful long-term planning and instructional coherence. For districts using extended-year calendars, the Matemáticas grado 1 días adicionales del año escolar (ADSY) provides guidance for up to 30 additional days of instruction. The ADSY resources include 25 targeted lessons and five flexible instructional days, along with accompanying assessments. These lessons are designed to be used during summer, during the regular school year, or for intervention, offering districts flexibility in implementation.

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 grade 1 mathematics materials articulate the rationale behind the sequence of modules and how mathematical concepts build coherently throughout the year. The instructional design intentionally supports teachers in understanding how student thinking evolves and how earlier knowledge is deepened through later content. Such instructional design ensures both conceptual continuity and readiness for future learning. The Guía del curso explains how foundational concepts such as number decomposition, doubles, and counting are introduced early and serve as the foundation for more complex topics such as comparing numbers, two-digit addition, and place value in later modules. These connections support a cohesive learning experience that aligns with students’ developmental progression. The "Explicación de la secuencia de módulos en grado 1" section provides insights into the strategic placement of modules. For example, Module 5, which focuses on geometry and measurement, is deliberately positioned between two number-intensive modules to give students time to internalize numerical concepts and apply such concepts in a different context. In Module 2, one unit begins with concrete strategies such as "make ten" to solve unknown result problems. The unit then transitions into abstract problem solving, demonstrating the careful scaffolding of concepts. Additionally, the "Desarrollo de la fluidez en grado 1" resource offers a chart detailing where the materials embed fluency TEKS throughout the modules. This resource emphasizes a developmental progression in numeracy and demonstrates the logical flow of the curriculum.

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

The grade 1 materials include clear protocols and guidance to support unit and lesson internalization. Each module’s Versión del maestro includes a "Contenido general del módulo" section that previews standards, objectives, vocabulary, and assessments. The section also addresses common misconceptions and suggested tools. The materials feature a structured four-step internalization process for both modules and lessons. The materials outline this process in the "Protocolo de internalización de módulos para el líder de instrucción" and the "Protocolo de internalización de lecciones para el líder de instrucción" sections. These protocols detail specific steps, time recommendations, and the purpose behind each step, ensuring educators understand instructional coherence and TEKS alignment.

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

The grade 1 materials offer robust support for instructional leaders to guide teachers in effectively implementing the curriculum as designed. These leader-facing tools are clearly aligned with teacher practices and student learning outcomes, promoting structured and sustained implementation. These tools empower leaders to coach teachers in content delivery and support them in building strong instructional habits, ensuring fidelity to the curriculum while addressing student needs. The Guía del programa e implementación includes explicit protocols for both unit and lesson internalization. The "Protocolo de internalización de módulos para el líder de instrucción" and "Protocolo de internalización de lecciones para el líder de instrucción" sections provide leaders with a step-by-step process that includes guidance on pacing, purpose, and key instructional priorities. These four-step protocols help leaders facilitate teacher understanding of both overarching goals and lesson-level details. The K–5 Math Program and Implementation Guide provides further guidance, offering structured agendas for internalization meetings. These agendas are designed to help leaders support teachers in examining lesson sequences, understanding objectives, and preparing for instruction through deep dives into content and pacing. Additionally, the "Herramienta de observación" resource supports instructional leaders in providing targeted, observation-based feedback on implementation. The Guía del protocolo outlines a process for reviewing student artifacts and monitoring progress, providing support to leaders on collaborating with teachers to analyze student work.

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 grade 1 materials provide comprehensive unit overviews that support teacher understanding and instructional planning. The units include both background content knowledge and academic vocabulary for each module. This integration of vocabulary, visuals, and teacher-facing explanations ensures that educators are equipped with the necessary tools to deliver conceptually rich and linguistically accessible instruction. Each module begins with conceptual background information. For example, Module 1 of the Versión del maestro includes a "Contenido general" section that provides strategies and guidance for teaching addition and subtraction within ten. The section also anticipates common student misconceptions and suggests ways to address these misconceptions. Academic vocabulary is clearly presented in each module under the "Terminología" section. The materials define these terms, such as contar a partir de un número, dobles, expresión, componer, and descomponer, using simple, student-friendly language. Visual supports often accompany the terms. For bilingual learners, the materials include cognates in parentheses, such as centímetro (centimeter) and gráfica de barras (bar graph), to support dual language connections and enhance instructional clarity.

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

The grade 1 materials include bilingual family supports for each unit. Such supports provide accessible guidance in both Spanish and English to help families reinforce learning at home. For each module, families have access to a Family Guide that mirrors content in both languages. This guide contains a general overview of the curriculum, descriptions of key concepts, and examples of problems students may encounter. ensuring parents understand the mathematical focus of the unit. The guide's documents include illustrated academic vocabulary, sample problems, and TEKS alignment, helping families understand how content connects to grade-level expectations. Sections such as "Consejos para las familias" (Spanish) and "Tips for Families" (English) suggest specific at-home activities and games (e.g., "Partes de la moneda de un centavo" or "Missing Part"). These activities and games directly align with the skills students develop in class. Located in the K–5 Family Guide and Guía de programa e implementación, these resources offer a consistent format across grades K–5 and ensure equitable access for families, regardless of language preference. The materials include resources in both Spanish and English, ensuring all families are empowered to support their child's progress.

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 grade 1 materials provide comprehensive, structured, and detailed lesson plans that include all necessary components for effective daily instruction. Each lesson plan includes clear, TEKS-aligned daily learning objectives that are listed in the "Contenido general de los temas del módulo y objetivos de la lección" section. For example, Module 3, Lesson 4's stated objective is, "Ordenar, medir y comparar la longitud de objetos antes y después de medir con cubos de 1 centímetro." This objective directly aligns with TEKS 1.7A. Each lesson also specifies the required materials and includes checks for understanding, providing teachers with a structured framework to meet content and language objectives. Structured tasks and instructional routines, such as the "Grupo de problemas" tasks, allow students to practice identifying geometric figures and applying measurement strategies using manipulatives. The materials pair these tasks with teacher prompts and discourse questions to guide mathematical conversations. Formative assessment opportunities include exit tickets that check for understanding of the lesson's objective. For instance, students might be asked, "¿Cuántos vértices y lados rectos tiene cada una de las siguientes figuras?" to determine their understanding of geometry standards. Built-in debriefing segments provide teachers with scripted, open-ended questions, such as "¿Qué figuras planas fueron las más difíciles de agrupar? ¿Por qué?" These questions support critical thinking and oral language development.

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 grade 1 materials provide clear and detailed lesson overviews that list all necessary teacher and student materials, along with suggested timing for each component of the lesson. The materials consistently include these elements throughout the modules to support effective lesson delivery. This structure ensures teachers are well-prepared and able to effectively implement lessons using the appropriate materials and timing for each component. Each module includes a "Lista de materiales del módulo" resource that specifies the materials that teachers and students need for each lesson. For example, in Module 4, Lesson 14, the listed teacher materials include "cinco barras de diez" and "cartulina," while student materials include a "pizarra blanca individual" and a "juego personal de herramientas matemáticas." The lesson overviews provide a breakdown of the daily instructional components and their suggested duration. This structure is consistent across modules. For instance, in Module 3, Lesson 1, the timing breakdown is as follows: "Práctica de fluidez—10 minutes"; "Problema de aplicación—5 minutes"; "Desarrollo del concepto—35 minutes"; "Reflexión—10 minutes." Additionally, in each module, the Versión del maestro includes charts detailing the number of days required per topic, lesson titles, and associated TEKS, further supporting lesson planning and pacing.

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

The grade 1 materials provide structured and aligned opportunities for extended practice, including homework and guided independent activities that reinforce lesson objectives. These supports are available across various components and include specific scaffolds to promote student success beyond the core lesson. Additionally, lesson debriefs prompt students to process and articulate their learning, which reinforces conceptual understanding and prepares students for independent work. These materials collectively ensure that students can meaningfully extend their learning beyond the classroom in a way that is developmentally appropriate and clearly connected to the lesson’s goals. Each lesson includes a "Tarea" section. In Module 1, Lesson 1, students complete a number bond that aligns with the day’s learning objective: "Analizar y describir números incorporados (hasta el 10) utilizando grupos de cinco y vínculos numéricos." Triunfar, versión del estudiante is a student workbook that provides additional aligned practice for each lesson. Activities follow a familiar structure, such as the read-draw-write problem-solving approach. Activities include visual aids such as speech bubbles, drawings, and place value charts, as evidenced in Module 6, Lesson 3. The "Ayuda para la tarea" sections in the Triunfar workbook offer scaffolds to help students understand and complete their homework independently. These supports break down problems into simpler language and provide visual cues to reinforce conceptual understanding. The Matemáticas K–5 Guía de programa e implementación and Guía de navegación de componentes provide guidance to teachers on the use of these materials. These guides explicitly state that the Triunfar workbook can be used for homework or extended practice, depending on student needs.

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 comprehensive range of instructional assessments at both the unit and lesson levels. Diagnostic assessments, administered at the start of each module, feature varied question types, such as open-ended responses and multiple-choice items. These assessments evaluate students’ prior knowledge and readiness. For example, in Module 1, the diagnostic assessment asks students to solve addition problems and identify quantities using prompts such as "Resuelve los problemas de suma. Muestra tu trabajo" and "Marca el número que representa la cantidad." The materials embed formative assessments throughout daily lessons, including exit tickets, problem sets, and observation checklists. Such assessments allow teachers to monitor student understanding in real time and tailor instruction accordingly. These tasks progressively increase in complexity, offering differentiated opportunities for students to demonstrate understanding through drawing, comparison, labeling, and short written explanations. For instance, Module 3, titled "Evaluación continua," includes activities in which students compare object lengths and justify their reasoning. Summative assessments conclude each module. These assessments evaluate student mastery of content using a blend of procedural and conceptual tasks. For example, the "Lesson final del módulo" in Module 3 assesses students’ problem-solving and conceptual understanding via tasks aligned to module objectives. The materials also provide mid-module formative assessments that support instructional decisions. The "Sugerencias para la implementación" section guides teachers to analyze assessment data and adjust support based on student needs.

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

The materials clearly define formative, summative, and diagnostic assessments and explain their distinct purposes. Formative assessments (such as exit tickets, problem sets, and debriefing activities embedded throughout lessons) are designed to monitor student progress, identify misconceptions, and inform real-time instructional adjustments. For example, the "Lesson final del módulo" and "Evaluación continua" sections include debriefing activities at the end of daily lessons. Such activities encourage students to synthesize their learning and discuss their thinking, supporting deeper understanding. Diagnostic assessments, including mid-module evaluations labeled "Evaluación de la mitad del módulo," cover about half of the learning objectives and help identify student misconceptions early in the instructional sequence. Teachers use the data from these assessments for targeted intervention and planning. Summative assessments appear at the end of each module in the "Evaluación final del módulo" section and measure students' overall mastery of TEKS-aligned content. These assessments combine both procedural and conceptual tasks, ensuring students are tested on the full range of skills developed throughout the unit. The materials also include detailed guidance on assessment formats and scoring within the "Rúbricas de evaluación" section of the Guía de evaluación. This section offers rubrics and explanations for multiple-choice, multiple-selection, and constructed-response items. Such guidance supports teachers in analyzing student responses, identifying common errors, and making instructional decisions. For example, in Module 1, mid-module assessments serve a diagnostic purpose by evaluating students on partial module content. End-of-module assessments comprehensively evaluate student learning. Lessons include debriefing prompts and problem sets such as "Boleto de salida" and "Grupo de problemas" to reinforce formative goals, thus encouraging students to articulate their thinking and apply concepts in varied contexts. The scoring rubrics in the assessment guide provide clear criteria for evaluating student work consistently.

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

The materials provide clear guidance to support consistent and accurate assessment practices. The materials direct teachers to regularly administer assessments as part of the instructional routine, including daily formative checks, mid-module evaluations, and end-of-module evaluations. The Guía del programa e implementación and the "Materiales de instrucción" document outline when and how assessments should be used and analyzed. Each assessment includes detailed rubrics and scoring guides that define levels of student performance. These rubrics include examples of correct and incorrect responses across item types (e.g., multiple choice, constructed response) and describe observable behaviors at each proficiency level. The scope and sequence offers sufficient time for teachers to administer assessments, analyze student work, and thoughtfully respond to learning needs. While students typically complete evaluations independently within one class period, the program allows several days for teachers to review results and provide targeted feedback or interventions. Assessment guidance also emphasizes equitable practices, ensuring all students receive the same assessments, including daily exit tickets and mid- and end-of-module evaluations. Such equity ensures consistency in monitoring progress. The materials encourage teachers to follow local guidelines alongside the provided rubrics to address individual student needs.

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

The materials demonstrate alignment between assessments, the TEKS, and instructional objectives. Each module includes a clear mapping of lesson objectives to specific TEKS, which diagnostic, formative, and summative assessments directly assess. For example, rubrics and assessment overviews identify the targeted TEKS for each module and lesson, ensuring that tasks (such as pictograph analysis or comparing numbers with symbols) are aligned with grade-level standards. The materials connect lesson objectives to formative assessments such as exit tickets and problem sets. Mid- and end-of-module assessments revisit those same TEKS to measure student growth over time. Teacher guidance includes charts and tables that clearly connect assessment items to instructional goals.

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

The materials provide a variety of TEKS-aligned assessment items that range in complexity from basic recall to advanced reasoning and justification. For example, in Module 1, students explain their thinking with drawings and number sentences to solve problems such as the following: "¿Por qué Jennifer no puede resolver 9 − 6 = ____ sumando 9 + 6?" Later, in Module 5, tasks include identifying and justifying whether figures are triangles and matching shapes to names. As the "Evaluaciones: contenido general de la evaluación" section explains, assessment formats include multiple choice, multiple selection, text entry, and constructed responses. Rubrics in documents such as "Matemáticas K–5 evaluaciones del grado 1" define three levels of question complexity, guiding teachers in evaluating student mastery. For instance, early Module 1 exit tickets focus on analyzing numbers up to ten, while later tickets require analyzing addition tables and creating related operations. Formative and summative assessments in Module 4 include varied item types, such as multiple-choice questions on place value ordering, text entries converting tens and ones, and open responses explaining number decompositions. These diverse tasks support the assessment of TEKS-aligned foundational skills and deeper mathematical understanding.

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

The grade 1 materials provide detailed guidance for interpreting student performance through structured assessments, clear rubrics, and tools that support both teacher evaluation and student reflection. For example, the Guía del curso del grado 1 includes the "Herramienta de reflexión sobre la evaluación" section, which offers pre- and post-assessment prompts and sample teacher scripts to guide students in reflecting on their learning. After administering assessments, teachers use the "Paso del estudiante" form to document performance levels, record evidence of mastery, and identify areas requiring further support. Such resources ensure a systematic approach to interpreting assessment data. The "Matemáticas K–5 evaluaciones del grado 1" section includes embedded scoring guidance. Rubrics define specific criteria for various proficiency levels, identify common misconceptions, and outline how student responses should be evaluated. Rubrics also clarify how to assess responses in relation to the standards and describe how progress is shown de izquierda a derecha (from emerging to proficient levels). In the Guía de programa e implementación, the "Enfoque de las evaluaciones" section emphasizes how the assessment data serves as evidence of student learning, thus informing future instruction and program decisions.

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

The grade 1 materials provide explicit guidance for teachers to respond to student trends in assessment data through targeted tasks and instructional support. Each module includes a "Solución colaborativa de problemas de conceptos erróneos de los estudiantes" table, which outlines common misconceptions by TEKS, along with suggested guiding questions and instructional strategies. This three-step routine helps teachers stimulate student thinking, validate the student's level of understanding, and ensure accurate conceptual understanding using assessment results. The materials guide teachers to use the "Progreso hacia el dominio" rubric to evaluate levels of mastery. Both mid- and end-of-module assessments include this rubric. The rubric presents student performance on a continuum and helps identify trends in conceptual understanding. Topics are clearly labeled with focus standards, enabling teachers to connect performance data directly to relevant instructional resources and reteaching opportunities. Additionally, the Guía del protocolo de análisis del trabajo del estudiante–5 provides a step-by-step protocol for teachers, coaches, or administrators to collaboratively analyze student work. The protocol guide includes prompts for identifying patterns in student reasoning, determining gaps in knowledge or skills, and deciding on appropriate next instructional steps. This process supports data-driven decision-making at both the classroom and program levels, satisfying student learning needs through intentional and targeted instruction.

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 grade 1 materials include a variety of tools that support both teachers and students in tracking progress and growth over time. The materials provide teachers with structured opportunities to monitor student performance. For example, the "Reflexión después de la evaluación" section of the Guía del curso del grado allows teachers to document topic-specific mastery and determine remediation or regrouping needs. In addition, the mid- and end-of-module assessments include rubrics that outline expected levels of performance according to the evaluated standards. These rubrics describe what mastery looks like at different levels and include examples of student work to help teachers determine progress and diagnose learning needs. The materials assist students in monitoring their own growth through age-appropriate self-reflection activities. Before and after assessments, students engage with visual tools, such as circling images that reflect how confident or prepared they feel about the content. Such tools encourage metacognition. The materials also include individualized rubrics and debriefing forms that allow students to identify areas of strength and set goals for improvement.

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 embedded teacher guidance for providing differentiated instruction to support students who have not yet reached proficiency on grade-level content and skills. For example, in the Guía del curso del grado, the "Solución colaborativa de problemas de conceptos erróneos de los estudiantes" section in each module outlines common student misconceptions by TEKS and provides scaffolded strategies and discussion prompts for reteaching. In Module 3, this support is further organized in a structured table for Topics A–C, enabling teachers to target instruction based on observed errors. The Versión del maestro integrates scaffolded lesson routines to gradually build student understanding through hands-on learning and teacher modeling. In Module 3, Lesson 4, students begin by ordering objects by length without measuring, and then transition to measuring with centimeter cubes. The teacher models how to record and compare measurements while prompting students with guiding questions, such as, "¿Qué puedes decir del lápiz de color en comparación con el crayón?" Throughout the modules, margin notes offer targeted instructional strategies for students who require additional academic support. In Module 4, Lesson 8, the guidance advises teachers to use place value charts and connecting cubes to help students distinguish between numbers such as 12 and 21 or 14 and 40. Similarly, in Module 6, Lesson 2, the guidance encourages teachers to reduce number size or integrate visuals to support students working through comparison problems with unknown variables. The margin notes offer a variety of support for students who have not yet reached proficiency, such as chunking tasks, allowing peer verbal explanations, and adapting language complexity to ensure access to the content.

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 embed vocabulary support throughout lessons using a combination of visuals, manipulatives, and teacher guidance to ensure students understand and apply academic terms in context. In the Versión del maestro, each module includes a "Terminología" section that previews essential terms (e.g., centímetro, pictograma, vértice, and rombo). These terms often include definitions, visual representations, and paired informal/formal language (such as esquina/vértice) to reinforce understanding. The materials introduce vocabulary through hands-on experiences before applying formal terminology. For example, Module 5, Lesson 1 asks students to use sticks to form shapes and discuss their characteristics before introducing the terms figura abierta, figura cerrada, and atributos. Similarly, Module 3, Lesson 2 engages students in measuring activities with centimeter cubes before encountering terms such as unidades de longitud and aproximadamente, allowing the vocabulary to be anchored in experience. Teacher guidance provides embedded vocabulary support within daily instruction. In Module 6, Lesson 7, the margin note guides teachers to create a vocabulary table comparing units and expanded number forms (e.g., 112). In Module 5, Lesson 11, the margin note prompts teachers to highlight key geometry terms such as mitad, cuarto, and cuarto de círculo to prepare students for new concepts. The modules revisit and reinforce vocabulary through tasks and application. For instance, Module 3, Lesson 1 includes a "Problema de aplicación" section. The lesson connects new vocabulary to prior learning from grade K, such as comparing lengths. Such connections help reinforce and build upon students’ foundational language in mathematical contexts.

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

The materials include embedded teacher guidance for providing enrichment and extension opportunities to students who have demonstrated proficiency with grade-level content. These suggestions are woven throughout daily lessons using margin notes. These margin notes provide targeted strategies for deepening student understanding through open-ended questions, increased complexity, and extended tasks. For example, Module 6, Lesson 5 includes a "Desarrollo del concepto" section. The margin notes guide teachers to challenge confident students by asking them to start at 120 and complete a count-back table, extending the standard activity. Similarly, Module 6, Lesson 8 asks students who demonstrate readiness to explore alternate place value combinations, such as using nine tens and 16 ones instead of seven tens and 11 ones. These illustrated extensions promote flexible thinking and a deeper understanding of numerical relationships. In Module 1, Lesson 22, the teacher guidance provides differentiated number sets (such as using numbers up to 20) for students demonstrating advanced proficiency. Module 4, Lesson 8 challenges students to generate multiple coin combinations to make 40 cents. Module 4, Lesson 15 recommends inviting students to solve a problem using a variety of tools and strategies, promoting strategic decision-making. The Guía del curso del grado and the Guía de navegación de componentes encourage productive struggle and emphasize analyzing student reasoning. Modules (including Module 5) enrich learning by incorporating exploratory tasks in geometry, such as composing figures with pattern blocks or connecting shape attributes to time concepts. Such inclusions offer rich opportunities for advanced learners to extend mathematical reasoning beyond standard expectations.

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

The materials provide detailed, explicit prompts and guidance to support teachers in modeling and explaining key mathematical concepts. For example, Module 5, Topic A directs teachers to model the classification of two-dimensional figures by attributes. Teachers use concrete tools such as a comprobador de esquinas cuadradas and precise vocabulary such as ángulo recto and vértice. This clear, step-by-step modeling helps teachers demonstrate geometric concepts effectively. Module 3, Topic A provides teachers with scripted language and guidance for introducing measurement with one-centimeter cubes. The teacher explains important measurement principles, such as measuring sin separaciones y sin encimarse. The materials support this explanation with prompts such as "¿Qué nos dice el quinto cubo?" These prompts scaffold students’ understanding of proper unit placement and accuracy in measurement. The materials also provide rich, scripted interactions for place value concepts. For instance, in Module 4, Lesson 4, the teacher guides students to compose numbers with tens and ones using manipulatives such as ten-longs and unit cubes. This activity prompts students to build number bonds and generate number sentences. Teachers circulate the classroom to support and challenge students appropriately. Additionally, lessons include explicit guidance for explaining data representation. In Module 3, Lessons 10 and 11, the materials prompt teachers to model creating and interpreting picture and bar graphs with the class. Scripts encourage teachers to highlight important features, such as spacing and grouping, while asking reflective questions that deepen students’ understanding of how graphs represent information. Across the program, the teacher guides provide scaffolded language and actionable prompts designed to support clear explanations, foster student engagement, and promote conceptual clarity in topics ranging from geometry to measurement to data representation.

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

The materials provide comprehensive teacher guidance and recommendations for effective lesson delivery, incorporating a range of instructional approaches to support diverse learner needs. For example, the program emphasizes a collaborative problem-solving routine that guides teachers to use questioning strategies, validation, and bridging techniques to address misconceptions and deepen student understanding. The materials embed this strategy across multiple modules. Module 5 encourages teachers to use the lee-dibuja-escribe strategy, which integrates reading, visual representation, and verbal or written expression. Such a strategy exemplifies a multimodal instructional approach that supports problem solving and language development simultaneously. The Program and Implementation Guide outlines a clear four-part lesson structure that progresses from simple to complex tasks. Each lesson balances fluency, application, and conceptual understanding, culminating in a student debrief in which students reflect on their learning. Lessons intentionally embed opportunities for discourse and debriefing through strategies such as turn-and-talk, think–pair–share, and error analysis, fostering high-level and flexible thinking by sharing multiple solution strategies. Margin notes and scaffolds provide teachers with suggestions for differentiation and accommodation, ensuring access for all learners and enabling responsive facilitation throughout the lessons. Teacher materials include explicit pacing guidance, discussion prompts, and structured debriefing questions. For example, in Module 3, Lesson 4, the "Reflexión" section encourages students to articulate problem-solving strategies: "¿Qué hicimos para averiguar con precisión cuánto más largo o más corto era un objeto que otro el día de hoy?" The materials thus support metacognition and consolidate conceptual understanding. Additional examples include debriefing questions in Module 3, Lesson 11 that connect counting strategies to mathematical expressions. Module 3, Lesson 2 also includes exit ticket recommendations that help teachers quickly assess student understanding while maintaining instructional flow.

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 varied practice opportunities, including guided, independent, and collaborative formats. The materials also provide clear teacher guidance with recommended instructional structures to promote effective implementation. For example, in Module 3, lessons guide teachers to balance whole group instruction during lesson openings, small group work for activities like data sorting, and independent practice with tools such as rulers and cubes. In Module 5, teacher guidance directs students to practice individually when sorting figures, collaborate with partners to construct shapes, and engage in group discussions to compare problem-solving approaches. Materials such as tarjetas de figuras and bloques de patrones facilitate the flexible use of different practice formats. The Program and Implementation Guide highlights the benefits of varied student groupings—whole group, pairs, small groups, and individualized instruction—as effective ways to meet diverse learner needs. For example, in Module 2, Lesson 2, students first work in whole groups, then work in small groups, in pairs, and individually while completing problem sets and debriefing activities. The materials also incorporate a "Lesson Internalization Protocol," as outlined in the Matemáticas K–5 guía de programa e implementación. This protocol supports teachers in organizing lessons with a mix of instructional approaches. These approaches include yo hago (teacher modeling), nosotros hacemos (collaborative practice), and ustedes hacen (independent practice). Such a structure helps anticipate student needs, manage pacing, and maintain engagement. Practical examples include partner activities. For example, in Module 3, Lesson 3, students practice measuring with one-centimeter cubes and a ruler in pairs. Module 6, Lesson 23 includes independent tasks. For example, students independently determine the total value of coins.

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 (such as 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 (for example, 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 curricula, in which 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, which includes strategies such as pre-teaching vocabulary, visuals, and cognates. The section also includes 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 such built-in resources, the materials do not meet the criteria for this indicator. The materials provide clear, embedded guidance to support teachers in effectively implementing instruction in bilingual and ESL settings. The Guía del curso del grado 1 outlines strategies for early language development and scaffolding, including examples for adapting instruction based on students' communication and reading levels. The materials provide teachers with explicit permission to orally administer assessments when appropriate, supporting emergent bilinguals in alignment with local guidelines. Teacher-facing resources consistently highlight best practices for bilingual/ESL classrooms, including the use of structured routines, strategic grouping, and opportunities for cross-linguistic transfer. These elements equip educators with tools to create a language-rich environment that aligns with the goals of state-approved bilingual education models.

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 teacher-facing guidance to support emergent bilingual students in developing academic vocabulary and comprehension through oral and written discourse. For example, the Guía del curso del grado 1 includes model dialogue that promotes reasoning and precise academic language, such as "¿Puedes contarme más sobre tu razonamiento sobre este problema?" Lesson materials explicitly introduce key terms such as centímetro, unidad de longitud, and gráfica de barras with definitions and visuals, supporting teachers in building both background knowledge and conceptual understanding through structured oral interaction and written tasks. Across lessons, the "Desarrollo del concepto" section provides embedded prompts and scripts for teachers to scaffold student learning through speaking and writing. In Module 1, Lesson 21, teachers guide students in using manipulatives and partner conversations to discover the meaning of dobles, thus connecting physical interaction to mathematical language. In Module 2, Lesson 4, guidance supports teachers in helping students decompose numbers using pictorial models, label their drawings, and articulate their thinking using the term descomponer. The materials thus reinforce vocabulary through multiple modalities and written discourse. Margin notes across modules encourage cross-linguistic connections by pairing cognates and formal/informal terms (e.g., vértice and esquina). The "Terminología" sections support teachers in helping students preview new terms. The section reinforces comprehension through debriefing questions that prompt students to apply recently introduced vocabulary. For instance, Module 1 presents the term total with its English cognate and a corresponding number bond illustration. In Module 5, Lesson 2, teacher debriefing prompts include newly introduced terms like rombos and hexágonos, helping students apply vocabulary in context and strengthen comprehension through structured discussion. Integrated tasks support teachers in building academic language across all four modalities—speaking, listening, reading, and writing. In Module 5, Lesson 12, the "Problema de aplicación" section prompts students to read, draw, and write to solve a math problem. A teacher note highlights this process as an opportunity to apply the vocabulary that students learned throughout the lesson, reinforcing comprehension and promoting oral and written discourse in an authentic context.

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 the Matemáticas K–5 guia de programa e implementación, the materials provide a "Cross-Linguistic Connections" section. This section details how the materials support linguistic approaches for both students who are native speakers of the Spanish language and those who are learning Spanish, such as in a DLI program. The materials include instructional strategies and sample activities, allowing teachers to provide opportunities for metalinguistic transfer. Such strategies and activities may be embedded into any lesson across the modules. The instructional strategies include tips in fluency, application problems, concept development, student debriefing 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 multiple TEKS-aligned practice opportunities that promote and deepen conceptual understanding throughout each lesson and unit. Lessons follow a structured progression from concrete to pictorial to abstract representations, helping students build fluency and reasoning over time. For instance, in Module 1, Lesson 13, students participate in the activity "Diez y esconde." Students use their fingers to compose ten, an activity aligned with TEKS 1.3C. In Lesson 36, students use number bonds in the activity "Vínculos numéricos de diez," creating math drawings to represent their thinking and reinforce their understanding of composing numbers. Practice tasks across lessons reinforce strategies such as making ten, decomposing numbers, and applying the commutative property. For example, in Lesson 3, students solve problems such as "María tiene nueve bolas de nieve y Tony tiene seis." Students decompose and solve this problem as "9 + (1 + 5) = 10 + 5 = 15," demonstrating how to use number composition to reach ten. Instructional assessments, such as the "Evaluación de la mitad del módulo" and "Evaluación final del módulo," evaluate students’ ability to apply these strategies independently. Each lesson includes a four-part structure involving fluency practice, concept development, application problems, and a student debrief. This structure supports learning through a daily progression from simple to complex concepts. In Module 4's "Contenido general" section, students begin with concrete and pictorial strategies to compose and decompose numbers up to 40, developing their understanding of place value and operational fluency. The "Student Debrief" component at the end of each lesson provides an intentional opportunity for students to reflect on and discuss their mathematical thinking, further reinforcing conceptual understanding aligned with grade-level 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 provide a clear, intentional progression of tasks that increase in rigor and complexity, supporting students’ mastery of grade-level TEKS. Lessons begin with concrete representations and foundational skills, then build toward abstract reasoning and multistep problem solving. For example, in Module 1, Topic A, students begin by solving basic addition problems such as " 9 + 1 + 4" in Lesson 1. Then, in Lessons 2–6, they progress to applying properties of operations to decompose numbers and solve more complex equations. This progression continues in Topic C, in which students move from solving unknown addend problems (e.g., "3 + [ ] = 7") to explaining equivalency in equations such as "12 – 7 = 3 + 2." In Module 2, Topic A, students shift from counting on to strategies such as making ten to solve unknown total problems. Tasks such as problem sets, fluency exercises, and exit tickets support this growth. In Lesson 1, students use number bonds to describe numbers. By Lesson 39, they analyze sum tables to identify related operations. Fluency activities also evolve. Students skip counting by twos to 20 in Lesson 8, then to 40 and back in Lesson 29. In Module 5, lessons progress from identifying flat shapes in Lesson 1 to classifying three-dimensional shapes in Lesson 6. The materials regularly prompt students to reflect on their learning and explain their strategies. For example, in Module 6, Lesson 13, students consider what made a problem difficult and how they solved it. This structure helps students develop their conceptual understanding and mathematical reasoning in alignment with the TEKS.

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

The grade 1 materials demonstrate strong coherence across units by explicitly connecting recurring strategies, concepts, and mathematical relationships that build on one another over time. A central topic is the conceptualization of "ten" as a unit. In Module 1, students begin by grouping ten objects and using strategies like hacer diez and tomar de diez to add and subtract within ten. This understanding deepens in Module 2, where ten is introduced as a countable unit (1.2A, 1.2B), setting the stage for students to compose, decompose, and compare numbers up to 100 in Module 6. Module 4 revisits place value by requiring students to solve addition and subtraction problems up to 40. Such problems ask students to apply their earlier understanding of tens and ones. Instructional routines also connect concrete manipulatives to abstract thinking. For example, in Module 2, Topics A and B, students use counting strategies alongside the "make ten" and "take from ten" approaches to solve unknown-result and unknown-total problems.

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 grade 1 materials clearly demonstrate coherence across grade levels by purposefully linking content to skills that students learned in grade K and skills that they will need in grade 2. In Module 2, students transition from the grade K focus on representing numbers with objects (K–2E, K–2F) to recognizing ten ones as una decena, bridging concrete understanding with formal place value concepts. Such connections prepare students for a more advanced understanding of tens and ones in Module 6. In this module, students count, compare, and compose numbers up to 120, laying the foundation for regrouping and multi-digit operations in grade 2 (e.g., G2–M3, G2–M4). The materials also build conceptual continuity across grades through lesson objectives, tasks, and academic language. For example, in Module 3, Lesson 4, students use centimeter cubes to measure length and solve comparison problems. Such an activity builds on grade K's informal measurement activities and progresses toward the eventual use of standard tools in grade 2. The materials consistently integrate terminology such as contar a partir de un número, descomponer, and expresión across modules to support students' language development and mathematical reasoning over time. Additionally, the materials explicitly state how a strategy such as hacer diez serves as a conceptual bridge to later skills, such as using mental math with three-digit numbers and unit-based measurement conversions. The materials thus reinforce a coherent learning trajectory from one grade to the next.

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 grade 1 materials demonstrate strong coherence at the lesson level by intentionally connecting students’ prior knowledge—both from earlier in the grade and from grade K—to new mathematical skills and concepts. For example, in Module 2: Topic A, Lessons 1–11, students build on their grade K understanding of numbers 11–19 using finger counting, ten-frames, and groupings of five and ten to conceptualize place value (1.2B). The materials carry these strategies forward from grade K's work with number representation, laying the foundation for understanding two-digit numbers. The materials deliberately design fluency activities within lessons to activate students' prior knowledge. In Module 6, Lesson 1, students begin with familiar addition and subtraction facts before using them to solve more complex comparison problems, reinforcing connections between procedural fluency and conceptual understanding. Additionally, the materials gradually extend students' strategies across modules. For instance, lessons in Topic A prepare students to use the counting-on strategy, which students then apply to solve unknown-addend problems in Topic B (1.3D). Throughout the curriculum, teacher-facing materials such as the "Contenido general" section and the "Progresión de conceptos matemáticos" chart clearly outline how each lesson builds on previously taught content while introducing new concepts in a logical sequence. This approach ensures that students are not learning in isolation; instead, they are making meaningful connections between past and current learning.

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

The grade 1 materials provide intentional and structured opportunities for spaced retrieval by consistently revisiting previously learned skills and concepts across lessons and units. Each lesson includes a "Práctica de fluidez" component, which includes tasks categorized by mantenimiento (review), preparación (current focus), and anticipación (upcoming content). Such inclusions ensure that students routinely engage with prior learning while building toward new understanding. For example, activities such as "Renombra la decena" and "A la mitad en la recta numérica" reappear throughout the year to reinforce previously taught strategies. The materials introduce key concepts such as place value and operations early on. The materials also spiral these concepts throughout the curriculum. Students begin working with sums and differences within ten in Module 1, extend to 20 in Module 2, progress to 40 in Module 4, and ultimately reach 100 by Module 6. Similarly, the materials introduce place value in Module 2 and revisit this concept in Modules 4 and 6, allowing students to deepen their understanding over time through repeated exposure. The materials also integrate spaced retrieval through real-world problem solving. For example, in Module 6, Lesson 16, students revisit skip-counting by twos and fives, reinforcing fluency and supporting the long-term retention of foundational math skills.

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

The grade 1 materials provide consistent interleaved practice opportunities by strategically blending previously learned concepts with new content across lessons and units. Each lesson begins with a "Práctica de fluidez" section that asks students to engage in brief, targeted activities that revisit prior skills and prepare students for upcoming learning. For example, in Module 4, Lesson 1, the fluency activity "Descomponer los números" revisits decomposing numbers five through nine (a concept that Module 1 introduced). This activity supports fluency with sums and differences within ten. Similarly, in Module 6, Lesson 3, the activity "Restar con tarjetas" requires students to subtract within ten, reinforcing earlier learning in a new context. The materials also include tools (such as TEKS-aligned charts) in the Guía del curso del grado 1. Such charts show how the materials address standards across multiple modules. For example, students practice Standard 1.1A in Modules 1, 5, and 6. This structured mapping articulates a focus on interleaved practice throughout the year. In addition, the Triunfar student book offers practice problems that align from lesson to lesson and integrate skills from earlier grades. The materials thus promote consistent interleaved review across grade levels.

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

The materials include consistent opportunities for students to interpret, analyze, and evaluate visual models and mathematical representations across tasks and assessments. Students engage with multiple representations—such as drawings, number bonds, equations, maps, and pictographs—to make sense of mathematical situations, compare quantities, and justify their reasoning. For example, Module 1 asks students to represent a real-life story problem using a picture, a number bond, and an equation. In the mid-module assessment, students evaluate two peers' claims about an equation and must defend their answer using drawings, words, or numbers. Such inclusions support critical thinking and reinforce the use of models to explain mathematical relationships. Lessons also ask students to use models to evaluate measurement concepts. In Module 3, Lesson 1, students estimate and measure items using line models and visual maps. In Module 3, Lesson 10, students analyze a pictograph they create in order to answer questions such as the following: "¿A cuántos estudiantes les gustó más el chocolate que la vainilla?" These tasks require students to extract and interpret data from their representations. The "Problemas de aplicación" section asks students to analyze and evaluate models in meaningful contexts. For example, Module 5, Lesson 1 asks student pairs to determine the total number of palitos by interpreting a given situation and using visual representations to arrive at a total. In Module 3, students analyze a drawing of an ant and an elephant to compare their lengths using appropriate measurement vocabulary. Teacher guidance highlights how the task revisits grade K concepts while extending learning. Lesson materials, such as the "Grupo de problemas" and "Tarea" sections, include scaffolded prompts within classwork and homework to deepen students' interpretations of models. For example, Module 3, Lesson 6 asks students to select and compare three objects from a data table to determine their order by length. Such activities emphasize model analysis as a foundational component of concept development.

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

The materials provide frequent and explicit opportunities for students to create models that represent mathematical situations. Tasks and teacher-guided activities across modules support students in constructing number bonds, strip diagrams, drawings, number lines, and place value charts to model their thinking and solve problems. For example, Module 4 and Module 6 guide students to use strip diagrams to represent problem scenarios. In Module 6, students solve unknown-difference comparison problems using double strip diagrams, helping them visualize relationships and clarify problem structures. The lesson materials consistently require students to generate multiple models to support their understanding of addition and subtraction. Module 5, Lesson 1 includes a "Problema de aplicación" section, which asks students to model a story scenario involving palitos. Students use manipulatives and a strip diagram to find the total. The "Boletos de salida" section reinforces model creation. Module 2, Lesson 1 asks students to draw and label a mathematical model to represent a word problem, including circling a group of ten to support their solution process. Students use models to represent place value and number relationships as well. Module 4, Lesson 12 asks students to construct a place value chart to show how many rocks Carl had at the beginning of the story. In Lesson 11, students draw a number line to order numbers and represent comparisons. These tasks help bridge conceptual understanding and procedural fluency through model making.

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

The materials include a range of tasks and scenarios that require students to apply conceptual understanding in new problem situations and real-world contexts. The materials embed these opportunities throughout modules using concrete, pictorial, and abstract representations, thus supporting the transfer of learning. For example, Module 3 asks students to apply their knowledge of measurement and data interpretation to real-life scenarios. Students collect and organize data using pictographs, then answer questions such as "How many students were surveyed in total?" and "How many more students preferred broccoli to beans?" In the "Grupo de problemas" section, students compare measurement paths using thread and interpret graphs that were created with class data. Tasks frequently prompt students to use previously learned strategies with flexibility. Module 2, Lesson 1 asks students to complete an exit ticket that requires them to interpret a real-life scenario about Toby’s dimes. Students then write an equation to represent the situation. In another example from the same lesson, students discuss and solve how to use cubes or ten-rods to show how many cans were collected, allowing students to apply their skills in addition and place value. Module 6 tasks challenge students to apply their understanding of coins and place value to financial and business contexts. In Lesson 20, students determine how Pedro could have more money than Leo using drawings and their knowledge of coin values. Lesson 11 includes an activity called "Cindy’s Candy Shop," in which students record candy bar sales by writing numbers into a place value chart. Additional application tasks promote problem solving through discussion and modeling. For example, students use number bonds to explore different combinations that add to six or ten. Students justify their thinking through peer conversations and teacher prompts, which include the question "What numbers did we join to make six?" These activities connect familiar strategies to new mathematical situations.

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

The lessons incorporate structured fluency routines in every module to help students develop the automaticity required for grade-level problem solving. For example, in Module 6, daily fluency activities focus on counting strategies, number bonds, and number patterns within 100. These tasks include timed partner work and quick-response games that emphasize both speed and accuracy, helping students build mental math skills and confidence with larger numbers. The carefully designed fluency tasks within each lesson reinforce key number relationships and support flexible thinking. In Module 3, Lesson 2, students roll number cubes to add to six, count by twos to 40, and break apart numbers (e.g., 14 into tens and ones to subtract from 20). This lesson strengthens students' foundational addition and subtraction strategies. Similarly, in Module 1, Lesson 23, students build fluency by creating number bonds under time constraints and racing to reach a sum of nine. Such tasks help students internalize number combinations through repetition and engagement. The K–5 guía de programa e implementación emphasizes daily "Práctica de fluidez" activities as essential to developing both procedural fluency and conceptual understanding. Across modules, students move from "counting all" to more advanced strategies such as counting on, decomposing, and composing numbers within 10 and 20. In later modules, activities such as "Contar centavos con los dedos" and "Suma hasta el 20" build on this foundation, enabling students to complete increasingly complex tasks with efficiency and accuracy.

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 embed opportunities for students to apply mathematical procedures with increasing efficiency and flexibility across lessons and units. For example, in Module 4, students practice decomposing numbers into tens and ones to solve addition and subtraction problems more efficiently. The module introduces multiple strategies—including making ten, using number bonds, and counting on—so students can approach the same task in different ways, thus supporting flexible problem solving. Daily application problems prompt students to apply learned strategies in new contexts, encouraging students to choose procedures that make sense to them. In Module 1, Lesson 14, students solve a scenario involving apples falling into a basket. Students must draw, decompose, and write a matching number sentence. In Module 2, Lesson 3, a problem involving Jasmine’s pennies invites students to solve for an unknown addend using any method, reinforcing accuracy and strategic thinking in real-world contexts. The materials also include guided problem sets that ask students to reflect on the efficiency of their methods. In Module 3, students compare measurements using different non-standard units and explain discrepancies in the results. The lessons include prompts to help students evaluate the appropriateness of strategies and refine their procedural understanding. One of these prompts reads, "¿Por qué medimos con unidades de longitud del mismo tamaño?" Fluency practice activities across modules provide additional opportunities for repeated and accurate application. For instance, in Module 6, Lesson 22, students complete a "Check for Standards" sprint in which they choose strategies to solve addition problems within 20. Similarly, in Module 3, Lesson 9, a repeated subtraction sprint allows students to build speed and confidence through structured practice.

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 embed structured opportunities for students to reflect on and evaluate their own mathematical thinking. For example, in Module 6, whole group discussions prompt students to compare strategies to determine which were the most efficient. During fluency routines, students engage in error analysis tasks to identify and correct mistakes, fostering greater accuracy and a deeper understanding of solution paths. The materials integrate debriefing questions throughout lessons to support student metacognition. In Module 6, Lesson 14, the teacher guide includes prompts such as: "¿Cómo encontraste el total en el problema 1?," "¿Cómo usaste tus decenas y unidades para resolver el problema 3?," and "¿Por qué hacer la siguiente decena es una buena estrategia para sumar?" These questions help students consider the efficiency and flexibility of different strategies and justify their reasoning. Module 3 asks students to analyze their data and graphing strategies for efficiency, flexibility, and accuracy. In Lesson 11, debriefing prompts ask students to compare different graph types and evaluate how they used counting and addition to interpret results. Questions throughout the lessons guide students to connect procedures to mathematical reasoning. One such question reads, "¿Cómo se relaciona el uso de la estrategia de contar con el uso de una oración numérica de suma?" Across modules, teacher prompts encourage students to compare solution methods and reflect on transferable strategies. In Module 4, Lesson 9, students evaluate how solving one problem supported their approach to another. In Module 2, Lesson 18, students reflect on different subtraction strategies for similar problems, strengthening their problem-solving flexibility. The materials also support the evaluation of efficiency in practical contexts. In Module 6, Lesson 8, students discuss faster counting methods by comparing strategies such as grouping by tens. In Lesson 20, students explore coin combinations, evaluating which sets represent equivalent values in order to reinforce procedural accuracy and flexible thinking.

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

The materials provide embedded supports for teachers to guide students toward increasingly efficient approaches for problem solving. Lesson guidance and side notes provide teachers with prompts, questioning strategies, and instructional suggestions designed to move students toward approaches that require fewer steps and reduce mental effort. For example, in Module 2, the guidance prompts teachers to ask reflective questions to promote strategic thinking and flexibility. These questions include "¿Esta estrategia siempre funcionará?" and "¿Puedes resolverlo de otra forma más rápida?" Throughout the modules, the lessons include embedded supports to help diverse learners remove language and conceptual barriers and improve efficiency. For instance, in Module 2, Lesson 6, the "Desarrollo del concepto" section includes conversation starters to help students clearly articulate their mathematical reasoning. These conversation starters include "Mi estrategia fue…" and "Un error en tu trabajo fue…" Similarly, in Module 4, Lesson 18, an embedded teacher note suggests acting out unfamiliar contexts with volunteers before problem solving. This process supports student comprehension and advances more streamlined problem-solving efforts. Additional embedded tools help teachers address misconceptions and shift students toward more effective strategies. In Module 2, a guidance table in the "Solución colaborativa de problemas de conceptos erróneos de los estudiantes" section outlines how to support and adjust student thinking. For example, students explore subtraction strategies such as tomar de diez. They solve the problem "15 – 9" by decomposing 15 into ten and five. Lessons across modules also include embedded prompts that promote precise and efficient mathematical communication. In Module 3, Lesson 4, prompts encourage teachers to ask questions in order to push students toward more accurate and efficient descriptions. These questions include, "¿Qué podemos hacer para describir sus longitudes de forma más precisa?" In Module 2, Lesson 10, the materials encourage the use of the hacer diez strategy and guide teachers to prompt students accordingly: "el Compañero A escribe la relación básica igual a 10 + ___."

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

The materials clearly articulate how the conceptual and procedural emphasis of the TEKS is addressed. The Guía del curso del grado 1 outlines a progression of concepts such as hacer diez, contar hacia adelante, as well as composing and decomposing numbers to build number relationships. Lessons embed procedural practice through structured fluency routines such as "count on" and "take from ten." Lessons also embed this practice through the consistent use of number sentences and step-by-step problem solving. Module overviews and lesson objectives provide explicit alignment to the TEKS. For example, in Module 3, students move from informal comparisons to measuring with centimeter cubes and standard rulers (TEKS 1.7A). Lessons guide students through placing cubes, interpreting measurement as a count of unit lengths, and connecting measurement to numeric comparisons and equations. Similarly, Module 4 introduces place value using tens and ones to build numbers up to 40 with coins, place value charts, and expanded notation, emphasizing both conceptual understanding and procedural fluency. The modules consist of structured lesson components, such as daily objectives, fluency practice, application problems, concept development, problem sets, debriefs, and exit tickets. These components consistently reinforce the conceptual and procedural focus of the materials. For instance, in Module 4, Lesson 16, students use strip diagrams to represent and solve result unknown and total unknown problems, directly supporting TEKS 1.3B. Teacher guidance helps students visualize the relationship between parts and the whole, write corresponding number sentences, and explain their reasoning, reinforcing both conceptual understanding and procedural fluency through integrated lesson routines. Teacher guidance materials highlight the TEKS that each module targets. The materials also describe common misconceptions alongside strategies for conceptual clarity. For example, in Module 3, the "Solución colaborativa de problemas de conceptos erróneos de los estudiantes" section guidance supports TEKS 1.7A by helping teachers address the misconception that "length is not a measurable distance." The materials suggest strategies such as emphasizing the use of measurement units and encouraging precise reasoning with standard tools such as centimeter cubes and rulers. These supports help teachers explicitly reinforce the connection between the TEKS expectations and student understanding.

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 include questions and tasks that incorporate concrete, pictorial, and abstract representations, as required by the TEKS. Students use hands-on tools such as linking cubes, pennies, sticks, and tangram pieces to explore concepts including shape attributes, place value, and composition. For example, in Module 5, Lesson 1, students construct figures using sticks, then identify and describe their attributes through discussion and guided activities. Lesson and problem sets embed pictorial representations across the materials. Students draw two- and three-dimensional shapes, create strip diagrams, use tally marks and number bonds, and complete visual models to represent their thinking. In Module 6, Lesson 15, students reinforce conceptual understanding by counting by twos using drawings of eyes, animals, and socks, which are arranged in repeated visual structures. The materials integrate abstract representations throughout lessons and problem sets. Students write equations, expressions, and number sentences that align with concrete and pictorial tasks. Teacher prompts such as "Escribe la oración numérica, empezando por la parte más grande" guide students in making the connection between visual models and symbolic notation. Tasks involving comparison symbols (">," "<," and "=") and place value equations such as "39 – 10 = 29" support TEKS-aligned expectations for abstract reasoning.

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 provide strong support for students to connect and create concrete and representational models that bridge to abstract mathematical concepts. For example, students use visual models such as vínculos numéricos (number bonds) and decenas rápidas (quick tens) to write and explain related number sentences and equations, such as transforming a part-part-whole model into "7 + 2 = 9." Lessons encourage students to define and articulate their mathematical thinking through sentence stems and discussion prompts. Such prompts include "¿Cómo lo sabes?" and "¿Qué parte representa el número desconocido?" These supports help develop student understanding from hands-on or pictorial representations to symbolic reasoning. The materials offer guidance to teachers on initially presenting concepts in a concrete fashion by using manipulatives like counters, connecting cubes, ten-frames, or even fingers. For instance, in Module 2, Lesson 8, the materials ask students to use cubes (grouped by fives) and ten-frames to find sums. Students then draw pictorial models and write number sentences, reinforcing the connection between concrete and abstract concepts. The materials also include fluency practice and problem sets that guide students in applying their understanding by drawing models and using comparison symbols such as ">" and "<." For example, in Module 4, Lesson 1 of the Versión del maestro, students build fluency by progressing from counting all to more abstract strategies such as decomposing and composing numbers, thus supporting TEKS-aligned fluency development.

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 opportunities for students to develop academic mathematical language through the use of visuals and structured language development strategies. Throughout the modules, lessons incorporate visual supports such as gráficas, pictografías, and tablas to help students interpret data and represent numerical relationships. For example, in Module 3, Topic C, students use graphs to analyze data, building both conceptual understanding and mathematical vocabulary related to data interpretation. Students use manipulatives throughout the lessons to support math language and conceptual development. Students regularly work with connecting cubes, rekenrek bracelets, clips, cubos de uno centímetro, and bloques de patrones to model math problems and explain their reasoning. In Module 1, Lesson 8, students use number bracelets with ten beads to represent and discuss number combinations that make ten. Similarly, in Module 4, Lesson 1, students count collections of 20 to 40 objects using connecting cubes grouped into tens and ones. This activity deepens students' understanding of place value and supports their use of terms such as decena and unidad. The materials also include clear strategies for math language development. Teacher guidance includes prompts and routines to encourage students to use academic language in context. For instance, in Module 4, Lesson 5, students respond to prompts such as "¿Cuántas cuentas hay?" and "Di una oración de suma que modele cuántas cuentas hay, empezando por diez." Such prompts help students articulate equations such as "10 + 4 = 14" with the correct terminology. Additionally, lessons promote peer discussion and encourage students to justify their reasoning, further supporting language development. Module 6, Lesson 7 prompts teachers to create a vocabulary table showing a number in both unit and expanded form, reinforcing vocabulary through written representation.

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 include embedded teacher guidance that effectively scaffolds and supports students’ development and use of academic mathematical vocabulary in context. For example, in Module 5, Topic A, the materials guide teachers to explicitly connect everyday language with formal mathematical terms such as vértice and lado when describing geometric attributes. The lesson guidance includes prompts such as "¿Tiene la figura cuatro lados de la misma longitud?" to guide student reasoning and reinforce their vocabulary use during discourse. In addition, the "General Content Overview" for this module emphasizes the importance of pairing informal terms (e.g., corners) with formal terminology (e.g., vertices) to support understanding. As students describe squares and rectangles, they clarify that concepts such as square corners are distinct from vertices. Such clarification supports precise language and conceptual clarity. The lessons consistently include guidance to support math vocabulary development. For example, Module 5, Lesson 11's guidance directs teachers to introduce students to terms such as mitad and cuarto using familiar contexts such as pizza slices. Visual models like circular and rectangular pizzas engage students in conversations about equal parts, helping them connect the vocabulary to the concept of fractional parts of a whole. The materials also include strategies for students who need additional support. Module 6, Lesson 2 encourages teachers to use smaller numbers and visual models to scaffold math vocabulary related to comparison problems. In Module 5, Lesson 4, teacher guidance recommends sentence stems such as "Mi figura tiene...," "Veo ____ esquinas y ____lados rectos," and "Ya sé..." to help students articulate their observations about shapes using precise terminology. Module 1, Lesson 21's teacher guidance explicitly models the use of vocabulary such as dobles and includes prompts for student discussion. Such inclusions help reinforce students' vocabulary through repetition and meaningful contexts. Similarly, in Module 4, Lesson 11, the margin notes suggest using gestures along the number line to support students' understanding of directional terms such as izquierda and derecha.

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 that supports the application of appropriate mathematical language, including vocabulary, syntax, and discourse. For example, across modules and lessons, the "Desarrollo del concepto" sections consistently provide teachers with sample questions, sentence frames, and prompts to model and reinforce precise academic language. This guidance helps teachers scaffold student responses, facilitate peer discussions, and promote the use of formal mathematical terms in context. Module 5 prompts teachers to use formal terms, guiding students to describe attributes using precise geometric language. For example, one prompt reads, "Describe sus atributos utilizando lenguaje geométrico formal." Instruction bridges informal and formal syntax, gradually introducing students to correct mathematical structures. The "Solución colaborativa de problemas" routine fosters opportunities for students to practice and refine vocabulary through structured peer dialogue and error correction. At the same time, prompts and questions help guide student thinking and responses using targeted academic language. In Module 4, Lesson 2, the "Práctica de fluidez" section includes embedded teacher guidance to support the application of appropriate mathematical language. The materials provide sample student responses for a money exchange task in which students work in pairs to trade ten pennies for one dime. The materials prompt teachers to model and reinforce precise language, such as "ten pennies equal one dime" and "20 pennies equal two dimes." This guidance enables teachers to facilitate structured mathematical conversations, allowing students to hear and practice accurate vocabulary and syntax in context while building fluency. Similarly, in Module 3, Lesson 4, the "Desarrollo del concepto" section provides teachers with guidance to support academic discourse as students compare the lengths of three objects using one-centimeter cubes. The materials include sample student responses such as the following: "The pencil is ten centimeters long. The crayon is six centimeters long. The book is 20 centimeters long. The order from shortest to longest is crayon, pencil, and book." These responses guide teachers in prompting students to articulate mathematical relationships using precise terminology and correct sentence structure, supporting the development of students’ mathematical language over time. Additional embedded prompts throughout the materials support discourse and vocabulary development. In Module 4, Lesson 13, teachers model formal comparisons using phrases such as "37 es mayor que 28" while introducing comparison symbols. In Module 1, Lesson 32, guidance includes debriefing questions to prompt students to explain their reasoning. One of these prompts reads, "¿Cuando utilizan diferentes estrategias, encuentran siempre el número desconocido en el mismo lugar en su oración numérica? Den un ejemplo para explicar su pensamiento." The materials include embedded teacher guidance to help initiate and sustain mathematical discussions that build students’ academic language over time. For example, in the "Problema de aplicación" section of Module 3, Lesson 1, teachers receive specific prompts, such as "¿Qué palabras pueden utilizar para comparar...?" These prompts encourage students to explore and articulate mathematical relationships. Lesson 2 of the same module guides teachers to ask the following question: "¿Con qué unidad de longitud hemos medido hoy?" This question prompts a debrief on measurement tools and vocabulary. These structured questions support teachers in fostering ongoing mathematical discourse and provide students with repeated opportunities to hear, refine, and use precise mathematical language in context.

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

The materials consistently integrate the TEKS process standards across lessons to promote mathematical reasoning, problem solving, and communication. Throughout daily instruction, the materials guide students to use models and representations. The materials also guide students to debrief in order to analyze, justify, and connect math concepts. In Module 1, the materials introduce the leer-dibujar-escribir problem-solving model to help students make sense of problems, select appropriate strategies, and justify their thinking. This structured approach appears in the "Contenido general" section and supports students in developing a consistent method for reasoning through tasks. Fluency routines also embed TEKS process standards. For example, in hacer diez exercises, students use manipulatives, number bonds, and equations to justify their strategies, directly supporting TEKS 1.1E and 1.1G. The materials appropriately integrate TEKS process standards into instruction by guiding students to represent and justify their mathematical thinking. For example, in Module 2, Lesson 1, students apply the associative and commutative properties to compose equations in different forms. The teacher’s materials include a story problem that prompts students to solve "1 + 9 + 5" using various groupings, supporting flexible thinking and reinforcing conceptual understanding in alignment with TEKS expectations. The materials integrate TEKS process standards throughout Module 3 by guiding students in hands-on measurement activities that develop their reasoning and communication skills. Early lessons engage students with concrete tools such as one-centimeter cubes, paper clips, meter sticks, and string to compare lengths and explain why using consistent measurement units matters. As the module progresses, Lesson 5 applies these skills to real-world problem solving through subtraction in the "Problema de aplicación" section. Later, in Lesson 8, teachers facilitate reflective discussions that encourage students to use precise mathematical language to clearly communicate their ideas, further supporting TEKS expectations for mathematical process standards.

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

The materials clearly describe how the TEKS process standards are intentionally incorporated and connected across the course. The Guía de programa e implementación explains that TEKS process standards are seamlessly woven into the lesson structure to promote the level of thinking and behaviors the standards represent. Instructional practices such as the use of models, numeric representations, drawings, and precise language are key tools for fostering reasoning, modeling, and justification. The Guía del curso del grado 1 includes a table under the "Alcance y secuencia" section that outlines each module’s focus, instructional days, and targeted standards. The materials list the TEKS process standards alongside the focus TEKS in the module overviews. In addition, lessons include embedded prompts and structured tasks that align with the TEKS process standards. The materials also describe how process standards build across topics and modules. As the Guía del curso del grado 1 notes, reasoning strategies that appeared alongside comparison language and visual models in early measurement tasks are later applied in data analysis and financial literacy lessons. Such connections illustrate how the materials integrate TEKS process standards within each lesson and throughout the year.

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 clear descriptions for each unit that explain how the TEKS process standards are incorporated and connected throughout the unit. The materials include these descriptions in several resources, including the Versión del maestro, the Matemáticas K–5 guía de programa e implementación, and the "Alcance y secuencia de grado 1" section. Each module overview details the mathematical focus and explicitly identifies the TEKS process standards embedded within the instructional sequence. For example, in Module 4, students engage with process standards such as 1.1E and 1.1G by using tablas de valor de posición and monedas to communicate mathematical reasoning and justify their thinking using precise language. The "Contenido general del módulo" section highlights how students create their own math tools to organize and communicate their ideas. Students also apply the leer-dibuja-escribe process to problem-solving tasks using tools such as strip diagrams. The materials include a description of how TEKS process standards are incorporated and connected throughout Module 5, which links geometry and time-telling concepts. The unit explains that students identify, compose, and divide shapes while applying reasoning skills to communicate about halves and fourths (TEKS 1.1E). The unit also describes how the module culminates in problem solving related to telling time to the hour and half-hour (TEKS 1.7E). Students use clocks as tools and explain their reasoning by applying the leer-dibuja-escribe problem-solving model (TEKS 1.1B). The "Contenido general del módulo" section (and associated tables listing the TEKS) provide descriptions concerning lesson objectives and the number of instructional days. Additionally, the "Alcance y secuencia de grado 1" resource clarifies that each module emphasizes process standards.

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

The materials consistently provide an overview of the TEKS process standards incorporated into each lesson. Each module features a detailed table that maps specific TEKS process standards to individual lessons, making the standards visible and actionable for teachers. This organization helps clarify how students engage in problem solving, mathematical communication, and connections across multiple representations throughout instruction. The materials include an overview of the TEKS process standards incorporated into each lesson. For example, in Module 1, Lesson 3, the overview highlights how students engage in mathematical discussions about embedded numbers and the concept of "one more" (TEKS 1.3D). Students learn to express one more as "+1" and develop foundational counting strategies. In Module 6, Lessons 1 and 2, the lesson overviews emphasize comparison problems with unknown differences using double-strip diagrams, supporting students' use of precise mathematical language during whole-class discussions. Similarly, lesson overviews located in the teacher guides specify the TEKS process standards that each activity addresses. For instance, in Module 3 of the Versión del maestro, Lesson 4 aligns with TEKS 1.7A by guiding students to order, measure, and compare lengths using one-centimeter cubes while solving comparison problems with unknown differences. In Module 5 of the Versión del maestro, Lesson 9 highlights TEKS 1.4A and 1.4C as students practice addition and subtraction with units and tens. Additionally, the materials include a clear reference table that shows which lessons cover which TEKS process standards throughout the year. This table helps teachers quickly find the specific standards that each module or lesson covers. For example, one standard appears in lessons at the end of Module 1 and several lessons in Module 6. The materials address another standard in lessons across Module 4 and Module 6. This organization supports teachers in planning instruction that covers all required skills.

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

The materials provide consistent opportunities for students to think mathematically, persevere through solving problems, and make sense of mathematics through thoughtfully designed tasks that incorporate visual models, real-world contexts, and debriefing prompts. For example, in Module 1, Lesson 9, students solve a real-world problem about beads on a bracelet by building on their understanding of number combinations. Students represent the problem using drawings, number bonds, and number sentences, then explain their reasoning. This approach supports students' conceptual understanding and perseverance through problem solving. Students also develop flexible strategies to make sense of mathematics. In Module 2, Lesson 1, they use a "make-ten" strategy with number bonds to solve problems, reinforcing number relationships and promoting strategic thinking. In Lesson 19, subtraction tasks are more complex. Students use tools such as number paths to reason through solutions, showing how the materials scaffold problem solving and support persistence. The materials continue to provide meaningful problem-solving experiences in later modules. In Module 4, students compare coin values, a task that requires critical thinking and precise reasoning. In Module 6, students use strategies such as leer-dibujar-escribir and bar diagrams to solve comparison problems. This work further supports students in making sense of mathematical relationships and justifying their thinking.

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 meaningful activities across modules that allow them to explore, compare, and reflect on different strategies and representations, thus strengthening their conceptual understanding and analytical thinking. For example, in Module 2, Lesson 21, students solve equations using a strategy of their choice and then explain their reasoning. Debriefing prompts guide students to compare their own work with that of a partner, reinforcing the idea that different approaches can be equally valid. Similarly, Lesson 19 prompts students to justify their preferred strategy—such as counting on or taking from ten—while teachers affirm that both strategies are effective, further promoting acceptance of multiple valid methods. In Module 3, tasks continue to support students in recognizing and justifying multiple ways to solve problems. In Lesson 8, students write their own problems to match both a drawing and an equation, highlighting how various representations can express the same concept. In Lesson 6, students explore how measurement results can vary when using different units, prompting students to reason about the importance of consistency and the implications of different approaches. The materials also incorporate collaborative and real-world tasks to reinforce understanding. For instance, students analyze data from class surveys and solve comparison problems such as "¿Cuánto más largo es el lápiz que el marcador?" Such tasks provide students with authentic contexts for exploring and justifying multiple solution paths through conversation and visual models.

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

The materials are intentionally designed to require students to make sense of mathematics through multiple opportunities to do, write about, and discuss math with peers and teachers. For example, in Module 3, Lesson 4, students complete math problems by measuring a popsicle using centimeter cubes, then write about their thinking by recording a number sentence and a written explanation. Similarly, in Lesson 7, students use concrete models and compose written statements that explain their reasoning. This approach supports conceptual understanding by combining manipulatives with verbal and written expression. Such tasks align with the leer-dibujar-escribir strategy, which consistently bridges visual models and mathematical writing. The materials also provide frequent opportunities for students to discuss math with peers and teachers through collaborative activities. In Module 5, Lesson 8, students use tangram pieces to form composite shapes, then engage in structured partner discussions to describe the new shapes they created. In Module 3, Lesson 11, students analyze strip graphs and pictographs, then reflect on and discuss similarities and differences. Students thus use math vocabulary to explain their observations and draw conclusions. The materials also integrate writing and discussion into computation-focused lessons. In Module 4, Lesson 15, students solve problems such as "18 + 2" or "25 + 7" by drawing and sharing tens. Students then explain their strategies orally and in writing. Debriefing prompts guide students to articulate and justify their thinking, ensuring that math discourse is purposeful and supports sense-making.

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 provide consistent and intentional support for teachers to guide students in sharing and reflecting on their mathematical thinking. Embedded instructional routines such as "Solución colaborativa de problemas" promote classroom conversations. In these conversations, students explain their strategies, justify their reasoning, and consider alternative approaches. To guide these conversations, the materials include teacher prompts such as "¿Qué pasaría si hicieras ____ en lugar de ____?" and "¿Puedes contarme más sobre tu razonamiento sobre este problema?" Such prompts help students reflect on their process, evaluate their thinking, and revise misconceptions. Lesson reflections provide targeted opportunities for students to compare strategies and clarify their reasoning. For example, in Module 5, Lesson 3, students reflect on geometric drawings by considering which shapes were easier to draw and why, what attributes define each shape, and how figures are alike or different. Such reflection promotes both conceptual understanding and mathematical argumentation. In Module 6, Lesson 1, students solve comparison problems using part-part-whole diagrams. The materials guide teachers to ask questions to students, which prompt them to reflect on their model choice and the reasoning behind their solution. Similarly, in Module 2, Lesson 18 and Module 1, Lesson 32, "Debrief" sections ask students to analyze structure and justify where the unknown number appears in a number sentence. Such reflections strengthen students' ability to articulate strategies and make mathematical connections.

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

The materials provide comprehensive support for teachers to deliver explanatory feedback by anticipating common student misconceptions and offering targeted prompts to address such misconceptions. Each module includes a section titled "Solución colaborativa de problemas de conceptos erróneos de los estudiantes," which outlines specific student misunderstandings that are aligned to the TEKS. This section offers recommended teacher actions and guiding questions. For example, in Module 1, the materials guide teachers to address the misconception that keywords in word problems always indicate the correct operation (for example, that "more" means "add"). Instead of relying on such shortcuts, the materials prompt teachers to ask clarifying questions such as "¿Qué nos dice el cuatro en la historia?" and "¿Estamos buscando una parte o el total?" Such questions help students meaningfully connect models and story contexts. In Module 2, the materials address the misconception that numbers must be added from left to right or smallest to largest. The materials encourage teachers to model flexible strategies using manipulatives and visual aids, such as grouping numbers to make ten. For example, when students solve "8 + 2 + 3," teachers show them how to rearrange addends as "(8 + 2) + 3" to simplify the problem. Scripted teacher prompts also support in-the-moment explanatory feedback based on student responses. In Module 3, Lesson 2, during a measurement activity, the materials prompt teachers to intentionally model incorrect spacing between cubes to spark discussion. Teachers then affirm correct reasoning with the following guided feedback: "Los cubos de uno centímetro tienen que estar todos conectados, sin espaciamientos ni separaciones." Additionally, the materials offer suggestions for providing explanatory feedback on anticipated misconceptions by supporting students regarding potentially confusing vocabulary. For example, teachers explain the term aproximadamente to students, ensuring that teachers are prepared to clarify both conceptual and language-based misunderstandings.