Aprendizaje Bluebonnet Matemáticas K-5 Grado 5

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

The materials include a detailed scope and sequence table under "Alcance y secuencia de grado 5" that breaks down each module. This table highlights how the Texas Essential Knowledge and Skills (TEKS) are introduced in each module and throughout the year. The materials include two scope and sequence tables—one for 150 instructional days and another for 165 instructional days. Each table presents the title of the lesson, a summary of the lesson, the essential ideas, the corresponding TEKS, and the number of instructional days allocated for each lesson. These tables provide a structured overview that supports effective pacing and ensures alignment with the TEKS.

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

The materials include a suggested pacing calendar at the start of each module, which can be found in the "Grade-level matematicas K–5" section of the Versión del maestro. The materials include an "Additional Days School Year" section, which can be found in the Matemáticas K–5 guía de programa e implementación. This section notes the modules that provide additional flexible-use days, which serve as a supplement to the core curriculum. The materials provide 30 additional instructional days that include 25 extra lessons, a pre-evaluation, a post-evaluation, and three flexible days. The materials outline this information in the "Matemáticas grado 5, días adicionales del año escolar (ADSY)" document in the Versión del maestro. The materials thus include suggested pacing to support effective 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 materials provide reasoning for the rationale of unit order, showing how each topic builds on prior knowledge in each of the six modules. This information can be found in the "Contenido general" section of the Versión del maestro. For example, in grade 5, Module 4, "Multiplicación y división de fracciones," the Versión del maestro describes how the module begins by introducing fraction multiplication, which allows students to review what they previously learned in grade 4 (Topic A). Students then apply this knowledge to fractions of a set and division (Topic B). Last, students use this knowledge in word problems and expressions (Topic C).

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

The "Protocolo de internalización de módulos para el maestro" section in the Matemáticas K–5 guía de programa e implementación provides unit internalization guidance through a step-by-step process that supports teachers in understanding each module before instruction begins. This section helps teachers understand the concept objective, the structure of the module, the lesson progression, and the organization of resources. In the "Grade-level matemáticas K–5 aprender" section of the Versión del maestro, the beginning of the module offers an overview of the content that the teacher will deliver to students. The "Contenido general" section includes a table with common misconceptions that students may have, methods for addressing misconceptions, focus standards, fundamental standards, process TEKS, information on the general content of modules, lesson objectives, and a vocabulary preview.

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

The Matemáticas K–5 guía de programa e implementación includes an "Observation Tool" table, which serves as a resource for coaches to document their observations of teachers' instruction and the implementation of materials. This tool is structured into sections that identify activities the coach should look for before, during, and after the classroom visit, accompanied by checkboxes to indicate the presence or absence of observed evidence.

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

The grade 5 Versión del maestro provides a detailed explanation of each module's general content. This information also provides background knowledge that students will apply, as well as instructional strategies that the teacher can implement.

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

The materials include strategies and activities for families in English and Spanish. For example, the Guía del curso includes a "Tips for Families" section for each of the grade 5 modules. This section features key terminology, visuals, and clearly defined objectives for families that outline the content that students will review throughout the module. This information helps families support their child's progress at home. The "Recursos por nivel de programa" provide letters to families in both English and Spanish. These letters explain the vision of the materials and provide information on available resources.

Evaluation for 1.3a
Materials include comprehensive, structured, detailed lesson plans that include daily objectives, questions, tasks, materials, and instructional assessments required to meet the content and language standards of the lesson (aligned with the TEKS and the ELPS).

In grade 5, Modules 1–6 of the Versión del maestro, the materials include detailed and comprehensive lesson plans with clear, consistent structures. Each lesson begins with a specific objective and incorporates fluency practice, application problems, concept development, and a student debrief. Each lesson includes a suggested timing for instructional pacing. The materials provide teachers with summaries, planning notes, and material lists to support preparation. Interactive activities encourage student discussion, while exit tickets at the end of each lesson help assess student understanding and guide instruction.

Evaluation for 1.3b
Materials include a lesson overview listing the teacher and student materials necessary to effectively deliver the lesson, and the suggested timing for each lesson component.

The materials include all the teacher and student resources needed to deliver each lesson. For example, in Module 4, Lesson 11, the "Desarrollo del concepto" section includes a lesson overview listing the specific materials needed for the lesson. The materials are labeled with an "M" for maestro and an "E" for estudiante, clearly showing which materials each group needs for the lesson.

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

The Matemáticas K–5 guía de programa e implementación provides a "Lesson Structure" resource that includes a "Homework" section. This section details the goals for assignments and information on effectively implementing homework. The Versión del maestro offers extensions to lessons. For example, the materials provide a homework sheet after each lesson, which requires students to independently apply what they learned on a particular day.

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

In grade 5, the "Evaluaciones" section of the Versión del maestro identifies mid-module assessments as diagnostic and end-of-module assessments as summative. These assessments include multiple-choice, fill-in-the-blank, and open-ended questions that inform instruction and reveal misconceptions. For example, the "Evaluación final del Módulo 4: Multiplicación y división de fracciones" asks students to interpret a graph, solve real-world problems, and draw a model to justify their reasoning. The materials include varied formative and summative assessments at the lesson level. Problem sets engage students in plotting points, drawing lines, and solving real-world fraction problems with open-ended responses and visuals. Each lesson ends with a student debrief and exit ticket. The grade 5 "Evaluaciones" section of the Versión del maestro states the following: "La reflexión está diseñada para invitar a los estudiantes a pensar y al procesamiento activo." The materials thus reinforce the use of formats that promote deeper thinking.

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

The Matematicas K–5 guía de programa e implementación defines the purpose of each assessment type embedded in instruction. Exit tickets function as brief, daily formative assessments that uncover misconceptions and guide next-day instruction. Problem sets act as formative checks that help teachers monitor student progress in real time. Mid-module and end-of-module assessments provide learning evidence that teachers use to adjust instruction or measure content mastery. In grade 5, the "Evaluaciones" resource of the Versión del maestro includes a "Contenido general de las evaluaciones de grado 5" section. This section explains that mid-module assessments serve a diagnostic purpose—they check understanding of the first half of the module and reveal misconceptions. End-of-module assessments serve a summative purpose and measure mastery of the module's TEKS.

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

The grade 5 Versión del maestro includes a "Sugerencias para la implementación" section. This section guides teachers on instructional assessments, such as when to administer mid- and end-of-module evaluations. The materials emphasize that assessments should be completed independently in class and should be unfamiliar to students. The "Enfoque de las evaluaciones" section of the Matematicas K–5 guía de programa e implementación provides teachers with guidance on consistently administering assessment materials. For example, the materials state the following: "In these instructional materials, assessment becomes a regular part of the classroom routine in the form of daily, mid-module, and end-of-module assessment tasks." The "Enfoque de las evaluaciones" section of the Matematicas K–5 guía de programa e implementación explains how to accurately administer tests. For example, the materials state the following: "Mid-module and end-of-module assessment tasks should be completed independently by students within one class period. These tasks should also be new to the students and not preceded by analogous problems."

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

The materials include diagnostic and summative assessments that are aligned to the TEKS and the objectives of the course, unit, and lesson. In grade 5, teachers can reference the "Evaluación y estándares evaluados" chart, which they can find in the "Evaluaciones" section of the Versión del maestro. This chart lists the specific TEKS and learning objectives that the materials assess. The chart supports alignment by identifying the TEKS addressed in each question for both mid-module and end-of-module assessments, helping teachers track which standards students are mastering. The materials include formative assessments at the beginning and end of each lesson. The materials align these assessments to the TEKS and the stated objectives in the module overview. For example, in grade 5, Module 5, Lesson 15 of the Versión del maestro, the lesson objective is to draw trapezoids to clarify and define their attributes. An exit ticket provides a two-part task: students first use a ruler to draw a trapezoid, then explain in writing which attributes must be present. This two-part task directly assesses each student's ability to complete the lesson objective.

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

The "Evaluación del final del Módulo 5," which can be found in the "Evaluaciones" section of the grade 5 Versión del maestro, includes tasks that demonstrate more than two levels of complexity. For example, students compute with decimals, interpret data in a table, and explain relationships between values. These tasks are rigorous and require students to apply, interpret, and justify their thinking in multiple ways. The "Evaluación del final del Módulo 3," which can be found in the "Evaluaciones" section of the grade 5 Versión del maestro, contains items that reflect more than two levels of complexity. Students solve multistep problems involving fractions, interpret number lines, and justify equivalence between fractional forms. These tasks require students to demonstrate understanding through computation, representation, and reasoning.

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

In the "Evaluaciones" section of the grade 5 Versión del maestro, instructional assessments provide clear guidance for interpreting student performance through the use of a progress rubric. This rubric describes how students demonstrate increasing levels of conceptual understanding and mathematical reasoning across four categories, which range from "Poca evidencia" to "Evidencia de razonamiento sólido." The materials guide teachers to use this tool diagnostically to identify misconceptions and strengths, enabling targeted instruction and reflection on student needs. Scoring information in the "Evaluaciones" section of the grade 5 Versión del maestro includes detailed rubrics that guide educators in evaluating student work. The materials include a four-tier performance rubric that is aligned to the TEKS, which is titled "Progreso hacia el dominio." This rubric includes specific descriptors that distinguish levels of reasoning and accuracy. Such tools support the teacher's ability to interpret whether student performance is proficient, helping the teacher determine students' strengths and weaknesses. The materials thus personalize instruction to meet students' needs for intervention and enrichment.

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

The grade 5 materials include clear guidance for using specific tasks to address student trends in performance. For example, the "Contenido general" resource in each module includes a "Solución colaborativa de problemas de conceptos erróneos de los estudiantes" section. This section includes a table that identifies common misconceptions aligned to the TEKS and suggests concrete instructional responses to correct these errors. The "Solución colaborativa de problemas de conceptos erróneos de los estudiantes" section offers teachers a structured, three-step process. This process encourages teachers to "(1) stimulate student thinking," "(2) validate partially correct reasoning," and "(3) bridge toward improved understanding." The section maps common student misconceptions to their related TEKS, and pairs each misconception with targeted guidance and sample questions or representations to address misunderstandings. For example, when students mistakenly believe that "814 × 39 ≈ 32,000" is a valid estimation strategy, the materials suggest leading a discussion contrasting exact versus estimated values. This discussion helps students reason about number sense and accuracy.

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

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

The materials include clear teacher guidance for differentiated instruction and activities for students who have not reached proficiency on grade-level content and skills. The Matemáticas K–5 guía de programa e implementación in the Versión del maestro includes a "Diferenciación y soportes" section. This section outlines how to use margin notes (embedded throughout lessons) to address the needs of emergent bilinguals, students with disabilities, and students requiring additional practice. The materials provide teachers with strategy activities such as breaking tasks into smaller parts, using graphic organizers, offering sentence stems, and making real-world connections. The materials include teacher guidance for differentiated, scaffolded instruction through a structured routine designed to address student misconceptions in real time. For example, Modules 1–6 of the grade 5 Versión del maestro includes a "Solución colaborativa de problemas de conceptos erróneos de los estudiantes" section. This section provides a three-step process that stimulates student thinking, validates student ideas, and guides students toward deeper understanding. The materials provide teachers with targeted strategies, visuals, and sample prompts to scaffold learning based on specific student needs, thus supporting small group and paired instruction for students who have not reached proficiency.

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

The materials pre-teach unfamiliar academic vocabulary through the "Terminología" section, which teachers can find in the "Contenido general del módulo" resource across Modules 1–6 of the Versión del maestro. This section clearly defines newly introduced mathematical terms, uses cognates when applicable, and provides visual representations for all learners. Modules 1–6 of the grade 5 Versión del maestro include embedded supports in the "Notas sobre las diferentes formas de representación." Teachers can use these notes to clarify unfamiliar references for students through multilingual scaffolds, visual examples, and academic language support. Such resources offer guidance for helping students access and understand academic terms in context.

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

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

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

Grade 5, Module 5 of the Versión del maestro includes explicit prompts that guide teachers in modeling and explaining volume using labeled diagrams, formula applications, and real-world problem contexts. In Lesson 7's "Desarrollo del concepto" section, the materials direct teachers to support students through structured steps such as "¿Pueden dibujar algo?," "¿Qué pueden dibujar?," "¿Qué conclusiones pueden sacar de su dibujo?," as well as prompts such as the following: "M: Mida la base del macetero. ¿Qué fórmula usarán para calcular el volumen?" These steps include teacher-led prompts for students to follow. The materials thus ensure that teachers guide students throughout the lesson's progression, breaking down the concepts to be learned. Grade 5, Module 5 of the Versión del maestro includes embedded teacher guidance that supports modeling through diagrams, application-based problems, and marginal notes. For example, Lesson 7's "Notas sobre las diferentes formas de participación" and "Notas sobre las diferentes formas de expresión" suggest that students use isometric dot paper, physical models, or digital tools to support visual and spatial reasoning when calculating and designing rectangular prisms. These supports help teachers scaffold volume concepts and promote accurate, meaningful modeling for a range of learners.

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

Grade 5, Module 4 of the Versión del maestro includes teacher guidance that supports effective facilitation through a variety of instructional approaches. For example, Lesson 16's "Desarrollo del concepto" section prompts teachers to use direct instruction with scripted modeling, structured peer discussion, and visual models (such as strip diagrams and fractional equivalence representations). These approaches provide multiple entry points for students and support teachers in delivering the lesson through explicit teaching, discourse, visual representation, and peer interaction. Grade 5, Module 4 of the Versión del maestro includes teacher guidance and recommendations for effective lesson delivery and facilitation using more than two instructional approaches. For example, Lesson 21's "Desarrollo del concepto" section prompts teachers to engage students in multiple strategies, including verbal explanation, diagram drawing, partner discussion, and writing story problems that match strip diagrams. The teacher script supports varied delivery methods. These methods include posing guiding questions (e.g., "¿Cuál es el entero en el diagrama?"), using diagrams for conceptual understanding, and prompting students to verify their solutions with multiplication.

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

The Matemáticas K–5 guía de programa e implementación in the Versión del maestro includes more than two types of practice to support effective implementation. For instance, the "Estructura de la lección" section outlines guided practice through teacher-student dialogue and the use of manipulatives. Students engage in independent practice during the "Grupo de problemas" section, in which students apply conceptual understanding on their own. The materials embed collaborative learning through structured peer discussions, such as the "Expliquen a su compañero" discussion. The materials include these discussions daily during the "Reflexión" portion of the lesson. The materials provide teacher guidance to support effective implementation through step-by-step instructional dialogue, questioning, and anticipated student responses for whole-group instruction across all seven modules. For example, the Matemáticas K–5 guía de programa e implementación in the Versión del maestro outlines detailed prompts in the "Desarrollo del concepto" section. This section includes teacher cues that are labeled with an "M," including "¿Qué ven, y qué debemos hacer?" The section also includes instructional tips that emphasize aligning mathematical strategies. The materials label expected student responses with an "E." The materials recommend multiple instructional structures to support effective implementation. The Matemáticas K–5 guía de programa e implementación in the Versión del maestro states that the "Desarrollo del concepto" section is designed for whole-group instruction and includes interactive modeling and discourse. The "Grupo de problemas" section supports independent work time while encouraging teachers to adapt the number and complexity of problems to meet student needs, which may include differentiated small groups. The lesson concludes with an individual "Boletos de salida" activity.

Evaluation for 3.3a
Materials include teacher guidance on providing linguistic accommodations for various levels of language proficiency [as defined by the English Language Proficiency Standards (ELPS)], which are designed to engage students in using increasingly more academic language.

This guidance is not applicable because the Spanish program does not require guidance on providing linguistic accommodations.

Evaluation for 3.3b
Materials include implementation guidance to support teachers in effectively using the materials in state-approved bilingual/ESL programs.

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

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

The materials include embedded guidance for teachers to support emergent bilingual students in developing academic vocabulary through oral discourse. In Module 2, Lesson 5's "Desarrollo del concepto" section, the teacher facilitates oral discourse by prompting students with "¿Por qué hay paréntesis?" The teacher then encourages turn-and-talk interactions. Lesson 9's "Reflexión" section requires students to orally discuss multiplication models and decomposition strategies using targeted terms such as modelo de área and productos parciales. The margin "Notas sobre las diferentes formas de participación" and "Notas sobre las diferentes formas de acción y expresión" suggest using sentence stems such as the following: "Los modelos de área...son iguales porque…." These sentence stems help scaffold structured math discussions. The materials guide teachers to review terms aloud and leverage cognates (such as producto, estimación, and suma) to reinforce cross-linguistic connections. The materials embed frequent opportunities for written discourse that help emergent bilingual students develop academic vocabulary, increase comprehension, and build background knowledge. In Module 2, Lesson 5's "Desarrollo del concepto" section, students record numeric expressions to represent diagrams and unknown values using academic terms such as expresión and cantidad desconocida. In Lesson 9's "Grupo de problemas" section, students write full solutions with equations and written justifications, such as "Se imprimirán 72,160 libros" and "El costo total es $17,178." In Lesson 11's "Grupo de problemas" section, students solve multistep problems and express answers using precise written responses, such as "Leah ganó $1,996 más que Gemma." In Lesson 31's "Reflexión" section, students write complete statements such as "Cero y siete décimas mililitros de suero hay en cada recipiente pequeño." Such statements demonstrate students' use of academic vocabulary and concept comprehension. The lesson's marginal notes encourage using math word walls, written sentence stems, and posters that highlight bilingual academic language, supporting cross-linguistic connections and reinforcing meaning across Spanish and English.

Evaluation for 3.3d
If designed for dual language immersion (DLI) programs, materials include resources that outline opportunities to address metalinguistic transfer from English to the partner language.

The materials include multiple resources that promote metalinguistic transfer from English to the partner language. The materials explicitly guide students to build connections between the two languages. Students develop a bilingual glossary using targeted vocabulary words, which offers opportunities to recognize and analyze cognates and false cognates while incorporating visuals to reinforce meaning. A student-facing "KWHL" chart further supports this process, which stands for "Know," "Want to Know," "How Can I Learn," and "What Did I Learn." Learners first write in their primary language to activate their prior knowledge. They then reflect on how these ideas connect to the partner language. Such activities encourage students to draw direct links between languages, enhancing their comprehension and language development. The materials also provide resources for instructional strategies that strengthen oral proficiency in the partner language through structured practice. For example, teachers use choral response activities in which students repeat vocabulary words in their primary language and then practice them in the partner language. Lessons consistently integrate opportunities for metalinguistic transfer in the "Fluency," "Application Problems," and "Concept Development" sections, in which students read, engage in discourse, and apply vocabulary in both languages. In the K–5 Program and Implementation Guide, the materials explicitly prompt educators to "encourage students to solve math problems in the language of their choice, while making explicit connections to the strategies, vocabulary, or reasoning they have used in the partner language." This guidance fosters metalinguistic awareness and supports students in transferring conceptual understanding across languages.

Evaluation for 4.1a
Practice opportunities over the course of a lesson and/or unit (including instructional assessments) require students to demonstrate depth of understanding aligned to the TEKS.

Modules 1–6 of the grade 5 Versión del maestro include practice opportunities that promote deep, TEKS-aligned understanding. In Module 3, the materials emphasize numerical reasoning and logical argumentation. For example, in Topic C, students estimate sums and differences with fractions by asking questions such as the following: "Will your sum be less than or greater than one half? One? How do you know?" These questions encourage students to reason, reflect, and justify before solving. Modules 1–6 of the grade 5 Versión del maestro provide TEKS-aligned assessments at the lesson and unit level. Each lesson includes exit tickets that assess key learning, while mid- and end-of-module assessments use varied question types and challenge levels. These assessments require students to demonstrate understanding through estimation, explanation, and strategy use, supporting deep learning across the module.

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

The materials include tasks and assessments in modules that provide students with scaffolding as support. The materials progressively increase in rigor and complexity, incorporating grade-appropriate question sets that lead to grade-level proficiency. In Module 3 of the grade 5 Versión del maestro, Lesson 8 shows how tasks increase in rigor and complexity. The lesson begins with a "Práctica de fluidez" section to review prior learning. During the "Desarrollo del concepto" section, students move from identifying equivalent fractions to solving more complex problems that involve adding and subtracting fractions with unlike denominators. The lesson concludes with a debrief that supports critical thinking and discussion. In Module 2 of the grade 5 Versión del maestro, Lesson 33 presents a clear progression in rigor and complexity. Problem sets begin with basic unit conversions in Problem 1 and advance to more complex problems in Problem 3, in which students use area to determine perimeter. Problem 4 demonstrates a further increase in rigor by requiring unit conversions between kilometers and meters while solving for area based on perimeter values.

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

The grade 5 materials demonstrate coherence across units by connecting place-value understanding developed in earlier grades to operations with decimals. In Module 1, students extend patterns from whole number place value to decimals and use these patterns to solve real-world metric measurement problems. The grade 5 Guía del curso states the following: "Los patrones de números enteros con discos numéricos en la tabla de valor de posición se generalizan fácilmente a números decimales." This guidance supports conceptual continuity from prior grade levels using manipulatives, allowing students to progress from concrete to representational to abstract models. The materials also connect students' understanding of fractions to volume, area, and algebraic thinking across modules. In Module 5, the grade 5 Guia del curso explains that students apply their prior fraction knowledge to measure area and volume with fractional side lengths. In the final module, students investigate numerical relationships on the coordinate plane. This progression builds conceptual bridges between geometry, numbers, and algebra. The grade 5 Guía del curso states the following: "Los estudiantes conectan la geometría plana con el trabajo numérico para investigar las relaciones…lo que anticipa el razonamiento proporcional de grado 6." The materials thus make explicit connections across mathematical concepts.

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 materials build on familiar content and language models from earlier grades to support new learning in grade 5. For example, in Module 3, students connect their prior understanding of part-to-whole relationships and unit equivalence from grade K through grade 4, such as adding "ones to ones" or "liters to milliliters." Students apply this knowledge to their addition and subtraction of fractions using unlike denominators. Visual tools such as rectangular fraction models, tape diagrams, and number lines help students apply earlier mathematical language in more complex contexts. Module 3 of the grade 5 Versión del maestro explicitly prepares students for middle school algebra by shifting from base-ten units to fractional units as the foundational building blocks of mathematical reasoning. For example, the "Contenido general" section of Module 3 states the following: "Este módulo marca un cambio significativo desde la centralidad de las unidades de base diez en K–4 hacia el estudio y el uso del entero completo de unidades fraccionarias a partir de 5to grado, especialmente en su aplicación al álgebra." This statement connects what students are currently learning to what they will learn in the future, making purposeful connections to the TEKS across vertical grade levels.

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..

Module 5 of the grade 5 Versión del maestro demonstrates coherence within the current grade level by sequencing instruction to build on prior learning from earlier lessons. In grade 5, Module 5, Topic B, students apply an understanding of volume that they developed in earlier lessons by transitioning from the concrete counting of unit cubes to using multiplication to determine the volume of rectangular prisms. The materials state the following: "Comprensión concreta del volumen y razonamiento multiplicativo (TEKS 5.6A) se unen en el Topic B a medida que el recuento sistemático del Topic A conduce de forma natural a fórmulas para encontrar el volumen de un prisma rectangular…." The materials thus draw upon students' prior knowledge from previous lessons. The materials demonstrate vertical coherence by explicitly connecting grade 5 content to foundational learning from grade 3. In Module 5, Topic B, students use their prior understanding of area and multiplication from grade 3 to reason about volume in three dimensions. The materials reference this connection directly in a chart that states "Coherencia - Se desprende de: G3–M4 multiplicación y área." This chart shows how students make connections between previously learned concepts (such as multiplication and area) to new on-grade-level learning. Students apply their prior knowledge to solve for the volume of shapes.

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

The grade 5 materials provide spaced retrieval opportunities through fluency. For example, Module 5, Lesson 6 begins with a 12-minute fluency section that revisits prior skills, including multiplying a fraction by a whole number (TEKS 5.3I), counting by cubic centimeters (TEKS 5.6A), and finding volume (TEKS 5.6B). These tasks directly reinforce content taught in earlier modules, such as fraction operations in Module 4 and foundational volume concepts from grade 3. The materials thus offer spaced retrieval opportunities across multiple grade levels and units. The materials in grade 5, Module 5 incorporate the intentional and systematic spaced retrieval of key mathematical concepts, particularly the concept of volume as both additive and multiplicative. In Lesson 6, students revisit and deepen their conceptual understanding of volume from earlier lessons by applying the formulas "V = l × a × h" and "V = Bh" to complex figures.

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

The materials provide strong interleaved practice by embedding previously taught skills—such as multiplication, area, and unit conversions—within new applications involving volume and composite figures. This integration occurs across multiple topics and reinforces students' procedural fluency through varied problem types. For example, Module 5 of the grade 5 Versión del maestro states the following: "Los estudiantes combinan los conocimientos previos sobre el área con los recién adquiridos sobre la multiplicación de fracciones para determinar el área de figuras rectangulares con longitudes laterales fraccionarias." This statement explains how students practice and apply previously learned skills in the context of new learning. The materials reinforce conceptual understanding across lessons by intentionally revisiting foundational volume concepts that students learned in earlier units. For example, Module 5 of the grade 5 Versión del maestro includes a "Contenido general" section, which states the following: "Los estudiantes solidifican la conexión del volumen como empacado con el volumen como llenado…comparando la cantidad de líquido que llena un recipiente con el número de cubos que pueden agruparse en él…La complejidad aumenta a medida que los estudiantes utilizan sus conocimientos de que el volumen es aditivo." This statement explains how the materials prompt students to draw on previously learned concepts to determine that volume is composed of unit cubes that fill the inside of a shape.

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

In grade 5, Module 2, the"Aprender operaciones con números enteros de varios dígitos y fracciones decimales" section of the Aprender versión del estudiante includes questions and tasks that require students to interpret and evaluate area models for multiplication problems, such as "34 × 21" and "434 × 21." Students must make sense of how each section of the model represents parts of the multiplication expression. This type of model interpretation appears consistently across all seven student modules in the grade 5 Aprender version del estudiante. Grade 5, Module 2 of the Aprender versión del estudiante includes an "Aprender operaciones con números enteros de varios dígitos y fracciones decimales" section. This section includes questions and tasks that require students to analyze area models by drawing arrows to match partial products with the corresponding parts of the standard algorithm. Modules 1–6 in the Aprender version del estudiante include similar opportunities for model analysis.

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

The materials consistently require students to create models to demonstrate understanding. In grade 5, Module 1, Lesson 1, the "Problema de aplicación" section of the Aprender versión del estudiante asks students to do the following: "Expliquen su razonamiento utilizando palabras, números o imágenes." This open-ended prompt encourages students to generate their own visual or numerical models, supporting conceptual understanding through student-created representations. This type of question appears throughout Modules 1–7 of the Aprender versión del estudiante. Tasks throughout Modules 1–7 of the Aprender versión del estudiante include opportunities for students to create models that represent mathematical concepts. For instance, in Module 1, Lesson 1, the "Grupo de problemas" section asks students to do the following: "Haz un dibujo de cómo era la tabla de valor de posición al principio." This task prompts students to construct a visual representation of place value, demonstrating their understanding of digit placement and numerical operations.

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

The materials include questions that require students to apply their conceptual understanding in new problem contexts. For example, in grade 5, Module 1, Lesson 2 of the Version del estudiante, the "Problema de aplicación" section asks students to do the following: "Un distrito escolar encargó 247 cajas de lápices...Dibujen una tabla de valor de posición para mostrar su razonamiento." This task challenges students to extend their understanding of place value and multiplication to a real-world application. Questions such as this appear consistently across Modules 1–7 of the Versión del estudiante. The materials include tasks that push students to apply their conceptual understanding in unfamiliar contexts. For example, in grade 5, Module 1, Lesson 2, the "Grupo de problemas" section of the Versión del estudiante prompts students to do the following: "Escriban una ecuación que cambie el valor del dígito 7 a 7 centésimas." This task requires students to manipulate decimal values conceptually rather than procedurally, demonstrating place value knowledge. The materials consistently embed this type of task across grade 5, Modules 1–7 of the Versión del estudiante, providing multiple opportunities for students to apply their knowledge to new contexts.

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

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

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

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

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

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

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

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

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

Modules 1–6 of the grade 5 Versión del maestro include "Topic" sections, which outline how to address the conceptual emphasis of the TEKS. For example, in Module 5, Topic A, the materials guide students to develop an understanding of volume as a measurable attribute of three-dimensional space. Students engage in hands-on experiences with unit cubes, construct and decompose rectangular prisms, and make predictions about the number of cubes required to fill a figure. These experiences build students' conceptual understanding before introducing formal formulas. The program emphasizes the relationship between volume, spatial structuring, and repeated addition or multiplication, reinforcing the TEKS-aligned focus on reasoning and the real-world application of mathematical ideas. Instruction intentionally sequences tasks to promote conceptual development before procedural practice. The materials state how the procedural emphasis of the TEKS is addressed by sequencing lessons in a manner that transitions from conceptual understanding to procedural fluency. In grade 5, Module 5, Topic B, students use formulas such as "V = l × w × h" and "V = Bh" to calculate the volume of rectangular prisms, including cubes as a special case. The materials offer repeated opportunities to practice applying formulas in varied contexts, reinforcing procedural accuracy and alignment with TEKS 5.6B and 5.4G. Instruction includes guided practice, visual models, and sentence frames to support students in verbalizing the steps used to solve problems. After instruction, students apply such procedures independently.

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.

Modules 1–6 of the grade 5 Versión del maestro include activities that require students to use concrete models to represent mathematical ideas across lesson tasks. For example, in Module 2, Lesson 5's "Desarrollo del concepto" section, the teacher directs students to use individual whiteboards to draw tape diagrams and model expressions such as "3 veces la suma de 26 y 4." The "Desarrollo del concepto" section repeatedly provides such modeling with hands-on tools. The materials frequently use pictorial representations to support students' conceptual understanding. In Module 5, Lesson 9's "Reflexión" section and Lesson 11's "Desarrollo del concepto" section, students interpret and draw area models and decompose rectangles to visualize multiplication problems such as "600 × 10" and "400 + 60 + 3." The materials consistently present abstract mathematical representations across lessons. For example, in Module 2, Lesson 28's "Grupo de problemas" section and Lesson 31's "Reflexión" section, students solve problems using equations such as "54 ÷ 90" and "14.7 ÷ 21." Students estimate quotients and justify decimal placement using numeric strategies. These tasks provide multiple opportunities to engage with symbolic and algorithmic representations, as required by the TEKS.

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

The materials support students in connecting concrete and pictorial models to abstract mathematical ideas. In Module 5, Lesson 9's "Reflexión" section, students compare decompositions shown in area models to the standard algorithm and explain which method they prefer. This task strengthens students' understanding of the relationship between models and symbolic notation. In Lesson 11's "Desarrollo del concepto" section, the lesson guides students to relate their visual models to numeric expressions, reinforcing abstract connections. The materials provide structured opportunities throughout all of the modules for students to create both concrete and pictorial models from abstract expressions. For example, in Module 2, Lessons 5 and 28 require students to build strip diagrams and area models to represent numerical problems such as "(26 + 4) × 3" or "463 × 21." Such tasks prompt students to interpret verbal or numeric expressions and translate them into visual or constructed representations. The materials prompt students to define and explain the relationship between concrete or pictorial models and abstract concepts. In Module 2, Lesson 5's "Desarrollo del concepto" section and Lesson 9's "Reflexión" section, teachers ask students to respond to questions such as "¿Por qué hay paréntesis alrededor de 26 + 4?" and "¿Cuál modelo prefieres y por qué?" These prompts require students to articulate their mathematical thinking and explain how models represent symbolic relationships.

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

In grade 5, Module 1, Lesson 1 of the Versión del maestro, the materials embed multiple opportunities for students to engage with consistent visuals. These visuals include "tablas de valor de posición con etiquetas para centenas, décimas y milésimas" to support students' conceptual understanding and mathematical language. The materials emphasize manipulatives such as "discos de valor de posición" as a core tool for students to represent place value relationships across units, tenths, hundredths, and thousandths. Additionally, the lesson embeds language routines such as chorally renaming units, saying "10 unidades = 1 decena," sentence stems, and repeated oral practice to reinforce vocabulary and syntactic structures. These strategies, which can be found across all modules, build students' academic mathematical language through multiple language development strategies. In grade 5, the lessons across Modules 1–6 of the Versión del maestro consistently incorporate visuals to support student understanding. For example, grade 5, Module 5, Lesson 9 of the Versión del maestro utilizes visuals and area models to review fractional multiplication and area. The materials prompt students to draw and decompose rectangles using visual models with dimensions in fractional units. The materials encourage teachers to use mosaicos concretos or dibujos en la pizarra to reinforce vocabulary and visual understanding. Structured partner talk (e.g., "Hablen con su compañero…") and sentence scaffolds (e.g., "La regla nos permite medir los lados…") further support students' language development. These strategies build both conceptual and linguistic skills.

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

The materials embed teacher-facing guidance that supports the development of academic mathematical vocabulary. For example, in the "Desarrollo del concepto" section of grade 5, Module 1, Lesson 1 in the Versión del maestro, the materials include prompts such as the following: "¿Qué patrones observan en la forma en que se nombran las unidades en nuestro sistema de valor de posición?" The materials guide educators to foster mathematical vocabulary by using scaffolds for students as support. For example, in the "Problema de aplicacion," teachers tell students to "expliquen su razonamiento utilizando palabras, números o imágenes," providing students with multiple ways to show their answers. The materials also guide teachers to model mathematical terms and encourage students to label the numerical positions, such as, "Etiqueten la posición de las milésimas." Such guidance helps students use the terms meaningfully in context. Teachers model specific vocabulary for students to use during peer discussions and explicitly expect students to use these terms in context. Visual prompts and teacher cues, which the materials embed throughout all lessons across all modules, support students in using and internalizing academic vocabulary related to area.

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.

All modules and lessons consistently promote student discourse through repeated partner talk and embedded teacher questioning strategies. For example, the materials incorporate teacher prompts such as "Compartan su respuesta" and "Expliquen su razonamiento." Such prompts demonstrate how teachers guide student responses. The materials weave sentence structure and academic modeling throughout the lessons, helping students incorporate mathematical reasoning into their responses. The materials guide teachers to prompt explanations of area equations using visuals and manipulatives, reinforcing content and language development. The materials provide exemplar responses to support accurate and complete student responses during both guided instruction and independent practice. The "Desarrollo del concepto" teacher script includes explicit vocabulary modeling of mathematical language across all units in the materials. For example, grade 5, Module 1, Lesson 1 of the Versión del maestro includes terms such as milésima, centésima, and décima. The lesson also includes instructions for students to articulate relationships using complete statements, such as "1 unidad de millón ÷ 10 = 1 centena de millar." The materials support syntax through sentence frames and modeled equations, which are embedded in the teacher's explicit modeling. The materials promote discourse through partner conversations, whole-group chorals, and peer explanations using prompts such as "Hablen con su compañero y utilicen su tabla para encontrar el cociente." These structures guide students to apply precise math language in increasingly independent ways.

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

The materials integrate the TEKS process standards appropriately throughout instructional routines and module activities. The grade 5 Guía del curso emphasizes collaborative problem-solving to address student misconceptions using a three-step routine: "estimular el pensamiento en los estudiantes, validar lo que el estudiante hizo bien y crear un puente a una mejor comprensión." This guidance reflects the integration of the TEKS process standards, such as analyzing student thinking (5.1F) and using problem-solving strategies (5.1A). Modules embed this three-step routine in math tasks and dialogue, reinforcing the continuous use of process standards in instruction. In grade 5, Modules 1–6 of the Versión del maestro, the materials integrate the TEKS process standards appropriately across lessons. Students represent, communicate, and justify mathematical ideas using models, tools, and problem-solving strategies. For example, in Module 5, Lesson 9, students estimate, measure, decompose, and calculate the area of rectangles with fractional side lengths using rulers, visual models, and partner discussions. The materials guide teachers to ask questions such as "¿Cuál es el área? ¿Cómo lo sabes?" The materials also guide teachers to encourage students to explain their thinking using visual and numerical representations. These opportunities align with the TEKS process standards, including reinforcing appropriate tool use (5.1B), mathematical communication (5.1C), and the representation of ideas through concrete and pictorial models (5.1G).

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

The grade 5 Guía del curso in the Versión del maestro outlines how the materials embed the TEKS process standards across the year. The "Perfil de un estudiante de matemáticas de grado 5" section explains that instruction is designed around esfuerzo productivo, in which students explain their reasoning, analyze mistakes, and engage in mathematical discourse. All modules sustain this approach using teacher behaviors and prompts (e.g., "Me gustaría que explicaras tu razonamiento…") to promote process standards such as 5.1B and 5.1F. These behaviors and prompts can be found in the "Curso de aprendizaje en grado 5," which also describes reflective routines that help students track their thinking before and after assessments. The materials thus align with expectations concerning the TEKS process standards. The grade 5 Guía del curso in the Versión del maestro connects process standards across modules by emphasizing recurring instructional structures and cognitive routines. For example, the materials describe how reasoning strategies that were introduced in earlier modules, such as place value using decimals, are extended and connected to fraction work in later modules. The module progression in the materials explicitly builds on earlier skills and reuses instructional dialogue strategies. In doing so, the module progression demonstrates vertical and conceptual connections between process standards, such as justifying solutions and using representations across different content areas.

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

The grade 5 Guía del curso in the Versión del maestro includes an "Estándares" section, which appears in the "Alcance y secuencia de grado 5" within each module. This section highlights the TEKS content and process standards. For example, Module 1 lists TEKS 5.1A, 5.1B, 5.1E, 5.1F, and 5.1G (among others)—process standards that are intentionally planned for use in decimal operations. The teacher's instructional guidance directly applies these standards through problem-solving, modeling, and student explanation tasks, which are embedded in each unit's design. The grade 5 Guía del curso in the Versión del maestro includes module descriptions that show a clear connection of process standards across and within units. For instance, in Module 2, students extend their understanding of multiplication and division by applying estimation and algorithmic strategies. TEKS 5.1A, 5.1F, and 5.1D support these strategies. Each module incorporates the "Solución colaborativa de problemas" routine, illustrating the continued connection of process skills to content, assessment, and error analysis throughout the unit's progression.

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

The grade 5 Guía del curso in the Versión del maestro includes a comprehensive chart titled "Estándares de procesos matemáticos de grado 5 por lección de cada módulo." This chart maps each TEKS process standard, such as 5.1A–5.1G, to specific lessons throughout Modules 1–6. The chart provides teachers with an at-a-glance reference to identify where and how the materials address each process standard, ensuring alignment with the TEKS framework. Modules 1–6 in the Versión del maestro include a "Contenido general del modulo" section. This section references the TEKS process standards that the materials integrate throughout each module's instruction. The module overview explicitly cites how students engage with standards such as 5.1C, 5.1D, and 5.1F. Moreover, it explains how students apply repeated reasoning, justify their thinking, select tools, and communicate mathematical ideas while working in fraction multiplication and personal finance contexts. This module-level overview supports planning and demonstrates how the materials intentionally embed process standards across lessons.

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

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

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

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

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

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

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

The materials include teacher-facing prompts and structures that guide students to explain and justify their problem-solving approaches. The "Discurso y elaboración" section of the K–5 guía de programa e implementación instructs teachers to use prompts such as "Comenten con sus compañeros, ¿Qué acaba de ocurrir?" and "Explícale a tu compañero los pasos que tomaste para resolverlo." These prompts encourage student-generated explanations and mathematical arguments during class discussions. The materials provide multiple embedded opportunities for students to reflect on their reasoning and strategy selection. The "Reflexión" section outlines how teachers guide students to connect their choices to prior problems, lesson goals, and mathematical models. Sample teacher questions include the following: "¿Cómo nos ayudaron nuestras actividades de fluidez…con nuestro trabajo de redondeo hoy?" Such questions support structured reflection that is linked to problem solving.

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

The materials include scripted feedback prompts within the "Rutinas de resolución de problemas" section. These prompts help teachers respond to student misconceptions in real time. For example, the materials prompt teachers to say, "Veo cómo empezaste con un enfoque y cuando eso no funcionó, en vez de rendirte, intentaste una estrategia diferente." Another prompt directs teachers to say, "¿Qué es lo que ya sabes? ¿Qué es lo que pregunta el problema?" These prompts explicitly acknowledge and productively redirect students' thinking. The prompts model how to affirm effort while guiding students toward conceptual clarity. The materials include multiple forms of teacher-facing guidance for responding to student reasoning. Margin notes labeled "Notas sobre diferentes formas de representación" and "Participación" offer suggestions for adjusting instruction based on observed student responses. Prompts such as "Resalte la palabra por y el signo x con otro color" help teachers reinforce meaning when students misinterpret symbols. The materials also highlight ways to extend feedback through metacognitive prompts such as "¿Cómo muestra tu dibujo la manera en que resolviste el problema?"