enVision+ Texas Matemáticas, 05

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

The Guía del ritmo de enseñanza, grado 5 includes “Contenido y secuencia” documents for 165-day, 180-day, and 210-day instructional pathways. These resources delineate the sequential order of mathematical concepts such as place value, fractions, and decimals. A Texas Essential Knowledge and Skills (TEKS) correlation table in the Guía del maestro program overview itemizes every grade 5 mathematics TEKS and identifies the specific lessons in which each TEKS is introduced, practiced, and assessed.

Additionally, in the Guía del maestro section “Vistazo del tema,” the “TEKS” column connects the standards to the corresponding lessons. In lesson 1-1, “Valor de posicion,” students apply TEKS 5.2B along with process standards 5.1D and 5.1F. The Guía del ritmo de enseñanza outlines both the standards and the course concepts. This resource identifies the specific topics students encounter throughout the year, including place value, operations, fractions, measurement, and financial literacy.

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 the Guía del ritmo de enseñanza, which provides differentiated pathways, utilizing “Essential” lessons for compressed 135-day schedules and “Extension” activities for expanded 210-day calendars. Furthermore, the grade 5 scope and sequence outlines the number of instructional days and TEKS covered per unit, organized by topic and lesson.

Additionally, the materials include an instructional sequence organized by topic in the Guía del maestro program overview. The “Contenido y secuencia” tables correlate TEKS coverage with suggested instructional days per unit. These tables embed specific days for differentiation and evaluation while providing suggested pacing, calculated in minutes per lesson, for 135-, 165-, 180-, and 210-day school calendars.

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.

In the program overview, the “Grade 5 Content Organization Rationale” explains the sequence of units and demonstrates how mathematical concepts connect throughout the course. The topics are organized around key concepts to support coherence, sequence content to connect new learning to prior knowledge, and spiral TEKS across multiple lessons to reinforce connections. For example, topics 1–6 focus on place-value patterns, whole-number operations, and decimal relationships to build computation fluency, which directly supports the subsequent fraction and decimal strategies in topics 8–9. Additionally, the “Key Concept” and “Connections” sections, along with the “Organized to Build Connections” chart, outline the progression and development of these mathematical ideas across all units.

Also in the Guía del maestro, “Contexto matemático: conceptos clave” and “Coherence” sections at the start of each topic connect the TEKS across prior, current, and future learning. The materials outline the rationale for the unit order, while the “Looking Back,” “In This Topic,” and “Looking Ahead” subsections show how mathematical concepts progress. In topic 1, “Entender el valor de la posición,” the “Vuelve atrás” and “Más adelante” fields state how grade 5 students build on prior skills to learn decimal number operations and fraction multiplication and division. The text details how this learning connects to grade 6, where students relate decimals to percents, and to topic 4, in which students evaluate expressions containing fraction multiplication and solve one-step equations with fraction operations.

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

The “Protocolo de internalización del tema” provides a framework to analyze pacing, TEKS integration, learning progression, differentiation, and material preparation. The “Protocolo de internalización de la lección” outlines lesson objectives, vocabulary, formative assessments, and lesson resources to align daily plans with instructional goals. Additionally, the “Protocolo de análisis del trabajo de los estudiantes” contains steps for educators to evaluate student work, identify misconceptions, and determine subsequent instructional steps.


Additionally, the materials include internalization protocols and implementation guides for student work analysis, such as the “Protocolo de análisis del trabajo del estudiante para líderes de la enseñanza,” which provides a framework to identify patterns, address misconceptions, and set instructional priorities. For example, lesson 1-3, “Comparar números decimales,” includes lesson and language objectives, TEKS alignment, vocabulary support, manipulatives, and guidance for connecting prior learning.

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

The “Protocolos de internalización y herramientas para observación” contains specific tracking and review resources, such as the “Protocolo de internalización de la lección para los líderes de la enseñanza” and the “Protocolo de análisis del trabajo del estudiante para los líderes de la enseñanza.” These tools, along with the “Protocolo de análisis del trabajo de los estudiantes,” allow instructional leaders to systematically review assessments and student work to identify misconceptions, analyze student thinking, and plan targeted instructional next steps based on student achievement.


Additionally, the materials include administrator observation guides with specific look-fors that help administrators document key indicators during classroom observations. The “Protocolos de internalización y herramientas de observación” include indicators related to educator preparation and practice, student preparation, and action plans after the administrator walkthrough.

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 materials provide comprehensive unit overviews containing the background content knowledge and academic vocabulary necessary to teach the concepts in each unit. At the beginning of each topic in the Guía del maestro, the “Contexto matemático” section details mathematical content, outlines instructional sequencing, and introduces essential terminology. For example, in topic 2, “Contexto matemático,” the text introduces academic vocabulary, including representing,estimation, decimals, and explains the instructional progression from decimals place-value to addition, subtraction, and multiplication of decimals.

Additionally, each unit overview includes a “Coherence” section that maps TEKS alignment across grades using “Looking Back,” “In This Topic,” and “Looking Ahead” frameworks. Furthermore, at the start of each topic in the Guía del maestro, the “Adaptaciones del lenguaje” section provides vocabulary scaffolding. For example, in topic 2, this section details required topic terminology, identifies critical prerequisite and upcoming academic vocabulary, and outlines instructional guidance for teaching targeted words in context to enable student comprehension.

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 provide unit-level family engagement resources in both English and Spanish to support student progress. For example, on the digital platform, the “Participación de la familia” (“Family Engagement”) section features topic-level overviews outlining lesson goals, video guides, worked-out mathematical examples, and at-home learning tasks. These resources outline everyday practice suggestions, such as calculating calories in multiple food servings or finding the total cost of monthly household bills, to reinforce multiplication skills at home.


Additionally, the “De la escuela al hogar” (“Home–School Connection”) letter provides families with an overview of topic concepts, learning goals, and lesson examples. To reinforce skills at home, these bilingual letters detail instructional activities and guidance for practicing with everyday materials and mathematical language.

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).

On the digital platform, each grade 5 lesson includes a lesson plan overview titled “Elaboremos.” This overview outlines the instructional foundation of the lessons by breaking it down into three core components: “Conceptos clave,” which defines the content objectives; “Coherencia,” which contextualizes the lesson within the broader curriculum, and “Equilibrio,” which addresses conceptual understanding.

Additionally, at the start of every lesson, the Guía del maestro outlines the TEKS alignment, daily learning objectives, and necessary materials. The lesson structure integrates targeted questions, tasks, and instructional assessments. Lessons include concept and language objectives, discussion questions within the “Aprendizaje visual” section, hands-on tasks using manipulatives, and instructional assessments such as “Comprobación rápida,” exit tickets, and guided practice.

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 Guía del maestro materials include editable lesson plans that list the required materials and provide time management suggestions for each component. The first page of the lesson overview in “Planes de lecciones” lists the specific educator and student materials needed for delivery. Additionally, the materials provide pacing for exploration, visual learning, practice, and assessment activities.

Furthermore, the lesson plans outline the layout of the instructional day by providing the suggested lesson timing, denoted in minutes, for each part of the lesson within the “Cronología de la lección” section. Throughout the lesson, clocks and time stamps at the top of the pages identify the recommended pacing for each component.

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

In the Guía del maestro, the step 4 component “Evaluar y diferenciar” contains a “Comprobación rápida” formative assessment. Student results from this assessment guide remediation, practice, or extension opportunities. The “Actividad de intervención” section provides educator support for students who need additional intervention, while the “Práctica adicional” section provides printable and automatically graded activities for continued student practice.

The materials also identify resources for extended practice and enrichment, including the “Reteach to Build Understanding” activities, enrichment activities, “Build Mathematical Literacy” activities, and the “Biblioteca de diferenciación,” which offers projects, math and literacy connections, collaborative problem-solving activities, games, and fluency practice.

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 Cuaderno de evaluación features diagnostic exams, unit-specific tests, and lesson-level formative tools to evaluate student performance throughout the course. For example, topic 9, “Entender la multiplicación y la división con fracciones,” includes a multiple-choice and fill-in-the-blank evaluation, an evaluación del tema, tareas de rendimiento, autoevaluaciones, and exit tickets. These tools establish evaluation checkpoints across the course material by utilizing different assessments, task types, and question formats.

Additionally, each lesson in the Guía del maestro contains embedded formative assessment opportunities. For example, the “Guided Practice” section follows visual learning to measure initial student understanding, the “Quick Check” provides data for daily differentiation, and the “Exit Ticket” section provides data for upcoming lessons.

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

Within the Cuaderno de evaluación, an assessment guide section specifies the types of evaluations, which include progress monitoring, diagnostic, formative, and summative assessments. Furthermore, this component explains the purpose and administration schedules for each assessment type. It outlines and details the intended instructional outcomes associated with these evaluations.

Additionally, each lesson within the Guía del maestro includes a formative assessment, or exit ticket, to support student learning and guide instruction. Furthermore, every lesson features an evaluation and differentiation section containing a “Comprobación rápida” to assess mastery of the lesson content.

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

The Cuaderno de evaluación contains a “How to Administer Assessments” section detailing the purpose, timeline, content, and methodology of the evaluation process. This component provides recommended time allotments, protocols for dividing assessments across class periods, step-by-step procedures for preparation and monitoring, and directions for educators to read aloud to students during testing.

Additionally, the Guía del maestro provides administration guidance for each lesson’s “Exit ticket,” detailing its specific use and purpose.This guidance continues into the step 4 “Assess and Differentiate” section, in which “Quick Check” pages provide specific directions on administering and scoring assessments to determine differentiated instruction.

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

The Cuaderno de evaluación contains item analysis charts that map each question on progress monitoring, diagnostic, and summative evaluations to its corresponding TEKS and objectives. In addition, materials include diagnostic tests, incorporate formative assessments such as “Quick Check” and “Exit Ticket” activities, as well as a topic assessment and topic performance task for summative evaluation.


Additionally, within the Guía del maestro, the step 4, “Assess and Differentiate” section in each lesson includes an additional practice assessment to reinforce skills, alongside an item analysis chart aligning each problem set with the TEKS.

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

The Cuaderno de evaluación includes item analysis charts that align each question in the progress monitoring, diagnostic, and summative assessments with a specific Depth of Knowledge (DOK) level. For example, the “Evaluación para observar el progreso, Forma A” evaluates course content through diverse item types, including multiple-choice, text-entry, and open-response questions. The “Tabla de análisis de las preguntas” identifies the specific TEKS aligned to each assessment item to verify consistency between instruction and assessment expectations.


Additionally, within the Guía del maestro, step 4 of each lesson includes a practice assessment to reinforce skills, along with an item analysis table that categorizes exercises by problem complexity levels and designates the core mathematical standard tested.

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

The Cuaderno de evaluación includes assessment and data resources that help educators examine and discuss student work on assessments. This resource explains how to use assessment data criteria for forming groups and making decisions on differentiation, and it includes printable versions of all topic- and lesson-level assessments.


Additionally, the “Guía de puntaje: evaluación para observar el progreso” tool provides completed sample responses, correct answers, and a “Tabla de análisis de las preguntas” to identify aligned TEKS for each lesson. For instance, the scoring guide for the topic 1 performance task aligns each specific theme task with TEKS 5.2.A, 5.2.B, and 5.2.C and process standards 5.1.D and 5.1.G.

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 Cuaderno de evaluación, accessible from the online platform, includes item analysis charts, answer keys, and performance task scoring rubrics. These rubrics provide performance criteria to help educators evaluate whether the student demonstrates conceptual understanding to identify and address misconceptions. The “Tabla de análisis de las preguntas” is a diagnostic tool that pairs assessment items with intervention lessons and the corresponding TEKS, providing data to inform instructional decisions.

Additionally, the Guía del maestro includes an “Hablemos de matemáticas” section for each lesson that features a TEKS-aligned warm-up activity. For example, lesson 5-5, “Usar cocientes parciales para dividir,” offers guidance on having students analyze and describe equations and work in pairs to collaborate on the inverse relationship between multiplication and division aligned with TEKS 5.3C.

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 “Herramientas del maestro para supervisar el progreso del estudiante” tool set allows educators to track student understanding and progress sequentially throughout each topic. In addition, the materials feature student progress and growth monitors to document growth before, during, and after topic instruction. For instance, in lesson 1-2, the tool displays student self-assessments to determine student progress in representing the value of digits in decimals in different ways, alongside recording whether a student is working on, almost meeting, or meeting each aligned TEKS.


Additionally, in the Guía del maestro, the materials integrate lesson overviews with TEKS-aligned exit tickets that offer a quick formative assessment. Educator notes explain how to use these results for targeted support, including a student self-assessment rubric.

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

In the Guía del maestro, lesson 6-1, “Describir patrones para dividir con números decimales,” contains the section “Práctica guiada,” which delivers targeted support for students who demonstrate difficulty understanding why dividing by 50 produces a smaller quotient. The materials provide guiding questions, visual representations, and instructional suggestions to address student misconceptions. Additionally, the section “Actividad de intervención” provides a scaffolded, educator-directed activity that uses number cards and decimal models to reinforce the concept and offer additional practice. Furthermore, the materials direct educators to use place-value charts and guided practice to demonstrate how the decimal point shifts when dividing by 10 and 100. This activity incorporates educator explanations, visual models, and scaffolded questions to connect place-value concepts to decimal division.

Additionally, the online platform includes a “Sistema de intervención,” which provides mini-lessons to address skills and content for which students have not yet demonstrated proficiency. For example, the mini-lesson “Comparar y ordenar números racionales” incorporates instructional materials, vocabulary terms, manipulatives, and pictorial models. Within the guided practice, the material provides educator guidance to address student errors, deliver intervention strategies, offer extended activities, and utilize formal evaluations to monitor student progress.

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

In the Guía del maestro, the section “Adaptaciones de lenguaje” delivers contextual explanations for cognates, meta-linguistic transfer, and topic-specific academic vocabulary. In topic 6, “Usar modelos y estrategias para dividir números decimales,” the topic opener incorporates pre-teaching activities to review mathematical terms and directs educators on how to introduce foundational academic language, including terms such as residuo and datos and contextual vocabulary such as convertir.

Additionally, the online platform and educator materials provide pre-teaching and embedded vocabulary supports to reinforce mathematical terms. For example, the online platform features a “Mis tarjetas de palabras” section in which vocabulary cards introduce key mathematical terms using visual models, examples, and student-friendly definitions. Students interact with this resource by matching terms to definitions, connecting terms to mathematical concepts, and creating their own explanations. During this process, participants use the words on the front of the cards to complete the definitions on the reverse. To reinforce these concepts, the Guía del maestro includes a language support activity within each “Elaboremos” section.

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.

Each lesson includes an “Early Finishers” component, such as the “Comprobación rápida” feature, which directs educators to assign targeted enrichment activities based on student performance. For example, in topic 7, lesson 7-5, “Hacer gráficas de barras,” students scoring 4–5 points on the “Comprobación rápida” transition to advanced tasks within “Práctica adicional.” In these tasks, students create, analyze, and interpret bar graphs; compare datasets; and apply mathematical reasoning to complex data-representation tasks. Additionally, the “Hablemos de matemáticas” activity and the “Apoyo al lenguaje” section provide discussion prompts to facilitate data analysis, data-set comparison, and communicating mathematical ideas.

Furthermore, the “Biblioteca de diferenciación” contains resources for enrichment and extension, including “Pick a Project” activities. Within these activities, the first project in each topic directs students to develop a “Math Walk” to highlight real-world mathematical applications. For example, project 1D, “Investiga medidas en nuestro sistema solar,” instructs students to research the distance from the Sun to each planet using print or digital resources. Students create a table to record each distance in miles and write each number in standard, word, and expanded forms. The project also requires students to research and record additional planetary measurements, such as the distance Mercury travels around the Sun in one year, the size of Jupiter’s Great Red Spot, or the orbital period of Neptune, to apply place-value and data collection concepts in a real-world context.

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

In lesson 7-3, “Hacer diagramas de puntos,” within the “Apoyo del lenguaje” section, the materials scaffold academic vocabulary by providing a specific script with questions that ask what the word ocurrir means in a daily-life context versus a mathematical context, along with expected student responses to guide the explanation of data frequency. Furthermore, under the “Hablemos de matemáticas” section, the materials outline a clear, explicit instructional routine for data collection and representation aligned with TEKS 5.9.A. This feature instructs educators to systematically collect numerical data, display all responses, and model the collaborative creation of a dot plot, ensuring that the conceptual transition from raw data to visual representation is explicitly structured and conceptually grounded for learners.

Additionally, in lesson 7-1, “Reunir, representar y analizar datos” features an investigation section that provides actionable instructions for setting up mathematical investigations. For example, the “Anticipar” section directs educators to front-load instruction by considering how students might use prior knowledge to solve problems, guiding them with real examples of student work. In the “Presentar la investigación” section, the materials model the exact use of digital tools, specifically diapositivas de revelación lenta, to break down information sequentially. This section also provides precise text for guiding questions like “¿Qué notan?” and “¿Qué se preguntan?” (“What do you notice? What do you wonder?”). Finally, to bridge student understanding and amplify student ideas, the materials embed an explicit script under the “Potenciar la voz del estudiante” section, which gives educators targeted prompts to systematically connect personal experiences to statistical concepts.

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

In lesson 7-7, “Hacer gráficas de tallo y hoja,” the “Explorar y comentar” section directs the educator through an initial inquiry-based strategy. The lesson transitions into collaborative peer structures in the “Supervisar, seleccionar y poner en secuencia” section for small groups and transitions in a shared synthesis during the “Relacionar” whole-class activity. The “Hablar sobre las ideas matemáticas” section incorporates a think-pair-share routine, while the “Apoyo al lenguaje” and “Rutina de lenguaje” sections provide targeted linguistic scaffolds. Finally, the materials prompt educators to manage misconceptions in the “Prevenir malentendidos” section, sequence student work from concrete to abstract, and wrap up concepts using the “Volver a la pregunta esencial” protocol.

Additionally, the Guía del maestro materials describe three explicit lesson types, “Investiguemos,” “Elaboremos,” and “Representémoslo en 3 actos,” and outline how educators can deliver instruction through a variety of teaching methods in each format. For example, the “Investiguemos” lesson structure utilizes problem-based and exploratory learning guided by educator-facilitated questioning and discussion. The “Elaboremos” lesson framework focuses on direct instruction paired with guided practice and collaborative discourse. Finally, the “Representémoslo en 3 actos” format engages students in inquiry-based learning and problem solving through real-world scenarios

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.

On the online platform, the program overview outlines instructional structures for each activity and specifies whether the activity utilizes guided, independent, or collaborative practice. This guidance defines opportunities for varying instructional groupings and outlines how each practice type develops conceptual understanding, procedural fluency, and problem-solving skills. The directions guide educators to organize instruction using these grouping structures throughout the lessons. For example, materials include a table that maps the practice opportunities available in the program to specific instructional structures. The table establishes how resources such as “Math Talks,” “Guided Practice,” “Practice and Problem Solving,” and more function in whole-group, small-group, and individual settings to facilitate guided, independent, and collaborative practice.

Additionally, the Guía del maestro materials provide multiple practice formats alongside instructional guidance and structural frameworks for lesson implementation. The “Biblioteca de diferenciación” tool contains a collection of hands-on games aligned to each topic for collaborative pair or small-group execution, along with activities in which students work together to solve mathematical problems. For example, in the Guía del maestro, topic 2, the “Biblioteca de diferenciación” outlines a math-based story, two small-group “Levántate y razona” problem-solving activities, two partner games, and an independent fluency practice page.

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.

Topic 4 provides strategies to develop “mathematical understanding and academic language related to multiplying decimal numbers.” These resources support language acquisition by identifying current, prior, and upcoming topic vocabulary along with contextualized definitions and multiple meanings of mathematical terms. The guidance also includes transferable and non-transferable language competencies, cognates, and false cognates, alongside recommended terms, activities, and instructional strategies. These integrated supports help educators develop students’ listening, speaking, reading, and writing skills to help them master grade-level mathematics content.

Additionally, in the Guía del maestro for lesson 1-2, “Valor de posición decimal,” the “Apoyo al lenguaje” section directs educators to connect content with students’ prior linguistic knowledge by outlining differences in word endings and sounds. For example, the section explains that the Spanish suffix -ésimas indicates a fraction, using the example of millares versus milésimas. The section also contains educator instructions for a collaborative peer-learning structure (“Pida a los estudiantes que trabajen de a dos . . .”) in which students alternate oral and written roles to use academic vocabulary. The materials also include different mathematical representations, such as fractional forms, standard notation, and expanded notation paths, to address the transition between everyday language and formal mathematical discourse.

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

In the topic 4 “Adaptaciones del lenguaje” section, the materials define words in different contexts and provide instructional steps for student oral and written mathematical ideas. The materials categorize mathematical words into groups titled “Vocabulario del tema (Potencia de 10),” “Términos previos,” and “Próximos términos.” A two-column word list titled “Vocabulario en contexto” displays the mathematical meaning next to the everyday meaning for words such as compatible, producto, and dimensión. A section titled “Transferencia metalingüística al inglés lists skills that transfer between languages, including abbreviations for measurements such as sq mi/square miles, and highlights language skills that do not transfer due to structural grammar differences. In addition, the lesson lists cognates with similar spelling and meaning in both languages, such as table/tabla and product/producto. The materials also list false cognates such as support versus soportar to address translation errors.

Additionally, in the Guía del maestro, the “Para el vocabulario académico” section provides instructional guidance for teaching academic vocabulary through definitions, examples, sentence frames, and synonyms. The materials give students opportunities to discuss and write about vocabulary terms. Additionally, the materials contain activities that connect vocabulary to mathematical contexts and prompt students to explain their reasoning to build comprehension and background knowledge. The materials also provide tools to monitor vocabulary development, such as the “Guía para verificar el desarrollo del vocabulario académico,” which tracks student progress.

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.

This guidance is not applicable because the program is not designed for dual language immersion (DLI) programs.

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 Cuaderno de evaluación contains topic assessments consisting of selected-response and constructed-response items. The “Tabla de análisis de las preguntas” links each assessment item to its corresponding TEKS standard and lists specific intervention lessons for incorrect responses. The educator materials outline steps to analyze student data and address identified learning gaps. The topic 9 assessment contains problems covering data analysis, fraction operations, measurement, equation writing, and numerical reasoning, which requires students to select and execute strategies across these concepts. Additionally, the “Evaluación del tema 12” section “Medir figuras y sólidos” includes a correlation chart mapping each assessment item to readiness standard TEKS 4H while documenting the cognitive complexity and DOK levels for each task.

Additionally, within the Guía del maestro “Evaluación y diferenciación” section for each unit, materials feature opportunities for students to demonstrate depth of understanding aligned to the TEKS. For example, in topic 3, “Multiplicar números enteros de varios dígitos con fluidez,” lesson 3-3, “Multiplicar números de 3 dígitos por números de 2 dígitos, paso 4” includes a five-question “Comprobación rápida” aligned to TEKS 5.3A. Based on student performance, educators assign either an intervention activity or an extension activity. Additionally, the “Práctica adicional” section includes an educator reference chart that identifies the TEKS alignment and corresponding DOK level for each item to support practice at varying levels of cognitive complexity.

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

The program overview organizes and sequences topics 1 through 13, providing tasks that increase in complexity. Topics 1 through 6 progress from basic place value to operations with whole numbers before extending those computational strategies to decimals, and these topics serve as the foundation for multidigit operations in topic 7. For example, in the Guía del maestro for lesson 3-7 “Elaboremos: resolver problemas de un paso y varios pasos con números enteros,” the materials guide students toward independent mastery of TEKS 5.3B by moving from concrete visual models to strategic reasoning and multistep problem solving. The “Apoyo del lenguaje” section of this lesson features use of counters, concrete visual models, and linguistic scaffolding to reinforce the concept of multiplicative comparison before transitioning to procedural and algebraic reasoning within the “Hablemos de matemáticas” section, in which tasks require students to estimate products and determine whether to use mental math or a written algorithm. The lesson includes a “Boleto de salida” activity, which requires students to solve multistep, real-world scenarios; interpret data formatted in tables; and apply the conventional multiplication algorithm for two- and three-digit numbers.

Additionally, the materials provide tasks throughout lessons, topics, and assessments that increase in complexity to support student proficiency in the TEKS. In the Guía del maestro, each unit includes a “Representémoslo en 3 actos” section in which tasks increase in complexity across three structured stages. For example, in topic 3, “Multiplicar números enteros de varios dígitos con fluidez,” the “Representémoslo en 3 actos” section begins with “Elevar al cuadrado,” in which tasks require students to estimate the number of figures needed to balance a scale. Then, during “El modelo,” students use the information they gathered to develop an explanatory model and communicate their mathematical reasoning and strategies. Finally, students learn the actual result and engage in verification and reflection.

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

The “Contexto matemático: coherencia” section for topic 3, “Multiplicar números enteros de varios dígitos con fluidez,” connects prior understanding of place value, estimation, and multiplication from grade 4 to current learning about multiplying multidigit whole numbers. The materials outline how estimation strategies in lesson 3-1 support multiplication with larger numbers and how area models and partial products in lessons 3-2 and 3-3 connect to the conventional multiplication algorithm. The “Math Background: coherence” section at the beginning of every topic utilizes “Looking Back,” “In This Topic,” and “Looking Forward” features to map these connections over time. For example, in topic 3, the “Looking Back” text reviews rounding whole numbers, estimation, and foundational multiplication concepts. The section then focuses on estimating products and using models or algorithms to multiply two-digit numbers before extending these skills to three-digit numbers. The “Looking Forward” component connects these concepts to future learning, demonstrating how students apply multiplication strategies to powers of 10 and decimal operations across grade levels.


Additionally, in the Guía del maestro topic 5 section “Vistazo del tema: dividir números enteros con destreza,” the materials connect place-value structures and numerical patterns across consecutive lessons. Lesson 5-1 introduces mental math and place-value patterns, which establish the basis for estimating quotients using compatible numbers in lesson 5-2. The material grounds these numerical relationships visually in lesson 5-3 through concrete area models and arrays. As the unit progresses from lesson 5-4 to lesson 5-8, tasks present division by two-digit divisors as an extension of single-digit principles. This progression links partial quotients, place-value distribution, and estimation to develop the conventional division algorithm for three- and four-digit dividends, relating the tasks to the foundation of place-value properties.

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.

In the Guía del maestro for topic 5, “Dividir números enteros con destreza,” the “Adaptaciones del lenguaje” section outlines términos previos, vocabulario del tema, academic vocabulary, and upcoming terms. This section connects previously introduced base 10 concepts such as potencias de diez, multiplication, place value, and estimation to current tasks involving division, cociente, divisor, residuo, cociente parcial, compatible numbers, and the conventional division algorithm. The material provides this vocabulary in context across consecutive lessons to pair mathematical language with content tasks. Additionally, the material organizes dual-meaning mathematical terms, metalinguistic transfers to English, cognates, and false cognates to align linguistic development with the operational structures and problem-solving scenarios required in subsequent grade levels.



In topic 7, “Reunir, organizar, mostrar e interpretar datos numéricos,” the “Estrategias para reunir, representar y analizar datos” section connects to prior learning by referencing student familiarity with collecting data and formatting it into tables and bar graphs. The materials establish grade 5 proficiency by requiring students to construct and interpret dot plots, stem-and-leaf plots, and scatter plots to analyze datasets and answer mathematical questions. Additionally, the “Conceptos avanzados para el maestro” section links current tasks to future grade-level requirements, outlining how the curriculum extends data representation, pattern and cluster recognition, and statistical conclusions in subsequent grades. These features connect previous data concepts, current expectations, and future statistical reasoning across 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..

In topic 3, lesson 3-1, “Estimar productos de factores de varios dígitos,” the materials structure a progression across four distinct steps. During step 1, “Explorar y comentar,” students review rounding strategies to estimate multiplication products. In step 2, “Aprendizaje visual,” students practice rounding techniques and apply new strategies for rounding down. During step 3, “Práctica y resolución de problemas,” students complete guided practice before applying these estimation concepts independently. Finally, in step 4, “Evaluación y diferenciación,” students complete assessment tasks aligned to the TEKS to determine if they require targeted intervention or extension activities. The materials apply this same coherent structure in lesson 3-2 “Investiguemos: multiplicar con números más grandes.” In this lesson, the “Coherencia” section links foundational mathematical knowledge to new grade-level concepts. Under the “Vuelve atrás” subsection, the materials connect the lesson to prior knowledge from earlier units and grade levels, including multiplying large numbers by multiples of 10 and 100, estimating products with multidigit factors, and multiplying by one-digit numbers. The lesson transitions to current grade-level content in the “En esta lección” section, in which students use these procedural skills to investigate area models for multidigit numbers, moving from conceptual visual representations to calculations. Finally, the “Más adelante” section outlines how this groundwork connects to subsequent skills, specifically developing the standard conventional algorithm for multidigit multiplication over the next two lessons.


Additionally, in the “Math Background: coherence” section at the beginning of each topic, the “Looking Back,” “In This Topic,” and “Looking Forward” features outline how mathematical concepts connect across and within lessons. For example, in topic 4, “Usar modelos y estrategias para multiplicar números decimales,” the “Looking Back” section revisits concepts including multiplying whole numbers, rounding, and estimation. The current unit uses these skills to introduce number sense and strategies for multiplying decimals. Finally, the “Looking Forward” section outlines the foundational skills students need to divide decimal numbers in subsequent coursework.

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

In the Guía del maestro for lesson 3-5, “Multiplicar números enteros con ceros,” the “Vuelve atrás” section requires students to retrieve place-value understanding and the standard multiplication algorithm from previous lessons to multiply three-digit numbers by two-digit numbers. This section also revisits estimation as a strategy to determine the reasonableness of products before students apply these skills to factors containing zeros. Within the same lesson’s “Elaboremos” framework, the “Hablemos de matemáticas” component contains the “Alinea los datos” activity, which requires students to collect, organize, and compare numerical data from least to greatest and write mathematical statements to describe their results. The educator guidance for this activity directs students to use the multiplication and estimation strategies they acquired earlier in the unit to determine and justify their answers.


Additionally, in the Guía del maestro, lesson 8-5, “Restar fracciones con distintos denominadores,” the “Coherencia” section includes the “Vuelve atrás” component. This section notes that students previously added fractions with different denominators, requiring them to retrieve and apply their understanding of equivalent fractions and common denominators to subtract fractions with unlike denominators. In topic 6, “Usar modelos y estrategias para dividir números decimales,” the “Repasa lo que sabes” section requires students to retrieve previously learned skills before beginning the unit, including dividing whole numbers and multiplying and dividing decimals. Within this same section, students review foundational concepts, including decimal-place value, related academic vocabulary, and visual decimal models. This structure requires students to recall and apply knowledge from earlier lessons and previous units to connect prior learning to the upcoming topic content.

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

In the Guía del maestro, topic 12, “Medir figuras y sólidos,” the curriculum integrates basic geometric properties and math fluency throughout the unit. For example, the “Comprender el vocabulario” section pairs geometric classifications (trapecios and cuadrados) directly with spatial measurement concepts (volumen and prisma rectangular). Lessons 12-3 and 12-4 expand this practice by requiring students to use hierarchical classification models such as Venn diagrams for quadrilaterals, along with algebraic computation skills, applying geometric attributes and algebraic formulas to solve multistep perimeter and area problems. Topic 6 in the “Repasa lo que sabes” section provides further interleaved review of prior concepts. In this section, students evaluate vocabulary words, execute whole-number operations, round decimals, solve decimal word problems, and calculate operations with decimals.


Additionally, at the end of each topic in the Guía del maestro, review pages offer interleaved practice for students to apply prior content in new contexts. For example, in topic 4, “Usar modelos y estrategias para multiplicar números decimales,” the “Repaso del tema” section reinforces whole-number multiplication strategies from topic 3 and extends them to decimal operations. Students multiply decimals by multiples of 10, whole numbers, and other decimals. Additionally, students utilize models, partial products, and estimation from earlier units to connect prior learning to current mathematical concepts, supporting conceptual understanding.

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

In the Guía del maestro, the “Representémoslo en 3 actos” section in each unit engages students in creating, analyzing, and evaluating mathematical models to represent real-world situations. For example, in topic 10, “Álgebra, patrones y el plano de coordenadas,” lesson 10-8 “Representémoslo en 3 actos: juego de apilamiento,” “Acto 1” introduces a video showing two students stacking cups at different starting times. Students interpret the visual data, analyze the mathematical context, and make a baseline prediction regarding the number of cups stacked in two minutes. In “Acto 2,” students observe physical models of stacked cups and heights to obtain mathematical variables. Working in small groups, students collaborate to design, develop, and compare a graph or a table to represent the relationships, subsequently sharing their methods and evaluating structural differences between the two modeling formats. In “Acto 3,” students verify their mathematical models against a video solution, evaluate potential sources of error, assess how altering foundational assumptions shifts outcomes, and determine model validity in alternate situations. Students extend their mathematical reasoning by constructing a new, mathematically parallel problem. Similarly, in lesson 8-1 “Elaboremos: estimar sumas y diferencias de fracciones,” the “Hablemos de matemáticas” section includes an analytical task in which students evaluate four progressing dot plots under the prompt “Mira de cerca.” This task requires students to interpret how the addition of new data points transforms the data representation. Additionally, the “Apoyo al lenguaje” section requires students to analyze a dual-model representation in which a fraction strip maps directly onto a 0-to-1 number line. This task requires students to interpret how abstract fractions align with critical benchmark fractions. The “Boleto de salida” task evaluates this conceptual modeling through concrete evaluation questions. Question 1 requires students to evaluate and round fractions to estimate a sum using benchmark fractions. Question 2 requires students to use the same analytical process to estimate a fractional difference.

Additionally, questions and tasks require students to analyze and evaluate mathematical models and representations to test geometric and algebraic relationships. For example, in topic 12, “Medir figuras y sólidos,” lesson 12-1, “Clasificar triángulos,” students analyze the side lengths and interior angles of visual triangle representations to classify them. In the “Hablemos de matemáticas” section, students evaluate abstract geometric concepts to justify why an equilateral triangle is always an acute triangle. Finally, the “Sentido numérico” task requires students to evaluate a mathematical proposition regarding time measurement conversions to determine if the statement is true or false.

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

In topic 9, lesson 9-1, “Multiplicar con fracciones,” the materials provide structured tasks that require students to use and connect models to represent mathematical situations, directly aligning with TEKS 5.3i. In the real-world scenario “Hacer sándwiches,” students solve problems involving multiplying a whole number by a unit fraction, such as calculating the total pounds of turkey needed to make a sandwich. To represent these mathematical situations, the materials require students to complete and analyze data tables that map out the relationship between the total number of sandwiches and the fractional outcomes. Additionally, the Guía del maestro lesson overview directs students to investigate these fractional parts of whole numbers using concrete and pictorial models, including fraction strips, area models, number lines, and two-color counters, ensuring that students actively create and interpret representations to conceptualize fraction multiplication. In lesson 9-4, “¡Comamos pizza!,” students model a real-world scenario to determine the total number of pizzas required for six guests if each guest receives two-thirds of a pizza. The educator guidance in the “Desarrollar un modelo” section prompts students to select an appropriate representation. The material includes student work exemplars demonstrating how to construct pictorial fraction models by partitioning circles into thirds using drawings, repeated addition, or fraction multiplication. Within the “Comentar estrategias de solución” section, tasks require students to utilize their models to justify the solution, explain their mathematical reasoning, and compare the different student-generated models.


Additionally, in the Guía del maestro for lesson 8-2, “Denominadores comunes,” students resolve a real-world problem regarding space allocation in a shopping center. Within the “Investiguemos” section, the materials require students to illustrate proportional sections of the center using original visual diagrams and fractional representations. Accompanying student work exemplars show students how to create area models by partitioning a whole into equal sections, labeling distinct regions, and utilizing those models to combine fractional values. Furthermore, the educator guidance in the “Relacionar” section outlines multiple student-generated models and strategies, including partitioning geometric planes into equal regions, applying equivalent fractions, and using visual fraction models. Finally, in the “Reflexión” section, students evaluate their constructed models and explain how these visual tools demonstrate equivalent fractions and common denominators.

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

In the Guía del maestro, lesson 10-9, “Patrones,” the “Investiguemos” section anchors the mathematical concept of algebraic relationships and numerical patterns, aligned with TEKS 5.4D, within the real-world context of a physical education class in which students jump across block tile patterns. The materials transition students from a concrete visual scenario using cubes to construct physical models to abstract mathematical representations, including structured data tables and coordinate graphing. “Anticipar” and “Tres lecturas” language routine sections prompt educators to systematically guide students through contextual comprehension by asking probing questions such as, “¿De qué se trata la tarea?” and “¿Qué información se da en la tarea?” These target questions challenge students to generalize their mathematical reasoning beyond the immediate data, requiring them to predict outcomes by finding the number of blocks for design numbers 10 and 20, and to articulate their own real-world contexts to transfer conceptual knowledge to new problem-solving situations. Similarly, in topic 8, lesson 8-4, “Sumar y restar fracciones y números mixtos con fluidez,” the “Hablemos de matemáticas” task presents mathematical statements regarding fractions and common denominators. The activity requires students to evaluate whether each statement is true or false and articulate specific strategies to justify their reasoning. Following the “Aprendizaje visual” conceptual development section, the “Hablemos sobre las ideas matemáticas” component requires students to apply the newly introduced concept to an entirely different problem situation or context, establishing a direct connection between core mathematical concepts and new applications.

Additionally, in lesson 6-2, “Estimar cocientes decimales,” students develop a conceptual framework for estimating quotients using rounding and compatible numbers. The tasks then require students to apply that understanding to estimate decimal quotients within a real-world scenario comparing water usage. Furthermore, in the Guía del maestro for lesson 8-7, “Sumar números mixtos,” within the “Explorar y comentar” section, tasks require students to apply their understanding of equivalent fractions, common denominators, mixed numbers, and visual models to a real-world scenario involving distances traveled on a walking trail. The exercises direct students to represent and combine fractional distances, utilize number lines or fraction bars to justify their calculations, and resolve a novel situational problem requiring the addition of mixed numbers with unlike denominators.

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

The Guía del maestro features a “Desarrollar la fluidez” component within topic 8, “Sumar y restar fracciones y números mixtos con fluidez,” which includes a “Señalar y marcar” partner game that provides repeated practice multiplying three-digit numbers by two-digit numbers. The activity requires students to solve multiple multidigit multiplication problems, verify their calculated solutions using inverse division operations, and apply estimation strategies to assess the reasonableness of their answers. This structured, repetitive practice requires students to develop computational precision and efficiency using previously acquired skills that support current grade-level learning. Furthermore, in the Guía del maestro for the topic 4 "Biblioteca de diferenciacion,” the “Práctica de fluidez: multiplicar números de hasta 3 dígitos por números de 2 dígitos” activity has students use a five-section spinner labeled “A,” “B,” “C,” “D,” and “E” to select and solve multidigit multiplication problems from a card.


In the topic 6 “Vistazo a la biblioteca de diferenciación,” the “Mantener la comprensión y fluidez” section incorporates spaced practice designed to transition students from conceptual understanding to procedural efficiency. Specifically, the materials provide fluency tasks such as “Carrera loca,” which targets multidigit multiplication fluency, and “Práctica de fluidez,” in which students divide up to four-digit numbers by two-digit numbers. Digital games on the online platform, such as “Duelo de decimales,” provide practice for dividing decimals to support fluent execution of core mathematical operations throughout topic 6.

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.

Within the “Elaboremos” section of each lesson, the “Hablemos de matemáticas” component requires students to apply mathematical procedures while comparing strategies with peers. For example, in lesson 8-10, “Representar problemas de un paso y de varios pasos con fracciones,” the “Detectives de números” activity requires students to use mathematical clues to identify a mystery fraction. As students work collaboratively, they apply fraction concepts, evaluate different solution strategies, and use strip diagrams and equations to represent and solve problems. Students then apply these procedures to solve one-step and multistep problems involving fraction addition and subtraction. In lesson 6-5, “Dividir números decimales,” tasks require students to solve decimal division problems using multiple solution methods, including area models, partial quotients, repeated subtraction, and the standard algorithm. Across the sequential phases of the lesson, which include exploration, conceptual connections, and problem-solving practice, students analyze varied solution strategies, evaluate the efficiency of each method, and select the most efficient procedure for a given problem. Instructional prompts require students to justify their mathematical reasoning and evaluate alternative approaches, establishing multiple opportunities to apply flexible operational procedures.


Additionally, in lesson 6-4, “Dividir por un número entero de 1 dígito,” tasks in the “Práctica guiada” section require students to calculate decimal positions within quotients and complete division problems using the standard algorithm. Students then apply these operational procedures to solve division problems, justify their mathematical reasoning, and utilize decimal quotients within real-world contexts involving measurements and monetary values.

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

In the Guía del maestro for topic 8, “Sumar y restar fracciones y números mixtos con fluidez,” lesson 8-11, the “Representémoslo en 3 actos” section “La receta” requires students to evaluate mathematical approaches across three stages. For the “Acto 1” activity, students watch a video prompt and collaborate as a class to establish a primary mathematical question. In “Acto 2,” students gather data, build mathematical models, and apply procedures to determine whether the given ingredients will fit into a mixing bowl. In “Acto 3,” a solution video reveals the final answer, and students compare their results to the outcome to evaluate solutions and refine their processes. In the “Comentar estrategias de solución” section, students examine sample work involving estimation and exact calculations to evaluate the accuracy and reasonableness of different solution strategies. In the “Práctica y resolución de problemas” section of lesson 9-8, “Representar problemas con fracciones,” tasks require students to analyze worked mathematical examples, evaluate whether a solution process correctly represents a given scenario, identify and correct operational errors, and justify their conclusions using visual models and equations.

Additionally, in lesson 4-9 of topic 4, “Usar modelos y estrategias para multiplicar números decimales,” the “Hablemos de matemáticas” section presents a series of computational problems. The tasks require students to collaborate with partners to analyze, select, and justify the most efficient strategies for each mathematical scenario. Following the “Aprendizaje visual” conceptual phase, the “Hablemos sobre las ideas matemáticas” component requires peer work to articulate a solution path, represent the problem using an equation, and evaluate the underlying mathematical reasoning. These peer discussions require students to evaluate the validity of their work, confirm the accuracy of their solutions, and assess the efficiency and flexibility of different mathematical approaches.

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

The Guía del maestro for topic 9, “Entender la multiplicación y la división con fracciones,” lesson 9-1, “Multiplicar con fracciones” includes specific instructional strategies within the “Investiguemos” section. Step 1 guides educators to ask assessing and advancing questions while monitoring student work to direct students toward streamlined mathematical methods. Additionally, the “Seleccionar y poner en secuencia” subsection directs educators to present student solutions in a specific progression that builds understanding of efficient pathways. Educators first present and discuss solutions that use concrete drawings and objects, followed by number lines or bar models, and finally solutions that use numerical reasoning and patterns. In step 2, the lesson supplies further embedded questioning and instructional strategies to reinforce these efficient mathematical approaches. In addition, the “Aprendizaje visual” section of lesson 9-8, “Representar problemas de un paso y de varios pasos con fracciones,” includes guidance that prompts students to contrast visual models with equations. These tasks require students to evaluate why a specific representation resolves a problem more efficiently than another and explain how selecting that appropriate representation simplifies the solution path. Furthermore, the material provides target discussion prompts designed to transition students from foundational, less efficient representations to strategic algorithmic methods while maintaining mathematical precision throughout the lesson.

Additionally, in the lesson 6-9 section “Comentar estrategias de solución,” subsection “Crear llaveros,” the educator guidance outlines a comparative analysis of two student methods for determining string length. The task requires students to contrast a visual partitioning model against the standard division algorithm, prompting students to connect concrete representations directly to abstract numerical division procedures. Similarly, each “Representémoslo en 3 actos” lesson includes targeted educator prompts that require students to evaluate the efficiency and accuracy of their solution strategies and refine their mathematical models. For example, in topic 3, “Multiplicar números enteros de varios dígitos con fluidez,” lesson 3-4, “Elevar al cuadrado,” students apply multiplication and numerical relationships to determine how structural changes affect a balance scale. Across the three instructional sections, educator guidance outlines specific discussion questions that require students to analyze the scenario, justify their models, and contrast the efficiency of different strategic approaches. As students compare their solutions against the final result, educators prompt them to refine their mathematical reasoning. Finally, the tasks require students to construct a new mathematical problem that applies these same concepts within an alternative context, enabling educators to reinforce efficient operational procedures.

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

The Guía del maestro for topic 6, “Usar modelos y estrategias para dividir números decimales,” features the core balance between conceptual comprehension and procedural skills. Under the “Comprensión de conceptos” subsection, the materials identify the conceptual emphasis by explaining how students develop number sense and understand decimal division through place-value patterns, area models, estimation, properties of operations, and the relationship between multiplication and division. In the “Destrezas en procesos” subsection, the materials identify the procedural expectations. This includes describing how students utilize base 10 blocks, partial quotients, estimation, strategies for dividing decimals by multiples of 10, and the standard division algorithm to solve decimal division problems within real-world contexts related to TEKS 5.3F and 5.3 G. In the Guía del maestro for lesson 6-4, “Dividir por un número entero de 1 dígito,” the “Equilibrio” section outlines that conceptual understanding focuses on generalizing the standard algorithm to place the decimal point directly above the dividend. The materials prompt mathematical discourse through true-or-false tasks and reinforce this focus with specific questions in the “Apoyo del lenguaje” section and the “Boleto de salida.”


Additionally, in topic 5, the “Comprensión de conceptos” section outlines how students construct a conceptual understanding of equations, inequalities, variables, and mathematical relationships, and the “Destreza en procesos y fluidez” section details how students develop procedural fluency by applying inverse operations. Similarly, at the lesson level, lesson 7-6, “Leer diagramas de tallo y hoja,” outlines this dual instructional focus. The introductory text outlines the conceptual emphasis by explaining how a stem-and-leaf plot organizes numerical data according to place value, defining the stems and leaves by their respective place values. Concurrently, the materials establish the procedural emphasis by modeling how to construct, read, and interpret these data displays; identify the data key; and calculate values such as the minimum and maximum data points to resolve situational problems.

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 program overview on the online platform states that progression from concrete to pictorial to abstract occurs both across and within lessons. Students begin each lesson with tasks using concrete materials such as counters, cubes, place-value blocks, tiles and pictorial representations, including number lines, arrays, grids, and strip diagrams. Additionally, integrated digital manipulative resources replicate three-dimensional cubes, two-dimensional tiles, and one-dimensional number lines for students to use at any time. For example, the program applies this structured Concrete–Representational–Abstract sequencing to scaffold the grade 5 extension of place-value concepts to larger numbers and decimals. Furthermore, In the Guía del maestro for topic 12, “Representar el volumen,” lesson 12-6 requires students to utilize multiple mathematical representations. Students first use concrete models and manipulatives by using physical unit cubes and place-value blocks to build and fill rectangular prisms. In the “Aprendizaje visual” section, students transition to pictorial representations by drawing rectangular prisms and analyzing three-dimensional diagrams that display the layers, rows, and columns of unit cubes. In addition, students use abstract representations by writing numerical calculation expressions and multiplication equations, such as length × width × height or layers × cubes per layer, to determine and represent the total volume mathematically.


Additionally, in the Guía del maestro, topic 2, lesson 2-7, within the “Hablemos de matemáticas” section, the materials guide educators to display specific images and equations. Educators ask students what they notice and wonder about the visual representations and corresponding equations to guide analysis of how the images are partitioned, shaded, and crossed out to represent subtraction and identify the difference. In lesson 5-10, “Representar y resolver problemas de un paso y varios pasos,” students use pictorial representations, including diagrams, tables, drawings, and bar models, to organize information and represent multistep division problems.

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 program overview within the online platform states that instruction progresses from concrete models and manipulatives to pictorial representations, abstract numbers, symbols, and procedures across and within lessons. During the “Explore” and “Let’s Build” lesson segments, students use physical manipulatives such as counters, cubes, place-value blocks, and tiles to construct models. As lessons progress, tasks require students to represent their thinking using drawings, diagrams, and visual models. The materials also include digital manipulatives with text detailing their educational advantages, and the “Visual Learning” section instructs educators to guide students in connecting these pictorial representations to abstract processes. For example, in lesson 2-6, “Usar estrategias para restar números decimales,” students utilize base 10 blocks and decimal grids to model a subtraction problem and connect these concrete and visual representations to a subtraction algorithm. During the “Aprendizaje visual” section, students interpret place-value models while relating them to numerical calculations. Tasks require students to create their own models using blocks or drawings to represent decimal subtraction and explain how the models correspond to the subtraction process. Furthermore, the materials prompt students to describe how their models display subtraction, explain the relationship between the representational models and the abstract equation, and justify their solutions.


Additionally, in the Guía del maestro lesson 7-2, “Leer diagramas de puntos,” educators guide students to interpret and connect data represented in tables, dot plots, number lines, and verbal descriptions across the “Explorar,” “Aprendizaje visual,” “Práctica,” and “Evaluación” components. Educators direct students to explain how tabular data translates to a dot plot, compare data across multiple representations, justify conclusions using visual models, and communicate their mathematical reasoning during class discussions. Students apply these skills during guided practice, independent practice, and intervention activities to synthesize data, solve problems, and interpret graphical representations. Furthermore, in topic 4, “Usar modelos y estrategias para multiplicar números decimales,” lesson 4-5, “Usar modelos para multiplicar un número decimal y un número decimal,” the student progression moves from concrete and pictorial models to abstract representations. During step 1, “Explorar y comentar,” students use grid paper to construct arrays that model decimal multiplication. In step 2, “Aprendizaje Visual,” students analyze matrix models, connect the visuals to partial products and place-value relationships, and explain how the representations correspond to the symbolic multiplication process. For step 3, “Práctica y resolución de problemas,” students apply these models to solve problems, justify reasoning, and represent solutions using abstract numerical methods to develop conceptual understanding.

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

In the Guía del maestro, topic 9, “Entender la multiplicación y la división con fracciones,” the “Repasa lo que sabes” activity at the start of the topic provides a vocabulary review. Students complete fill-in-the-blank exercises to reinforce prerequisite terms, including denominador común, fracciones equivalentes, and múltiplo. The “Actividad de vocabulario” section directs educators to use a graphic organizer called “Mapa de palabras” to help students define, illustrate, and record target terms such as fracción unitaria and recíproca. In this activity, students place a term in the center, add examples to the left, write related words to the right, and explain the concept at the bottom. The “Vocabulario académico” section provides educator guidance for explicitly teaching and using academic verbs, including establecer, experimentar, and inferir, promoting discussion and prompting students to use visual models and drawings to explain fraction concepts. In the Guía del maestro, topic 11, lesson 11-1, “Convertir unidades de longitud del sistema usual,” the materials include an “Aprendizaje visual” section, in which students use visual models, conversion diagrams, number lines, and measurement representations to connect mathematical vocabulary to equivalent customary units. The “Apoyo al lenguaje” guidance prompts educators to ask scaffolded questions using terms such as pies, pulgadas, yardas, and millas, while students explain relationships between units using complete mathematical language. The lesson also incorporates repeated educator questioning, structured discussion, and opportunities for students to justify their reasoning using academic vocabulary before applying the concepts independently. These embedded visual representations and language supports intentionally develop students’ mathematical vocabulary while strengthening conceptual understanding of customary unit conversions.



Additionally, in the Guía del maestro, topic 4, lesson 4-10, the “El parque” component of the “Representémoslo en 3 actos” lesson structure requires students to explain and justify mathematical concepts using visual models and real-world problems. During “Acto 1,” students analyze situations, predict outcomes, and discuss area-estimation strategies. In “Acto 2,” students perform calculations and generate visual representations to construct a solution model, apply decimal multiplication concepts, and communicate mathematical reasoning. During “Acto 3,” students compare their models to the actual result, reflect on their reasoning, and write a new problem to apply the concepts in an alternate context. In the Guía del maestro for topic 8, “Sumar y restar fracciones y números mixtos con fluidez,” the digital platform component “Biblioteca de diferenciación” includes the section “Actividades con materiales digitales manipulables.” Within this section, the activity “Hallar los números mixtos” requires students to use fraction tiles to determine mixed numbers with different denominators from a given addition. Additionally, in the activity “Hormas de queso,” students use fraction circles to represent strategies for subtracting mixed numbers with different denominators.

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

In the Guía del maestro, lesson 2-1, “Elaboramos: usar el cálculo mental para sumar y restar,” the “Apoyo del lenguaje” section utilizes graphic organizers, visual representations, and prior-knowledge connections to introduce vocabulary. Specifically, the “Apoyo al lenguaje” section directs educators to use problems from the “Apoyo visual” layout to build linguistic links between related words such as associative property and associate. Step 2, “Aprendizaje visual,” guides educators to ask targeted questions prompting students to explain how they grouped numbers, why addend order can change, and which mental strategies optimize efficiency. This educator guidance embeds academic terms directly into instruction, prompting students to use the expressions propiedad asociativa de la suma, propiedad conmutativa de la suma, números compatibles, and compensación during mental computation problem solving. Furthermore, the “Rutina del lenguaje” instructs educators to have students explain how compatible numbers simplify mental computation and identify when to execute specific mental strategies. Finally, during “Hablar sobre las ideas matemáticas,” educators facilitate discussions in which students compare computation strategies, justify mathematical reasoning, and use guided questions such as “¿Cómo puedes explicar la propiedad asociativa con tus propias palabras?” to apply precise vocabulary.


Additionally, the Guía del maestro embeds this guidance at the end of each unit within the “Repaso del tema” section, specifically through the “Comprender el vocabulario” and “Usar el vocabulario” activities. These components offer structured opportunities to introduce, reinforce, and assess content vocabulary within the context of the unit’s mathematical concepts. For example, in topic 4, “Usar modelos y estrategias para multiplicar números decimales,” the “Comprender el vocabulario” activity requires students to match examples to corresponding mathematical terms from a word bank. In the subsequent “Usar el vocabulario” activity, educators direct students to write a paragraph explaining the steps to solve a problem using those same terms. Similarly, the topic 7 “Repaso del tema: reunir, organizar, mostrar e interpretar datos numéricos” section scaffolds vocabulary through the “Lenguaje oral” section. In this section, educators facilitate the review game “¿Cuál es mi palabra?,” in which one student provides a clue about a mathematical term while peers listen and identify the word. Educator guidance continues in the “Escritura en matemáticas” section, in which students create their own vocabulary clues using lesson terminology, such as datos, gráfico de barras, gráfico de puntos, gráfico de líneas, diagrama de tallo y hojas, intervalo, frecuencia, and encuesta. Students then exchange clues with classmates to identify the correct term based on the written description, requiring them to apply academic vocabulary within meaningful mathematical contexts.

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

In the Guía del maestro, topic 2, lesson 2-8, “Representar y resolver problemas de varios pasos,” the “Reforzar el vocabulario” section introduces the terms ecuación and diagrama de tiras. To support syntax and discourse, the “Apoyo al lenguaje” section provides questions and model responses to connect student models to academic vocabulary, instructing educators to ask how a strip diagram represents the problem and connects to the corresponding equation. During step 2, “Aprendizaje visual,” in the “Convención en la clase” and “Pregunta” sections, educators have students explain each step of the solution process, justify the strip diagram representation, and compare solution methods. Furthermore, in the “Rutina de lenguaje: cada vez más sólido y claro,” educators have students explain a diagram to a partner, listen to a peer’s explanation, and revise their own reasoning. The “Hablar sobre las ideas matemáticas” section provides prompts for students to justify why different representations model the same problem and explain model efficiency, and the “Prevenir malentendidos” section outlines questioning strategies to redirect misconceptions. Finally, during step 3, “Práctica y resolución de problemas”, the “Práctica guiada,” “Errores e intervención,” and “Conversaciones en grupos pequeños” sections include exemplar responses, sample student reasoning, and follow-up prompts to convert informal language into mathematical communication.



Additionally, in lesson 5-4, “La división con divisores más grandes,” the “Supervisar, seleccionar y poner en secuencia,” and “Relacionar estrategias de solución” sections guide educators to facilitate discussions by comparing student solution strategies. The materials provide specific discussion prompts, including “¿Cómo obtuviste la respuesta?” and “¿Qué otra manera hay de resolver el problema?” to help students justify their reasoning. In the “Hablar sobre las ideas matemáticas” section, students discuss the relationship between area models, multiplication, and division during partner and whole-class conversations. The “Ejemplos del trabajo de los estudiantes” section provides sample responses paired with suggested educator follow-up questions. Additionally, the “Repaso del tema” section contains oral and written language tasks to reinforce academic language. For example, in topic 4, “Usar modelos y estrategias para multiplicar números decimales,” the “Comprender el vocabulario” activity directs students to match mathematical examples to terms in a word bank. In the “Usar el vocabulario” activity, educators direct students to write a paragraph explaining problem-solving steps using those word-bank terms. In an oral language task, educators give students clues to identify mathematical terms, and in a writing activity, students write down mathematical terms they hear without reference materials and exchange papers with a partner to review errors.

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

In the Guía del maestro, “Estandares de procesos matematicos” and “Vistazo del tema” sections feature a scope and sequence chart showing that process standards are embedded within every content theme rather than taught in isolation. For example, TEKS 5.1C (selecting tools, mental math, and estimation) integrates into lessons 2-1 and 2-2, which prompt students to use mental math and estimation strategies to solve word problems, such as estimating the price differences between objects. TEKS 5.1G (explaining and justifying mathematical ideas) integrates questions and language objectives that require students to explain, both orally and in writing, how they use place-value structures or partial sums to compute results. The materials include student prompts such as “¿Cómo puedes estimar la diferencia de precio entre dos objetos?” and “¿Cómo se pueden comparar tus respuestas?” These prompts require students to select tools and strategies and justify their mathematical reasoning under TEKS 5.1G.


Additionally, in topic 3, “Multiplicar números enteros de varios dígitos con fluidez,” the “Estándares de los procesos matemáticos de los TEKS” section incorporates TEKS 5.1B (problem-solving models) and TEKS 5.1F (analyzing mathematical relationships) while providing specific educator questioning strategies. Similarly, topic 5, “Dividir números enteros con destreza,” integrates TEKS 5.1D and 5.1G as the focal process standards for whole-number division. The accompanying educator guidance outlines observable student behaviors for these standards, such as utilizing models, images, and mathematical language to communicate reasoning. Furthermore, the materials direct educators to prompt students to explain multiplication–division relationships, justify solutions using pictorial representations, and apply precise mathematical vocabulary to describe quotients and remainders.

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

The Guía del maestro table of contents and topic contents identify the specific content standards alongside one or more process standards, from TEKS 5.1A through TEKS 5.1G, for every lesson. This alignment provides a roadmap showing how these standards reinforce grade-level instruction across all topics and lesson types, including “Elaboremos,” “Investiguemos,” and “Representémoslo en 3 actos”. For instance, the overview for topic 1, “Valor de posición,” includes a dedicated section titled “Estándares de procesos matemáticos de los TEKS” to identify embedded process standards before instruction begins. The table of contents maps these process standards to content standards for every lesson, demonstrating how students repeatedly apply mathematics to real-world situations under TEKS 5.1A, use problem-solving models under TEKS 5.1B, and select and use representations under TEKS 5.1C.


Additionally, within the “Estándares de los procesos matemáticos de los TEKS” section of topic 13, “Comprensión de finanzas personales,” the materials display a chart detailing how students develop mathematical reasoning behaviors through TEKS 5.1A, applying mathematics to problems arising in everyday life, society, and work, and TEKS 5.1G, displaying, explaining, and justifying mathematical ideas and arguments using precise mathematical language. To support these connections at the unit and lesson levels, the materials incorporate real-world analytical questions. For example, tasks require students to compare and contrast gross versus net income, justify choices for specific payment methods, and explain the financial significance of balancing a budget, which requires students to apply mathematical process standards to financial literacy context.

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

Each unit includes an “Estándares de los procesos matemáticos de los TEKS” section that features a dedicated unit overview detailing how core process standards will be developed and evaluated across each topic. For example, in topic 4, “Usar modelos y estrategias para multiplicar números decimales,” the materials feature an overview that outlines the integration of TEKS 5.1A, applying mathematics to daily life, society, and work, and TEKS 5.1E, creating and using representations to organize, record, and communicate mathematical ideas. To provide evidence of these connections, the materials incorporate real-world questions and reflective prompts throughout the unit. For instance, to support TEKS 5.1A, tasks prompt students to apply decimal operations to financial scenarios, such as calculating the total cost of produce, to evaluate the reasonableness of a given solution equation. To support TEKS 5.1E, the materials include a task requiring students to use area models, decimal grids, strip diagrams, and equations to represent partial products, execute the conventional algorithm, and communicate their mathematical reasoning.


Additionally, the “Planes de la lección para Texas” resource within the online platform identifies the TEKS process standards for each lesson and outlines how those standards embed throughout instruction. Each lesson includes specific educators guidance across phases such as “Explore/Investigate” and “Practice and Problem Solving” to direct students to explain mathematical thinking, communicate ideas, analyze relationships, connect representations, and solve problems. For instance, topic 1, “Valor de posición,” includes a “Conocimientos y destrezas esenciales de Texas (TEKS)” section for each lesson. Within this topic, lesson 1-1, “Elaboremos: valor posicional de números enteros,” incorporates content standard TEKS 5.2B along with process standards TEKS 5.1D, TEKS 5.1E, and TEKS 5.1F. This structural layout details the direct correlation between process standards and mathematical content across all lessons within the unit.

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

The Guía del maestro and Libro del estudiante lesson 2-4, “Sumar y restar números decimales,” includes process standards TEKS 5.1D, TEKS 5.1F, and TEKS 5.1G, which directly correlate with the primary content target TEKS 5.3K. Throughout the student prompts and exercises, students apply mathematical skills to real-world problems, such as budgeting a $10 meal. This application connects to TEKS 5.1D and TEKS 5.1G. Furthermore, the “Relacionar” section contains analytical prompts, and the “Justificar” question directs students to compare adding money decimals to whole decimal numbers. Questions require students to map connections between decimal place-value patterns and whole number place-value patterns. The “Práctica y resolución de problemas” section features multistep, real-world applications, including estimation. For example, students calculate how much money they will have left after purchasing a book, which integrates TEKS 5.1F by requiring students to analyze problem situations, select appropriate strategies, and evaluate the reasonableness of their solutions.


Additionally, the Guía del maestro outlines integrated TEKS content and process standards within specific lesson overview sections. In lesson 3-1, “Estimar productos de factores de varios dígitos,” the “Conocimientos y destrezas esenciales de Texas (TEKS)” section aligns with TEKS 5.3A and TEKS 5.3B to connect conceptual multiplication strategies with procedural skills. Each lesson within the “Estándares de los procesos matemáticos de los TEKS” section specifies supportive process standards, including TEKS 5.1A (everyday problem solving), TEKS 5.1C (tool selection), TEKS 5.1D (communication), and TEKS 5.1G (justification). Similarly, lesson 6-1, “Describir patrones para dividir con números decimales,” embeds these process standards directly into student tasks. In problem 2, students analyze multiplication-division patterns and apply TEKS 5.1D by explaining whether dividing by 10 or 50 produces a greater quotient. In problem 28, students apply TEKS 5.1G by identifying and justifying patterns in expressions involving multiplication and division by powers of 10.

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

In the Guía del maestro, in lesson 13-4, “Evaluar y seleccionar métodos de pago,” step 1, “Explorar y comentar,” direct students to analyze financial scenarios and determine appropriate payment methods. To support making sense of mathematics, educator guidance includes protocols to monitor and sequence student thinking, alongside prompts that require students to evaluate the advantages of cash, checks, debit cards, credit cards, and electronic payments. In step 2, “Aprendizaje visual,” students examine real-life financial transactions to apply mathematical reasoning to consumer decisions. During step 3, “Práctica y resolución de problemas,” students demonstrate perseverance through problem solving by completing multistep tasks and higher-order reasoning problems in which they must refine strategies, defend their reasoning, and verify fund sufficiency. Educators provide targeted questions to promote reasoning and intervention steps that direct students to revise their thinking. Finally, step 4, “Evaluar y diferenciar,” uses “Quick Check” assessment data to deliver systematic intervention, independent practice, or enrichment tasks.

Additionally, in the Guía del maestro, topic 1, lesson 1-1, “Valor de posición de números enteros,” step 1, “Explorar y comentar,” provides opportunities for students to think mathematically and facilitates instruction that values multiple paths to a solution. To support mathematical thinking and perseverance, educators give students “time to face challenges” and note that conceptual understanding emerges as students grapple with complex ideas. By encouraging collaboration and featuring sample student work, educators guide a whole-class “Relacionar” discussion in which students compare strategies. In the “Relacionar” section, students share, expand, and justify their thinking, and in the “Investigar” section, students explore content through problem-based learning tasks, choosing their own approach and drawing on prior knowledge. Students work in small groups while educators facilitate productive struggle. Furthermore, lesson 8-2, “Denominadores comunes,” step 1, “Investigar,” presents students with a real-world problem involving fractional parts of a secondhand shopping center and asks them to determine and compare areas using fractions with unlike denominators. Students develop and explain multiple solution strategies, and educators ask questions that probe student thinking, identify misconceptions, and encourage students to justify and refine their reasoning. In step 2, “Relacionar,” educators show different student solution methods, facilitating discussions that compare strategies, connect equivalent fractions and common denominators, and help students analyze why different approaches lead to the same conclusion. In step 3, “Práctica y resolución de problemas,” students apply their understanding to increasingly complex problems, and educators address common errors, prompt students to revise incorrect reasoning by using equivalent fractions, and encourage students to verify the reasonableness of their solutions. Finally, step 4, “Evaluar y diferenciar,” uses the “Quick Check” results to provide targeted intervention, differentiated practice, and enrichment so students continue strengthening conceptual understanding while persevering through mathematical tasks.

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

In the Guía del maestro, lesson 10-10, “Patrones de suma,” the “Hablemos de matemáticas” routine requires students to analyze coordinate graphs and justify which ordered pairs do not belong, establishing alternative solution pathways. During step 1, “Explorar y comentar,” students analyze addition patterns by generating input–output tables and coordinate graphs. The educator materials provide sample student work and protocols directing students to compare alternative strategies, explain how ordered pairs communicate identical growing patterns, and evaluate why a graph matches its corresponding table. In step 2, “Aprendizaje visual,” students synthesize tables, equations, ordered pairs, and coordinate graphs, and educators instruct students to explain how each format displays a constant rate of change. During step 3, “Práctica y resolución de problemas,” students independently construct tables, graph ordered pairs, derive algebraic rules, and justify solutions across multiple representations. Finally, in step 4, “Evaluar y diferenciar,” performance data reinforces student proficiency in translating and verifying mathematical relationships. Similarly, in lesson 12-5, “Volumen,” the “Bloques para enviar” activity presents an open-ended scenario in which students arrange 120 wooden blocks into rectangular prisms based on the student prompt “¿De qué tres maneras puedo ordenar los bloques para enviarlos?” The educator-facing guidance facilitates mathematical discourse and student justification by showcasing distinct solution strategies, including pictorial multiplication models, concrete structural arrangements linked to multiplication equations, and multiplicative comparisons. Furthermore, the materials provide an explicit example of a student misconception involving an attempt to construct a cube that exceeds the 120-block limitation. The educator guidance includes evaluative questions such as “¿Cómo sabes que tienes 120 bloques?,” directing educators to have students analyze, critique, and verbally justify the mathematical validity of different geometric representations.


Additionally, in the Guía del maestro, lesson 6-5, “Dividir números decimales,” students examine multiple solution strategies for dividing decimals. In step 1, student work samples illustrate different approaches, including using grid paper and partial products, patterns and place value, repeated subtraction, and the conventional algorithm to solve identical division problems. In step 2, “Relacionar,” students compare these strategies, document how they are alike and different, and explain why each method is valid. In step 3, “Reflexión,” students use an area model to connect multiplication and division, explaining how decomposing the dividend and combining partial quotients leads to the final quotient.

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

In the Guía del maestro, lesson 11-4 “Investiguemos: convertir unidades métricas,” the multistep instructional flow directs students to solve contextualized, real-world problems using diverse strategies such as strip diagrams, unit conversions, and multidigit operations. The “Supervisar” and “Seleccionar y poner en secuencia” sections guide educators to ask open-ended questions such as “¿Cómo puedes decirme o mostrarme lo que hiciste?” and “¿Qué significan estos dibujos?” These prompts require students to articulate their mathematical reasoning in small-group and whole-class settings. The materials instruct students to write about mathematics in the “Hablar sobre las ideas matemáticas” section, in which they must independently write a concrete conversation on an index card, explicitly noting how the decimal point moves, and then share and compare their written work with classmates. In lesson 12-6, “Representar el volumen,” the “Hablemos de matemáticas” routine requires students to work in pairs to analyze a geometric solid and determine its volume.

Additionally, in the Guía del maestro, topic 4, lesson 4-6, “Usar modelos y estrategias para multiplicar números decimales,” the “Investiguemos” section includes a three-step investigation utilizing concrete, pictorial, and abstract representations. In step 1, “Investigar,” students use place-value blocks and 100 grids to construct concrete models of decimal multiplication and explain how these representations illustrate place-value relationships. Within lesson 4-6, the “Rutina del lenguaje” guides students to read the task, explain it, and discuss their understanding with their educator and classmates. In step 2, “Relacionar,” students analyze and compare their strategies while connecting concrete models to pictorial representations and symbolic methods. In step 3, “Práctica y resolución de problemas,” students solve decimal multiplication problems, create pictorial representations for new situations, record solutions using numerical expressions and equations, and compare approaches with others. Additionally, in the Guía del maestro, lesson 5-4, “La división con divisores más grandes,” the “Investigar” section requires students to solve a division task using manipulatives, record their work, and explain their reasoning. The “Ejemplos del trabajo de los estudiantes” section provides student solution strategies for analysis, comparison, and discussion, and the materials direct educators to ask questions prompting students to justify their methods and critique alternative approaches. In “Práctica y resolución de problemas,” students solve division problems, complete area models, write equations, and document how partial quotients relate to multiplication and division, while the “Reflexión” section requires students to write out connections among representations.

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

In lesson 10-9, “Patrones,” the “Rutinas del lenguaje” section provides explicit protocols for educators to have students explain the assignment in their own words, clarifying understanding and establish mathematical communication. During the “Investigar” segment, students analyze sample student work, identify patterns, extend data tables, and generate predictions. Within this component, the educator materials provide “Preguntas de evaluación” and “Preguntas para profundizar” to prompt students to explain their pattern representations, justify their derived rules, and evaluate alternative solution methods. In the “Relacionar” section, embedded prompts instruct educators to have students analyze multiple approaches, justify their procedural decisions, and connect mathematical ideas across investigation strategies. The “Hablar sobre las ideas matemáticas” section structures partner and whole-class discourse in which students defend their isolation of the mathematical rule and demonstrate how their chosen representations support their thinking. Finally, during “Práctica y resolución de problemas” and the subsequent “Reflexión” phase, the educator facilitates ongoing evaluation by directing students to describe tabular patterns, generate ordered pairs, define variable relationships, and justify mathematical predictions for additional data values. Furthermore, the instructional materials provide structured educator guidance within the digital platform’s “Modelo de resolución de problemas” to facilitate mathematical discourse and student reflection on problem-solving approaches. The online educator materials include specific discussion prompts that instruct students to reflect about their strategies. These embedded digital prompts guide students to explain how they solved a problem, compare multiple solution strategies, explain why a strategy is effective, and support their reasoning with mathematical evidence. Throughout the online problem-solving routine, the platform directs students to defend their solutions, evaluate alternative strategies, and refine their thinking based on evaluation of their progress.

Additionally, the Guía del maestro includes a “Representémoslo en 3 actos” lesson for each topic with embedded educator guidance. For example, in topic 3, “Multiplicar números enteros de varios dígitos con fluidez,” the lesson 3-4 “Elevar al cuadrado” section has students apply multiplication and numerical relationships to determine how changes to a balance scale affect the overall balance. In “Acto 1,” educators prompt students to analyze the situation, predict how many figures must be added to change the balance, and explain their initial reasoning. In the “Acto 2” activity, educators prompt students to develop, represent, and justify solution models, explain their strategies, and compare methods with peers. In step 3, educators have students compare solutions with the actual result, reflect on the effectiveness of their approaches, and justify adjustments to their reasoning. Finally, students extend their understanding by creating a new problem that applies the same mathematical concepts to a different situation.

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

The Guía del maestro for lesson 10-10, “Patrones de suma,” features a “Supervisar, seleccionar y poner en secuencia” section that provides protocols for educators to monitor student strategies. Included prompts instruct educators, “Observe a los estudiantes mientras trabajan” and “Seleccione soluciones para que los estudiantes las presenten” to identify errors such as missing graph labels or misaligned axes. Additional prompts guide educators to ask questions that require students to explain pattern representations. The “Conversación en la clase” and “Hablar sobre las ideas matemáticas” sections provide discussion prompts for educators to direct student analysis of relationships across tables, graphs, and equations, instructing, “Pida a los estudiantes que participen en una actividad de pensar, trabajar en parejas.” The “Errores e intervención” section contains follow-up questions to clarify student thinking and reinforce mathematical reasoning, directing, “Pregunte a los estudiantes cómo se relaciona la longitud de un lado de un cuadrado con su perímetro.” Within each “Let’s Build” lesson, the “Prevent Misconceptions” feature outlines possible student errors and provides prompts for explanatory feedback. The subsequent “Práctica guiada” section provides error-intervention strategies that direct educators to recognize calculation mistakes, ask follow-up questions, and clarify concepts, while the exit ticket guidance identifies prerequisite-skill gaps. Additionally, in the Guía del maestro, lesson 12-5, “Volumen,” the “Ejemplos del trabajo de los estudiantes” section presents strategies for determining the volume of a rectangular prism, showcasing approaches that organize cubes into layers, rows, or columns along with multiplication methods. The educator guidance contains questions to analyze student reasoning and deliver explanatory feedback to build a conceptual understanding of volume. During step 1, “Supervisar,” the sections “Preguntas de evaluación” and “Preguntas para profundizar” direct educators to interpret student responses, assess whether students understand the relationships among geometric attributes, and ask follow-up questions to extend mathematical reasoning. The “Errores e intervención” section targets common misconceptions, such as counting only visible cubes or misidentifying prism dimensions, and instructs educators to guide students to isolate the number of layers, rows, and columns before calculating the total number of unit cubes.

The Guía del maestro for lesson 5-4, “La división con divisores más grandes,” features an “Investigar” section that requires students to solve a division task scenario using manipulatives while recording and explaining their reasoning. The “Ejemplos del trabajo de los estudiantes” section presents multiple solution strategies for student analysis, comparison, and discussion. It asks students to justify methods and evaluate different approaches. In the “Práctica y resolución de problemas” section, students solve division problems, complete area models, write equations, and document how partial quotients relate to multiplication and division. In the “Reflexión” section, prompts instruct educators to ask, “¿De qué manera se representa 192 dividido por 16 en un modelo de área? ¿De qué manera se podría escribir esto como un problema de multiplicación?” Educators support struggling students by directing them to draw an area model to represent the problem, which enables students to record connections among mathematical representations.