enVision+ Texas Matemáticas, 04

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 4 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, reading and writing numbers up to billions, and describing place-value relationships. Also, a Texas Essential Knowledge and Skills (TEKS) correlation table in the Guía de maestro program overview itemizes every grade 4 mathematics TEKS and identifies the specific lessons that introduce, practice, and assess each TEKS.

Additionally, in the Guía de maestro topic planner section titled “Vistazo del tema,” the “TEKS” column connects the standards to the corresponding lessons. In lesson 1-1, “Números hasta mil millones,” students apply TEKS standard 4.2B alongside process standards 4.1A and 4.1D. 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, decimals, geometry, 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 guide, which provides differentiated pathways, utilizing “Essential” lessons for compressed 135-day schedules and “Extension” activities for expanded 210-day calendars. Furthermore, the grade 4 scope and sequence outlines the number of instructional days and TEKS covered per unit, organized by topic and lesson.


Additionally, the Guía de maestro program overview includes an instructional sequence organized by topic. Within this component, the “Contenido y secuencia” tables correlate TEKS coverage with suggested instructional days per unit. These tables provide suggested pacing—calculated in minutes per lesson—for 135-, 165-, 180-, and 210-day school calendars while embedding specific days for differentiation and evaluation. For example, in topic 1, “Entender el valor de posición,” the table designates seven days for instruction, two days for differentiation, and three days for revision and evaluation within class periods ranging from 45 to 75 minutes per day.

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 section titled “Grade 4 Content Organization Rationale” outlines how topics group concepts to connect new learning to prior knowledge. For instance, the guide specifies that topics 1–2 focus on patterns, relationships, and place value to develop addition and subtraction fluency. This structure connects to the multiplication, division, fraction, and decimal strategies in topics 3–8. Furthermore, the “Organized to Build Connections” chart shows the sequence and development of these mathematical ideas across subsequent units.

Additionally, the “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 posición,” the “Vuelve atrás” and “Más adelante” fields state how students in previous grades explored place-value relationships and composed and decomposed numbers. The text details how grade 4 students extend this work to compare, order, and round whole numbers and decimals.

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

The grade 4 materials feature separate planning documents for unit and lesson analysis and internalization. The digital platform hosts these resources within the folder “Protocolos de internalización y herramientas de observación.” The “Protocolo de internalización del tema” outlines instructional pacing, topic learning progressions, and materials preparation. The “Protocolo de internalización de la lección” contains directions for analyzing lesson objectives, transition preparation, and lesson resources. Furthermore, the “Protocolo de análisis del trabajo de los estudiantes” provides instructions for evaluating student work, identifying misconceptions, and planning subsequent instructional steps.

Additionally, lesson 1-1 “Investiguemos: entender el valor de posición en números enteros” provides instructional delivery notes. For lesson 1-2, “Valor de posición,” the text outlines objectives, TEKS alignment, vocabulary, manipulatives, and place-value relationships. The educator notes contain discussion prompts, student misconceptions, and questions to guide lessons. Furthermore, the internalization protocols provide guidance for student work analysis to inform data decisions.

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” in the online platform offer 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 grade 4 “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.

At the beginning of each topic in the grade 4 Guía del maestro, the “Contexto matemático” section outlines mathematical content, instructional sequencing, and terminology. For example, the topic 2 “Contexto matemático” section lists academic vocabulary, including estimation, regrouping, and inverse operations, and details the instructional progression from estimation strategies to standard algorithms.


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 grade 4 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, the “Participación de la familia” 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.


The grade 4 topic 1 “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 place value and comparing numbers using 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 4 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 grade 4 Guía del ritmo de enseñanza 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.

For grade 4, the 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. For example, lesson 1-1 “Elaboremos: de números a mil millones” lists resources such as place-value blocks and charts, while lesson 3-1, “Multiplicar por 10 y 100,” includes place-value blocks and 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 timestamps at the top of the pages identify the timing suggestions 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 grade 4 Guía del ritmo de enseñanza, the step 4 component titled “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.

Furthermore, the materials identify resources for extended practice and enrichment, including “Reteach to Build Understanding,” “Enrichment,” and “Build Mathematical Literacy” activities and the “Differentiation Library” tool. For example, the “Biblioteca de diferenciación” includes 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 materials include the Cuaderno de evaluación, which features diagnostic exams, unit-specific tests, and lesson-level formative tools to evaluate student performance throughout the course. For example, topic 1 “Entender el valor de posición” includes multiple-choice and fill-in-the-blank evaluations, as well as “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, for each lesson in the Guía del maestro, the Guía del ritmo de enseñanza outlines embedded formative assessment opportunities. For example, the “Guided Practice” section follows visual learning to measure initial student understanding, the “Quick Check” section 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, for each lesson within the Guía del maestro, the Guía del ritmo de enseñanza 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” tool to assess mastery of the lesson content.

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

Specifically, the Cuaderno de evaluación contains the section “Assessment Guide: How to Administer Assessments,” 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 ritmo de enseñanza 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, where the “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 grade 4 materials include diagnostic, formative, and summative assessments aligned with the TEKS and lesson objectives. The Cuaderno de evaluación contains item analysis charts that map each question from the 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 of 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” and “Examen de preparación” evaluate course content through diverse item types, including multiple-choice, text-entry, and open-response questions. Furthermore, 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 “Assess and Differentiate” in each lesson includes the “Additional Practice” assessment to reinforce skills, alongside 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 guide educators to examine and discuss student work on assessments. This resource guides educators on how to use assessment data criteria for forming groups and making decisions on differentiation and 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 grade 4 scoring guide for the topic 3 performance task aligns each topic-specific task with the corresponding TEKS 4.5A and process standards 4.1.D, 4.1.E, and 4.1.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 includes item analysis charts, answer keys, and performance task scoring rubrics. These rubrics provide performance criteria to guide educators in evaluating whether the student demonstrates conceptual understanding to identify and address misconceptions. Furthermore, materials include the “Tabla de análisis de las preguntas,” which serves as a diagnostic tool pairing assessment items with intervention lessons and corresponding TEKS and provides 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, grade 4 lesson 5-1, “Usar cálculo mental para dividir,” includes educator guidelines to help students analyze visual data in alignment with the TEKS.

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” track student progress throughout each topic. Because the concepts are sequential, educators track whether students develop understanding gradually to reach proficiency by the end of the topic. Furthermore, the materials feature student progress and growth trackers to document growth before, during, and after topic instruction. For instance, for lesson 1-2, “Place Value,” the tool displays student self-assessments to determine student progress in investigating patterns in place values of numbers while recording whether a student is working on, almost meeting, or meeting each aligned TEKS.

Additionally, the materials integrate lesson overviews with a TEKS-aligned “Exit Ticket” component in each lesson that serves as a quick formative assessment, while accompanying educator notes guide the use of these results for targeted support alongside 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.

Each “Let’s Build” and “Let’s Investigate” lesson contains an educator-led intervention activity within the “Assess and Differentiate” section, utilizing small-group tasks and concrete models to scaffold foundational concepts. For example, in the grade 4 Guía del maestro, topic 7, lesson 7-6, “Representar la suma y resta de números mixtos,” provides an intervention activity using fraction models and guided practice for students requiring additional instructional support.

Additionally, the grade 4 online platform includes the component “Sistema de intervención,” which provides mini-lessons to address skills and content for which students have not yet demonstrated proficiency. For example, minilesson F-1, “Maneras de representar los números,” incorporates guided practice, for which the materials instruct educators to “Recuerde a los estudiantes que hallen el número de centenas, decenas y unidades en cada número. Déles más palillos si es necesario.” The lesson also includes an instructional materials list, specific vocabulary terms such as forma desarrollada and forma estándar, manipulatives, and pictorial models. Within the “Guided Practice” section, the materials provide 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 grade 4 Guía del maestro, the “Adaptaciones lingüísticas” section provides contextual explanations for cognates, English metalinguistic transfer, and topic-specific academic vocabulary. In topic 7, “Sumar y restar fracciones y números mixtos,” the topic opener contains pre-teaching activities to review mathematical terms and guides educators on introducing foundational academic language for each lesson.

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, where 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. To reinforce these concepts, the Guía del maestro includes a “Language Support Activity” within each “Elaboremos” section to provide support for lesson understanding

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 grade 4 lesson includes an “Early Finishers” component to challenge students who have mastered the core content. For example, the educator notes in the Guía del maestro for topic 7, lesson 7-6, “Representar la suma y la resta de números mixtos,” provide a real-life problem-solving question for early finishers. The “Hablemos de matemáticas” activity prompts students to evaluate expressions, justify whether two quantities are equivalent, and explain their reasoning using mathematical language. The “Apoyo al lenguaje” section provides discussion prompts that encourage students to analyze solution strategies and make connections between visual models and symbolic representations


Additionally, in the Guía del maestro, topic 7, lesson 7-6, “Representar la suma y la resta de números mixtos,” the “Quick Check” or “Comprobación rápida” feature provides instructional directions for educators to assign targeted enrichment activities that expand upon core lesson concepts. Educators utilize this tool to route students scoring 4–5 points to specific enrichment tasks within “Práctica adicional.” In this section, students solve complex problems, explain their reasoning, and apply concepts in new contexts.

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 “Aprendizaje visual,” educators are provided with questions and sample responses to model how fractions can be decomposed into equivalent sums. For example, in topic 7, lesson 7-1, “Descomponer fracciones,” within the “Explorar y comentar” section, educators are directed to ask questions such as “¿Qué representaciones usan los estudiantes?” to elicit student thinking and connect visual models to the concept.

In lesson 7-5, “Sumar y restar números mixtos,” within the step 1 “Investiguemos” component, the “Lesson Launch” assists educators in engaging students in a mathematical investigation. The “Anticipar” section within this launch guides educators to predict possible student misconceptions by considering how students utilize prior knowledge to approach the task. Furthermore, the Guía del maestro for topic 4, “Multiplicar por números de 2 dígitos,” contains a sample classroom conversation within the “Desarrollar G.R.I.T.” section. This feature delivers scripted educator language and direct instructional prompts to demonstrate how to multiply two-digit numbers using multiple mathematical strategies.

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

Each lesson incorporates instructional approaches and provides guidance to support educators in facilitating instruction. For example, in lesson 7-7, “Sumar números mixtos,” the “Elaboremos” begins with step 1, “Explore and Share,” where students draw on prior knowledge to explore lesson concepts. The lesson includes an “Apoyo al lenguaje” section that recommends reviewing mathematical vocabulary and engaging students in lesson discussions.


Additionally, the materials include educator guidance for lesson facilitation and delivery using more than two instructional approaches. For instance, in lesson 3-1, step 2, “Aprendizaje visual,” students and educators follow an instructional sequence to consolidate learning. During this step, students participate in a think-pair-share activity using models and partial products to solve problems while educators observe for and correct possible misunderstandings.

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

The online platform includes a program overview that features a chart identifying instructional structures for each activity and indicating whether the activity supports guided, independent, or collaborative practice. This guidance specifies opportunities for whole-group, small-group, and individual instruction while describing how each practice type supports the development of conceptual understanding, procedural fluency, and problem-solving skills.

Additionally, in the Guía del maestro, the “Vistazo a la Biblioteca de diferenciación” section for topic 3, “Multiplicar números por 1 dígito,” provides guidance and resources that support guided, independent, and collaborative practice. Furthermore, activities and games show educators how to organize instruction using various groupings and structures throughout the lesson.

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

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

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

The grade 4 materials outline lesson-specific vocabulary and provide instructional recommendations for listening, speaking, reading, and writing to build academic language throughout the topic. For example, in topic 3, “Multiplicar números de 1 dígito,” the “Transferencia metalingüística al inglés” section guides educators through metalinguistic transfer, cognates, false cognates, and transferable versus non-transferable language features between Spanish and English. Key components include explicit cognate connections such as distancia/distance and calendario/calendar to assist students in connecting home language features to grade-level mathematical content.

Additionally, the grade 4 materials identify topic vocabulary, prior terms, upcoming terms, vocabulary in context, and academic vocabulary associated with the unit. Each topic includes an “Adaptaciones del lenguaje” section that outlines strategies to support language development and content learning. For instance, instructions direct educators to read the problem aloud, have students identify familiar words that resemble words in their home language, and discuss the meanings of cognates.

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 topic 6, the “Adaptaciones del lenguaje” section provides language supports to develop student understanding of mathematical vocabulary related to the equivalence and comparison of fractions. This section identifies topic vocabulary, prior and upcoming terms, and academic vocabulary while clarifying mathematical meanings alongside everyday meanings for words such as fracción, sombrear, and reescribir. Furthermore, the “Transferencia metalingüística al inglés” section promotes cross-linguistic connections by identifying transferable and non-transferable language structures, false cognates, and cognates such as “park/parque” and “distance/distancia.” These integrated features connect language development to grade-level mathematical content.

Additionally, each topic includes lesson-specific vocabulary previews that outline background knowledge. For example, the “Adaptaciones lingüísticas” section in topic 6 contains a chart that compares the usage of identical terms across both a common language context and a mathematical context. This comparative chart includes words such as fracción, sombrear, and reescribir. Finally, explicit Spanish–English language transfer guidance, cognates, and false cognates establish cross-linguistic connections.

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.

In grade 4, the Cuaderno de evaluación provides topic assessments consisting of selected-response and constructed-response items aligned to grade-level standards. Educators track student performance using the “Tabla de análisis de las preguntas,” which links every item to its corresponding TEKS and specifies targeted intervention lessons for incorrect responses. The educator materials provide direct guidance to analyze student data and address identified learning gaps. In addition, the cumulative assessment for topics 1–6 features assessment items from diverse mathematical domains, including place value, fractions, decimals, operations, measurement, and geometry. The assessment layout requires students to evaluate, select, and apply different problem-solving strategies.

Additionally, within each unit of the grade 4 Guía del maestro, the “Evaluación y Diferenciación” section for step 4 contains assessments to monitor student mastery of the unit TEKS. For example, in topic 4, “Multiplicar por números de 2 dígitos,” lesson 4-1, “Usar el cálculo mental para multiplicar por múltiplos de 10,” paso 4 includes a five-question “Comprobación rápida,” which aligns to TEKS 4.4B and 4.4D. The educator materials direct educators to assign either an intervention or extension activity based on student performance data. Furthermore, the “Práctica adicional” section features an educator reference chart detailing the specific TEKS alignment and corresponding DOK level for every item to enable instruction and assessment across multiple 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 grade 4 Guía del maestro structures each unit sequentially around a four-step instructional framework. For instance, in topic 3, “Multiplicar por números de 1 dígito,” lesson 3-2 “Usar el cálculo mental para multiplicar” tasks outline a progression: step 1, “Explorar y comentar,” requires students to review prior multiplication strategies; step 2, “Aprendizaje visual” introduces the associative, commutative, and distributive properties of operations; and step 3, “Práctica y resolución de problemas,” transitions students from educator-guided examples to independent practice. Students justify their thinking in the “Hablemos de matemáticas” activity and evaluate solution reasonableness using multiple properties in the “Boleto de salida.” Finally, during step 4, “Evaluación y diferenciación,” students complete assessment tasks aligned to TEKS 4D, where performance data guides educators to deliver targeted interventions or above-grade-level extension tasks. These extensions require students to apply multistep operational properties to multidigit factors and non-routine algebraic contexts aligned with grade 4 standards.


Additionally, the program overview outlines how the curriculum sequences topics to connect new content to prior knowledge and repeats TEKS within and across topics. The “Coherence” and “Balance” sections specify that students build understanding through cross-grade, cross-topic, and cross-lesson connections using problem-based learning, visual learning, mathematical modeling, and procedural fluency. This progression utilizes the Concrete–Representational–Abstract (CRA) instructional model. This model requires students to solve problems using concrete manipulatives, diagrams, and models before connecting their understanding to abstract equations and procedures. For example, lesson 6-3 begins with students using area models to explore equivalent fractions. Students then transition to explaining “why different models represent the same fraction” to apply this understanding to create and identify equivalent fractions, and ultimately solve abstract problems using those models.

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

In the “Math Background: Coherence” section at the start of every topic, the “Looking Back,” “In This Topic,” and “Looking Forward” sections describe how mathematical concepts relate across units and topics. For example, in topic 3, “Multiplicar por números de 1 dígito,” the materials connect relationships between mathematical concepts across grade levels. The materials establish horizontal coherence within grade 4 by anchoring content in place-value understanding and progression from concrete estimation and partial products, using the distributive property, to the conventional multiplication algorithm. This progression builds on foundational skills from grade 3, where students used area models and repeated addition to multiply. Furthermore, the materials outline future learning trajectories, showing how single-digit multiplication in topic 3 connects to multidigit multiplication, multistep problem solving, and equivalent fractions later in grade 4. Additionally, the materials connect this content to multidigit fluency in grade 5, presenting mathematical skills within an integrated framework to support algebraic and proportional reasoning.

Additionally, in topic 5, “Dividir por números de 1 dígito,” the materials connect prior knowledge of multiplying and dividing multiples of 10 and 100 to multidigit division tasks instead of introducing topics in isolation. The progression routes foundational place-value concepts and mental math strategies into the standard division algorithm, where tasks require multidigit numbers to be broken down by place value. Across consecutive lessons, the materials feature concrete visual models such as area models, arrays, place-value blocks, and strip diagrams paired with abstract numerical procedures. This structure requires students to apply division as an extension of place value, estimation, and properties of operations.

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 “Adaptaciones del lenguaje” section for topic 3, “Multiplicar por números de 1 dígito,” the materials build upon términos previos from earlier grade levels, including properties of addition and strategies such as counting forward, counting backward, and compensation. These mathematical foundations connect to the current fourth-grade vocabulario del tema, where tasks require students to apply concepts to multiplication through terms such as associative property, commutative property, and distributive property alongside visual models like matriz and modelo de área. Furthermore, the material connects with future mathematical learning by previewing próximos términos such as cuadrado perfecto, which relies on the single-digit and multidigit multiplication skills practiced in this unit.

Additionally, in topic 8, “Representar, comparar, sumar y restar números decimales,” the “Contexto matemático y coherencia” section references prior knowledge from grade 3, including whole-number place value, addition, subtraction, and locating fractions on a number line, and connects these to grade 4 concepts such as equivalent fractions and comparing fractions with like denominators. These concepts connect to current grade 4 learning goals, where tasks require students to use decimal notation for tenths and hundredths, fractional forms, conventional algorithms, and grid models to add and subtract decimals. This linguistic and conceptual progression transitions into the “Más adelante” section, which links current work to grade 4 financial literacy concepts and establishes the trajectory for grade 5, where the curriculum extends place value to thousandths, requires rounding decimals, and introduces operational strategies with decimals.

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

In the Guía del maestro, each unit follows an instructional progression through the “Elaboremos” framework. For example, in topic 4, “Multiplicar por números de 2 dígitos,” lesson 4-1, “Usar el cálculo mental para multiplicar por múltiplos de 10,” the materials structure a progression across four distinct steps. During step 1, “Explorar y comentar,” students review multiplication strategies and models to estimate products involving multiples of 10. In step 2, “Aprendizaje visual,” students use associative, commutative, and distributive properties alongside place-value understanding to develop mental multiplication strategies. During step 3, “Práctica y resolución de problemas,” students complete guided practice before applying their learning independently. Finally, in paso 4, “Evaluación y diferenciación,” students complete assessment tasks aligned with the TEKS to determine if they require targeted intervention or extension activities. The materials apply this same coherent structure in lesson 4-3 “Investiguemos” section “Estrategias para multiplicar números de 2 dígitos.” In this lesson, the “Vuelve atrás” section links two-digit multiplication skills to foundational skills from previous lessons, including place value, basic multiplication facts, and estimation strategies like rounding and compatible numbers. The “En esta lección” section activates prior procedural knowledge to meet TEKS 4.4C. This section requires students to use concrete visual representations such as matrices and area models to decompose numbers into partial products.


Additionally, the Guía del maestro materials for topic 5, lesson 5-11 build on students’ prior understanding of division by linking partial quotients, place value, and equal groups. During the lesson, students compare a place-value model directly to the conventional algorithm. Students then apply place-value concepts to extend these procedures, using the conventional algorithm to divide two- and three-digit dividends by one-digit divisors to solve division problems.

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 topic 2, lesson 2-6, “Sumar números de varios dígitos,” the “Coherencia” section connects multidigit addition to prior skills. The “Vuelve atrás” component notes that students have previously practiced adding and subtracting whole numbers using the standard algorithm, requiring them to retrieve these foundational skills. This prior knowledge is activated in the “En esta lección” section, where students apply the standard algorithm and place-value structures to add numbers up to 1,000,000. Furthermore, the “Más adelante” section outlines future instructional blocks where students use the standard algorithm to solve multidigit subtraction. In addition, the materials provide additional spaced retrieval opportunities through the “Hablemos de matemáticas” section titled “Detective de números.” This component requires students to retrieve previously learned place-value understanding, estimation, and addition strategies to identify a mystery number. Through this design, the materials require students to use prior knowledge regarding number relationships and mathematical operations within a new problem-solving context.


Additionally, in the online platform, the grade 4 materials outline opportunities for students to retrieve previously learned skills through components such as fluency practice, review-what-you-know practice, spiral review, adaptive practice, topic review, and hands-on games. The overview includes a structural table specifying whether these retrieval opportunities occur during individual, whole-group, or small-group settings. Additionally, this table details when each component occurs within the instructional sequence, mapping the activities across guided, independent, or collaborative lesson blocks.

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 7, “Sumar y restar fracciones y números mixtos,” the materials integrate foundational vocabulary and concepts into problem-solving exercises across multiple lessons. For instance, the “Vocabulario” section connects mathematical terminology, including denominador, numerador, and número mixto, to visual representations. Students apply these conceptual definitions while decomposing fractions in lesson 7-1. This integration continues into lessons 7-2 and 7-3, where students utilize their understanding of common denominators to perform operations. Finally, in lesson 7-4, the materials utilize fractional concepts for estimation and reasonableness checks. By embedding vocabulary review, visual grouping models, and computational skills alongside new objectives within the “Topic Review,” the materials revisit and apply previous learning to reinforce procedural fluency. Furthermore, in the grade 4 Guía del maestro, topic 5, “Presentación del tema: dividir por números de 1 dígito,” the “Repasa lo que sabes” section combines foundational content acquired across previous units. This component requires students to review division vocabulary, solve division equations, round whole numbers to the nearest hundred, use compatible numbers, and apply the distributive property. Rather than practicing a single mathematical skill in isolation, students must evaluate mixed problem types to determine which previously learned operational and place-value strategies to apply. This structure enables students to reinforce prior knowledge to prepare for upcoming division concepts.

Additionally, at the end of each topic in the Guía del maestro, the “Repaso del tema” section provides interleaved practice for students to apply prior content in new contexts. For example, in topic 4, “Multiplicar por números de 2 dígitos,” the “Repaso del tema” section requires students to review multiplication strategies from topic 3. Additionally, tasks within this section require students to use models and partial products developed in earlier units to solve current mathematical problems.

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

The “Representémoslo en 3 actos” sections within the Guía del maestro include tasks that require students to create, analyze, and evaluate mathematical models of real-world situations. For example, in topic 9, “Reunir, organizar, mostrar e interpretar datos,” lesson 9-8, “Representémoslo en 3 actos: línea aelgada,” students compare data from two dot plots, analyze the information, and make predictions. In “Acto 2,” students collaborate to develop a mathematical model by applying problem-solving and communication strategies. In “Acto 3,” the solution is revealed, allowing students to verify results and reflect on their reasoning. Furthermore, students create a new problem like the one solved. Similarly, in lesson 8-2 “Elaboremos: entender y representar números decimales,” students analyze and evaluate mathematical models. The “Hablemos de matemáticas” section presents the open-ended task “¿Cuál no pertenece?,” featuring three suitcases labeled with different decimal masses. This task requires students to evaluate numerical representations, identify patterns, and justify their reasoning based on place-value by comparing tenths, hundredths, and thousandths. Additionally, the “Boleto de salida” evaluates student understanding through targeted questions requiring direct interpretation of mathematical notation. Question 1 asks students to interpret an expanded notation expression, “¿Cuál de los siguientes es igual a . . . ?” and match it to its standard decimal numeral representation. Question 2 asks students to determine the place-value of a specific digit within a real-world context: “La distancia desde la escuela hasta la casa de Milo es 3.57 millas. ¿Cuál es el valor del dígito . . . ?” This task requires students to analyze the positional value of the tenths and hundredths places.

Additionally, in lesson 5-9, “Usar la repartición para dividir,” students interpret and analyze multiple representations of division throughout the lesson. In step 1 and step 2, students use place-value models, drawings, and manipulatives to represent and solve division problems. In step 3, students create models to justify their solutions, and in step 4, they analyze division models, identify remainders, and explain the division process.

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

In the Guía del maestro, lesson 8-4, “Comparar y ordenar números decimales,” the “Comprensión de conceptos” and “Materiales” sections require students to construct and use place-value blocks, 100 grids, and number lines to represent and compare decimal values to the hundredths place. Lessons present real-world mathematical situations where students use these tools to model the lengths of various insects. Additionally, the “Anticipar” and “Evaluar la comprensión” sections direct educators to ask, “¿De qué se trata la tarea?,” “¿Qué están midiendo los estudiantes?,” and “¿Qué herramientas serán útiles en esta investigación?” These prompts require students to select and construct mathematical models to interpret the scenario.


Additionally, in lesson 6-2, “Fracciones equivalentes,” students create visual models to represent and analyze equivalent fractional amounts. In step 1, students manipulate area models and fraction strips to demonstrate different ways to represent the same value and compare equivalent fractions. Furthermore, the “Paso 3” section requires students to construct and use original visual models to explain and justify fraction equivalence.

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, “Investiguemos,” lesson 9-2, “Diagramas de puntos,” students analyze a real-world multicolumn data table showing weekly recycling totals in pounds. Rather than including formulas, the open-ended task directs students, “Muestra cómo podrías organizar los datos sobre el reciclaje. Luego, escribe algunas cosas que notes sobre los datos.” The framework combines three language routines with the educator prompt “¿Cómo podrían organizar los datos sobre cuánto se recicla?,” requiring students to identify mathematical relationships in unfamiliar datasets. Similarly, in the Guía del maestro, lesson 9-5, “Leer diagramas de tallo y hojas,” students interpret a stem-and-leaf plot of test scores by organizing values by place value. The “Explorar y comentar” and “Aprendizaje visual” sections require students to connect place-value concepts to data interpretation rather than performing isolated procedural skills. Students then apply this conceptual understanding to independent practice tasks involving new context datasets, including dog weights and baseball statistics.


Additionally, in the Guía del maestro, lesson 8-4, “Comparar y ordenar números decimales,” students analyze aquatic animal measurements to compare and order values using models, 100 grids, or number lines. The tasks require students to identify equivalent decimal representations such as 8, 8.0, and 8.00 or 7.5 and 7.50 to determine greater or lesser values. During independent practice, students interpret and order decimal numbers across varied real-life datasets. Similarly, in lesson 6-5, “Usar la multiplicación para hallar fracciones equivalentes,” exercise 24, students apply fraction equivalence to a new context. The problem requires students to calculate total flower bouquets purchased by using multiplication and equivalent fractions to analyze fractional parts containing different flower types.

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

In the Guía del maestro, under the “Biblioteca de diferenciación” for topic 5, “Dividir por números de 1 dígito,” the “Mantener la comprensión y la fluidez” section provides resources to develop grade 4 division fluency through print and digital formats. Specifically, the materials include games such as “Sumar tres, restar tres,” where students divide multidigit numbers by divisors from 2 to 9, and “Girar para mostrar,” which focuses on dividing numbers up to four digits by a single-digit divisor. Additionally, the platform integrates digital fluency vocabulary, escape games, and dedicated “Práctica de fluidez” tasks targeting four-digit by one-digit division to support accurate, flexible, and efficient computation skills. Furthermore, in topic 8, the “Desarrollar la fluidez” section features an “Emparejalo” activity that requires students to divide four-digit dividends by one-digit divisors and match quotients to provided clues. To solve these problems, students execute estimation, mental math strategies, and the standard division algorithm.

Additionally, The “Biblioteca de diferenciación” in the Guía de maestro features hands-on fluency games for each topic. For example, topic 3 includes multiplication games, including “Multiplicar por varios dígitos” for groups of three and “Carrera loca,” where student pairs multiply four-digit numbers by one-digit numbers. This fluency segment requires students to complete a summative practice worksheet immediately following game play.

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.

Materials provide opportunities for students to practice the application of efficient, flexible, and accurate mathematical procedures within the lesson and throughout a unit. Materials utilize area models to transition students from concrete grid counting to abstract multidigit multiplication. In lesson 4-3, “Estrategias para multiplicar números de 2 dígitos,” students partition a 13 × 15 grid into four smaller rectangles in multiple ways to practice procedural flexibility. The materials support formative assessment by including strategic educator prompts such as “¿Cómo están los estudiantes descomponiendo los factores?” and “¿Existe otra manera de resolver el problema?” Furthermore, the “Relacionar” and student work analysis sections reinforce efficiency and accuracy. In these sections, students compare diverse strategies, including decomposing by place value, and answer analytical questions. This sequence guides students throughout the unit to identify place-value decomposition as a progression toward standard algorithm multiplication. Furthermore, in the Guía del maestro for topic 7, lesson 7-1 embeds these procedural practice tasks into the beginning of lessons through “Hablemos de matemáticas” routines. These included structured activities feature specific exercise types, including “Detective de números.” The initial lesson routines require students to execute diverse mental calculation strategies to verify procedural accuracy and operational efficiency prior to beginning the core lesson content.


Additionally, in the Guía del maestro, topic 10, lesson 10-5, this procedural development occurs during “Investigator” lessons. In step 1, students apply prior mathematical methods to solve introductory problems. During the strategy comparison phase, the tasks require students to evaluate operational efficiency by transitioning from additive strategies to multiplication procedures to build procedural fluency and conceptual accuracy.

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 topic 8, “Representar, comparar, sumar y restar números decimales,” the lesson layout requires students to use previous mental math and estimation strategies before introducing concrete models, place-value blocks, and 100 grids for decimal operations. In lesson 8-9, “Elaboremos Usar modelos para sumar y restar números decimales,” the materials reinforce accuracy and efficiency by anchoring student understanding in place-value concepts, including reminders that 10 hundredths equal 1 tenth, and 10 tenths equal one whole. To guide students to evaluate processes and justify solutions, the “Hablemos de matemáticas” section includes analytical discussion questions, including “¿Qué notas sobre los modelos?,” “¿Cuál es la suma de las barras?,” and “¿Cuántas centésimas hay?” In addition, the unit assesses individual accuracy and application through the “Boleto de salida” section, which features word problems and calculation questions. Furthermore, in the Guía del maestro for topic 8, “Representar, comparar, sumar y restar números decimales,” lesson 8-13, “Resolver problemas sobre dinero,” the “Representémoslo en 3 actos” section embeds this evaluation framework. In “Acto 1,” students watch an introductory video to establish a collective question. In “Acto 2,” students gather data to build mathematical models and apply calculation procedures. In “Acto 3,” the video reveals the final answer, requiring students to analyze their mathematical solutions and modify their initial calculation processes for accuracy and efficiency.

Additionally, in the Guía del maestro, lesson 6 -11, the “Práctica guiada” section includes “Errores e intervención” exercise 1, in which students analyze a common misconception regarding equivalent fractions. The instructions direct educators to prompt students to plot mixed numbers on a number line to verify mathematical reasoning. In this task, students analyze why the fractions do not represent identical points on the number line and modify their final conclusions based on the visual evidence.

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

In topic 8, “Representar, comparar, sumar y restar números decimales,” lesson 8-4, the “Investiguemos” section includes targeted educator monitoring guidance during step 1. The instructions supply specific assessing and advancing questions designed to redirect students from procedural errors to optimized mathematical strategies. Furthermore, the material outlines a systematic framework for selecting and sequencing student solutions to highlight procedural efficiency. The lesson concludes with additional embedded questioning matrices and pedagogical strategies in step 2 to reinforce standard operational approaches. Similarly, lección 8-13, “Suena el timbre” utilizes the “Representémoslo en 3 actos” mathematical modeling framework to build procedural efficiency. In “Acto 1: el anzuelo,” educator guidance prompts the activation of prior knowledge through estimation without formal calculations by using the open-ended question “¿Quién presionó el timbre más cerca de los tres segundos?” In “Acto 2: el modelo,” the materials instruct educators to prompt students to identify the necessary information before providing the exact decimal values for four students. In “Acto 3: la solución,” educator guidance instructs educators to direct students toward a number line representation to visually compare how close each decimal value is to the whole number three. The three acts transition from estimation to quantitative modeling and visual number line comparison to scaffold student reasoning toward efficient mathematical approaches.

Additionally, in lesson 6-9, “Desafío de chocolate,” the “Comentar estrategias de solución” section provides explicit educator guidance to analyze and contrast diverse student mathematical methods for determining fractional value greatness. This structured instructional framework directs educators to facilitate peer discussions regarding individual student approaches. The instructional notes then outline specific scaffolding steps to transition students from a reliance on concrete visual models to more efficient symbolic comparison strategies.

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

In the Guía del maestro for lesson 3-1, “Elaboremos: multiplicar por 10 y 100,” the introductory section features the core balance between conceptual comprehension and procedural skill. The lesson establishes conceptual understanding by requiring students to utilize basic operations alongside place-value patterns. Concurrently, the materials prompt procedural skills by prompting students to perform calculations built upon place-value foundation. This focus is reinforced through embedded discussion prompts, such as the conceptual question in the “¡Convénceme!” section: “¿Cómo restar de un número con un cero en el lugar de la decena?” Procedural application is further assessed via the exit ticket, which features multiple-choice formative questions such as “¿Cuáles estrategias usarías para multiplicar 8 × 50?” These elements connect the multiplication tasks to TEKS 4.4B, which requires students to determine products of a number and 10 or 100 using mental math, properties of operations, and place-value understandings. The “Contexto matemático” section for topic 3 outlines the conceptual framework, detailing how students construct an understanding of one-digit multiplication through place value, arrays, equal groups, estimation, and the distributive property. This section also links prior knowledge to future grade-level concepts. Furthermore, the “Equilibrio” section establishes the procedural emphasis by detailing how students develop mathematical fluency through mental computation, partial products, and the standard multiplication algorithm, thereby illustrating how conceptual understanding supports procedural proficiency.


Additionally, in lesson 5-7, “Usar cocientes parciales para dividir dividendos más grandes,” the content builds conceptual understanding through area models, place-value reasoning, and partial quotients. Concurrently, the materials establish procedural proficiency by requiring students to apply estimation strategies and divide larger dividends using partial quotients. In addition, the step 2, “Aprendizaje visual” section of less 7-9, within the Guía del maestro develops conceptual understanding by including how decomposing mixed numbers and utilizing equivalent fractions enables students to add and subtract fractions with like denominators. The materials then build procedural proficiency by modeling multiple solution strategies, including decomposing mixed numbers, renaming fractions, and using number lines to solve problems. Furthermore, embedded educator prompts guide students to explain the mathematical reasoning behind a strategy before applying those procedures to solve similar 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 grade 4 Guía del maestro for lesson 6-2, “Fracciones equivalentes,” integrates concrete, pictorial, and abstract representations. The materials use pictorial representations through a fraction strip diagram that provides a visual layout of area models to compare lengths. This diagram serves as a bridge to concrete manipulatives, as the educator guide instructs the incorporation of physical fraction strips for hands-on learning. These visual and physical models support the transition to abstract representations, where tasks require students to translate the visual segments of a pictorial fraction wall into symbolic fractional notation and write down the equivalent numerical fraction to solve real-world problems. Furthermore, the program overview includes the CRA instructional model, outlining a progression from concrete manipulatives such as counters, cubes, place-value blocks, and tiles to drawings and then transitioning to abstract numerical symbols and procedures. Lessons embed multiple representations across and within individual lessons to transition students from conceptual visualization to abstract application. Additionally, the materials provide digital manipulatives to support representational transitions during instruction.

In lesson 5-9, “Usar la repartición para dividir,” students use physical place-value blocks and digital manipulatives to model division situations. The tasks require students to construct and interpret pictorial representations, including drawings and place-value models, to demonstrate the division of quantities into equal groups. Students then connect these visual models to abstract mathematical representations by writing and solving division equations. In lesson 7-10 “Representémoslo en 3 actos,” the “Solo agrega agua” section introduces a real-world scenario featuring three liquid containers, establishing a concrete contextual baseline for fraction comparison. During “Acto 2,” the student work exemplars and educator guidance prompt students to represent these volumetric quantities using visual fraction drawings. In “Acto 3,” students compare and justify the amounts by generating equivalent fractions and symbolic mathematical expressions to determine the container with the greatest volume. This instructional sequence connects concrete, pictorial, and abstract representations within a single lesson.

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 includes the CRA instructional model, outlining a systematic progression from manipulatives to pictorial illustrations and abstract numerical symbols across and within lessons. Specifically, during the “Explore” and “Let’s Build” sections, students manipulate concrete tools including counters, cubes, place-value blocks, and tiles to construct physical models. As instruction progresses, the materials direct students to transfer their mathematical reasoning into pictorial drawings, diagrams, and visual models. Finally, during the “Visual Learning” section, the educator guidance provides targeted instructional prompts that require students to connect these concrete and pictorial representations directly to abstract symbols, numbers, and algebraic procedures. For example, in lesson 2-2, “Hallar sumas y diferencias con cálculo mental,” students use base 10 blocks and corresponding drawings to resolve subtraction tasks. Within the “Aprendizaje visual” section the materials require students to connect these models to the standard subtraction algorithm by performing and recording each regrouping step across hundreds, tens, and ones places. Embedded prompts direct students to explain their mathematical reasoning, evaluate model-based against algorithmic solutions, and analyze how place-value patterns relate to regrouping. Furthermore, the “Actividad de intervención” requires students to generate and contrast solutions using both physical blocks and the standard algorithm, reinforcing the relationship between place-value models and abstract numerical procedures.

Additionally, in lesson 6-3, “Fracciones equivalentes con modelos de área,” students use concrete fraction strips alongside geometric area models including circles, rectangles, and triangles to represent equivalent fractions. Within the “Aprendizaje visual,” the materials require students to connect pictorial models of pizzas and geometric shapes to abstract written fractions by comparing and explaining why they represent identical portions of a whole. In the “Trabajo del estudiante” section, students construct original area models to represent equivalent fractions, justifying how the numerators and denominators correspond to the shaded regions. The lesson further requires students to articulate why fractions are equivalent by describing how different models represent the same fractional amount. During the “Actividad de intervención,” students manipulate fraction strips to generate equivalent fractions and write corresponding symbolic equations, reinforcing the connections between manipulatives, visual representations, and abstract fractional concepts.

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 2, “Sumar y restar números enteros de varios dígitos,” “Presentación del tema,” “Repasa lo que sabes,” students use a visual review page to connect prerequisite mathematical concepts with grade-level academic vocabulary, including algoritmo, propiedad conmutativa de la suma, propiedad asociativa de la suma, compensación, estimación, números compatibles, variables, and operaciones inversas. Educator guidance for this section includes a vocabulary activity where students complete a Frayer organizer for each term to record definitions, characteristics, examples, and visual representations. Additionally, In the Guía del maestro, lesson 10-6, “Equivalencia con unidades métricas de longitud,” the “Apoyo al lenguaje” section directs educators to facilitate oral and written explanations. The materials incorporate manipulatives and visuals, explicitly instructing educators to utilize metric rulers so students can compare markings and relative sizes of units. The lesson includes guided questions to prompt student reasoning, such as “¿Cuál es la relación entre centímetros y milímetros?” and “¿Qué son las pequeñas líneas entre cada una de las marcas de centímetros en la regla?” Furthermore, the materials feature an extension discussion under “Hablemos de matemáticas” that asks, “¿Qué significa que algo sea una libra?” Finally, the independent assessment section, “Boleto de salida,” requires students to identify the appropriate metric unit to measure a laptop and complete a conversion of a specific distance in metros.

Additionally, in the Guía del maestro, lesson 8-13, “Representémoslo en 3 actos: suena el timbre,” begins with a visual model, a video, and pictures to establish a concrete context for observing, making predictions, and connecting mathematical ideas to real-world situations. The “Reforzar el vocabulario” section directs educators to provide manipulatives and concrete models that support conceptual development. Throughout “Acto 1,” “Acto 2,” and “Acto 3,” educator prompts facilitate structured academic discussions. Specifically, educators use guiding questions such as “¿Quién presionó el timbre más cerca de los 3 segundos?” and “¿Por qué creen que su predicción es la respuesta a la pregunta principal?” to guide students in discussing predictions, explaining reasoning, comparing strategies, and justifying solutions using precise terminology. Furthermore, each unit in the Guía del maestro includes a “Representémoslo en 3 actos” lesson. In topic 3, “Multiplicar por números de 1 dígito,” lesson 3-10, “Torre de pancakes,” students apply multiplication concepts to determine ingredient ratios. Students analyze visual data in “Acto 1,” build and justify a mathematical model using academic vocabulary in “Acto 2,” and compare solutions with actual results to analyze efficiency in “Acto 3.” Beyond these units, the “Biblioteca de diferenciación” includes juegos de vocabulario to reinforce terminology, while actividades con materiales digitales manipulables such as “Montar el juego” utilize area models and the distributive property to build conceptual understanding. Finally, the “Matemáticas y lectoescritura” resources blend math with literacy tasks, while juegos prácticos and juegos digitales provide systematic contextual reinforcement.

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 2-3, “Hallar sumas y diferencias con cálculo mental,” under step 2, “Aprendizaje visual,” the text embeds vocabulary instruction directly within mathematical tasks. The section directs educators to use the problem presented in “Apoyo visual” to make linguistic connections between propiedad asociativa de la suma and the root word asociar. Educators use scripted questions to prompt students to explain what it means to associate numbers, identify which property applies to a given expression, and compare the propiedad conmutativa de la suma, propiedad asociativa de la suma, and propiedad de identidad de la suma. Furthermore, students apply compensación, contar hacia adelante, and contar hacia atrás while solving mental computation problems. Additional guidance in “Rutina del lenguaje” directs educators to have students explain how these properties simplify computation, while the “Hablar sobre las ideas matemáticas” section guides educators to facilitate discussions where students communicate their mathematical reasoning using the targeted vocabulary terms throughout the lección. Furthermore, in the Guía del maestro, “Repaso del tema 2: sumar y restar números enteros de varios dígitos,” the materials provide specific strategies to reinforce vocabulary before and after task completion. The oral language review directs educators to facilitate the activity “¿Correcto o incorrecto?” to reinforce the word list verbally. Additionally, the “Escritura en matemáticas” section scaffolds writing by directing students to create riddles using propiedad asociativa, propiedad conmutativa, and algoritmo. Within the student materials, contextual items measure language development by requiring students to circle the property represented in specific questions and respond to open-ended prompts using at least three formal vocabulary words from a word bank to explain a peer’s mental math strategy.

Furthermore, in the Guía del maestro, lesson 5-1, “Usar cálculo mental para dividir,” the “Explorar y comentar” section prompts educators to ask, “¿Cómo usan los estudiantes estrategias de cálculo mental para ayudarlos a dividir?” The guidance directs educators to connect informal strategies to academic terminology by integrating valor de posición, cálculo mental, multiplicación, división, decenas, centenas, and cociente into student discussions. Additionally, in the topic 7 “Repaso del tema,” the “Repaso del vocabulario” section provides structured review strategies. The “Lenguaje oral” subsection directs educators to facilitate an oral vocabulary game where students listen to clues, identify mathematical terms, and justify responses within the context of adding and subtracting fractions. The lesson continues this scaffold in “Escritura en matemáticas,” where educators direct student pairs to author vocabulary clues and exchange them with peers to apply precise language. Similarly, the Guía del maestro includes embedded vocabulary scaffolds within the end-of-unit “Repaso del tema” sections through “Comprender el vocabulario” and “Usar el vocabulario” activities.

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 2-2, “Restar números enteros,” the ”Repaso del tema” section, “Reforzar el vocabulario,” identifies the academic term algoritmo convencional for student application. Under step 2, “Aprendizaje visual,” the “Ampliar las matemáticas” section provides questions prompting students to explain regrouping and justify estimates using complete sentences. The text builds mathematical syntax through the routine “Rutina de lenguaje: cada vez más sólido y claro,” instructing educators to have students document their solution methods, discuss ideas with a partner, listen to peer explanations, and revise their written responses. To develop mathematical discourse, “Hablar sobre las ideas matemáticas” directs educators to facilitate discussions regarding valor de posición and reagrupación, while the “Pensar emparejar compartir” routine in “Apoyo al lenguaje” requires students to explain and compare the steps used to subtract three-digit numbers. For corrective feedback, “Prevenir malentendidos” identifies anticipated misconceptions and provides questioning guidance to correct inaccurate language. Throughout “Explorar y comentar” and step, “Práctica y resolución de problemas,” the “Práctica guiada,” “Errores e intervención,” and “Escoger estrategias eficientes” sections provide “Ejemplos del trabajo de los estudiantes” and sample prompts to model precise vocabulary and complete mathematical statements.

Additionally, in the Guía del maestro, lesson 8-11, “Elaboremos: usar el algoritmo convencional para restar números decimales,” the materials provide discussion prompts in step 1, “Explorar y comentar,” that require students to explain operational choices and compare solution methods. The text directs educators to ask questions such as “¿Qué operación usan los estudiantes?” to connect mental math strategies with the conventional algorithm. Student work samples and educator prompts provide exemplar responses to guide educators in responding to student thinking. During step 2, “Aprendizaje visual,” the lesson introduces academic vocabulary, including reagrupar, punto decimal, décimas, centésimas, and algoritmo convencional, alongside scripted questions that prompt students to explain regrouping and place value. The “Rutina de lenguaje” directs students to discuss reasoning with a partner to refine language through peer discussion. Finally, the “Hablemos de las ideas matemáticas” section instructs educators to have students compare solution strategies and justify their reasoning.

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

The grade 4 materials integrate the TEKS mathematical process standards (TEKS 4.1A through 4.1G) directly within grade-level content across lessons, units, instructional days, and program assessments. The Guía del ritmo de enseñanza features a scope and sequence chart showing that process standards are embedded throughout every content theme rather than taught in isolation. For example, lesson 1-1 and lesson 1-2 tie content standards TEKS 4.2B and 4.2C with process standards TEKS 4.1A, 4.1B, 4.1C, and 4.1G, directing educators to use concrete tools like place-value blocks and tables for numbers up to 1 billion. Additionally, lesson 1-4, “Comparar números enteros,” integrates TEKS process standards 4.1A, 4.1B, 4.1F, and 4.1G, requiring students to analyze mathematical relationships and apply comparative terms, including mayor que and menor que, to justify how whole numbers are ordered. To support daily instruction, the section “Estándares de procesos matemáticos de los TEKS en la enseñanza” provides a problem-solving model instructing educators to guide students through analyzing information, developing solution strategies, justifying reasoning, and communicating conclusions using multiple representations. Furthermore, the section “Estándares de procesos en problemas y evaluaciones” dictates that mathematical tasks require the simultaneous application of multiple process standards, supported by the Manual de resolución de problemas which supplies a structured model requiring students to analyze data, select operational strategies, and justify solutions.

Additionally, in the Guía del maestro, each topic begins with an “Estándares de los procesos matemáticos de los TEKS” page that highlights two process standards integrated into the lessons. The section describes how students use these processes to acquire and demonstrate mathematical understanding and provides educator questioning strategies to support student proficiency. In topic 3, “Multiplicar por números de 1 dígito,” this section identifies TEKS 4.1.B (problem-solving models) and TEKS 4.1.F (analyzing mathematical relationships to connect and communicate ideas). Similarly, the “Estándares de los procesos matemáticos de los TEKS” page for topic 8 outlines how students apply mathematics to solve everyday problems and communicate mathematical ideas using symbols, diagrams, graphs, and precise language. The educator guidance includes grade-level learning experiences where students solve real-world decimal problems, compare and order decimals, and justify their reasoning. Additionally, the section provides discussion prompts requiring students to analyze, communicate, and justify their mathematical thinking.

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 identifies the TEKS process standards aligned with each lesson throughout the program. The topic 1, “Valor de posición,” overview includes a section titled “Estándares de procesos matemáticos de los TEKS” to outline embedded educator actions. The table of contents structures these instructional actions alongside the content TEKS for every lesson across all structural formats, including “Elaboremos,” “Investiguemos,” and “Representémoslo en 3 actos.” This layout identifies where educators prompt students to apply mathematics to real-world situations (TEKS 4.1.A), select and use representations (TEKS 4.1.C), and communicate mathematical ideas and reasoning (TEKS 4.1.D). By listing the process standards (1A–1G) alongside the lesson content, the materials demonstrate how these standards integrate with grade-level instruction across all topics and lesson types rather than in isolated lessons.


Additionally, at the beginning of each topic in the Guía del maestro, the “Estándares de los procesos matemáticos de los TEKS” page identifies process standards and details how students apply them to develop mathematical understanding. This page also provides educator questioning strategies to support student proficiency during content engagement. For example, topic 6, “Equivalencia y comparación de fracciones” utilizes an “Estándares de los procesos matemáticos de los TEKS” section to highlight specific standards, including selecting appropriate tools (TEKS 4.1.C) and analyzing mathematical relationships (TEKS 4.1.F), to connect these processes directly to fraction concepts. Similarly, topic 3, “Multiplicar por números de 1 dígito” emphasizes TEKS 4.1.B (using a problem-solving model) and TEKS 4.1.F to link instructional content to student learning. Finally, the “From the Authors: TEKS Mathematical Process Standards” section of the program overview confirms that materials integrate these daily processes into lessons, tasks, assessments, and the Manual de resolución de problemas rather than presenting them as isolated skills.

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

In the overview for topic 8 “Representación, comparación, suma y resta de decimales,” the “Estándares de procesos matemáticos” section states that opportunities to practice these standards are embedded across the topic. The materials include a table outlining how students demonstrate the standards throughout the unit, such as using place value for money calculations or explaining decimal comparisons, highlighting standards TEKS 4.1.A and TEKS 4.1.D. Furthermore, the materials provide guiding questions for educators to integrate throughout lessons to prompt reflection on fractional and decimal relationships, representations, estimations, and place-value strategies. Similarly, the overview for topic 12, “Comprensión de las finanzas personales,” outlines opportunities for students to apply the process standards, specifically highlighting instructional focuses on TEKS 4.1.C and TEKS 4.1.G. Overview charts within this topic explain how students connect these processes to financial literacy content, such as using mental math to calculate profits, comparing home versus bank savings, and distinguishing between fixed and variable expenses. Additionally, the materials include a set of guiding reflection questions for educators to use across the unit.


Furthermore, the “Planes de la lección para Texas” section within the online platform identifies the TEKS process standards for each lesson and describes how those standards embed throughout instruction. Each lesson includes educator guidance across the “Explore/Investigate,” “Visual Learning or Relate,” “Practice and Problem Solving,” and “Evaluate and Differentiate” phases to direct students to explain mathematical thinking, communicate ideas, analyze relationships, connect representations, and solve problems. For instance, topic 1, “Entender el valor de posición” includes a “Conocimientos y destrezas esenciales de Texas (TEKS)” section per lesson. Within this topic, lesson 1-1 “Elaboremos: de números a mil millones” incorporates TEKS 4.1.A (apply mathematics to problems arising in everyday life, society, and the workplace) and TEKS 4.1.D (communicate mathematical ideas, reasoning, and their implications using multiple representations, including symbols, diagrams, graphs, and language as appropriate). This structural layout identifies the correlation between process standards and content across all lessons within the unit.

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

Within the Libro del estudiante, lesson 4-3, “Investiguemos: estrategias para multiplicar números de 2 dígitos” targets content standards TEKS 4.4.C and TEKS 4.4.D and lists TEKS process standards 4.1.A, 4.1.C, and 4.1.F. The materials guide students to apply a mathematical problem-solving model, decompose numbers using area models, and explain their reasoning. In the Guía del maestro, lesson 4-1, “Elaboremos: usar el cálculo mental para multiplicar por múltiplos de 10,” includes an “Análisis de los ejercicios: práctica y resolución de problemas” table and an “Análisis de los ejercicios: práctica adicional” table. These tables identify the content TEKS, corresponding process standards, and problem complexity levels for each group of practice problems and assessment items across all “Let’s Build” and “Let’s Investigate” lessons.


Additionally, each lesson in the Guía del maestro includes a “Conocimientos y destrezas esenciales de Texas (TEKS)” section to identify targeted knowledge and skills alongside a separate “Estándares de los procesos matemáticos de los TEKS” section. For instance, in lesson 3-1, “Multiplicar por 10 y 100,” these sections identify content TEKS 4.4.B and supporting process standards TEKS 4.1.A (applying mathematics to everyday problems), TEKS 4.1.F (analyzing mathematical relationships to connect and communicate mathematical ideas), and TEKS 4.1.G (displaying, explaining, and justifying mathematical ideas using precise mathematical language). Similarly, within the Libro del estudiante, lesson 6-3, “Fracciones equivalentes con modelos de área,” identifies the process standards within the lesson objective. During this lesson, students use area models and fraction strips to determine equivalent fractions, explain why 3/4 and 9/12 are equivalent, and complete practice problems, which include State of Texas Assessments of Academic Readiness (STAAR) practice items.

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

The materials in the Guía del maestro for topic 12, “Comprensión de finanzas personales,” provide opportunities for students to think mathematically, persevere through solving problems, and make sense of mathematics. Within the “GRIT” section, under “Desarrollar confianza,” the materials guide educators to support students as they evaluate financial choices, including saving and investing for future needs. Furthermore, the “Seguir intentando: resiliencia” section prompts students to distinguish between fixed expenses, such as rent or car payments, and variable expenses, such as grocery or electricity bills. Students also practice perseverance by managing time, calculating profits, organizing items by cost, and comparing sale prices with purchase prices. Throughout these activities, the materials remind educators to emphasize consistent practice as students strengthen their understanding. The “Ejemplo de la conversación de clase” section models a multistep financial decision in which students partition a total amount into categories for saving, spending, and sharing. This structure helps students make sense of mathematics by applying budgeting concepts to personal finance decisions. Additionally, every lesson in the Guía del maestro includes tasks for students to develop mathematical sense while solving problems. For example, in topic 12, lesson 12-2 “Elaboremos: gastar, ahorrar y compartir” begins with step 1, “Explora y comenta,” where students analyze situations using prior knowledge, discuss strategies, and justify ideas with peers before formal instruction. Students refine their reasoning to think mathematically in step 3, “Práctica y resolución de problemas,” by applying concepts in guided and independent activities, explaining solution methods, and connecting mathematical strategies. In the “Hablemos de matemáticas” section, students analyze four distinct sets of coins, identify the outlier, and justify their reasoning. The task allows for multiple mathematical justifications to prompt higher-order thinking and algebraic reasoning over routine computation. Finally, the “Boleto de salida” section presents multistep financial literacy word problems that require students to calculate remaining allowance after spending and lending from a fixed budget. These items require students to persevere through executing multiple operations, contextualize abstract quantities, and interpret real-world mathematical applications.


Additionally, in order to think mathematically, lesson 6-2, “Fracciones equivalentes,” prompts students to investigate multiple ways to represent equivalent fractions using area models, fraction strips, and visual models. In step 1, students compare different solution strategies, explain their reasoning, and determine whether different-sized tiles represent the same fractional amount. To make sense of mathematics, in step 2, students analyze classmates’ work, justify why fractions are equivalent, and connect models to mathematical ideas. In order to persevere through solving problems, in step 3, “Práctica y resolución de problemas,” students solve real-world and visual problems, reflect on how different representations show the same value, and explain their thinking. Furthermore, in the Guía del maestro, topic 3, “Multiplicar por números de 1 dígito,” lesson 3-4, the “Investiguemos” section prompts students to complete a three-step investigation utilizing concrete, pictorial, and abstract representations. In step 1, “Investigar,” students use two-colored square tiles or grid paper to construct concrete models of multiplication and explain how their representations illustrate the mathematical concepts. In step 2, “Relacionar,” students analyze, justify, and compare their developed strategies, connecting their concrete models to pictorial representations and symbolic multiplication methods. Furthermore, to persevere through solving problems, in step 3, “Práctica y resolución de problemas,” students apply their understanding by solving multiplication problems using the provided models, creating pictorial representations of new situations, and recording solutions with numerical expressions and equations.

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 8-2, “Entender y representar números decimales,” students investigate decimal representations using standard form, expanded notation, word form, place-value charts, and decimal grids. In step 1, “Explora y comenta,” students determine which mass does not belong to a suitcase by comparing and subtracting decimals. They evaluate multiple strategies, such as 100-grid drawings, equations, mixed numbers, and decimal notation. In step 2, “Relacionar,” the “Aprendizaje visual” section demonstrates how these different forms represent the same value, accompanied by educator prompts directing students to compare the approaches. In step 3, “Práctica y resolución de problemas,” students convert between representations and justify why different forms describe identical quantities. Furthermore, in lesson 11-1, “Rectas, semirrectas y ángulos,” students investigate and compare roof designs by representing angles through drawings, visual models, sketches, and geometric comparisons to determine their relationship to a right angle. During step 1, “Investigar,” students analyze sample work showing different representations, including sketches, traced right angles, and direct visual comparisons, while educator guidance prompts students to explain how each representation supports their thinking. In step 2, “Relacionar,” students discuss similarities and differences among solution methods, sequence strategies from simple to complex, and justify why different representations lead to the same mathematical conclusion. Step 3, “Práctica y resolución de problemas,” and step 4, “Evaluar y diferenciar,” extend this work through differentiated activities where students classify angles, defend their reasoning, and explain why a specific representation is appropriate for a given situation.


Additionally in the Guía del maestro, topic 3, “Multiplicar por números de 1 dígito,” lesson 3-12, “Pila de panqueques,” each section features a ”Representémoslo en 3 actos” subsection where students apply mathematical concepts to localized task scenarios. In “Acto 1,” students analyze the initial scenario and formulate predictions based on the information provided. In “Acto 2,” students construct, model, and justify different solution pathways while mapping numerical multiplication concepts to the scenario context. In “Acto 3,” students compare their finalized solution sets against the baseline mathematical result and document observations regarding their reasoning. Finally, students complete an extension task by constructing a new problem that utilizes the identical underlying mathematical processes and justifying how to use a mathematical model representation to solve the self-created problem.

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

Every “Elaboremos” lesson in the Guía del maestro includes an “Hablemos de matemáticas” routine that structures whole-class, partner, and small-group discussions where students solve problems, explain their reasoning, and evaluate various solution strategies. In topic 12, lesson 12-4, “Elaboremos: gastos fijos y variables,” in the Hablemos de matemáticas” section, students analyze a scenario regarding the price of an item and the change received, determine the validity of a statement, and engage in a whole-class discussion to compare and justify their solution strategies. In the “Apoyo al lenguaje” section, students utilize a Frayer model to define and contrast fixed and variable expenses, discuss real-world examples with a partner, and verbally explain their classification reasoning. Students then apply prior knowledge in step 1, “Explora y comenta,” to classify real-world expenses, record their solutions, and respond to educator-led prompts to defend their classifications, while the educator guide directs the analysis of sample student work to evaluate multiple mathematical approaches. This process continues in step 2, “Aprendizaje visual,” where students organize and record examples of fixed and variable expenses, using precise mathematical language to document how they determined each category. In step 3, “Práctica y resolución de problemas,” students apply their understanding by solving contextual financial literacy problems, generating written responses, and discussing final solutions with peers to validate their mathematical discourse. Furthermore, in the Guía del maestro, lesson 10-5, “Investiguemos: unidades métricas,” a structured instructional sequence embeds educator guidance to anticipate, monitor, select, and sequence student work. This framework supports mathematical discourse by guiding educators to ask targeted evaluation and probing questions, prompting students to explain or demonstrate how to convert larger metric units to smaller ones. In addition, the materials require students to critique and discuss mathematical thinking by analyzing authentic student work samples, such as identifying a misconception regarding meters and centimeters or evaluating a peer-created visual bar diagram converting kilograms to grams. This focus on communication extends to the “Hablar sobre las ideas matemáticas” section, which provides explicit prompts for think-pair-share activities where students discuss and justify to a partner why converting measurements to a common unit is necessary before comparing them.

Additionally, in the Guía del maestro, topic 1, lesson 1-1, the “Hablemos de matemáticas” sección features a “¿Cuál no pertenece?” challenge where students analyze four different base 10 and numeric representations, discuss choices with peers, and orally justify decisions based on number relationships. Following this, the corresponding “Boleto de salida” prompts students to independently write a large whole number in expanded form (50,000 + 1,000 + 300 + 10 + 2) and word form. Furthermore, in lesson 7-10, “Solo agrega agua,” students complete a three-act lesson layout. In “Acto 1,” students discuss observations from an introductory video, formulate mathematical predictions, and explain their initial reasoning. In “Acto 2,” students identify mathematical information, construct models, compare fractional quantities, analyze sample work, and justify their solution strategies during partner, small group, and whole-class discussions. In “Acto 3,” students justify their final solution, compare multiple representations, evaluate the efficiency of different methods, record reflections on their reasoning, and construct and solve a related student-created problem

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

The “Modelo de resolución de problemas” found in the online platform features a problem-solving model that provides students and educators with a step-by-step framework for approaching and solving challenging mathematical problems. The educator materials include specific discussion prompts that instruct students to share their problem-solving approaches with partners or the entire class. These prompts guide students to explain how they solved a problem, compare multiple solution strategies, and justify why a strategy supports their reasoning with mathematical evidence. Throughout the problem-solving routine, the materials direct educators to facilitate discourse by requiring students to defend their solutions, analyze and respond to classmates’ reasoning, evaluate alternative strategies, and refine their own thinking based on peer input. Additionally, in the Guía del maestro, lesson 9-2, “Diagramas de puntos,” the “Investigar” section prompts students to organize, represent, and compare recycling data. The educator materials include “Preguntas de evaluación” and “Preguntas para profundizar” sections to guide students in explaining data representations, justifying organizational choices, and describing conclusions. Furthermore, the “Hablar sobre las ideas matemáticas” section structures partner and whole-class discussions for students to defend their reasoning and analyze how visual representations support data interpretation. Within the “Reflexiónar” component, educators instruct students to explain how frequency tables and dot plots organize data, compare multiple solution strategies, and refine their thinking after considering alternative methods. Additionally, the “Rutinas del lenguaje” section guides educators to have students explain assignments in their own words to clarify understanding, while the “Relaciona” and “Práctica y resolución de problemas” sections provide explicit prompts for students to justify why a strategy is effective and support their reasoning with mathematical evidence.

Additionally, in the Guía del maestro, lesson 8-4, “Comparar y ordenar números decimales,” the materials include tiered questions within the “Supervisar” and “Relacionar” sections that prompt students to explain their mathematical representations, asking, “¿Pueden decirme o mostrarme cómo lo hicieron?” and “¿Cómo obtuvieron su respuesta?” The lesson provides guidance for educators to help students identify alternative pathways to solve problems. Furthermore, the materials facilitate classroom discourse through the “Seleccionar y poner en secuencia” section, instructing educators to guide peer discussions where students compare and critique different peer approaches, such as contrasting student-created 100 grids with number lines and numerical reasoning models. Additionally, the guide provides concrete student work models to help educators identify and target misconceptions such as consecutive decimal place-value misunderstandings by probing student thinking with targeted follow-up questions such as, “¿Cómo representarían 0.3?”

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

In the Guía del maestro, lesson 9-3, “Leer diagramas de puntos,” the sections “Prevenir malentendidos” and “Rutina del lenguaje: apoyos para la discusión” direct educators to have students compare interpretations and clarify how dot plots represent numerical values. To build conceptual understanding of statistical formatting, the educator guidance explicitly directs, “Guíe a los estudiantes para que reconozcan que los valores en un diagrama de puntos pueden ser denotados con un punto o una X.” Additionally, the “Errores e intervención“ section targets specific misconceptions, such as confusing the highest-frequency value with the maximum value, and provides follow-up questions to help students justify and correct their thinking. Within each “Let’s Build” lesson, the “Prevent Misconceptions” feature outlines predictive student errors and provides prompts for explanatory feedback. Following this, the “Aprendizaje visual” component includes a sequential series of prompts designed to test basic comprehension and immediately provide conceptual feedback, asking “¿Qué muestra la tabla?” and “Muestra las distancias en la tabla.” Finally, during small-group instruction within the “Supervisar y poner en secuencia” section, the materials prompt the educator to closely monitor how students interpret data points by asking, “¿Cómo los estudiantes interpretan cada punto encima de la recta numérica?” Furthermore, in lesson 10-5 “Investiguemos: unidades métricas,” the section “Ejemplos del trabajo de los estudiantes” presents correct and incorrect metric conversion strategies, focusing on errors involving multiplying or dividing by powers of 10. During step 1, “Supervisar,” the sections “Preguntas de evaluación” and “Preguntas para profundizar” include analysis prompts to evaluate student understanding of metric unit relationships. The corresponding “Errores e intervención” section provides prompts for direct intervention if students struggle with comparing relative values, directing educators, “Si los estudiantes hallan la medida equivalente, entonces recuérdeles que el signo de mayor significa que la medida de la izquierda será mayor que la medida de la derecha.” Similarly, in the section “Seleccionar y poner en secuencia,” the materials instruct educators to sequence student work to address systematic errors: “Comience con soluciones que muestren el error común de descomponer la cantidad en unidades más pequeñas que hay en cada unidad más grande”

Additionally, in the Guía del maestro, lesson 2-5, “Sumar y restar números enteros,” the “Anticipar” section guides educators to identify alternate student solution pathways utilizing prior knowledge before beginning the core lesson tasks. Furthermore, the “Presentar la investigación” and “Evaluar la compresión” sections provide explicit instructional prompt questions, including “¿En qué consiste la tarea?” and “¿Qué les pide la tarea que hallen?,” to guide students through the “Maratón de lectura” task. Additionally, the materials provide targeted intervention resources, such as G13, “Estimar sumas y diferencias de números más grandes;” G15, “Restar números de cuatro dígitos;” and G17, “Sumar números de cuatro dígitos,” outlining sequential instructional pathways to address student performance needs.