enVision+ Texas Matemáticas, 06

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

La guía del ritmo de enseñanza, grado 6 includes “Contenido y secuencia” documents for 165-day, 180-day, and 210-day instructional pathways. These resources delineate the sequential order of mathematical concepts, such as place value, fractions, and decimals. Additionally, a Texas Essential Knowledge and Skills (TEKS) correlation table in the Guía del maestro program overview itemizes every grade 6 mathematics TEKS and identifies the specific lessons where each TEKS is introduced, practiced, and assessed.

Additionally, the Guía del maestro topic planner section “Vistazo del tema” includes a “TEKS” column to align state standards with specific lessons. In lesson 1-1, “Patrones de valor de posición en números enteros y decimales,” students apply TEKS content standard 6.3E alongside mathematical process standards 6.1B, 6.1C, 6.1D, and 6.1F. Additionally, the “Contenido y secuencia” section within the Guía del maestro details both the content and process standards for grade 6 mathematics. This guide structures instruction around core mathematical strands, including numbers and operations, proportionality, and expressions and equations.

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 digital platform provides access to the Guía del ritmo de enseñanza. The guide provides differentiated pathways, utilizing “Essential” lessons for compressed 135-day schedules and “Extension” activities for expanded 210-day calendars. Furthermore, grade 6 scope and sequence outlines the number of instructional days and TEKS covered per unit, organized by topic and lesson.

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

Evaluation for 1.1c
Materials include an explanation for the rationale of unit order as well as how concepts to be learned connect throughout the course.

The “Content Organization Rationale” section within the program overview describes how topics group together to link new learning to prior knowledge. For example, in topics 1–3, students connect mathematical concepts to rational numbers. In topics 4–5, this structure requires students to extend their understanding of algebraic expressions. The “Key Concept” and “Connections” sections detail how these ideas progress across units, while recurring TEKS appear within and across topics to reinforce mathematical relationships.

Additionally, the “Contexto matemático: conceptos clave” section outlines how students develop an understanding of rational number operations through sequential decimal and fraction lessons, while the “Conceptos avanzados para el maestro” section contains advanced content knowledge for instruction. Furthermore, the “Math Background” section at the beginning of each topic details the core concepts, while the “Coherence” section includes how concepts and TEKS connect to prior learning, the current topic, and future learning through “Looking Back,” “In This Topic,” and “Looking Ahead” subsections.

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

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

Additionally, the materials include internalization protocols and implementation guides for student work analysis, such as the grade 6 “Protocolo de análisis del trabajo del estudiante para líderes de la enseñanza,” which provides a framework to identify patterns, address misconceptions, and set instructional priorities. For example, lesson 1-3, “Dividir numeros enteros y numeros decimales con fluidez,” includes lesson language support, TEKS alignment, vocabulary support, manipulatives, and guidance for connecting prior learning.

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

The “Protocolos de internalización y herramientas para observación” tools in the online platform contain 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. Furthermore, the grade 6 “Protocolos de internalización y herramientas de observación” tools 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 6 Guía del maestro, the “Contexto matemático” section details mathematical content, outlines instructional sequencing, and introduces essential terminology. For example, in the topic 2 “Contexto matemático,” the text introduces academic vocabulary, including rational number and integer number, and explains the instructional progression from integer numbers to rational numbers and operations, preparing students for grade 7.

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 6 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 grade 6 “Participación de la familia” (“Family Engagement”) section features topic-level overviews outlining lesson goals, video guides, worked-out mathematical examples, and at-home learning tasks. These resources outline everyday practice suggestions, such as applying addition and subtraction skills in real-world situations to compare prices and find total costs while shopping.

Additionally, the grade 6 “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 at home with everyday materials and mathematical language.

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

On the digital platform, each grade 6 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 6 Guía del maestro outlines the TEKS alignment, daily learning objectives, and necessary materials. The lesson structure integrates targeted questions, tasks, and instructional assessments. Lessons include concept and language objectives, discussion questions within the “Aprendizaje visual” section, hands-on tasks using manipulatives, and instructional assessments such as “Comprobación rápida,” exit tickets, and guided practice.

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

The grade 6 “Planes de lecciones” overview lists educator and student resources on the first page, while editable lesson plans outline the instructional day by providing suggested timing in minutes for each segment. For example, lesson 1-1 “Vamos a investigar: patrones de valor posicional en números enteros y decimales” establishes lesson pacing through the “Cronología de la lección,” which assigns specific minute allocations to the investigating, connecting, practice and problem solving, and evaluation 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 recommended pacing for each component.

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

In the grade 6 Guía del maestro, 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 the “Reteach to Build Understanding,” “Enrichment,” and “Build Mathematical Literacy” activities. Additionally, the “Biblioteca de diferenciación” provides projects, math and literacy connections, collaborative problem-solving activities, and instructional videos.

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 online platform contains a Cuaderno de evaluación designed to evaluate student performance throughout the course. For example, topic 4, “Expresiones numéricas y algebraicas,” includes a multiple-choice evaluación de preparación, a fill-in-the-blank evaluación de mitad del tema, autoevaluaciones, and exit tickets. These tools establish evaluation checkpoints across the course material by utilizing different assessments, task types, and question formats.

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

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

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

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

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

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

Additionally, the Guía del maestro provides administration guidance for each lesson’s exit ticket, detailing its specific use and purpose. This guidance continues into the step 4 “Assess and Differentiate” section, 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 Cuaderno de evaluación contains item analysis charts that map each question on progress monitoring, diagnostic, and summative evaluations to its corresponding TEKS and objectives. In addition, materials include diagnostic tests, incorporate formative assessments such as “Quick Check” and “Exit Ticket” activities, as well as a “Topic Assessment” and “Topic Performance Task” for summative evaluation.


Additionally, within the Guía del maestro, step 4 (“Assess and Differentiate”) 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”) of each lesson includes an “Additional Practice” assessment to reinforce skills, alongside an item analysis table that categorizes exercises by problem complexity levels and indicates 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 provides completed sample responses, correct answers, and a “Tabla de análisis de las preguntas” to identify the aligned TEKS for each lesson. For instance, the grade 6 scoring guide for the topic 4 performance task aligns each specific topic task with the corresponding TEKS 6.7.A and 6.7.D, as well as process standards 6.1.B, 6.1.D, and 6.1.F.

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

The Cuaderno de evaluación, accessible within the online platform, contains assessment data resources, item analysis charts, answer keys, and performance task scoring rubrics that specify intervention system lessons based on student performance on each assessment item. The “Tabla de análisis de las preguntas” serves as a diagnostic tool that pairs assessment items with intervention lessons and corresponding TEKS, which provides data to inform instructional decisions.

Additionally, the Guía del maestro includes an “Hablemos de matemáticas” section for each lesson featuring a TEKS-aligned warm-up activity. For example, grade 6 lesson 5-7, “Entender y escribir desigualdades,” provides guided discussion questions for the educator, such as having students interpret data to apply algebraic thinking aligned with TEKS 6.3D.

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” tools 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, in lesson 1-2 on fluently adding, subtracting, and multiplying decimals, the tool displays student self-assessments to determine student progress in adding, subtracting, and multiplying decimals while recording whether a student is working on, almost meeting, or meeting each aligned TEKS.

Additionally, in the Guía del maestro, the materials integrate lesson overviews with a TEKS-aligned “Exit Ticket” component in each lesson to serve as a quick formative assessment. 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.

The Guía del maestro for topic 10, lesson 10-4, “Entender los informes de crédito,” delivers point-of-use instructional support, scaffolding tools, and remediation strategies. The lesson incorporates a diagnostic exit ticket, “Support Student Understanding” strategies within step 2, and post-lesson “Reteach to Build Understanding” activities within step 4 to monitor progress. Additionally, this component includes the section “Biblioteca de diferenciación,” which provides supplemental videos and digital resources to reinforce lesson content and address diverse learning needs.


Additionally, within the online platform, grade 6 materials provide access to the Manual de resolución de problemas to support students who do not demonstrate mastery of the content. The material directs educators to use the designated model to demonstrate problem solutions. For students who encounter difficulties during problem-solving tasks, the materials provide specific diagnostic questions to identify misconceptions and guide them toward a solution. Furthermore, the manual outlines the sequential steps required to implement the problem-solving model.

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

The Guía del maestro contains the section “Adaptaciones de lenguaje,” which delivers contextual explanations for cognates, metalinguistic transfer, and topic-specific academic vocabulary. In topic 5, “Representar y resolver ecuaciones y desigualdades,” the topic opener incorporates pre-teaching activities to review mathematical terms and directs educators on how to introduce foundational academic language, including vocabulary in context such as ecuación, solución, and desigualdad.


Additionally, the grade 6 materials include pre-teaching or embedded supports for unfamiliar vocabulary and references in text. Each “Let’s Build” lesson incorporates a “Language Support Activity” to facilitate guided partner discussions. For example, in lesson 2-2, the “Apoyo al lenguaje” feature includes an activity to help students become familiar with words like entero and opuesto. This section directs educators to have students record the words in their word bank, write a description of each term, and then compare and contrast their definitions with classmates.

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 6 math lesson includes a component to challenge students who master core content. For example, the educator notes in the Guía del maestro for topic 7, lesson 7-1, “Entender porcentajes,” provide a real-life problem-solving question for early finishers. Furthermore, lesson-level assessment tools offer extension opportunities based on student performance. The “Quick Check” feature in each lesson provides instructional directions to help educators assign targeted enrichment activities that expand upon core lesson concepts.

The grade 6 materials contain resources for enrichment and extension, including the topic “Pick a Project” activities, where the first project in each topic asks students to develop and highlight real-world mathematical applications. For example, project 3D, “Entre las estrellas,” provides an extension where students investigate the locations of objects in the solar system, create a data representation showing distances from Earth at different points in time, describe positive and negative directions relative to Earth, and apply the addition and subtraction of integers to model changes in distance.

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

In lesson 5-12, “Relacionar tablas, gráficas y ecuaciones,” the materials provide direct instructional actions to help educators bridge concrete and graphical representations of mathematical ideas. In the “Apoyo al lenguaje” section, the materials instruct educators to guide students to identify and label variables across three distinct formats: a table, an equation, and a graph. Under the “Hablemos de matemáticas” section, the materials provide educators with direct, scripted questions to drive mathematical discourse and surface conceptual understanding such as “¿Cuál es la variable independiente?” (“Which is the independent variable?”), “¿Cuál es la variable dependiente?” (“Which is the dependent variable?”), and “How can you use the relationship in a table or graph to write an equation?” Furthermore, under the “Prevenir malos entendidos” section, the materials deliver explicit guidance on how to interpret student errors on the exit ticket by explaining exactly why students might select an incorrect option, allowing the educator to immediately clarify and remodel the problem context.


Additionally, in lesson 2-6, “Representar la ubicación en el plano de coordenadas,” the materials provide educators with direct support in the “Anticipar” section, prompting them to evaluate various ways students might use coordinate plane positions to solve problems and directing them to concrete examples of student work. In the “Presentar la investigación” section, under “Usar las diapositivas de revelación lenta,” the materials model and explain the execution of a digital slow-reveal strategy. This feature provides educators with direct prompts such as “¿Qué notan?” (“What do you notice?”) and “¿Qué se preguntan?” (“What do you wonder?”) to guide student observations systematically before revealing all problem details.

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

In the Guía del maestro, “Let’s Build” lessons begin with step 1, “Explore and Share,” where the materials provide opportunities for students to activate prior knowledge and evaluate new concepts. In step 2, “Visual Learning,” the materials outline structured instructional guidance for educators to execute concept development before independent practice. For example, in the Guía del maestro, topic 9, lesson 9-4, “Hallar áreas de paralelogramos y rombos,” the step 1, “Explore and Share” section prompts students to review the calculation of rectangle areas and other geometric figures. In step 2, “Visual Learning,” the lesson outlines the visual decomposition of parallelograms and rhombuses into previously studied geometric figures to connect new concepts to existing student knowledge.

Additionally, in the Guía del maestro for lesson 9-4, the “Supervisar, seleccionar y poner en secuencia” section instructs educators to monitor student strategies, ask questions such as “¿Para qué figuras pueden hallar el área?” and sequence student work to establish the relationship between rectangles and parallelograms. This section contains a subsection titled “Relacionar estrategias de solución.” Finally, the “Aprendizaje visual” section outlines group discussions where students compare solution strategies and demonstrate how rearranging a parallelogram forms an equivalent rectangle.

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 grade 6 materials provide multiple practice formats alongside instructional guidance and structural frameworks for lesson implementation. For example, in lesson 7-3, “Aprendizaje visual,” “Elaboremos: Representar porcentajes mayores que 100 o menores que 1,” the materials direct educators to ask questions where students explain how to convert percentages less than 1 into equivalent fractions and decimals. The lesson also includes collaborative learning through the “Rutina del lenguaje: tres lecturas” protocol, where students reread the problem and discuss the mathematical context with a partner. Additionally, the “Hablar sobre las ideas matemáticas” section promotes student discourse and reasoning by directing educators to facilitate discussions that compare percentages, fractions, and decimals.

Furthermore, the “Biblioteca de diferenciación” section in the Guía del maestro contains a collection of hands-on games aligned to each topic for collaborative pair or small-group, alongside activities where students work together to solve mathematical problems. In the grade 6 Guía del maestro, topic 2, the “Biblioteca de diferenciación” outlines a math-based story, two small-group “Levántate y razona” problem-solving activities, two partner games, and an independent fluency practice page.

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

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

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

In the Guía del maestro, each topic features an “Adaptaciones del lenguaje” section. This section provides guidance to develop “mathematical understanding and academic language related to razón, tasa, and términos” in topic 6. These resources identify current, prior, and upcoming topic vocabulary alongside contextualized definitions and multiple meanings of mathematical terms per lesson. Furthermore, the guidance includes transferable and non-transferable language competencies, metalinguistic connections to English, cognates, and false cognates, alongside recommended instructional strategies. These integrated supports assist educators in developing students’ listening, speaking, reading, and writing skills to provide access to grade-level mathematics content.

Additionally, in lesson 2-1, “Clasificar números,” under the “Apoyo al lenguaje” section, the materials prompt students to connect abstract vocabulary such as enteros, números enteros no negativos, and números racionales to concrete daily experiences in “Experiencias de la vida diaria.” Furthermore, the materials feature peer activities guiding educators, “Pida a los estudiantes que trabajen en parejas,” along with math talk routines like “Igual pero diferente.” This routine directs educators to provide 1–2 minutes of independent think time before facilitating small-group and whole-class discussions about equivalent representations. The materials target metalinguistic comprehension by addressing conceptual misconceptions in the “Errores frecuentes” section, where instructions direct educators to use a visual Venn diagram to illustrate the relationships between subsets of rational numbers, supporting students to connect, explain, and justify mathematical ideas orally and in writing.

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

In the topic 8 “Adaptaciones del lenguaje” section, the materials outline word definitions across different contexts. Under this same section, the text outlines instructional steps for students to express oral and written mathematical ideas. The materials categorize mathematical vocabulary into three distinct groups: “Vocabulario del tema,” “Términos previos,” and “Próximos términos.” A two-column word list titled “Vocabulario en contexto” displays mathematical definitions adjacent to everyday meanings for the terms moda, media, and tabla. Additionally, the materials detail how skills connect between English and Spanish in a section titled “Transferencia metalingüística al inglés.” This section identifies skills that transfer between languages and explains linguistic elements that do not transfer due to structural grammar differences. Furthermore, the lesson highlights words with similar spellings and meanings in both languages, such as explore and multiple. To mitigate translation errors, the materials list false cognates under the section “Falsos cognados,” contrasting word pairs such as rest and restar.


Additionally, within the grado 6 digital resource “Vocabulario académico,” the materials provide step-by-step support for introducing and reinforcing academic vocabulary through definitions, examples, sentence stems, related words, and opportunities for discussion. The materials include sentence frames such as “When I ___, I need to ___” to help students justify their thinking. Educators are guided to have students explain the meaning of words, use them in oral and written responses, and apply them in mathematical contexts.

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 the grade 6 Cuaderno de evaluación section “Evaluaciones del tema 7,” students solve problems involving percents using different models and equivalent representations, such as pictorial models, fractions, decimals, word problems, and tables. Students select and use strategies for each problem across these concepts. The Cuaderno de evaluación provides educator guidance for analyzing student performance in the “Tarea de rendimiento de mitad del tema,” managing lesson intervention and tracking alignment with TEKS 6.2D and TEKS 6.1A. This guidance includes “Tabla de análisis de preguntas” tools that feature cognitive complexity and DOK levels.

Additionally, the materials include practice opportunities and instructional assessments across lessons and units. For example, the topic 9 assessment contains problems covering data analysis, fraction operations, measurement, equation writing, and numerical reasoning. Students select and execute strategies for each problem across these concepts. In lesson 5-1, step 3, exercises 5–8 require students to determine whether given values satisfy equations and justify their reasoning. The lesson includes discussion questions regarding equations with no solutions and those with multiple solutions, requiring students to analyze mathematical relationships and explain their thinking.

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

The grade 6 lessons utilize a multitier framework that transitions from foundational concepts to problem solving. For instance, lesson 2-4 requires students to demonstrate an understanding of the absolute value of rational numbers. Lessons introduce concepts using an entry-level hook within the “Explorar y comentar” section. Additionally, the “Apoyo al lenguaje” section includes contextual questions using real-world scenarios, such as banking applications, to direct students to activate prior knowledge. Within the “Aprendizaje visual” and “Hablemos de matemáticas” sections, the materials introduce mathematical notation such as subsets of rational numbers, diagrams, and structured vocabulary routines. Furthermore, the materials include independent tasks located in the “Boleto de salida” which align with TEKS 6.2B. The components in the “Hablar sobre las ideas matemáticas” protocols require students to analyze, justify, and verbally explain how alterations to a dataset or a number line transformation impact the mathematical structure.

Additionally, in the Guía del maestro, each unit includes a “Representémoslo en 3 actos” section where tasks change in complexity. For example, in the topic 4, Expresiones numéricas y algebraicas,” lesson 4-6 activity “La excursión,” students engage in a three-act task designed to build conceptual understanding. In “Acto 1,” students estimate the number of students attending the excursion and the amount of money needed for the trip. In “Acto 2: el modelo,” students share their reasoning and use the available information to develop a model that represents the cost of the excursion. Students select tools, including paper, rulers, calculators, spreadsheets, or other electronic devices, to create and modify their models. In the “Acto 3” activity, the result is displayed, and students compare their estimates and models with the solution. Following verification and reflection, students create a new problem independently using the strategies and concepts from the lesson.

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

In topic 6, “Entender y usar razones y tasas,” the “Math Background: Coherence” section at the start of the topic connects prior knowledge from grade 5 about the conceptual understanding of fraction operations and unit conversions to introduce the foundational patterns of ratios and rates. The materials connect to grade 6 standards by guiding students from concrete representations, such as equivalent ratio tables, diagrams, and double number lines, to abstract concepts like using a coordinate plane to graph ratios and understanding percentage as a rate per 100. This progression connects to grade 7, where students apply these foundational patterns to rates with fractions. By connecting these concepts, the materials present skills within a structured mathematical framework across units and grade bands.

Additionally, the materials establish coherence across units by connecting patterns, core concepts, and relationships between mathematical concepts. For example, in topic 5, the “Vistazo al tema” overview outlines a progression from understanding equations and solutions to applying properties of equality, solving one-step equations, solving equations with rational numbers, using mathematical models, and writing and interpreting inequalities. The program overview groups and sequences topics to build content connections. In topics 4–5, students use mathematical process standards to extend their understanding of rational numbers, including integers, by writing, evaluating, and generating equivalent numerical and algebraic expressions. Students use variables as changing quantities or unknown values to represent situations algebraically and model mathematical and real-world scenarios using equations and inequalities. Also, the materials introduce dependent and independent variables to represent relationships between quantities.

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 topic 8, “Mostrar, describir y resumir datos,” the materials reference términos previos such as percentage to establish the basis for data representation strategies. This foundation connects to the current grade 6 vocabulario del tema, where tasks introduce data analysis concepts, including pregunta estadística, measures of central tendency media, mediana, and moda; and variability measurements rango and desviación absoluta, alongside data displays like histograms and box plots. Furthermore, the unit connects to future courses by listing próximos términos, such as factor de escala and geometric terms, distinguishing mathematical definitions from everyday language to sequence content for subsequent algebraic reasoning and data interpretation.


Additionally in the “Conceptos clave del tema” section of topic 7, “Entender y usar porcentajes,” the materials connect prior understanding of fractions, decimals, ratios, and proportional relationships to the development of percent concepts. The material outlines how tasks utilize equivalent fractions, decimal representations, and ratio reasoning to represent, compare, estimate, and solve problems involving percentages. Tasks connect previously introduced concepts by relating percentages to fractions and decimals through visual models, number lines, and proportional reasoning to determine percentages, wholes, and parts. Additionally, the material introduces percentages greater than 100% and less than 1% to establish the trajectory for future work with proportional relationships, algebraic reasoning, statistics, and financial mathematics.

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 7, “Entender y usar porcentajes,” lesson 7-1, “Entender porcentajes,” the materials structure a progression across four distinct steps. During step 1, “Explorar y comentar,” students review the meaning of percentages and their visual representations. In step 2, “Aprendizaje visual,” students use this foundation to learn new techniques for representing percentages. During step 3, “Práctica y resolución de problemas,” students complete guided practice before applying these percentage concepts independently. Finally, in step 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 3-1 “Investiguemos: relacionar enteros y sus opuestos.” In this section, the “Coherencia” subsection links prior conceptual understanding to new skills and subsequent mathematical learning by connecting to students’ prior knowledge from topic 2, where students used integers to represent real-world quantities and identified opposite values or directions. In the “En esta lección” section, the materials build upon this foundation to introduce the grade-level standard TEKS 6.3C. The lesson requires students to connect opposite numbers directly to the concept of absolute value and to combine opposite quantities to equal zero on a number line. Additionally, the “Más adelante” section outlines how this groundwork prepares students to use integers and rational numbers to solve problems later in the topic


Additionally, In the “Math Background: Coherence” section at the beginning of each topic, the “Looking Back,” “In This Topic,” and “Looking Forward” features outline how mathematical concepts connect across and within lessons. For example, in topic 4, “Expresiones numéricas y algebraicas,” the “Looking Back” section revisits evaluating, writing, and interpreting numerical expressions. The current unit uses these skills to introduce numerical and algebraic expressions, exponents, and equivalent expressions. Finally, the “Looking Forward” section outlines the foundational skills required to solve equations and inequalities in subsequent coursework.

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

Within the “Elaboremos” framework in the Guía del maestro, the “Hablemos de matemáticas” component includes spiral review activities. In lesson 5-5, the “Cadena algebraica” activity requires students to connect their prior understanding of multiplication and division with fractions to inverse operations and the properties of equality used to isolate a variable. This design requires students to retrieve and apply foundational algebraic concepts within the current lesson structure to establish a progression for solving equations. In the Guía del maestro for topic 1, “Usar números racionales positivos,” the “Vuelve atrás” section requires students to retrieve grade 5 foundational skills, including decimal operations to the hundredths place and basic fraction models. This content is then reviewed across lesson 1-2, lesson 1-5, and lesson 1-9 to transition students from conceptual models to algorithms. Furthermore, the “Más adelante” section outlines future practice across topic 4 through topic 9, requiring students to retrieve and reapply these core rational number skills in subsequent units for applications including algebraic equations, rate conversions, and geometric volume calculations.

Additionally, within each unit, the “Repasa lo que sabes” section requires students to retrieve concepts and skills learned in previous lessons and units before introducing new content. In topic 3, “Operaciones con enteros,” the “Repasa lo que sabes” section requires students to review mathematical vocabulary from previous units using a sentence-based definition exercise. This section also requires students to complete integer operations, including addition, subtraction, multiplication, and division, alongside word problems that require the application of these skills. Additionally, the Guía del maestro includes a structural table that identifies the TEKS alignment for each exercise mapping current standards to prior units, lessons, and grade levels, alongside the corresponding level of difficulty.

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 6, “Explorar relaciones de suma y multiplicación,” the materials build on prior knowledge of tables, graphs, and equations. Students apply these foundational concepts to distinguish numerically and verbally between additive and multiplicative rules. The lessons integrate continuous vocabulary development, including razones, and incorporate multiple practice formats such as problem-solving exercises, conceptual checks like “Comprobación rápida,” and targeted differentiation resources. The “Repasa lo que sabes” section in topic 6 distributes practice across multiple domains, requiring students to generate equivalent fractions, write equations from patterns, select units of measure, convert customary measurements, and analyze foundational concepts such as factors, multiples, and ratios. Furthermore, in the Guía del maestro, topic 10, “Matemáticas de finanzas,” the “Repasa lo que sabes” section features mixed prerequisite tasks, including vocabulary evaluations, decimal operations, equivalent rational numbers, and percentage problems. Because these tasks feature a combination of content from prior units, students select the appropriate mathematical strategy for each problem.


In the Guía del maestro, topic 4, “Expresiones numéricas y algebraicas,” the “Repaso del tema” section requires students to apply numerical expression evaluations, simplifications, and equivalent expression generations while integrating integer operations from topic 3 and rational number operations from topic 1. Additionally, in lesson 8-4, “Mostrar datos en tablas de frecuencias e histogramas,” the “Coherencia” section directs students to connect prior line plot and stem-and-leaf plot representations with newly introduced equal intervals, frequency tables, and histograms. During the “Hablemos de matemáticas” routine within this lesson, students compare and evaluate different data representations to determine which display best communicates the dataset, integrating previously learned representations with newly acquired display methods.

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

In the Guía del maestro, topic 4, “Expresiones numéricas y algebraicas,” the lesson 4-6 section “Representémoslo en 3 actos: la excursión” has students complete a three-act mathematical modeling task. In the “Acto 1” activity, students view a video, formulate mathematical questions regarding the cash required for an excursion, and predict the total cost. In “Acto 2,” students collaborate as a whole class to extract relevant details, including bus pricing, admission fees, and passenger constraints, to develop an algebraic expression and determine which quantities require variables and which require numerical values before evaluating different solution methods against an exemplar. In “Acto 3,” students verify their solutions by assessing the accuracy of their models, identifying calculation errors, and explaining in small groups how their representations optimized the problem-solving process. In lesson 6-2 “Elaboremos: entender razones,” the “Hablemos de matemáticas” section presents students with 3D concrete and visual representations of cubes and cylinders. The section asks analytical questions, including “¿En qué se parecen las imágenes?,” “¿En qué se diferencian?,” and “¿Cómo describirías las imágenes a alguien que tuviera los ojos cerrados?” These prompts require students to analyze the structure of models and evaluate how different visual setups represent the same part-to-part ratio. Furthermore, the “Boleto de salida” section contains a formal assessment question regarding a theater club with four grade 6 students, five grade 7 students, and nine grade 8 students. The task asks, “¿Qué razones comparan la cantidad de estudiantes de sexto grado con la cantidad total de estudiantes del grupo de teatro?” To solve this problem, students must interpret the word problem, evaluate part-to-whole relationships, and select the correct symbolic representation. Finally, the “Apoyo al lenguaje” table directs students to translate fractions and ratios into spoken language and visual block diagrams to connect multiple mathematical representations.


Additionally, in the Guía del maestro, the lesson 7-1 section “Explorar y comentar” prompts students to interpret rectangular visual models representing fractional portions of two pizzas to determine relative quantities. Students analyze the relationships among 100 grids, tape diagrams, number lines, fractions, ratios, and percentages to explain how different representations describe identical part-to-whole relationships. Furthermore, within the Guía del maestro, the “Elaboremos” framework embedded throughout topic 3, “Operaciones con enteros,” lesson 3-3, “Restar enteros,” structures this analysis across four sequential instructional steps. In step 1, “Explora y comenta,” students analyze a real-world problem involving negative integers to connect the scenario to integer subtraction. In step 2, “Aprendizaje visual,” students interpret positive integer subtraction models to evaluate alternative solution strategies. Students complete guided practice in step 3, “Práctica y resolución de problemas,” before working on targeted assessment tasks in step 4, “Evaluación y diferenciación,” to verify and justify their mathematical conclusions.

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

In the Guía del maestro, lesson 4-7, “Expresiones equivalentes,” the “Investiguemos” section requires students to generate and analyze concrete models to represent algebraic situations. During the activity “Cosecha saludable,” students use algebra tiles to build visual and physical models representing the number of plants across different garden plots over a specific number of weeks. Students use these tools to write algebraic expressions and explain why different pictorial representations are equivalent, connecting concrete modeling with abstract algebraic reasoning. The materials challenge students with the task “¿Después de cuántas semanas tienen todos los macizos la misma cantidad de plantas? Explícalo,” which guides students to use their models to solve a multistep algebraic problem and justify their mathematical reasoning. In the Guía del maestro, lesson 8-5, “Representémoslo en 3 actos: rango vocal,” students create a data representation model to evaluate scores from a singing competition. In “Acto 2,” students select and utilize mathematical tools, including dot plots and histograms, to organize and display the contestants’ dataset. In “Acto 3,” students apply their finalized data displays to evaluate the outcomes, verify their mathematical predictions, and justify their conclusions.


Additionally, within the Guía del maestro, the “Elaboremos” framework for topic 3, “Operaciones con enteros,” lesson 3-3, “Restar enteros,” requires students to construct and apply mathematical models across sequential steps. In step 1, “Explora y comenta,” students construct number-line and grid-paper models to represent integer subtraction. In step 2, “Aprendizaje visual,” students utilize these number lines to analyze positive and negative number relationships. Students complete guided and independent application tasks in step 3, “Práctica y resolución de problemas,” to justify their reasoning. Similarly, in lesson 5-2, “Aplicar propiedades de la igualdad,” students manipulate balance models, algebra tiles, and coins to model linear equations and visually justify how properties of equality maintain balance on both sides of an equation.

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

In the Guía del maestro, lesson 4-7, “Expresiones equivalentes,” the “Investiguemos” section transitions students through a Concrete–Representational–Abstract (CRA) instructional sequence. During the activity “Cosecha saludable,” students use algebra tiles to construct and evaluate visual expressions representing varying growth rates of garden plants. Students apply this algebraic concept within the “Utilizar un modelo de resolución de problemas” task, which requires them to calculate rates of change to answer the question, “¿Después de cuántas semanas tienen todos los macizos la misma cantidad de plantas? Explícalo.” Furthermore, the “Conectar ideas matemáticas” prompt requires students to generalize the concept by responding to the question, “Si reemplazas el mismo valor de x en dos expresiones equivalentes, ¿siempre tendrán el mismo valor? Explícalo.” These tasks require students to connect visual representations to algebraic variables and justify the underlying mathematical relationships. Furthermore, within the Guía del maestro, in topic 9, “Usar área y volumen,” lesson 9-4, students compare and contrast the properties of rectangles and parallelograms to calculate and evaluate their areas, transferring previously learned geometric concepts to analyze relationships between shapes. Subsequently, the “Aprendizaje visual” and the “Hablemos sobre las ideas matemáticas” component requires students to apply this newly developed conceptual understanding to a distinct mathematical scenario to extend and justify their reasoning.

Additionally, within the Guía del maestro, lesson 6-1, “Explorar relaciones de suma y de multiplicación,” students analyze additive and multiplicative relationships using data tables, coordinate graphs, and algebraic rules. Students then apply this conceptual understanding to real-world scenarios, such as evaluating balloon counts at a fair, to determine and justify whether the underlying mathematical relationship represents addition or multiplication.

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 topic 3, “Operaciones con enteros,” the “Biblioteca de diferenciación” activities on the online platform apply mathematical concepts through varied application-based games and projects. For example, the math game “Acierta el número” builds fluency and automaticity by requiring students to rapidly add and subtract integers to reach a target objective of zero. The repetitive nature of drawing cards, executing calculations, and evaluating numerical distances over a structured five-round cycle provides procedural practice. Furthermore, the materials include educator and student prompts embedded in the “Ampliación” project extensions that require higher-order thinking. For example, project 3A asks, “What did you see and what question did you explore?” Additionally, project 3D requires students to predict when the Sun is closest to the Earth and explain the meaning within a daily life context. Combined, these elements pair fluency drills with contextual, evaluative questions that require grade 6 students to explain and justify their mathematical reasoning. Furthermore, in the Guía del maestro, within the “Desarrollar la fluidez” activity located at the end of topic 2, “Los enteros y el plano de coordenadas,” students complete the “Pista escondida” task to build computational efficiency. Students resolve multiple positive rational number computation problems, requiring them to repeatedly add and subtract decimals. Students then apply these numerical solutions as ordered pairs to plot coordinates on a plane, which reveals a hidden image and directly reinforces the accuracy and automaticity needed for grade-level coordinate geometry.


Additionally, within the “Biblioteca de diferenciación” in the Guía del maestro, topic 3 materials include hands-on fluency games to build computational efficiency. Students work in pairs to play “Zonas de mareas” to practice integer operations and “Adivina el número” to repeatedly add or subtract integers to hit a targeted numerical value before completing a practice worksheet covering integer addition, subtraction, multiplication, and division. Similarly, in the Guía del maestro for topic 8, within the “Práctica de fluidez” section, students complete the “Reordenar la adivinanza” activity by performing repeated additions and subtractions of positive rational numbers. Students then utilize those final calculations to order decimal values, estimate the overall reasonableness of their solutions, and plot the numbers to decode a hidden message.

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

Within the Guía del maestro, the “Hablemos de matemáticas” component of the “Elaboremos” framework for topic 2, lesson 2-3, “Representar números racionales en la recta numérica,” requires students to apply mathematical procedures to write fractions, decimals, and mixed numbers. Students use these procedures concurrently to connect multiple representations of rational numbers, plot them on a number line, and compare different solution strategies with peers. In the “Práctica adicional” section, students continue practicing these procedures with more complex rational numbers to compare, order, and reinforce procedural accuracy and flexibility. Furthermore, in the Guía del maestro for lesson 1-6, “Entender la división con fracciones,” the lesson structure transitions from foundational concrete models to abstract algorithmic thinking. To practice procedural flexibility, students solve a core task using multiple strategies in the “Trabajo del estudiante 1–6” section. These strategies include repeated subtraction, fraction bar models, number lines, area models, and multiplying by the reciprocal. To reinforce accuracy and efficiency, the educator materials embed guiding questions that require students to evaluate their chosen pathways. For example, the materials ask, “¿Es este método eficiente?” during an analysis where students determine that multiplying by the reciprocal is faster. Furthermore, the lesson features analytical prompts such as “¿Qué es mejor para representar los modelos: con fichas cuadradas o usar resta repetida?” and “¿Qué patrón ven?” This progression combines procedural practice with real-world application throughout the lesson.

Additionally, within the Guía del maestro, lesson 5-1, “Entender ecuaciones y soluciones,” students use multiplication and division equations to determine whether a given value makes an equation true to solve a real-world scenario. Students analyze work, evaluate different solution strategies, identify mathematical errors, and justify correct solutions. Similarly, in lesson 7-5, “Resolver problemas de porcentajes,” students solve percent problems using multiple procedures, including visual models, equations, proportions, and percent relationships. Students compare different solution strategies, determine which procedure is most appropriate for specific problems, justify why a strategy is efficient, and apply their selected method during guided and independent practice.

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

Within the Guía del maestro, lesson 5-3, “Escribir y resolver ecuaciones de suma y de resta,” step 3, “Práctica y resolución de problemas,” and step 4, “Evaluación y diferenciación,” require students to determine whether equations represent problem situations correctly. Students verify the value of a variable by substituting it back into the equation, identify incorrect solution processes in worked examples, and explain why a solution is valid or invalid. Furthermore, in the “Comprobación rápida” section, students analyze and correct mathematical errors before completing additional practice tasks to evaluate the accuracy of their solutions. Similarly, in the grade 6 Guía del maestro for topic 9, “Usar área y volumen,” the “Representémoslo en 3 actos” framework for lesson 9-7, “Fichas de tabla de trapecio” requires students to evaluate mathematical approaches across three stages. During “Acto 1,” students watch a video prompt and collaborate as a class to establish a primary mathematical question. In “Acto 2,” students gather data, build mathematical models, and apply procedures to determine how many one-inch square tiles are needed to cover a trapezoid-shaped table. In “Acto 3,” a solution video reveals the final answer, and students compare their predictions with the revealed solution, analyze possible sources of error in their models, and discuss how to refine their procedures and processes for improved efficiency and accuracy.

Additionally, within the Guía del maestro, lesson 6-11, “Práctica y resolución de problemas,” the “Errores e intervención: ejercicio 11” component requires students to evaluate a conversion mistake involving centiliters and liters. Students identify the error, correct the work, and explain the validity of the correct mathematical procedure. Similarly, in lesson 7-1, “Multiplicar con fracciones,” students compare different representations and solution methods during whole-class discussions to justify whether the procedures accurately model a multiplication scenario. During step 3, “Práctica y resolución de problemas,” and step 4, “Evaluación y diferenciación,” the “Comprobación rápida” component requires students to verify that their solutions are reasonable, identify calculation errors, and revise incorrect procedures before completing additional practice tasks.

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

Within the Guía del maestro, the “Investiguemos” framework in topic 5, “Representar y resolver ecuaciones y desigualdades,” lesson 5-1 provides embedded guidance during step 1. The materials outline specific assessing and advancing questions for educators to use while monitoring students, alongside strategies to select and sequence student solutions. Furthermore, in lesson 5-3, “Escribir y resolver ecuaciones de suma y de resta,” the Guía del maestro embeds instructional prompts within the “Supervisar, seleccionar y poner en secuencia,” “Relacionar,” “Aprendizaje visual,” “Hablar sobre las ideas matemáticas,” and “Práctica y resolución de problemas” sections. This guidance prompts educators to compare student representations, connect visual balance models to symbolic equations, question the application of inverse operations, and sequence student work from concrete models to abstract algebraic methods. In addition, the Guía del maestro for topic 3, “Operaciones con enteros,” lesson 3-2, “Sumar enteros,” provides specific instructional scaffolding across activities 1 through 4. Throughout these activities, the materials provide educators with mathematical questioning, prompts for classroom discourse, and explicit guidance to address common misconceptions. Specifically, the “Relacionar estrategias de solución” section guides educators to discuss and compare different student approaches to determine if a sum is positive or negative. To facilitate this progression, the materials instruct educators to “have students first use patterns in a table to make predictions and then connect those patterns to reasoning with opposites and number lines.” This structure supports educators in moving student reasoning from concrete representations to increasingly efficient abstract mathematical approaches.


Additionally, within the Guía del maestro, each “Representémoslo en 3 actos” task provides structured prompts for educators to facilitate classroom discussions that transition students from initial informal representations toward formal mathematical reasoning. In topic 4, “Expresiones numéricas y algebraicas,” lesson 4-6 “La Excursión,” these embedded prompts direct educators to guide students to analyze a real-world trip scenario, develop and justify algebraic expressions, and evaluate the efficiency of their models against the actual solution. Similarly, in lesson 7-1, “Multiplicar con fracciones,” the Guía del maestro embeds instructional guidance within the “Supervisar,” “Preguntas de evaluación,” “Preguntas para profundizar,” and “Seleccionar y poner en secuencia” sections. These supports direct educators to compare student representations, explain why specific strategies optimize calculation speed, and intentionally sequence student work to move from visual drawings to abstract, generalizable fraction multiplication methods.

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

Within the Guía del maestro, each topic includes a “Contexto matemático: coherencia y equilibrio” section that outlines conceptual and procedural expectations. For instance, in topic 5, “Representar y resolver ecuaciones y desigualdades,” the “Comprensión de conceptos” component details how the materials build student understanding of equations, inequalities, the properties of equality, independent and dependent variables, and the multirepresentational relationships across tables, coordinate graphs, and verbal descriptions. Concurrently, the “Destreza en procesos y fluidez” component defines procedural expectations by tracking how students solve one- and two-step equations and inequalities using inverse operations, properties of equality, and symbolic representations to isolate variables and resolve real-world scenarios. Similarly, in the Guía del maestro for lesson 2-3, “Elaboremos: representar números racionales en la recta numérica,” the “Conocimientos y destrezas esenciales de Texas (TEKS)” section cites and correlates TEKS 6.2C, which requires students to locate, compare, and order rational numbers on a number line. The materials align this content alongside process standards TEKS 6.1A and TEKS 6.1C. Under the “Equilibrio” section, the materials detail how students build conceptual understanding using visual models before transitioning to procedural application by representing real-world data on a number line. Furthermore, the educator guidelines include embedded formative assessment questions to gauge student comprehension, such as “¿Qué pasos realizó el estudiante para escribir cada expresión?”


Additionally, within the Guía del maestro, lesson 8-3, “Mostrar datos en diagramas de tallo y hojas,” the “Comprensión de conceptos” component defines the conceptual emphasis by explaining how students develop an understanding of data representation and interpretation using stem-and-leaf plots. Concurrently, the “Objetivos de matemáticas” component outlines the procedural emphasis by explaining how students perform numerical calculations to construct a stem-and-leaf plot and analyze the data to solve questions in context. Similarly, in lesson 5-7, “Entender y escribir desigualdades,” the materials define the conceptual focus by explaining the mathematical meaning of inequality symbols, while the procedural focus specifies tasks where students write inequalities to model different mathematical and real-world scenarios.

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.

Within the Guía del maestro, lesson 2-1, “Clasificar números,” students draw upon real-world contexts, such as weighing grapes, to connect abstract numerical classifications to real-life student experiences. Pictorial representations include Venn diagrams and number lines, which serve as the visual transition to help students map out and analyze the relationships among non-negative integers, whole numbers, and rational numbers. Students progress to abstract mathematical notation in the “Igual pero diferente” task, where they evaluate how a single abstract value can be represented both as a whole integer and as a symbolic rational fraction. Finally, in the “Boleto de salida” section, students complete explicit multiple-choice tasks that evaluate this progression by requiring them to translate abstract numerical symbols into their corresponding pictorial Venn diagram classifications. Furthermore, the program overview features the CRA instructional model and details how the curriculum structures progressions from concrete manipulatives to pictorial representations and abstract symbols both across and within lessons. To implement this progression, the materials provide visual learning activities and digital manipulatives designed for students to create, explain, and connect mathematical ideas across all three representational phases.



Additionally, within the Guía del maestro, the “Investiguemos” framework in topic 4, “Expresiones numéricas y algebraicas,” lesson 4-7, ”Expresiones equivalentes,” guides students through a three-step progression. In step 1, “Investigar,” students manipulate algebra tiles to build concrete models of equivalent numerical expressions. In step 2, “Relacionar,” students analyze their strategies to link these concrete models to pictorial drawings and symbolic equations. In step 3, “Práctica y resolución de problemas,” students apply these models to simplify expressions and record their final solutions abstractly. Similarly, in the lesson 7-1 “Entender y explorar” section, students begin by manipulating paper strips and 100 grids. During step 3, “Práctica y resolución de problemas,” students represent percentages using these 100 grids, area models, circle models, and number lines before writing equivalent fractions, decimals, and percentages, transitioning directly from pictorial formats to abstract numerical reasoning.

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

In the grade 6 Guía del maestro for lesson 4-7, “Investiguemos: expresiones equivalentes,” the lesson structure utilizes the CRA framework to transition from physical models to algebraic notation. These materials align with TEKS 6.7C, which requires students to determine if two expressions are equivalent using concrete models, pictorial models, and algebraic representations. The lesson embeds concrete algebra tiles and pictorial arrays to illustrate variables and constant unit values, guiding students to define, create, and connect these visual aids to symbolic expressions. To assist students in explaining these concepts, the materials provide structured language routines in “Rutina de lenguaje” along with explicit educator prompts, including “¿Quién puede reformular este razonamiento de otra manera?” Additionally, the lesson embeds contextual application tasks where students determine the number of weeks required for three agricultural plots to contain an identical number of plants based on their corresponding algebraic expressions and predict if the plots will share an identical quantity of plants after week four. In addition, within the online platform, the program overview outlines the CRA instructional model embedded throughout the program. The framework guides educators to introduce topics using concrete manipulatives, transition to visual drawings through the “Aprendizaje visual” component, and link those illustrations to abstract algebraic procedures. Furthermore, the material provides discussion prompts for educators to guide students in explaining the structural relationships among these formats.


Additionally, within the Guía del maestro, lesson 8-6, “Comunicar con datos,” the instructional materials prompt educators to guide students to analyze, compare, and select appropriate statistical representations, including dot plots, histograms, boxplots, data tables, and numerical datasets. Throughout the lesson framework, the materials provide specific questions and discussion prompts that require students to explain how each display communicates identical data, evaluate the strengths of different graphs, and justify which representation optimizes data communication for a given context. Students link these graphical representations to abstract calculations by interpreting the median and range within each display to solve problems and communicate mathematical reasoning across the “Investigar,” “Relacionar,” “Práctica,” and assessment components of the lesson.

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

In the online platform under “Recursos apoyo de vocabulario” and “Más apoyo de vocabulario 1-1,” students complete vocabulary tables by matching terms with definitions and visual representations for geometric concepts, including ángulos adyacentes, ángulos complementarios, and ángulos suplementarios. The section directs students to solve crossword puzzles using geometry vocabulary and utilize a graphic organizer to record definitions, facts, examples, and non-examples for specific mathematical terms such as porcentaje. Throughout the course, these lesson activities require students to classify concepts, complete graphic organizers, analyze diagrams, and apply academic language while connecting terms to visual models. Furthermore, in lesson 1-7, students identify and use mathematical terminology, including fracción, número mixto, cociente, divisor, recíprocos, razón, tasa por unidad, fórmula, volumen, and números racionales, to compare related concepts and explain mathematical relationships.


Additionally, in the Guía del maestro, topic 7, lesson 7-1, “Entender porcentajes,” the materials introduce unit vocabulary such as porcentaje. The “Apoyo al lenguaje” section connects vocabulary to prior knowledge by requiring students to describe a 100 grid and explain how shaded and unshaded regions represent percentages. In the “Conexiones de lenguaje y matemáticas” section, student partners identify vocabulary, discuss the meaning of terms, and explain their mathematical reasoning. Throughout step 2, students respond to the prompts “Hablemos de matemáticas,” “Pregunta esencial,” “Concepto clave,” and “Hablar sobre las ideas matemáticas.” These prompts require oral and written usage of precise academic vocabulary, including porcentaje, cuadrícula de centésimos, denominador, fracción equivalente, and razón. Furthermore, in the Guía del maestro, topic 3 “Operaciones con enteros,” the digital platform component “Biblioteca de diferenciación” includes the section “Actividades con materiales digitales manipulables.” Within this section, the activity “Asombrosos peces voladores” requires students to use number lines to model the height of a flying fish to relate the addition and subtraction of rational numbers. Additionally, in the activity “Un sapo muy saltarín,” students construct a number line model to demonstrate multiplication with positive and negative numbers.

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, topic 6, “Entender y usar razones y tasas,” the “Repaso del tema” educator guidance reinforces academic vocabulary after students complete the topic. This support is located in the “Repaso del vocabulario,” “Lenguaje oral,” and “Escritura en matemáticas” sections. The educator guidance directs educators to engage students in discussions using vocabulary, including razón, tasa, precio por unidad, factor de conversión, and análisis dimensional. The “Lenguaje oral” routine instructs the educator to facilitate conversations where one student describes a ratio using the vocabulary while classmates ask clarifying questions and evaluate the mathematical statement. In the “Escritura en matemáticas” section, educators instruct students to work with a partner, select terms from the vocabulary review, compose written responses using the terms, and exchange papers to verify vocabulary usage. Additionally, in lesson 6-4, “Comparar razones,” the “Apoyo al lenguaje” section provides educator guidance to introduce and reinforce vocabulary related to ratio tables, double number lines, and bar diagrams. The materials instruct educators to guide students to discuss connections between representations, create matching diagrams, and complete the sentence frame “Creo que usar una____ para comparar razones es mas eficiente porque____.”


Additionally, in the Guía del maestro, lesson 5-2, “Aplicar propiedades de la igualdad,” the “Explorar y comentar” section directs educators to ask questions such as “¿Cómo pueden simplificar sus resultados para ver si la ecuación es verdadera?” and instructs students to explain which operations keep an equation true. This guidance supports the use of academic vocabulary in context by reinforcing terms such as ecuación, igualdad, verdadera, simplificar, and ambos lados while students explain, compare, and justify their reasoning. Similarly, in the Guía del maestro for topic 7, lesson 7-4, “Estimar para hallar porcentajes,” the lesson reinforces vocabulary within the “Reforzar el vocabulario” section using terms such as números compatibles, estimación, fracciones equivalentes, and redondeo. During step 2, “Aprendizaje visual,” the “Apoyo al lenguaje,” “Conceptos clave,” and “Hablemos de matemáticas” sections prompt the educator to ask questions such as “¿Por qué 100 es un número compatible para 94?,” “¿Qué otros porcentajes y fracciones equivalentes están cerca de 27% y son compatibles con 300?,” and “¿Cómo escriben una fracción equivalente de un porcentaje si no pueden hacerlo mentalmente?”

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, lesson 6-6, “Entender tasas y tasas por unidad,” the “Reforzar el vocabulario” section introduces the terms tasa and tasa por unidad before students engage in mathematical discussions. During step 1, “Explorar y comentar,” the materials provide guiding questions directing educators to have students compare solution strategies, explain why strategies are equivalent, and justify their reasoning using the terms tasa, tasa por unidad, and razones equivalentes. The educator’s guidance prompts discussion with questions, including “¿Cómo usan los estudiantes las tasas para hallar el tiempo de juego por $30?” In the “Relacionar estrategias de solución” section, the materials instruct educators to have students explain why a unit rate applies to the problem and compare approaches. The “Ejemplos del trabajo de los estudiantes” section provides exemplar responses for educators to reference. During step 2, “Aprendizaje visual,” the “Pregunta esencial,” “Concepto clave,” “Hablar sobre las ideas matemáticas,” and “¿Lo entiendes? ¿Cómo hacerlo?” sections provide prompts for students to explain relationships between ratios and unit rates using complete mathematical statements. Furthermore, the “Práctica y resolución de problemas” and “Práctica adicional” sections include exemplar responses, error analysis, and educator guidance for addressing misconceptions to correct student vocabulary, syntax, and discourse.


Additionally, in the Guía del maestro, lesson 5-11, “Entender variables independientes y dependientes,” the “Supervisar, seleccionar y poner en secuencia” and “Comentar las soluciones de los estudiantes” sections provide educators with targeted questions that prompt students to explain and justify their reasoning. For example, educators ask questions such as, “¿Cómo describen los estudiantes el impacto del tamaño y contenido de la caja en su peso?” to deepen classroom discourse. These prompts facilitate whole-class conversations about dependent and independent variables, which allow students to hear, refine, and use academic vocabulary with peers. Finally, the “Ejemplos del trabajo de los estudiantes” section includes exemplar student responses alongside educator follow-up questions and anticipated answers to guide instructional support.

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

In Guía del maestro, within topic 2, “Los enteros y el plano de coordenadas,” process standards are embedded into the core content rather than serving as separate tasks. Integrating TEKS 6.1C, the materials prompt students to select tools, including graph paper, coordinate grids, mental math, and estimation, to plot and identify points across all four quadrants. Educator guided questions support this strategy through prompts such as, “¿Qué representa cada marca y línea de la cuadrícula?” and “¿Cómo puede aplicar su comprensión de los números racionales positivos para diagramar, comparar y ordenar números racionales negativos?” Concurrently, the materials emphasize TEKS 6.1D by requiring students to communicate mathematical reasoning through multiple representations, including symbols, diagrams, and precise language. The materials support this standard by instructing educators to ask questions like, “¿Cómo puede justificar su razonamiento matemático?” By structuring lessons around these reflective questions, the materials require students to justify their reasoning, interpret visual representations, and use accurate mathematical language integrated to TEKS 6.1D.

Additionally, at the beginning of each topic, the Guía del maestro highlights mathematical process standards and describes how students use these processes to acquire and demonstrate understanding. In topic 3, “Operaciones con enteros,” the “Estándares de los procesos matemáticos de los TEKS” section identifies TEKS 6.1B, which focuses on using a problem-solving model, and TEKS 6.1F, which emphasizes analyzing mathematical relationships to connect and communicate ideas.

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

The topic 1, “Usar números racionales positivos” overview features an “Estándares de procesos matemáticos” section that identifies the specific process standards embedded throughout the topic before instruction begins. Furthermore, the Guía del maestro table of contents lists the process standards alongside the content standards for every individual lesson. This layout establishes how students repeatedly engage in mathematical processes across different mathematical domains, such as applying mathematics to problems arising in everyday life under TEKS 6.1A, using problem-solving models under TEKS 6.1B, and selecting and using representations under TEKS 6.1C. By embedding process standards, including TEKS 6.1B through TEKS 6.1G, directly into daily lesson outlines, from foundational concepts like “Entender y representar exponentes” to algebraic tasks like “Evaluar expresiones algebraicas” and “Simplificar expresiones algebraicas,” the materials connect these process standards to each lesson rather than presenting them as separate skills.


Additionally, the “From the Authors: TEKS Mathematical Process Standards” section of the program overview states that process standards are integrated into lesson instruction. Specifically, the materials place these practices within dedicated mathematical process standards pages, instructional tasks, assessments, topic performance tasks, and a Manual de resolución de problemas, while marking them across the Libro del estudiante and Guía del maestro. Finally, the overview outlines the implementation of these practices across instruction, practice, and assessment to present the process standards as connected features throughout the course rather than isolated skills. Furthermore, in the Guía del maestro, topic 6, “Entender y usar razones y tasas,” includes an “Estándares de procesos matemáticos” overview section that outlines how these process standards integrate into the lessons. The educator guidance highlights TEKS 6.1D for communicating ideas and TEKS 6.1F for analyzing relationships, connecting both to ratio and rate concepts through sample student behaviors and instructional questions used across the unit.

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 Guía del maestro, each topic begins with an “Estándares de procesos matemáticos” overview page that details how the process standards are embedded into topic instruction and connect to the mathematical content. For example, the topic 9 unit overview explains how students apply TEKS 6.1F and TEKS 6.1G while developing an understanding of area and volume. This section identifies required mathematical expectations including constructing arguments, explaining and justifying reasoning, analyzing mathematical relationships, and communicating ideas, and provides educator questioning strategies, classroom discussion examples, and instructional guidance. Similarly, the topic 1, “Usar números racionales positivos,” “Estándares de procesos matemáticos” overview section explains how process standards embed throughout decimal and fraction relationship analysis. This guidance details expected student behaviors, such as using place value to add and subtract decimal numbers and using algorithms to calculate decimals and fractions. Finally, students explain and justify their reasoning, use equations and formulas to support solutions, identify structural relationships among multiplication and division of fractions, and construct mathematical arguments using accurate mathematical language.


Additionally, the “Planes de la lección para Texas” resource within the online platform identifies the TEKS process standards for each lesson and outlines how those standards are embedded throughout instruction. Each lesson includes specific 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, “Usar números racionales positivos,” includes a “Conocimientos y destrezas esenciales de Texas (TEKS)” section for each lesson. Within this topic, lesson 1-1, the “Elaboremos” activity on place value patterns in whole numbers and decimals guides students to use mathematical processes to acquire and demonstrate mathematical understanding. The materials incorporate content standard TEKS 6.3E along with process standards TEKS 6.1G and TEKS 6.1D. This structural layout details the direct correlation between process standards and mathematical content across all lessons within the unit.

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

In lesson 4-1, “Entender y representar exponentes, the materials list process standards TEKS 6.1B, TEKS 6.1D, TEKS 6.1F, and TEKS 6.1G alongside the primary content standard TEKS 6.7A. On the introductory page, an “Análisis de relaciones matemáticas” prompt directs students to connect the physical folding of paper to exponents. Furthermore, the assessment and discussion sections feature targeted questions under “Analizar relaciones matemáticas.” Specifically, question 2 requires students to determine how many times a factor is used under “Explicar ideas matemáticas,” compare power values, and justify mathematical statements under “Comunicar ideas matemáticas.” Advanced problem-solving sections also utilize “Razonamiento de orden superior” and “Comunicar el razonamiento” to ensure students apply process standards, such as reasoning, modeling, and communicating mathematical ideas. Similarly, in topic 8, “Mostrar, describir y resumir datos,” the step 3, “Práctica y resolución de problemas” section includes an “Análisis de ejercicios” table that identifies the TEKS content and process standards addressed for each group of student practice problems. For example, in exercise 17, “Comunicar ideas matemáticas,” students create a frequency table and histogram from a dataset and explain how changing interval ranges affects the graph, which reinforces process TEKS 6.1D. Furthermore, the lesson provides a second analysis table for the “Additional practice” activities, allowing educators to identify where each mathematical process standard embeds throughout the lesson.

Additionally, every lesson in the Guía del maestro includes a “Conocimientos y destrezas esenciales de Texas (TEKS)” section that identifies the targeted knowledge and skills while connecting TEKS expectations to mathematical concepts and procedures. For example, lesson 3-1, “Operaciones con enteros” lists TEKS 6.2B and TEKS 6.3C to connect conceptual understanding of rational number operations and problem solving to procedural skills. In addition, each unit contains an “Estándares de los procesos matemáticos de los TEKS” section that outlines the supporting process standards, including TEKS 6.1C for selecting tools, TEKS 6.1F for analyzing relationships, and TEKS 6.1G for justifying ideas with precise language.

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

Materials in the Guía del maestro for topic 4, “Expresiones numéricas y algebraicas,” provide opportunities for students to think mathematically, persevere through solving problems, and make sense of mathematics. In the Guía del maestro, lesson 5-1, “Entender ecuaciones y soluciones,” step 1, “Investigar,” students analyze a real-world planting scenario.

Additionally, materials in the Guía del maestro for topic 4, “Expresiones numéricas y algebraicas,” provide opportunities for students to think mathematically, persevere through solving problems, and make sense of mathematics. Within the section “Perseverancia (GRIT),” the materials introduce resilience checkpoints that prompt educators to guide students when encountering problems that require identifying more than one correct solution. Additionally, in lesson 4-7, “Expresiones equivalentes” the section “Anticipar” challenges students to represent real-world scenarios, such as modeling plant patches, requiring sustained effort even when an initial approach is unclear. Students also make sense of mathematics by bridging abstract algebraic concepts with concrete visual tools and substitution strategies. An example of this conceptual sense-making occurs in “Conversación de la clase,” where students unpack the meaning behind the least common multiple and greatest common divisor by connecting them to multiplication products and factor trees. Finally, the lesson guidelines support this by directing students to utilize algebra tiles to visually represent terms, alongside a substitution table feature in “Trabajo del estudiante” that maps out values over multiple weeks to prove mathematically that different expressions yield an identical value, targeting their understanding of algebraic equivalence.

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

The grade 6 materials support students in understanding, explaining, and justifying multiple ways to represent and solve problems and complete tasks. In topic 5, lesson 5-2, “Aplicar propiedades de la igualdad,” students solve and justify equivalent equations using addition, subtraction, multiplication, and division properties of equality, alongside balance scales and algebra tiles. In step 1, students compare solution strategies to explain why an equation remains true only when applying the same operation to both sides. In step 2, “Aprendizaje visual” connects symbolic equations with balance models, requiring students to explain how different properties produce equivalent equations, compare multiple representations, and justify property usage. In step 3, students apply properties to solve equations, explain their reasoning, and verify that solutions maintain equality. Additionally, every “Elaboremos” lesson in the Guía del maestro includes an “Hablemos de matemáticas” routine. This routine begins as a whole-class discussion and extends to partner or small-group conversations where students elaborate on reasoning, compare approaches, and respond to peer ideas. In lesson 5-2, students use this routine to compare equations and determine variations. The lesson continues with step 1, “Explora y comenta,” where students analyze problems, reflect on reasoning, revise approaches, and compare solution methods illustrated through sample student work.Furthermore, materials in order to represent, In the Guía del maestro, lesson 9-3, “Investiguemos: estrategias para hallar áreas de polígonos,” step 1, “Investigar,” students evaluate sample work demonstrating different decomposition methods. In step 2, “Relacionar,” students select problems and compare structural composition and decomposition approaches. During step 3, “Práctica y resolución de problemas,” students model their work with diagrams and calculations to find the area of composite figures. Then, to solve, students calculate area by decomposing polygons across all lesson phases. They apply alternative decomposition methods to solve composite figure problems in step 3 and complete application tasks within step 4, “Evaluar y diferenciar.” Finally, to explain and justify, educator prompts in step 1 direct students to compare methods, explain each strategy, and verify that different decompositions yield identical area measurements. Students explain the validity of each method in step 2, justify their final solutions in step 3, and present formal mathematical reasoning during the practice and intervention tasks in step 4.




Additionally, in the Guía del maestro, lesson 5-1, “Entender ecuaciones y soluciones,” students determine whether a value is a solution to an equation using writing and solving equations, ratios, and substitution. In step 1, students analyze student work samples using these strategies to identify correct and incorrect reasoning and explain why a solution is valid. In step 2, “Relacionar,” students compare solution strategies, discuss how substitution verifies an equation, and explain why different approaches lead to the same conclusion. In step 3, students solve and check equations by substituting values and justifying their reasoning. Similarly, in lesson 8-6, “Comunicar con datos,” students create and analyze a single dataset using dot plots, box plots, and histograms. In step 1, “Investigar,” educator guidance prompts students to compare the strengths and limitations of each representation, determine which display best communicates the data depending on the purpose, and explain their reasoning. In step 2, “Relacionar,” students discuss and justify why one representation is more appropriate than another for identifying the median or range. In step 3, “Práctica y resolución de problemas,” students select and use representations to solve problems and justify their choices by evaluating multiple representations to fit the context.

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

The grade 6 materials require students to analyze mathematical concepts through regular opportunities to perform operations, write solutions, and discuss concepts with peers and educators. In the Guía del maestro, lesson 5-10 “Resolver desigualdades usando la multiplicación o la división,” the “Explorar y comentar” section requires students to determine values that satisfy an inequality, compare distinct solution strategies, justify their reasoning, and evaluate the accuracy of contrasting solutions. During “Aprendizaje visual,” students solve inequalities, graph solutions on a number line, explain why the inequality symbol reverses when multiplying or dividing by a negative number, and verify solutions using substitution. Additionally, in the “Práctica y resolución de problemas” section, students solve, represent, and justify solutions to inequalities within mathematical and real-world contexts. Furthermore, in lesson 2-6, “Representar la ubicación en el plano de coordenadas,” the materials require students to investigate a real-world problem by graphing and reflecting points on the coordinate plane, analyzing ordered pairs, and determining how reflections modify point locations. Throughout the lesson, students record mathematical thinking by graphing points, writing ordered pairs, analyzing sample student work, and completing guided and independent practice tasks. Within the “Comentar las soluciones de los estudiantes” section, educators guide students to explain and justify their reasoning, compare multiple solution strategies, discuss core mathematical concepts in whole group, evaluate if the given information is enough to solve the featured problem, and communicate ideas using mathematical vocabulary.


Additionally, in the Guía del maestro, lesson 10-6, “Explorar cómo generar ingresos,” students engage in financial literacy and data analysis. In the “Apoyo del lenguaje” section, students work in small groups to observe and contrast different professions using the sentence frame, “La gente que trabaja como ___ gana más ingresos ___.” This verbal activity transitions into written analysis during the “Hablemos de matemáticas” section, where students evaluate a “¿Cuál no pertenece?” prompt comparing the required education, training hours, and salary of a bus driver versus an airline pilot. The lesson includes a “Boleto de salida” section, requiring students to independently analyze data tables contrasting education levels across multiple occupations—such as doctors, educators, and chefs—and answer questions demonstrating how education impacts yearly salaries.

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

In Guía del maestro, topic 4, “Expresiones numéricas y algebraicas,” lesson 4-7, “Expresiones equivalentes,” the “Supervisar” section provides “Preguntas de evaluación” and “Preguntas para profundizar,” including “¿Qué les está pidiendo que hagan el problema?,” “¿Qué representan las fichas de álgebra?,” and “¿Cómo pueden usar fichas de álgebra como ayuda para escribir expresiones equivalentes?” These prompts direct educators to have students explain expression equivalence, describe how algebra tiles model expressions, and justify mathematical reasoning. Furthermore, the “Comentar las soluciones de los estudiantes” and “Relacionar” sections direct educators to lead discussions where students compare solution strategies, explain expression equivalence, and defend conclusions using models and substitution. Additionally, the “Comprobar la comprensión: comparar y relacionar” routine provides prompts requiring students to state whether they agree or disagree with a solution and explain their reasoning. The “Rutina del lenguaje: comparar y relacionar” activity requires student pairs to solve tasks using distinct methods, identify structural similarities, and debate which conceptual path is most efficient. To facilitate reflection before the “Práctica y resolución” de problemas phase, the materials provide closing discussion prompts, including: “¿Quién puede reformular este razonamiento de otra manera?” and “¿Están de acuerdo o en desacuerdo? ¿Por qué?” These embedded prompts require students to analyze alternative solution pathways and provide mathematical justifications. Furthermore, the grade 6 instructional materials provide structured educator guidance within the digital platform’s Manual de resolución de problemas to facilitate mathematical discourse and student reflection on problem-solving approaches. The online educator materials include specific discussion prompts that instruct students to reflect on their strategies. These embedded digital prompts guide students to explain how they solved a problem, compare multiple solution strategies, justify why a strategy is effective, and support their reasoning with mathematical evidence. Throughout the online problem-solving routine, the platform directs students to defend their solutions, evaluate alternative strategies, and refine their own thinking based on evaluation of their own progress.


Additionally, in the Guía del maestro, lesson 5-2, “Aplicar propiedades de la igualdad,” the “¿Lo entiendes? ¿Cómo hacerlo?” section includes educator prompts asking students, “¿Cómo pueden determinar la cantidad de bloques x necesarios en el lado izquierdo para que la balanza de platillos esté equilibrada?” Students explain what operation was performed on both sides of an equation and justify why the equation remains balanced. The “Apoyar la comprensión de los estudiantes” section guides educators to have students verify that the same property of equality was applied correctly by explaining and repeating the process with new equations. Additionally, the “Errores e intervención” guidance provides questions that prompt students to defend whether a property was applied correctly and explain why an incorrect solution does not preserve equality. Similarly, in lesson 7-6, “Sobresalir en los exámenes,” educators guide students to explain the information needed to solve problems, develop and defend mathematical models, and justify predictions using percentages and mathematical evidence. Educators lead discussions where students compare solution methods, analyze sample student work, and evaluate whether different models represent the situation. During the “Comentar estrategias de solución,” “Comprobar conclusiones,” and “Reflexionar sobre el razonamiento” sections, students reflect on problem-solving approaches by explaining reasoning, evaluating alternative strategies, and justifying revisions to their models.

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 1-8, “Dividir números mixtos,” the “Rutina del lenguaje: evaluar, corregir y aclarar” and “Hablar sobre las ideas matemáticas” sections provide discussion prompts, including “¿Puedes hallar el cociente de dos números mixtos dividiendo primero las partes de un entero, luego dividiendo las partes fraccionarias, y después sumando esos cocientes?” These prompts require students to explain, justify, and evaluate the reasonableness of their quotients. To address anticipated misconceptions, such as calculating the reciprocal of only the fractional component of a mixed number or confusing repeated multiplication, the “Apoyar la comprensión de los estudiantes” guidance supplies corrective questions and explanations to clarify mathematical concepts. Additionally, the “Elaboremos: dividir números mixtos” lesson structure contains the “Ejemplos del trabajo de los estudiantes” section, which presents multiple student solution strategies using visual models and fractional algorithms. During step 1, “Supervisar, seleccionar y poner en secuencia,” the materials provide educators with specific diagnostic prompts: “¿Cómo usan los estudiantes un modelo para representar el problema?,” “¿Qué operaciones usan los estudiantes para resolver el problema?,” “¿Cómo pueden convertir un número mixto en una fracción?,” and “¿Pueden hacer un modelo para que los ayude?” During step 2, “Aprendizaje visual,” the “Pregunta esencial” and “Hablar sobre las ideas matemáticas” sections provide follow-up prompts to guide explanatory feedback, including “¿Por qué hacen una estimación del cociente?” and “¿Por qué usan el recíproco del divisor para volver a escribir el problema de división como un problema de multiplicación?” Following the visual learning component, the “Prevenir malentendidos” section features “Guided Practice” error intervention strategies in case students selected the incorrect responses and exit tickets that provide embedded guidance to help educators interpret student inputs, recognize common errors, and deliver explanatory feedback on prerequisite skills. Furthermore, in the Guía del maestro, lesson 6-7, “Investiguemos: usar tasas para comparar” section, the “Errores e intervención” subsection identifies a common student misconception where students misinterpret a better economic value as a greater numerical value instead of a lower unit price. To address this misconception, the materials provide educators with explicit, sequential guiding questions, such as asking whether students prefer a higher or lower price per flyer and comparing $0.30 to $0.26 to anchor understanding. The “Comprobación rápida” section provides data-driven feedback pathways based on assessment scores. For students scoring zero to three points, the platform directs educators to assign reinforcement tasks and vocabulary support. For students scoring four to five points, the platform directs educators to transition students to an extension activity called “Actividad de ampliación” to deepen mastery. Additionally, the materials include bilingual support with a specific instructional callout recommending that educators use the “Developing Math Competency” activity for emergent bilingual students.

Additionally, in lesson 9-3, “Estrategias para hallar áreas de polígonos,” the section “Anticipar” directs educators to consider the methods students use to decompose composite shapes before the lesson starts to prepare for varied mathematical reasoning. The section “Supervisar” contains formative tools, providing evaluation questions for educators to ask, such as “¿Qué hicieron para hallar el área antes?,” and instructional prompts such as “¿Qué grupos no pueden llenar el polígono con bloques?” These provisions prompt educators to monitor and be aware of misconceptions by addressing incorrect responses. Furthermore, the section “Comentar las soluciones de los estudiantes” features reflective prompts for educators to guide students to evaluate efficiency, recognize why non-standard figures must be broken down into familiar shapes, and understand why external areas are subtracted in a subtraction strategy. These integrated prompts and structured evaluation questions within the materials provide a framework for educators to manage mathematical discourse and address geometric comprehension.