enVision+ Texas Matemáticas, Adv 06

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

The “Documentos del contenido y secuencia” tab includes four files for school years of varying lengths: 135, 165, 180, and 210 days. Each file outlines topics taught in the course, broken down into individual lessons that indicate the Texas Essential Knowledge and Skills (TEKS) addressed. For example, “Alcance y secuencia de 165 días de grado 6A” details topic 1,”Utiliza números racionales positivos,” as a 10.5-day lesson that teaches TEKS 6AM.3A, 6AM.3B, 6AM.3C, 6AM.3F. This same topic spans 9 days, 10.5 days, and 15.5 days in the respective 135-, 180-, and 210-day “Contenido y secuencia” files.

Additionally, the “Contenido y secuencia” in the “Páginas finales” section of the enVision+ Texas Mathematics 2027 grade 6 advanced Guía del maestro provides a vertical scope and sequence, including “Grados 6–8 Avanzados,” “Geometría,” and “Álgebra II” sections detailing, “Las declaraciones en Contenido y secuencia provienen de los TEKS. El cuadro está organizado para mostrar progresiones a lo largo de ejes similares.” For example, the scope and sequence chart contains 17 “Eje” sections, such as “Números y operaciones” and “Círculos,” highlighting that 6 of the 17 strands are taught in the grade 6 advanced course.

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).

In the “Pacing Guides” under the “Browse” heading, there are four separate files with pacing guides for school years of varying lengths (135, 165, 180, and 210 days) that include the topics, the number of days each topic should take to teach, and which TEKS are covered. The days allocated to each topic vary depending on the length of the instructional calendar. Specifically, topic 10, “Financial Math,” requires 12 days under the 180-day instructional calendar and 9 days under the 165-day instructional calendar.

Likewise, there are four separate files of “Documentos del Contenido y secuencia” for school years of varying lengths (135, 165, 180, and 210 days) that include the suggested number of days allocated to each topic for each respective school year length. For example, topic 1, “Utiliza números racionales positivos,” suggests 9 instructional days and 2 assessment days for the 135-day calendar and 15.5 instructional days and 3.5 assessment days for the 210-day calendar.

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 article “Advanced Grade 6 Content Organization Rationale” in the “Grados 6–8: vistazo al programa” states that “Topics are sequenced to support mathematics progressions that connect new content to prior knowledge” and explains that the TEKS recur in multiple lessons within and across topics to reinforce more connections.

Furthermore, in the program overview, a graphic organizer provides the rationale for the content grouping and how it builds mathematical connections. It states that topics 5 (“Integers and the Coordinate Plane”) and 6 (“Integer Operations”) are grouped because “Students extend the number system to integers, identifying a number, its opposite, and its absolute value. Students represent absolute values on number lines and use these relationships of distance and direction, as well as other models, to add and subtract integers. They generalize these understandings to fluently add, subtract, multiply, and divide integers.”

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

In the “Protocolos de internalización y herramientas para observación” section, a document titled “Protocolo de internalización del tema para el maestro” guides educators to internalize each unit and lesson by providing a four-part protocol with detailed steps for “Alcance y secuencia y ritmo,” “Preparándose para enseñar el tema,” “Evaluación del tema,” and “Reúne y prepara materiales.” For example, in the “Alcance y secuencia y ritmo” section, step 1 guides educators, “Consulta tu ámbito y secuencia para situar este tema en el contexto del currículo anual,” and step 3 of the “Preparándose para enseñar el tema” section guides educators, “Identifica las relaciones entre las lecciones y cómo construyen hacia una cobertura exitosa de TEKS.”

Additionally, the Guía del maestro provides a “Contexto matematico” for each topic. Specifically, topic 1, “Utiliza números racionales positivos” guides the educator through key concepts, balance and coherence, process standards, and linguistic accommodations for the unit. Furthermore, the Guía del maestro provides side-by-side guidance on lesson internalization for each page of the lesson that corresponds to the Libro del estudiante.

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

In the Protocolos de internalización y herramientas para observación, several links are provided as resources for instructional leaders to support educators in implementing the materials as designed, including internalizing topics and lessons, with step-by-step guidance on topic and lesson internalization. For example, the “Protocolo de internalización de la lección para los líderes de la enseñanza” resource document contains an “Orientación” section, broken down into three parts, such as “Implementación,” with guidance to “...facilita discusiones sobre conceptos y habilidades fundamentales abordadas en la lección y cómo se evalúan a través de la práctica de la lección y los Tickets de Salida.”

Furthermore, “Protocolos de internalización y herramientas para observación” section provides the “Protocolo de análisis del trabajo del estudiante para los líderes de la enseñanza,” a document that offers step-by-step guidance for analyzing student work. Specifically, guidance is provided for implementation to coach educators, “Identifica no solo qué TEKS están dirigidos, sino qué breakout específico del TEKS” so that educators can “ordenar y categorizar el trabajo de los estudiantes” to “crear categorías significativas basadas en estrategias de solución, conceptos erróneos comunes, niveles de razonamiento, completitud de la solución.”

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

The Guía del maestro provides a “Contexto matemático: conceptos clave” section at the beginning of topic 2, “Analizar relaciones geometricas,” including guidance on key concepts, such as “Hallar medidas que faltan” and “Hallar el área,” and academic vocabulary, including “Adaptaciones linguisticas” for terms such as factor de escala, descomponer, and cometa. For example, the guidance states that the “Vocabulario en contexto” includes “volumen,” with a “Significado matemático” of “la cantidad de espacio que ocupa un objeto tridimensional en unidades cúbicas” and other meanings, such as “cuán fuerte es un sonido.”

Moreover, the “Contexto matemático: coherencia” section explains how concepts connect to what students in grade A6 learned previously, such as “Propriedades de las figuras” and “Volumen” in grade 5 and “Representar punto en el plano de coordenadas” and “Evaluar expresiones algebraicas” earlier in grade A6. It also specifies how concepts such as “Dibujos a escala” and “Área de un triangulo” in topic 2 lead to concepts such as “Resolver problemas de medición” and “Área y área de la superficie” in grade A7.

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.

On the online platform, there is a “Participación de la familia” section that provides families with access to the concepts in each lesson within the units. For example, for lesson 1-5, “Multiplicar fracciones,” families have access to two tutorial videos and are directed to key vocabulary, including multiplicar fracciones unitarias. The language may be changed from Spanish to English by toggling the language selection at the top right of the window.

Additionally, each topic provides a “De la escuela al hogar” letter with detailed support and suggestions, in English and Spanish, that families can use to help their student understand and practice the topic’s concepts. For example, the “De la escuela al hogar Tema 1” provides an activity for families to challenge their student to identify the operation (multiplication or division) used with two fractions to obtain a solution. At the bottom of the letter, it suggests, “Déle su apoyo para que reconozca que el problema 5 entre 1/2 quiere decir ‘¿Cuántas mitades hay en 5?’ y entienda que el cociente, 10, es mayor que el dividendo.”

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

In the grade 6 advanced “Planes de la lección para Texas” document, lesson 1-1, “Vamos a investigar: patrones de valor posicional en números enteros y decimales,” correlates with TEKS 6AM.3F for “Objetivos de las matemáticas,” requiring students to “utilizar números enteros para estimar soluciones decimales” and “Sumar, restar y multiplicar decimales.” The lesson includes questions such as “¿Cómo decides dónde está el decimal en el producto?” and uses a “Comprobación rápida” from the Cuaderno de evaluación as an instructional assessment that aligns with the objectives.

Additionally, the lesson 6-2 component “Elaboremos: sumar enteros” includes adding positive and negative integers and modeling integer addition in real-life applications as daily objectives, which correlates with TEKS 6AM.3D and 6AM.3E. In the lesson, students use number lines as materials to identify additive inverses and opposite integers and answer questions, including “¿Qué notan acerca de los sumandos cuando la suma es cero?” An exit ticket assessing achievement in adding integers prompts students to identify the total change in temperature after two drops in temperature during the day, aligning with the objective.

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.

There are lesson plans in the grade A6 “Planes de la lección para Texas” tab for all lessons in the course. The plans provide the number of days allocated to each lesson, which are then broken down into detailed steps, with minutes allocated to each step. The document also includes the educator and student materials necessary for each lesson. For example, for lesson 1-2, “Vamos a construir: sumar, restar y multiplicar decimales,” the plan indicates the lesson should take one day, with four steps that are broken down into the number of minutes for each step, and lists necessary materials as the “Diapositivas de presentación de la lección enVision on the Go” for educators and rejillas decimales and manipuladores de cubos decimales for students.

Similarly, each topic in the Guía del maestro begins with a “Plan del tema” section that presents a chart of the lessons, citing the objectives, materials required for educators and students to deliver each lesson effectively, and the number of days allocated for each lesson within the topic. For example, the topic 2 “Plan del tema: analizar relaciones geométricas” section includes “Investiguemos 2-4: estrategias para hallar áreas de polígonos,” which should take two days, and lists the necessary materials as “bloques de patrón, opcional: papel cuadriculado, lápices de colores, tijeras.”

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

Step 4 in most lessons in the Guía del maestro includes a “Comprobación rapida” formative assessment with guidance for educators on extended practice based on student performance, including suggested resources. For example, if a student scores 0–3 points, the educator is guided to use “Refuerzo para mejorar la comprensión y actividades de ‘Más apoyo de vocabulario.’” If a student scores 4–5 points, the “Actividad de ampliación” should be used as an extension.

Moreover, the grade A6 “Planes de la lección para Texas” tab includes the lesson plans for all lessons in the course. The document includes a blue plus sign symbol as educator guidance to indicate opportunities for extended practice in each step of the lesson. For example, in lesson 6-3, “Vamos a construir: restar enteros,” step 2, “Aprendizaje visual,” a blue plus sign labeled “Ampliar el pensamiento del estudiante” challenges students to add three integers, two of which have the same sign.

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.

Materials for grade A6 include a variety of instructional assessments at the unit and lesson level (including diagnostic, formative, and summative assessments) that vary in types of tasks and questions in the Cuaderno de evaluación. For example, the “Tarea de rendimento de mitad del tema” serves as a formative assessment in each topic, exhibiting question types such as multiple choice, open ended, fill in the blank, and graphing. While the Cuaderno de evaluación includes an “Evaluación de preparación” as a diagnostic assessment at the beginning of each topic, all of these assessments contain 12 multiple-choice questions that vary in question type, including problem solving, calculations, and real-world situations.

Furthermore, in lesson 1-1, step 4, “Evaluar y diferenciar,” the “Comprobación rápida” (a lesson-level formative assessment) provides differentiated follow-up activities based on student performance using a variety of questions and tasks, such as multiselect, text-entry, and multiple-choice questions.

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

The Cuaderno de evaluación includes the definitions and intended purposes for diagnostic, formative, and summative assessments in a chart that indicates the “Why” and “When” for each type of assessment. For example, it states the following for diagnostic assessment: “Why: Diagnose students’ readiness for learning by assessing prerequisite content. When: Before instruction,” and goes on to provide “Instructional Outcomes Informed by Assessment Results” as “develop individual study plans, make grouping decisions, and prescribe specific activities to fill gaps in understanding of prerequisite content.”

Additionally, in the Cuaderno de evaluación “How to Assess” section, the materials explain how observation assessments, portfolio assessments, performance-based tasks, and program assessments are used to evaluate student readiness, understanding, complex thinking, and mastery of content.

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

The grade A6 materials include a Cuaderno de evaluación that guides educators on consistent and accurate administration of instructional assessments. For example, the section “How to Administer Assessments” guides educators to prepare for assessments by understanding and scheduling time for the assessment, ensuring a proper testing environment, and monitoring assessments actively, including making accommodations for emergent bilingual students.

Similarly, the “Explorar y comentar” section in lesson 3-11 provides explicit educator directions for moving through the observational assessment, including questions such as “¿Cómo escogen los estudiantes un factor de conversion para usar?” Additionally, the “Supervisar, seleccionar y poner en secuencia” section asks, “¿Cómo evaluan los estudiantes el razonamiento de Linus?” when assessing a small group of students, providing guidance for monitoring and responding to student understanding during the activity.

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

In the Cuaderno de evaluación, all types of assessments throughout the course are provided with answer keys indicating the TEKS that align with each question as they correspond to the objectives in each lesson and unit. For example, each topic begins with an “Evaluación de preparación” as a diagnostic tool for the specific TEKS and objectives students will learn during the unit. Throughout the topic, formative assessments such as the “Comprobación rapida” and “Boleto de salida” are used to gauge students’ achievement of the TEKS and objectives aligned with the individual lessons in the unit. Finally, each topic concludes with an “Evaluación” and a “Tema de rendimiento,” which serve as summative assessments aligned with the unit’s TEKS and objectives.

Additionally, the course begins with the “Evaluación de preparación” as a diagnostic tool to gauge students’ performance on the specific objectives they learned in grade 5, aligned with the grade 5 TEKS, such as 5.3E and 5.6B. Throughout each topic in grade A6, formative assessments such as the “Boleto de salida” are used to measure students’ achievement of the TEKS and objectives aligned with the individual lessons in the unit. Finally, the “Tarea de rendimiento” serves as a summative assessment that aligns with all the unit’s TEKS and objectives. For example, lesson 3-3 has an objective for students to “usar la multiplicación y la división para hallar razones equivalentes” using TEKS 6AM.6A, 6AM.5C, and 6AM.5D, with a “Comprobación rápida” that assesses both the objective and the TEKS with a problem requiring students to “seleccionar todos los enunciados que indiquen una operación que dará una razón equivalente a 8 a 20.” The “Tema de rendimiento” for topic 3 aligns with the objectives and TEKS within all lessons in the topic, including 6AM.6A.

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

In the Cuaderno de evaluación, each assessment includes an answer key showing the Depth of Knowledge (DOK) level and TEKS for each item-type question. For example, the “Tema 1 evaluación” includes 11 questions (one DOK-1, eight DOK-2, and two DOK-3), some of which are multiple choice, while others are open ended or multiselect.

Furthermore, each lesson provides TEKS-aligned items at varying levels of complexity. For example, the lesson 7-1, “Entender y representar exponentes,” assessment requires students to interpret exponents, connect exponents to repeated multiplication, evaluate exponents, and apply concepts in context, demonstrating varying cognitive complexity while remaining aligned to TEKS 6AM.3G.

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

In step 4 of each lesson, students answer five questions in an online “Comprobación rápida” that is automatically scored, and based on student performance, a remediation, practice, or enrichment activity is assigned. The Guía del maestro provides a scoring interpretation for the “Comprobación rápida” to guide educators to “usar la versión del Cuaderno de evaluación para asignar la remediación o la ampliación.” For example, the scoring interpretation guides educators to use “Refuerzo para mejorar la comprension y actividades de ‘Más apoyo de vocabulario’” for students who score 0–3 points.

Additionally, instructional assessments and scoring information guide educators in interpreting student performance on the “Boleto de salida” in lesson 5-2, “Entender enteros.” The guidance includes identifying common errors and interpreting misconceptions, helping educators determine why students may be struggling and how to respond instructionally.

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

In the Cuaderno de evaluación, each assessment includes an answer key with a “Lección de intervención” tied to each question or task to support students in that concept. For example, if a student does not correctly answer the questions in the “Comprobación rápida” for lesson 3-8, the educator is guided to use “Lección de intervención M28” for that student.

Moreover, the materials provide guidance for the use of included tasks and activities to respond to student trends in performance on assessments in lesson 5-5, “Comprender valores absolutos de números racionales.” For example, the lesson includes a “Prevenir malentendidos” section connected to the “Boleto de salida” that identifies a likely student misconception and provides specific reteaching guidance educators can use when assessment results reveal that misunderstanding.

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 para supervisar el progreso del estudiante y del maestro” allows educators to mark student progress and growth according to the TEKS for each lesson, using symbols such as “x trabajando en ello,” “- casi llegado,” and “+ lo tengo.” Likewise, students can track their own progress and growth “Antes del tema,” “Durante el tema,” and “Después del tema” using the “Herramienta para supervisar el progreso y crecimiento del estudiante” for each lesson objective with selections such as “Puedo,” “Con ayuda,” and “Aun no.”

Furthermore, in the “Autoevaluación” section of the “Tarea de rendimiento de mitad del tema,” students self-assess their understanding of both the mathematics and language objectives using a structured rating scale, providing a tool for monitoring their progress and identifying areas where additional support may be needed. For example, on the “Boleto de salida” for lesson 1-6, “Entender la división con fracciones,” students select between three self-assessment indicators, such as “Lo entendi,” “Necesito ayuda,” and “Sigo trabajando,” to respond to the “Objetivo de matemáticas: puedo investigar divisiones con fracciones.”

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

In the Guía del maestro, the section “Apoyar la comprensión de los estudiantes” in lesson 3-4, “Elaboremos: comparar razones” guides the educator to practice another ratio problem with students who need more practice. It states, “Algunos estudiantes pueden necesitar práctica adicional en la comparación de razones,” and guides educators on setting up two ratios to represent “el puesto de productos agrícolas A” and “el puesto de productos agrícolas B,” including their prices for an ear of corn. The materials then guide the educator in assisting students through the steps that use ratios to determine which farm stand offers a better deal for 12 ears of corn. The educator uses a set of three questions to guide students in understanding that the farm stand that has a lower price when both ratios represent 12 ears of corn offers a better deal.

Additionally, in “Grados 6–8: sistema de intervención,” the intervention lesson K1, “Patrones que se repiten,” explicitly guides educators in supporting students who need additional instruction. The lesson includes “Enseñanza guiada,” “Práctica,” “Errores e intervención,” and “Si tiene más tiempo” sections that describe how educators should scaffold learning, address common misconceptions, and provide additional practice opportunities. The “Errores e intervención” section specifically guides educators to have students verbalize and chant patterns when they struggle to identify repeating sequences, providing targeted support for students who have not yet reached proficiency.

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

The grade A6 materials include pre-teaching and embedded supports for unfamiliar vocabulary and references within the text in the Guía del maestro in the “Adaptaciones del lenguaje” section at the beginning of each topic. For example, in topic 3, the “Vocabulario para poner en contexto” section offers pre-teaching supports that state, “Los estudiantes se encontrarán con los siguientes términos en este tema; asegúrese de que comprendan su significado para poder entender la situación o el problema.” It continues with terms for each lesson, such as grupo sanguineo and concesionario in lesson 3-2. Items 9–14 of the “Práctica y resolución de problemas” section include a chart depicting all different blood types and how many donors of each blood type are represented and then has students complete a variety of ratio comparisons between numbers of donors of the different blood types and the total number of donors. Likewise, the “Vocabulario en contexto” subsection of the “Adaptaciones de lenguaje” section provides the meanings of the word tasa, including the significado matemático as “un tipo especial de razón que compara cantidades con distintas unidades de medida” and the alternative meaning of “una cantidad de dinero que se paga por algo.”

Additionally, the lesson 5-2 “Elaboremos: entender enteros” section includes a “Vocabulario nuevo” section on the first page that explicitly introduces the terms entero and opuesto before students engage with the lesson content. The corresponding section in the Guía del maestro includes an “Apoyo al lenguaje” section, which provides embedded vocabulary support by directing educators to discuss mathematical terms and connect new unfamiliar vocabulary and references to prior knowledge. For example, the materials state, “Antes de que los estudiantes conozcan el término entero, puede resultarles útil hacer un repaso del término matemático contar números y el significado no matemático de la palabra opuesto. Pida a los estudiantes que trabajen con un compañero para sumar estas palabras a sus bancos de palabras y que escriban una descripción de cada término junto con el ejemplo correspondiente.” The guidance also explains that there are additional language-development resources to support unfamiliar vocabulary and references with the specific guided examples in the lesson, such as “Palabras no matemáticas desconocidas” with in example 3.

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

The grade A6 materials guide educators in differentiated instruction, enrichment, and extension activities for students who have demonstrated proficiency in grade-level content and skills throughout each lesson. For example, in the Guía del maestro, lesson 5-1, “Clasificar números,” step 1, “Explorar y comentar,” guides the educator to ask, “¿Cómo cambia el conjunto de datos si el robot midiera la estatura de las personas, en pies, que hay en cada habitación de una oficina?” in the section “Para estudiantes rápidos,” providing an extension for students that finish their work early.

Additionally, the “Biblioteca de diferenciación” tool offers educators multiple enrichment activities for students who have demonstrated proficiency in grade-level content and skills, including “Escoge un proyecto,” “Levántate y razona,” and “Contribuciones asombrosas.” The page describes extended learning opportunities such as investigating gear mechanisms, analyzing statistics, experimenting with color combinations, exploring relationships between addition and multiplication, and examining the contributions of mathematician Georg Joachim Rheticus. These activities require students to extend their learning beyond the core lesson and engage in deeper exploration, application, and problem solving.

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

The Guía del maestro uses scripted questions to provide direct instructional guidance, including sample responses and discussion prompts in lesson 8-11, “Elaboremos: relacionar tablas, gráficas y ecuaciones,” step 2, “Aprendizaje visual,” example 2, “Relacionar una ecuación que contiene dos operaciones con una tabla y una gráfica.” Specifically, the example asks students to graph the change in temperature for one day, and the Guía del maestro prompts the educator to ask, “¿Qué representa 2c en la ecuación?” and “Usando la gráfica, ¿después de cuántas horas es la temperatura de 12 grados C? Explíquelo.” The materials also guide educators in assisting struggling students and extending the example for students who understand in the sections “Apoyar la comprensión de los estudiantes” and “Ampliar el razonamiento de los estudiantes.” For example, the “Apoyar la comprensión de los estudiantes” section guides the educator, “Algunos estudiantes pueden necesitar práctica adicional para relacionar la información dada en una situación de la vida diaria,” and provides guiding questions that the educator can use to support the students with the example.

Additionally, every “Investiguemos” lesson includes a “Paso 1: Investigar” page that explicitly guides educators through the sections “Anticipar,” “Introducir la investigación,” “Usar las diapositivas de revelación lenta,” and “Comprobar la comprensión.” These sections include specific questions, facilitation prompts, anticipated student responses, and guidance for discussion to help educators introduce, model, and explain the lesson’s concepts. For example, the lesson 6-1, “Investiguemos: relacionar enteros y sus opuestos,” “Anticipar” section guides the educator, “Piense en distintas maneras en que los estudiantes razonarán sobre la posición original del sensor,” and the “Usar las diapositivas de revelación lenta” prompts the educator to ask, “¿Qué notan? ¿Qué se preguntan?”

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

The Guía del maestro provides guidance for facilitating student exploration, classroom discussion, observational analysis of student work, mathematical discourse, visual learning, and whole-group instruction. For example, lesson 2-5 “Elaboremos: hallar areas paralelogramos y rombos” begins with step 1, “Explorar y comentar,” which guides educators to introduce the lesson with a whole-class inquiry-based exploration and discussion about what parallelograms are, have students find the area of a rectangle on a coordinate plane, and then have them move the top two vertices four units to the right to make a parallelogram and find the area of that new shape. The materials guide the educator to “Observe a los estudiantes mientras trabajan,” and ask, “¿Cómo hallan los estudiantes el área de cada figura?” followed by suggestions of what students might do. Next, step 2, “Aprendizaje visual” includes explicit recommendations for lesson delivery using guided examples with visual modeling, questioning strategies, and educator-facilitated explanations, such as example 1, “Hallar la formula del area de un paralelogramo,” which guides the educator to ask “¿Cómo saben que la altura, h, del paralelogramo es igual al ancho, a, del rectangulo? ¿Por qué el lado inclinado del paralelogramo e se considera su altura?” and “¿Cómo saben que el paralelogramo y el rectángulo tienen la misma área?”

Additionally, the beginning of each lesson guides educators with recommendations in the Guía del maestro through the sections “Apoyo al lenguaje,” “Hablemos de matemáticas,” “Boleto de salida,” “Reforzar el vocabulario,” and “Recursos para el maestro.” These sections support lesson facilitation through academic language development, mathematical discourse, vocabulary reinforcement, formative assessment, and technology-enhanced instruction using presentation slides and visual learning resources. For example, in the lesson 6-2 section “Elaboremos: sumar enteros,” the “Recursos para el maestro” subsection of the tells the educator to use four resources to effectively deliver the lesson, including “Diapositivas de presentación de la lección” and “Usar manipulables: sumar enteros,” and then supports the educators in facilitating the “Explorar y comentar” engaging piece of the lesson using the guidance in the “Apoyo al lenguaje” section. This section guides the educator, “Si [los estudiantes] saben lo que es la evaporación, guíelos para que reconozcan que es un cambio de agua líquida a vapor de agua y resulta en la pérdida de agua de la piscina,” when the engaging piece asks students to calculate the change in water level before and after evaporation. This provides recommendations for facilitating instruction using multiple instructional approaches, including language supports, discussion-based learning, visual modeling, vocabulary development, and assessment-driven instruction.

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 “Practice in enVision+ Texas Mathematics” page in the program overview uses a chart to identify multiple types of practice, including whole-group, small-group, and individual practice, that connect to a variety of program components such as “Math Talks,” “Fluency Practice,” “Topic Review,” and “Hands-On Games” using guided, independent, and collaborative practice structures. For example, the page guides the educator in using different structures, such as a whole-group structure to “promote mathematical discourse and classroom conversations as students practice and apply new and previously learned concepts.” At the same time, the chart recommends whole-group and small-group structures for “Math Talks” using guided or collaborative practice and recommends whole-group, small-group, or individual structures for “Topic Review,” using guided, collaborative, or independent practice.

Additionally, in lesson 5-4, “Elaboremos: representar números racionales en la recta numérica” provides opportunities for multiple types of practice using different instructional structures. For example, the “Apoyo al lenguaje” section directs students to collaborate with a partner to discuss and explain how to represent a rational number on a number line. The “Hablemos de matemáticas” section facilitates guided whole-group mathematical discourse through educator-led questioning and discussion about representing negative rational numbers on a number line, while the “Boleto de salida” can be used any time after example 1 as independent practice for individual students.

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

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

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

The “Adaptaciones del lenguaje: los números racionales y el plano de coordenadas” page of the Guía del maestro guides educators in language development opportunities within the topic using sections such as “Apoyo para el vocabulario del tema,” “Transferencia metalingüística al inglés,” “Cognados,” and “Vocabulario académico” to support multilingual learners. The page includes specific guidance on language integration to effectively use the materials in state-approved bilingual programs. For example, the materials state, “Las actividades de este tema ofrecen experiencias diversas y atractivas con vocabulario matemático para fomentar la confianza y brindar apoyo a todos los estudiantes, pero especialmente a los estudiantes bilingües emergentes (BE) en el desarrollo tanto de sus habilidades académicas como lingüísticas.”

Additionally, each lesson guides educators in effectively using the materials in state-approved bilingual/ESL programs. For example, in lesson 7-1, “Elaboremos: entender y representar exponentes,” step 4, “Evaluar y diferenciar,” provides explicit implementation guidance to support emergent bilingual students in the “Comprobación rápida” results by using assessment data to determine appropriate next steps. Specifically, the materials note, “los estudiantes bilingües emergentes pueden beneficiarse de la actividad de ‘Desarrollar la competencia matemática.’” The page also points educators to additional supports available through the “Biblioteca de diferenciación” and “Videos de apoyo” components on the digital platform, providing clear guidance on incorporating language-support resources into instruction based on student needs.

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 Guía del maestro, under the “Adaptaciones lingüísticas: los números racionales y el plano de coordenadas” page, “Apoyo para el vocabulario del tema: vocabulario en contexto” provides embedded language supports to help educators develop academic vocabulary and increase comprehension in oral and written discourse by defining mathematical terms. For example, the term racional is defined as “Significado matemático: todo número que puede escribirse como fracción,” and “Otros significados: basado en la razón en lugar de las emociones.” The “Vocabulario para poner en contexto” section also informs educators that “los estudiantes se encontrarán con los siguientes términos en este tema, asegúrese de que comprenden su significado para que puedan entender la situación o problema.” The materials support comprehension in oral and written discourse throughout the lessons, providing specific terms in each lesson, such as lesson 5, “Más lejos, estrategia, representar.” To support educators with embedded guidance on cross-linguistic connections in oral and written discourse for the topic, the “Cognados” section lists robot/robot, persona/person, and negativo/negative as cognates that students will use in the topic.

Additionally, in lesson 5-4 “Elaboremos: representar números racionales en la recta numérica,” the “Apoyo al lenguaje” section supports emergent bilingual students through oral and written discourse of academic vocabulary development while increasing comprehension and building background knowledge. For example, the section guides educators in pre-teaching the term renombrar by having students write the term and underline the prefix re- connecting the concept to students’ prior knowledge about the meaning of the prefix as “volver a hacer.” This leads into a discussion about renaming rational numbers as mixed numbers to plot them on a number line. In the “Explorar y comentar” activity, students interpret the depths of different animals below the water’s surface and heights above water using positive and negative rational numbers to plot on a number line. The students use the cross-linguistic terms positivo and negativo, which are identified as cognates in the “Adaptaciones del lenguaje” section of the topic, in oral and written discourse to explore plotting rational numbers on a number line.

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.

Each topic includes lessons that contain a “Práctica y resolución de problemas” section that challenges students’ depth of understanding in solving problems aligned to the TEKS of the lesson’s concept(s). Each topic ends with an “Evaluación del tema” section that uses scaffolded DOK-leveled questions aligned to the topic’s TEKS to assess students’ learning. For example, in lesson 7-1, “Elaboremos: entender y representar exponentes” uses a variety of questions aligned to TEKS 6AM.3G in the “Práctica y resolución de problemas” section. These questions require students to calculate expressions with exponents, apply and analyze exponent calculations in real-world questions, and demonstrate depth of understanding to compare and contrast expressions with exponents. The Cuaderno de evaluación provides an “Evaluación del tema” for topic 7, with questions that have students demonstrate depth of understanding to analyze exponent expressions and solve a real- world evaluation aligned to 6AM.3G. Additionally, problems require students to simplify one-variable expressions and evaluate and identify multiple one-variable expressions with the same solution, demonstrating depth of understanding aligned with TEKS 6AM.7C.

Additionally, in lesson 2-1, “Elaboremos: dibujar triángulos con condinciones dadas” begins with step 1, “Explorar y comentar,” in which students use physical materials such as rulers, compasses, straws, and scissors to explore which combinations of three side lengths can form a triangle. This activates conceptual thinking and mathematical reasoning before formal instruction begins with TEKS 6AM.1C and 6AM.1E. During step 2, “Aprendizaje visual,” students engage with five sequenced examples that progressively increase in complexity, from drawing and comparing triangles with given side lengths using Desmos to analyzing triangles given only three angle measures. The embedded “¡Inténtalo!” prompts for each guided example require students to justify their thinking. Next, the “¿Lo entiendes?/¿Cómo hacerlo?” section and the “Conceptos clave” sections further consolidate understanding by requiring students to articulate the three sets of conditions that always determine a unique triangle. During step 3, “Práctica y resolución de problemas,” students engage with practice exercises spanning DOK levels 1 through 3, including higher-order thinking problems such as items 17 and 22, which require students to draw multiple triangles under given conditions and explain their reasoning, demonstrating a depth of understanding of TEKS 6AM.12D.

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

In the Guía del maestro, lesson 5-1, “Elaboremos: clasificar números” uses scaffolded steps, including “Explorar y comentar” and “Aprendizaje visual,” that guide educators in using a variety of strategies and visual models, such as Venn diagrams and concentric circles, to represent and classify numbers. Next, the students use a number line to locate whole numbers, integers, and rational numbers. The “Práctica y resolución de problemas” questions begin with classifying whole numbers, integers, and rational numbers in a Venn diagram and progressively increase in rigor, requiring students to communicate mathematical reasoning for number classifications. The materials also challenge students to solve real-world problems, such as “Una cuenta bancaria tiene un saldo de $0, un retiro de -$50, una transferencia de -$2.50 y un depósito de $20.50. Clasifica cada monto en números enteros no negativos, enteros y racionales,” leading to proficiency in TEKS 6AM.2A.

Additionally, in lesson 2-1, “Elaboremos: dibujar triángulos con condiciones dadas” includes questions and tasks that progressively increase in rigor and complexity from foundational exploration through higher-order reasoning. In step 1, “Explorar y comentar,” students begin at a concrete, exploratory level by physically testing combinations of wood pieces to determine which can form a triangle, building an intuitive understanding of the triangle inequality before any formal rule is introduced. In step 2, “Aprendizaje visual,” the five examples provided systematically increase in complexity. Specifically, the first example guides students to use Desmos to observe and compare triangles with given side lengths and identify that they are identical regardless of orientation. Each consecutive example increases in rigor. First, students determine possible triangle side lengths based on the rule that the sum of the two shorter sides must be greater than the longest side, and then they draw triangles given the side lengths and an angle measure to evaluate if multiple triangles can be formed before moving into more complex guided examples. In example 4, students use non-routine reasoning to analyze why two side lengths and a non-included angle do not always determine a unique triangle and use geometry software to explore multiple possibilities. Finally, in example 5, students reason that three angle measures without side lengths cannot determine a unique triangle formation and justify their answer using proportional reasoning and equations. The embedded “¡Intentalo!” prompts reinforce this progression by requiring students to write and solve equations to find missing angle measures, write three side lengths that do and do not form a triangle, and explain their reasoning, leading to grade-level proficiency in TEKS 6AM.12D.

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

Each topic in the Guía del maestro begins with guiding pages to prepare educators to teach its concepts, such as the “Contexto matemático: coherencia” page. This page connects the topic’s concepts to patterns, big ideas, and relationships that students previously learned in grade A6 and highlights how they connect to concepts that students will learn later in grade A6. For example, the “Contexto matemático: coherencia” page for topic 3, “Entender y usa razones y tasas,” explains in the “Anteriormente en el grado 6 avanzado: cálculos con números racionales” section, “En el Tema 1, los estudiantes adquirieron fluidez en la suma, la resta, la multiplicación y la división de números racionales.” This connects to topic 3, “Razonamiento de razones” because students “usan razones para describir relaciones de multiplicación y aprenden a razonar sobre razones usando razones equivalentes.” Students also learn about rates, create equivalent rates, compare rates, and solve unit rate problems, demonstrating coherence in the section “Más adelante en el grado 6 avanzado: comprender y usar porcentaje.” This section explains, “En el Tema 4, los estudiantes comprenderán el porcentaje como una tasa en la que se compara con 100,” and “En Tema 11, los estudiantes usarán porcentajes mientras resumen distribuciones de datos.”

Additionally, each lesson in the Guía del maestro contains a “Coherencia” section that explicitly maps what students learned previously within the topic and across prior units, what they are learning in the current lesson, and where their learning is headed later in the topic and course. For example, in lesson 5-1, “Clasificar números,” the “Coherencia” section explains a cross-unit connection to the big idea from the previous topic, in which students added, subtracted, multiplied, and divided rational numbers to solve problems. Building directly on that prior unit’s work with rational numbers, this lesson connects the pattern to classifying numbers as whole numbers, integers, and/or rational numbers using a Venn diagram and locating numbers on a number line based on their classification. Looking ahead within the topic, the “Coherencia” section notes that students will locate, order, and compare relationships between integers and rational numbers using a number line and use rational numbers to locate points on the coordinate plane. In lesson 5-2, “Entender enteros,” the “Coherencia” section notes that students will connect patterns, big ideas, and relationships between mathematical concepts by reading, writing, comparing, and ordering rational numbers later in the topic.

Evaluation for 4.2b
Materials demonstrate coherence across units by connecting the content and language learned in previous courses/grade levels and what will be learned in future courses/grade levels to the content to be learned in the current course/grade level.

The grade A6 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. For example, in the in the Guía del maestro, topic 11, “Mostrar, describir y resumir datos,” begins with several pages that prepare educators to teach the topic’s lessons, including “Contexto matemático: coherencia” and “Adaptaciones del lenguaje.” The “Contexto matemático: coherencia” page is separated into three columns, titled “¡Vuelve atrás!,” “Tema 11,” and “Más adelante.” The “¡Vuelve atrás!” section connects the content learned in grade 5 and earlier in grade A6 to the content students are learning in topic 11, demonstrating the mathematical language that connects the concepts. For example, the text states, “Grado 5: Los estudiantes representaron datos numericos usando diagramas de puntos. Las experiencias de los estudiantes creando y analizando estas representaciones de datos marcaron el inicio de su análisis de las distribuciones de datos.” An additional section states, “Anteriormente en el grado 6 avanzado: En el Tema 1, los estudiantes adquirieron fluidez con la suma, resta, multiplicación y división de números decimales . . . Estas habilidades de cálculo permitirán a los estudiantes calcular medidas estadísticas.” The “Tema 11” section headers “Representaciones de datos” and “Distribuciones de datos” uses mathematical terms to describe the content students will learn throughout lessons in topic 11. The subsection “Medidas estadísticas” describes how students will determine the mean, median, and mode, which are measures of center, and learn how to find the first and third quartiles of a dataset. Finally, the “Más adelante” section explains how the content and language students will learn in topic 11 connect to grade A7, when students learn to use samples to draw inferences about a population for comparison among populations and use measures of center and measures of variability from random samples to make informal inferences comparing two populations.

Additionally, each lesson begins with a “Coherencia” section that maps the progression of mathematical content and a “Vocabulario” section that indicates whether language is being introduced for the first time or reinforced from prior learning. For example, the “Coherencia” section on the first page of lesson 2-5, “Hallar áreas de paralelogramos y rombos,” in the Guía del maestro notes that students used the formula for the area of a rectangle to solve problems in grades 4 and 5, connecting to deriving the formula for the area of a parallelogram to solve real-world and mathematical problems. The “Reforzar el vocabulario” section connects to the previously learned mathematical language, including área de un paralelogramo, paralelogramos, and rombos. Lesson 2-9, “Resolver problemas con volumen de prismas,” includes a “Coherencia” section to connect the content, such as “hallan el volumen de ortoedros con longitudes de aristas fraccionarias,” to vocabulary, including cubo, longitudes de aristas fraccionarias, prisma rectangular recto y volumen. The section additionally connects to the content students will learn in grade 7, such as solving real-world and mathematical problems involving the volume of more complex three-dimensional figures.

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

The grade A6 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, as outlined in the “Coherencia” component on the first page of each lesson in the Guía del maestro. For example, the first page of lesson 7-1, “Elaboremos: entender y representar exponentes” explains, “En grado 5, los estudiantes aprendieron cómo usar exponentes para denotar potencias de 10.” This connects to the lesson because students “amplían su comprensión de exponentes para incluir otras bases” in grade A6. Likewise, the section highlights that students “aprenderán cómo escribir y evaluar expresiones con exponentes de números enteros no negativos,” which connects to concepts later in the topic, where students “escribirán y evaluarán tanto expresiones numéricas como expresiones algebraicas que contienen exponentes.”

Additionally, in the Guía del maestro, lesson 9-2, “Representar soluciones de desigualdades,” the “Coherencia” section demonstrates coherence by connecting students’ prior knowledge of concepts and procedures from grade 5. For example, the section connects the use of greater-than, less-than, and equal-to symbols to the new mathematical knowledge and skills of the current lesson to write inequalities to represent mathematical and real-world situations before solving inequalities later in the topic. Lesson 9-4, “Resolver desigualdades usando multiplicación y división,” connects students’ prior knowledge of graphing solutions of inequalities and solving them using the addition and subtraction properties of inequality from earlier in the topic to the new mathematical knowledge and skills of using the multiplication and division properties of Inequality and graphing solutions on a number line.

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

The grade A6 materials provide spaced retrieval opportunities with previously learned skills and concepts across lessons and units, as demonstrated in a Venn diagram on the “Space and Interleaved Practice in enVision+ Texas Mathematics” page in the program overview. This page compares the sections within the materials that offer spaced and interleaved practice, identifying that “Math Talks” and “Fluency Practice” both provide spaced retrieval opportunities. For example, the “Hablemos de matemáticas” section in lesson 1-7, “Elaboremos: dividir fracciones” in the Guía del maestro asks students to identify mistakes in the steps used to divide the mixed number 2½ by the fraction ⅘, providing spaced retrieval of skills and concepts that were previously learned in grades 4 and 5. The “Práctica de fluidez” at the end of topic 1, “Usar números racionales positivos,” provides spaced retrieval practice for the skills and concepts of adding, subtracting, multiplying, and dividing rational numbers that students learned throughout the topic.

Additionally, the materials include a “Repasa lo que sabes” section for each topic in the Libro del estudiante that uses spaced retrieval to activate prior knowledge and allows students to practice the prerequisite skills for that topic. For example, in topic 3, “Entender y usar razones y tasas,” the “Repasa lo que sabes” section asks students to recall vocabulary and skills related to equivalent fractions, equations, units of measure, and measurement conversions. The “Análisis de los ejercicios: repasa lo que sabes” table maps these exercises to TEKS standards 3.3F, 4.3C, 6AM.9B, 4.8A, and 5.7A. In topic 4, “Entender y usar porentajes,” the “Repasa lo que sabes” section requires students to retrieve skills related to rates, decimal computation, and equivalent ratios. The exercises are mapped to TEKS standards 6AM.2A, 6AM.5B, 6AM.3F, and 6AM.2E, providing spaced retrieval opportunities across lessons and units.

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

The grade A6 materials provide interleaved practice opportunities with previously learned skills and concepts across lessons in the “Práctica y resolución de problemas” and “Repasa lo que sabes” components. For example, the “Práctica y resolución de problemas” section of lesson 10-8, “Elaboremos: entender el impuesto sobre la renta,” provides interleaved practice across lessons to calculate income tax, such as directly multiplying percent tax rates and whole dollar amounts; using a table to determine tax rates; subtracting, multiplying, and adding values to calculate tax amounts; and using proportions to solve income tax amounts. The “Repasa lo que sabes” section of topic 10, “Matemáticas de finanzas,” provides interleaved practice across topics. For example, the “Vocabulario” section prompts students to use terms such as precio por unidad, ecuación de porcentaje, porcentaje, and equivalentes. The “Operaciones con números decimales” section has students multiply and divide money decimal amounts. The “Números racionales equivalentes” section has students convert rational numbers between decimals and percents. Finally, the “Resolver problemas con porcentajes” section challenges students to solve word problems involving money and percentages.

Additionally, each “Elaboremos” lesson includes step 3, “Práctica y resolución de problemas,” as part of the four-step instructional process, providing students with opportunities to review and apply previously taught concepts while engaging with new mathematical content. For example, the step 3, “Práctica y resolución de problemas,” section in lesson 10-8, “Entender el impuesto sobre la renta,” allows students to recall previously learned skills in multiplying decimals and percents while applying these concepts to the new topic of income tax. By connecting prior knowledge to unfamiliar contexts, students strengthen their understanding of previously learned concepts while developing new mathematical knowledge.

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

The “Representémoslo en 3 actos” lessons for each topic in the Guía del maestro require students to create models to solve problems involving mathematical concepts and situations and to interpret, analyze, and evaluate their models to find efficient solutions. For example, lesson 7-5, “Representémoslo en 3 actos: la excursión” presents students with a 30-second video about an educator preparing for a field trip. After students watch the video, they are tasked to write a question they can solve using a model, guided by questions such as “Después de mirar el video, ¿cual es la primera pregunta que te viene a la mente? Escribe la pregunta principal a la que responderás. Haz una predicción para responder a esa pregunta principal. Explica tu predicción,” followed by a number line model with boxes on the ends labeled “Demasiado pequeño” and “Demasiado grande.” In the second part of the lesson, students receive the detailed information they need to calculate the total cost of a field trip to the museum, including bus fare and museum admission prices based on participant age, as well as the number of students and chaperones attending. Students then interpret how their model can be used with the given information to solve the total cost of the field trip and analyze the variables of the problem to create and solve an algebraic equation. In the third part of the lesson, students evaluate their model once the answer has been revealed using questions 11 and 12, which ask, “¿Coincide tu respuesta con la respuesta del video? Si no, ¿qué razones explican la diferencia?” and “¿Cambiarías tu modelo ahora que sabes la respuesta? Explícalo.”

Additionally, in the Guía del maestro, lesson 3-3, “Investiguemos: patrones en razones equivalentes,” students are directed to engage with multiple representations, including ratio tables, double number lines, and bar diagrams. In step 1, “Investigar,” the “Comprobar la compresión” section uses a language routine called “Elaborar preguntas en conjunto,” in which students interpret a real-world context involving public transportation data, generate mathematical questions about equivalent ratios, and compare their questions with a partner before the class discusses them. In step 2, “Relacionar,” students analyze how different models represent the same mathematical relationships. The educator guidance states, “Comparar estrategias mejora la comprensión de diferentes maneras de hallar razones equivalentes. Pida a los estudiantes que se enfoquen en los distintos modelos que se pueden usar y cómo esos modelos relacionan las cantidades que se están usando.” Students then evaluate, “¿Es 6:8 equivalente a 30:40? Explíquenlo,” and are required to justify their reasoning. In step 3, “Práctica y resolución de problemas,” students interpret the structure of a ratio table through questions such as “A medida que avanzan por cada fila, ¿qué representa cada uno de los números?,” moving students from using a model to analyzing the mathematical relationships embedded within it.

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

The Guía del maestro for grade A6 includes questions and tasks that require students to create models to represent mathematical situations in the “Representémoslo en 3 actos” lessons in each topic. For example, lesson 11-7, “Representémoslo en 3 actos: rango vocal” presents students with a 37-second video of two contestants on a singing show, each scoring 24 points from three judges. After students watch the video, they are tasked to write a question they can solve using a model, guided by questions such as “Después de mirar el video, ¿cuál es la primera pregunta que te viene a la mente? Escribe la pregunta principal a la que responderás. Haz una predicción para responder a esa pregunta principal. La persona que debería ganar la competición es ________,” followed by a question asking students to justify their prediction. In the second part of the lesson, students receive detailed information about the scores each contestant received from three judges each week for six weeks. Students then create a statistical model to represent the given information to determine which contestant should win the competition.

Additionally, in lesson 3-2, “Elaboremos: entender razones, “Explorar y comentar,” “Construyamos” in the Libro del estudiante, students create a bar diagram to represent the relationship between the numbers of pop songs and R&B songs and use the model to compare the quantities. Students further create models when they respond to the prompt, “Ahora el álbum tiene 2 canciones pop y 10 canciones de R&B. Dibuja un diagrama de barras que podrías usar para representar la relación entre el número de canciones pop y el número de canciones de R&B.” In “Relacionar estrategias de solución,” students create additional bar diagrams comparing pop songs to the total number of songs and represent the relationship in multiple ways, including “3 a 5,” “3:5,” and “3/5.”

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

The materials for grade A6 include questions and tasks that provide opportunities for students to apply conceptual understanding to new problem citations and contexts in the “Investiguemos” lessons throughout the topics. For example, lesson 7-6, “Investiguemos, Expresiones equivalentes,” in the Libro del estudiante begins with a guided activity, “Cosecha saludable,” using algebra tiles to represent two gardens with 10 plants and 2 more added weekly, as well as a third garden with 2 plants and 4 more added weekly. Students write equations to represent the situation and determine how many weeks it will take for the three gardens to have the same number of plants. Then, students use algebra tiles to create new arrangements of the gardens, solidifying their conceptual understanding that the gardens remain equivalent even when arranged differently. Next, students select a new problem from the “Escoger un problema” section that contains four similar contexts, including selecting different expressions that are equivalent using variables L and W to represent the perimeter of a rectangle, selecting equivalent expressions that represent the extension of a square patio x feet, determining if two sets of algebra tiles arranged differently represent the same expression, and using algebra tiles to determine if three expressions containing the variable x are equivalent. A guiding question asks students, “¿En qué se parecen las estrategias que usaste en ‘Escoger un problema’ y en ‘Cosecha saludable’? ¿En qué se diferencian?”

Additionally, the Libro del estudiante provides opportunities for students to apply their understanding of the order of operations, exponents, and grouping symbols to unfamiliar real-world and mathematical situations in lesson 7-3, “Investiguemos: usar expresiones numéricas,” step 2, “Relacionar,” and step 3, “Práctica y resolución de problemas.” Students apply conceptual understanding to new contexts by solving problems that require them to use the order of operations in new situations. In step 2, “Escoger un problema,” students analyze errors, determine appropriate placement of grouping symbols, write expressions for geometric situations, and justify solutions. In step 3, “Práctica y resolución de problemas,” students apply the order of operations to new real-world contexts involving pricing, fundraising, measurements, and STAAR-style tasks. Examples include problem C, in which students determine how grouping symbols change the value of an expression, and exercise 20, in which students modify an expression with parentheses to produce a specified value. These activities require students to transfer their conceptual understanding to novel situations rather than repeat a previously demonstrated procedure.

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

The grade A6 materials provide tasks designed to build student automaticity and fluency necessary to complete grade-level tasks, such as the “Práctica de fluidez” component at the end of each topic in the Libro del estudiante. For example, in topic 5, “Los números racionales y el plano de coordenadas,” “Práctica de fluidez” is designed to build automaticity in adding and subtracting rational numbers to simplify coordinates and plot them on the coordinate plane. Students use this fluency later in lessons that require them to plot coordinates in the grade-level tasks of topic 8, “Representar y resolver ecuaciones.”

Additionally, the materials include a dedicated juego de fluidez in the “Biblioteca de diferenciación” that provides repeated practice of mathematical skills. For example, “Juego de fluidez, tema 2: ¡Rebota!” provides repeated practice in adding and subtracting decimal numbers to the hundredths place through structured gameplay. The activity builds the automaticity necessary to complete grade-level tasks by repeatedly requiring students to form decimal numbers and match them to equivalent decimal expressions appearing on the game board. The activity builds fluency by having students repeatedly apply addition and subtraction of decimals to the hundredths place while creating decimal values, checking solutions, and continuing play over multiple turns. The objective explicitly states, “Los jugadores suman y restan decimales hasta las centésimas para reclamar espacios en el tablero,” and the game requires students to continually compute and verify decimal expressions throughout the activity.

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

The grade A6 materials provide opportunities for students to practice the application of efficient, flexible, and accurate mathematical procedures within lesson 5-4, “Elaboremos: representar números racionales en la recta numerica.” For example, the Guía del maestro guides the educator in explaining to students in the “Apoyo al lenguaje” section that it is more efficient to plot rational numbers on a number line by first renaming them as mixed numbers. Then, in the examples, students practice applying flexible mathematical procedures, including using number lines in horizontal and vertical orientations to plot rational numbers, accurate procedures using a number line to compare positive and negative rational numbers, and efficient procedures using a number line to order negative temperatures from warmest to coldest.

Additionally, in lesson 4-4, “Elaboremos, Estimar para hallar porcentajes,” the materials provide multiple structured opportunities across all four steps for students to practice and refine estimation procedures using equivalent fractions, rounding, and compatible numbers. In step 1, “Explorar y comentar,” students apply estimation procedures flexibly using two possible approaches, including rounding 78 percent to the nearest 10 and using the part-to-whole fraction model or rewriting 78 percent as a compatible fraction and multiplying. The materials also include educator guidance to help students identify whether both strategies produce reasonable estimates and explain how each model supports the estimation. In step 2, “Aprendizaje visual,” students practice two different procedures across different examples. For example, in example 1, students apply equivalent fractions as estimation tools across a pie chart context, and in example 2, students practice both rounding and compatible number procedures side by side for the same problem.

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

The grade A6 Guía del maestro provides opportunities for students to evaluate procedures, processes, and solutions for efficacy, flexibility, and accuracy within the “Representémoslo en 3 actos” lessons in each topic. For example, lesson 2-8, “Representémoslo en 3 actos: fichas de tabla de trapecio,” presents students with an 18-second video about using small square tiles to fill a large trapezoid shape on a table. After students watch the video, they are tasked to write a question they can solve using a model, guided by questions including, “Después de mirar el video, ¿cuál es la primera pregunta que te viene a la mente? Escribe la pregunta principal a la que responderás. Haz una predicción para responder a esa pregunta principal,” followed by a question asking students to justify their prediction. In the second part of the lesson, students receive detailed information about the dimensions of the square tiles and the trapezoid’s height and bases. Students then use various procedures and processes to solve how many small tiles it will take to fill the large trapezoid area. After some time, the educator reveals the solution, and students compare and evaluate their procedures, processes, and solutions for efficacy, flexibility, and accuracy, including possible errors, in small groups.

Additionally, the materials provide explicit opportunities for students to analyze solution strategies, evaluate incorrect and correct reasoning, compare different mathematical representations, and discuss how mathematical procedures support valid conclusions in lesson 6-1, “Relacionar enteros y sus opuestos,” step 1, “Investigar.” For example, students examine multiple samples of student work, including both correct and incorrect solutions, and educators sequence solutions strategically, beginning with correct reasoning, addressing misconceptions, and concluding with a correct solution that uses additive inverses and a number line. Students discuss errors, justify reasoning, and evaluate whether solutions appropriately represent the problem situation. The lesson also supports evaluation processes and procedures for flexibility because students compare multiple representations and solution methods, including discussing how additive inverses, number lines, and integer reasoning can be used to solve the same problem and answering the question “¿Qué modelo pueden usar cómo ayuda para resolver problemas relativos a los enteros positivos y negativos?” Students also compare different approaches during the “Relacionar estrategias de solución” and “Comentar las soluciones de los estudiantes” sections. Finally, the lesson provides opportunities for students to evaluate processes and procedures for efficiency by evaluating which mathematical relationships and procedures provide the most direct path to a solution. In exercise 4, students reason that opposite values combine to 0 and use this relationship to determine a score without calculating every individual value. Students are encouraged to use the relationships among integers, opposites, additive inverses, and absolute value to justify and simplify solutions, thereby requiring them to evaluate the effectiveness of different procedures and representations when solving problems.

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

The grade A6 materials contain embedded supports for educators to guide students toward increasingly efficient approaches in the step 1, “Explorar y comentar” and step 2, “Aprendizaje visual” sections of the “Elaboremos” lessons. For example, the Guía del maestro embeds support for the educator in lesson 6-2, “Elaboremos: sumar enteros,” to guide students through looking for patterns in adding positive and negative integers. In step 1, “Explorar y comentar,” students discuss strategies for making predictions or reasoning so they will realize “ambas estrategias indican que si se suma un número negativo que es menor que el opuesto del número positivo, el resultado será negativo.” Students revisit adding two negative integers after using a number line in step 2, “Aprendizaje visual” to verify their prediction. Next, students use two-color counters to model adding integers with different signs before using a number line to model the abstract algorithm for adding integers with different signs. Before students move on to individual practice, the embedded questions “¿En qué se parece sumar enteros negativos a sumar enteros positivos?” and “¿Cómo pueden representar modelos de la suma de enteros con signos diferentes?” guide students toward the most efficient approaches.

Additionally, in the Guía del maestro, lesson 3-3, “Investiguemos: patrones en razones equivalentes,” step 1, “Investigar,” provides embedded guidance for monitoring students’ thinking, sequencing solution strategies, and connecting equivalent-ratio representations. Educators begin with “una solución correcta que usa razones equivalentes” and then examine incorrect strategies before presenting “una recta numérica doble . . . y relacionar esas representaciones con el uso de razones equivalentes.” Additional educator guidance is provided in step 2, “Relacionar” through “Presentar y analizar” questions such as “¿Cómo pueden usar la multiplicación . . .?” and “¿Cómo pueden usar la división . . . ?” to guide students toward increasingly efficient approaches.

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

The grade A6 Guía del maestro explicitly states how the conceptual and procedural emphasis of the TEKS are addressed in the “Contexto matemático” pages at the beginning of each topic. For example, in topic 8, “Representar y resolver ecuaciones,” the “Contexto matemático: equilibrio” page explicitly states in “Comprensión de conceptos: entender las ecuaciones y las propiedades de la igualdad” that “los estudiantes aprenden los requisitos conceptuales para resolver ecuaciones. Los estudiantes entienden la definición de ecuación, usan sustitución para determinar la solución de una ecuación e identifican cómo se usan las propiedades de la igualdad para generar ecuaciones equivalentes. Un concepto clave es que los términos a ambos lados del signo igual (=) deben equilibrarse (6AM.8A).” In the “Destreza en procesos y fluidez” section, “Resolver ecuaciones de suma y de resta” explicitly states, “Los estudiantes usan los conceptos de ecuaciones e igualdad para resolver ecuaciones de suma y resta. Los estudiantes reconocen que una operación tiene una relación inversa con la otra (6AM.8D).”

Additionally, the Guía del maestro explicitly addresses the conceptual emphasis of TEKS 6AM.2B in lesson 5-6, “Representémoslo en 3 actos: el disco volador,” which requires students to identify a number, its opposite, and its absolute value. The “Conocimientos esenciales” and “Comprensión de conceptos” sections explain that real-world situations can be represented with mathematical models, while recognizing that a model may not perfectly represent a situation. Students use their understanding of rational numbers and absolute value to develop and evaluate mathematical models, supporting conceptual understanding of the mathematics underlying the problem. The materials explicitly address the procedural emphasis of TEKS 6AM.2G, which requires students to order a set of rational numbers arising from mathematical and real-world contexts. The “Objetivos de matemáticas” and “Aplicación” sections require students to use mathematical models to represent a situation, propose a solution, test whether the model is appropriate, and explain the results, providing explicit procedural expectations for applying mathematics to solve real-world problems.

Evaluation for 5.3b
Questions and tasks include the use of concrete models and manipulatives, pictorial representations (figures/drawings), and abstract representations, as required by the TEKS.

The program overview describes the progression of concrete to pictorial (representational) to abstract models in the article “Concrete, Representational, Abstract (CRA) Instructional Model.” It details, “‘Explore and Share’ in ‘Let’s Build’ lessons and ‘Let’s Investigate’ lessons ask students to solve a problem that embeds new ideas and to solve it any way they choose. Students might use concrete materials (counters, geoboards, AngLegs, algebra tiles) [or] pictorial representations (number lines, arrays, grids, strip diagrams).” Students have access to digital manipulatives through the Brainingcamp program embedded in the materials for use as concrete models, and the Brainingcamp Live feature allows educators to view each student’s work with the digital manipulatives in real time.

Additionally, in the Libro del estudiante, lesson 4-4, “Elaboremos: estimar para hallar porcentajes,” students progress through concrete, pictorial, and abstract representations through the lesson. Step 1, “Explorar y comentar,” presents concrete models and manipulatives, with the “Ejemplos del trabajo de los estudiantes” section prompting students to use fraction strips and unit fractions as physical models to represent 78 percent as a compatible fraction before multiplying to estimate the number of correct exam questions. In step 2, “Aprendizaje visual,” presents pictorial representations, with example 1 using a pie chart displaying eye color data for 500 students, from which students identify approximate equivalent fractions and use those visual proportions to estimate percentages before transitioning to calculation. Example 2 presents abstract representations, prompting students to apply rounding and compatible numbers without visual supports to estimate percents algebraically. The “Concepto clave” section highlights equivalent fractions, compatible numbers, and rounding as parallel abstract strategies.

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

The program overview describes the progression of concrete to pictorial (representational) to abstract in the article, “Concrete, Representational, Abstract (CRA) Instructional Model.” It details, “‘Explore and Share’ in ‘Let’s Build’ lessons and ‘Let’s Investigate’ lessons ask students to solve a problem that embeds new ideas and to solve it any way they choose. Students might use concrete materials (counters, geoboards, AngLegs, algebra tiles) [or] pictorial representations (number lines, arrays, grids, strip diagrams) . . . When students share and discuss solutions, rich conversations deepen conceptual understanding of connections between concrete, pictorial, and abstract.” The article explains in the “Visual Learning” section that “The ‘Visual Learning’ in a ‘Let’s Build’ lesson provides explicit instruction that connects students’ work in the ‘Explore and Share’ to new ideas taught and shows pictures of concrete materials, drawings of concrete materials, diagrams, or some combinations of those to represent math concepts. The ‘Visual Learning’ connects these representations to abstract numbers, symbols, and procedures.” Students have access to digital manipulatives through the Brainingcamp program embedded in the materials, which serve as concrete models they can connect to abstract concepts. The Brainingcamp Live feature also allows educators to view each student’s work with the digital manipulatives in real time. Moreover, the Desmos digital program offers representational models that students can use to connect to abstract concepts. In each “Elaboremos” lesson, the progression from “Explorar y comentar” to “Aprendizaje visual” supports students in connecting and creating concrete and representational models to connect with abstract concepts. Then, in the final guided examples, students discuss how to define and explain the abstract concepts they connect to the concrete and representational models.

Additionally, lesson 2-4, “Investiguemos: estrategias para hallar área de polígonos,” uses step 2, “Relacionar” to support students in connecting to and creating concrete and representational area models by composing and decomposing polygons with pattern blocks and by drawing figures on a coordinate plane to determine area abstractly using addition and subtraction. Prompts in the Guía del maestro guide the educator to help students explain how composing and decomposing pattern-block models support an abstract understanding of a polygon’s area. In the “Escoge un problema: presentar y analizar” section, students explain how they use the concrete pattern blocks and representational area models to obtain the abstract area by composing and decomposing polygons. The “Concepto clave” component explains that students can decompose the representational model of a polygon into known shapes and add their areas, or draw a larger shape and subtract the areas of the regions that are not part of the polygon to find the abstract area.

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

The grade A6 materials provide opportunities for students to develop their academic mathematical language using visuals and manipulatives within lessons, along with other language development strategies, within the “Más apoyo de vocabulario” section under the “Recursos” tab of the Savvas Realize digital program. For example, in lesson 5-1, “Elaboremos: classifIcar números,” students use visuals and digital manipulatives, including a list of numbers, a Venn diagram, and a number line, to write about and discuss how to classify different types of numbers. The “Más apoyo de vocabulario” section provides worksheets to accompany the lesson, helping students develop their academic mathematical language through other language development strategies, including cloze sentences, mapping diagrams, and Frayer models.

Additionally, the materials provide opportunities to develop academic mathematical language in lesson 8-2, “Elaboremos: aplicar propiedades de la igualdad,” using visuals, such as an animated visual lesson; a balance-scale model illustrating the properties of equality, equations, mathematical expressions; and color-coded representations while defining and applying the properties of equality. The Guía del maestro also provides opportunities to develop academic mathematical language using manipulatives in example 1, which references algebra tiles that can be used as virtual manipulatives to help students develop the academic mathematical language of balancing an equation. Finally, the materials provide opportunities to develop academic mathematical language using other language development strategies with the “Rutina del lenguaje: evaluar, corregir y aclarar” section, which provides structured opportunities for students to develop academic mathematical language using other language development strategies such as evaluating a partner’s solution, explaining why a solution is or is not correct, justifying corrections using the sentence stem “No estoy de acuerdo con tu solución porque . . . ,” and revising their responses based on peer feedback.

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

The grade A6 materials include embedded educator guidance to scaffold and support students’ development and use of academic mathematical vocabulary in context within the “Repaso del vocabulario” section of the “Repaso del tema” at the end of each topic. For example, in the Guía del maestro, the “Repaso del vocabulario” section contains embedded educator guidance in the topic 3 “Entender y usar razones y tasas: repaso del tema” section that directs educators to have students use the academic mathematical vocabulary terms, including razón, precio por unidad, and tasa, in context orally and in writing to scaffold and support their development of the terms. The “Lenguaje oral” embedded guidance directs educators, “Pida a un estudiante voluntario que escriba una razón que incluya unidades en la pizarra,” before students complete the page. Further guidance instructs, “Luego, pida al estudiante voluntario que haga preguntas a los otros estudiantes sobre la razón, como ‘¿Es esta una velocidad?,’ ‘¿Por qué es este un precio por unidad?’ y ‘¿Qué tipo de tasa es esta?’” and then repeat the activity with other student volunteers. Next, the “Escritura en matemáticas” embedded guidance adds another level of support after the students complete the page: “Pida a los estudiantes que trabajen con un compañero. Cada compañero escribe una pregunta de matemáticas que usa un término de vocabulario. Luego, los estudiantes intercambian papeles y dan una respuesta escrita que usa el término de vocabulario.”

Additionally, in the Guía del maestro, topic 5, “Los números racionales y el plano de coordenadas,” the “Adaptaciones del lenguaje” page guides educators in building academic vocabulary for the topic. The “Apoyo para el vocabulario del tema” section organizes vocabulary into tiers, identifying new terms such as enteros, números racionales, opuestos, and valor absoluto; prior terms students should already know; and upcoming terms students will encounter later, thereby scaffolding vocabulary development within a coherent progression. The “Vocabulario en contexto” table guides educators in addressing potential confusion between mathematical and everyday meanings of key terms, supporting students’ development and use of academic mathematical vocabulary in context. For example, racional in mathematics means any number that can be written as a fraction, while in everyday Spanish, it refers to reasoning without emotion. The “Vocabulario para poner en contexto” section maps specific contextual vocabulary lesson by lesson, which gives educators guidance for pre-teaching situational language students will need to access problems in the topic.

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

The grade A6 materials include embedded educator guidance within “Elaboremos” lessons to support the appropriate academic mathematical vocabulary, syntax, and discourse that support mathematical conversations, providing opportunities for students to hear, refine, and use math language with peers, developing their math language toolkit over time. Additionally, “Ejemplos del trabajo de los estudiantes” guides educators to support student responses using exemplar responses to questions and tasks. For example, in the Guía del maestro, lesson 8-2, “Elaboremos: aplicar propiedades de la igualdad” includes an “Apoyo al lenguaje” section with educator guidance instructing, “Pida a cada estudiante que escriba una ecuación y una ecuación equivalente usando una de las propiedades de la igualdad. En el reverso, pídales que escriban y describan, usando oraciones matemáticas, la propiedad que usaron y por qué. Luego, pida a los estudiantes que trabajen con un compañero para compartir sus tarjetas de apuntes. Pida al primer compañero que levante su tarjeta y pregúntele: ¿Qué propiedad usó para hacer esta ecuación equivalente? El compañero responde, describiendo la propiedad usada. Si el compañero responde incorrectamente, el primer compañero comparte la respuesta correcta y explica por qué. Luego el segundo compañero toma un turno. Después de que ambos presenten sus tarjetas de apuntes, pida a los estudiantes que hallan nuevos compañeros y repitan la actividad.” This supports student discourse using appropriate academic vocabulary and syntax, providing opportunities for students to hear, refine, and use math language with peers and develop their math language toolkit over time. In the “Explorar y comentar” section of the lesson, students begin with a simple equation, “4 + 8 = 12,” and make specific changes to the equation, including adding, subtracting, multiplying, and dividing either side of the equation by given values, before determining whether the equation still remains true. The Guía del maestro provides “Ejemplos del trabajo de los estudiantes” with exemplar responses, including, “Nick muestra sus cálculos e indica qué cálculos mantienen la igualdad. Amanda completa correctamente cada cálculo y luego indica si la ecuación resultante es verdadera.”

Additionally, in the Guía del maestro, lesson 5-3, “Investiguemos, entender números racionales negativos,” provides materials that guide educators in using the “Rutina de lenguaje: recopilar y mostrar” to “Comenten la definición de números racionales con la clase” and “pida a los estudiantes que expresen de otra manera la definición con sus propias palabras y escriban tres ejemplos.” The activities build vocabulary, syntax, and discourse together, as students define and use the term números racionales precisely, moving beyond casual language to formal terminology, and write complete explanatory sentences justifying why a number is or is not rational rather than simply stating an answer. The guidance directs educators, “pida a varios estudiantes que pasen al pizarrón, escriban uno de sus números y expliquen a la clase por qué es racional,” giving students the opportunity to hear their peers’ phrasing, refine their own explanations, and develop their math language over the course of the lesson. Embedded exemplar responses give educators a clear guide for the depth and precision expected in student explanations. The question “¿Por qué escogieron crear la recta numérica de esta manera?” provides the exemplar response “Para poder ubicar las fracciones que creamos en el juego de mesa, tendremos que convertirlas en números decimales,” and the question “¿Por qué piensan que 3/6 se convierte en un decimal finito cuando otras fracciones con un denominador de 6 no lo hacen?” provides the examplar response “Porque 3 es la mitad de 6, por tanto, es igual a 0.5.”

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

The grade A6 materials appropriately integrate the TEKS process standards, as discussed in the “Estándares de procesos matemáticos en la enseñanza” subsection in the “Páginas preliminares” section of the Guía del maestro. For example, the article explains how the TEKS process standards are integrated into lessons, problems, and assessments in four sections with specific information, including “Los estándares de procesos matemáticos están integrados y explícitamente resaltados en la enseñanza de la lección usando tipo de letra color verde azulado.” Also, the Savvas Realize digital program appropriately integrates the TEKS process standards into the materials using a “Modelo de resolución de problemas” that students can use at any time to support their problem solving.

Additionally, the Guia del maestro explicitly identifies where the mathematical process standards are incorporated in each topic and lesson, including daily instruction, guided and independent practice, problem-solving activities, and formative and summative assessments. For example, in lesson 11-9, “Elaboremos: resumir y comparar distribuciones de datos,” the first page of the lesson identifies the TEKS mathematical process standards addressed, including 6AM.1C, 6AM.1D, 6AM.1E, 6AM.1F, and 6AM.1G. These standards emphasize “seleccionar herramientas, incluyendo tecnología, según sea apropiado”; “comunicar ideas matemáticas; analizar relaciones matemáticas”; and “mostrar, explicar y justificar ideas y argumentos matemáticos utilizando un lenguaje matemático preciso”.

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

The grade A6 materials include a description of how the TEKS process standards are incorporated and connected throughout the course, as discussed in the “Estándares de procesos matemáticos en la enseñanza” subsection of the “Páginas preliminares” section in the Guía del maestro. For example, the article explains, “Énfasis especial en dos estándares de procesos por tema: En la Guía del maestro, una página de ‘Estándares de procesos matemáticos de los TEKS’ al principio de cada tema proporciona sugerencias que puede implementar para dar un énfasis especial en dos estándares de procesos del tema.” The text continues to describe how the process standards are connected throughout the course by stating, “Todas las tareas matemáticas evocan la selección, el uso y la gestión de múltiples procesos matemáticos” and “Las preguntas que evalúan contenido también involucran a los estudiantes en el uso de estándares de procesos. Las tareas de rendimiento del tema son oportunidades especialmente buenas para evaluar la competencia de los estudiantes con los estándares de procesos.”

Additionally, the Guía del ritmo de enseñanza de 165 días explicitly states that “Los estándares de procesos matemáticos de los TEKS están integrados a lo largo de cada tema: 6AM.1A, 6AM.1B, 6AM.1C, 6AM.1D, 6AM.1E, 6AM.1F, 6AM.1G.” The pacing guide shows that the process standards are intentionally embedded across all 11 topics while content TEKS and English Language Proficiency Standards (ELPS) are identified for each topic, demonstrating that the mathematical process standards are consistently integrated throughout the entire grade A6 course rather than taught as isolated skills. In the Guía del maestro, “Contenido” pages in the “Páginas preliminares” sections corroborate this by listing the process standards for each lesson across the topics in bold.

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

The grade A6 materials include a description for each unit of how the TEKS process standards are incorporated and connected throughout each topic in the Guía del maestro on “Estándares de prácticas matemáticas” page at the beginning of the topic. For example, topic 2, “Analizar relaciones geométricas,” uses the “Estándares de prácticas matemáticas” page to describe how 6AM.1G is incorporated and connected throughout the topic, including “Los estudiantes competentes en matemáticas construyen argumentos con definiciones y terminología correctas relacionadas con las áreas de paralelogramos y triángulos,” “explican cómo hallar el área de un trapecio y justificar su solución usando fórmulas y ecuaciones,” and “construyen argumentos para explicar cómo usar la cantidad de cubos fraccionarios en un prisma rectangular para hallar el volumen.” The page clarifies that 6AM.1F is incorporated and connected throughout the topic because “los estudiantes competentes en matemáticas determinan cómo se relacionan las áreas de paralelogramo y un rectángulo descomponiendo el paralelogramo y usando las partes para componer un rectángulo, analizan la estructura de trapecios y cometas para determinar cómo descomponerlos en figuras para las cuales se conocen las fórmulas de área y construyen argumentos para defender la aplicación de fórmulas a situaciones nuevas.”

Additionally, in the Guía del maestro, topic 5, “Números racionales y el plano coordenadas,” the “Estándares de procesos matemáticos” page of the “Vistazo al tema” emphasizes the process standards with guidance explaining that students develop proficiency through these process standards as they engage in lessons throughout the topic. The materials include a description of how the TEKS process standards are connected and reinforced throughout the topic through mathematical reasoning, communication, multiple representations, modeling, and problem solving. The accompanying educator questioning and topic guidance connect these mathematical behaviors across the sequence of lessons, demonstrating that the process standards are intentionally developed throughout the unit rather than addressed as isolated skills.

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

The grade A6 materials include an overview of the TEKS process standards incorporated into each lesson in the Guía del maestro in the “Análisis de los ejercicios: práctica y resolución de problemas” answer key in the “Práctica y resolución de problemas” section. For example, in lesson 2-2, “Elaboremos: entender los ángulos y las longitudes de los lados de los triángulos,” the “Análisis de los ejercicios: práctica y resolución de problemas” answer key provides an overview showing that TEKS 6AM.1B is integrated into example 1 and exercises 7, 12, 15, and 18; 6AM.1D is integrated into example 2 and exercises 8, 9, 14, and 15; and 6AM.1G is incorporated into example 3 and exercises 10, 11, 13, 16, and 17.

Additionally, in the Guía del maestro, the first page of each “Elaboremos” lesson lists the TEKS content standards and the “Estándares de procesos matemáticos” addressed in the lesson. For example, lesson 11-1, “Reconocer preguntas estadísticas” identifies TEKS process standards 6AM.1B, 6AM.1C, 6AM.1D, 6AM.1E, and 6AM.1F as incorporated throughout the lesson. These process standards support students in acquiring and demonstrating mathematical understanding as they engage with the lesson content. This overview enables educators to easily identify the TEKS mathematical process standards incorporated throughout the lesson.

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

The grade A6 materials provide opportunities for students to think mathematically, persevere through solving problems, and to make sense of mathematics in “Elaboremos” lessons, such as lesson 4-5, “Elaboremos: resolver problemas de porcentajes.” For example, the Guía del maestro shows that in step 1, “Explorar y comentar,” students think mathematically to use the meaning of percent and number sense to solve percent problems, including “¿Cuánto es 50% de 400? ¿Cuánto es 5% de 400?” Students persevere through solving percent problems and make sense of mathematics in a whole-class setting using benchmark fractions and double number lines in step 2, “Aprendizaje visual,” example 1 to estimate and then solve for the part when given percentages and whole numbers, followed by individual “¡Inténtalo!” problems.

Additionally, each topic includes a “Desarrollar GRIT” section that provides educators with concrete talking points and a modeled classroom dialogue to cultivate a growth mindset, resilience, self-efficacy, and time management as students work through multistep, real-world math tasks. For example, in topic 10, “Matemáticas de finanzas,” the “Desarrollar GRIT” section centers on financial mathematics, reminding educators to build students’ confidence with complex problems like credit card balances and interest; to encourage flexible problem solving and organizational strategies such as tables, diagrams, and color-coding; and to connect financial terms to real-life decision-making. This is modeled through a sample dialogue in which the educator guides a student, Kai, to persevere through a credit-limit budgeting problem by reflecting on his process and reasoning step-by-step toward a solution, rather than simply being given the answer.

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 A6 materials use the “Hablemos de matemáticas” and “Explorar y comentar” activities in the “Elaboremos” lessons to support students in understanding, justifying, and explaining that there can be multiple ways to represent and solve problems and complete tasks. For example, lesson 8-2, “Elaboremos, aplicar propiedades de la igualdad” in the Guía del maestro uses the “Hablemos de matemáticas” opening task, which presents a set of four equations with variables and different operations and asks students to determine “¿Cuál no pertenece?” Educator prompts support students in understanding that there can be multiple ways to represent and solve problems and complete tasks, such as “¿Qué saben sobre dos expresiones que estan unidas por un signo igual?,” “¿Qué significa para un número ser una solución a una ecuación?,” “¿Cómo podrían comprobar si 7 es una solución para cada ecuación?,” and ¿Cómo saben cuándo no lo es?” Next, the step 1, “Explorar y comentar,” activity supports students in using a graphic organizer that shows four ways to manipulate the left side, right side, or both sides of the equation “4 + 8 = 12” using different whole-number computations and to work in small groups to explain and justify that there can be multiple ways to represent and solve problems. The “Relacionar estrategias de solución” section of the Guía del maestro instructs educators to have students discuss as a whole class what they noticed about which computations kept the equations true and which made them false and then have them explain how the pattern could be used to predict the result for any computation instructions. The “Ejemplos del trabajo de los estudiantes” page that accompanies the activity shows how students can justify how and when computations kept the equations true or made them false.

Additionally, lesson 3-3, “Investiguemos: patrones en razones equivalentes,” step 1, “Investigar,” supports students in understanding, explaining, and justifying multiple ways to represent and solve problems. For example, the section “Seleccionar y poner en secuencia” in the Guía del maestro directs educators, “Empiece con una solución correcta que use razones equivalentes para determinar la cantidad de autobuses adicionales necesarios por distrito (Trabajo del Estudiante 1).” The text then guides educators, “Muestre soluciones con estrategias incorrectas (Trabajos del Estudiante 2 y Estudiante 3) y aclare cualquier concepto erróneo” and “muestre otras estrategias de solución correctas, como usar una recta numérica doble (Trabajo del Estudiante 4) y relacionar esas representaciones con el uso de razones equivalentes para determinar la cantidad de autobuses adicionales que se necesitan por distrito.” The educator then prompts students to justify their thinking during “Comentar las soluciones de los estudiantes” with questions such as “¿En qué se parece determinar si dos razones son equivalentes a determinar si dos fracciones son equivalentes?” and “¿Cómo saben que hay suficiente información?”

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 A6 materials include an “Hablemos de matemáticas” component in every “Elaboremos” lesson, providing multiple opportunities for students to make sense of mathematics and discuss it with their peers and educators. For example, in the Guía del maestro, lesson 9-4, “Elaboremos: resolver desigualdades usando la multiplicación y la división,” includes an “Hablemos de matemáticas: cadenas algebraícas” activity that shows the steps for simplifying a one-step, one-variable inequality problem by dividing both sides by three in each step until the coefficient of x becomes -1, with the instruction “Busca un patrón” on the first slide. The second slide reveals the last step, showing that the coefficient of x is no longer negative but that the inequality of x becomes negative, and uses a question mark to require students to make sense of the mathematics and discuss as a whole class what appropriate symbol should be used to represent the inequality. Examples 2 and 3 model the same concept, providing the opportunity for students to do math with their educator. The “Conectar” questions within multiple “Investiguemos” lessons, such as those in lesson 3-3, “Investiguemos: patrones en razones equivalentes,” provide opportunities for students to make sense of mathematics, to do and write about mathematics with their peers and educators. For example, the Guía del Maestro directs educators to group students with peers who chose the same problem to solve, so they can discuss solution strategies as they do the required mathematics and write their strategies and solutions. Then, the whole class answers questions about selecting strategies, representing ideas, analyzing relationships, and evaluating reasonableness, providing opportunities for students to write about math with their educator.

Additionally, the materials provide opportunities for students to do and write about math with peers and educators in the Guía del maestro through the “Apoyo al lenguaje” section of lesson 10-4, “Elaboremos: construir una declaración de patrimonio neto,” where students work in pairs or small groups to record assets and liabilities in a financial statement; classify each item, sorting them into appropriate categories; and complete a net worth statement. The activity requires students to collaboratively apply mathematical concepts while the educator facilitates and monitors learning. The “Boleto de salida” section requires students to complete a written task by analyzing a financial statement and recording mathematical responses. Students discuss math with peers and educators in the “Hablemos de matemáticas” section, where educators prompt discussion with questions such as “¿Cuál no pertenece?” and “¿Cuál no pertenece? Preste atención a los estudiantes . . .” Students justify which financial item does not belong, explain their reasoning, and compare responses during whole-class discussion. The “Apoyo al lenguaje” guidance also directs educators, “Facilite un debate en toda la clase sobre tipos de bienes y obligaciones financieras,” requiring students to discuss and defend their mathematical thinking with peers and the educator.

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

The grade A6 materials include a “Modelo de resolución de problemas” tool on the digital platform that supports educators in guiding students to share and reflect on their problem-solving approaches using guiding questions. For example, guiding questions for reflecting on problem-solving approaches are broken into categories to support explanations, arguments, and justifications, such as “Analizar la información dada,” “Determinar una solución,” and “Justificar la solución y evaluar si es razonable.” Students use their answers to questions such as “¿Qué operaciones se necesitan?” and “¿Tienen sentido mis representaciones?” to share explanations and arguments about their problem-solving approaches. Students then use answers to questions such as “¿Responde mi solución a la pregunta?” and “¿Justifiqué mi solución usando terminología correcta que otros puedan comprender?” to share their justification.

Additionally, in lesson 10-3, “Elaboremos: entender los informes de crédito,” students read through a real-world finance problem and explain their reasoning as they consider how Blythe’s credit decisions could affect her budget, with the Guía del maestro prompting, “¿Si Blythe decide usar todo el crédito que le queda para el viaje, cómo podría afectar esto su presupuesto de los meses siguientes?” Students then explain and argue their strategies as a whole class, with the educator selecting solutions that propose paying for the trip with a credit card so students can discuss how each strategy affects Blythe’s budget. Later, in the “Hablemos de matematicas” activity, students justify why a given piece of information, such as an employer’s stated salary or an old address, does or does not belong in a credit report, with the Guía del maestro explaining that “cada una de estas ideas demuestran un razonamiento valido” and prompting the educator to have students share their justification. In the “Aprendizaje visual” section, students reason why the length of time that information remains on a credit report matters, explaining that “el informe de crédito de una persona se ve mejor después de que no queden datos negativos.” The educators pushes students to argue about how a credit report can affect financial decisions, with the “¡Inténtalo!” questions asking students to explain how making up for late payments can affect one’s ability to rent an apartment.

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

The grade A6 materials include a “Prevenir malentendidos” section for the “Boleto de salida” in every “Elaboremos” lesson, which supports educators with prompts and guidance for providing explanatory feedback based on student responses and anticipated misconceptions. For example, in lesson 1-7, “Elaboremos: dividir fracciones,” the “Boleto de salida” gives students four choices (3, 6, 24, and 32) for the correct answer to how many one-eighth-pound containers can be filled using three-quarters of a pound of almonds. The “Prevenir malentendidos” section of the Guía del maestro guides the educator that if students selected 24, they may not have used the reciprocal of the divisor, and provides prompts, including “¿Cómo se modifica el divisor al dividir fracciones?” In the “Explorar y comentar” activity at the beginning of the lesson, students work in small groups to solve how many one-and-three-eighth-inch pieces can be cut from a five-and-one-half-inch strip. In the Guía del maestro, the “Supervisar, seleccionar y poner en secuencia” section guides the educator to observe the students working and consider how they use a model and which operations they use to represent the problem, giving potential student responses. For example, the guidance states, “Los estudiantes pueden usar un modelo de barras para mostrar el problema,” and “Los estudiantes que usan modelos pueden resolver el problema mediante sumas o resta repetidas.” Prompts with explanatory feedback, such as “¿Cómo pueden hacer un dibujo que muestre el problema?” and “¿Qué operación matemática sería útil para resolver el problema?,” support educators in anticipating misconceptions.

Additionally, every “Elaboremos” lesson includes an “Evitar errores frecuentes” feature that provides prompts and guidance to support educators in providing explanatory feedback based on student responses and addresses anticipated misconceptions. For example, in lesson 11-1, “Elaboremos: reconocer preguntas estadísticas,” the “Evitar errores frecuentes” feature explicitly guides educators in explaining that a question is statistical if it has a variety of possible responses. The Guía del maestro prompts educators to ask clarifying questions such as, “En A, ¿estás preguntando a todos los estudiantes de la clase o solamente a una persona? ¿Qué sucede en B?” Through this discussion, students recognize that in part A, the question is being asked to everyone in the class, and because a variety of responses can be collected, the question is statistical.