enVision+ Texas Matemáticas, 03

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

The Guía del maestro includes a scope and sequence for 14 Temas aligned with the Texas Essential Knowledge and Skills (TEKS) in “Contenido y secuencia” for 135-day, 165-day, 180-day, and 210-day instructional calendars. “Contenido y secuencia” for the instructional calendars includes a table with the concepts for each Tema. For example, Tema 1 “Significados de la multiplicación y división” includes the lessons, concepts, and TEKS addressed within the progression of content throughout the year, with instructional pacing varying according to each instructional calendar for the academic year.

Additionally, the Guía del maestro includes a scope and sequence that outlines the TEKS in “Correlación con los conocimientos y destrezas esenciales de Texas.” In the grade 3 Guía del maestro, “Contenido y secuencia” includes a table with the TEKS and aligned lessons and pages from the Libro del estudiante and Guía del maestro. For example, the grade 3 scope and sequence follows an instructional pathway with números y operaciones, razonamiento algebraico, geometría y medición, análisis de datos, and comprensión de finanzas personales, with the TEKS presented in a table for instruction throughout the 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).

The grade 3 Guía del ritmo de enseñanza includes a suggested pacing guide for 135-day, 165-day, 180-day, and 210-day instructional calendars in the online platform. Each instructional calendar includes a table with TEKS integration across the 14 Temas of the academic year in the materials, the days of instruction, and the TEKS for each topic. For example, the materials provide the 165-day Guía del ritmo de enseñanza with suggested pacing for 14 Temas of TEKS-aligned instruction throughout 165 days of instruction.


Furthermore, the Savvas Realize online platform includes the suggested instructional calendar tabs in “Contenido y secuencia” for 135, 165, 180, and 210 days. Tema 3 “Multiplicación: Operaciones derivadas,” in “Contenido y secuencia: 135 días,” includes a table with the suggested pacing of the materials, including the days of instruction, the TEKS, differentiation, review, and evaluation. The table also includes materials such as “Elaboremos,” “Vamos a investigar,” “Representémoslo en 3 actos,” and “Investiguemos.”

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.

Program overview materials include the “Grade 3 Content Organization Rationale” organized in 14 Temas with mathematical key concepts and student connections, including a “Grade 3 Content Organized to Build Connections” table with each Tema in unit order. For instance, Temas 1–4 focus on joining and separating equal quantities through multiplication and division, while Temas 5 focuses on interpreting and representing data in graphs. Grade 3 materials include key concept description with the intentional purpose of each unit and conceptual connections across Temas.

Additionally, in the grade 3 Guía del maestro, the “Contexto matemático: coherencia” section at the beginning of each Tema explains how concepts connect to prior and future learning through the “¡Vuelve atrás!” and “Más adelante” components. For example, in Tema 3 “Multiplicación: Operaciones derivadas,” the “Contexto matemático: conceptos clave” section outlines the progression of the Tema and what is taught before and after.

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

The Savvas Realize online platform includes “Protocolos de internalización y herramientas de observación” in the tools section, which provides “Protocolo de internalización del tema para el maestro” and “Protocolo de internalización de la lección para el maestro.” The grade 3 materials include guidance for unit and lesson internalization that includes 13- and 16-step processes providing a thorough understanding of key learning objectives, sequencing, and instructional strategies.

Furthermore, the Guía del maestro includes “Elaboremos,” “Investiguemos,” and “Representémoslo en 3 actos” lesson types with internalization guidance for previewing the unit to understand key standards, unit objectives, vocabulary, and assessments. For example, expanded notes in grade 3 appear in each of the three lesson types in Tema 1 of the Guía del maestro. The materials provide a process for educators to connect lesson objectives to the TEKS, identify vocabulary and prerequisite skills, plan formative assessments, differentiate instruction, and plan lesson materials.

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

The Savvas Realize platform contains the “Protocolos de internalización y herramientas de observación,” which are observation tools and internalization protocols that include support and guidance for educators from instructional leaders. Resources for grade 3 instructional leaders include “Herramienta de observación para líderes de la enseñanza,” “Protocolo de internalización del tema para líderes de la enseñanza,” “Protocolo de internalización de la lección para líderes de la enseñanza,” and “Protocolo de análisis del trabajo del estudiante para líderes de la enseñanza.”For instance, “Herramienta de observación para líderes de la enseñanza” is an observation and analysis tool for instructional leaders in the format of a checklist to answer “Yes,” “Partially,” or “No,” serving as a resource for material implementation supporting educators.

Additionally, the grade 3 materials provide notes at the beginning of each lesson in the Guía del maestro titled “Elaboremos,” “Investiguemos,” or “Representémoslo en 3 actos.” The expanded notes in the first of each of the three lesson types in Tema 1 explain the key components of the program, such as problem-based learning, visual learning, and differentiated instruction, to allow instructional leaders to support educators. The materials outline the unit structure by incorporating a list of materials, new vocabulary, and resources for instructional leaders to support educators in implementing the materials effectively.

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

The grade 3 materials in the Guía del maestro include a “Contexto matemático: conceptos clave” section that explains the progression of the Tema. In the “Contexto matemático: coherencia” section, the materials explain how concepts and the TEKS connect across previous courses, within current courses, and in possible future courses.

Additionally, “Adaptaciones del lenguaje” sections incorporate vocabulary in context with mathematical meaning and outline the critical prerequisite vocabulary. For example, each Tema in grade 3 includes “Adaptaciones del lenguaje y discurso oral/escrito,” “Apoyo para el vocabulario del tema,” and “Transferencia metalingüística al inglés y cognados.” These sections focus on vocabulary that will be introduced in the unit along with previously taught vocabulary and what will be introduced in the upcoming unit. The materials provide a breakdown of academic vocabulary by lesson to support effective instruction of the concepts.

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

The online platform provides family engagement resources for each Tema and unit in the “Participación de la familia” (“Family Engagement”) section. Resources include digital resources, an overview of lesson learning goals, video tutorials, examples, and at-home learning activities in English and Spanish. For example, families will view a welcome page in the online platform with the Temas of the grade level in the “Soporte del capítulo” tabs, where families can select the Tema to support their student and find the engagement resources in both English and Spanish.

Furthermore, in the “Plan del tema” under “Participacion de familia,” each Tema includes a family letter with guidance and support resources. Materials provide suggestions for how families can support student progress and achievement in the grade level for each unit in a “De la escuela al hogar” letter in English and Spanish. These materials provide strategies and activities for families to use at home for each Tema, such as Tema 1 “Significados de la multiplicación y la división,” which includes a short letter in both English and Spanish and a section where families can make observations.

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).

“Planes de lecciones” can be found in the digital resource that includes lesson objectives, the TEKS correlations, and tasks, questions, and assessments aligned to the lesson objectives. For example, each lesson includes a table with a summary of the lesson and the steps in the lesson plan, such as paso 1 “Explorar y comentar,” paso 2 “Aprendizaje Visual,” paso 3 “Práctica y resolucion de problemas,” and paso 4 “Evaluar y diferenciar.” Materials support the effective implementation of grade-level instructions to facilitate mastery of content.

Furthermore, at the beginning of each “Elaboremos” lesson in the Guía del maestro, the grade 3 materials include critical lesson information, including TEKS alignment, lesson objectives, and materials. For example, in lección 2-1 “Como Factor,” “Elaboremos” includes “Comprobación rápida” and “Boleto de salida” to assess students in alignment with the TEKS.

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

The online platform for grade 3 in “Plan de lecciones” provides materials required for instruction and the suggested timing for each lesson component in “Cronología de la lección.” For example, the grade 3 materials include a table with “Tiempo,” “Propósito,” and “Materiales” for the steps of the lesson in the lesson overview. The guidance in the lesson overview provides lesson pacing and suggested timing for each component of the lesson cycle to support educators in effectively delivering instruction.

Furthermore, the “Plan de tema” section of the Guía del maestro includes suggested time allocations for each lesson component with clocks at the top of all pages. For example, grade 3 materials in Tema 5, lección 5-2 “Elaboremos: Diagramas de puntos” include a suggested lesson timing of one day.

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

In the grade 3 Guía del maestro, the paso 4 “Evaluar y diferenciar” section provides formative assessment guidance with interventions, enrichment, and additional practice resources. For example, “Comprobación rápida” is a formative assessment in the paso 4, “Evaluar y diferenciar” section with a point rubric with educator guidance on the effective use of the assessment resources in the materials, as well as “Actividad de intervención” and “Práctica adicional.”

The Guía del maestro “Biblioteca de diferenciación” includes extended practice in the form of intervention, reteach-to-build, enrichment, and build-mathematical-literacy activities, as well as additional practice pages. For example, in grade 3 Tema 1 “Vistazo a la Biblioteca de diferenciación,” the materials feature sections for enrichment activities of “Escoge un proyecto,” “Matemáticas y lectoescritura,” “Contribuciones asombrosas,” and “Levántate y razona,” which include routines such as “Juegos prácticos” and “Práctica de fluidez.”

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

The grade 3 Cuaderno de evaluación includes a “Why and When to Assess” section that features observation tools, quick checks, exit tickets, Tema assessments, and cumulative assessments available as digital and printed materials. The instructional assessments for grade 3 include varying question types and tasks, such as multiple choice, text entry, and constructed responses. For example, educators give students diagnostic assessments at the start of the academic year and the beginning of each Tema, formative assessments during lessons and at the end of each lesson, and summative assessments at the end of each Tema, after a group of Temas, and at the end of the year.

The grade 3 Guía del maestro includes guided practice to check for understanding, quick check activities for differentiation needs, and exit tickets to assess student learning at the end of the lesson. The “Examen de preparación” diagnostic assessment contains 36 multiple-choice questions, including word problems, matching number sentences to visuals, telling time, place value, fractions, and more. Exit tickets are available at the lesson level, with the exit tickets for Tema 2 consisting of two questions for each lesson along with a check-in for the students. The unit-level assessment follows the exit ticket in the guide and includes 12 questions with multiple-choice, constructed-response, and text-entry question types.

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

The materials for grade 3 in the Cuaderno de evaluación define each assessment and the intended purpose of diagnostic, summative, and formative assessments in a table. For instance, the grade 3 materials provide a “Why and When to Assess” section for each Tema included and define diagnostic assessments as assessments to be administered before instruction to measure student readiness.

The grade 3 materials in the Cuaderno de evaluación also provide a table that includes definitions of the varying types of assessments, the recommended time to administer the assessments, and the names of the assessments in the instructional materials. For example, formative assessments during a lesson are “Herramientas de evaluación observacional,” “Práctica guiada,” and “Comprobaciones rápidas.” “Boletos de salida” are defined as formative assessments for the end of the lesson and intended to assess student lesson comprehension. The Guía del maestro describes diagnostic assessments administered at the beginning of the year to measure student readiness, formative assessments used during lessons to monitor student progress, and summative assessments administered at the end of a Tema to measure student learning.

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

The grade 3 materials in the Cuaderno de evaluación include the sections “Why and When to Assess,” “How to Assess,” “Assessment Data,” “Assessment Practice,” and “How to Administer Assessments,” with tables that provide guidance for educators. For example, the materials for grade 3 include a table with assessment administration guidance in “How to Administer Assessments.” Additionally, the guide provides direction on how to score the assessments along with the answer keys.

The materials for grade 3 in the Cuaderno de evaluación also include a table that provides guidance on the observation assessment, portfolio assessment, performance-based task, and program assessments. Guidance includes timeframes for assessments and recommendations for a proper testing environment. For observation assessments, the materials suggest that the educator “Walk around and observe students reply to questions in class,” while for a portfolio assessment the educator should “collect samples of student work.” The materials also contain a “Boleto de salida” formative assessment within each lesson and includes directions for administering the print and digital materials with guided intervention support, directions for reviewing student responses, identifying misconceptions related to fractions in the case of lección 9-1, and using assessment results to determine instructional support. Educator guidance also includes a script of directions.

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

The grade 3 Cuaderno de evaluación includes a “Guía de puntaje” with item analysis charts that identify the TEKS aligned to the varying assessment types included in the materials. Assessment Sourcebook materials include “Examen de preparación,” “Evaluación para observar el progreso,” “Boleto de salida,” “Evaluación,” “Evaluación acumulativa,” and “Tarea de rendimiento.” For example, the item analysis charts connect individual assessment items for formative assessments in “Evaluacion para observar el progresso,” “Formas A–C,” and “Evaluación del tema” summative assessments to the assessed TEKS and corresponding intervention lessons. The “Examen de preparación” diagnostic assessment takes place at the start of the year and “Repasa lo que sabes” at the start of a Tema. In addition, the “Guía de Puntaje” provides a table for the “Evaluación acumulativa,” covering three Temas at a time, and a cumulative assessment table for Temas 1–14 at the end of the guide in alignment with the TEKS.

The grade 3 Cuaderno de evaluación “Evaluación para observar el progreso” section includes summative assessment items aligned to grade-level TEKS and lesson objectives. The grade 3 “Práctica de los TEKS” assessments include summative assessment items aligned to the grade-level TEKS, lesson objectives, and mathematical process standards. For example, the “Práctica de los TEKS 3.4k” assessment includes items connected to lesson objectives that require students to solve multiplication, division, and perimeter problems using equations, visual models, constructed-response items, and multiple-choice response formats aligned to the TEKS expectations. Formative assessments can be found in the grade 3 Guía del maestro with an educator provided answer key. For example, the exit ticket for lección 4-6 “División con 0 y 1” assesses TEKS 3.4K and process standard 3.1A for question 1 and TEKS 3.4F and process standard 3.1D for question 2.

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

The materials in the grade 3 Cuaderno de evaluación and “Guía de puntaje” include a “Tabla de análisis,” which features an item analysis chart that lists the Depth of Knowledge (DOK) level on the progress monitoring, diagnostic, and summative assessments for the materials. For example, the “Evaluación del Tema 1” contains an item analysis chart that aligns assessment items to the TEKS and (DOK) levels while performance tasks require students to solve multiplication problems, analyze data tables, explain mathematical relationships, and justify responses using equations, visual models, and written explanations with multiple scoring criteria. The Tema 14 “Tarea de rendimiento” includes open-ended questions that require students to explain and justify their answers. Meanwhile, the “Evaluación acumulativa de referencia” for Temas 1–14 includes a variety of TEKS-aligned question types, including multiple-choice and multiple-response items.

The grade 3 materials in the “Evaluaciones del curso” resources include diagnostic, progress-monitoring, and summative assessments aligned to the TEKS with varying levels of complexity. For instance, “Evaluación para observar el progreso, Formas A–C,” features TEKS-aligned items at varying levels of complexity, with multiple-choice and text-entry response formats administered at the beginning, middle, and end of the year to measure student understanding. Furthermore, the Tema 1 assessment consists of 12 questions. Five of the 12 questions are multiple-choice, while the other questions require the student to draw or write an answer. For example, question nine of the assessment asks students to draw an array as their answer when being given the following word problem: There are 24 students in a class. The educator divides them into six equal groups. Draw an array that shows how many students are in each group.

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

The materials for grade 3 include the Cuaderno de evaluación “Guía de puntaje” for all Tema- and lesson-level assessments, with a scoring guide and answer keys. For example, the grade 3 “Guía de puntaje” explains how educators use online assessment reports to analyze standards mastery, group students based on performance data, and identify instructional support based on assessment results. The scoring guide addresses how students earn points, with one or two points awarded based on the expected response.

Furthermore, the Guía del maestro provides instructional assessments and scoring information for interpreting student performance. The grade 3 Guía del maestro includes guidance for analyzing assessment results and determining instructional responses based on student performance. For example, in lección 11-8, paso 4 “Evaluar y diferenciar,” the included scoring guidance for “Comprobación rápida” identifies scores for intervention and extension activities. The “Boleto de salida” then includes a self-assessment response and guidance for using student results to determine instructional support. Additionally, for each Tema, the grade 3 materials offer guidance on student performance before, during, and after the Tema with the “Mi progreso y crecimiento” document.

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

The grade 3 Cuaderno de evaluación “Guía de puntaje” includes scoring guidance, item analysis charts, and instructional support connected to student assessment results. For instance, the item analysis charts connect the TEKS assessed to corresponding intervention lessons and provide instructional support within the Intervention System (IS) based on student performance trends.

Additionally, the grade 3 Guía del maestro assessment analysis tools include instructional guidance based on student assessment performance. For example, in Tema 10, lección 10-1, the scoring guidance for “Comprobación rápida” identifies intervention and extension activities based on student scores and connects the assessment results to instructional support and differentiation activities. Lección 6-9 also contains guidance for educators to support students through the “Boleto de salida.” In the same lesson, if a student scores 0–3 points, they are assigned an intervention or reinforcement activity to improve their comprehension. If a student scores 4–5 points, they are assigned an enrichment lesson. The “Biblioteca de diferenciación” also includes guidance and a variety of differentiated projects for educators to choose from in response to student trends in performance on assessments.

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 materials for grade 3 include progress monitoring tools to document student performance before, during, and after instruction in the “Herramienta para profesores de progreso y crecimiento del alumno” section. For example, the “Antes del tema,” “Durante el tema,” and “Tras el tema” resources help educators record student performance across the TEKS-aligned lessons and objectives. The grade 3 materials also include a student self-assessment in “Boleto de salida” to track progress for the lesson objective. The student tracker consists of three options for students to select: “Puedo,” “Con ayuda,” or “No todavia,” with the student tracker listing each assessed unit and their corresponding lessons. Students can view the lesson objective and evaluate their progress before, during, and after the lesson.

Additionally, the grade 3 materials include student-facing progress monitoring tools in the Cuaderno de evaluación “Boleto de salida” that allow students to reflect on and document their comprehension of the lesson objectives. For example, in Tema 4, lección 4-2, the “Mi progreso y crecimiento” section contains self-assessment options for students to monitor their progress, including a check-in of “Puedo,” “Con ayuda,” or “No todavia.” In Guía del maestro, the “Datos de las evaluaciones” include online data that tracks student progress and growth for individual students and the class overall. For instance, the educator tracker lists each unit and its corresponding lessons, and the table names the lessons, TEKS standards, objectives, and how students performed before, during, and after the unit.

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.

Materials in the grade 3 Guía del maestro include the paso 4 “Evaluar y diferenciar” section, which contains an “Actividad de intervención” at the end of each lessons and an additional “Video de apoyo,” where students can reinforce and review the lesson content. Additionally, materials include “Refuerzo para mejorar la comprensión” resources in each lesson with step-by-step guidance, additional practice activities, and answer keys to support reteaching. For example, grade 3 “Refuerzo para mejorar la comprensión, R 2-2” requires students to identify factors and multiples, complete multiplication patterns, represent multiplication using equal groups, and solve multiplication problems using tables, models, and number relationships. Lección 7-1, paso 3 “Práctica y resolución de problemas” includes guidance for “Práctica guiada,” where students are expected to use an addition table and select a 3x3 square to determine if sums would be the same regardless of the numbers selected. The guidance under “Errores e intervención, Ejercicio 1” states, “Si los estudiantes no entienden el patrón, entonces pídales que comparen las sumas de los números de las esquinas en diagonal.” In paso 4 “Evaluar y diferenciar,” the “Biblioteca de diferenciación” and “Actividad de intervención” include additional resources to support varying virtual learning styles and provide materials and steps for intervention. For example, in “Actividad de intervención” for grade 3, lección 8-1 provides a hands-on activity for students to complete in pairs using a partial addition table.

The materials for grade 3 in paso 4 “Evaluar y diferenciar,” “Comprobación rápida,” include “Actividad de intervención” as an assigned enrichment activity for a small group of students. The materials include the Tema 12 “Biblioteca de diferenciación,” which provides targeted support through a variety of instructional formats, such as differentiated activities, resources, and additional practice for students at varying levels of proficiency, as well as projects and electronic games. The “Refuerzo para mejorar la comprensión” is also included with educator guidance on scaffolded lessons and differentiated instruction. Additionally, the grades K–3 “Sistemas de intervención, Librito A” resource provides a resource book with educator guidance and activities designed to support students through differentiated instruction and targeted intervention. For example, “Errores e intervención” activities address common misconceptions and provide opportunities for students to practice and strengthen skills they have not yet mastered.

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

In the Guía del maestro, the “Adaptaciones del lenguaje” section provides a breakdown of vocabulary support in “Apoyo para el vocabulario del tema,” “Transferencia metalingüística al inglés,” “Cognados,” and “Vocabulario académico.” In “Apoyo para el vocabulario del tema,” there are three sections labeled “Vocabulario del tema,” “Términos previos,” and “Próximos términos” which provide support for unfamiliar vocabulary in grade 3. A “Vocabulario en contexto” table includes the vocabulary word, math definition, and other meanings. Tema 11 materials provides the mathematical meanings and alternate meanings of the words longitud, tira, and valor, as well as Tema vocabulary such as fracción equivalente and fracción de referencia. Some sections include metalinguistic transfers between Spanish and English. The “Presentación del tema” features a vocabulary activity that guides the educator to use a graphic organizer to have students write the word and create an illustration. In the Tema 4 lección 4-7 “Elaboremos” section, the “Hablemos de matemáticas” subsection guides the educator to facilitate a math discussion where students can express their ideas and strategies using the given lesson vocabulary. Additionally, the Tema 11 “Cognados” section identifies cognates including fractions/fracciónes, symbol/símbolo, and division/división, while the “Falsos cognados” section defines the word notice. The “Vocabulario académico” section then introduces the academic language terms identificar and explorar and provides definitions for each term.

In addition, grade 3 “Recursos Vocabulario académico” includes educator guidance and student activities that provide explicit instruction for academic language. The materials direct educators to show the word, model how to say the word using the audio provided, give the definition of the word, and to use the word in a sentence. The Spanish Academic Vocabulary Teacher’s Guide includes teaching suggestions for 40 words along with digital resources. For example, in the “Repetir” lesson in Guía del maestro, students are introduced to the term through a definition, contextual examples, discussion prompts, and using the word in a sentence. Additionally, grade 3 “Tarjetas de vocabulario” provide academic vocabulary with pictures and instructions for educators on how to use the cards to support student learning with visuals and application examples, including sentence frames to complete sentences using academic vocabulary. The vocabulary cards define and illustrate terms including ecuación, multiplicación, grupos iguales, factores, producto, recta numérica, matriz, and fila.

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.

In grade 3, the “Biblioteca de diferenciación” contains varying resources for students for differentiated instruction and enrichment and extension activities. For example, the 14 Temas include “Escoge un proyecto,” “Levantate y razona,” “Juegos prácticos,” and “Práctica de fluidez” activities, which provide grade-level content and skill proficiency by having students apply mathematical reasoning, complete collaborative problem-solving tasks, develop fluency, and connect mathematical concepts to real-world situations aligned to Tema objectives and the TEKS. Additionally, materials in lección 7-2 also include “Práctica adicional” as an enrichment and extension activity for students to practice “Usar patrones para sumar” using “a tabla para sumar.” “Escoge un proyecto” allows students the opportunity to further enhance their understanding of the lesson. “Matemáticas y lectoescritura” includes an extension activity in “Ampliación,” which provides educator guidance for having students practice repeated addition and multiplication equations. In lección 7-2, paso 4 “Evaluar y diferenciar,” the “Comprobación rápida” section provides guidance on the activity to be completed after the quick check, depending on students’ scores: if students score 0–3 points, they are assigned an intervention or reinforcement activity, and if they score 4–5 points, they are assigned an enrichment activity with a required partial addition table to work on with a partner, where one student chooses the numbers, while the other student finds the corresponding number on the table. Students will repeat with numbers that are three units less than the sum they previously had, then add the two sums.

Furthermore, the grade 3 “Biblioteca de diferenciación” contains educator guidance that includes mathematics and literacy resources connected to classification, counting, patterns, and problem-solving skills. For example, Tema 3 includes “Matemáticas y lectoescritura” activities such as “Serpientes sigilosas” and “Sacudir el producto” that require students to analyze informational text, solve subtraction problems using decomposition and visual models, and explain mathematical thinking through written responses. In lección 7-8, the extension titled “Mostrar patrones,” presents students with a partial addition table. Students are to find examples for each pattern and explain why it is an example. The Libro del estudiante includes the section “Escoge un proyecto” at the end of Tema 1 that provides extension opportunities for students to apply and extend their learning. Students may select from photographs depicting real-world situations and respond to project-based questions that promote critical thinking, creativity, and the application of mathematical concepts. Sample questions include: “¿En qué situaciones de la vida diaria ves las Matemáticas?” “¿Cual es el edificio más alto del lugar en donde vives?” The grade 3 Guía del maestro “Práctica adicional” guides educators to allow students to work on problems that will extend into future learning within the Tema, such as with lección 7-2, where students practice using patterns to solve problems by using associative property and the compensation strategy for addition problems.

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

In the grade 3 Guía del maestro, paso 2 “Aprendizaje visual” and paso 3 “Práctica y resolución de problemas,” the materials provide prompts and guidance for modeling lesson concepts. Lección 10-1 “Dividir regiones en partes iguales,” includes educator-directed questions, sample responses, and discussion prompts throughout the lesson. In paso 2 “Aprendizaje visual,” the educator is prompted to ask, “Cuántas partes iguales hay en cada entero?” and ¿Cómo saben que cada una de las partes es igual?” and provided sample responses for each question. The “Conversación en la clase” section includes prompts for discussing how figures are divided into equal parts and the “Rutina de lenguaje” section directs students to explain and justify their responses. The “Apoyo al lenguaje” section includes educator questions and sample responses related to equal parts and area. Materials for lección 7-1 provide explicit prompts under “Conversación en la clase.” The prompts are in blue font followed by the expected student response in brackets, with a total of four questions to facilitate this section. Question A is as follows: “¿Cuando han trabajado anteriormente con propiedades? [Al multiplicar].” Following the class conversation, there is guidance for the educator to prevent misunderstandings, which states: “Observe a los estudiantes que cambian los sumandos ellos mismos para facilitar la suma en lugar de cambiar el orden o de agrupar los sumandos.” These structured prompts and guidance support educators in facilitating mathematical discussions, developing students’ observational skills, and strengthening conceptual understanding.

In addition, the Guía del maestro for grade 3, Tema 2, “Estándares de procesos matemáticos de los TEKS,” provides educator guidance and discussion prompts to support mathematical reasoning, such as “¿Qué patrones ven?” “¿Cómo hallaron el producto?” and “¿Qué información necesitan para resolver el problema?” The “Presentación del tema” in the Guía del maestro Tema 2 includes a “Paseo de matemáticas” section with educator-prompted questions such as “¿Qué notaron?” “¿Qué se preguntaron?” and “¿Qué pregunta del video intenta responder la persona?” Educator guidance can be found in the Guía del maestro Tema 8, lección 8-1, after the following sections: “Práctica guiada,” “Práctica y resolución de problemas,” “Comprobación rápida,” “Biblioteca de diferenciación,” and “Actividad de intervención.” The guided sections are part of paso 3 and paso 4 of a given lesson. Additionally, in “Algunas sugerencias para usar el Modelo de resolución de problemas,” educators are given guidance on how to assist students with using the problem-solving mode. Educators support students who are struggling to understand concepts by demonstrating how to use the model in order for students to be successful in solving problems independently.

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

The materials for grade 3 in Guía del maestro include lesson structures, instructional routines, and teaching practices that support educators in facilitating mathematical discussion, modeling concepts, and guiding student learning. For example, in Tema 7 “Usar estrategias y propiedades para sumar y restar,” paso 1 “Explorar y comentar,” the “Supervisar, Seleccionar y poner en secuencia” section provides educator guidance for effective lesson delivery, including placing students in small groups to use various strategies to add 36 + 24. Paso 2 “Aprendizaje visual” instructs educators to structure conversations using an animated visual to support students in analyzing varying strategies and instructional approaches for the given concept. Additionally, the Guía del maestro describes three lesson types: “Investiguemos,” “Elaboremos,” and “Representémoslo en 3 actos.” Each lesson incorporates a different instructional approach. “Investiguemos” uses a problem-based learning approach, “Elaboremos” emphasizes direct instruction, and “Representémoslo en 3 actos” includes a real-world approach. Materials additionally include guidance for instructional routines such as “Anticipar,” “Supervisar,” “Seleccionar y poner en secuencia,” “Relacionar,” and “Hablar sobre las ideas matemáticas.” The “Prácticas de enseñanza efectivas” section identifies instructional approaches used throughout the program, including facilitating mathematical discussions, using and connecting mathematical representations, supporting productive struggle, and posing purposeful questions during instruction.

Furthermore, “Planes de la lección para Texas” for grade 3, lección 1-3 includes lesson pacing, instructional routines, educator prompts, sample responses, intervention support, and differentiation guidance throughout the lesson. Paso 2 “Aprendizaje visual” includes “Conversación en la clase” prompts and sample responses that guide students in explaining arrays, rows, columns, and multiplication equations, and “Rutina de lenguaje” questions that support discussions and explanation of arrays and equal groups. Additionally, Brainingcamp tasks incorporate educator guidance for an additional instructional approach with virtual manipulative integration, such as the “How Many Arrays” activity, which includes online manipulatives that allow students to use two-color-counters to represent arrays. The activity also provides extension opportunities that encourage students to generate fact families. Lección 7-3 “Elaboremos” then guides educators on the use of “Boleto de salida” and supporting students based on their results to facilitate instruction with reminders such as “Apoyar a los estudiantes según sea necesario, recordándoles que pueden usar diferentes estrategias como descomposición y compensación para facilitar la suma de números de varios dígitos.”

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 Grades 3–5 program overview includes guided, independent, and collaborative practice in a table featuring practice opportunities and recommended structures for approaches, with the section including the definition of the program for whole group, small group, and the individual. Whole-group is defined as “practice opportunities to promote mathematical disclosure and classroom conversation as students practice and apply new and previously learned concepts.” The materials include a table with practice opportunities, such as math talks, spiral review, fluency practice, and Tema review. Next to each practice opportunity are the recommended structures. Spiral review is guided, stand-up-and-think is guided and collaborative, and Tema review is guided, independent, and collaborative.

Additionally, the grade 3 Guía del maestro, lección 4-3 includes whole-group and small-group instructional structures, educator prompts, and guidance for facilitating discussions and monitoring student understanding. Paso 1 “Explorar y comentar” includes the instructional structures “Introducción Toda la clase,” “Supervisar, seleccionar y poner en secuencia en grupos pequeños,” and “Relacionar toda la clase,” which provide guidance for questioning students, monitoring student strategies, selecting student responses for discussion, and connecting student representations to multiplication and division relationships. In lección 6-3, paso 2 “Aprendizaje visual” includes the “Hablar sobre las ideas Matemáticas” section, in which the educator is guided to have students participate in a think-pair-share activity in a small group where students compare their explanations on why they should start counting with the dollar bill or coin of higher value first while the educator actively listens to student conversations to support with skip counting to support their answer. Furthermore, the “Biblioteca de Diferenciación” includes four projects with educator guidance and recommended structures. Students complete the projects collaboratively across multiple lessons aligned to the Tema, such as Project 1B, which requires students to write addition and multiplication equations that describe an array after it has been rotated. This activity provides opportunities for collaborative practice, mathematical reasoning, and application of concepts learned throughout the Tema.

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

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

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

In the grade 3 Guía del maestro, Tema 4 and Tema 9 include the “Adaptaciones del lenguaje” section at the beginning of each topic, with implementation guidance for educators to effectively use the materials with emergent bilingual students. The section includes “Adaptaciones del lenguaje oral/escrito,” “Apoyo para el vocabulario del tema,” “Transferencia metalingüística al inglés,” “Cognados,” and “Vocabulario académico.” Tema 9 “Adaptaciones del lenguaje” includes guidance for vocabulary development, academic language support, oral and written discourse, and metalinguistic transfer between Spanish and English. The “Transferencia metalingüística al inglés” for Tema 9 includes “Competencias transferibles” and “Cognates,” including “Polígono/Polygon” and “Pentágono/Pentagon,” while the “Vocabulario académico” and “Vocabulario en contexto” sections provide academic terms, contextualized vocabulary support, and lesson-specific language guidance. Tema 4 “Entender la suma” contains a table of vocabulary words, their mathematical meanings, and their alternate meanings in other contexts. Additionally, Tema 4 includes the “Vocabulario académico” and “Vocabulario en contexto” sections that provide academic terms, contextualized vocabulary support, and lesson-specific language guidance to support bilingual and emergent bilingual students during instruction. Lección 1-3 includes the “Organizador gráfico” implementation guidance for educators to use “Explorar y comentar” concepts from the materials with a Frayer model as a graphic organizer for unknown vocabulary or terms.

The grade 3 materials include the “Apoyo al lenguaje” section in the Guía del maestro, Tema 4, lección 4-3 which provides guidance for discussing and comparing data presented in a graph before students solve the problem independently, as well as sentence stems for students to practice using the words taught during “Aprendizaje visual.” The guidance directs educators to use bloques de valor de posición, connect the activity to the “Aprendizaje visual” section, and prompt students to explain how the models represent addition strategies. Additionally, the beginning of each new Tema has a “Repasa lo que sabes” section, which provides language and vocabulary support for educators to implement with students to deepen their understanding. The words and phrases aligned with the lesson are provided as well as vocabulary activities. Furthermore, materials include a program overview, which describes the sections “Supporting Emergent Bilingual Students” and “Additional Resources for Teachers,” which include a Language Support Handbook. For example, one support for emergent bilingual students is the “Language Support Activity,” which provides targeted language support at specific points during the lesson. Finally, each Tema’s “Linguistic Accommodations” section provides vocabulary and metalinguistic transfer support through Spanish-English cognates, as well as academic vocabulary development to help students access content and strengthen language proficiency.

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 grade 3 Guía del maestro Tema 11 “Adaptaciones del lenguaje,” the materials include a variety of embedded guidance to support emergent bilingual students. For example, in “Adaptaciones del lenguaje oral/escrito,” emergent bilinguals interact with the vocabulary words in the Tema to increase comprehension through oral and written discourse and develop academic vocabulary. This section includes vocabulary that is relevant to the topic, along with vocabulary from previous and future Temas. A table titled “Vocabulario en contexto” includes the vocabulary word, mathematical definition, and other meanings. For example, in Tema 6, the provided mathematical definition for the word Desarrollada is “ampliada, extendida, que ha alcanzado un mayor grado de complejidad,” while another meaning is “una ciudad desarrollada cuenta con infraestructura moderna y servicios avanzados.” The section further breaks down the words by lesson including metalinguistic support with transferable and nontransferable information to English in “Competencias transferibles.” Cognates and false cognates are also listed as Calendar/Calendario and Taller/Taller.

Furthermore, the program overview includes language routines and language support activities. Language routines include “Collect and Display” for developing mathematical vocabulary and discourse, “Three Reads” for making sense of mathematical situations and problems, and “Compare and Connect” for analyzing mathematical concepts, representations, and language. In the activities guide, educators support emergent bilinguals in developing academic vocabulary, increasing comprehension, building background knowledge, and making cross-linguistic connections. For example, in the “Co-Craft Questions and Problems” activity, the students use conversation skills and content vocabulary while working in groups to generate questions, problems, and situations. The educator presents a mathematical equation and students write a math story that matches the given problem. Additionally, “Supporting Emergent Bilingual Students” identifies a “Language Support Activity” that provides lesson-specific opportunities for students to discuss mathematical concepts, explain their thinking, and communicate mathematical ideas through speaking and writing. “Presentacion del tema” includes a vocabulary activity that guides the educator to use a frayer model to interact with vocabulary words both orally and by writing. The section includes the definition, characteristics, examples and nonexamples. The Guía del Maestro lección 1-2 “Multiplicación, suma y la recta numérica” includes a section titled “Notas detalladas sobre las lecciones de Elaboremos,” where Note B references an online glossary available in both English and Spanish that provides visual representations of vocabulary terms and opportunities for oral language practice, supporting students in developing academic vocabulary both orally and in written form. Online materials include a Spanish Academic Vocabulary Teacher’s Guide, which includes teaching suggestions for 40 words, including aproximar, calcular, and preciso. The guide supports the digital materials for these words with the student version of these materials that includes pronunciation, a student-friendly definition, a brief activity which uses the word in context, and an opportunity for students to use the word in a sentence for emergent bilinguals to practice oral and written discourse.

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.

Materials in the grade 3 Cuaderno de evaluación include all instructional assessments for the grade level, such as the “Examen de preparación,” “Evaluación para observar el progreso” with various forms, “Evaluación del tema,” “Tarea de rendimiento del tema,” and “Evaluación acumulativa/de referencia,” that all contain a “Tabla de análisis de las preguntas,” which display the specific question, the DOK, and the TEKS that students practice. For example, “Tarea de rendimiento del Tema 13” provides an opportunity for students to demonstrate their depth of understanding at DOK level 3 with “Ejercicio 6” aligned to TEKS 3.7C. The materials include a scoring guide that provides the TEKS alignment for each assessment. The Cuaderno de evaluación includes cumulative assessments with multiple item types that require students to solve multi-step problems, analyze mathematical models, represent equations, interpret data, and apply grade-level concepts related to multiplication, fractions, geometry, area, and measurement. For example, grade 3 “Evaluación acumulativa/de referencia: Temas 1 a 11” includes assessment items aligned to TEKS 3.2C, 3.4A, 3.5B, and 3.6D, and the “Tabla de análisis de las preguntas” identifies the corresponding TEKS and DOK levels for each item.

Additionally, the grade 3 Guía del maestro includes opportunities for students to model mathematical thinking and explain reasoning through exploration and visual practice in lección 6-1. In paso 1 “Explorar y comentar,” paso 2 “Aprendizaje visual,” and paso 3 “Práctica y resolución de problemas,” students represent numbers up to 100,000 using place value and compare multiple solution strategies through discussion prompts and visual models aligned with TEKS 3.2A, 3.2B, 3.1C, and 3.1E. In lección 3-2 “La propiedad distributiva,” students begin with paso 1 “Explorar y comentar” by dividing an array into two smaller arrays and explaining their division strategy. Next, the lesson moves to paso 2 “Aprendizaje visual,” where students decompose different arrays using the distributive property, followed by paso 3’s “Práctica guiada,” “Práctica y resolución de problemas,” and “Comprobación rápida.” The Guía del maestro materials give students multiple opportunities to demonstrate and deepen their understanding of comparison concepts and problem-solving strategies.

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

The program overview contains questions and tasks that increase progressively in complexity and rigor using concrete, representational, and abstract instructional models. For example, in grade 3 students use concrete models and place-value blocks during the “Explore” and “Share” tasks, transition to pictorial and visual representations in the “Visual Learning” activities, and then apply abstract strategies and equations through digital manipulatives and Brainingcamp activities. The Guía del maestro materials, paso 1 “Explorar y comentar,” paso 2 “Aprendizaje visual,” paso 3 “Práctica y resolución de problemas,” and paso 4 “Evaluar y diferenciar,” provide questions and tasks that progressively increase in rigor and complexity. For example, in lección 3-2, paso 1, students decompose an array into two smaller arrays using distributive property. In paso 4, they decompose an array into two smaller arrays using distributive property and write the new operations for the arrays, including writing the operations without the visual representations of the arrays, progressively increasing the rigor and complexity of the TEKS for the grade level.


Additionally, the grade 3 corresponding student activity book includes lessons with questions and tasks that progressively increase in rigor and complexity. For example, lección 6-1 “Números hasta 100,000” begins with paso 1 “Explorar y comentar,” where students are given a word problem and asked to represent 5,400 in as many ways as they can in the space provided. As students progress to the guided practice, they are initially prompted to use the place value chart to determine the expanded form for 62,539. Questions then transition to removing the visual support for students. In Tema 1 “Sumar y restar hasta 20,” the “Contexto matemático: Conceptos clave” section describes how the materials increase rigor throughout the lessons and demonstrate how students work with increasingly complex concepts over time. In Tema 1 lección 1-1, students investigate different ways to combine equal groups, building a foundation for understanding multiplication. In lección 1-4, the materials progress to “Propiedad conmutativa de la multiplicación,” where students observe that arrays can be rotated 90 degrees while maintaining the same product, developing an understanding of the commutative property as they progress to lección 1-8 “La relación inversa de la multiplicación y la división,” where students use arrays to represent multiplication and division equations and explore the relationship between the two operations as materials progress in rigor and complexity.

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

The grade 3 materials demonstrate coherence across units by establishing connections between patterns, big ideas, and relationships among mathematical concepts explicitly by including a “Contexto matemático: coherencia” section, with “¡Vuelve atrás!” and “Más adelante” subsections, in each Tema. Tema 3 “Operaciones de multiplicación derivadas” explains how the unit relates to what students have previously learned and what students will be learning in the future. For example, this Tema includes the TEKS 2.7A and 2.6A, which regard the development of an understanding of even and odd numbers and equations for arrays for equal groups. In the future TEKS 3.4J and 3.4F, students will begin to develop fluency with operations of division using multiplication operation relationships and continue developing fluency with operations of multiplication while exploring the concept of area. Additionally, the “Grade 3 Content Organization Rationale” provides key concepts and connections between Temas. For example, the key concept for Temas 10–11 is “A fraction is a number that can be used to represent a part of a whole, a part of a set, or a point or distance on the number line.”

Additionally, the grade 3 materials in Guía del maestro include coherence across the Temas, explicitly connecting patterns, big ideas, and relationships among mathematical concepts in the “Elaboremos” section of the Temas. The materials in “Contexto matemáticó,” include three sections of “Conceptos clave,” “Coherencia,” and “Equilibrio,” demonstrating the coherence in Temas. The Tema 5 “¡Vuelve atrás!” and “Más adelante” sections connect previously learned content from grade 2 pictographs and bar graphs to grade 3 data organization, representation, and interpretation skills while also preparing students for future grade 4 concepts involving frequency tables, dot plots, and fractional data representations. Furthermore, Tema 11 “Comparación y equivalencia de fracciones” has a connection with grade 4. “Más adelante,” in reference to grade 4, states, “Equivalencia de fracciones: En el Tema 6, los estudiantes generarán fracciones equivalentes multiplicando o dividiendo el numerador y el denominador por el mismo número distinto de cero TEKS 4.3C.”

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

In Guía del maestro, the grade 3 materials coherently connect units through the content and language learned in previous grades, learned throughout the current academic year, and to be learned in the future. In Tema 11 “Contexto matemático: Coherencia” connects prior grade 2 concepts, such as partitioning equal parts and using number lines to compare numbers, to grade 3 concepts involving equivalent fractions, comparing fractions, and representing fractions on a number line. The materials also demonstrate coherence with grade 3 fraction concepts to future grade 4 learning involving generating equivalent fractions, comparing fractions with different denominators, and adding and subtracting fractions with like denominators. Tema 2 “Multiplicación: Operaciones básicas” has three sections that demonstrate coherence connecting content and language in “Adaptaciones del lenguaje,” through the “Vocabulario del tema,” “Términos previos,” “Próximos términos,” “Vocabulario en contexto,” and “Vocabulario para poner en contexto” sections. For example, in the grade 3 materials the “Términos previos” includes terms such as ecuaciones, multiplicación, grupos iguales, factores, producto, división, and matriz, and “Próximos términos” include upcoming terms like propiedad distributiva and propiedad asociativa de la multiplicación.

Additionally, in Guía del maestro, Tema 6 “Valor de posición: Números hasta 100,000,” the materials include “Repasa lo que sabes” in “Análisis de los ejercicios,” along with the sections “Palabras de vocabulario,” “Actividad de vocabulario,” and “Vocabulario académico.” The “Palabras de vocabulario” section lists key vocabulary terms, including componer, punto decimal, descomponer, dígito, símbolo del dólar, forma desarrollada, notación desarrollada, valor de posición, ordenar, redondear, forma estándar, and en palabras. The “Actividad de vocabulario” section provides opportunities for students to deepen their understanding of these terms through the “Elemento didáctico 5: Mapa de palabras,” which allows students to review and reinforce mathematical vocabulary. The “Contexto matemáticó: Coherencia” section includes information on what has been previously taught and how it connects to the current unit and connections to the unit or grade level ahead. For example, Tema 11 “Comparación y equivalencia de fracciones” connects to grade 4. “Más adelante” states, “Equivalencia de fracciones: En el Tema 6, los estudiantes generarán fracciones equivalentes multiplicando o dividiendo el numerador y el denominador por el mismo número distinto de cero TEKS 4.3C.” Meanwhile, the “¡Vuelve atrás!” section explains that students previously used a number line to compare numbers and divide a figure into equal parts in grade 2 and develop an understanding of fractions in grade 3, demonstrating coherence across previously learned and future units since learning about equal parts and how to represent fractions.

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

In Guía del maestro, lección 3-5 “La propiedad asociativa” includes three sections that demonstrate coherence at the lesson level by connecting prior student knowledge to new knowledge and skills: “Conceptos clave,” “Coherencia,” and “Equilibrio.” “Conceptos clave” includes a mathematics objective for new knowledge and skills for lección 3-5, in which students focus on decomposing factors of unknown multiplication operations into factors of known multiplication operations and multiplying the products of the known operations. The “Coherencia” section includes “¡Vuelve atrás!” “En esta lección,” and “Más adelante,” where the lesson includes students’ previous knowledge of commutative property for multiplication, and building on their previous knowledge for new mathematical knowledge and skills by learning to use associative property for multiplication.

Additionally, the materials for grade 3 provide coherence at the lesson level by connecting students’ prior knowledge from the current and previous grade to new mathematical skills and knowledge of concepts and procedures. Lección 2-4 requires students to use their prior knowledge of skip counting, multiplication facts, and number patterns to identify relationships within multiplication tables, compare patterns in rows and columns, and explain connections between repeated addition and multiplication. Furthermore, in lección 11-2 “Usar modelos para representar fracciones equivalentes,” the “¡Vuelve atrás!” section states, “Previamente, los estudiantes aprendieron que las fracciones nombran partes iguales de un entero.” Then, the “En esta lección” section states, “Los estudiantes usan modelos para mostrar que dos fracciones son equivalentes.” Materials continue to demonstrate coherence at the lesson level in “Más adelante,” stating, “Más tarde, los estudiantes representarán fracciones equivalentes en la recta numérica.” Additionally, in Tema 3, lección 3-1, paso 1 “Investigar,” the “Ejemplos del trabajo de los estudiantes” include “El problema de la feria local A,” which contains a task in which students represent an array of 3 rows by 4 columns and determine the total number of counters in two different ways by decomposing the array into smaller parts and finding the sum of the quantities in each section. The materials provide examples of students’ solutions, each demonstrating the application of previously learned concepts and procedures. For example, one student drew lines to decompose the array into three separate rows with four counters each and then used repeated addition to find the total, 4 + 4 + 4 = 12. The solutions require students to apply concepts and procedures introduced in grade 1, lección 1-3 “Sumar y juntar,” and grade 1, lección 3-3 “Dobles y casi dobles,” as well as the understanding of equal groups developed in grade 2, lección 5-3 “Grupos iguales.”

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

The grade 3 materials include spaced retrieval opportunities. The “Elaboremos” section of each lesson includes an “Hablemos de matemáticas” subsection for students to engage in mathematical discourse using previously learned skills and concepts across lessons and Temas. In lección 1-4 “Matrices y la propiedad conmutativa de la multiplicación,” the “Hablemos de matemáticas” section has students select a non belonging group or arrays where they must justify their answers. Students use previous knowledge included in the materials in “Coherencia” and the “¡Vuelve atrás!” component, where students previously learned how arrays can represent multiplication, to the application of the strategies to meeting the objective of understanding and using commutative property for multiplication. Additionally, the program overview for the “Spaced and Interleaved Practice” section features math talks, fluency practice, review-what-you-know, and Tema review activities with spaced opportunities that allow students to repeatedly practice and apply previously learned concepts and skills across lessons and Temas. Materials include a Venn diagram with the names of spaced and interleaved practice, or a combination of the two found in math talks and fluency practice. In combination with interleaved practice, opportunities are also found in review-what-you-know, spiral review, adaptive practice, stand-up-and-think, Tema review, and hands-on games.

Additionally, the grade 3 materials include “Desarollar automaticidad” activities in the Libro del estudiante that revisit previously taught addition and subtraction skills through repeated computation and problem-solving practice embedded within Temas. For example, Tema 6, “Desarollar automaticidad” requires students to apply previously learned multiplication and division relationships, fact families, and missing-number equations while practicing multiplication and division within 100. Additionally, “Repaso en espiral” is available digitally by lesson or as a print file for each lesson with 6–10 questions in each. The questions include both multiple-choice and open-ended questions. The “Repaso en espiral” for lección 2-1 consists of eight questions. Some questions are related to multiplication, including repeated addition, and division, and time to the hour. This shows spaced retrieval opportunities with previously learned lessons and units as students are still working with material learned in the previous unit.

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

The grade 3 materials provide practice opportunities interleaved with previously learned skills and concepts across lessons and units in “Repaso del tema” and “Repasa lo que sabes.” In Tema 4 “Operaciones de división: Pensar en la multiplicación,” the “Repasa lo que sabes” section include instructions for students to fill in the blank with vocabulary words and solve division problems and equations as they review previously learned concepts. The materials also include an “Análisis de los ejercicios” table for “Repasa lo que sabes” that identifies the TEKS being reviewed, such as 3.4D, 3.4H, and 3.4J for the Tema. Additionally, the Tema 10 “Repaso del tema” includes review activities from lecciónes 10-1, 10-2, and 10-4 that require students to apply previously learned concepts related to equal parts, unit fractions, fractions as numbers, fractions on a number line, and fraction of regions.

Furthermore, the materials include interleaved practice opportunities in “Levántate y razona,” which requires multiplication, division, equal groups, equations, and real-world problem-solving concepts from lecciónes 1-2 through lecciones 1-6 to represent and solve cafeteria and trophy-sharing scenarios using multiple solution strategies. In lección 11-2 “Usar modelos para representar fracciones equivalentes,” the “Práctica y resolución de problemas” activity consists of twelve questions that gradually release support. For example, all questions provide interleaved practice opportunities with previously learned skills and concepts in grade 3. The first two questions provide visual representations of the fractions students are given in order to write an equivalent fraction. The next four questions are similar to the first two questions without visual support, but students are reminded that manipulatives or drawings may be used. The following two questions are related with equivalent fractions and a word problem in which students have to provide their reasoning. The last question is a STAAR practice question in which students are to select all the answer choices that include equivalent fractions with the support of fraction strips.

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

In the Guía del maestro, the “Representémoslo en 3 actos” section presents “Acto 1,” “Acto 2,” and “Acto 3,” where students interpret, analyze, and evaluate models and representations for mathematical concepts and situations. For example, in lección 10-9 “Búsqueda en un mapa matemático,” “Acto 1, El anzuelo,” students are provided with tasks to interpret mathematical concepts and situations, formulating mathematical questions with guidance such as “¿Qué pregunta les resulta más interesante?” and “¿Qué pregunta podríamos responder con las matemáticas?” Additionally, students are required to analyze mathematical concepts by making predictions with educator guidance such as “¿Por qué creen que su predicción es la respuesta a la Pregunta principal?” and “¿Quién tiene una predicción similar?” Materials also include tasks requiring students to evaluate models and representations for mathematical concepts and situations, such as in “Acto 2, El modelo,” where students create a model stating, “El inicio está en 0 y el final está en 1” and “¿Cómo podrían localizar 3/8 en la recta numérica?” with included student examples of open number lines and their selected point responding to the question. In Tema 11, lección 11-9, students analyze fraction strip and circle models used by Madison and Tobías to compare fractions. Students interpret the representations to determine which fraction is greater, analyze the strategies used in each model, and evaluate the effectiveness of their problem-solving approaches through reflection questions such as “¿Cómo podrían analizar y evaluar la eficacia del enfoque que escogieron para resolver el problema?” Students also explain how the models represent the situation and justify their reasoning when comparing fractions.

Additionally, in the grade 3 Tema 2 “Bibliotéca de diferenciación” “Levántate y razona” section, students interpret visual representations of coin values and product prices, analyze sample student work that uses multiplication and skip-counting strategies, and determine which products can be purchased using only one type of coin. Students participate in a gallery walk to examine multiple solution methods and are asked to comment, explain, and debate the processes used, requiring them to evaluate the validity and efficiency of different mathematical representations and approaches. In lección 5-8 “Columpios y toboganes,” the content objective is for students to use their conceptual comprehension of data represented in graphs to solve a problem. The materials state, “Los estudiantes tienen la tarea de determinar si se deben agregar columpios o toboganes al área de juegos de una escuela, a partir de datos de tres encuestas.” Students participate in a question brainstorm after watching the video to respond to the “Pregunta principal,” sharing their individual predictions while they discusing their reasoning for why they believe their prediction is correct. Students also reflect on answers that are unreasonable and determine which model to use to represent the problem as they receive more information. Students are able to analyze and evaluate their models as they transition from “Acto 2” to “Acto 3.” After the reflection, students have the opportunity to create and solve a problem similar to the one they solved. Furthermore, the “Manual de resolución de problemas” includes a problem-solving model that supports students in developing mathematical reasoning and problem-solving skills. The model consists of five sections that guide students through the problem-solving process by providing strategies for representing mathematical situations, such as drawing pictures, creating diagrams, using tables or graphs, and writing equations. The resource includes completed examples of student work that demonstrate how students interpret, analyze, and evaluate mathematical models and representations. Additionally, in the “Evaluar el proceso” section, the students reflect on the effectiveness of the strategy by writing, “Mi estrategia funcionó. Me di cuenta de que la parte que falta siempre es la diferencia entre la cantidad total y la otra parte. Puedo usar diagramas para resolver problemas de resta y suma en el futuro.”

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

The grade 3 materials include various questions and tasks that require students to create models to represent mathematical situations. For example, in lección 8-6, “Representémoslo en 3 actos, Recolección de sueteres,” the “Acto 2, El modelo” section includes questions and tasks for students to create models to represent mathematical situations. In “Desarrollar un modelo,” the materials prompt students to create their models with questions such as “¿Pueden usar la cantidad recolectada en el día 1 para predecir la cantidad recolectada en los días 2 o 3?” The materials also include student examples such as a grade 3 model representing strategies to complete a word problem to solve how many sweaters are needed, with a goal of 750 sweaters, if there were 299 sweaters collected on day 1, 158 sweaters collected on day 2, and 255 sweaters were collected on day 3. Student examples include the use of place value to add and count forward to find the missing quantity and mental math and subtraction to find the difference. The answer to the problem is revealed in “Acto 3,” where students confirm their answer or are able to adjust their model, continuing to represent mathematical situations.

Additionally, in the Libro del estudiante, Tema 3, lección 3-8 “Escoger una estrategia para resolver operaciones básicas de multiplicación,” students analyze a situation involving boxes of paper towel rolls and determine the total number of rolls in each package. Students select a strategy, such as decomposing factors, using multiplication, or combining quantities, to create a mathematical model that represents the situation and supports their solution. In lección 11-1, the “Desarrolla GRIT” activity includes the prompt, “Usa tiras de fracciones para hallar otros ejemplos en los que un conjunto de fracciones del mismo tamaño tenga la misma longitud que otra fracción.” This task requires students to use and create mathematical models with fraction strips to represent and identify equivalent fractions. Additionally, in lección 11-2, the “Otro ejemplo” section guides the problem: “Puedes representar fracciones de distintas maneras,” and provides multiple representations, including fraction strips, diagrams, and area models. In the “Práctica guiada,” students are given two fractions and asked to draw a strip diagram to represent them. By drawing it, students create models to represent equivalent fractions. In Cuaderno de práctica adicional, “Activity 1-3” directs students to work on multiplication and arrays, with question 7 presenting the following word problem: “Scott pone algunas calcomanías de deportes en filas. Hace 6 filas con 5 calcomanías en cada fila. ¿De qué otra manera podría ordenar sus calcomanías en filas y columnas?” Students are then asked to choose a tool to create a model to solve and are given the opportunity to communicate their mathematical thinking through tangible representations and figures or drawings.

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

The grade 3 materials include questions and tasks that provide opportunities for students to apply conceptual understanding to new problem situations and contexts in Guía del maestro. For example, in Tema 9, lección 9-5 “Clasificar y agrupar figuras tridimensionales,” students analyze nets of three-dimensional figures and classify them based on attributes such as faces, edges, and vertices. Student work samples show different methods for grouping the figures, including classifying by the number of faces and by the presence of edges. The lesson also prompts students to explain and compare classification strategies using attributes of three-dimensional figures. In lección 8-2 “Usar el valor de posición para sumar,” the “Hablemos de matemáticas” section provides questions and tasks with opportunities for grade 3 students to apply “Resolución de problemas” by displaying two separate sums and asking if it is true or false that the sum of 413 + 325 is equal to the sum of 325 + 413. Additionally, the materials task students to apply conceptual understanding to new problem situations and contexts, with students taking turns to present their decisions and justify their final answers and their reasoning in small groups.

Furthermore, in Guía del maestro Tema 10, lección 10-2 “Explorar fracciones como números,” students analyze flags composed of fractional parts and then create their own flag design using at least three fractional parts. Students describe their designs using fraction vocabulary and explain how the fractional parts represent the whole, applying their understanding of fractions in a new context. In lección 5-4 “Representar datos,” paso 2 “Relacionar” in the “Hablar sobre las ideas matematicas” section, students apply conceptual understanding to new problem situations and contexts by working through problems where they have to answer how they organized the data and why they chose that graph, followed by comparing their work to their peers to find differences and similarities in their representations. Finally, they participate in think-pair-share activities to communicate why bar or picture graphs make it easier to answer data questions. In Tema 14 “Vistazo a la Biblioteca de diferenciación,” the materials provide opportunities for students to apply their mathematical understanding through a variety of projects and contexts. The “Escoge un proyecto” section includes four project options to demonstrate understanding in different ways. Project 14B asks students to design a savings game, while Project 14C asks students to write a story about going shopping. To complete these projects, students apply their conceptual understanding of counting, coins, money, addition, subtraction, and saving in authentic, real-world situations.

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

In the grade 3 Guía del maestro, each Tema includes a “Desarrollar fluidez” section to provide students with tasks designed to build automaticity and fluency in mathematics for the grade level. For example, Tema 7 “Usar estrategias y propiedades para sumar y restar” includes the activity in alignment with the TEKS 3.4A and asks students to work with a partner to select a different color between dark purple with a square or light purple with a star and pick a number at a time from the column to add. Additionally, the materials include another activity in “Otra actividad” and an enrichment activity in “Desafío adicional” aligned to TEKS 3.4A. The materials include fluency games that provide repeated opportunities for students to develop accuracy and efficiency with addition and subtraction within 100. These activities engage students in repeated practice solving computation problems and recalling addition and subtraction facts while participating in structured mathematical games. For example, in Tema 3 “Biblioteca de diferenciación,” “Juego de fluidez: Carrera loca,” students solve addition and subtraction problems such as 14 + 53, 31 – 12, 46 + 35, and 56 – 19 as they move through a game board. Students repeatedly compute sums and differences within 100, verify solutions with a partner, and solve multiple equations throughout the game. These tasks include repeated practice with addition and subtraction within 100 through a fluency game format.

The Tema 3 “Desarrollar fluidez” activity focuses on subtraction up to 100. The activity provides 25 solved facts with an embedded maze, where the correct path requires the facts to be solved correctly. For example, 75 – 13 = 62 is a part of the path, while 39 – 21 = 12 is not a part of the path since it is not correct. The guide for the corresponding activity provides extensions with “Otra actividad” and “Desafío adicional” using the same sheet. In Tema 4 “Desarrollar automaticidad,” students solve multiple multiplication and division equations and match each expression to an equivalent fact. This activity provides repeated practice with multiplication and division within 100 and supports fluency with related facts and fact families. In Guía del maestro lección 2-6, paso 3 “Práctica y resolución de problemas,” students demonstrate their comprehension of the content and fluently apply their knowledge to solve the multiplication problems. The interactive activity builds in rigor with students representing and solving a word problem using strip diagrams. The activity continues with practice and problem-solving where students use strip diagrams and write equations for solving multiplication problems. Students continue to solve problems using higher-order thinking skills and the activity concludes with a STAAR assessment practice question for grade-level tasks for automaticity and fluency.

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.

Mathematics procedures in the Guía del maestro include varying opportunities for students to practice the application of efficient, flexible, and accurate procedures in lección 7-7 “Elaboremos, Estrategias para estimar sumas.” The “Mira de cerca” activity in “Hablemos de matemáticas” has students analyze the hints to figure out the mystery numbers with provided clues. Materials provide opportunities for practicing application of efficient, flexible, and accurate mathematical procedures by providing clues for mathematical thinking and discourse to take place such as “El número es mayor que 374 – 123,” “El dígito de las decenas del número es mayor que el dígito de las decenas de 374 – 123,” “El número es menor que 367 – 94,” “El dígito de las decenas del número es menor que el dígito de las decenas de 364 -–94,” and “El digito de las unidades del número es menor que el dígito de las unidades de 364 – 94.” In Tema 10, lección 10-8 “Fracciones y conjuntos,” students identify and represent fractions of a set, determine the fraction represented by a subset of objects, and explain how the numerator and denominator relate to the part and whole. The lesson includes “Apoyo al lenguaje,” “Hablemos de matemáticas,” and a “Boleto de salida” that provides additional opportunities for students to practice fraction procedures and represent fractional relationships using sets of objects.

In Tema 4, lección 4-3 “Usar la multiplicación para dividir con 2, 3, 4 y 5,” students solve a division problem involving 16 students seated in pairs. Students’ samples demonstrate different procedures, including drawing equal groups and using the relationship between multiplication and division to determine that 16 ÷ 2 = 8. The lesson requires students to use representations and equations to solve and explain division situations with the application of efficient, flexible, and accurate mathematical procedures. Additionally, in lección 11-1 “Fracciones equivalentes,” the “¡Investiguemos!” section directs students to investigate equivalent fractions using fraction strips and provides the opportunity to find efficient mathematical procedures during paso 1 “Investigar.” The materials include student examples in the Guía del maestro for how fraction strips can be used to find equivalent fractions, with opportunities for students to practice the application of efficient, flexible, and accurate mathematical procedures. It is anticipated that some students use the fraction strips based on size rather than denominators or are able to successfully find equivalent fractions and are able to describe them. In the Libro del estudiante, the lección 5-1 “Recopilar y organizar datos” section, “Elaboremos,” provides opportunities for students to solve problems using efficient, flexible, and accurate mathematical procedures by prompting them to survey their classmates to determine the most popular season by collecting responses from at least 10 students, recording the data in a table, and creating a graph to represent the results.

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 Guía del maestro provides multiple opportunities for students to evaluate procedures, processes, and solutions for efficiency, flexibility, and accuracy within the lesson or throughout the Tema. For example, the “Representémoslo en 3 actos” section includes “Acto 1, El anzuelo,” “Acto 2, El modelo,” and “Acto 3, La solución,” providing opportunities for students to use a video to develop questions from procedure evaluation, create models using mathematical processes and solutions for efficiency, flexibility, and accuracy within the lesson and throughout the Temas. For example, in lección 8-6, “Representémoslo en 3 actos, Recolección de sueteres,” “Acto 1, El anzuelo” provides the opportunity for students to formulate predictions as they evaluate procedures and formulate questions. Educators ensure students have varied predictions and evaluate procedures including comprehension of the importance of thinking of unreasonable predictions. The section “Acto 2, El modelo” allows students to incorporate mathematical processes and solutions for efficiency, flexibility, and accuracy when creating their own model to represent and respond to the question. Students also apply the provided information prior to creating their models in “Revelar la información.” In “Acto 3, La solución,” the materials include using the provided video to reveal the answer to the initial question. The materials also include three sections to support opportunities for students to evaluate solutions for efficiency, flexibility, and accuracy with “Comprobar conclusiones” and “Reflexionar sobre el razonamiento,” where students must represent, explain, prove, and finally “Crear un problema.” Furthermore, in Tema 4, lección 4-2 “Relacionar operaciones de multiplicación y división,” the sections “Seleccionar y poner en secuencia,” “Relacionar estrategias de solución,” and “Hablar sobre las ideas matemáticas” guide students to compare multiple representations and strategies for solving multiplication and division problems. Students continue evaluating solution methods through “Práctica y resolución de problemas,” “Reflexión,” and “Práctica adicional,” where they analyze relationships between multiplication and division and determine whether solutions are reasonable.

Additionally, in the Libro del estudiante, Tema 7, lección 7-4, students solve a subtraction problem and justify their reasoning using place-value blocks or another strategy of their choice. In the “Conectar” activity, students explain the strategy used to determine what additional items Kai can purchase, identify tools that could be used to solve 500 – 227, and evaluate Kai’s approach of thinking about addition to solve a subtraction problem. The lesson concludes with a discussion of different ways to think about subtraction, providing opportunities for students to compare and evaluate solution methods. Additionally, in lección 6-6 “Redondear números enteros,” students complete the following task: “De todos los estados de EE. UU., Texas tiene la mayor cantidad de condados: ¡254! ¿Qué número puedes usar para describir aproximadamente cuántos condados hay? Explica tu decisión.” The materials also include two examples of student work that demonstrate different solution strategies. Students use different procedures, as they apply place-value reasoning and estimation strategies to justify their answers. The activity provides opportunities for students to compare and discuss different solution methods and evaluate the effectiveness of each approach. These opportunities promote efficiency by encouraging students to select a strategy that allows them to estimate quickly and effectively. They promote flexibility by allowing multiple valid estimation strategies, such as using a number line or skip counting. The task also supports accuracy because students must justify their estimates using place-value reasoning and verify that their chosen number is the most reasonable approximation. In lección 5-8 “Columpios y toboganes,” the content objective is for students to use their conceptual comprehension of data represented in graphs to solve a problem. The materials state, “Los estudiantes tienen la tarea de determinar si se deben agregar columpios o toboganes al área de juegos de una escuela, a partir de datos de tres encuestas.” Students participate in a question brainstorm after watching the video for this lesson to respond to the “Pregunta principal of “¿La escuela debería adquirir columpios o toboganes para el área de juegos?” Students share their individual predictions while discussing their reasoning for why they believe their prediction is correct and reflecting on unreasonable answers. Students determine which model to use to represent the problem as they receive more information and then analyze and evaluate their models as they transition from “Acto 2” to “Acto 3.” After the reflection, students have the opportunity to create and solve a problem similar to the one they solved.

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

The grade 3 Guía del maestro includes embedded supports for educators to guide students toward increasingly efficient approaches. For example, in lección 8-7 “Estrategias para sumar y restar,” paso 1 “Investigar” includes “Presentar la investigación,” which guides educators to use slides to reveal information and provide prompted questions such as “¿Qué notan?” and “¿Qué se preguntan?” The “Supervisar” section includes prompts and guiding questions for educators to use within the lesson in “Preguntas de evaluación” and “Preguntas para profundizar.” Questions include: “¿Qué representan los números en tus ecuaciones?” and “¿Cuál es otra manera de sumar los números que puede ser más eficiente?” Additionally, paso 2 “Hablar sobre las ideas matemáticas” includes embedded supports to guide students’ approaches, for example, “Pida a los estudiantes que participen en una actividad de pensar-trabajar en parejas-compartir para comentar las estrategias de suma y resta. Esté atento a los estudiantes que mencionan sumas parciales y diferencias parciales, compensación u otra estrategia de valor de posición.” In lección 12-11, students develop models to estimate the number of words typed in a given amount of time. During “Acto 3,” students compare their predictions to the revealed solution, discuss how their models could be revised, and evaluate whether different approaches produced reasonable results. The educator guidance also prompts students to compare solution strategies and explain how models helped solve the problem.

Additionally, the grade 3 materials provide embedded support in Tema 12 lección 12-7 “La multiplicación como comparación.” The “Seleccionar y poner en secuencia” section directs educators to sequence student responses from direct comparison statements to comparison strategies involving numerical relationships and to address misconceptions. The “Relacionar estrategias de solución” section further guides educators to compare addition, subtraction, and multiplication strategies and discuss how multiplication can be used to compare lengths, supporting students’ development of increasingly efficient approaches. Additionally, the Tema 3 “Estándares de Procesos Matemáticos de los TEKS” includes embedded educator supports designed to guide students’ mathematical thinking. At the bottom of the page, the materials provide a list of guiding questions that educators use to deepen students’ understanding of efficient mathematical approaches to solving multiplication problems. For example, the materials include questions such as: “¿Qué patrones notan?” “¿Cómo pueden ayudarlos a multiplicar?” “¿Cómo pueden representar el problema?” “¿Cómo pueden descomponer un factor para usar operaciones conocidas?” “¿Qué estrategia de multiplicación usarán?” “¿Qué representan los factores?” “¿Qué representa el producto?” and “¿Cómo saben que pueden multiplicar para resolver el problema?”

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

The grade 3 Guía del maestro explicitly states the conceptual and procedural emphasis of the TEKS in “Contexto matemático: Coherencia” and “Contexto matemático: Equilibrio” sections in each Tema. “Comprensión de conceptos” and “Destrezas en procesos y automaticidad” directly address the conceptual and procedural emphasis of the TEKS within the materials. In Tema 3 “Multiplicación: Operaciones derivadas, Comprensión de conceptos,” students learn basic multiplication operations using various strategies to build fluency aligned to TEKS 3.4E and 3.4K. Students comprehend the distributive property aligned to TEKS 3.4D and 3.4K as they create arrays to deepen comprehension. As students comprehend the associative property aligned to TEKS 3.4K, they use symbolic representation with parentheses. Additionally, the “Destrezas en procesos y automaticidad” section identifies how the procedural emphasis of the TEKS is addressed, such as with students practicing the use of strategies and properties to solve multiplication operations, acquiring fluency for Tema 3. In Tema 1 “Contexto matemático: Equilibrio - Significados de la multiplicación y la división,” the “Comprensión de conceptos” section identifies conceptual expectations, including understanding multiplication through equal groups and arrays, applying properties of operations, and recognizing the relationship between multiplication and division. The “Destrezas en procesos y fluidez” section identifies procedural expectations, including using repeated addition, skip counting, and repeated subtraction to develop multiplication and division fluency.

Additionally, Tema 11 “Presentación del tema: Contar hasta 100” includes the essential question “¿Cuáles son algunas maneras distintas de comparar fracciones?” and connects instruction to TEKS process standard 3.1A through the “Paseo de matemáticas.” The Tema also provides a prerequisite review activity aligned to TEKS 3.2D, 3.3C, 3.2D, 3.3A, and 3.5B in the “Análisis de los ejercicios: Repaso lo que sabes” table. In Tema 4, lección 4-5, the materials include an “Análisis de ejercicios: Práctica y resolución de problemas” table, which explicitly identifies the exercise, PDC, the content TEKS, and the process TEKS addressed in the accompanying student practice. The table supports the purpose of the “Práctica y resolución de problemas” section of the Libro del estudiante by identifying the TEKS associated with problems 5–20. The materials clearly distinguish between the content TEKS 3.4J, 3.4F, 3.4K, and 3.5B and the process TEKS 3.1D, 3.1E, and 3.1F, explicitly identifying the mathematical content and process standards addressed by each exercise for the conceptual and procedural emphasis of each task. Furthermore, in lección 2-1 “Elaboremos,” students use their understanding of patterns to develop strategies to build 2s facts in multiplication. This concept connects to a greater conceptual understanding of multiplication strategies as indicated in lección 2-7, where students use what they know about the concept to begin using a mathematical model such as an array and equal groups 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 grade 3 Guía del maestro includes questions and tasks that use concrete models and manipulatives, pictorial representations, and abstract representations. Each lesson includes four steps: paso 1 “Explorar y comentar,” paso 2 “Aprendizaje visual,” paso 3 “Práctica y resolución de problemas,” and paso 4 “Evaluar y diferenciar.” Lección 1-8 “Relacionar la multiplicación y la división” features concrete models in paso 1 “Explorar y comentar” as students use double colored chips to represent the digits in the multiplicative equation and show how those digits relate to the digits in the division equation. In paso 2 “Aprendizaje visual,” materials include pictorial representations as an array for students to use the visual for a multiplication and a division equation. Additionally, in paso 3 and paso 4, students create multiplication and division equations using arrays, number families, and groups of numbers to create the equation in “Práctica y resolución de problemas” and “Práctica adicional.” The program overview explains that instruction follows a Concrete-Representational-Abstract (CRA) instructional model that moves students from hands-on experiences to visual representations and symbolic notation. The program overview for the CRA Instructional Model states that students use concrete materials such as counters, cubes, and place-value blocks; pictorial representation such as drawings, diagrams, and visual models; and abstract representations including numbers, symbols, and procedures. Visual learning lessons and Brainingcamp digital manipulatives resources support students in connecting these representations throughout instruction.

Additionally, in the Libro del estudiante Tema 4, lección 4-5 sections, “Aprendizaje visual” and “Práctica guiada,” students solve division problems using groups of objects represented by pajillas, draw diagramas de tiras to model equal groups and unknown quantities, and write related multiplication and division equations such as 7 x 8 = 56, 56 ÷ 8 = 7, and 9 x 6 = 54. The guided practice directs students to use multiplication equations to determine quotients and record solutions using numerical equations. In Tema 7, lección 7-4, paso 1 “Maneras de pensar la resta,” students work toward the objective of exploring different strategies for subtraction. The materials present a problem-solving task and instruct students to use base 10 blocks to model and solve the problem. Students are encouraged to choose any strategy that helps them represent their thinking, providing opportunities to use concrete manipulatives, pictorial representations, or abstract representations. Additionally, the materials include four samples of student work demonstrating multiple representations for solving the same problem. For example, Hua uses base-ten blocks as concrete manipulatives and a number line as a representational model. Kevin uses mental math, demonstrating an abstract representation, while Juan and Nellie solve the problem using standard addition and subtraction algorithms, representing abstract mathematical procedures. In the “Manual de Resolución de problemas,” the materials provide a problem-solving guide and sheet for students to refer to and use when solving problems. This tool supports student understanding of TEKS-aligned concepts and allows them to engage further with the material by increasing the rigor.

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 “Concrete, Representational, Abstract Instructional Model” program overview includes various supports for students to connect, create, and define mathematical models in “Progression within and Across Lessons,” “Tasks at the Start of Lessons,” “Visual Learning,” and “Visual Learning Animations” sections. The materials guide students in using concrete objects such as counters, cubes, place-value blocks, and tiles, or pictorial models such as number lines, arrays, grids and strip diagrams in the explore and share sections of “Let’s Build” lessons, as well as the investigate sections of “Let’s Investigate” lessons. Additionally, the materials include abstract concepts in the lesson with supports for students, such as “When students share and discuss solutions, rich conversations deepen conceptual understanding of connections between concrete, pictorial, and abstract.” In Guía del maestro, lección 2-6, students work on solving problems involving multiplication facts. During the “Explorar y comentar” section of the lesson, students are prompted to represent math ideas by using objects or drawings to represent the multiplication problem and can solve it any way they choose. The student samples provided show one student using a strip diagram to solve using addition only, and the other using pictures to represent and solve using both addition and multiplication. Following the completion of the task, the educator facilitates a whole-group discussion connecting the solution strategies used in the student work samples. The conversation allows students to make connections between the concrete, representational, and abstract by understanding that while both answers were correct, the model that used multiplication to solve was more efficient than addition.

Additionally, the grade 3 materials support students as they connect, create, define, and explain concrete and representational models and abstract mathematical concepts through a structured problem-solving process aligned to the TEKS. The Guía del maestro includes lección 1-8 “Explorar y comentar,” where the “Elaboremos” provides solar panels as visual representations to help students connect the model to arrays and multiplication and division concepts. Students use counters to create arrays and develop an understanding of the relationship between multiplication and division. After modeling the arrays with concrete manipulatives, students create a multiplication equation and a related division equation using fact families, connecting the concrete and representational models to abstract symbolic representations. The materials also prompt students to explain their mathematical thinking by responding to questions such as “¿Cómo decidieron la cantidad de filas?” “¿Qué representa cada uno de los números en la ecuación de multiplicación?” and “¿Cómo se relacionan con los números de la ecuación de división?” These questions require students to define the meaning of the models, explain the relationships among the representations, and connect concrete and representational models to abstract mathematical concepts and procedures. Additionally, the “Manual de resolución de problemas” provides students with a problem-solving process that includes analyzing information, selecting representations, determining solutions, justifying reasoning, and evaluating the problem-solving process. The accompanying “Hoja de anotaciones” guides students to organize known and unknown information, select representations such as diagrams and equations, and explain their solutions. The “Diagramas de tiras” provide visual models for addition, subtraction, multiplication, division, and comparison situations and connect these representations to equations such as 13 + 30 = 43, 78 – 49 = 29, 4 x ? = 36, and 14 x 8 = 112, supporting students in relating visual models to abstract numerical representations. At the beginning of each Tema, the materials provide a math background to guide understanding of key concepts that develop over the course of the Tema. For example, in Tema 1, lección 1-2 and lección 1-3, students use different models to represent multiplication problems such as equal groups, equal lengths on a number line, and arrays. Students investigate ways to join equal groups, which allows them to develop a foundation for understanding multiplication. In lección 1-4, students connect their knowledge from the previous lesson and use abstract thought when given visuals showing the commutative property in multiplication. Students make observations and notice the array can be rotated 90 degrees and the product will remain the same.

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

The grade 3 Guía del maestro provides various opportunities for students to develop academic mathematical language through visuals, manipulatives, and other language development strategies, such as in the Tema 2 “Multiplicación: Operaciones básicas” “Repasa lo que sabes” section. For example, the “Presentación del tema” includes the “Actividad de vocabulario” and “Vocabulario académico,” which reinforce academic mathematical language as students practice with classmates or in a virtual setting. “Actividad de vocabulario” provides varying language development activities, such as having students use images, words, numbers, or symbols that they believe signify the vocabulary words, for example, drawing images and writing multiplication operations to illustrate the identity property or the property of zero in multiplication. “Vocabulario académico” includes online activities that use visuals, manipulatives, and other language development strategies to present or review words in the Tema. Lección 8-1 has students use bloques de valor de posición to represent numbers and discuss how the place-value blocks are used to find partial sums. Students then use the place-value block models to connect mathematical language to the visual representation of 378 + 243 while discussing the addition strategy.

Additionally, in Libro del estudiante, the materials provide opportunities for students to develop their academic mathematical language through visual representation and mathematical discussion. In lección 6-4, the “Aprendizaje visual” section introduces the terms componer and descomponer through visual models and mathematical explanations where students use place-value charts, pictorial models, expanded notation, and discussion prompts to represent, compose, and decompose numbers in multiple ways while explaining their mathematical thinking. In Guía del maestro, lección 7-5 “Usar una recta numérica para restar,” the use of rectas numéricas with “Elemento didáctico 33” is optional, and students have the opportunity to develop their academic mathematical language using manipulatives in the “Explorar y comentar” section of “Elaboremos” lessons. Students have to solve a word problem subtracting 365 and 149, in which they can use the number line as a manipulative. In lección 13-4, paso 1 “Investigar” provides students with visuals of different measurement tools and academic vocabulary and students respond to questions that engage them in using that academic vocabulary. In the section “Potenciar la voz del estudiante: Involucrar a los estudiantes en el contexto,” the materials provide opportunities for students to contribute their own experiences and ideas by responding to questions such as: “¿Qué herramientas para medir tienes en casa?” “¿Cómo se usan?” and “¿Por qué se usan herramientas para medir cuando las personas hacen u hornean algo?” These questions allow students to share their experiences while reinforcing academic vocabulary.

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

The materials for grade 3 include embedded educator guidance in Guía del maestro to scaffold and support student development and use of academic vocabulary throughout the academic school year. In lección 1-3 “Elaboremos: Leer, formar y escribir 1, 2, 3” the “Apoyo al lenguaje” section includes embedded educator guidance to scaffold and support students’ development and use of academic mathematical vocabulary in context. For example, the materials include the following prompts: “Diga a los estudiantes que expliquen la división en sus propias palabras.” and “Muestra la palabra división y pida a los estudiantes que piensen sobre cómo la división representa separar.” Tema 11 “Repaso del Tema: Comparación y equivalencia de fracciones” includes a “Repaso de vocabulario” section with educator guidance for reviewing vocabulary through partner discussions, oral language practice, and mathematics writing activities. The guidance directs educators to have students define Tema vocabulary, use the terms in context with a partner, and reinforce vocabulary through a writing activity that connects mathematical terms to the concepts reviewed in the Tema.

Additionally, Tema 3 includes an “Actividad de vocabulario” that directs students to represent the associative and distributive properties using images, words, symbols, or manipulatives and explain their examples. “Vocabulario académico” educator guidance includes prompts that support students in using academic vocabulary such as argumentar, ordenar, distribuir, and distributiva while discussing mathematical ideas. The guidance instructs educators to use the “Actividades de vocabulario académico” available online to introduce or review the vocabulary terms before students apply them throughout the lesson. Each “Repaso del tema” includes a “Repaso de vocabulario” section in which students have the opportunity to engage in oral and written review of words. For Tema 5 “Recopilar, organizar, mostrar e interpretar datos,” the “Lenguaje oral” section guides the educator to play “¿Verdadero o Falso?” a game in which the educator or a student uses a vocabulary word in a sentence and the class has to determine if the word was used correctly or not. This practice is done before the activity sheet to reinforce oral language with the game. The “Escritura en matemáticas” section includes what students will say and write with the vocabulary words and students exchange their papers to see if the word was written correctly using spelling rules. Students can use a list of the words to reference them.

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 3 materials include embedded educator guidance in the Guía del maestro to support students’ application of appropriate mathematical language, such as through discourse opportunities. In lección 1-3, “Elaboremos: dobles y casi dobles,” educator guidance supports student responses to questions and tasks through the use of mathematical language, such as “Los estudiantes deben determinar qué se les pide que hallen, qué información se les da y cuál es la pregunta escondida. Organice a los estudiantes en pequeños grupos para que comenten el problema con sus propias palabras.” Additionally, the “Hablemos de matemáticas” section prompts educators to support the application of appropriate mathematical language with the following guidance: “Pida a los estudiantes que analicen las pistas, una por una, y que piensen cuál podría ser el número misterioso después de revelar cada pista” and “Los estudiantes deben comentar sus estrategias en parejas antes de unirse a una discusión en clase.” In paso 1 “Explorar y comentar,” the materials guide educators to support student responses using exemplar responses to questions and tasks in the “Supervisar, seleccionar y poner en secuencia” section, where students compare lengths and use linking cubes with provided student example responses. Educators provided guided questions with appropriate mathematical language such as “¿Cómo saben si un objeto será más grande o más pequeño?” and “¿Cómo pueden mover su tren de cubos para ayudar a encontrar esto?” Lección 9-2 “Describir y comparar objetos por longitud y altura” introduces the vocabulary altura, longitud, más largo, más bajo, and más alto. The “Apoyo al lenguaje” section guides educators to facilitate discourse in which students compare objects using prompts such as “¿Cuál es más largo?” and “¿Cuál es más alto?” The “Hablemos de matemáticas” section provides educator prompts and example discussion questions that encourage students to describe, explain, and justify their observations while using appropriate mathematical language with a partner. The lección 3-8 “Escoger una estrategia para resolver operaciones básicas de multiplicación” “Apoyo al lenguaje” section includes the “Discurso del estudiante” activity, which should be used during the “Práctica guiada” section of the lesson to help students communicate about strategies used to solve the problems. Students are encouraged to justify their answers using educator-provided sentence frames to support the application of appropriate syntax: “Resuelvo usando . . . porque . . . ” “Para este problema, yo . . . ” “La . . . estrategia tiene sentido porque . . . ” Students are encouraged to work through differences respectfully.

Additionally, lección 5-4 “Representar datos” includes the “Rutina de lenguaje: Tres lecturas,” which guides educators to ask questions such as “¿En qué consiste la tarea?” “¿Sobre qué recopila datos Jada?” “¿Qué información se proporciona en la tarea?” and “¿Qué les pide encontrar la tarea?” The lesson also includes “Potenciar la voz del estudiante,” providing discourse prompts that encourage students to connect the mathematics to their own experiences and explain their thinking during mathematical conversations. In paso 1 “Investigar,” the “Ejemplos del trabajo de los estudiantes” include varying student responses and educator guidance for questions such as “¿Por qué decidiste hacer las barras con cuadrados apilados?” and “¿Cómo puedes asegurarte de haber mostrado todos los datos en tu tabla de conteo?” Each “Repaso del tema” includes a “Repaso de vocabulario” section in which students have the opportunity to engage in oral and written review of words. For Tema 5 “Recopilar, organizar, mostrar e interpretar datos,” the “Lenguaje oral” section guides the educator to play “¿Verdadero o Falso?” a game in which the educator or a student uses a vocabulary word in a sentence and the class has to determine if the word was used correctly or not. This practice is done before the activity sheet to reinforce oral language with the game. The “Escritura en matemáticas section” includes what students will say and write with academic vocabulary words, supporting the application of appropriate syntax as students exchange their papers to see if the word was written correctly using spelling rules. Students can use a list of the words to reference them. Furthermore, the “Argumento” section provides educator guidance by including sentence starters that support students as they explain their mathematical thinking and engage in discussions with their peers.

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

The grade 3 Guía del maestro includes the TEKS process standards integrated throughout the materials. The “Estándares de procesos matemáticos de los TEKS en la enseñanza” section includes four subsections that explain how the TEKS process standards are integrated into the materials: “Estándares de procesos matemáticos de los TEKS en la enseñanza,” “Estándares de procesos en problemas y evaluaciones,” “Estándares de procesos y el Manual de resolución de problemas,” and “Estándares de proceso y uso de diagramas de tiras para resolver problemas.” In “Estándares de procesos en problemas y evaluaciones,” the materials include “Estándares de procesos matemáticos de los TEKS en evaluaciones,” which states, “Los ejercicios que evalúan contenido también animan a los estudiantes a usar Estándares de procesos.” Tema 9 “Estándares de procesos matemáticos de los TEKS: Geometría” highlights TEKS 3.1B and 3.1C and describes observable student behaviors such as using problem-solving models to represent and solve geometry problems, identifying relevant information, describing, classifying, and grouping geometric figures using their attributes, selecting appropriate mathematical tools, and determining the areas and perimeter of figures.

Additionally, Tema 10 “Vistazo al tema,” identifies the mathematical objectives, language objectives, vocabulary, content TEKS, and corresponding “Estándares de procesos matemáticos” for each lesson, including TEKS 3.1B, 3.1D, 3.1E, 3.1G, demonstrating that the TEKS process standards are intentionally incorporated throughout instruction rather than addressed in isolation. This organization is provided in the “Vistazo al tema” for each Tema throughout the program. This section lays out the specific TEKS for the unit in an “Estándares de procesos matemáticos resaltados en las lecciones del Tema” table. For Tema 5 “Recopilar, organizar, mostrar e interpretar datos,” the materials state, “Se espera que el estudiante comunique ideas matemáticas, su razonamiento y sus implicaciones utilizando múltiples representaciones cuando sean apropiadas, incluyendo símbolos, diagramas, gráficas y el lenguaje común TEKS 3.1D.” The column then lists how the breakout is reflected in the unit, for example, “recopilan datos y los representan mediante una tabla de frecuencias, un diagrama de puntos, una pictografía o una gráfica de barras, clasifican los datos en diferentes categorías y los representan en una gráfica o tabla de frecuencias, resumen y comunican sus ideas sobre los datos representados de diferentes maneras. . . ” Lección 2-2 includes the TEKS mathematical process standards 3.1A, 3.1C, 3.1D, and 3.1F. The “Boleto de salida” activity identifies process standard 3.1A, which states, “Aplique las matemáticas a los problemas que surgen en la vida diaria, la sociedad y el trabajo.”

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

The materials for grade 3 include a description of how the TEKS are integrated and connected throughout the course in each Tema’s “Contenido” section. For example, Tema 1 “Significados de la multiplicación y la división,” includes a table that shows the order of the lessons and how the TEKS are incorporated throughout the topic. For lección 1-2 “Multiplicación, suma y la recta numérica,” the TEKS are 3.4E, 3.4D, 3.4K, 3.1C, 3.1E, and 3.1F. Temas 1 and 2’s “Contenido” sections list the content TEKS and corresponding TEKS process standards for every lesson, such as lección 1-1 “Maneras de juntar grupos iguales,” which includes the TEKS 3.4E, 3.4D, 3.1F, 3.1G and lección 2-6 “Resolver problemas que involucran operaciones de multiplicación,” which contains the TEKS 3.5B, 3.4D, 3.4E, 3.4K, 3.1B, 3.1E, 3.1F. This organization continues throughout all Temas, demonstrating the incorporation of the TEKS process standards across the course.

The grade 3 Guía del maestro also includes a description of how TEKS are incorporated and connected throughout the course. For example, in the program overview, the “TEKS Process Standards” and the “Problem-Solving Handbook” explain how the teal-colored process standards appear throughout the student edition and educator edition and identify the “Problem-Solving Model,” “Problem-Solving Model Recording Sheet,” and “Strip Diagrams” as resources that support multiple TEKS process standards. The overview also identifies the mathematical processes: apply math, plan, check, select tools, communicate, represent, analyze, connect, explain, and justify. Each unit overview within the Guía del maestro includes the “Vistazo al tema,” which contains the TEKS for each lesson, and the “Contexto matemático: Coherencia” sections, with the “Vuelve atras,” “Tema . . . ” and “Más adelante” subsections. These components identify the TEKS aligned to what was taught before, during, and after the topic. The 165-day Guía del ritmo de enseñanza includes a table stating that the “Estándares de procesos matemáticos de los TEKS están integrados a lo largo de cada tema.” For example, the guide lists the process TEKS 3.1A, 3.1B, 3.1C, 3.1D, 3.1E, 3.1F, and 3.1G, indicating that these standards are integrated across all Temas rather than taught in isolation. This guidance helps educators understand how the TEKS process standards are incorporated and connected from Temas 1–14.

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

Each unit in the grade 3 Guía del maestro materials includes a description of how the TEKS are incorporated within the Tema through the “Estándares de procesos matemáticos destacados en las lecciones.” In Tema 8 “Sumar y restar hasta 1,000 con fluidez,” the “Estándares de procesos matemáticos de los TEKS” table describes how the TEKS process standards are incorporated and connected throughout the Tema and includes student mathematical expectations for each standard. For TEKS 3.1A, for example, the materials state, “Reconocen cuando pueden aplicar las matemáticas para ayudarse a resolver problemas.” Tema 11 “Comparación y equivalencia de fracciones” highlights TEKS 3.1A and 3.1D, describes observable student behaviors aligned to each process standard, and includes educator questioning strategies that connect the process standards to fraction comparison and equivalence throughout the unit.

Additionally, the 165-day Guía del ritmo de enseñanza states that TEKS process standards 3.1A-3.1G are integrated throughout each Tema and provides a pacing guide that aligns every Tema with its corresponding content TEKS across all 14 Temas, demonstrating how the process standards continue throughout the course. In Tema 4, “Vistazo del tema: Resolver más problemas usando estrategias numéricas,” the materials include an overview table that organizes the instructional components of the unit. At the bottom of the table, a section labeled “TEKS” identifies the content and process standards addressed in each lesson. For example, in the “Investiguemos” section, the materials identify process TEKS 3.1C, 3.1D, and 3.1E.

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

The grade 3 Guía del maestro includes an overview of the TEKS process standards incorporated into each lesson. Paso 3 “Práctica y resolución de problemas” and paso 4 “Evaluar y diferenciar” both include an “Análisis de los ejercicios” table that provides an overview of the TEKS process standards incorporated into lección 6-1 “Elaboremos: Números hasta 100,000.” For example, paso 3’s “Análisis de los ejercicios: Relacionar; Práctica y resolución de problemas” table includes the TEKS 3.2A and 3.2B. Paso 4’s “Análisis de los ejercicios: Práctica adicional” table includes the incorporated process TEKS 3.2A and 3.2B. Additionally, lección 12-1 “Multiplicar por múltiplos de 10” lists TEKS process standards 3.1A-3.1C in the “Estándares de procesos matemáticos section.”

Furthermore, the Guía del maestro and Libro del estudiante include an overview of the TEKS process standards incorporated into each lesson. The Libro del estudiante lección 11-1 “Fracciones equivalentes” lists the content TEKS 3.3F and the TEKS process standards 3.1C, 3.1F, and 3.1G on the lesson opener. Students then use fraction strips to identify equivalent fractions, explain their reasoning, and compare fractional relationships during the lesson activities. Each lesson in the Guía del maestro includes a “Conocimientos y Destrezas Esenciales de Texas (TEKS)” section that identifies the knowledge and skills addressed in the lesson and connects the TEKS expectations to the mathematical concepts and procedures students are expected to develop.

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

The grade 3 Guía del maestro includes opportunities for students to think mathematically, persevere through solving problems, and make sense of mathematics. Lección 14-1 “Elaboremos: Ocupaciones e ingresos” includes guided support for each lesson to encourage mathematical thinking in paso 1 “Explorar y comentar,” where students identify various professions and the years of study needed to complete the studies. The materials ask: “¿Pueden pensar en un momento en el que hayan visto a alguien hacer un trabajo y hayan pensado que te gustaría hacerlo?” Students then use mathematical thinking to solve the problem. In paso 3 “Práctica y resolución de problemas,” students think mathematically through “Práctica guiada” and “Práctica y resolución de problemas.” The materials direct educators to provide the following guidance: “Pídales que identifiquen la profesión con una cantidad de años de estudio similar y pregúnteles qué notan sobre los ingresos.” Students apply their mathematical thinking in “Práctica y resolución de problemas” to solve problems. In Tema 14, lección 14-4, the “Investigar” section in “Gastos previstos y no previstos” provides four samples of student work that demonstrate different approaches to solving the same problem, giving students opportunities to think mathematically and analyze multiple solution strategies. Each student solves the problem using a different strategy, allowing students to compare and evaluate different mathematical approaches. The materials include educator prompts that encourage deeper mathematical thinking, such as “¿Son cosas que comprarias semanal o mensualmente?” and “¿De qué manera estos elementos son gastos no previstos?” These questions prompt students to reason about mathematical context to persevere through solving problems and justify their thinking.

Additionally, the Guía del maestro and Libro del estudiante provide opportunities for students to persevere through solving problems and think mathematically to make sense of mathematical content. For example, in the Libro del estudiante, lección 2-1 “Como factor” provides opportunities for students to think mathematically by engaging them in identifying multiplication patterns, organizing objects into equal groups, explaining how doubling and skip counting can be used to find products, and solving problems with missing factors and products. Students are prompted to develop a plan, explain their reasoning, and represent their solutions using models and equations. In Guía del maestro Tema 4 “Desarrollar GRIT, Operaciones de división: Pensar en la multiplicación” provides opportunities for students to develop confidence, resilience, and self-efficacy while solving mathematical problems. The materials include explicit educator guidance that encourages students to persevere as they work through challenging tasks such as “A medida que resuelven los problemas de división con 0 y 1, recuérdeles que el GRIT les ayudará a tener éxito.” Additionally, the materials include an example of a class conversation between the educator and a student named Mae that models how educators can guide students to think mathematically, reflect on their reasoning, and make sense of mathematical concepts.

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

The materials for grade 3 in Guía del maestro include support for students to understand, justify, and explain that solving problems and completing tasks can be done in a variety of ways. In lección 11-7 “Usar estrategias y puntos de referencia para comparar fracciones,” students see a table and an open number line. The instructions ask students to use the given data to find out who had the greatest distance by using the number line to show the fractions. The educator observes which strategies were used to compare fractions. The next section in the lesson, “Aprendizaje visual,” asks an essential question and is followed by class conversation with questions such as “¿Qué saben acerca de la cantidad de tela que Talia necesita para hacer cada bolsa de compras reutilizable?” This section includes a think-pair-share during “Hablar sobre las ideas matemáticas,” where students have the opportunity to share and explain how a number line can be used to compare fractions, leading to an opportunity to understand that problems can be approached in multiple ways as they justify their responses. The lesson continues with “Práctica guiada” and “Práctica y resolución de problemas.” In Tema 11, lección 11-7, the “Hablemos de matemáticas” section provides opportunities for students to develop mathematical understanding by explaining and justifying their thinking. Students are frequently encouraged to justify and explain their solutions with peers or in small-group discussions. Students work on a problem titled “¿Cuál no pertenece?” in which they develop their understanding of fractions and are asked to identify the fraction sequence that does not belong and justify their reasoning. The materials explicitly acknowledge that there are multiple correct answers because there are different ways to represent and interpret fractions.

Additionally, in Tema 9, lección 9-3, the “Aprendizaje visual” section in paso 2 “Conversación en la clase” provides opportunities for students to analyze, communicate, compare answers with their partners, and justify their mathematical thinking while exploring the essential question: “¿Qué figuras ven en la clase que parezcan cuadriláteros?” Students also participate in a think-pair-share routine where they discuss and compare their ideas about how the names of quadrilaterals help them identify and describe the attributes of each shape. During these discussions, students explain and justify their reasoning while considering different perspectives to deepen mathematical understanding. Additionally, the materials include a language routine in which students answer and justify prompts such as: “¿Un rectángulo es un cuadrado o un cuadrado es un rectángulo? Explíquenlo.” In Tema 3 “Multiplicar por números de 1 dígito,” lección 3-12 “Pila de Panqueques,” the “Representémoslo en 3 Actos” section has students apply their understanding of multiplication to determine how many pancakes can be made from a given set of ingredients and quantities. In “Acto 1” students analyze the situation and make predictions based on the information provided. In “Acto 2” they use mathematical reasoning to develop, represent, and justify solution models while applying multiplication concepts in a real-world context. Students may use different representations and strategies to solve the problem while explaining and justifying their mathematical reasoning. In “Acto 3,” students compare their solutions with the actual result and reflect on their reasoning. Finally, students extend their understanding by creating a new problem that applies the same mathematical concepts in a different situation, providing an opportunity to transfer their conceptual understanding to a new context.

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

The grade 3 Guía del maestro provides varying opportunities for students to do, write about, and discuss math with their peers and educators to make sense of mathematics. For example, lección 12-6 “Elaboremos: Representar el volumen” includes the “Hablemos de matemáticas section with “Vistazo rápido,” where students make sense of mathematics by presenting an image for five seconds and asking others to discuss what they saw as they ask questions such as “¿Qué forma tiene la figura?” “¿Cuál es la longitud?” and “¿Cuál es el volumen?” The materials prompt the educator to support students in making sense of mathematics through discussion and writing with “Organice a los estudiantes en parejas y pidales qie conversen y escriban sus respuestas.” In lección 13-6 “Medir el volumen líquido usando unidades usuales,” the students observe a fish tank and measuring cups (quart, pint, and cup) with instructions to decide which measuring cup should be used to fill the fish tank and justify how many more times it would take to fill the fish tank with the other measuring cups. The “Supervisar, seleccionar y poner en secuencia” small group activity guides the educator to work with students with prompting questions or by providing extensions for the students who may finish quicker. The “Aprendizaje visual” section follows with an essential question and a whole-class conversation, such as “Si Izaak llenó una taza de medir 8 veces para llenar otra pecera, ¿cuántos galones entran en la pecera?” This section also includes a think-pair-share activity during “Hablar sobre las ideas matemáticas,” where students have the opportunity to discuss what they know about capacity and measurement with their peers and the educator.

Additionally, Tema 4 lección 4-11 includes the “Representémoslo en 3 actos” activity, “En el jardín,” which engages students in mathematical thinking through discussion, written work, and collaborative problem-solving. In “Acto 1,” the “Lluvia de ideas para preguntar” section prompts students to consider the question: “¿Qué pregunta les resulta más interesante?” In “Acto 2, El modelo,” students solve the problem in writing and then participate in a whole-class discussion with peers and the educator to compare and explain their solution strategies. The materials include examples of two students, Marco and Marisol, who use different strategies to solve the problem. Students analyze these examples, discuss the different approaches with their peers and educator, and explain their mathematical reasoning. In “Acto 3,” students create and write a new mathematical problem related to “Acto 1.” Lección 2-7’s “Representémoslo en 3 actos” also requires students to make sense of mathematics through opportunities to do, write about, and discuss math with peers and educators through making predictions, having students develop and represent a mathematical model, compare their predictions to the total number of cookies, and identify relevant information. Additionally, students represent the situation using mathematical models, compare and discuss different solution strategies with their peers and educator, justify how their models solve the problem, evaluate the effectiveness of their approach, and create and solve a related mathematical problem.

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

The grade 3 Guía del maestro and “Modelo de resolución de problemas” include support for educators in guiding students to share and reflect on their problem-solving approaches. Lección 14-1 “¡Investiguemos! Ocupaciones e ingresos” includes four steps where educators guide students in their problem-solving approaches as they explain, argue, and justify their responses. In paso 1 “Investigar,” the materials prompt educators with questions to guide students to share and explain, such as “¿Qué cosas disfrutan hacer?” and “¿Pueden pensar en un momento en el que hayan visto a alguien hacer un trabajo y hayan pensado que te gustaría hacerlo?” The “Seleccionar y poner en secuencia” section includes “Relacionar estrategias de solución,” where educators guide students to identify the similarities and differences in the problem-solving strategies others used, as the materials lead into “Hablar sobre las ideas matemáticas” for students to share and reflect on their problem-solving approaches. Additionally, paso 3 “Práctica y resolución de problemas” includes a “Reflexión” section, which includes educator-prompted questions to guide students and an “Errores e intervención” section for students having difficulty with the exercise. In Tema 3, lección 3-1 includes an “Investigar” section with “Ejemplos del trabajo de los estudiantes,” which provides educator guidance for facilitating student reflection and discussion about problem-solving strategies. The materials present four samples of student work for the “Problema de la feria local A y B,” along with educator prompts that encourage students to reflect, explain, and justify their thinking. Questions include: “¿Cómo cambiarían los cálculos si dividieras la matriz en 1 columna y 3 columnas?” and “¿Por qué separaste las fichas de esta manera?” The prompts guide students in explaining their reasoning, evaluating the accuracy of their solutions, and arguing and justifying the strategies they used to solve the problem.

Additionally, in lección 13-3, “Actos 2–3” direct educators to have students share and compare different strategies for determining an ending time, explain how models such as number lines or clocks helped solve the problem, argue and justify why their solution is reasonable, and reflect on the effectiveness of their chosen approach while creating and solving related problems. Similarly, “¡Investiguemos!” sections provide supports for educators in guiding students through problem-solving. The paso 1 “Investigar” section, “Anticipar,” helps educators be prepared with support students may need as they work through the investigation by including student examples included in the materials. Educators are also prompted to pose questions such as “¿Puedes decirme o mostrarme lo que hiciste?” for students to explain, argue, and justify their problem-solving approaches. There is a small group opportunity in which student examples are referenced with suggestions on how to help the student and in which order. Students persevere through solving problems in aso 2 “Conectar” and paso 3 “Práctica y resolución de problemas.” The reflection section then guides the educator to challenge students to solve the problem in different ways and reflect on their problem-solving approaches. Students also participate in “Hablar sobre las ideas matemáticas,” a think-pair-share activity with their peers, with opportunities to explain, argue, and justify their solution strategies for the activity. In Tema 6, lección 6-5 includes the “Aprendizaje visual” section, where students solve three mathematical problems and respond to educator-guided questions that encourage them to reflect on their thinking, explain their reasoning, and justify their answers beginning with the essential question: “¿Qué notas sobre la recta numérica?” Students work through three problems involving estimation on a number line using problem-solving approaches. Throughout the lesson, the materials include educator prompts such as: “¿Sería 15,600 una estimación razonable? ¿Por qué?” These questions encourage students to explain their reasoning, evaluate the reasonableness of their solutions, and justify their responses using mathematical evidence to argue their responses for their problem-solving approach.

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 3 Guía del maestro includes prompts and guidance to support educators in providing explanatory feedback based on student responses and anticipated misconceptions. Lección 12-3 “Elaboremos: Estimar productos” includes “Prevenir malentendidos” in paso 2 “Aprendizaje visual,” which provides prompts and guidance for educators on how to give feedback based on student responses and anticipated misconceptions. The materials state, “Recuerde a los estudiantes que lo normal es redondear al número mayor cuando el número que se redondea es mayor que el punto medio.” In “Hablar sobre las ideas matemáticas,” the materials additionally include educator prompts and guidance such as “Pida a los estudiantes que compartan ideas en parejas para comentar otras maneras de estimar productos. Preste atención a las conversaciones sobre buscar patrones en los números o usar el dígito inicial en uno de los factores.” Additionally, in lección 12-3, students work on estimating products, and educators monitor and support students by preventing misconceptions and guiding students in developing a deeper conceptual understanding. Educators watch for misconceptions and provide explanatory feedback, such as with students who may forget how to round, and remind them that when rounding, they should round to the highest number when the number they are rounding is greater than the halfway point. During “Aprendizaje visual,” the materials support educators through the classroom conversation where anticipated student responses are included. For example, in Step A, the educator asks the student, “¿Por qué estimariamos un producto?” Student’s anticipated response: “Se estimaría si no tenemos números exactos para multiplicar, si no necesitamos una respuesta exacta o cuando queremos comprobar que la respuesta a un problema sea razonable.” To further develop the student’s understanding, the educator follows up with, “¿Por qué es útil redondear 36 a 40?” and the student’s response may be, “Este es uno de los sumandos.” The materials include explanatory educator feedback: “Sabemos cómo multiplicar 7 x 40 porque podemos usar una operación conocida.”

Additionally, in Tema 2, lección 2-5, the materials include educator guidance in paso 3 “Práctica y resolución de problemas” within the “Práctica guiada” section. The “Errores e intervención, Ejercicio 5” subsection identifies a common student misconception and provides explicit guidance for educators on how to address it. For example, the materials state, “Si los estudiantes tienen dificultad para responder a este ejercicio, entonces recuérdeles el trabajo que hicieron con la propiedad del cero de la multiplicación y la propiedad de identidad de la multiplicación. Si multiplico cualquier número por 1, ¿cuál es el producto? [Ese número]. Ahora, ¿qué pasa si multiplico ese mismo número por 0? ¿Cuál es el producto? [0]. ¿Por qué?” This guidance helps educators provide explanatory feedback by directing students to revisit the problem, analyze the relationship described in the task, and reconsider their initial response. In the lección 1-3 “Explorar y comentar” activity, students work on investigating how an array can represent a multiplication problem. The activity requires students to find a solution for arranging 12 patches on a poster in columns and rows. The materials guide educators to ensure students are arranging counters to represent equal rows. If students are unsure how to arrange the rows, the educator may ask, “¿Cómo pueden comprobar que todas las filas tienen la misma cantidad de parches en ellas?” To support the class in solving the problem, educators select possible solutions from two students related to multiplication, providing explanatory feedback. Though both students multiplied, they used a different amount in the columns and rows. By making this distinction, educators can demonstrate there are multiple ways to represent and solve a word problem using multiplication. The materials prompt educators to ensure students understand that the number of patches in a row is the same for each row by anticipating misconceptions.