enVision+ Texas Matemáticas, 01

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

Grade 1 materials in the Guía del maestro include a scope and sequence for 13 Temas aligned with the Texas Essential Knowledge and Skills (TEKS) in “Contenido y secuencia” for 135 days, 165 days, 180 days, and 210 days. The “Contenido y secuencia” for the instructional calendars includes a table with the concepts for each Tema. For example, Tema 1 focuses on “Comprender la suma y la resta” and includes the lessons, concepts, and the TEKS addressed within the progression of content throughout the year, varying accordingly in instructional pacing for each instructional calendar for the academic year.

Additionally, the Guía del maestro includes a scope and sequence outline with “Correlación con los conocimientos y destrezas esenciales de Texas.” Materials in the grade 1 Guía del maestro for “Contenido y secuencia” include a table with the TEKS and aligned lessons and pages from the Libro del estudiante and the Guía del maestro. For example, the grade 1 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 a table listing the TEKS taught 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 Guía del ritmo de enseñanza, grado 1 includes “Contenido y secuencia” documents for 135-day, 165-day, 180-day, and 210-day instructional calendars. Each instructional calendar includes a table with TEKS integration in the 13 Temas of the academic year in the materials, the days of instruction, and the TEKS for each Tema. For example, the materials include the 165-day Guía del ritmo de enseñanza sequence, with a suggested pacing of 13 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 “Operaciones de suma hasta 20: Usar estrategias” in “Contenido y secuencia: 135 días,” contains a table for the suggested pacing of the materials, including the days of instruction, the TEKS, differentiation, review, and evaluation. The table also includes materials to be used, 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 1 Content Organization Rationale” organized in 13 Temas with mathematical key concepts and student connections, including a “Grade 1 Content Organized to Build Connections” table with each Tema in unit order. For instance, Temas 1-5 focus on basic addition and subtraction facts, while Tema 6 focuses on patterns in data and graph representations. Grade 1 materials include key concept description with the intentional purpose of each unit and conceptual connections across Temas.

Additionally, materials in the Guía del maestro include a “Math Background and Coherence” section at the beginning of each Tema explaining how concepts connect to prior and future learning in the “Vuelve atrás” and “Más adelante” sections. For example, in “Contexto matemático: Conceptos clave - Operaciones de suma hasta 20: Usar estrategias,” the materials break down the progression of the Tema, including what students learn before and after it.

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

The online platform includes the “Protocolos de internalización y herramientas de observación” in a tools section that also provides resources such as “Protocolo de internalización del tema para el maestro” and “Protocolo de internalización de la lección para el maestro.” The grade 1 materials include guidance for unit and lesson internalization consisting of 13 and 16 steps, providing a thorough understanding of key learning objectives, sequencing, and instructional strategies.

Additionally, the Guía del maestro includes an “Elaboremos,” “Investiguemos,” and “Representémoslo” section for each lesson in the materials with internalization previewing the unit to understand key standards, unit objectives, vocabulary, and assessments. For example, expanded notes 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 online platform Savvas Realize includes “Protocolos de internalización y herramientas de observación” with observation tools and internalization protocols that include support and guidance for educators from instructional leaders. Resources for 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 1 materials provide notes at the beginning of each lesson in the Guía del maestro titled “Elaboremos,” “Investiguemos,” or “Representémoslo.” 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 to implement 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 1 Guía del maestro includes a math background section in “Contexto matemático: Conceptos clave” that breaks down 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, in “Adaptaciones del lenguaje,” the grade 1 materials incorporate vocabulary in context with mathematical meaning and outline the critical prerequisite vocabulary. For example, each Tema includes “Adaptaciones de lenguaje y discurso oral/escrito,” “Apoyo para el vocabulario del tema,” and “Transferencia metalingüística al inglés y cognados” sections. 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 Temas also break down the academic vocabulary by lesson to effectively teach 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” section. Materials 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 “La suma y la resta,” 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, in Guía del maestro at the beginning of each lesson, the “Elaboremos” section includes critical information for the lesson including TEKS alignment, lesson objectives, and other materials. For example, in lección 2–1 “Elaboremos,” the grade 1 materials include “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 1 in the “Plan de lección” provides materials required for instruction and the suggested timing for each lesson component in “Cronología de la lección.” For example, the grade 1 materials include a table that includes “Tiempo,” “Propósito,” and “Materiales” for the steps of the lesson in the lesson overview. The guidance in the lesson overview outlines the pacing of lessons and the lesson cycle within a given timeframe, which supports the educator in effectively delivering instruction of the materials.

Furthermore, in the “Plan de tema” section of the Guía del maestro, suggested time allocations are included for each lesson component with clocks at the top of all pages. For example, grade 1 materials in Tema 5, “Elaboremos, 5-2 Hallar los números desconocidos,” have a suggested timing for the lesson 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 1 Guía del maestro, the paso 4 “Evaluar y diferenciar” section provides formative assessment guidance with interventions, enrichment, and additional practice resources. For example, the “Comprobación rápida” is a formative assessment in paso 4 “Evaluar y diferenciar” with a point rubric that includes guidance for educators on 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 1 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 1 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 1 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 1 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 18 multiple choice questions with administration instructions at the bottom of the assessment. The unit level assessment follows the exit ticket in the guide and includes multiple choice, student 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 1 in the Cuaderno de evaluación assessment guide define each assessment and the intended purpose for diagnostic, summative, and formative assessments in a table. For instance, the grade 1 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.

Grade 1 materials in the Cuaderno de evaluación also provide a table with the definition for the varying types of assessments, including the type of assessment, the recommended time to administer the assessments, and the name 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.

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

The grade 1 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 under each section with guidance for educators. For example, the table in “How to Administer Assessments,” categorized as “Administration of Instructional Assessments,” provides educator guidance for preparing and monitoring assessments.

The materials for grade 1 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.

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

The grade 1 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” and “Evaluacion 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 1–13 at the end of the guide in alignment with the TEKS.

The grade 1 Cuaderno de evaluación “Evaluación para observar el progreso” section include summative assessment items aligned to grade-level TEKS and lesson objectives. Forma B includes items connected to lesson objectives that require students to compare lengths, interpret data from pictographs, and solve money problems using visual models, constructed-response items, and multiple-choice response formats aligned to TEKS expectations. “Boleto de salida” are formative assessments included in the grade 1 Guía del maestro with an educator-provided answer key. For example, lección 3-10 “Resolver problemas verbales con operaciones hasta 20” assesses TEKS 1.3B and 1.1B. Diagnostic assessment “Repasa lo que sabes” appears at the start of each Tema as a guided educator assessment. For example in Tema 4, lección 4-1 “Operaciones de resta hasta 20: Usar estrategias,” there are six guided educator questions that are TEKS-aligned for the grade level included in an “Análisis de los ejercicios” table.

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

The materials in the 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. The guide includes the table of item types in and performance tasks explaining the varying item types, such as text entry, inline choice, hot spot, drag and drop, multi-select, and more. Performance tasks require students to solve problems, explain responses, and represent mathematical thinking using drawings, equations, and written responses with multiple scoring criteria. The materials for grade 1 include varying levels of complexity with TEKS-aligned items, for instance, the Tema 10 “Tarea de Rendimiento” features opportunities for students to explain and justify their answers and the “Evaluación para observar el progreso, Forma C” includes multiple-response items.

The grade 1 materials in the “Evaluaciones del curso” resources include diagnostic, progress-monitoring, and summative assessments aligned with the TEKS with varying levels of complexity. The “Evaluación para oservar el progreso, Formas A-C” features TEKS-aligned items ranging in complexity levels with multiple-choice and text-entry response formats administered at the beginning, middle, and end of the year to measure student understanding. For example, the Tema 1 assessment consists of 12 questions. Eight of the 12 questions are multiple choice, while the other questions require the student to draw or write in their answer.

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

The materials for grade 1 include the Cuaderno de evaluación and “Guía de puntaje” for all Tema and lesson-level assessments with a scoring guide and answer keys. For example, the “Guía de puntaje” explains how educators use online assessment reports to interpret student mastery, group students based on performance data, and identify instructional support based on the instructional 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 Guía del maestro also includes guidance for analyzing assessment results and determining instructional responses based on student performance. For example, in lección 11-9, paso 4 “Evaluar y diferenciar,” the scoring guidance for “Comprobacion rápida” identifies scores for intervention and extension activities. The “Boleto de salida” includes a self-assessment response and guidance for using student results to determine instructional support. For each Tema, the grade 1 materials include a “Mi progreso y crecimiento” document to offer guidance on student performance before, during, and after the Tema.

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 1 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 1 Guía del maestro assessment analysis tools include instructional guidance based on student assessment performance. For example, in Tema 10, lección 10-2, 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. There are also quick checks within the lesson, where students complete a reinforcement activity if they receive a 0–3 score and an enrichment lesson if they score 4–5 points. 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 “Herramienta para profesores de progreso y crecimiento del alumno” includes progress monitoring tools to document student performance before, during, and after instruction. 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. In “Boleto de salida,” materials include a student self-assessment to track progress for the objective of the lesson. For instance, the student tracker consists of three options of “Puedo,” “Con ayuda,” or “No todavia,” with the student tracker listing each assessed unit and their corresponding lessons.

Additionally, in the Cuaderno de Evaluación, there are student-facing progress monitoring tools in the “Boleto de salida” that allow students to reflect on and document their comprehension of the lesson objectives. For example, in the “Mi progreso y crecimiento” exit ticket tool in Tema 4, lección 4-2, the self-assessment options for students to monitor their progress include a check-in of “Puedo,” “Con ayuda,” or “No todavia.” In the Guía del maestro, “Datos de las evaluaciones” include online data that track student progress both for individual students and the class. For instance, the educator tracker lists each unit and their corresponding lessons, the table names, the lessons, the TEKS, and objectives, as well as 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 1 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 and additional practice activities. For example, “Refuerzo para mejorar la comprensión, R 2-9” requires students to use counting-back strategies to solve subtraction problems, complete subtraction equations, and represent numerical relationships using numerals and manipulatives. Additionally, lección 7-1, paso 3 “Practica y resolución de problemas” includes guidance for “Práctica guiada.” Originally, students were expected to use count by tens using ten frames, then write how many tens make up the number. However, if they are having difficulty, the guidance under “Errores e intervención ejercicio 2” states, “Si los estudiantes tienen dificultad para contar de 10 en 10, entonces pídales que rotulen cada marco de diez 1, 2 y 3. Luego agregan un 0 después de cada número para mostrar 10, 20 y 30.”

Furthermore, the materials for grade 1 paso 4 “Evaluar y diferenciar: Comprobación rapida” include an “Actividad de intervención” as an assigned enrichment activity to be done with a small group of students. Tema 9, lección 9-2 features educator-led “Actividad de intervención” and “Práctica adicional” activities that require students to compare two-digit numbers using base 10 blocks, determine greater than and less than relationships, and justify comparisons using place-value reasoning. The materials include “Biblioteca de diferenciación” in Guía del maestro Tema 9 to provide targeted support through a variety of instructional formats. For example, the “Biblioteca de diferenciación” includes differentiated activities and resources and additional practice for students at varying levels of proficiency, such as projects and electronic games. The “Refuerzo para mejorar la comprensión” is also included in “Biblioteca de diferenciación” with included educator guidance on scaffolded lessons and differentiated instruction.

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

The grade 1 Guía del maestro includes a section titled “Adaptaciones del lenguaje” with a breakdown of vocabulary supports in sections of “Apoyo para el vocabulario del tema,” “Transferencia metalingüistica al inglés,” “Cognados,” and “Vocabulario Académico.” “Apoyo para el vocabulario del tema” contains three sections for the Tema’s unfamiliar vocabulary: “Vocabulario del tema,” “términos previos,” and “próximos terminos.” Additionally, a “Vocabulario en contexto” table includes the vocabulary word, math definition, and other meanings. For example, in Tema 8, the provided math definition for the word separar is “separar un numero” while another meaning is “establecer distancia.” The section further breaks down the words by lesson. In the Tema 8, lección 4-4 “Elaboremos” section of “Hablemos de matematicas,” the educator facilitates a math discussion where students are able to express their ideas and strategies using the given lesson vocabulary.

In addition, “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. In the “Valor” lesson, students are introduced to the term through a definition, contextual examples, discussion prompts, and opportunities to use the word in a sentence. The educator guide includes related vocabulary and discussion questions connected to mathematical concepts. The Spanish Academic Vocabulary Teacher’s Guide K–2 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 1 “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.

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 1, the “Biblioteca de diferenciación” contains varying resources for students for differentiated instruction and enrichment and extension activities. For example, the 13 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 8-6, paso 1 “Explorar y comentar, Para estudiantes rápidos” provide an extension activity for students to use a pattern to represent 115 in a variety of ways with base 10 blocks. Lección 8-6, paso 4 “Evaluar y diferenciar” provides guidance on the activity to be completed after the “Comprobación rápida” activity, depending on the score. If students scored 0–3 points. they complete an intervention or reinforcement activity, and if they scored 4–5 points, they complete an enrichment activity. Students are given the number 120 to compose with the blocks. After filling in the information on the table, the educator assigns a different way to compose 120 by using zero hundreds, 12 tens, and zero ones. Ultimately, students compose 120 a total of three different ways and then repeat the process with the numbers 103 and 110.

Furthermore, the "Biblioteca de diferenciación" features educator guidance that includes mathematics and literacy resources connected to classification, counting, patterns, and problem-solving skills. For example, in Tema 3, there are “Matemáticas y lectoescritura” activities such as “El gol,” “Adivinanza de fútbol,” “Dobles y casi dobles,” “Hacer un gol,” and “Terence Tao,” which require students to solve addition problems, apply doubles and near-doubles strategies, analyze informational text, identify number patterns, and explain mathematical thinking through written responses and visual representations. In lección 8-6 for “Grado 1: Ampliación,” the extension activity “Mostrar números en tres en fila” adapts a tic-tac-toe game so that each space contains a different way to compose 107, 117, and other numbers. Students are to place an X on the spaces that compose 117 and circles on the spaces that compose 107. Additionally, 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: “¿Dónde ven las matemáticas en la vida diaria?” The grade 1 Guía del maestro “Práctica adicional” directs educators to allow students to work on problems that will extend into future learning within the Tema, such as lección 8-6 “Más sobre formar números de diferentes maneras,” where the materials have students illustrate using base 10 blocks and tables to create three-digit numbers.

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 1 Guía del maestro paso 2 “Aprendizaje visual” and paso 3 “Práctica y resolución de problemas,” the materials provide prompts and guidance for modeling concepts of the lesson. For example, lección 8-1 provides explicit prompts under “Conversación en la clase” in a blue font, followed by what the student should say in brackets. There are a total of four questions to facilitate this section. Question A “seleccionar herramientas” includes prompts and guidance such as, “Pida a los estudiantes que usen bloques de valor de posición para cada paso. Cuando suman 1 a 47, ¿cambia el dígito de las unidades o de las decenas? [El dígito de las unidades].” The “Hablemos de matemáticas” section in each Tema provides guidance for introducing and explaining lesson concepts. Additionally, the “Resolución de problemas” activity provides specific prompts and discussion questions to guide student interactions and mathematical discourse. For example, students are instructed to interview a classmate using prompts such as “Cuéntame todo lo que sabes sobre sumar y restar decenas.” The materials also provide sample responses and follow-up questions, including “¿Qué sabes tú sobre sumar y restar?” In lección 10-2, the “Interpretación de datos” includes educator guidance for the “Mira de cerca” activity, where the materials direct the educator to display images and prompt students to observe, discuss, and describe what they notice.

In addition, the Guía del maestro for grade 1 Tema 2 “Estandares de procesos matemáticos de los TEKS” includes educator guidance and discussion prompts to support mathematical reasoning, such as “¿Qué números y símbolos pueden usar para representar sus fichas o dibujos?” “¿Cómo ayuda pensar en la suma a resolver un problema de resta?” and “¿Cómo pueden usar una recta numérica para sumar o restar?” In Guía del maestro Tema 1, the “Presentación del Tema” 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 also be found in Guía del maestro Tema 8, lección 8-1, after the following sections: “Práctica guíada,” “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.

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 the grade 1 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 lección 8-3, the paso 1 “Explorar y comentar” section guides educators to create groups and have students use base 10 blocks or illustrations to create 2 decenas and 20 unidades, having students discuss how the quantities are similar and different. Paso 2 “Aprendizaje visual” includes educator guidance for structured conversations using an animated visual to support students and analyze varying strategies and instructional approaches for the given concept. Additionally, the Guía del maestro describes three lesson types: “Investiguemos,” “Elaboremos,” and “Representemos en 3 actos.” Each lesson incorporates a different instructional approach. “Investiguemos” uses a problem-based learning approach, “Elaboremos” emphasizes direct instruction, and “Representemos en 3 actos” includes a real-world approach. Additionally, the materials 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, the “Planes de la lección para Texas” in lección 1-1 include lesson pacing, instructional routines, educator prompts, sample responses, intervention support, and differentiation guidance through the lesson. Paso 2 “Apredizaje visual” includes a “Conversación en la clase” section, featuring prompts and sample responses that guide students in identifying and comparing patterns for numbers 0–10. Additionally, Brainingcamp tasks incorporate educator guidance for an additional instructional approach with virtual manipulative integration. The “Counting on to Subtract” activity, specifically, includes online manipulatives that allow students to use linking cubes and a number line to count on to subtract within 20. The activity also provides extension opportunities that encourage students to generate fact families. Lección 8-4 “Elaboremos” guides educators to use the “Boleto de salida” to support students based on their results and to facilitate instruction with reminders such as, “Asegurese de que los estudiantes entiendan que en los números de dos dígitos, el dígito de las decenas siempre se escribe a la izquierda del dígito de las unidades.”

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 K–2 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.” For example, guided practice, adaptive practice, fluency practice, spiral review, math talks, and hands-on games include recommended implementation structures for each practice type. The materials recommend spiral review for guided practice, stand-up-and-think for guided and collaborative practice, and Tema review for guided, independent, and collaborative practice.

Additionally, grade 1 Guía del maestro lección 4-1 includes whole 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 of “Introducción toda la clase and 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 the lesson objectives with guided instruction. In lección 6-3, paso 2 “Aprendizaje visual, Hablar sobre las ideas matemáticas,” the educator has students participate in a think-pair-share small group activity, where students compare a table and a bar graph and point out similarities and differences. Paso 3 “Práctica y resolucion de problemas” includes digital and print practice for students to complete independently and directs educators to asks students to “Recuerde a los estudiantes que presten atención a los números en la parte inferior o en el costado de una gráfica de barras mientras construyen una gráfica de barras usando datos en una tabla.” Additionally, 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 1D,” where students work collaboratively to create a collage using items found in nature. They then use the objects in their collage to create and represent an equation, providing opportunities for hands-on, collaborative, and application-based learning.

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 1 Guía del maestro Tema 6, the materials at the beginning for each Tema include the “Adaptaciones de lenguaje” section with implementation guidance for educators to effectively teach the materials for emergent bilinguals. Sections include “Adaptaciones del lenguaje oral/escrito,” “Apoyo para el vocabulario del tema,” “Transferencia metalingüística al ingles,” “Cognados,” and “Vocabulario académico.” Grade 1 materials include the “Términos recomendados” of “Representar and Interpretar” for Tema 6. Tema 4 “Entender la suma” provides a table of vocabulary words, their mathematical meanings, and their alternate meanings in other contexts. In “Transferencia metalingüística al inglés,” “Competencias transferibles” states, “Tanto en inglés como en español usan las letras b y v. Los sonidos son más diferentes en inglés que en español: basketball/basquetbol; visit/visita.” “Competencias no transferibles” says, “Mientras que en español la posesión suele describirse mediante una frase preposicional, en inglés se usa un apóstrofe + s. Charlie’s brother/el hermano de Charlie.” Additionally, Tema 6 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.


Additionally, Tema 11, lección 11-7 also includes the “Apoyo al lenguaje” section, which provides guidance for building vocabulary and oral language through number patterns and counting discussions. The guidance directs educators to use groups of 10 objects and leftover ones to support counting and number representation and provides additional support for students who confuse tens and hundreds by using a block 10 during instruction. Additionally, the beginning of each new Tema has a section titled “Repasa lo que sabes” that provides language and vocabulary support for educators to implement with students to deepen understanding. The lesson includes aligned words and phrases 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.

The Guía del maestro Tema 6 section “Adaptaciones del lenguaje” includes a variety of embedded guidance for emergent bilingual support. For example, in “Adaptaciones del lenguaje y discurso oral/escrito,” emergent bilinguals will 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 unit along with previous and future units. A table titled “Vocabulario en contexto” includes the vocabulary word, math definition, and other meanings. For example, in Tema 6, the provided math definition for the word interpretar is “explicar algo,” while another meaning is “interpretar una pieza musical o un papel en una obra de teatro.” The section further breaks down the words by lesson, supporting emergent bilingual students in developing academic vocabulary, increasing comprehension, and building background knowledge with the terms in context with the Tema and real-life context. Additionally, the materials for grade 1 include “Transferencia metalingüistica al inglés” and “Cognados” with an embedded guidance to make oral and written cross-linguistic connections. The “Apoyo para el vocabulario del tema” section allows educators to provide emergent bilingual students with guidance on academic vocabulary in context within the Tema, building on and increasing their background knowledge.


Furthermore, the K–2 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 1-1 “Patrones espaciales para los numeros hasta el 10” 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 oral and written. Online materials include a Spanish Academic Vocabulary Teacher’s Guide K–2, which includes teaching suggestions for 40 words. 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 1 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 11” provides the practice opportunity of having students demonstrate their depth of understanding with a DOK level 2 with “Ejercicio 4,” as aligned to TEKS 1.7E. The materials include a scoring guide where the TEKS alignment can be found for each assessment. The Cuaderno de evaluación contains a performance assessment at the end of each Tema. “Tarea de rendimiento del tema 8” includes six questions and the corresponding scoring tables, “Tabla de análisis de las preguntas,” identifies the corresponding TEKS and DOK levels for each item. In the “Guía de puntaje,” the materials provide a cumulative evaluation for Temas 1–6. Students are evaluated on various skills, including addition and subtraction to 20, solving equations, and representing/interpreting data.

Additionally, the grade 1 Guía del maestro includes opportunities for students to model mathematical thinking and explain reasoning through exploration and visual practice in paso 1 “Explorar y comentar” and paso 2 “Aprendizaje visual.” For example, in lección 8-1, students use place value blocks and a hundreds chart to determine one more, one less, 10 more, and 10 less than a given number, explain how digits change in the tens and ones place, and justify solutions using models and discussion prompts aligned to the TEKS 1.5C and 1.1C. Furthermore, the Guía del maestro includes “Práctica guiada,” “Práctica y resolución de problemas,” and “Comprobación rápida” for additional practice opportunities over the course of the lesson with the inclusion of a formative assessment, such as in Tema 2 “Contar y comparar números del 0 al 10” in “Resolución de problemas,” where students count to find the number that is one more and one less than the number provided. Tema 8, lección 8-5 provides an extension opportunity for students who finish early, allowing them to continue practicing by representing the number 37 in two different ways. The activity includes the aligned TEKS, 1.2B and 1.2C, ensuring that students have multiple opportunities to demonstrate and deepen their understanding of place value concepts through concrete representations.

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, grade 1 includes concrete models, visual representations, and abstract reasoning where students first solve problems using concrete manipulatives such as counters, cubes, and place-value blocks during “Explore” and “Investigate” tasks, then transition to pictorial and visual models in the “Visual Learning” activities and animation before applying abstract mathematical symbols and procedures 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 “Explorar y comentar,” students count forward up to 20 using chips, linking cubes, or number lines as a strategy with a provided equation such as 7+4=11. In paso 4 “Evaluar y diferenciar,” students use a number line to solve the sum and complete an equation like 4+8=12, progressively increasing the rigor and complexity of the TEKS for the grade level. The sequencing in the materials progressively increases in rigor and complexity throughout the grade level.

Additionally, in lección 4-2, students first use ten frames during “Aprendizaje visual” to model the “make 10” subtraction strategy and explain how the strategy works. Students then complete guided and independent practice problems using ten frames before applying their understanding in real-world problem-solving tasks, higher-order reasoning questions, and practice activities that require them to analyze equations, represent subtraction strategies, and apply grade-level mathematical reasoning. In lección 1-1 students use different patterns to recognize quantities within 1–10. The content then progresses to “Situaciones de sumar y juntar” in lección 1-2, where students use concrete objects and visual models to develop an understanding of two types of addition situations. Furthermore, in lección 7-1 “Elaboremos, Contar de 10 en 10 hasta 120,” students were previously taught about numbers 11-19 and how each number was composed of a ten and some ones. The lesson’s rigor increases with the new material of place value and the understanding of how the numbers 10-120 are made of 10s and as students continue to build toward future learning, counting one by one to 120.

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

The grade 1 Guía del maestro coherently establishes a connection of patterns, big ideas, and relationships between mathematical concepts throughout all units using the “Contexto matemático, Coherencia” section, which includes the “¡Vuelve atrás!” and “Más adelante” subsections for the Temas. Tema 5 “Trabajar con ecuaciones de suma y resta” focuses on how the unit relates to what students have previously learned and what students will be learning in the future. For example, the TEKS K.2G in the previous grade includes students developing comprehension about whether two groups of objects are equal in number when comparing two numbers between 1 and 10, while the future TEKS 1.2G includes students using symbols such as >, <, and = to compare numbers. Additionally, the “Grade 1 Content Organization Rationale” features key concepts and connections between Temas, such as the key concept for Tema 11 “El dinero, partes iguales y la hora” and Tema 12 “Medir la longitud” for measuring and representing money, time, and length.

Additionally, the Guía del maestro includes coherence across the Temas, explicitly connecting patterns, big ideas, and relationships between mathematical concepts in the “Elaboremos” sections. The materials include the three sections of “Conceptos clave,” “Coherencia,” and “Equilibrio,” demonstrating the coherence in the Temas. The lección 4-7 “Escoger una estrategia para restar hasta 20” subsection, “¡Vuelve atrás!” highlights previously learned concepts, noting that students have already learned different strategies to solve problems involving subtraction. In the “En esta lección” subsection, students select subtraction strategies to solve problems such as counting, form tens, and use addition strategies. In the “Más adelante” subsection, the materials describe future learning. For example, in the following two lessons, students will apply addition or subtraction strategies to solve verbal problems. The Tema 12 “Medir la longitud” section “Más adelante,” references grade 2, stating, “Estimar mediciones: En el Tema 7, los estudiantes explorarán estimar longitudes (2.9A, 2.9E).” Furthermore, in reference to grade 3, it states, “Perimetro y area: En el Tema 9, los estudiantes usan su conocimiento sobre la medición de longitud para hallar el perímetro y el área de las figuras (3.6B, 3.7B).”

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.

Grade 1 Guía del maestro materials include coherence across units connecting the content and language students will learn in the future to the content learned throughout the academic year. In Tema 6 “Contexto matemático: Coherencia,” the materials connect prior grade K concepts such as comparing groups and categorizing objects to grade 1 skills involving data analysis, interpreting tables and pictographs, and solving comparison problems. The materials also connect current grade 1 concepts to future grade 2 learning involving bar graphs, pictographs, and data interpretation. Tema 4 has three sections that demonstrate coherence connecting content and language in “Adaptaciones del lenguaje,” where there are sections of “Vocabulario del tema,” “Términos previos,” “Próximos términos,” “Vocabulario en contexto,” and “Vocabulario para poner en contexto.” For example, in the grade 1 materials, the “Términos previos” includes “operaciones de dobles y más, operaciones inversas” and “Forma 10.” For “Próximos términos,” the upcoming term is sumando.

Additionally, in Guía del maestro Tema 4 “Presentacion del tema: Entender la suma,” the materials include the sections “Análisis de los ejercicios: Repasa lo que sabes,” “Palabras de vocabulario,” “Actividad de vocabulario,” and “Vocabulario académico.” The “Palabras de vocabulario” section lists key vocabulary words, including marcas de conteo, datos, encuesta, pictografía, tabla de conteo, and gráfica de barras. The “Actividad de vocabulario” section provides opportunities for students to deepen their understanding of these terms through the “Elemento didáctico 2, Vocabulario, Tabla de palabras,” which supports the spiraling and reinforcement of mathematical vocabulary. The “Contexto matematico, Coherencia” section includes information on what has been previously taught and how it connects to the current unit, as well as connections to the unit or grade level ahead. “Vuelve atrás” mentions that students have learned how to describe and compare two objects by their length and height in grade K and have an understanding of addition and subtraction from grade 1.

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..

Grade 1 Guía del maestro lección 3-2 “Contar hacia adelante para sumar hasta 20” includes three sections that demonstrate coherence at the lesson level connecting prior student knowledge to new knowledge and skills: “Conceptos clave,” “Coherencia,” and “Equilibrio.” “Conceptos clave” includes lesson objectives for new mathematical knowledge and skills, such as the lesson’s mathematics objective of counting forward to add using a number line. The “Coherencia” section includes “¡Vuelve atrás!” “En esta lección,” and “Más adelante,” where the lesson includes students’ previous knowledge of counting forward to add in addition operations up to 10 with a number line and having students use prior knowledge of concepts and procedures to apply for a sum up to 20.

In addition, lección 2-1 requires students to use their prior knowledge of counting forward and counting from a given number to solve addition problems and compare solution strategies, including counting on from the greater addend to find the total. Furthermore, the lección 12-2 “Medir con unidades de diferentes longitudes” section “¡Vuelve atrás!” says, “Previamente, los estudiantes compararon las longitudes de los objetos, de manera directa e indirecta.” The lesson also states, “Los estudiantes usan cubos y clips como unidades para medir la longitud de diferentes objetos.” Additionally, “Más adelante” states, “Luego los estudiantes usarán unidades estándar y una regla para medir la longitud de los objetos.” Tema 8, lección 8-2, paso 1 “Investigar” contains “Ejemplos del trabajo de los estudiantes,” which includes “Problema A” and its two tasks. In the first task, students represent the number 57 in tens and ones. The materials provide examples of students’ solutions, each demonstrating the application of previously learned concepts and procedures. For example, one student used 57 counters to fill five ten frames and represent seven additional ones. Solutions require students to apply prior knowledge of ten frames and base 10 representations, concepts and procedures that were first introduced in grade K, lección 2-6, and reinforced in grade 1, lección 7-1.

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

The Guía del maestro includes spaced retrieval opportunities with the application of previously learned skills and concepts in the lecciones and Temas. The “Elaboremos” section for each lección includes an “Hablemos de matemáticas” section for students to have mathematical discourse with previously learned skills and concepts across lessons and units. In lección 7-6 “Contar salteado hasta 120,” the “Hablemos de matemáticas” section has students select a number table that does not belong from three number charts and justify why it does not belong. Students use previous knowledge included in the materials in “Coherencia” and “¡Vuelve atrás!” where students previously counted one by one and 10 by 10, to the application of the strategies to meet the objective of counting by two by two, five by five, and 10 by 10 up to 120. 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 1 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 addition and subtraction within 20 while matching equivalent equations and practicing fact relationships through a partner activity. In Tema 7 “Repaso,” students retrieve information from lecciones 7-1, 7-2, 7-4, and 7-5, while reviewing concepts from lecciones 7-6 and 7-7. Additionally, “Repaso en espiral” is available digitally or as a print file for each lesson with 2–4 accompanying questions, including both multiple-choice and open-ended questions.

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

The materials also provide interleaved practice opportunities with previously learned skills and concepts across lessons and units in “Repaso del tema” and “Repasa lo que sabes” sections. In Tema 7 “Presentación del tema, Números hasta 120,” the materials in “Repasa lo que sabes” include instructions for students to review vocabulary including suma, total, and partes, as well as word problems, as they review previously learned concepts. There is also an “Análisis de los ejercicios: Repasa lo que sabes” table, which lists the TEKS being reviewed in the lesson, such as 1.5D and 1.5F. Additionally, Tema 10 “Repaso del tema” includes review activities from lecciónes 10-1 through 10-4 that require students to classify and group two-dimensional figures, identify attributes that define shape, compare geometric attributes, and create two-dimensional figures using geometric vocabulary and representations. Tema 7 “Repasa lo que sabes” also gives students the opportunity to demonstrate and practice their different problem-solving abilities by switching between problem types and strategies. The unit review begins with vocabulary comprehension and ends with solving word problems. The interleaved practice promotes flexible thinking and gradually increases in complexity.

Furthermore, the materials provide interleaved practice opportunities with previously learned skills and concepts in the grade 1 Guía del maestro and “Biblioteca de diferenciación.” In the Guía del maestro, interleaved practice opportunities are found in “Levántate y razona,” which requires students to use previously learned concepts and procedures.

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 9-8 “Inversión de dígitos,” “Acto 1, El anzuelo,” students interpret mathematical concepts and situations by formulating mathematical questions with guidance such as “¿Qué pregunta les resulta más interesante?” and “¿Qué pregunta podríamos responder con las matemáticas?” Additionally, students 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, as they are asked, “¿Qué suposición necesitan hacer para usar un modelo matemático?” The section features student examples of ordering numbers from least to greatest, including student errors. In Tema 3 lección 3-7, students analyze the work of Taylor and Benjamín as they use ten-frame models and equations to determine the results of two spins in a game. Students interpret the representations to identify the numbers shown, analyze the strategies used to solve the problem, and evaluate whether the solutions correctly answer the question. Reflection questions such as “¿Tiene sentido el trabajo de Taylor?” and “¿Tiene sentido la respuesta de Benjamín?” require students to assess the validity and effectiveness of the models and reasoning used to solve the problem.

Additionally, in grade 1 Guía del maestro lección 6-7 “Gomitas deliciosas,” the content objective is to use addition to solve a problem that may arise in everyday life. In short, “Los estudiantes tienen la tarea de determinar cuántas gomitas de cada color hay en ambas bolsas, dada la información sobre el número de gomitas de cada color en cada bolsa.” Students participate in a question brainstorm after watching the video for this lesson. The “Pregunta principal” is “¿Cuántas gomitas de cada color hay en ambas bolsas?” As a whole group, students discuss their individual predictions while they share 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 then analyze and evaluate their models as they transition from “Acto 2” to “Acto 3.” In Tema 2 “Levántate y razona,” students interpret information from a problem involving two vases with the same number of flowers, analyze possible totals using drawings and other representations, and justify their reasoning. Students examine sample student work that uses pictures and counting representations to solve problems and participate in a gallery walk to analyze multiple solution methods. The educator then facilitates opportunities for students to comment, explain, and debate strategies, requiring them to evaluate the validity and effectiveness of different mathematical representations and approaches. Furthermore, in “Refuerzo para mejorar la comprensión,” activity 1-2, students interpret the model shown and observe how to add the given number of ducks. Students then analyze the next problem where they are given a total (five books) and must choose one strategy to help them solve how many books are on the desk and in the backpack. Finally, students are given a problem where there are five dolls and four trucks. Students must determine how many in all and to draw the parts by solving any way they choose.

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

The grade 1 materials include varying questions and tasks that require students to create models to represent mathematical situations. For example, in lección 7-8 “Representémoslo en 3 actos, Súper Selfie,” 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 model with questions like, “¿Qué suposición deben hacer para usar un modelo matemático?” The materials also include student examples, such as their grade 1 models representing a “selfie” with the required information for their models. Examples include one student creating an array and another making connections from ones to tens. Furthermore, in Tema 5, lección 5-8 “Demasiado pesado,” students model a balancing-scale situation to determine how to make both sides equal. During “Acto 2,” students create models using drawings and counters to represent the number of erasers on each side of the balance and determine the difference between two quantities. Student work samples demonstrate multiple representations, including drawings, counters, and equations, used to model the situation and justify solutions. In “Acto 3,” students use their models to explain how adding or removing erasers affects the balance and to verify their solutions.

Additionally, in the Libro del estudiante Tema 5, lección 5-5 “Resolver problemas verbales con tres sumandos,” students use information about pears, apples, and oranges to solve an addition problem involving three addends. Students create two different addition equations to represent the situation and determine the total number of fruits, modeling the mathematical relationships among the quantities in the problem. Furthermore, the “¡Investiguemos! Lecciones” consists of 4 steps: paso 1 “Investigar,” paso 2 “Relacionar,” paso 3 “Práctica y resolución de problemas,” and paso 4 “Evaluar y diferenciar.” For lección 10-1 “Clasificar y agrupar figuras bidimensionales,” the content objective states that students will investigate how to join figures to create drawings, using their prior knowledge of identification and comparison of circles, triangles, rectangles, and squares. Paso 1 starts by asking if they have ever made a card for a friend or family, and they describe the drawings they made on the card. The corresponding student activity book has a designated space for students to draw an animal using three or more figures, with visual representations of the shapes that can be used. In the second activity, students draw the figures that they used and circling the figures that have straight sides.

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

The grade 1 Guía del maestro provides questions and tasks for students to apply conceptual understanding to new problem situations and contexts. For example, in Tema 9, lección 9-5 “Ordenar numeros en una recta numérica,” students determine the location of numbers on a number line by using their understanding of tens, ones, and benchmark numbers. Student work samples show students using a hundreds chart and a number line to identify the position of 23 and explain why it is closer to 20 than 30. The lesson also prompts students to justify their reasoning using place value and number relationships in lección 5-4 “Elaboremos, Hacer ecuaciones verdaderas.” The “Hablemos de matemáticas” section provides grade 1 students with questions, tasks, and opportunities to apply sentido numérico by incorporating TEKS 1.5E and 1.5F to describe the pattern and complete three equations answering the following questions, “¿Qué número hace verdadera cada ecuación?” and “¿Cuál será la siguiente ecuación?” Additionally, the materials include guidance for educators to direct students to discuss their responses in small groups and identify, describe, and extend the pattern as they apply conceptual understanding to new problem situations and contexts.

Additionally, the Guía del maestro and Recursos para Desarrollar la competencia matemática include questions and tasks that provide opportunities for students to apply conceptual understanding to new problem situations and contexts. For example, in lección 6-4 “Representar e interpretar datos,” students use information about animals observed in a natural park to organize data and represent the results using a table, pictograph, bar graph, or tally chart. Students then analyze the data to answer questions and compare quantities, applying their understanding of data representation and interpretation in a contextualized setting. The lesson prompts students to apply their understanding of measurable attributes in a new context and communicate conclusions. In lección 8-2 “Números formados con decenas y unidades,” paso 2 “Relacionar,” students apply conceptual understanding to new problem situations and contexts by working through problems in which they decompose numbers such as 46 into four tens and six ones. Students are also challenged to decompose 46 in different ways. In the “Hablar sobre las ideas matemáticas” section, students participate in think-pair-share activities to compare different ways tens and ones can represent a number. In Tema 7 “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 5D asks students to answer the question, “¿Quién obtuvo más fichas después de jugar a las damas?” This task requires students to apply their conceptual understanding of addition to solve a real-world problem in a new context. The materials also include a table summarizing all four projects (5A, 5B, 5C, and 5D), across which students are expected to create, cut, draw, investigate, and play while applying previously learned mathematical concepts in new situations. These project-based tasks encourage students to transfer their conceptual understanding to meaningful contexts and demonstrate their learning.

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

Grade 1 materials provide tasks that are designed to build the automaticity and fluency necessary for students to complete grade-level tasks through the “Desarrollar automaticidad” section included in each Tema. For example, Tema 9 “Partes iguales y fracciones” contains an activity for TEKS 2.4B for students to find the sum or the difference and shade a route to the “salida/meta” following only even numbers moving upward, downward, or to the left and right. Additionally, there is an additional activity in “Otra actividad” and an enrichment activity in “Desafío adicional” aligned to TEKS 2.1C, 2.4B. In Tema 7’s “Biblioteca de diferenciación” “Juego: ¿Cuánto más largo?” students compare the lengths of objects using rulers, determine how much longer one object is than another, and move game pieces based on correct responses. Students repeatedly solve measurement comparison problems involving pencils, clips, nails, screws, crayons, and glue sticks while using centimeter measurements to determine the difference in length. These tasks include repeated practice with comparing and measuring lengths using standard units.

Additionally, the grade 1 Guía del maestro includes tasks to build students’ automaticity and fluency through the paso 3 “Práctica y resolución de problemas,” where students demonstrate their comprehension of the content and fluently apply their knowledge in order to find the solution. The interactive activity builds in rigor, beginning with a guided practice solving an addition problem before continuing with solving basic addition math facts, solving addition word problems, solving problems using higher-order thinking skills, and concluding with a STAAR Assessment practice question. In the Libro del estudiante, the “Desarrollar fluidez” section provides a task designed to help students develop automaticity and fluency with two-digit addition and subtraction within 100. The materials include a table containing two-digit addition and subtraction problems. The activity also features a section titled “Sigue la ruta,” which directs students to, “Sombrea una ruta que vaya desde la salida hasta la meta. Sigue las sumas y diferencias que sean números pares.” Students may move only up, down, left, or right as they identify the correct path based on even-numbered sums and differences. Students build automaticity and fluency by solving multiple two-digit addition and subtraction problems within 100.

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 8-4 “Elaboremos, Formar números con grupos de decenas y unidades” and the “Detective de números” activity in “Hablemos de matemáticas,” which has students analyze hints to figure out the mystery numbers with provided clues. Materials provide opportunities for practicing the application of efficient, flexible, and accurate mathematical procedures by providing clues for mathematical thinking and discourse to take place, such as “El primer número es 10 más que el segundo número,” “El segundo número es 1 menos que el tercer número,” and “El tercer número es 16.” In Tema 10, lección 10-8 “Atributos que definen y atributos que no definen figuras tridimensionales,” students analyze three-dimensional figures using a table that organizes attributes such as faces, vertices, edges, and the ability to roll. Students discuss similarities and differences during “Hablemos de matemáticas” and apply their understanding in the “Boleto de salida” by identifying attributes that define or do not define three-dimensional figures.

Additionally, in Tema 4, lección 4-1 “Contar para restar,” students solve a subtraction problem involving 13 dumplings and five eaten dumplings. Student work samples demonstrate different procedures, including counting backward on a number line and crossing out objects in a drawing to determine that eight dumplings remain. The lesson supports the use of multiple representations to solve and verify subtraction problems. Additionally, in the Libro del estudiante, the lección 5-2 “Hallar los números desconocidos” section “Elaboremos” provides opportunities for students to solve problems using efficient, flexible, and accurate mathematical procedures. Students solve the following problem: “Halla el número que falta en la ecuación 7 + . . . = 13. Explica cómo hallaste el número que falta.” The task supports flexibility by allowing students to select and apply different solution strategies. The materials include two examples of student work demonstrating different approaches to solving the problem. The task also supports efficient mathematical procedures because students may use either counting-on or the inverse relationship between addition and subtraction to determine the unknown number. In addition, the activity promotes accuracy because students must correctly apply their chosen strategy and verify that the completed equation is true.

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 8-10 “Representémoslo en 3 actos, ¡Tantos vehiculos!” “Acto 1 El anzuelo” includes 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 5, lección 5-1 “Expresiones iguales,” the “Seleccionar y poner en secuencia” section guides educators to present student work that includes misconceptions and correct reasoning related to equivalent expressions. Students compare different strategies, determine whether expressions have the same value, and explain their reasoning during the “Relacionar estrategias de solución” discussion. Additionally, students have opportunities to evaluate solutions through “Práctica y resolucion de problemas,” “Reflexión,” “Comprobación rápida,” and “Práctica adicional,” where they verify answers, analyze expressions, and justify whether equations are true.

Additionally, in the Libro del estudiante, Tema 2, lección 2-1, students determine the total number of beads on bracelets using different strategies and representations. The lesson directions state that students may use any strategy to find the total number of beads and then explain their strategy. Students also create and solve a new bracelet problem using different methods and discuss why using different strategies to find a sum can be useful. Furthermore, in Guía del maestro lección 6-7 “Gomitas deliciosas,” the content objective is to use addition to solve a problem that may arise in everyday life, including using data. The lesson states, “Los estudiantes tienen la tarea de determinar cuántas gomitas de cada color hay en ambas bolsas, dada la información sobre el número de gomitas de cada color en cada bolsa.” Students participate in a question brainstorm after watching the video for this lesson to respond to the “Pregunta principal of “¿Cuántas gomitas de cada color hay en ambas bolsas?” As a whole group, 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. Students can 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 already solved. In Tema 3, lección 3-2 “Contar hacia adelante para sumar hasta 20,” students complete the task: “Abby tiene 4 cubos. Salina le da 7 cubos más. ¿Cuántos cubos tiene Abby ahora? Muestra tu razonamiento.” The materials include two student samples that show different solution strategies. The activity provides opportunities for students to share and compare their solutions, evaluate different procedures, and discuss how each strategy leads to the same answer. These opportunities promote efficiency because students can practice counting and applying a strategy. They promote flexibility because students use different representations, such as a number line and counters. The task also supports accuracy because students must verify that both procedures correctly show a total of 11 cubes.

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

The grade 1 Guía del maestro includes embedded supports to help educators guide students toward increasingly efficient approaches. For example, lección 9-1 “Mayor que,” 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: “¿Existe otra manera de resolver el problema?” Additionally, the materials in paso 2 “Hablar sobre las ideas matemáticas” contain embedded supports to guide students in approaches, such as “Pida a los estudiantes que participen en una actividad de pensar-trabajar en parejas-compartir para discutir cómo indicar si un número es mayor que el otro. Esté atento a los estudiantes que usan los términos mayor que o menor que para comparar los dígitos en la posición de las decenas y los dígitos en la posición de las unidades.” In Tema 13, lección 13-5, students determine which jar contains more money by modeling and calculating the value of different coin collections. During “Acto 2,” students use different strategies to organize and count coins, and the educator prompts students to discuss how their methods helped solve the problem efficiently. In “Acto 3,” students compare their solutions to the revealed answer, evaluate the effectiveness of their approaches, and consider how their models could be improved.

Additionally, the grade 1 materials provide embedded support in the Tema 12, lección 12-1 “Seleccionar y poner en secuencia” section, which directs educators to present student work in a progression from solutions that do not align objects with the train of 10 cubes, to solutions showing objects with approximately the same length, and finally to solutions showing objects that are longer than the train of 10 cubes. Additionally, “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 and promote increasingly efficient mathematical approaches. For example, the materials include questions such as: “¿Qué información se brinda en este problema verbal?” “¿Qué saben?” “¿Qué hay que hallar?” “¿Cómo podrían resolver este problema?” “¿Han visto este tipo de problema verbal antes? ¿Cómo lo resolvieron?” “¿Se pueden usar objetos?” “¿Se puede hacer un dibujo?” “¿Se puede escribir una ecuación?” “¿Usaron la suma para resolver este problema? ¿Y la resta?” and “¿Tiene sentido la solución? ¿Cómo se puede comprobar?”

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

The materials for grade 1 explicitly state 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 5 “Trabajar con ecuaciones de suma y resta,” “Comprensión de conceptos,” students use objects or colored chips to represent quantities on both sides of the equation aligned to TEKS 1.5E, 1.5F, and 1.3D. Additionally, in “Destrezas en procesos y automaticidad,” materials explicitly state the procedural emphasis of the TEKS, such as using the associative property to add, for example, “Al sumar múltiples sumandos, los estudiantes a veces pueden encontrar que es más fácil empezar con un doble o dos sumandos para formar 10,” for Tema 5. In Tema 9 “Contexto matemático, Equilibrio - Comparar y ordenar números,” the “Comprensión de conceptos” section identifies conceptual expectations, including comparing and ordering numbers using symbols and a number line while developing an understanding of place value. The “Destrezas en procesos y automaticidad” section identifies procedural expectations, including using place-value concepts and base 10 representations to compare numbers and determine whether a number is greater than, less than, or equal to another number. The “Aplicaciones” section connects these concepts and procedures to comparison situations in real-world contexts.

Additionally, Tema 11 “Presentación del tema: El dinero, partes iguales y la hora” includes the essential questions “¿Cómo puedes contar el tiempo y decir la hora?” and “¿Cómo puedes describir partes iguales?” These questions connect instruction to the TEKS process standard 1.1A through the “Paseo de matemáticas” and provides a prerequisite review activity aligned to the TEKS 1.6A, 1.6D, and 1.5A in the “Análisis de los ejercicios” table. In Tema 4, lección 4-5, the materials include a table titled “Análisis de ejercicios: Práctica y resolución de problemas.” This table explicitly identifies the exercise, PDC, content TEKS, and Ppocess 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 3–9. The materials distinguish between the content TEKS and the process TEKS, explicitly identifying the mathematical content and process standards addressed by each exercise and explicitly communicating the conceptual and procedural emphasis of each task. Furthermore, in “¡Investiguemos! Lección 3-1,” students begin to develop an understanding of why counting on is used and how they can count on to find the sum for addition facts. This concept connects to a greater conceptual understanding of addition as indicated in lección 3-8, where students use what they know to solve addition facts within 20 using various tools and strategies such as counting on, making 10, and near-doubles facts.

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 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 1-3 “Sumar y juntar” features concrete models in paso 1 “Explorar y comentar” as students use colored chips or linking cubes to work with concrete objects to add four dogs and three more dogs. Paso 2 “Aprendizaje visual” also includes pictorial representations for students to recognize pictorial models representing the sum of 4 + 2 = 6. Additionally, in paso 3 and paso 4, students use abstract representations of addition as they employ strategies to create an addition 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 8, lección 8-1 “Aprendizaje visual” and “Práctica guiada,” students use a tabla de 100 and bloques de valor de posición to determine numbers that are 1 more, 1 less, 10 more, and 10 less than a given number. Students analyze highlighted numbers on the hundred chart and place-value models and then record numerical responses to complete the guide practice tasks. The lesson includes concrete model place-value blocks, pictorial representations of the hundred chart and place-value visuals, and abstract representations of numerical responses. In Tema 8, lección 8-2, paso 1 “Investigar, Cómo formar números con decenas y unidades de diferentes maneras,” students represent numbers using tens and ones in multiple ways. The materials present a problem-solving task and instruct students to use connecting cubes or counters to represent and explain their answers. Students are encouraged to choose any strategy that helps them model the problem, providing opportunities to use concrete manipulatives, pictorial representations, or abstract representations. In the “Manual de Resolución de problemas,” the materials provide a problem-solving guide and sheet for students to refer to and utilize 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.

Each lesson’s program overview includes supports for students in connecting, creating, defining, and explaining concrete and representational models to abstract concepts as aligned to the TEKS. 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 3-8, students work on choosing strategies to add within 20. During the “Explorar y comentar” section of the lesson, students can choose between using objects, drawings, or words to solve an addition problem. Two student samples are shown in which one student uses counters and an equation to solve and represent, and the other uses linking cubes and an equation to solve and represent. In the “Relacionar” portion of the lesson, the educator facilitates a whole-group conversation referencing student work and has students make the connection from the concrete and representational task when solving the problem to abstract concepts.

Additionally, the grade 1 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. In Tema 1 “Aprendizaje Visual,” the lesson begins with the question, “¿Cómo pueden observar y usar patrones de puntos para saber la cantidad de puntos sin contar?” Students observe visual models and use counters as concrete models to represent and practice different ways to make 5. Finally, students write the numeral 5 as an abstract representation. Throughout the lesson, students connect visual representations, concrete manipulatives, and abstract symbols to develop a conceptual understanding of the number 5. In “Modelo de resolución de problemas: Hoja de anotaciones,” students analyze information, select a representation such as drawing, diagrams, tables, graphs, or equations, and determine a solution. The annotation sheet includes a student example that represents a problem about marbles using drawing and numerical representations, connects the model to the equation 8 + 2 = 10 and 10 + 2 = 12, and includes a written justification explaining why the solution is reasonable and an evaluation of the problem-solving process. In Tema 1, the lesson builds in rigor and provides opportunities for students to demonstrate their knowledge of the concepts, connecting tasks by using concrete and representational models to solve problems. For example, in lección 1-2, students use concrete tools like linking cubes or counters, as well as visual models or drawings, to build their understanding of how to represent the two types of addition problems: adding to and putting together. In lección 1-4, students extend their understanding of addition to solve more abstract problems, such as part-part-whole, where both addends are unknown.

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

The Guía del maestro provides students with varying opportunities through the use of visuals, manipulatives, and other language development strategies to develop academic mathematical language, such as in Tema 2 “Sumar y restar hasta 10.” The materials provided in “Presentación del tema” include the “Actividad de vocabulario” and “Vocabulario académico” sections, which include reinforcements in academic mathematical language where students practice with other classmates or in a virtual setting. In “Actividad de vocabulario,” the materials provide varying activities for language development through language development activities such as having students use images, words, numbers, or symbols to demonstrate what the vocabulary words mean. In “Vocabulario académico,” the materials provide online activities through visuals, manipulatives, and other language development activities to present or review words in the Tema. The lección 2-2 “Apoyo al lenguaje” section has students use a number line visual and manipulative to model a sum by identifying one addend and counting forward to represent the second addend. Students respond to educator questions about why they begin counting from the larger addend, explain how the number line represents the counting strategy, and read the equation aloud to identify the sum.

Additionally, the Libro del estudiante “Aprendizaje visual” section introduces mathematical vocabulary through visual models and guided mathematical discussion. In lección 3-3, students use manipulatives with connecting cube models and equations to compare sumas de dobles and sumas de casi dobles, explain how a doubles fact helps solve a near doubles fact, and respond to the “Hablar sobre las ideas matemáticas” prompt by explaining how knowing 7 + 7 helps solve 7 + 8. In Tema 4, lección 4-1 “Investigar,” paso 1 provides students with visuals of different vehicles with different numbers of wheels. In the “Presentar la investigación” section, students work on “Representar la suma” and practice academic vocabulary such as contar and número. In “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 “¿Cuál de estos vehículos han visto?” “¿Pueden adivinar cuál es el monociclo?” “¿Pueden contar sobre un vehículo con ruedas que tengan o hayan probado?” and “¿Cuántas ruedas tiene?” These questions allow students to share their experiences while reinforcing academic vocabulary. The materials include four examples of students’ work, providing students with opportunities to explain their solutions through the use of manipulatives and visuals using counters and drawings 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 grade 1 Guía del maestro contains embedded educator guidance to scaffold and support student development and use of academic vocabulary throughout the academic school year. In lección 12-4 “Elaboremos, Operaciones con 5 en un marco de diez,” the “Apoyo al lenguaje” section features embedded instruction that guides the educator to scaffold and support students’ development and use of academic mathematical vocabulary in context. For example, the materials say to ask students, “¿Por qué creen que se llama un marco de 10?” and direct the educator to “Pida a los estudiantes que trabajen de manera autónoma el uso del marco de 10 para resolver operaciones de suma.” Embedded educator guidance incorporates oral language and mathematics writing activities that provide structured opportunities for students to review, discuss, define, and apply academic vocabulary connected to the mathematical concepts in the Tema. Tema 12 “Repaso del tema, Medir la longitud” includes a “Repaso de vocabulario” section with educator guidance that directs students to compare classroom objects using the vocabulary terms más largo and más corto during an oral language activity and a mathematics writing activity in which students compare the lengths of shoes and write comparison statements using vocabulary from the Tema, reinforcing the use of mathematical language in context.

Additionally, the materials for grade 1 include embedded educator guidance that scaffolds academic mathematical vocabulary for students in context, providing structured vocabulary activities that support students in defining, discussing, and applying mathematical vocabulary through graphic organizers, collaborative discussions, and digital resources. Tema 8 includes an “Actividad de vocabulario” that directs educators to use “Elemento didáctico 4, Organizador gráfico: Dibujar la palabra” to help students represent vocabulary terms with pictures and record the corresponding word. Students draw place value tables to demonstrate mathematical concepts related to the vocabulary terms. The “Vocabulario académico” section directs educators to use the online academic vocabulary activities to introduce or review vocabulary before students apply the terms throughout the lesson. In Tema 3, lección 3-2 “Aprendizaje visual: Conversación en la clase” includes educator guidance for “Hablar sobre las ideas matemáticas” to facilitate mathematical discussions by asking students to explain their thinking and listen to where classmates begin counting and how many ones they count on while solving addition problems. The materials also provide questions that support students’ oral use of academic mathematical vocabulary. For example, educators ask, “¿Qué notan sobre la recta numérica? ¿De qué otra manera podrían usar la recta numérica para hallar 3 + 8? Expliquen. ¿Cómo ayuda comprender los términos menor y mayor a resolver problemas de suma usando la recta numérica?” These educator-guided discussions scaffold students’ use of academic vocabulary, including recta numérica, sumar, contar hacia adelante, mayor, and menor.

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 1 materials include embedded educator guidance supporting student application of appropriate mathematical language, such as discourse opportunities. The Guía del maestro lección 2-2 “Elaboremos, Contar hacia adelante para sumar hasta 10” features educator guidance to support student responses with questions and tasks with the use of mathematical language such as “¿Por qué número empezarán a contar hacia adelante?” and “¿Cómo pueden mostrar el conteo hacia adelante usando la recta numérica?” Additionally, the materials include the “Hablemos de matemáticas” section, which prompts educators to support the application of appropriate mathematical language through student discourse with, “Divida a los estudiantes en parejas y pídales que compartan el método que usaron para determinar cuántos hay,” and questions for students such as, “Cómo contaron hacia adelante?” Additionally, lección 9-2 “Compara números” introduces the vocabulary mayor que (>) and menor que (<); and the “Apoyo al lenguaje” section guides educators to ask questions such as, “¿Cuántas placas de centenas hay?” “¿Cuál es el valor de 1 placa de centenas?” and “¿Qué número tiene más unidades?” while providing example responses in brackets. The “Hablemos de matemáticas” section directs educators to facilitate classroom discussion by asking students to explain their reasoning about the images and the “Boleto de salida” reinforces students’ use of comparison language with place-value models. “Actividad de intervención” embeds educator guidance to support the application of mathematical language, including syntax, with the following: “Pídales que digan y anoten un enunciado para comparar sus números en este formato: 12 es menor que 16.”

Additionally, Guía del maestro lección 6-4 “Representar e interpretar datos,” includes the “Rutina de lenguaje, Tres lecturas,” which guides educators to ask questions such as “¿De qué trata la tarea?” “¿Qué animales ven Naomi y Roshan?” “¿Qué información se da en la tarea?” and “¿Qué necesitan escribir?” The lesson also includes “Potenciar la voz del estudiante,” providing discussion prompts that encourage students to connect mathematics to their experiences and participate in mathematical discourse using appropriate mathematical vocabulary. Additionally, each “Repaso del tema” includes a “Repaso de vocabulario” section in which students have the opportunity to engage the use of appropriate mathematical language, including vocabulary, syntax, and discourse. For Tema 5 “Trabajar con ecuaciones de suma y resta,” the “Lenguaje oral” section embeds educator guidance to group students in pairs and ask for a volunteer. One student from the group will be the word while their partner is the definition. The students are to randomly share their word or definition with the class and the class is to pair the matching word and definitions. The “Escritura en matemáticas” section prompts educators to say words while students write them down, applying appropriate syntax. The students are to use the word in a short and long sentence and then draw a representation for each sentence.

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

The Guía del maestro explains how the TEKS process standards are integrated into the materials in the “Estándares de procesos matemáticos de los TEKS en la enseñanza.” The section includes four distinct subsections on how the TEKS process standards integrate properly into the materials. In “Estándares de procesos en problemas y evaluaciones,” the materials include “Estándares de procesos matemáticos de los TEKS en evaluaciones,” stating “Los ejercicios que evalúan contenido también animan a los estudiantes a usar Estándares de procesos.” Tema 9 “Estándares de procesos matemáticos de los TEKS: Comparar y ordenar números” highlights TEKS 1.1B and 1.1C and describes observable student behaviors that demonstrate how the process standards are applied throughout the Tema, such as justifying comparisons using place-value blocks and number lines, determining the order of numbers, selecting appropriate mathematical tools, and solving comparison and ordering problems using place-value models and number lines.

Additionally, Tema 13 “Vistazo al tema” identifies the mathematical objectives, language objectives, vocabulary, content TEKS, and corresponding “Estándares de procesos matemáticos” for each lesson, 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. In Tema 5, lección 5-1 “Expresiones iguales” explicitly identifies the TEKS process standards addressed in the lesson through the “Estándares de procesos matemáticos” section, which explains the process skills students use to acquire and demonstrate mathematical understanding. The materials explicitly list process TEKS 1.1E, 1.1F, and 1.1G and provide opportunities for students to generate and use representations to organize, record, and communicate mathematical ideas. Students also analyze mathematical relationships to make connections and communicate their mathematical thinking, explain and justify their mathematical ideas and arguments using precise mathematical language in both oral and written forms.

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

The materials for grade 1 include a description of how the TEKS are integrated and connected throughout the course in each Tema’s “Contenido” section. In Tema 1 “Comprender la suma y la resta,” the materials are included in a table form, showing the order of the Tema and how the TEKS are incorporated throughout. For lección 1-1 “Elaboremos, Patrones espaciales para los números hasta 10,” the TEKS are 1.2A, 1.1B, 1.1D, and 1.1G. Tema 1 and 2’s “Contenido” sections list the content TEKS and corresponding TEKS process standards for every lesson, such as lección 2-13 “Resolver problemas verbales hasta 10,” which includes TEKS 1.3B, 1.5D, 1.3D, 1.3E, 1.1A, 1.1B, and 1.1E.

The grade 1 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. 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.” The guide lists the process TEKS 1.1A, 1.1B, 1.1C, 1.1D, 1.1E, 1.1F, and 1.1G, indicating that these standards are integrated across all Temas, with guidance for educators to understand how the TEKS process standards are incorporated and connected from Temas 1–13.

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 1 Guía del maestro materials includes a description of how the TEKS are incorporated within the Tema. For example, Tema 4 “Estándares de procesos matemáticos de los TEKS, Operaciones de resta hasta 20: Usar estrategias,” includes a table for each Tema in the materials for “Estándares de procesos matemáticos destacados en las lecciones.” Tema 4 “Operaciones de resta hasta 20: Usar estrategias, Estándares de procesos matemáticos de los TEKS” contains a table regarding how the TEKS process standards are incorporated and connected throughout the Tema with the included student math expectations for the TEKS, such as, for TEKS 1.1A, “Aplican el conteo hacia atrás en una recta numérica para resolver problemas de resta.” In Tema 10, the “Estándares de procesos matemáticos de los TEKS: Geometría” highlights TEKS 1.1E and 1.1F to describe observable student behaviors aligned to each process standard and includes educator questioning strategies that connect the process standards to geometry throughout the unit.

Additionally, the “Vistazo al tema” includes the TEKS for each lesson, and the “Contexto matematico: Coherencia” sections includes subsections titled “Vuelve atras,” Tema . . .” and “Más adelante.” This section is specific to the TEKS, aligned to what was taught before, during, and after the unit, throughout the course or grade level. In Tema 4 “Vistazo del tema: Operaciones de resta hasta 20: Usar estrategias,” 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 1.1B, 1.1E, and 1.1G. The “Paseo de matemáticas” section in the grade 1 Guía del maestro Tema 3 provides the process standard connected to the activity. Process standard 1.1A states, “Se espera que el estudiante aplique las matemáticas a problemas que surgen en la vida diaria, la sociedad y el trabajo.” Students watch a video in which they take a math walk to plan a picnic, answer how many picnic tables they saw, and use their addition strategies to solve, with the process standard incorporated for students to make connections to everyday life and continue to develop their mathematical thinking when solving problems throughout the unit.

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

The grade 1 Guía del maestro includes an overview of the TEKS within the lessons. For example, paso 3 “Práctica y resolución de problemas” and paso 4 “Evaluar y diferenciar” contain a table for each of the steps titled “Análisis de los ejercisios” that includes an overview of the TEKS process standards incorporated into lección 3-4 “¡Investiguemos! Formar 10.” Paso 3’s “Análisis de los ejercisios: Relacionar; Práctica y resolucion de problemas” table includes TEKS such as 1.3E, and paso 4’s table includes the incorporated the process TEKS, such as 1.3D and 1.3E. Additionally, lección 12-2 “Medir con unidades de diferentes longitudes” lists the TEKS process standards 1.1C, 1.1D, and 1.1F in the “Estándares de procesos matemáticos” section of the lesson.

Additionally, 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 10-1 “Clasificar y agrupar figuras bidimensionales” lists the content TEKS 1.6A, 1.6C, and 1.6F and the TEKS process standards 1.1D, 1.1F, and 1.1G in the opening part of the lesson, where students classify and compare two-dimensional figures, explain how figures can be grouped, and communicate their reasoning during the lesson activities. Furthermore, in lección 4-1 “Contar para restar,” the process standards are identified in a blue-shaded section at the bottom of the lesson. The materials identify the process TEKS 1.1A and 1.1D, noting that students use the mathematical process standards to acquire and demonstrate mathematical understanding. In addition, the “Boleto de salida” for each lesson identifies the applicable process TEKS, such as 1.1D in lección 4-1.

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

The grade 1 Guía del maestro includes varying opportunities for students to think mathematically and persevere through solving problems to make sense of mathematics. In lección 13-2 “Elaboremos, Deseos y necesidades,” the materials include guided support for each lesson to encourage mathematical thinking.

Additionally, the Guía del maestro and Libro del estudiante provide opportunities where students persevere through solving problems and think mathematically to make sense of mathematical content. For example, in the Libro del estudiante, lección 3-1 “Usar el conteo hacia adelante” engages students in counting strategies to solve addition problems, comparing two methods for finding a sum, justifying which strategy they prefer, and representing their solutions using numbers, equations, drawings, or other representations as they make sense of mathematics through problem-solving. Students are prompted to explain their reasoning and communicate how they determine their solutions. In lección 1-2 students work on different ways to solve addition problems when both addends are given. In the word problem, the addends 4 and 3 are provided and students must find the total number of blocks. Educators guide the class in thinking mathematically to overcome challenges they may face when dealing with comprehension or strategies for solving. During the lesson, educators may ask questions to help students develop a greater understanding of the concepts. For example, in one of the student samples, Samira drew a tower of four blocks and then a second tower on top with three blocks. The educator asks, “¿Cómo hallaste tu respuesta a la pregunta?” which allows the student to verbalize how they worked through the problem to make sense of mathematics.

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

The grade 1 Guía del maestro materials include support for students to understand, justify, and explain that solving problems and completing tasks can be done in a variety of ways. Lección 8-2 “Elaboremos, Entender y representar números decimales” includes the “Hablemos de matemáticas” section, which features a “Sentido numérico” task where students must understand how to explain and justify why they believe the mass of the suitcase does not belong using different ways to respond to the question. Additionally, in paso 1 “Explorar y comentar,” students can use multiple ways to represent and solve problems with support to understand, explain, and justify grade-level tasks. In “Supervisar, seleccionar y poner en secuencia,” educators are guided to encourage varied ways to represent and solve problems, such as “¿Cómo pueden usar la relación que hay entre los números decimales y las fracciones como ayuda para resolver el problema?” with included possible responses, including the use of manipulatives such as a hundreds square or drawings. In Tema 10, lección 10-7 also includes the “Hablemos de matemáticas” section, which provides opportunities for students to develop mathematical understanding by explaining and justifying their thinking. Students are frequently encouraged to elaborate on their solutions with peers or in small-group discussions. For example, students work on a problem titled “¿Cuál no pertenece?” in which they develop geometric sense when asked to identify the shape that does not belong and explain and justify their reasoning. In addition, the materials explicitly acknowledge that there are multiple correct answers and varying ways to represent the problems and tasks.

Additionally, the "Biblioteca de diferenciación" and Guía del maestro include support for students in understanding, explaining, and justifying that there can be multiple ways to represent and solve problems and complete tasks. In “Biblioteca de diferenciación,” Tema 8 “Levántate y razona, Adivina mi número,” students use clues to determine a possible mystery number and show their solution in two different ways. Students also explain how they identified the number and represent their thinking using different mathematical models. Furthermore, “¡Investiguemos!” lessons similarly provide supports for students to understand, explain, and justify that problems can be solved in multiple ways. Paso 1 “Investigar” provides the opportunity for students to explain their answers to a partner during the investigation. As students work through the investigation, the Guía del maestro provides student examples to better support student needs as they solve problems using a variety of representations before they go into small group instruction. Lesson materials also provide prompting questions for the educator such as “¿Cómo podrían hacer una bandera diferente que siga las reglas?” Students persevere through solving problems in paso 2 “Conectar” and paso 3 “Práctica y resolución de problemas.” The reflection section guides the educator to challenge students to solve the problem in different ways. In Tema 11, lección 11-5 includes the “Aprendizaje visual” section in paso 2 “Conversación en la clase,” which provides opportunities for students to analyze, communicate, and compare answers with their partners, and justify their mathematical thinking while exploring the essential question: “Cuando dividen una figura en 2 o 4 partes iguales, ¿cómo describen las partes?” Students participate in a think-pair-share routine, where they discuss and compare their ideas about what fraction of a rectangle is shaded green. During these discussions, students explain and justify their reasoning while considering different perspectives.

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 1 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. Lección 12-2 “Elaboremos, Medir con unidades de diferentes longitudes” includes the “Hablemos de matemáticas” section with “Detective de números,” where students make sense of mathematics by examining the clues one at a time to determine the mysterious longitude. The materials prompt the educator to support students in making sense of mathematics through discussion with their peers and educators, stating, “Pida a los estudiantes que discutan su razonamiento en parejas antes de participar en un debate de toda la clase.” In the same lesson, the students see a pencil to be measured and must estimate the length of the pencil using small and large paper clips. The “Supervisar, seleccionar y poner en secuencia” small group activity guides the educator to work with students with prompting questions. The next section in the lesson is “Aprendizaje visual,” which starts with an essential question followed by a peer and educator class conversation, with questions such as, “¿Qué observas en los clips que estan debajo del segundo marcador?” This section also includes a think-pair-share activity, making sense of mathematics, during “Hablar sobre las ideas matematicas” where students have the opportunity to share and explain how to correctly measure the length of an object.

Additionally, the materials for grade 1 in the Guía del maestro require students to make sense of mathematics as they do, write about, and discuss math with peers and teachers. In Tema 5, Lección 5-8, the materials include the “Representémoslo en 3 actos” activity, “Demasiado pesado,” 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 preguntas podríamos responder con las matemáticas?” In Acto 2, "El modelo," students solve the problem in writing and then participate in a whole-class discussion to compare and explain their solution strategies. The materials include examples of two students, Luis and Lin, who use different strategies to solve the problem. Students analyze these examples, discuss the different approaches with their peers and teacher, and explain their mathematical reasoning. Finally, in Acto 3, students create a new mathematical problem in writing and explain how they would use mathematical models to solve it.

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 Guía del maestro and “Modelo de resolución de problemas” resource include support for educators in guiding students to share and reflect on their problem-solving approaches. Lección 11-8 “¡Investiguemos! La hora y datos” 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 the educator with questions to guide students to share and explain, such as “¿Cuándo han tenido que seguir un cronograma?” and “¿De qué manera fue útil?” The “Seleccionar y poner en secuencia” section includes “Relacionar estrategias de solución,” where the educator guides students to identify similarities and differences in the problem-solving strategies they 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 to reflect on their problem-solving approaches and an “Errores e intervención” section for students having difficulty within the exercise. Each “¡Investiguemos!” lesson includes educator guidance that prompts students to explain and compare their solution strategies throughout the lesson. The “Relacionar estrategias de solución” and “Hablar sobre las ideas matemáticas” section engages students in discussing different approaches and justifying their reasoning, while “Práctica y resolución de problemas” provides opportunities for students to reflect on the mathematical concepts they used and explain how they solved the problems. Lección 9-1 asks students to explain how they determined which two-digit number is greater using tens and ones, compare different solution strategies, argue and justify why one number is greater than another, and reflect on how place-value models support their reasoning.

Additionally, lección 9-8, “Actos 2-3” support educators in guiding students to share and compare strategies for determining which fractional pieces are larger, explaining how models represent equal parts, justifying why one fraction is greater than another, arguing why it is greater, evaluating the effectiveness of different solution approaches, and creating a related problem that requires applying the same mathematical reasoning. In Tema 11, lección 11-9 includes the “Aprendizaje visual” section, in which students solve four 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: “¿Cómo muestran las manecillas de un reloj las 5 en punto?” Students work through four problems related to identifying and using coins. Throughout the lesson, the materials provide educator prompts such as: “Se usa un término especial cuando la manecilla apunta a las 12, ¿saben cuál es?” and “¿Cómo saben qué hora muestra el reloj?” Students explain their thinking, compare mathematical ideas, and justify their responses by using evidence as they reflect on the strategies they use to solve the problems.

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 1 Guía del maestro includes prompts and guidance to support educators in providing explanatory feedback based on student responses and anticipated student misconceptions. For example, lección 11-9 “Elaboremos, Entender la manecilla de la hora y el minutero” includes “Prevenir malentendidos” in paso 2 “Aprendizaje visual,” where there are prompts and guidance for educators in providing feedback based on student responses and anticipated misconceptions, such as “Observe a los estudiantes que confunden la manecilla de la hora y el minuto en el reloj. Recalque que la manecilla de la hora es más corta y muestra la hora, mientras que el minutero es más largo y apunta a los minutos.” In the “Hablar sobre las ideas centrales,” the materials additionally include educator prompts and guidance such as “Esté atento a las conversaciones sobre cómo la manecilla de la hora es más corta y muestra la hora, mientras que la de los minutos es más largo y muestra los minutos.” In Tema 13, lección 13-1 includes educator guidance for providing targeted feedback during the “Investigar” section. In paso 3 “Reflexión,” the materials include a subsection titled “Errores e intervención, Ejercicio 5,” which identifies a common student misconception and provides instructional guidance for addressing it. The materials state: “Si los estudiantes no pueden determinar cuánto ganó Amber, pídales que usen cubos conectables para representar el ingreso total y luego quiten 6 cubos para representar el ingreso del viernes para dejar lo que representa el ingreso del sábado.”

Additionally, in Tema 8, lección 8-8 includes educator guidance in paso 3 “Práctica y resolución de problemas” within the “Práctica guiada” section. This section includes a subsection titled “Errores e intervención, Ejercicio 2,” which identifies a common student misconception and provides explicit guidance for educators on how to address it. Educator explanatory feedback states, “Si los estudiantes suman unidades al dígito de las decenas, entonces pídales que cuenten de 10 en 10, empezando con el número de un dígito. Diga, Empiecen en el 6. Muevanse 2 filas hacia arriba para sumar 20. 20+6=26.” In the lección 7-2 “Explorar y comentar” activity students work on counting by ones up to 120. The task requires students to determine which three numbers come after 100 when counting. Educators look for students who did not count by ones and, to prevent any further misconceptions, provide explanatory feedback such as “Cuando cuentan en orden, ¿qué dígito cambia primero?” and “¿Cómo saben cuál es el siguiente número?” To support the class in counting strategies, educators select solutions for students to present and first choose one that shows students counting by 10s before selecting solutions that count by ones. The materials provide educator guidance to prevent misconceptions about why counting by 10s as a solution would not work for this problem. Educators then teach students to understand that counting numbers greater than 100 follows the same counting pattern as counting numbers that are less than 100.