enVision+ Texas Matemáticas, 02

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

The Guía del maestro includes a scope and sequence for 13 Temas aligned with the Texas Essential Knowledge and Skills (TEKS) in “Contenido y secuencia” for 135-day, 165-day, 180-day, and 210-day instructional calendars. “Contenido y secuencia” for the instructional calendars includes a table with the concepts for each Tema. For example, Tema 1 “Sumar y restar hasta 20” includes the lessons, concepts, and TEKS addressed within the progression of content throughout the year, with instructional pacing varying according to each instructional calendar for the academic year.

Additionally, the Guía del maestro includes a scope and sequence that outlines the TEKS in “Correlación con los conocimientos y destrezas esenciales de Texas.” In the grade 2 Guía del maestro, “Contenido y secuencia” includes a table with the TEKS and aligned lessons and pages from the Libro del estudiante and Guía del maestro. For example, the grade 2 scope and sequence follows an instructional pathway with números y operaciones, razonamiento algebraico, geometría y medición, and comprensión de finanzas personales, with the TEKS presented in a table for instruction throughout the course.

Evaluation for 1.1b
Materials include suggested pacing (pacing guide/calendar) to support effective implementation for various instructional calendars (e.g., varying numbers of instructional days - 165, 180, 210).

The Guía del ritmo de enseñanza, grado 2 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 across the 13 Temas of the academic year in the materials, the days of instruction, and the TEKS for each topic. For example, the materials provide the 165-day Guía del ritmo de enseñanza with suggested pacing for 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 “Restar hasta 100 usando estrategias,” in “Contenido y secuencia: 135 días,” includes a table with the suggested pacing of the materials, including the days of instruction, the TEKS, differentiation, review, and evaluation. The table also includes materials such as “Elaboremos,” “Vamos a investigar,” “Representémoslo en 3 actos,” and “Investiguemos.”

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

Program overview materials include the “Grade 2 Content Organization Rationale” organized in 13 Temas with mathematical key concepts and student connections, including a “Grade 2 Content Organized to Build Connections” table with each Tema in unit order. For instance, Temas 1–5 focus on equal and unequal quantities using addition and subtraction strategies, while Temas 6–7 focus on representing money, time, and length in equivalent forms. Grade 2 materials include key concept description with the intentional purpose of each unit and conceptual connections across Temas.

Additionally, in the Guía del maestro, the “Contexto matemático: coherencia” section at the beginning of each Tema explains how concepts connect to prior and future learning through the “¡Vuelve atrás!” and “Más adelante” components. For example, in Tema 3 “Restar hasta 100 usando estrategias,” the “Contexto matemático: conceptos clave” section, “Usar estrategias,” outlines the progression of the Tema and what is taught before and after.

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

The Savvas Realize online platform includes “Protocolos de internalización y herramientas de observación” in the tools section, which provides “Protocolo de internalización del tema para el maestro” and “Protocolo de internalización de la lección para el maestro.” The grade 2 materials include guidance for unit and lesson internalization that includes 13- and 16-step processes providing a thorough understanding of key learning objectives, sequencing, and instructional strategies.

Furthermore, the Guía del maestro includes “Elaboremos,” “Investiguemos,” and “Representémoslo en 3 actos” lesson types with internalization guidance for previewing the unit to understand key standards, unit objectives, vocabulary, and assessments. For example, expanded notes in grade 2 appear in each of the three lesson types in Tema 1 of the Guía del maestro. The materials provide a process for educators to connect lesson objectives to the TEKS, identify vocabulary and prerequisite skills, plan formative assessments, differentiate instruction, and plan lesson materials.

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

The Savvas Realize platform contains the “Protocolos de internalización y herramientas de observación,” which are observation tools and internalization protocols that include support and guidance for educators from instructional leaders. Resources for grade 2 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 2 materials provide notes at the beginning of each lesson in the Guía del maestro titled “Elaboremos,” “Investiguemos,” or “Representémoslo en 3 actos.” The expanded notes in the first of each of the three lesson types in Tema 1 explain the key components of the program, such as problem-based learning, visual learning, and differentiated instruction, to allow instructional leaders to support educators. The materials outline the unit structure by incorporating a list of materials, new vocabulary, and resources for instructional leaders to support educators in implementing the materials effectively.

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

The grade 2 materials in the Guía del maestro include a “Contexto matemático: conceptos clave” section that explains the progression of the Tema. In the “Contexto matemático: coherencia” section, the materials explain how concepts and the TEKS connect across previous courses, within current courses, and in possible future courses.

Additionally, “Adaptaciones del lenguaje” sections incorporate vocabulary in context with mathematical meaning and outline the critical prerequisite vocabulary. For example, each Tema in grade 2 includes “Adaptaciones del lenguaje y discurso oral/escrito,” “Apoyo para el vocabulario del tema,” and “Transferencia metalingüística al inglés y cognados.” These sections focus on vocabulary that will be introduced in the unit along with previously taught vocabulary and what will be introduced in the upcoming unit. The materials provide a breakdown of academic vocabulary by lesson to support effective instruction of the concepts.

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

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

Furthermore, in the “Plan del tema” under “Participacion de familia,” each Tema includes a family letter with guidance and support resources. Materials provide suggestions for how families can support student progress and achievement in the grade level for each unit in a “De la escuela al hogar” letter in English and Spanish. These materials provide strategies and activities for families to use at home for each Tema, such as Tema 1 “Sumar y restar hasta 20,” which includes a short letter in both English and Spanish and a section where families can make observations.

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

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

Furthermore, at the beginning of each “Elaboremos” lesson in the Guía del maestro, the grade 2 materials include critical lesson information, including TEKS alignment, lesson objectives, and materials. For example, in lección 2-1, “Elaboremos,” the 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 2 in “Plan de lecciones” provides materials required for instruction and the suggested timing for each lesson component in “Cronología de la lección.” For example, the grade 2 materials include a table with “Tiempo,” “Propósito,” and “Materiales” for the steps of the lesson in the lesson overview. The guidance in the lesson overview provides lesson pacing and suggested timing for each component of the lesson cycle to support educators in effectively delivering instruction.

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

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

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

The Guía del maestro “Biblioteca de diferenciación” includes extended practice in the form of intervention, reteach-to-build, enrichment, and build-mathematical-literacy activities, as well as additional practice pages. For example, in grade 2 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 2 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 2 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 2 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 24 multiple-choice questions, including word problems, matching number sentences to visuals, graphs, place value, two-dimensional shape identification, and more. Exit tickets are available at the lesson level, with the exit tickets for Tema 2 consisting of two or three questions for each lesson along with a check-in for the students. The unit-level assessment follows the exit ticket in the guide and includes 14 questions with multiple-choice, constructed-response, and text-entry question types.

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

The materials for grade 2 in the Cuaderno de evaluación define each assessment and the intended purpose of diagnostic, summative, and formative assessments in a table. For instance, the grade 2 materials provide a “Why and When to Assess” section for each Tema included and define diagnostic assessments as assessments to be administered before instruction to measure student readiness.

The grade 2 materials in the Cuaderno de evaluación also provide a table that includes definitions of the varying types of assessments, the recommended time to administer the assessments, and the names of the assessments in the instructional materials. For example, formative assessments during a lesson are “Herramientas de evaluación observacional,” “Práctica guiada,” and “Comprobaciones rápidas.” “Boletos de salida” are defined as formative assessments for the end of the lesson and intended to assess student lesson comprehension. The Guía del maestro describes diagnostic assessments administered at the beginning of the year to measure student readiness, formative assessments used during lessons to monitor student progress, and summative assessments administered at the end of a Tema to measure student learning.

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

The grade 2 materials in the Cuaderno de evaluación include the sections “Why and When to Assess,” “How to Assess,” “Assessment Data,” “Assessment Practice,” and “How to Administer Assessments,” with tables that provide guidance for educators. For example, the materials for grade 2 include a table with assessment administration guidance in “How to Administer Assessments.” Additionally, the guide provides direction on how to score the assessments along with the answer keys.

The materials for grade 2 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. Additionally, the materials contain instructions for collecting assessment data for online and printed use, as well as preparing and monitoring assessments, including time frames, recommendations for a proper and secure testing environment, and a script of directions.

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

The grade 2 Cuaderno de evaluación includes a “Guía de puntaje” with item analysis charts that identify the TEKS aligned to the varying assessment types included in the materials. Assessment Sourcebook materials include “Examen de preparación,” “Evaluación para observar el progreso,” “Boleto de salida,” “Evaluación,” “Evaluación acumulativa,” and “Tarea de rendimiento.” For example, the item analysis charts connect individual assessment items for formative assessments in “Evaluacion para observar el progresso,” “Formas A–C,” and “Evaluación del tema” summative assessments to the assessed TEKS and corresponding intervention lessons. The “Examen de preparación” diagnostic assessment takes place at the start of the year and “Repasa lo que sabes” at the start of a Tema. In addition, the “Guía de Puntaje” provides a table for the “Evaluación acumulativa,” covering three Temas at a time, and a cumulative assessment table for Temas 1–13 at the end of the guide in alignment with the TEKS.

The grade 2 Cuaderno de evaluación “Evaluación para observar el progreso” section includes summative assessment items aligned to grade-level TEKS and lesson objectives. “Forma A” includes items connected to lesson objectives that require students to solve addition and subtraction problems, interpret pictographs, identify points on a number line, and classify geometric figures using multiple-choice and constructed-response formats aligned to TEKS expectations. “Boletos de salida” are formative assessments included in the grade 2 Guía del maestro with an answer key, the TEKS standards, and lesson objective alignment. For example, lección 3-10 “Escoger una estrategia para restar hasta 100” assesses TEKS 2.4B and 2.1A. The “Repasa lo que sabes” diagnostic assessment appears at the start of each Tema as a guided educator assessment. Then Tema 3, lección 3-7 “Restar hasta 100 usando estrategias” contains six guided educator questions that are TEKS-aligned for the grade level 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 grade 2 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 2 include varying levels of complexity with TEKS-aligned items. For instance, the “Evaluación acumulativa de referencia” for Temas 1–13 includes opportunities for students to explain and justify their answers and “Evaluación para observar el progreso, Formas B and C,” include multiple-response and multiple-choice items.

The grade 2 materials in the “Evaluaciones del curso” resources include diagnostic, progress-monitoring, and summative assessments aligned to the TEKS with varying levels of complexity. For instance, “Evaluación para observar el progreso, Formas A–C,” features TEKS-aligned items at varying levels of complexity, with multiple-choice and text-entry response formats administered at the beginning, middle, and end of the year to measure student understanding. Furthermore, the Tema 1 assessment consists of 12 questions. Four of the 12 questions are multiple-choice, while the other questions require the student to draw or write an answer. For example, question six of the assessment shows a blank double ten frame. The students are asked to show ten in order to solve for 16 − 8.

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

The materials for grade 2 include the Cuaderno de evaluación “Guía de puntaje” for all Tema- and lesson-level assessments, with a scoring guide and answer keys. For example, the grade 2 “Guía de puntaje” explains how educators use online assessment reports to analyze standards mastery, group students based on performance data, and identify instructional support based on assessment results. The scoring guide addresses how students earn points, with one or two points awarded based on the expected response.

Furthermore, the Guía del maestro provides instructional assessments and scoring information for interpreting student performance. The Guía del maestro also includes guidance for analyzing assessment results and determining instructional responses based on student performance. For example, in lección 11-11, paso 4 “Evaluar y diferenciar,” the included scoring guidance for “Comprobación rápida” identifies scores for intervention and extension activities. The “Boleto de salida” then includes a self-assessment response and guidance for using student results to determine instructional support. Additionally, for each Tema, the grade 2 materials offer guidance on student performance before, during, and after the Tema with the “Mi progreso y crecimiento” document.

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

The grade 2 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 2 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. Lección 6-3 also contains guidance for educators to support students through the “Boleto de salida.” In the same lesson, if a student scores 0–3 points, they are assigned an intervention or reinforcement activity to improve their comprehension. If a student scores 4–5 points, they are assigned an enrichment lesson. The “Biblioteca de diferenciación” also includes guidance and a variety of differentiated projects for educators to choose from in response to student trends in performance on assessments.

Evaluation for 2.2c
Materials include tools for teachers to track student progress and growth, and tools for students to track their own progress and growth.

The materials for grade 2 include progress monitoring tools to document student performance before, during, and after instruction in the “Herramienta para profesores de progreso y crecimiento del alumno” section. For example, the “Antes del tema,” “Durante el tema,” and “Tras el tema” resources help educators record student performance across the TEKS-aligned lessons and objectives. The grade 2 materials also include a student self-assessment in “Boleto de salida” to track progress for the lesson objective. For instance, in Tema 4 lección 4-2, the student tracker consists of three options for students to select: “Puedo,” “Con ayuda,” or “No todavia,” with the student tracker listing each assessed unit and their corresponding lessons. Students can view the lesson objective and evaluate their progress before, during, and after the lesson.

Additionally, the grade 2 materials include student-facing progress monitoring tools in the Cuaderno de evaluación “Boleto de salida” that allow students to reflect on and document their comprehension of the lesson objectives. In the Guía del maestro, the “Datos de las evaluaciones” include online data that tracks student progress and growth for individual students and the class overall. For instance, the educator tracker lists each unit and its corresponding lessons, and the table names the lessons, TEKS standards, objectives, and how students performed before, during, and after the unit.

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

Materials in the grade 2 Guía del maestro include the paso 4 “Evaluar y diferenciar” section, which contains an “Actividad de intervención” at the end of each lessons and an additional “Video de apoyo,” where students can reinforce and review the lesson content. Additionally, materials include “Refuerzo para mejorar la comprensión” resources in each lesson with step-by-step guidance, additional practice activities, and answer keys to support reteaching. For example, grade 2 “Refuerzo para mejorar la comprensión, R 1–6” requires students to use number lines, count forward and backward, and solve subtraction problems by representing differences and explaining mathematical reasoning. Lección 7-1, paso 3 “Práctica y resolución de problemas” includes guidance for “Práctica guiada.” Students select shapes that show halves and cross out those that do not. Students also complete a problem with fourths and eighths. The guidance under “Errores e intervención ejercicio 1” states, “Si los estudiantes dicen que la segunda figura muestra mitades, entonces pídales que coloreen cada parte del círculo de un color diferente y pregunte: ¿Cuántas partes iguales forman el círculo completo? [2] ¿Las partes son iguales? [No], ¿Cómo se llaman 2 partes iguales? [Mitades]. Ayude a los estudiantes a entender que si dos partes de un entero no tienen el mismo tamaño, entonces la imagen no está dividida en mitades.” In paso 4 “Evaluar y diferenciar,” the “Biblioteca de diferenciación” and “Actividad de intervención” include additional resources to support varying virtual learning styles and provide materials and steps for intervention. For example, in “Actividad de intervención” for grade 2, lección 9-1 provides activity materials and guidance for educators to create shape task cards divided into equal halves, fourths, and eighths and unequal halves, fourths, and eighths, for pairs of students to determine equal and unequal parts.

Furthermore, the materials for grade 2 in paso 4 “Evaluar y diferenciar,” “Comprobación rápida,” include “Actividad de intervención” as an assigned enrichment activity for a small group of students. Grade 2, Tema 1, lección 1-2 includes an educator-led “Actividad de intervención” using connectable cubes to model addition equations and “Práctica adicional” activities that require students to solve addition problems, represent equations, and explain mathematical reasoning. “Actividad de intervención” includes an activity for a small group of students in which the educator draws a variety of shapes on index cards, such as triangles, squares, and rhombuses. Some of the cards have shapes divided into halves, fourths, and eighths, while other cards have the shapes divided into unequal parts for students to determine if the card they choose shows equal or unequal parts. The materials include “Biblioteca de diferenciación” in the Guía del maestro Tema 12, to provide targeted support through a variety of instructional formats. For example, “Biblioteca de diferenciación” includes differentiated activities and resources and additional practice for students at varying levels of proficiency, such as projects and electronic games. “Refuerzo para mejorar la comprensión” is also included in “Biblioteca de diferenciación” with 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).

In the Guía del maestro, the “Adaptaciones del lenguaje” section provides a breakdown of vocabulary support in “Apoyo para el vocabulario del tema,” “Transferencia metalingüística al inglés,” “Cognados,” and “Vocabulario académico.” In “Apoyo para el vocabulario del tema,” there are three sections labeled “Vocabulario del tema,” “Términos previos,” and “Próximos términos” which provide support for unfamiliar vocabulary in grade 2. A “Vocabulario en contexto” table includes the vocabulary word, math definition, and other meanings. Tema 7 materials include a math definition for the word fila as “conjunto de cosas o personas dispuestas en línea horizontal,” while another meaning is “conjunto de personas que esperan su turno.” Some sections include metalinguistic transfers between Spanish and English. The “Presentación del tema” features a vocabulary activity that guides the educator to use a graphic organizer, have students write the word longitud in the center, then write all the units of measurement that they will use throughout the unit. In the Tema 7 lección 7-3 “Elaboremos” section, the “Hablemos de matemáticas” subsection guides the educator to facilitate a math discussion where students can express their ideas and strategies using the given lesson vocabulary. Additionally, the Tema 9 “Cognados” section identifies cognates including fraction/fracción, equal/igual, and divide/dividir, while the “Falsos cognados” section defines the word notice. The “Vocabulario académico” section then introduces the academic language terms identificar and explorar and provides definitions for each term.

In addition, grade 2 “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 2 “Tarjetas de vocabulario” provide academic vocabulary with pictures and instructions for educators on how to use the cards to support student learning with visuals and application examples, including sentence frames to complete sentences using academic vocabulary. The vocabulary cards define and illustrate terms including ecuación, suma, dobles, casi dobles, and diferencia.

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 2, 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 7-8 also include “Práctica adicional” as an enrichment and extension activity for students to practice “Comparando longitudes.” “Escoge un proyecto” allows students the opportunity to further enhance their understanding of the lesson. “Matemáticas y lectoescritura” includes an extension activity in “Ampliación,” which provides educator guidance for having students draw pictures and write number sentences that match their illustrations. In lección 7-8, paso 4 “Evaluar y diferenciar,” the “Comprobación rápida” section provides guidance on the activity to be completed after the quick check, depending on students’ scores: if students score 0–3 points, they are assigned an intervention or reinforcement activity, and if they score 4–5 points, they are assigned an enrichment activity. The educator cuts strips of paper ahead of time and gives each student a strip. In pairs, students measure the length of their strip of paper to the nearest centimeter and label the length, then connect their strips of paper and add the measurements. For example, six cm + three cm = nine cm. Students can then compare their findings with their partners and find the difference of their measurements.

Furthermore, the grade 2 “Biblioteca de diferenciación” contains educator guidance that includes mathematics and literacy resources connected to classification, counting, patterns, and problem-solving skills. For example, Tema 3 includes “Matemáticas y lectoescritura” activities such as “Sky Brown: campeona olímpica,” “Estrategias para restar: descomponer,” “Estrategias para restar: usar modelos,” and “Leonhard Euler” that require students to analyze informational text, solve subtraction problems using decomposition and visual models, and explain mathematical thinking through written responses. In lección 7-8, the extension titled “En la cocina de Denzel,” presents students with visuals of a variety of kitchen objects and asks them to order the items from shortest to longest, then complete the sentences provided. 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?” In “Crea tu propio paseo de las matemáticas,” sample questions include “¿Qué tiene 8 patas y es grande y peludo?” and “¿Cómo dependen las personas y las plantas del agua?” The grade 2 Guía del maestro “Práctica adicional” allows students to work on problems that extend into future learning within the topic, such as with lección 7-8, “Comparar longitudes,” where the materials have students create and solve equations for length.

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 2 Guía del maestro, paso 2 “Aprendizaje visual” and paso 3 “Práctica y resolución de problemas,” the materials provide prompts and guidance for modeling lesson concepts. Lección 10-2 “Sólidos” includes educator-directed questions, sample responses, and discussion prompts throughout the lesson. In paso 2 “Aprendizaje visual,” educators are prompted to ask “¿Cuántas superficies planas tiene un cono?” and “¿Cuántas caras tiene un prisma rectangular?” and provided sample responses for each question. The “Conversación en la clase” section includes prompts for discussing the attributes of three-dimensional figures and the “Rutina de lenguaje” section directs students to explain and justify their responses. The “Apoyo al lenguaje” section includes educator questions and sample responses related to similarities and differences between cones and cylinders. For example, materials for lesson 9-1 provide explicit prompts below “Conversación en la clase.” The prompts are in blue font followed by the expected student response in brackets, with a total of four questions to facilitate this section. Question A is as follows: “¿Por qué las 2 partes del primer círculo se llaman mitades? [Son 2 partes iguales del todo]. ¿Por qué las 2 partes del siguiente círculo no son mitades? [Cada parte es de un tamaño diferente].” Lección 9-1 includes educator guidance stating, “Esté atento a los estudiantes que tienen problemas para entender que el entero son todas las partes iguales.” The materials also include guiding questions for educators to use during the “Vistazo rápido” activity, such as “¿Cuántas secciones había en total?” “¿Cuántas estaban sombreadas?” and “¿Cuántas no estaban sombreadas?” These structured prompts support educators in facilitating mathematical discussions, developing students’ observational skills, and strengthening conceptual understanding.

In addition, the Guía del maestro for grade 2, Tema 2, “Estándares de procesos matemáticos de los TEKS,” provides educator guidance and discussion prompts to support mathematical reasoning, such as “¿Qué estrategia podrían usar para resolver el problema?” “¿Pueden escribir una ecuación que muestre su solución?” and “¿Cómo saben cuándo hay que reagrupar para sumar?” The “Presentación del tema” in the Guía del maestro Tema 1 includes a “Paseo de matemáticas” section with educator-prompted questions such as “¿Qué notaron?” “¿Qué se preguntaron?” and “¿Qué pregunta del video intenta responder la persona?” Educator guidance can be found in the Guía del maestro Tema 8, lección 8-1, after the following sections: “Práctica guiada,” “Práctica y resolución de problemas,” “Comprobación rápida,” “Biblioteca de diferenciación,” and “Actividad de intervención.” The guided sections are part of paso 3 and paso 4 of a given lesson. Additionally, in “Manual de resolución de problemas,” educators are provided guidance on how to assist students in solving problems with educator prompts in the “Formular un plan” section, which contains ideas for educators to remind students of ways in which they have solved problems and which strategies they may use.

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

The materials for grade 2 in the Guía del maestro include lesson structures, instructional routines, and teaching practices that support educators in facilitating mathematical discussions, modeling concepts, and guiding student learning. For example, in lección 9-3, the paso 1 “Explorar y comentar” section provides educator guidance on instructional approaches for effective lesson delivery. The materials direct educators to create small groups and have students divide a square into equal parts by creating two lines down the middle in each direction or four vertical lines. Paso 2 “Aprendizaje visual” instructs educators to structure conversations using an animated visual to support students in analyzing varying strategies and instructional approaches for the given concept. Additionally, the Guía del maestro describes three lesson types: “Investiguemos,” “Elaboremos,” and “Representémoslo en 3 actos.” Each lesson incorporates a different instructional approach. “Investiguemos” uses a problem-based learning approach, “Elaboremos” emphasizes direct instruction, and “Representémoslo en 3 actos” includes a real-world approach. Materials additionally include guidance for instructional routines such as “Anticipar,” “Supervisar,” “Seleccionar y poner en secuencia,” “Relacionar,” and “Hablar sobre las ideas matemáticas.” The “Prácticas de enseñanza efectivas” section identifies instructional approaches used throughout the program, including facilitating mathematical discussions, using and connecting mathematical representations, supporting productive struggle, and posing purposeful questions during instruction.

Furthermore, “Planes de la lección para Texas” for grade 2, lección 1-1 includes lesson pacing, instructional routines, educator prompts, sample responses, intervention support, and differentiation guidance throughout the lesson. Paso 1 “Investigar” features “Preguntas de evaluación,” “Preguntas para profundizar,” and “Seleccionar y poner en secuencia las soluciones de los estudiantes” to guide educators in monitoring student thinking, questioning students about strategies, and facilitating mathematical discussions. Additionally, Brainingcamp tasks incorporate educator guidance for an additional instructional approach with virtual manipulative integration, such as the “Take Apart Problem” activity, which includes online manipulatives that allow students to use two-color counters to model and solve a take-apart problem. The activity also provides extension opportunities that encourage students to generate fact families. The Guía del maestro lección 9-4 “Elaboremos” section guides educators in the use of “Boleto de salida” and supporting students based on their results to facilitate instruction with reminders such as “Apoyar a los estudiantes cuando sea necesario, recordándoles que cuando se divide un entero en fracciones, cuanto más pequeña la parte fraccionaria, mayor es la cantidad de partes, y cuanto más grande es la parte fraccionaria, menor es la cantidad de partes.”

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.” The materials include a table with practice opportunities, such as math talks, spiral review, fluency practice, and Tema review. Next to each practice opportunity are the recommended structures. Math talks can be used with whole or small groups, while spiral review is recommended for individual practice.

Additionally, the grade 2 Guía del maestro, lección 4-2 includes whole-group and small-group instructional structures, educator prompts, and guidance for facilitating discussions and monitoring student understanding. Paso 1 “Explorar y comentar” includes the instructional structures “Introducción Toda la clase,” “Supervisar, seleccionar y poner en secuencia en grupos pequeños,” and “Relacionar toda la clase,” which provide guidance for questioning students, monitoring student strategies, selecting student responses for discussion, and connecting student representations to addition and subtraction problem-solving strategies with unknown values. In lección 6-3, paso 2 “Aprendizaje visual” includes the “Hablar sobre las ideas matemáticas” section, in which the educator is guided to have students participate in a think-pair-share activity in a small group and share their ideas on how to compare the value of a dollar bill and a dollar coin. The educator actively listens to student conversations to ensure that they understand that each is worth 100 cents. Paso 3 “Práctica y resolución de problemas” includes digital and print practice for students to complete independently and includes educator guidance on what to ask students to do, for example, “Si los estudiantes presentan dificultades, pídales que intenten con 3 monedas al azar.” 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 topic, such as project 1D, where students work together to explain one of their solution strategies in writing.

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 2 Guía del maestro, Tema 4 includes the “Adaptaciones del lenguaje” section at the beginning of each topic, with implementation guidance for educators to effectively use the materials with emergent bilingual students. The section includes “Adaptaciones del lenguaje oral/escrito,” “Apoyo para el vocabulario del tema,” “Transferencia metalingüística al inglés,” “Cognados,” and “Vocabulario académico.” The grade 2 materials include the recommended terms representar and interpretar in “Vocabulario académico” for Tema 6. Tema 9 “Adaptaciones del lenguaje,” includes guidance for vocabulary development, academic language support, oral and written discourse, and metalinguistic transfer between Spanish and English. In “Transferencia metalingüística al inglés” for Tema 4, “Competencias transferibles” states, “Tanto en inglés como en español se usan oraciones que comienzan con una preposición. Marta and Kai see flies and bees in the garden. / Marta y Kay ven moscas y abejas en el jardín.” “Competencias no transferibles” says, “El español no usa el sonido /sh/: show, sharks, she.” Tema 4 “Entender la suma,” provides a table of vocabulary words, their mathematical meanings, and their alternate meanings in other contexts. Additionally, Tema 6 includes the “Vocabulario académico” and “Vocabulario en contexto” sections, which provide academic terms, contextualized vocabulary support, and lesson-specific language guidance to support bilingual and emergent bilingual students during instruction.

The grade 2 materials include the “Apoyo al lenguaje” section in the Guía del maestro, Tema 8, lección 8-6, which provides guidance for discussing and comparing data presented in a graph before students solve the problem independently. The guidance directs educators to review vocabulary related to comparar, use the visual model from the “Aprendizaje visual” section, and facilitate small-group discussions about the collections of estampillas represented in the graph. Additionally, at the beginning of each new topic, the “Repasa lo que sabes” section provides language and vocabulary support for educators to implement with students to deepen their understanding. The words and phrases aligned with the lesson are provided, along with vocabulary activities. Furthermore, materials include a program overview, which describes the sections “Supporting Emergent Bilingual Students” and “Additional Resources for Teachers,” which include a Language Support Handbook. For example, one support for emergent bilingual students is the “Language Support Activity,” which provides targeted language support at specific points during the lesson. Finally, each Tema’s “Linguistic Accommodations” section provides vocabulary and metalinguistic transfer support through Spanish-English cognates, as well as academic vocabulary development to help students access content and strengthen language proficiency.

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

In the grade 2 Guía del maestro, Tema 6, “Adaptaciones del lenguaje,” the materials include a variety of embedded guidance to support emergent bilingual students. For example, in “Adaptaciones del lenguaje oral/escrito,” emergent bilinguals interact with the vocabulary words in the Tema to increase comprehension through oral and written discourse and develop academic vocabulary. This section includes vocabulary that is relevant to the topic, along with vocabulary from previous and future Temas. A table titled “Vocabulario en contexto” includes the vocabulary word, mathematical definition, and other meanings. For example, in Tema 6, the provided mathematical definition for the word valor is “cuanto vale una moneda o un billete,” while another meaning is “la cualidad de ser útil o importante.” The section further breaks down the words by lesson, supporting emergent bilingual students in developing academic vocabulary, increasing comprehension, and building background knowledge by presenting the terms in the context of the Tema and real-life situations. Additionally, the materials for grade 2, Tema 12, “Adaptaciones del lenguaje” include “Transferencia metalingüística al inglés” guidance for transferable and nontransferable competencies related to numbers and place value concepts, while the “Cognados,” “Vocabulario académico,” and “Vocabulario en contexto” sections provide academic terms, contextualized definitions, and lesson-specific vocabulary support for emergent bilingual students during instruction.

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 1-2 “Estrategias de suma” includes a section titled “Notas detalladas sobre las lecciones de Elaboremos,” where Note B references an online glossary available in both English and Spanish that provides visual representations of vocabulary terms and opportunities for oral language practice, supporting students in developing academic vocabulary both orally and in written form. Online materials include a Spanish Academic Vocabulary Teacher’s Guide 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 2 Cuaderno de evaluación include all instructional assessments for the grade level, such as the “Examen de preparación,” “Evaluación para observar el progreso” with various forms, “Evaluación del tema,” “Tarea de rendimiento del tema,” and “Evaluación acumulativa/de referencia,” that all contain a “Tabla de análisis de las preguntas,” which display the specific question, the DOK, and the TEKS that students practice. For example, “Tarea de rendimiento del Tema 13” provides an opportunity for students to demonstrate their depth of understanding at DOK level 3 with “Ejercicio 7” aligned to TEKS 2.11B. The materials include a scoring guide that provides the TEKS alignment for each assessment. The Cuaderno de evaluación contains a performance assessment at the end of each Tema. “Evaluación acumulativa/de referencia: Temas 1 a 13” includes assessment items aligned to TEKS 2.4C, 2.8C, 2.10B, and 2.11A, and the “Tabla de análisis de las preguntas” identifies the corresponding TEKS and DOK levels for each item. In the “Guía de puntaje,” the “Tarea de rendimiento del Tema 4” includes questions 1, 2A, 2B, 3, 4A, and 4B with their corresponding scoring tables and detailed criteria that include references to the question number, DOK, and aligned TEKS.

Additionally, the grade 2 Guía del maestro includes opportunities for students to model mathematical thinking and explain reasoning through exploration and visual practice in lección 9-1. In paso 1 “Explorar y comentar,” paso 2 “Aprendizaje visual,” and paso 3 “Práctica y resolución de problemas,” students fold paper models to create equal parts, determine whether figures represent halves, fourths, and eighths, compare solution strategies, and explain why some models do not represent equal parts using pictures and discussion prompts aligned to TEKS 2.3A and 2.3D. In Tema 4, lección 4-3, paso 1 “Explorar y comentar,” students investigate different ways to solve comparison problems with unknown values. Students who finish early can solve another problem and show their work. These activities align to TEKS 2.7C, 2.4B, and 2.4C.

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 2 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 backward or add to subtract on an empty number line and represent 56 − 24 = 32. In paso 4 “Evaluar y diferenciar,” students use an empty number line to solve 73 − 45, using strategies such as counting by tens and ones to represent and solve the problem. These activities progress from modeling subtraction strategies to independently applying the strategies to solve problems.

In the grade 2 Guía del maestro lección 6-2 “Resolver problemas con monedas,” paso 1 “Explorar y comentar,” students are given an addition word problem involving coins and asked to solve it while showing their work in the space provided. The lesson transitions to “Aprendizaje visual,” where coins are introduced with pictures, names, and values, and students are guided to place coins in order from greatest to least value before counting using lines placed under each coin as a visual to find the total. In Tema 1 “Sumar y restar hasta 20,” the “Contexto matemático: conceptos clave” section describes how the materials increase rigor throughout the lessons and how students work with increasingly complex concepts over time. In lección 1-1 “Usar y escoger estrategias de suma,” students analyze addition patterns and use manipulatives and number lines to model their thinking as the materials progress to lección 1-2, “Estrategias de suma,” where students use strategies to count on and add numbers in any order. Furthermore, in lección 4-1 “Problemas verbales sin números,” students use models, draw pictures, and write equations to represent and solve one- and two-step word problems. The lesson’s rigor increases as students develop an understanding of the meaning of word problems with or without numbers before progressing to one- and two-step word problems that involve adding, subtracting, and comparing numbers.

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

In the grade 2 Guía del maestro, each Tema includes a “Contexto matemático: coherencia” section, with “¡Vuelve atrás!” and “Más adelante” subsections. Tema 3 “Restar hasta 100 usando estrategias” explains how the Tema relates to what students have previously learned and what students will learn in the future. For example, the TEKS 1.2B in Tema 8 for the previous grade level includes students developing an understanding of tens and ones, while future learning in the TEKS 2.9E will include students adding and subtracting up to 100 to solve one- and two-step problems. Additionally, the “Grade 2 Content Organization Rationale” program overview section provides key concepts and connections between Temas. For example, the key concept for Temas 6 and 7, “Trabajar con el dinero y la hora” and “Medición,” is “Most expressions of money, time, and length can be represented in different but equivalent forms.”

Additionally, in the grade 2 Guía del maestro, “Contexto matemático” demonstrates the connections between Temas through three sections: “Conceptos clave,” “Coherencia,” and “Equilibrio.” In Tema 5, lección 5-3 “Grupos iguales,” the “¡Vuelve atrás!” subsection highlights previously learned concepts, noting that students learned about even and odd quantities in the previous lesson, which serves as a foundation for understanding equal groups. In the “En esta lección” subsection, students use manipulatives, drawings, and numbers to represent and organize equal groups. In the “Más adelante” subsection, the materials describe future learning, such as how students will develop the concepts of adding and subtracting equal groups in the following three lessons. Furthermore, Tema 3 “Restar hasta 100 usando estrategias,” demonstrates connections between grade 2 and grade 3. “Más adelante,” in reference to grade 2, states, “Sumar y restar hasta 100 para resolver problemas: En el Tema 4, los estudiantes sumarán y restarán hasta 100 para resolver problemas de un paso y de dos pasos. En el Tema 7, sumarán y restarán hasta 100 para resolver problemas verbales relativos a longitudes TEKS 2.9E.” In reference to grade 3, it states, “Sumar y restar hasta 1,000: En el Tema 7, los estudiantes usarán la comprensión del valor de posición, las propiedades de las operaciones y la relación entre suma y resta para sumar y restar hasta 1,000 TEKS 3.4A.”

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

In the grade 2 Guía del maestro, Tema 7 “Contexto matemático: coherencia” connects prior grade 1 concepts, such as comparing lengths, using measurement tools, and representing addition and subtraction on a number line, to grade 2 measurement concepts involving estimating and measuring length, using different measurement units, solving measurement problems, and representing addition and subtraction on a number line. The materials also connect current grade 2 concepts to future grade 3 learning involving fractions on a number line, perimeter, and multistep measurement problem-solving. Tema 3 “Restar hasta 100 usando estrategias” includes language connections in “Adaptaciones del lenguaje” through the “Vocabulario del tema,” “Términos previos,” “Próximos términos,” “Vocabulario en contexto,” and “Vocabulario para poner en contexto” sections. For example, the grade 2 “Términos previos” include decenas, recta numérica abierta, suma parcial, unidades, and compensación, and “Próximos términos” include ninguno.

Additionally, the Guía del maestro Tema 7 “Presentación del tema: entender la suma” includes “Repasa lo que sabes” in “Análisis de los ejercicios,” along with the sections “Palabras de vocabulario,” “Actividad de vocabulario,” and “Vocabulario académico.” The “Palabras de vocabulario” section lists key vocabulary words, including metro, pulgada, pie, yarda, centímetro, longitud, and unidad cuadrada, and provides opportunities for students to estimate and measure lengths, describe measurement tools and units, and use mathematical language to explain measurement concepts that support current learning in measurement and geometry. 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 matemático: coherencia” section includes information on what students previously learned, how it connects to the current topic, and connections to future Temas and grade levels. For example, Tema 3 “Restar hasta 100 usando estrategias,” connects to a later Tema in grade 2 and to grade 3. “Más adelante” states, “Sumar y restar hasta 100 para resolver problemas: En el Tema 4, los estudiantes sumarán y restarán hasta 100 para resolver problemas de un paso y de dos pasos.” In reference to grade 3, it states, “Sumar y restar hasta 1,000: En el Tema 7, los estudiantes usarán la comprensión del valor de posición, las propiedades de las operaciones y la relación entre suma y resta para sumar y restar hasta 1,000 TEKS 3.4A.” The “¡Vuelve atrás!” section explains that students learned to understand place value in grade 1 and add up to 100 in grade 2.

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

In the grade 2 Guía del maestro, lección 3-2 “Contar hacia atrás o sumar para restar en una recta numérica vacía” includes the sections “Conceptos clave,” “Coherencia,” and “Equilibrio.” “Conceptos clave” includes a mathematics objective for lección 3-2 in which students use an open number line to count backward or add to subtract up to 100. The “Coherencia” section includes “¡Vuelve atrás!” “En esta lección,” and “Más adelante.” “¡Vuelve atrás!” connects to students’ prior knowledge of using an open number line to add tens and ones, and “En esta lección” builds on that knowledge as students use an open number line to subtract.

Additionally, lección 2-1 requires students to use their prior knowledge of counting forward and counting by ones, fives, and tens, decomposing numbers, and using a hundred chart to solve addition problems involving increments of 25 and compare multiple solution strategies. Furthermore, in lección 13-2 “Los beneficios de ahorrar,” the “¡Vuelve atrás!” section states, “Anteriormente, los estudiantes aprendieron la diferencia entre ahorrar y gastar.” “En esta lección” says, “Los estudiantes se centran en el ahorro y en cómo contribuir al ahorro a lo largo del tiempo aumentará la cantidad total. Usan lo aprendido sobre gráficas de barras para visualizar las contribuciones al ahorro a lo largo del tiempo.” “Más adelante” says, “Más adelante, los estudiantes aprenderán la diferencia entre depósitos y retiros, préstamos y otorgamientos, y entre productores y consumidores.” Additionally, in Tema 6, lección 6-1, paso 1 “Investigar,” the “Ejemplos del trabajo de los estudiantes” include “Contar monedas, Problema A,” which contains two tasks where students identify coins to determine the value of four nickels. The materials provide examples of students’ solutions, each demonstrating the application of previously learned concepts and procedures. For example, one student uses nickels and counts by fives to determine a total value of 20 cents, while another student uses a number line to skip-count by fives four times. The solutions require students to apply prior knowledge of counting by fives, coin values, and skip-counting on a number line.

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

In the grade 2 Guía del maestro, the “Elaboremos” section of each lesson includes an “Hablemos de matemáticas” subsection for students to engage in mathematical discourse using previously learned skills and concepts across lessons and Temas. In lección 2-10 “Sumar más de dos números de 2 dígitos,” the “Hablemos de matemáticas” section has students select a number table that does not belong from three number charts and justify why the table does not belong. The “Coherencia” section includes the “¡Vuelve atrás!” component, which notes that students previously counted one by one and 10 by 10, requiring them to retrieve and apply this knowledge to meet the objective of counting 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 2 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 100 while identifying even-number solutions and following number patterns through a fluency game activity. Additionally, “Repaso en espiral” is available digitally by lesson or as a print file for each lesson with 4–10 questions in each. The questions include both multiple-choice and open-ended questions. The “Repaso en espiral” for lección 2-1 contains four questions and the first consists of a word problem while the answer choices are a variety of addition and subtraction number sentences. The second question also consists of a subtraction word problem in which the student selects the answer choice that solves the problem. This provides spaced retrieval of previously learned skills as students continue to work with material learned in the previous topic.

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

In the grade 2 Guía del maestro, “Repaso del tema” and “Repasa lo que sabes” provide interleaved practice opportunities with previously learned skills and concepts across lessons and Temas. In Tema 3 “Presentación del tema: Restar hasta 100 usando estrategias,” the “Repasa lo que sabes” includes instructions for students to decompose, regroup, complete a strip diagram, use open number lines, and solve a word problem as they review previously learned concepts. The materials also include an “Análisis de los ejercicios” table for “Repasa lo que sabes” that identifies the TEKS being reviewed, such as 2.2A, 2.2B, 2.4B, and 2.4C for the Tema. Additionally, the Tema 10 “Repaso del tema” materials review lecciones 10-1 through 10-4 and require students to identify and describe attributes of two-dimensional figures and three-dimensional solids, compare and classify shapes and solids, and compose new solids using geometric attributes and vocabulary.

In the grade 2 Guía del maestro and “Biblioteca de diferenciación,” the “Levántate y razona” requires students to apply addition, subtraction, number relationships, number line representations, and part-part-whole concepts from lecciones 1-1 through 1-3 to create equations, represent quantities, and solve real-world problems involving groups of chickens and classroom stickers. Lección 13-2 “Los beneficios de ahorrar” consists of six questions that gradually release support. For example, the first two questions provide a visual representation in the form of a bar graph for students to use to identify how much money was earned over six months and answer a comparison question. The last two questions are STAAR practice questions that require students to answer multiple-choice questions. In the first question, students find the difference in the amount of money earned, while the second question requires a higher level of thinking.

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

In the Guía del maestro, the “Representémoslo en 3 actos” section presents “Acto 1,” “Acto 2,” and “Acto 3,” where students interpret, analyze, and evaluate models and representations for mathematical concepts and situations. For example, in lección 10-10, “¡A emparejarlo!” “Acto 1, El anzuelo,” students are provided with tasks to interpret mathematical concepts and situations and formulate mathematical questions with guidance such as “¿Qué pregunta les resulta más interesante?” and “¿Qué pregunta podríamos responder con las matemáticas?” Additionally, students are required to analyze mathematical concepts by making predictions with educator guidance such as “¿Por qué creen que su predicción es la respuesta a la Pregunta principal?” and “¿Quién tiene una predicción similar?” The 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 and are asked, “¿Qué suposición deben hacer para usar un modelo matemático?” The materials include student examples of creating a model with two triangles, two trapezoids, and one hexagon. In Tema 11, lección 11-12, students examine models created by Marco and Erica to determine the value of a collection of coins and interpret the representations to identify the quantities and values shown, analyze the different strategies used to organize and count the coins, and evaluate the efficiency of each approach through questions such as “¿Cómo podría Erica ser más eficiente?” and “¿Cómo podrían analizar y evaluar la eficacia del enfoque que escogieron para resolver el problema?” Students explain how the models support the solution and justify their reasoning when comparing strategies.

Additionally, in the grade 2 “Manual de resolución de problemas,” the materials include a problem-solving model that supports students in developing mathematical reasoning and problem-solving skills, guiding students through the problem-solving process by providing strategies for representing mathematical situations, such as drawing pictures, creating diagrams, using tables or graphs, and writing equations. The resource includes completed examples of student work. These representations help students organize and analyze the quantities in the problem, and students determine a solution using the representations created. Additionally, in “Biblioteca de diferenciación,” the materials include questions and tasks that require students to interpret, analyze, and evaluate models and representations for mathematical concepts and situations. In Tema 2 “Levántate y razona,” students interpret information from a food drive scenario, analyze possible totals using the given quantities, and create representations to justify their reasoning. Students examine sample student work that uses equations and place-value models to represent solutions and participate in a gallery walk to analyze multiple approaches. Furthermore, in the Guía del maestro, lección 5-8 “¡Cuántas manzanas!” the content objective is for students to add or count to find the number of objects in an array. The materials state, “A los estudiantes se les asigna la tarea de determinar cuántas manzanas hay en una matriz, con la información que tienen disponible sobre la cantidad de manzanas en cada fila y columna.” Students participate in a question brainstorm after watching the video to respond to the “Pregunta principal,” “¿Cuántas manzanas hay?” Students share their individual predictions and explain why they believe their predictions are correct. Students also reflect on unreasonable answers and then determine which model to use to represent the problem as they receive more information and analyze and evaluate their models as they transition from “Acto 2” to “Acto 3.” After the reflection, students have the opportunity to create and solve a problem similar to the one they solved.

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

The grade 2 materials include various questions and tasks that require students to create models to represent mathematical situations. For example, in lección 9-6 “Representémoslo en 3 actos, Tiras de papel,” the “Acto 2, El modelo” section includes questions and tasks for students to create models to represent mathematical situations. In “Desarrollar un modelo,” the materials prompt students to create their models with questions such as “¿Cómo pueden usar las matemáticas para modelar el problema?” The materials also include student examples, such as a grade 2 model representing fourths and eighths with drawn fraction bars and another model labeling the fraction with the type of paper based on the information in “Acto 2.” The answer to the problem is revealed in “Acto 3,” where students confirm their answers or adjust their models to continue representing the mathematical situation.

Additionally, in the Libro del estudiante Tema 3, lección 3-2 “Contar hacia atrás o sumar para restar en una recta numérica vacía,” students solve a problem about insects with and without wings and use an open number line to model the relationship between the total number of insects and the number of insects without wings. Students represent their solution on the number line to determine how many insects have wings, creating a mathematical model to represent and solve the situation. Furthermore, the Libro del estudiante materials include lección 7-2 “Elaboremos: usar modelos para unidades usuales,” where students work toward the objective, “Puedo hallar la longitud de los objetos usando diferentes unidades.” In the “Explorar y comentar” activity, the materials present the following task: “Encuentra tres objetos en el salón de clases que midan aproximadamente lo mismo que un clip. Dibuja esos objetos debajo.” This task requires students to first use a paper clip as a concrete model of a standard unit of measurement to compare the lengths of classroom objects. Students then create model representations by drawing the objects and the paper clips used to measure them and discuss their findings with their classmates. In lección 11-8 “Patrones de valor de posición con números,” the “Investiguemos” content objective states that students will compose and compare three-digit numbers using their prior knowledge of three-digit numbers, place value, and pictorial and concrete representations. Paso 1 begins by asking students whether they have ever played a game where they had to keep score, which games did not require keeping score, and how the winning score was determined. The corresponding student activity book has a designated space for students to play a game and collect digits to represent numbers. After collecting the digits, students use them to compose a three-digit number with hundreds, tens, and ones, creating a model that represents the mathematical situation.

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

The grade 2 Guía del maestro includes questions and tasks that provide opportunities for students to apply conceptual understanding to new problem situations and contexts. For example, in Tema 9, lección 9-5 “Fracciones mayores que 1,” students determine how many fourths can be formed from two whole crackers divided into equal parts. Student work samples show students partitioning each whole into fourths and using the fractional parts to represent a quantity greater than one whole. The lesson also prompts students to explain how multiple wholes can be represented using fractional units and to justify their solutions. In lección 12-3 “Sumar en una recta numérica vacía,” the “Hablemos de matemáticas” section provides opportunities for students to apply “Resolución de problemas” by presenting two related mathematical problems one at a time and having students share their strategies and solutions for each problem. Additionally, in activities incorporating TEKS 2.4C and 2.7B, students engage in discourse about the relationships within and between both problems, applying their conceptual understanding to new problem situations and contexts.

Additionally, in the Guía del maestro Tema 5, lección 5-3 “Grupos iguales,” students use a school sports context to determine how 12 students can be organized into equal groups and analyze groupings of two and three, determine the number of teams that can be formed, and consider whether other equal-group arrangements are possible. Students represent and justify their solutions using words, numbers, models, or drawings, applying their understanding of equal groups in a contextualized problem-solving situation. In lección 3-6 “Valor de posición y resta con números de dos dígitos,” paso 2 “Relacionar,” students apply conceptual understanding to new problem situations and contexts by determining which subtraction problems require regrouping and explaining how they came to that conclusion. In the “Hablar sobre las ideas matemáticas” section, students participate in a think-pair-share activity to communicate how they used place value in the problems they solved. In Tema 8 “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 for students to demonstrate their understanding in different ways. Project 8B asks students to create a graph showing the flowers found in their neighborhood, for example. To complete the project, students apply their conceptual understanding of counting, data collection, and data representation by organizing information into tables, picture graphs, or bar graphs in a new context.

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

The grade 2 Guía del maestro provides tasks designed to build students’ automaticity and fluency. For example, Tema 9 “Partes iguales y fracciones” includes an activity aligned to TEKS 2.4B in which students find the sum or difference and shade a route to the “salida/meta” following only even numbers and moving upward, downward, left, or right. Additionally, the materials include an activity in “Otra actividad” and an enrichment activity in “Desafío adicional” aligned to TEKS 2.1C and 2.4B. Tasks in the “Biblioteca de diferenciación” feature the following sections for each unit: “Escoge un proyecto,” “Matemáticas y lectoescritura,” “Contribuciones asombrosas,” “Levántate y razona,” “Juegos prácticos,” and “Práctica de fluidez.” “Juegos prácticos” includes games with colorful game boards aligned with the content from the unit. The materials state, “Cada tema también incluye un juego de fluidez. . . Los juegos de fluidez pueden ser jugados en cualquier momento.” “Práctica de fluidez” includes practice sheets with 19 problems, with the one featured in Tema 1, for example, focusing on addition and subtraction up to 20 to build fluency.

Additionally, the grade 2 Guía del maestro includes tasks to build students’ automaticity and fluency through lección 2-2, paso 3 “Práctica y resolución de problemas.” In this interactive activity, students build rigor and demonstrate their comprehension of the content and fluently apply their knowledge, beginning with guided practice using a 100 chart to solve addition equations. The activity continues with practice and problem-solving using a 100 chart, solving addition word problems, applying higher-order thinking skills, and concluding with a STAAR assessment practice question. In the Libro del estudiante, Tema 7 “Desarrollar fluidez,” students engage in repeated practice with addition and subtraction within 100 to develop accuracy, efficiency, and flexibility with computation. Students solve multiple addition and subtraction equations and match each expression to clues describing sums and differences. The activity provides repeated practice with two-digit computation and supports fluency with addition and subtraction within 100, providing 45 facts, and including an embedded maze, in which the even-number answers are the correct path. The Guía del maestro for the corresponding activity also includes extensions called “Otra actividad” and “Desafío adicional” using the same sheet.

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

The grade 2 Guía del maestro provides opportunities for students to practice the application of efficient, flexible, and accurate mathematical procedures. For example, in lección 11-5 “Números hasta 1,200 en la recta numérica,” the “Hablemos de matemáticas” section includes the “Número misterioso” activity, which requires students to analyze clues to determine mystery numbers. The materials provide clues that promote mathematical thinking and discourse, such as “El número está entre 200 y 250” and “El número tiene el mismo número de centenas, decenas y unidades.” In Tema 7, lección 7-11 “Medir el área,” students use square tiles to cover rectangles and count the total number of unit squares to determine area. The lesson’s “Apoyo al lenguaje” and “Hablemos de matemáticas” sections require students to identify rows and columns and explain how area is measured, as well as the “Boleto de salida,” which requires students to apply these procedures to determine the area of a rectangle using square units.

Additionally, in Tema 12, lección 12-3 “Sumar en una recta numérica vacía,” students solve 598 + 123 using an open number line and decompose 123 into hundreds, tens, and ones. Student samples demonstrate different procedures, including adding 100, 20, and three in sequential jumps and starting from different numbers on the number line to determine a sum of 721. Additionally, the Libro del estudiante, lección 10-2 “Sólidos” provides opportunities for students to solve problems using efficient, flexible, and accurate mathematical procedures, including two examples of student work demonstrating different approaches to completing the task. The task promotes flexibility because students may use different approaches and levels of mathematical language to describe the same three-dimensional shapes. It supports accuracy because students must correctly identify the defining attributes of each shape and relate them to appropriate real-world objects. The task also promotes efficient mathematical procedures because students use the properties and attributes of the shapes.

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

The grade 2 Guía del maestro includes 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 11-12 “Tener centavos,” the “Representémoslo en 3 actos” section includes “Acto 1, El anzuelo,” which provides students the opportunity to formulate predictions as they evaluate procedures and formulate questions. Educators ensure students have varied predictions and evaluate procedures including comprehension of the importance of thinking of unreasonable predictions. The section “Acto 2, El modelo” allows students to incorporate mathematical processes and solutions for efficiency, flexibility, and accuracy when creating their own model to represent and respond to the question. Students also apply the provided information prior to creating their models in “Revelar la información.” In “Acto 3, La solución,” the materials include using the provided video to reveal the answer to the initial question. The materials also include three sections to support opportunities for students to evaluate solutions for efficiency, flexibility, and accuracy with “Comprobar conclusiones” and “Reflexionar sobre el razonamiento,” where students must represent, explain, prove, and finally “Crear un problema.” Furthermore, in Tema 4, lección 4-1 “Problemas verbales sin números,” the “Seleccionar y poner en secuencia,” “Relacionar estrategias de solución,” and “Reflexión” sections guide students to examine multiple approaches for solving a problem, identifying errors in student work, and explaining how different representations can be used to determine a solution. Students continue evaluating solution methods through “Práctica y resolución de problemas,” “Comprobación rápida,” and “Práctica adicional,” where they analyze solutions and justify their reasoning.

Additionally, in Libro del estudiante, Tema 9, lección 9-2, students create multiple plans for partitioning a lasagna and a pan de maíz into fourths and determine how many parts remain and how many are given away. In the “Relacionar” activity, students evaluate whether the parts in Plans A, B, C, and D represent equal fourths and explain their reasoning. Students also analyze a pizza divided into four parts and determine whether the pieces are equal, justifying their conclusion. These tasks require students to examine and compare solutions based on the mathematical requirement that fourths must be equal parts. In the Guía del maestro, Tema 5, lección 5-8 “¡Cuántas manzanas!” the content objective is to add or count to determine the number of objects in an array. The materials state, “A los estudiantes se les asigna la tarea de determinar cuántas manzanas hay en una matriz, con la información que tienen disponible sobre la cantidad de manzanas en cada fila y columna.” After watching the lesson’s video, students participate in a question brainstorm, responding to the “Pregunta principal:” “¿Cuántas manzanas hay?” Students share their individual predictions and their reasoning for why they believe their predictions are correct while also reflecting on unreasonable answers. Then students determine which model to use to represent the problem as they receive more information and analyze and evaluate their models as they transition from “Acto 2” to “Acto 3.” After the reflection, students have the opportunity to create and solve a problem similar to the one they solved.

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

The grade 2 Guía del maestro includes embedded supports for educators to guide students toward increasingly efficient approaches. For example, in lección 8-1 “Organizar datos,” 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: “¿Cómo puedes contar la cantidad de votos para hámster en la pictografía?” and “¿Qué gráfica prefieres para obtener información?” Additionally, paso 2 “Hablar sobre las ideas matemáticas” includes embedded supports to guide students’ approaches, for example, “Pida a los estudiantes que participen en una actividad de pensar-trabajar en parejas-compartir sobre las gráficas. Esté atento a los estudiantes que afirman que cuanto más largas las barras o cuantas más imágenes, más datos.” In Tema 13, lección 13-6, students determine the amount of money that must be repaid after purchasing an item. During “Acto 2,” students use different strategies to represent and solve the problem, including drawings, equations, and calculations with coin values. Educator guidance prompts students to compare solution methods and discuss how different representations support problem-solving. In “Acto 3,” students evaluate their solutions against the revealed answer and consider the efficiency and accuracy of their approaches.

Additionally, the grade 2 materials provide embedded support in Tema 12, lección 12-2, in the “Seleccionar y poner en secuencia” section, which directs educators to present student solutions in a progression from common errors to strategies that use place value to form three-digit numbers and determine a sum within a target range. The “Relacionar estrategias de solución” section further guides educators to compare representations and discuss how place-value strategies can be used to solve the problem, supporting students’ development of increasingly efficient approaches. 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 necesitan resolver primero para resolver este problema?” “¿Qué estrategia pueden usar para resolver el problema?” “¿Cómo restaban números antes?” “¿Existe otra manera de resolver el problema?” “¿Su solución es razonable?” “¿Por qué escogieron esa estrategia?” and “¿Qué otra estrategia pueden usar para que restar sea más fácil?”

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

The grade 2 Guía del maestro explicitly states the conceptual and procedural emphasis of the TEKS in “Contexto matemático: Coherencia” and “Contexto matemático: Equilibrio” sections in each Tema. “Comprensión de conceptos” and “Destrezas en procesos y automaticidad” directly address the conceptual and procedural emphasis of the TEKS within the materials. In Tema 5 “Trabajar con grupos iguales,” “Comprensión de conceptos,” students learn to recognize number pairs as numbers that can be identified by counting by twos and represented by two equal rows of objects, ultimately comprehending the relationship between equal groups as repeated addition or repeated subtraction aligned to the TEKS 2.6A, 2.7A, and 2.6B. Additionally, the “Destrezas en procesos y automaticidad” section identifies how the procedural emphasis of the TEKS is addressed, such as with students practicing addition operations up to 20 and creating equations that represent number pairs, odd numbers, and equal groups with the expectation of addition and subtraction automaticity up to 20 using basic operations for Tema 5. In Tema 7 “Contexto matemático: equilibrio,” the “Comprensión de conceptos” section identifies conceptual expectations, including understanding the measurement process, relationships among customary and metric units, and the relationships between the size of a unit and the number of units needed to measure an object. The “Destrezas en procesos y fluidez” identifies procedural expectations, including using measurement tools to measure to the nearest unit and using a number line to solve addition and subtraction problems. The “Aplicaciones” section connects these concepts and procedures to real-world measurement situations involving length and distance.

Additionally, Tema 11 “Presentación del tema: explorar números hasta 1,200,” includes the essential question “¿Cómo puedes contar, leer y mostrar números hasta 1,200?” and connects instruction to the TEKS process standard 2.1A through the “Paseo de matemáticas.” The page includes the “Repasa lo que sabes” section, which reviews prerequisite skills related to place value, number composition, and comparison, and an “Análisis de los ejercicios para el diagnóstico y la corrección” table that identifies the specific TEKS addressed throughout the topic, including 2.5A, 2.5B, 2.2B, 2.7C, and related readiness and supporting standards. In Tema 4, lección 4-4, the table “Análisis de ejercicios: práctica y resolución de problemas” explicitly identifies the exercise, DOK level, content TEKS, and process TEKS addressed in the accompanying student practice. The table supports the purpose of the “Práctica y resolución de problemas” section of the Libro del estudiante by identifying the TEKS associated with problems 2–6. The materials clearly distinguish between the content TEKS 2.4C and 2.7C and the process TEKS 2.1D, explicitly identifying the mathematical content and process standards addressed by each exercise for the conceptual and procedural emphasis of each task. Furthermore, in lección 3-1 “Elaboremos,” students begin to develop number sense by noticing patterns on a 100 chart to subtract numbers and develop mental math. Then, lección 3-12 connects this learning to the conceptual understanding of subtraction strategies when students use what they know about subtraction to find how many objects are missing from a group and create a mathematical model.

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

The grade 2 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 7-11 “Medir el área” features concrete models in paso 1 “Explorar y comentar” as students use double colored squares to find a solution for how many can fit inside a rectangle. In paso 2 “Aprendizaje visual,” pictorial representations are included as an array for students to find the area of the rectangle by finding the units in the rectangle. Additionally, in paso 3 and 4, students use abstract representations of multiplication to find the area of rectangles using varying strategies and reasoning 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 12, lección 12-7 sections, “Aprendizaje visual” and “Práctica guiada,” students use bloques de valor de posición to model subtraction of hundreds and tens from three-digit numbers. The lesson includes pictorial representations of place-value blocks with units crossed out to show the subtraction process and directs students to write corresponding equations such as 368 − 30 = 338 and 368 − 200 = 168. In the guided practice, students use place-value blocks or mental math to solve subtraction problems and record solutions using numerical equations. In Tema 6, lección 6-1 “Resolver problemas sobre dinero,” paso 1 “Investigar” presents a problem-solving task and instructs students to use coins and a die to model and solve the problem. Students are encouraged to choose any strategy that helps them represent their thinking, providing opportunities to use concrete manipulatives, pictorial representations, or abstract representations. The materials also include four samples of student work demonstrating multiple representations for solving the same problem. In the “Manual de resolución de problemas,” the materials provide a problem-solving guide and sheet for students to refer to and use when solving problems. This tool supports student understanding of the TEKS-aligned concepts and allows them to engage further with the material by increasing the rigor.

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

The “Concrete, Representational, Abstract Instructional Model” program overview includes various supports for students to connect, create, and define mathematical models in “Progression within and Across Lessons,” “Tasks at the Start of Lessons,” “Visual Learning,” and “Visual Learning Animations” sections. The materials guide students in using concrete objects such as counters, cubes, place-value blocks, and tiles, or pictorial models such as number lines, arrays, grids and strip diagrams in the explore and share sections of “Let’s Build” lessons, as well as the investigate sections of “Let’s Investigate” lessons. Additionally, the materials include abstract concepts in the lesson with supports for students, such as “When students share and discuss solutions, rich conversations deepen conceptual understanding of connections between concrete, pictorial, and abstract.” Furthermore, the “Progression Within and Across Lessons” section explains that “there is a progression from concrete to pictorial to abstract that occurs across lessons and within lessons,” with opportunities for students to connect their work from the “Explore and Share” activities to newly introduced mathematical ideas. This section incorporates illustrations of concrete manipulatives and representational diagrams that support students in creating, explaining, and defining mathematical models before transitioning to abstract reasoning. The materials also provide digital manipulatives that allow students to create and manipulate concrete and representational models as they develop conceptual understanding.

Additionally, the grade 2 materials support students as they connect, create, define, and explain concrete and representational models and abstract mathematical concepts through a structured problem-solving process aligned to the TEKS. The Guía del maestro includes “Elaboremos” lessons that start with “Explorar y comentar.” For example, in lección 9-3, students use crayons to represent three-fourths of a square. In “Aprendizaje visual,” students begin to connect concrete representations to pictorial representations. The tasks become more abstract in “Práctica guiada” and “Práctica y resolución de problemas.” At the beginning of each topic, the materials provide a math background to guide understanding of key concepts that develop over the course of the topic. For example, in Tema 1, lección 1-1, students choose and use strategies to solve word problems using prior knowledge for solving addition within 20, analyze addition and fact patterns, and use tools like counters and number lines to represent their thinking. This understanding connects to more abstract concepts in lección 1-4, where students develop an understanding of different strategies such as counting on, applying the commutative property, making ten, and using doubles and near doubles.

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

The grade 2 Guía del maestro provides various opportunities for students to develop academic mathematical language through visuals, manipulatives, and other language development strategies, such as in the Tema 2 “Suma hasta 100 usando estrategias” “Repasa lo que sabes” section. For example, the “Presentación del tema” includes the “Actividad de vocabulario” and “Vocabulario académico,” which reinforce academic mathematical language as students practice with classmates or in a virtual setting. “Actividad de vocabulario” provides a variety of activities for language development, such as having students write the word decenas and create a model to demonstrate their knowledge of the word. “Vocabulario académico” includes online activities that use visuals, manipulatives, and other language development strategies to present or review words in the Tema. The “Apoyo al lenguaje” section in lección 9-1 introduces the multiple meanings of the terms igual and partes iguales before the lesson. Students use visual models of rectangles, circles, and triangles divided into equal parts to distinguish the meaning of the terms in a mathematical context and describe the representations using the vocabulary during class discussion.

Additionally, in the Libro del estudiante, the “Aprendizaje visual” section introduces mathematical vocabulary through visual models and guided mathematical discussion. In lección 5-1, students use connecting cubes and a hundreds chart to determine whether numbers are par or impar, explain how equal groups identify even numbers, and respond to the “Hablar sobre las ideas matemáticas” prompt by explaining whether a quantity is even or odd using mathematical vocabulary. The Guía del maestro lección 12-5 “Sumar usando el valor de posición y sumas parciales” provides students with opportunities to develop mathematical language through the use of manipulatives, including bloques de valor de posición with “Elemento didáctico 70” and tablas de sumas parciales with “Elemento didáctico 32.” Students have the opportunity to develop their academic mathematical language using manipulatives in the “Explorar y comentar” section of “Elaboremos” lessons. Students can solve 248 + 325 using a strategy of their choice, including manipulatives. In lección 1-1 “Usar y escoger estrategias de suma,” students solve an addition word problem in which they need to find how many red dragons and yellow dinosaurs could be in the piñata shown in the graphic. Students use counters as support and may use words, numbers, or a drawing when choosing their strategy to solve the problem and show their work. To be successful, students use the counters as a visual representation of their counting by connecting mathematical terms to concrete objects.

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

The materials for grade 2 include embedded educator guidance in the Guía del maestro to scaffold and support students’ development and use of academic vocabulary throughout the school year. In lección 2-2 “Elaboremos: sumar decenas y unidades en una tabla de 100,” the “Apoyo al lenguaje” section includes embedded educator guidance to scaffold and support students’ development and use of academic mathematical vocabulary in context. For example, the materials state, “Agrupe en un banco de palabras de términos clave con los estudiantes para ayudarles a escribir o comentar cómo sumar números de dos dígitos utilizando una tabla de 100” and “Pida a los estudiantes que hallen las palabras que les gustaría agregar al banco de palabras, como jugada, tabla de 100, arriba, adelante, atrás y fila.” In Tema 11 “Explorar números hasta 1,200,” the “Repaso del tema” section includes a “Repaso de vocabulario” section with educator guidance for reviewing Tema vocabulary through an oral language game in which students provide clues and identify mathematical terms. The guidance also directs students to write mathematics questions using vocabulary from the topic, exchange questions with a partner, and use correct mathematical vocabulary and spelling while explaining their responses.

Additionally, the Guía del maestro Tema 5 includes an “Actividad de vocabulario” that directs educators to use a Frayer model, the “Elemento didáctico 1,” to help students analyze vocabulary terms by recording definitions, characteristics, examples, and nonexamples. The guidance also instructs educators to have students work collaboratively to complete additional Frayer models for other vocabulary terms and directs students to an online vocabulary game available in the “Centro de juegos” to reinforce vocabulary development. Each “Repaso del tema” also includes a “Repaso de vocabulario” section in which students have the opportunity to engage in oral and written review of words. For Tema 6 “Trabajar con el dinero y la hora,” the “Lenguaje oral” section guides educators to play “¿Correcto o incorrecto?” a game in which an educator or a student uses a vocabulary word in a sentence and the class determines whether the word was used correctly. The “Escritura en matemáticas” section directs educators to have students work in pairs to have each student write a question using a vocabulary word. The students must then exchange papers and write their answers to the questions. In Tema 4, the “Vocabulario académico” section instructs educators to help students look at the targeted word in different ways by guiding them in creating a word web using academic mathematical vocabulary in context. Students work in pairs and write the targeted word in the center oval along with an equation. They then write several more related equations around the oval, being sure to include addition and subtraction as well as different ways to write the same equation.

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 2 materials include embedded educator guidance in the Guía del maestro to support students’ application of appropriate mathematical language, such as through discourse opportunities. In lección 1-3, “Elaboremos: dobles y casi dobles,” educator guidance supports student responses to questions and tasks through the use of mathematical language, such as “Pida a los compañeros que comparen sus trenes de cubos para ver si están de acuerdo. Repita para casi dobles” and “Luego, pida a los estudiantes que comenten por qué puede haber más de una respuesta correcta para casi dobles.” Additionally, the “Hablemos de matemáticas” section prompts educators to support the application of appropriate mathematical language with the following guidance: “Muestre a los estudiantes las filas de ranas y luego pídales que hallen la cantidad de ranas que haya en cada fila. Pídales que describan el patrón en la cantidad de ranas junto a un compañero.” In paso 1 “Explorar y comentar,” the materials guide educators to support student responses using exemplar responses to questions and tasks in the “Supervisar, seleccionar y poner en secuencia” section, where students find a relationship between two equations using colored fichas. The materials provide student example responses and educator-guided questions that use appropriate mathematical language, such as “¿En qué son semejantes las dos ecuaciones?” and “¿En qué se diferencian?” Lección 7-2 “Usar modelos para unidades usuales” introduces the vocabulary words estimación, pie, pulgada, longitud, unidad, and yarda. The “Apoyo al lenguaje” section then provides educator questions that use these vocabulary words, such as “¿Qué mide aproximadamente un pie de longitud?” and “¿Qué mide aproximadamente una yarda de longitud?” In paso 3 “Práctica y resolución de problemas,” questions 7 and 10 include embedded educator guidance in the “Responder” and “Razonamiento de orden superior” sections to support the application of syntax.

Additionally, lección 8-1, paso 1 “Investigar,” includes the “Rutina de lenguaje: tres lecturas,” which guides educators to ask questions such as “¿De qué trata la tarea?” “¿Qué información se da en la tarea?” and “¿Qué les está pidiendo hallar la tarea?” The lesson also contains “Potenciar la voz del estudiante,” which provides discourse prompts with mathematical vocabulary that encourage students to share ideas, connect mathematics to their experiences, and participate in mathematical conversations during instruction. Paso 1 “Investigar” includes the “Ejemplo de trabajo de los estudiantes” section with varying student responses and educator guidance using exemplar responses to questions and tasks, such as “¿De qué maneras diferentes las gráficas muestran los votos?” In Tema 6 “Trabajar con el dinero y la hora,” the “Lenguaje oral” section guides educators to play “¿Correcto o incorrecto?” a game in which an educator or a student uses a vocabulary word in a sentence and the class determines whether the word was used correctly. The “Escritura en matemáticas” section directs educators to have students work in pairs. Each student writes a question using a vocabulary word, including the application of appropriate syntax. The students exchange papers and write their answers to the questions. Lección 4-2 asks students to describe two strategies they would use to solve 12 + 27 + 28 + 35. Educators provide students with language supports by having them incorporate sentence starters in their responses, such as “Una estrategia que usé fue. . . ” “Otra estrategia que usé fue. . . ” and “Escogí estas estrategias porque. . . ” After sharing their strategies, students further refine and use their mathematical vocabulary by critiquing, defending, and clarifying their strategies.

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

The grade 2 Guía del maestro includes the TEKS process standards integrated throughout the materials. The “Estándares de procesos matemáticos de los TEKS en la enseñanza” section includes four subsections that explain how the TEKS process standards are integrated into the materials: “Estándares de procesos matemáticos de los TEKS en la enseñanza,” “Estándares de procesos en problemas y evaluaciones,” “Estándares de procesos y el Manual de resolución de problemas,” and “Estándares de proceso y uso de diagramas de tiras para resolver problemas.” In “Estándares de procesos en problemas y evaluaciones,” the materials include “Estándares de procesos matemáticos de los TEKS en evaluaciones,” which states, “Los ejercicios que evalúan contenido también animan a los estudiantes a usar Estándares de procesos.” Additionally, Tema 9 “Estándares de procesos matemáticos de los TEKS: partes iguales y fracciones” highlights TEKS 2.1B and 2.1C and describes observable student behaviors such as using visual models to divide figures into equal parts, comparing equivalent fractions, representing fractions with models, estimating fractional values, and justifying solutions while solving fraction problems.

Additionally, Tema 7 “Vistazo al tema,” identifies the mathematical objectives, language objectives, vocabulary, content TEKS, and corresponding “Estándares de procesos matemáticos” for each lesson, including TEKS 2.1A–2.1G, demonstrating that the TEKS process standards are intentionally incorporated throughout instruction rather than addressed in isolation. In “Estándares de procesos matemáticos resaltados en las lecciones del Tema” for Tema 6 “Trabajar con el dinero y la hora,” the table includes a column that states the following: “Seleccionar herramientas cuando sean apropiadas, incluyendo objetos reales, manipulativos, papel y lápiz, y tecnología, además de técnicas cuando sean apropiadas, incluyendo el cálculo mental, la estimación y el sentido numérico, para resolver problemas TEKS 2.1C.” The column then lists how the breakout is reflected in the Tema. For example, “usan monedas para ayudar a resolver problemas de dinero, hallan colecciones de monedas que sean equivalentes a $1.00, usan el conteo salteado y el conteo hacia adelante para hallar el valor de un grupo de monedas.” Lección 3-1 includes the TEKS mathematical process standards 2.1E, 2.1F, and 2.1G. The “Boleto de salida” activity identifies process standard 2.1E, which states, “genere y utilice representaciones para organizar, anotar, y comunicar ideas matemáticas.” In the “Boleto de salida,” students apply the process standard in question 1 by using a 100 chart to solve 59 − 23.

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

The materials for grade 2 include a description of how the TEKS are integrated and connected throughout the course in each Tema’s “Contenido” section. For example, Tema 1 “Sumar y restar hasta 20” includes a table that shows the order of the lessons and how the TEKS are incorporated throughout the topic. Lección 1-1 “Elaboremos: usar y escoger estrategias de suma” includes the TEKS 2.4A, 2.1B, 2.1D, and 2.1E. Temas 1 and 2’s “Contenido” sections list the content TEKS and corresponding TEKS process standards for every lesson, such as lección 1-1 “Usar y escoger estrategias de suma,” which includes the TEKS 2.4A, 2.1B, 2.1D, and 2.1E, and lección 2-11 “Resolver problemas verbales de uno y dos pasos,” which contains the TEKS 2.4C, 2.7C, 2.4B, 2.1A, 2.1B, and 2.1E.

The grade 2 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 “Contenido y secuencia: 135 días” section lists each Tema throughout the grade level and includes each process standard that will be used throughout the Temas. For example, process standards 2.1A–2.1G are integrated into every grade 2 Tema and connected throughout lessons, helping students build critical thinking skills and math fluency over time. The scope and sequence also includes a brief description of the tools used in each lesson, which connects to process standard 2.1C, in which students use a tool to solve problems. In the Guía del maestro, “Vistazo al tema” includes the TEKS for each lesson, and “Contexto matemático: coherencia” includes the components “¡Vuelve atrás!” “Tema. . . ” and “Más adelante.” These components identify the TEKS aligned to what was taught before, during, and after the topic.

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 2 Guía del maestro materials includes a description of how the TEKS are incorporated within the Tema through the “Estándares de procesos matemáticos destacados en las lecciones.” In Tema 4 “Resolver más problemas usando estrategias numéricas,” the “Estándares de procesos matemáticos de los TEKS” table describes how the TEKS process standards are incorporated and connected throughout the Tema and includes student mathematical expectations for each standard. For TEKS 2.1A, for example, the materials state, “Usan la información en un problema verbal para determinar si deben sumar o restar para resolver el problema.” Tema 10 “Geometría” highlights TEKS 2.1D and 2.1F, which describe observable student behaviors aligned to each process standard and includes educator questioning strategies that connect the process standards to geometry throughout the topic.

Additionally, the 165-day Guía del ritmo de enseñanza states that TEKS process standards 2.1A–2.1G are integrated throughout each Tema and provides a pacing guide that aligns every Tema with its corresponding content TEKS across all 13 Temas, showing how the process standards are addressed throughout the course. In Tema 4 “Vistazo del tema: Resolver más problemas usando estrategias numéricas,” the materials include an overview table that organizes the instructional components of the topic. 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 2.1A, 2.1D, and 2.1F. Additionally, Tema 3 provides the process standard connected to the activity. TEKS 2.1A in the materials 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 visit a skyscraper and must use their subtraction strategies to solve the question, “¿Cuántos pisos más hay hasta la cima?” The activity allows students to make connections to everyday life and continue to develop their mathematical thinking when solving problems throughout the topic.

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

The grade 2 Guía del maestro includes an overview of the TEKS process standards incorporated into each lesson. Paso 3 “Práctica y resolución de problemas” and paso 4 “Evaluar y diferenciar” both include an “Análisis de los ejercicios” table that provides an overview of the TEKS process standards incorporated into lección 2-7 “Elaboremos: sumar con sumas parciales y usar el valor de posición.” For example, paso 3’s “Análisis de los ejercicios: Relacionar; Práctica y resolución de problemas” table includes the TEKS 2.4B. Paso 4’s “Análisis de los ejercicios: Práctica adicional” table includes the TEKS 2.4B and the process TEKS 2.1A. Additionally, lección 12-1 “Sumar decenas y centenas” lists TEKS process standards 2.1D and 2.1F in the “Estándares de procesos matemáticos” section.

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 9-1 “Ver fracciones en figuras” lists the content TEKS 2.3D and the TEKS process standards 2.1D and 2.1E in the opening section of the lesson. Students then explore equal parts and identify figures that represent halves, fourths, and eighths. In Guía del maestro lección 4-2 “Elaboremos: resolver problemas de suma y resta con valores desconocidos,” the process standards are identified in a blue-shaded section at the bottom of the lesson. For this lesson, the materials identify the process TEKS 2.1A, 2.1D, and 2.1F, 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 the TEKS 2.1F for lección 4-2.

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

The grade 2 Guía del maestro includes opportunities for students to think mathematically, persevere through solving problems, and make sense of mathematics. Lección 13-2 “Elaboremos: los beneficios de ahorrar” includes guided support that encourages mathematical thinking in paso 1 “Explorar y comentar,” where students count cents to find an amount that was saved. The materials ask, “¿Hay una manera más eficiente de encontrar la respuesta?” Students then use mathematical thinking to solve the problem. In paso 3 “Práctica y resolución de problemas,” students think mathematically through “Práctica guiada” and “Práctica y resolución de problemas.” The materials direct educators to provide the following guidance: “Recuerde a los estudiantes que, para los problemas que se formulan como ‘cuánto más’, deben usar la resta para ayudar a resolver el problema.” Students apply their mathematical thinking in “Práctica y resolución de problemas” to solve problems and make sense of mathematics. In Tema 13, lección 13-1, the “Investigar” section in “Ahorrar y gastar” provides four samples of student work that demonstrate different approaches to solving the same problem, giving students opportunities to think mathematically and analyze multiple solution strategies. Each student solves the problem using a different strategy, allowing students to compare and evaluate different mathematical approaches. The materials include educator prompts that encourage deeper mathematical thinking, such as “¿Hay otra palabra para guardar dinero? ¿Y para dar dinero?” and “¿Si cada vaso de limonada costó 5 centavos, cuánto ganó?” These questions prompt students to reason about the mathematical context and justify their thinking.

Additionally, the Guía del maestro and Libro del estudiante provide opportunities for students to persevere through solving problems and think mathematically to make sense of mathematical content. For example, in the Libro del estudiante, lección 3-1 “Restar decenas y unidades en una tabla de 100” engages students in using a 100 chart to solve subtraction problems, comparing two solution strategies, explaining how counting forward or backward can be used to find the difference, and solving problems involving unknown values. Students are prompted to explain their reasoning and represent their solutions using equations and a 100 chart. Additionally, the Guía del maestro “Investiguemos” lessons similarly provide opportunities for students to think mathematically. Paso 1 “Investigar” provides students with opportunities to think mathematically as they persevere through solving problems and working through the investigation as they move into small-group instruction. Students also continue to persevere through solving problems in paso 2 “Conectar” and paso 3 “Práctica y resolución de problemas.” In Tema 4 “Resolver más problemas usando estrategias numéricas,” the materials provide opportunities for students to develop confidence, resilience, and self-efficacy while solving mathematical problems. The materials include explicit educator guidance that encourages students to persevere as they work through challenging tasks. The materials state, “Anímelos a que creen sus propios problemas verbales, fomentando la creatividad y una comprensión más profunda de los conceptos matemáticos.”

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.

All criteria for guidance met.

The grade 2 Guía del maestro includes support for students to understand, explain, and justify that they can solve problems and complete tasks in a variety of ways. Students are presented with new material in the “Explorar y comentar” section of the lesson. In lección 8-6 “Escribir y resolver problemas usando datos,” students see a picture graph. The instructions ask students to use the given data to write and solve a data problem using the table that shows how much money was spent over the course of three weeks. Educators observe which questions students write and ask which data questions students have previously solved. The next section in the lesson, “Aprendizaje visual,” asks an essential question and is followed by class conversation with questions such as “¿Por qué pueden restar para hallar la respuesta a este problema?” where students explain and justify how they can subtract to find the answer. This section also includes a think-pair-share activity during “Hablar sobre las ideas matemáticas,” where students have the opportunity to share and explain how they used the graph to write and solve their own problem, supporting their understanding that problems can be approached in multiple ways. Tema 8, lección 8-6 includes the “Hablemos de matemáticas” section, which provides opportunities for students to develop mathematical understanding by explaining and justifying their thinking. Students have opportunities to explain and justify their solutions with peers or in small-group discussions. For example, students work on a problem titled “¿Cuál no pertenece?” in which they develop their understanding of data representations. Students are asked to identify the representation that does not belong and justify their reasoning. The materials explicitly acknowledge that there are multiple correct answers because there are different ways to represent and interpret the same data.

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 2 Guía del maestro provides varying opportunities for students to do, write about, and discuss math with their peers and educators to make sense of mathematics. For example, lección 12-3 “Elaboremos: sumar en una recta numérica vacía” includes the “Hablemos de matemáticas” section with “Cadenas numéricas,” where the materials present two related math problems one at a time and have students share strategies and solutions with a partner or in small groups. The materials prompt educators to support students in making sense of mathematics through a whole-class discussion with the guidance “Represente las estrategias de los estudiantes y facilite el debate sobre las relaciones dentro y entre los problemas.” Lección 4-1, paso 2 “Relacionar” then requires students to make sense of mathematics by explaining their reasoning about a problem involving caterpillars and butterflies, writing and solving a related story problem using words or pictures, determining whether a statement about the problem is true or false, and justifying their response. Students have opportunities to do, write about, and discuss math with peers and educators as they record their solutions, explain their thinking, and discuss different representations and solution strategies.

Additionally, lección 3-12 “Representémoslo en 3 actos” requires students to make sense of mathematics as they make predictions, identify relevant information, develop and represent a mathematical model, compare their predictions to a solution, explain how their model helped solve the problem, reflect on their reasoning, and create and solve a related mathematical problem. Students record their mathematical thinking and discuss their strategies and conclusions throughout the lesson with their peers and educators. In Tema 1, lección 1-12 includes the “Representémoslo en 3 actos” activity, “Perder canicas,” 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?” Students discuss possible mathematical questions with their peers and the educator, encouraging them to make sense of the situation before solving the problem. 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, Marco and Nathalie, who use different strategies to solve the problem. Students analyze these examples and discuss the different approaches with their peers and educators and conclude with “Acto 3,” where students create a new problem in writing and explain 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 grade 2 Guía del maestro and “Modelo de resolución de problemas” include support for educators in guiding students to share and reflect on their problem-solving approaches. Lección 13-2 “¡Investiguemos! Los beneficios de ahorrar” includes four steps where educators guide students in their problem-solving approaches as they explain, argue, and justify their responses. In paso 1 “Investigar,” the materials prompt educators with questions to guide students to share and explain, such as “¿Hay una manera más eficiente de encontrar la respuesta?” The “Seleccionar y poner en secuencia” section includes “Relacionar estrategias de solución,” where educators guide students to identify the similarities and differences in the problem-solving strategies others used, as the materials lead into “Hablar sobre las ideas matemáticas” for students to share and reflect on their problem-solving approaches. Additionally, paso 3 “Práctica y resolución de problemas” includes a “Reflexión” section, which includes educator-prompted questions to guide students and an “Errores e intervención” section for students having difficulty with the exercise. In Tema 12, lección 12-2 includes an “Investigar” section with “Ejemplos del trabajo de los estudiantes,” which provides educator guidance for facilitating student reflection and discussion about problem-solving strategies. The materials present four samples of student work for the “Torre hasta 1000,” Problems A and B, along with educator prompts that encourage students to reflect on and justify their thinking. Questions include: “¿Cómo usaste la reagrupación cuando hallaste la suma?” and “¿Cómo supiste que tu suma sería mayor que 997?” The prompts guide students in explaining their reasoning, evaluating the accuracy of their solutions, and arguing and justifying the strategies they used to solve the problem.

Additionally, in Tema 13, lección 13-3 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. The materials present the essential question “¿Cómo afectan los depósitos y retiros al dinero que tienen en una cuenta?” Students work through four problems involving deposits, withdrawals, and account balances. The included questions support educators in guiding students to analyze the information, explain how deposits and withdrawals affect the account balance, and justify their calculations: “¿Cuánto dinero tenía Melissa al principio en el banco?” and “¿Cuánto dinero tenía Kyle al principio en el banco?” The embedded educator guidance supports meaningful mathematical discussions that deepen students’ conceptual understanding of money and financial transactions. In lección 10-10, students solve real-world problems using their understanding of the attributes of two-dimensional shapes. Students are shown a video and asked what they notice and wonder about what they saw. They then predict what a design may look like when given information about the shapes and the number of shapes used. The class works together to brainstorm ideas and ask questions. Educator guidance for students includes questions such as “¿Cómo podría verse el diseño?” Students must determine the information needed to correctly predict while educators provide the sentence stem “Si supiera. . . , podría averiguar. . . ” Students are then provided the information needed to solve the problem and show their work using pattern blocks to justify and argue their answers. Finally, educators have students discuss and explain their solution methods as a class.

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 2 Guía del maestro includes prompts and guidance to support educators in providing explanatory feedback based on student responses and anticipated misconceptions. Lección 12-3 “Elaboremos: sumar en una recta numérica vacía” includes “Prevenir malentendidos” in paso 2 “Aprendizaje visual,” which provides prompts and guidance for educators on how to give feedback based on student responses and anticipated misconceptions. The materials state, “Observe a los estudiantes que siempre empiezan con el sumando mayor y cuentan centenas, decenas y unidades para sumar el otro sumando. Explique que es posible sumar números en cualquier orden y aún obtener la misma suma.” In “Hablar sobre las ideas matemáticas,” the materials additionally include educator prompts and guidance such as “Pida a los estudiantes que participen en una actividad de pensar-trabajar en parejas-compartir para comparar explicaciones sobre cómo el conteo salteando ayuda a resolver problemas de suma usando una recta numérica. Incentive conversaciones sobre el valor de posición y el conteo salteado de centenas, decenas y unidades.” Additionally, “Conversación en la clase” includes anticipated student responses and questioning guidance for educators. For example, in paso A, educators ask students, “¿Qué número se muestra primero en la recta numérica abierta?” The questioning guidance concludes paso A with “¿Cómo se usa la recta numérica abierta para sumar 481 y 122?”

In Tema 5, lección 5-7 includes educator guidance in paso 3 “Práctica y resolución de problemas” within the “Práctica guiada” section. The “Errores e intervención, Ejercicio 1” subsection identifies a common student misconception and provides explicit guidance for educators on how to address it. For example, the materials state, “Si los estudiantes no pueden escribir una ecuación para resolver el cuento, entonces pídales que usen fichas para representar el problema. ¿Cuántas fichas usarán en total? [10] ¿Cuántos grupos iguales deberán formar? [5] ¿Cuántas fichas hay en cada grupo?” This guidance provides explanatory feedback by directing students to revisit the problem, analyze the relationship described in the task, and reconsider their initial response. In the lección 4-2 “Explorar y comentar” activity, students investigate ways to model problems using equations with an unknown. Students are provided with a word problem to solve with the addition equation ? + 18 = 44 and determine the unknown by demonstrating varying samples of work. The materials guide educators on what to look for, such as which students may use subtraction to solve and which may use counting on. If students are unsure how to solve or if educators anticipate misconceptions, educators provide explanatory feedback and may ask, “Piensen en las estrategias que aprendieron para resolver un problema de sumandos que faltan. ¿Qué estrategias pueden ayudar a resolver el problema?” To support the class in strategies for finding an unknown, educators select solutions for counting on to subtract and breaking apart to subtract.