Kiddom Texas: Matemáticas en Español – Grado 2

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

The materials include a scope and sequence that outlines the TEKS and concepts taught in the course and can be found in the document titled Grado 2 Alcance y Secuencia. The scope and sequence is organized by unit number and lesson number and includes column titles such as “Kiddom Unidad Número,” “Kiddom Lección Número,” “TEKS cubiertos en la lección,” and “Objetivos de Aprendizaje.” For example, unit 1, lesson 1 covers TEKS 2.2A and lists “Reconozcan que cada centena está compuesta por 100 unos o 10 decenas” as the concept to be taught.

The document Grado 2 Alcance y Secuencia presents the TEKS in an organized format, including columns that clearly identify each unit and the corresponding lessons within each unit. This document provides detailed information for units 1–10, specifying the TEKS alignment and instructional focus for every lesson. For example, in unit 7, lesson 7, “Partes fraccionarias más allá de un entero,” the identified TEKS include 2.3A and 2.3D. The associated student learning concept is “Amplía la comprensión de los números enteros en la recta numérica para ver fracciones en una recta numérica.”

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 scope and sequence presents the units in an organized format and includes the unit number, number of lessons, number of additional practice days, evaluation days, and flex days. This document provides detailed information for three different academic calendars: 165, 180, and 210 days. For example, the suggested pacing for unit 4, “Datos, tiempo y dinero” in the 180-day instructional calendar includes 24 lessons, one evaluation day, and three flex days, for a total of 28 instructional days. The document also includes suggested activities for use during flex days.

The materials include suggested pacing of various units and concepts taught throughout the course. The document Guía de planificación de matemáticas de Texas K–2 presents the units in a format organized by instructional week and includes the recommended number of days allocated for each unit. This document provides detailed information for units 1–10, specifying the focus of each unit and the expected duration of instruction. For example, unit 9, “Multiplicación y división,” is designed to span approximately 14 instructional days and is scheduled to occur during weeks 31–33 of the school year.

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

The resources include an overview of the curriculum and specific information describing how mathematical ideas build on one another across units. For example, the document Guía de recursos para maestros states that the program offers “acceso a las matemáticas a través de una progresión coherente y ofrece a los maestros la oportunidad de profundizar su conocimiento de las matemáticas.”

The materials include a K–2 pacing guide titled Guía de planificación de matemáticas de Texas K–2 that identifies the unit number and the recommended weeks of instruction for each unit across grades K–2. Additionally, the materials provide a rationale for the sequence of units and explain how concepts are connected and developed throughout the course through a flowchart.

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

The materials include a section planning guide titled Guía de planificación de la sección for each unit. Each planning guide includes an overview of the lessons within the unit, is organized into sections based on the number of lessons in the unit, identifies learning objectives for each section, and incorporates visual supports. For example, section A, “El valor de cuatro dígitos” provides an overview of lessons 1–11 and includes two learning objectives, while section B, “Comparar y ordenar números dentro de 1,000” provides an overview of lessons 12–17 and includes two learning objectives.

In unit 9, lesson 2, “Compartir equitativamente 2,” the lesson overview supports educator planning and lesson internalization by providing guidance on the instructional purpose, sequence, and expectations. It includes the TEKS addressed, learning objectives, lesson narrative, required materials, reflections, activity links, and printable resources. The materials also provide protocols that guide educators to review the objective, key vocabulary, and success criteria before implementation.

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

The materials include an educator resource guide titled Guía de recursos para maestros that provides general information about the components of a math lesson, supports for emergent bilingual (EB) students and students with disabilities, assessment guidance, and key instructional structures within the course. However, the materials do not include guidance for instructional leaders to support educators in implementing the materials as designed.

The materials include resources that support educators during implementation. However, the materials do not provide guidance for instructional leaders on how to use the curriculum to support educators. The materials do not include professional learning resources or training modules designed to build instructional leaders’ capacity to support educators in implementing the curriculum with fidelity.

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 unit 4 overview provides background content knowledge by explaining key concepts across data interpretation, time, and money, including how students represent and analyze data using graphs and tables, read and tell time to the nearest minute, and understand coin values and equivalencies. It also describes developmental progressions and how students apply operations such as addition and subtraction within contextual problem-solving situations.

The unit overview for “Leer, escribir y representar números hasta 1,200” provides educators with background content knowledge explaining the progression of learning across the unit, including place value, composing and decomposing numbers, multiple number representations, comparing and ordering numbers, and using number lines. For example, the overview explains that students begin by “reconociendo que cada centena está compuesta por 100 unos o 10 decenas,” establishing the mathematical foundation educators need to then explain how students progress from representing numbers with base 10 blocks and expanded form. In addition, the “Términos clave” section defines unit-specific academic vocabulary, including componer, descomponer, forma desarrollada, and recta numérica, with mathematical explanations and examples.

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

The materials include supports for families in English and Spanish for each unit within an FAQ document. For example, the FAQ for grade 2, unit 1 provides families with responses to questions such as “What are the main ideas in this unit?,” “What representations are used within this unit?,” “What specific skills or methods are addressed in this unit?,” “What can I do to support my student at home?,” “How does this content connect to the world around us?,” and “How does the content prepare students for college and career readiness?” This FAQ framework is included in every unit.

Each unit of the materials includes an FAQ document in English and Spanish with subsections on how families can support students at home. For example, the Spanish FAQ for grade 2, unit 1 includes the question “¿Qué puedo hacer para apoyar a mi estudiante en casa?” The document provides an overview of the main ideas of the unit, the representations used, and the specific skills and methods addressed in the lessons, as well as how the content prepares students for college and career readiness. It also helps families understand how the mathematics content connects to the world around them.

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).

The grade 2 materials include structured and detailed lesson plans with clearly stated learning objectives, TEKS alignment, lesson tasks and questions connected to the objectives, and opportunities for instructional and formative assessment through educator observation, questioning, and monitoring of student understanding throughout the lesson. For example, unit 1, lesson 1, “Cómo formar una centena,” includes lesson objectives, the TEKS correlation (111.4.b.2.A), guided questions for educators during student exploration, and formative assessment opportunities embedded throughout the lesson.

Each lesson within the materials identifies the TEKS addressed and incorporates materials and tasks needed to meet the objectives. For example, in unit 2, lesson 3, the lesson targets TEKS 2.3B and lists the necessary materials, including poster board, scissors, crayons or markers, glue, and provided PDF resources such as pizza slices and fraction strips. The lesson includes two sequenced instructional tasks that build on one another to support students in developing strategies for solving problems involving fractions.

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.

In grade 2, unit 1, lesson 4, the materials list includes bloques de base diez, which are needed to effectively deliver the lesson. Additionally, the suggested timing for each lesson component is included. For example, the warm-up is allotted 10 minutes, activities are 15–20 minutes in length, and the cooldown should be five minutes in duration.

In unit 9, lesson 2, the materials needed for implementation are listed under the section titled “Materiales requeridos.” The list of required materials for each activity includes all supporting resources, such as PDFs that include story templates and digital presentations.

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

The materials provide guidance for educators on using lesson activities as continued independent practice after instruction. The TX Math Teacher Course Guide K–5 explains the purpose of independent work and describes how students continue applying newly learned concepts while the educator monitors progress and uses formative assessment to determine next instructional steps. This guidance supports the effective use of lesson materials as extended practice beyond direct instruction. For example, in the TX Math Teacher Course Guide K–5, “What’s in a Kiddom Lesson” explains that “El entrenamiento . . . ofrece oportunidades para que los estudiantes comiencen a trabajar en el aprendizaje durante aproximadamente 5 minutos mientras el maestro . . .” and further notes that “La evaluación formativa . . . proporciona a los maestros respuestas específicas de los estudiantes para informar la enseñanza.”

In unit 4, lesson 24, “¿Qué es un gráfico de puntos?,” the “Narrativa de la lección” provides explicit guidance for using the lesson as an extension after instruction, stating, “Esta lección opcional solo digital está fuera del alcance de aprendizaje para el segundo grado, pero puede usarse para extender a aquellos que están listos para conceptos más avanzados.” This guidance directs educators to use the optional lesson as enrichment for students who are ready to extend their learning beyond grade-level expectations. Through collecting measurement data, creating a dot plot, and interpreting how each x represents a measurement and how the scale communicates the units used, students deepen their understanding while educators use the lesson materials to provide continued learning beyond the core instruction.

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.

At the unit level, the materials provide section checkpoint checklists and end-of-unit assessments with notes for evaluating responses, giving educators clear tools to track student understanding across the unit. For example, in grade 2, unit 3, the materials include an end-of-unit assessment that includes multiple-choice, short-answer, fill-in-the-blank, and written-response questions. It also includes educator guidance for evaluating student responses.

In unit 3, after lesson 4, the materials include a checkpoint titled “Chequeo de la sección A de la unidad 3” that incorporates open-ended questions and multipart questions. Furthermore, unit 3 has two additional checkpoints titled “Chequeo de la sección B de la unidad 3” and “Chequeo de la sección C de la unidad 3” that also vary in types of tasks and questions.

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

The materials include the definition and intended purpose for the types of instructional assessments, specifically the warm-ups, lesson checkpoints, and end-of-unit assessments. For example, TX Math Teacher Course Guide K–5 ES states that “the cool-down serves as a brief formative assessment to determine if students understood the lesson.” Additionally, the materials explain that educators use student responses during the cooldown to make adjustments to instruction.

The materials include the purpose and importance of assessments in supporting educators with lesson planning, delivering instruction, monitoring student progress, and making data-driven instructional decisions throughout the school year. For example, the Guía de recursos para maestros highlights the availability of assessment guidance at the lesson, section, and unit levels. It explains that each unit includes a summative assessment that students complete independently to evaluate their progress toward the unit’s learning objectives and grade-level standards. Additionally, all assessment items are aligned to the relevant grade-level standards, ensuring that student mastery is accurately measured.

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

The materials provide guidance for educators on administering assessments consistently and accurately. For example, in the Guía de recursos para maestros, the section “Oportunidad de evaluación sumativa” includes specific administration directions, stating, “En los grados K a 2, lee en voz alta la evaluación a los estudiantes. Los ítems pueden leerse en voz alta a estudiantes de otros grados, según sea necesario.” This guidance directs educators to read assessments aloud to students in grades K–2 and, when appropriate, to students in higher grades, helping ensure consistent administration.

The materials provide clear educator guidance that supports the consistent administration of assessments across lessons and units. Educators are given explicit information on how to use assessments, what to observe in student responses, and how to interpret student understanding. For example, in the Guía de recursos para maestros, guidance is given to support educators in consistently monitoring student understanding and responding to incomplete learning. These structured supports help ensure that assessment practices are implemented with fidelity and that instructional decisions are aligned to student needs.

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

The materials show alignment between diagnostic, formative, and summative assessments and the TEKS and lesson or unit objectives. The TEKS are identified throughout lessons, practice problems, and assessments through sections such as “Abordando,” while lesson objectives are outlined in “Objetivos de aprendizaje.” The materials also include multiple assessment opportunities, including warm-ups, educator questioning, practice problems, activities, cooldowns, checkpoints, and end-of-unit/course assessments. For example, in unit 2, “Punto de control de la sección A de la unidad 2,” each question includes standard tags, which list the TEKS being addressed (111.4.b.6.B, 111.4.b.7.A).

The materials include formative assessments such as unit checkpoints that are aligned to the TEKS and objectives of the unit. For example, the “Chequeo de la sección A de la unidad 3” assesses TEKS 2.4D and 2.7B. TEKS 2.4D states that students will generate and solve problem situations for a given mathematical number sentence involving addition and subtraction of whole numbers within 1,000, while TEKS 2.7B states that students will use an understanding of place value to determine the number that is 10 or 100 more or less than a given number up to 1,200. In unit 3, “Overview,” the checkpoint aligns to the unit objective “Sumar y restar dentro de 1,000 con y sin componer y descomponer números.”

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

The materials include summative assessments such as end-of-unit tests that include a variety of TEKS-aligned item types that vary in complexity. For example, in unit 3, the “Evaluación de fin de unidad 3” is an eight-question test assessing TEKS 2.4B and 2.4D. The test includes item types that vary in complexity, such as multiple-select, multiple-choice, multipart, short-answer, and written-response items.

Assessments incorporate both formative and summative components and feature a range of item types, including multiple-choice, text-entry, and open-response questions, all aligned to the TEKS. Additionally, the materials provide access to an online assessment bank that includes technology-enhanced items such as inline choice, hot spot, and multi-select, allowing students to demonstrate understanding in diverse ways. For example, the course guide explains that end-of-unit evaluations include a variety of problem types, such as multiple-choice, multiple-response, and short-answer questions, and these problems vary in difficulty and depth of knowledge, ensuring that students are assessed across a range of complexity levels.

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

The materials include instructional assessments and scoring information that provide guidance for interpreting student performance in the educator-facing section of each unit exam titled “Note for Evaluating Responses.” For example, the “Evaluación final de la unidad 4,” part A, has a “Note for Evaluating Responses” that gives educators guidance for scoring student responses related to adding money. The guidance for interpreting student performance on this question states, “42: 1 quarter equivale a 25 centavos y 3 nickels son 5, 10, 15 centavos. Eso hace un total de 40 centavos. Luego, 2 pennies más hacen 2 centavos o 42 centavos en total.”

The materials provide guidance for scoring assessments and interpreting student performance through a combination of formative and summative supports, including observational tools, progress monitoring checklists, and suggested instructional next steps that are aligned to student understanding and the grade-level TEKS. For example, in the TX Math Teacher Course Guide K–5, the section “Guía para la evaluación final de la unidad” provides sample observations that highlight areas of incomplete student learning. It also includes “Apoyo para la siguiente unidad,” which offers strategies, guiding questions, and instructional supports to help educators address learning gaps identified through assessment data.

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 TX Math Teacher Course Guide K–5 ES has a “Guía de la evaluación.” However, it does not provide explicit guidance for educators on how to respond to student assessment results or identify a task or activity that should follow.

In “Grading and Reporting,” the materials include a section titled “How Do I Provide Feedback to Students?” However, this section does not include explicit tasks and activities to respond to students based on their 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 provide educators with clear and comprehensive tools to monitor student progress and growth over time. Educators can access multiple reporting features, including the Assignment View, Scoreboard, Scorecard, Question View, and Standards View, which offer data on both individual student performance and class-wide achievement across assignments, assessment items, and standards. For example, the resource “What Do My Reports Mean?” provides explicit guidance for interpreting and using key reporting tools, including the Class Grade Average line graph, Mastery Groups pie chart, Class Standard Mastery tracker, and Student Standard Progress reports. These features allow educators to analyze changes in student performance over time, monitor mastery of specific standards, group students according to performance levels, and track individual growth toward learning goals.

The materials provide tools that enable students to monitor their own progress and growth. Students have access to reports that display class grade averages, standards mastery, assignment performance, and progress trends over weekly or monthly periods. For example, students can view Class Standard Mastery reports that present color-coded mastery levels, allowing them to track their progress over time. Students can also select specific standards to access related assignments, grades, and educator feedback. These features support students in actively tracking their learning, reflecting on their performance, and understanding their progress across standards and assignments.

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

The materials provide multiple pathways for students to access the mathematical concepts, including the use of concrete and visual representations, structured peer discussions, and targeted educator facilitation. For example, in grade 2, unit 3, lesson 12, the “Enfriamiento: ampliar el pensamiento del estudiante” section identifies students who are struggling (“si los estudiantes tienen dificultades . . .”), provides reteaching guidance (“refuerza el concepto de representar cantidades con barras”), suggests scaffolding and instructional prompts (“guíalos a ver tendencias o patrones”), recommends targeted follow-up practice (“proporciona práctica adicional con la interpretación y el dibujo de gráficos de barras”), and connects to prior lessons (“repasa el concepto de marcas de conteo o pictogramas”).

In the “Enfriamiento” under the section “Ampliar el pensamiento del estudiante,” the materials state, “Si un estudiante tiene dificultades con la estimación o complica la tarea tratando de calcular el número exacto, el apoyo al día siguiente podría implicar volver a explicar el concepto de estimación y sus aplicaciones en la resolución de problemas del mundo real. Para apoyo de unidades anteriores, reforzar el concepto de volumen y espacio puede ser beneficioso.” The educator guidance supports students who struggle with estimation by recommending reteaching the concept the following day and reinforcing prior learning related to volume and space.

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

The materials include pre-teaching and embedded supports for unfamiliar vocabulary in text. For example, in grade 2, unit 7, lesson 1, activity 1, the lesson explicitly introduces and reinforces academic terms such as mitad, cuarto, and octavo through educator modeling, guided questioning, and hands-on folding activities that connect language to concrete representations. During instruction, the educator directly defines the term octavo, stating, “Cuando una figura está dividida en ocho partes iguales, cada parte se llama un octavo,” while also prompting students to explain and identify halves, fourths, and eighths as they fold and compare paper models.

The materials include embedded supports for unfamiliar non-mathematical vocabulary through “Math Language Routine 6: Tres lecturas.” For example, in unit 4, lesson 3, activity 2, the “Narrativa de la actividad” uses this routine. According to the TX Math Teacher Course Guide K–5, “Math Language Routine 6: Tres lecturas” is a routine that supports reading comprehension, interpretation, and meta-awareness of mathematical language. In this routine, students are supported in reading and interpreting a mathematical text, situation, diagram, or graph three times, each time with a particular focus. During the first reading, educators focus on “What is this situation about?” while students describe the situation or context. The course guide notes that this is the time to identify and resolve any difficulties with non-mathematical vocabulary.

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

In unit 4, lesson 24, “¿Qué es un gráfico de puntos? (opcional),” the materials provide educator guidance for enrichment and extension through an optional digital lesson designed for students who are ready for more advanced concepts. The lesson narrative notes, “Esta lección opcional solo digital está fuera del alcance de aprendizaje para el segundo grado, pero puede usarse para extender a aquellos que están listos para conceptos más avanzados.” The lesson extends learning by introducing students to ways a dot plot can be used to represent data collected through measurement, providing an opportunity for students who have demonstrated proficiency with grade-level content to engage with additional, advanced learning opportunities.

In unit 7, lesson 7, “A la recta numérica (opcional),” the “Narrativa de la lección” provides educator guidance for extending learning by identifying the lesson as optional and explaining that its purpose is for students to “amplíen su comprensión de los números enteros en la recta numérica mientras trabajan con rectas numéricas divididas en fracciones.” The guidance further states that students learn “que las cantidades que no son números enteros también pueden representarse en la recta numérica.” Because the lesson is designated as optional and extends previously learned concepts through connections to fractions on the number line, it provides an enrichment opportunity that deepens students’ mathematical understanding.

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 grade 2, unit 9, lesson 4, activity 2, educators guide students to use concrete manipulatives to represent multiplication as equal groups and connect those models to symbolic representations. The lesson also includes targeted questions that prompt educators to deepen student thinking about structure and prediction. For example, the educator asks, “Si agregamos otro conjunto de 4 bloques, ¿cómo cambiaría nuestro modelo de multiplicación? ¿Puedes predecir el número total de bloques sin contar cada uno?” These questions help students understand how adding equal groups affects the total in a multiplication situation.

Within the Guía de recursos para maestros is a section titled “Rutinas de instrucción” that provides details on the specific routines used in the curriculum. This section also states that “to help identify when a particular routine appears in the curriculum, each activity is labeled with the routine’s name, allowing educators to look for upcoming opportunities to try out or focus on a specific instructional routine. Professional learning for the curriculum materials includes videos of the routines in action in classrooms, helping educators understand what the routines look like when implemented.” Furthermore, this section of the Guía de recursos para maestros provides guidance for 20 instructional routines.

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

The materials provide educator guidance for delivering lessons through a variety of instructional approaches, including discourse routines, collaborative learning, problem-solving, and mathematical sense-making. The TX Math Teacher Course Guide K–5 explains the purpose and implementation of instructional routines and provides recommendations for how educators should facilitate student learning and discussion. For example, the materials state, “Las lecciones que incluyen esta rutina permiten a los estudiantes resolver problemas de maneras que tengan sentido para ellos. Monitorea para descubrir y fomentar comprensiones conceptuales durante la actividad” when describing the “5 Practices” routine, giving educators explicit guidance for facilitating student-centered problem-solving and discussion.

The grade 2, unit 7, lesson 8, “Calentamiento” incorporates the instructional routine “Observa y pregúntate,” independent thinking time, partner discussion, whole-class sharing, and educator-facilitated concept development. The materials provide explicit guidance for how educators should introduce the task, facilitate student discourse, and guide students toward the lesson objective. For example, the lesson directs the educator to have students observe figures divided into equal and unequal parts, discuss their observations with a partner, and then facilitate a synthesis discussion that states, “guía la conversación hacia la comprensión de las partes iguales y el concepto básico de fracciones,” while introducing academic vocabulary such as mitades, cuartos, and octavos.

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 materials support multiple types of practice, including independent thinking, collaborative discussion, and whole-group participation, and provide educators with explicit guidance for implementing instructional structures. For example, in grade 2, unit 1, lesson 1, “Calentamiento,” students independently count by 1s starting at 90. The materials state, “Cuenta de 1 en 1, comenzando en 90. Anota mientras los estudiantes cuentan. Anota 10 números en cada fila. Luego comienza una nueva fila justo debajo. Detén la cuenta y el registro en 120.” The educator records the count as students participate, organizes the numbers into rows, and guides students to continue the sequence up to 120, supporting structured engagement and consistent practice.

The materials support multiple types of practice, including independent thinking, collaborative discussion, and whole-group reflection, while also providing educators with recommended instructional structures for implementation. For example, the TX Math Teacher Course Guide K–5 explains that instructional routines are used to structure interactions between educators and students and describes routines such as “Clasificación de tarjetas,” where students work independently or in groups to analyze and categorize mathematical representations while educators monitor and facilitate discussion.

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

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

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

The materials include implementation guidance that supports educators in effectively serving emergent bilingual students through embedded multilingual learner supports integrated into lesson delivery and classroom discourse. For example, grade 2, unit 4, lesson 14, activity 2 includes “Math Language Routine 8: Apoyos para la conversación,” directing educators to have students repeat and discuss questions created by their peers, providing structured opportunities for language production and mathematical communication during collaborative work. The materials also include guidance for facilitating peer discussions, whole-group sharing, and language development within the mathematical task, supporting implementation in bilingual and ESL instructional settings.

The materials include guidance to support educators in effectively using the materials in state-approved bilingual/ESL programs. Grade 2, lesson 1, activity 2, “Apoyo para estudiantes que aprenden inglés,” includes an activity in which students explain their reasoning and discuss when they do not agree. The support for students who are learning English states, “Mientras los estudiantes explican su razonamiento para cada coincidencia a su compañero, muestra las siguientes oraciones para que todos las vean: ‘Noté _____, así que las comparé’. Anima a los estudiantes a cuestionarse mutuamente cuando no estén de acuerdo.”

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

The materials provide embedded support for emergent bilingual (EB) students through oral discourse, particularly in developing academic vocabulary, increasing comprehension, and building background knowledge. For example, in grade 2, unit 4, lesson 14, activity 2, the “Math Language Routine 8: Apoyos para la conversación” guidance directs students to repeat and discuss questions with partners, providing opportunities to produce mathematical language and deepen understanding through structured interaction. The lesson also requires students to explain their reasoning, justify whether questions can be answered with available data, and participate in multiple rounds of peer discussion. Furthermore, the materials provide evidence of cross-linguistic connections, such as cognates, language comparisons, and guidance for connecting English and Spanish. There is support for developing vocabulary, comprehension, and background knowledge through written discourse, as students primarily record and answer questions with explicit language-development scaffolds for writing.

In activity 2, “¿Qué figura podría ser?,” the materials direct educators to use “Math Language Routine 2: Recopilar y mostrar” to revisit and expand a language display with academic vocabulary such as atributo, cuadrilátero, and pentágono during partner conversations. The materials support background knowledge and comprehension by connecting terms such as cuadrilátero, pentágono, and hexágono to prior lessons. The “Conexiones translingüísticas” guidance explicitly identifies cognates, including atributo/attribute, cuadrilátero/quadrilateral, pentágono/pentagon. Educators also connect the shared Greek prefixes penta-, hexa-, and octa- across both languages. Students apply these connections through oral and written discourse by discussing and comparing figures with a partner and labeling their drawings with figure names in both languages.

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.

The materials provide practice opportunities that require students to demonstrate depth of understanding aligned to the TEKS by engaging in hands-on partitioning tasks that emphasize the meaning of equal parts. In grade 2, unit 7, lesson 1, activity 1, “Doblar partes iguales,” students fold and cut rectangles into halves, fourths, and eighths, then explain how they know the parts are equal. These practice opportunities require students to justify their reasoning through questions such as “¿Cómo pueden comprobar si son iguales?” and “¿Cómo saben que las piezas son iguales?” rather than just identifying fractional parts. Students move beyond recognizing fraction vocabulary by demonstrating the underlying concept that fractional parts must be equal-sized portions of a whole. The instructional assessments also provide practice opportunities for students to create and verify equal partitions, explain their thinking, and compare their representations with a partner, demonstrating conceptual understanding of fractions and alignment to the TEKS.

For example, in grade 2, unit 1, section A checkpoint, “Place Value Representations,” the assessment prioritizes conceptual understanding over identifying correct answers. Students demonstrate mastery by connecting base 10 models, drawings, place-value language, and symbolic notation to represent and explain their thinking. Throughout the checkpoint tasks, students interpret quantities shown with manipulatives, flexibly compose and decompose numbers, and justify equivalent representations. The embedded scoring guidance provides educators with insight into student reasoning and supports analysis of students’ understanding of the relationships among hundreds, tens, and ones, ensuring that assessment of learning goes beyond procedural accuracy to measure conceptual understanding.

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

The materials include questions and tasks that progressively increase in rigor and complexity, leading students toward grade-level proficiency with partitioning shapes into equal fractional parts. Students begin by dividing a rectangle into two equal parts (halves), then progress to four equal parts (fourths), and finally eight equal parts (eighths). The lesson also requires students to verify that the parts are equal, compare their work with a partner, and explain their reasoning, increasing both conceptual understanding and mathematical communication. For example, the grade 2, unit 7, lesson 1, activity 1, “Narrativa de la actividad” states that students first divide rectangles into halves, then fourths, and finally eighths, while the “Synthesis” asks students to explain why parts are equal and analyze examples where the parts are not equal.

In grade 2, unit 1, lesson 8, activity 1, students use place value models and manipulatives to solve equations that progressively increase in complexity. Students begin by using concrete representations to reason about composing and decomposing numbers within hundreds, tens, and ones. The activity states, “Para hallar el número que hace verdadero 2 centenas + 9 decenas + 17 unidades, los estudiantes explican usando bloques de base diez o diagramas de valor posicional,” requiring students to find the missing value and explain their reasoning using base 10 blocks or place-value diagrams. Students then transition to more abstract equations that require them to apply place-value relationships, such as regrouping units into tens and tens into hundreds. For example, students solve “Encuentra el número que hace que cada ecuación sea verdadera. 5 cientos + _____ decenas + 6 unidades = 5 cientos + 5 decenas + 16 unidades,” which requires them to recognize that equivalent representations can be composed and decomposed in different ways. Students continue to develop their reasoning by solving missing-value problems and creating their own equations, “crea tu propia ecuación con un valor faltante para tu compañero,” demonstrating their understanding by applying place value concepts in new contexts.

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

In grade 2, unit 1, lesson 1, students identify patterns within the base 10 system and develop an understanding of the relationship among ones, tens, and hundreds. Students build on prior learning from the TEKS 1.2B, where they composed and decomposed numbers up to 120, by extending their understanding of place value relationships. The lesson emphasizes the connection and reinforces the pattern that units can be regrouped to create larger units. For example, the materials state, “En esta actividad, mostraste que sabes que 10 unidades son iguales a 1 decena. Así como 10 unidades son iguales a 1 decena, 10 decenas son iguales a 1 centena” and “Una centena es una unidad que está formada por 10 decenas.” The coherence in the materials supports students’ understanding of the base 10 system and prepares them for future learning with larger numbers, addition and subtraction strategies, and multi-digit operations.

The materials demonstrate coherence by connecting financial literacy concepts to previously learned addition and subtraction concepts. Students apply their understanding of operations to analyze how deposits and withdrawals affect account balances, reinforcing the relationship between mathematical operations and real-world financial literacy. For example, in grade 2, unit 10, lesson 2, activity 2, the “Narrativa de la actividad” has students determine whether a scenario represents a depósito or retiro and identify how the action changes the account balance. The introduction connects deposits to addition through the statement “sumo la cantidad de dinero” and withdrawals to subtraction through “resto el monto total.” By applying addition and subtraction within the context of financial decisions, students connect prior mathematical learning to new concepts and recognize relationships between operations, quantities, and everyday financial situations.

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

The materials demonstrate coherence by connecting previous content and language to current learning while preparing students for future mathematical concepts. Students use prior experiences with grouping and counting objects to develop an understanding of even and odd numbers and equal groups, which serve as foundations for future multiplication concepts. Mathematical vocabulary such as pares, impares, grupos iguales, and arreglo is developed consistently throughout the unit. For example, in grade 2, unit 2, Guía de planificación a nivel de sección, section A explains that students organize objects into equal groups and states that they will learn more about the organization of arrays and the term arreglo in the next section, explicitly linking current learning to future concepts.

In grade 2, unit 4, lesson 15, “Narrativa de la lección” states that students build on their grade 1 understanding of telling and writing time to the hour and half-hour as they learn to tell time to the nearest quarter-hour using the terms quarter past and quarter to. The lesson also connects prior learning about halves by linking analog clock representations to circles partitioned into equal parts. In “Calentamiento: ¿Qué sabes sobre las formas de decir la hora?,” students activate prior knowledge and mathematical language related to telling time. Activity 1, “Decir la hora en punto y la media hora,” provides a review of previously learned grade 1 content before extending students’ understanding to quarter-hours. By connecting halves and quarters on analog clocks to partitioned circles and fractional language, the lesson prepares students for future learning involving fractions, equivalent parts, and the interpretation of fractional relationships.

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

The materials demonstrate coherence at the lesson level by connecting students’ prior understanding of place value, addition, subtraction, and numerical relationships to new learning with numbers within 1,000. Students apply previously learned strategies, including counting on, using number lines, decomposing numbers, and representing quantities with base 10 models, to develop more advanced addition and subtraction methods. For example, in grade 2, unit 3, the Guía de planificación a nivel de sección, section C, the materials explain that students subtract within 1,000 using place-value strategies and state that “este trabajo se basa en su experiencia previa de restar números de dos dígitos por valor posicional y descomponer una decena.” This approach explicitly connects students’ previous work with two-digit subtraction and place-value reasoning to current learning with larger numbers.

In grade 2, unit 2, section B, students build on their understanding of addition and subtraction by developing strategies for solving problems within 20, including finding unknown addends and writing equations with unknown values. In this section, students explore the relationship between addition and subtraction and use concrete objects to represent quantities, compose and decompose numbers, and break numbers into tens and ones to support efficient strategies. These experiences connect to prior learning with number composition and place value while preparing students for future work with mental strategies and addition of multiple two-digit numbers. The section supports the progression from foundational addition and subtraction concepts to more advanced problem-solving and mathematical reasoning with numbers within 100.

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

The materials provide spaced retrieval opportunities by revisiting previously learned skills and concepts across lessons and units. For example, in grade 2, unit 4, lesson 11, activity 2, students build on prior experiences with pictographs and extend their understanding to bar graphs by applying familiar data analysis strategies in a new representation. Students retrieve and apply previously learned skills, including interpreting visual data, comparing quantities, and using addition and subtraction to solve one-step problems. The lesson connects to prior learning through the statement “Hemos visto cómo los pictogramas . . . ,” reminding students that pictographs and bar graphs both represent data that can be analyzed to answer questions.

For example, in grade 2, unit 6, “Problemas de práctica de la sección A,” students apply previously learned concepts and skills related to measurement, place value, operations, and problem-solving within the same practice set. Students revisit measurement concepts by measuring and comparing the lengths of objects using concrete models and rulers, estimating lengths, and performing calculations involving length, and applying place value strategies and algorithms to add and subtract two-digit numbers. Students also retrieve prior problem-solving strategies by representing and solving addition and subtraction word problems with unknowns in various positions. By integrating multiple previously learned skills within a single practice opportunity, the materials provide repeated opportunities for students to recall, apply, and strengthen concepts across contexts and reinforce learning over time.

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

The materials provide interleaved practice opportunities with previously learned skills and concepts across lessons and units by integrating multiple mathematical concepts and strategies within a single practice set. For example, in grade 2, unit 6, “Problemas de práctica de la sección A,” students apply measurement, comparison, estimation, addition, subtraction, number lines, equations, and problem-solving skills across varied tasks. Students are required to move between different mathematical concepts rather than practice one skill in isolation. Tasks include comparing lengths, measuring figures, estimating and verifying measurements, solving subtraction word problems, and writing equations to represent measurement situations, such as using 32 − 17 = 15 to determine a rectangle’s length. Additionally, the assessment intentionally integrates multiple previously learned mathematical ideas, requiring students to apply concepts and skills from both current and prior units in varied contexts.

In grade 2, unit 1, lesson 11, activity 2, students revisit their understanding of hundreds, tens, and ones while extending their thinking through multiple representations and decompositions. Students use base 10 blocks to represent numbers in conventional and nonconventional ways, such as representing 345 as three hundreds, four tens, and five ones or as two hundreds, 14 tens, and five ones, requiring them to apply prior knowledge of composing and decomposing numbers. Students then use these understandings to determine numbers that are 10 more, 10 less, 100 more, and 100 less, reinforcing patterns within the base 10 system. The activity supports interleaved practice by requiring students to connect prior place value concepts with new problem types rather than practicing a single procedure in isolation.

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

In grade 2, unit 3, lesson 4, activity 2, “Suma o resta con forma desarrollada,” students interpret and analyze the work of two hypothetical students who use different strategies to solve the same problem using expanded form. Educator questions such as “¿Dónde ves cada número en su trabajo?,” “Prueba la manera de Andre y la manera de Diego,” and “¿Cuál forma prefieres? ¿Por qué?” require students to compare methods and evaluate the effectiveness of each representation, justifying their reasoning. By examining multiple solution strategies and defending their conclusions, students engage in interpreting, analyzing, and evaluating mathematical representations.

The materials require students to interpret and analyze real-world scenarios involving deposits and withdrawals by determining how each transaction affects an account balance. In grade 2, unit 10, lesson 2, activity 2, “Escenarios bancarios: Depósitos y retiros,” students read banking scenarios and determine whether each transaction is a deposit or withdrawal and how it changes the account balance. Students connect these situations to mathematical operations to analyze changes in value and reason about the relationships between actions and account balances.

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

In grade 2, unit 4, lesson 4, activity 2, “Representar ideas matemáticas en gráficos,” students are given survey data and are asked to create bar graphs that accurately represent the information. Educator prompts such as “Crea un gráfico de barras para representar los datos” require students to generate their own mathematical representations rather than interpret pre-existing graphs. As students organize data, determine appropriate categories, and construct bars to show quantities, they create mathematical models that represent and communicate numerical relationships within a data set, as well as develop their understanding of data representation.

For example, in grade 2, unit 7, lesson 1, activity 1, “Formar mitades, cuartos y octavos,” the materials give students hands-on opportunities to model math scenarios by partitioning shapes. Students build their own physical representations of halves, fourths, and eighths as they fold, cut, compare, and adjust their work to explore equal shares. The task encourages students to test and evaluate their models by comparing individual pieces and discussing whether the partitions are truly equal. Through repeated construction and reflection, students develop understanding of fractions by connecting physical models to math vocabulary and spatial reasoning.

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

For example, in grade 2, unit 1, lesson 17, activity 2, “Compara de diferentes maneras,” the materials challenge students to apply their understanding of place value to tasks using multiple representations. Students extend their knowledge of hundreds, tens, and ones to number lines, base 10 diagrams, and symbolic comparison statements, explaining how each representation supports their mathematical thinking. By estimating values on a number line, interpreting visual models, and selecting appropriate representations, students apply place-value concepts flexibly rather than relying on procedural rules. The activity supports conceptual transfer by prompting students to justify their answers and connect representations to quantities in new contexts.

In grade 2, unit 2, lesson 3, activity 2, “Comparte las canicas,” students apply their understanding of equal groups to determine whether a set of 16 to 20 objects can be separated into two equal groups. Students use counters and create representations, including diagrams and equations, to model and justify their thinking. By representing the same situation in multiple ways, students apply their conceptual understanding of equal groups to a new problem context and explain how their models support their solutions.

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

The materials provide tasks that support both automaticity and fluency by giving students repeated opportunities to count by tens, recognize patterns in multiples of 10 and 100, and represent hundreds in different ways using base 10 blocks. Students practice counting by 10 beyond 120, connect 10 tens to 100, and use this understanding to build and represent numbers such as 90, 110, 150, 200, and 300. For example, in grade 2, unit 1, lesson 2, the “Calentamiento” directs students to count by tens and identify patterns, while activity 1, “Formar centenas,” has students use base 10 blocks to form multiples of 100 and determine how many tens are needed to build each number.

In grade 2, unit 2, lesson 17, activity 2, “Resta estratégica,” students build automaticity and fluency with two-digit subtraction by using mental math and place value strategies to solve problems efficiently. Students first solve each problem independently and then verify their thinking with a partner. The activity directs students to use their understanding of place value to subtract the smaller number from the larger one as they mentally solve problems such as 82 − 57, 62 − 28, 91 − 56, and 85 − 47. This repeated practice with efficient strategies strengthens fluency with two-digit subtraction and supports the automaticity needed for grade-level computation tasks.

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.

In grade 2, unit 3, lesson 4, activity 1, “Cero decenas y cero unidades,” students analyze two different methods for subtracting from a multiple of 100. Students compare using a number line to count up from 387 to 500 with using expanded form to subtract 300, 80, and 7 from 500. During the “Síntesis de la actividad,” students explain which method they prefer and why, then apply each method to new problems, including 600 − 476 and 400 − 134. By comparing strategies and applying them to additional problems, students practice selecting and using subtraction procedures accurately and flexibly.

In unit 4, lesson 21, activity 2, “El valor de un dólar,” students solve problems involving coin combinations that equal 100 cents. Students use strategies such as grouping like coins, making tens, and counting on to determine totals in different ways. Students choose and apply strategies for each situation and explain their methods during partner discussions. Students engage in repeated practice with varied coin combinations and apply these strategies across similar money and addition tasks.

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.

In grade 2, unit 1, lesson 1, activity 2, “Diferentes maneras de ver 100,” students evaluate different representations of 100 by matching base 10 block diagrams to statements such as “Veo 100 unidades,” “Veo 10 decenas,” and “Veo 1 centena.” Students explain how each diagram represents the same quantity using different place-value representations. To support students who need additional guidance, “Promover el pensamiento del estudiante” prompts educators to ask, “¿Cómo decidiste qué afirmación coincidía con cada diagrama?” and “¿Qué tienen de similar o diferente estos diagramas?” During the “Síntesis de la actividad,” students also evaluate efficiency as the educator asks, “¿Cómo podrías representar el 100 en la expresión con la menor cantidad de bloques?,” encouraging students to compare representations and determine the most efficient way to model the same value.

The materials provide opportunities for students to evaluate flexible and accurate processes for equal sharing. Students use objects, drawings, and different grouping strategies to divide items equally and discuss how the strategies support fair sharing. For example, in grade 2, unit 9, lesson 1, activity 2, “Dividir el botín,” students divide 12 coins among 4 pirates, then solve related sharing problems with 32 gems and 42 pieces of gold. Next, the activity synthesis asks students to review how each group divided their objects and discuss different strategies for dividing objects into equal groups.

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

The materials include embedded educator supports that guide students in connecting concrete models, base 10 diagrams, equations, and place-value reasoning when solving story problems. Educator guidance prompts students to move beyond counting or drawing all objects by using tens and ones to represent and solve problems. For example, in grade 2, unit 5, lesson 4, activity 2, educator guidance prompts students who are not grouping tens and ones to consider, “¿Cómo podrías usar lo que sabes sobre decenas y unidades para sumar o restar?” and the synthesis directs the educator to compare cube representations with base 10 drawings.

In unit 10, lesson 9, activity 1, “Productores y consumidores: producción simple de artículos,” the instructional materials provide educators with supports to help students use efficient ways to solve problems. Educators guide students with simple directions such as “lee cada escenario” and ask students to decide if it is a “productor o consumidor.” If students struggle, educator guidance includes step-by-step assistance in adding costs to find the total. Students work with a partner to compare and improve their thinking. Educators also reinforce key ideas by asking students to explain how they found the total cost, such as “calcula el costo total.”

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

In grade 2, unit 3, lesson 2, activity 1, the “Narrativa de la lección” explains that students add and subtract three-digit numbers and multiples of 10 or 100 using base 10 blocks (conceptual understanding) and equations (procedural fluency). The narrative explains that the structure of the base 10 blocks helps students recognize that hundreds are combined with hundreds and tens are combined with tens, strengthening place-value understanding. Students represent their thinking with equations, connecting concrete models to addition and subtraction procedures. The activity notes that the numbers are selected so students can focus on place-value relationships without composing or decomposing a hundred. Through base 10 models, equations, and discussion of how the value of the blocks changes, students connect conceptual understanding with procedural fluency.

The materials explicitly address the conceptual emphasis by explaining that students learn how symbols communicate mathematical ideas and represent relationships in problems. The procedural emphasis is addressed as students solve addition and subtraction problems and represent both the problems and solutions using symbols such as plus, minus, and equal signs. For example, in grade 2, unit 5, lesson 5, the “Narrativa de la lección” explains that students communicate mathematical ideas using multiple representations, including symbols, and solve problems using symbols when appropriate.

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.

In grade 2, unit 5, lesson 6, activity 1, “Interpretar el diagrama,” students use pictorial and abstract representations as they interpret strip diagrams and connect them to comparison and part-part-whole word problems. Students use strip diagrams to represent relationships among quantities, providing a pictorial representation of addition and subtraction situations. Students also engage with abstract representations as they analyze known and unknown quantities and explain how the diagrams represent addition and subtraction relationships.

In grade 2, unit 9, lesson 12, activity 1, “¿Cuántos cuadrados?,” students partition rectangles into equal-sized squares to determine the total number of squares, as required by the TEKS. Students begin by using inch tiles to build arrays and rectangles, providing a concrete model of rows, columns, and equal groups. Students then create pictorial representations by shading squares on grids and partitioning rectangles with and without grid lines. Students finish by recording abstract equations to represent the total number of squares by rows or columns.

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 materials support students in connecting concrete base 10 models and representational diagrams to abstract addition and subtraction concepts. Students use base 10 blocks or base 10 diagrams to solve story problems, explain their methods, and connect their representations to equations. For example, in grade 2, unit 5, lesson 4, activity 1, “Diversión en el zoológico,” students use base 10 blocks or base 10 diagrams to show addition and subtraction with tens and ones, then connect their work to equations such as 20 + 1 = 21 or 50 − 30 = 20.

In grade 2, unit 9, lesson 5, activity 2, “Agrupar objetos para multiplicarlos,” students use physical objects to create equal groups and model multiplication. Students divide a set of 20 objects into equal groups, determine the number of groups and the number of objects in each group, and then write a multiplication equation to represent their model. During the “Síntesis de la actividad,” students share their groupings and multiplication sentences, explaining how their concrete models connect to the abstract multiplication equation. This progression builds students’ connections between hands-on models and symbolic representations of multiplication.

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

For example, in grade 2, unit 6, lesson 4, “Medir y estimar en centímetros,” students develop academic mathematical language through the use of manipulatives, visual models, oral discussion routines, and targeted language supports. While analyzing rulers and measurement strategies, students use measurement vocabulary such as length, estimate, centimeter, accuracy, and comparison to describe and justify their thinking. MLRs provide structured opportunities for students to rehearse ideas orally, share observations with peers, and clarify their reasoning before writing. Educator prompts and visual models support students in connecting measurement vocabulary to concrete tools and representations, allowing students to apply precise mathematical language as they communicate their reasoning.

In grade 2, unit 8, lesson 4, activity 1, “Muchas maneras de componer figuras,” the materials provide opportunities for students to develop academic mathematical language through the use of visuals, manipulatives, and structured mathematical discussion. Students use pattern blocks to compose the same hexagon in multiple ways while creating a butterfly and describe their models using mathematical vocabulary from previous lessons, such as “Usé 1 trapecio y 3 triángulos para hacer un hexágono.” During the “Síntesis de la actividad,” students share and compare different compositions, reinforcing geometry vocabulary as they discuss how equal-sized pieces can be combined to form a hexagon.

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

In grade 2, unit 4, lesson 19, “Dólares, decimales y centavos,” the educator implements embedded guidance that supports students’ development and use of academic mathematical vocabulary through opportunities to work with coins and explain their strategies. The educator facilitates collaborative discussions in which students use mathematical language to describe strategies for “determinen el valor de una colección de monedas hasta un dólar,” including “conteo por saltos” and “conteo hacia adelante.” Educator guidance reinforces vocabulary by prompting students to use symbols and terms such as “signo de dólar” and “punto decimal” when representing money amounts. Throughout the lesson, the educator prompts students to justify their reasoning as they group coins and explain how they determined a total within 100. These embedded supports scaffold students’ use of precise mathematical vocabulary in context and strengthen their ability to communicate and justify their mathematical thinking.

For example, in grade 2, unit 5, lesson 4, activity 1, “Diversión en el zoológico,” educator guidance is provided to scaffold and support students’ academic mathematical vocabulary through structured discussion routines, analysis of representations, and peer communication. “Math Language Routine 6: Three Reads” guides educators in supporting students as they interpret mathematical language, identify key quantities, and analyze problem structures before solving. Educator prompts encourage students to use place-value vocabulary in context as they explain how representations and equations show tens and ones, compare solution methods, and communicate their reasoning. Additionally, structured partner discussions, targeted synthesis questions, and educator monitoring guidance provide ongoing support for students to develop and apply precise mathematical language while explaining strategies and analyzing relationships between representations and operations.

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

In grade 2, unit 5, lesson 11, activity 2, “¿Cuál es la pregunta?,” students interpret two story problems and analyze student work to determine which question was answered and which calculation strategies were used. Embedded educator guidance supports students’ mathematical discourse by providing questions that prompt students to explain, justify, and refine their reasoning. The educator asks questions such as “¿Cómo supiste que el estudiante estaba tratando de encontrar una cantidad total?,” “¿Por qué crees que el estudiante sumó 51 y 19 en lugar de 51 y 18?,” “¿Cómo supiste que la pregunta podría tratar sobre comparar? ¿Por qué no una pregunta sobre quitar?,” and “¿Qué estrategias puedes usar para calcular 51 − 19 − 18?” Students use mathematical language to discuss problem structures, strategies, and representations with peers. The lesson includes exemplar responses, such as “El diagrama de cinta y el trabajo del estudiante muestran suma,” “Hacen 70 juntos. De esa manera, no hay necesidad de formar una decena cuando sumas el tercer número,” “El diagrama ayuda a ver que es una comparación,” and “Usa la recta numérica. Haz un dibujo. Resta 20 y suma 1, resta 20 más y suma 2,” which provide guidance for educators in supporting students’ mathematical explanations and discourse.

The materials include embedded educator guidance that supports students’ vocabulary, syntax, and discourse related to equal sharing and early division concepts. Students hear, use, and refine mathematical language such as compartir equitativamente, grupos iguales, partes iguales, and dividir as they discuss how objects can be shared fairly. The tasks provide opportunities for students to use mathematical language with peers while working with objects, drawings, and contextual situations. For example, in grade 2, unit 9, lesson 1, “Calentamiento,” students analyze a collection of jewels, determine the number of objects, and discuss how the treasures could be shared equally among four pirates. The materials include exemplar responses that describe how students might count, group, and divide the objects, providing educators with guidance to support student responses and facilitate mathematical conversations. These supports help students develop and apply a mathematical language toolkit over time.

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

For example, in grade 2, unit 8, lesson 4, activity 1, “Muchas maneras de componer figuras,” the activity integrates the TEKS process standards by engaging students in problem-solving, mathematical communication, representation, and reasoning about geometric relationships. Using pattern blocks, students model mathematical ideas, analyze how composite figures are constructed, and use precise geometric language to explain and justify their reasoning. Educator prompts and discussion routines guide students to explore how different combinations of shapes can compose the same figure and to defend their mathematical thinking. Through hands-on representations and collaborative discussions, students apply the TEKS process standards as they make sense of problems, use tools and representations, communicate ideas, and justify their reasoning within the context of geometry.

In grade 2, unit 9, lesson 11, activity 2, “Hacer cuadrados del mismo tamaño,” students engage in the TEKS mathematical process standards as they divide rectangles into equal squares and use drawings, shading, and organized representations to model and communicate their mathematical thinking. Students analyze the structure of their models by identifying rows and columns and explain relationships between the visual representations and the quantities represented. Educator prompts such as “¿Cómo podrías hallar el número total de cuadrados . . . ?” encourage students to justify their reasoning and connect models to equations. Students write equations such as “5 + 5 + 5 + 5 = 20” to represent their work, demonstrating how they use representations, reasoning, and mathematical communication to solve problems.

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

The TX Math Teacher Course Guide K–5 describes how the TEKS mathematical process standards are incorporated and connected throughout the course through a problem-based approach that engages students in reasoning, problem-solving, mathematical discourse, and the use of representations. The guide explains that students learn mathematics by doing mathematics and that they will regularly engage in practices such as interpreting problems, constructing arguments, critiquing reasoning, modeling with mathematics, and using tools strategically. Educator guidance highlights how these practices are embedded in daily instruction through discussions, questioning, sharing strategies, and lesson syntheses. The materials also describe how students revisit and build these mathematical practices over time through modeling, problem-solving, and communication experiences that develop across units and grade levels. This course-level description demonstrates how the TEKS mathematical process standards are intentionally incorporated and connected throughout the instructional program.

In grade 2, unit 1, Guía de planificación a nivel de sección, section A, “El valor de cuatro dígitos,” students use base 10 models and other representations to explore place value. Students explain relationships between place values as they read, write, and decompose three-digit numbers, promoting mathematical reasoning, communication, and connections among representations. The progression from composing and decomposing numbers prepares students to apply these process standards in future lessons and units. This demonstrates how the materials connect the TEKS mathematical process standards across the course by building mathematical practices through increasingly complex applications.

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

The materials describe how the TEKS mathematical process standards are incorporated throughout the unit as students explore even and odd numbers, equal groups, and addition and subtraction within 100. Students use objects, diagrams, equations, and visual representations to explain mathematical relationships and solve problems. The Guía de planificación a nivel de sección connects process standards across the unit by moving from pairing and equal groups to equations, unknowns, and place-value strategies. For example, in grade 2, unit 2, the Guía de planificación a nivel de sección, section B, “Narrativa,” explains that students communicate their reasoning using diagrams and visual representations to build connections between numbers and operations.

The materials describe how the TEKS mathematical process standards are incorporated and connected throughout unit 3 as students solve addition and subtraction problems within 1,000. Students use number lines, base 10 blocks, base 10 diagrams, expanded form, and equations to represent, analyze, and justify sums and differences. The unit guidance connects these processes across sections by showing how students progress from strategies that do not require composing or decomposing to more flexible place-value methods. For example, in grade 2, unit 3, the Guía de planificación a nivel de sección, section B, “Narrativa,” explains that students analyze and use base 10 blocks, base 10 diagrams, expanded form, and equations to connect conceptual understanding with place-value reasoning. This unit description demonstrates how the TEKS mathematical process standards are intentionally incorporated and connected as students develop increasingly sophisticated problem-solving and representation strategies.

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

At the beginning of each lesson, the materials outline the TEKS that will be addressed, the materials needed, and a brief overview of the lesson. The lesson overview also includes learning objectives, suggested educator questions, and activities to guide instruction. These components describe how students should think and work mathematically while learning the content, including opportunities for reasoning, problem-solving, communication, and the use of strategies and tools. For example, in grade 2, unit 2, lesson 6, “Comunicar ideas matemáticas usando diagramas,” students “resuelven un problema matemático y luego dibujan un diagrama que representa su proceso de Pensamiento.” This lesson overview identifies the mathematical processes students will use as they engage with the content.

The materials include individual lessons’ lists of the TEKS in the “Abordando” section and connect them to the lesson purpose, objectives, and student tasks. These lesson overviews identify the process standards emphasized and show how students apply them through real-world contexts, representations, tools, and mathematical explanations. For example, in grade 2, unit 9, lesson 1, the “Abordando” section lists the TEKS addressed, and students use objects, drawings, and discussion to explore how objects can be shared equitably into equal groups. This provides educators with an overview of the TEKS mathematical process standards incorporated within the lesson and how students will apply them during instruction.

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

The materials provide opportunities for students to think mathematically, persevere through solving problems, and make sense of mathematics by engaging them in a non-routine measurement task. In grade 2, unit 6, lesson 9, activity 1, “El problema del cuaderno,” students determine how Kai and Jada both measured the same notebook even though the ruler does not begin at zero. Students reason about the relationship between the starting and ending measurement points, connect their measurements to equations, and explain why both methods produce the same length. As students work through an unfamiliar measurement situation, they justify their reasoning and use measurement tools appropriately, supporting mathematical thinking, perseverance, and conceptual understanding.

In grade 2, unit 9, lesson 12, activity 2, “Dividir rectángulos,” students think mathematically as they partition rectangles into equal-sized squares using tiles to plan their work before drawing their partitions and writing equations to represent the total number of squares. Students first collaborate with a partner and then independently partition additional rectangles before comparing their solution strategies. Educator prompts such as “¿Cómo decidiste qué rectángulo dibujado usar?” and “¿Qué estrategias usaste para hacer que todos tus cuadrados fueran del mismo tamaño?” encourage students to explain and refine their reasoning, while educator guidance suggests using tiles or a ruler to revise their work when needed.

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.

In grade 2, unit 4, lesson 1, activity 1, “¿Cómo llegamos a la escuela?,” the materials support students in understanding, explaining, and justifying that data can be represented and interpreted in multiple ways. Students use hands-on tools, such as Unifix cubes and pictures, to organize and represent class data before discussing the effectiveness of different representations. Educator prompts such as “¿Cómo podríamos averiguar cuántos estudiantes . . . ?” and questions about whether the graph is easy to read encourage students to explain and justify their thinking. As students compare different ways to organize the same data, they recognize that mathematical information can be represented in multiple valid ways while reaching the same conclusions.

In grade 2, unit 5, lesson 22, activity 2, “Paseo por el salón de problemas narrativos,” students engage in a gallery walk to understand, explain, and justify how problems can be completed in various ways. During the gallery walk, students examine classmates’ posters that feature different story problems, representations, and solution strategies before discussing what they notice and wonder about each approach. Prompts such as “¿Qué tenían en común los enfoques?” and “¿Cómo eran diferentes?” encourage students to compare representations, explain how different strategies solve the same problem, and justify why multiple approaches are mathematically valid. Students also provide feedback, ask questions, and revise their own posters based on insights gained from their peers, reinforcing that mathematical problems can have multiple correct representations and solution methods.

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.

In grade 2, unit 7, lesson 1, activity 1, “Doblar partes iguales,” the materials require students to make sense of mathematics through opportunities to do, write about, and discuss mathematics. Students do mathematics by folding and cutting rectangles into equal parts to compare their sizes, write about their mathematical thinking by recording the names of the equal parts, such as halves, fourths, and eighths, and discuss their reasoning with peers as they explain how they know the pieces are equal. During the activity synthesis, the educator facilitates discussion by having students share and compare examples of rectangles partitioned into equal parts, helping students build conceptual understanding through hands-on exploration, written responses, and mathematical discourse.

In grade 2, unit 4, lesson 24, activity 2, “Interpretar nuestros datos numéricos,” students make sense of mathematics by interpreting a class dot plot through opportunities to do, write about, and discuss mathematics. Students do mathematics by analyzing measurement data displayed on the dot plot, write about their thinking by answering questions and recording observations about the data, and discuss their interpretations with classmates and the educator during whole-class conversations. The lesson begins with an educator-led discussion of the graph’s title, labels, and units of measure before students independently analyze the data. During the “Síntesis de la actividad,” educator prompts such as “¿Qué representan los números en nuestro gráfico de puntos?,” “¿Qué envergadura de mano fue la más común?,” and “¿Qué medida nadie en nuestra clase tenía para su mano?” encourage students to explain, justify, and compare their reasoning, supporting mathematical sense-making through meaningful discussion and written reflection.

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

In grade 2, unit 6, lesson 6, activity 2, “Adivina mis reptiles,” the materials provide educator supports that guide students in sharing and reflecting on their problem-solving approaches through mathematical explanations, arguments, and justifications. Conversation stems such as “Comparé _____ y _____ porque . . .” and “Nuestras comparaciones son diferentes porque . . .” encourage students to explain and compare their reasoning with a partner. The materials also direct educators to facilitate productive disagreement and use prompts such as “¿Tu diagrama coincide con el problema de narrativa que creaste? ¿Por qué o por qué no?” and “¿Sumaste o restaste para hallar el otro reptil? ¿Cómo te ayudó tu diagrama?” to encourage students to defend their conclusions using diagrams and equations. These supports help students communicate their strategies, evaluate different approaches, and reflect on how representations support their problem-solving.

In grade 2, unit 9, lesson 11, activity 2, “Hacer cuadrados del mismo tamaño,” the materials support educators in guiding students to share and reflect on their problem-solving approaches through explanations, arguments, and justifications. As students partition rectangles into equal-sized squares and represent the total number of squares with equations, the educator is directed to pair students who use different techniques and have them “comparen sus técnicas y prueben las técnicas de los demás para completar una fila o columna de cuadrados.” This guidance encourages students to explain their strategies, evaluate the reasoning of others, and reflect on how different approaches can be used to solve the same problem. During the “Síntesis de la actividad,” “Math Language Routine 8: Apoyos para la conversación” guides educators to provide time for students to ensure that “todos los miembros de su grupo puedan explicar cómo saben cuántos cuadrados llenarán el rectángulo” and rehearse their explanations before sharing with the class. The educator’s question, “¿Cómo podrías hallar el número total de cuadrados que llenarían este rectángulo sin dibujar las líneas?” further prompts students to justify their reasoning by using the structure of rows and columns, strengthening their ability to communicate and defend their mathematical thinking.

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

In grade 2, unit 5, lesson 3, activity 2, “Resuelve problemas de comparación,” the materials provide prompts and guidance that support educators in giving explanatory feedback based on students’ responses and anticipated misconceptions. The lesson directs educators to monitor the different representations students use to solve comparison problems, including strip diagrams, equations, and drawings, and to select student work that highlights varied approaches for discussion. Educator prompts such as “¿Qué tienen en común sus representaciones? ¿Qué es diferente?” and “¿Cómo te ayudó tu representación a decidir si debías sumar o restar?” help educators build on students’ thinking and support deeper understanding of comparison situations. The lesson also anticipates a common misconception by noting that students may create equations that do not match the context of the word problem. In response, educators are guided to ask students to explain what each quantity represents and, when needed, to provide an unlabeled strip diagram to help students connect representations to the problem situation.

In grade 2, unit 9, lesson 10, activity 2, “Organizar vegetales para formar matrices,” the materials provide educator guidance for responding to student strategies and addressing anticipated misconceptions through explanatory feedback. Students create arrays, write repeated-addition equations, and compare different arrangements that represent the same quantity. The materials direct educators to monitor students’ strategies, select students with different array representations to share, and model a 4 × 4 array if students do not generate one before discussing the related repeated-addition equation. Educator prompts such as “¿Qué ecuación representaría el arreglo usando sumandos iguales?,” “¿Los sumandos representan el número de semillas de zanahoria en cada fila o en cada columna?,” and “¿Puedes hallar otra ecuación que muestre el número en cada fila o en cada columna?” encourage students to connect representations and explain their reasoning. The lesson also anticipates the misconception that students may create arrays with only one row or rows of one and provides the prompt “¿Hay otra manera de organizar los cultivos para que haya al menos 2 filas?” to guide students toward more complete representations and deeper understanding.