Kiddom Texas: Matemáticas en Español – Grado 3

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 3 Alcance y Secuencia. The scope and sequence is organized by unit and lesson number and includes column titles such as “Número de unidad en Kiddom,” “Número de lección en Kiddom,” “TEKS cubiertos en la lección,” and “Objetivos de aprendizaje.” For example, unit 1, lesson 1 covers TEKS 3.2A and has the corresponding concept taught, “Representa números hasta 1,000 de diferentes formas usando el valor posicional.”

The document Grado 3 Alcance y Secuencia presents the TEKS in an organized format, including columns that identify each unit and the corresponding lessons within each unit. This document provides information for units 1–9, specifying the TEKS alignment and instructional focus for each lesson. For example, in unit 8, lesson 11, “Geometría,” the identified TEKS include 3.7B. The associated concepts are “Encuentra el perímetro de figuras bidimensionales” and “Comprende que muchas figuras diferentes pueden tener el mismo perímetro.”

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 materials include three instructional calendars titled Calendario de 165 días, Calendario de 180 días, and Calendario de 210 días. Each calendar includes the number of lessons, evaluation days, additional flexible days, total days, and suggested ideas for flexible days to support effective implementation of the materials. For example, in the 165-day calendar, unit 1 includes eight lessons, one additional evaluation day, and one flexible day, for a total of 10 instructional days.

The scope and sequence documents present the units in an organized format, including the unit, number of lessons, number of additional practice days, evaluation days, and flex days. The document provides detailed information for three academic calendars: 165, 180, and 210 days. For example, in the 165-day instructional calendar, the suggested pacing for unit 5, “Resolver problemas,” includes a total of 19 lessons, one evaluation day, and two flex days, for a total of 22 instructional days.

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 materials provide a clear rationale for the sequencing of units and an explanation of how concepts are interconnected 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 pacing guide titled Guía de planificación de matemáticas de Texas 3–5 that outlines the unit order by number and the weeks they should be taught across grades 3–5. For example, grade 3 begins with unit 1 titled “Valor posicional hasta 100,000.” The materials include a guide for the order in which units are to be taught. The materials also include a rationale for the unit order, and they explain how the concepts connect 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 por 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, and includes learning objectives for each section and visual supports. For example, “Sección A: Composición de números” provides an overview of lessons 1–6 and includes two learning objectives, while “Sección B: Comparar y clasificar” provides an overview of lessons 7–8 and includes one learning objective.

In unit 8, lesson 1, “¿Qué atributos ves?,” 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 the educator. 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 materials include unit overviews that provide educator background knowledge related to the mathematical concepts. For example, the grade 3, unit 4 overview provides strong background content knowledge by explaining key concepts related to division, including equal groups, types of division problems (“¿cuántos grupos?” and “¿cuántos en cada grupo?”), the inverse relationship between multiplication and division, and the use of visual models such as arrays, strip diagrams, and equations. It also describes how students progress from conceptual understanding to applying division in real-world contexts and connecting it to known multiplication facts.

The materials explicitly identify and embed the academic vocabulary necessary to teach the unit within the unit overviews. For example, in unit 1, “Valor posicional hasta 100,000,” the “Overview” tab contains the objectives, narrative for the unit, and the following key terms: ecuación, forma desarrollada, and multiplicación. Academic vocabulary for the grade level is also included in “Términos de glosario.”

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 3, 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 3, 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 careers. 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 materials provide comprehensive, structured, and detailed lesson plans that include lesson objectives, TEKS correlation, tasks and questions aligned to the objectives, and instructional assessments aligned to the lesson objectives. For example, unit 1, lesson 1 covers TEKS 3.2A, addresses the lesson objectives “Relaciona (oralmente) diagramas de base diez, expresiones, nombres de números y números de tres dígitos que representan el mismo valor” and “Representa maneras de descomponer el mismo número de tres dígitos, utilizando expresiones,” and includes a drag-and-drop question aligned to TEKS 3.2A.

The materials include comprehensive, structured, and detailed lesson plans that incorporate lesson objectives, guiding questions, instructional activities, required materials (such as presentations and printable resources), and evaluation questions. Each lesson clearly identifies the TEKS being addressed and includes informal assessments to monitor student understanding throughout the lesson. For example, in unit 5, lesson 7, the identified TEKS is 3.4K. Required materials include base 10 blocks and provided resources such as “Compare Stage 4 Division Cards” and standards-based graphing paper. The lesson includes two instructional activities that build on one another to support student learning and the development of multiple strategies for solving problems.

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 materials include a lesson overview that lists required materials, materials to be copied, required preparation, and the lesson schedule. For example, in grade 3, unit 1, lesson 1, the required materials include “Bloques de base diez: Actividad 1, Actividad 2; tarjetas para clasificar números en sus diferentes formas: Actividad 1; hoja de registro para la mesa redonda de números en diferentes formas: Actividad 2.” Additionally, the lesson overview provides suggested timing for each component: “Calentamiento,” 10 minutes; “Actividad 1,” 15 minutes; “Actividad 2,” 20 minutes; “Estimación/síntesis,” 10 minutes; and “Enfriamiento,” 5 minutes.

The materials include a lesson overview that lists the educator and student materials necessary to effectively deliver the lesson. The structure of the lesson is clearly outlined. For example, in unit 8, lesson 1, activity 1, the materials include a lesson overview, a list of required materials for each activity, and all supporting resources, such as shape sorting cards and presentations, needed to deliver the lesson.

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, 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 2, lesson 9, activity 3, “Mi manera,” the “Narrativa de la actividad” provides explicit guidance for using the activity as extended practice after instruction, stating, “Esta actividad es opcional porque no aborda nuevos estándares matemáticos de contenido. Sin embargo, les brinda a los estudiantes una oportunidad para aplicar destrezas previas de modelado matemático.” This guidance directs educators to use the optional activity as additional practice for reinforcing previously taught mathematical modeling skills. Students apply prior learning by representing and solving two-step subtraction problems in real-world contexts using strategies that make sense to them, supporting educators in extending learning beyond the core lesson through continued application of previously learned concepts.

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 materials include a variety of instructional formative assessments at the lesson level that vary in types of tasks and questions. For example, in unit 3, after lesson 6, the materials include a checkpoint titled “Punto de control de la sección A” that incorporates a drag-and-drop of manipulatives, an open-ended question with multiple answers, and a multipart question. Furthermore, unit 3 has two more checkpoints titled “Punto de control de la sección B” and “Punto de control de la sección C” that also vary in types of tasks and questions.

The materials include a variety of instructional assessments at both the unit and lesson levels, including diagnostic and formative assessments, with a variety of tasks. For example, in unit 1, lesson 1, “Enfriamiento,” students are asked to identify the many ways a given number can be represented. This task serves as an effective formative and diagnostic assessment at the lesson level, as it allows educators to monitor student understanding and misconceptions. The materials provide “what to look out for” and “next steps” guidance for supporting students before the following day’s lesson.

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 state that the purpose of assessment is for educators to use student responses during the cooldown to make adjustments to instruction.

The materials demonstrate a clear understanding of 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, in the Guía de recursos para maestros, the materials highlight the availability of assessment guidance at the lesson, section, and unit levels. The guide explains that each lesson includes an “Enfriamiento” (cooldown) in the form of an exit ticket. It further defines how this activity serves as a brief check to determine if students understand the main concepts of the lesson and explains how to use the formative assessment to plan future instruction.

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 include educator guidance to ensure the consistent and accurate administration of instructional assessments, including specific recommendations for the amount of time students should be given to complete each assessment. For example, unit 3, lesson 5, “Enfriamiento: tarjetas de Clare,” states that the exit ticket should take approximately five minutes to complete.

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 the “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 grade 3, unit 2, “Problemas de práctica de la sección A,” each question includes standard tags, which list the TEKS being addressed (111.5.b.1.C, 111.5.b.5.A, 111.5.b.4.A, 111.5.b.2.D, 111.5.b.1.F, 111.5.b.1.G).

The materials include formative assessments titled “unit checkpoints” that are aligned to the TEKS and objectives of the unit. For example, unit 3, “Punto de control de la sección A” assesses TEKS 3.4D and 3.5B. TEKS 3.4D states that students will determine the total number of objects when equal-sized groups of objects are combined or arranged in arrays up to 10 by 10. TEKS 3.5B states that students will represent and solve one- and two-step multiplication and division problems within 100 using arrays, strip diagrams, and equations. This checkpoint aligns to the unit objectives “Interpretar la multiplicación como grupos iguales a través de representaciones visuales, arreglos y diagramas” and “Conectar los conceptos de área y multiplicación.”

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, unit 3, “Grado 3.3: Evaluación de fin de unidad,” is an eight-question test assessing TEKS 3.4K, 3.5B, and 3.6C. The test also includes the following item types that vary in complexity: short-answer, drawing, multiple-choice, and multipart 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 TX Math Teacher Course Guide K–5 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, in unit 4, “Evaluación final de la unidad 3.4,” a “Note for Evaluating Responses” appears after question 3 and gives educators guidance related to evaluating student responses for dividing. The guidance for interpreting student performance on this question states, “Los estudiantes pueden dibujar una imagen o usar la expresión de 36 dividido por 6 para encontrar que Kai pondrá 6 imágenes en cada página.”

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, no explicit guidance is shared for educators to use to respond to how students scored on the assessment and the task or activity that would 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 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.

Within the materials, if a student has difficulty with a concept, the materials provide guidance for differentiated instruction. For example, in a unit about estimation, if a student does not understand the task and tries to calculate the exact number, the educator support provided the next day could involve re-explaining the concept of estimation and its applications in solving real-world problems. Within 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 materials provide supports for students who have not yet reached proficiency and include differentiation for multilingual students and students with disabilities. For example, in unit 3, lesson 4, activity 1, the “Apoyo para estudiantes multilingües” section instructs educators to display key vocabulary such as row, column, each, times each, 3 by 5, and 5 by 3, along with diagrams and annotations, and to allow multilingual students to reference and add to this language throughout the lesson. To support students with disabilities, the “Apoyo para estudiantes con discapacidades” section encourages educators to make visible connections between representations and to have students use gestures or drawings when explaining correspondences between matrices and expressions, such as explaining how numbers represent rows and groups. These supports focus on differentiated accessibility during tier-one instruction.

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

The materials include embedded supports for unfamiliar vocabulary in text. In grade 3, unit 6, lesson 2, activity 1, the lesson incorporates “Math Language Routine 2: Collect and Display,” which provides educator guidance for collecting, displaying, and reinforcing mathematical vocabulary as students engage with the task. For example, educators are directed to display and revisit terms such as partir, dividir, partes iguales, mitades, tercios, cuartos, and entero and to encourage students to use the displayed language when describing and classifying figures. The lesson also prompts educators to refine students’ language and highlight precise mathematical terminology during the “Síntesis de actividad” section.

The materials include pre-teaching or embedded supports for academic language. This lesson builds student vocabulary by design. It provides structured guidance to help educators introduce terms through collaborative discussion, peer response comparisons, and explicit definitions. In grade 3, unit 1, lesson 1, “Representar números de diferentes maneras,” students learn to represent numbers using base 10 blocks, base 10 diagrams, expanded form, numbers, and word form, thereby building their vocabulary schema.

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

In grade 3, unit 4, lesson 13, “Resolver misterios de ecuaciones,” the materials provide teacher guidance for extending learning through an activity that goes beyond grade-level expectations. The lesson notes that interpreting data represented in a gráfico de líneas may be considered “una extensión más allá del nivel de grado.” Students analyze and discuss information displayed in a line graph while applying multiplication and division within 100 to solve real-world problems and represent their thinking with equations. By incorporating mathematical concepts beyond the previous grade’s expectations and connecting them to problem-solving and mathematical reasoning, the lesson provides an extension opportunity for students who are ready for more advanced learning.

In unit 5, lesson 3, activity 3, “Juega cerca de 100 multiplicación (opcional),” the materials provide educator guidance for an optional activity that extends students’ multiplication learning beyond the core lesson. The lesson states, “Esta actividad es opcional porque ofrece práctica adicional para multiplicar por factores que son números de los adolescentes y factores mayores que 20. Dependiendo del tiempo disponible, los estudiantes pueden jugar 1 o 2 juegos.” By engaging students in multiplication with teen numbers and factors greater than 20, the optional activity provides an opportunity for educators to extend learning and reinforce multiplication strategies through additional application and practice for students who are ready to deepen their 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.

The materials provide explicit prompts, questioning strategies, discussion starters, and educator language that support consistent lesson delivery across classrooms. For example, in unit 4, lesson 3, activity 1, students match division situations to drawings of equal groups. The materials direct educators to say, “Vas a emparejar seis situaciones y dibujos que podrían representarlas. Toma unos minutos para decidir qué dibujo corresponde a cada situación.” The lesson includes time for independent thinking and discussion, and during synthesis educators ask, “¿Cómo puede el mismo dibujo representar ambas situaciones?” with sample student responses such as, “No vimos cómo se hicieron los grupos, pero al final, se hicieron el mismo número y tamaño de grupos en ambas situaciones.” These supports help educators facilitate mathematical discourse and guide students in connecting division situations to representations of equal groups.

The materials provide guidance to support the educator in facilitating mathematical discussions and developing conceptual understanding through instructional routines. The materials explain the purpose of routines, describe how they support student thinking, and identify how educators should monitor and engage students during instruction. For example, in the TX Math Teacher Course Guide K–5, the description of the “Conversación numérica” routine explains that students share strategies, make connections, and build conceptual understanding while educators facilitate discussion around mathematical structure and reasoning.

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

Grade 3, unit 7, lesson 4, activity 1 combines collaborative learning, data collection, student discourse, and whole-class discussion through a structured sequence of group work, class data analysis, and reflection. The educator is given guidance for facilitating each phase of instruction, including group organization, discussion prompts, and synthesis questions. For example, the lesson directs students to work in “grupos de 4” to collect and organize categorical data from classmates and then guides the educator to facilitate a whole-class discussion using prompts such as “¿Qué es útil de tener estos datos en forma de lista?” to help students analyze and make sense of the data.

The materials include the use of exit tickets to monitor student understanding. These supports help educators effectively assess student comprehension and make instructional decisions based on student performance. For example, in unit 2, lesson 21, “Enfriamiento,” students complete a two-question exit ticket designed to assess their understanding of the lesson content. The materials also provide educators with guidance for responding to assessment results. For instance, educators are prompted to review student responses to evaluate their understanding of addition strategies within 1,000. The next-day guidance recommends providing targeted review activities with smaller sums for students who are struggling before returning to larger addition problems. Additionally, educators are encouraged to revisit foundational concepts related to base 10 understanding and properties of operations through hands-on activities and prior-unit support.

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, while providing educators with explicit guidance for implementing recommended instructional structures. For example, grade 3, unit 1, lesson 1, “Calentamiento,” directs students to explain the meaning of any terms they use. The materials state, “Durante la discusión, pídeles a los estudiantes que expliquen el significado de cualquier término que usen, como valor posicional, cientos, decenas, unidades, suma o diagrama de base diez.” These structured opportunities support active engagement and effective lesson implementation.

The materials support multiple types of practice, including guided, independent, and collaborative learning, and provide structured guidance for implementation. The TX Math Teacher Course Guide K–5 notes that the “Inicio” often involves partner or small-group work to promote discussion and engagement, and that students regularly work individually, with a partner, and in small groups. It also explains that the “Enfriamiento” is typically completed independently as a formative assessment. In addition, routines such as “Math Language Routine 2: Recolectar y mostrar” can be implemented in whole-group or small-group settings. These structures support students in both independent application and collaborative discussion of mathematical ideas.

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 provide explicit implementation guidance for supporting EB students and students learning English through the use of Mathematical Language Routines (MLRs). The TX Math Teacher Course Guide K–5 explains the purpose of the routines, when and how educators should use them, how they support language development alongside mathematics learning, and how educators can adjust the supports based on students’ language needs and proficiency levels. For example, the materials state that educators should use the suggested MLRs and language strategies “para proporcionar a los estudiantes acceso a una actividad sin reducir las demandas matemáticas de la tarea,” and explain that educators can modify the supports as students develop greater proficiency in English.

Within the Guía de recursos para maestros is a section titled “Rutinas de lenguaje matemático” that provides eight routines to support multilingual students. Unit 6, lesson 2, activity 1, for example, notes that the use of “Math Language Routine 2: Recolectar y mostrar” is for educators to circulate and listen to students as they converse in pairs, small groups, or as a whole class during the discussion. Educators note down the words and phrases students use, along with any useful sketches or diagrams, and capture a variety of language uses to connect with the lesson’s content objectives. Educators organize the collected material into a display to refer to during whole-class discussions throughout the unit.

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 guidance for supporting EB students through oral discourse, including routines such as MLR1, MLR2, MLR5, MLR6, MLR7, and MLR8 that promote academic vocabulary development, comprehension, and background knowledge building through structured mathematical discussions. For example, in the TX Math Teacher Course Guide K–5, “Math Language Routine 2: Recolectar y mostrar” directs educators to collect and display student language to support the development of mathematical vocabulary, while “Math Language Routine 6: Tres lecturas” strengthens comprehension by guiding students through multiple readings of mathematical situations before solving problems. Additionally, the materials provide evidence of explicit cross-linguistic connections, such as cognates and comparisons between English and Spanish, through either oral or written discourse.

In unit 8, lesson 1, activity 1, “Clasificación de tarjetas: figuras,” the materials embed “Math Language Routine 2: Recopilar y mostrar” and explicit cross-linguistic guidance. For example, educators collect and display students’ academic language for describing and classifying figures, including lados iguales, longitudes iguales, esquinas, diagonal, recta, curva, and inclinada, and students are encouraged to borrow this language during discussion. The “Conexiones translingüísticas” guidance explicitly identifies transferable cognates such as ángulo/angle, atributo/attribute, categoría/category, and pentágono/pentagon. Students build comprehension through visual figures and the vocabulary display, then apply the language through partner classification, explanation, guessing categories, and a written response explaining their categories. Overall, students are given repeated opportunities to read, discuss, explain, and record mathematical language.

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 over the course of a lesson that require students to demonstrate depth of understanding aligned to the TEKS by determining the value of coin collections using multiple strategies. These practice opportunities require students to apply skip counting, multiplication, and place-value reasoning to solve problems and explain and justify their methods rather than only provide a total. For example, in grade 3, unit 7, lesson 10, activity 2, students determine the value of a collection of coins and share their reasoning. The “Lesson Synthesis” highlights strategies such as labeling coin values, using multiplication to find groups of like coins, and counting by intervals. The instructional assessments also require students to apply their understanding of coin values and efficient counting strategies to increasingly complex coin collections. Educator guidance prompts students to practice these skills by explaining how they found the total, identifying the value of each coin, and describing how they organized the collection, demonstrating conceptual understanding and alignment to the TEKS.

The materials include multiple opportunities for practice across lessons and units, including embedded assessments that require students to demonstrate depth of understanding. These assessments are aligned to the rigor of the TEKS and provide educators with meaningful data on student proficiency. For example, in grade 3, unit 2, the materials focus on developing students’ understanding of addition and subtraction within 1,000 through one- and two-step problem-solving. Students practice through pictorial models, equations, and number lines to represent problems and build fluency. Students then estimate and evaluate the reasonableness of their answers.

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

In unit 6, lesson 18, the lesson begins with students counting from one-fourth to sixteen-fourths and discussing patterns they observe before being introduced to the vocabulary of numerator and denominator. In activity 1, “Conozcamos Number Line Scoot: Mitades, Tercios y Cuartos,” students use unit cubes to model fractions on a number line, connecting concrete representations to fractional values. In activity 2, “Fracciones en la recta numérica,” students apply this understanding by locating and labeling fractions on a number line. The lesson concludes with students partitioning a number line into equal parts, marking but not labeling a fraction, and then exchanging their work with a partner to identify the fraction represented. This sequence of tasks progresses from developing fraction vocabulary and recognizing patterns to modeling, representing, and reasoning about non-unit fractions on a number line, supporting students’ development toward grade-level proficiency.


In grade 3, unit 7, lesson 10, activity 2, the “Narrativa de la actividad” explains that students skip count using “conteo saltado de cinco, diez o 25 y el valor posicional” to determine the value of collections of coins. The activity synthesis prompts students to compare strategies, including labeling coin values, using multiplication, and counting by groups. Students begin by determining the value of a smaller collection of coins and then apply increasingly efficient strategies to analyze larger collections. The tasks increase in rigor and complexity as students move from counting individual coins to using skip counting, multiplication, and problem-solving strategies to represent and justify their thinking.

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

In unit 3, lesson 8, activity 1, students connect multiplication and division through drawings, word problems, and equations. The activity states, “El propósito de esta actividad es que los estudiantes solidifiquen lo que han aprendido sobre la relación entre la multiplicación y la división,” emphasizing the relationship between the two operations. Students write both multiplication and division equations using the same equal groups, allowing them to recognize patterns and understand that the same situation can be represented in multiple ways. The discussion question, “Al mirar tu papel, ¿qué conexiones notas entre la multiplicación y la división?” prompts students to identify relationships between operations, including that multiplication and division can represent the same context and that unknown quantities appear in different positions within equations.

The materials demonstrate coherence by explicitly connecting big ideas such as skip counting, multiplication, place value, and money across mathematical concepts. Students apply counting by 5s, 10s, and 25s, along with multiplication and grouping strategies, to determine the value of coin collections, reinforcing relationships among mathematical concepts in a real-world context. For example, in grade 3, unit 7, lesson 10, activity 2, students use “el conteo saltado de cinco, diez o 25 y el valor posicional” to determine the value of a collection of coins. The synthesis further connects multiplication, grouping, and counting strategies by highlighting how students can use these relationships to efficiently find the total value of coins.

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 grade 3, unit 2, Guía de planificación a nivel de sección, section D, the section explains the connection between addition and subtraction and previously learned strategies to solve more complex two-step problems. Students build on prior understanding of addition, subtraction, place value, and algorithms as they apply these concepts to multistep problem-solving situations and estimation. The materials also maintain consistent mathematical language, including suma, resta, valor posicional, and redondeo, to connect prior and current learning.

The materials demonstrate coherence across units and grade levels by connecting the content and academic language students use to describe and classify geometric figures. In grade 3, unit 8, students develop foundational understanding by identifying, describing, and classifying two-dimensional figures based on attributes such as sides, angles, and symmetry while using mathematical language including rectangle, rhombus, square, and quadrilateral. Students build an understanding that figures can share attributes and belong to multiple categories, establishing relationships among geometric classifications. This learning is extended in grade 4, unit 7, lesson 1, where students build on prior geometric language and move toward more precise terminology, including point, line, and line segment. Students apply more formal definitions, such as recognizing that a line segment has endpoints, while connecting these descriptions to their previous understanding of geometric attributes.

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 knowledge of equal groups, repeated addition, and numerical reasoning to new learning involving multiplication, arrays, area, and multiplicative representations. Students use familiar concepts and procedures to develop increasingly sophisticated understandings of multiplication and its applications. For example, in grade 3, unit 3, Guía de planificación a nivel de sección, section A, “Narrativa de la sección” states that students “relacionan la idea de grupos iguales con la estructura de un arreglo,” connecting previously learned concepts of equal groups to multiplication with arrays. The unit then extends this understanding in section B by connecting multiplication to area and in section C by applying multiplication to diagrams and real-world situations.

In grade 3, unit 4, lesson 7, students build on previously learned multiplication and division concepts as they analyze related equations and expressions involving equal groups. In earlier lessons, students learned strategies for solving multiplication and division problems separately. In this lesson, students connect those procedures by using their understanding of factors, products, and equal groups to make sense of division equations and unknown values. Students analyze the relationship between multiplication and division and recognize how the same situation can be represented by both operations. The lesson also introduces the mathematical term cociente, connecting students’ prior understanding of division to more precise academic language.

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 and reinforcing previously learned skills through structured centers across lessons and units. For example, in grade 3, unit 3, lesson 1, the materials include activities such as “Atrapa cuadrados (Etapa 4: resta dentro de 20)” and “Cinco en fila (Etapa 6: suma dentro de 100 con composición),” which require students to retrieve and apply prior addition and subtraction strategies in different contexts. In “Atrapa cuadrados,” students revisit subtraction within 20, strengthening fluency with decomposing numbers and solving related problems. In “Cinco en fila,” students build on previous addition learning by composing numbers within 100 and applying strategies that combine tens and ones. Because these centers are revisited across lessons and units, students have repeated opportunities to recall familiar procedures while extending their understanding to new number ranges and problem types. The center-based structure also allows educators to observe student strategies and monitor students’ application of skills over time.

The materials provide spaced retrieval opportunities with previously learned skills and concepts across lessons and units, including multiplication and division. For example, in grade 3, unit 5, lesson 15, the warm-up routine provides an opportunity for students to revisit prior learning through the “True or False” activity. Students retrieve and apply their understanding of multiplication and division relationships developed in units 3 and 4 before engaging with more complex multistep problems. This review connects previous concepts to current learning and provides students with an opportunity to recall and apply foundational skills across lessons and units.

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 across units by connecting previously learned multiplication concepts to new learning about division. For example, in grade 3, unit 4, lesson 7, the warm-up activity “Conectemos las ecuaciones de división con las ecuaciones de multiplicación” prompts students to retrieve their prior understanding of multiplication while developing an understanding of division. Through the “Notice and Wonder” routine, students compare multiplication and division equations that use the same numbers, allowing them to recognize relationships between the two operations and connect new learning to existing knowledge. This interleaved practice requires students to move between multiplication and division reasoning, apply known relationships, and analyze how the operations represent related situations. Within lesson 7, students identify missing values and discuss connections between equations. The “teacher synthesis” reinforces these connections by highlighting division as a missing-factor relationship, helping students integrate multiplication and division concepts rather than treating them as separate skills.

The materials provide interleaved practice opportunities with previously learned skills and concepts across lessons and units by requiring students to apply multiple mathematical processes and data representations within a single practice set. Students interpret and create pictographs, dot plots, and bar graphs, compare quantities, solve multistep problems, use addition and subtraction, and apply measurement concepts in data contexts. Rather than practicing one skill in isolation, students move between representations and strategies as they analyze and represent data. For example, in grade 3, unit 7, “Problemas de práctica de la sección A,” question 1 requires students to interpret a table and identify a matching pictograph, question 2 requires students to analyze a dot plot and compare quantities, question 3 asks students to create a dot plot from a frequency table, and questions 5 and 6 require students to interpret bar graphs and pictographs while using addition and subtraction to answer data-analysis questions.

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

In unit 5, lesson 15, “Calentamiento: Verdadero o falso: multiplica por 10,” students interpret numerical representations, analyze relationships among numbers, and evaluate whether equations are true or false by justifying their reasoning. In activity 1, “Preguntas sobre una situación,” students interpret a mathematical context, analyze the information presented to generate questions that can be answered from the situation, and evaluate the representations and relationships within the context before solving problems. Across both activities, students interpret, analyze, and evaluate mathematical models and situations by making sense of representations, examining relationships, and justifying their conclusions.

The materials require students to interpret, analyze, and evaluate multiple representations, including tables, pictographs, and dot plots. Students interpret data displays, analyze relationships among representations, and evaluate which pictograph correctly represents a data table. For example, in grade 3, unit 7, “Problemas de práctica de la sección A,” question 1, students analyze a data table and determine which pictograph accurately represents the information, requiring them to evaluate multiple representations before selecting a correct answer.

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

In unit 3, lesson 2, activity 2, “Organizar en matrices,” students create arrays using physical objects to model multiplication situations. Students build arrays representing six groups of five, as well as additional arrays using 20 and 24 cubes to represent different equal-group situations. By constructing arrays with physical objects, students create mathematical models that represent multiplication concepts and equal-group situations.

The materials require students to create models that represent mathematical situations by constructing their own scaled pictographs from collected data. Students determine how to represent the data, select symbols, create a key, and organize information into a graphical representation. For example, in grade 3, unit 7, lesson 4, activity 2, “Haz un pictograma a escala,” the “Narrativa de la actividad” directs students to “representar los datos que recopilaste en tu propio pictograma a escala donde cada imagen representa a 2 estudiantes,” and question 1 requires students to draw their pictogram on a canvas.

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

In unit 3, lesson 9, activity 1, “Expresiones y áreas de coincidencia,” students apply their understanding of equal groups and multiplication to a new context by connecting multiplication expressions to rectangular arrays. Students decompose rectangles to identify equal groups, relate the rows and columns to the factors in a multiplication expression, and match each expression to the appropriate rectangle displayed around the room. By applying their conceptual understanding of multiplication to area models, students make connections between visual representations and symbolic expressions in a new mathematical context.

In grade 3, unit 4, lesson 11, activity 2, “Visualizar la división con diagramas de tiras,” students apply their understanding of division and equal groups to represent and solve a two-step problem involving cupcakes, boxes, and shelves. Students use strip diagrams to model the situation, first determining how many boxes can be made from 16 cupcakes when each box contains 2 cupcakes and then determining how many boxes can be placed on each of 2 shelves. By representing the situation with strip diagrams and connecting their models to equations such as 16 ÷ 2 = 8 and 8 ÷ 2 = 4, students apply previously learned concepts of division in a new problem situation. Through using a visual model to represent a multistep context and making connections between division and multiplication, students apply conceptual understanding across new representations and mathematical contexts.

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

In unit 3, “Problemas de práctica de la sección A,” students build automaticity and fluency with multiplication concepts through repeated practice with arrays and equal groups. The practice set provides focused opportunities to create arrays, determine whether arrays represent even or odd numbers, and write multiplication equations from array models. Specifically, questions 1, 4, and 5 require students to create arrays, questions 2 and 3 focus on identifying even and odd numbers using arrays, and questions 6 and 7 have students write multiplication equations based on arrays. This repeated practice with related multiplication concepts helps students develop fluency and automaticity.

In grade 3, unit 5, lesson 4, “Día del centro de multiplicación,” students reflect on their multiplication fluency by sorting facts into categories based on whether they know them immediately, can find them quickly, or are still developing them. Students then identify unknown products, consider efficient strategies for finding those products, and practice applying those strategies. Through evaluating their current level of fluency, practicing multiplication facts, and using known facts and number relationships to determine unknown products, students strengthen both automatic recall and strategic thinking. As students build fluency with multiplication within 100, they develop the foundational skills needed to engage successfully in grade-level problem-solving, division, and other more complex mathematical 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 unit 2, lesson 3, activity 1, “Estrategias para sumar,” students practice applying efficient, flexible, and accurate addition procedures by solving sums within 1,000 using strategies of their choice. Students may add hundreds, tens, and ones by place value, reason with numbers close to 100, use mental math, or model their thinking with base 10 cubes, number lines, or paper-and-pencil methods. As students work with a partner, they explain and justify their chosen strategy and representation. During the “Síntesis de la actividad,” the educator asks, “¿Qué representaciones muestran la misma idea o nos ayudan a encontrar la suma de la misma manera?,” prompting students to compare methods and evaluate the efficiency of different approaches.

The materials provide opportunities for students to practice efficient, flexible, and accurate mathematical procedures by connecting multiplication expressions to rectangular area models. Students use rows, columns, equal groups, and area models to determine products, compare representations, and explain how multiplication relates to the total number of squares. For example, in grade 3, unit 3, lesson 9, activity 2, “Crear a partir de expresiones,” students draw rectangles to represent multiplication expressions, label the rectangles with numbers, and explain why multiplying the numbers in each expression gives the area of the rectangle. This activity supports efficient multiplication strategies, flexible use of models, and accurate connections between factors, products, and area.

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 materials provide opportunities for students to evaluate procedures, processes, and solutions for efficiency, flexibility, and accuracy by comparing two subtraction algorithms. Students analyze how each algorithm records decompositions, discuss similarities and differences, and explain how and why each method works. For example, in grade 3, unit 2, lesson 11, activity 1, “Un nuevo algoritmo de resta,” students compare Andre’s and Clare’s algorithms for 528 − 271, complete both algorithms, and discuss what they did differently while solving each one.

In grade 3, unit 5, lesson 2, “Formas de representar la multiplicación de números de dos cifras,” students compare multiple strategies for multiplying numbers from 11 to 19 using different representations. Students analyze and evaluate how each strategy supports solving the same problem and determine which methods are more efficient or effective. The warm-up synthesis question prompts students to justify which strategy is most helpful and why, supporting evaluation of approaches used to solve multiplication problems.

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

In unit 2, lesson 4, activity 2, “¿Cómo sumarías?,” students choose an algorithm or other strategy to add numbers within 1,000 while educators guide them toward increasingly efficient approaches. The activity encourages students to consider the structure of each problem and select the strategy that is most appropriate for the numbers involved. The “Narrativa de la actividad” states that the goal is for students to choose a strategy or algorithm they can use efficiently and accurately for each problem. Student directions reinforce this by stating, “Usa la estrategia que prefieras para hallar el valor de cada suma. Escribe los pasos que seguiste para encontrar el valor de la suma.”

In unit 7, lesson 15, “Calentamiento: Verdadero o falso: comparaciones,” students determine whether statements such as “56 centavos > 61 centavos,” “100 centavos = $1.00,” “$456 > $452,” and “$13.45 < $14.98” are true or false using a strategy of their choice. During the “Síntesis de la actividad,” educator guidance prompts students to explain how they made their comparisons. The educator facilitates discussion by asking, “¿Cómo los comparaste?” and supports students in sharing and comparing different strategies. These embedded educator prompts guide students to consider and discuss different approaches for comparing monetary values.

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

In the TX Math Teacher Course Guide K–5, the section “Desarrollando comprensión conceptual y fluidez procedimental” explains that conceptual understanding, procedural fluency, and application are developed simultaneously throughout the materials. It describes how conceptual understanding is built through connections between new representations, mathematical language, and prior learning, while procedural fluency is developed through warm-ups, routines, practice problems, and centers. The guide further explains that students apply both conceptual understanding and procedural fluency to new mathematical problems in real-world and non-real-world contexts, showing how the materials are designed to integrate conceptual and procedural expectations of the TEKS across instruction.

The materials explicitly address the conceptual emphasis by explaining that students analyze division strategies and strengthen their understanding of place value, properties of operations, and the relationship between multiplication and division. The materials address the procedural emphasis as students divide within 100 using strategies based on place value and properties of operations, including writing equations to represent and solve for unknown quotients. For example, in grade 3, unit 5, lesson 7, students analyze diverse strategies for representing division and extend this work by writing equations to determine the quotient.

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 unit 3, lesson 3, activity 1, “Ordenar tarjetas: matrices,” students connect pictorial representations of equal groups to arrays by matching drawings with corresponding array models. As students sort the cards, they identify arrays that show the same number of objects in each row or column as the number of objects in each group. Within this task, students use multiplication language to explain the relationships they observe, connecting visual models to abstract multiplication concepts and equations.

In grade 3, unit 6, lesson 14, activity 2, “Comparar fracciones,” students use concrete, pictorial, and abstract representations as they compare fractions and justify their reasoning. Students use fraction bars as concrete manipulatives to model and compare the size of fractions. They create visual models to show why one fraction is greater than another, and an abstract representation is evident when students are asked to explain their answers by creating models.

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.

For example, in grade 3, unit 3, lesson 2, “Organizar objetos en matrices,” the materials guide students through connected representations of multiplication by sequencing physical manipulation, sketching arrays, and describing their reasoning. Students first use objects to build arrays, then sketch their models, and finally explain how the rows and columns represent equal groups. This progression supports students in connecting concrete models to pictorial representations and explaining mathematical ideas using language.

In unit 7, lesson 2, activity 2, “Doblar y nombrar,” students fold rectangular strips of paper into equal parts to create thirds, sixths, fourths, and eighths before formally learning the terms sixths and eighths. As they manipulate the paper, students observe that thirds can be partitioned into sixths and fourths into eighths, connecting the concrete model to the representational idea of equal partitions. During the “Síntesis de la actividad,” educator questions such as “¿Cómo utilizaste las particiones de _____ partes iguales para partir en _____ partes iguales?” and “¿Alguien quiere añadir una observación sobre la forma en que _____ dividió?” guide students to explain how their models represent the new fractional concepts and connect them to the mathematical language of sixths and eighths.

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

In unit 8, lesson 13, “Problemas de perímetro,” students use geometric figures to explore perimeter and develop academic mathematical language through visuals, problem-solving, and mathematical discussions. Students strengthen vocabulary related to perimeter and measurement as they solve problems involving unknown side lengths and explain their reasoning, including “hallen longitudes de lados desconocidos dado el perímetro de una figura.” Students communicate their ideas using mathematical language through hands-on activities, such as drawing in response to “¿Puedes dibujarlo?” and comparing figures by discussing “¿En qué se parecen?”

In unit 5, lesson 13, activity 2, “Representar, Resolver, Explicar,” students develop academic mathematical language through the use of visual models, structured discussions, and language routines. Students represent situations using models such as strip diagrams to support their understanding of relationships between quantities and the equations they create. The activity supports mathematical discourse by prompting students to explain and justify their solutions through questions such as “¿Cuáles son algunas maneras en que podrás determinar si tu respuesta tiene sentido?,” “¿Qué se puede contar o medir en esta situación?,” and “¿Cómo podrías representar el problema?” Students engage in partner discussions to compare strategies and equations by responding to prompts including “¿En qué se parecen y en qué se diferencian esas ecuaciones?” and “¿Alguien resolvió el problema de una manera diferente?” Additionally, the “Math Language Routine 5: Co-crear preguntas” provides a language development strategy that supports students in generating, discussing, and refining mathematical questions before solving the task.

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 include embedded educator guidance that scaffolds students’ development and use of academic vocabulary related to multiplication and area. Students use and explain terms such as factores, producto, filas, columnas, grupos iguales, and área while matching multiplication expressions to rectangular models. For example, in grade 3, unit 3, lesson 9, activity 1, the “Lesson Synthesis” guides educators in asking students how they identify each factor in the rectangle and how the product is represented by the model. These educator prompts support students in connecting mathematical vocabulary to visual representations and applying academic language while explaining their reasoning.

In unit 3, lesson 12, “Lesson Synthesis,” the educator provides embedded guidance to introduce and scaffold students’ use of academic vocabulary related to multiplication. The educator displays the expression 3 × 5 and the equation 3 × 5 = 15 and explicitly identifies the parts of each representation using the terms factores and producto. Educator questioning, including “¿En qué se parecen las expresiones y ecuaciones de multiplicación?,” “¿En qué se diferencian las expresiones y ecuaciones de multiplicación?,” and “¿Cuándo sería útil cada una?,” supports students in using mathematical vocabulary in context as they compare and discuss multiplication expressions and equations. These guided questions provide opportunities for students to use mathematical vocabulary in context as they compare and discuss multiplication expressions and equations.

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 materials include embedded educator guidance that supports mathematical vocabulary, syntax, and discourse related to multiplication and area. Students hear, refine, and use terms such as factores, producto, filas, columnas, grupos iguales, and área as they match multiplication expressions to rectangular area models. Educator guidance prompts students to explain how each factor appears in the rectangle and how the product represents the total number of squares. For example, in grade 3, unit 3, lesson 9, activity 1, students match expressions such as 9 × 5, 8 × 2, and 7 × 10 to rectangular models and prepare to explain their reasoning. The materials include exemplar responses that identify rows, columns, groups, and total squares, providing educators with guidance for supporting student explanations and mathematical conversations.

The materials include embedded educator guidance that supports vocabulary, syntax, and discourse as students connect multiplication and division strategies. Students hear and use academic language such as división, cociente, estrategia, multiplicación, and expresión during a number talk and while explaining how they found each value. Educator guidance supports mathematical conversations by prompting students to repeat a peer’s reasoning, explain a strategy in a different way, compare strategies, and add on to another student’s thinking. For example, in grade 3, unit 5, lesson 7, “Calentamiento,” students participate in a “Conversación numérica” with multiplication and division expressions while the educator asks questions such as “¿Quién puede repetir el razonamiento de _____ de una manera diferente?” The materials also include exemplar responses for expressions such as 3 × 5, 6 × 5, 10 × 5, and 65 ÷ 5, providing educators with guidance for supporting student responses during mathematical discussions.

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

The materials integrate the TEKS mathematical process standards by engaging students in using models, making connections, and communicating mathematical reasoning about multiplication and area. Students connect multiplication expressions to rectangular area models and explain how factors relate to rows and columns. The lesson includes opportunities for students to reason about why a rectangle matches a given expression and how the product represents the total number of squares. For example, in grade 3, unit 3, lesson 9, activity 1, “Expresiones y áreas de coincidencia,” students match multiplication expressions such as 9 × 5, 8 × 2, and 7 × 10 to rectangular area models and explain their reasoning.

In unit 5, lesson 13, activity 2, “Representar, resolver, explicar,” students engage in the TEKS mathematical process standards by solving story problems involving unknown quantities and representing situations with equations that include a symbol, such as a box or question mark. Students select strategies, including tape diagrams, number lines, or other previously learned methods, to solve the problems and explain why their solutions make sense. Through selecting representations, connecting mathematical work to the context of the problem, and explaining their reasoning, students use mathematical tools, representations, problem-solving, and communication throughout the activity.

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

The materials describe how students connect multiplication, arrays, area models, diagrams, and equations across the unit. The section guide explains that students begin with equal groups and arrays, then connect those representations to area and later to diagrams and real-world multiplication situations. These connections incorporate the TEKS mathematical process standards through the use of representations, reasoning, communication, and connections among mathematical ideas. For example, in grade 3, unit 3, Guía de planificación a nivel de sección, section B, the narrative explains that students explore area using rectangular models and connect multiplication to the number of rows and columns in a rectangle.

In grade 3, unit 5, Guía de planificación a nivel de sección, the guide describes how the TEKS mathematical process standards are embedded throughout the course by engaging students in problem-solving, representation, reasoning, and mathematical communication. For example, in section A, students use base 10 blocks, area diagrams, properties of operations, and place-value strategies to develop multiplication and division understanding. In section B, students analyze patterns and relationships in paired-number tables and communicate their observations. Section C extends these process skills as students represent and solve two-step word problems using equations, strip diagrams, arrays, and other models. The guide describes how students apply representations, analyze relationships, use problem-solving strategies, and communicate mathematical thinking across sections of the unit.

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 through problem-solving, strategy selection, representations, and explanation of reasoning with whole-number operations. Students represent addition and subtraction problems using pictorial models, number lines, equations, and algorithms. The guide connects the process standards across sections by describing how students move from one-step problems to more complex two-step problems and then use rounding to evaluate reasonableness. For example, in grade 3, unit 2, Guía de planificación a nivel de sección, section D, “Narrativa,” students represent two-step addition and subtraction problems in multiple ways and apply strategies based on place value, properties of operations, and the relationship between addition and subtraction.

In grade 3, unit 1, Guía de planificación a nivel de sección, section A, “Composición de números,” students represent and explain multi-digit numbers using place value models, expanded form, standard form, and word form. Students use mathematical reasoning to compare, order, and describe numbers up to 1,000,000. Students use tools and equations to represent place-value relationships and explain how each digit is worth ten times the digit to its right. The unit materials describe how students use these process standards as they develop place value understanding across the unit.

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

The Grado 3 Alcance y Secuencia provides evidence of how the TEKS mathematical process standards are incorporated into individual lessons by identifying the specific process standards and outlining the mathematical practices connected to the lesson objectives. For example, in grade 3, unit 2, lesson 22, the materials identify TEKS 3.1A and state that students will “Sumar y restar dentro de 1,000 para resolver problemas del mundo real.” This lesson objective identifies the mathematical process students apply as they use addition and subtraction to solve real-world problems.

The materials include individual lessons that provide supporting evidence through the “Abordando” section and lesson narratives that identify the standards addressed and explain how students apply them during instruction. The tasks require students to use models, connect representations, and communicate mathematical reasoning. For example, in grade 3, unit 3, lesson 9, “Representar productos como áreas,” the “Abordando” section lists the TEKS addressed, and students connect multiplication expressions to rectangular area models by explaining how rows, columns, factors, and products are represented.

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

In grade 3, unit 2, lesson 18, “¿Tiene sentido?,” the materials provide opportunities for students to think mathematically, persevere through problem-solving, and make sense of mathematics by analyzing whether solutions are reasonable. During the “Calentamiento: Verdadero o falso: ¿Es mayor?,” students determine whether expressions are true or false and reflect on when rounding is an effective strategy for estimating. In activity 1, “Estimaciones rápidas,” students evaluate the reasonableness of a sample student’s estimate before applying estimation strategies to multistep addition and subtraction story problems. In activity 2, “Resuelve y razona,” students exchange their work with a partner, analyze whether their partner’s solution makes sense, and provide feedback that can be used to revise the solution.

The materials provide opportunities for students to think mathematically, persevere through solving problems, and make sense of mathematics by analyzing and comparing multiple strategies for division. Students connect division concepts to multiplication, place value, base 10 blocks, diagrams, and equations as they develop and explain their reasoning. For example, in grade 3, unit 5, lesson 7, “Calentamiento: Conversación numérica: multiplicación y división,” students use a number talk and strategy discussion to solve division expressions such as 65 ÷ 5 and explain how multiplication can support their division strategies. As students consider classmates’ methods, explain how strategies work, and apply their thinking to unfamiliar division situations, they develop persistence and deepen their understanding of the relationship between operations and representations.

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 unit 2, lesson 3, “Suma a tu manera,” activity 1, the materials support students in understanding, explaining, and justifying that there are multiple ways to represent and solve mathematical problems. Students add within 1,000 using strategies that make sense to them, including adding hundreds to hundreds, tens to tens, and ones to ones, reasoning with numbers close to one hundred, and using mental math strategies. Students also choose from multiple representations and tools, such as base 10 blocks, number line diagrams, pencil-and-paper methods, and calculators, to represent their thinking and verify their solutions. As students explain and compare different approaches, they develop an understanding that the same problem can be solved using multiple valid strategies. Educator reflection prompts that highlight the variety of student methods further support students in recognizing the value of flexible mathematical thinking and strategic problem-solving.

In grade 3, unit 6, lesson 1, activity 2, “Creando modelos de fracciones,” the materials support students in understanding, explaining, and justifying that fractions can be represented in multiple valid ways. Educators provide hands-on materials and model strategies for creating fraction representations, while students fold paper to show different fractions and explain their reasoning through educator questions such as “¿Cómo representaste un tercio?” Partner discussions provide opportunities for students to compare their models, describe how they created and colored their representations, and justify why their models accurately show the same fraction.

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 3, unit 3, lesson 9, activity 1, “Expresiones y áreas de coincidencia,” the materials require students to make sense of mathematics through opportunities to do, write about, and discuss mathematical ideas. Students do mathematics by connecting multiplication expressions to rectangular area models and analyzing how rows, columns, factors, and products are related. Students write about mathematics by recording their matches and creating or identifying representations that show the relationship between multiplication expressions and area models. They discuss mathematics with peers as they explain how they interpret each model and compare their reasoning with others. Educator prompts about how the model represents multiplication and how the product connects to the total number of squares encourage students to explain their thinking and deepen their understanding through mathematical discussion and reflection.

In unit 10, lesson 9, activity 1, “Elección de números para tiempo de carnaval,” students make sense of mathematics through opportunities to do, write about, and discuss mathematical reasoning in the context of elapsed-time situations. Students do mathematics by selecting reasonable numbers and times for real-world carnival scenarios, solving the resulting problems, and justifying their choices. Students write about mathematics by recording their selected values and solutions, and they discuss mathematics with peers by explaining their reasoning and comparing strategies within their groups. The educator monitors students’ justifications and facilitates whole-class discussions with prompts such as “¿Cómo decidiste qué números (o tiempos) escoger para cada problema?,” “¿Por qué estos números (o tiempos) tienen sentido para esta situación?,” and “¿Qué números (o tiempos) no tendrían sentido en esta situación?”

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 3, unit 9, lesson 11, activity 2, “Distancia alrededor,” the materials support educators in guiding students to share and reflect on their problem-solving approaches through explanations, arguments, and justifications. Students solve perimeter problems independently by explaining or showing their reasoning and then share their solutions with a partner. The educator monitors a variety of strategies, including counting individual units, adding the lengths of all sides, and using multiplication to efficiently combine equal side lengths. During the “Síntesis de la actividad,” the educator selects students to present strategies in a progression from counting individual units to using operations and records the approaches for the class to compare. Educator questions such as “¿Cómo estás encontrando la distancia alrededor de la figura?,” “¿Cómo podrías llevar la cuenta de las longitudes de los lados mientras trabajas?,” and “¿Qué forma, C, D o E, tiene el perímetro mayor?” prompt students to explain and justify their reasoning. The guidance to “Identifica conexiones entre estrategias que dan los mismos resultados pero utilizan enfoques diferentes” supports students in comparing, discussing, and reflecting on multiple valid approaches for finding perimeter.

In unit 4, lesson 9, activity 1, “Ordenar tarjetas: multiplicación,” the materials provide educator support for guiding students to share and reflect on their problem-solving approaches through explanation, argumentation, and justification. Educator prompts encourage students to explain what it means to find a product efficiently, share multiplication strategies with partners, and compare different approaches for finding unknown products. The materials support mathematical argumentation by encouraging students to consider classmates’ ideas, discuss the effectiveness of different strategies, and revise their thinking based on evidence from the discussion. Reflection opportunities, including prompts such as “¿Cuáles fueron algunas estrategias útiles para hallar productos que aún no conocías?” and the “Math Language Routine 8” synthesis statement “La próxima vez que multiplique _____ por _____, haré . . . ,” guide students in justifying effective strategies and reflecting on how their approaches can support future problem-solving.

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 3, unit 2, lesson 21, activity 1, “Práctica de fluidez de un paso,” the materials provide prompts and guidance that support educators in giving explanatory feedback based on students’ mathematical thinking and anticipated misconceptions. Educator prompts such as “¿Por qué seleccionaste esta estrategia para resolver este problema?,” “¿Alguien abordó este mismo problema de manera diferente?,” and “¿Alguien quiere añadir a la estrategia de _____?” encourage students to explain their reasoning and allow educators to build on students’ strategies during discussion. The lesson anticipates that students may have difficulty identifying the appropriate operation and guides educators to ask, “¿Su tarjeta tiene un valor total o necesitan resolver para hallar un valor total?” to help students determine whether addition or subtraction is needed. Educators are also directed to monitor strategies based on place value, operation properties, and the relationship between addition and subtraction so they can select student work that highlights efficient methods and support students in comparing and refining their approaches.

In grade 3, unit 6, lesson 13, “¿Mismas fracciones, resultado diferente?,” the materials provide educator guidance for responding to student thinking, addressing misconceptions, and providing explanatory feedback that deepens understanding. The lesson directs educators to monitor for students who recognize that Kai and Lin reached different conclusions because the wholes represented on the number lines are different and to select those students to share their reasoning. Educator prompts such as “¿Qué entendieron Lin y Kai acerca de representar fracciones en una recta numérica?” help educators build on students’ responses and support further explanation of fraction representation. The lesson also anticipates the misconception that fractions can be compared without considering the size of the whole and provides guidance for educators to address this misunderstanding by emphasizing that fraction comparisons are only meaningful when the fractions refer to the same whole. Through the use of number lines, fraction strips, and mathematical discussion, educators are supported in providing targeted feedback that helps students clarify, revise, and strengthen their reasoning about fractions.