Kiddom Texas: Matemáticas en Español – Grado 5

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

The grade 5 materials include a scope and sequence that outlines the specific order of the math TEKS and concepts taught throughout the instructional year. For example, unit 1, lesson 1, “Valor posicional y expresiones,” section A, “Valor posicional decimal,” includes the lesson titled “¿Qué es una milésima?” These materials align with TEKS 5.1C and 5.2A, and the lesson objective is to understand the relationship between tenths, hundredths, and thousandths.

The materials include a scope and sequence outlining the ELPS and the concepts taught in the course. The scope and sequence includes a total of 10 units with associated ELPS and concepts identified for instruction. For example, in unit 6, lesson 2, “Suma y resta de decimales,” the lesson is associated with ELPS 3D and 5G. The grade 5 scope and sequence states that the concepts to be taught in this lesson are “suma y resta decimales hasta las centésimas utilizando estrategias basadas en el valor posicional.”

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 suggested pacing to support three instructional calendars for 165, 180, and 210 days. The calendar options document includes lessons and activities for a full year of instruction. The implementation of units aligns with the time constraints of a school year. In the 165-day calendar, unit 1, “Valor posicional y expresiones,” includes 14 lessons allotted 16 days. In the 180-day calendar, unit 1, “Valor posicional y expresiones,” is allotted 17 days. In the 210-day calendar, the same unit is allotted 20 days.

The grade 5 materials include a suggested pacing guide to support effective implementation. This suggested pacing guide outlines the concepts in each unit and the suggested pacing for each unit. For example, in Guía de planificación de matemáticas de Texas 3–5, unit 1, “Valor posicional hasta 100,000,” will take 10 days. Unit 1 has been allotted “semanas 1 y 2” to be completed. Unit 2, “Suma y resta,” provides a timeline of “semanas 3 hasta 7” for the educator to complete the instruction, for a total of 24 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.

In grade 5, the materials include a rationale for unit order that explains why units are sequenced as they are and how each unit contributes to an overarching learning goal. In the course guide, the section “Principios del diseño del currículo de matemáticas de Kiddom” states, “Cada unidad, lección y actividad tiene la misma estructura de diseño general: El aprendizaje comienza con una invitación a las matemáticas, seguida de un estudio profundo de conceptos y procedimientos, y concluye con una oportunidad para consolidar la comprensión de las ideas matemáticas.” This guidance explains that each unit, lesson, and activity follows the same overall design structure. Learning begins with an invitation to mathematics, followed by an in-depth study of concepts and procedures, and concludes with an opportunity to consolidate understanding of mathematical ideas.

Additionally, within the TX Math Teacher Course Guide K–5 ES, the section titled “Principios del diseño del currículo de matemáticas de Kiddom” provides an explanation of the logic behind unit progression and the conceptual connections across units. For example, the materials state, “students are supported in making connections with prior knowledge and upcoming grade-level work, emphasizing the importance of educators understanding the progressions within the materials.”

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

In grade 5, the materials include protocols and guidance that support unit internalization through previewing key standards, objectives, vocabulary, and assessments. For example, in unit 1, the Guía de planificación a nivel de sección is organized into two sections that support educator planning. Section 1 covers lessons 1–9 and focuses on valor posicional decimal, guiding students to reason about decimals through the thousandths place. Section 2 covers lessons 10–13 and focuses on expresiones, with students solving two-step word problems and simplifying numerical expressions using the order of operations.

The materials include protocols with corresponding guidance for lesson internalization by clearly identifying the mathematical purpose, instructional sequence, student grouping, materials, and educator monitoring expectations for unit 13, lesson 7, activity 3. The activity guidance explains that students solve two proportional allocation problems involving school advisors and connect the mathematics to prior work with distributing computers and assigning congressional representatives. Educators are directed to organize students in groups of two to four, provide calculators as needed, introduce the context explicitly, and monitor the different strategies students use to assign advisors fairly. The lesson also includes targeted supports for students with disabilities and multilingual learners, including breaking the task into manageable parts and using “Math Language Routine 2: Recopilar y mostrar” to capture and display language such as proporcional, tasas, and _____ por _____. Response notes, anticipated strategies, and discussion guidance support educators in understanding the central mathematical idea that proportional allocation may require rounding and adjustment and that a completely fair solution may not always be possible when school populations vary.

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

In grade 5, the materials do not fully provide guidance for instructional leaders to support curriculum implementation and address instructional challenges. While the materials include support for using the rostering system to organize student information and data, they do not include resources that help instructional leaders support effective classroom instruction. Additionally, the materials do not provide tools for monitoring implementation, leadership frameworks, or professional learning resources designed to build instructional leaders’ capacity to support educators in implementing the curriculum.

The materials do not include resources that support educators during implementation or guidance for instructional leaders on how to use the curriculum to support educators. The materials also 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.

In unit 1, the materials provide a comprehensive unit overview with the academic vocabulary necessary to effectively teach place value and decimal concepts. For example, the overview defines milésima as the size of a part when a hundredth is divided into 10 equal parts and valor posicional as the value of a digit based on its position in a number. The materials provide clear definitions for these two vocabulary words, demonstrating that the materials equip educators with the essential vocabulary and content knowledge needed to effectively teach the unit.

In unit 3, the Guía de planificación a nivel de sección provides educators with the necessary background knowledge to understand how students’ prior learning about volume connects to the development of concepts in section C, lessons 13–17. The guide states, “En esta sección, los estudiantes aplican su comprensión del volumen para resolver problemas del mundo real y matemáticos. Se encuentran con figuras sólidas que están compuestas por dos o más prismas rectangulares rectos, lo que refuerza su comprensión de la naturaleza aditiva del volumen.” This overview supports effective instruction by identifying the key mathematical concepts and vocabulary, such as volumen, figuras sólidas, prismas rectangulares rectos, and naturaleza aditiva del volumen, that educators need to effectively teach the unit.

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 grade 5 materials include family support resources in both English and Spanish for each unit. These resources inform families about unit objectives and provide suggestions for supporting student progress and achievement. For example, in unit 3, the Materiales de apoyo familiar include information in both languages. The materials state, “Los estudiantes explorarán sobre el área y la multiplicación para introducir el concepto de volumen.” This information helps families understand the unit’s learning goals and support student learning at home.

English and Spanish resources provide families with information about upcoming learning and ways to support student success. For example, in unit 4, “Multiplicación y división con números enteros no negativos,” the Materiales de apoyo familiar describe specific skills students will learn during the unit. The materials state, “Los estudiantes aprenderán y usarán el algoritmo estándar para la multiplicación para resolver problemas con números más grandes.” This guidance gives families insight into the procedural skills students are expected to develop and practice.

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).

Each grade 5 Spanish math lesson follows a four-step instructional framework designed to support TEKS-aligned instruction. The warm-up, referenced as the “Calentamiento,” activates prior knowledge. Activities 1 and 2 provide high-utility tasks in which students engage with the content through guided instruction, student-facing tasks, and activity synthesis, with guiding questions for discussion. The “Síntesis de la lección” provides an educator-led opportunity to consolidate key understandings. Instructional assessments are included as the cooldown, serving as a daily formative assessment aligned to the lesson’s target TEKS to monitor students’ mastery.


The materials provide educators with guidance through a lesson plan structure that includes the necessary information for effective implementation of grade-level instruction aligned with the TEKS and appropriate lesson objectives. For example, in unit 2, lesson 2, “Milésimas en cuadrículas y en palabras,” the objective is “Representa fracciones y decimales hasta milésimas en planos de cienavos. Escribe fracciones y decimales hasta milésimas para representar cantidades sombreadas en planos de cienavos,” and it aligns with TEKS 111.7.D.1B, 111.7.D.1G, and 111.7.D.2A.

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 lesson overviews that identify the educator and student materials needed for instruction and specify the suggested timing for each lesson component. For example, in unit 1, lesson 1, activity 1, “¿Qué sabes sobre las milésimas?,” the materials list chart paper and colored pencils, crayons, or markers as required resources. The lesson narrative and “Inicio” provide guidance for using these materials during instruction. The activity is designed for a 20-minute instructional block in which students discuss their understanding of tenths and hundredths and begin exploring the concept of thousandths.

In grade 5, the materials include guidance on the suggested timing of lesson components, including inquiry, direct instruction, guided practice, independent work, and collaborative learning. For example, in unit 1, lesson 1, “¿Qué es una milésima?,” the lesson presentation includes digital slides with embedded educator notes that support lesson pacing. These notes provide recommendations for transitioning between instructional components and indicate the amount of time to spend on specific slides and discussion prompts to help maintain the lesson’s intended pace.

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

In unit 6, lesson 12, activity 2, “Completar el espacio en blanco (opcional),” the materials provide guidance for using an optional activity as extended practice to deepen students’ understanding of fraction equations. The materials state, “El propósito de esta actividad es que los estudiantes encuentren el valor faltante en ecuaciones que involucran un número entero y una fracción. Encuentran factores o productos faltantes para que las ecuaciones sean verdaderas.” The guidance explains that the activity supports students in reasoning about fraction relationships by interpreting a fraction a/b in terms of division by the denominator and multiplication by the numerator. This optional activity provides educators with an opportunity to extend students’ learning by engaging them in additional problem-solving and reasoning with fractions beyond the core lesson.

In unit 6, lesson 12, “Situaciones del área,” the materials provide guidance for using an optional enrichment activity to extend students’ understanding of fractions as quotients and multiplication of fractions. In activity 2, “Completar el espacio en blanco (opcional),” students solve problems involving fractions by finding missing values in equations with whole numbers and fractions. The materials state, “El propósito de esta actividad es que los estudiantes encuentren el valor faltante en ecuaciones que involucran un número entero y una fracción. Encuentran factores o productos faltantes para que las ecuaciones sean verdaderas.” The guidance explains that the activity encourages students to reason about fractions by interpreting a fraction a/b in terms of division by the denominator and multiplication by the numerator. This optional activity provides educators with an opportunity to extend students’ learning through additional problem-solving and deeper reasoning about fraction relationships.

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.

In grade 5, the materials include a variety of instructional assessments at the unit level, including a formative assessment that varies in question types. The materials include varying types of questions, such as text-entry and multiple-choice questions, which can be found in “Grado 5.2 Chequeo de la sección A.” For example, one of the questions within this assessment asks students to calculate the total miles driven by adding numbers up to the thousands place. The question states, “Priya condujo 1,384.9 millas el sábado y 2,903.34 millas el domingo. ¿Cuántas millas condujo en total?” Students have a text field to enter their response.

Assessments include mid-unit checks for understanding that measure a combination of skills from multiple lessons. For example, in unit 7, “Multiplicar y dividir fracciones,” “5.7 Chequeo de la sección A” is a formative assessment covering lessons 1–6. The assessment includes varied item types, such as word problems that require students to model and explain their reasoning. One example item states, “En la fiesta de cumpleaños de Priya, se pidieron 10 pizzas. 7/8 de cada pizza fue comida. ¿Cuántas pizzas se comieron en total? Usa un modelo para resolver.” This item requires students to apply fraction multiplication in a real-world context and represent their thinking using a model and a short written response.

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

The materials define the purpose of each assessment type and explain how the results should be used. Formative assessments, such as “Enfriamientos” and “Section Checks,” are intended to monitor student understanding and inform instructional decisions. Summative assessments, such as unit assessments and the end-of-course assessment, are designed to measure students’ mastery of grade-level standards and learning objectives. The assessment guide provides specific guidance for interpreting student performance and planning next steps for instruction. For example, the materials state that the “Enfriamiento” (cooldown) is “a brief check to determine whether students understand the main concepts of the lesson” and should be used “as a formative assessment to plan future instruction.”

The materials define 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 explains that this activity serves as a brief check to determine whether students understand the main concepts of the lesson and 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 Guía de recursos para maestros, the section “Oportunidad de evaluación sumativa” includes specific directions for administration that state, “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 Descripción del curso and “Guía de la evaluación” provide information about the assessment types used throughout the course and explain how and when they should be administered. For example, the materials state, “Cada unidad incluye una Evaluación final escrita que los estudiantes completan individualmente para evaluar su progreso hacia los objetivos de aprendizaje de la unidad y los estándares del nivel de grado para el curso. Los ítems están alineados con los estándares relevantes del nivel de grado.” This guidance identifies the assessment format (written), specifies that students complete the assessment individually, and describes its use within each unit, supporting consistent administration across classrooms.

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

In grade 5, the materials include formative assessments that are explicitly aligned to the TEKS and unit objectives. The alignment is shown by labeling assessment items with the corresponding TEKS standard. For example, in unit 4, “Suma y resta de fracciones,” “Punto de control de la sección A,” students solve fraction addition and related word problems such as “Encuentra el valor de la expresión 2/8 + 3/8. Explica o muestra tu razonamiento” and “Kai lavó los platos en su casa. 2/8 de los platos vinieron de su habitación y 3/8 de los platos vinieron de sus hermanos. ¿Cuál enunciado es verdadero?” These questions are aligned to TEKS 111.6.b.3.F.

In grade 5, diagnostic, formative, and summative assessments are aligned to the TEKS and the learning objectives identified throughout the scope and sequence. Each lesson lists the specific TEKS and corresponding learning goals, ensuring that assessments measure the intended knowledge and skills. Formative assessments, such as “Enfriamientos” and “Section Checks,” monitor student progress toward lesson and section objectives, while unit and end-of-course assessments evaluate mastery of the TEKS. This alignment provides a coherent system for measuring student learning from individual lessons through the entire course.

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

In grade 5, “5.7 Chequeo de la sección A” includes TEKS-aligned assessment items that vary in complexity and measure students’ understanding of fraction multiplication and area. The items range from computing fractional quantities using standard procedures to applying fraction concepts in real-world and geometric contexts. Students are also asked to use visual models and written explanations to support their answers, which increases the level of cognitive demand beyond computation alone. This combination of calculation, modeling, and explanation requires students to demonstrate both procedural fluency and conceptual understanding at different levels of complexity.

The materials include formative and summative assessments with multiple-choice, text-entry, and open-response items aligned to the TEKS. In unit 4, “Multiplicación y división con números enteros no negativos,” the “Grado 5.4 Evaluación de fin de unidad” includes a range of item types that require different levels of thinking, from multiple-choice selections to writing to explain mathematical reasoning. For example, the item “Andre dice que 834 × 21 es aproximadamente 17,000. ¿Estás de acuerdo?” requires students to evaluate the reasonableness of an estimate and justify their thinking, which involves higher-level reasoning beyond basic computation.

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

In unit 2, “Suma y resta,” the progress-monitoring assessment titled “Punto de control de la sección A” includes scoring information that supports educators in evaluating student responses. The materials provide answer keys, expected responses, and item-specific scoring notes for both selected-response and open-ended questions, which outline how each item should be scored. This information gives educators clear criteria for determining whether student answers are correct and aligned to the learning objectives being assessed.

In unit 10, “Educación financiera personal,” the assessment titled “Grado 5.10 Evaluación y recursos de fin de curso” includes a section for educator instructions. This section, titled “Instrucciones para el maestro,” explains how to use assessment tasks and how they relate to student understanding over time. The materials state, “Los ejercicios incluidos aquí pueden usarse antes de la unidad final para enfocar el tiempo restante del año o para evaluar la comprensión de los estudiantes al final del año. No se recomienda que estos recursos se usen todos a la vez.” This guidance helps educators interpret the purpose of the assessment tasks and understand how student performance reflects overall proficiency and learning progress.

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 materials include tasks and activities for responding to trends in performance. However, the materials do not include guidance on the use of these tasks and activities. The materials do not include guidance that supports the educator in utilizing results from assessments to support the purposeful planning of tasks and activities for the appropriate grade level.

This resource does not include differentiation in the lesson. The materials do not include instructional guidance for tasks and activities to target various skills, as determined by assessment data. For example, the materials do not provide guidance for educators to group students based on assessment results and provide targeted activities to address specific skills.

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.

In unit 5, lesson 5, “Multiplicar más decimales,” educators receive guidance to support students who are not yet proficient in multiplying decimals and explaining why equivalent expressions have the same value. For example, the materials state, “Los estudiantes aún no explican por qué las expresiones tienen el mismo valor. Apoyos para el día siguiente. Crea un póster con términos y expresiones importantes de este enfriamiento.” The materials guide educators to provide additional support by creating an anchor chart or poster that highlights key terms and expressions from the lesson’s cooldown. This targeted scaffold helps students strengthen their understanding of equivalence and mathematical vocabulary while addressing areas where they need additional support to reach proficiency.

In unit 5, lesson 8, “Dividir números enteros entre decimales,” educators receive guidance to support students who have not yet mastered dividing whole numbers by decimals. For example, the materials state, “¿Qué sabes sobre dos décimas? Muestra a los estudiantes un plano de centésimas. ¿Cuántos grupos de dos décimas hay en 1?” The materials guide educators to activate students’ prior knowledge of two-tenths, use visual representations such as hundredths grids, and support students in determining how many groups of two-tenths are contained in one whole. These instructional supports provide scaffolding that helps students build conceptual understanding of decimal division and progress toward mastery of the grade-level skill.

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

In grade 5, lesson plans incorporate structured “Turn and Talk” or “Math Chat” opportunities tied to academic vocabulary development. For example, in unit 6, lesson 10, “Descomponer el área,” educators facilitate collaborative mathematical discourse during partner work: “Grupos de 2, 1–2 minutos: tiempo de trabajo independiente, 8–10 minutos: trabajo con un compañero,” and monitor students as they “etiquetan las longitudes de los lados con números mixtos” and “descomponen los rectángulos más grandes en dos rectángulos más pequeños.” Discussion prompts such as “¿En qué se parecen estas expresiones? ¿En qué se diferencian?” and “¿Cómo podemos determinar cuál jardín tiene un área más grande sin evaluar las expresiones?” support students in using academic vocabulary, comparing expressions, and explaining their mathematical reasoning.

The TX Math Teacher Course Guide K–5 provides sentence frames aligned to unit problem-solving tasks, along with sample educator talk that models how to introduce and use the frames to support academic language during math discussions. For example, in unit 6, lesson 11, “Área y propiedades de las operaciones,” students use the sentence frame “Noté _____, así que relacioné _____” as they explain connections between representations and justify their reasoning. The lesson directs educators to facilitate partner discussions in which, “Los estudiantes deben turnarse para encontrar una correspondencia y explicar su razonamiento a su compañero” and to “Anime a los estudiantes a cuestionarse entre sí cuando no estén de acuerdo.” These supports encourage students to articulate mathematical thinking, use academic language, and engage in meaningful discussion about properties of operations and area.

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 2, lesson 2, “Estimar y sumar,” the materials provide educator guidance for differentiated instruction, enrichment, and extension activities for students who have demonstrated proficiency with grade-level content and skills. Students are encouraged to use a variety of strategies, including place-value reasoning, estimation, and the standard algorithm, to solve decimal addition problems. For students who demonstrate proficiency, the materials provide enrichment opportunities that require them to explain and justify their reasoning orally and in writing, compare different methods, and evaluate the reasonableness of solutions. The lesson incorporates “Math Language Routine 1: Stronger and Clearer Each Time,” which supports students in refining mathematical explanations and engaging in deeper mathematical discourse. Additionally, center activities such as “Tres en raya circular,” “El más grande de todos,” and “Saltar la recta” provide extension opportunities for advanced learners to apply decimal concepts in new contexts, strengthen fluency, and extend their understanding through strategic problem-solving.

In unit 6, lesson 16, “Problemas de conversión de varios pasos: volumen métrico de líquidos,” students engage in extension tasks that require them to solve complex, multistep problems involving metric liquid volume. The materials explain that “Los estudiantes también tienen la opción de convertir a mililitros o litros y hay diferentes momentos en los cálculos en los que pueden elegir hacer la conversión,” encouraging flexible problem-solving and strategic decision-making. These activities deepen students’ understanding of decimal operations and metric conversions by requiring them to apply their knowledge in real-world contexts.

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 5, the materials provide explicit prompts to support educators in modeling and explaining mathematical concepts. For example, in unit 2, lesson 1, “Interpretar la suma decimal,” educators receive structured guidance for introducing decimal addition through a game that emphasizes place-value reasoning. The lesson directs educators to read the game instructions with students, model a complete round, think aloud about strategic choices, and record equations so students can observe how decimals are added in tenths and hundredths. Educators are also provided with prompts that encourage discussion about how changing a digit’s place value affects the total and helps students get closer to the target number of 1. Reflection questions and sample responses, such as “Elegí demasiadas décimas y me pasé,” “No me acerqué a 1 porque tenía miedo de pasármelo,” and “Elegí demasiadas centésimas,” further support students in explaining their strategies and developing a deeper understanding of decimal magnitude and place-value relationships.

In grade 5, the materials provide explicit educator guidance and visual supports to model and explain mathematical concepts. For example, in unit 5, lesson 1, “Multiplicar decimales y números enteros,” educators use a visual representation to introduce multiplication of decimals by whole numbers. The lesson directs educators to “Muestra la imagen del libro de trabajo del estudiante” and ask questions such as “¿Cuántos ves?” before facilitating a brief partner discussion. Educators then connect the diagram to the expression “2 × 0.3” by asking, “¿Cómo representa el diagrama la expresión?” and guiding students to recognize that “Hay 2 grupos de 0.3 sombreados.” These supports help educators explicitly model the relationship between the visual representation and the multiplication expression.

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

In grade 5, the materials provide educator guidance and recommendations for effective lesson delivery through a variety of instructional approaches to include drawing diagrams to solve problems. For example, in unit 6, lesson 2, “Interpretar ecuaciones,” students solve a problem about sharing 2 liters of water equally among 3 dancers to develop their understanding of division and equation interpretation. The lesson includes “5 minutos: tiempo de trabajo independiente, 5 minutos: conversa con un compañero” and directs educators to observe students as they “dibujen un diagrama para determinar la cantidad de agua que bebe cada bailarín si 3 bailarines comparten 2 litros de agua” and “revisen su solución sobre cuánta agua recibe cada bailarín después de explicar por qué la respuesta de Mai no tiene sentido.” These supports guide educators in facilitating independent and collaborative problem-solving while helping students use diagrams, interpret equations, and evaluate mathematical reasoning in a meaningful real-world context.

The materials include educator guidance that supports effective lesson delivery by providing a variety of structured routines such as “Represéntalo,” “Conteo grupal,” “Exploración de estimación,” and “¿Cuántos ves?,” each designed to activate prior knowledge through different mathematical entry points. These routines guide educators to facilitate student engagement using multiple instructional approaches, including storytelling, visual representation, estimation, and number-sense activities that connect language to mathematical thinking. The guidance recommends that educators encourage discussion through prompts like “¿Qué observas?” and “¿Qué te preguntas?” and support students in explaining reasoning during routines such as “Conversación numérica,” where strategies are shared and connected.

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.

In unit 5, lesson 5, “Dividir para multiplicar fracciones unitarias,” educators use the routine “Comparar y conectar” to help students solve real-world problems involving whole numbers and unit fractions. The materials explain that the instructional structure of the lesson is to be completed independently and then in pairs. The materials state, “Grupos de 2, 1–2 minutos: tiempo para pensar individualmente, 5 minutos: tiempo de trabajo con un compañero.” These supports help educators structure brief independent thinking followed by partner discussion while scaffolding students’ understanding of unit fraction multiplication in context.

In grade 5, the materials support multiple types of practice, including independent and collaborative work, and provide educators with recommended instructional structures such as partner activities. For example, in unit 6, lesson 4, “Relacionar división y multiplicación,” students develop understanding of the relationship between division and multiplication by modeling real-world situations. The materials explain that students connect division and multiplication by recognizing that a three-mile race shared equally by two people can also be represented as each person running half of the distance. The lesson provides students with time to think individually and in partners. The materials state, “Grupos de 2, 2 minutos: tiempo para pensar individualmente, 5–8 minutos: tiempo de trabajo con un compañero” to support individual reflection followed by collaborative discussion as students build and explain these connections.

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.

Educators are provided with strategies to support emergent bilingual (EB) students’ linguistic and academic development while maintaining alignment with state standards. In unit 5, lesson 6, “Feria del libro,” educators use “Math Language Routine 6: Tres lecturas” to scaffold comprehension and problem-solving. For example, the materials include the following steps for following this routine: “MLR6 Tres lecturas. Mantén los libros o dispositivos cerrados. Muestra solo el enunciado del problema, sin revelar las preguntas. ‘Vamos a leer esta pregunta 3 veces’. Después de la 1.ª lectura: ‘Dile a tu compañero o compañera de qué se trata esta situación’. Después de la 2.ª lectura: ‘Haz una lista de las cantidades. ¿Qué se puede contar o medir?’. Revela la(s) pregunta(s). Después de la 3.ª lectura: ‘¿Qué estrategias podemos usar para resolver este problema?’” The materials guide educators to structure a three-read routine where students first discuss the situation, then identify measurable quantities before seeing the question, and finally determine strategies to solve the problem.

In unit 1, lesson 1, activity 2, the materials provide targeted supports for EB students that promote mathematical communication and language development through structured discussion. The lesson includes explicit educator prompts that guide students to compare, contrast, and connect different solution strategies while reflecting on the language used to interpret mathematical representations. Educators are directed to facilitate partner conversations using questions such as “What types of details or language helped you understand the representations?” and “Did anyone solve the problem the same way but explain it differently?,” which encourage academic discourse and multiple forms of mathematical expression. These supports help EB students develop vocabulary related to decimals, fractions, and place value while strengthening their ability to represent, explain, and communicate mathematical reasoning.

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 include embedded guidance for educators to support EB students in developing academic vocabulary, increasing comprehension, and building background knowledge through oral and written discourse. For example, in unit 2, lesson 11, educators are guided to support EB students using a three-read routine, “Math Language Routine 6: Apoyo para estudiantes multilingües.” The materials guide students to keep their books closed and view only the problem statement. During the first reading, the materials state, “Dile a tu compañero de qué se trata esta situación,” and during the second reading, they state, “Haz una lista de las cantidades. ¿Qué se puede contar o medir?” After the third reading, students discuss problem-solving strategies. Through this structured interaction, students increase their comprehension and academic language by making lists of measurable attributes and engaging in oral discourse while drawing on their background knowledge by solving problems within the relatable context of preparing a recipe and sharing ingredients they like to use on salads.

In unit 3, lesson 12, “Unidades cúbicas de medida,” the materials include embedded supports for making cross-linguistic connections as students learn about geometry. In “Calentamiento: Observa y pregúntate: dos prismas,” the materials explicitly identify words that transfer between Spanish and English and provide a pattern students can use to make connections between the two languages. For example, the materials state, “Conexiones translingüísticas: Palabras que se transfieren: El vocabulario del volumen es casi todo cognado, con el patrón -ico → -ic: cúbico / cubic, volumen / volume, unidad cúbica / cubic unit, prisma / prism, rectangular, estimación / estimate, exponente / exponent. Las unidades métricas también: centímetro / centimeter, metro / meter.” By explicitly identifying cognates and the -ico → -ic pattern, the materials support students in connecting Spanish and English academic vocabulary and using their existing linguistic knowledge to build understanding of new geometry concepts.

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.

In unit 1, “Valor posicional y expresiones,” “Chequeo de la sección A,” the materials provide educators with guidance to assess students’ understanding of decimals. The practice opportunities within the assessment require students to apply place-value knowledge and rounding strategies to demonstrate understanding of decimal concepts. An example of one of the assessment questions is “¿Cuánto es 13.728 redondeado a la décima más cercana? ¿Y a la centésima más cercana? Usa la recta numérica si es útil.” The question asks students to round 13.728 to the nearest tenth and nearest hundredth and use a number line to support their reasoning if needed. This practice opportunity aligns with TEKS 111.7.b.2.C, which requires students to round decimals to tenths or hundredths. The task requires students to demonstrate understanding of decimal place value and apply rounding procedures rather than simply identify a decimal value.

In grade 5, unit 2, lesson 1, “Números decimales,” students move beyond identifying decimals by interpreting tenths and hundredths using unit-square grids and explaining the relationship among fraction notation, decimal notation, and fraction names. For example, students represent 35 hundredths on a grid, identify it as 35/100, and write it as 0.35 while explaining how each representation describes the same quantity. These practice opportunities require students to demonstrate conceptual understanding by reasoning about equivalence, connecting multiple representations, and communicating their mathematical thinking using precise mathematical language.

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

In unit 3, “Geometría,” lesson 17, “Mucha y mucha basura,” students move from making an initial estimate to applying mathematical reasoning, modeling, and evaluating assumptions to refine their solutions. Students estimate the number of shipping containers on a fully loaded cargo ship and then analyze the arrangement of containers to create a more accurate estimate. The task states, “Los estudiantes estimen el número de contenedores de envío en un barco de carga completamente cargado. Luego hacen muchas suposiciones sobre la disposición de los contenedores en el barco para llegar a una mejor estimación.” Educator guidance supports this progression through questions such as “¿Cuántos contenedores hay en el barco de carga?,” “¿Cuál es una suposición razonable que sea demasiado alta?,” “¿Demasiado baja?,” and “¿Cómo podrías mejorar tu estimación?” These tasks increase complexity by requiring students to justify their thinking, evaluate solutions, and apply mathematical concepts in a real-world context.

The section titled “Complejidad de la tarea” in the Guía del Curso K–5 explains how mathematical tasks increase in complexity by considering students’ prior knowledge, experiences, and the demands of the mathematical context. It states, “Las tareas matemáticas son complejas de diferentes maneras, con la fuente de complejidad variando según los conocimientos previos, antecedentes y experiencias de los estudiantes. En el currículo, se presta especial atención a la complejidad de los contextos, números y cálculos requeridos, así como a la posible familiaridad de los estudiantes con los contextos y representaciones dadas.” This guidance reflects how the materials structure tasks to increase complexity through changes in contexts, numbers, calculations, and representations while building on students’ developing mathematical understanding.

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

In unit 4, lesson 5, the materials demonstrate coherence by explicitly connecting students’ prior understanding of place value, partial products, and the distributive property to the standard multiplication algorithm. Students analyze two different methods for solving 413 × 21 and identify how the same six partial products appear in both representations, reinforcing the mathematical relationship that different strategies can represent the same computation. The lesson builds on concepts developed earlier in the unit, where students used place-value reasoning and partial products to multiply multi-digit numbers, and prepares students for future fluency with the standard algorithm. For example, students are asked, “Se muestran dos algoritmos para hallar el valor de 413 × 21. ¿En qué se parecen los dos algoritmos?,” “¿En qué se diferencian?,” “Explica o muestra dónde ves cada paso del primer algoritmo en el segundo algoritmo,” and “¿Cómo se comparan los pasos finales en los dos algoritmos?” These questions guide students to compare the structure of two multiplication methods by identifying similarities, differences, and connections between the steps. Through this comparison, students develop a deeper understanding of multiplication strategies and how mathematical ideas build across lessons.

In unit 5, lesson 9, “Dividir decimales entre números enteros,” the materials demonstrate coherence across grade-level concepts by connecting whole-number division strategies to decimal division through place-value relationships and equivalent representations. Students build on their prior understanding of whole-number quotients and apply those strategies to reason about decimal quotients, strengthening connections among operations, place value, and mathematical representations. The lesson emphasizes how place-value patterns and operational relationships allow students to extend familiar division strategies to new contexts involving decimals. For example, students solve division problems such as 0.45 ÷ 5 and use their reasoning to explain their strategies. The materials provide educators with questions to support student reflection, such as “¿Podrías usar un diagrama para hallar estos cocientes?,” and “¿Cómo te ayudó pensar en 0.7 y 0.45 como centésimas a hallar el valor de estas expresiones?” These questions encourage students to connect visual models and place-value reasoning to their strategies for dividing decimals.

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 Guía del Curso K–5 section “Progresión coherente” explains that the curriculum is designed to support connections across units and grade levels. It states, “Para apoyar a los estudiantes a hacer conexiones con conocimientos previos y trabajos de grado próximos, es importante que los maestros comprendan las progresiones en los materiales. Las narrativas de grado, unidad, lección y actividad describen decisiones sobre la organización de las ideas matemáticas, conexiones con trabajos previos y próximos de grado, y el propósito de cada lección y actividad.” The document also explains that students first use their own language to interpret mathematical ideas before formal language is introduced, stating, “Se basa en conocimientos previos y anima a los estudiantes a usar su propio lenguaje para interpretar las ideas antes de que se introduzca el lenguaje formal.” This approach supports a progression in which students connect prior understanding, develop precise mathematical vocabulary, and communicate increasingly complex mathematical ideas across units and grade levels.

The materials demonstrate connections among content and mathematical language across grade levels by building on students’ prior understanding of place value, multiplication, and division to develop more advanced decimal concepts. For example, in unit 5, “Multiplicación y división con decimales,” lesson 11, the lesson narrative explains that students previously learned that in multi-digit whole numbers, a digit represents ten times the value of the digit to its right. The materials state, “En grados anteriores, los estudiantes reconocieron que en un número entero de varios dígitos, un dígito en un lugar representa diez veces lo que representa en el lugar a su derecha. En la unidad anterior, los estudiantes vieron que este mismo patrón continúa hacia la derecha del decimal.” Students extend this understanding by applying multiplication, division, and place-value reasoning to describe how decimal digits relate to one another, recognizing that each digit represents ten times the value of the place to its right and one-tenth of the place to its left. Throughout the lesson, students use consistent mathematical language related to place value and decimal relationships while practicing how multiplying decimals shifts digits on the place-value chart. This learning builds from previous concepts and prepares students for future work with multiplying decimals in grade 6.

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 connections to students’ prior knowledge by building on previously learned multiplication strategies and procedures to develop new skills. For example, in unit 4, lesson 4, “Algoritmo estándar,” the lesson narrative explains that students use prior understanding of multiplying one-digit numbers by multi-digit numbers to strengthen their use of the standard algorithm. The materials state, “En cuarto grado, los estudiantes interpretaron el algoritmo estándar para la multiplicación y lo compararon con un algoritmo de productos parciales para multiplicar números de un dígito por números de varios dígitos.” In this lesson, students revisit the standard algorithm by applying it to multiply three-digit numbers by one-digit numbers while strengthening understanding of place value and composing new units. This learning builds toward future work with multiplying three-digit numbers by two-digit numbers as described in TEKS 5.3(B), connecting previous multiplication concepts and procedures to new mathematical skills.

In grade 5, unit 7, lesson 1, “Una pieza de una parte,” the “Narrativa de la lección” demonstrates coherence at the lesson level by connecting students’ prior understanding of multiplying whole numbers by fractions using tape diagrams and area models to new interpretations of fractional parts within contextual problems. Students build on earlier grade-level work with equal groups and fraction models as they represent and explain how a whole can be partitioned into multiple fractional parts using visual representations. The lesson extends this prior knowledge by asking students to interpret what it means to take multiple fractional pieces of the same whole, strengthening conceptual understanding of fraction multiplication. Students apply and refine these ideas by creating and discussing their own models, preparing them to connect visual representations to multiplication and division expressions. For example, students draw and explain a diagram representing a mac-and-cheese situation involving fractional parts of a whole, such as showing 3/4 of a pan being shared across two groups and explaining how each group receives fractional portions from the same whole.

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 applying previously learned fraction concepts, equivalence strategies, and operational reasoning across lessons and units. For example, in unit 2, “Suma y resta con números racionales,” lesson 15, “¿Verdadero o falso?,” students retrieve prior understanding of equivalent fractions, unlike denominators, and fraction addition and subtraction strategies to analyze and create mathematical statements. The “True or False” activity requires students to repeatedly apply fraction relationships and reasoning across multiple equations rather than practice a single procedure. The lesson narrative states, “El propósito de esta actividad es que los estudiantes razonen sobre la suma y resta de fracciones con denominadores distintos. Los estudiantes crean ecuaciones para completar una actividad de ¿Verdadero o falso?.” Students use previously learned fraction concepts to determine whether equations are true, create their own examples, and explain their reasoning.

In unit 4, lesson 3, the “Narrativa de la lección” explains how students transfer prior learning from multiplication strategies to solving with partial products. The materials state, “En lecciones anteriores, los estudiantes multiplicaron números de tres dígitos y números de dos dígitos, utilizando estrategias basadas en el valor posicional y las propiedades de las operaciones.” Students retrieve their understanding of place value, multiplication strategies, and area models as they move from using diagrams to recording partial products with an algorithm. The lesson also states, “Los estudiantes relacionan expresiones de productos parciales con diagramas y luego analizan una forma sistemática de registrar productos parciales.” By revisiting and applying previous multiplication concepts in a new context, students strengthen connections among representations, procedures, and mathematical reasoning while preparing for future work with the standard algorithm.

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 by combining previously learned fraction concepts, equivalence strategies, mixed-number reasoning, subtraction procedures, and properties of operations within a single learning experience. For example, in unit 2, lesson 10, “Diferentes formas de restar,” students apply and compare multiple strategies for subtracting mixed numbers while connecting equivalent fractions, common denominators, and mathematical reasoning. Rather than practicing one procedure in isolation, students analyze different approaches and representations to determine how strategies relate. The activity synthesis states, “El objetivo de la síntesis de la actividad es comparar y conectar varias estrategias diferentes y considerar los beneficios y retos de cada estrategia.” Students revisit prior fraction knowledge while evaluating methods such as separating parts, renaming fractions, or using addition, requiring them to switch between strategies and apply previously learned concepts in varied contexts.

The materials provide interleaved practice opportunities by requiring students to apply previously learned area concepts, measurement skills, and problem-solving strategies within new contexts. For example, in unit 6, lesson 12, “Brecha de información: área,” students collaborate to solve area problems that require them to determine missing information and select appropriate strategies. Students use prior knowledge of area formulas, rectangular models, and measurement relationships while discussing different approaches for solving the problems. For example, “Tarjeta de problema 1. Una toalla de papel es rectangular. La longitud de la toalla de papel es de 11 pulgadas. ¿Cuál es el área de la toalla de papel?” requires students to determine the missing width in order to calculate the area. This task requires students to connect multiple mathematical ideas, reason through an incomplete scenario, and apply previously learned skills in a real-world context aligned with TEKS 111.7.b.1.A.

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

In unit 2, lesson 15, students analyze and evaluate fraction equations involving addition and subtraction with unlike denominators to determine whether mathematical statements are true or false. Within this task, students interpret symbolic representations of fractions and reason about equivalence, common denominators, and the meaning of the equal sign. In this lesson, students also justify their conclusions and critique the reasoning of others through collaborative discussion. For example, students might evaluate an equation such as 1/2 + 1/4 = 3/4 as true or determine that a non-equivalent fraction statement is false, using fraction relationships and mathematical reasoning to support their decisions.

In unit 9, “El plano de coordenadas,” lesson 9, students interpret, analyze, and evaluate mathematical models and representations through tables, coordinate graphs, and numerical relationships. In activity 2, students respond to prompts and questions such as, “Grafica los datos en el plano de coordenadas. Utiliza un color diferente al del gráfico de la Actividad 1. ¿Qué relaciones ves entre tus gráficos? Explica tu pensamiento. Basado en la relación que descubriste, ¿cuál es otro conjunto de puntos de datos que podría añadirse a tu gráfico?” Students plot data on the coordinate plane, identify relationships between graphs, explain their reasoning, and suggest additional data points. Through comparing representations, students distinguish between additive and multiplicative relationships and analyze how tables and graphs represent corresponding values.

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

In unit 2, lesson 14, students use visual and mental fraction models to represent and reason about subtraction situations involving fractions with unlike denominators. Through discussion and comparison of strategies, students create equivalent fraction representations and use these models to explain relationships between fractions and differences. For example, students recognize that two fractions are equivalent and use that relationship to represent and solve a subtraction expression by renaming fractions with common denominators before finding the difference. As students share and justify their strategies, they develop a deeper understanding of fraction equivalence and subtraction while using mathematical models to represent and make sense of fraction operations.

In unit 5, lesson 7, “Dividir decimales: modelos pictóricos y modelos de área,” students create concrete and visual models to represent decimal division situations using area models on graph paper. Students construct representations of decimal quantities, partition areas into equal groups, and use visual modeling to explain quotient relationships and place-value reasoning. Through these tasks, students use models to represent mathematical situations involving decimal division, connecting concrete representations to conceptual understanding of division and place value.

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

In unit 1, lesson 1, students extend their prior understanding of tenths and hundredths to the concept of thousandths by representing and comparing decimal quantities in multiple ways. Students apply previously learned concepts about fractions, decimals, base 10 relationships, and number lines to reason about the size and meaning of thousandths in unfamiliar contexts. For example, students create posters showing that one tenth can be represented as 1/10, 0.1, a point on a number line, or a shaded region of a whole, and then use these representations to infer that one thousandth can be written as 0.001 and is smaller than one hundredth. Through discussions about real-world uses of decimals and representation challenges, students apply their conceptual understanding of decimal place value to new contexts.

In unit 10, lesson 6, “Equilibrar presupuestos cuando los gastos superan los ingresos,” students apply conceptual understanding of operations, budgeting, and financial reasoning to real-world financial situations. Students analyze income and expenses, evaluate financial decisions, and use mathematical strategies to propose solutions for balancing a budget. For example, students respond to prompts such as, “¿Cuál es el total de los gastos de Clare para el mes?,” “¿Cuánto está desequilibrado su presupuesto?,” and “¿Qué gastos puede Clare reducir para equilibrar su presupuesto?” Students interpret financial information, justify recommendations, and connect mathematical reasoning to authentic decision-making contexts involving budgeting.

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

In unit 2, lesson 13, students practice adding fractions with unlike denominators while reasoning about how numerators and denominators affect fraction size. The game structure provides repeated practice opportunities that support fluency by requiring students to select numbers strategically, generate equivalent fractions, and determine common denominators across multiple rounds. For example, students place numbers such as four, five, or six in the numerator and one or two in the denominator to create larger fractions and then find common denominators to calculate and compare sums. Through repeated gameplay and discussion of solution methods, students strengthen computational fluency with the addition of fractions.

In unit 5, lesson 5, “Multiplicar más decimales,” students are provided repeated practice opportunities to build fluency and automaticity with decimal multiplication using place-value reasoning. Students share and explain their solutions and respond to prompts such as, “¿Cómo usaste tu comprensión del valor posicional para hallar los productos?,” and “¿En qué se parece el último producto a los otros productos que has hallado? ¿En qué se diferencia?” Through repeated computation of decimal products and discussion of strategies, students refine efficiency and accuracy while connecting place-value understanding to multiplication of decimals.

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 1, lesson 4, “Explorar las relaciones del valor posicional,” the materials provide educators with guidance on creating practice opportunities for students to apply efficient, flexible, and accurate mathematical procedures within the unit on place value. In activity 1, students evaluate mathematical representations, models, and solutions for efficiency, flexibility, and accuracy through analysis of decimal place-value relationships. Students determine which decimal representations are most efficient while maintaining accuracy and equivalence. For example, students are asked: “Un pepita de oro pesa 0.2 onzas. ¿Cuál es un conjunto de pesas que podrías usar para equilibrar la pepita? ¿Cuál es otro conjunto de pesos que podrías usar para pesar la pepita? ¿Cuántos pesos de 0.01 onzas necesitarías para equilibrar la pepita? ¿Y cuántos pesos de 0.001 onzas?” Students critique and compare different weight combinations to determine which are more efficient while still representing the same decimal value.

In unit 2, lesson 10, “Diferentes formas de restar,” students are provided practice opportunities to apply efficient, flexible, and accurate mathematical procedures when subtracting rational numbers. In activity 2, students find the difference between mixed numbers using strategies of their choice. The materials state, “Se debe animar a los estudiantes a encontrar las diferencias de una manera que les haga sentido. Esto puede significar elegir una estrategia diferente dependiendo del problema, pero también podría significar escribir cada diferencia como una diferencia de fracciones y luego hallar un denominador común.” Students select and apply different strategies depending on the problem, including rewriting differences as fractions with common denominators.

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 unit 1, lesson 2, “Milésimas en cuadrículas y en palabras,” the materials provide educators with guidance on creating practice opportunities for students to evaluate procedures, processes, and solutions for efficiency, flexibility, and accuracy within the unit on place value. In activity 2, students evaluate mathematical representations, models, and solutions by analyzing multiple interpretations of the same decimal representation. Students determine which student claims correctly represent a shaded region, justify equivalence relationships between decimals and fractions, and critique inaccurate reasoning related to place-value concepts. For example, “Varios estudiantes observan el diagrama y describen la región sombreada de diferentes maneras. ¿Con quién estás de acuerdo? ¿Por qué?” Through these practice opportunities, students critique interpretations of decimal models and justify accurate representations using place-value reasoning.

In unit 2, lesson 11, students are provided practice opportunities to estimate and compute sums and differences of fractions in the context of a salad dressing recipe while evaluating the reasonableness of their solutions. Students compare estimation strategies, analyze the precision of fractional calculations, and consider how different mathematical decisions affect a real-world outcome. For example, students evaluate Priya’s claim that borrowing 1/16 cup of olive oil is close enough to the required amount and justify whether the difference meaningfully affects the recipe. Through discussion of strategies, comparison of estimates and exact calculations, and critique of solutions, students develop flexibility and accuracy in fraction operations.

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

In unit 1, lesson 6, the materials include educator-embedded supports that guide students toward increasingly efficient and accurate strategies for comparing and ordering decimals using place value and number lines. Embedded prompts support educators in monitoring how students place decimals, selecting students to share different reasoning strategies, and facilitating discussions about how position on a number line determines value. For example, educators ask, “¿Qué corredor corrió la distancia más larga? ¿Cómo lo muestra la recta numérica?” prompting students to explain that Mai ran the farthest because 0.561 is located farthest to the right on the number line, showing it is greater than 0.54, 0.52, and 0.50. Through questioning, discussion, and visual models, students are guided toward more efficient and flexible decimal comparison strategies.

In unit 4, lesson 18, “Multiplicación y división con números enteros no negativos,” the materials provide educator-embedded supports that guide students toward increasingly efficient approaches for division using partial quotients and the standard algorithm. Educators support students in analyzing how different choices of partial quotients affect efficiency, comparing the number of steps in different methods, and evaluating strategies for accuracy and mental computation. The materials explain that students divide three- and four-digit dividends by two-digit divisors using partial quotients and the standard algorithm, and that using larger multiples of the divisor can reduce unnecessary steps. The activity synthesis reinforces efficient decision-making by prompting students to critique and refine their approaches to division.

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, “Enseñanza y aprendizaje basados en problemas,” the materials explain how the conceptual and procedural emphasis of the TEKS is addressed through problem-based instruction and mathematical practices. Students learn mathematical concepts and procedures while engaging in reasoning, problem-solving, modeling, discourse, and strategic tool use. For example, “Los estudiantes aprenden matemáticas haciendo matemáticas, en lugar de ver a alguien más hacer matemáticas o que les digan qué hacer. ‘Hacer matemáticas’ significa aprender conceptos y procedimientos matemáticos mientras se participa en las prácticas matemáticas . . . interpretar problemas, razonar de manera abstracta y cuantitativa, construir argumentos y criticar el razonamiento de otros, modelar con matemáticas, usar herramientas apropiadas estratégicamente, prestar atención a la precisión en el uso del lenguaje, buscar y aprovechar la estructura, y expresar regularidad en el razonamiento repetido.” Students learn mathematics through active engagement in both conceptual understanding and procedural application within problem-based learning experiences.

In unit 2, lesson 7, students develop conceptual understanding by sorting fraction expressions into categories based on attributes such as operation type, mixed numbers, and whether denominators are the same or different. Students also develop procedural understanding by identifying which expressions can be solved directly and which require strategies such as finding common denominators. For example, students compare 2/3 − 1/3 and 2/3 − 1/6, explaining that the first can be solved directly because the denominators are the same, while the second requires equivalent fractions. Embedded educator prompts, fraction strips, and partner discussions support students in justifying their reasoning and developing both conceptual understanding and procedural fluency.

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 1, lesson 3, “Milésimas en notación extendida,” the materials provide guidance on implementing questions and tasks that include the use of concrete models, pictorial representations (figures/drawings), and abstract representations to support students’ understanding of place value as required by the TEKS. In activity 1, students interpret shaded grid models, connect visual representations to decimal fractions and decimal notation, and represent quantities using expanded-notation expressions. For example, “Explica o muestra por qué la región sombreada representa (4 × 0.1) + (1 × 0.01) + (9 × 0.001). ¿Qué número decimal representa la región sombreada?” Students translate shaded decimal grids into symbolic decimal expressions and expanded notation, strengthening connections between representations.

In unit 2, lesson 12, students use representations and reasoning to evaluate different strategies for finding common denominators before adding fractions. The task supports pictorial and concrete reasoning by allowing students to show their thinking with drawings, diagrams, and visual models while connecting those representations to abstract fraction expressions. For example, students analyze 4/6 + 5/8 and determine valid common denominators such as 24 and 48, while recognizing that 18 is not valid because it is not a multiple of eight. Students then rewrite fractions using equivalent forms, such as 16/24 + 15/24 = 31/24 or 32/48 + 30/48 = 62/48, demonstrating connections among visual reasoning, equivalent fractions, and symbolic procedures.

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.

In unit 2, lesson 3, students connect place-value understanding to the abstract algorithm for adding decimals by analyzing why digits must be aligned according to decimal place value. The lesson supports students in explaining symbolic calculations through representational reasoning, estimation, and precise mathematical language such as punto decimal, décimas, and centésimas. For example, students compare Elena’s incorrect calculation with Andre’s correct solution for 621.45 + 72.30, explaining that Andre’s answer, 693.75, is reasonable because he aligns digits by place value and uses an estimate of about 620 + 70 = 690. Through “Math Language Routine 3” within this lesson, students critique, correct, and clarify explanations, strengthening the connection between conceptual understanding of decimal place value and the standard addition algorithm.


In unit 3, lesson 7, “Medir volumen,” the materials support students in connecting and explaining concrete and representational models and linking them to abstract concepts of volume, including symbolic, numeric, and algorithmic representations, as required by the TEKS. In activity 1, students transition from hands-on cube models and spatial representations to abstract reasoning about volume formulas. Educator guidance prompts students to explain counting strategies, analyze cube arrangements, and relate grouped structures to multiplication-based formulas. For example, “Los estudiantes se enfocan solamente en prismas rectangulares. Mientras cuentan, los estudiantes deberán asegurarse de contar cada cubo una vez y solo una vez. Observa estas estrategias: Tocar cada cubo mientras lo cuentan, Contar los cubos por capas (incluyendo cuando hay diferentes números de cubos en cada capa), Usar suma o multiplicación cuando los cubos están organizados en capas.” The activity supports students in moving from concrete cube models to abstract formulas and symbolic reasoning about volume.

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

In unit 1, lesson 1, “¿Qué es una milésima?,” students develop academic mathematical language using visuals, manipulatives, and language development strategies to explore place value. Students work in pairs using hundredths grids, graph paper, and colored pencils, crayons, or markers to create a poster representing tenths, hundredths, and thousandths. For example, “En grupos de 2, dales a los estudiantes acceso a cuadrículas de centésimas de las copias de recursos. Dales a los estudiantes acceso a papel para gráficos y lápices de colores, crayones o marcadores. Trabaja con tu compañero para hacer un cartel que muestre lo que sabes sobre los números 1 décimo, 1 centésimo y 1 milésimo.” The lesson also includes language supports through a visible vocabulary display. For example, “Mantén una exhibición visible para registrar el vocabulario nuevo. Invita a los estudiantes a sugerir detalles (palabras o imágenes) que les ayuden a recordar el significado de los milésimos y la conexión de los milésimos con las décimas y centésimas.”

In unit 3, lesson 5, activity 1, “El ajuste correcto,” students develop academic mathematical language using visual representations, geometric tools, and mathematical discussions. Students use triangle cards, grids, and protractors to identify and classify triangles while discussing geometric attributes. Educator prompts include “¿Cómo determinaste cuáles triángulos tienen ángulos de 90 grados?” and “¿Cómo podemos estar seguros de que un triángulo es un triángulo rectángulo?” Students use vocabulary such as triángulos rectángulos, ángulos, and lados as they describe figures and explain their reasoning.

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

In unit 8, lesson 3, “Representar fracciones en un diagrama de puntos,” the materials provide embedded educator guidance to scaffold and support students’ development and use of academic mathematical vocabulary related to representing data. In activity 2, the materials incorporate the “Math Language Routine 8: Apoyos para la conversación” to guide students in explaining their reasoning, interpreting equations, and discussing mathematical claims. For example, “Antes de resolver los problemas, invita a los estudiantes a comprender las situaciones y a turnarse para compartir su comprensión con su compañero. Escucha y aclara cualquier pregunta sobre el contexto.” Educator prompts also guide students in using mathematical vocabulary as they explain their reasoning, including “¿Cómo usaste tu diagrama de puntos para saber cuántos huevos pesó Jada?,” “¿Cómo decidiste si su afirmación era correcta?,” and “¿Cómo representan estas ecuaciones el razonamiento de Jada?”

In unit 9, lesson 1, activity 1, “¿Puedes dibujarlo? Figuras en el plano de coordenadas,” the materials provide educator guidance to support students’ use of academic mathematical vocabulary while describing and drawing figures on a coordinate plane. Students work with a partner to replicate rectangles, with one student using precise mathematical language to describe the figure and the other drawing it based on the verbal description. The materials state, “El propósito de esta actividad es que los estudiantes utilicen la estructura del plano de coordenadas para comunicar y dibujar figuras. Los estudiantes trabajan con un compañero para replicar rectángulos dados. Un compañero utiliza un lenguaje preciso y describe los rectángulos y el otro los dibuja basándose en la descripción verbal de su compañero.”

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 unit 7, lesson 6, “Imágenes de mosaico,” the materials include embedded educator guidance that supports the application of appropriate mathematical language through vocabulary, syntax, and discourse as students solve fraction multiplication problems in context. In activity 2, the educator uses “Math Language Routine 1: Cada vez más fuerte y más claro” to support mathematical conversations in which students explain their reasoning, receive peer feedback, and revise their explanations using increasingly precise mathematical language. The materials state, “El propósito de esta actividad es que los estudiantes apliquen su comprensión de multiplicar números enteros por fracciones mayores que 1 para determinar el costo de hacer un mosaico con diferentes materiales. Anima a los estudiantes a usar estrategias de estimación. Anima a los estudiantes a interpretar la fracción con respecto al dinero.” This guidance provides opportunities for students to hear, refine, and use mathematical language with peers while educators support student responses during discussion.

In unit 8, lesson 4, activity 1, “Brecha de información: recolectar fruta,” the materials include embedded educator guidance that supports vocabulary, syntax, and discourse as students communicate mathematical ideas about data represented in dot plots. Students work collaboratively to identify missing information, ask questions, and explain their reasoning using mathematical language. Educator guidance directs educators to monitor students as they request information, complete a dot plot, and justify their responses. For example, the materials state, “Esta actividad Brecha de información ofrece a los estudiantes la oportunidad de resolver problemas sobre datos representados en gráficos de puntos. Supervisa a los estudiantes que: solicitan toda la información de la tarjeta de datos y crean un gráfico de puntos completo que pueden usar para responder la pregunta; solo solicitan la información que necesitan para responder la pregunta sobre el albaricoque más pesado y el peso más común.” This guidance supports mathematical conversations as students hear, refine, and use mathematical language with peers.

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

In unit 1, lesson 5, “Valores por diez,” the materials integrate the TEKS mathematical process standards as students analyze place-value relationships, construct equations, interpret mathematical patterns, and communicate their reasoning. In activity 2, students use equations and multiple representations to explain how the value of the same digit changes across different numbers. For example, “En esta actividad, los estudiantes interpretan las relaciones entre los valores del mismo dígito en diferentes números y escriben ecuaciones de multiplicación y división para representar estas relaciones.” Students explain their reasoning through partner discussions, written responses, and mathematical representations, supporting problem-solving, mathematical communication, and connections among mathematical ideas.

In unit 3, lesson 10, activity 3, “¿Cuál es la pregunta?,” the materials integrate the TEKS mathematical process standards as students communicate mathematical ideas using multiple representations while measuring the volume of rectangular prisms. Students use linking cubes, equations, and mathematical vocabulary to interpret representations, formulate questions, and explain their reasoning. For example, the materials state, “Conecta el lenguaje informal con los términos matemáticos longitud, ancho, alto y área de una base. Los estudiantes tienen que interpretar las ecuaciones y formular la pregunta cuya respuesta está dada. Los números se eligen específicamente para motivar a los estudiantes a considerar la estructura de los prismas rectangulares.” These opportunities engage students in reasoning, representation, problem-solving, and mathematical communication.

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 ES, the grade 5 section titled “Qué hay en una lección de matemáticas de Kiddom,” describes how the TEKS mathematical process standards are incorporated and connected throughout the course. The course guide explains that students engage in mathematical discourse, reasoning, problem-solving, and representation through warm-ups, collaborative activities, lesson synthesis discussions, and independent application opportunities. The guidance demonstrates that process standards are embedded within daily instruction and connected to conceptual understanding and procedural development across learning pathways. For example, in unit 8, lesson 10, students describe rectangular prisms in terms of their side lengths, find volume by multiplying side lengths, and connect this strategy to finding volume by multiplying the base area by the height.

In the Guía de planificación a nivel de sección for unit 3, “Geometría,” “Narrativa de la sección A,” the materials describe how the TEKS mathematical process standards are incorporated through opportunities for students to reason, represent, and communicate mathematical ideas while developing content understanding. The guidance indicates how students classify quadrilaterals and triangles by category and study their relationships through the use of physical models. For example, the materials state, “En esta sección, los estudiantes clasifican cuadriláteros y triángulos en diferentes categorías y estudian las relaciones entre ellas. Comienzan ordenando un gran conjunto de cuadriláteros de una manera que les resulte lógica, usando atributos como las medidas de ángulos (especialmente ángulos rectos) y pares de lados paralelos. Luego, se enfocan en relacionar los atributos de trapecios, rectángulos, paralelogramos, cuadrados y rombos . . . . Construyen estas figuras con palillos y ven que un cuadrado es un tipo especial de rombo y un rectángulo es un tipo especial de paralelogramo. A medida que aprenden más sobre las relaciones entre las categorías de cuadriláteros, los estudiantes utilizan un diagrama de Venn para resaltar su comprensión.”

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

In unit 3, “Geometría,” the unit overview describes how the TEKS mathematical process standards are incorporated and connected throughout the unit through opportunities for students to develop conceptual understanding and apply mathematical skills related to measuring the volume of solid figures. The materials explain how students build understanding of volume through exploration, representation, and reasoning: “Esta unidad introduce a los estudiantes al concepto de volumen basándose en su comprensión del área y la multiplicación. Aquí, los estudiantes aprenden que el volumen de una figura sólida es el número de cubos encajables que la llenan sin huecos ni superposiciones. Primero, miden el volumen contando los cubos encajables y observan su naturaleza aditiva. También aprenden que diferentes figuras sólidas pueden tener el mismo volumen.” This demonstrates how the unit connects the TEKS mathematical process standards to content development through mathematical modeling, reasoning, and application throughout the learning progression.

In unit 6, Guía de planificación a nivel de sección, the materials provide a description of how the TEKS mathematical process standards are incorporated and connected throughout the unit on fractions as quotients and multiplication of fractions. The guide highlights opportunities for students to represent mathematical relationships, analyze structures, communicate reasoning, solve problems, interpret models, justify strategies, and connect multiple representations throughout the unit progression. For example, the materials state, “Los estudiantes aprenden a ver una fracción como un cociente, resultado de dividir el numerador por el denominador. Resuelven una secuencia de problemas sobre situaciones que implican compartir un número entero de objetos por igual. A través del razonamiento repetido, observan regularidad en el resultado de la división y generalizan eso.” This demonstrates how the unit intentionally embeds the TEKS mathematical process standards through reasoning, problem-solving, representation, and mathematical communication.

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

In grade 5, the materials include an overview of the TEKS mathematical process standards incorporated into each lesson by embedding opportunities for students to problem-solve, represent, communicate, and justify mathematical thinking. In unit 2, lesson 4, students select and apply strategies that make sense to them, such as using hundredths grids, equations, and place-value reasoning to subtract decimals, supporting mathematical problem-solving and strategic tool use. The lesson incorporates “Math Language Routine 7: Comparar y conectar,” requiring students to create visual representations, compare solution methods, and discuss similarities and differences among approaches. Educator guidance includes discussion prompts such as “¿Qué es lo mismo y qué es diferente sobre las estrategias usadas para hallar el valor de la diferencia?” to support students in analyzing multiple representations and justifying their reasoning.

In unit 4, “Multiplicación y división de números enteros no negativos,” Guía de planificación a nivel de sección, the materials provide an overview of the TEKS mathematical process standards incorporated into the lessons by describing how students apply problem-solving, reasoning, and mathematical representations as instruction progresses. For example, the materials state, “Esta sección introduce el algoritmo estándar para la multiplicación, extendiendo el trabajo previo de los estudiantes sobre la multiplicación. En cuarto grado, los estudiantes usaron diagramas y algoritmos de productos parciales para hallar el producto de un número de un dígito y un número de hasta cuatro dígitos y el producto de 2 números de dos dígitos.” This overview explains how lessons build from visual models and partial products to the standard algorithm, embedding the TEKS mathematical process standards through reasoning, problem-solving, and increasingly abstract representations across the lesson sequence.

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

In unit 7, lesson 6, activity 2, “Costo del mosaico,” the materials provide opportunities for students to think mathematically, persevere through problem-solving, and make sense of mathematics by applying multiplication of whole numbers and fractions greater than 1 to solve an authentic cost problem. Students select a preferred material, use rectangle models to represent a mosaic, estimate or calculate total area and cost, and determine a reasonable solution using mathematical strategies. The activity connects visual models, numerical expressions, estimation, and fractional dollar amounts as students analyze and solve the problem. Through the “Math Language Routine 1: Cada vez más fuerte y más claro,” students explain their reasoning, receive peer feedback, revise their work, and clarify their mathematical arguments. Educator guidance supports students in exploring different solution strategies, using estimation, and writing expressions that represent their thinking, allowing students to engage in productive struggle and make sense of mathematical relationships.

In unit 10, lesson 5, “Administrar las finanzas personales mediante el presupuesto y el ahorro,” the materials provide opportunities for students to think mathematically, persevere through problem-solving, and make sense of mathematics through personal finance scenarios. In activity 1, “Bienestar financiero: equilibrio de un presupuesto,” students analyze budget information, make decisions, and create and balance a sample budget. The materials state, “En esta actividad, los estudiantes lanzarán un dado para determinar su presupuesto de muestra. Luego revisarán una lista de ocho categorías de presupuesto, cada una con diferentes opciones. Los estudiantes usarán estas opciones para administrar sus finanzas creando y equilibrando un presupuesto simple.” Students interpret mathematical information and justify decisions as they work through a non-routine problem-solving task. The activity requires students to reason through financial situations and persist in applying mathematical understanding rather than only following a set procedure.

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 3, lesson 9, activity 2, “Encontrar el volumen de diferentes maneras,” the materials support students in understanding, explaining, and justifying that there are multiple valid ways to represent and solve the same mathematical problem. Students analyze rectangular prisms using interlocking cubes and represent volume using different decompositions, including horizontal and vertical layers. Through the “Math Language Routine 7: Comparar y conectar” routine, students create visual displays of their strategies, compare representations with classmates, and explain how different expressions represent the same volume. Educator prompts such as “¿Cómo representa esta expresión el volumen del prisma?” and “¿Alguien resolvió el problema de la misma manera pero lo explicó de forma diferente?” support students in justifying their reasoning, connecting models to expressions, and recognizing equivalent solution methods.

In unit 4, lesson 10, “Los factores como un factor en nuestra elección de estrategia,” the materials support students in understanding, explaining, and justifying that there are multiple ways to represent and solve multiplication and division problems with non-negative integers. In activity 2, “Comparar estrategias,” students compare mental computation strategies, decomposition methods, and standard algorithms while explaining why different approaches may be useful depending on the numbers and context. The materials state, “El propósito de esta actividad es que los estudiantes prueben nuevas ideas de la actividad anterior y practiquen la multiplicación utilizando el algoritmo estándar. Compara tus estrategias con tu grupo pequeño. ¿Dónde usaron la misma estrategia? ¿Dónde usaron una estrategia diferente?” Educator prompts and discussion questions support students in explaining their strategies, comparing approaches, and justifying why different methods can be used to solve the same mathematical problem.

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 unit 8, lesson 4, activity 1, “Brecha de información: recolectar frutas,” the materials require students to make sense of mathematics through opportunities to do, write about, and discuss mathematics with peers and the educator. Using the “Math Language Routine 4: Brecha de información” routine, students collaborate in pairs to ask questions, gather missing information, complete dot plots, and solve problems involving the heaviest fruit, the most common weight, and missing data. Students record their mathematical reasoning by explaining how they identified missing measurements and justified conclusions using completed data displays. Educator prompts, including “¿Qué tipo de preguntas fueron más útiles?” and “¿Alguien resolvió el problema de otra manera?,” support students in reflecting on strategies, comparing approaches, and communicating mathematical ideas during discussions.

In unit 9, lesson 1, “Explora el plano de coordenadas,” the materials require students to make sense of mathematics through multiple opportunities to do, write about, and discuss mathematical ideas with peers and educators. In activity 1, “¿Puedes dibujarlo? Figuras en el plano de coordenadas,” students use the coordinate plane to communicate and draw figures while working with a partner. The materials state, “El propósito de esta actividad es que los estudiantes utilicen la estructura del plano de coordenadas para comunicar y dibujar figuras. Los estudiantes trabajan con un compañero para replicar rectángulos dados. Un compañero utiliza un lenguaje preciso y describe los rectángulos y el otro los dibuja basándose en la descripción verbal de su compañero.” Students interpret descriptions, create and refine representations, and discuss mathematical ideas using precise language. The “Math Language Routine 2: Recolectar y mostrar” supports students in sharing their thinking, using academic vocabulary, and refining explanations through peer and whole-class discussions.

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 unit 2, lesson 2, activity 2, “Estimar y averiguar el valor,” the materials provide educators with structured guidance for helping students share and reflect on their problem-solving approaches through explanations, arguments, and justifications when working with addition and subtraction of rational numbers. Students estimate decimal sums before determining exact values using the standard algorithm or place-value reasoning, then explain and compare the strategies they used. During the lesson synthesis, educator guidance prompts students to share their approaches, identify similarities and differences among strategies, and justify their reasoning. Educator questions such as “¿Qué tienen en común sus estrategias?,” “¿En qué se diferencian?,” and “¿Cómo les ayudó la estimación con el cálculo?” support students in evaluating strategies and connecting estimation to precise computation. Reflection supports, including the sentence stem “La próxima vez que estime sumas de números decimales de varias cifras, prestaré atención a . . .,” guide educators in helping students reflect and communicate mathematical reasoning and justifications.

In grade 5, unit 7, lesson 13, activity 1, “Mayor o menor que 1,” the materials provide educators with structured guidance for helping students share and reflect on their problem-solving approaches through explanations, arguments, and justifications. Students first determine whether quotients are greater than or less than 1 without calculating exact values, then write an explanation describing how the relationship between the dividend and divisor supports their reasoning. The “Math Language Routine 1: Cada vez más fuerte y más claro” directs educators to facilitate structured partner discussions in which students present their thinking, ask clarifying questions, provide constructive feedback, and revise their explanations based on peer input. Educator prompts such as “Can you give an example to help show your thinking?” and “How can you use the words dividend and divisor in your explanation?” guide students to strengthen mathematical arguments using precise vocabulary and evidence. These embedded instructional supports help educators foster a classroom environment where students regularly communicate, justify, refine, and reflect on their mathematical reasoning while learning from the perspectives of their peers.

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 5, unit 2, lesson 3, activity 1, “Comparar cálculos,” the materials provide educators with prompts and guidance for providing explanatory feedback based on student responses and an anticipated misconception about aligning decimal numbers incorrectly. The lesson presents Elena’s incorrect calculation, in which digits are aligned to the right rather than by place value, allowing educators to address why tenths must be added to tenths and hundredths to hundredths. Through “Math Language Routine 3: Criticar, corregir, aclarar,” educators guide students to identify what is unclear, incorrect, or incomplete in Elena’s reasoning and revise the explanation with a partner. Prompts such as “What parts of this response are unclear, incorrect, or incomplete?” and criteria requiring students to use terms such as decimal point, tenths, and hundredths support educators in guiding students toward more precise mathematical explanations. These embedded supports help educators address misconceptions, use student responses to guide feedback, and strengthen students’ conceptual understanding of decimal operations.

In unit 10, lesson 6, “Equilibrar presupuestos cuando los gastos superan los ingresos,” the materials provide prompts and guidance to support educators in providing explanatory feedback based on student responses and anticipated misconceptions related to personal finance problem-solving. In activity 2, “Equilibrar el presupuesto: hacer ajustes,” students evaluate proposed actions to balance a budget and explain their reasoning. Educator guidance includes prompts to help students analyze unsuccessful strategies and consider alternative solutions. The materials state, “Incentiva a los estudiantes a pensar críticamente sobre la efectividad de sus acciones propuestas. Si sus acciones no lograron equilibrar el presupuesto, pídeles que consideren por qué y qué acciones adicionales podrían tomar. Si los estudiantes tienen dificultades para equilibrar el presupuesto, guíalos a considerar otras estrategias como aumentar los ingresos o hacer recortes más significativos en los gastos no esenciales.” These supports help educators address misconceptions, ask clarifying questions, and guide students in refining their explanations and mathematical reasoning when making financial decisions.