Math Journeys Texas, Kindergarten (Spanish)

Evaluation for 1.1a
Materials include an alignment guide outlining the TEKS, ELPS, and concepts covered, with a rationale for learning paths across grade levels (vertical alignment) and within the same grade level (horizontal alignment) as designed in the materials.

The TEKS Correlation Guide in the Math Journeys program outlines the TEKS corresponding to each lesson, including both the content and process standards for educators. Additionally, the “Scope and Sequence” document—which is organized into different sections called “journeys” that tie the program together—describes the TEKS and ELPS. The Journey Instructional Guide presents a detailed rationale for each journey. For example, section 2 of the guide provides the vertical rationale for how the current journey builds upon the previous one and how it prepares students for the next concept(s) to be taught. The A2 Journey Instructional Guide, which involves identifying numbers and counting from 1–100, extends the skills of counting, comparing, ordering, and estimating from the previous journey, which focuses on numbers 1–20. Section 3 contains the horizontal rationale, explaining how learning moves from concrete to representational to abstract models of number sense.

The “Alcance y secuencia” (“Scope and Sequence”) document in the Math Journeys program outlines the TEKS, process standards, and mathematical concepts corresponding to each lesson across the curriculum. Additionally, the scope and sequence shows how concepts are connected and developed across lessons and grade levels. The materials present a detailed progression of mathematical learning by demonstrating how educators introduce and extend foundational skills in later lessons. Early lessons focus on foundational concepts and representations, while later ones build toward more complex mathematical reasoning and problem-solving. The vertical alignment within the scope and sequence shows how each concept builds upon previous learning and prepares students for future mathematical understanding. The horizontal alignment is reflected through the connections between concepts, process standards, and multiple representations used throughout the lessons and activities.

Evaluation for 1.1b
Materials include an implementation guide with usage recommendations and strategies for effective educator use in various contexts, such as just-in-time supports, advanced learning, or as a course.

The Program Guide in the Math Journeys program provides comprehensive guidance for implementation, including the three-step framework of “build,” “consolidate,” and “practice.” Each lesson is designed to start with an educator-led, small-group lesson followed by logsheets for students to complete independently with educator feedback, and then further optional practice on Atlas Math, an adaptive digital platform. Additionally, the “Lesson Internalization and Planning” section describes ways to plan for variability among students, including explanations for multiple entry points, just-in-time supports, extensions, and multiple representations and modes of expression.

The Guía del programa outlines strategies and usage recommendations for adapting instruction across a variety of instructional settings and contexts. Additionally, the guide provides support for differentiated instruction as well as flexible lesson implementation throughout the grade K curriculum. The materials also include Atlas Math, a personalized adaptive digital platform that allows students to work at their own pace while participating in support or extension activities based on their individual learning needs. The guide explains how grade K educators can adapt instruction to support varying levels of understanding while keeping students engaged with grade-level mathematical concepts and processes.

Evaluation for 1.1c
Materials include a TEKS correlation guide with recommended skill entry points based on diagnostic assessment results.

The TEKS Correlation Guide of the Math Journeys Spanish program recommends skill entry points based on the results of diagnostic assessment. The program aligns journeys and lessons with TEKS content and process standards. The TEKS Correlation Guide helps educators implement instruction by connecting lessons and activities to specific standards within each journey. There is also a report template for diagnostic assessment and placement that suggests skill entry points and helps educators identify appropriate instructional starting points, targeted interventions, and differentiated learning opportunities based on data from individual students’ performance.

The Guía del programa contains strategies and usage recommendations for adapting instruction across a variety of instructional settings and contexts. The guide also supports differentiated instruction and flexible lesson implementation throughout the grade K curriculum. The materials include “práctica adicional” through the adaptive digital platform Atlas Math, which allows students to practice, review previously taught concepts, and learn new concepts based on their individual learning needs. The materials also provide templates for “informes del progreso,” reports that describe individual students’ progress and performance on TEKS-aligned activities. The guide shows how grade K educators can monitor students’ learning and adapt instruction to support varying levels of understanding while keeping them engaged with grade-level mathematical concepts and processes.

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

The Math Journeys program provides protocols and guidance for internalizing both units and lessons through the “Lesson Internalization and Planning” section of the Program Guide. In the “Preparing for a Journey” section, educators learn how each journey builds upon prior learning, review lesson objectives and mastery criteria, identify scaffolds and enrichment opportunities, gather materials, and analyze learning progression before starting instruction. The materials also include protocols for internalizing lessons in the sections “Preparing for a Building Session,” “Preparing for a Consolidating Session,” and “Preparing for an Additional Practice Session.” These sections help educators clarify objectives, anticipate students’ thinking and misconceptions, prepare materials, identify opportunities for formative assessment, analyze students’ responses, and use progress monitoring data to inform future instruction.

The Math Journeys grade K program contains protocols and implementation guidance that help educators internalize units and lessons throughout the curriculum. Additionally, the materials explain how to prepare for instruction through sections such as “Internalización y planificación de lecciones,” “Preparándose para un journey,” and preparation protocols for sessions focused on construction, consolidation, and additional practice. The materials outline lesson objectives, vocabulary, instructional strategies, preparation of materials, opportunities for formative assessment, and step-by-step activities that help educators understand how concepts are developed during instruction. The implementation guidance also helps educators analyze learning progression, anticipate students’ thinking, identify opportunities for scaffolding and differentiation, and prepare materials needed for lesson delivery. This guidance shows how grade K educators can internalize unit and lesson expectations while confidently planning instruction aligned with grade-level mathematical concepts and students’ learning needs.

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

The Math Journeys program offers resources to help instructional leaders assist educators with implementing it. The “Hands on Partnership” section of the Program Guide contains examples of how a math success manager can partner with, and provide guidance to, instructional leaders, such as “facilitation of PLC [professional learning community] sessions, student work and progress monitoring analysis, aligning instructional practices, and developing a long-term tier two math model.”


The Latin American (es-LA) Spanish version of the Math Journeys Coaching Guide for Instructional Leaders provides specific resources and guidance for instructional leaders to help educators implement the Math Journeys program as designed. The “How to Use It” section establishes a clear coaching protocol that instructional leaders can use during classroom observations, during the post-observation conversation, and when collaboratively planning the next lesson with the educator. For example, while observing, the instructional leader can use the Stage 1 Observation Tool to determine whether the educator is following the intended lesson structure and using manipulatives, conversations, logsheets, and other program resources at appropriate times. This tool also helps the instructional leader verify that lesson objectives have been met. Following observation, the instructional leader can use the reflection rubric to facilitate the coaching conversation as well as the lesson preparation guide to jointly plan subsequent instruction, including lesson objectives, TEKS, prerequisites, anticipated student errors, strategies, and instructional adjustments. Together, these resources provide instructional leaders with actionable guidance for observing implementation, providing targeted feedback, and helping educators maintain the intended design of Math Journeys.

Evaluation for 1.2a
If designed to be static, materials include detailed lesson plans with learning objectives, teacher and student materials, lesson components with suggested timeframes, and assessment resources aligned with the TEKS and ELPS.

The Guía del programa of the Math Journeys Texas program breaks down the instructional components within each journey lesson and suggests timeframes for each part of the lesson. The materials outline components such as educator-led instruction, student exploration, discussion, and practice activities to support consistent implementation of the program as designed. Additionally, the Guía del programa describes multiple assessment resources, including diagnostic and progress monitoring tools. The “Digital Practice Progress” report provides TEKS-aligned assessment data by identifying student performance for each TEKS to support instructional decision-making and monitor student growth.

The Math Journeys grade K program contains lesson plans that outline the learning objectives, TEKS alignment, vocabulary, educator and student materials, instructional resources, and lesson components across the curriculum. Additionally, instruction is organized into lesson-based sections such as “Planteamiento,” “Nudo,” and “Desenlace,” which guide educators through the progression of instruction and student learning. The materials provide a sequence of instructional activities aligned with the lesson objectives and TEKS, helping educators understand how concepts are introduced, developed, and reinforced during a lesson. For example, in journey A0, session 14, the learning objective focuses on finding pairs of numbers that add up to five, while the warm-up, development, and wrap-up activities provide instructional guidance to support students throughout the learning process. This guidance shows how grade K educators can internalize lesson expectations, prepare instructional materials, and facilitate instruction aligned with grade-level mathematical concepts and skills.

Evaluation for 1.2b
If designed to be adaptive, materials include responsive learning objectives, lesson components with suggested timeframes, and assessment resources aligned with the TEKS and ELPS.

The Math Journeys program explains how to plan lessons through clearly organized lesson components within the program’s structure. The materials outline the three-step framework of “build,” “consolidate,” and “practice” and suggest timeframes for each part of the lesson to support effective pacing and implementation. The framework helps educators teach in a consistent and purposeful way while providing students with a structured learning routine. The organization of the lesson components helps educators manage their instructional time effectively and ensures that each stage of learning is addressed throughout the lesson.

The Math Journeys grade K program contains lesson plans that outline the learning objectives, TEKS alignment, vocabulary, educator and student materials, instructional resources, and lesson components across the curriculum. Instruction is organized into lesson-based sections such as “Planteamiento,” “Nudo,” and “Desenlace,” which guide educators through the progression of instruction and student learning. The materials provide a sequence of instructional activities aligned with the lesson objectives and the TEKS, helping educators understand how concepts are introduced, developed, and reinforced during the lesson. For example, in journey A1, session 2, the learning objective focuses on practicing acoustic counting from one to 10, while the warm-up, development, and wrap-up activities provide instructional guidance to support students throughout the learning process. This guidance shows how grade K educators can internalize lesson expectations, prepare instructional materials, and facilitate instruction aligned with grade-level mathematical concepts and skills.

Evaluation for 1.2c
Materials contain support for families in Spanish and English for each unit, with suggestions on supporting the progress of their student(s).

The Math Journeys program provides resources for families within each journey to help caregivers support students’ learning at home. The materials include a template for a family letter in Spanish that contains guidance, questions, vocabulary, and suggested activities connected to the lesson concepts being taught in class. Additionally, educators can change the language of the letter by using the language toggle located in the top right corner, allowing families to access the information in their preferred language. The letter is designed to strengthen the connection between school and home by providing caregivers with specific strategies and conversation prompts to reinforce students’ understanding outside the classroom.

The Math Journeys grade K program provides a template for a family letter in both English and Spanish that offers support for families throughout each journey or unit within the curriculum. The letter outlines the mathematical topics, vocabulary, definitions, examples, and learning goals addressed during the unit. The materials also include suggested activities and opportunities for practice that families can complete at home to reinforce students’ learning and support the development of grade-level mathematical concepts. This guidance shows how families with grade K students can support their children’s progress as well as strengthen connections between classroom instruction and learning at home.

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

The Math Journeys grade K program includes the definition and intended purpose of the “Prueba del final de journey” assessment, which measures students’ understanding of the concepts and skills taught throughout a particular journey. The materials guide educators on how to administer the assessment, review students’ performance, and use the results to identify students who are ready to continue learning or who may need additional support and practice.

The Math Journeys grade K program includes the definition and intended purpose of formative instructional assessment integrated into the lesson plans. The materials include opportunities to activate previous knowledge and conduct checks for understanding during a lesson in order to detect misconceptions and make real-time instructional adjustments to support students in the learning process.

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

The Math Journeys grade K program helps educators assess students consistently and accurately using the Guía de implementación for the “Prueba del final de journey” assessment. The materials explain the assessment’s purpose and characteristics, describe its components and question types, and outline clear administration procedures as well as expectations for the testing environment. This guidance helps educators assess students uniformly across all grade K classrooms.

The Math Journeys grade K program ensures that educators consistently and accurately administer instructional assessments through detailed guidelines. The materials include information about the assessment, suggested administration time, and step-by-step procedures for implementing it. For example, at the end of journey A1, the Guía de implementación for the “Prueba del final de journey” assessment helps educators complete the evaluation by explaining how to check for necessary information before the test, administer procedures during the test, and interpret the results afterward.

Evaluation for 2.1c
Digital assessments include printable versions and accommodations, including text-to-speech, content and language supports, and calculators, that educators can enable or disable to support individual students.

The Math Journeys grade K program provides accommodations for digital assessment as well as accessibility supports to meet individual students’ needs, including text-to-speech functionality, content and language supports, and digital calculators. The materials also explain how students can access accessibility features within the platform to support equitable access during assessment. However, educators are not able to independently change students’ language settings or manage individualized accessibility features within the platform’s settings.

Evaluation for 2.1d
Materials include diagnostic assessments with TEKS-aligned tasks or questions, including interactive item types with varying complexity levels.

The Math Journeys program contains resources for diagnostic assessment designed to measure students’ understanding of grade-level mathematical concepts and skills through TEKS-aligned tasks. The materials provide interactive assessment activities with different levels of complexity that require students to apply mathematical reasoning and problem-solving skills. In addition, the materials include numeric response tasks that help students understand place value concepts and computation strategies through real-world applications.

The Math Journeys grade K program contains diagnostic and end-of-journey assessments with TEKS-aligned tasks and varying levels of complexity. For example, questions progress from factual knowledge to procedural knowledge to problem-solving tasks. In another instance, the digital Journey Test A0 includes assessment items aligned with the TEKS, and the “Muestra de informe de prueba” shows journey levels connected to TEKS and student performance data. The materials also help educators use assessment reports to make instructional decisions and determine the support students may need to improve and advance to the next journey.

Evaluation for 2.1e
Materials include a variety of formative assessments with TEKS-aligned tasks or questions, including interactive item types with varying complexity levels.

The Math Journeys grade K program provides a variety of formative assessments with TEKS-aligned tasks and questions, including interactive item types with varying levels of complexity. The materials contain assessment items that measure students’ understanding of addition and subtraction concepts through equations, visuals, and word problems. Students solve missing number equations and simple story problems using pictures and mathematical reasoning.

The materials also contain “Hojas de registro” for each journey at different levels of complexity. Educators use these formative assessment activities to support or extend students’ learning based on individual needs. For example, in journey B2, session 17, educators assign the “Hojas de registro de apoyo” to students who need extra support and the “Hojas de registro de ampliación” to students who perform above level, preparing them for the next journey. These resources help educators differentiate instruction and respond to student performance through formative assessment tasks at varying levels of complexity.

Evaluation for 2.2a
Instructional assessments include scoring information and guidance for interpreting student performance, including rationale for each correct and incorrect response.

Using features such as performance levels, score ranges, and detailed descriptions of student understanding to help educators identify strengths, misconceptions, and instructional needs, the Guía de puntuación a nivel de evaluación of the Math Journeys program provides scoring information and guidance for interpreting student performance. The materials also include the “Muestra de informe de prueba de nivel,” which explains how educators can analyze assessment results to guide instruction.

The Guía de implementación for the “Prueba del final de journey” assessment of the Math Journeys grade K program contains scoring information and guidance for interpreting student performance. For example, printables like the Guía formativa for the “Prueba del final de journey: solucionario o clave de respuestas” provide answer keys, scoring guidance, and rationales for correct and incorrect responses. The materials also include levels of achievement, possible misconceptions, related TEKS, and additional support suggestions to help educators interpret assessment results and make instructional decisions.

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 Math Journeys program explains how to use the included tasks and activities to respond to trends in student performance on assessments through grouping recommendations and instructional pathways. For example, the “Ubicación en trayectorias” report helps educators analyze student data, group students based on learning needs, and select targeted instructional tasks and activities for focused instruction.

The Math Journeys grade K program helps educators use resources, activities, and strategies based on trends in student performance on assessments. The Guía de implementación for the “Prueba del final de journey” assessment and the Guía formativa for the “Prueba del final de journey: solucionario o clave de respuestas” provide educators with guidance beyond just answer keys. The materials highlight possible misconceptions, related TEKS, areas that need reinforcement, and suggestions for extra support. These features help educators identify instructional needs and choose targeted activities to support student learning.

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 Math Journeys grade K program includes tools for educators to track students’ progress and growth through the “Classroom Manager” platform and “Student Progress” reports. The Guía de implementación for the “Prueba del final de journey” assessment explains how educators can access assessment results, review student performance data, interpret levels of mastery, and use the information to make instructional decisions and provide differentiated support. However, the materials do not contain tools for students to independently track or monitor their own progress and growth.

The Math Journeys grade K program provides tools for students to track their own progress through digital practice activities on the Atlas Math platform. Students can view their scores after completing an activity within the applets. However, the scores can no longer be seen after the activity is finished, which limits students’ ability to independently monitor and track their progress and growth over time.

Evaluation for 2.2d
If designed to be static, materials provide prompts and guidance to support educators in conducting frequent checks for understanding at key points throughout each lesson or activity.

The Math Journeys grade K program provides prompts and guidance to help educators conduct frequent checks for understanding at key points during each lesson or activity. Educator prompts and questioning opportunities help educators monitor student thinking and understanding during instruction. For example, in the lesson “El medidor de cubos,” educators are prompted to ask questions such as “¿Crees que tu herramienta de medida encaja mejor así o de esta otra manera junto al objeto?” and “¿Podrías explicar cómo estás utilizando tu herramienta de cubitos para medir la longitud?” to assess student understanding during the activity. In addition, development activity 2 helps students check each other’s answers and collaboratively identify mistakes or misconceptions. Frequent opportunities for formative assessment are also embedded throughout the lessons.

The Math Journeys grade K program contains prompts and guidance to help educators conduct frequent checks for understanding at key points throughout each lesson. Targeted questions and observation opportunities help educators identify misconceptions, analyze student performance, observe different problem-solving strategies, and determine whether the learning objective has been met. For example, in journey A0, session 9, the “Desenlace” prompts and guidance help educators monitor student understanding throughout the lesson.

Evaluation for 2.2e
If designed to be adaptive, materials provide frequent checks for understanding at key points throughout each lesson or activity.

The Math Journeys grade K program provides frequent checks for understanding at key points throughout each lesson or activity through interactive adaptive activities on the Atlas Math platform. Applets and math activities with milestone trackers allow students to monitor their progress and receive immediate feedback after submitting their responses. Correct answers are marked with a green check, while incorrect answers are identified with a question mark, supporting ongoing formative assessment and helping students check their understanding during the activity.

Targeted questions and observation opportunities allow educators to monitor student understanding and make instructional adjustments as needed throughout the lesson. For example, in journey A0, session 9, educators have multiple opportunities to conduct checks for understanding during instruction.

Evaluation for 3.1a
Materials include explicit educator guidance for lessons or activities scaffolded for students who have not yet reached proficiency in prerequisite or grade-level concepts and skills.

The Math Journeys grade K program provides educators with explicit guidance to scaffold lessons and activities for students who have not yet reached proficiency in prerequisite or grade-level concepts and skills. The supports help educators provide additional resources, targeted assistance, and scaffolded learning opportunities to strengthen students’ understanding of foundational concepts. For example, in the activity “Escribimos la secuencia numérica hasta el 20,” the “Apoyo” section guides educators to provide “tarjetas 0–50” to students who need support with number formation and sequencing. This scaffolded support helps students access the activity and develop an understanding of numbers in sequence.

Additionally, the supports help educators provide simplified representations and targeted practice to strengthen students’ understanding of foundational concepts. For example, in lesson A1, session 15, the “Hoja de actividad de apoyo” contains scaffolded activities designed to help students reach proficiency. The student “Cuaderno” (notebook) includes activities in which students count objects from mixed groups, while the support logsheet provides smaller quantities with the objects separated. These scaffolded supports help students develop counting skills and accurately represent quantities while enabling them to access grade-level learning.

Evaluation for 3.1b
Materials include explicit educator guidance for language supports, including pre-teaching and embedded supports for developing academic vocabulary and unfamiliar references in text.

The Math Journeys grade K program explicitly guides educators on language supports to help students acquire and use academic vocabulary as well as understand unfamiliar concepts. Lesson activities contain pre-teaching opportunities and embedded supports for developing vocabulary. For example, in the lesson “Estimamos cuántos niños y niñas caben en un cuadrado de 1 m de lado,” educators are directed to discuss the attributes of a square, connect the concept to prior learning in “Espacio y forma,” and use questioning prompts before students start the activity. The materials also include visual models, hands-on activities, discussion prompts, and guidance for emergent bilingual (EB) students that reinforce academic vocabulary and mathematical reasoning throughout the lesson.

The Math Journeys “A0 Language Banks and Redirections” explicitly guides educators on pre-teaching and embedded language supports that develop academic vocabulary and address unfamiliar references in the text. The language support routines provide educators with specific guidance for introducing and reinforcing mathematical language through modeling, repetition, gestures, visuals, manipulatives, and sentence structures. For example, routine 6, “Unfamiliar Reference Quick Bridge,” directs educators to pre-teach the context of an unfamiliar song, story, game, or object before beginning the math by displaying an image, real object, or brief clip; explaining the reference in one sentence; and having students repeat key vocabulary. The lesson-by-lesson guidance identifies specific unfamiliar references and provides an explicit bridge for each. For example, before Math Journeys lesson A0.7, educators introduce the unfamiliar musical hoops game by showing the hoops, explaining the rule, and allowing students to complete a practice round before starting the lesson. These supports explicitly guide educators on developing academic language while ensuring that unfamiliar references do not prevent students from accessing Math Journeys lesson content.

Evaluation for 3.1c
Materials include explicit educator guidance for enrichment and extension activities for students who have demonstrated proficiency in grade-level and above grade-level content and skills.

The Math Journeys A0 Enrichment and Extension Guide explicitly guides educators on how to identify students who have demonstrated proficiency as well as provide appropriate enrichment and extension opportunities. The guide identifies three observable indicators for determining when a student is ready for extension, including completing the core task with correct reasoning and time remaining, accurately completing the standard logsheet while justifying responses, and demonstrating sustained proficiency across three consecutive sessions. The guide also clearly explains how to facilitate the extension tips by identifying the purpose of each task, the student’s expected response, and specific evidence that shows mastery. For example, in A0.2, students extend their learning by working with a new range of quantities (three, four, and five). This requires them to recount, compare, and match each quantity to its numeral, and to justify the order rather than relying on the previously modeled sequence. When a student is proficient for three consecutive sessions, the guide directs the educator to administer the end-of-journey test early. A score above 75 percent allows students to move on to the next journey, where they continue learning with more advanced content and skills.

Evaluation for 3.1d
Digital materials include accommodations, including text-to-speech, content and language supports, and calculators that educators can enable or disable to support individual students.

The Math Journeys Spanish program does not provide digital accommodations to support individual students’ needs. The digital materials do not include text-to-speech, content and language supports, or calculator features that educators can enable or disable for individual students. As a result, the materials do not contain the embedded supports for digital accessibility required by this indicator.

Evaluation for 3.1e
Materials include educator guidance on offering options and supports for students to demonstrate understanding of mathematical concepts in various ways, such as perform, express, and represent.

The Math Journeys grade K program guides educators on how to offer options and supports for students to show understanding of mathematical concepts in various ways, such as by performing, expressing, and representing mathematical thinking. Students have opportunities to demonstrate learning through movement, verbal discussion, physical models, and symbolic representations. For example, in “Representamos la canción con el cuerpo,” students act out a subtraction situation using their bodies and bottles, verbally explain what happens as bottles fall, and connect the experience to subtraction expressions and equations. The materials also guide educators to support students as they represent their thinking through songs, physical actions, manipulatives, oral responses, and written equations.

Students have opportunities to show learning through stories, manipulatives, measurement activities, verbal discussions, and visual representations. For example, in lesson A0.9, students begin by listening to a story to count, review length, and compare the heights of towers. Next, they participate in hands-on activities using number cards with symbols, cubes, and objects to measure. Finally, students apply their learning by measuring objects on an activity page using visual representations. The materials help them show mathematical understanding through multiple formats and instructional experiences.

Evaluation for 3.2a
Materials include explicit (direct) prompts and guidance for educators to build knowledge by activating prior knowledge, anchoring big ideas, and highlighting and connecting key patterns, features, and relationships through multiple means of representation.

The Math Journeys grade K program provides educators with explicit prompts and guidance to build knowledge by activating prior knowledge; anchoring big ideas; and highlighting and connecting key patterns, features, and relationships through multiple means of representation. Students have opportunities to connect mathematical concepts through oral discussion, visual representations, story contexts, and concrete models. For example, in “El medidor de cubos,” students observe visual representations, listen to the story being narrated, and respond to educator-guided questions on comparing height, length, and size. The materials also direct educators to pause throughout the story to discuss key vocabulary and relationships such as más alto, más bajo, and igual, helping students make connections among mathematical ideas through multiple representations.

Students have opportunities to connect counting concepts through movement, concrete models, visual representations, and oral discussion. For example, in lesson A2-1, the warm-up activity activates prior knowledge of counting by tens as students use arm movements to represent number sequences while counting forward and backward between 20 and 50. Next, in development activity 1 (“Nudo: actividad 1”), students use number cards to identify the ones digit and skip count by tens. Then, students begin with a different number card and count backward by tens to explore number patterns. As a result, students recognize the relationship that only the tens digit changes when counting forward or backward by ten, helping them make connections among number patterns through multiple representations.

Evaluation for 3.2b
If designed to be static, materials include educator guidance for effective lesson delivery and facilitation using various instructional approaches.

The Math Journeys grade K program guides educators on how to effectively deliver and facilitate lessons using various instructional approaches. Number sense and counting concepts are reinforced by whole-group instruction, collaborative games, songs, movement, oral discussion, visual supports, and independent participation. The materials also provide step-by-step facilitation guidance, questioning strategies, hands-on activities, and opportunities for student discourse through songs, gestures, games, and number identification tasks.

Multiple instructional approaches help students move from concrete to representational understanding while developing subtraction concepts. For example, in lesson B2-2, the warm-up activity is facilitated through whole-group instruction. The development activities incorporate hands-on learning experiences that transition from whole-group instruction to small-group collaboration and then to independent work. Students also receive guidance through the use of cubes, cards, magic pads, and visual representations to build mathematical understanding based on multiple instructional approaches.

Evaluation for 3.2c
Materials include multi-tiered intervention methods for various types of practice and structures and educator guidance to support effective implementation.

The Math Journeys grade K program provides multi-tiered intervention methods through a variety of instructional practices as well as teaching structures designed to support diverse learning needs. Across the lessons, educators have opportunities for guided, independent, and educator-supported practice using whole-group as well as individual teaching structures. Educators also receive guidance on implementation through questioning prompts, manipulatives, visual models, digital resources, support options, and extension opportunities. For example, grade K students participate in subitizing activities using fingers, cubes, ten frames, images, and applets while educators adjust quantities, pacing, and questioning based on student readiness and performance. In addition, independent recording tasks and scaffolded supports allow educators to monitor student understanding and provide differentiated intervention as needed.

Assessment data and instructional recommendations help educators identify student needs and select appropriate intervention supports. For example, the “Placement Test” report (“Prueba de nivel: muestra de informe”) provides educators with student performance data that they can use to make instructional decisions, reteach specific skills in whole-group settings, create intervention groups, or assign individualized learning pathways based on student needs. The materials help educators implement targeted interventions to address learning gaps and promote student growth.

Evaluation for 3.2d
Materials include enrichment and extension methods that support various forms of engagement, and guidance to support educators in effective implementation.

The Math Journeys grade K program provides enrichment and extension methods that support a variety of opportunities for student engagement throughout the lessons. The materials contain differentiated supports through the “Apoyo” and “Ampliación” sections embedded within instructional activities, allowing educators to extend learning based on student readiness and performance. The lessons also guide educators on effective implementation through questioning prompts, movement-based activities, partner discussions, visual models, number cards, and opportunities for independent practice. For example, students engage in counting, ordering, and identifying numbers through whole-group, partner, and individual activities, while extension tasks encourage students to apply mathematical reasoning with increasing complexity. In addition, scaffolded support and enrichment opportunities help educators differentiate instruction while maintaining engagement with grade-level mathematical concepts and skills.

Students have opportunities to extend their learning through hands-on activities, multiple problem-solving strategies, and challenging extension tasks. For example, in lesson A2-8, students engage with manipulatives such as an applet, a 20-bead string, and number cards to explore mathematical concepts. In addition, extension tips encourage students to demonstrate different strategies, and “Actividades de ampliación” provide more challenging activities for students who are ready to deepen their understanding.

Evaluation for 3.2e
Materials include prompts and guidance to support educators in providing timely feedback during lesson delivery.

The Math Journeys program contains prompts and guidance to support timely feedback while delivering grade K lessons such as “Estimar y comparar.” Educators are provided with questioning routines, discussion prompts, and opportunities for students to make predictions, explain their reasoning, and compare estimates with actual results throughout the lesson. For example, students formulate hypotheses about quantities, record their estimates, and discuss their thinking as educators monitor understanding and provide immediate feedback. Additionally, the lesson includes guidance statements that help educators facilitate mathematical discussions, connect concepts, and address student thinking during instruction. The materials encourage ongoing feedback through partner discussions, group conversations, estimation checks, and reflection activities that allow educators to respond to student understanding in real time.

Anticipated responses, misconceptions, and strategies for redirection help educators respond to student thinking and address misunderstandings during instruction. For example, the A0 Journey Language Bank (“A0 Banco de lenguaje y redirecciones”) includes a “Banco de respuestas previas, ideas erróneas y redirecciones” section that provides suggested feedback and ideas for redirection based on lesson content. In lesson A0.1, if a student is unable to connect a body representation to the corresponding number word, the materials guide educators to show the appropriate number of fingers and say aloud, “Esto es 2, ahora hay 2 flores.” The materials help educators provide immediate, targeted feedback that enables students to strengthen their number sense and mathematical understanding.

Evaluation for 3.3a
If designed to be static, materials include educator guidance on providing and incorporating linguistic accommodations for all 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 does not apply because the program is not designed to be static.

Evaluation for 3.3b
If designed to be adaptive, materials include embedded linguistic accommodations for all 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 to the program because it is not designed to be adaptive.

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

The “Documento complementario de ELPS a nivel de lección” of the Math Journeys program guides educators on using the materials in bilingual/ESL programs effectively. The materials include lesson-level language objectives, linguistic demands, expected oral and written production, and suggested educator supports aligned with the TEKS and ELPS. For example, the companion document for journey A1 guides educators on how to help students develop their listening, speaking, and writing skills through sentence stems, oral language supports, and instructional notes that enable educators to integrate language acquisition strategies during math instruction.

The Texas Bilingual/ESL Implementation Guide (“Guía de implementación para estudiantes bilingües”) and the “Journey A0 Addendum” (“Anexo de journey A0”) provide model-specific steps for implementation aligned with the mathematical content and language demands of each session. The materials also include differentiated support based on the type of bilingual or ESL program. For example, for transitional bilingual early-exit and late-exit programs, journey A0 supports bilingual instruction through visual models and predictable part-whole structures, and the materials recommend using the student’s home language to support comprehension of unfamiliar vocabulary before transitioning to mathematical language in English. Lesson A0.2, “Encontrar el número 4,” guides educators to preview comparison vocabulary in Spanish, requires numerical matching in English, and provides extended opportunities for partner discussion before students restate the sequence in English.

Evaluation for 3.3d
Materials include embedded guidance 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 Math Journeys grade K program contains embedded guidance to help EB students develop their academic vocabulary, increase comprehension, build background knowledge, and make cross-linguistic connections through oral and written discourse. The materials include academic vocabulary, discussions on estimation, collaborative conversations, and written representation activities that support students’ language development during math instruction. For example, in the lesson “Estimar y comparar,” students use vocabulary such as metro, estimación, más que, and menos que while making predictions, explaining their reasoning, comparing quantities, and recording their responses through drawings and numbers. The support section “Estudiantes bilingües emergentes” provides structured oral language prompts as well as opportunities for students to revise, clarify, and explain their mathematical thinking using comparison language during classroom discussions.

The materials include academic vocabulary, structured partner discussions, supports for EB students, and guiding questions that provide students with opportunities to explain their mathematical thinking orally as well as in writing. For example, in lesson A2.8, “Contamos con el collar de bolas,” students review and practice vocabulary such as entre, contar hacia adelante, contar hacia atrás, saltar, and colocar; discuss strategies for locating numbers using a 20-bead string as a model to represent numbers on a number line; and record their representations in their “Cuaderno.” The materials help students develop mathematical language and conceptual understanding through both oral and written discourse.

Evaluation for 3.3e
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 does not apply because the program is not designed for dual language immersion (DLI) programs.

Evaluation for 4.1a
Practice opportunities throughout learning pathways (including instructional assessments) require students to demonstrate depth of understanding aligned to the TEKS.

The Math Journeys grade K program provides opportunities for practice as well as instructional assessments throughout the broader learning pathway that require students to show a depth of understanding aligned with the TEKS. In journey B1, “Descomposición de números, y sumas y restas mediante conteo,” students engage in “Nudo: actividad 1—Investigamos cómo resolver un problema de matemáticas” and “Desenlace: llevamos a cabo una puesta en común,” where they solve a real-world problem involving toys with a total of 10 wheels; represent multiple solutions using drawings, manipulatives, and equations; and explain and justify their reasoning during partner as well as whole-group discussions. Students are encouraged to identify multiple combinations, model their thinking, and communicate their mathematical reasoning, providing opportunities for them to demonstrate a depth of understanding aligned with the TEKS. In addition, individualized digital activities associated with the broader learning pathway require students to independently apply lesson concepts and show their understanding. Student performance data from these activities is collected and reported through educator-accessible reports, including “Progreso de la semana” and “Resultados de la semana,” which provide information about student progress and performance based on the TEKS. Through these practice opportunities and instructional assessments, students demonstrate a depth of understanding aligned with the TEKS throughout the broader learning pathway.

The progression of activities in journey B2.1, “Sumamos 1 y 2,” allows students to learn and show their understanding of adding one and two through different strategies and representations. During the “Planteamiento,” students use a game board and number chart to identify the number that comes next and the number that comes after that when given a specific number, helping them represent the concepts of adding one and two. In “Nudo: actividad 1,” students use snap cubes to model addition, verbally explain their thinking, and write corresponding equations. In activity 2, students transition from using snap cubes to number cards to represent addition situations. In activity 3, students create mathematical representations of addition and record equations that match their models. Throughout the lesson, educators use guidance and prompts to facilitate discussions that encourage students to explain their reasoning and make connections among the representations, supporting a deeper understanding of adding one and two rather than simply identifying an answer.

Evaluation for 4.1b
Questions and tasks, including enrichment and extension materials, increase in rigor and complexity, leading to grade-level and above grade-level proficiency in the mathematics TEKS.

The Math Journeys grade K program includes questions and tasks that increase in rigor and complexity, leading to grade-level and above-grade-level proficiency in the mathematics TEKS. In journey B1, “El número 10 (parte 2),” students build on prior learning from earlier sessions in which they decomposed numbers and represented quantities in multiple ways. In “Nudo: actividad 1—Encontramos parejas de números que suman 10,” students work collaboratively to identify pairs of numbers that compose 10, organize the pairs systematically, and analyze relationships among the addends to determine whether all possible combinations have been found. The educator prompts students with questions such as “¿Creen que tenemos todas las parejas posibles? ¿Qué podríamos hacer para saberlo?” and “¿Ordenar las parejas de números podría ayudarnos?” These questions require students to move beyond finding answers and engage in mathematical reasoning about completeness, patterns, and relationships among numbers. Students are also asked to justify their reasoning and explain how organizing the pairs helps verify their solutions. In “Nudo: actividad 2—Presentamos ‘La mona,’” students apply their understanding of number pairs that sum up to 10 within a game context, requiring them to recall, identify, and use complementary pairs fluently. During “Hacemos una representación en una página en blanco” (“Desenlace”), students independently represent decompositions of 10 using drawings, numbers, and equations. An “Ampliación” activity encourages students to move from pictorial representations to more abstract and symbolic representations, including recording equations such as 3 + 7 = 10 and 0 + 10 = 10. Across the broader learning pathway, students progress from composing and decomposing numbers to analyzing patterns, justifying mathematical relationships, and representing solutions symbolically, increasing the rigor and complexity of the tasks and supporting both grade-level and above-grade-level proficiency in the mathematics TEKS.

Journey B2.11 provides differentiated activities that progressively increase the rigor and complexity of composing and decomposing numbers up to 10. In “Nudo: actividad 1—Descomponemos números menores que 10 como suma de dos números,” students use additive part-part-whole frames (cajitas aditivas) to represent equations such as 2 + 3 = 5. Students are then challenged to determine additional ways to decompose five. The activity includes multiple levels of complexity as students may identify one or more addition combinations, order number pairs that make five, and decompose 5 using subtraction equations, introducing subtraction as the inverse of addition. In activity 2, students use snap cubes alongside additive part-part-whole frames to model number compositions and decompositions. In activity 3, students increase their reasoning skills by using a handkerchief to cover one addend and represent the missing part on the additive part-part-whole frame without counting the snap cubes one by one. During “Desenlace,” the “Ampliación” activity further extends learning by asking students to decompose a number using zero and to identify six different ways to decompose a number. These activities provide students with opportunities to engage with increasingly complex tasks while extending their mathematical thinking beyond the core lesson expectations.

Evaluation for 4.2a
Materials demonstrate coherence across concepts horizontally within the grade level by connecting patterns, big ideas, and relationships.

The Math Journeys grade K program demonstrates coherence across concepts horizontally within the grade level by connecting patterns, big ideas, and relationships. In lesson A1.15, “Contaje resultativo,” the materials explicitly connect acoustic and cardinal counting by stating that “el conteo acústico es el prerrequisito para trabajar el conteo resultativo,” helping students understand how reciting a number sequence supports determining the quantity of objects in a set. In “Nudo: actividad 1—Comparamos cantidades con objetos del aula,” students apply counting to determine how many objects are in a collection. In “Nudo: actividad 2—Comparamos colecciones de objetos y decidimos cuál contiene más elementos,” students use one-to-one correspondence and comparison strategies to determine which collection contains more or fewer objects. The lesson further connects these concepts by introducing the comparison relationships represented by mayor que (>), menor que (<), and igual (=). Across the lesson, students connect counting, cardinality, comparison, and symbolic representations, demonstrating coherence across mathematical concepts within the grade level.

Journey B1.13, “El número 9 (parte 2),” shows coherence across concepts within the grade level by connecting manipulatives, representations, and the relationship between addition and subtraction. In “Nudo: actividad 1—Jugamos a encontrar la pareja de números que suman 9,” students receive a number card (such as three) and determine the missing number needed to make nine. Students first represent the quantities using snap cube towers placed over numerals on a mat displaying the numbers 0–9. The lesson then transitions to a different representation as students use number cards instead of snap cubes to model the same mathematical relationships. In activity 2, “Creamos frases matemáticas con el 9,” students use number cards and operation symbol cards (+/−) to create multiple addition and subtraction equations that equal nine. Through these activities, students make connections among concrete models, symbolic representations, and related addition and subtraction concepts, supporting a coherent understanding of number composition and decomposition across the grade level.

Evaluation for 4.2b
Materials demonstrate coherence vertically across concepts and grade bands, including connections from grade K–6, by connecting patterns, big ideas, and relationships.

The Math Journeys grade K program demonstrates coherence vertically across concepts and grade bands by connecting patterns, big ideas, and relationships. In the “Vista general de tramo—A: conteo y números,” the “Progresión de contenidos” section outlines how foundational concepts develop across the broader learning pathway, connecting students’ early experiences with recognizing, representing, and comparing quantities to later understandings of counting, number relationships, place value, and number composition and decomposition. The materials show how concepts introduced in earlier learning experiences are expanded upon and applied in subsequent journeys to support future addition and subtraction strategies. The “Contexto matemático” section further illustrates vertical coherence by connecting concrete counting models to increasingly sophisticated representations, including bead strings, number lines, and place-value models. The overview explains how these representations evolve across later journeys, helping students connect cardinality, counting, number decomposition, and place-value concepts over time. Through the documented progression of concepts, representations, and mathematical relationships, the materials demonstrate vertical coherence across concepts and grade bands.

Journey B2.6, “Suma y resta: saltando,” establishes vertical coherence by bridging students’ prior knowledge of jumping forward and backward on a number board to add and subtract with current grade-level content involving the use of a 20-bead string. The lesson also builds connections to future learning, where students use larger bead strings and represent addition and subtraction on number lines. During the “Planteamiento,” students jump forward and backward on a number board to solve addition and subtraction problems. In the “Nudo: actividad 1—Representamos la suma y la resta de dos números sobre el collar de 20,” students transition from using the number board to using a 20-bead string to model addition and subtraction. Students use two clothespins to locate numbers on the bead string and count beads forward or backward to determine sums and differences. They then label the numbers on paper to represent the 20-bead string, helping them connect concrete models to visual representations that support future work with bead strings and number lines in subsequent grade levels. Through these learning experiences, students build on previously learned concepts while developing foundational understanding to support future mathematical learning.

Evaluation for 4.2c
Materials demonstrate coherence across lessons or activities by connecting students’ prior knowledge of concepts and procedures to the mathematical concepts to be learned in the current grade level and future grade levels.

This guidance statement does not apply to the program because grade K does not have a preceding course with prior knowledge to connect to the current grade level as well as future grade levels.

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

The Math Journeys grade K program provides opportunities for students to develop and apply mathematical knowledge and skills through distributed practice over time. In lesson B1.15, “El número 10 (parte 2),” students revisit and apply number decomposition relationships developed throughout earlier sessions in journey B1. During “Nudo: actividad 1—Encontramos parejas de números que suman 10,” students use previously learned decompositions to identify, organize, and justify all pairs of numbers that sum to 10. Educators prompt students to consider, “¿Creen que tenemos todas las parejas posibles? ¿Qué podríamos hacer para saberlo?” and “¿Ordenar las parejas de números podría ayudarnos?” These questions require students to retrieve previously learned number relationships and apply them to determine whether all possible combinations have been found. In “Nudo: actividad 2—Presentamos ‘La mona,’” students continue applying these number relationships while playing a card game that requires identifying complementary pairs that total 10. The distributed practice extends to subsequent lessons, where students use these same decomposition relationships to solve new mathematical situations and verify solutions using ten frames. Through repeated opportunities to retrieve, apply, and extend previously learned concepts across multiple sessions, the materials support distributed practice over time.

Another opportunity for retrieval practice is provided in journey B1.9, “El número 8 (parte 1),” where students revisit and apply strategies and concepts introduced in earlier lessons throughout section B1. Students represent and decompose the number eight using familiar approaches, including counting and building towers with snap cubes, finding number pairs with number cards, creating pictorial representations, and writing equations. In “Nudo: actividad 1—Encontramos las combinaciones de dos torres mágicas,” students work in groups to determine how many combinations can be used to make eight, and then represent their solutions using cards or equations. These activities draw upon strategies previously used to compose and decompose the numbers five through seven in earlier sessions, allowing students to retrieve and apply prior learning while extending their understanding of number relationships. Through these repeated opportunities, students strengthen their mathematical understanding and fluency across the broader learning pathway.

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

The Math Journeys grade K program provides opportunities for interleaved practice with previously learned skills and concepts across the learning pathways. In the “Vista general de tramo—A: conteo y números,” the “Contexto matemático” and “Progresión de contenidos” sections describe how students progress from counting methods to increasingly flexible arithmetic strategies across the broader learning pathway. Students revisit and apply previously learned approaches, including bridging through 10, combining jumps in different directions, and optimizing jumps of 10 when solving related mathematical situations. Rather than practicing a single strategy in isolation, students draw on skills developed across multiple sessions and learning experiences, selecting and applying different approaches to solve problems efficiently. The learning progression highlights a shift from simple counting to strategic and flexible computation, requiring students to connect previously learned concepts and procedures throughout the general pathway. Using opportunities to revisit, apply, and integrate multiple strategies developed over time, students engage in interleaved practice with previously learned skills and concepts across the learning pathways.

Journey B1.13, “El número 9 (parte 2),” provides students with opportunities to apply multiple strategies introduced throughout section B1 while learning new content. Across the broader learning pathway, students compose and decompose numbers as well as solve addition and subtraction situations using manipulatives, number cards, part-part-whole frames, and number sentences. Rather than practicing each strategy in isolation, the lessons integrate previously learned approaches with new learning opportunities. In “Nudo: actividad 1,” students receive a number card, such as three, and determine the missing number needed to make nine. Students first represent the quantities by placing snap cube towers on numerals displayed on a mat containing the numbers 0–9. The activity then shifts to a different representation as students use number cards instead of snap cubes to model the same number relationships. These strategies were used previously with other numbers throughout section B1, allowing students to revisit and apply prior learning while extending their understanding of number composition and decomposition.

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

The Math Journeys grade K program provides opportunities for students to interpret, analyze, and evaluate models and representations of mathematical concepts and situations in B1.3, “Situaciones matemáticas.” During the “Planteamiento,” students interpret photographs by answering questions such as “¿Qué ven?,” “¿Qué pasó?,” “¿Cuántos hay arriba?,” “¿Cuántos hay abajo?,” and “¿Cuántos hay en total?” to describe and make sense of the mathematical situation represented in the images. In “Nudo: actividad 2,” students analyze the same situation using multiple representations, including photographs, manipulatives, and the cajita aditiva, connecting concrete models to a more abstract representation. The educator prompts students with questions such as “¿Qué pasó?,” “¿Cuántos bajaron?,” and “¿Cuántos quedan arriba?” as they model and explain their thinking. Students then evaluate mathematical representations by determining which equations accurately represent the situation, including 5 − 2 = 3, 5 = 2 + 3, and 5 − 3 = 2. In activity 3 and the “Desenlace,” students create additional situations and corresponding mathematical sentences, demonstrating their ability to interpret, analyze, and evaluate models and representations of mathematical concepts and situations.

The materials include questions and tasks that provide students with opportunities to interpret, analyze, and evaluate models and representations of mathematical concepts and situations. In journey B1.17, “Nudo: Development activity 1—Descomponemos el 10: investigamos cómo resolver un problema de matemáticas,” students view images of cars, scooters, and tricycles, and solve a problem involving a family that purchased toys with a total of 10 wheels. Students must determine which toys could have been purchased and interpret how the tools provided (including paper, ten frames, and tiles) can be used to represent the wheels and support their problem-solving. Students use manipulatives and pictorial representations to explore possible solutions and discuss their reasoning with peers. The Teacher Guide contains questions such as “¿Qué tipos de juguetes compró la familia?,” “¿Cuántos juguetes de cada tipo compraron?,” and “En total, ¿cuántos juguetes compró la familia?” to help students interpret representations and explain their thinking. Activity 2, “Encontramos más soluciones del problema,” encourages students to identify additional solutions, prompting them to analyze different combinations of wheels that total 10. The guide further supports this process with questions such as “¿Qué herramienta—marco de diez, cubos o dibujo—te ayudó a resolver el problema y por qué la elegiste?” and “¿Puedes escribir una oración matemática para mostrar cuántas ruedas hay?” After identifying multiple solutions, students determine a maximum of five and a minimum of three toys the family could have purchased and evaluate which solutions satisfy those mathematical conditions. These opportunities require students to interpret representations, analyze possible solutions, and evaluate the reasonableness of their results.

Evaluation for 5.1b
Questions and tasks provide opportunities for students to create concrete models and pictorial representations to represent mathematical situations.

The Math Journeys grade K program provides students with opportunities to create concrete models and pictorial representations of mathematical situations in B1.3, “Situaciones matemáticas.” During “Nudo: actividad 2,” students use bear counters and a construction piece to model situations represented in photographs of children moving on and off a platform. Students physically recreate the situations, represent changes in quantity, and use the manipulatives to determine unknown amounts. The educator prompts students with questions such as “¿Qué pasó?,” “¿Cuántos bajaron?,” and “¿Cuántos quedan arriba?” as they build their models. In activity 3, students create their own mathematical situations using the manipulatives and additive frame, recording as many corresponding mathematical sentences as possible. During the “Desenlace,” students complete and create representations in the additive frame and connect those representations to equations such as 5 − 1 = 4, 5 − 4 = 1, and 4 + 1 = 5. These activities require students to create both concrete models and pictorial representations of mathematical situations.

Similarly, the materials include questions and tasks that provide opportunities for students to create concrete models and pictorial representations to represent mathematical situations. In journey B1.13, “Nudo: Development activity 1—El número 9 (parte 2): jugamos a encontrar la pareja de números que suman 9,” students write the numbers zero to nine on a strip of paper, draw a number card, and use cubes to represent the selected number and determine the missing number needed to make nine. This activity provides opportunities for students to create and use concrete models as they represent different decompositions of nine with snap cubes. During the “Desenlace,” students transition from concrete to pictorial representations by drawing the cube towers they created and writing equations that represent the decomposition of nine. These opportunities allow students to create, connect, and explain both concrete models and pictorial representations to represent mathematical situations and relationships.

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

The Math Journeys grade K program provides students with opportunities to apply conceptual understanding to new problem situations and contexts in B1.15, “Investigamos cómo resolver un problema de matemáticas.” Students encounter a real-world problem involving toy cars, scooters, and tricycles with a total of 10 wheels and must determine possible combinations the family could have purchased. Rather than following a prescribed procedure, students apply the previously learned concepts of counting, composing and decomposing numbers, and combinations that make 10 to generate and justify solutions. In activity 2, students extend their reasoning by finding and representing additional combinations using drawings, manipulatives, ten frame structures, and mathematical expressions. The lesson encourages students to determine whether all possible solutions have been found and discuss the minimum and maximum number of toys that could be purchased. During the “Desenlace,” students share and compare solutions with classmates, demonstrating their application of conceptual understanding in a new mathematical context.

The materials include questions and tasks that provide students with opportunities to apply conceptual understanding to new problem situations and contexts. In journey B1.14, “Nudo: Development activity 1—El número 10 (parte 1): preparamos el espacio para jugar a los bolos,” students apply their understanding of decomposition in a new context beyond the cubes, number cards, and counting activities used in previous lessons. Working in groups, students explore and test different arrangements of 10 bottles or cans to use as bowling pins and determine which arrangement allows them to knock down the most pins. As they organize the bottles, they create groups that compose 10, applying previously learned concepts in a hands-on, real-world situation. Students also mark a throwing line 10 feet away, providing an additional opportunity to count to 10 in a meaningful context. In activity 2, “Jugamos al juego de los bolos,” students use ten frame representations to record the pins that were knocked down and count the total. These opportunities require students to transfer and apply their conceptual understanding of counting, composing numbers, and representing quantities to new problem situations and real-world contexts.

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

The Math Journeys grade K program contains tasks designed to help students build the automaticity and fluency needed to complete grade-level mathematical tasks. In journey A2.2, “Conteo acústico hacia adelante y hacia atrás (1–100),” students engage in repeated practice activities that develop fluency with counting and number relationships. During the “Planteamiento,” students recite number sequences forward by ones from 20 to 100 and forward by tens from 10 to 100 while incorporating movement. In the “Nudo: actividad 1,” students use number cards to identify the next and previous number for values between 20 and 100, strengthening automatic recall of number sequences. In activity 2, students recite number sequences backward by ones and tens, providing additional practice with counting patterns. In activity 3, students order number cards from least to greatest and greatest to least, reinforcing number order and relationships. During the “Desenlace,” students complete missing-number sequences and count by tens, extending opportunities for practice and application. Through repeated counting, sequencing, and ordering activities, students develop automaticity and fluency with number patterns and counting skills that support future mathematical learning.

The materials provide tasks designed to build the automaticity and fluency needed to complete grade-level mathematical tasks. In journey B1.13, “Nudo: Development activity 1—El número 9 (parte 2): jugamos a encontrar la pareja de números que suman 9,” students write the numbers zero to nine on a strip of paper, draw a number card, and use cubes to determine the missing number needed to make nine. Through repeated rounds of identifying number pairs that compose nine, students develop automaticity and fluency with number combinations. Students may initially use cubes and then rely on number cards as their understanding becomes more efficient. In activity 2, “Creamos frases matemáticas con el 9,” students work collaboratively to create addition and subtraction equations using number and operation cards. By generating equations such as 4 + 5 = 9 and 9 − 5 = 4, students repeatedly apply relationships among numbers and operations, strengthening their fluency with composing and decomposing numbers. These opportunities ensure repeated practice with number combinations and equations, supporting the development of automaticity and fluency in addition and subtraction within 10.

Evaluation for 5.2b
Materials provide opportunities for students to practice the application of efficient, flexible, and accurate mathematical procedures throughout learning pathways.

The Math Journeys grade K program provides students with opportunities to practice applying efficient, flexible, and accurate mathematical procedures throughout the learning pathways. In journey B1.15, “El número 10 (parte 2),” students apply multiple strategies to identify and represent pairs of numbers that sum to 10. During the “Nudo: actividad 1,” students use number cards to find combinations that make 10 and discuss strategies to determine whether all possible pairs have been identified. The educator prompts students with questions such as “¿Creen que tenemos todas las parejas posibles? ¿Qué podríamos hacer para saberlo?” and “¿Ordenar las parejas de números podría ayudarnos?” to encourage students to organize the pairs systematically and justify their reasoning. In activity 3, students participate in a memory game that requires them to recognize number combinations that equal 10 and apply efficient strategies to identify matching pairs. During the “Desenlace,” students create representations of the combinations they have found using drawings, equations, and other mathematical models. Through these activities, students practice selecting, applying, and explaining mathematical procedures while demonstrating flexibility and accuracy in composing numbers that make 10.

The materials provide students with opportunities to practice applying efficient, flexible, and accurate mathematical procedures throughout the learning pathways. In journey B1.8, “Nudo: Development activity 1—El número 7 (parte 2): representamos nuestro puntaje con cubitos y una frase matemática,” students use data from a previous activity to represent how many hoops an individual landed over a cone and how many the individual missed. Students use multiple strategies and tools to decompose seven, such as snap cubes, drawings, and mathematical equations like 2 + 5 = 7, demonstrating the same mathematical relationship through different representations. The educator prompts students with questions such as “¿Puedes mostrarme cómo tus cubitos coinciden con tu frase matemática?” and “¿Cómo utilizaste los números para mostrar las diferentes partes que forman 7?” to encourage them to explain and compare their approaches. In activity 2, “Buscamos parejas de cartas que suman 7 y las ordenamos,” students work collaboratively to identify pairs of number cards that compose seven and then organize the pairs in a systematic order. Through educator-facilitated discussions, students compare ordering strategies and analyze their effectiveness. Students are guided to recognize that arranging the pairs in order is an efficient way to determine whether all decompositions of seven have been identified. These opportunities help students apply efficient, flexible, and accurate mathematical procedures while justifying their reasoning and refining their problem-solving strategies.

Evaluation for 5.2c
Materials provide opportunities for students to evaluate mathematical representations, models, strategies, and solutions for efficiency, flexibility, and accuracy throughout learning pathways.

The Math Journeys grade K program provides students with opportunities to evaluate mathematical representations, models, strategies, and solutions for efficiency, flexibility, and accuracy throughout the learning pathways. In journey B1.8, “El número 7 (parte 2),” students represent decompositions of seven using cubes, drawings, score tables, and number sentences. During the “Nudo: actividad 1,” students model their scores from a game using connecting cubes and record corresponding mathematical expressions. In activity 2, students identify pairs of numbers that sum up to seven and discuss whether they have found all possible combinations. The educator prompts students with questions such as “¿Creen que las tienen todas?” and “¿Ordenarlas podría ayudarnos?” to encourage them to evaluate the effectiveness of organizing number pairs as a strategy. Students then reflect on the process used to order the cards and justify how organizing the pairs helps verify that all decompositions of seven have been identified. During the “Desenlace,” students create their own representations of the combinations that make seven and share their solutions with their classmates. Through these activities, students evaluate mathematical representations and strategies for accuracy and efficiency while developing an understanding of number relationships.

The materials provide students with opportunities to evaluate mathematical representations, models, strategies, and solutions for efficiency, flexibility, and accuracy throughout the learning process. In journey B2.5, “Nudo: Development activity 2—Resta: conteo hacia atrás: restamos mediante situaciones de cambio decreciente,” students solve subtraction situations by representing a quantity with snap cubes, covering the cubes with a handkerchief, and removing some cubes. For example, students cover seven cubes, remove two cubes, and determine how many cubes remain under the handkerchief. As students solve the problem, they may use different strategies such as counting back, counting on, or reasoning about the quantities, providing opportunities to develop flexibility while finding accurate and efficient solutions. The educator prompts students with questions that encourage them to explain and compare their thinking and solutions. In activity 3, “Comparamos torres de cubitos,” students compare towers of 12 and seven snap cubes and determine how much taller one tower is than the other. Students evaluate and apply different strategies to solve the problem, such as using a missing-addend equation, 7 + ? = 12, or representing the situation as a subtraction problem, 12 − 7 = ?. By discussing and comparing their solutions, students consider the efficiency, flexibility, and accuracy of different approaches while justifying their mathematical reasoning. These opportunities help them evaluate mathematical representations, models, strategies, and solutions throughout the learning process.

Evaluation for 5.2d
Materials contain guidance to support students in selecting increasingly efficient approaches to solve mathematics problems.

The Math Journeys grade K program contains guidance to help students select increasingly efficient approaches to solve mathematical problems. In journey A2.8, “Contamos con el collar de bolas I,” students use a 20-bead string to represent and locate numbers from one to 20. During the “Nudo: actividad 1,” students place a clothespin on the bead string to identify a given number and discuss strategies for locating numbers efficiently. The educator prompts students with questions such as “¿Desde qué punto de referencia empezarías a contar para colocar este número y por qué lo elegirías?” and “¿Cómo te ayuda saber dónde están el cinco, el 10 y el 15 para encontrar otros números?” to encourage them to use benchmark numbers and the structure of the bead string, rather than counting each bead individually. The materials also state that students should use numbers close to complete tens because these numbers help students use reference points within the bead string structure. During the “Desenlace,” the materials explicitly note that “Esta actividad no permite al alumnado contar las bolas de una en una; así les promueve que las cuenten utilizando el patrón cromático,” guiding students toward a more efficient counting strategy. Through these supports, students develop increasingly efficient approaches for locating and representing numbers.

The materials contain guidance to help students select increasingly efficient approaches to solve math problems. In journey A1.11, “Nudo: Development activity 2—Agrupar objetos de 10 a 19: hacemos paquetes de 10 elementos,” students create groups of 10 pencils or craft sticks and secure each group with a rubber band. In activity 3, “Representamos cantidades con material,” students use these groups to represent teen numbers such as 12, 15, and 18 by showing one group of 10 and the remaining ones. With guidance from educators, students are encouraged to use a more efficient counting strategy by beginning with the group of 10 and counting on, rather than recounting all objects from one. As students represent and discuss quantities, they develop an understanding of the structure of teen numbers as “10 and some more.” The educator prompts students with questions such as “¿Observan cómo podemos usar nuestro grupo de 10 para ayudarnos a contar números como 12, 15 o 18?” and “¿Pueden pensar en otra manera de representar el número 14 usando decenas?” to help them analyze number relationships and recognize efficient counting strategies. Additional supports in the Emergent Bilingual Guide provide differentiated sentence stems and prompts that encourage students to describe quantities using tens and ones, progressing from identifying groups to explaining generalizations about teen numbers. These opportunities help students select increasingly efficient approaches for representing, counting, and reasoning about numbers from 10 to 20.

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

The Math Journeys grade K program explicitly states how the conceptual and procedural emphasis of the TEKS is addressed in the “Vista general de tramo—A: conteo y números.” The overview identifies the conceptual emphasis by describing how students develop an understanding of number relationships, quantity, place value, and multiple representations. For example, students will “identificar y comparar números representados con cantidades en el rango 1–10, comprendiendo las relaciones entre su numeral y cantidad” and “trabajar el valor posicional de las cifras.” The overview also identifies the procedural emphasis by outlining the skills students will practice throughout the broader learning pathway, such as “practicar la cantinela de identificar números en el rango 1–10”; identifying, comparing, and ordering numbers; and representing numbers using different models. Through the “Vista general de tramo—A: conteo y números,” the Math Journeys grade K program clearly communicates both the conceptual understanding and procedural skills addressed within the TEKS.

The materials clarify how the conceptual and procedural emphases of the TEKS are addressed. In journey B2.4, “Nudo: Development activity 1—Suma: conteo hacia adelante II: sumamos mediante situaciones de cambio creciente,” students view an image of snap cubes representing a tower of 10 and two additional cubes and determine the total quantity. After identifying the quantity, students observe three more cubes being added and connect the representation to a mathematical equation. This activity develops conceptual understanding of addition as a joining or “adding to” situation while introducing procedures for adding when the first addend is greater than 10. In activity 2, “Sumamos usando cubitos,” students count and cover 14 snap cubes with a handkerchief, add three more cubes, and determine the total number of cubes. The handkerchief prevents students from recounting all the cubes one by one and instead encourages them to view the hidden 14 cubes as a single quantity and use the counting on strategy. The educator prompts students with questions such as “¿Cómo se relacionan los 14 cubitos escondidos, los tres cubitos que puedes ver y el total?” and “¿Piensas en los 14 cubitos escondidos como cubitos individuales o como un solo grupo? ¿Por qué?” to help them connect their conceptual understanding of quantity with the procedural strategy of counting on. These opportunities explicitly link the conceptual understanding of addition as combining quantities with efficient procedures for solving addition problems involving teen numbers.

Evaluation for 5.3b
Questions and tasks provide opportunities for students to use concrete models, pictorial representations, and abstract models as required by the TEKS.

The questions and tasks in the Math Journeys grade K program provide students with opportunities to use concrete models, pictorial representations, and abstract models as required by the TEKS. In journey B1.17, “Descomponemos el 10,” students solve a problem involving toys with a total of 10 wheels by using multiple representations. During the “Nudo: actividad 1,” students use concrete models such as ten frames (hueveras de 10), counters, chips, cubes, and bottle caps to represent different combinations of toys and verify that the total number of wheels equals 10. The materials provide examples of using the ten frame to model combinations such as 2 + 2 + 2 + 2 + 2 = 10 and 2 + 2 + 2 + 4 = 10. Students also create pictorial representations by drawing diagrams and sketches to model possible solutions. Students may use “dibujos o esquemas” to represent their thinking. As students identify solutions, they transition to abstract models by recording mathematical expressions and equations representing the combinations they found. During the “Desenlace,” students share and represent their solutions using both verbal explanations and mathematical equations. Through these activities, students use concrete models, pictorial representations, and abstract representations to develop an understanding of composing and decomposing 10.

Similarly, the materials contain questions and tasks that provide students with opportunities to use concrete models, pictorial representations, and abstract models as required by the TEKS. In journey B1.12, “El número 9 (parte 1),” students engage in a sequence of activities centered on a situational problem involving a bus with nine seats in which they determine how many seats are occupied and how many are empty. The lesson begins with a pictorial representation of the bus as students listen to the story and respond to guiding questions that reinforce the decomposition of nine. In “Nudo: Development activity 2—Escenificamos un autobús de 9 plazas,” the educator creates a nine-seat bus in the classroom, and students act out the story as passengers getting on and off the bus. Through this concrete experience, students represent different combinations of occupied and empty seats while the educator records the corresponding pairs of numbers that compose nine. This activity supports the transition from concrete experiences to representational models. In activity 3, “Apuntamos de qué maneras podemos llenar el autobús,” students use snap cubes and a resource sheet displaying nine cubes and a recording table to model and document the combinations they find. Students then connect these concrete representations to abstract ones by recording number pairs and equations that total nine. During the “Desenlace,” students use pictorial representations of the bus activity and connect them to abstract representations of decomposing nine. These opportunities help students use and connect concrete models, pictorial representations, and abstract mathematical representations to develop a conceptual understanding of number relationships.

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

The Math Journeys grade K program helps students connect concrete, representational, and abstract models in B1.3, “Situaciones matemáticas.” Students first use photographs and real-world situations involving children getting on and off a platform to interpret the context. They then represent the situation concretely using bears and a construction piece, allowing them to model the quantities and actions described in the story. Next, students connect these concrete models to the cajita aditiva (part-part-whole frame), which the materials describe as a more abstract representation of the same situation. Finally, students write and interpret symbolic equations such as 5 − 2 = 3, 2 + 3 = 5, and 5 − 3 = 2, explaining how the numbers and operations correspond to the context, the manipulatives, and the additive frame. Through these connections, the materials help students move from concrete and representational models to abstract mathematical notation as required by the TEKS.

The materials contain supports to help students connect, create, define, and explain concrete and representational models as well as abstract concepts, as required by the TEKS. In journey B2.4, “Suma: conteo hacia adelante II,” the educator guide provides questions, discussions, and instructional supports that help students move from concrete models to pictorial representations and abstract mathematical concepts. In “Nudo: Development activity 1—Sumamos mediante situaciones de cambio creciente,” students view an image of snap cubes representing a tower of 10 and two additional cubes and determine the quantity shown. The image then displays three more cubes being added and connects the model to a mathematical equation, helping students link visual representations to abstract notation. The EB supports provide differentiated sentence frames, such as “Veo ___ cubitos. Agrego ___ más” to help students describe and explain the mathematical actions represented in the model. In activity 2, “Sumamos usando cubitos,” students count and cover 14 snap cubes with a handkerchief, add three more cubes, and determine the total number of cubes. Rather than recounting all the cubes individually, students are encouraged to view the hidden 14 cubes as a single quantity and connect that quantity to the additional three cubes. The educator prompts students with questions such as “¿Cómo se relacionan los 14 cubitos escondidos, los tres cubitos que puedes ver y el total?” and “¿Piensas en los 14 cubitos escondidos como cubitos individuales o como un solo grupo? ¿Por qué?” to help them explain the relationship between the concrete model and the abstract addition process. These supports help students connect, create, define, and explain concrete and representational models while developing an understanding of abstract mathematical concepts and procedures.

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

The Math Journeys grade K program provides opportunities for students to develop academic mathematical language using visuals, manipulatives, and other language development strategies. In the “Vista general de tramo—A: conteo y números,” the materials include a dedicated vocabulary section that introduces mathematical terms such as número, numeral, cifra, cantidad, comparar, ordenar, and contar. The overview also incorporates visual representations such as collections of objects, finger patterns, bead strings, number paths, and multiple number representations to support students’ understanding and use of mathematical language. Throughout the broader learning pathway, students discuss quantities, identify and compare numbers, represent numbers using different models, and describe relationships between numerals and quantities. The materials provide opportunities for students to engage in mathematical conversations using visuals and manipulatives while developing vocabulary related to counting, comparing, ordering, and representing numbers. Through these supports, students develop academic mathematical language aligned with the TEKS.

The materials provide opportunities for students to develop academic mathematical language by using visuals, manipulatives, and other language development strategies. In journey A1.8, “Estimar y comparar,” lessons begin with hands-on experiences, visual supports, and guiding questions that introduce and reinforce the terms estimar and comparar. The educator introduces the concept of estimation by showing students a cup containing snap cubes and asking, “¿Cuántos cubitos creen que necesitamos para llenar el vaso?” After students share their predictions, the educator facilitates discussion using language involving comparison through questions such as “¿El resultado es más grande o más pequeño de lo que te habías imaginado?” and “¿Qué diferencia hay? Es decir, ¿cuántos cubitos más o menos habías dicho en tu hipótesis?” These discussions encourage students to use mathematical vocabulary to describe, compare, and justify their thinking. Additional supports for EB students are provided through the “critique, correct, clarify” routine, which prompts students to explain their estimates, provide their reasoning, and use terms of comparison such as más que, menos que, and cantidad igual. Students then reflect on how their estimates compare to the actual quantity and discuss what they would change after counting the snap cubes. These opportunities help students develop academic mathematical language by connecting vocabulary to concrete experiences, visual representations, and mathematical discourse.

Evaluation for 5.4b
Materials include embedded educator guidance to scaffold, support, and extend students’ use of academic mathematical vocabulary in context when communicating with peers and educators.

The Math Journeys grade K program provides educators with embedded guidance to scaffold, support, and extend students’ use of academic mathematical vocabulary in context when communicating with peers and educators. The “B1, Journey Language Banks” (“Bancos de lenguaje y redirecciones”) provide educators with guidance, sentence stems, discussion prompts, and redirection to help students use mathematical vocabulary in classroom conversations. The materials suggest language for discussing mathematical concepts, explaining strategies, describing representations, and justifying solutions. This guidance helps educators scaffold students’ use of academic vocabulary by modeling precise mathematical language and prompting students to communicate their thinking using appropriate terms. The language banks also provide follow-up questions and redirection that extend students’ responses and encourage deeper mathematical discussions with peers and educators. Through these embedded supports, the Math Journeys grade K program promotes the development and application of academic mathematical vocabulary within meaningful mathematical contexts.

The materials provide educators with embedded guidance to scaffold, support, and extend students’ use of academic mathematical vocabulary in context when communicating with peers and educators. In journey B2.1, “Sumamos 1 y 2,” students develop mathematical language related to addition as they associate adding one with el siguiente and adding two with el siguiente del siguiente, while also learning to represent addition using the symbols + and =. Throughout the lesson, the educator models and reinforces the meaning of these terms by connecting them to the counting sequence and explicitly discussing how the next number represents adding one and the number after that represents adding two. The EB supports prompt the educator to explain concepts by using language such as “El siguiente número significa que sumamos uno. El número después de ese significa que sumamos dos” and by having students repeat complete mathematical statements such as “12 más 1 son 13.” The educator further models mathematical vocabulary and notation by representing equations with snap cubes and verbalizing statements such as “Si tenemos seis cubitos y añadimos uno, tenemos siete cubitos” before introducing the symbolic representation 6 + 1 = 7. As students progress through the lesson, they use snap cubes, number cards, and operation cards to discuss and represent addition situations with peers. In the final activity, students record addition expressions on their whiteboards while the educator encourages them to communicate their thinking using complete mathematical sentences rather than simply stating answers. These embedded supports help students develop, practice, and extend academic mathematical vocabulary while communicating mathematical ideas in meaningful contexts.

Evaluation for 5.4c
Materials include embedded guidance to support student application of appropriate mathematical language and academic vocabulary in discourse.

The Math Journeys grade K program provides embedded guidance to support students’ application of appropriate mathematical language and academic vocabulary in discourse. In activity 2 of journey B1.13, “El número 9 (parte 2)—Creamos frases matemáticas con el 9,” students construct and discuss mathematical sentences using numbers and symbols to represent decompositions of nine. The materials contain embedded guidance for educators, such as “Comunicar ideas usando lenguaje matemático preciso,” and prompts such as “¿Cómo lo supiste?” and “¿Cómo lo resolviste?” that require students to explain their reasoning using mathematical language. Students discuss addition and subtraction expressions, justify solutions, and communicate relationships between numbers using terms such as suma, resta, igual, descomposición, and frase matemática during mathematical discourse with peers and the educator.

As students progress through journey B2.4, “Suma: conteo hacia adelante II,” Math Journeys embeds guidance to help students apply appropriate mathematical language and academic vocabulary during mathematical discourse. Students relate addition in “adding to” situations and counting on by using manipulatives while communicating their thinking with mathematical vocabulary. In “Nudo: actividad 1—Sumamos mediante situaciones de cambio creciente,” the educator shows 12 snap cubes and asks students how many cubes there will be when three more are added. Students solve 12 + 3 by counting on from 12 with snap cubes and explain how they determined the total. The EB support guides educators to scaffold mathematical discourse by providing sentence stems for different levels of English proficiency during the counting on task, including: “Veo ___ cubitos. Añado ___ más” (inicial); “Empecé con ___ cubitos y añadí ___, así que ahora tengo ___” (intermedio); “Había ___ cubitos ocultos, así que conté desde ___ y conseguí ___” (avanzado); and “Como había ___ cubitos ocultos, conté ___ más para obtener el total, que coincide con ___ + ___ = ___” (avanzado alto). Later on in the lesson, during activity 2, “Sumamos usando cubitos,” students use the handkerchief strategy to add a hidden group of 14 snap cubes and three visible cubes, allowing them to begin counting from 14 instead of recounting every cube. The educator prompts students to communicate their mathematical reasoning by asking, “¿Qué relación hay entre los 14 cubitos ocultos, los tres cubitos que puedes ver y el total?” and “¿Piensas en los cubitos ocultos como cubitos individuales o como un solo grupo? ¿Por qué?” This encourages students to use precise mathematical language to explain the relationship between the addends and the total.

Evaluation for 5.4d
Materials include embedded guidance to facilitate mathematical conversations allowing students to hear, refine, and use math language with peers.

The Math Journeys grade K program contains embedded guidance to facilitate mathematical conversations in B1.2, “El número 5 (parte 2).” For example, during activity 2, students work collaboratively to identify pairs of cards that sum up to five and discuss their reasoning with their peers. The materials provide the educator with prompts such as “¿Por qué esa carta va a formar primero y por qué?” and “¿Podrías explicar cómo sabes cuántas cartas suman cinco?” to encourage students to explain and justify their thinking. During activity 3, students participate in a whole-group discussion where they share combinations that make five while the educator records representations using numbers, symbols, and drawings. The lesson also includes sentence frames for EB students (such as “__ más __ suman cinco” and “Agrupé estas dos cartas porque __ más __ suman cinco”) to help them refine and use mathematical language during peer interaction. Through these structured discussions and language supports, students hear, refine, and use mathematical language with their peers.

Throughout journey A1.16, “Contar a simple vista,” the Math Journeys grade K program embeds guidance that facilitates mathematical conversations and encourages students to hear, refine, and use mathematical language with their peers. Students practice identifying quantities through subitizing by using manipulatives and visual models before sharing their thinking with their classmates. They work in groups to count the dots on dice and cubes, determine the total, and connect the visual grouping to the corresponding number. The educator prompts students to explain their mathematical thinking by asking, “¿Podrías explicar cómo agrupaste los objetos para encontrar el total rápidamente?” and “¿Observas algún patrón en la disposición de los puntos de los dados?” to encourage students to describe the strategies they used. To further support mathematical discourse, the EB guidance directs educators to implement the “collect and display” strategy as students represent numbers with their fingers and use phrases such as “Vi cinco y dos” or “La fila de arriba estaba llena y dos más.” The educator then displays sentence frames, including “cinco y ___ más” and “Fila completa y ___ más,” so that students can refine and consistently use precise mathematical language during discussions with their peers.

Evaluation for 5.4e
Materials include embedded guidance to anticipate a variety of student answers including exemplar responses to questions and tasks, including guidance to support and/or redirect inaccurate student responses.

The Math Journeys grade K program contains embedded guidance to help educators anticipate a variety of answers from students, including exemplar responses to questions and tasks as well as guidance to support and redirect inaccurate student responses. In lesson B1.3, “Situaciones matemáticas,” students interpret visual representations of children moving on and off a raised surface and use additive part-part-whole representations to solve addition and subtraction situations. The materials provide exemplar responses from students as well as mathematical equations (such as 5 − 1 = 4, 4 + 1 = 5, and 5 − 2 = 3) to illustrate expected reasoning and methods for solution. The lesson also includes embedded guidance and prompts for educators to ask questions such as “¿Qué ven?,” “¿Qué pasó?,” “¿Cuántos bajaron?,” and “¿Cuántos quedaron arriba?” to help students explain their thinking and connect visual models to mathematical representations. In addition, the materials provide redirection for incomplete responses by prompting students to write the corresponding mathematical sentence when they give only a numerical answer. These supports help educators anticipate students’ thinking, address misconceptions, and guide students toward accurate mathematical reasoning.

As students explore multiple ways to decompose numbers in journey B1.13, “El número 9 (parte 2),” the Math Journeys grade K program embeds guidance that enables educators to anticipate a variety of responses from students. The program also helps educators to provide feedback that builds on students’ thinking and redirects inaccurate responses. Students decompose the number nine by finding pairs of numbers that equal nine and creating mathematical sentences with manipulatives and number cards. As students communicate their mathematical thinking by modeling decompositions with cubes and symbolic representations, the educator asks questions such as “¿Podrías mostrar esta oración numérica con tus cubitos?” and “¿Conoces otra manera de escribir esta historia numérica?” to elicit student responses and check for understanding. To support instructional feedback, the Teacher Guide provides exemplar responses by explaining that students may represent the decomposition of nine using equations such as 4 + 5 = 9, 5 + 4 = 9, 9 − 4 = 5, and 9 − 5 = 4. This helps educators anticipate multiple acceptable responses during instruction. The lesson also directs educators to “check the answers as a class, highlighting the relationships between addition and subtraction, as well as the use of the + and − symbols,” and to “be sure to highlight any math sentences involving subtraction.” As a result, educators receive explicit guidance to reinforce accurate mathematical understanding and redirect incomplete or inaccurate student responses.

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

The Math Journeys grade K program integrates the TEKS mathematical process standards appropriately within grade-level content-based instruction. In lesson B1.5, “Cantidad 0–6,” students participate in the “Cuadrado y ángulo” game where they apply problem-solving strategies to determine scores based on the location of tossed objects; analyze the results; and represent their thinking using drawings, symbols, numbers, and mathematical expressions. During the lesson, students discuss scoring outcomes, answer questions about possible point totals, and explain how they determined their answers. In the closure section, students create representations of game results and share their reasoning with their peers, providing opportunities to communicate, justify, and refine mathematical ideas. Through problem-solving, representation, reasoning, and mathematical communication embedded within the lesson activities, the materials appropriately integrate the TEKS mathematical process standards with content learning.

As students build knowledge of addition strategies in journey B2.4, “Suma: conteo hacia adelante II,” the Math Journeys grade K program appropriately integrates the TEKS mathematical process standards within grade-level content-based instruction. During “Nudo: actividad 2—Sumamos usando cubitos,” TEKS Process Standard 1.F is embedded as students analyze the relationship between the 14 snap cubes hidden under a handkerchief and the three visible cubes to determine the total. Rather than counting every cube individually, students begin counting from the known quantity of 14 and then count on three more to find the sum. The educator prompts students with questions such as “¿Qué relación hay entre los 14 cubitos ocultos, los tres cubitos que puedes ver y el total?” and “¿Piensas en los cubitos ocultos como cubitos individuales o como un solo grupo? ¿Por qué?” to encourage them to analyze the relationship between the addends and explain their mathematical reasoning. Later, during the “Desenlace,” TEKS Process Standard 1.A is embedded as students apply math to solve real-world addition problems, such as determining how many people are on a bus after more passengers board and how many markers are in a box after additional markers are added. The educator extends students’ thinking by asking, “¿Podrías explicar cómo te ayudan los cubitos encajables a resolver el problema del autobús?” and “¿Ves cómo este problema se conecta con situaciones de la vida real?” This prompts students to connect their mathematical strategies to authentic situations.

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

The Math Journeys grade K program describes how the TEKS mathematical process standards are incorporated and connected across the learning pathways. In the B1 Journey Instructional Guide, “Descomposición de números, y sumas y restas mediante conteo,” the materials provide a vertical justification that explains how students engage in problem-solving, reasoning, mathematical communication, representations, and connections while developing additive thinking throughout the journey. The guide also includes a lesson-by-lesson alignment table identifying where specific TEKS mathematical process standards are embedded in the broader pathway, demonstrating how these standards are incorporated across multiple sessions rather than taught in isolation. In addition, the guide describes how process standards support the progression of content learning and provides examples of students using mathematical representations, discussing strategies, solving problems, and justifying their reasoning. These descriptions show how the process standards are intentionally incorporated and connected throughout the broader learning pathway.

As students decompose nine in journey B1.13, “El número 9 (parte 2),” the Math Journeys grade K program describes how the process standards connect throughout the broader learning pathway. The Teacher Guide explicitly labels the TEKS Process Standards 1.D and 1.G, and students apply these standards across the lesson activities. In activity 2, “Creamos frases matemáticas con el 9,” students engage with Process Standard 1.D by communicating the same mathematical idea through multiple representations such as cubes, number cards, and the written equation 4 + 5 = 9. Students connect the concrete model to the abstract mathematical sentence and then create additional equations with symbol cards, such as 5 + 4 = 9, 9 − 4 = 5, and 9 − 5 = 4. Additionally, students engage with Process Standard 1.G as they display, explain, and justify their mathematical sentences using precise mathematical language. Students read equations aloud using terms such as plus, minus, and equals and explain step by step how each equation represents a decomposition of nine.

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

The Math Journeys grade K program contains an overview of the TEKS mathematical process standards incorporated into each lesson. In lesson B1.5, “Cantidad 0–6,” the materials explicitly identify the process standard “1B, usar un modelo de resolución de problemas” within the lesson activities. The lesson overview describes how students apply the process standard while participating in the game, representing scores, analyzing results, and communicating their mathematical thinking. The guidance for educators explains how students use problem-solving, reasoning, and representations to make sense of the scoring situations and record their ideas. By identifying the process standard and describing how it is applied during instruction, the materials provide an overview of the TEKS mathematical process standards incorporated into the lesson.

As students participate in journey A0.7, “Juegos con el número 5,” the Math Journeys grade K program provides an overview of the TEKS mathematical process standards incorporated across the lesson. The Teacher Guide explicitly identifies TEKS Process Standards 1.B and 1.D, helping educators recognize where students apply each standard during instruction. In activity 1, “Jugamos a hacer paquetes,” Process Standard 1.B guides students as they use a problem-solving model to analyze the target group size of five, plan how to gather the correct number of classmates, determine how many additional students they need to complete the group, and justify whether their solution matches the number on the card. The educator supports students’ reasoning by asking questions such as “¿Tienes algún plan para averiguar cuántos amigos más necesitas en tu grupo?” and “¿Podrías explicar cómo sabes que necesitas más personas para formar un grupo de cinco?” Later, in activity 2, “Jugamos a los aros musicales,” Process Standard 1.D guides students as they communicate a quantity using multiple representations. Students connect the numeral shown on the card to the corresponding quantity of balls placed in the hoop, showing that the same number can be represented as both a written symbol and a countable set of objects.

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

In lesson B1.9, “El número 8 (parte 1),” students think mathematically, persevere through solving problems, and make sense of math. They engage in an open-ended challenge to create “torres mágicas” using eight cubes and investigate multiple combinations that satisfy the task conditions. The lesson contains guiding questions such as “¿Creen que hay más de una solución?” and “¿Pueden encontrar otras soluciones?” that encourage students to continue exploring and refining their strategies. Students analyze relationships among tower heights, record combinations that total eight, discuss their reasoning with their peers, and create representations of their solutions, supporting mathematical thinking, perseverance, and sense-making.

In journey B1.12, “El número 9 (parte 1),” students use a nine-seat bus problem to explore different ways passengers can get on and off the bus. They use cubes to model and show how to break apart nine into two numbers for occupied and empty seats. As students find combinations that total nine, the educator encourages them to look for more solutions. Box 1A suggests that educators ask, “¿Crees que puede haber más maneras de llenar los asientos?” and “¿Podrías encontrar una manera diferente de colocar a los pasajeros en el autobús?” After students share several solutions, the educator helps them figure out if they have found all possible combinations by asking, “¿Creen que tenemos todas las parejas posibles?,” “¿Qué podríamos hacer para saberlo?,” and, if needed, “¿Ordenar las parejas de números podría ayudarnos?” These questions prompt students to think mathematically, persevere, and systematically find every way possible to break apart nine.

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

Lesson B1.9, “El número 8 (parte 1),” of the Math Journeys grade K program helps students see that there are many ways to solve problems. Students build “torres mágicas” with eight cubes and find different combinations such as seven and one, six and two, or five and three. They compare their strategies with their classmates. Educators ask questions such as “Si una torre usa cinco cubos, ¿cuántos necesita la otra torre? ¿Cómo lo sabes?,” “¿Creen que hay más de una solución?,” and “¿Pueden encontrar otras soluciones?” to prompt students to explain their thinking and justify their answers. Students join group discussions to share combinations, check if their solutions meet the requirements, and defend their reasoning. During the “Desenlace,” students show their solutions in different ways and prove that they can solve problems using multiple strategies.

In journey B1.13, “El número 9 (parte 2),” students use manipulatives and number cards to break apart the number nine in different ways. They build pairs of cubes that total nine, then write matching mathematical sentences and explain their thinking. Box 1D shows how students use several representations for the same idea, such as building nine with five and four cubes and then writing the equation 4 + 5 = 9. This helps them connect hands-on models to abstract math sentences. Educators prompt students with questions such as “¿Podrías mostrar esta oración numérica con tus cubitos?” and “¿Conoces otra manera de escribir esta historia numérica?” to encourage new representations. Students keep exploring ways to split nine with models and equations, explaining and justifying their reasoning. Educators further support math talk by asking, “¿Podrías leer tu oración numérica utilizando palabras matemáticas?” and “¿Puedes contarnos paso a paso cómo la resolviste?” These prompts help students understand, explain, and prove that there are many valid ways to solve and represent the same math 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/or educators.

The Math Journeys grade K program helps students make sense of math by doing, writing about, and discussing math with their peers and the educator. In lesson B1.7, “El número 7 (parte 1),” students work in small groups to play a hands-on ring toss game. They throw seven rings, count how many land inside and outside the cone, and explore different ways to break apart the number seven. During the activity, educators ask questions such as “¿Cuántos hay fuera?,” “¿Cuántos hay dentro?,” and “¿Hay tantos aros en el cono como fuera?” to encourage mathematical thinking. During the “Desenlace,” students draw, write numbers and symbols, and use mathematical representations to demonstrate how they can compose and decompose seven in different ways. Finally, students explain and compare their work with their classmates during a group discussion, sharing solution-based strategies and math-related ideas.

In journey B1.14, “El número 10 (parte 1),” students learn to break apart 10 into pairs by playing a bowling game. In activity 1, students work together to arrange the bowling pins in different ways and test which setup knocks down the most pins. They share ideas with their group, and the educator asks questions such as “¿Crees que podrías encontrar otra manera de colocar los bolos?” and “¿Podrías probar un patrón diferente para derribar más bolos?” to guide their thinking. In activity 2, students play the game and mark the number of pins they knock down on a printable ten frame, using an “X” for each pin. They see how the ten frame shows the total pins. Afterward, students join a class discussion to interpret their ten frames, compare different combinations, and explain their reasoning. The educator asks questions such as “¿Cuántos bolos has tirado?” and “¿Alguien tiene alguna otra combinación?” These activities get students to explore math through hands-on play, record their thinking with ten frame models, and discuss their ideas with classmates and the educator.

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

In lesson B1.7, “El número 7 (parte 1),” students explain and discuss their problem-solving strategies with their peers and the educator. They work in groups to play a ring toss game, count how many rings land inside and outside the cone, and use those numbers to break apart seven. The educator asks questions such as “¿Cuántos hay fuera?,” “¿Cuántos hay dentro?,” and “¿Hay tantos aros en el cono como fuera?” to get students to explain their answers and justify their reasoning. During the “Desenlace,” students draw, write numbers, use symbols, and add words to show different ways to break apart seven. They present their work to the class, describing how their drawings or numbers display the rings inside and outside the cone and how these represent a decomposition of seven. As students compare their work, they discuss how their approaches are similar or different and reflect on how different representations can show the same math-based idea.

In journey B1.15, “El número 10 (parte 2),” students work in groups to find all pairs of number cards that add up to 10. Educators ask questions that push students to explain, justify, and reflect on their thinking as they search for every possible combination. After students find several pairs, educators ask, “¿Creen que tenemos todas las parejas posibles?” and “¿Qué podríamos hacer para saberlo?” If students need help, educators ask, “¿Ordenar las parejas de números podría ayudarnos?” to encourage students to organize and check their work. In activity 2, “Presentamos ‘La mona,’” students play a card game with two sets of number cards (zero through ten) and look for pairs that make 10. Educators model the game by thinking aloud and asking questions such as “Si la carta es un ocho, ¿ocho y qué número suman 10?” and “Sonia emparejó un seis y un cuatro. ¿Suman 10?” Educators prompt students to explain their reasoning with questions such as “Marina, ¿qué robaste?,” “Un tres,” and “¿Puedes descartar cartas?” These prompts help students share, reflect on, and justify their strategies while discussing math with their classmates and the educator.

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

In lesson B1.8, “El número 7 (parte 2),” educators prompt students to explain their thinking and address misconceptions as they work. Students use connecting cubes to build scores and write mathematical sentences that equal seven. Educators ask, “¿Podrías mostrarme cómo tus cubitos coinciden con tu frase matemática?” and “¿Cómo usaste los números para mostrar las distintas partes que forman el siete?” to get students to connect their models to equations. To ensure that students find every way possible to break apart seven, educators ask, “¿Creen que las tienen todas?” and “¿Qué podríamos hacer para saberlo?” Students organize number cards, compare combinations, and explain how ordering the pairs helps them check for all decompositions of seven. These prompts allow educators to respond to students’ thinking, give clear feedback, and help students address misconceptions by thinking through questions instead of just receiving answers.

In journey B1.9, “El número 8 (parte 1),” students work in pairs to build two magical towers of different heights using eight snap cubes. As students share their solutions, educators ask, “¿Creen que hay más de una solución?,” “¿Pueden encontrar otras soluciones?,” and “Investíguenlo con ocho cubitos más” to encourage them to find more ways to break apart eight. Box 1F directs educators to explain that when one tower gets taller, the other must get shorter, so students notice the pattern and move from seven and one, to six and two, to five and three. The Teacher Guide helps educators handle common student responses and misconceptions. For example, if students suggest four and four, educators explain that while four and four make eight, the towers are not magical because they are the same height. If students suggest eight and zero, educators lead a discussion about why this combination does not work since it only makes one tower. These prompts and explanations help educators give feedback, address misconceptions, and deepen students’ understanding of number decomposition.