Math Journeys Texas, Grado 1 (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 of the Math Journeys grade 1 program outlines the TEKS corresponding to each of the lessons, including both the content and process standards for educators. Additionally, the TEKS and ELPS are incorporated into the scope and sequence document, which is organized into different sections called “Journeys.” The Journey Instructional Guide provides a detailed rationale for each journey. For example, section 2 of the guide describes the vertical rationale for how the current journey builds upon the previous one and how it prepares students for subsequent concepts. The A2 Journey Instructional Guide, which focuses on identifying numbers and counting from 1–100, extends the concepts of counting, comparing, ordering, and estimating from the previous journey, which involves numbers 1–20. The horizontal rationale is provided in section 3, which explains how learning moves from concrete to representational to abstract models of number sense.

The “Alcance y secuencia” scope and sequence document of the Math Journeys grade 1 program describes the TEKS, process standards, and mathematical concepts corresponding to each grade 1 session throughout the curriculum. Additionally, the scope and sequence is organized to show how concepts are connected and developed across lessons within the grade level. The materials outline a detailed progression of mathematical learning by demonstrating how foundational grade 1 skills are introduced and extended in later sessions. For example, early sessions focus on foundational number sense and representations, while later sessions 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 in 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 of the Math Journeys grade 1 program provides comprehensive instruction for implementation, including the three-step framework of “build,” “consolidate,” and “practice.” Each lesson begins with an educator-led, small-group lesson followed by logsheets for students to complete independently with educator feedback, and then further optional practice in Atlas Math, an adaptive digital platform. In addition, the “Lesson Internalization and Planning” section of the guide describes how 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 for effective educator practices across a variety of instructional settings and contexts. In addition, the guide supports differentiated instruction and flexible lesson implementation throughout the grade 1 curriculum. The materials provide guidance for small-group instruction through activities such as “Secuencia de ricas actividades matemáticas,” which are designed to support the development of specific mathematical skills, including reasoning and comprehension. The guide shows how grade 1 educators can adapt instruction to meet varying student needs 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. The materials also include a diagnostic assessment and placement report, which recommends skill entry points and helps educators identify appropriate instructional starting points, targeted interventions, and differentiated learning opportunities based on the performance data of individual students.

The Guía del programa outlines strategies and usage recommendations for adapting instruction across a variety of instructional settings and contexts. In addition, the guide supports differentiated instruction and flexible lesson implementation throughout the grade 1 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 individual learning needs. The materials also contain “Informes del progreso,” which provide updates on individual students’ progress and performance on TEKS-aligned activities. The guide shows how grade 1 educators can monitor student learning and adapt instruction to support varying levels of understanding while keeping students 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 grade 1 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 on 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 lesson internalization protocols 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 student thinking and misconceptions, prepare materials, identify formative assessment opportunities, analyze student responses, and use progress monitoring data to inform future instruction.

The Math Journeys grade 1 program provides journeys, which are labeled with a letter to identify the cluster or unit and a number to identify the lesson. In addition, each journey serves as an educator guide that outlines the learning objectives, TEKS, vocabulary, instructional resources, and sequence of lesson activities throughout instruction. The materials provide instructional strategies and organized lesson components that help educators understand the progression of concepts and prepare for instruction. The guidance demonstrates how grade 1 educators can preview lessons, internalize instructional objectives, and adapt teaching practices to support varying student needs while keeping students engaged with grade-level mathematical concepts and skills.

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

The Math Journeys grade 1 program contains resources to help instructional leaders assist educators with implementing it. The “Hands on Partnership” section of the Program Guide provides examples of how a math success manager can partner with and provide guidance to instructional leaders. Examples include “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 Spanish (es-LA) edition of the Math Journeys Coaching Guide for Instructional Leaders provides resources and explicit guidance for instructional leaders to help grade 1 educators implement the Math Journeys program as designed. The “How to Use It” section establishes a clear coaching protocol that instructional leaders use during classroom observation, during the post-observation conversation, and when collaboratively planning the next lesson with the educator. For example, during a Math Journeys grade 1 classroom observation, an 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 the appropriate times. The tool also helps the leader verify that lesson objectives have been met. Following the observation, the instructional leader can use the reflection rubric to guide the coaching conversation as well as the lesson preparation guide to collaboratively plan subsequent instruction, including lesson objectives, TEKS, prerequisites, anticipated student errors and strategies, and instructional adjustments. Together, these resources provide instructional leaders with actionable guidance for observing implementation, providing targeted feedback, and supporting grade 1 educators in maintaining the intended design of the Math Journeys program.

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 provides detailed guidance for implementing lessons, 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. In addition, the materials contain multiple assessment resources described within the Guía del programa, including diagnostic and progress monitoring tools. The digital practice progress reports specifically provide TEKS-aligned assessment data by identifying student performance for each TEKS to support instructional decision-making and monitor student growth.

The Math Journeys grade 1 program contains lesson plans outlining the learning objectives, TEKS alignment, vocabulary, educator and student materials, instructional resources, and lesson components throughout the curriculum. In addition, the materials organize instruction into lesson 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 the lesson. For example, in journey A2, session 6, the learning objective focuses on practicing resultative counting to 100 with an emphasis on grouping by tens, while the development and wrap-up activities provide aligned instructional guidance to support students throughout the learning process. This guidance demonstrates how grade 1 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 grade 1 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. In addition, the lesson framework is designed to help educators deliver instruction in a consistent, purposeful manner while providing students with a structured learning routine. The organization of the lesson components helps educators manage instructional time effectively and ensure that each stage of learning is addressed throughout the lesson.

The Math Journeys grade 1 program contains lesson plans that outline the learning objectives, TEKS alignment, vocabulary, educator and student materials, instructional resources, and lesson components throughout the curriculum. In addition, the materials organize instruction into lesson 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 B2, session 4, the learning objective focuses on practicing addition with increasing change situations, while the warm-up, development, and wrap-up activities provide aligned instructional guidance to support students throughout the learning process. This guidance shows how grade 1 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 grade 1 program provides family resources within each journey to help caregivers support students’ learning at home. The family letter offers guidance, questions, vocabulary, and suggested activities connected to the concepts of the lesson being taught in class. Additionally, educators can change the language of the family letter using the language toggle located in the top right corner, allowing families to access the information in their preferred language. The family 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 of the classroom.

The “F1 Carta para familias” of the Math Journeys grade 1 program provides support for families throughout each journey or unit within the curriculum. Additionally, the family letter explains student learning goals, academic vocabulary, and mathematical concepts in family-friendly language to support understanding of grade-level content. The materials include discussion questions, examples, and at-home practice activities that families can use to reinforce learning and support students’ understanding outside of the classroom. This guidance shows how grade 1 families can support students’ progress and strengthen the 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 1 program contains resources for diagnostic assessment to support instructional decision-making and identify student learning needs. The materials provide educators with the definition and purpose of the “Prueba de nivel” assessment, which measures students’ mathematical reasoning and problem-solving skills at the beginning of instruction. In addition, the materials help educators interpret assessment results and use student performance data to support instructional planning. For example, grade 1 educators can use the “Prueba de nivel” report sample to group students, identify learning gaps, and place students into the appropriate journeys for targeted instruction and intervention. The materials also help educators monitor student progress and select instructional pathways based on assessment results.

The Math Journeys grade 1 program contains resources for summative assessment to evaluate students’ understanding and support instructional decision-making at the end of a journey. The materials provide the Instrucciones y guía for the “Prueba del final de journey” in both printable and digital formats and include the intended purpose of the assessment. In addition, the materials explain how to administer the assessment, interpret student performance data, and use assessment results to inform instruction. For example, educators use the assessment guide to administer the summative assessment, analyze the results, and identify areas where students may need additional support or review before moving on to the next journey. The materials also help educators monitor mastery of grade-level mathematical concepts and skills through structured assessment practice.

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

The Math Journeys grade 1 program guides educators to administer assessments consistently and accurately using the Guía de implementación of the “Prueba de nivel.” The materials explain the assessment’s purpose and characteristics, describe the assessment’s components and question types, and outline clear administration procedures as well as expectations for the testing environment. The guide helps educators implement assessments uniformly across all grade 1 classrooms. In addition, the materials help educators administer assessments and establish appropriate testing environments, ensuring accurate and consistent implementation across classrooms. For example, grade 1 educators follow the guide to understand assessment procedures, prepare students for the testing environment, and administer the diagnostic assessment according to program expectations. The materials help educators implement assessment practices consistently so that they gather meaningful data on student performance.

The Math Journeys grade 1 program contains resources for summative assessment to help educators administer assessments effectively and make instructional decisions. The A2 Instrucciones y guía of the “Prueba del final de journey” provide guidance on using manipulatives and other instructional supports to ensure that educators successfully implement the assessment. Additionally, the materials explain how to administer the assessment, understand intended use cases, and interpret student performance data from the summative assessment.

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 1 program offers digital supports designed to address individual students’ accessibility needs during assessment. The supports include text-to-speech functionality, content and language supports, or calculators on the digital assessment platform. Additionally, the materials describe how students can access accessibility features to support equitable participation during digital assessments. For example, grade 1 students can use embedded digital supports while completing assessment activities within the platform. However, educators cannot 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 grade 1 program provides resources for diagnostic assessment to measure students’ understanding of grade-level mathematical concepts and skills through TEKS-aligned tasks. For example, interactive assessment activities with different levels of complexity require students to apply their mathematical reasoning and problem-solving skills. In addition, visual assessment tasks help students demonstrate their understanding of place-value concepts through multiple representations. For example, in grade 1, students interpret place value models and identify numbers represented on the abacus through visual assessment questions that require mathematical reasoning and understanding of place value. The materials also help educators monitor students’ comprehension and identify instructional needs through structured activities for diagnostic assessment.

The Math Journeys grade 1 program includes resources for summative assessment to measure student mastery of TEKS-aligned mathematical concepts and skills through a variety of levels of complexity. The materials contain end-of-journey assessments that include questions ranging from factual knowledge to procedural understanding to problem-solving. Additionally, the materials provide educators with guidance and reporting tools that help them interpret student performance data and make instructional decisions. For example, the digital Journey Test A2 includes assessment items aligned with the TEKS, while the “Muestra de informe de prueba” displays journey levels aligned with the TEKS and identifies levels of student performance. The materials also help educators use assessment reports to strategically determine which supports students may need and identify whether they are ready to 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 1 program provides TEKS-aligned resources for formative assessment to measure students’ understanding through interactive tasks and multiple levels of complexity. Digital assessment activities allow students to demonstrate mathematical reasoning, number sense, and conceptual understanding through a variety of interactive item types. Additionally, students have opportunities to apply mathematical learning using question formats that extend beyond basic recall. For example, grade 1 students complete digital tasks such as matching quantities to numerals and applying number sense through interactive response activities. The materials also help educators monitor students’ understanding and identify instructional needs through ongoing opportunities for formative assessment.

Students have opportunities to participate in peer discussions, answer open-ended questions, and complete interactive learning tasks in every lesson. Educators use formative assessment tasks to prompt students to apply mathematical reasoning and communicate their thinking in different ways. For example, in the “Conteo acústico hacia adelante” journey activities, students discuss their ideas with peers and answer open-ended questions that cover a range of levels of mathematical complexity. The materials help educators monitor students’ understanding and adjust instruction based on the results of formative assessment.

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

The Math Journeys grade 1 program equips educators with assessment scoring resources that help them interpret student performance and make instructional decisions. The Guía de puntuación a nivel de evaluación provides educators with performance levels, score ranges, and detailed descriptions of student understanding so they can identify students’ strengths, misconceptions, and instructional needs. The “Muestra de informe de la prueba de nivel” helps educators analyze assessment results and use student data to plan instruction. For example, educators review performance reports to find areas where students need extra support or targeted intervention. These resources help educators monitor student progress and plan instruction based on assessment outcomes.

The Math Journeys grade 1 program contains assessment scoring resources to help educators interpret student performance and make instructional decisions. The Instrucciones y guía of the “Prueba del final de journey” include printable assessment resources. The “Prueba del final de journey” also has an answer key and formative guide. Additionally, educators receive support for instructional planning through answer rationales, achievement levels, scoring information, and formative assessment guidance. For example, grade 1 educators can use the answer key and formative guide to analyze correct and incorrect responses, identify possible student misconceptions, review related TEKS, and determine additional instructional supports needed after the journey A2 assessment. The materials also help educators use assessment data to guide their next instructional steps and make decisions about targeted intervention.

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 grade 1 program contains resources for assessment reporting to help educators respond to trends in student performance and make instructional decisions. The “Ubicación en trayectorias” report helps educators analyze student assessment data and identify learning needs. Additionally, educators receive guidance for grouping students and selecting targeted instructional tasks and activities to provide focused support and intervention. For example, educators can use student performance results from the “Ubicación en trayectorias” report to place students into appropriate instructional pathways and determine differentiated learning supports. The materials also help educators monitor student progress and plan targeted instruction based on assessment data.

The Math Journeys grade 1 program contains resources for instructional support to help educators respond to trends in student performance on assessments and provide targeted intervention. The Instrucciones y guía of the “Prueba del final de journey” include printable assessment resources. The “Prueba del final de journey” also has an answer key and formative guide. Additionally, educators receive guidance to identify student misconceptions, review related TEKS, determine areas needing reinforcement, and select additional instructional supports and activities. For example, educators can use the assessment guide following the journey A2 assessment to analyze student responses, identify learning gaps, and implement targeted activities to help students in specific skill areas. The materials also help educators make instructional decisions and provide differentiated interventions based on assessment results.

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 1 program provides educators with tools to track student progress and growth through the “Progreso general” dashboard on the “Classroom Manager” platform. The dashboard provides data on weekly progress, completed activities, time spent, course grades, and content mastery levels to help educators monitor student performance and analyze growth data. Educators can also use the dashboard to review whether students have completed an activity, monitor mastery of mathematical concepts, and identify areas where additional instructional support may be needed to guide instruction and intervention decisions. However, there are no tools that allow students to independently track or monitor their own progress and growth.

The Math Journeys grade 1 program provides digital progress monitoring tools to allow students to view performance information during interactive math activities. The materials provide access to scores and feedback within the “Atlas Math Biblioteca de applets,” which students use to practice Math Journeys skills and concepts. Additionally, students can view their results immediately after completing applet activities. However, the scores are not stored or displayed over time, making it difficult for students to independently track their long-term progress and growth across activities.

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 1 program provides guidance on formative assessment to help educators conduct checks for understanding across lesson activities through educator prompts, observation opportunities, and discussion questions. Educators also receive guidance to encourage students to explain their thinking, justify their responses, and participate in mathematical discussions during instruction. For example, in the lesson “Conteo resultativo (hasta 20),” educators observe whether students use groups of ten or continue counting one by one to monitor their understanding of place-value concepts and counting strategies. To encourage students to explain their reasoning and justify their responses, the materials include prompts such as “¿Observas algún patrón relacionado con la posición de los números menores y mayores cuando contamos?” and “Cuando comparas 13 y 15, ¿cuál aparece primero al contar hacia adelante?” Additionally, the materials help educators conduct ongoing formative assessment through partner discussions, observation, and student explanations throughout the lesson.

The Math Journeys grade 1 program provides educators with guidance on formative assessment to help them conduct frequent checks for understanding throughout lesson instruction. Educator prompts, targeted questioning strategies, and observation opportunities help educators monitor students’ understanding and identify misconceptions during learning activities. Additionally, educators receive guidance to analyze student performance, observe multiple problem-solving strategies, and determine whether lesson objectives have been met. For example, in the “Desenlace” of journey B2, session 1, targeted questions and observation prompts help educators identify misconceptions, analyze student responses, observe the different methods that students use to solve problems, and determine mastery of the learning objective. The materials also help educators use ongoing practices for formative assessment to guide instructional decisions and provide targeted support as needed.

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 1 program contains resources for formative assessment to facilitate frequent checks for understanding throughout lesson activities. Interactive digital applets within Atlas Math allow students to solve math problems and receive immediate feedback during instruction. Additionally, milestone trackers and response indicators support ongoing formative assessment and help students monitor their understanding while completing activities. For example, in applet A16, students solve addition problems and receive immediate feedback after submitting their responses, with correct answers marked by a green check and incorrect answers identified with a question mark.

Targeted questions, observation opportunities, and discussion prompts help educators monitor students’ understanding and make instructional adjustments during lessons. Additionally, educators have ongoing opportunities to analyze student responses and identify areas where additional support may be needed. For example, in journey B2, session 1, educators receive multiple opportunities during the lesson to conduct checks for understanding through targeted questions and student observations to adjust instruction as needed. The materials also help educators use formative assessment practices to guide instruction and respond to student learning needs during lesson activities.

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 1 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 adjust instruction, provide additional representations, and reinforce foundational concepts based on student needs. For example, in the lesson “Contamos con el collar de bolas I,” educators are guided to adjust pacing, encourage the use of benchmark numbers such as 5, 10, and 15 to support counting strategies, and implement additional supports through the “Apoyo” section by using number cards or writing numbers on the board. Guiding questions help students make connections among number relationships and develop more efficient counting strategies.

The supports help educators provide opportunities for additional practice, simplified representations, and targeted instruction based on student needs. For example, in lesson B2, session 17, the “Hoja de actividad de apoyo” provides scaffolded activities to help students reach proficiency. The support logsheet includes part-part-whole frames for addition and subtraction as well as opportunities to write equations using number cards with values up to seven, while the student “Cuaderno” activities require students to subtract using part-part-whole frames and write equations with number cards up to 20. These scaffolded supports strengthen students’ understanding of addition and subtraction concepts while providing access to 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 1 program provides educators with explicit guidance for language supports in order to help students acquire and use academic vocabulary as well as understand mathematical concepts. The “Vocabulario clave” section introduces academic vocabulary such as descomponer, salto, recta numérica, estrategia, and decenas. In addition, interactive applets, number lines, visuals, educator modeling, and guided discussions support students’ understanding of mathematical concepts and problem-solving strategies.

The Math Journeys A2 Language Bank provides educators with explicit guidance for grade 1 pre-teaching and embedded language supports that help students develop their academic vocabulary and address unfamiliar references in the text. The language support routines provide educators with specific steps for introducing mathematical vocabulary, including modeling and pronouncing a word, defining it in student-friendly language, using it immediately in the context of the lesson, and checking for understanding. For example, the guide identifies academic terms such as digit, segment, reference number, locate, and decompose, and identifies the Math Journeys lessons in which these terms should be supported. In addition, routine 4, “Unfamiliar Reference Quick Bridge,” directs educators to pre-teach the context of an unfamiliar song, story, game, or object by showing an image, real object, or brief clip, explaining the reference in one sentence, having students repeat key vocabulary, and then returning to the math. The lesson-by-lesson guidance identifies specific unfamiliar references and provides an explicit bridge for each. For example, before lesson A2.14, the educator introduces the unfamiliar reference of an abacus by showing the object, explaining how its columns and beads are used to represent numbers, having students repeat the academic vocabulary abacus and column, and allowing students to move a bead before beginning the mathematical task. These supports provide grade 1 educators with explicit guidance for helping students develop 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 A2 Enrichment and Extension Guide provides educators with explicit guidance for grade 1 enrichment and extension activities for students who have shown proficiency in current and above-level content and skills. The guide mentions three observable indicators for determining which students should receive extension, including completing the core task with correct reasoning and time remaining, accurately completing the standard logsheet without support and justifying one’s responses, and demonstrating sustained proficiency with standard and extension activities across three consecutive sessions. The guide also contains explicit guidance for facilitating and evaluating extension logsheets and tips by identifying the purpose of each task, what educators should listen for, expected responses, and evidence of mastery. For example, in Math Journeys A2.3, students extend their understanding of number relationships by finding all numbers whose digits sum up to 7, 11, or 13, comparing the number of solutions, and identifying patterns when the numbers are represented on a hundreds chart. Students show mastery when they systematically generate the complete sets, justify that no solutions are missing, and describe the resulting diagonal pattern. When a student demonstrates sustained proficiency for three consecutive sessions, the guide directs the educator to administer the end-of journey test early. A score above 75 percent enables the student to move on to journey B1 for continued 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 provide 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 include 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 1 program explains how to offer options and supports for students to show their understanding of mathematical concepts in various ways, including performing, expressing, and representing mathematical thinking. Students have opportunities to use concrete, visual, verbal, and symbolic representations to demonstrate their understanding of mathematical concepts. For example, students represent numbers using cubes, groups of tens, money models, and written numerals while explaining how each representation connects to place-value concepts. The materials also guide educators to ask questions, compare representations, and identify incorrect models to help students express and represent mathematical understanding in multiple ways.

Students have opportunities to demonstrate their learning through concrete models, collaborative activities, and visual representations. For example, in lesson A2-7, students start by identifying numbers using a color-coded 20-bead string during whole-group instruction. Students then work in groups to match number cards using a clothespin and, finally, identify numbers on an activity page using visual representations. The materials help students show mathematical understanding through multiple formats and instructional experiences.

2ND

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 1 program provides explicit prompts and guidance for educators to build students’ knowledge by activating their prior knowledge, anchoring big ideas, and highlighting and connecting key patterns, features, and relationships through multiple means of representation. Students have opportunities to connect previously learned concepts to new learning through concrete models, visual representations, and oral discussions. For example, in “Representamos números con el collar de 100,” students link previously used collars of 20 and 50 to create a 100-bead necklace and utilize the model to represent numbers between 50 and 100. The materials also highlight patterns (such as color changes every 10 beads) and help students make connections among counting, place value, and number representation through multiple representations.

Students have opportunities to connect previously learned concepts to new learning through concrete models, visual representations, and mathematical discussions. For example, in lesson B2-12, the “Planteamiento” activity connects doubles addition equations to coloring magic pads and identifying patterns. In development activity 1, students link concrete representations using cubes to a visual model through a part-part-whole frame to explore the relationship between addition and subtraction. The materials help students make connections among mathematical concepts 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 1 program explains how to effectively deliver and facilitate lessons using various teaching approaches such as whole-group instruction, collaborative learning opportunities, oral counting routines, movement-based activities, hands-on use of manipulatives, visual representations, independent practice, and mathematical discourse. Educators also receive step-by-step guidance on facilitation, educator questioning prompts, and differentiated supports through the embedded “Apoyo” and “Ampliación” sections to support students’ engagement and mathematical understanding.

Multiple instructional approaches help students move from concrete to representational understanding while developing number concepts to 100. For example, in lesson A2-13, the educator facilitates the warm-up activity 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 money models, connecting cubes, and activity-page representations to build mathematical understanding using 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 1 program contains multi-tiered intervention methods for various types of practice as well as teaching structures and educator guidance to support effective implementation. The materials provide guided, collaborative, independent, and educator-supported opportunities for practice through whole-group, partner, and individual teaching structures designed to address diverse student learning needs. In addition, educators receive guidance through questioning prompts, manipulatives, visual models, applets, support options, and extension opportunities to assist with implementation. For example, students represent, compare, and order numbers using abacuses, place-value models, and digital resources while educators facilitate discussions, scaffold student reasoning, and adjust instruction based on student performance. The materials also include independent application tasks and differentiated supports that enable educators to monitor understanding and provide targeted intervention as needed.

Assessment data and instructional recommendations help educators identify student needs and select appropriate intervention supports. For example, the “Muestra de informe de la prueba de nivel” 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 1 program provides enrichment and extension methods that support a variety of opportunities for student engagement across the lessons. The “Apoyo” and “Ampliación” sections, embedded within instructional activities, contain differentiated supports and allow educators to extend learning based on student readiness and performance. Additionally, the lessons guide educators on effective implementation through questioning prompts, movement-based activities, number cards, partner discussions, visual models, and opportunities for independent practice. For example, students engage in counting forward and backward, identifying and ordering numbers, and completing numerical sequences 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 keeping students engaged 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 instance, in lesson A2-9, students engage with manipulatives such as 20-bead and 50-bead strings as well as magic pads 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 grade 1 program provides educators with prompts and guidance to support timely feedback during lesson delivery in grade 1 lessons such as “Representamos números con bloques base 10.” Educators can access questioning routines, validation prompts, and opportunities for students to explain and represent numbers using multiple models throughout the lesson. For example, students represent numbers with base 10 blocks, compare quantities, explain place-value relationships, and justify their representations while educators monitor their understanding and provide immediate feedback. Additionally, the lesson includes guidance statements that help educators address misconceptions, such as regrouping units into tens, and validate students’ responses during whole-group and individual activities. Support and extension options allow educators to adjust feedback and instruction based on student needs throughout the lesson.

Anticipated responses, misconceptions, and redirection strategies help educators respond to student thinking and address misunderstandings during instruction. For example, the A2 Journey Language Bank (“A2 Banco de lenguaje y redirecciones”) contains a section called “Banco de respuestas previas, ideas erróneas y redirecciones” that suggests feedback and ideas for redirection based on lesson content. In lesson A2.12, if a student states that 78 + 5 = 84 because the bridge to the next ten is not accounted for, the materials guide educators to ask the student to represent the jump to the next 10 on a number line using arrows (“representa +2 hasta 80 y +3 hasta 83 usando flechas para los saltos”). The materials help educators provide immediate, targeted feedback that enables students to refine their mathematical reasoning and 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 Math Journeys grade 1 program provides implementation guidance to help educators use the materials in bilingual/ESL programs effectively. For example, the “Banco de lenguaje y redirecciones” contains language routines, discourse supports, sentence stems, and writing supports to help emergent bilingual (EB) students participate in mathematical discussions and explain their thinking. For example, the A2 language bank offers guidance for pair conversations, quick writing activities, instructional routines, and educator prompts that help students develop (oral) language and acquire academic vocabulary during math instruction.

The Texas Bilingual/ESL Implementation Guide and the Journey A2 Addendum provide model-specific implementation guidance 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 A2 moves from concrete mathematical experiences toward explanations in English, and the materials recommend using the English portion of the lesson as a bridge from Spanish to English. In lesson A2.3, “Escritura de números hasta 100,” educators review Spanish terms such as dígito, segmento, and suma and provide extended bilingual think time before students talk about patterns 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 1 program contains embedded guidance to help EB students develop their academic vocabulary, increase their comprehension, build background knowledge, and make cross-linguistic connections through oral and written discourse. The materials include academic vocabulary, structured partner discussions, oral language routines, and opportunities for students to explain their mathematical thinking using precise mathematical language. For example, in the lesson “Conteo acústico hacia adelante y hacia atrás (1–50),” students practice using terms such as secuencia, siguiente, anterior, and decena while participating in counting discussions, ordering numbers, and justifying their responses. The “Estudiantes bilingües emergentes” support section provides sentence stems, repeated oral practice, and opportunities for collaborative discourse to help students strengthen their comprehension and develop mathematical language during instruction.

Academic vocabulary, structured partner and group discussions, supports for EB students, and guiding questions provide opportunities for students to explain their mathematical thinking orally as well as in writing. For example, in lesson A2.14, “Representamos números en el ábaco,” students review and practice terms such as ábaco, columna de las decenas, columna de las unidades, and valor posicional, discuss strategies for representing two-digit numbers on an abacus, and record their representations in their “Cuaderno.” The materials help students develop their 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 1 program provides opportunities for practice and instructional assessments throughout the broader learning pathway that require students to show a depth of understanding aligned with the TEKS. In lesson B2.7, “Suma: paso por el 10,” students engage in “Nudo: actividad 1—Practicamos la estrategia del paso por el 10 en el contexto de las hueveras” and “Nudo: actividad 2—Usamos la estrategia del paso por el 10 en el contexto de las hueveras.” Students use ten frame models, manipulatives, and equations to apply the Make Ten strategy to addition problems. Students explain how many counters must be moved to complete a group of ten, represent their thinking using multiple representations, and connect concrete models to symbolic equations. In “Registramos lo que aprendimos,” students independently complete ten frame representations and corresponding equations to demonstrate their understanding of the strategy. This closure activity serves as an instructional assessment that requires students to apply the strategy independently and demonstrate a depth of understanding aligned with the TEKS.

Journey B1.14, “Situaciones contextualizadas de suma y resta: situaciones de cambio creciente y decreciente,” provides students with opportunities to demonstrate their understanding of addition and subtraction through discussions, manipulatives, representations, and problem-solving tasks. In “Nudo: actividad 1,” students solve an addition word problem using bead strings, represent the jumps on a number line, and write a corresponding expression. Students then apply the same process to solve and represent a subtraction word problem. These activities require students to move beyond recalling facts by demonstrating an understanding of increasing and decreasing quantities within contextualized situations. In activity 2, students engage with addition and subtraction equations and create their own word problems to match the number sentences. This task requires students to apply mathematical concepts in meaningful contexts and show a deeper understanding of the relationship between equations and real-world situations. Throughout the lesson, educator guidance and discussion prompts help students explain their reasoning and make connections among representations and mathematical concepts.

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 1 program contains questions and tasks that increase in rigor and complexity, leading to grade-level and above grade-level proficiency in the mathematics TEKS. In lesson A2.1, “Conteo acústico hacia adelante y hacia atrás (1–50),” students progress from counting forward and backward within 50 to identifying missing numbers, completing number sequences, comparing quantities, and ordering numbers from least to greatest. In “Nudo: actividad 1—Contamos hacia adelante y hacia atrás de 10 en 10 a partir de un número determinado,” students identify patterns in counting sequences and analyze relationships among numbers while counting forward and backward by tens. To require students to justify their reasoning and use mathematical language to explain number relationships, the educator uses prompts such as “¿Cómo puedes estar seguro de que el número va aquí?” and “¿Cómo puedes usar palabras como decenas y unidades para justificar por qué colocaste estas cartas en este orden?” In “Nudo: actividad 2—Identificamos y ordenamos números de menor a mayor,” students apply this understanding to compare and order numbers. During “Registramos lo que aprendimos,” students independently complete number sequences, count by tens, identify the least and greatest numbers, and order numbers from least to greatest. The materials include “Ampliación” opportunities that extend learning by having students generate their own number sequences and additional extension resources for students who are ready for greater challenges. Across the lesson, questions, tasks, and extension materials increase in rigor and complexity and support grade-level as well as above grade-level proficiency in the mathematics TEKS.

Journey B3.8, “Resta: saltando y cruzando el 10 II,” provides activities that progressively increase the rigor and complexity of subtracting by combining jumps greater than 10 and crossing tens when subtracting units. In “Nudo: actividad 1,” students solve problems such as 65 − 17 by representing jumps of tens and ones on an empty number line. The activity includes multiple levels of complexity as students may use different strategies to represent subtraction. For example, students may bridge through ten using one jump of seven from 55 to 48, or decompose the jump into smaller parts by subtracting five to reach 50 and then subtracting two more to reach 48. These opportunities encourage students to analyze and compare efficient solutions while developing flexibility in their mathematical thinking. During the “Desenlace,” the “Ampliación” activity extends learning by asking students to create six different two-digit minus one-digit subtraction equations using three given number cards. These tasks provide opportunities for students to engage with increasingly complex mathematical reasoning and extend their understanding beyond the core expectations of the lesson.

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 1 program demonstrates coherence across concepts horizontally within the grade level by connecting patterns, big ideas, and relationships. In lesson B2.7, “Suma: paso por el 10,” students connect decomposition, place-value structure, and addition through the Make Ten strategy. The lesson explicitly states that using the strategy requires understanding both the decomposition of 10 and the decomposition of digits. In “Nudo: actividad 1—Practicamos la estrategia del paso por el 10 en el contexto de las hueveras,” students use ten frame models to decompose an addend and transform expressions such as 9 + 6 into 10 + 5, connecting number decomposition to efficient addition strategies. In “Nudo: actividad 2—Usamos la estrategia del paso por el 10 en el contexto de las hueveras,” students represent addition situations using manipulatives, ten frame models, and equations such as 10 + 3 = 13, linking concrete, pictorial, and symbolic representations. The educator further reinforces these connections by asking questions such as “¿Cómo cambian los números de tu ecuación al mover los cubitos?” and “¿Cómo te ayuda escribir 10 + 3 = 13 a mostrar lo que haces con los cubitos encajables?” Across the lesson, students connect decomposition, benchmark numbers, addition strategies, and multiple representations, demonstrating coherence across mathematical concepts within the grade level.

Another illustration of this can be seen in journey A2.16, “Representamos números con bloques base 10 I,” where students make connections among manipulatives, money, pictorial representations, expanded notation, and number lines to develop a coherent understanding of place value and number relationships. During the “Planteamiento,” students represent numbers using $1 and $10 bills to connect ones and tens. In “Nudo: actividad 1—Presentamos los bloques base 10,” students represent numbers using flats, rods, and units. In activity 2.1, students create pictorial representations to match the base 10 blocks. In activity 2.2, students are introduced to decomposing numbers using expanded notation, such as representing 87 as 80 + 7. These concepts are extended in activity 3, where students compare numbers using expanded notation, locate numbers on a number line, and use comparison symbols to justify their reasoning. Through these connected learning experiences, students form relationships among multiple representations of numbers and apply place-value understanding across different mathematical contexts within 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 1 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 counting and number concepts develop throughout the broader learning pathway and support future mathematical learning. The materials connect students’ understanding of counting, cardinality, number relationships, and place value to increasingly sophisticated concepts and strategies introduced in subsequent journeys. The overview also highlights how representations evolve across learning experiences, including the use of bead strings, number lines, and place-value models to support the development of number sense and computation. The “Contexto matemático” section further explains how these representations are revisited and extended to deepen students’ understanding of counting patterns, number decomposition, and additive reasoning. By explicitly connecting prior knowledge, current learning, and future mathematical concepts through a documented learning progression, the materials show vertical coherence across concepts and grade bands.

Journey B2.9, “Suma: huevera y collar de bolas,” establishes vertical coherence by connecting students’ previous experiences using cubes and bead strings to represent and add numbers with current grade-level learning involving addition by bridging through 10. The lesson also supports future learning by preparing students to use bead strings and number lines to represent operations with larger numbers. In “Nudo: actividad 1,” students move from using two clothespins on a 20-bead string to using three clothespins to represent the next ten as they bridge through 10 when adding. In activity 2, students connect bead string representations to ten frames to model addition across a ten. Students also record and label the numbers represented by the clothespins on paper, linking concrete and pictorial representations. Through these experiences, students build on previously learned strategies while developing understanding that supports future work with number lines and more advanced addition concepts in later grade levels.

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.

The Math Journeys grade 1 program shows coherence across lessons and activities by connecting students’ prior knowledge of concepts and procedures to current and future mathematical learning. In lesson B2.7, “Suma: paso por el 10,” students build on prior conceptual knowledge of number decomposition and the understanding of 10 as a benchmark number. The lesson explicitly states that using the Make Ten strategy requires students to understand both the decomposition of 10 and the decomposition of digits. In “Nudo: actividad 1—Practicamos la estrategia del paso por el 10 en el contexto de las hueveras,” students apply previously learned concepts to transform addition expressions such as 9 + 6 into 10 + 5, connecting prior knowledge of decomposition to a new addition strategy. In “Nudo: actividad 2—Usamos la estrategia del paso por el 10 en el contexto de las hueveras,” students use manipulatives, ten frame models, and equations to apply previously learned procedures for decomposing and recomposing numbers. The lesson connects these current grade-level concepts and procedures to future mathematical learning by helping students develop efficient computation strategies, flexible number sense, and place-value reasoning that support later work with larger numbers and more advanced addition methods. Through explicit connections among prior knowledge, current learning, and future mathematical concepts and procedures, the materials demonstrate coherence across lessons and activities.

Journey A2.12, “Línea numérica: de los colores a la línea vacía (1–100),” connects students’ prior experiences using bead strings to represent numbers and addition with new learning involving empty number lines. In “Nudo: actividad 1.1,” students locate a number on a bead string using a clothespin and determine the result of a forward jump of five units. Students then represent the same addition on an empty number line, connecting a familiar model to a more abstract representation. In activity 1.2, students complete a similar task without the bead string, representing the forward jump directly on the empty number line. Through this progression, students move from concrete and visual models to more abstract representations of addition. These experiences build on previously learned concepts from section A2 and support future learning in sections B2–B5, where students apply number line strategies to add and subtract greater numbers and develop more advanced computational reasoning.

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

The Math Journeys grade 1 program provides students with opportunities to develop and apply mathematical knowledge and skills through distributed practice over time. In lesson B2.7, “Suma: paso por el 10,” students retrieve previously learned knowledge of number decomposition and the structure of 10 as a benchmark number. During “Nudo: actividad 1—Practicamos la estrategia del paso por el 10 en el contexto de las hueveras,” students apply this prior learning to transform addition expressions such as 9 + 6 = 10 + 5 and explain how decomposing an addend helps create a complete group of 10. To require students to connect previous decomposition knowledge to a new computation strategy, educators use prompts such as “¿Podrías explicar qué ocurre cuando movemos huevos de una huevera a otra?” and “¿Qué patrón observas en las sumas cuyo resultado es mayor que 10?” In “Nudo: actividad 2—Usamos la estrategia del paso por el 10 en el contexto de las hueveras,” students continue applying the strategy using manipulatives, ten frame models, and equations such as 8 + 5 = 10 + 3 = 13. The distributed practice continues through the independent work in the “Desenlace,” where students complete multiple addition problems using the same strategy. Through repeated opportunities to retrieve, apply, and extend previously learned concepts and procedures across multiple activities, the materials support distributed practice over time.

Similarly, journey A2.11, “Línea numérica: de las bolas a los colores (1–100),” provides students with opportunities to revisit and apply strategies introduced earlier in section A2 while extending their understanding of number representation to 100. Throughout the broader learning pathway, students use bead strings and number lines to locate, represent, and reason about numbers. In activities 1 and 2, students use a 100-bead string and two-color number lines to represent numbers up to 100. These activities build on strategies previously used with 20-bead and 50-bead strings as well as number lines colored in groups of five. By revisiting familiar models and extending them to larger numbers, students retrieve and apply prior learning while developing a new understanding of number relationships and place value. These opportunities for spaced retrieval help students connect previously learned concepts to new content across the general learning pathway.

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

The Math Journeys grade 1 program provides opportunities for interleaved practice with previously learned skills and concepts across learning pathways. In the “Vista general de tramo—B: pensamiento aditivo,” the “Progresión de contenidos” and “Contexto matemático” sections describe how students revisit and apply previously learned counting, decomposition, number relationship, and place-value concepts while developing increasingly sophisticated addition and subtraction strategies. The materials encourage students to use multiple strategies across the broader learning pathway—such as Count On, decomposition, number-line reasoning, and place-value approaches—rather than practicing a single strategy in isolation. As students progress through the cluster, they repeatedly apply skills and concepts introduced in earlier sessions to solve new types of problems and justify their reasoning. The overview highlights how additive thinking develops by integrating previously learned concepts and procedures, requiring students to connect and apply multiple strategies across their learning experiences. Based on opportunities to revisit, integrate, and apply previously learned skills and concepts across the broader pathway, the materials enable interleaved practice throughout the broader learning pathway.

Journey B2.10, “Resta: huevera y collar de bolas,” provides students with opportunities to apply multiple strategies introduced throughout section B2 while building their understanding of subtraction. Across the broader learning pathway, students engage with addition and subtraction concepts using manipulatives, number cards, ten frames, bead strings, and number sentences. Rather than practicing each strategy in isolation, the lessons integrate previously learned approaches with new learning experiences. In “Nudo: actividad 1,” students use a 20-bead string and clothespins to locate numbers and model subtraction. They then connect the bead string to a color number line and represent subtraction by making backward jumps. In activity 2, students use the bead string to model bridging through ten and connect their representations to ten frames. These activities build on strategies previously introduced in journeys B2.2 through B2.9, allowing students to revisit and apply prior learning while deepening their understanding of subtraction concepts and representations.

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 1 program provides opportunities for students to interpret, analyze, and evaluate models and representations of mathematical concepts and situations in B2.7, “Suma: paso por el 10.” During “Nudo: actividad 1,” students interpret egg-carton models and manipulatives to determine how many cubes they must move to complete a group of ten and represent the resulting equation. Students analyze how decomposing an addend transforms equations such as 9 + 6 into 10 + 5 and 8 + 5 into 10 + 3, making connections among visual models, manipulatives, and symbolic representations. To require students to examine and explain the relationships represented in the models, educators ask questions such as “¿Cómo cambian los números de tu ecuación al mover los cubitos?” and “¿Cómo te ayuda escribir 10 + 3 = 13 a mostrar lo que hiciste con los cubitos encajables?” In the “Desenlace,” students complete independent tasks using egg-carton representations to determine missing values and verify sums, evaluating whether the visual and symbolic representations accurately model the Make Ten strategy. These activities require students to interpret, analyze, and evaluate mathematical models and representations throughout the lesson.

The materials contain questions and tasks that provide students with opportunities to interpret, analyze, and evaluate models and representations for mathematical concepts and situations. In journey B2.12, development activity 1, students use an additive part-part-whole frame to find four different ways to decompose 13 snap cubes into two groups. Students analyze the relationships between parts and wholes, interpret the representations they create, and record corresponding equations. The educator then introduces a situation that can be represented as either addition or subtraction, such as 4 + 12 = 16 or 16 – 4 = 12, prompting students to analyze how the same model can represent different operations. In activity 2, “Calculamos una parte de una combinación conociendo la otra parte y el total,” students receive a total of seven snap cubes divided into two groups covered by handkerchiefs. After uncovering one group, students use an additive part-part-whole frame to identify the missing part. Students evaluate different solutions by finding the missing amount through subtraction and verifying their answer through addition, helping them interpret the inverse relationship between the two operations. In activity 3, students solve a word problem involving a comparison of ages and use an additive part-part-whole frame to determine the difference. As they solve the problem, students evaluate whether the situation is best represented through addition or subtraction and justify their reasoning. These opportunities require students to interpret representations, analyze relationships among quantities, and evaluate mathematical models to deepen their understanding of addition and subtraction as inverse operations.

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 1 program provides students with opportunities to create concrete models and pictorial representations of mathematical situations in A2.16, “Representamos números con bloques base 10.” During “Nudo: actividad 1,” students use base 10 blocks to represent numbers and identify the value of each digit through tens and ones. In “Nudo: actividad 2,” students construct numbers such as 35, 23, 41, 112, and 120 using concrete base 10 materials and then represent those quantities on their “pizarrita mágica” using drawings and symbols, including squares, segments, and crosses. Students create multiple representations of the same number and connect the concrete models to pictorial representations. The lesson also asks students to represent number decompositions through equations, such as 67 = 60 + 7, further connecting models and representations. During the “Desenlace,” students identify numbers represented with base 10 models and complete visual representations by adding the necessary tens and ones. These activities require students to create both concrete models and pictorial representations of mathematical situations.

Similarly, the materials contain questions and tasks that provide students with opportunities to create concrete models and pictorial representations to represent mathematical situations. In journey A2.14, development activity 1, students practice representing two-digit numbers using an abacus. As students model numbers, the educator uses prompts such as “¿Por qué colocamos tres cuentas en la columna de las unidades para representar el número 23?” to encourage students to connect the model to the quantity represented. In activity 2, “Representamos números en el ábaco,” students view “Applet A18 Pack 1,” which displays a symbolic representation of an abacus, and work with a partner to identify and record the number shown. In activity 2.2, the educator calls out numbers between 20 and 99, and students work in pairs to represent the numbers using different forms. One student records the numeral while the other forms a pictorial representation by drawing the abacus. Based on this sequence of activities, students create and connect concrete models using the abacus and pictorial representations through drawings to represent two-digit numbers and demonstrate their understanding of place value.

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 1 program provides students with opportunities to apply conceptual understanding to new problem situations and contexts in B2.14, “Situaciones contextualizadas de suma y resta: situaciones de cambio creciente y decreciente.” In activity 1, students solve contextualized addition and subtraction situations using the bead string model, including scenarios involving passengers on a bus, candies in a jar, bees leaving a hive, and money. The materials explicitly direct students to return to the context of the problem and interpret what the quantities represent rather than focus only on computation. In activity 2, students are presented with expressions such as 7 + 6, 11 – 4, and 5 + 20 and must create their own real-world situations that can be represented by each equation before solving them. The lesson emphasizes that solving an operation is different from solving a problem, requiring students to connect mathematical representations to meaningful contexts. Through creating, solving, and interpreting contextual situations, students apply their conceptual understanding in new problem situations and contexts.

The materials contain questions and tasks that provide students with opportunities to apply their conceptual understanding to new problem situations and contexts. In journey B2.16, development activity 2, students begin by applying addition strategies and number relationships developed in previous lessons (B2.7–B2.15) to solve sums within 20. As the activity progresses, students encounter a new situation that extends their understanding of equality. Students use number cards and operation symbols to identify two different addition expressions that result in the same sum, such as 4 + 7 and 5 + 6, and then represent the relationship as 4 + 7 = 5 + 6. Rather than using the equal sign to show the answer to a calculation, students apply their conceptual understanding in a new context by interpreting the equal sign as representing a balance or equivalence between two expressions. The educator prompts students to discuss and justify why both sides of the equation are equal and how they know that the expressions represent the same quantity. These opportunities require students to transfer previously learned addition concepts to a new mathematical situation, deepening their understanding of equality and the meaning of mathematical symbols.

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 1 program contains tasks designed to help students build the automaticity and fluency needed to complete grade-level mathematical tasks. In journey B2.16, “Práctica productiva: suma hasta 20,” students engage in repeated practice with addition facts and number relationships through a variety of activities. During the “Nudo,” students use number cards to create addition expressions, predict sums, and justify their reasoning with their peers. Students then identify different number combinations that produce the same sum and record multiple equivalent equations, such as 3 + 2 = 1 + 4 and 4 + 7 = 5 + 6. These repeated opportunities help students develop flexibility and efficiency with addition facts while strengthening their understanding of number relationships. During the “Desenlace,” students continue practicing combinations that equal 10, complete missing-addend equations, and generate additional number combinations using cards they are given. Through repeated exposure to addition facts and related number patterns, students build the automaticity and fluency needed to complete grade-level mathematical tasks.

The materials contain tasks to build the automaticity and fluency needed to complete grade-level mathematical tasks. In journey A2.5, “Conteo resultativo (hasta 50),” the “Planteamiento” uses “Applet A1 Pack 18” to provide students with repeated opportunities to identify the number that comes after a given number, strengthening their fluency with counting sequences. In development activity 1, students work together to organize collections of 20–50 snap cubes into groups of ten and then determine the total quantity by counting tens and ones. Students also respond to educator prompts by building collections that match numbers between 10 and 40, reinforcing efficient counting strategies. Through repeated practice grouping objects into tens and counting by tens rather than counting individual cubes, students develop automaticity and fluency with place-value concepts and number quantities. In activity 2, “Identificamos la decena con cubitos encajables,” students view images of towers of ten and individual cubes, with portions of the tens partially hidden, and determine the total number of cubes represented. This activity encourages students to recognize groups of ten as a unit and efficiently count by tens and ones to identify quantities. These opportunities provide repeated practice with counting, grouping, and place-value reasoning, supporting the development of automaticity and fluency with numbers through 50.

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 1 program provides students with opportunities to practice applying efficient, flexible, and accurate mathematical procedures throughout learning pathways. In journey B2.3, “Suma: conteo hacia adelante I,” students compare and apply different strategies for finding sums. During “Nudo: actividad 1,” students determine the total number of cubes in two collections and discuss the strategies they used to find the answer. The educator guides students to evaluate the efficiency of their approaches by asking questions such as “¿Podrías explicar por qué nos puede ser difícil contar si tenemos que contar todos?” and “¿Por qué es más fácil empezar por el 14 y contar 3 más que empezar por el dos y contar 14 más?” Students compare the Count All and Count On strategies and discuss which methods are more efficient. In activity 2, students model addition with cubes and use Count On to determine sums, reinforcing flexible and accurate procedures for solving addition problems. During the “Desenlace,” students continue applying these strategies to addition situations and reflect on which approaches were most efficient. Through these activities, students practice selecting and applying mathematical procedures while comparing strategies for efficiency, flexibility, and accuracy.

The materials provide students with opportunities to practice applying efficient, flexible, and accurate mathematical procedures throughout learning pathways. In journey B2.11, development activity 1, students use snap cubes and part-part-whole boxes to decompose numbers less than 10 into two parts. Students then represent the same relationships using both addition and subtraction equations, such as 3 + 2 = 5 and 5 − 2 = 3, demonstrating flexibility in their use of mathematical procedures. The educator uses prompts that encourage students to approach the task systematically by considering whether there is a combination that begins with 0, then 1, and continues through all possible numbers. Through discussion and educator guidance, students are encouraged to recognize that organizing the number pairs in order is an efficient way to determine whether all decompositions have been found. Students apply these same procedures with larger numbers from 6 to 10, providing additional opportunities to practice and refine their strategies. These opportunities help students develop efficient, flexible, and accurate procedures while analyzing patterns and relationships among numbers.

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 1 program provides students with opportunities to evaluate mathematical representations, models, strategies, and solutions for efficiency, flexibility, and accuracy throughout learning pathways. In journey B2.3, “Suma: conteo hacia adelante I,” students compare different strategies for solving addition problems and discuss the effectiveness of each approach. During “Nudo: actividad 1,” students determine the total number of cubes in two collections and explain the strategy they used to find the sum. The educator records students’ approaches and facilitates discussions about which strategies are more efficient. Students evaluate the Count All and Count On strategies through questions such as “¿Podrías explicar por qué nos puede ser difícil contar si tenemos que contar todos?” and “¿Por qué es más fácil empezar por el 14 y contar 3 más que empezar por el 2 y contar 14 más?” In activity 2, students continue solving addition problems using cubes and discuss how starting with the larger addend can make finding the sum more efficient. During the “Desenlace,” students reflect on their solutions and identify which addition problem seemed easiest while discussing the efficiency of different strategies. Through these activities, students evaluate mathematical procedures and solutions for efficiency, flexibility, and accuracy.

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 B2.15, development activity 1, students use snap cubes, number cards, and operation symbols to represent and solve addition expressions involving three addends, such as 3 + 4 + 5 = 12. As students explore different ways to find the sum, they evaluate multiple representations and strategies, including decomposing numbers to make 10. For example, students may decompose 7 into 4 + 3 to transform 6 + 7 into 6 + 4 + 3, allowing them to use the Make Ten strategy to calculate more efficiently and accurately. In activity 2, “Reflexionamos sobre cómo el orden de los sumandos puede facilitar el cálculo,” students analyze an image representing 3 + 4 + 6 and discuss which numbers they chose to add first and why. The educator uses prompts that encourage students to explain and compare solutions, such as identifying pairs of numbers that make 10 and discussing how rearranging the addends can simplify the calculation. Through these discussions, students evaluate the efficiency of different strategies and recognize that combining 6 + 4 first to make 10 and then adding 3 can lead to a quicker, more accurate solution. These opportunities help students evaluate mathematical models, representations, strategies, and solutions while developing efficient, flexible, and accurate approaches to computation.

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

The Math Journeys grade 1 program contains guidance to help students select increasingly efficient approaches to solve math problems. In journey B2.3, “Suma: conteo hacia adelante I,” students compare strategies for solving addition problems and are guided toward more efficient counting methods. During “Nudo: actividad 1,” students determine the total number of cubes in two collections and discuss the strategies used to find the sum. The materials explicitly state, “Con el pañuelo evitamos que los niños y niñas cuenten los cubitos uno a uno y, por tanto, pretendemos que expliquen la cantidad inicial para resolver la suma.” This encourages students to move beyond counting all objects individually. To help students evaluate more efficient approaches, the educator uses prompts such as “¿Podrías explicar por qué nos puede ser difícil contar si tenemos que contar todos?” and “¿Por qué es más fácil empezar por el 14 y contar tres más que empezar por el 2 y contar 14 más?” In activity 2, the materials state, “Pretendemos que el alumnado llegue a la conclusión de que, antes de resolver una suma como 2 + 9 contando a partir del primer sumando (dos), es más fácil hacer 9 + 2,” guiding students to count on from the larger addend. During the “Desenlace,” students reflect on the efficiency of different strategies and identify addition methods that are easier and more effective. Through these supports, students develop increasingly efficient approaches for solving addition problems.

The materials contain guidance to help students select increasingly efficient approaches to solve math problems. In journey B2.10, development activity 1, students solve subtraction problems such as 12 − 5 using clothespins on a 20-bead string. Rather than counting back one bead at a time, students are guided to use a more efficient strategy by decomposing five into two and three, allowing them to make a jump of two to reach 10 and then a jump of three to reach seven. To encourage students to analyze and compare solution strategies, the educator uses prompts such as “¿Puedes explicar por qué dividir el salto en dos partes ayuda a resolver el problema?” and “¿Puedes encontrar otra manera de descomponer el número cinco para facilitar la resta?” In activity 2, “Relacionamos el paso por el 10 sobre el collar con las hueveras,” students represent the same subtraction problem using ten frames and connect the strategy of bridging through 10 across different models. The educator further supports students’ understanding with questions such as “¿Puedes explicar cómo pasar por el 10 funciona de la misma manera en la huevera y en el collar de bolas?” and “¿Cómo te ayudan los cambios de color a identificar el 10 en ambas herramientas?” Through these opportunities, students compare representations, justify their reasoning, and recognize that decomposing numbers to bridge through 10 is more efficient than counting back one at a time. These supports help students select increasingly efficient strategies for solving subtraction problems while developing conceptual understanding across multiple mathematical models.

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

The Math Journeys grade 1 program explicitly states how the conceptual and procedural emphases of the TEKS are addressed in the “Vista general de tramo—B: pensamiento aditivo.” The overview identifies the conceptual emphasis by describing how students develop an understanding of addition and subtraction relationships, composing and decomposing numbers, and the connections between different representations and strategies used to solve additive situations. For example, the materials describe how students build understanding of part-whole relationships and represent addition and subtraction situations using concrete, pictorial, and symbolic models. The overview also identifies the procedural emphasis by outlining the skills students will practice throughout the broader learning pathway, including solving addition and subtraction problems, using counting strategies, representing operations with models and equations, and applying strategies to determine unknown quantities. Through the “Vista general de tramo—B: pensamiento aditivo,” the Math Journeys grade 1 program explicitly communicates both the conceptual understanding and procedural skills addressed within the TEKS.

The materials explicitly state how the conceptual and procedural emphases of the TEKS are addressed. In journey B2.8, development activity 1, students use a ten frame widget to solve subtraction problems such as 12 − 5. The activity develops conceptual understanding of decomposition and the Make Ten strategy while also building procedural fluency with subtracting across ten. Students decompose the subtrahend to determine how many eggs they must remove from the second ten frame and how many additional eggs they must remove from the first ten frame to bridge through 10. To help students connect the procedure to the underlying mathematical concepts, the educator uses prompts such as “Si necesitas quitar cinco huevos, ¿cuántos debes quitar de la segunda huevera?,” “¿Cuántos más necesitas quitar de la primera huevera?,” and “¿Cuántos huevos quedan en la primera huevera?” In activity 2, “Usamos la estrategia del paso por el 10 en el contexto de las hueveras,” students use ten frames and snap cubes to solve problems such as 14 − 5 by decomposing the subtrahend and applying the Bridge through Ten strategy (14 − 4 = 10; 10 − 1 = 9). Based on educator-guided questioning and hands-on modeling, students connect their conceptual understanding of place value, decomposition, and Make Ten with the procedural steps required to efficiently solve subtraction problems that cross ten.

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 1 program provide students with opportunities to use concrete models, pictorial representations, and abstract models as required by the TEKS. In journey A2.16, “Representamos números en el ábaco II / Representamos números con bloques base 10,” students represent numbers using multiple representations as they develop place-value understanding. During “Nudo: actividad 1,” students use concrete models, including base 10 blocks, to build and represent numbers composed of hundreds, tens, and ones. In activity 2.1, students construct numbers such as 35 using base 10 blocks and then create pictorial representations on their “pizarrita mágica,” where “representaremos la centena con un cuadrado, las decenas con segmentos y las unidades con cruces.” Students then transition to abstract representations by writing numerals and recording numbers represented by the models. In activity 2.2, students represent numbers with manipulatives, draw equivalent pictorial models, and express the same quantities using numerals and expanded notation. The lesson further extends abstract thinking as students compare numbers using the symbols > and < and represent number decompositions as sums. Through these activities, students use concrete models, pictorial representations, and abstract representations to develop their understanding of place value and number relationships.

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 B2.8, development activity 2, students use snap cubes placed on printed ten frames to represent and solve 14 − 5, providing a concrete model of the subtraction situation. Students remove four cubes from the second ten frame and then one cube from the first ten frame, demonstrating how the subtrahend can be decomposed to bridge through 10. As students manipulate the cubes, they connect the concrete model to pictorial representations on the ten frames and then record the solution using the abstract equation 14 − 5 = 9 on their magic pads. To help students make connections among the different representations, the educator uses prompts such as “¿Cómo representa la acción de quitar cubitos la resta que escribimos?” and “¿Puedes explicar qué representa cada número en la expresión 14 − 5 = 9 usando los cubitos de tus hueveras?” These opportunities help students use and connect concrete models, pictorial representations, and abstract mathematical notation to develop a deeper understanding of subtraction across 10.

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 1 program provides supports for students to connect, create, define, and explain concrete and representational models to abstract concepts as required by the TEKS. In journey B2.7, “Suma: paso por el 10,” students use ten frames (hueveras) and counters to model addition problems and connect these representations to abstract equations. During “Nudo: actividad 1,” students represent the sum 9 + 6 using ten frames and determine how many counters they must move to complete a group of ten. The materials explicitly connect the model to the symbolic representation by asking, “¿Qué nueva suma obtenemos al pasar 1 huevo de la segunda a la primera? (10 + 5).” In activity 2, students model sums such as 8 + 5 with counters and ten frames, move counters to make 10, and record the resulting equation on their “pizarrita mágica.” The materials explain that “La descomposición del 10 es fundamental para completar la primera huevera” and that decomposing numbers helps students determine the remaining quantity, supporting them in defining and explaining the strategy. Students create representations, connect concrete models to equations, and explain how decomposing an addend results in an equivalent addition expression. Through these supports, students connect, create, define, and explain concrete and representational models as well as abstract mathematical concepts.

The materials provide supports for students to connect, create, define, and explain concrete and representational models as well as abstract concepts, as required by the TEKS. In journey B2.8, “Resta: paso por el 10,” the educator uses questions, discussions, and instructional supports that guide students from concrete models to pictorial representations and abstract mathematical concepts. In development activity 2, students use snap cubes on printed ten frames to represent 14 − 5, providing a concrete model of the subtraction situation. To help students as they decompose the subtrahend and apply the Bridge through Ten strategy, the educator uses prompts such as “¿Cuántos cubitos puedes quitar de la segunda huevera?,” “¿Cuántos necesitas quitar de la primera huevera?,” and “¿Cuántos cubitos quedan en la huevera?” Students remove four cubes from the second ten frame and then one cube from the first ten frame, demonstrating how the decomposition of five can be represented using the model. Students then connect this concrete representation to pictorial and abstract representations by recording the subtraction equation 14 − 5 = 9 on their magic pads. The educator further supports these connections with questions such as “¿Cómo representa la acción de quitar cubitos la resta que escribimos?” and “¿Puedes explicar qué representa cada número en la expresión 14 − 5 = 9 usando los cubitos de tus hueveras?” These supports help students connect, create, define, and explain the relationships among concrete models, visual representations, and abstract mathematical notation while developing a conceptual understanding of subtraction across 10.

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 1 program provides students with opportunities to develop academic mathematical language using visuals, manipulatives, and other language development strategies. In the “Vista general de tramo—B: pensamiento aditivo,” the materials include dedicated vocabulary sections that introduce mathematical terms related to addition, subtraction, composing and decomposing numbers, and additive situations. The overview incorporates visual representations such as additive boxes, number lines, equations, and other mathematical models that help students develop and use academic mathematical language. Throughout the broader learning pathway, students discuss strategies, explain the relationships between quantities, represent addition and subtraction situations using multiple models, and communicate their mathematical reasoning. These opportunities encourage students to listen, speak, read, and write using mathematical vocabulary while making connections between visual models and mathematical concepts.

While participating in journey A1.8, “Estimar y comparar,” students develop academic mathematical language through visuals, manipulatives, and language development strategies. The educator introduces the academic term estimar by showing students a cup containing snap cubes and asking, “¿Cuántos cubitos creen que necesitamos para llenar el vaso?” Students make estimates, share their predictions, and use manipulatives to test their ideas. To encourage students to compare their estimates with the actual quantity and explain their reasoning using precise mathematical language, the educator then introduces the word comparar by asking 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/menos habías dicho en tu hipótesis?” Additionally, the EB guidance recommends using the “critique, correct, clarify” strategy, prompting the educator to read a student’s estimation statement and help students identify the estimate, justify their reasoning, use comparative terms such as más que, menos que, or cantidad igual, and explain what they would change after counting the snap cubes.

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 1 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 B2 Journey Language Bank (“Banco de lenguaje y redirecciones”) provides educators with sentence stems, discussion prompts, vocabulary supports, and redirection to help students communicate mathematical ideas using precise mathematical language. The materials contain guidance for discussing addition and subtraction strategies, composing and decomposing numbers, representations, and mathematical relationships. Educators are provided with prompts that encourage students to explain their reasoning, justify their solutions, compare strategies, and communicate their thinking during partner, small-group, and whole-group discussions. The Journey Language Banks also include follow-up questions and redirection that extend students’ responses and support deeper mathematical discourse. Through these embedded supports, the Math Journeys grade 1 program scaffolds and extends students’ use of academic mathematical vocabulary when communicating with peers and educators.

During journey A2.16, “Representamos números con bloques base 10 I,” students strengthen their use of academic mathematical vocabulary through embedded guidance that scaffolds, supports, and extends mathematical communication with peers and the educator. Students represent numbers from one to 120 with base 10 blocks, decompose numbers into tens and ones, and use place-value language as they connect concrete models to written numerals. The educator introduces rods as groups of ten and models how each digit represents a specific place value. To encourage students to explain and justify their representations using academic mathematical vocabulary, the educator then prompts students to communicate their understanding by asking, “¿Podrías explicar qué nos dice la cantidad de barras y cubitos sobre el valor del número?” and “¿Podrías pensar en otra manera de representar este número y mostrarla?” Additionally, the EB guidance recommends the Stronger and Clearer Each Time strategy by asking students to write an initial response to “¿Cómo muestra el valor posicional la representación del 36 con bloques base 10?” Students exchange responses with a partner, explain their reasoning, receive feedback, and revise their explanations using more precise mathematical language. To extend students’ understanding, the lesson asks students to represent 40 so they can discuss the meaning of the zero in the ones place and explain why the representation contains no individual unit blocks.

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 1 program provides embedded guidance to help students apply appropriate mathematical language and academic vocabulary in discourse. In journey B2.7, “Suma: paso por el 10,” students use concrete models such as “hueveras” and connecting cubes to represent addition situations and apply the Make Ten strategy. Students discuss how moving cubes changes the quantities in the addends, create representational models on their “pizarrita mágica,” and connect those models to abstract equations such as 8 + 5 = 13 and 10 + 3 = 13. To require students to explain their reasoning using mathematical language, the materials include embedded guidance for the educator such as “Comunicar ideas usando lenguaje matemático preciso” and prompts such as “¿Cómo cambia los números de la ecuación al mover los cubitos?” and “¿Cómo te ayuda escribir 10 + ? = 13 mostrar lo que hiciste con los cubitos originales?” Students justify how the Make Ten strategy works, describe the relationships among concrete models, drawings, and equations, and communicate their thinking using academic terms such as suma, decena, unidades, ecuación, estrategia, and descomposición during mathematical discourse with their peers and the educator.

Within journey B2.12, “Conectamos suma y resta I,” students apply appropriate mathematical language and academic vocabulary during mathematical discourse through embedded instructional guidance. During “Nudo: actividad 1— Encontramos algunas descomposiciones de números mayores que 10,” students use part-part-whole frames to decompose 13, record multiple addition expressions, and explain how they determined each decomposition. To encourage students to use precise mathematical vocabulary as they describe their strategies, the educator prompts students to communicate their mathematical thinking by asking, “¿Podrías explicar cómo has encontrado diferentes maneras de obtener 13?” and “¿Cómo te ayuda tu plan a saber si has encontrado todos los pares?” Next, in activity 2, “Calculamos una parte de una combinación conociendo la otra parte y el total,” students work together with snap cubes and the handkerchief strategy to solve subtraction problems and discuss how they determined the unknown part. To further support mathematical discourse, and to scaffold students’ use of academic mathematical vocabulary as they explain their reasoning to their peers and the educator, the EB guidance prompts the educator to ask questions such as “¿Cuál es la cantidad total?” and “¿Cuántos hay?” while providing sentence stems such as “Si restamos ___ de ___, obtenemos ___.”

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 1 program provides embedded guidance to facilitate mathematical conversations in B2.7, “Suma: paso por el 10.” During activity 2, students work in pairs using egg-carton models and connecting cubes to apply the Make Ten strategy while discussing their reasoning with a partner. The materials provide structured opportunities for students to explain how moving cubes changes the equation and how the new representation relates to the original sum. To encourage students to communicate and justify their thinking using mathematical language, the educator uses prompts such as “¿Cómo cambian los números de tu ecuación al mover los cubitos?” and “¿Cómo te ayuda escribir 10 + 3 = 13 a mostrar lo que hiciste con los cubitos encajables?” In addition, the Math Language Routines (MLR) guidance prompts students to compare strategies, explain how quantities changed, and connect concrete actions to symbolic representations. Through peer discussions and educator-supported prompts, students hear, refine, and use mathematical language with their classmates.

Throughout journey A2.16, “Representamos números con bloques base 10 I,” students participate in mathematical conversations that allow them to hear, refine, and use mathematical language with their peers through embedded guidance. Students represent numbers from one to 120 by decomposing them into tens and ones with base 10 blocks before sharing their thinking with their group. For example, students represent 36 using three rods and six unit cubes, draw a pictorial representation, and record the decomposition 30 + 6. As students connect the concrete model to the written numeral, in order to encourage students to explain what each digit represents and compare different representations, the educator prompts mathematical discussion by asking, “¿Podrías explicar qué nos dice la cantidad de barras y cubitos sobre el valor del número?” and “¿Podrías pensar en otra manera de representar este número y mostrarla?” To strengthen mathematical communication, the EB guidance recommends the Stronger and Clearer Each Time strategy by asking students to write an initial response to “¿Cómo muestra el valor posicional la representación del 36 con bloques base 10?” Students then exchange explanations with a partner, receive feedback, revise their responses using more precise mathematical language, and present their refined explanations during a whole-class share-out. This routine provides multiple opportunities for students to hear mathematical language, refine their explanations based on peer feedback, and communicate their mathematical thinking with increasing precision.

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 1 program provides embedded guidance, including exemplar responses to questions and tasks, to help educators anticipate a variety of student answers and support and redirect inaccurate responses. In lesson B2.7, “Suma: paso por el 10,” students use ten frame representations and manipulatives to apply the Make Ten strategy when solving addition problems. The materials provide anticipated responses and exemplar solutions, including identifying that one counter must be moved to transform 9 + 6 into 10 + 5, and that two counters must be moved to transform 8 + 5 into 10 + 3. Embedded prompts allow educators to guide students in explaining how the quantities change when counters are moved and how the new equation represents the action shown in the model. The lesson also contains support guidance that encourages the use of ten frames and connecting cubes when students need further assistance. This helps educators address misconceptions and redirect students toward accurate mathematical reasoning.

Journey A2.14, “Representamos números en el ábaco I,” provides embedded guidance, including exemplar answers, to help educators anticipate a variety of student responses and address inaccurate responses. Students connect two-digit numerals to quantities represented on an abacus by applying their understanding of place value. As the educator models the number 23 on the abacus, students respond to the question, “¿Por qué creen que no se pueden poner 10 bolas en la columna de la derecha?” The materials provide an anticipated student response: “no tiene sentido poner 10 bolas en la columna de la derecha porque 10 billetes de un dólar equivalen a 1 billete de 10 dólares,” which the educator can use to reinforce place-value concepts or redirect misconceptions. Later, in activity 2, “Representamos números en el ábaco,” students use seven beads to represent numbers on their individual abacuses and share their representations with the class. The Teacher Guide anticipates all possible correct responses (7, 16, 25, 34, 43, 52, 61, and 70), prompts educators to identify any missing representations with the class, and provides the exemplar sequence 7 < 16 < 25 < 34 < 43 < 52 < 61 < 70 to support feedback as students compare and order the numbers from least to greatest.

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

The Math Journeys grade 1 program integrates the TEKS mathematical process standards appropriately within grade-level content instruction. In lesson B2.7, “Suma: paso por el 10,” students apply the Make Ten strategy to solve addition problems using ten frames, connecting cubes, drawings, and equations. Students analyze the relationships between quantities by determining how many counters they must move to complete a ten and then represent the resulting sums using mathematical models and symbolic notation. Throughout the lesson, students explain how the numbers change when moving counters, share their solutions with their peers, and record their reasoning on individual whiteboards. The lesson explicitly connects mathematical representations, problem-solving, communication, and reasoning while students use appropriate tools and strategies to solve addition problems, demonstrating appropriate integration of the TEKS mathematical process standards with content learning.

Throughout journey B2.10, “Resta: huevera y collar de bolas,” the Math Journeys grade 1 program integrates the TEKS mathematical process standards within grade-level content instruction. During “Nudo: actividad 1—Recuperamos la representación de la resta de dos números sobre el collar de 20,” TEKS process standard 1.B is embedded as students use a problem-solving model to solve 12 − 5 on the bead string. Students analyze the backward jump of five, decompose it into two and three to bridge through 10, place clothespins at 12, 10, and seven, and justify why the two-part jump produces the correct solution. The educator supports students’ mathematical reasoning by asking, “¿Podrías explicar por qué dividir el salto en dos partes ayuda a resolver el problema?” and “¿Puedes encontrar otra manera de descomponer el número cinco para facilitar la resta?” Next, in activity 2, “Relacionamos el paso del 10 por el collar de las hueveras,” TEKS process standard 1.F is embedded as students analyze the relationship between bridging through 10 with the ten frame and the bead string. The educator extends students’ understanding by asking, “¿Podrías explicar cómo el paso por el 10 funciona de la misma manera en la huevera y en el collar de bolas?” and “¿Cómo te ayudan los cambios de color a encontrar el 10 en ambas herramientas?” This prompts students to analyze the mathematical connections between the two representations and explain how each model supports the same subtraction strategy.

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

The Math Journeys grade 1 program describes how process standards are incorporated and connected throughout the broader learning pathway. In the B2 Journey Instructional Guide, the materials explain the TEKS mathematical process standards. The guide contains sections on vertical as well as horizontal alignment that describe how mathematical reasoning, problem-solving, communication, and representations are developed across the journey. The guide also includes a lesson-by-lesson alignment chart identifying where process standards are embedded within each session and how they connect to content development. These descriptions show that process standards are intentionally incorporated throughout the broader learning pathway and linked across lessons to support students’ mathematical understanding.

Throughout journey A2.15, “Representamos números en el ábaco II,” the Math Journeys grade 1 program describes how the TEKS mathematical process standards connect and build across the broader learning pathway. The Teacher Guide explicitly identifies TEKS process standards 1.B and 1.F, which students apply across multiple lesson activities. In activity 1, “Investigamos qué pasa al añadir una bola al ábaco,” students engage with process standard 1.F by analyzing how the position of a bead on the abacus changes the value of a number. For example, students begin with 35, determine that adding one bead to the ones column creates 36, and recognize that adding one bead to the tens column creates 45, demonstrating that the position of the bead determines whether it represents one or 10. Later, in activity 2, “Representamos en el ábaco números que cumplan ciertas condiciones,” students engage with process standard 1.B by using a problem-solving model to represent numbers with exactly eight beads while meeting conditions such as creating a number greater than 40. Students analyze the given information, plan how to distribute the beads between the tens and ones columns, find a solution, and verify whether their representation satisfies all of the stated conditions before revising their approach when needed. By connecting students’ understanding of place value to increasingly complex problem-solving tasks, the lesson shows how process standards 1.F and 1.B work together throughout the general learning pathway.

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

The Math Journeys grade 1 program provides an overview of the TEKS mathematical process standards incorporated into the lesson. In lesson B2.12, “Conectamos suma y resta,” the materials explicitly identify process standard “1B, usar un modelo de resolución de problemas” and describe how students apply the standard throughout the lesson. Students use additive boxes, manipulatives, equations, and contextualized situations to represent mathematical relationships, determine missing values, and connect addition and subtraction as inverse operations. The lesson guidance explains that students apply a problem-solving process by modeling situations, selecting representations, communicating mathematical ideas, and justifying their solutions while solving increasingly complex tasks.

Within journey B2.17, “Práctica productiva: resta hasta 20,” the Math Journeys grade 1 program provides an overview of the TEKS mathematical process standards incorporated throughout the lesson. The Teacher Guide explicitly identifies TEKS process standards 1.E and 1.G, helping educators recognize where students apply each standard during instruction. During the “Planteamiento,” students complete mathematical sentences using the symbols <, >, or =. Process standard 1.G guides students as they explain and justify why a comparison statement is true by using precise mathematical language. To support students’ mathematical reasoning, the Teacher Guide contains an exemplar explanation and prompts educators to ask questions such as “¿Podrías explicar por qué este símbolo hace que la expresión sea verdadera?” and “¿Qué significa el signo mayor que en esta expresión?” Later, in activity 1, “Recordamos las cajitas aditivas,” process standard 1.E guides students as they create and use mathematical representations to organize and communicate the relationship between addition and subtraction. Students place numbers in an addition square to demonstrate related equations, such as 7 + 5 = 12, 12 − 5 = 7, and 12 − 7 = 5, making the inverse relationship between addition and subtraction visible through a mathematical representation.

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

In lesson B2.15, “Sumamos tres números” of the Math Journeys grade 1 program, students think mathematically, persevere through solving problems, and make sense of math as they explore strategies for adding three addends. Students use manipulatives, drawings, and equations to represent sums, investigate how decomposing and reordering numbers can simplify calculations, and explain the reasoning behind their strategies. The lesson includes educator prompts such as “¿Puedes explicar cómo tu solución muestra lo que hiciste con los tres grupos de cubos?,” “¿Cómo se relacionan los tres grupos de cubos con cada número de tu ecuación?,” “¿Puedes explicar con tus propias palabras lo que hiciste con los tres grupos de cubos?,” and “¿Ves un par de números que suman 10? ¿Por qué sería útil empezar por ellos?” These prompts “incentivan a los estudiantes a justificar su pensamiento, analizar las relaciones entre los números y comparar métodos de solución.” Students participate in whole-group discussions to share and defend their strategies, explain how they represented their solutions, and evaluate different approaches for finding sums. During independent practice, students generate multiple combinations that satisfy specific conditions, such as creating different combinations that total 10, demonstrating perseverance, mathematical reasoning, and conceptual understanding of addition.

In journey B2.16, “Práctica productiva: suma hasta 20,” students build two addition equations with number cards, making sure both sides have the same sum. For example, they pair 4 + 7 and 5 + 6 because each adds up to 11. Students check both sides of the equation to confirm that the sums match. Educators ask questions such as “¿Cuál es la suma del lado izquierdo?,” “¿Cuál es la suma del lado derecho?,” and “¿Son iguales?” and keep the equations visible so students can compare and see that different expressions can be equal. Students experiment with different card combinations, test whether their equations are equivalent, and revise their choices as needed. This activity challenges students to persevere and understand mathematical relationships.

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 B2.3, “Suma: conteo hacia adelante I” of the Math Journeys grade 1 program helps students understand, explain, and justify that there can be multiple ways to solve problems and complete tasks. Students explore addition strategies by representing and solving problems using cubes, number cards, drawings, and equations. During the lesson, students compare strategies for adding collections, including counting all objects and using the Count On strategy. The lesson includes educator prompts such as “¿Cuántos cubitos tenemos entre los dos conjuntos?,” “¿Qué estrategia empleó para llegar a la solución?” and “Si lo tuvieran que hacer ustedes, ¿qué pañuelo levantarían primero?” These prompts “incentivan a los estudiantes a explicar su razonamiento, comparar enfoques y justificar por qué una estrategia puede ser más eficiente.” Students discuss how starting with the greater number can make solving addition problems easier. They continue applying different strategies during partner and independent activities. These opportunities allow students to understand that problems can be solved in multiple ways and help them explain and defend their mathematical reasoning.

In journey B2.9, “Suma: huevera y collar de bolas,” students apply the Bridging through Ten strategy by jumping forward along the 20-bead string and using ten frames to add numbers. In development activity 1, students solve 9 + 5 by decomposing five into one and four, first jumping one to make 10 and then jumping four to reach 14. In activity 2, “Relacionamos el paso por el 10 sobre el collar con las hueveras,” students use ten frames to solve 8 + 6 by decomposing six into two and four, completing the first ten frame with eight and two before adding the remaining four to the second ten frame. Students compare the 20-bead string and ten frames as different representations for solving the same problem. Box 1F explains that students analyze the mathematical relationship between the bead string and the ten frame to connect and communicate the same Bridging through Ten strategy. To encourage students to explain, justify, and compare multiple solutions, the educator uses prompts such as “¿Podrías explicar por qué el paso por el 10 funciona de la misma manera en el collar de bolas y en la huevera?” and “¿Qué patrón observas en la manera en la que descomponemos los números para formar primero el 10?”

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.

Throughout lesson B2.7, “Suma: paso por el 10” of the Math Journeys grade 1 program, students make sense of math through multiple opportunities to do, write about, and discuss math with their peers and the educator. Students first do math by using egg-carton models, counters, and the widget “hueveras” to apply the Make Ten strategy. They move counters from one egg carton to another, solve addition problems such as 9 + 6 and 8 + 5, and model how decomposing one addend creates an equivalent addition expression. To prompt students to explain their mathematical reasoning, the educator asks questions such as “¿Cuántos huevos de la segunda huevera deben pasar a la primera para completarla?” and “¿Qué nueva suma obtenemos?” Students then write about math by recording their new equations and solutions on their “pizarrita mágica” and by completing the independent practice in the “Desenlace,” where they represent and solve additional Make Ten problems. Finally, students discuss math by working with partners to explain how they moved the counters, compare solution strategies, and share their mathematical thinking during educator-led, whole-group conversations.

In journey B2.16, development activity 2, students play a card game to add numbers. Students place the cards face down, randomly select two cards to add, independently determine the sum, and record their answers on their individual whiteboards. After all students finish, they share and justify their solutions with their group. Students then deepen their understanding by comparing two addition expressions and creating a mathematical sentence using number cards and + and = symbol cards. They discuss and justify their reasoning by showing that both sides of the equation represent the same sum, providing opportunities to do math, write about their thinking, and engage in mathematical discussions with their peers.

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

As students progress through lesson B2.7, “Suma: paso por el 10” of the Math Journeys grade 1 program, they share and reflect on their problem-solving approaches by explaining, justifying, and discussing their mathematical thinking with their peers and the educator. Students first use egg-carton models, counters, and the widget “hueveras” to solve addition problems using the Make Ten strategy. To prompt students to explain how moving counters changes the addition expression and justify why the new equation is equivalent to the original problem, the educator asks questions such as “¿Cuántos huevos de la segunda huevera deben pasar a la primera para completarla?” and “¿Qué nueva suma obtenemos al pasar dos cubitos de la segunda huevera a la primera?” While working in pairs, students record their new equations and solutions on their “pizarrita mágica,” then raise their boards to share their work with the class so that the educator and classmates can compare and discuss different possible solutions. During the lesson, to encourage students to reflect on the relationship between their concrete models and written equations as well as explain why the Make Ten strategy works, the educator asks, “¿Cómo cambian los números de la ecuación al mover los cubitos?” and “¿Cómo te ayuda escribir 10 + 3 = 13 a mostrar lo que hiciste con los cubitos encajables?”

In journey B2.8, development activity 2, students use snap cubes and ten frames to solve 14 − 5 by applying the Make Ten strategy introduced in activity 1. As students remove five snap cubes, the educator guides them with questions such as “¿Cuántos cubitos puedes quitar de la segunda huevera?,” “¿Cuántos necesitas quitar de la primera huevera?,” and “¿Cuántos cubitos quedan en la huevera?” Students then write a mathematical sentence to represent the subtraction and explain how the equation models the actions they performed with the cubes. Box 1D explains that students communicate the mathematical idea behind 14 − 5 = 9 using multiple representations by connecting their actions with the snap cubes to the symbols in the equation. To help students share, explain, and justify their problem-solving approaches, the Teacher Guide provides prompts such as “¿Cómo representa la retirada de los cubitos la resta que escribimos?” and “¿Podrías explicar qué significa cada número de 14 − 5 = 9 utilizando los cubitos encajables de tus hueveras?”

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

Throughout lesson B2.7, “Suma: paso por el 10” of the Math Journeys grade 1 program, prompts guide educators to provide explanatory feedback based on student responses and anticipated misconceptions. As students use egg-carton models, counters, and the widget “hueveras” to apply the Make Ten strategy, in order to elicit student thinking and provide feedback that connects the concrete model to the new addition equation, the educator asks questions such as “¿Cuántos huevos de la segunda huevera deben pasar a la primera para completarla?” and “¿Qué nueva suma obtenemos al pasar dos cubitos de la segunda huevera a la primera?” The lesson also anticipates misconceptions about how moving counters changes the expression by prompting the educator to ask, “¿Cómo cambian los números de la ecuación al mover los cubitos?” and “¿Cómo te ayuda escribir 10 + 3 = 13 a mostrar lo que hiciste con los cubitos encajables?” These questions help educators address misunderstandings by guiding students to explain why the new equation is equivalent to the original addition problem, rather than simply identifying the correct answer. Students then share their equations on their “pizarrita mágica,” allowing the educator to respond to student work with explanatory feedback and reinforce the relationship between the concrete model and the symbolic representation.

In journey A2.14, “Representamos números en el ábaco I,” educators guide students to show the number 23 on an abacus with tens and ones columns. To help students realize that ten beads in the ones column equal one bead in the tens column, educators ask, “¿Por qué creen que no se pueden poner 10 bolas en la columna de la derecha?” Box 1G tells students to justify putting two beads in the tens column and three in the ones column because each bead in the tens column stands for a group of ten, and each bead in the ones column stands for one unit. To encourage reasoning, educators also prompt students with questions such as “¿Puedes explicar qué significa cada bola en las distintas columnas?” and “¿Por qué ponemos tres bolas en la columna de las unidades para representar el número 23?” In activity 2.3, students use seven beads to represent all possible numbers on the abacus. Educators address the misconception that a number with a smaller ones digit may be greater by having students order numbers from least to greatest (7 < 16 < 25 < 34 < 43 < 52 < 61 < 70). The materials help educators give feedback and support to deepen students’ understanding of place value.