Math Journeys Texas, Grado 3 (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 3 program outlines the TEKS corresponding to each of the lessons, including both content and process standards for educators. The scope and sequence document is organized into sections called “Journeys” and identifies the TEKS and ELPS addressed in each. The Journey Instructional Guide provides a detailed rationale for each journey. For example, section 2 of the guide explains the vertical rationale for how the current journey builds on 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. Section 3 describes the horizontal rationale, showing how learning progresses from concrete to representational and abstract models of number sense.

The Math Journeys Spanish Instructional Guide explains how each journey connects to prior and future learning through both vertical and horizontal alignment. The guide describes each journey’s specific role within the overall learning progression and illustrates how concepts build across grade levels as well as within the same grade. This organization shows how learning experiences are intentionally sequenced and interconnected to reinforce and extend students’ understanding.

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 Math Journeys grade 3 Spanish provides comprehensive instruction on implementation, including the three-step framework of “build,” “consolidate,” and “practice.” Each lesson starts with an educator-led, small-group lesson, followed by logsheets for students to complete independently with educator feedback and then further optional practice on Atlas Math, an adaptive digital platform. In addition, the “Lesson Internalization and Planning” section explains how to plan for student variability, including explanations for multiple entry points, just-in-time supports, extensions, and multiple representations and modes of expression.

Within each journey, instructional activities provide opportunities for enrichment, small-group instruction, and targeted supports. Guidance is included for adapting instruction based on students’ needs through additional practice, intervention resources, and differentiated instructional approaches. These supports are designed to address varying student needs across instructional settings while maintaining access to grade-level content.

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

The TEKS Correlation Guide identifies recommended skill entry points based on the results of diagnostic assessment and aligns lessons within each journey to TEKS content and process standards. The guide supports instructional planning by helping educators connect lessons and activities to specific standards addressed within each journey. Additionally, reports for diagnostic assessment and placement provide recommended skill entry points, targeted interventions, and instructional supports based on individual student performance, allowing educators to determine appropriate starting points and instructional pathways for students.

The placement test report sample for Math Journeys grade 3 Spanish outlines the TEKS Correlation Guide with recommended skill entry points based on the results of diagnostic assessment. The report clearly identifies the TEKS that were assessed and includes a “Proposed Group Distribution” section that suggests grouping structures based on assessment data, along with a recommended entry point for each group. Furthermore, the report contains a page for a given student that provides a snapshot of that student’s current understanding and a suggested entry point tailored to the student’s performance. This allows the educator to personalize instruction and address individual learning needs from the beginning.

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

The Math Journeys grade 3 Spanish program contains protocols with corresponding guidance for internalizing both units and lessons through the “Lesson Internalization and Planning” section of the Program Guide. The “Preparing for a Journey” section explains how to internalize units by helping educators: understand how the current journey builds upon prior learning, review lesson objectives and mastery criteria, identify scaffolds and enrichment opportunities, gather materials, and analyze the learning progression before starting instruction. In addition, the sections “Preparing for a Building Session,” “Preparing for a Consolidating Session,” and “Preparing for an Additional Practice Session” describe how to internalize lessons. These sections help educators clarify objectives, anticipate students’ thinking and misconceptions, prepare the materials, identify opportunities for formative assessment, analyze students’ responses, and use progress monitoring data to inform future instruction.

The “Lesson Internalization and Planning” section of the Program Guide contains additional support for internalizing lessons. The sections “Preparing for a Building Session,” “Preparing for a Consolidating Session,” and “Preparing for an Additional Practice Session” help educators clarify objectives, anticipate students’ misconceptions, organize the materials, and use assessment information to inform instruction and respond to students’ needs.

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

The Math Journeys grade 3 Spanish program provides resources to help instructional leaders assist educators with implementing the program. The “Hands on Partnership” section in the Program Guide contains examples of how a math success manager can partner with and provide guidance to instructional leaders. The materials offer extra guidance for instructional leaders in the Math Journeys Coaching Guide.

The Math Journeys grade 3 Spanish program provides resources and implementation guidance that help instructional leaders assist educators with using the materials as designed. The training materials include on-demand videos that model specific instructional strategies, such as Let’s Add by Breaking Down. Although these videos are not exclusively intended for instructional leaders, they serve as a valuable resource for both educators and leaders who need further support with specific instructional routines. Instructional leaders can leverage these videos to help educators build their understanding of embedded strategies and promote consistent, effective implementation across classrooms.

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, which outlines the instructional components of each lesson and suggests timeframes for implementation, provides detailed guidance on how to deliver lessons. Lesson materials identify components such as educator-led instruction, student exploration, discussion, and practice activities that support consistent implementation across the program. The Guía del programa describes multiple resources for assessment such as diagnostic and progress monitoring tools. The digital practice progress reports provide TEKS-aligned student performance data for each TEKS to help educators make instructional decisions and monitor students’ growth.

Assessment resources within the Math Journeys grade 3 Spanish program are aligned with the TEKS identified in each lesson overview. Formative assessments embedded throughout the lesson overviews clearly identify the aligned TEKS. End-of-journey assessments are also aligned with the TEKS. The answer key lists the TEKS corresponding to each assessment. Because the Math Journeys grade 3 Spanish program is a Spanish-language math curriculum, ELPS alignment does not apply and is therefore not referenced in the assessment materials.

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 3 Spanish program contains detailed lesson overviews that identify TEKS-aligned learning objectives, student materials, educator resources, and lesson components. Each lesson overview contains key vocabulary and cognates to support language development. The “Inside a Journey” section of the Program Guide suggests timeframes for lesson components, allowing educators to plan and pace instruction according to students’ needs.

The Math Journeys grade 3 Spanish program refers to assessment resources in each lesson overview that are aligned with the TEKS. The lesson overviews contain formative assessments that clearly identify the aligned TEKS, allowing educators to make direct connections between instructional activities and the standards being assessed. End-of-journey assessments are also aligned with the TEKS, and the answer key lists the corresponding TEKS. Because the Math Journeys grade 3 Spanish program is a Spanish-language math curriculum, alignment with the ELPS does not apply and is therefore not referenced in the assessment materials.

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).

Each journey offers families support in both Spanish and English through the family letter, which contains information about student learning, questions to discuss at home, vocabulary to reinforce concepts, and suggestions for extending learning outside the classroom. For example, the journey C1 family letter provides an Array Builder activity that uses buttons, coins, beans, or crackers to create rows and columns and prompts families to discuss the total number represented. Families can access the letter in either Spanish or English using the language toggle in the upper-right corner of the platform. This helps ensure that all families can access the resource.

Each journey contains “Cartas para familias,” which consist of a general letter about the unit and individual letters about each topic covered throughout the unit. These resources contain organized sections with unit and topic overviews, questions families can ask at home, home practice activities, and important vocabulary words that support students’ learning and progress. Families can use the language toggle in the upper-right corner of the platform to access the letters in Spanish or English, depending on their language preference.

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

The “Evaluación y monitoreo del progreso” section of the Program Guide defines and explains the curriculum’s instructional assessment types. The materials describe the intended purposes of diagnostic, formative, and summative assessment and clarify how each assessment type supports different stages of instruction. This guidance helps educators plan lessons, deliver targeted instruction, monitor students’ progress, and make data-informed instructional decisions throughout the school year.

The Math Journeys grade 3 Spanish program defines and explains the intended purpose of each type of instructional assessment used throughout the curriculum. The materials combine diagnostic assessments at the start of and throughout the year to establish a baseline for students’ understanding and monitor ongoing progress. Daily formative assessments embedded in classroom activities allow educators to continuously monitor students’ understanding during instruction. Educators administer summative assessments at the end of each journey to evaluate students’ learning and their mastery of the concepts covered. Together, these three assessment types provide a comprehensive, purposeful system for monitoring students’ progress and informing instructional decisions throughout the school year.

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

The Placement Test Implementation Guide helps educators administer instructional assessments both consistently and accurately. The guide describes administration procedures in detail such as the estimated testing time, the educator’s role during administration, and the recommended materials needed for implementation. For example, the “Administration Guidance” section explains that “In grades 3–5, students complete the assessment independently in a self-paced format” and suggests using paper and pencil to support students’ thinking and working memory during the assessment. This explicit guidance promotes consistent administration practices and helps ensure that educators collect diagnostic assessment results accurately across classrooms.

The End-of-Journey Test: Instructions and Guide provides educators with detailed instruction on how to administer the end-of-journey summative assessment. The document is organized into three sections: preparation and expectations for the day before testing, administration procedures and directions for the day of testing, and follow-up actions for the day after testing. By providing step-by-step guidance across all phases of the assessment process, the materials help educators consistently and accurately administer the end-of-journey assessment across classrooms.

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 “Prueba del final de journey” section within each journey gives educators access to printable versions of digital assessments. By selecting an assessment from the “Descargar imprimibles” dropdown menu, educators can download and print each topic assessment for offline administration. This option increases accessibility by ensuring that students who may benefit from or require a paper-based testing format are accommodated. Although the materials provide printable assessment versions, they do not contain additional accessibility features such as text-to-speech functionality, calculators, or language supports for assessment content.

The Math Journeys grade 3 Spanish program references accommodations embedded within the digital platform. The “Accommodations in Assessment” section of the Program Guide states that certain accommodations, such as text-to-speech functionality, are built into the digital platform. However, the platform does not offer calculators or content language supports. In addition, the ability to choose the testing language is not considered a content language support, as such supports are intended to provide linguistic scaffolds that help students access and demonstrate understanding of the content. Therefore, this indicator is only partially met as not all required accommodations are available or fully functional within the digital assessment platform.

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 3 program contains a diagnostic placement test available to students through the Atlas Math app. This assessment is TEKS-aligned and includes questions in digital format with a variety of interactive item types, allowing students to show their understanding in multiple ways. Item types include multiple-choice, constructed-response, and number-line interaction items, representing more than two unique interactive item types. The levels of complexity vary as students demonstrate mastery or reveal learning gaps, ensuring that the assessment is adjusted to capture each student’s level of understanding.

The diagnostic assessment incorporates a variety of interactive question types that allow students to show their understanding in multiple ways. More than two unique item formats are included, such as multiple-choice, graphing, inline choice, hot spot, drag-and-drop, and fraction models. By incorporating diverse question formats, the assessment provides students with multiple opportunities to demonstrate mathematical understanding while generating meaningful, comprehensive data that educators can use to identify students’ entry points and inform instructional decisions.

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.

Throughout the activity section of each lesson, students respond to multiple TEKS-aligned questions that progressively increase in complexity, moving from foundational understanding to higher-order thinking tasks. Atlas Math, which incorporates interactive item types, including drag-and-drop activities that allow students to show their understanding in varied and engaging ways, provides additional opportunities for formative assessment through Weekly Practice. Collectively, these opportunities for formative assessment provide educators with meaningful evidence of learning that they can use to monitor students’ understanding and inform instructional decisions.

The “Wrap-up” section of each lesson overview contains a formative assessment that incorporates the items found in the printable log books, along with an answer key and guidance to support instructional decision-making. Across a given journey, the wrap-up activities include at least three different question types and three varying levels of complexity, indicating that students engage with more than two unique item formats and levels of cognitive demand. These varied opportunities for formative assessment allow students to show their understanding in multiple ways while providing educators with meaningful evidence of learning to inform instruction.

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

The placement test report sample provides educators with detailed scoring information and guidance for interpreting student performance data. The report displays individual student scores and identifies the corresponding performance categories, including low, medium-low, medium-high, and high achievement levels. In addition to summarizing performance outcomes, the report offers recommendations for instructional placement based on assessment results. The guidance further notes, “Use this report alongside what you see in class—student talk, written work, and tasks over time. Scores summarize performance on this instrument and administration. They can miss strengths that timed or online formats do not capture.” By pairing assessment data with ongoing classroom evidence, the materials help educators make informed, individualized instructional decisions that align with students’ learning needs.

The Math Journeys grade 3 Spanish program provides “scoring information and guidance for interpreting student performance” through the placement test report for individual students. This report contains detailed scoring information based on the strand and process standard on a scale of 0–100. Specific guidance for interpreting students’ results is organized by domain and proficiency level, including low, medium, or high, along with the percentage of correct responses received for each learning target. The “Suggested Instructional Focus” section at the bottom of each report shows TEKS-tested guidance by skill, rather than by the entire TEKS, allowing educators to target students’ deficits since many TEKS include multiple learning targets. This level of detail ensures that educators have actionable data required to make informed, individualized instructional decisions based on each student’s specific areas of need.

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 Placement Test Implementation Guide helps educators administer the diagnostic assessment efficiently and use the resulting data to inform instruction. The guide outlines the estimated testing time, the educator’s role during administration, and the recommended materials needed for implementation. By providing these administration procedures and expectations, the materials help educators analyze trends in student performance, determine appropriate instructional placement, and identify next steps for individual students and groups.

The placement test report sample helps educators respond to trends in student performance and plan purposeful instruction. The report includes a chart that identifies the TEKS, the process standards involved, the class percentage of correct responses, and the percentage of correct responses for students using the Innovamat program. These data allow educators to identify class-wide trends and prioritize TEKS that require further instructional attention. Additionally, the “Placement in Journeys” section organizes students under a “Proposed Group Distribution” and recommends an appropriate journey entry point for each group. This guidance enables educators to respond directly to assessment data by assigning targeted tasks and activities that address the specific learning needs of individual students and groups.

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 3 Spanish program provides multiple assessment tools that help educators track students’ progress and growth over time. The Teacher Guide describes how educators can use diagnostic, formative, and summative assessments throughout the program to monitor learning, identify strengths and areas of need, and inform instructional decisions. The materials also note that “Students are also able to track their own progress and growth.” Through Weekly Practice on Atlas Math, students receive immediate feedback on their responses, enabling them to monitor their performance and reflect on their understanding over time.

The Math Journeys grade 3 Spanish program provides some progress monitoring tools through the digital platform. The digital platform enables educators to track students’ progress and growth through a general overview as students work through their activities on the app. Students receive immediate feedback on their performance as they complete activities. However, the platform lacks a log or tracker that allows them to revisit and monitor their own progress and growth over time. Therefore, this indicator is only partially met as the materials include tools for educators to track students’ progress but do not provide students with a dedicated tool to independently track and reflect on their own progress and growth over time.

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

The Math Journeys grade 3 Spanish program provides prompts and guidance to help educators frequently check students’ understanding throughout each lesson. Activities 1 and 2 include embedded guidance for educators to check students’ understanding at key points during instruction. Additionally, in the final step of a given lesson, students work together to review each other’s answers, allowing them to identify and address errors and misconceptions together. This collaborative structure provides educators with an additional opportunity to observe students’ understanding in real time and address any misconceptions before moving forward.

Supports embedded in each lesson help educators frequently check students’ understanding and respond to students’ needs as they arise. Within the “Desenlace” section, the materials include and link to a supported worksheet version for struggling students, allowing educators to identify misconceptions and provide timely intervention. In addition, the “Apoyo” section at the end of each lesson offers specific recommendations for manipulatives and instructional strategies to clarify concepts and provide further support. Collectively, these resources equip educators with guidance for monitoring students’ understanding at key points during instruction as well as for making responsive instructional adjustments based on students’ needs.

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

Educators frequently check students’ understanding throughout the lessons and activities during embedded opportunities for formative assessment as well as when giving immediate feedback during digital practice. Within lesson activities, educators encounter strategically placed questions for monitoring students’ understanding. In addition, educators provide opportunities to determine whether students are ready to progress to new content. During applet activities, students receive immediate feedback based on their responses, and the program adjusts the sequence of follow-up activities based on educator pacing and student performance.

The materials do not contain adaptive checks for understanding within an activity. Although the sequence of follow-up applet activities may change based on students’ performance, the current activity does not adjust the level of rigor, modify question types, or provide additional instructional supports in response to individual students’ answers. Thus, educators frequently check students’ understanding but do not fully engage in adaptive checks, which help educators adjust instruction in real time during each lesson or activity.

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 3 program provides educators with explicit guidance for supporting students who have not yet shown proficiency with prerequisite or grade-level concepts and skills. In each lesson, educators can access printable “Material de apoyo” resources from the right-side panel and distribute them to students who need additional scaffolding and support. These resources provide foundational learning supports that help students access grade-level content while enabling educators to differentiate instruction according to individual students’ needs.

Throughout each lesson, the Math Journeys grade 3 program provides explicit guidance to help students who have not yet reached proficiency in grade-level concepts and skills. The “Desenlace” section includes and links to a worksheet version with embedded supports that offers struggling students an accessible entry point into the content. In addition, the “Apoyo” section at the end of each lesson recommends specific manipulatives and instructional strategies to clarify concepts for students who need additional assistance. Together, these embedded supports equip educators with clear guidance for identifying and responding to students’ learning needs.

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 3 program provides educators with explicit guidance to support students’ language development and access to grade-level math content. In the left-side panel, educators can access the “Adaptaciones lingüísticas” section, which includes the “Guía bilingüe/ESL” resource for implementing language scaffolds during instruction. This resource offers guidance for enabling students to develop their language in math and helps reduce barriers to accessing and engaging with grade-level content. Additionally, lesson overviews contain key vocabulary and cognates to support the development of academic language.

The Math Journeys grade 3 program embeds dedicated supports for emergent bilingual (EB) students throughout each lesson. These supports identify specific opportunities to reinforce key vocabulary and provide educators with intentional, targeted guidance for promoting language development during math instruction. For example, sentence stems in activity 1.1 help students explain their mathematical thinking through oral discourse. The materials also suggest using gestures and visual representations to reinforce vocabulary throughout a given lesson, ensuring that EB students have multiple opportunities to access and develop academic language. These supports provide meaningful guidance for increasing comprehension and building academic vocabulary.

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 grade 3 program gives educators explicit guidance to extend learning for students who have shown proficiency with grade-level content and skills. In the “Desenlace” section of each lesson, the “Ampliación” component offers extension activities and questions that encourage students to apply their understanding beyond the lesson objectives. For example, one lesson prompts students to solve an additional problem that was not addressed during instruction, challenging them to extend their thinking and deepen their conceptual understanding. These embedded supports equip educators with guidance for keeping students engaged and promoting deeper learning for students who have mastered grade-level content.

The Math Journeys grade 3 program successfully supports advanced students by providing educators with explicit guidance as well as extension activities in the “Recursos” section of a given lesson. The curriculum includes a printable “Ampliación” worksheet for students proficient in above grade-level content and skills. This resource extends learning by tasking students with identifying patterns, analyzing numerical relationships, and applying advanced mathematical concepts. Furthermore, the materials include clear instructional guidance for educators, offering actionable strategies for implementing, facilitating, and scaffolding extension activities to deepen students’ understanding.

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 grade 3 program does not meet the requirements of this indicator. The digital materials do not include text-to-speech functionality, content and language supports, or calculators that educators can enable or disable to address individual students’ needs. As a result, the materials do not provide the embedded supports for digital accessibility required by this indicator.

The digital materials do not contain text-to-speech functionality, content and language supports, or calculators.

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 3 program helps educators offer multiple ways for students to demonstrate their understanding of mathematical concepts. For example, in lesson 14 of journey C1, activity 1 displays pictures that help students connect to the story’s context, providing a concrete, visual representation of the math before students transition to an equation. This progression from visual representations to symbolic notation allows students to show their understanding in multiple ways as they move from concrete pictorial understanding to abstract mathematical expression. The embedded supports enable educators to offer students multiple entry points to access and demonstrate their understanding of mathematical content.

The Math Journeys grade 3 program provides educators with support that allows students to show their understanding of mathematical concepts through multiple modes of expression. During instruction, students practice multiplying numbers between one and 1,000 by single-digit numbers using several forms of representation. Students first discuss a given problem and explain their mathematical thinking through oral discourse. They then use manipulatives and multiplicative frames to represent problems concretely and visually. Finally, students represent and solve problems independently using the area model. Together, these opportunities to express, represent, and perform mathematical thinking provide educators with guidance for giving students multiple ways to show their understanding throughout the lesson.

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 3 program embeds prompts and guidance that help educators activate students’ prior knowledge, highlight patterns and relationships, and connect mathematical ideas through multiple representations. In grade 3 lessons, students compare and order sums without calculating, explain strategies using place-value reasoning, and analyze incorrect solutions using number lines and equations. Educators pose questions that help students justify the relationships among numbers and operations while connecting symbolic expressions, visual models, and verbal reasoning. These embedded supports equip educators to help students make meaningful connections among mathematical concepts and representations throughout instruction.

Through embedded prompts and questioning strategies, the Math Journeys grade 3 program helps educators build students’ mathematical understanding by activating their prior knowledge, anchoring big ideas, and connecting relationships through multiple representations. Learning activities ask students to analyze and compare mathematical relationships, explain their reasoning, and evaluate solution strategies using visual models, equations, and other representations. The materials also help educators facilitate discussions that promote justification and deepen students’ conceptual understanding by strengthening the connections among symbolic, visual, and verbal representations. Together, these supports help educators foster deep and connected mathematical understanding throughout each lesson.

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 3 program clearly explains how to effectively deliver and facilitate lessons through multiple instructional approaches embedded across the program’s components. Grade 3 lessons incorporate whole-group instruction, collaborative learning experiences, oral counting routines, movement-based activities, hands-on use of manipulatives, visual representations, independent practice, and mathematical discourse. The embedded “Apoyo” and “Ampliación” sections provide step-by-step guidance for facilitation, questioning prompts, and differentiated supports that promote student engagement and mathematical understanding. Collectively, these instructional approaches enable educators to effectively deliver lessons that address the diverse learning needs of grade 3 students.

The Math Journeys grade 3 program enables educators to deliver lessons effectively by embedding multiple instructional approaches within each lesson. During instruction, students practice multiplying numbers between one and 1,000 by single-digit numbers through a sequence of instructional experiences. Students first discuss a given problem, creating opportunities for mathematical discourse and collaborative learning. They then use manipulatives and multiplicative frames to represent problems through hands-on and visual experiences. Finally, students solve problems using the area model, transitioning from concrete and visual representations to more abstract mathematical thinking. Together, these instructional approaches provide educators with clear guidance for facilitating lessons through multiple teaching methods.

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

Through varied practice structures and embedded educator supports, the Math Journeys grade 3 program incorporates multi-tiered intervention methods that promote effective implementation. Lessons include collaborative partner work and whole-group discussions throughout instructional activities. Students also engage in individualized, self-paced practice activities that become available after marking “Sesión completada,” allowing for practice opportunities to align with individual needs. The embedded “Apoyo” and “Ampliación” sections provide tiered supports for scaffolding instruction and extending learning. Together, these structures help educators address students’ diverse learning needs throughout each lesson.

Multiple instructional practices and learning structures create opportunities for educators to implement multi-tiered interventions. The lessons incorporate guided, collaborative, independent, and educator-facilitated practice across whole-group, partner, and individual learning contexts. Questioning strategies, manipulatives, models, and visual representations further support instruction across multiple tiers. In addition, the embedded “Apoyo” and “Ampliación” sections provide targeted scaffolds for students who need additional support and extension opportunities for students who have shown mastery. These differentiated supports help educators monitor students’ understanding and respond to their individual learning needs.

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

Differentiated supports and enrichment opportunities found throughout grade 3 lessons promote meaningful student engagement. The “Apoyo” and “Ampliación” sections allow educators to scaffold or extend learning based on students’ readiness and performance. The lessons also include implementation guidance through questioning prompts, manipulatives, number lines, partner discussions, visual models, and opportunities for independent practice. For example, students solve problems using multiple strategies, calculate distances on number lines, compare solution methods, and justify their mathematical reasoning through whole-group, partner, and individual activities. These scaffolded supports help educators differentiate instruction while keeping students engaged with grade-level mathematical concepts and skills.

Within the “Desenlace” section of each lesson, the “Ampliación” component provides extension activities and questions for students who have demonstrated proficiency with the content and skills. For example, one lesson asks students to explain how the outcome would change if the initial number were different from that of the previous example, challenging them to apply their understanding in a new context and extend their mathematical thinking beyond the lesson objectives. These embedded supports provide educators with actionable guidance to keep students engaged and deepen learning for those who have mastered the content and skills taught.

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

The Math Journeys grade 3 program offers prompts and guidance to help educators provide timely feedback during lessons. Within each lesson overview, a dedicated section under the activities lists specific prompts and guidance for educators to use with students during instruction. These embedded prompts allow educators to pause at key moments during the lesson to check students’ understanding, address misconceptions, and provide immediate, meaningful feedback in real time. This support ensures that educators are equipped with the tools needed to deliver responsive instruction and keep students on track toward meeting lesson objectives.

The Math Journeys grade 3 program offers prompts and guidance to help educators provide timely feedback during lessons. The lessons include embedded prompts that encourage educators to facilitate discussions in which students are asked to explain their thinking. This allows educators to explicitly assess whether students are showing understanding of the content based on their responses. The materials provide specific instruction on what educators should expect to see and hear from students when they demonstrate understanding, giving educators a clear benchmark for evaluating students’ responses in real time. These embedded moments within the lesson serve as intentional checkpoints where educators can provide timely, targeted feedback to students, ensuring that educators address misconceptions and confirm students’ understanding before moving forward.

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 is not applicable because the program is not designed to be static.

Not applicable.

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.

Not applicable.

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

Language support resources provide educators with guidance that they can access through the “Gestor de aula.” By navigating to the “Adaptaciones lingüísticas” tab in the left-side panel, educators can locate lesson-level language support documents for each journey. For example, journey D6 includes the “Lesson Level ELPS Companion” in the “Documentation” section. Although this document references the ELPS, it appears to be a direct translation of the ELPS in English. In Texas, the ELPS are designed for EB students developing English proficiency and do not apply to Spanish-language math instruction.

Implementation resources in the Math Journeys grade 3 program help educators use the materials in state-approved bilingual program models. The ESL/Bilingual Implementation Guide provides detailed language guidance for each journey, including instructional routines, strategies, activities, and implementation recommendations designed to support bilingual instruction. These resources provide educators with targeted, actionable guidance for using the materials in bilingual settings while promoting both language development and mathematical understanding among EB students.

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.

Language supports embedded throughout the Math Journeys grade 3 Spanish program help EB students develop their academic vocabulary, build background knowledge, increase their comprehension, and make cross-linguistic connections through oral and written discourse. Each lesson overview presents key academic terms along with definitions and visual representations that support the development of mathematical language in Spanish. The “Antes de empezar” section helps educators activate and build students’ background knowledge before introducing new content, preparing students to engage with grade-level mathematical concepts. Discussion prompts and partner conversations provide opportunities to develop oral language, while printable log books support written discourse by prompting students to record and explain their mathematical thinking. Additionally, cognates embedded in lesson vocabulary help students make connections between Spanish and English mathematical terms.

Dedicated support for EB students in each lesson provides educators with guidance for developing academic vocabulary and promoting cross-linguistic connections through oral and written discourse. The supports identify intentional opportunities to reinforce key vocabulary in meaningful, targeted ways. For example, activity 1.3 recommends recording students’ statements using key vocabulary to help them develop and apply academic language. The materials also guide educators in highlighting cognates in Spanish to reinforce vocabulary meaning and strengthen the connections between Spanish and English mathematical terms.

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 is not applicable because the program is not designed for dual language immersion (DLI) programs.

Not applicable.

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

In grade 3, students engage in practice opportunities throughout the broader learning pathway that require them to demonstrate a depth of understanding aligned with the TEKS. For example, the final lesson of journey C1, which focuses on multiplication using an array model, progresses through the “Planteamiento,” activities 1 and 2, and the “Desenlace,” enabling students to move from concrete to representational and abstract thinking. Students first analyze a pictorial array to determine a total and explain their reasoning. In activity 1, they connect multiplication to real-world situations, while activity 2 extends their understanding through the use of manipulatives in another real-world context. The “Desenlace” then connects multiplication to division, reinforcing the relationships between operations. This sequence of activities provides multiple opportunities for students to deepen their conceptual understanding during a single lesson.

Assessments embedded throughout the broader learning pathway require students to demonstrate a depth of understanding aligned with the TEKS. Practice opportunities such as identifying patterns, generating equivalent numbers, and solving problems with multiple solution paths engage students with increasingly complex mathematical concepts. Embedded instructional assessments—including “pizarrita” responses and problem-solving tasks that require students to explain and apply mathematical ideas—provide evidence of conceptual understanding beyond procedural recall.

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 3 Spanish program contains questions and tasks that increase in rigor and complexity, supporting both grade-level proficiency and opportunities to extend learning beyond grade-level expectations. In each lesson, the activities intentionally progress from pictorial and concrete representations in activity 1 to more abstract mathematical thinking in activity 2, followed by the “Desenlace.” The “Ampliación” section, embedded in the “Desenlace,” provides extension tasks that further increase rigor for students who have shown grade-level proficiency. This progression from concrete to abstract learning, combined with structured extension opportunities, provides increasing levels of challenge throughout the lesson.

The Math Journeys grade 3 Spanish program provides students with opportunities to build on their prior knowledge as lessons increase in rigor. For example, in lesson 2 of journey C3, students begin the warm-up by practicing multiplication fact fluency, sorting equations as greater than, less than, or equal to specific factors. Students then extend that understanding by multiplying larger numbers, recognizing patterns, and applying previously learned strategies to new problem situations. The “Apoyo” and “Ampliación” sections further increase rigor by guiding educators to extend questioning and encourage students to explore multiple solution strategies that lead to the same result.

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

Multiplication tables and related division facts demonstrate horizontal coherence by connecting patterns, big ideas, and relationships across multiplication and division concepts. During the “Planteamiento,” students use number cards to construct multiplication equations, activating their understanding of the relationship between factors and products. The lesson then connects multiplication to an additive framework as students use concrete snap cubes and write corresponding addition and multiplication equations to represent relationships such as “twice as many.” In the “Desenlace,” students connect multiplication comparisons to measurement by using linear scales and real-world phrases of comparison. By integrating multiplication, division, and measurement in a single lesson, the Math Journeys grade 3 Spanish program presents these concepts as interconnected rather than isolated, demonstrating horizontal coherence within the grade level.

The Math Journeys grade 3 Spanish program demonstrates horizontal coherence within the grade level. The “Vista general de tramo” explains the progression of concepts across previous, current, and future learning clusters within a given topic. For example, the cluster C document, “Pensamiento multiplicativo,” explains that students have previously moved away from counting by ones toward thinking in groups and mastered the idea that totals can be broken down and rearranged. In the current cluster, students build upon that foundation by working with equal groups using strategies such as arrays and equal jumps on the number line. The following cluster then extends this understanding by focusing on partitioning, sharing, and working with larger numbers and more complex grouping, showing a coherent progression that builds upon previous concepts and moves toward more complex mathematical ideas.

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.

In grade 3, a lesson on foundational multiplication in pathway C1, lesson 14, illustrates how the materials build vertical coherence across grade bands by connecting patterns, big ideas, and relationships throughout grades K–6. Students develop multiplication concepts using concrete and representational tools, building a foundation that is extended in pathway C3, lesson 14, where grade 5 students apply area models to multiply and transition to the standard algorithm. By building multiplication concepts along a strategic progression across grade bands, the materials help students see multiplication as a continuous, connected idea that deepens in complexity rather than a set of isolated skills, showing vertical coherence from grades K–6.

The Math Journeys grade 3 Spanish program demonstrates coherence vertically across grade levels. For example, in the “Planteamiento,” students activate their prior knowledge regarding pictorial models of fractions, drawing on their understanding that fraction pieces within a whole must be equal. Building on that foundation, the lesson extends students’ understanding by exploring fractions that make up a whole using the length model and applying fraction concepts to real-world situations. The materials show coherence vertically across grade levels by connecting previously learned concepts to current understanding and strengthening more complex mathematical ideas.

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 3 Spanish program demonstrates coherence across lessons by connecting students’ prior knowledge of concepts and procedures to the mathematical concepts to be learned in the current grade level as well as future grade levels. In pathway C1, lesson 1, students explore doubling two-digit numbers using base 10 blocks. Educator notes connect this lesson to students’ prior understanding of odd and even numbers, using the doubling activity as an opportunity to revisit the concept. The materials connect prior knowledge of place-value composition by guiding students to see that doubling a two-digit number requires doubling the tens and the ones separately. To enable students to analyze relationships across place-value concepts and apply that understanding to new numbers, building a foundation for multi-digit multiplication strategies in future grade levels, educators use prompts such as “¿Podrías explicar qué ocurre con las decenas y las unidades cuando haces el doble de 24?” and “¿Cómo te ayuda esa relación a encontrar el doble de un número diferente, como 37?”

The Math Journeys grade 3 Spanish program demonstrates coherence vertically across grade bands through the progression of concepts outlined in the “Vista general de tramo.” For example, the cluster C document, “Pensamiento multiplicativo,” explains that students have previously moved away from counting by ones toward thinking in groups and mastered the idea that totals can be broken down and rearranged. In the current cluster, students build upon that foundation by working with equal groups using strategies such as arrays and equal jumps on the number line. The following cluster then extends this understanding by focusing on partitioning, sharing, and working with larger numbers and more complex grouping, showing a coherent vertical progression that builds from previous concepts toward more complex mathematical ideas.

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

The Math Journeys grade 3 Spanish program provides spaced retrieval opportunities by revisiting previously learned skills and concepts throughout the learning pathways. The lessons follow a consistent structure that begins with the “Planteamiento,” continues through the activities, and concludes with the “Desenlace.” This sequence introduces and develops new learning while intentionally prompting students to recall and apply knowledge from earlier pathways. By revisiting previously learned concepts over time, the materials contain opportunities for spaced retrieval across the broader learning pathway.

The Math Journeys grade 3 Spanish program incorporates opportunities for spaced retrieval by revisiting multiplication strategies across multiple contexts. For example, students apply decomposition strategies and partial products (e.g., 32 × 8 = 30 × 8 + 2 × 8) through rectangular arrays, guided practice, and independent word problems. The lessons also reinforce multiplication concepts, such as equal groups and arrays, by engaging students in contextual problem-solving and multiple representations. These recurring opportunities encourage students to retrieve prior learning while strengthening their conceptual understanding over time.

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

The Math Journeys grade 3 Spanish program provides opportunities for interleaved practice by integrating previously learned skills and concepts throughout the learning pathways. Across the reviewed lessons, multiplication and division concepts are intentionally connected across the pathways. For example, in pathway C1, lesson 1, doubling concepts connect to place-value understanding, while in pathway C2, lesson 2, multiplicative comparison is combined with additive reasoning. Later, pathway C3, lesson 14, and pathway C4, lesson 6 integrate multiplication concepts with area models and division strategies, requiring students to apply prior learning as they engage with new content. This progression encourages students to connect previously learned ideas with new mathematical learning, rather than exploring each concept in isolation.

The Math Journeys grade 3 Spanish program provides opportunities for distributed practice that strengthen both procedural fluency and conceptual understanding. For example, students repeatedly apply addition, subtraction, and multiplication while generating, reversing, and operating with three-digit capicúa numbers, reinforcing fluency with standard algorithms. Lessons also connect operations to place value, patterns, and symmetry as students analyze reversals and identify capicúa structures. By integrating conceptual reasoning with repeated practice across tasks, the materials support distributed practice throughout the broader learning pathway.

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

Students can interpret, analyze, and evaluate models and representations for mathematical concepts and situations via questions and tasks embedded throughout the materials. Students interpret models and representations as they make sense of shaded grids and fraction manipulatives to determine fractional values and equivalence. They analyze models and representations by comparing multiple representations of the same quantity, identifying patterns in numerators and denominators, and examining how partitioning affects equivalence. Students also evaluate models and representations by determining which representations are not equivalent, critiquing the role of the unit, and justifying the accuracy of models using geometric and numerical reasoning. This progression from interpreting to analyzing to evaluating models and representations shows that the Math Journeys grade 3 Spanish program provides opportunities for students to engage with fraction concepts at increasing levels of cognitive demand.

The Math Journeys grade 3 Spanish program contains questions and tasks that require students to interpret, analyze, and evaluate models and representations for mathematical concepts and situations. Students interpret models and representations as they use fraction pieces, area models, and geometric figures to determine fractional values and represent parts of a whole. They analyze models and representations by generating equivalent fractions, examining divisibility relationships between denominators, and comparing multiple representations of the same quantity. Students also evaluate models and representations as they justify why they can or cannot represent certain fractions with given partitions and defend the validity of their representations using visual and numerical reasoning.

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 3 Spanish program contains questions and tasks that provide students with opportunities to create concrete models and pictorial representations to represent mathematical situations. For example, in journey C1, station 8, students build equal-group models by drawing circles and placing colored tiles in each one, then use the concrete model to represent multiplication. Students also create arrays with tiles as an additional concrete representation of multiplication. The logsheets then require students to draw the array, creating a pictorial representation of a given multiplication statement. Embedded questions in the lesson plan support connecting representations to the mathematical situation, asking students to explain how the numbers of circles and tiles relate to their multiplication equation and to identify what each number in the equation represents in the tile arrangement.

The Math Journeys grade 3 Spanish program contains questions and tasks that provide students with opportunities to create concrete models and pictorial representations that show mathematical situations. Students create concrete models as they use base 10 blocks to build and manipulate quantities, representing doubles by combining equal groups and halves through partitioning into two equal groups. Students also create pictorial representations by drawing and modeling numbers on their boards, demonstrating visually how quantities are composed and decomposed to represent doubling and halving.

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

Students in grade 3 have opportunities to apply their conceptual understanding to new problem situations and contexts. For example, in the activity involving equal groups, students transition from placing tiles in circles to a new context by drawing rectangles that symbolize egg cartons and determining how many eggs fit in a given number of cartons. This task requires students to apply their conceptual understanding of equal groups, built with concrete models, to a new real-world situation. A second task extends this transfer further, asking students to determine the number of passengers a specified number of cars could transport. Both tasks require students to move beyond the original concrete context and apply their understanding of multiplication to unfamiliar, real-world problem situations, showing that the materials meet the criterion for applying conceptual understanding to new contexts.

The Math Journeys grade 3 Spanish program contains questions and tasks that provide opportunities for students to apply their conceptual understanding to new problem situations and contexts. In activity 1.2, students move from placing tiles in circles to a new context by drawing rectangles that symbolize egg cartons and determining how many eggs fit in a given number of cartons, applying their understanding of equal groups to an unfamiliar real-world situation. The Teacher Guide extends this further by presenting a new context involving cars and passengers, requiring students to transfer the same multiplicative concept across multiple novel real-world situations and contexts.

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

The Math Journeys grade 3 Spanish program provides students with opportunities to develop and demonstrate procedural fluency. For example, in the “Planteamiento,” applet A95, pack 9, asks students to rapidly identify which of four multiplication equations matches a displayed product, building automatic fact retrieval across the two, four, five, and eight times tables. Activity 1.1 then has pairs of students place colored tiles into circles and write equations such as 6 × 4 = 24 repeatedly across changing group sizes, building fluency through varied practice with equal groups. The Teacher Guide further supports fluency development by directing educators to monitor whether students are counting by ones and intervening to guide students toward more efficient multiplicative strategies.

The Math Journeys grade 3 Spanish program provides students with opportunities to develop and demonstrate procedural fluency. For example, students engage in repeated practice identifying and representing multiplication through rectangular arrays, equal groups, and real-world contexts such as counting wheels, arranging seats, and organizing objects. These tasks require students to consistently apply multiplication facts and related reasoning, including finding unknown factors, thus supporting the development of efficient strategies and strengthening recall over time. The progression from guided whole-group practice to structured application in groups and individual tasks promotes accuracy, flexibility, and efficiency in multiplication, providing clear opportunities to develop both fluency and automaticity aligned with grade-level expectations.

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 3 Spanish program provides students with opportunities to develop and demonstrate flexibility in procedural competency. For example, in activity 1, working in pairs, students solve 3,455 + 1,280 using both the decomposition and “Jumping along the Number Line” strategies, then swap methods, directly practicing flexible selection of procedures. The Teacher Guide prompts students to discuss which strategy they find more efficient for solving the given addition operation, building accurate and flexible application of procedures. The independent work in the “Desenlace” reinforces this flexibility by asking students to choose their own strategies for subtraction, sustaining the development of procedural efficiency across the broader learning pathway.

The Math Journeys grade 3 Spanish program provides students with opportunities to develop and show flexibility in procedural competency. For example, activity 1.2 presents two fractions in different models and asks students to compare strategies, including representing both fractions with the same model or converting to fraction notation to check for shared numerators or denominators. Activity 2 then asks groups to find fractions greater than and less than 2/6 using fraction circles, evaluating which representations make comparisons most efficient. The Teacher Guide prompts students to select the tool or technique that best helps them compare fractions and explain their accuracy by confirming that their chosen approach yields a defensible and correct ordering, reinforcing both flexibility and precision in procedural application.

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.

Activity 1 requires students to work in pairs to solve 3,455 + 1,280 using both the decomposition and “Jumping along the Number Line” strategies, then exchange Magic Pads to verify accuracy and identify errors. Next, students discuss which strategy they find more efficient for the given addition problem, evaluating flexibility by selecting the better method based on the numbers’ structure. Students repeat the same process for subtraction, justifying procedural efficiency and confirming that both approaches yield the same results. By asking students to compare strategies, check each other’s work, and argue for the most efficient method across both operations, the Math Journeys grade 3 Spanish program provides students with opportunities to evaluate mathematical strategies and solutions for efficiency, flexibility, and accuracy throughout learning pathways.

The Math Journeys grade 3 Spanish program provides students with opportunities to evaluate the reasonableness of their results and the efficiency of their procedures. For example, activity 1.2 presents two fractions in different models and asks students to compare strategies, including representing both fractions with the same model or converting to fraction notation to check for shared numerators or denominators. Activity 2 then asks groups to find fractions greater than and less than 2/6 using fraction circles, evaluating which representations make comparisons most reasonable and efficient. The Teacher Guide prompts students to select the tool or technique that best helps them compare fractions and explain their accuracy by confirming that their chosen approach yields a defensible and correct ordering, reinforcing the importance of evaluating both the reasonableness of results and the efficiency of procedures.

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

The Math Journeys grade 3 Spanish program provides students with opportunities to apply procedural fluency by selecting and using the most efficient strategy for a given problem. For example, activity 1 presents 1,000 − 754 and asks students which strategy is most efficient among jumping backward, finding distance, decomposing, and simplifying. To encourage students to move toward the equivalent-subtraction approach, the Teacher Guide directs educators to ask “What if you came to the store with $1 less, but what you bought also cost $1 less?” Students apply this reasoning by selecting the most efficient strategy for each new subtraction problem based on the characteristics of the numbers, thus reinforcing the connection between number structure and strategic efficiency.

The Math Journeys grade 3 Spanish program provides students with opportunities to apply procedural fluency by selecting and using the most efficient strategy for a given problem. For example, activity 1 directs educators to ask students which strategies they can use for 345 ÷ 6, distinguishing between mental and written approaches based on problem complexity. The Teacher Guide instructs educators to help students recognize that when dividing by 6 and the dividend is greater than 60, the calculation extends beyond multiplication facts, thus steering students toward written strategies. Students then select between the column diagram and decomposition strategies, discussing which approach is most efficient for the given numbers, reinforcing the importance of matching strategy selection to the structure and complexity of the problem.

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

The Math Journeys grade 3 Spanish program clearly explains how the conceptual and procedural emphases of the TEKS are addressed. For example, in “Introducción y representación de fracciones,” the “Antes de empezar” section states the conceptual progression of the lesson by noting that students have previously approached fractions through the area model, where the unit is a continuous geometric figure, and that the current lesson introduces the set model, where the unit is composed of independent, discrete elements. This explicit articulation of prior and current conceptual emphases helps educators understand how the lesson builds on students’ existing understanding of area models while extending their conceptual understanding to a new representation of fractions.

The Math Journeys grade 3 Spanish program clearly explains how the conceptual and procedural emphases of the TEKS are addressed. For example, the materials communicate the conceptual emphasis by helping students understand multiplication and division through arrays (filas y columnas), visual models, and the relationship between factors and products. The materials thus highlight the reasoning behind operations, such as multiplication when counting elements in rectangular arrangements and division when determining missing dimensions. The materials simultaneously address the procedural emphasis through structured practice using cajitas multiplicativas, writing equations such as 2 × 6 = 12, and solving for unknown factors. This allows students to develop fluency in representing and solving multiplicative situations. By explicitly connecting conceptual understanding through models and meaning with procedural skills via calculating and representing operations, the program clearly communicates both components of the TEKS emphases.

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 Math Journeys grade 3 Spanish program contains questions and tasks that provide students with opportunities to use concrete models, pictorial representations, and abstract models as required by the TEKS. For example, in C5, “Introducir la tabla del 5,” students use pictorial representations of hands and dice to support counting by fives, connecting visual models to the concept of equal groups. The lesson guides students through repeated iterations of the activity using images from the resource and concludes with the abstract reasoning prompt “¿Qué pasa cuando la cantidad de dados es un número par?” This requires students to move beyond the pictorial model and apply their understanding of equal groups in order to analyze patterns and draw conclusions about even quantities.

The Math Journeys grade 3 Spanish program provides students with consistent opportunities to use concrete, pictorial, and abstract models as required by the TEKS. For example, students engage with concrete models by using pattern blocks and cutting materials to physically partition wholes and represent fair-sharing situations. Students then connect these hands-on experiences to pictorial representations by drawing fractions, coloring parts of shapes, and interpreting models such as hexagons and food contexts. Students then link these concrete and pictorial experiences to abstract models by using fraction notation such as 3/4, symbolic representations, and mathematical terms such as numerator and denominator. By intentionally integrating and connecting all three representations throughout the lesson, the materials provide students with a coherent progression from concrete to pictorial to abstract understanding.

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.

Students have explicit, structured opportunities to connect, create, define, and explain both concrete and representational models leading to abstract concepts, as required by the TEKS. For example, students physically manipulate base 10 blocks to represent multi-digit values, actively assigning place value to each block to construct quantities. The materials incorporate process standard 1F to prompt students to analyze and explain relationships of structural place value that make regrouping mathematically viable, using prompts such as “Do you understand why we can exchange 10 rods for 1 flat?” and “Could you explain how the value stays the same when we regroup?” The lesson further supports this progression by helping students transition from using concrete tools to representational models through sketching base 10 block symbols. The lesson concludes by connecting these experiences to abstract notation through an expanded algorithm, creating a direct bridge between physical, visual, and symbolic processes.

The Math Journeys grade 3 Spanish program contains explicit, structured opportunities for students to connect, create, define, and explain both concrete and representational models, moving toward abstract concepts as required by the TEKS. For example, students connect concrete models, such as pattern blocks and physical partitioning of food, and representational models, such as drawings and shaded figures, to abstract fraction notation by linking parts of a whole to symbols like 3/4. Students create both concrete and pictorial models by building hexagons, cutting shapes, and modeling fair-sharing situations, then recording these experiences as fractions. The lesson further helps students define and explain their thinking by requiring them to justify how the parts relate to the whole, interpret the numerator and denominator, and describe equivalences across representations.

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

The “Vista general de tramo—B: pensamiento aditivo” introduces and defines mathematical terms such as tens, units, and values, providing students with the foundational vocabulary needed to engage with additive thinking concepts. The materials also include linguistic supports that help students identify and interpret mathematical symbols. This ensures that they develop both the academic language and symbolic literacy needed to access and communicate mathematical ideas throughout the broader learning pathway. Together, explicit vocabulary instruction and symbolic literacy support demonstrate that the Math Journeys grade 3 Spanish program includes clear instruction on mathematical terms and academic language.

Lesson 12 of journey C1 provides students with opportunities to develop mathematical language in several places. The lesson opens by identifying key vocabulary, orienting students to the academic language they will encounter throughout the lesson. In activity 1.3, a dropdown box titled “Estudiantes bilingües emergentes” explains a language strategy for educators to utilize, helping linguistically diverse students access mathematical content. The embedded strategy “Recopilar y mostrar” guides students to participate in language discourse using the lesson’s vocabulary while the educator records their responses for later review, reinforcing both oral language production and the use of academic vocabulary. Together, these layered language supports—vocabulary introduction, an explicit strategy for EB students, and structured discourse with educator documentation—show that the Math Journeys grade 3 Spanish program contains explicit instruction in mathematical vocabulary and academic language.

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.

Educators receive guidance to scaffold, support, and extend students’ use of academic mathematical vocabulary through dedicated Journey Language Banks housed in the “Adaptaciones bilingües” section. For example, the B2 Journey Language Bank provides educators with how-to guidance for using the banks, multiple instructional routines, and a guide for discussion and writing. This combination of routines and discourse instruction equips educators with concrete tools to help students practice and apply academic vocabulary in context, both when communicating with their peers and when responding to the educator.

The materials contain embedded guidance for educators to scaffold, support, and extend students’ use of academic mathematical vocabulary in context when communicating with peers and educators. In “Representing Fractions Area Model,” key terms are posted to serve as supports and scaffolds for all students, including fraction, numerator, denominator, equal parts, thirds, and sixths, alongside Spanish cognates such as fracción, numerador, and denominador. In activity 1.3, embedded guidance connects fraction notation to a familiar sharing context. To scaffold students’ use of fraction vocabulary as they explain their reasoning, the educator asks “Could you explain how your drawing shows the way you shared the cookies?” and “How does the fraction help you show that each friend gets the same amount of cookie?” In activity 2.2, embedded guidance extends academic language further by directing educators to record students’ statements and sketches on a chart while they share cookies in thirds and sixths. This reinforces terms such as equal parts, numerator, and denominator and provides differentiated sentence frames, which range from labeling thirds or sixths at the beginning level to comparing two shares using numerator and denominator in a complete sentence at the advanced high level. These supports are embedded both as students explain their thinking to their peers and as they respond to educator questioning.

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

Students in the Math Journeys grade 3 Spanish program apply academic mathematical vocabulary in discourse through embedded prompts and anticipatory guidance built into lesson activities. In C2.3, “Introducimos la cajita multiplicativa,” before students write down any equation, the tip on EB students directs educators to ask “How many rows and columns?” This requires precise mathematical language in spoken responses prior to symbolic recording. This embedded sequence ensures that terms such as factor, product, and total appear in students’ conversations before students transition to written notation. In activity 1.3, anticipated student responses, such as “The missing number is 3, because 3 times 5 or 5 times 3 equals 15,” embed factor and product vocabulary directly into oral reasoning. This helps students apply accurate mathematical language as they justify their thinking to their peers.

The lesson plans contain embedded guidance to help students apply appropriate mathematical language and academic vocabulary during discourse. In journey C2, station 3, “Introducing the Multiplicative Frame,” guiding questions prompt students to reason around the multiplicative relationship using precise mathematical terms. The lesson presents an array and asks students how many rows, columns, and dots they see in total, followed by prompts involving embedded language support such as “What is the total?” and “Why did you place this number here?” The embedded guidance also directs educators to “revoice responses with precise language,” providing a sample restatement such as “So you’re saying that multiplying two by seven gives a product of 14?” The guidance further recommends having partners restate the sentence using the same vocabulary, reinforcing independent application of precise mathematical language. Together, these layered supports, including guiding questions, educator revoicing, and peer restatements, show that the materials include embedded guidance to help students apply appropriate mathematical language and academic vocabulary in discourse.

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

Educators facilitate mathematical conversations that allow students to hear, refine, and use mathematical language with their peers through embedded guidance on discussions within the lesson. The Teacher Guide directs educators to ask students to name each part aloud using questions such as “¿Cuántas filas? ¿Cuántas columnas? ¿Cuál es el total?” and “¿Por qué decidiste colocar este número aquí?” while keeping terms such as fila, columna, factor, producto, and total visible for students to reference as they describe their thinking process. Educators then revoice students’ responses using precise language. For example, they might ask “Entonces, ¿estás diciendo que multiplicar 2 por 7 da como producto 14?” and encourage students to ask a peer to repeat the sentence using the same vocabulary before moving to the next problem. This structured sequence ensures that students hear accurate mathematical language modeled in context and actively refine and use it with their peers.

Educators can reference embedded prompts and guidance in the lessons to facilitate math-related conversations. The “Planteamiento” in journey D1, station 12, “Comparing Fractions,” asks students to explain how two students could have traveled different fractions of the distance if they started from the same place and are now at the same point along the way. The lesson plan explains that because the two fractions 2/3 and 1/3 are not equivalent, the only possible explanation is that their endpoints differ, thus helping educators support students’ reasoning around the discrepancy. The embedded prompts further assist educators in helping students refine and use mathematical language, including “Could you explain why we can’t compare these fractions directly?” and “How can you justify that Ethan’s home must be closer to school, using the fractions 2/3 and 1/3?” The lesson plan notes that “this discussion provides an opportunity to observe whether students listen to their peers’ arguments and evaluate their reasoning,” positioning the conversation as a tool for developing language as well as assessing reasoning. Together, these prompts demonstrate that the materials contain guidance for educators to facilitate math-related conversations.

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.

Educators receive support through anticipated student responses and embedded guidance on redirection that prepare them to address conceptual misconceptions and advance students’ reasoning during instruction. In activity 1, the Teacher Guide anticipates that students may claim two tangram parts are not halves because they differ in shape, providing an exemplar response explaining that equal area—not identical shape—defines halves. When students resist this concept, the guide redirects educators to ask “Can you explain why these two parts are equal even though they look different?” This encourages students to move beyond visual appearance toward reasoning about area. Support notes further direct educators to physically overlap the pieces to verify equal area when students continue to struggle, anchoring the conceptual redirect in a concrete, hands-on experience. This layered guidance ensures that educators can anticipate where student thinking may break down and respond with targeted support that helps students move toward accurate mathematical understanding.

Activity 1 anticipates a variety of student responses, including the misconception that two tangram parts “aren’t halves” because they differ in shape, and provides the exemplar response that equal area—not identical shape—defines halves. The Teacher Guide redirects this inaccurate reasoning by having educators ask “Can you explain why these two parts are equal even though they look different?” This encourages students to reconsider the relationship between area and shape. Support notes further direct educators to physically overlap the pieces to verify equal area when students resist the concept, providing a concrete strategy to support and redirect inaccurate responses. Together, this anticipated misconception, exemplar response, and redirection strategy demonstrate that the materials contain embedded guidance to help educators anticipate a variety of student answers as well as support and redirect inaccurate student responses.

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

Students in the Math Journeys grade 3 Spanish program apply TEKS mathematical process standards through tasks that integrate mathematical reasoning with real-world contexts across the lesson sequence. In activity 1, students place 4 colored tiles on each of 6 sheets and write the equation 6 × 4 = 24, connecting a concrete equal-groups model directly to multiplication notation. Activity 1.2 extends this by having pairs of students draw 5 circles and place 8 colored tiles in each (5 × 8 = 40), then represent cars with passengers and egg cartons with eggs as multiplication situations. To encourage students to articulate the connection between their drawings and the real situation, the Teacher Guide directs the educator to ask “Could you explain how your drawing shows the real situation with the cars and passengers?” and “Do you see how your equation represents the number of eggs in all the egg cartons?” Process standard 1A is explicitly tagged in activity 2, where students apply multiplication to problems that arise in everyday life, translating real-world details into multiplication equations that match the situations they have drawn. The “Desenlace” then transfers this work to independent word problems, completing the concrete-to-abstract progression in a real-world context.

Lesson 12 in journey C1 explicitly lists the process standards at the start of the lesson, with activity 1.2 including a dropdown box that states process standard 1E. The materials go beyond simply labeling the standard, offering guiding questions within the dropdown box that prompt students to explain how their representation connects to the product they have found. This deeper level of support ensures that students do not simply identify a process standard in name only but rather actively engage with it as they reason through and communicate their mathematical thinking.

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

Educators receive support to understand how process standards are incorporated and connected throughout the learning pathways via specific documentation in the Guía de instrucciones del journey B4. This guide identifies which process standards are present in each lesson of the journey, providing educators with a clear map of where and how process standards appear across the broader learning pathway. The horizontal rationale explains how the standards are connected throughout the general learning pathway, while the session alignment details how the standards build upon and work off of each other across lessons. Together, these three layers of documentation—lesson-level identification, the horizontal rationale, and session alignment—ensure that educators understand not only which process standards are present but how they function together to support learning across the journey.

The cluster overview D and D1 instructional guide describe how process standard 1A is incorporated in sharing contexts and connected across sessions about the area, set, and length models throughout the D1 learning pathway. D1.3 tags 1A, linking cookie-sharing situations to fraction notation, and the D1 instructional guide notes that this language recurs in D1.4 and D1.5. The D1 scope and sequence further shows 1A, 1E, and 1G each appearing across multiple lessons. Thus, the materials describe and reinforce these connections throughout sessions across the broader learning pathway.

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

Educators receive a clear overview of the TEKS mathematical process standards incorporated into each lesson through explicit tagging in the session header. The session header tags process standard 1A, signaling to the educator that students will apply math to everyday contexts, such as counting passengers and eggs, before instruction begins. The Teacher Guide then connects this tag directly to tasks where students write multiplication equations that match real-world equal-groups drawings, demonstrating that the tagging is purposeful and tied to specific instructional moments. This per-lesson overview allows educators to anticipate which process standards are active and how they will be enacted in the lesson’s tasks and activities.

Activity 1 embeds process standard 1A as students apply fraction reasoning to a real-world context of sharing cookies equally among friends, translating the situation into fraction notation using appropriate numerators and denominators. The Teacher Guide further integrates process standard 1D by directing the educator to connect graphical, verbal, and numerical representations so that students can move between pictorial models, spoken explanations, and symbolic fraction notation. Students write fractions such as 3/4 and explain the meaning of the numerator and denominator within the sharing context, strengthening their ability to represent mathematical ideas across multiple forms. This embedded tagging provides educators with a clear overview of which process standards are incorporated into the lesson and how they connect to specific instructional tasks.

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

Students persevere through solving problems by engaging in tasks that require mathematical reasoning before committing to a solution path. During independent work, students are asked to estimate whether 400 lb of feed is enough without calculating an exact result, positioning thinking mathematically as a prerequisite to solving the problem. The prompt “Which answer is closest to the solution without calculating the exact result?” reinforces perseverance by directing the educator to have students eliminate unreasonable answer choices through reasoning rather than computation. In activity 2, the Teacher Guide instructs educators to use the “Three Reads” routine, guiding students to continuously revisit the problem and make sense of what each quantity represents in context. Together, these structures provide students with opportunities to think mathematically, persevere through multi-step reasoning, and build meaning from the problem before arriving at a solution.

Educators provide students with opportunities to think mathematically by giving groups fraction pieces in activity 1 and asking them to find different ways to represent one-half, requiring students to test combinations without a prescribed method. Students persevere as they reposition physical pieces, make marks, and revisit placements until the areas match. To prompt students to construct meaning from their own discoveries rather than being told the relationship directly, in tip 1F, the guide directs the educator to ask “Do you notice a pattern in how the numerators and denominators are related?” Together, these supports require students to reason flexibly, persevere through trial and adjustment, and make sense of fraction relationships on their own.

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

Students understand, explain, and justify that there are multiple ways to solve problems through a structured routine of partner comparison, which they apply to both addition and subtraction. In activity 1, partners are each assigned a different strategy for solving 3,455 + 1,280—one using decomposition and the other using “Jumping along the Number Line”—then exchange Magic Pads to verify that both routes lead to the same answer and correct any discrepancies. In this way, students build an understanding that there are multiple valid solution paths. The Teacher Guide prompts educators to ask students to discuss which strategy they find more efficient and notes that the Number Line strategy is more efficient here, requiring one forward jump of 1,000, another of 300, and a final backward jump of 20. This gives students a model for how to explain strategy preference with mathematical reasoning. Activity 2 repeats this structure with subtraction (3,455 − 1,280), requiring students to compare and justify their preferred strategy a second time across a new operation. Process standard 1C is tagged, directing students to select the technique that best helps them solve the problem after applying and comparing both methods.

Activity 1.1 helps students understand that there can be multiple ways to complete a task by asking groups to distribute 35 colored tiles into five circles, then record every equation the arrangement produces, surfacing both 5 × 7 = 35 and 35 ÷ 5 = 7 from one model. The Teacher Guide directs educators to write all suggested equations on the board and ask students which multiplicative frame combines all the equations, prompting students to explain the relationships among them. Students then create word problems for a new frame, justifying how a single set of three numbers supports four distinct operations. Together, these supports require students to understand, explain, and justify multiple ways one model can represent different operations.

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.

Students make sense of math through doing, writing, and discussing in a single multiplication activity. In activity 1.1, pairs physically build snap cube towers, count tiles, and write equations such as 2 × 8 = 16 on their Magic Pads, making sense of doubling through hands-on doing. Students then discuss with their partners whether a new tower is “twice as many” or “three times as tall,” using sentence frames such as “The new tower has __ times as many cubes” to structure oral reasoning around multiplicative comparison. The Teacher Guide embeds written equations alongside this oral justification, ensuring that students record their thinking in addition to discussing it. By requiring students to build a physical model, document it in an equation, and defend their interpretation with a partner, activity 1.1 integrates doing, writing, and discussing math in a single coherent task.

Small groups use scissors and “Printable 1” to physically distribute cookie cutouts equally, doing math concretely before writing fraction notation. The Teacher Guide directs the educator to have students write the fraction that each child receives and then explain their distribution using terms like numerator and denominator with their partners. This requires students to write about and discuss math with their peers. Discussion is further structured through prompts asking groups to share their strategies, ensuring that students hear, refine, and use fraction-related terms with one another. Together, these supports require students to make sense of math by doing, writing, and discussing it 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.

Educators receive guidance to help students share and reflect on their problem-solving approaches, including explanations, arguments, and justifications. In a lesson on comparing fractions, activity 1 prompts educators to ask “Which fraction is greater?” and then directs students to raise their hands and explain their reasoning, eliciting shared explanations and arguments from the whole group. The Teacher Guide further anticipates students’ responses and directs the educator to ask “Could you explain another reason why this shape might not belong?” This encourages students to reflect on and refine their initial justifications rather than simply confirming a correct answer. Activity 2 extends both sharing and reflection by asking students to find fractions less than 3/8 and defend their choices using same-numerator or same-denominator reasoning. This requires students to construct, share, and revisit mathematical justifications grounded in fraction structure. By guiding educators to elicit explanations, press for arguments, and require students to reflect on and refine their justifications across multiple activities, the Math Journeys grade 3 Spanish program supports both the sharing and reflecting dimensions required by the criterion.

Activity 1 prompts students to work in pairs to solve 3,455 + 1,280 using both decomposition and the “Jumping along the Number Line” strategy, then exchange Magic Pads to verify accuracy and identify errors in each other’s work. This provides a structured opportunity for students to share and reflect on their reasoning with a peer. Students then discuss “which strategy they find more efficient for solving the given addition operation,” evaluating the flexibility of each approach and building an argument for the better method given the specific number structure. Students repeat the same steps for subtraction, requiring them to justify the efficiency of their chosen strategy and confirm that both approaches yield identical correct results. This reinforces students’ ability to reflect on and validate their problem-solving process. By requiring students to check their partner’s work, discuss efficiency, and justify their strategy choices in both addition and subtraction, the materials help students share and reflect on their problem-solving approaches, as required by the criterion.

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

The Math Journeys grade 3 Spanish program contains both prompts and guidance to help educators provide students with explanatory feedback based on students’ responses and anticipated misconceptions. In activity 1, the Teacher Guide anticipates a specific and common misconception: students may write the multiplication equation with reversed factor order—recording 8 × 5 = 40 instead of 5 × 8 = 40—and clarifies that “while the result is the same, it does not represent the same problem.” This is not a general caution to watch out for errors—it is a named, explained misconception with a specific corrective rationale that educators can relay directly to students. The accompanying note on process standard 1A reinforces this guidance with scripted follow-up prompts, including “Could you explain how your drawing shows the real situation with the cars and passengers?” and “Do you see how your equation represents the number of eggs in all the egg cartons?” directing the educator to return students to the contextual meaning of each factor position rather than simply marking the answer wrong. Together, the anticipated misconception and scripted prompts enable educators to provide explanatory, situation-grounded feedback based on students’ responses.

The Math Journeys grade 3 Spanish program guides educators to provide explanatory feedback through scripted responses to anticipated misconceptions rather than simply naming the error. In the warm-up, when students struggle to locate a fraction on the number line, the guide directs educators to provide a precise, conceptual explanation that the denominator shows how many equal parts make up the unit, and the numerator shows how many of those parts to count, paired with a worked example for placing 3/4. In activity 2, when students only propose fractions with a denominator of six, the guide instructs educators to redirect students to find other fractions that satisfy the conditions using different denominators. Both responses equip educators with the corrective language needed to explain why a student’s response is incomplete and guide the student toward a more complete understanding.