Program Information
- ISBN
- 9791370378110
- Technical Specifications: Checklist
- Tech Specs: Checklist (pdf 1.28 MB)
- Technical Specifications: Professional Development
- Tech Specs: Professional Development (pdf 180.62 KB)
Math Journeys Texas, Grado 6 (Spanish)
Supplemental Math (Spanish) Grade 6
IMRA 2026
Publisher: Innovamat Education, Inc.
Copyright: 2026
Rubric: Supplemental Mathematics 6–12 (Spanish) | 2025 (Download Not Available)
* Some programs submit evidence for only part of a standard, while others submit all sections. A 100% score means this program met all the expectations it submitted.
Quality Review
Standards Alignment
Rubric Section
| Grade | TEKS % | ELPS % |
|---|---|---|
| Grade 6 | 100% | N/A |
Criteria for Quality
Rubric Section 1
Intentional Instructional Design
Materials support educators in effective implementation through intentional course, unit, and lesson-level design.
Total
100% (23 out of 23 points)
Evaluation for 1.1a
The TEKS Correlation Guide of the Math Journeys grade 6 Spanish program identifies the TEKS associated with each lesson, including both content and process standards. The scope and sequence describes the aligned TEKS and ELPS, and organizes instruction into “Journeys” across the curriculum. In addition, the Journey Instructional Guide explains how learning progresses across the journeys through both vertical and horizontal alignment. For example, the A2 journey describes how learning extends from identifying and counting numbers 1–20 to counting, comparing, ordering, and estimating numbers through 100. The Journey Instructional Guide also clarifies how instruction progresses from concrete representations to increasingly abstract models of number sense.
The Math Journeys grade 6 Spanish program contains a scope and sequence that shows TEKS-aligned learning progression and conceptual organization across the curriculum.
Evaluation for 1.1b
The Program Guide provides direction on implementation through the three-step instructional framework of “build,” “consolidate,” and “practice.” Lessons begin with an educator-led, small-group lesson, followed by independent student work in logsheets with educator feedback and further optional practice on Atlas Math, an adaptive digital learning platform. The “Lesson Internalization and Planning” section supports student variability by providing guidance for multiple entry points, just-in-time supports, extensions, and multiple representations and modes of expression.
The Math Journeys grade 6 Spanish program provides opportunities for small-group instruction, independent logsheets, and adaptive digital practice through Atlas Math to support student variability and various intervention settings.
Evaluation for 1.1c
The TEKS Correlation Guide of the Math Journeys grade 6 Spanish program identifies recommended skill entry points based on diagnostic assessment results. Lessons within each journey are aligned with TEKS content and process standards, and the guide supports implementation by connecting lessons and activities to specific standards. In addition, the report for diagnostic assessment and placement recommends skill entry points based on student performance data. Following completion of the digital diagnostic assessment, the report suggests starting points for instruction, targeted interventions, and appropriate journeys to assign. The report supports differentiated instruction by identifying learning opportunities based on individual student performance.
The “Prueba de nivel” report provides recommendations for grouping students based on performance data and individualized strand analysis to help identify instructional entry points.
Evaluation for 1.1d
The “Lesson Internalization and Planning” section of the Program Guide contains protocols on how to internalize units and lessons. The “Preparing for a Journey” protocol helps educators understand how each 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. The protocols “Preparing for a Building Session,” “Preparing for a Consolidating Session,” and “Preparing for an Additional Practice Session” provide additional support for internalizing lessons.
The Cluster Overview Guide, available in the “Digital Manager,” describes protocols for internalizing units. The guide provides educators with an overview of the learning progression, the unit learning trajectory, the core mathematical objectives, vocabulary, and ELPS language goals to support internalization of the concepts covered in the lessons. Additionally, this guide includes lesson-level direction on internalization for each instructional session type. The Program Guide directs educators to prepare for the “Building,” “Consolidating,” and “Additional Practice” sessions by clarifying objectives, preparing materials, anticipating student thinking and misconceptions, identifying opportunities for formative assessment, and using student evidence and Atlas Math performance data to inform instructional next steps.
Evaluation for 1.1e
The Math Journeys grade 6 Spanish program contains resources that instructional leaders may use to support implementation. The “Hands-on Partnership” section of the Program Guide provides examples of how a math success manager may collaborate with and offer guidance to instructional leaders.
The Program Guide identifies the Classroom Manager as a platform available to educators and administrators that provides access to lesson plans, instructional videos, training resources, virtual manipulatives, assessment tools, and reporting features. In addition, student progress reports offer recommendations for differentiated instruction and enable educators and instructional leaders to review student performance data.
Evaluation for 1.2a
The Guía del programa—which outlines instructional components and suggests timeframes for each lesson—provides detailed guidance on implementation. Lesson materials identify educator-led instruction, student exploration, discussion, and practice activities that support consistent implementation. The Guía del programa also describes multiple assessment resources, including diagnostic and progress monitoring tools. Digital practice progress reports provide TEKS-aligned student performance data for each TEKS, supporting instructional decision-making, and ongoing monitoring of student growth.
The Math Journeys grade 6 Spanish program contains lesson-specific instructional guides within each journey station that identify the TEKS mathematical process standards addressed in the lesson. The materials include TEKS-aligned learning objectives, lists of lesson materials, digital teaching guides, answer keys, guided-practice log books, instructional supports, and concept-introduction videos. Together, these resources support lesson implementation, instructional planning, and student practice by providing educators with the materials needed for instruction.
Evaluation for 1.2b
The Math Journeys grade 6 Spanish program provides detailed lesson overviews for each journey station that identify learning goals, key vocabulary, required materials, and lesson components. The Program Guide explains that lessons are organized into the “Build,” “Consolidate,” and “Additional Practice” sections and suggests timeframes for implementation. The “Additional Practice” section incorporates Atlas Math, an adaptive digital learning platform that offers interactive activities, fluency practice, immediate feedback, and adaptive learning opportunities based on student progress.
The scope and sequence and cluster overviews align lessons with TEKS content standards, TEKS mathematical process standards, and the ELPS. Cluster overviews describe the learning progression, learning milestones, lesson objectives, language goals, and vocabulary associated with each station within a journey. In addition, the program uses a concrete-representational-abstract (CRA) instructional approach that incorporates physical manipulatives and digital representations throughout structured lesson segments, including warm-ups, core activities, and wrap-ups.
Evaluation for 1.2c
Within each journey, families receive support through a family letter available in both Spanish and English. This letter contains questions for families to discuss at home, vocabulary that reinforces learning, and particular suggestions for supporting student progress outside the classroom. Families can access the resource in their preferred language using the language toggle in the upper-right corner of the platform.
The Math Journeys grade 6 Spanish program contains both cluster-level and journey-level letters that provide information on the mathematical background, learning goals, vocabulary, questions families can discuss with students, and suggestions to support learning at home. For example, the “Expressions and Equations Family Letter” includes a “How Can We Support From Home?” section with activities and guidance aligned with concepts taught during the journey. These letters also support communication with families through language-toggle options that make the resources available in both English and Spanish.
1.1 Course-Level Design
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.
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.
4 out of 4 points
Evaluation for 1.1a
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.
4 out of 4 points
The Math Journeys grade 6 Spanish program contains a scope and sequence that shows TEKS-aligned learning progression and conceptual organization across the curriculum.
1.1b
Materials include an implementation guide with usage recommendations and strategies for effective educator use, such as just-in-time supports, advanced learning, or as a course.
Materials include an implementation guide with usage recommendations and strategies for effective educator use, such as just-in-time supports, advanced learning, or as a course.
3 out of 3 points
Evaluation for 1.1b
Evaluation for 1.1b
Materials include an implementation guide with usage recommendations and strategies for effective educator use, such as just-in-time supports, advanced learning, or as a course.
3 out of 3 points
The Math Journeys grade 6 Spanish program provides opportunities for small-group instruction, independent logsheets, and adaptive digital practice through Atlas Math to support student variability and various intervention settings.
1.1c
Materials include a TEKS correlation guide with recommended skill entry points based on diagnostic assessment results.
Materials include a TEKS correlation guide with recommended skill entry points based on diagnostic assessment results.
2 out of 2 points
Evaluation for 1.1c
Evaluation for 1.1c
Materials include a TEKS correlation guide with recommended skill entry points based on diagnostic assessment results.
2 out of 2 points
The “Prueba de nivel” report provides recommendations for grouping students based on performance data and individualized strand analysis to help identify instructional entry points.
1.1d
Materials include protocols with corresponding guidance for unit and lesson internalization.
Materials include protocols with corresponding guidance for unit and lesson internalization.
2 out of 2 points
Evaluation for 1.1d
Evaluation for 1.1d
Materials include protocols with corresponding guidance for unit and lesson internalization.
2 out of 2 points
The Cluster Overview Guide, available in the “Digital Manager,” describes protocols for internalizing units. The guide provides educators with an overview of the learning progression, the unit learning trajectory, the core mathematical objectives, vocabulary, and ELPS language goals to support internalization of the concepts covered in the lessons. Additionally, this guide includes lesson-level direction on internalization for each instructional session type. The Program Guide directs educators to prepare for the “Building,” “Consolidating,” and “Additional Practice” sessions by clarifying objectives, preparing materials, anticipating student thinking and misconceptions, identifying opportunities for formative assessment, and using student evidence and Atlas Math performance data to inform instructional next steps.
1.1e
Materials include resources and guidance for instructional leaders to support educators with implementing the materials as designed.
Materials include resources and guidance for instructional leaders to support educators with implementing the materials as designed.
2 out of 2 points
Evaluation for 1.1e
Evaluation for 1.1e
Materials include resources and guidance for instructional leaders to support educators with implementing the materials as designed.
2 out of 2 points
The Program Guide identifies the Classroom Manager as a platform available to educators and administrators that provides access to lesson plans, instructional videos, training resources, virtual manipulatives, assessment tools, and reporting features. In addition, student progress reports offer recommendations for differentiated instruction and enable educators and instructional leaders to review student performance data.
1.2 Lesson-Level Design
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.
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.
5 out of 5 points
Evaluation for 1.2a
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.
5 out of 5 points
The Math Journeys grade 6 Spanish program contains lesson-specific instructional guides within each journey station that identify the TEKS mathematical process standards addressed in the lesson. The materials include TEKS-aligned learning objectives, lists of lesson materials, digital teaching guides, answer keys, guided-practice log books, instructional supports, and concept-introduction videos. Together, these resources support lesson implementation, instructional planning, and student practice by providing educators with the materials needed for instruction.
1.2b
If designed to be adaptive, materials include detailed lesson overviews with learning objectives, lesson components with suggested timeframes, and assessment resources aligned with the TEKS and ELPS.
If designed to be adaptive, materials include detailed lesson overviews with learning objectives, lesson components with suggested timeframes, and assessment resources aligned with the TEKS and ELPS.
3 out of 3 points
Evaluation for 1.2b
Evaluation for 1.2b
If designed to be adaptive, materials include detailed lesson overviews with learning objectives, lesson components with suggested timeframes, and assessment resources aligned with the TEKS and ELPS.
3 out of 3 points
The scope and sequence and cluster overviews align lessons with TEKS content standards, TEKS mathematical process standards, and the ELPS. Cluster overviews describe the learning progression, learning milestones, lesson objectives, language goals, and vocabulary associated with each station within a journey. In addition, the program uses a concrete-representational-abstract (CRA) instructional approach that incorporates physical manipulatives and digital representations throughout structured lesson segments, including warm-ups, core activities, and wrap-ups.
1.2c
Materials contain support for families in Spanish and English for each unit, with suggestions on supporting the progress of their student(s).
Materials contain support for families in Spanish and English for each unit, with suggestions on supporting the progress of their student(s).
2 out of 2 points
Evaluation for 1.2c
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).
2 out of 2 points
The Math Journeys grade 6 Spanish program contains both cluster-level and journey-level letters that provide information on the mathematical background, learning goals, vocabulary, questions families can discuss with students, and suggestions to support learning at home. For example, the “Expressions and Equations Family Letter” includes a “How Can We Support From Home?” section with activities and guidance aligned with concepts taught during the journey. These letters also support communication with families through language-toggle options that make the resources available in both English and Spanish.
Rubric Section 2
Progress Monitoring
Materials support educators in effective implementation through frequent, strategic opportunities to monitor and respond to student progress.
Total
86% (18 out of 21 points)
Evaluation for 2.1a
The “Assessment and Progress Monitoring” section of the Program Guide defines the assessments and describes their intended purpose. For example, the curriculum defines the diagnostic assessment as a tool used at the start of instruction to identify prior knowledge and determine which journey to place students in. Formative assessments, such as warm-ups, logsheets, and embedded checks for understanding, are intended to inform real-time instructional adjustments. Finally, the materials define summative assessments, such as the end-of-journey tests and cumulative progress reports, as opportunities to evaluate student mastery of targeted skills and determine readiness for advancement within the instructional pathways.
The Program Guide defines the purpose of diagnostic assessment and identifies the placement test as a diagnostic evaluation given at the beginning of instruction to determine students’ current level of mathematical understanding and establish an appropriate entry point within the broader pathway. The guide explains that assessment results align with the curriculum’s learning progression and are used to place students in the most appropriate journey based on their learning needs. Additionally, the materials provide examples of how diagnostic results can inform instructional planning and support grouping students for targeted instruction.
Evaluation for 2.1b
The Math Journeys grade 6 Spanish program helps educators consistently and accurately administer instructional assessments. The Placement Test Implementation Guide provides clear, detailed directions for educators to administer the diagnostic assessment precisely and reliably. The guidance includes the estimated testing time, the educator’s role during administration, and suggested materials. For example, the “Administration Guidance” section of the Placement Test Implementation Guide clarifies that “In grades 3–5, students complete the assessment independently in a self-paced format” and that “paper and pencil are recommended to support student thinking and working memory during the assessment.” This level of detail ensures that all educators administer the diagnostic assessment in a consistent, accurate manner across classrooms.
The placement test process, described in the Program Guide, explains how to correctly and reliably administer as well as use instructional assessments. The guide clarifies that all students complete the placement test at the beginning of the year through their Atlas Math accounts and details how assessment results are mapped to the curriculum’s learning progression. The guide further outlines how educators can use the results to assign students to an appropriate starting journey based on their demonstrated understanding. This guide promotes standardized administration procedures and supports the consistent interpretation and use of assessment results across classrooms.
Evaluation for 2.1c
The Math Journeys grade 6 Spanish program offers digital and print versions of the end-of-journey and formative assessments, or logsheets. For example, each end-of-journey assessment contains a link to download printables, including the assessment, answer key, and instructional guide. The program does not allow educators to enable and disable text-to-speech functionality, content and language supports, or calculators for individual students. However, students can access text-to-speech functionality, and the educator can toggle the assessment language to English or Spanish. The “Accommodations in Assessment” section of the Program Guide explains that the assessment platform provides embedded text-to-speech functionality as well as content and language supports, including setting the language to English or Spanish, and specifies when calculators can be used. For example, the guide states, “Calculators are not provided within the digital interface. Instead, they are provided and managed by educators during test administration.” The Program Guide clearly outlines the embedded accommodations but does not allow educators to enable or disable them.
The Program Guide identifies several accommodations for digital assessment, including embedded text-to-speech functionality as well as content and language supports within the assessment platform. Educators can designate each student’s language of instruction through the Classroom Manager. This setting applies across content, practice, and assessments. However, students activate text-to-speech functionality through a speaker icon rather than the educator enabling or disabling it for individual students. Additionally, calculators are not embedded within the digital assessment platform. Instead, the Program Guide states that educators provide and manage calculators during test administration. Thus, the curriculum includes some digital assessment accommodations but does not allow educators to enable or disable text-to-speech functionality, content and language supports, or calculators for individual students as required by the rubric.
Evaluation for 2.1d
The Math Journeys grade 6 Spanish program provides diagnostic assessments with TEKS-aligned tasks or questions. In the placement test report sample, the diagnostic assessment identifies student performance across multiple mathematical strands and processes, and connects results to specific instructional pathways within the curriculum’s progression. The report organizes student outcomes by strand and process, demonstrating alignment between the diagnostic tasks and TEKS-based mathematical content. In addition, the Placement Test Implementation Guide identifies multiple item types in the diagnostic assessment, including multiple-choice, number-line, constructed-response, and other interactive response formats. The guide also describes questions at multiple levels of complexity, including DOK 1 (Factual Knowledge), DOK 2 (Procedural Knowledge), and DOK 3 (Reasoning and Problem-Solving), providing students with opportunities to show their understanding through tasks that require recall, procedural application, and mathematical reasoning.
The Placement Test Implementation Guide describes diagnostic assessments that incorporate varying levels of complexity and multiple interactive item types. The guide identifies three levels of cognitive demand within the diagnostic assessment: DOK 1 (Factual Knowledge), DOK 2 (Procedural Knowledge), and DOK 3 (Reasoning and Problem-Solving). It also identifies multiple item formats such as multiple-choice, constructed-response, number-line, and other interactive response formats. These diagnostic tasks require students to demonstrate their understanding across a range of cognitive demands, from recalling facts and procedures to applying mathematical reasoning and problem-solving strategies.
Evaluation for 2.1e
The Math Journeys grade 6 Spanish program provides a variety of formative assessments with TEKS-aligned tasks or questions. The TEKS Correlation Guide identifies lessons connected to specific TEKS. For example, F2, “First Steps into Equations,” session 9, “Equations with Scales,” aligns with TEKS 7.11.A and 8.8.C, demonstrating that the formative tasks in the session are TEKS-aligned. In addition, the item types involve interactive formative assessment at varying levels of complexity. For example, student logsheets and digital activities contain multiple-choice questions, graphing tasks, number-entry tasks, text-entry tasks, and number-line activities. Furthermore, the grade 6 materials provide differentiated tasks for formative assessment to address multiple levels of student readiness. As is evident in journey E, “Powers and Integers,” E2, “Integers,” station 2, “Negative Numbers on the Number Line,” the downloadable student logsheets include Version X, Y, and Z activities. Specifically, Version X provides scaffolded support, Version Y contains grade-level tasks, and Version Z includes more complex, non-routine problem-solving tasks. Together, these formative assessments provide students with opportunities to engage in TEKS-aligned content through multiple interactive formats and increasing levels of cognitive demand.
The “XYZ” activities provide a variety of formative assessments with TEKS-aligned tasks that incorporate multiple interactive item types and varying levels of complexity. These activities include number-line representation tasks, sequence-completion tasks, card-placement activities, sentence-completion tasks, and multi-step constructed-response questions that require students to explain or justify their reasoning. The activities are organized into X, Y, and Z versions that progress from supported practice to grade-level application and more complex, non-routine problem-solving. This structure engages students with mathematical concepts through varied task formats while increasing cognitive demand across the assessment activities.
Evaluation for 2.2a
The Math Journeys grade 6 Spanish program explains in detail how to interpret student performance data in the placement test report sample. The instructional assessment report displays each student’s score and identifies the corresponding performance category (i.e., low, medium-low, medium-high, and high). In addition to stating performance outcomes, the sample offers recommendations for instructional placement based on assessment results. The guidance emphasizes using “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.” This comprehensive approach helps educators make informed, individualized instructional decisions aligned with students’ learning needs.
The end-of-journey answer key provides scoring information and rationales for correct as well as incorrect responses. The answer key identifies the correct answer for each assessment item and explains why the correct response is valid. In addition, the answer key clarifies common incorrect responses and associated misconceptions, helping educators understand potential student errors and identify subsequent instructional steps. These item-by-item rationales help educators interpret student performance, analyze misunderstandings, and provide targeted feedback and intervention.
Evaluation for 2.2b
The instructional materials provide guidance for responding to trends in student performance through the placement test report. In the section “Placement in Journeys,” the report explains how educators can use assessment results to support instructional decision-making and student placement. Specifically, the placement test report helps educators group students for targeted instruction and determine appropriate placement within the Innovamat program. Based on students’ assessment performance, the report suggests starting points for each student within the journey’s progression, allowing educators to differentiate instruction according to demonstrated levels of understanding and academic readiness.
The placement test report contains information that informs how educators use assessment results to address trends in student performance. The report includes aggregated classroom data that identifies trends in student performance across mathematical domains and processes, highlighting areas where groups of students may require additional support. It also provides recommended instructional groupings and suggests intervention pathways based on assessment results. By connecting performance trends to specific instructional starting points within the curriculum’s progression, educators receive guidance to select targeted tasks and activities in order to address identified learning needs and support differentiated instruction.
Evaluation for 2.2c
The Math Journeys grade 6 Spanish program provides tools for educators to track students’ progress and growth through the placement test report sample and the end-of-journey tests dashboards. The “Results per Student,” “Class Distribution,” and “Question Details” reports allow educators to monitor trends in student performance, identify areas needing support, and make instructional decisions based on assessment data. In addition, “Suggested instructional focus” statements and recommended instructional placements connect to student performance outcomes. However, the program does not provide tools for students to independently track their own progress and growth over time.
The Classroom Manager provides tools that help educators track students’ progress and growth. This platform generates real-time reports for individual students as well as entire classes using data from formative assessment checkpoints, instructional assessments, and the Atlas Math adaptive digital learning platform. Educators can review trends in student performance across customizable date ranges and export reports in Excel or PDF format to support progress monitoring and instructional planning. Although students receive immediate feedback within Atlas Math activities through a milestone tracker that indicates correct and incorrect responses, the platform does not contain a student-facing dashboard, progress report, goal-setting tool, or longitudinal tracker that would allow students to independently monitor their progress and growth over time.
Evaluation for 2.2d
The Math Journeys grade 6 Spanish program provides valuable information on formative assessment to help educators frequently check students’ understanding throughout the lessons using prompts, observation opportunities, and discussion questions. In addition, the guidance encourages students to explain their thinking, justify their responses, and participate in mathematical discussions during instruction. For example, in the lesson “Conteo resultativo (hasta 20),” grade 1 educators observe whether students use groups of 10 or continue counting one by one to monitor their understanding of place-value concepts and counting strategies. To encourage students to explain their reasoning and justify their responses, the educator uses prompts such as “¿Observas algún patrón relacionado con la posición de los números menores y mayores cuando contamos?” and “Cuando comparas 13 y 15, ¿cuál aparece primero al contar hacia adelante?” In addition, the curriculum helps educators conduct ongoing formative assessment through partner discussions, observation, and student explanations across the lessons.
Throughout each lesson and activity, embedded prompts and instructional guidance help educators frequently check students’ understanding at key instructional points. For example, journey E, “Powers and Integers,” E2, “Integers,” station 1, “Introduction to Negative Numbers,” contains opportunities for educators to monitor students’ understanding during the “Warm-up,” “Development activity,” and “Wrap-up” sections. During the warm-up, students represent a picture with an equation, allowing educators to assess their prior understanding and identify misconceptions. The lesson also includes “Teacher Moves” guidance and targeted questions that help educators monitor students’ thinking throughout the learning process. Additionally, whole-class and partner tasks provide opportunities to check for understanding during and after the activity. In the wrap-up, educators use prompts, observation guidance, and suggested look-fors to evaluate whether students have met the lesson objective and to determine appropriate next instructional steps.
Evaluation for 2.2e
The Math Journeys grade 6 Spanish program enables educators to frequently check students’ understanding throughout lessons and activities using embedded opportunities for formative assessment and immediate feedback during digital practice. The Program Guide describes Atlas Math as an adaptive digital learning platform that adjusts the sequence of activities based on educator pacing and student performance. Within each journey station, the “Additional Practice” component uses Atlas Math to provide interactive activities, fluency practice, feedback, and individualized learning pathways that allow educators to monitor students’ understanding throughout instruction.
The Program Guide explains that Atlas Math adapts the sequence of activities based on educator pacing and student performance, rather than adapting checks for understanding within an activity. Students receive immediate feedback and may progress to different activities based on performance, but the curriculum does not show that the complexity of questions, item types, or instructional supports are adjusted in real time in response to individual students’ responses. Thus, the curriculum enables educators to frequently check students’ understanding, but does not fully allow educators to perform adaptive checks for understanding in each lesson or activity.
2.1 Instructional Assessments
2.1a
Materials include the definition and intended purpose for the types of instructional assessments.
Materials include the definition and intended purpose for the types of instructional assessments.
1 out of 1 points
Evaluation for 2.1a
Evaluation for 2.1a
Materials include the definition and intended purpose for the types of instructional assessments.
1 out of 1 points
The Program Guide defines the purpose of diagnostic assessment and identifies the placement test as a diagnostic evaluation given at the beginning of instruction to determine students’ current level of mathematical understanding and establish an appropriate entry point within the broader pathway. The guide explains that assessment results align with the curriculum’s learning progression and are used to place students in the most appropriate journey based on their learning needs. Additionally, the materials provide examples of how diagnostic results can inform instructional planning and support grouping students for targeted instruction.
2.1b
Materials include guidance to ensure consistent and accurate administration of instructional assessments.
Materials include guidance to ensure consistent and accurate administration of instructional assessments.
1 out of 1 points
Evaluation for 2.1b
Evaluation for 2.1b
Materials include guidance to ensure consistent and accurate administration of instructional assessments.
1 out of 1 points
The placement test process, described in the Program Guide, explains how to correctly and reliably administer as well as use instructional assessments. The guide clarifies that all students complete the placement test at the beginning of the year through their Atlas Math accounts and details how assessment results are mapped to the curriculum’s learning progression. The guide further outlines how educators can use the results to assign students to an appropriate starting journey based on their demonstrated understanding. This guide promotes standardized administration procedures and supports the consistent interpretation and use of assessment results across classrooms.
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.
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.
1 out of 2 points
Evaluation for 2.1c
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.
1 out of 2 points
The Program Guide identifies several accommodations for digital assessment, including embedded text-to-speech functionality as well as content and language supports within the assessment platform. Educators can designate each student’s language of instruction through the Classroom Manager. This setting applies across content, practice, and assessments. However, students activate text-to-speech functionality through a speaker icon rather than the educator enabling or disabling it for individual students. Additionally, calculators are not embedded within the digital assessment platform. Instead, the Program Guide states that educators provide and manage calculators during test administration. Thus, the curriculum includes some digital assessment accommodations but does not allow educators to enable or disable text-to-speech functionality, content and language supports, or calculators for individual students as required by the rubric.
2.1d
Materials include diagnostic assessments with TEKS-aligned tasks or questions, including interactive item types with varying complexity levels.
Materials include diagnostic assessments with TEKS-aligned tasks or questions, including interactive item types with varying complexity levels.
4 out of 4 points
Evaluation for 2.1d
Evaluation for 2.1d
Materials include diagnostic assessments with TEKS-aligned tasks or questions, including interactive item types with varying complexity levels.
4 out of 4 points
The Placement Test Implementation Guide describes diagnostic assessments that incorporate varying levels of complexity and multiple interactive item types. The guide identifies three levels of cognitive demand within the diagnostic assessment: DOK 1 (Factual Knowledge), DOK 2 (Procedural Knowledge), and DOK 3 (Reasoning and Problem-Solving). It also identifies multiple item formats such as multiple-choice, constructed-response, number-line, and other interactive response formats. These diagnostic tasks require students to demonstrate their understanding across a range of cognitive demands, from recalling facts and procedures to applying mathematical reasoning and problem-solving strategies.
2.1e
Materials include a variety of formative assessments with TEKS-aligned tasks or questions, including interactive item types with varying complexity levels.
Materials include a variety of formative assessments with TEKS-aligned tasks or questions, including interactive item types with varying complexity levels.
4 out of 4 points
Evaluation for 2.1e
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.
4 out of 4 points
The “XYZ” activities provide a variety of formative assessments with TEKS-aligned tasks that incorporate multiple interactive item types and varying levels of complexity. These activities include number-line representation tasks, sequence-completion tasks, card-placement activities, sentence-completion tasks, and multi-step constructed-response questions that require students to explain or justify their reasoning. The activities are organized into X, Y, and Z versions that progress from supported practice to grade-level application and more complex, non-routine problem-solving. This structure engages students with mathematical concepts through varied task formats while increasing cognitive demand across the assessment activities.
2.2 Data Analysis and Progress Monitoring
2.2a
Instructional assessments include scoring information and guidance for interpreting student performance, including rationale for each correct and incorrect response.
Instructional assessments include scoring information and guidance for interpreting student performance, including rationale for each correct and incorrect response.
3 out of 3 points
Evaluation for 2.2a
Evaluation for 2.2a
Instructional assessments include scoring information and guidance for interpreting student performance, including rationale for each correct and incorrect response.
3 out of 3 points
The end-of-journey answer key provides scoring information and rationales for correct as well as incorrect responses. The answer key identifies the correct answer for each assessment item and explains why the correct response is valid. In addition, the answer key clarifies common incorrect responses and associated misconceptions, helping educators understand potential student errors and identify subsequent instructional steps. These item-by-item rationales help educators interpret student performance, analyze misunderstandings, and provide targeted feedback and intervention.
2.2b
Materials provide guidance for the use of included tasks and activities to respond to student trends in performance on assessments.
Materials provide guidance for the use of included tasks and activities to respond to student trends in performance on assessments.
1 out of 1 points
Evaluation for 2.2b
Evaluation for 2.2b
Materials provide guidance for the use of included tasks and activities to respond to student trends in performance on assessments.
1 out of 1 points
The placement test report contains information that informs how educators use assessment results to address trends in student performance. The report includes aggregated classroom data that identifies trends in student performance across mathematical domains and processes, highlighting areas where groups of students may require additional support. It also provides recommended instructional groupings and suggests intervention pathways based on assessment results. By connecting performance trends to specific instructional starting points within the curriculum’s progression, educators receive guidance to select targeted tasks and activities in order to address identified learning needs and support differentiated instruction.
2.2c
Materials include tools for teachers to track student progress and growth, and tools for students to track their own progress and growth.
Materials include tools for teachers to track student progress and growth, and tools for students to track their own progress and growth.
1 out of 2 points
Evaluation for 2.2c
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.
1 out of 2 points
The Classroom Manager provides tools that help educators track students’ progress and growth. This platform generates real-time reports for individual students as well as entire classes using data from formative assessment checkpoints, instructional assessments, and the Atlas Math adaptive digital learning platform. Educators can review trends in student performance across customizable date ranges and export reports in Excel or PDF format to support progress monitoring and instructional planning. Although students receive immediate feedback within Atlas Math activities through a milestone tracker that indicates correct and incorrect responses, the platform does not contain a student-facing dashboard, progress report, goal-setting tool, or longitudinal tracker that would allow students to independently monitor their progress and growth over time.
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.
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.
2 out of 2 points
Evaluation for 2.2d
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.
2 out of 2 points
Throughout each lesson and activity, embedded prompts and instructional guidance help educators frequently check students’ understanding at key instructional points. For example, journey E, “Powers and Integers,” E2, “Integers,” station 1, “Introduction to Negative Numbers,” contains opportunities for educators to monitor students’ understanding during the “Warm-up,” “Development activity,” and “Wrap-up” sections. During the warm-up, students represent a picture with an equation, allowing educators to assess their prior understanding and identify misconceptions. The lesson also includes “Teacher Moves” guidance and targeted questions that help educators monitor students’ thinking throughout the learning process. Additionally, whole-class and partner tasks provide opportunities to check for understanding during and after the activity. In the wrap-up, educators use prompts, observation guidance, and suggested look-fors to evaluate whether students have met the lesson objective and to determine appropriate next instructional steps.
2.2e
If designed to be adaptive, materials provide frequent checks for understanding at key points throughout each lesson or activity.
If designed to be adaptive, materials provide frequent checks for understanding at key points throughout each lesson or activity.
0 out of 1 points
Evaluation for 2.2e
Evaluation for 2.2e
If designed to be adaptive, materials provide frequent checks for understanding at key points throughout each lesson or activity.
0 out of 1 points
The Program Guide explains that Atlas Math adapts the sequence of activities based on educator pacing and student performance, rather than adapting checks for understanding within an activity. Students receive immediate feedback and may progress to different activities based on performance, but the curriculum does not show that the complexity of questions, item types, or instructional supports are adjusted in real time in response to individual students’ responses. Thus, the curriculum enables educators to frequently check students’ understanding, but does not fully allow educators to perform adaptive checks for understanding in each lesson or activity.
Rubric Section 3
Supports for All Learners
Materials support educators in reaching all learners through design focused on engagement, representation, and action/expression for learner variability.
Total
91% (32 out of 35 points)
Evaluation for 3.1a
The Math Journeys grade 6 Spanish program explains how to scaffold lessons for students who have not yet reached proficiency in prerequisite or grade-level concepts and skills. In the Guía del profesor, E2.3, “Ordenación y saltos en la línea numérica,” the “Apoyo” section helps educators support students who need further assistance with ordering integers and using a number line. The support is embedded within instruction and provides scaffolding during learning.
The Math Journeys grade 6 Spanish program includes scaffolded activities for students who require additional support with grade-level concepts. In Guía del profesor, E2.4, “Representación de números enteros con fichas (I),” the “Resources” section contains XYZ activities for use during the “Consolidate” session. These activities provide visual representations and concrete models that support students’ understanding of integer concepts.
Evaluation for 3.1b
The Math Journeys grade 6 Spanish program clearly explains how to pre-teach academic vocabulary. In the Guía del profesor, E2.2, “Números negativos en la línea numérica,” the educator-facing lesson includes a “Key Vocabulary” section that identifies lesson-specific mathematical terminology. The curriculum also incorporates cognates and false cognates to support language development.
The Journey E2 Language Bank outlines routines that support the pre-teaching and development of mathematical language. This resource also includes an “Unfamiliar Reference Quick Bridge” routine and a lesson-by-lesson table that identifies unfamiliar references across eight lessons. Educators can use a corresponding bridge before students encounter the reference in the text. These additions clearly explain how to pre-teach the context of unfamiliar references while using existing language routines to support students’ development and use of academic vocabulary.
Evaluation for 3.1c
The Math Journeys grade 6 Spanish program contains extension opportunities that provide additional challenges as well as opportunities to engage in mathematical reasoning. The curriculum gives educators explicit guidance on enrichment and extension activities for students who have shown proficiency in grade-level content and skills. The new Enrichment and Extension Guide identifies three observable signals that educators can use to determine which students should receive extension work, and explains how to facilitate extension logsheets and extension tips, including the task intent, what educators should listen for, and evidence of mastery.
The Math Journeys grade 6 Spanish program contains XYZ activities with tasks involving increased complexity that are intended to provide additional challenges. The guide also outlines a process for students who demonstrate continued proficiency. After three consecutive sessions completed without difficulty, educators may administer the end-of-journey test early, and students who score above 75 percent may advance to the next journey.
Evaluation for 3.1d
The digital materials include student-facing accessibility and support features such as text-to-speech functionality and support icons. However, verified platform use indicates that educators cannot enable or disable content and language supports for individual students. The Program Guide explains that students can independently activate text-to-speech functionality through a speaker icon rather than through educator-controlled settings.
The Math Journeys grade 6 Spanish program does not provide an integrated calculator accommodation within the digital platform that educators can enable or disable for individual students. The Program Guide states that calculators are managed externally during assessment administration, and educator-controlled accommodation settings have not been confirmed.
Evaluation for 3.1e
The Math Journeys grade 6 Spanish program explains how to offer students options so they can demonstrate their understanding through multiple representations. In Guía del profesor, E2.4, “Representación de números enteros con fichas (I),” students use integer counters, discussion, and recorded representations to show their understanding. The lesson follows a concrete-to-representational progression that supports multiple methods for expressing mathematical understanding.
The Math Journeys grade 6 Spanish program provides students with opportunities to demonstrate their understanding through discussion, visual representation, and collaborative problem-solving. In Guía del profesor, E2.3, “Ordenación y saltos en la línea numérica,” students participate in group discussions, partner work, and number-line representations, allowing them to express their reasoning orally and represent their ideas visually.
Evaluation for 3.2a
The Math Journeys grade 6 Spanish program contains explicit prompts and guidance to help educators assist students with activating their prior knowledge and connecting it to new learning. In the Guía del profesor, E2.3, “Ordenación y saltos en la línea numérica,” students revisit their prior understanding of number order and location on a number line before extending it to integers. Educator-facing prompts guide educators to help students connect their prior learning to new concepts and identify patterns as well as relationships among representations.
The Math Journeys grade 6 Spanish program clearly explains how to anchor instruction in key mathematical ideas through multiple representations. In the Guía del profesor, E2.4, “Representación de números enteros con fichas (I),” students represent integers using counters, number lines, verbal explanations, and symbolic notation. Educator-facing guidance helps students identify relationships among representations and connect concrete models to abstract mathematical concepts.
Evaluation for 3.2b
The Math Journeys grade 6 Spanish program explains how to deliver lessons effectively using multiple instructional approaches. In the Guía del profesor, E2.3, “Ordenación y saltos en la línea numérica,” the lesson incorporates whole-group discussion, guided questioning, collaborative learning, and independent application. Educator-facing prompts help educators facilitate mathematical discourse and monitor students’ understanding throughout instruction.
The Math Journeys grade 6 Spanish program contains guidance for transitioning among instructional approaches while implementing a lesson. In Guía del profesor, E2.6, “Suma y resta de números enteros con fichas,” students engage in hands-on exploration with counters, collaborative discussion, educator-facilitated questioning, and independent practice. The lesson structure helps educators facilitate each phase of instruction while supporting student engagement.
Evaluation for 3.2c
The Math Journeys grade 6 Spanish program provides multi-tiered intervention methods through multiple teaching structures and practice opportunities. In the Guía del profesor, E2.6, “Suma y resta de números enteros con fichas,” students participate in educator-led instruction, guided practice, collaborative learning, and independent application. Embedded supports and differentiated practice opportunities enable educators to address varying student needs throughout the lesson.
The Math Journeys grade 6 Spanish program explains how to effectively implement multi-tiered intervention methods. The Program Guide describes the three-step framework of “build,” “consolidate,” and “additional practice.” “Build” supports educator-guided instruction and mathematical discussion. “Consolidate” provides opportunities for independent practice and differentiated resources. “Additional Practice” relies on Atlas Math to provide adaptive learning pathways as well as individualized practice based on student performance.
Evaluation for 3.2d
The Math Journeys grade 6 Spanish program contains enrichment and extension methods that support student engagement through mathematical reasoning and problem-solving. In Guía del profesor, E2.7, “Práctica de suma y resta de números enteros (I),” extension opportunities encourage students to explore multiple solution strategies, justify their mathematical reasoning, and engage in mathematical discussion beyond lesson expectations. These activities provide opportunities for deeper engagement with the content.
The Math Journeys grade 6 Spanish program contains additional enrichment opportunities through differentiated practice resources and adaptive learning tools. The Program Guide describes “Additional Practice” on Atlas Math, which provides individualized activities and increasingly complex tasks based on student performance. These opportunities allow students to engage with content beyond the core lesson expectations while continuing to develop their conceptual understanding.
Evaluation for 3.2e
The Math Journeys grade 6 Spanish program provides educator-facing prompts to help educators monitor students’ understanding and provide timely feedback. In Guía del profesor, E2.4, “Representación de números enteros con fichas (I),” educators are directed to ask questions that require students to explain patterns, justify strategies, and communicate their mathematical reasoning. The prompts provide opportunities for educators to give immediate feedback during instruction.
The Math Journeys grade 6 Spanish program explains how to observe students’ thinking and address misconceptions throughout the lesson. In Guía del profesor, E2.2, “Números negativos en la línea numérica,” educator-facing questions and observation opportunities help educators monitor how students represent, compare, and sequence integers on a number line. The guide enables educators to provide feedback as students engage in discussion, modeling, and independent practice.
Evaluation for 3.3a
This guidance is not applicable because the program is not designed to be static.
This indicator does not apply to the grade 6 Spanish materials.
Evaluation for 3.3b
This guidance is not applicable to the program because it is not designed to be adaptive.
This indicator does not apply to the grade 6 Spanish materials.
Evaluation for 3.3c
The Math Journeys grade 6 Spanish program provides implementation guidance to help educators use the materials effectively in bilingual/ESL programs. The Texas Bilingual / ESL Implementation Guide explains how to implement instruction for emergent bilingual (EB) students and includes recommendations on how to make mathematical language accessible while maintaining the rigor of grade-level content. The guide helps educators plan opportunities for students to develop language alongside math instruction.
The Math Journeys grade 6 Spanish program provides further implementation guidance through the “Lesson-Level ELPS Companion.” This resource contains lesson-specific language objectives, language demands, expected oral and written student output, and suggested educator supports. This companion helps educators plan instruction that supports language development while engaging students in grade-level mathematical learning.
Evaluation for 3.3d
The Math Journeys grade 6 Spanish program contains embedded guidance to help EB students develop their academic vocabulary and increase their comprehension through oral discourse. In Guía del profesor, E2.6, “Suma y resta de números enteros con fichas,” the “Key Vocabulary” section identifies mathematical vocabulary and provides cognates, sentence frames, and discussion opportunities that help students use academic language while explaining their mathematical thinking. These supports help students deepen their comprehension and make connections between English and Spanish through classroom discourse.
The Math Journeys grade 6 Spanish program contains embedded guidance to support EB students through written discourse and cross-linguistic connections. The “Lesson-Level ELPS Companion” provides opportunities for students to record their observations, justify their mathematical reasoning, and explain solutions using academic vocabulary. The curriculum supports connections between English and Spanish mathematical terms through cognates, structured language supports, and written-response opportunities, thereby strengthening both language development and mathematical understanding.
Evaluation for 3.3e
This guidance is not applicable because the program is not designed for dual language immersion (DLI) programs.
This indicator does not apply to the grade 6 Spanish materials.
3.1 Differentiation and Scaffolds
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.
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.
1 out of 1 points
Evaluation for 3.1a
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.
1 out of 1 points
The Math Journeys grade 6 Spanish program includes scaffolded activities for students who require additional support with grade-level concepts. In Guía del profesor, E2.4, “Representación de números enteros con fichas (I),” the “Resources” section contains XYZ activities for use during the “Consolidate” session. These activities provide visual representations and concrete models that support students’ understanding of integer concepts.
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.
Materials include explicit educator guidance for language supports, including pre-teaching and embedded supports for developing academic vocabulary and unfamiliar references in text.
4 out of 4 points
Evaluation for 3.1b
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.
4 out of 4 points
The Journey E2 Language Bank outlines routines that support the pre-teaching and development of mathematical language. This resource also includes an “Unfamiliar Reference Quick Bridge” routine and a lesson-by-lesson table that identifies unfamiliar references across eight lessons. Educators can use a corresponding bridge before students encounter the reference in the text. These additions clearly explain how to pre-teach the context of unfamiliar references while using existing language routines to support students’ development and use of academic vocabulary.
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.
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.
2 out of 2 points
Evaluation for 3.1c
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.
2 out of 2 points
The Math Journeys grade 6 Spanish program contains XYZ activities with tasks involving increased complexity that are intended to provide additional challenges. The guide also outlines a process for students who demonstrate continued proficiency. After three consecutive sessions completed without difficulty, educators may administer the end-of-journey test early, and students who score above 75 percent may advance to the next journey.
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.
Digital materials include accommodations, including text-to-speech, content and language supports, and calculators that educators can enable or disable to support individual students.
0 out of 3 points
Evaluation for 3.1d
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.
0 out of 3 points
The Math Journeys grade 6 Spanish program does not provide an integrated calculator accommodation within the digital platform that educators can enable or disable for individual students. The Program Guide states that calculators are managed externally during assessment administration, and educator-controlled accommodation settings have not been confirmed.
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.
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.
2 out of 2 points
Evaluation for 3.1e
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.
2 out of 2 points
The Math Journeys grade 6 Spanish program provides students with opportunities to demonstrate their understanding through discussion, visual representation, and collaborative problem-solving. In Guía del profesor, E2.3, “Ordenación y saltos en la línea numérica,” students participate in group discussions, partner work, and number-line representations, allowing them to express their reasoning orally and represent their ideas visually.
3.2 Instructional Methods
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.
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.
5 out of 5 points
Evaluation for 3.2a
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.
5 out of 5 points
The Math Journeys grade 6 Spanish program clearly explains how to anchor instruction in key mathematical ideas through multiple representations. In the Guía del profesor, E2.4, “Representación de números enteros con fichas (I),” students represent integers using counters, number lines, verbal explanations, and symbolic notation. Educator-facing guidance helps students identify relationships among representations and connect concrete models to abstract mathematical concepts.
3.2b
If designed to be static, materials include educator guidance for effective lesson delivery and facilitation using various instructional approaches.
If designed to be static, materials include educator guidance for effective lesson delivery and facilitation using various instructional approaches.
2 out of 2 points
Evaluation for 3.2b
Evaluation for 3.2b
If designed to be static, materials include educator guidance for effective lesson delivery and facilitation using various instructional approaches.
2 out of 2 points
The Math Journeys grade 6 Spanish program contains guidance for transitioning among instructional approaches while implementing a lesson. In Guía del profesor, E2.6, “Suma y resta de números enteros con fichas,” students engage in hands-on exploration with counters, collaborative discussion, educator-facilitated questioning, and independent practice. The lesson structure helps educators facilitate each phase of instruction while supporting student engagement.
3.2c
Materials include multi-tiered intervention methods for various types of practice and structures and educator guidance to support effective implementation.
Materials include multi-tiered intervention methods for various types of practice and structures and educator guidance to support effective implementation.
3 out of 3 points
Evaluation for 3.2c
Evaluation for 3.2c
Materials include multi-tiered intervention methods for various types of practice and structures and educator guidance to support effective implementation.
3 out of 3 points
The Math Journeys grade 6 Spanish program explains how to effectively implement multi-tiered intervention methods. The Program Guide describes the three-step framework of “build,” “consolidate,” and “additional practice.” “Build” supports educator-guided instruction and mathematical discussion. “Consolidate” provides opportunities for independent practice and differentiated resources. “Additional Practice” relies on Atlas Math to provide adaptive learning pathways as well as individualized practice based on student performance.
3.2d
Materials include enrichment and extension methods that support various forms of engagement, and guidance to support educators in effective implementation.
Materials include enrichment and extension methods that support various forms of engagement, and guidance to support educators in effective implementation.
2 out of 2 points
Evaluation for 3.2d
Evaluation for 3.2d
Materials include enrichment and extension methods that support various forms of engagement, and guidance to support educators in effective implementation.
2 out of 2 points
The Math Journeys grade 6 Spanish program contains additional enrichment opportunities through differentiated practice resources and adaptive learning tools. The Program Guide describes “Additional Practice” on Atlas Math, which provides individualized activities and increasingly complex tasks based on student performance. These opportunities allow students to engage with content beyond the core lesson expectations while continuing to develop their conceptual understanding.
3.2e
Materials include prompts and guidance to support educators in providing timely feedback during lesson delivery.
Materials include prompts and guidance to support educators in providing timely feedback during lesson delivery.
2 out of 2 points
Evaluation for 3.2e
Evaluation for 3.2e
Materials include prompts and guidance to support educators in providing timely feedback during lesson delivery.
2 out of 2 points
The Math Journeys grade 6 Spanish program explains how to observe students’ thinking and address misconceptions throughout the lesson. In Guía del profesor, E2.2, “Números negativos en la línea numérica,” educator-facing questions and observation opportunities help educators monitor how students represent, compare, and sequence integers on a number line. The guide enables educators to provide feedback as students engage in discussion, modeling, and independent practice.
3.3 Support for Emergent Bilingual Students
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.
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.
Not applicable.
Evaluation for 3.3a
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.
Not applicable.
This indicator does not apply to the grade 6 Spanish materials.
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.
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.
Not applicable.
Evaluation for 3.3b
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.
Not applicable.
This indicator does not apply to the grade 6 Spanish materials.
3.3c
Materials include implementation guidance to support educators in effectively using the materials in state-approved bilingual/ESL programs.
Materials include implementation guidance to support educators in effectively using the materials in state-approved bilingual/ESL programs.
1 out of 1 points
Evaluation for 3.3c
Evaluation for 3.3c
Materials include implementation guidance to support educators in effectively using the materials in state-approved bilingual/ESL programs.
1 out of 1 points
The Math Journeys grade 6 Spanish program provides further implementation guidance through the “Lesson-Level ELPS Companion.” This resource contains lesson-specific language objectives, language demands, expected oral and written student output, and suggested educator supports. This companion helps educators plan instruction that supports language development while engaging students in grade-level mathematical learning.
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.
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.
8 out of 8 points
Evaluation for 3.3d
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.
8 out of 8 points
The Math Journeys grade 6 Spanish program contains embedded guidance to support EB students through written discourse and cross-linguistic connections. The “Lesson-Level ELPS Companion” provides opportunities for students to record their observations, justify their mathematical reasoning, and explain solutions using academic vocabulary. The curriculum supports connections between English and Spanish mathematical terms through cognates, structured language supports, and written-response opportunities, thereby strengthening both language development and mathematical understanding.
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.
If designed for dual language immersion (DLI) programs, materials include resources that outline opportunities to address metalinguistic transfer from English to the partner language.
Not applicable.
Evaluation for 3.3e
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.
Not applicable.
This indicator does not apply to the grade 6 Spanish materials.
Rubric Section 4
Depth and Coherence of Key Concepts
Materials are designed to meet the rigor of the standards while connecting concepts within and across grade levels/courses.
Total
94% (15 out of 16 points)
Evaluation for 4.1a
Students develop their reasoning with integers through practice opportunities that help them move from concrete models to symbolic representations. In E2, “Números enteros,” students use “Actividades XYZ” to represent integer subtraction with fichas, complete symbolic models, solve expressions, compare results, identify patterns, and determine missing values in equations. These activities require students to connect representations, analyze relationships among integers, and generalize mathematical ideas while demonstrating understanding aligned with the TEKS.
Opportunities for formative assessment in E2, “Números enteros,” require students to solve subtraction expressions, compare related results, identify patterns, and complete equations involving integer values. Students document their observations and explain the relationships among solutions while using logsheets and “Actividades XYZ” to consolidate their learning. These assessment tasks show students’ understanding through representation, comparison, and generalization of integer relationships, rather than through procedural computation alone.
Evaluation for 4.1b
Across the E2, “Números enteros” pathway, questions and tasks increase in rigor and complexity, leading students toward grade-level proficiency. Students begin with negative numbers and integer representations, then use fichas to model integers, add and subtract integers, identify patterns in integer operations, multiply and divide integers, and complete combined operations. This progression helps students move from concrete representations to symbolic operations and generalizations, and includes the increasing rigor and complexity needed for grade-level proficiency.
Some tasks extend beyond grade 6 expectations, but the enrichment and extension resources do not provide structured support that helps students achieve above grade-level proficiency. In E2, “Números enteros,” “Actividades XYZ,” students represent integer subtraction with fichas, connect models to symbolic expressions, solve expressions such as 6 − 9, 9 − 6, 24 − 32, and 32 − 24, compare related results, identify patterns, and complete equations with missing integer values. These tasks increase complexity by requiring students to analyze relationships and generalize patterns rather than complete isolated computations, and the pathway extends into future-grade expectations involving integers. However, the resources do not contain a structured sequence of guidance, scaffolds, or follow-up tasks that systematically enables students to develop above grade-level proficiency. Thus, the materials meet the criteria for increasing rigor toward grade-level proficiency and include tasks that extend beyond grade 6 expectations, but they do not meet the criterion for structured support leading to above grade-level proficiency.
Evaluation for 4.2a
Coherence across grade 6 concepts is developed within the E2, “Números enteros,” pathway as students progress from understanding negative numbers and integer representations to performing operations and identifying patterns among integer relationships. Learning experiences build from concrete models and visual representations to symbolic operations and mathematical generalizations. This progression connects integer magnitude, representation, operations, and pattern recognition within a coherent grade-level sequence.
Educators help students reinforce connections among integer concepts through E2, “Números enteros,” “Actividades XYZ.” Students represent subtraction with fichas, complete symbolic models, solve integer expressions, compare related results, identify patterns, and determine missing values in equations. These tasks connect concrete representations, symbolic notation, integer operations, comparison of results, and generalization, thus supporting coherence across grade 6 integer concepts.
Evaluation for 4.2b
The Math Journeys grade 6 Spanish program demonstrates vertical coherence across concepts and grade bands by connecting patterns, big ideas, and relationships across grades 3–12. Within cluster E, “Powers and Integers,” the updated Learning Progression explicitly identifies prerequisite learning from grades 3–5 and connects the understanding built in those grades to the development of powers and integers in the current grade. The progression also identifies how these concepts and related strategies extend into future learning in Algebra I, Geometry, and Algebra II. These clear connections show how mathematical ideas and relationships develop across grade levels and courses.
The planning resources demonstrate vertical coherence by explicitly connecting prior, current, and future mathematical learning. The cluster F Learning Progression identifies foundational work from grades 3–5, connects it to learning within the current grade band, and extends the progression into Algebra I, Geometry, and Algebra II. The progression highlights mathematical relationships and identifies the area model as a strategy carried across the grade span, showing how a common representation connects increasingly complex mathematical ideas from earlier grades through high school coursework.
Evaluation for 4.2c
The Math Journeys grade 6 Spanish program demonstrates coherence across lessons and activities by connecting students’ prior knowledge of concepts and procedures to mathematical concepts and procedures in the current as well as future grade levels. The Connections and Misconceptions Teacher Companion identifies the prior knowledge students bring to each session, the new concepts or procedures developed, and where learning returns in subsequent grades and courses. For example, work with integer addition and subtraction in E2.6–E2.8 connects students’ current learning to grade 7 rational number fluency as well as Algebra I, explicitly showing how current concepts and procedures support future mathematical learning.
The Math Journeys grade 6 Spanish program connects current mathematical procedures to future grade-level concepts and procedures. The cluster D Connections and Misconceptions Teacher Companion identifies prior knowledge, new learning, and future applications at the session level. For example, work with percent of a quantity in D3.11–D3.12 connects to rate and proportional reasoning in grades 6–7, while fraction multiplication procedures developed in D5.8–D5.9 and D5.15–D5.16 are linked to future work with rational expressions in Algebra I. These clear connections show how students develop their conceptual and procedural knowledge across lessons, grade levels, and future courses.
Evaluation for 4.3a
Students revisit previously learned skills and concepts throughout E2, “Números enteros,” session 9, “Práctica de suma y resta de números enteros (II).” During the warm-up, students return to integer addition and subtraction concepts from earlier lessons by inserting positive and negative signs into an expression to generate different results. Activity 2 then revisits sequence and pattern concepts as students analyze integer sequences and identify rules. These experiences require students to retrieve prior learning after intervening instruction and apply it within new mathematical contexts.
The TEKS Correlation Guide provides opportunities for spaced retrieval across the grade 6 Spanish learning pathways by identifying where content standards and mathematical process standards recur throughout journeys and sessions. This resource shows when previously introduced concepts reappear in later lessons, allowing students to revisit and apply their prior understanding of integers, patterns, and related mathematical ideas over time.
Evaluation for 4.3b
Students encounter opportunities for interleaved practice in E2, “Números enteros,” session 15, “Operaciones combinadas con números enteros.” Students simplify expressions involving addition, subtraction, multiplication, and division of integers while applying the order of operations. They determine whether mathematical statements are true, analyze errors, and revise expressions when necessary. These activities require students to coordinate prior arithmetic skills, integer concepts, operation rules, and algebraic reasoning within a single learning experience.
The cluster E overview, titled “Potencias y números enteros,” describes how students extend their prior arithmetic understanding into the study of integers and apply the concepts they have learned in a variety of contexts. Throughout the pathway, students connect computation skills, integer representations, operation rules, and contextual reasoning while developing new understanding. Recurring connections provide opportunities for them to simultaneously engage with multiple mathematical ideas, thus supporting opportunities for interleaved practice across the learning progression.
4.1 Depth of Key Concepts
4.1a
Practice opportunities throughout learning pathways (including instructional assessments) require students to demonstrate depth of understanding aligned to the TEKS.
Practice opportunities throughout learning pathways (including instructional assessments) require students to demonstrate depth of understanding aligned to the TEKS.
2 out of 2 points
Evaluation for 4.1a
Evaluation for 4.1a
Practice opportunities throughout learning pathways (including instructional assessments) require students to demonstrate depth of understanding aligned to the TEKS.
2 out of 2 points
Opportunities for formative assessment in E2, “Números enteros,” require students to solve subtraction expressions, compare related results, identify patterns, and complete equations involving integer values. Students document their observations and explain the relationships among solutions while using logsheets and “Actividades XYZ” to consolidate their learning. These assessment tasks show students’ understanding through representation, comparison, and generalization of integer relationships, rather than through procedural computation alone.
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.
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.
3 out of 4 points
Evaluation for 4.1b
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.
3 out of 4 points
Some tasks extend beyond grade 6 expectations, but the enrichment and extension resources do not provide structured support that helps students achieve above grade-level proficiency. In E2, “Números enteros,” “Actividades XYZ,” students represent integer subtraction with fichas, connect models to symbolic expressions, solve expressions such as 6 − 9, 9 − 6, 24 − 32, and 32 − 24, compare related results, identify patterns, and complete equations with missing integer values. These tasks increase complexity by requiring students to analyze relationships and generalize patterns rather than complete isolated computations, and the pathway extends into future-grade expectations involving integers. However, the resources do not contain a structured sequence of guidance, scaffolds, or follow-up tasks that systematically enables students to develop above grade-level proficiency. Thus, the materials meet the criteria for increasing rigor toward grade-level proficiency and include tasks that extend beyond grade 6 expectations, but they do not meet the criterion for structured support leading to above grade-level proficiency.
4.2 Coherence of Key Concepts
4.2a
Materials demonstrate coherence across concepts horizontally within the grade level by connecting patterns, big ideas, and relationships.
Materials demonstrate coherence across concepts horizontally within the grade level by connecting patterns, big ideas, and relationships.
1 out of 1 points
Evaluation for 4.2a
Evaluation for 4.2a
Materials demonstrate coherence across concepts horizontally within the grade level by connecting patterns, big ideas, and relationships.
1 out of 1 points
Educators help students reinforce connections among integer concepts through E2, “Números enteros,” “Actividades XYZ.” Students represent subtraction with fichas, complete symbolic models, solve integer expressions, compare related results, identify patterns, and determine missing values in equations. These tasks connect concrete representations, symbolic notation, integer operations, comparison of results, and generalization, thus supporting coherence across grade 6 integer concepts.
4.2b
Materials demonstrate coherence vertically across concepts and grade bands, including connections from grades 3–12, by connecting patterns, big ideas, and relationships.
Materials demonstrate coherence vertically across concepts and grade bands, including connections from grades 3–12, by connecting patterns, big ideas, and relationships.
1 out of 1 points
Evaluation for 4.2b
Evaluation for 4.2b
Materials demonstrate coherence vertically across concepts and grade bands, including connections from grades 3–12, by connecting patterns, big ideas, and relationships.
1 out of 1 points
The planning resources demonstrate vertical coherence by explicitly connecting prior, current, and future mathematical learning. The cluster F Learning Progression identifies foundational work from grades 3–5, connects it to learning within the current grade band, and extends the progression into Algebra I, Geometry, and Algebra II. The progression highlights mathematical relationships and identifies the area model as a strategy carried across the grade span, showing how a common representation connects increasingly complex mathematical ideas from earlier grades through high school coursework.
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.
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.
4 out of 4 points
Evaluation for 4.2c
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.
4 out of 4 points
The Math Journeys grade 6 Spanish program connects current mathematical procedures to future grade-level concepts and procedures. The cluster D Connections and Misconceptions Teacher Companion identifies prior knowledge, new learning, and future applications at the session level. For example, work with percent of a quantity in D3.11–D3.12 connects to rate and proportional reasoning in grades 6–7, while fraction multiplication procedures developed in D5.8–D5.9 and D5.15–D5.16 are linked to future work with rational expressions in Algebra I. These clear connections show how students develop their conceptual and procedural knowledge across lessons, grade levels, and future courses.
4.3 Coherence and Variety of Practice
4.3a
Materials provide spaced retrieval opportunities with previously learned skills and concepts across learning pathways.
Materials provide spaced retrieval opportunities with previously learned skills and concepts across learning pathways.
2 out of 2 points
Evaluation for 4.3a
Evaluation for 4.3a
Materials provide spaced retrieval opportunities with previously learned skills and concepts across learning pathways.
2 out of 2 points
The TEKS Correlation Guide provides opportunities for spaced retrieval across the grade 6 Spanish learning pathways by identifying where content standards and mathematical process standards recur throughout journeys and sessions. This resource shows when previously introduced concepts reappear in later lessons, allowing students to revisit and apply their prior understanding of integers, patterns, and related mathematical ideas over time.
4.3b
Materials provide interleaved practice opportunities with previously learned skills and concepts across learning pathways.
Materials provide interleaved practice opportunities with previously learned skills and concepts across learning pathways.
2 out of 2 points
Evaluation for 4.3b
Evaluation for 4.3b
Materials provide interleaved practice opportunities with previously learned skills and concepts across learning pathways.
2 out of 2 points
The cluster E overview, titled “Potencias y números enteros,” describes how students extend their prior arithmetic understanding into the study of integers and apply the concepts they have learned in a variety of contexts. Throughout the pathway, students connect computation skills, integer representations, operation rules, and contextual reasoning while developing new understanding. Recurring connections provide opportunities for them to simultaneously engage with multiple mathematical ideas, thus supporting opportunities for interleaved practice across the learning progression.
Rubric Section 5
Balance of Conceptual and Procedural Understanding
Materials are designed to balance conceptual understanding, procedural skills, and fluency.
Total
92% (35 out of 38 points)
Evaluation for 5.1a
Within the grade 6 Journey Instructional Guide for journey F1, station 3, “Expresiones algebraicas equivalentes,” students interpret different visual groupings of the same growing pattern by identifying what each part of the figure represents algebraically. Students analyze why expressions such as 2n + n + 1 + 2 and 3n + 3 describe the same model and determine whether 3(n + 1) is also equivalent. The task requires students to connect the visual representation to symbolic expressions and justify the relationships among them.
In the grade 6 Journey Instructional Guide for journey D3, station 12, “Calcular porcentajes I,” students interpret percentage relationships using benchmark values such as 50 percent, 25 percent, and 10 percent. Students analyze how tables, verbal descriptions, and numerical expressions represent the same part-whole relationship. In the extension, students evaluate whether A% of B = B% of A across examples, requiring them to justify the representation’s structure, rather than only calculate a percentage.
Evaluation for 5.1b
Within the grade 6 Journey Instructional Guide for journey F1, station 2, “Patrones visuales,” activity 1 asks students to construct the sixth step of a growing pattern with snap cubes before recording an arithmetic expression that represents the structure. Students then draw the first four stages of additional patterns in their notebooks, creating pictorial representations that correspond to the concrete models. This activity requires students to construct and record multiple representations of the same mathematical situation.
In the grade 6 Journey Instructional Guide for journey E2, station 6, “Sumar y restar enteros con fichas,” students model integer addition and subtraction with positive and negative counters before representing each operation with drawings in their notebooks. The lesson connects the concrete counter models to pictorial representations by having students sketch the quantities and zero pairs used to solve each problem. Educator guidance emphasizes recording the models on paper to support the transition from manipulatives to visual representations.
Evaluation for 5.1c
Within the grade 6 Journey Instructional Guide for journey D3, station 13, “Resolver problemas con porcentajes,” students apply their understanding of percentages to new real-world situations by representing world population data with snap cubes before extending their reasoning to family budget scenarios. Students determine unknown percentages by using part-whole relationships established earlier in the lesson and explain how the same conceptual understanding applies across different contexts.
In the grade 6 Journey Instructional Guide for journey E2, station 16, “Números racionales negativos,” students extend their understanding of integer ordering by classifying rational numbers represented as fractions, decimals, and mixed numbers. Students apply the concepts of valor absoluto and número opuesto to unfamiliar rational values before placing them accurately on a number line using benchmark integers as reference points.
Evaluation for 5.2a
Within the grade 6 Journey Instructional Guide for journey E2, station 8, “Suma y resta de números enteros usando la recta numérica,” students revisit integer addition and subtraction during the warm-up before applying number-line strategies throughout the lesson. Repeated opportunities to determine sums and differences using positive and negative integers reinforce efficient procedures while strengthening automatic recall of integer operations needed for later work with expressions and equations.
In the grade 6 Journey Instructional Guide for journey E1, station 8, “Práctica productiva: orden de operaciones I,” students solve multiple numerical expressions that require consistently applying the order of operations. Repeated practice with increasingly varied expressions supports procedural fluency by having students determine the correct sequence of operations accurately and efficiently throughout the lesson.
Evaluation for 5.2b
Within the grade 6 Journey Instructional Guide for journey E1, station 8, “Práctica productiva: orden de operaciones I,” students solve a variety of numerical expressions by applying the order of operations accurately across multiple practice opportunities. This lesson requires students to determine the sequence of operations for expressions with different structures, reinforcing procedural accuracy while providing opportunities to apply the same procedure in varied situations.
In the grade 6 Journey Instructional Guide for journey D5, station 18, “Dividimos fracciones II,” students complete multiplicative frames and choose among related division equations to solve each situation. Students compare approaches involving scaling, common denominators, and multiplying by the reciprocal when solving fraction-division problems. This lesson provides opportunities to apply different strategies, but does not consistently require students to reflect on or compare the efficiency of these strategies across the broader learning pathway.
Evaluation for 5.2c
Within the grade 6 Journey Instructional Guide for journey E2, station 1, “Introducción a los números negativos,” students arrange historical dates on a timeline and determine whether each placement accurately represents positive and negative values. Students then interpret thermometer models displaying temperatures during a historical polar cold wave and explain how crossing zero on the number line supports the solution strategy. These activities require students to verify the accuracy of mathematical representations and justify their reasoning.
In the grade 6 Journey Instructional Guide for journey F1, station 3, “Expresiones algebraicas equivalentes,” students determine whether different algebraic expressions represent the same visual growing pattern by comparing symbolic and visual representations. Students generate additional equivalent expressions using the commutative and associative properties, and evaluate whether simplified forms more efficiently communicate the pattern while maintaining accuracy.
Evaluation for 5.2d
The grade 6 Journey Instructional Guide for journey F1, station 3, “Expresiones algebraicas equivalentes,” directs educators to ask students to compare different expressions representing the same visual pattern and determine whether they are equivalent. Students use the structure of the expression together with the commutative and associative properties to move from visual groupings to more efficient symbolic representations without recounting each part of the figure.
In the grade 6 Journey Instructional Guide for journey E2, station 8, “Suma y resta de números enteros usando la recta numérica,” the Teacher Guide helps educators assist students in using direction, distance, and zero as reference points when representing integer operations. This instruction helps students move beyond counting individual jumps toward recognizing sign relationships and number-line structure, supporting increasingly efficient approaches for solving integer addition and subtraction problems.
Evaluation for 5.3a
Within the scope and sequence document, the grade 6 Spanish program aligns the TEKS with specific journeys and stations throughout the curriculum. The document identifies where standards are addressed and supports instructional planning. However, it does not clearly explain how students develop their conceptual understanding alongside the procedural emphasis identified in the TEKS.
The TEKS Correlation Guide identifies instructional topics aligned with TEKS 6.7A, including lessons involving equivalent numerical expressions, the order of operations, exponents, and prime factorization. Although the guide identifies where the standard is addressed, it does not explicitly state the conceptual or procedural emphases, nor does it clarify how the two emphases are connected, as required by the indicator.
Evaluation for 5.3b
In the grade 6 Journey Instructional Guide for journey E2, station 6, “Sumar y restar enteros con fichas,” students manipulate positive and negative counters to model operations such as −7 + 4. Students then create drawings of the counter models before recording symbolic equations, including −7 − (−5) = −2. These activities provide opportunities to progress from concrete models to pictorial representations and abstract notation, as required by TEKS 6.3C and 6.3D.
In the grade 6 Journey Instructional Guide for journey F1, station 4, “Representar expresiones algebraicas,” students use bags, snap cubes, frames, boxes, and counters to construct concrete models of algebraic expressions. Students then sketch the models before writing equivalent symbolic expressions such as 2(2x + 3) and 4x + 6. The lesson connects concrete, pictorial, and abstract representations while supporting the expectations of TEKS 6.7C and 6.7D.
Evaluation for 5.3c
In the grade 6 Journey Instructional Guide for journey E2, station 6, “Sumar y restar enteros con fichas,” students use positive and negative counters to create concrete models of integer operations before recording drawings of the models and writing the corresponding symbolic equations. The educator asks students to explain how zero pairs, counter removal, and movement between positive and negative values relate to equations such as −7 + 4 = −3 and −7 − (−5) = −2, thus supporting connections between concrete models and abstract notation.
In the grade 6 Journey Instructional Guide for journey F1, station 3, “Expresiones algebraicas equivalentes,” students analyze pictorial growing patterns before recording algebraic expressions representing each figure. Students construct snap-cube models, generate equivalent symbolic expressions, and explain why expressions such as 3(n + 1) and 3n + 3 represent the same pattern by applying the distributive property. These activities help students connect, create, define, and explain representational models while developing abstract algebraic concepts.
Evaluation for 5.4a
In E1, “Powers and Order of Operations,” students define base and exponent, translate notation blocks into verbal expressions, and interpret square and cube models that connect powers to area and volume. As they explain repeated multiplication through these geometric representations, they apply academic vocabulary to the mathematical structure shown in each model.
In journey E2, “Integers,” colored counters, zero pairs, and number lines make signed-number relationships visible, while contexts involving sea level, elevator floors, bank balances, and thermometers connect these ideas to familiar situations. Students draw upon the models and contexts to explain signs, direction, distance from zero, and the relationships between values using precise mathematical language.
Evaluation for 5.4b
In journey E2, “Integers,” station 3, “Ordering & Jumping on the Number Line,” the “Emergent Bilingual Students” section directs educators to use Math Learning Routine (MLR) 7, “Compare and Connect,” with sentence frames that support discussion of input, output, opposite, direction, and number-line relationships. Students compare jump-machine representations with their peers while educators guide them toward using increasingly precise explanations. The “Extension” advances this vocabulary work by requiring verbal justifications of structural number-line properties and domain restrictions.
The E2 Journey Language Bank helps educators plan language development across the journey through pre-teach routines, embedded supports, discourse and writing frames, and redirects for misconceptions. The guidance supports students as they classify signed quantities, explain distance and direction, describe zero pairs, and justify sign patterns during peer and educator interactions. Later lessons extend this language into integer operations, conjectures, and comparisons involving negative rational numbers.
Evaluation for 5.4c
In journey F1, “Algebraic Expressions,” station 8, “From Natural Language to Algebra,” the “Emergent Bilingual Students” section directs educators to use MLR 1, “Stronger and Clearer Each Time,” as students rehearse mathematical expressions aloud before a partner dictation task. During the “In Pairs” activity, communication rules require students to describe expressions with precise natural-language terms while avoiding letters and brackets. This structure prompts students to apply academic vocabulary as they clarify meaning and communicate algebraic relationships with a partner.
In E2.6, educators prompt students to describe actions with counters, explain why zero pairs do not change value, and record the matching integer equation. While discussing the model and their reasoning, students apply terms such as positive, negative, zero pair, value, and equation to connect concrete representations with symbolic expressions in oral and written discourse.
Evaluation for 5.4d
In activity 2 of journey F1, “Algebraic Expressions,” station 3, “Equivalent Algebraic Expressions,” the educator asks, “Are the algebraic expressions we came up with as a class equivalent to each other?” Students compare peer-generated expressions and discuss equivalence through vocabulary such as distributive property and like terms. The guide then directs the educator to “ask several students to state a general rule,” giving their classmates the opportunity to hear varied algebraic reasoning before refining their own explanations and recording agreements.
In E2.8 and E2.9, students compare counter and number-line models, explain why the representations match, and discuss patterns in integer addition and subtraction. Educator-guided comparisons create repeated peer exchanges in which students listen to model-based explanations, revise their reasoning, and apply language related to positive and negative values, zero pairs, integer operations, and number-line movement.
Evaluation for 5.4e
In journey F1, “Algebraic Language,” station 3, “Equivalent Algebraic Expressions,” the Teacher Guide anticipates multiple valid expressions for the same visual pattern, including 2n + n + 1 + 2 and n + n + n + 3. When a student writes 3n + 6 instead of 3n + 3, the guide directs educators back to the visual model and then to ask, “What does each term count in the picture?” This prompt reconnects the inaccurate expression to the constant tiles and helps students revise their reasoning.
In F1.8, “From Natural Language to Algebra,” educators can anticipate different translations of natural-language statements into algebraic expressions, including confusion between “double the successor of a number” and “the successor of double a number.” The lesson supports redirection by having students reread each phrase, identify the operation words, and compare the verbal structure with the corresponding algebraic expression, thus helping them distinguish the order and grouping of operations.
Evaluation for 5.5a
In journey F1, “Algebraic Language,” station 2, “Visual Patterns,” students analyze geometric sequences, organize values in tables, predict later terms, and formulate verbal or algebraic rules. TEKS process standard 1.F operates within the algebraic work as students connect step numbers to total quantities, compare expressions for the same pattern, and explain why different representations describe an equivalent relationship.
In journey E2, “Integers,” station 6, “Adding and Subtracting Integers with Counters,” students model −7 + 4 with counters, cancel zero pairs, and record −7 + 4 = −3. The activity integrates TEKS process standard 1.D as students communicate integer operations through concrete and symbolic representations. They apply the same representational connection to subtraction, including −7 − (−5) = −2, linking each counter action to its corresponding equation.
Evaluation for 5.5b
The E2 Guía instruccional del recorrido describes how TEKS mathematical process standards connect across the integers pathway through a session-by-session alignment that identifies the content focus, primary TEKS, mathematical process standards, ELPS focus, and instructional purpose. The progression moves from classifying signed contexts and locating integers to using counters, operating with integers, reasoning about sign patterns, and extending these ideas to negative rational numbers. This sequence explains how mathematical reasoning, representation, communication, and justification develop across the connected stages of the journey.
The “Alcance y secuencia” document lists sessions in instructional order and identifies the TEKS mathematical process standards associated with each lesson. Across the broader learning pathway, recurring standards engage students in analyzing information, selecting tools, communicating with representations, organizing mathematical ideas, connecting relationships, and justifying arguments. The ordered entries show how these processes continue across sessions and connect mathematical thinking throughout the general grade 6 Spanish pathway.
Evaluation for 5.5c
In journey F1, “Algebraic Language,” station 2, “Visual Patterns,” the lesson overview identifies TEKS mathematical process standard 1.F alongside the content standards. The guidance connects the standard to students’ analysis of geometric sequences as they extend patterns, organize values, predict later terms, and formulate rules such as 3n + 1 and 2n − 1. This lesson-level overview clarifies how relational analysis supports the algebraic work in the grade 6 Spanish materials.
In journey E2, “Integers,” station 5, “Expressions with Multiple Operations I,” the lesson overview highlights mathematical process standard 1.G and explains how students apply precise mathematical language while comparing expressions such as 14 + 7 × 2 and (14 + 7) × 2. The guidance connects justification to the role of parentheses and the order of operations, showing educators how the process standard supports students’ explanations of why the expressions produce different results.
5.1 Development of Conceptual Understanding
5.1a
Questions and tasks provide opportunities for students to interpret, analyze, and evaluate mathematical concepts and complex, real-world situations.
Questions and tasks provide opportunities for students to interpret, analyze, and evaluate mathematical concepts and complex, real-world situations.
3 out of 3 points
Evaluation for 5.1a
Evaluation for 5.1a
Questions and tasks provide opportunities for students to interpret, analyze, and evaluate mathematical concepts and complex, real-world situations.
3 out of 3 points
In the grade 6 Journey Instructional Guide for journey D3, station 12, “Calcular porcentajes I,” students interpret percentage relationships using benchmark values such as 50 percent, 25 percent, and 10 percent. Students analyze how tables, verbal descriptions, and numerical expressions represent the same part-whole relationship. In the extension, students evaluate whether A% of B = B% of A across examples, requiring them to justify the representation’s structure, rather than only calculate a percentage.
5.1b
Questions and tasks provide opportunities for students to create concrete models and representations of mathematical situations.
Questions and tasks provide opportunities for students to create concrete models and representations of mathematical situations.
2 out of 2 points
Evaluation for 5.1b
Evaluation for 5.1b
Questions and tasks provide opportunities for students to create concrete models and representations of mathematical situations.
2 out of 2 points
In the grade 6 Journey Instructional Guide for journey E2, station 6, “Sumar y restar enteros con fichas,” students model integer addition and subtraction with positive and negative counters before representing each operation with drawings in their notebooks. The lesson connects the concrete counter models to pictorial representations by having students sketch the quantities and zero pairs used to solve each problem. Educator guidance emphasizes recording the models on paper to support the transition from manipulatives to visual representations.
5.1c
Questions and tasks provide opportunities for students to apply conceptual understanding to new problem situations and contexts.
Questions and tasks provide opportunities for students to apply conceptual understanding to new problem situations and contexts.
1 out of 1 points
Evaluation for 5.1c
Evaluation for 5.1c
Questions and tasks provide opportunities for students to apply conceptual understanding to new problem situations and contexts.
1 out of 1 points
In the grade 6 Journey Instructional Guide for journey E2, station 16, “Números racionales negativos,” students extend their understanding of integer ordering by classifying rational numbers represented as fractions, decimals, and mixed numbers. Students apply the concepts of valor absoluto and número opuesto to unfamiliar rational values before placing them accurately on a number line using benchmark integers as reference points.
5.2 Development of Fluency
5.2a
Materials provide tasks that are designed to build student automaticity and fluency necessary to complete grade-level mathematical tasks.
Materials provide tasks that are designed to build student automaticity and fluency necessary to complete grade-level mathematical tasks.
2 out of 2 points
Evaluation for 5.2a
Evaluation for 5.2a
Materials provide tasks that are designed to build student automaticity and fluency necessary to complete grade-level mathematical tasks.
2 out of 2 points
In the grade 6 Journey Instructional Guide for journey E1, station 8, “Práctica productiva: orden de operaciones I,” students solve multiple numerical expressions that require consistently applying the order of operations. Repeated practice with increasingly varied expressions supports procedural fluency by having students determine the correct sequence of operations accurately and efficiently throughout the lesson.
5.2b
Materials provide opportunities for students to practice the application of efficient, flexible, and accurate mathematical procedures throughout learning pathways.
Materials provide opportunities for students to practice the application of efficient, flexible, and accurate mathematical procedures throughout learning pathways.
2 out of 3 points
Evaluation for 5.2b
Evaluation for 5.2b
Materials provide opportunities for students to practice the application of efficient, flexible, and accurate mathematical procedures throughout learning pathways.
2 out of 3 points
In the grade 6 Journey Instructional Guide for journey D5, station 18, “Dividimos fracciones II,” students complete multiplicative frames and choose among related division equations to solve each situation. Students compare approaches involving scaling, common denominators, and multiplying by the reciprocal when solving fraction-division problems. This lesson provides opportunities to apply different strategies, but does not consistently require students to reflect on or compare the efficiency of these strategies across the broader learning pathway.
5.2c
Materials provide opportunities for students to evaluate mathematical representations, models, strategies, and solutions for efficiency, flexibility, and accuracy throughout learning pathways.
Materials provide opportunities for students to evaluate mathematical representations, models, strategies, and solutions for efficiency, flexibility, and accuracy throughout learning pathways.
3 out of 3 points
Evaluation for 5.2c
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.
3 out of 3 points
In the grade 6 Journey Instructional Guide for journey F1, station 3, “Expresiones algebraicas equivalentes,” students determine whether different algebraic expressions represent the same visual growing pattern by comparing symbolic and visual representations. Students generate additional equivalent expressions using the commutative and associative properties, and evaluate whether simplified forms more efficiently communicate the pattern while maintaining accuracy.
5.2d
Materials contain guidance to support students in selecting the most efficient approaches when solving mathematics problems.
Materials contain guidance to support students in selecting the most efficient approaches when solving mathematics problems.
1 out of 1 points
Evaluation for 5.2d
Evaluation for 5.2d
Materials contain guidance to support students in selecting the most efficient approaches when solving mathematics problems.
1 out of 1 points
In the grade 6 Journey Instructional Guide for journey E2, station 8, “Suma y resta de números enteros usando la recta numérica,” the Teacher Guide helps educators assist students in using direction, distance, and zero as reference points when representing integer operations. This instruction helps students move beyond counting individual jumps toward recognizing sign relationships and number-line structure, supporting increasingly efficient approaches for solving integer addition and subtraction problems.
5.3 Balance of Conceptual Understanding and Procedural Fluency
5.3a
Materials explicitly state how the conceptual and procedural emphasis of the TEKS are addressed.
Materials explicitly state how the conceptual and procedural emphasis of the TEKS are addressed.
0 out of 2 points
Evaluation for 5.3a
Evaluation for 5.3a
Materials explicitly state how the conceptual and procedural emphasis of the TEKS are addressed.
0 out of 2 points
The TEKS Correlation Guide identifies instructional topics aligned with TEKS 6.7A, including lessons involving equivalent numerical expressions, the order of operations, exponents, and prime factorization. Although the guide identifies where the standard is addressed, it does not explicitly state the conceptual or procedural emphases, nor does it clarify how the two emphases are connected, as required by the indicator.
5.3b
Questions and tasks provide opportunities for students to use concrete models, pictorial representations, and abstract models as required by the TEKS.
Questions and tasks provide opportunities for students to use concrete models, pictorial representations, and abstract models as required by the TEKS.
3 out of 3 points
Evaluation for 5.3b
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.
3 out of 3 points
In the grade 6 Journey Instructional Guide for journey F1, station 4, “Representar expresiones algebraicas,” students use bags, snap cubes, frames, boxes, and counters to construct concrete models of algebraic expressions. Students then sketch the models before writing equivalent symbolic expressions such as 2(2x + 3) and 4x + 6. The lesson connects concrete, pictorial, and abstract representations while supporting the expectations of TEKS 6.7C and 6.7D.
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.
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.
6 out of 6 points
Evaluation for 5.3c
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.
6 out of 6 points
In the grade 6 Journey Instructional Guide for journey F1, station 3, “Expresiones algebraicas equivalentes,” students analyze pictorial growing patterns before recording algebraic expressions representing each figure. Students construct snap-cube models, generate equivalent symbolic expressions, and explain why expressions such as 3(n + 1) and 3n + 3 represent the same pattern by applying the distributive property. These activities help students connect, create, define, and explain representational models while developing abstract algebraic concepts.
5.4 Development of Academic Mathematical Language
5.4a
Materials provide opportunities for students to develop academic mathematical language using visuals, manipulatives, or other language development strategies.
Materials provide opportunities for students to develop academic mathematical language using visuals, manipulatives, or other language development strategies.
1 out of 1 points
Evaluation for 5.4a
Evaluation for 5.4a
Materials provide opportunities for students to develop academic mathematical language using visuals, manipulatives, or other language development strategies.
1 out of 1 points
In journey E2, “Integers,” colored counters, zero pairs, and number lines make signed-number relationships visible, while contexts involving sea level, elevator floors, bank balances, and thermometers connect these ideas to familiar situations. Students draw upon the models and contexts to explain signs, direction, distance from zero, and the relationships between values using precise mathematical language.
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.
Materials include embedded educator guidance to scaffold, support, and extend students’ use of academic mathematical vocabulary in context when communicating with peers and educators.
2 out of 2 points
Evaluation for 5.4b
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.
2 out of 2 points
The E2 Journey Language Bank helps educators plan language development across the journey through pre-teach routines, embedded supports, discourse and writing frames, and redirects for misconceptions. The guidance supports students as they classify signed quantities, explain distance and direction, describe zero pairs, and justify sign patterns during peer and educator interactions. Later lessons extend this language into integer operations, conjectures, and comparisons involving negative rational numbers.
5.4c
Materials include embedded guidance to support student application of appropriate mathematical language and academic vocabulary in discourse.
Materials include embedded guidance to support student application of appropriate mathematical language and academic vocabulary in discourse.
1 out of 1 points
Evaluation for 5.4c
Evaluation for 5.4c
Materials include embedded guidance to support student application of appropriate mathematical language and academic vocabulary in discourse.
1 out of 1 points
In E2.6, educators prompt students to describe actions with counters, explain why zero pairs do not change value, and record the matching integer equation. While discussing the model and their reasoning, students apply terms such as positive, negative, zero pair, value, and equation to connect concrete representations with symbolic expressions in oral and written discourse.
5.4d
Materials include embedded guidance to facilitate mathematical conversations allowing students to hear, refine, and use math language with peers.
Materials include embedded guidance to facilitate mathematical conversations allowing students to hear, refine, and use math language with peers.
2 out of 2 points
Evaluation for 5.4d
Evaluation for 5.4d
Materials include embedded guidance to facilitate mathematical conversations allowing students to hear, refine, and use math language with peers.
2 out of 2 points
In E2.8 and E2.9, students compare counter and number-line models, explain why the representations match, and discuss patterns in integer addition and subtraction. Educator-guided comparisons create repeated peer exchanges in which students listen to model-based explanations, revise their reasoning, and apply language related to positive and negative values, zero pairs, integer operations, and number-line movement.
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.
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.
2 out of 2 points
Evaluation for 5.4e
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.
2 out of 2 points
In F1.8, “From Natural Language to Algebra,” educators can anticipate different translations of natural-language statements into algebraic expressions, including confusion between “double the successor of a number” and “the successor of double a number.” The lesson supports redirection by having students reread each phrase, identify the operation words, and compare the verbal structure with the corresponding algebraic expression, thus helping them distinguish the order and grouping of operations.
5.5 Process Standards Connections
5.5a
TEKS process standards are integrated appropriately into the materials.
TEKS process standards are integrated appropriately into the materials.
1 out of 1 points
Evaluation for 5.5a
Evaluation for 5.5a
TEKS process standards are integrated appropriately into the materials.
1 out of 1 points
In journey E2, “Integers,” station 6, “Adding and Subtracting Integers with Counters,” students model −7 + 4 with counters, cancel zero pairs, and record −7 + 4 = −3. The activity integrates TEKS process standard 1.D as students communicate integer operations through concrete and symbolic representations. They apply the same representational connection to subtraction, including −7 − (−5) = −2, linking each counter action to its corresponding equation.
5.5b
Materials include a description of how process standards are incorporated and connected throughout the learning pathways.
Materials include a description of how process standards are incorporated and connected throughout the learning pathways.
2 out of 2 points
Evaluation for 5.5b
Evaluation for 5.5b
Materials include a description of how process standards are incorporated and connected throughout the learning pathways.
2 out of 2 points
The “Alcance y secuencia” document lists sessions in instructional order and identifies the TEKS mathematical process standards associated with each lesson. Across the broader learning pathway, recurring standards engage students in analyzing information, selecting tools, communicating with representations, organizing mathematical ideas, connecting relationships, and justifying arguments. The ordered entries show how these processes continue across sessions and connect mathematical thinking throughout the general grade 6 Spanish pathway.
5.5c
Materials include an overview of the TEKS process standards incorporated into each lesson.
Materials include an overview of the TEKS process standards incorporated into each lesson.
1 out of 1 points
Evaluation for 5.5c
Evaluation for 5.5c
Materials include an overview of the TEKS process standards incorporated into each lesson.
1 out of 1 points
In journey E2, “Integers,” station 5, “Expressions with Multiple Operations I,” the lesson overview highlights mathematical process standard 1.G and explains how students apply precise mathematical language while comparing expressions such as 14 + 7 × 2 and (14 + 7) × 2. The guidance connects justification to the role of parentheses and the order of operations, showing educators how the process standard supports students’ explanations of why the expressions produce different results.
Rubric Section 6
Productive Struggle
Materials support students in applying disciplinary practices to productive problem-solving, including explaining and revising their thinking.
Total
100% (21 out of 21 points)
Evaluation for 6.1a
The Math Journeys grade 6 Spanish program provides students with opportunities to think mathematically, persevere through problem-solving, and make sense of math in journey F1, “Algebraic Language,” station 2, “Visual Patterns.” Activity 1 asks students to determine how many segments the next fence has without providing a formula. The Teacher Guide extends the investigation by asking students to determine the number of segments in a fence with 100 sections and later explain how to calculate the total number of segments for any step n. These tasks connect visual patterns to equivalent algebraic expressions through conceptual reasoning.
The Math Journeys grade 6 Spanish program helps students develop their mathematical reasoning in journey E2, “Integers,” station 9, “Integer Addition and Subtraction Practice (II).” The warm-up challenges students to place positive and negative signs into an expression to generate every possible outcome before investigating long-term numerical patterns. Students analyze why the sequence alternates between positive and negative values and use those observations to explain patterns in integer operations instead of relying on memorized procedures.
Evaluation for 6.1b
The Math Journeys grade 6 Spanish program helps students understand, explain, and justify multiple solution methods in journey D5, “Pensamiento multiplicativo con fracciones,” station 18, “Dividir fracciones II.” Students solve fraction-division tasks using different approaches, compare their strategies during class discussions, and explain why dividing by a fraction produces the same outcome as multiplying by its reciprocal. The lesson concludes by asking students to justify why different representations and procedures lead to equivalent solutions.
The Math Journeys grade 6 Spanish program provides another opportunity in journey E2, “Integer Addition and Subtraction Practice (II).” During the warm-up, students discover multiple outcomes from the same set of numbers by organizing signs in different ways and using physical cards, counter models, or tree diagrams. Students compare these approaches, explain their reasoning, and justify why different organizational methods and conjectures produce mathematically valid results.
Evaluation for 6.1c
The Math Journeys grade 6 Spanish program requires students to make sense of math in journey F1, “Lenguaje Algebraico,” station 2, “Patrones Visuales.” Partners build geometric sequences with snap cubes, complete step-count tables, and record algebraic rules for the growing patterns. During the “Share and Discuss” routine, students explain why different expressions represent the same pattern, compare peer reasoning, and refine their mathematical thinking through whole-class discussion.
The Math Journeys grade 6 Spanish program provides another opportunity in journey E2, “Integers,” station 6, “Adding and Subtracting Integers with Counters.” Students work with partners to model integer operations using counters, draw the corresponding representations, and record symbolic equations. Throughout the lesson, they explain the meaning of each counter action, discuss solution strategies with their peers and the educator, and connect concrete models to symbolic representations through written and verbal reasoning.
Evaluation for 6.2a
The Math Journeys grade 6 Spanish program helps educators guide students to share and reflect on their problem-solving approaches in journey F1, “Algebraic Language,” station 3, “Equivalent Algebraic Expressions.” During the “Share and Discuss” routine, the educator prompts students to explain how different visual groupings generate equivalent expressions and asks whether the class-generated expressions represent the same quantity. Students justify their reasoning with the distributive and associative properties and extend their thinking by generating additional equivalent expressions while reflecting on alternative solution paths.
The Math Journeys grade 6 Spanish program also supports mathematical reflection in journey E2, “Representing Integers with Counters (I).” Educators use structured discussion routines, “Teacher Moves,” and MLR 2, “Collect and Display,” to guide students as they explain zero-pair cancellation, defend why irreducible counter models represent an integer’s absolute value, and compare equivalent counter arrangements. Real-world contexts, manipulatives, symbolic representations, and extension tasks provide multiple points of entry while encouraging students to reflect on different approaches to representing integers.
Evaluation for 6.2b
The Math Journeys grade 6 Spanish program contains prompts and guidance that support explanatory feedback based on student responses in journey E2, “Integers,” station 3, “Ordering & Jumping on the Number Line.” “Teacher Moves,” the “Share and Discuss” routine, and observation prompts guide educators as students explain number-line placements and justify relationships among integers. The curriculum also supports explanatory feedback in journey F1, “Algebraic Language,” station 3, “Equivalent Algebraic Expressions.” Educators use discussion prompts and observation guidance to respond to students’ explanations about equivalent expressions and visual patterns.
The Math Journeys grade 6 Spanish program provides prompts and guidance for explanatory feedback within the broader algebra learning pathway. In the cluster F Connections and Misconceptions Teacher Companion, block 2 identifies anticipated misconceptions for individual sessions and provides a specific prompt and educator response for each. For example, in F2.6, the curriculum anticipates that students may interpret an equation such as 2n = 2n as having no solution because they view the equal sign as a direction to calculate. In F2.15, the curriculum anticipates that students may incorrectly multiply only the first term inside the parentheses. For each misconception, the companion provides a ready-to-use question and corresponding educator guidance to help educators address the error and provide explanatory feedback.
6.1 Student Self-Efficacy
6.1a
Materials provide opportunities for students to think mathematically, persevere through solving problems, and to make sense of mathematics.
Materials provide opportunities for students to think mathematically, persevere through solving problems, and to make sense of mathematics.
3 out of 3 points
Evaluation for 6.1a
Evaluation for 6.1a
Materials provide opportunities for students to think mathematically, persevere through solving problems, and to make sense of mathematics.
3 out of 3 points
The Math Journeys grade 6 Spanish program helps students develop their mathematical reasoning in journey E2, “Integers,” station 9, “Integer Addition and Subtraction Practice (II).” The warm-up challenges students to place positive and negative signs into an expression to generate every possible outcome before investigating long-term numerical patterns. Students analyze why the sequence alternates between positive and negative values and use those observations to explain patterns in integer operations instead of relying on memorized procedures.
6.1b
Materials support students in understanding, explaining, and justifying that there can be multiple ways to solve problems and complete tasks.
Materials support students in understanding, explaining, and justifying that there can be multiple ways to solve problems and complete tasks.
3 out of 3 points
Evaluation for 6.1b
Evaluation for 6.1b
Materials support students in understanding, explaining, and justifying that there can be multiple ways to solve problems and complete tasks.
3 out of 3 points
The Math Journeys grade 6 Spanish program provides another opportunity in journey E2, “Integer Addition and Subtraction Practice (II).” During the warm-up, students discover multiple outcomes from the same set of numbers by organizing signs in different ways and using physical cards, counter models, or tree diagrams. Students compare these approaches, explain their reasoning, and justify why different organizational methods and conjectures produce mathematically valid results.
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.
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.
3 out of 3 points
Evaluation for 6.1c
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.
3 out of 3 points
The Math Journeys grade 6 Spanish program provides another opportunity in journey E2, “Integers,” station 6, “Adding and Subtracting Integers with Counters.” Students work with partners to model integer operations using counters, draw the corresponding representations, and record symbolic equations. Throughout the lesson, they explain the meaning of each counter action, discuss solution strategies with their peers and the educator, and connect concrete models to symbolic representations through written and verbal reasoning.
6.2 Facilitating Productive Struggle
6.2a
Materials support educators in guiding students to share and reflect on their problem-solving approaches, including explanations, arguments, justifications, and multiple points of entry.
Materials support educators in guiding students to share and reflect on their problem-solving approaches, including explanations, arguments, justifications, and multiple points of entry.
8 out of 8 points
Evaluation for 6.2a
Evaluation for 6.2a
Materials support educators in guiding students to share and reflect on their problem-solving approaches, including explanations, arguments, justifications, and multiple points of entry.
8 out of 8 points
The Math Journeys grade 6 Spanish program also supports mathematical reflection in journey E2, “Representing Integers with Counters (I).” Educators use structured discussion routines, “Teacher Moves,” and MLR 2, “Collect and Display,” to guide students as they explain zero-pair cancellation, defend why irreducible counter models represent an integer’s absolute value, and compare equivalent counter arrangements. Real-world contexts, manipulatives, symbolic representations, and extension tasks provide multiple points of entry while encouraging students to reflect on different approaches to representing integers.
6.2b
Materials include prompts and guidance to support educators in providing explanatory feedback based on student responses and anticipated misconceptions.
Materials include prompts and guidance to support educators in providing explanatory feedback based on student responses and anticipated misconceptions.
4 out of 4 points
Evaluation for 6.2b
Evaluation for 6.2b
Materials include prompts and guidance to support educators in providing explanatory feedback based on student responses and anticipated misconceptions.
4 out of 4 points
The Math Journeys grade 6 Spanish program provides prompts and guidance for explanatory feedback within the broader algebra learning pathway. In the cluster F Connections and Misconceptions Teacher Companion, block 2 identifies anticipated misconceptions for individual sessions and provides a specific prompt and educator response for each. For example, in F2.6, the curriculum anticipates that students may interpret an equation such as 2n = 2n as having no solution because they view the equal sign as a direction to calculate. In F2.15, the curriculum anticipates that students may incorrectly multiply only the first term inside the parentheses. For each misconception, the companion provides a ready-to-use question and corresponding educator guidance to help educators address the error and provide explanatory feedback.