Program Information
- ISBN
- 9791370378028
- Technical Specifications: Checklist
- Tech Specs: Checklist (pdf 1.28 MB)
- Technical Specifications: Professional Development
- Tech Specs: Professional Development (pdf 174.72 KB)
Math Journeys Texas, Grade 6
Supplemental Math (English) Grade 6
IMRA 2026
Publisher: Innovamat Education, Inc.
Copyright: 2026
Series includes:
Rubric: Supplemental Mathematics 6–12 (English) | 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
96% (27 out of 28 points)
Evaluation for 1.1a
The TEKS Correlation Guide identifies the TTEKS addressed in each lesson, including both content and process standards. The scope and sequence aligns lessons to the TEKS and ELPS, and organizes instruction into “Journeys.” Each Journey Instructional Guide explains the purpose of the journey and its place within the learning progression, describing how learning builds on prior knowledge and prepares students for upcoming concepts. Within each journey, the materials illustrate a progression from foundational understanding to increasingly sophisticated applications, providing a rationale for both vertical and horizontal alignment across grade levels.
In the Program Guide, the “Program Structure” section describes the intervention pathway as a series of grade-agnostic journeys organized around learning progressions rather than isolated grade-level skills. The materials explain how concepts connect across and within grade levels through structured learning pathways. The scope and sequence and journey organization demonstrate how students develop understanding over time, supporting both vertical and horizontal alignment.
Evaluation for 1.1b
Implementation guidance in the Program Guide centers on a three-phase instructional model of build, consolidate, and practice. Lessons begin with educator-led instruction and guided learning before progressing to independent practice through logbooks and optional activities in Atlas Math. The “Lesson Internalization and Planning” section describes multiple entry points, intervention options, and alternative representations to support implementation across instructional contexts. Guidance for learning variability, just-in-time supports, and differentiated instruction further assists educators in adapting lessons to address a range of student needs and instructional settings.
The materials in Math Journeys include a Program Guide that explains how educators use the Math Journeys intervention structure to diagnose unfinished learning, select appropriate journeys based on placement data, follow targeted learning pathways, and monitor student progress through reports and end-of-journey assessments. The materials provide recommendations for adapting instruction based on student needs and support implementation as a supplemental intervention pathway through differentiated instructional supports and progress-monitoring tools.
Evaluation for 1.1c
Diagnostic assessment results connect directly to instructional entry points through recommendations provided in the TEKS Correlation Guide. The guide identifies recommended skill entry points and aligns journeys and lessons to the TEKS content and process standards. By connecting lessons and activities to specific standards within each journey, the guide supports instructional planning and implementation. Additionally, the materials include a diagnostic assessment and a placement report that outline recommended skill entry points based on diagnostic results. After students complete the digital diagnostic placement assessment, the program generates an educator report that recommends skill entry points and journeys to assign, supporting targeted instruction and differentiated learning opportunities based on individual student needs.
The placement test measures students’ current mathematical understanding and organizes students into instructional groupings based on performance data. The diagnostic assessment and placement report provide individualized analyses of mathematical strands and identify learning gaps to support targeted intervention and differentiated instruction. The Program Guide explains how diagnostic and placement data are used to match students to the most appropriate journey within the Math Journeys learning pathway.
Evaluation for 1.1d
The materials in the Math Journeys Program Guide, “Lesson Internalization and Planning” section, include protocols and guidance for both unit and lesson internalization. The “Preparing for a Journey” section supports unit internalization by guiding educators to examine how each journey builds on prior learning, review lesson objectives and success criteria, identify scaffolds and enrichment opportunities, gather materials, and analyze learning progressions before instruction begins. The materials also provide lesson internalization protocols through the “Preparing for a Building Session,” “Preparing for a Consolidating Session,” and “Preparing for an Additional Practice Session” sections. These sections guide educators in clarifying instructional goals, anticipating student thinking and misconceptions, preparing materials, identifying formative assessment opportunities, analyzing student responses, and using progress-monitoring data to inform future instruction.
The materials in Math Journeys provide protocols for unit internalization through the Cluster Overview Guide available in the digital manager. The guide provides educators with an overview of the learning progression, the unit learning trajectory, core mathematical objectives, vocabulary, and the ELPS language goals to support internalization of the concepts covered in the lessons. Additionally, the materials include lesson-level guidance on internalization for each instructional session type. The Program Guide directs educators to prepare for building, consolidating, and additional practice sessions by clarifying objectives, preparing materials, anticipating student thinking and misconceptions, identifying formative assessment opportunities, and using student evidence and Atlas Math performance data to guide instructional next steps.
Evaluation for 1.1e
The materials in Math Journeys do not include resources to support instructional leaders in implementing the program. In the Program Guide, the “Hands on Partnership” section provides examples of how a math success manager can partner with and provide guidance to instructional leaders. The materials themselves, however, do not provide additional guidance for instructional leaders.
Resources available through the Program Guide may be accessed by instructional leaders to support implementation. The guide identifies the Classroom Manager License as a platform that provides access to lesson plans, instructional videos, training materials, virtual manipulatives, assessment tools, and reporting features. The materials also include student progress reports that provide recommendations for differentiated instruction and allow educators and leaders to review student performance data. However, the materials do not provide guidance for instructional leaders on how to support educator implementation. The materials do not include leader-facing implementation protocols, observation tools, coaching resources, monitoring rubrics, professional learning community facilitation guidance, or professional development specifically designed for instructional leaders.
Evaluation for 1.2a
The materials include detailed lesson plans with learning objectives, educator and student materials, lesson components with suggested timeframes, and assessment resources aligned with the TEKS and ELPS. Each journey includes lesson-specific instructional guides with learning objectives, the TEKS and ELPS alignment, materials, instructional components, student resources, and suggested timeframes. The E1 Lesson-Level ELPS Companion provides lesson-level language objectives, ELPS codes, language demands, expected oral and written output, and corresponding Atlas Math adaptive practice pathways. Additionally, the assessment support documents identify both the TEKS and ELPS aligned to each end-of-journey test question, providing explicit TEKS and ELPS alignment within the assessment resources.
The materials include lesson-level guidance that explicitly connects learning objectives and instructional components to the TEKS and ELPS. In the F1 Lesson-Level ELPS Companion, each lesson identifies the primary concept, the TEKS content and process standards, the ELPS focus, language objective, language demand, expected oral and written student output, and suggested use within the corresponding Teacher Guide lesson. For example, F1.15, “Ratios, Rates, and Proportionality,” identifies TEKS 7.4.B, 7.4.C, and 7.4.E, and the ELPS for speaking, reading, and writing. The lesson provides a language objective requiring students to describe ratios or rates and use proportionality tables to solve for unknown quantities, along with expected oral and written responses. The companion also connects the lesson to Atlas Math adaptive practice and identifies ELPS 1.C and 3.C for the audio and written prompts provided within each activity. These resources provide explicit TEKS and ELPS alignment within the lesson-level instructional guidance and associated student practice.
Evaluation for 1.2b
The materials include detailed adaptive lesson overviews with learning objectives, lesson components with suggested timeframes, and assessment resources aligned with the TEKS and ELPS. The Program Guide provides the instructional sequence, learning goals, materials, and suggested timeframes, while Atlas Math provides adaptive practice pathways that respond to student performance. The Lesson-Level ELPS Companion connects each lesson’s adaptive Atlas Math pathways to language objectives, specific ELPS codes, language demands, and expected oral and written output. Assessment support documents further identify the TEKS and ELPS associated with individual assessment questions, providing explicit standards alignment for the assessment resources.
The materials include a detailed lesson overview with learning objectives and adaptive practice aligned to the TEKS and ELPS. In the F1 Lesson-Level ELPS Companion, F1.16, “Practicing Direct Proportion,” identifies TEKS 7.4.A and 7.7.A, along with related grade 6 and grade 8 TEKS, and identifies the ELPS for speaking, reading, and writing. The language objective requires students to determine whether a situation is directly proportional and explain connections among a table, graph, and expression. The lesson also specifies the language demand and expected oral and written student outputs. The Atlas Math adaptive practice is organized into Core, Explore, and Reinforcement pathways so students can continue at their individual level. The companion identifies ELPS 1.C and 3.C for the spoken and written prompts presented in every adaptive activity.
Evaluation for 1.2c
Within each journey, the materials include support for families in Spanish through a family letter offering suggestions for caregivers to support learning at home. The letter includes questions to ask, vocabulary to use, and specific ideas for families to support learning. The language of the letter can be changed to Spanish or English using the language toggle in the top right corner.
Cluster- and journey-level family letters provide families with mathematical background information, learning goals, vocabulary, questions to ask students, and suggestions for supporting learning at home. For example, the “F Expressions and Equations” family letter includes a “How Can We Help from Home?” section with specific activities and guidance connected to the concepts taught within the journey. The family letters also support communication with caregivers through language toggle options 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.
5 out of 5 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.
5 out of 5 points
In the Program Guide, the “Program Structure” section describes the intervention pathway as a series of grade-agnostic journeys organized around learning progressions rather than isolated grade-level skills. The materials explain how concepts connect across and within grade levels through structured learning pathways. The scope and sequence and journey organization demonstrate how students develop understanding over time, supporting both vertical and horizontal alignment.
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 materials in Math Journeys include a Program Guide that explains how educators use the Math Journeys intervention structure to diagnose unfinished learning, select appropriate journeys based on placement data, follow targeted learning pathways, and monitor student progress through reports and end-of-journey assessments. The materials provide recommendations for adapting instruction based on student needs and support implementation as a supplemental intervention pathway through differentiated instructional supports and progress-monitoring tools.
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 placement test measures students’ current mathematical understanding and organizes students into instructional groupings based on performance data. The diagnostic assessment and placement report provide individualized analyses of mathematical strands and identify learning gaps to support targeted intervention and differentiated instruction. The Program Guide explains how diagnostic and placement data are used to match students to the most appropriate journey within the Math Journeys learning pathway.
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 materials in Math Journeys provide protocols for unit internalization through the Cluster Overview Guide available in the digital manager. The guide provides educators with an overview of the learning progression, the unit learning trajectory, core mathematical objectives, vocabulary, and the ELPS language goals to support internalization of the concepts covered in the lessons. Additionally, the materials include lesson-level guidance on internalization for each instructional session type. The Program Guide directs educators to prepare for building, consolidating, and additional practice sessions by clarifying objectives, preparing materials, anticipating student thinking and misconceptions, identifying formative assessment opportunities, and using student evidence and Atlas Math performance data to guide 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.
1 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.
1 out of 2 points
Resources available through the Program Guide may be accessed by instructional leaders to support implementation. The guide identifies the Classroom Manager License as a platform that provides access to lesson plans, instructional videos, training materials, virtual manipulatives, assessment tools, and reporting features. The materials also include student progress reports that provide recommendations for differentiated instruction and allow educators and leaders to review student performance data. However, the materials do not provide guidance for instructional leaders on how to support educator implementation. The materials do not include leader-facing implementation protocols, observation tools, coaching resources, monitoring rubrics, professional learning community facilitation guidance, or professional development specifically designed for instructional leaders.
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.
7 out of 7 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.
7 out of 7 points
The materials include lesson-level guidance that explicitly connects learning objectives and instructional components to the TEKS and ELPS. In the F1 Lesson-Level ELPS Companion, each lesson identifies the primary concept, the TEKS content and process standards, the ELPS focus, language objective, language demand, expected oral and written student output, and suggested use within the corresponding Teacher Guide lesson. For example, F1.15, “Ratios, Rates, and Proportionality,” identifies TEKS 7.4.B, 7.4.C, and 7.4.E, and the ELPS for speaking, reading, and writing. The lesson provides a language objective requiring students to describe ratios or rates and use proportionality tables to solve for unknown quantities, along with expected oral and written responses. The companion also connects the lesson to Atlas Math adaptive practice and identifies ELPS 1.C and 3.C for the audio and written prompts provided within each activity. These resources provide explicit TEKS and ELPS alignment within the lesson-level instructional guidance and associated student practice.
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.
5 out of 5 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.
5 out of 5 points
The materials include a detailed lesson overview with learning objectives and adaptive practice aligned to the TEKS and ELPS. In the F1 Lesson-Level ELPS Companion, F1.16, “Practicing Direct Proportion,” identifies TEKS 7.4.A and 7.7.A, along with related grade 6 and grade 8 TEKS, and identifies the ELPS for speaking, reading, and writing. The language objective requires students to determine whether a situation is directly proportional and explain connections among a table, graph, and expression. The lesson also specifies the language demand and expected oral and written student outputs. The Atlas Math adaptive practice is organized into Core, Explore, and Reinforcement pathways so students can continue at their individual level. The companion identifies ELPS 1.C and 3.C for the spoken and written prompts presented in every adaptive activity.
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
Cluster- and journey-level family letters provide families with mathematical background information, learning goals, vocabulary, questions to ask students, and suggestions for supporting learning at home. For example, the “F Expressions and Equations” family letter includes a “How Can We Help from Home?” section with specific activities and guidance connected to the concepts taught within the journey. The family letters also support communication with caregivers through language toggle options 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
In the Program Guide, the “Assessment and Progress Monitoring” section includes the definition and intended purpose of the assessments. For example, the materials explicitly define the diagnostic assessment as a tool used at the start of instruction to identify prior knowledge and to determine in which journey to place students. 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 assessments and identifies the placement test as a diagnostic assessment administered at the beginning of instruction to determine students’ current level of mathematical understanding and establish an appropriate entry point within the Math Journeys pathway. The guide explains that assessment results align with the Math Journeys progression and are used to place students in the most appropriate journey based on their learning needs. Additionally, examples within the materials demonstrate how diagnostic results can be used to group students for targeted instruction and inform instructional planning.
Evaluation for 2.1b
The materials in Math Journeys include guidance to ensure consistent and accurate administration of instructional assessments. The Placement Test Implementation Guide provides clear, detailed guidance for educators for administering the diagnostic assessment consistently and accurately. This guidance includes the estimated test length, the instructor’s role during administration, and the suggested materials. For example, the “Administration Guidance” section clarifies that “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 and accurate manner across classrooms.
The Program Guide embeds guidance for the consistent and accurate administration and use of instructional assessments within the placement test process. The guide explains 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 Math Journeys progression. The materials further describe how results are used to assign students to an appropriate starting journey based on their demonstrated understanding. This guidance promotes consistent administration procedures and supports the consistent interpretation and use of assessment results across classrooms.
Evaluation for 2.1c
Digital and print versions of the end-of-journey assessments and formative assessment logsheets are available within the materials. For example, each end-of-journey assessment includes an End-of-Journey Test: Instructions and Guide that provides a link to download printables, including the assessment, answer key, and instruction guide. In the Program Guide, the “Accommodations in Assessment” section states that the assessment platform provides embedded text-to-speech functionality and content and language supports, including setting the assessment language to English or Spanish and specifying when calculators can be used. Students can access text-to-speech, and educators can toggle the assessment language between English and Spanish. The guide states, “Calculators are not provided within the digital interface; instead, they are provided and managed by educators during test administration.” Although the Program Guide clearly explains the embedded accommodations, the materials do not allow educators to enable or disable text-to-speech, content and language supports, or calculators for individual students.
The materials include some digital assessment accommodations, but do not provide educator-controlled accommodation settings required by the indicator. The Program Guide identifies embedded text-to-speech and content and language supports within the assessment platform. Educators can designate each student’s language of instruction through the Classroom Manager, and that setting applies across content, practice, and assessments. However, text-to-speech is student-activated through a speaker icon rather than enabled or disabled by the educator for individual students. Additionally, calculators are not provided on the digital assessment platform. Instead, the Program Guide states that educators supply and manage them during test administration. Therefore, the materials do not allow educators to enable or disable text-to-speech, content and language supports, or calculators for individual students as required by the rubric.
Evaluation for 2.1d
The placement test report sample demonstrates that the diagnostic assessments include TEKS-aligned tasks and questions, identify student performance across multiple mathematical strands and processes, and connect results to specific instructional pathways within the Math Journeys progression. The report organizes student outcomes by strand and process, demonstrating alignment between the diagnostic tasks and the TEKS-based mathematical content. Additionally, the Placement Test Implementation Guide identifies multiple item types within 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 Depth of Knowledge (DOK) 1, Factual Knowledge; DOK 2, Procedural Knowledge; and DOK 3, Reasoning and Problem Solving. These levels provide students with opportunities to demonstrate 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, including multiple-choice, constructed response, number line, and other interactive response formats. These diagnostic tasks require students to demonstrate 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 materials include 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 to TEKS 7.11.A and 8.8.C, demonstrating that the formative tasks in the session align with the TEKS. Additionally, the materials include interactive formative assessment item types with varying complexity levels. For example, student logsheets and digital activities include multiple-choice questions, graphing tasks, number-entry tasks, text-entry tasks, and number line activities. Furthermore, the grade 6 materials include differentiated formative assessment tasks designed to address multiple levels of student readiness. As 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 includes grade-level tasks, and version Z includes more complex and nonroutine 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 multistep 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 to more complex, nonroutine problem solving. This structure engages students with mathematical concepts through varied task formats and increasing levels of cognitive demand.
Evaluation for 2.2a
The placement test report sample provides educators with detailed scoring information for interpreting student performance data. The instructional assessment report displays each student’s score and identifies the corresponding performance category, including low, medium-low, medium-high, and high achievement levels. In addition to reporting performance outcomes, the sample report provides recommendations for instructional placement based on assessment results. The guidance states, “Use this report alongside what you see in class—student talk, written work, and tasks over time. Scores summarize performance on this instrument and administration; they can miss strengths that timed or online formats do not capture.” This comprehensive approach supports educators in making informed, individualized instructional decisions aligned with student learning needs.
The end-of-journey test answer key provides scoring information and rationales for both correct and incorrect responses. The answer key identifies the correct answer for each assessment item and includes explanations describing why the correct response is valid. The answer key also explains common incorrect responses and associated misconceptions, helping educators understand potential student errors and identify instructional next steps. These item-by-item rationales support educators in interpreting student performance, analyzing misunderstandings, and providing targeted feedback and intervention.
Evaluation for 2.2b
The instructional materials provide guidance for responding to student performance trends through the placement test report. The “Placement in Journeys” section explains how assessment results can be used to support instructional decision-making and student placement. Specifically, the placement test report assists educators in grouping students for targeted instruction and determining appropriate placement within the program. Based on students’ assessment performance, the report generates suggested starting points for each student within the journey progression, allowing educators to differentiate instruction according to demonstrated levels of understanding and academic readiness.
The placement test report provides guidance for using assessment results to address student performance trends. 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. The report also provides recommended instructional groupings and suggested intervention pathways based on assessment results. By connecting performance trends to specific instructional starting points within the Math Journeys progression, the materials support educators in selecting targeted tasks and activities to address identified learning needs and provide differentiated instruction.
Evaluation for 2.2c
The materials include tools for educators to track student progress and growth through the placement test report sample and the end-of-journey test dashboard. The materials provide results per student, class distribution, and question detail reports that allow educators to monitor student performance trends, identify areas needing support, and make instructional decisions based on assessment data. The materials also include suggested instructional focus statements and recommended instructional placements connected to student performance results. However, the materials do not include tools for students to independently track their own progress and growth over time.
The Classroom Manager platform includes tools that help educators track student progress and growth. The platform generates real-time reports for individual students and entire classes using data from formative assessment checkpoints, instructional assessments, and the Atlas Math digital practice application. Educators can review student performance trends 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 materials do not include a student-facing dashboard, progress report, goal-setting tool, or longitudinal tracker that allows students to independently monitor their progress and growth over time.
Evaluation for 2.2d
Educator prompts, observation opportunities, and discussion questions provide formative assessment guidance to support educators in conducting checks for understanding throughout lessons. Embedded instructional supports also encourage students to explain their thinking, justify responses, and participate in mathematical discussions during instruction. For example, in one lesson, educators observe whether students use groups of 10 or continue counting one by one to monitor understanding of place value concepts and counting strategies. The lesson includes prompts that ask students to identify patterns in the order of numbers and determine which numbers appear first when counting forward, encouraging them to explain their reasoning and justify their responses. Additionally, partner discussions, educator observations, and student explanations support educators in conducting ongoing formative assessment throughout the lesson.
The materials provide prompts and guidance to support educators in conducting frequent checks for understanding at key points throughout each lesson or activity. For example, Journey E, “Powers and Integers,” E2, “Integers,” station 1, “Introduction to Negative Numbers,” includes opportunities for educators to monitor student understanding during the “Warm-Up,” “Development Activity,” and “Wrap-Up” sections. In the warm-up, educators prompt students to represent a picture with an equation, allowing educators to assess prior understanding and identify misconceptions. Additionally, the lesson includes “Teacher Moves” guidance and targeted questions that support educators in monitoring student thinking throughout the learning process. Furthermore, the materials provide whole-class and partner tasks that allow educators 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 met the lesson objective and to determine appropriate next instructional steps. Together, these embedded prompts and instructional supports enable educators to conduct ongoing formative assessment and respond to student understanding throughout the lesson.
Evaluation for 2.2e
The materials provide frequent checks for understanding throughout lessons and activities through embedded formative assessment opportunities and immediate feedback during digital practice. The Program Guide describes Atlas Math as an adaptive digital practice 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 student understanding throughout instruction.
However, the Program Guide explains that Atlas Math adapts the sequence of activities based on educator pacing and student performance rather than adapting the checks for understanding within an activity. Students receive immediate feedback and may progress to different activities based on performance, but the materials do not demonstrate that the complexity of questions, item types, or instructional supports adjust in real time in response to individual student responses. As a result, the materials provide frequent checks for understanding but do not fully demonstrate adaptive checks for understanding throughout 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 assessments and identifies the placement test as a diagnostic assessment administered at the beginning of instruction to determine students’ current level of mathematical understanding and establish an appropriate entry point within the Math Journeys pathway. The guide explains that assessment results align with the Math Journeys progression and are used to place students in the most appropriate journey based on their learning needs. Additionally, examples within the materials demonstrate how diagnostic results can be used to group students for targeted instruction and inform instructional planning.
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 Program Guide embeds guidance for the consistent and accurate administration and use of instructional assessments within the placement test process. The guide explains 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 Math Journeys progression. The materials further describe how results are used to assign students to an appropriate starting journey based on their demonstrated understanding. This guidance promotes consistent 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 materials include some digital assessment accommodations, but do not provide educator-controlled accommodation settings required by the indicator. The Program Guide identifies embedded text-to-speech and content and language supports within the assessment platform. Educators can designate each student’s language of instruction through the Classroom Manager, and that setting applies across content, practice, and assessments. However, text-to-speech is student-activated through a speaker icon rather than enabled or disabled by the educator for individual students. Additionally, calculators are not provided on the digital assessment platform. Instead, the Program Guide states that educators supply and manage them during test administration. Therefore, the materials do not allow educators to enable or disable text-to-speech, 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, including multiple-choice, constructed response, number line, and other interactive response formats. These diagnostic tasks require students to demonstrate 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 multistep 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 to more complex, nonroutine problem solving. This structure engages students with mathematical concepts through varied task formats and increasing levels of cognitive demand.
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 test answer key provides scoring information and rationales for both correct and incorrect responses. The answer key identifies the correct answer for each assessment item and includes explanations describing why the correct response is valid. The answer key also explains common incorrect responses and associated misconceptions, helping educators understand potential student errors and identify instructional next steps. These item-by-item rationales support educators in interpreting student performance, analyzing misunderstandings, and providing 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 provides guidance for using assessment results to address student performance trends. 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. The report also provides recommended instructional groupings and suggested intervention pathways based on assessment results. By connecting performance trends to specific instructional starting points within the Math Journeys progression, the materials support educators in selecting targeted tasks and activities to address identified learning needs and provide 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 platform includes tools that help educators track student progress and growth. The platform generates real-time reports for individual students and entire classes using data from formative assessment checkpoints, instructional assessments, and the Atlas Math digital practice application. Educators can review student performance trends 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 materials do not include a student-facing dashboard, progress report, goal-setting tool, or longitudinal tracker that allows 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
The materials provide prompts and guidance to support educators in conducting frequent checks for understanding at key points throughout each lesson or activity. For example, Journey E, “Powers and Integers,” E2, “Integers,” station 1, “Introduction to Negative Numbers,” includes opportunities for educators to monitor student understanding during the “Warm-Up,” “Development Activity,” and “Wrap-Up” sections. In the warm-up, educators prompt students to represent a picture with an equation, allowing educators to assess prior understanding and identify misconceptions. Additionally, the lesson includes “Teacher Moves” guidance and targeted questions that support educators in monitoring student thinking throughout the learning process. Furthermore, the materials provide whole-class and partner tasks that allow educators 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 met the lesson objective and to determine appropriate next instructional steps. Together, these embedded prompts and instructional supports enable educators to conduct ongoing formative assessment and respond to student understanding throughout the lesson.
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
However, the Program Guide explains that Atlas Math adapts the sequence of activities based on educator pacing and student performance rather than adapting the checks for understanding within an activity. Students receive immediate feedback and may progress to different activities based on performance, but the materials do not demonstrate that the complexity of questions, item types, or instructional supports adjust in real time in response to individual student responses. As a result, the materials provide frequent checks for understanding but do not fully demonstrate adaptive checks for understanding throughout 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
81% (35 out of 43 points)
Evaluation for 3.1a
Educator guidance for supporting students who need additional assistance is embedded within lesson plan E2.3, “Ordering and Jumping on the Number Line.” Within the “Warm-Up” section, the expandable support tip provides strategies for helping students order integers and interpret movement on a number line. The guidance is available during instruction and offers educators additional prompts and support at the point when students are engaging with the concept. This embedded scaffold allows educators to address misconceptions and reinforce prerequisite understandings as students work with integer relationships.
Additional support for students developing grade-level understanding of integers is available in lesson plan E2.4, “Representing Integers with Counters (I).” The “Resources” section includes XYZ activities that are used during the “Consolidate” session to reinforce learning. These activities use counters and visual models to represent positive and negative integers, allowing students to connect concrete representations to mathematical concepts. As students engage with the activities, they build understanding through hands-on experiences before progressing to more abstract representations of integer relationships.
Evaluation for 3.1b
The materials provide explicit educator guidance for both preteaching and embedding language supports during instruction. In the E2 Journey Language Bank, the “Unfamiliar References” section provides a “Quick Bridge Before the Lesson” section that directs educators to identify and clarify lesson-specific unfamiliar references before students encounter them in the text. The lesson-by-lesson table identifies the reference and provides a corresponding bridge educators can use to establish the necessary context.
These preteaching supports work alongside embedded vocabulary routines, sentence frames, discourse supports, and writing opportunities that reinforce academic mathematical language as students engage with lesson content, providing support for both academic vocabulary and unfamiliar references before and during instruction.
Evaluation for 3.1c
The materials provide explicit educator guidance for assigning and facilitating extension opportunities for students who demonstrate proficiency in grade-level content. The Enrichment and Extension Guide identifies three observable signals educators can use to determine readiness for extension and provides task-specific guidance for extension logsheets and extension tips, including the purpose of the task, what educators should listen for during student work, and evidence that demonstrates mastery. When students demonstrate proficiency across three consecutive sessions, the guide directs educators to administer the end-of-journey test early and allows students scoring above 75 percent to advance to the next journey. However, these procedures identify and extend students based on mastery of the current grade-level journey. The materials do not provide explicit educator guidance for enrichment or extension activities specifically designed for students who have already demonstrated proficiency in above grade-level content and skills.
The Enrichment and Extension Guide provides explicit educator guidance for implementing extension activities when students demonstrate proficiency in grade-level content, including observable indicators of readiness, guidance for facilitating extension tasks, and evidence educators can use to determine mastery. The guide also provides a pathway for students who consistently demonstrate proficiency to complete an end-of-journey test early and advance to the next journey based on their performance. However, advancing a student to the next journey does not constitute explicit educator guidance for enrichment and extension activities designed for students who have already demonstrated proficiency in above grade-level content and skills. Therefore, the materials meet the criterion for grade-level proficiency but do not meet the criterion for above grade-level proficiency.
Evaluation for 3.1d
Accessibility features are available within the platform to support student access to instructional content. These features include text-to-speech functionality and other support tools that students can access while engaging with digital materials. The Program Guide explains that students activate text-to-speech independently through a speaker icon, making the feature available during instruction and learning activities. Platform verification did not identify educator-controlled settings that allow content and language supports to be enabled or disabled for individual students. As a result, the available accessibility features are student activated rather than accommodations that educators can assign or manage for specific learners.
Calculator use is addressed in the Program Guide as a resource managed outside of the digital platform rather than as an integrated accommodation within the system. The guidance indicates that calculators are provided and managed separately during instruction or assessment activities. The materials do not demonstrate educator-controlled settings that allow calculators to be enabled or disabled for individual students. Similarly, platform verification did not identify educator-controlled options for managing text-to-speech or content and language supports at the individual-student level. As a result, the materials do not demonstrate integrated digital accommodations that educators can assign, enable, or disable for specific learners.
Evaluation for 3.1e
Multiple representations are incorporated into lesson E2.4, “Representing Integers with Counters (I),” as students develop and communicate their understanding of integer concepts. During the lesson students use integer counters to model values, discuss their reasoning with peers, and record their thinking in logsheets and related activities. The lesson sequence moves from concrete manipulatives to representational models, providing students with different ways to demonstrate understanding of the mathematical content. These opportunities allow students to communicate their learning through hands-on models, mathematical discussions, and written representations.
In lesson E2.3, “Ordering and Jumping on the Number Line,” students demonstrate their understanding of integer concepts through discussion, visual representations, and collaborative learning experiences. Throughout the lesson, students participate in partner and group discussions to explain their reasoning, compare strategies, and communicate mathematical ideas. Number line models are used to represent and justify solutions visually, while collaborative activities provide opportunities for students to refine their thinking through interaction with peers. These instructional experiences allow students to express understanding through oral communication, visual representations, and shared problem solving.
Evaluation for 3.2a
Prior knowledge is activated in lesson D3.11, “Knowing Percentages,” through a warm-up activity that asks students to identify a fraction that is not equivalent to the others before beginning work with percentages. This task prompts students to recall and apply their understanding of equivalent fractions as a foundation for new learning. Educator-facing guidance then supports students in generating equivalent fractions with a denominator of 100 and connecting fraction notation to percent notation. Throughout the lesson, relationships among fractions, equivalent fractions, and percentages are highlighted using multiple representations, allowing students to build on existing knowledge as they develop understanding of percentage concepts.
Key mathematical ideas are developed in lesson F1.4, “Representing Algebraic Expressions,” through connections among multiple representations of algebraic thinking. Educator-facing guidance supports students as they represent algebraic expressions and interpret the meaning of terms, coefficients, variables, and operations within those expressions. Throughout the lesson, written descriptions are connected to symbolic expressions, allowing students to examine how mathematical relationships are represented in different forms. These instructional experiences help students identify important features of algebraic expressions and recognize relationships across verbal and symbolic representations.
Evaluation for 3.2b
A variety of instructional approaches are incorporated into lesson E2.6, “Adding and Subtracting Integers with Counters,” to support lesson delivery and student engagement. The “Warm-Up” section provides educator-facing guidance for introducing integer concepts through whole-group discussion and direct instruction, creating a foundation for the lesson. In development activity 1, educators facilitate hands-on exploration using integer counters as students model operations, discuss strategies, and explain their mathematical reasoning. The lesson combines discussion, visual representations, and concrete manipulatives to support student understanding of integer addition and subtraction.
Instruction in lesson E2.7, “Integer Addition and Subtraction Practice (I),” employs multiple instructional approaches to support student learning throughout the lesson. The lesson begins with a whole-group discussion during the warm-up, where students engage with key concepts and share initial thinking. During the development activities, prompts guide educators in facilitating collaborative learning and guided practice as students apply integer operations and discuss solution strategies. The lesson concludes with independent learning opportunities in the wrap-up, allowing students to apply their understanding individually. Educator guidance throughout the lesson supports transitions among whole-group instruction, collaborative work, guided practice, and independent application.
Evaluation for 3.2c
Multiple instructional structures are incorporated into lesson E2.6, “Adding and Subtracting Integers with Counters,” to support students as they develop understanding of integer operations. The lesson begins with educator-led instruction during the warm-up, where key concepts are introduced and discussed. In development activity 1, students participate in guided hands-on practice using integer counters to model addition and subtraction, while collaborative discussions provide opportunities to explain reasoning and compare strategies. The lesson concludes with independent consolidation activities in the wrap-up, allowing students to apply their learning individually. These instructional experiences provide opportunities for guided, collaborative, and independent practice throughout the lesson.
Guidance for implementing instructional supports is outlined in the Program Guide through the Math Journeys framework of “build, consolidate, and additional practice.” The “Build” component focuses on educator-led instruction, mathematical discourse, and the development of new concepts through guided learning experiences. The “Consolidate” component provides opportunities for students to apply learning independently through logsheets and differentiated practice resources that reinforce lesson content. The “Additional Practice” component is delivered through Atlas Math, where students engage in digital practice activities that respond to student performance and provide feedback as they work. Together, these components establish a structure that incorporates educator-guided learning, independent practice, and digital learning opportunities to support students throughout the instructional process.
Evaluation for 3.2d
Additional challenge opportunities are embedded within lesson E2.7, “Integer Addition and Subtraction Practice (I),” through extension activities that encourage students to investigate mathematical ideas, justify reasoning, and engage in discussion. These activities extend learning beyond the core lesson by providing opportunities for students to explore concepts through multiple problem-solving approaches. Educator-facing extension prompts are incorporated into the lesson structure, supporting implementation while allowing students to engage with integer operations at a deeper level.
Opportunities for enrichment are incorporated throughout the Math Journeys instructional framework of build, consolidate, and additional practice. The Program Guide describes how students engage with lesson content through educator-led instruction, independent practice, and digital learning experiences. The “Additional Practice” components are provided through Atlas Math, where activities respond to student performance and present increasingly complex tasks as students demonstrate understanding. This structure provides opportunities for students to continue developing mathematical concepts through individualized learning experiences.
Evaluation for 3.2e
Ongoing opportunities for monitoring student understanding are embedded within lesson E2.4, “Representing Integers with Counters (I).” Prompts encourage educators to ask students to explain patterns, justify strategies, and communicate mathematical reasoning while working with integer models. These questions provide opportunities to gather evidence of student thinking during instruction and support immediate responses to misconceptions or emerging understanding as students engage with the lesson.
Student understanding is monitored throughout lesson E2.2, “Negative Numbers on the Number Line,” using observation opportunities and discussion prompts embedded within the lesson. Guidance directs educators to observe how students represent, compare, and sequence numbers on a number line while engaging in learning activities. These instructional checkpoints provide opportunities to identify misconceptions, assess student reasoning, and respond to student needs during the lesson.
Evaluation for 3.3a
The materials provide differentiated linguistic accommodations designed to support students’ progression toward increasingly academic mathematical language. The bilingual tip organizes educator guidance by the five current ELPS proficiency levels—pre-production, beginning, intermediate, high intermediate, and advanced—and provides a distinct accommodation at each level. The progression of supports gives educators guidance for adjusting linguistic demands according to students’ proficiency while maintaining engagement with grade-level mathematical content. These supports address the full range of language proficiency levels identified in the ELPS and provide educators with guidance for incorporating appropriate linguistic accommodations during instruction.
In session 8, “Ordering Decimals,” the materials provide educator guidance for incorporating linguistic accommodations across all five ELPS proficiency levels as students compare and order decimal numbers. The bilingual tip differentiates supports for pre-production, beginning, intermediate, high intermediate, and advanced students, providing educators with proficiency-appropriate accommodations for engaging students with lesson-specific academic language. The differentiated guidance supports students as they use terms such as greater than, less than, place value, digit, decimal point, compare, and order to communicate mathematical reasoning. By adjusting the linguistic support according to students’ proficiency levels while maintaining engagement with the same grade-level decimal concepts, the materials support students in progressing toward increasingly more academic mathematical language.
Evaluation for 3.3b
Adaptive digital resources described in the Program Guide include personalized practice opportunities and accessibility features that support student engagement with mathematical content. The guidance explains how adaptive activities respond to student performance and provide ongoing practice opportunities. There is no evidence demonstrating embedded linguistic accommodations aligned to all language proficiency levels as defined by the ELPS. The materials do not specify language supports differentiated by proficiency level within the adaptive components.
Supports for emergent bilingual (EB) students are embedded throughout grade 6, Journey E2 lessons through vocabulary development activities, visual models, sentence frames, and discussion opportunities. These resources provide educators with tools for supporting language development while students engage with grade-level mathematics content. The supports rely on educator implementation and facilitation. There do not appear to be student-facing linguistic accommodations embedded within the adaptive materials or organized according to ELPS proficiency levels.
Evaluation for 3.3c
Guidance for implementation in bilingual and ESL instructional settings is provided through the Texas Bilingual/ESL Implementation Guide. The guide describes strategies for maintaining the mathematical integrity of tasks while making content accessible to EB students. Educators are provided with recommendations for previewing essential language, supporting comprehension, and using lesson representations to strengthen language development during mathematics instruction.
Additional implementation support is provided through the E2 Lesson-Level ELPS Companion. These resources identify lesson-specific language objectives, language demands, expected oral and written student outputs, ELPS alignments, and suggested educator supports connected to the mathematics content. The companion serves as a planning resource that helps educators incorporate language supports while providing access to grade-level mathematical learning.
Evaluation for 3.3d
Academic vocabulary development is integrated into lesson E2.6, “Adding and Subtracting Integers with Counters,” through the use of lesson-specific terminology, including addend, sum, minuend, subtrahend, difference, zero pair, positive counter, and negative counter. Spanish cognates, sentence frames, and discussion opportunities are embedded within the lesson to support mathematical communication. These resources provide opportunities for students to use academic vocabulary while participating in oral discourse and explaining mathematical thinking.
Written discourse is supported through the E2 Lesson-Level ELPS Companion, which includes opportunities for students to record and annotate models of integer addition and subtraction using mathematical explanations and academic vocabulary. Lesson resources encourage students to connect English mathematical terminology with Spanish cognates while communicating their reasoning in writing. These activities provide opportunities for students to develop written explanations that incorporate both mathematical concepts and academic language.
Evaluation for 3.3e
This guidance is not applicable because the program is not designed for dual language immersion (DLI) programs.
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
Additional support for students developing grade-level understanding of integers is available in lesson plan E2.4, “Representing Integers with Counters (I).” The “Resources” section includes XYZ activities that are used during the “Consolidate” session to reinforce learning. These activities use counters and visual models to represent positive and negative integers, allowing students to connect concrete representations to mathematical concepts. As students engage with the activities, they build understanding through hands-on experiences before progressing to more abstract representations of integer relationships.
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
These preteaching supports work alongside embedded vocabulary routines, sentence frames, discourse supports, and writing opportunities that reinforce academic mathematical language as students engage with lesson content, providing support for both academic vocabulary and unfamiliar references before and during instruction.
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.
1 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.
1 out of 2 points
The Enrichment and Extension Guide provides explicit educator guidance for implementing extension activities when students demonstrate proficiency in grade-level content, including observable indicators of readiness, guidance for facilitating extension tasks, and evidence educators can use to determine mastery. The guide also provides a pathway for students who consistently demonstrate proficiency to complete an end-of-journey test early and advance to the next journey based on their performance. However, advancing a student to the next journey does not constitute explicit educator guidance for enrichment and extension activities designed for students who have already demonstrated proficiency in above grade-level content and skills. Therefore, the materials meet the criterion for grade-level proficiency but do not meet the criterion for above grade-level proficiency.
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
Calculator use is addressed in the Program Guide as a resource managed outside of the digital platform rather than as an integrated accommodation within the system. The guidance indicates that calculators are provided and managed separately during instruction or assessment activities. The materials do not demonstrate educator-controlled settings that allow calculators to be enabled or disabled for individual students. Similarly, platform verification did not identify educator-controlled options for managing text-to-speech or content and language supports at the individual-student level. As a result, the materials do not demonstrate integrated digital accommodations that educators can assign, enable, or disable for specific learners.
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
In lesson E2.3, “Ordering and Jumping on the Number Line,” students demonstrate their understanding of integer concepts through discussion, visual representations, and collaborative learning experiences. Throughout the lesson, students participate in partner and group discussions to explain their reasoning, compare strategies, and communicate mathematical ideas. Number line models are used to represent and justify solutions visually, while collaborative activities provide opportunities for students to refine their thinking through interaction with peers. These instructional experiences allow students to express understanding through oral communication, visual representations, and shared problem solving.
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
Key mathematical ideas are developed in lesson F1.4, “Representing Algebraic Expressions,” through connections among multiple representations of algebraic thinking. Educator-facing guidance supports students as they represent algebraic expressions and interpret the meaning of terms, coefficients, variables, and operations within those expressions. Throughout the lesson, written descriptions are connected to symbolic expressions, allowing students to examine how mathematical relationships are represented in different forms. These instructional experiences help students identify important features of algebraic expressions and recognize relationships across verbal and symbolic representations.
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
Instruction in lesson E2.7, “Integer Addition and Subtraction Practice (I),” employs multiple instructional approaches to support student learning throughout the lesson. The lesson begins with a whole-group discussion during the warm-up, where students engage with key concepts and share initial thinking. During the development activities, prompts guide educators in facilitating collaborative learning and guided practice as students apply integer operations and discuss solution strategies. The lesson concludes with independent learning opportunities in the wrap-up, allowing students to apply their understanding individually. Educator guidance throughout the lesson supports transitions among whole-group instruction, collaborative work, guided practice, and independent application.
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
Guidance for implementing instructional supports is outlined in the Program Guide through the Math Journeys framework of “build, consolidate, and additional practice.” The “Build” component focuses on educator-led instruction, mathematical discourse, and the development of new concepts through guided learning experiences. The “Consolidate” component provides opportunities for students to apply learning independently through logsheets and differentiated practice resources that reinforce lesson content. The “Additional Practice” component is delivered through Atlas Math, where students engage in digital practice activities that respond to student performance and provide feedback as they work. Together, these components establish a structure that incorporates educator-guided learning, independent practice, and digital learning opportunities to support students throughout the instructional process.
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
Opportunities for enrichment are incorporated throughout the Math Journeys instructional framework of build, consolidate, and additional practice. The Program Guide describes how students engage with lesson content through educator-led instruction, independent practice, and digital learning experiences. The “Additional Practice” components are provided through Atlas Math, where activities respond to student performance and present increasingly complex tasks as students demonstrate understanding. This structure provides opportunities for students to continue developing mathematical concepts through individualized learning experiences.
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
Student understanding is monitored throughout lesson E2.2, “Negative Numbers on the Number Line,” using observation opportunities and discussion prompts embedded within the lesson. Guidance directs educators to observe how students represent, compare, and sequence numbers on a number line while engaging in learning activities. These instructional checkpoints provide opportunities to identify misconceptions, assess student reasoning, and respond to student needs during the lesson.
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.
4 out of 4 points
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.
4 out of 4 points
In session 8, “Ordering Decimals,” the materials provide educator guidance for incorporating linguistic accommodations across all five ELPS proficiency levels as students compare and order decimal numbers. The bilingual tip differentiates supports for pre-production, beginning, intermediate, high intermediate, and advanced students, providing educators with proficiency-appropriate accommodations for engaging students with lesson-specific academic language. The differentiated guidance supports students as they use terms such as greater than, less than, place value, digit, decimal point, compare, and order to communicate mathematical reasoning. By adjusting the linguistic support according to students’ proficiency levels while maintaining engagement with the same grade-level decimal concepts, the materials support students in progressing toward increasingly more academic mathematical language.
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.
0 out of 4 points
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.
0 out of 4 points
Supports for emergent bilingual (EB) students are embedded throughout grade 6, Journey E2 lessons through vocabulary development activities, visual models, sentence frames, and discussion opportunities. These resources provide educators with tools for supporting language development while students engage with grade-level mathematics content. The supports rely on educator implementation and facilitation. There do not appear to be student-facing linguistic accommodations embedded within the adaptive materials or organized according to ELPS proficiency levels.
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
Additional implementation support is provided through the E2 Lesson-Level ELPS Companion. These resources identify lesson-specific language objectives, language demands, expected oral and written student outputs, ELPS alignments, and suggested educator supports connected to the mathematics content. The companion serves as a planning resource that helps educators incorporate language supports while providing access to 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
Written discourse is supported through the E2 Lesson-Level ELPS Companion, which includes opportunities for students to record and annotate models of integer addition and subtraction using mathematical explanations and academic vocabulary. Lesson resources encourage students to connect English mathematical terminology with Spanish cognates while communicating their reasoning in writing. These activities provide opportunities for students to develop written explanations that incorporate both mathematical concepts and academic language.
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.
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
The grade 6 learning pathway embeds depth of understanding through tasks that require students to analyze patterns, generalize relationships, and justify mathematical reasoning. In F1.2, “Visual Patterns,” students examine geometric sequences, identify relationships among figures, and develop algebraic expressions to predict future terms. Students compare different approaches, defend their reasoning, and connect visual representations to symbolic expressions. These learning experiences move beyond procedural work and require students to demonstrate conceptual understanding aligned to the TEKS.
Assessment opportunities within E2, “Integers,” session 7, “Integer Addition and Subtraction Practice (I),” require students to apply reasoning about integer operations in multiple contexts. Students record solutions, represent integer combinations, analyze relationships among positive and negative values, and explain how different combinations affect results. Logbook activities and XYZ activities serve as formative assessment opportunities in which students demonstrate their understanding through representations, problem solving, and mathematical explanations rather than through isolated computation.
Evaluation for 4.1b
Across the E2, “Integers,” pathway, students encounter increasingly rigorous questions and tasks as they develop proficiency with integer concepts and operations. Early sessions introduce negative numbers and use number lines to locate and order integers. Later sessions ask students to represent integers with counters, add and subtract integers through concrete and visual models, apply properties of integer operations, multiply and divide integers, and complete combined operations. This progression moves students from conceptual representations to increasingly abstract and complex applications of integer operations, and leads to grade-level proficiency.
Students also engage in tasks that extend the complexity of grade-level integer work. For example, in E2, session 7, “Integer Addition and Subtraction Practice (I),” students select two integer cards, determine different possible sums, and identify the highest and lowest possible results. The extension asks students to investigate all possible results from adding two cards, which requires them to analyze combinations, compare outcomes, and reason about integer relationships. The session aligns with TEKS 6.3.D and 7.3.A, extending the task into future-grade expectations. However, the enrichment and extension resources do not provide structured support that systematically leads students to above grade-level proficiency.
Evaluation for 4.2a
Coherence across grade 6 concepts is evident throughout the E2, “Integers,” pathway as students develop understanding from foundational integer concepts to increasingly complex operations. Early sessions focus on negative numbers, locating and comparing integers on a number line, and interpreting direction and magnitude. Later sessions build on these understandings through the use of counters; number line models; and properties of operations to add, subtract, multiply, and divide integers. This progression connects representations, operations, and integer relationships within a unified learning sequence.
Lesson-level tasks reinforce relationships among integer concepts by connecting multiple mathematical ideas. In E2, session 7, “Integer Addition and Subtraction Practice (I),” students use integer cards to generate different sums, determine the greatest and least possible results, and analyze how positive and negative values influence outcomes. These activities connect integer value, direction on the number line, addition patterns, and comparison of results, supporting coherence across grade 6 integer concepts.
Evaluation for 4.2b
The materials demonstrate 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 those understandings 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 explicit connections demonstrate how mathematical ideas and relationships develop across grade levels and courses.
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, demonstrating how a common representation connects increasingly complex mathematical ideas from earlier grades through high school coursework.
Evaluation for 4.2c
The Connections and Misconceptions Teacher Companion identifies the prior knowledge students bring to each session, the new concepts or procedures developed, and where the 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 and Algebra I, explicitly showing how current concepts and procedures support future mathematical learning.
The materials explicitly connect 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 and D3.12 connects to rate and proportional reasoning in grades 6 and 7. In addition, fraction multiplication procedures developed in D5.8, D5.9, D5.15, and D5.16 are connected to future work with rational expressions in Algebra I. These explicit connections demonstrate how students’ conceptual and procedural knowledge develops across lessons, grade levels, and future courses.
Evaluation for 4.3a
Students revisit previously learned skills and concepts throughout E2, “Integers,” session 9, “Integer Addition and Subtraction Practice (II).” During the warm-up students return to integer addition and subtraction concepts from earlier E2 lessons as they insert positive and negative signs into the expression (5 \square 4 \square 3 \square 2) to generate multiple results. Later in the lesson, activity 2 revisits sequence and pattern concepts introduced in E1.10 by asking students to analyze integer sequences, identify rules, and predict future terms. These tasks require students to retrieve and apply prior learning after intervening instruction, supporting long-term retention of mathematical concepts.
The program’s organizational resources also support spaced retrieval. The TEKS Correlation Guide identifies where content standards and mathematical process standards are introduced and revisited across journeys and lessons. By showing when related concepts reappear throughout the learning pathways, the guide supports instructional planning that allows students to return to previously learned skills and concepts in later learning experiences.
Evaluation for 4.3b
Interleaved practice is incorporated throughout E2, “Integers,” session 15, “Combined Operations with Integers.” Students simplify expressions involving additive and multiplicative integer operations while applying order of operations and reasoning about algebraic expressions. When statements are identified as false, students analyze errors and revise the expressions to create true mathematical statements. These activities require students to coordinate integer operations, operation hierarchy, algebraic reasoning, and error analysis within the same task rather than practice each skill independently.
The cluster overview for E, “Powers and Integers,” describes how students build on previously learned concepts such as multiplication, number lines, area models, and order of operations while developing understanding of powers and integers. Throughout the pathway students apply prior arithmetic knowledge in new contexts and combine multiple mathematical ideas within lessons and activities. This progression supports interleaved practice by requiring students to use previously learned skills alongside newly introduced concepts.
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
Assessment opportunities within E2, “Integers,” session 7, “Integer Addition and Subtraction Practice (I),” require students to apply reasoning about integer operations in multiple contexts. Students record solutions, represent integer combinations, analyze relationships among positive and negative values, and explain how different combinations affect results. Logbook activities and XYZ activities serve as formative assessment opportunities in which students demonstrate their understanding through representations, problem solving, and mathematical explanations rather than through isolated computation.
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
Students also engage in tasks that extend the complexity of grade-level integer work. For example, in E2, session 7, “Integer Addition and Subtraction Practice (I),” students select two integer cards, determine different possible sums, and identify the highest and lowest possible results. The extension asks students to investigate all possible results from adding two cards, which requires them to analyze combinations, compare outcomes, and reason about integer relationships. The session aligns with TEKS 6.3.D and 7.3.A, extending the task into future-grade expectations. However, the enrichment and extension resources do not provide structured support that systematically leads students 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
Lesson-level tasks reinforce relationships among integer concepts by connecting multiple mathematical ideas. In E2, session 7, “Integer Addition and Subtraction Practice (I),” students use integer cards to generate different sums, determine the greatest and least possible results, and analyze how positive and negative values influence outcomes. These activities connect integer value, direction on the number line, addition patterns, and comparison of results, 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
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, demonstrating 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 materials explicitly connect 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 and D3.12 connects to rate and proportional reasoning in grades 6 and 7. In addition, fraction multiplication procedures developed in D5.8, D5.9, D5.15, and D5.16 are connected to future work with rational expressions in Algebra I. These explicit connections demonstrate how students’ conceptual and procedural knowledge develops 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 program’s organizational resources also support spaced retrieval. The TEKS Correlation Guide identifies where content standards and mathematical process standards are introduced and revisited across journeys and lessons. By showing when related concepts reappear throughout the learning pathways, the guide supports instructional planning that allows students to return to previously learned skills and concepts in later learning experiences.
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 overview for E, “Powers and Integers,” describes how students build on previously learned concepts such as multiplication, number lines, area models, and order of operations while developing understanding of powers and integers. Throughout the pathway students apply prior arithmetic knowledge in new contexts and combine multiple mathematical ideas within lessons and activities. This progression supports interleaved practice by requiring students to use previously learned skills alongside newly introduced concepts.
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
In Journey F1, station 3, “Equivalent Algebraic Expressions,” students interpret different visual representations of the same growing pattern by identifying what each section represents algebraically. Students analyze why expressions such as 2n + n + 1 + 2 and 3n + 3 describe the same figure and determine whether 3(n + 1) is also equivalent. The activity requires students to connect visual representations to symbolic expressions and justify the relationships among them.
In Journey D3, station 12, “Calculating Percentages I,” students interpret benchmark percentages using numerical, tabular, and contextual representations. Students analyze relationships among multiple representations before investigating whether A% of B = B% of A. The extension asks students to justify their conclusions by comparing representations and explaining the mathematical relationship rather than relying only on computation.
Evaluation for 5.1b
In Journey F1, station 2, “Visual Patterns,” activity 1 asks students to build 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 logbooks, creating pictorial representations that correspond to the concrete models. The activity requires students to construct and record multiple representations of the same mathematical situation.
In Journey E2, station 6, “Adding and Subtracting Integers with Counters,” students model integer addition and subtraction with positive and negative counters before representing each operation with drawings in their logbooks. The lesson connects the concrete counter models to pictorial representations by having students sketch the quantities and zero pairs used to solve each problem. The educator guidance emphasizes recording the models on paper to support the transition from manipulatives to visual representations.
Evaluation for 5.1c
In Journey D3, station 13, “Solving Percentages: Word Problems,” students apply their understanding of percentages to new real-world situations by representing world population data with snap cubes before extending the same 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 Journey E2, station 16, “Negative Rational Numbers,” students extend their understanding of integer ordering by classifying rational numbers represented as fractions, decimals, and mixed numbers. Students apply concepts of absolute value and opposite numbers to unfamiliar rational values before placing them accurately on a number line using benchmark integers as reference points.
Evaluation for 5.2a
In Journey E2, station 8, “Adding and Subtracting Integers Using the Number Line,” 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 Journey E1, station 8, “Productive Practice: Order of Operations I,” students solve multiple numerical expressions that require consistent application of the order of operations. Repeated practice with increasingly varied expressions supports procedural fluency by requiring students to determine the correct sequence of operations accurately and efficiently across the lesson.
Evaluation for 5.2b
In Journey E1, station 8, “Productive Practice: Order of Operations I,” students solve a variety of numerical expressions by applying the order of operations accurately across multiple practice opportunities. The lesson requires students to determine the sequence of operations for different expression structures, reinforcing procedural accuracy while providing opportunities to apply the same procedure in varied situations.
In Journey D5, station 18, “Dividing Fractions 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. The lesson provides opportunities to apply different procedures. However, it does not consistently require students to reflect on or compare the efficiency of those strategies across the learning pathway.
Evaluation for 5.2c
In Journey E2, station 1, “Introduction to Negative Numbers,” students arrange historical figures on a timeline and determine whether each placement accurately represents the order of historical events using positive and negative values. Students then interpret thermometer models showing temperatures during a historical polar cold wave and explain how crossing zero on a number line supports the solution strategy. These activities require students to verify the accuracy of mathematical representations and justify the strategies used to interpret them.
In Journey F1, station 3, “Equivalent Algebraic Expressions,” students determine whether multiple 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 communicate the pattern more efficiently while maintaining mathematical accuracy.
Evaluation for 5.2d
In Journey F1, station 3, “Equivalent Algebraic Expressions,” the Teacher Guide directs students to compare multiple algebraic expressions representing the same visual pattern before using the commutative and associative properties to generate equivalent forms. The guidance supports students in moving from lengthy visual descriptions toward more efficient symbolic expressions by recognizing the structure of the pattern rather than recounting each component individually.
In Journey E2, station 8, “Adding and Subtracting Integers Using the Number Line,” the educator guidance emphasizes using direction, distance, and zero as reference points when modeling integer operations. Students progress from counting individual movements to 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, the grade 6 TEKS are aligned to specific journeys and stations throughout the instructional program. The document identifies where each TEKS is addressed and serves as a planning resource for lesson sequencing. However, it does not explicitly explain how the conceptual emphasis of the TEKS supports the procedural emphasis or how both are intentionally developed throughout instruction.
The TEKS Correlation Guide identifies instructional topics aligned to TEKS 6.7.A, including lessons addressing equivalent numerical expressions, order of operations, exponents, and prime factorization. Although the guide identifies where the standard is taught, it does not explicitly state the conceptual emphasis, procedural emphasis, or the relationship between the two.
Evaluation for 5.3b
In Journey E2, station 6, “Adding and Subtracting Integers with Counters,” students use positive and negative counters to model integer operations, such as −7 + 4. After manipulating the counters, students draw proportional representations of the models and record the corresponding symbolic equations, including −7 – (−5) = −2. The lesson intentionally progresses from concrete manipulatives to pictorial representations and abstract notation, supporting TEKS 6.3.C and 6.3.D.
In Journey F1, station 4, “Representing Algebraic Expressions,” students construct algebraic expressions using bags, snap cubes, frames, boxes, and counters before creating drawings of the same models. Students then represent each situation symbolically by writing equivalent algebraic expressions, such as 2(2x + 3) and 4x + 6. These questions and tasks provide opportunities to connect concrete, pictorial, and abstract representations required by TEKS 6.7C and 6.7D.
Evaluation for 5.3c
In Journey E2, station 6, “Adding and Subtracting Integers with Counters,” 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. Educators ask 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, supporting connections between concrete models and abstract notation.
In Journey F1, station 3, “Equivalent Algebraic Expressions,” students begin by analyzing pictorial growing patterns before recording algebraic expressions that represent 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 support students in connecting, creating, defining, and explaining representational models and abstract algebraic concepts.
Evaluation for 5.4a
In Journey F1, station 3, “Equivalent Algebraic Expressions,” activity 1 has students examine a geometric snap-cube sequence and translate the visual pattern into algebraic notation. While generating expressions through the commutative and associative properties, students apply terms related to like terms, the distributive property, and equivalent expressions. During the wrap-up substituting values allows students to verify equivalence and explain relationships across visual and symbolic representations.
In Journey E2, “Integers,” colored counters represent positive and negative values as students combine opposites to form zero pairs and model integer operations. Number lines and contexts involving bank balances, sea level, elevators, and thermometers further anchor signed-number concepts. Through these representations, students explain positive and negative values, opposites, absolute value, and integer relationships with academic mathematical language.
Evaluation for 5.4b
In Journey E2, station 3, “Ordering & Jumping on the Number Line,” the guide directs educators to focus on the symbols < and > as students order integers on a number line. During “Compare and Connect,” educators ask, “How is the representation different for each case?” to support discussion of opposites, absolute value, and direction as students compare jump-machine representations with peers. The wrap-up extends this language work by asking students to classify statements as true or false and correct inaccurate statements using inequality and absolute-value language.
The E2 Journey Language Bank guides educators through pre-teach and embedded language-support routines, discourse and writing supports, and redirections for anticipated responses and misconceptions. For example, routine 1 directs educators to use the routine before lessons that introduce or revisit signed real-world situations, including before lessons like E2.1 and E2.6. Across the journey, educators support students in classifying signed quantities, explaining distance and direction, describing zero pairs, and justifying sign patterns, then extend that vocabulary into operations, conjectures, and comparisons of negative rational numbers.
Evaluation for 5.4c
In Journey F1, “Algebraic Expressions,” station 8, “From Natural Language to Algebra,” the warm-up guides educators to facilitate a dictation routine in which students translate spoken phrases into algebraic expressions using terms such as successor, double, and square. Educator prompts draw attention to how intonation can change the meaning of an expression and encourage students to justify their interpretations. During “I Have One, Who Has the Other?” students state expressions aloud with precise mathematical language as they collaborate to locate matching cards.
In E2.6 the educator guidance prompts students to narrate their actions with counters, explain why zero pairs preserve value, and record the corresponding integer equation. As students discuss their reasoning, they apply terms such as positive, negative, zero pair, value, and equation to connect the concrete model with symbolic notation and communicate their reasoning aloud and in writing.
Evaluation for 5.4d
In Journey F1, station 3, “Equivalent Algebraic Expressions,” activity 2, educators ask, “Are the algebraic expressions we came up with as a class equivalent to each other?” Students evaluate peer-generated expressions and discuss relationships using terms such as equivalent expressions, distributive property, and like terms. The guide also directs educators to “ask several students to state a general rule,” allowing classmates to hear varied reasoning before refining their own explanations and recording shared conclusions.
In Journey F1, station 2, “Visual Patterns,” the share and discuss routine directs educators to “highlight the variety of patterns that fit the same general expression.” Students listen to classmates describe different counting strategies, compare those approaches, and generate new expressions from peer ideas using the commutative and associative properties. This sequence moves the conversation from hearing multiple strategies to refining and restating algebraic reasoning with peers.
Evaluation for 5.4e
In Journey F1, 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, giving educators exemplar responses for comparing student approaches. When a student writes 3n + 6 instead of 3n + 3, the guide redirects the reasoning to the visual pattern and prompts, “What does each term count in the picture?” This move helps educators address the inaccurate constant term by reconnecting each part of the expression to the geometric model.
Lesson F1.8, “From Natural Language to Algebra,” prepares educators for varied translations of natural-language statements into algebraic expressions. For example, students may distinguish between phrases such as “double the successor of a number” and “the successor of double a number” or confuse their algebraic structures. The guidance supports redirection by having students reread the phrase, identify the operation words, and match the verbal statement to the corresponding algebraic structure.
Evaluation for 5.5a
In Journey F1, station 2, “Visual Patterns,” students analyze geometric sequences, organize values in tables, predict later terms, and develop verbal or algebraic rules. Activity 1 integrates the TEKS process standard 1.F as students connect the step number to the total number of fence segments and compare expressions that represent the same pattern. Activity 2 extends the reasoning as students generate sequences for rules such as 3n + 1 and determine whether a specified output occurs, integrating analysis, representation, and justification within the algebraic content.
In Journey E2, station 6, “Adding and Subtracting Integers with Counters,” students represent -7 + 4 with counters, cancel zero pairs, and record the corresponding equation, -7 + 4 = -3. The task integrates the TEKS process standard 1.D by requiring students to communicate the same mathematical idea through concrete and symbolic representations. Students extend this connection to subtraction, including -7 - (-5) = -2, and explain how each counter action corresponds to the recorded equation.
Evaluation for 5.5b
The E2 Journey Instructional Guide describes how the TEKS mathematical process standards operate across the integers pathway through a session-by-session alignment that identifies each lesson’s content focus, the primary TEKS, mathematical process standards, ELPS focus, and “Why This Matters.” The sequence traces students from classifying signed contexts and locating integers to using counters, performing integer operations, analyzing sign patterns, and extending reasoning to negative rational numbers. By pairing process standards with the purpose of each session, the guide explains how reasoning, representation, communication, and justification develop alongside the mathematical content across the journey.
The scope and sequence maps sessions in instructional order and identifies the TEKS mathematical process standards connected to each entry. Across the pathway, standards 1.B, 1.C, 1.D, 1.E, 1.F, and 1.G recur as students analyze information, select tools, communicate through representations, organize ideas, connect relationships, and justify arguments. The ordered map documents how these mathematical processes reappear across sessions and connect students’ work from one stage of the learning pathway to the next.
Evaluation for 5.5c
In Journey F1, station 2, “Visual Patterns,” the lesson overview identifies the TEKS mathematical process standard 1F alongside the content standards before instruction begins. The mathematical process standards guidance explains that students analyze relationships as they extend geometric patterns, organize values, predict later terms, and generalize the patterns with expressions, such as 3n + 1 and 2n – 1. This lesson-level overview connects the identified process standard to the mathematical reasoning students apply throughout the session.
In Journey E1, station 8, “Productive Practice: Order of Operations I,” the lesson overview lists TEKS 6.7.A, 6.7.C, and 6.7.D with mathematical process standard 1C in the standards section. The accompanying guidance connects tool selection to the “Broken Calculator” task, where students choose operations and keystrokes to generate target numbers. By naming the process standard and describing its role in the task, the overview shows educators how students apply strategic tool use during the lesson.
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 Journey D3, station 12, “Calculating Percentages I,” students interpret benchmark percentages using numerical, tabular, and contextual representations. Students analyze relationships among multiple representations before investigating whether A% of B = B% of A. The extension asks students to justify their conclusions by comparing representations and explaining the mathematical relationship rather than relying only on computation.
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 Journey E2, station 6, “Adding and Subtracting Integers with Counters,” students model integer addition and subtraction with positive and negative counters before representing each operation with drawings in their logbooks. The lesson connects the concrete counter models to pictorial representations by having students sketch the quantities and zero pairs used to solve each problem. The 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 Journey E2, station 16, “Negative Rational Numbers,” students extend their understanding of integer ordering by classifying rational numbers represented as fractions, decimals, and mixed numbers. Students apply concepts of absolute value and opposite numbers 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 Journey E1, station 8, “Productive Practice: Order of Operations I,” students solve multiple numerical expressions that require consistent application of the order of operations. Repeated practice with increasingly varied expressions supports procedural fluency by requiring students to determine the correct sequence of operations accurately and efficiently across 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 Journey D5, station 18, “Dividing Fractions 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. The lesson provides opportunities to apply different procedures. However, it does not consistently require students to reflect on or compare the efficiency of those strategies across the 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 Journey F1, station 3, “Equivalent Algebraic Expressions,” students determine whether multiple 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 communicate the pattern more efficiently while maintaining mathematical 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 Journey E2, station 8, “Adding and Subtracting Integers Using the Number Line,” the educator guidance emphasizes using direction, distance, and zero as reference points when modeling integer operations. Students progress from counting individual movements to 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 to TEKS 6.7.A, including lessons addressing equivalent numerical expressions, order of operations, exponents, and prime factorization. Although the guide identifies where the standard is taught, it does not explicitly state the conceptual emphasis, procedural emphasis, or the relationship between the two.
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 Journey F1, station 4, “Representing Algebraic Expressions,” students construct algebraic expressions using bags, snap cubes, frames, boxes, and counters before creating drawings of the same models. Students then represent each situation symbolically by writing equivalent algebraic expressions, such as 2(2x + 3) and 4x + 6. These questions and tasks provide opportunities to connect concrete, pictorial, and abstract representations required by 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 Journey F1, station 3, “Equivalent Algebraic Expressions,” students begin by analyzing pictorial growing patterns before recording algebraic expressions that represent 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 support students in connecting, creating, defining, and explaining representational models and 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 represent positive and negative values as students combine opposites to form zero pairs and model integer operations. Number lines and contexts involving bank balances, sea level, elevators, and thermometers further anchor signed-number concepts. Through these representations, students explain positive and negative values, opposites, absolute value, and integer relationships with academic 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 guides educators through pre-teach and embedded language-support routines, discourse and writing supports, and redirections for anticipated responses and misconceptions. For example, routine 1 directs educators to use the routine before lessons that introduce or revisit signed real-world situations, including before lessons like E2.1 and E2.6. Across the journey, educators support students in classifying signed quantities, explaining distance and direction, describing zero pairs, and justifying sign patterns, then extend that vocabulary into operations, conjectures, and comparisons of 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 the educator guidance prompts students to narrate their actions with counters, explain why zero pairs preserve value, and record the corresponding integer equation. As students discuss their reasoning, they apply terms such as positive, negative, zero pair, value, and equation to connect the concrete model with symbolic notation and communicate their reasoning aloud and in writing.
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 Journey F1, station 2, “Visual Patterns,” the share and discuss routine directs educators to “highlight the variety of patterns that fit the same general expression.” Students listen to classmates describe different counting strategies, compare those approaches, and generate new expressions from peer ideas using the commutative and associative properties. This sequence moves the conversation from hearing multiple strategies to refining and restating algebraic reasoning with peers.
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
Lesson F1.8, “From Natural Language to Algebra,” prepares educators for varied translations of natural-language statements into algebraic expressions. For example, students may distinguish between phrases such as “double the successor of a number” and “the successor of double a number” or confuse their algebraic structures. The guidance supports redirection by having students reread the phrase, identify the operation words, and match the verbal statement to the corresponding algebraic structure.
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, station 6, “Adding and Subtracting Integers with Counters,” students represent -7 + 4 with counters, cancel zero pairs, and record the corresponding equation, -7 + 4 = -3. The task integrates the TEKS process standard 1.D by requiring students to communicate the same mathematical idea through concrete and symbolic representations. Students extend this connection to subtraction, including -7 - (-5) = -2, and explain how each counter action corresponds to the recorded 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 scope and sequence maps sessions in instructional order and identifies the TEKS mathematical process standards connected to each entry. Across the pathway, standards 1.B, 1.C, 1.D, 1.E, 1.F, and 1.G recur as students analyze information, select tools, communicate through representations, organize ideas, connect relationships, and justify arguments. The ordered map documents how these mathematical processes reappear across sessions and connect students’ work from one stage of the learning pathway to the next.
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 E1, station 8, “Productive Practice: Order of Operations I,” the lesson overview lists TEKS 6.7.A, 6.7.C, and 6.7.D with mathematical process standard 1C in the standards section. The accompanying guidance connects tool selection to the “Broken Calculator” task, where students choose operations and keystrokes to generate target numbers. By naming the process standard and describing its role in the task, the overview shows educators how students apply strategic tool use during the lesson.
Rubric Section 6
Productive Struggle
Materials support students in applying disciplinary practices to productive problem-solving, including explaining and revising their thinking.
Total
90% (19 out of 21 points)
Evaluation for 6.1a
The Math Journeys grade 6 materials provide opportunities for students to think mathematically, persevere through solving problems, and make sense of mathematics in Journey F1, station 2, “Visual Patterns.” In activity 1, students determine how many segments make up the next fence without first receiving a formula, requiring them to analyze the visual pattern before using algebraic notation. The Teacher Guide extends this reasoning by asking, “Without needing to represent the fence, how many segments make up the one with 100 sections?” Students then explain how to calculate the total number of segments for any step n, connecting the visual model to equivalent algebraic expressions.
Math Journeys grade 6 continues to promote mathematical thinking and perseverance in Journey E2, station 9, “Integer Addition and Subtraction Practice (II).” The warm-up asks students to place positive and negative signs into an expression to generate every possible outcome, requiring them to reason about signs and operations simultaneously. Later activities ask students to determine the results for distant steps, such as step 41 and step 42, and explain why the sequence alternates between positive and negative values.
Evaluation for 6.1b
The Math Journeys grade 6 materials support students in understanding, explaining, and justifying that mathematical problems can have multiple valid solution paths in Journey F1, station 3, “Equivalent Algebraic Expressions.” The lesson presents three expressions to represent the same visual pattern: 2n + n + 1 + 2, 3n + 3, and 3(n + 1). During the share and discuss segment, students compare the expressions, explain why each model represents the same pattern, and justify their conclusions by applying the associative and distributive properties. These discussions reinforce that different algebraic forms can describe the same mathematical relationship.
Math Journeys grade 6 continues to develop flexible problem solving in Journey D5, station 18, “Dividing Fractions II.” Students solve fraction-division tasks by using different representations and strategies before discussing their approaches during the share and discuss segment. The lesson asks students to defend why dividing by a fraction produces the same result as multiplying by its reciprocal, and to explain why different strategies produce equivalent solutions. These opportunities strengthen conceptual understanding while demonstrating that more than one valid method can solve the same problem.
Evaluation for 6.1c
The Math Journeys grade 6 materials require students to make sense of mathematics through collaborative work in Journey F1, station 2, “Visual Patterns.” Working in pairs, students build geometric sequences with snap cubes, record step-count tables, and develop algebraic rules for any step n in their logbooks. During the share and discuss segment, students explain why different expressions represent the same pattern, compare classmates’ reasoning, and refine their own ideas through whole-class discussion.
Math Journeys grade 6 provides another opportunity in Journey E2, station 6, “Adding and Subtracting Integers with Counters.” Partners model integer operations with counters, draw the counter representations, and record the corresponding symbolic equations. Throughout the lesson, students explain what each counter action represents while discussing their solutions with peers and the educator, connecting hands-on models, written work, and mathematical discourse.
Evaluation for 6.2a
The Math Journeys grade 6 materials support educators in guiding students to share and reflect on their problem-solving approaches in Journey F1, station 3, “Equivalent Algebraic Expressions.” During the share and discuss segment, educators ask students whether different algebraic expressions generated by the class are equivalent and prompt them to explain how different visual groupings produce the same expression. Students compare multiple solution paths, construct mathematical arguments using the associative and distributive properties, and justify why equivalent expressions represent the same quantity. The accompanying “As a Teacher, What Can I Observe?” guidance helps educators facilitate reflection as students generate additional equivalent expressions and defend their reasoning.
Math Journeys grade 6 provides another opportunity in Journey E2, “Representing Integers with Counters (I).” The lesson includes “Teacher Moves,” whole-class discussion routines, and MLR2, “Collect and Display,” that guide students to explain zero-pair cancellation, debate whether an odd number of counters can represent zero, and justify why irreducible counter models equal an integer’s absolute value. Multiple entry points—including real-world contexts, physical counters, symbolic representations, and extension tasks—allow educators to facilitate reflection on different mathematical pathways.
Evaluation for 6.2b
The Math Journeys grade 6 materials include prompts and guidance that support educators in providing explanatory feedback based on student responses in Journey E2, station 3, “Ordering & Jumping on the Number Line.” The “Teacher Moves,” share and discuss, and “As a Teacher, What Can I Observe?” segments direct educators to respond to students’ explanations as they compare integers, justify number line placements, and distinguish absolute value from position on the number line. These routines provide prompts and guidance for responding to student thinking during instruction. However, the lesson does not identify anticipated misconceptions or provide educator guidance for addressing common errors before they arise, such as ordering negative integers according to absolute value rather than their location on the number line.
Math Journeys grade 6 also provides explanatory feedback based on student responses in Journey F1, station 3, “Equivalent Algebraic Expressions.” The lesson prompts educators to ask students what each term represents in the visual pattern and uses “Teacher Moves,” share and discuss, and observation guidance to extend or clarify student explanations. Although these supports help educators respond to students’ reasoning, the materials do not include prompts or guidance that anticipate misconceptions, such as incorrectly combining unlike terms or misunderstanding why equivalent expressions represent the same quantity.
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
Math Journeys grade 6 continues to promote mathematical thinking and perseverance in Journey E2, station 9, “Integer Addition and Subtraction Practice (II).” The warm-up asks students to place positive and negative signs into an expression to generate every possible outcome, requiring them to reason about signs and operations simultaneously. Later activities ask students to determine the results for distant steps, such as step 41 and step 42, and explain why the sequence alternates between positive and negative values.
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
Math Journeys grade 6 continues to develop flexible problem solving in Journey D5, station 18, “Dividing Fractions II.” Students solve fraction-division tasks by using different representations and strategies before discussing their approaches during the share and discuss segment. The lesson asks students to defend why dividing by a fraction produces the same result as multiplying by its reciprocal, and to explain why different strategies produce equivalent solutions. These opportunities strengthen conceptual understanding while demonstrating that more than one valid method can solve the same problem.
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
Math Journeys grade 6 provides another opportunity in Journey E2, station 6, “Adding and Subtracting Integers with Counters.” Partners model integer operations with counters, draw the counter representations, and record the corresponding symbolic equations. Throughout the lesson, students explain what each counter action represents while discussing their solutions with peers and the educator, connecting hands-on models, written work, and mathematical discourse.
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
Math Journeys grade 6 provides another opportunity in Journey E2, “Representing Integers with Counters (I).” The lesson includes “Teacher Moves,” whole-class discussion routines, and MLR2, “Collect and Display,” that guide students to explain zero-pair cancellation, debate whether an odd number of counters can represent zero, and justify why irreducible counter models equal an integer’s absolute value. Multiple entry points—including real-world contexts, physical counters, symbolic representations, and extension tasks—allow educators to facilitate reflection on different mathematical pathways.
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.
2 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.
2 out of 4 points
Math Journeys grade 6 also provides explanatory feedback based on student responses in Journey F1, station 3, “Equivalent Algebraic Expressions.” The lesson prompts educators to ask students what each term represents in the visual pattern and uses “Teacher Moves,” share and discuss, and observation guidance to extend or clarify student explanations. Although these supports help educators respond to students’ reasoning, the materials do not include prompts or guidance that anticipate misconceptions, such as incorrectly combining unlike terms or misunderstanding why equivalent expressions represent the same quantity.