Program Information
- ISBN
- 9791370378103
- Technical Specifications: Checklist
- Tech Specs: Checklist (pdf 1.28 MB)
- Technical Specifications: Professional Development
- Tech Specs: Professional Development (pdf 180.62 KB)
Math Journeys Texas, Grado 5 (Spanish)
Supplemental Math (Spanish) Grade 5
IMRA 2026
Publisher: Innovamat Education, Inc.
Copyright: 2026
Series includes:
Rubric: Supplemental Mathematics K–5 (Spanish) | 2025 (Download Not Available)
* Some programs submit evidence for only part of a standard, while others submit all sections. A 100% score means this program met all the expectations it submitted.
Quality Review
Standards Alignment
Rubric Section
| Grade | TEKS % | ELPS % |
|---|---|---|
| Grade 5 | 100% | N/A |
Criteria for Quality
Rubric Section 1
Intentional Instructional Design
Materials support educators in effective implementation through intentional course, unit, and lesson-level design.
Total
100% (23 out of 23 points)
Evaluation for 1.1a
The TEKS Correlation Guide identifies the TEKS addressed in each lesson, including both the content and process standards. The scope and sequence document is organized into sections called “Journeys” and identifies the TEKS and ELPS addressed in each. The Journey Instructional Guide provides a detailed rationale for each journey. For example, section 2 of the A2 Journey Instructional Guide explains how the current journey focuses on identifying numbers and counting from 1–100, extending students’ understanding of counting, comparing, ordering, and estimating. These skills were developed in the previous journey, which involves numbers 1–20. Section 3 further clarifies how learning progresses from concrete experiences to representational models and ultimately to an abstract understanding of number sense.
Each Math Journeys Spanish Instructional Guide provides a rationale for the vertical and horizontal alignment of each journey. The vertical rationale explains why a given journey is strategically positioned within the materials and how learning connects across grade levels to build on prior knowledge and support future learning. The horizontal rationale illustrates how lessons within a journey build upon one another through an intentional sequence of interconnected concepts that reinforce and deepen students’ mathematical understanding within the same grade level.
Evaluation for 1.1b
Implementation guidance in the Program Guide is organized around the three-step instructional framework of “build,” “consolidate,” and “practice.” Lessons begin with educator-led, small-group instruction, followed by independent completion of logsheets with educator feedback and optional practice opportunities on Atlas Math, an adaptive digital platform. The “Lesson Internalization and Planning” section, which explains how to plan for student variability through multiple entry points, just-in-time supports, extensions, and multiple representations and modes of expression, contains additional implementation support.
Each journey contains specific instructions and activities for both enrichment and small-group instruction. The curriculum also clarifies how to use manipulatives to support problem-solving through concrete, hands-on learning experiences. The teaching strategies enable educators to adapt instruction across multiple contexts by providing enrichment opportunities for students who have shown mastery as well as targeted, small-group support for students who require additional practice.
Evaluation for 1.1c
The TEKS Correlation Guide, which connects lessons and activities within each journey to specific TEKS content and process standards, recommends skill entry points. A digital diagnostic assessment and placement report also identifies appropriate instructional starting points based on student performance data. After students complete the diagnostic assessment, the program generates a report that recommends specific skill entry points and journeys to assign. These suggestions support targeted instruction, differentiated learning opportunities, and instructional decision-making based on individual student performance.
The placement test report sample for grade 5 illustrates how diagnostic assessment results can be used to recommend skill entry points and guide instructional planning. The report identifies the assessed TEKS and includes a “Proposed Group Distribution” section that suggests grouping structures based on student performance data and recommends an appropriate entry point for each group. In addition, the report provides an individual student page that offers a snapshot of each student’s current understanding and a recommended starting point tailored to that student’s performance. These features enable educators to personalize instruction and address individual learning needs from the beginning of instruction.
Evaluation for 1.1d
The Math Journeys grade 5 Spanish program contains protocols with corresponding guidance for internalizing both units and lessons, available in the “Lesson Internalization and Planning” section of the Program Guide. The “Preparing for a Journey” section explains how to internalize units by directing educators to understand how the current journey builds on prior learning, review lesson objectives and mastery criteria, identify scaffolds and enrichment opportunities, gather materials, and analyze the learning progression before starting instruction. Furthermore, the sections “Preparing for a Building Session,” “Preparing for a Consolidating Session,” and “Preparing for an Additional Practice Session” contain protocols for internalizing lessons. These sections guide educators to clarify objectives, anticipate students’ thinking and misconceptions, prepare materials, identify opportunities for formative assessment, analyze students’ responses, and use progress monitoring data to inform future instruction.
The Math Journeys grade 5 Spanish program provides protocols with corresponding guidance for internalizing lessons. The “Lesson Internalization and Planning” section of the Program Guide contains three sections for use with each lesson component. “Preparing for a Building Session,” “Preparing for a Consolidating Session,” and “Preparing for an Additional Practice Session” help educators understand the lesson’s various components, ensuring that they are well prepared to deliver effective, responsive instruction to meet the needs of all students.
Evaluation for 1.1e
Resources within the Math Journeys grade 5 Spanish program provide instructional leaders with some support to put the curriculum into practice. The “Hands-on Partnership” section of the Program Guide describes ways a math success manager can collaborate with and support instructional leaders throughout the implementation process. Additional embedded guidance and dedicated implementation resources are designed specifically for instructional leaders.
On-demand videos provide training on specific instructional strategies such as Let’s Add by Breaking Down. Although these videos are not meant exclusively for instructional leaders, they serve as resources that both educators and leaders can use to deepen their understanding of the teaching methods embedded in the program. Instructional leaders can leverage these resources to help educators implement strategies consistently and effectively across classrooms.
Evaluation for 1.2a
The Guía del programa explains how to deliver lessons in detail, outlines the instructional components of each lesson, and suggests timeframes for implementation. Lesson materials identify components such as educator-led instruction, student exploration, discussion, and practice activities that support consistent implementation across the program. The Guía del programa also describes multiple assessment resources, including diagnostic and progress monitoring tools. Digital practice progress reports provide TEKS-aligned student performance data for each TEKS to support instructional decision-making and monitor student growth.
Each lesson overview in the Math Journeys grade 5 Spanish program identifies TEKS-aligned learning objectives, student materials, educator resources, and instructional components. The lesson overviews provide key vocabulary and cognates to support language development, and the “Inside a Journey” section of the Program Guide suggests timeframes for implementing lessons. This guidance helps educators plan and pace instruction according to students’ needs.
Evaluation for 1.2b
The Math Journeys grade 5 Spanish program contains detailed lesson overviews that identify TEKS-aligned learning objectives, student materials, educator resources, and lesson components. Each lesson overview provides key vocabulary and cognates to support language development. The “Inside a Journey” section of the Program Guide suggests timeframes for lesson components, allowing educators to plan and pace instruction according to students’ needs.
Each lesson overview provides assessment resources that are aligned with the TEKS. Formative assessments embedded throughout the lesson overviews clearly identify the aligned TEKS, enabling educators to make direct connections between instructional activities and the standards being assessed. End-of-journey assessments are also aligned with the TEKS, and the answer key lists the corresponding aligned TEKS. Because the Math Journeys grade 5 Spanish program is a Spanish-language math curriculum, alignment with the ELPS does not apply. Thus, ELPS alignment is not referenced in the assessment materials.
Evaluation for 1.2c
Within each journey, families receive support in both Spanish and English through the family letter, which includes information about student learning, questions to discuss at home, vocabulary to reinforce concepts, and suggestions to extend learning outside the classroom. For example, the journey C1 family letter contains an Array Builder activity that uses buttons, coins, beans, or crackers to create rows and columns and prompts families to discuss the total number represented. Families can access the letter in either Spanish or English using the language toggle in the upper-right corner of the platform. This helps ensure that all families can access the resource.
The Math Journeys grade 5 Spanish program provides multiple “Cartas para familias” within each journey, including a general family letter for the unit and individual letters for each topic covered throughout the unit. These resources contain organized sections with unit and topic overviews, questions families can ask at home, home practice activities, and key vocabulary to support students’ learning and progress. Families can use the language toggle in the upper-right corner of the platform to access the letters in Spanish or English, depending on their language preference.
1.1 Course-Level Design
1.1a
Materials include an alignment guide outlining the TEKS, ELPS, and concepts covered, with a rationale for learning paths across grade levels (vertical alignment) and within the same grade level (horizontal alignment) as designed in the materials.
Materials include an alignment guide outlining the TEKS, ELPS, and concepts covered, with a rationale for learning paths across grade levels (vertical alignment) and within the same grade level (horizontal alignment) as designed in the materials.
4 out of 4 points
Evaluation for 1.1a
Evaluation for 1.1a
Materials include an alignment guide outlining the TEKS, ELPS, and concepts covered, with a rationale for learning paths across grade levels (vertical alignment) and within the same grade level (horizontal alignment) as designed in the materials.
4 out of 4 points
Each Math Journeys Spanish Instructional Guide provides a rationale for the vertical and horizontal alignment of each journey. The vertical rationale explains why a given journey is strategically positioned within the materials and how learning connects across grade levels to build on prior knowledge and support future learning. The horizontal rationale illustrates how lessons within a journey build upon one another through an intentional sequence of interconnected concepts that reinforce and deepen students’ mathematical understanding within the same grade level.
1.1b
Materials include an implementation guide with usage recommendations and strategies for effective educator use in various contexts, such as just-in-time supports, advanced learning, or as a course.
Materials include an implementation guide with usage recommendations and strategies for effective educator use in various contexts, such as just-in-time supports, advanced learning, or as a course.
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 in various contexts, such as just-in-time supports, advanced learning, or as a course.
3 out of 3 points
Each journey contains specific instructions and activities for both enrichment and small-group instruction. The curriculum also clarifies how to use manipulatives to support problem-solving through concrete, hands-on learning experiences. The teaching strategies enable educators to adapt instruction across multiple contexts by providing enrichment opportunities for students who have shown mastery as well as targeted, small-group support for students who require additional practice.
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 report sample for grade 5 illustrates how diagnostic assessment results can be used to recommend skill entry points and guide instructional planning. The report identifies the assessed TEKS and includes a “Proposed Group Distribution” section that suggests grouping structures based on student performance data and recommends an appropriate entry point for each group. In addition, the report provides an individual student page that offers a snapshot of each student’s current understanding and a recommended starting point tailored to that student’s performance. These features enable educators to personalize instruction and address individual learning needs from the beginning of instruction.
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 Math Journeys grade 5 Spanish program provides protocols with corresponding guidance for internalizing lessons. The “Lesson Internalization and Planning” section of the Program Guide contains three sections for use with each lesson component. “Preparing for a Building Session,” “Preparing for a Consolidating Session,” and “Preparing for an Additional Practice Session” help educators understand the lesson’s various components, ensuring that they are well prepared to deliver effective, responsive instruction to meet the needs of all students.
1.1e
Materials include resources and guidance for instructional leaders to support educators with implementing the materials as designed.
Materials include resources and guidance for instructional leaders to support educators with implementing the materials as designed.
2 out of 2 points
Evaluation for 1.1e
Evaluation for 1.1e
Materials include resources and guidance for instructional leaders to support educators with implementing the materials as designed.
2 out of 2 points
On-demand videos provide training on specific instructional strategies such as Let’s Add by Breaking Down. Although these videos are not meant exclusively for instructional leaders, they serve as resources that both educators and leaders can use to deepen their understanding of the teaching methods embedded in the program. Instructional leaders can leverage these resources to help educators implement strategies consistently and effectively across classrooms.
1.2 Lesson-Level Design
1.2a
If designed to be static, materials include detailed lesson plans with learning objectives, teacher and student materials, lesson components with suggested timeframes, and assessment resources aligned with the TEKS and ELPS.
If designed to be static, materials include detailed lesson plans with learning objectives, teacher and student materials, lesson components with suggested timeframes, and assessment resources aligned with the TEKS and ELPS.
5 out of 5 points
Evaluation for 1.2a
Evaluation for 1.2a
If designed to be static, materials include detailed lesson plans with learning objectives, teacher and student materials, lesson components with suggested timeframes, and assessment resources aligned with the TEKS and ELPS.
5 out of 5 points
Each lesson overview in the Math Journeys grade 5 Spanish program identifies TEKS-aligned learning objectives, student materials, educator resources, and instructional components. The lesson overviews provide key vocabulary and cognates to support language development, and the “Inside a Journey” section of the Program Guide suggests timeframes for implementing lessons. This guidance helps educators plan and pace instruction according to students’ needs.
1.2b
If designed to be adaptive, materials include responsive learning objectives, lesson components with suggested timeframes, and assessment resources aligned with the TEKS and ELPS.
If designed to be adaptive, materials include responsive learning objectives, lesson components with suggested timeframes, and assessment resources aligned with the TEKS and ELPS.
3 out of 3 points
Evaluation for 1.2b
Evaluation for 1.2b
If designed to be adaptive, materials include responsive learning objectives, lesson components with suggested timeframes, and assessment resources aligned with the TEKS and ELPS.
3 out of 3 points
Each lesson overview provides assessment resources that are aligned with the TEKS. Formative assessments embedded throughout the lesson overviews clearly identify the aligned TEKS, enabling educators to make direct connections between instructional activities and the standards being assessed. End-of-journey assessments are also aligned with the TEKS, and the answer key lists the corresponding aligned TEKS. Because the Math Journeys grade 5 Spanish program is a Spanish-language math curriculum, alignment with the ELPS does not apply. Thus, ELPS alignment is not referenced in the assessment materials.
1.2c
Materials contain support for families in Spanish and English for each unit, with suggestions on supporting the progress of their student(s).
Materials contain support for families in Spanish and English for each unit, with suggestions on supporting the progress of their student(s).
2 out of 2 points
Evaluation for 1.2c
Evaluation for 1.2c
Materials contain support for families in Spanish and English for each unit, with suggestions on supporting the progress of their student(s).
2 out of 2 points
The Math Journeys grade 5 Spanish program provides multiple “Cartas para familias” within each journey, including a general family letter for the unit and individual letters for each topic covered throughout the unit. These resources contain organized sections with unit and topic overviews, questions families can ask at home, home practice activities, and key vocabulary to support students’ learning and progress. Families can use the language toggle in the upper-right corner of the platform to access the letters in Spanish or English, depending on their language preference.
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
Within the “Evaluación y monitoreo del progreso” section of the Program Guide, the materials define and explain the purposes of diagnostic, formative, and summative assessment. The guide describes how each assessment type is intended to be used throughout the program and helps educators plan lessons, deliver instruction, monitor student progress, and make data-informed instructional decisions across the school year.
The Math Journeys grade 5 Spanish program provides a comprehensive assessment system that clearly defines the purposes of diagnostic, formative, and summative assessment. Educators administer diagnostic assessments at the beginning of and throughout the year to establish a baseline understanding and monitor ongoing progress. Classroom activities involve daily formative assessments, enabling educators to continuously monitor students’ understanding during instruction. Educators administer summative assessments at the end of each journey to evaluate students’ learning and mastery of the concepts addressed. Collectively, these assessment types create a purposeful system for monitoring student progress and informing instructional decisions throughout the school year.
Evaluation for 2.1b
The Math Journeys grade 5 Spanish program contains guidance to ensure that educators administer instructional assessments both consistently and accurately. The Placement Test Implementation Guide explains how to administer the diagnostic assessment precisely and reliably. The guide covers the estimated testing time, the educator’s role during administration, and suggested materials. For example, the “Administration Guidance” section of the Placement Test Implementation Guide clarifies that “In grades 3–5, students complete the assessment independently in a self-paced format” and that “paper and pencil are recommended to support student thinking and working memory during the assessment.” This level of detail ensures that all educators administer the diagnostic assessment consistently and accurately across classrooms.
The Math Journeys grade 5 Spanish program explains how to consistently and accurately administer the end-of-journey summative assessment. The End-of-Journey Test: Instructions and Guide provides educators with detailed, step-by-step instructions on how to administer the assessment. The guide is organized into three sections: preparation and expectations for the day before the test, procedures and instructions for the day of the test, and follow-up steps for the day after the test. This comprehensive structure ensures that educators are fully prepared and supported at every stage of the assessment process, promoting consistency and quality in administration across all classrooms.
Evaluation for 2.1c
The Math Journeys grade 5 Spanish program provides printable versions of digital assessments to allow for flexible administration options and increase accessibility. Within each journey, the “Prueba del final de journey” section allows educators to download and print topic assessments by selecting them from the “Descargar imprimibles” dropdown menu. This feature ensures that educators can give assessments offline and accommodates students who may benefit from or require a paper-based format. However, the materials do not provide additional accessibility accommodations such as text-to-speech functionality, calculators, or language supports for assessment content.
The “Accommodations in Assessment” section of the Program Guide identifies accommodations embedded in the digital assessment platform, including text-to-speech functionality. However, calculators and content and language supports are not available on the platform. Additionally, the option to select a testing language does not constitute a content and language support because content and language supports are intended to provide linguistic scaffolds that help students access and demonstrate understanding of the assessed content. As a result, the indicator is only partially met because not all required accommodations are available and fully functional within the digital assessment platform.
Evaluation for 2.1d
The Atlas Math app provides students with a diagnostic placement test that is TEKS-aligned and includes digital questions with a variety of interactive item types, allowing students to show their understanding in multiple ways. Item types include multiple-choice, constructed-response, and number-line interaction items, representing more than two unique interactive item types. The levels of complexity vary as students demonstrate mastery or reveal learning gaps, ensuring that the diagnostic assessment is adjusted to capture each student’s level of understanding.
A variety of interactive question types in the diagnostic assessment allow students to demonstrate their understanding in multiple ways. The diagnostic assessment includes more than two unique interactive item types, such as multiple-choice, graphing, inline choice, hot spot, drag-and-drop, and fraction models. The variety of interactive item types ensures that students have multiple opportunities to show their understanding across different question formats while providing educators with meaningful, comprehensive data to inform instructional decisions and identify students’ entry points.
Evaluation for 2.1e
Throughout the activity section, students engage with TEKS-aligned questions that progress from foundational skills to higher levels of cognitive demand. Weekly Practice on Atlas Math provides additional opportunities for formative assessment through interactive item types, including drag-and-drop activities that allow students to demonstrate their understanding in varied ways. By incorporating questions with varying levels of complexity and multiple response formats, the formative assessments provide educators with meaningful evidence of student understanding that they can use to monitor progress and inform instructional decisions.
The “Wrap-up” section of each lesson overview contains a formative assessment that includes items from the printable log books, along with an answer key and educator guidance to support instructional decision-making. Across a given journey, the wrap-up activities incorporate at least three different question types and three levels of complexity. This shows that the formative assessments include more than two unique item formats and varying levels of cognitive demand. These assessment opportunities allow students to demonstrate their understanding in multiple ways while providing educators with meaningful evidence of learning in order to guide instructional decisions.
Evaluation for 2.2a
The placement test report sample provides detailed scoring information and guidance to help educators interpret student performance data. The report displays the individual student’s scores and identifies corresponding performance categories, including low, medium-low, medium-high, and high achievement levels. In addition to summarizing performance outcomes, the report offers recommendations for instructional placement based on assessment results. The guidance further emphasizes, “Use this report alongside what you see in class—student talk, written work, and tasks over time. Scores summarize performance on this instrument and administration. They can miss strengths that timed or online formats do not capture.” By combining assessment results with multiple sources of classroom evidence, the materials support informed, individualized instructional decisions that align with students’ learning needs.
The individual student placement test report provides detailed scoring information and guidance for interpreting student performance. The report displays scores by strand and process standard on a scale of 0–100 and organizes performance data by domain and proficiency level categorized as low, medium, or high. In addition, the report identifies the percentage of correct responses for each learning target. The “Suggested Instructional Focus” section at the bottom of the report provides guidance aligned with TEKS-tested skills rather than entire TEKS statements, recognizing that many standards encompass multiple learning targets. This level of specificity equips educators with actionable information to make informed, individualized instructional decisions based on each student’s identified areas of need.
Evaluation for 2.2b
The Placement Test Implementation Guide helps educators use diagnostic assessment results to understand trends in student performance and determine appropriate next steps for instruction. The guide outlines practical administration details, including the estimated testing time, the educator’s role during administration, and the recommended materials needed for implementation. By establishing consistent procedures and expectations for administration, the curriculum helps educators interpret assessment data, make decisions about instructional placement, and identify targeted supports for individual students as well as groups.
The placement test report sample helps educators use assessment results to plan purposeful tasks and activities aligned with the appropriate TEKS. The report contains a chart that displays the assessed TEKS, the process standards involved, the class percentage of correct responses, and the portion of correct responses for students using the Innovamat program. These data enable educators to identify class-wide performance trends and prioritize TEKS that require additional instructional attention. Furthermore, the “Placement in Journeys” section organizes students into a “Proposed Group Distribution” and recommends an appropriate journey entry point for each group. This information enables educators to respond directly to assessment data by assigning targeted tasks and activities that address the specific learning needs of individual students as well as groups.
Evaluation for 2.2c
The Math Journeys grade 5 Spanish program provides tools to help educators track students’ progress and growth. The Teacher Guide outlines the use of diagnostic, formative, and summative assessment to monitor students’ progress throughout the program. These tools allow educators to identify students’ strengths, address areas of need, and make informed instructional decisions. Students are also able to track their own progress and growth. When students engage in Weekly Practice on Atlas Math, the platform provides immediate feedback, allowing them to see how they are performing and monitor their understanding over time.
The Math Journeys grade 5 Spanish program provides progress monitoring tools on the digital platform that allow educators to track students’ progress and growth based on a general overview of progress as students work through the activities on the app. Students receive immediate feedback on their performance as they complete activities. However, the platform lacks a log or tracker that enables them to revisit and monitor their own progress and growth over time. Thus, this indicator is only partially met as the materials include tools for educators to track students’ progress but do not provide students with a dedicated tool to independently track and reflect on their own progress and growth over time.
Evaluation for 2.2d
Embedded guidance within activities 1 and 2 helps educators frequently check students’ understanding at key points during instruction. In the final step of the lesson, students collaborate to review one another’s responses, creating opportunities to identify and address errors and misconceptions together. This collaborative process also provides educators with an opportunity to observe students’ thinking in real time and address misconceptions before they move on to new learning.
The “Desenlace” section includes and links to a supported worksheet version for struggling students, enabling educators to identify misconceptions and respond to students’ needs in a timely manner. In addition, the “Apoyo” section at the end of each lesson provides recommendations for manipulatives and instructional strategies that help clarify concepts for students who require additional support. Together, these resources help educators monitor students’ understanding at key points during instruction and make responsive instructional adjustments as needed.
Evaluation for 2.2e
Educators can frequently check students’ understanding during the activities of a given lesson through embedded opportunities for formative assessment and immediate feedback during digital practice. Within activities, educators encounter strategically placed questions that help them monitor students’ understanding and provide opportunities to determine whether students are ready to move on to new content. During applet activities, students receive immediate feedback based on their responses, and the program adjusts the sequence of follow-up activities based on educator pacing and student performance.
The activities do not contain opportunities for adaptive checks to measure students’ understanding. Although the sequence of follow-up applet activities may be changed based on student performance, the current activity is not adjusted for the level of rigor, question types are not modified, and additional instructional supports are not provided in response to individual students’ answers. As a result, the activities of a given lesson allow educators to frequently check students’ understanding but do not provide full opportunities for adaptive checks that lead educators to adjust instruction in real time within 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 Math Journeys grade 5 Spanish program provides a comprehensive assessment system that clearly defines the purposes of diagnostic, formative, and summative assessment. Educators administer diagnostic assessments at the beginning of and throughout the year to establish a baseline understanding and monitor ongoing progress. Classroom activities involve daily formative assessments, enabling educators to continuously monitor students’ understanding during instruction. Educators administer summative assessments at the end of each journey to evaluate students’ learning and mastery of the concepts addressed. Collectively, these assessment types create a purposeful system for monitoring student progress and informing instructional decisions throughout the school year.
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 Math Journeys grade 5 Spanish program explains how to consistently and accurately administer the end-of-journey summative assessment. The End-of-Journey Test: Instructions and Guide provides educators with detailed, step-by-step instructions on how to administer the assessment. The guide is organized into three sections: preparation and expectations for the day before the test, procedures and instructions for the day of the test, and follow-up steps for the day after the test. This comprehensive structure ensures that educators are fully prepared and supported at every stage of the assessment process, promoting consistency and quality in administration across all 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 “Accommodations in Assessment” section of the Program Guide identifies accommodations embedded in the digital assessment platform, including text-to-speech functionality. However, calculators and content and language supports are not available on the platform. Additionally, the option to select a testing language does not constitute a content and language support because content and language supports are intended to provide linguistic scaffolds that help students access and demonstrate understanding of the assessed content. As a result, the indicator is only partially met because not all required accommodations are available and fully functional within the digital assessment platform.
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
A variety of interactive question types in the diagnostic assessment allow students to demonstrate their understanding in multiple ways. The diagnostic assessment includes more than two unique interactive item types, such as multiple-choice, graphing, inline choice, hot spot, drag-and-drop, and fraction models. The variety of interactive item types ensures that students have multiple opportunities to show their understanding across different question formats while providing educators with meaningful, comprehensive data to inform instructional decisions and identify students’ entry points.
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 “Wrap-up” section of each lesson overview contains a formative assessment that includes items from the printable log books, along with an answer key and educator guidance to support instructional decision-making. Across a given journey, the wrap-up activities incorporate at least three different question types and three levels of complexity. This shows that the formative assessments include more than two unique item formats and varying levels of cognitive demand. These assessment opportunities allow students to demonstrate their understanding in multiple ways while providing educators with meaningful evidence of learning in order to guide instructional decisions.
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 individual student placement test report provides detailed scoring information and guidance for interpreting student performance. The report displays scores by strand and process standard on a scale of 0–100 and organizes performance data by domain and proficiency level categorized as low, medium, or high. In addition, the report identifies the percentage of correct responses for each learning target. The “Suggested Instructional Focus” section at the bottom of the report provides guidance aligned with TEKS-tested skills rather than entire TEKS statements, recognizing that many standards encompass multiple learning targets. This level of specificity equips educators with actionable information to make informed, individualized instructional decisions based on each student’s identified areas of need.
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 sample helps educators use assessment results to plan purposeful tasks and activities aligned with the appropriate TEKS. The report contains a chart that displays the assessed TEKS, the process standards involved, the class percentage of correct responses, and the portion of correct responses for students using the Innovamat program. These data enable educators to identify class-wide performance trends and prioritize TEKS that require additional instructional attention. Furthermore, the “Placement in Journeys” section organizes students into a “Proposed Group Distribution” and recommends an appropriate journey entry point for each group. This information enables educators to respond directly to assessment data by assigning targeted tasks and activities that address the specific learning needs of individual students as well as groups.
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 Math Journeys grade 5 Spanish program provides progress monitoring tools on the digital platform that allow educators to track students’ progress and growth based on a general overview of progress as students work through the activities on the app. Students receive immediate feedback on their performance as they complete activities. However, the platform lacks a log or tracker that enables them to revisit and monitor their own progress and growth over time. Thus, this indicator is only partially met as the materials include tools for educators to track students’ progress but do not provide students with a dedicated tool to independently track and reflect on their own progress and growth over time.
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 “Desenlace” section includes and links to a supported worksheet version for struggling students, enabling educators to identify misconceptions and respond to students’ needs in a timely manner. In addition, the “Apoyo” section at the end of each lesson provides recommendations for manipulatives and instructional strategies that help clarify concepts for students who require additional support. Together, these resources help educators monitor students’ understanding at key points during instruction and make responsive instructional adjustments as needed.
2.2e
If designed to be adaptive, materials provide frequent checks for understanding at key points throughout each lesson or activity.
If designed to be adaptive, materials provide frequent checks for understanding at key points throughout each lesson or activity.
0 out of 1 points
Evaluation for 2.2e
Evaluation for 2.2e
If designed to be adaptive, materials provide frequent checks for understanding at key points throughout each lesson or activity.
0 out of 1 points
The activities do not contain opportunities for adaptive checks to measure students’ understanding. Although the sequence of follow-up applet activities may be changed based on student performance, the current activity is not adjusted for the level of rigor, question types are not modified, and additional instructional supports are not provided in response to individual students’ answers. As a result, the activities of a given lesson allow educators to frequently check students’ understanding but do not provide full opportunities for adaptive checks that lead educators to adjust instruction in real time within each lesson or activity.
Rubric Section 3
Supports for All Learners
Materials support educators in reaching all learners through design focused on engagement, representation, and action/expression for learner variability.
Total
91% (32 out of 35 points)
Evaluation for 3.1a
The Math Journeys grade 5 Spanish program guides educators to scaffold lessons and activities for students who have not yet reached proficiency in prerequisite or grade-level concepts and skills. Within each lesson, “Material de apoyo” resources are available in the right-side panel and can be printed and distributed to students who need additional scaffolding and support. These printable resources provide students with the foundational support required to access grade-level content and enable educators to differentiate instruction based on individual students’ needs.
The Math Journeys grade 5 Spanish program guides educators to support students who have not yet reached proficiency throughout each lesson. The “Desenlace” section of each lesson includes and links to a worksheet version with embedded supports for struggling students, providing an accessible entry point for students who need additional scaffolding to engage with the content. Furthermore, the “Apoyo” section at the end of each lesson provides educators with specific suggestions for manipulatives and strategies they can use to clarify concepts for students who need additional support. Together, these embedded supports ensure that educators receive the explicit guidance needed to identify and respond to the needs of students who have not yet reached proficiency in grade-level content and skills.
Evaluation for 3.1b
The Math Journeys grade 5 Spanish program explains how to use language supports to help students develop their academic vocabulary and access grade-level mathematical content. On the left-side panel of the platform, educators can access the “Adaptaciones lingüísticas” section, which includes a “Guía bilingüe/ESL” resource to help educators provide language scaffolds during instruction. This resource clarifies how to support students’ language development within the context of math instruction, ensuring that language barriers do not hinder students’ ability to access and engage with grade-level math content. Additionally, each lesson overview contains key vocabulary and cognates to help students develop their academic language during instruction.
Each lesson contains dedicated embedded supports for emergent bilingual (EB) students that identify specific moments throughout the lesson where the educator can reinforce important vocabulary words. Thus, the educator receives intentional, targeted guidance for supporting language development within the context of math instruction. For example, activity 1.1 provides sentence stems using key vocabulary to help students explain their mathematical thinking through oral discourse. The lesson also includes suggestions for educators to use gestures and visual representations to reinforce key vocabulary throughout instruction, ensuring that EB students have multiple opportunities to access and develop their academic language. These embedded supports show that the Math Journeys grade 5 Spanish program provides meaningful guidance for developing academic vocabulary and increasing comprehension. However, the program does not clearly explain how to pre-teach unfamiliar references in the text.
Evaluation for 3.1c
The Math Journeys grade 5 Spanish program provides educators with clear guidance on enrichment and extension activities for students who have shown proficiency in grade-level content and skills. In the “Desenlace” portion of each lesson, a dedicated section titled “Ampliación” explains how to offer extension activities and pose questions to students who have mastered the content. For example, in one lesson, the “Ampliación” extension activity directs educators to ask students to find the solution to an additional problem that was not solved during the lesson, thus challenging them to apply and extend their understanding beyond the core lesson objectives. This embedded guidance ensures that educators have the tools they need to keep students engaged and deepen learning for those who have demonstrated mastery of grade-level content and skills. Educators also receive explicit guidance on enrichment and extension activities for students who have shown proficiency in above grade-level content and skills.
The Math Journeys grade 5 Spanish program consistently supports advanced students by providing detailed guidance alongside targeted enrichment and extension activities. The “Recursos” section for lessons includes a printable “Ampliación” worksheet designed for students who have demonstrated proficiency in above grade-level content and skills. This resource effectively extends learning by tasking students with applying alternative numerical values and identifying patterns. Crucially, the materials pair this student-facing component with explicit guidance, equipping educators with clear instructional strategies to effectively implement and facilitate a given extension activity.
Evaluation for 3.1d
The Math Journeys grade 5 Spanish program does not meet the requirements of this indicator. The digital materials do not provide text-to-speech functionality, content and language supports, or calculators that educators can enable or disable to help individual students. Thus, the materials do not provide the embedded digital accessibility supports required by this indicator, and this indicator is not met.
The digital materials do not provide text-to-speech functionality, content and language supports, or digital calculators.
Evaluation for 3.1e
The Math Journeys grade 5 Spanish program explains how to offer options and supports to students so they can show their understanding of mathematical concepts in various ways. For example, in journey C1, lesson 14, grade 4, activity 1 includes pictures that allow students to visually connect to the story’s context, providing a concrete and visual representation of the mathematical concept before transitioning to an equation. This progression from visual representation to symbolic notation helps students demonstrate their understanding in multiple ways, moving from concrete pictorial understanding to abstract mathematical expression. This embedded support ensures that educators have the guidance needed to offer students multiple entry points to access and show their understanding of the mathematical content taught.
The Math Journeys grade 5 Spanish program explains how to offer options and supports to students so they can show their understanding of mathematical concepts in various ways. In one example, students are asked to practice multiplying numbers between one and 1,000 by single-digit numbers. The activities guide students through multiple modes of demonstration. In the first activity, students discuss a given problem, thus providing them with an opportunity to “express” their mathematical thinking through oral discourse. Students then use manipulatives and multiplicative frames to “represent” problems in a concrete, visual way. Finally, students represent and solve various problems using the area model, allowing them to “perform” their understanding through independent application.
Evaluation for 3.2a
The Math Journeys grade 5 Spanish program provides clear prompts and guidance to build students’ knowledge by activating their prior knowledge, highlighting patterns and relationships, and connecting mathematical ideas through multiple representations. In the grade 5 activities of a given lesson, students compare and order sums without calculating, explain strategies using place-value reasoning, and analyze incorrect solutions using number lines and equations. Educators ask questions that help students justify the relationships between numbers and operations while connecting symbolic expressions, visual models, and verbal reasoning.
The Math Journeys grade 5 Spanish program provides clear prompts and guidance to build students’ knowledge by activating their prior knowledge, anchoring big ideas, and highlighting and connecting relationships through multiple means of representation. Learning activities encourage students to analyze and compare mathematical relationships, explain their reasoning using conceptual understanding, and evaluate solution strategies through visual models, equations, and other representations. Educators also facilitate discussions and pose questions that promote mathematical justification, deepen conceptual understanding, and strengthen the connections among symbolic, visual, and verbal representations. Together, the embedded prompts and guidance ensure that educators are well equipped to help students build a deep, connected understanding of mathematical concepts throughout each lesson.
Evaluation for 3.2b
The Math Journeys grade 5 Spanish program explains how to effectively deliver and facilitate lessons using multiple instructional approaches within the static components of the program. Grade 5 lessons incorporate whole-group instruction, collaborative group activities, oral counting routines, movement-based learning, hands-on use of manipulatives, visual representations, independent practice, and mathematical discourse. The embedded “Apoyo” and “Ampliación” sections contain step-by-step guidance on facilitation, questioning prompts, and differentiated supports to increase student engagement and mathematical understanding. Together, these varied instructional approaches ensure that educators can deliver effective, engaging lessons that meet the diverse learning needs of all grade 5 students.
The Math Journeys grade 5 Spanish program explains how to effectively deliver and facilitate lessons using various instructional approaches within the static components of the program. In this lesson, students are asked to practice multiplying numbers between one and 1,000 by single-digit numbers. In activity 1, students discuss a given problem, providing them with an opportunity for mathematical discourse and collaborative learning. Students then use manipulatives and multiplicative frames to represent problems, incorporating a hands-on and visual instructional approach. Finally, students represent and solve various problems using the area model, helping them transition from concrete and visual representations to more abstract mathematical thinking. Together, these diverse teaching methods demonstrate that the curriculum provides educators with clear, specific guidance to effectively facilitate lessons using multiple instructional approaches throughout each lesson.
Evaluation for 3.2c
The Math Journeys grade 5 Spanish program contains multi-tiered intervention methods for various types of practice as well as structures with educator guidance to support effective implementation. The lessons include multiple types of practice, such as collaborative partner work and whole-group discussions embedded throughout the activities of a given lesson. Additionally, students engage in independent practice through individualized activities that are added when marking “Sesión completada,” thus providing them with self-paced practice opportunities based on their individual needs. The “Apoyo” and “Ampliación” sections embedded within the lessons provide educators with tiered guidance to scaffold instruction for students who need additional support or to extend learning for students who have demonstrated mastery. Together, these tiered supports and varied practice structures ensure that educators can meet the diverse learning needs of all students throughout each lesson.
The Math Journeys grade 5 Spanish program provides multi-tiered intervention methods through a variety of instructional practices and structures designed to support students’ diverse learning needs. Students have opportunities for guided, collaborative, independent, and educator-facilitated practice across whole-group, partner, and individual settings throughout the lessons. Educators receive implementation support through questioning strategies, manipulatives, models, and visual representations to facilitate effective instruction across multiple tiers of support. Furthermore, the embedded “Apoyo” and “Ampliación” sections contain differentiated supports that provide targeted intervention for students who need additional scaffolding as well as extension opportunities for students who have shown mastery. These differentiated supports and opportunities for independent application enable educators to assess students’ understanding and deliver targeted interventions when needed, ensuring that all students receive support at the appropriate level of instruction.
Evaluation for 3.2d
The Math Journeys grade 5 Spanish program contains enrichment and extension methods that support a variety of opportunities for student engagement throughout the lessons. The “Apoyo” and “Ampliación” sections, embedded within instructional activities, include differentiated supports, allowing educators to extend or scaffold learning based on individual student readiness and performance. The lessons also provide explicit guidance on effective implementation through questioning prompts, manipulatives, number lines, partner discussion, visual models, and opportunities for independent practice. For example, students solve problems using multiple strategies, calculate distances on number lines, compare solution methods, and justify their mathematical reasoning through whole-group, partner, and individual activities. These scaffolded supports and enrichment opportunities equip educators with the tools needed to differentiate instruction for grade 5 students while keeping students meaningfully engaged with grade-level mathematical concepts and skills.
The Math Journeys grade 5 Spanish program provides explicit guidance for enrichment and extension activities that support various forms of engagement for students who have shown proficiency in the content and skills taught. In the “Desenlace” portion of each lesson, a dedicated section titled “Ampliación” provides guidance on how to offer extension activities and pose questions to students who have mastered the content. For example, in one lesson, the “Ampliación” extension activity guides educators to ask students to explain what would happen if the initial number were different from the previous example, thus challenging students to apply their understanding by reasoning through a new scenario and extending their mathematical thinking beyond the core lesson objectives. This embedded guidance ensures that educators have the specific, actionable tools needed to keep students engaged and deepen learning for those who have demonstrated mastery of the content and skills taught.
Evaluation for 3.2e
Educators in the Math Journeys grade 5 Spanish program receive embedded prompts and guidance that support timely, responsive feedback during instruction. Within each lesson, a dedicated section beneath the activities provides them with prompts to use at key moments, such as when pausing to check for understanding, addressing misconceptions, or delivering immediate feedback in real time. This embedded support ensures that educators can respond to student thinking as it surfaces during the lesson, keeping students on track toward meeting lesson objectives.
The Math Journeys grade 5 Spanish lessons embed structured discussion points where educators prompt students to explain their thinking aloud, enabling educators to assess understanding in real time based on students’ responses. At these moments, educators receive guidance on what to expect to see and hear from students when they show understanding, creating clear checkpoints for delivering timely, targeted feedback. This detailed guidance helps educators recognize evidence of learning and respond meaningfully during instruction rather than afterward.
Evaluation for 3.3a
This guidance is not applicable because the program is not designed to be static.
Not applicable.
Evaluation for 3.3b
This guidance is not applicable to the program because it is not designed to be adaptive.
Not applicable.
Evaluation for 3.3c
The Math Journeys grade 5 Spanish program provides guidance on language support that educators can access within the “Gestor de aula.” By navigating to the “Adaptaciones lingüísticas” tab using the left-side panel, educators can locate documents for lesson-level language support within each journey. For example, within journey D6, the “Documentación” section contains the “Lesson-Level ELPS Companion.” Importantly, while this document references ELPS, it appears to be a direct translation of the English ELPS. In Texas, the ELPS are designed for EB students and do not apply to Spanish-language math instruction.
The Math Journeys grade 5 Spanish program contains implementation guidance to help educators use the materials effectively in state-approved bilingual programs. The ESL/Bilingual Implementation Guide provides detailed language instruction for each journey, highlighting specific routines, strategies, activities, and implementation guidance designed to support effective instruction within models of state-approved bilingual programs. This resource ensures that educators have the targeted, actionable guidance needed to effectively implement the curriculum in state-approved bilingual programs, thus supporting both language development and mathematical understanding for EB students.
Evaluation for 3.3d
The Math Journeys grade 5 Spanish program contains embedded guidance to help EB students develop their academic vocabulary, increase their comprehension, build background knowledge, and make cross-linguistic connections through oral and written discourse. Each lesson overview contains key academic vocabulary along with definitions and visual representations to help students develop mathematical language in Spanish. The “Antes de empezar” section of each lesson explains how to help students activate and build their background knowledge before introducing new content, ensuring that students are prepared to engage with grade-level mathematical concepts. Throughout the activities of a given lesson, embedded discussion prompts and opportunities for partner discussion help students develop and use academic language through oral discourse. Additionally, students engage in written discourse through the printable log books, in which they record and explain their mathematical thinking. The lesson vocabulary includes cognates, helping students make cross-linguistic connections between Spanish and English mathematical terms.
Each lesson contains dedicated embedded supports for EB students and provides educators with specific guidance to help them develop their academic vocabulary and make cross-linguistic connections through oral and written discourse. These embedded supports identify intentional moments throughout the lesson when educators can reinforce important vocabulary in meaningful, targeted ways. For example, activity 1.3 suggests that the educator record students’ statements using key vocabulary, helping them develop and apply academic language through oral and written discourse. Additionally, educators highlight cognates in Spanish to reinforce the meaning of key vocabulary, helping students make cross-linguistic connections between Spanish and English mathematical terms.
Evaluation for 3.3e
This guidance is not applicable because the program is not designed for dual language immersion (DLI) programs.
Not applicable.
3.1 Differentiation and Scaffolds
3.1a
Materials include explicit educator guidance for lessons or activities scaffolded for students who have not yet reached proficiency in prerequisite or grade-level concepts and skills.
Materials include explicit educator guidance for lessons or activities scaffolded for students who have not yet reached proficiency in prerequisite or grade-level concepts and skills.
1 out of 1 points
Evaluation for 3.1a
Evaluation for 3.1a
Materials include explicit educator guidance for lessons or activities scaffolded for students who have not yet reached proficiency in prerequisite or grade-level concepts and skills.
1 out of 1 points
The Math Journeys grade 5 Spanish program guides educators to support students who have not yet reached proficiency throughout each lesson. The “Desenlace” section of each lesson includes and links to a worksheet version with embedded supports for struggling students, providing an accessible entry point for students who need additional scaffolding to engage with the content. Furthermore, the “Apoyo” section at the end of each lesson provides educators with specific suggestions for manipulatives and strategies they can use to clarify concepts for students who need additional support. Together, these embedded supports ensure that educators receive the explicit guidance needed to identify and respond to the needs of students who have not yet reached proficiency in grade-level content and skills.
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
Each lesson contains dedicated embedded supports for emergent bilingual (EB) students that identify specific moments throughout the lesson where the educator can reinforce important vocabulary words. Thus, the educator receives intentional, targeted guidance for supporting language development within the context of math instruction. For example, activity 1.1 provides sentence stems using key vocabulary to help students explain their mathematical thinking through oral discourse. The lesson also includes suggestions for educators to use gestures and visual representations to reinforce key vocabulary throughout instruction, ensuring that EB students have multiple opportunities to access and develop their academic language. These embedded supports show that the Math Journeys grade 5 Spanish program provides meaningful guidance for developing academic vocabulary and increasing comprehension. However, the program does not clearly explain how to pre-teach unfamiliar references in the text.
3.1c
Materials include explicit educator guidance for enrichment and extension activities for students who have demonstrated proficiency in grade-level and above grade-level content and skills.
Materials include explicit educator guidance for enrichment and extension activities for students who have demonstrated proficiency in grade-level and above grade-level content and skills.
2 out of 2 points
Evaluation for 3.1c
Evaluation for 3.1c
Materials include explicit educator guidance for enrichment and extension activities for students who have demonstrated proficiency in grade-level and above grade-level content and skills.
2 out of 2 points
The Math Journeys grade 5 Spanish program consistently supports advanced students by providing detailed guidance alongside targeted enrichment and extension activities. The “Recursos” section for lessons includes a printable “Ampliación” worksheet designed for students who have demonstrated proficiency in above grade-level content and skills. This resource effectively extends learning by tasking students with applying alternative numerical values and identifying patterns. Crucially, the materials pair this student-facing component with explicit guidance, equipping educators with clear instructional strategies to effectively implement and facilitate a given extension activity.
3.1d
Digital materials include accommodations, including text-to-speech, content and language supports, and calculators that educators can enable or disable to support individual students.
Digital materials include accommodations, including text-to-speech, content and language supports, and calculators that educators can enable or disable to support individual students.
0 out of 3 points
Evaluation for 3.1d
Evaluation for 3.1d
Digital materials include accommodations, including text-to-speech, content and language supports, and calculators that educators can enable or disable to support individual students.
0 out of 3 points
The digital materials do not provide text-to-speech functionality, content and language supports, or digital calculators.
3.1e
Materials include educator guidance on offering options and supports for students to demonstrate understanding of mathematical concepts in various ways, such as perform, express, and represent.
Materials include educator guidance on offering options and supports for students to demonstrate understanding of mathematical concepts in various ways, such as perform, express, and represent.
2 out of 2 points
Evaluation for 3.1e
Evaluation for 3.1e
Materials include educator guidance on offering options and supports for students to demonstrate understanding of mathematical concepts in various ways, such as perform, express, and represent.
2 out of 2 points
The Math Journeys grade 5 Spanish program explains how to offer options and supports to students so they can show their understanding of mathematical concepts in various ways. In one example, students are asked to practice multiplying numbers between one and 1,000 by single-digit numbers. The activities guide students through multiple modes of demonstration. In the first activity, students discuss a given problem, thus providing them with an opportunity to “express” their mathematical thinking through oral discourse. Students then use manipulatives and multiplicative frames to “represent” problems in a concrete, visual way. Finally, students represent and solve various problems using the area model, allowing them to “perform” their understanding through independent application.
3.2 Instructional Methods
3.2a
Materials include explicit (direct) prompts and guidance for educators to build knowledge by activating prior knowledge, anchoring big ideas, and highlighting and connecting key patterns, features, and relationships through multiple means of representation.
Materials include explicit (direct) prompts and guidance for educators to build knowledge by activating prior knowledge, anchoring big ideas, and highlighting and connecting key patterns, features, and relationships through multiple means of representation.
5 out of 5 points
Evaluation for 3.2a
Evaluation for 3.2a
Materials include explicit (direct) prompts and guidance for educators to build knowledge by activating prior knowledge, anchoring big ideas, and highlighting and connecting key patterns, features, and relationships through multiple means of representation.
5 out of 5 points
The Math Journeys grade 5 Spanish program provides clear prompts and guidance to build students’ knowledge by activating their prior knowledge, anchoring big ideas, and highlighting and connecting relationships through multiple means of representation. Learning activities encourage students to analyze and compare mathematical relationships, explain their reasoning using conceptual understanding, and evaluate solution strategies through visual models, equations, and other representations. Educators also facilitate discussions and pose questions that promote mathematical justification, deepen conceptual understanding, and strengthen the connections among symbolic, visual, and verbal representations. Together, the embedded prompts and guidance ensure that educators are well equipped to help students build a deep, connected understanding of mathematical concepts throughout each lesson.
3.2b
If designed to be static, materials include educator guidance for effective lesson delivery and facilitation using various instructional approaches.
If designed to be static, materials include educator guidance for effective lesson delivery and facilitation using various instructional approaches.
2 out of 2 points
Evaluation for 3.2b
Evaluation for 3.2b
If designed to be static, materials include educator guidance for effective lesson delivery and facilitation using various instructional approaches.
2 out of 2 points
The Math Journeys grade 5 Spanish program explains how to effectively deliver and facilitate lessons using various instructional approaches within the static components of the program. In this lesson, students are asked to practice multiplying numbers between one and 1,000 by single-digit numbers. In activity 1, students discuss a given problem, providing them with an opportunity for mathematical discourse and collaborative learning. Students then use manipulatives and multiplicative frames to represent problems, incorporating a hands-on and visual instructional approach. Finally, students represent and solve various problems using the area model, helping them transition from concrete and visual representations to more abstract mathematical thinking. Together, these diverse teaching methods demonstrate that the curriculum provides educators with clear, specific guidance to effectively facilitate lessons using multiple instructional approaches throughout each lesson.
3.2c
Materials include multi-tiered intervention methods for various types of practice and structures and educator guidance to support effective implementation.
Materials include multi-tiered intervention methods for various types of practice and structures and educator guidance to support effective implementation.
3 out of 3 points
Evaluation for 3.2c
Evaluation for 3.2c
Materials include multi-tiered intervention methods for various types of practice and structures and educator guidance to support effective implementation.
3 out of 3 points
The Math Journeys grade 5 Spanish program provides multi-tiered intervention methods through a variety of instructional practices and structures designed to support students’ diverse learning needs. Students have opportunities for guided, collaborative, independent, and educator-facilitated practice across whole-group, partner, and individual settings throughout the lessons. Educators receive implementation support through questioning strategies, manipulatives, models, and visual representations to facilitate effective instruction across multiple tiers of support. Furthermore, the embedded “Apoyo” and “Ampliación” sections contain differentiated supports that provide targeted intervention for students who need additional scaffolding as well as extension opportunities for students who have shown mastery. These differentiated supports and opportunities for independent application enable educators to assess students’ understanding and deliver targeted interventions when needed, ensuring that all students receive support at the appropriate level of instruction.
3.2d
Materials include enrichment and extension methods that support various forms of engagement, and guidance to support educators in effective implementation.
Materials include enrichment and extension methods that support various forms of engagement, and guidance to support educators in effective implementation.
2 out of 2 points
Evaluation for 3.2d
Evaluation for 3.2d
Materials include enrichment and extension methods that support various forms of engagement, and guidance to support educators in effective implementation.
2 out of 2 points
The Math Journeys grade 5 Spanish program provides explicit guidance for enrichment and extension activities that support various forms of engagement for students who have shown proficiency in the content and skills taught. In the “Desenlace” portion of each lesson, a dedicated section titled “Ampliación” provides guidance on how to offer extension activities and pose questions to students who have mastered the content. For example, in one lesson, the “Ampliación” extension activity guides educators to ask students to explain what would happen if the initial number were different from the previous example, thus challenging students to apply their understanding by reasoning through a new scenario and extending their mathematical thinking beyond the core lesson objectives. This embedded guidance ensures that educators have the specific, actionable tools needed to keep students engaged and deepen learning for those who have demonstrated mastery of the content and skills taught.
3.2e
Materials include prompts and guidance to support educators in providing timely feedback during lesson delivery.
Materials include prompts and guidance to support educators in providing timely feedback during lesson delivery.
2 out of 2 points
Evaluation for 3.2e
Evaluation for 3.2e
Materials include prompts and guidance to support educators in providing timely feedback during lesson delivery.
2 out of 2 points
The Math Journeys grade 5 Spanish lessons embed structured discussion points where educators prompt students to explain their thinking aloud, enabling educators to assess understanding in real time based on students’ responses. At these moments, educators receive guidance on what to expect to see and hear from students when they show understanding, creating clear checkpoints for delivering timely, targeted feedback. This detailed guidance helps educators recognize evidence of learning and respond meaningfully during instruction rather than afterward.
3.3 Support for Emergent Bilingual Students
3.3a
If designed to be static, materials include educator guidance on providing and incorporating linguistic accommodations for all levels of language proficiency [as defined by the English Language Proficiency Standards (ELPS)], which are designed to engage students in using increasingly more academic language.
If designed to be static, materials include educator guidance on providing and incorporating linguistic accommodations for all levels of language proficiency [as defined by the English Language Proficiency Standards (ELPS)], which are designed to engage students in using increasingly more academic language.
Not applicable.
Evaluation for 3.3a
Evaluation for 3.3a
If designed to be static, materials include educator guidance on providing and incorporating linguistic accommodations for all levels of language proficiency [as defined by the English Language Proficiency Standards (ELPS)], which are designed to engage students in using increasingly more academic language.
Not applicable.
Not applicable.
3.3b
If designed to be adaptive, materials include embedded linguistic accommodations for all levels of language proficiency [as defined by the English Language Proficiency Standards (ELPS)], which are designed to engage students in using increasingly more academic language.
If designed to be adaptive, materials include embedded linguistic accommodations for all levels of language proficiency [as defined by the English Language Proficiency Standards (ELPS)], which are designed to engage students in using increasingly more academic language.
Not applicable.
Evaluation for 3.3b
Evaluation for 3.3b
If designed to be adaptive, materials include embedded linguistic accommodations for all levels of language proficiency [as defined by the English Language Proficiency Standards (ELPS)], which are designed to engage students in using increasingly more academic language.
Not applicable.
Not applicable.
3.3c
Materials include implementation guidance to support educators in effectively using the materials in state-approved bilingual/ESL programs.
Materials include implementation guidance to support educators in effectively using the materials in state-approved bilingual/ESL programs.
1 out of 1 points
Evaluation for 3.3c
Evaluation for 3.3c
Materials include implementation guidance to support educators in effectively using the materials in state-approved bilingual/ESL programs.
1 out of 1 points
The Math Journeys grade 5 Spanish program contains implementation guidance to help educators use the materials effectively in state-approved bilingual programs. The ESL/Bilingual Implementation Guide provides detailed language instruction for each journey, highlighting specific routines, strategies, activities, and implementation guidance designed to support effective instruction within models of state-approved bilingual programs. This resource ensures that educators have the targeted, actionable guidance needed to effectively implement the curriculum in state-approved bilingual programs, thus supporting both language development and mathematical understanding for EB students.
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
Each lesson contains dedicated embedded supports for EB students and provides educators with specific guidance to help them develop their academic vocabulary and make cross-linguistic connections through oral and written discourse. These embedded supports identify intentional moments throughout the lesson when educators can reinforce important vocabulary in meaningful, targeted ways. For example, activity 1.3 suggests that the educator record students’ statements using key vocabulary, helping them develop and apply academic language through oral and written discourse. Additionally, educators highlight cognates in Spanish to reinforce the meaning of key vocabulary, helping students make cross-linguistic connections between Spanish and English mathematical terms.
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.
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
100% (16 out of 16 points)
Evaluation for 4.1a
In grade 5, a lesson on powers and exponential growth within journey E1 provides practice opportunities that require students to demonstrate a depth of understanding aligned with the TEKS. During the “Planteamiento,” students reflect on exponential growth through a real-world pictorial model, engaging in a concrete, visual exploration of the concept. In activity 1, students determine the result of problems involving powers of 10 and connect the concept to expanded notation, bridging pictorial and abstract mathematical thinking. The “Desenlace” extends this progression by incorporating real-world examples, calculator use, and additional pictorial models, ensuring that students engage with the concept across multiple modalities and increasing levels of complexity. This structured movement across concrete, representational, and abstract levels in a single lesson shows that practice opportunities in the curriculum are aligned with the full rigor of the TEKS.
The Math Journeys grade 5 Spanish program provides practice opportunities throughout the broader learning pathway that require students to demonstrate a depth of understanding aligned with the TEKS, such as representing integers using counters, analyzing equivalent and irreducible representations, and explaining the relationships between positive and negative quantities. The lessons also embed instructional assessments that require students to show a depth of understanding aligned with the TEKS, including individual, partner, and group tasks in which students justify, represent, and apply their understanding of integer models.
Evaluation for 4.1b
The Math Journeys grade 5 Spanish program contains questions and tasks that increase in rigor and complexity, leading to grade-level proficiency in the mathematics TEKS. Within each lesson, the progression of activities is designed to increase in complexity, beginning with pictorial and concrete representations in activity 1 and gradually moving toward more abstract and representational mathematical thinking in activity 2 as well as the “Desenlace.” This structured progression ensures that students are consistently challenged at increasing levels of rigor as they move through each lesson. Additionally, the “Ampliación” section embedded within the “Desenlace” provides extension activities that increase in rigor and complexity beyond the core lesson objectives, challenging students who have shown grade-level proficiency to deepen their mathematical understanding.
The Math Journeys grade 5 Spanish program includes opportunities for students to build upon their prior knowledge as lessons increase in rigor. For example, in journey D4, lesson 14, students begin by estimating the placement of given fractions on a number line before building upon that knowledge by estimating answers to addition of fractions problems involving unlike denominators. Rather than focusing on finding exact answers, students apply logic and their prior knowledge about fractions to estimate reasonable solutions. This progression leads to the “Desenlace,” where students apply their estimation skills to real-world word problems. The “Apoyo” and “Ampliación” sections further demonstrate an increase in rigor by guiding educators to extend their questioning as well as prompting students to find different ways to obtain the same outcome.
Evaluation for 4.2a
The Math Journeys grade 5 Spanish program demonstrates coherence across concepts horizontally within the grade level by connecting patterns, big ideas, and relationships. In pathway C4, “Mastering Division: Bridging Strategies and Algorithms,” lesson 6, “Productive Practice: Sharing I,” tasks connect multiplication and division concepts across the lesson. During the warm-up, students analyze images to identify how distinct multiplication equations produce identical products, recognizing patterns within number sets. In the development activity, the materials link multiplication to division by presenting division as the operational inverse of equal groups, connecting concrete representations to abstract partial quotients.
The Math Journeys grade 5 Spanish program demonstrates coherence horizontally across grade bands. The “Vista general de tramo” explains the progression of concepts across previous, current, and future learning clusters within a given topic. For example, the cluster D document, “Números racionales,” explains that in the previous cluster, students worked with whole numbers, grouping units into rectangular arrays, and understanding a group as a single unit that can be repeated. In the current cluster, students build upon that foundation by recognizing that a whole can be divided into equal parts and begin exploring the connections between fractions, decimals, and percentages. The following cluster then extends this understanding by emphasizing a more abstract approach to these concepts and introducing abstract systems such as integers and powers, demonstrating a coherent progression that builds from previous concepts toward more complex mathematical ideas.
Evaluation for 4.2b
The Math Journeys grade 5 Spanish program demonstrates coherence vertically across concepts and grade bands by connecting patterns, big ideas, and relationships. Across grade levels, the materials build multiplication concepts along a strategic progression of learning. In pathway C1, lesson 14, grade 3 students develop foundational multiplication concepts using concrete and representational tools. These concepts are extended in pathway C3, lesson 14, where grade 5 students apply area models to multiply and transition to the standard algorithm. This vertical progression allows students to see multiplication as a continuous, connected idea that deepens in complexity across grade bands, rather than as a set of isolated skills.
The Math Journeys grade 5 Spanish program demonstrates coherence vertically across grade levels. For example, in journey D4, lesson 10, students begin by reviewing the addition of fractions with common denominators before building on that knowledge by simplifying results using both division and pictorial models. Students are then guided through problems involving the addition of fractions with unlike denominators, connecting to their prior learning that both fractions must share a common denominator before adding. In this context, students recognize that it makes sense to express tenths as hundredths by finding an equivalent fraction, thus applying their previous knowledge of common factors and like denominators to a more complex problem situation. The materials demonstrate coherence vertically across grade levels by requiring students to draw upon foundational skills and extend them toward the addition of fractions with unlike denominators.
Evaluation for 4.2c
The Math Journeys grade 5 Spanish program demonstrates coherence across lessons by connecting students’ prior knowledge of concepts and procedures to the mathematical concepts to be learned in the current grade level as well as future grade levels. In grade 5, students apply a problem-solving model to a contextual grouping situation involving 32 tokens. Students draw on their prior understanding of equal groups and division to analyze the given information, formulate a strategy, and determine how many complete groups can be formed. To enable students to justify their reasoning by connecting their prior knowledge of remainders and divisibility to the current problem’s context and thus work toward more complex division and algebraic reasoning in future grade levels, educators use prompts such as “¿Qué ocurre cuando no puedes formar otro grupo completo de 5 fichas?” and “¿Podrías explicar por qué sobran 2 fichas al agruparlas de 5 en 5 y no sobra ninguna al agruparlas de 4 en 4?”
The Math Journeys grade 5 Spanish program demonstrates coherence across lessons and activities by connecting students’ prior knowledge of concepts and procedures to current and future mathematical learning. For example, lessons build on students’ prior understanding of the order of operations with whole numbers to extend these concepts to integers, reinforcing procedures such as applying the hierarchy of operations and using parentheses. The materials support future learning by having students apply these procedures in problem-solving contexts and develop flexible reasoning with expressions, preparing them for more advanced algebraic thinking and the evaluation of expressions. These connections create a clear progression of concepts and procedures, helping students link their prior knowledge to current learning and thus preparing them for future mathematical concepts.
Evaluation for 4.3a
The Math Journeys grade 5 Spanish program contains spaced retrieval opportunities involving previously learned skills and concepts across the learning pathways. Lessons are structured around the “Planteamiento,” followed by development activities, and conclude with the “Desenlace,” which wraps up the current lesson’s learning. This consistent structure focuses on introducing and practicing new concepts within the lesson while including intentional opportunities for students to retrieve skills and concepts from earlier pathways at a later point in time. As a result, the materials provide opportunities for spaced retrieval of previously learned skills and concepts across the learning pathways.
The Math Journeys grade 5 Spanish program provides opportunities for spaced retrieval involving previously learned skills and concepts across the learning pathways. For example, lessons revisit students’ prior understanding of powers by having them calculate and analyze powers of 2, such as noticing patterns in the last digits (2, 4, 8, 6) and applying previously learned computation strategies across multiple tasks. Educators also reinforce previously learned concepts such as patterns and place value by engaging students in analyzing regularities, including adding zeros in powers and base 10 relationships, thus supporting opportunities for spaced retrieval across contexts and promoting deeper conceptual understanding.
Evaluation for 4.3b
The Math Journeys grade 5 Spanish program provides opportunities for interleaved practice with previously learned skills and concepts across the learning pathways. As an adaptive program, the curriculum is designed to mix previously learned skills and concepts within practice sessions based on student performance and progress. Throughout the reviewed lessons, the materials interleave multiplication and division concepts across the pathways, as evidenced in pathway C1, lesson 1, where doubling concepts connect to place-value skills, and in pathway C2, lesson 2, where multiplicative comparison is practiced alongside additive reasoning. In pathway C3, lesson 14, and pathway C4, lesson 6, the materials continue to interleave previously learned multiplication concepts with area models and division strategies. This requires students to draw upon skills from earlier pathways to engage with new content. This adaptive design ensures that students practice previously learned skills and concepts alongside new learning, rather than in isolation.
The Math Journeys grade 5 Spanish program provides students with opportunities to develop procedural fluency and conceptual understanding through distributed practice. For example, students repeatedly apply division strategies by using known facts (such as 100 ÷ 6 and 70 ÷ 7) to deduce unknown results (such as 99 ÷ 6 and 78 ÷ 7), thereby strengthening their fluency with quotients and remainders. The lessons also deepen conceptual understanding by connecting division to equal groups, multiplication relationships, and decomposition, thus integrating reasoning about the structure of division with procedural practice across multiple tasks.
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
The Math Journeys grade 5 Spanish program provides practice opportunities throughout the broader learning pathway that require students to demonstrate a depth of understanding aligned with the TEKS, such as representing integers using counters, analyzing equivalent and irreducible representations, and explaining the relationships between positive and negative quantities. The lessons also embed instructional assessments that require students to show a depth of understanding aligned with the TEKS, including individual, partner, and group tasks in which students justify, represent, and apply their understanding of integer models.
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.
4 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.
4 out of 4 points
The Math Journeys grade 5 Spanish program includes opportunities for students to build upon their prior knowledge as lessons increase in rigor. For example, in journey D4, lesson 14, students begin by estimating the placement of given fractions on a number line before building upon that knowledge by estimating answers to addition of fractions problems involving unlike denominators. Rather than focusing on finding exact answers, students apply logic and their prior knowledge about fractions to estimate reasonable solutions. This progression leads to the “Desenlace,” where students apply their estimation skills to real-world word problems. The “Apoyo” and “Ampliación” sections further demonstrate an increase in rigor by guiding educators to extend their questioning as well as prompting students to find different ways to obtain the same outcome.
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
The Math Journeys grade 5 Spanish program demonstrates coherence horizontally across grade bands. The “Vista general de tramo” explains the progression of concepts across previous, current, and future learning clusters within a given topic. For example, the cluster D document, “Números racionales,” explains that in the previous cluster, students worked with whole numbers, grouping units into rectangular arrays, and understanding a group as a single unit that can be repeated. In the current cluster, students build upon that foundation by recognizing that a whole can be divided into equal parts and begin exploring the connections between fractions, decimals, and percentages. The following cluster then extends this understanding by emphasizing a more abstract approach to these concepts and introducing abstract systems such as integers and powers, demonstrating a coherent progression that builds from previous concepts toward more complex mathematical ideas.
4.2b
Materials demonstrate coherence vertically across concepts and grade bands, including connections from grade K–6, by connecting patterns, big ideas, and relationships.
Materials demonstrate coherence vertically across concepts and grade bands, including connections from grade K–6, 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 grade K–6, by connecting patterns, big ideas, and relationships.
1 out of 1 points
The Math Journeys grade 5 Spanish program demonstrates coherence vertically across grade levels. For example, in journey D4, lesson 10, students begin by reviewing the addition of fractions with common denominators before building on that knowledge by simplifying results using both division and pictorial models. Students are then guided through problems involving the addition of fractions with unlike denominators, connecting to their prior learning that both fractions must share a common denominator before adding. In this context, students recognize that it makes sense to express tenths as hundredths by finding an equivalent fraction, thus applying their previous knowledge of common factors and like denominators to a more complex problem situation. The materials demonstrate coherence vertically across grade levels by requiring students to draw upon foundational skills and extend them toward the addition of fractions with unlike denominators.
4.2c
Materials demonstrate coherence across lessons or activities by connecting students’ prior knowledge of concepts and procedures to the mathematical concepts to be learned in the current grade level and future grade levels.
Materials demonstrate coherence across lessons or activities by connecting students’ prior knowledge of concepts and procedures to the mathematical concepts to be learned in the current grade level and future grade levels.
4 out of 4 points
Evaluation for 4.2c
Evaluation for 4.2c
Materials demonstrate coherence across lessons or activities by connecting students’ prior knowledge of concepts and procedures to the mathematical concepts to be learned in the current grade level and future grade levels.
4 out of 4 points
The Math Journeys grade 5 Spanish program demonstrates coherence across lessons and activities by connecting students’ prior knowledge of concepts and procedures to current and future mathematical learning. For example, lessons build on students’ prior understanding of the order of operations with whole numbers to extend these concepts to integers, reinforcing procedures such as applying the hierarchy of operations and using parentheses. The materials support future learning by having students apply these procedures in problem-solving contexts and develop flexible reasoning with expressions, preparing them for more advanced algebraic thinking and the evaluation of expressions. These connections create a clear progression of concepts and procedures, helping students link their prior knowledge to current learning and thus preparing them for future mathematical concepts.
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 Math Journeys grade 5 Spanish program provides opportunities for spaced retrieval involving previously learned skills and concepts across the learning pathways. For example, lessons revisit students’ prior understanding of powers by having them calculate and analyze powers of 2, such as noticing patterns in the last digits (2, 4, 8, 6) and applying previously learned computation strategies across multiple tasks. Educators also reinforce previously learned concepts such as patterns and place value by engaging students in analyzing regularities, including adding zeros in powers and base 10 relationships, thus supporting opportunities for spaced retrieval across contexts and promoting deeper conceptual understanding.
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 Math Journeys grade 5 Spanish program provides students with opportunities to develop procedural fluency and conceptual understanding through distributed practice. For example, students repeatedly apply division strategies by using known facts (such as 100 ÷ 6 and 70 ÷ 7) to deduce unknown results (such as 99 ÷ 6 and 78 ÷ 7), thereby strengthening their fluency with quotients and remainders. The lessons also deepen conceptual understanding by connecting division to equal groups, multiplication relationships, and decomposition, thus integrating reasoning about the structure of division with procedural practice across multiple tasks.
Rubric Section 5
Balance of Conceptual and Procedural Understanding
Materials are designed to balance conceptual understanding, procedural skills, and fluency.
Total
100% (38 out of 38 points)
Evaluation for 5.1a
The Math Journeys grade 5 Spanish program contains questions and tasks that require students to interpret, analyze, and evaluate models and representations for mathematical concepts and situations. Students interpret models and representations as they use area models, numerical expressions, and place value to make sense of decimal multiplication and the meaning of products. They analyze models and representations by connecting area models to multiplication strategies, examining patterns when multiplying by powers of 10, and relating representations across units. Students also evaluate models and representations as they use estimation and contextual reasoning to determine the reasonableness of results, justify placement of the decimal point, and critique procedural approaches that do not reflect underlying mathematical relationships.
The Math Journeys grade 5 Spanish program contains questions and tasks that require students to interpret, analyze, and evaluate models and representations for mathematical concepts and situations. Students interpret models and representations as they make sense of visual and contextual models, including groups, area representations, and fraction pieces, to understand multiplication of a whole number by a fraction. They analyze models and representations by comparing equivalent representations, decomposing fractions, and connecting visual models to multiplicative equations. Students also evaluate models and representations as they justify whether representations are equivalent or appropriate, determine which contexts correctly match a given multiplication, and defend their reasoning using visual and contextual evidence.
Evaluation for 5.1b
The Math Journeys grade 5 Spanish program includes questions and tasks that provide students with opportunities to create concrete models and pictorial representations in order to represent mathematical situations. Students create concrete models as they use fraction-circle pieces to physically build all possible decompositions of a fraction, representing repeated equal parts through hands-on manipulation. Students then create pictorial representations by drawing their groupings on their Magic Pads before writing the corresponding multiplication equation. This sequence of manipulating, drawing, and recording requires students to create both concrete and pictorial representations of the mathematical situation presented.
The Math Journeys grade 5 Spanish program contains questions and tasks that provide students with opportunities to create concrete models and pictorial representations in order to represent mathematical situations. Students create concrete models using fraction pieces and manipulatives to represent and combine fractions, making their understanding of denominators and equivalent fractions visible. Students also create pictorial representations, such as shaded figures and visual fraction models, to justify why common denominators are needed and how fractions are combined.
Evaluation for 5.1c
The Math Journeys grade 5 Spanish program contains questions and tasks that provide students with opportunities to apply their conceptual understanding to new problem situations and contexts. For example, students apply their understanding of decimal numbers and place value within the context of measurement by converting and representing lengths using decimal notation. Students interpret measurements, compare values, and connect expanded forms to real-world contexts, such as expressing 1.395 m as 1 m + 3 dm + 9 cm + 5 mm, thus demonstrating a transfer of understanding across representations and extending conceptual understanding beyond abstract computation to meaningful, contextualized situations.
The Math Journeys grade 5 Spanish program contains questions and tasks that provide students with opportunities to apply their conceptual understanding to new problem situations and contexts. For example, in development activity 1, students encounter a word problem about plant growth that requires them to apply fraction addition in a new measurement context. Students transfer the “Jumping along the Number Line” strategy from abstract practice to a real-world situation by determining the total height of a sprout that measured 3/8 inch and grew 4/8 inches more. The lesson guide supports this transfer by prompting students to consider how 3/8 + 4/8 helps them answer the question about how tall the plant is now.
Evaluation for 5.2a
The Math Journeys grade 5 Spanish program provides students with opportunities to develop and demonstrate procedural fluency. For example, the “Desenlace” independent work tasks students with repeatedly creating and solving addition and subtraction equations using number cards across four progressively focused tasks, thus providing the volume of practice needed to build automaticity with common denominator procedures. The Teacher Guide notes that an efficient strategy is to keep denominators the same across equations, allowing students to reuse the common denominator they calculated and reinforcing fluency through repeated application. Tasks 3 and 4 extend practice to subtraction and require students to find equations with matching results, thereby sustaining engagement while building accurate and automatic computation across both operations.
The Math Journeys grade 5 Spanish program provides students with opportunities to develop and demonstrate procedural fluency. For example, in applet 147, students solve multi-operation equations by applying the correct order of operations, building fluency and automaticity through repeated practice. The activity reinforces the importance of procedural accuracy by allowing students to observe how significantly a result changes when they do not follow the correct order of operations. This task provides the fluency needed to complete grade-level mathematical tasks by requiring students to automatically identify and apply the order of operations, thus supporting greater accuracy and efficiency in solving complex expressions.
Evaluation for 5.2b
The Math Journeys grade 5 Spanish program provides students with opportunities to develop and demonstrate flexibility in procedural competency. For example, the “Planteamiento” directs educators to have students solve 3 × 2/9 and identify all equivalent multiplication expressions. This requires flexible, accurate application of the procedure across multiple forms. Activity 1 then asks students to solve 1/3 × 6 using two different approaches—the fraction-of-a-set strategy and the commutative property—practicing flexible procedure application for the same problem type. Activity 2 reinforces this flexibility by presenting parallel word problems solved with 8 × 3/4 and 3/4 × 8, directing students to confirm identical results across both representations, and deepening their understanding of procedural equivalence.
The Math Journeys grade 5 Spanish program provides students with opportunities to develop and demonstrate flexibility in procedural competency. For example, activity 1.2 surfaces two solution paths for 2 ÷ 1/5—repeated grouping with the Fraction Pieces widget and recognizing the multiplication pattern—and asks students to evaluate which approach is more efficient. Activity 1.3 extends the same comparison to 2 ÷ 1/3, requiring students to evaluate accuracy by checking their results against the multiplicative frame. Activity 2 deepens this flexibility by asking students to assess whether multiplying by the denominator is always a valid strategy. This requires evaluating a generalized procedure for accuracy and reinforces the importance of both strategic efficiency and procedural reliability across division tasks.
Evaluation for 5.2c
The Math Journeys grade 5 Spanish program provides students with opportunities to evaluate the reasonableness of their results and the efficiency of their procedures. For example, activity 1 surfaces two distinct approaches to 1/3 × 6 and asks students to compare them for similarities and differences, requiring that strategies be evaluated for flexibility. Activity 2 presents the same problem as both “8 times 3/4 of an hour” and “3/4 of 8 hours,” directing students to evaluate whether both representations yield accurate outcomes. The Teacher Guide concludes by asking educators to have students evaluate which interpretation is more efficient for a given context, thus reinforcing the importance of both procedural accuracy and strategic efficiency across multiple representations of the same problem.
The Math Journeys grade 5 Spanish program provides students with opportunities to evaluate the reasonableness of their results and the efficiency of their procedures. For example, activity 1.2 surfaces two solution paths for 2 ÷ 1/5—repeated grouping with the Fraction Pieces widget and recognizing the multiplication pattern—and asks students to evaluate which approach yields the most reasonable and efficient outcome. Activity 1.3 extends the same comparison to 2 ÷ 1/3, requiring students to evaluate the accuracy of their results by checking them against the multiplicative frame. Activity 2 reinforces this by asking students to assess whether multiplying by the denominator is always a valid strategy. This requires students to evaluate a generalized procedure for reasonableness and accuracy across division tasks.
Evaluation for 5.2d
The Math Journeys grade 5 Spanish program provides students with opportunities to apply procedural fluency by selecting and using the most efficient strategy for a given problem. For example, activity 1 guides students from representing 1/3 × 6 with manipulatives to applying the commutative property and then interpreting the outcome as “one-third of a set,” thereby scaffolding students toward increasingly efficient approaches. To direct students to reflect on and select the most efficient strategy for a given problem, the Teacher Guide supports the progression by having the educator ask students, “Which approach helped you solve faster?” Additionally, the platform tracks strategy choices and recommends more efficient approaches based on problem complexity, thus reinforcing the development of strategic efficiency across multiplication tasks.
The Math Journeys grade 5 Spanish program provides students with opportunities to apply procedural fluency by selecting and using the most efficient strategy for a given problem. For example, activity 1.2 guides students from using the Fraction Pieces widget toward recognizing that each liter fills five glasses, thus supporting the selection of multiplication by the denominator as the more efficient approach. Activity 2 then presents the statement “to divide a whole number by a unit fraction, multiply by the denominator” and asks students to evaluate whether it is always true, guiding them to internalize an efficient general strategy and reinforcing the importance of selecting and applying the most effective procedure based on the structure of the problem.
Evaluation for 5.3a
The Math Journeys grade 5 Spanish program explains how the TEKS’ conceptual and procedural emphases are addressed. A lesson on decimal addition presents a contextualized situation in which students determine the total length of three ribbons measuring 9 cm, 8.3 cm, and 3.8 cm placed end to end, linking a conceptual understanding of decimal addition to a real-world measurement context. The curriculum addresses the procedural emphasis by prompting students to identify and apply multiple strategies for adding three numbers, such as using a vertical alignment scheme or adding two numbers first and then adding the third. The lesson provides a visual of decimals aligned by place value to support accurate addition and concludes by confirming that the total length of the three ribbons is 21.1 cm, creating a clear connection between the contextualized situation, the visual representation, and the abstract procedural strategy. This explicit link between the conceptual and procedural emphases within a single lesson shows that the Math Journeys grade 5 Spanish program addresses both dimensions of the TEKS as required by the criterion.
The Math Journeys grade 5 Spanish program explains how the conceptual and procedural emphases of the TEKS are addressed. For example, the lesson addresses the conceptual emphasis by helping students develop their understanding of multiplying decimals through the area model and connections to place value, highlighting the reasoning behind the operation by interpreting decimal multiplication as area and scaling. The lesson simultaneously addresses the procedural emphasis by guiding students to compute products of decimals using models, estimation, and the algorithm. By connecting a conceptual understanding through area models and reasoning with procedural skills through accurate calculation and application, the curriculum clearly communicates both components of the TEKS emphases within the lesson.
Evaluation for 5.3b
In grade 5, a lesson on division provides students with opportunities to use concrete, pictorial, and abstract models as required by the TEKS. Students begin by physically manipulating 200 interlocking cubes, grouped into towers of 10, and distributing them equally among nine towers to build a hands-on understanding of division through equal sharing. The materials connect this concrete experience to a pictorial representation through a triangle-shaped visual displaying two known numbers and one unknown number, thus helping students identify the relationship between the values. The lesson then transitions to abstract representation by recording each step of the distribution process using a condensed division scheme, creating a direct bridge between the concrete manipulation of cubes and the symbolic, algorithmic representation of division. This deliberate progression across concrete, pictorial, and abstract models in a single lesson demonstrates that the Math Journeys grade 5 Spanish program provides students with opportunities to engage with the full representational continuum required by the TEKS.
The Math Journeys grade 5 Spanish program gives students consistent opportunities to use concrete models, pictorial representations, and abstract models as required by the TEKS. For example, students engage with concrete models by using fraction pieces to physically combine and transform fractions when they find common denominators. Students then connect these hands-on experiences to pictorial representations by visualizing fractions with fraction circles and models to compare, decompose, and represent equivalent fractions. Next, students link these concrete and pictorial experiences to abstract models through symbolic work with equivalent fractions, common denominators, and fraction equations. By consistently integrating and connecting all three representations throughout the lesson, the curriculum provides students with a coherent progression from concrete to pictorial to abstract understanding.
Evaluation for 5.3c
The Math Journeys grade 5 Spanish program contains explicit, structured opportunities for students to connect, create, define, and explain both concrete and representational models leading to abstract concepts, as required by the TEKS. For example, during the warm-up, students independently analyze a pictorial representation of dollar bills and coins, assigning the correct place value to each to determine a total decimal value. Using process standard 1F in the development activity, the educator prompts students to explain the structural relationship between the money model and the decimal place-value system by asking, “How are the relationships between dollars, dimes, and pennies similar to the relationships between hundreds, tens, and ones?” and “Could you explain why we need to regroup when the number of cents in the subtrahend is greater than in the minuend?” The curriculum then helps students transition to representational models by requiring them to actively cross out subtrahend values and draw how whole bills are regrouped into 10 separate dimes, rather than simply viewing a completed static image.
The Math Journeys grade 5 Spanish curriculum contains explicit, structured opportunities for students to connect, create, define, and explain both concrete and representational models leading to abstract concepts, as required by the TEKS. For example, students connect concrete models, such as fraction pieces and manipulatives, and representational models, such as visual fraction diagrams, to abstract fraction operations by linking models to equivalent fractions and common denominators. Students create models by building and manipulating fraction pieces and visual representations to transform and combine fractions, developing a hands-on foundation for abstract understanding. The lesson further helps students define and clarify their reasoning by requiring them to justify why fractions must share a common denominator, explain equivalence through multiplying by one, and connect these ideas to symbolic procedures. By consistently engaging students in connecting, creating, and explaining across all three representations throughout a given lesson, the curriculum fully addresses all components of the indicator.
Evaluation for 5.4a
The Math Journeys grade 5 Spanish program contains explicit instruction on mathematical vocabulary and academic language. For example, the “Vista general de tramo—B: pensamiento aditivo” introduces and defines mathematical terms such as tens, units, and values, providing students with the foundational vocabulary needed to engage with additive thinking concepts. The curriculum also provides linguistic supports by introducing students to identifying and interpreting mathematical symbols, ensuring that students develop both the academic language and symbolic literacy required to access and communicate mathematical ideas throughout the broader learning pathway.
Activity 1 asks students to develop academic mathematical language by using manipulatives to represent all possible rectangles with 13 squares on the grid section of their Magic Pads, anchoring the terms factor and prime number to a visual arrangement. The Teacher Guide then directs educators to connect each rectangle to factor pairs before formally naming prime numbers, tying vocabulary to the physical model. “Video 30,” about the Sieve of Eratosthenes, reinforces these same terms through a visual elimination strategy across a 1–100 chart.
Evaluation for 5.4b
Educators receive guidance to scaffold, support, and extend students’ use of academic mathematical vocabulary through dedicated Journey Language Banks housed within the “Adaptaciones bilingües” documents. For example, the B2 Journey Language Bank explains how to use the bank, describes multiple instructional routines, and provides guidance on discussion and writing. This combination of routines and discourse instruction equips educators with concrete tools to help students practice and apply academic vocabulary in context, both when communicating with their peers and when responding to the educator.
In grade 5, the “Development” segment includes a dedicated Math Learning Routine (MLR) Sentence Frames sidebar that directs educators to scaffold students’ use of terms such as inverse, dividing, and multiplying through the tiered frames of “emerging,” “expanding,” and “bridging” in the context of verbally justifying why dividing by a whole number equals multiplying by its inverse. The Teacher Guide also directs educators to recast students’ language with precise mathematical vocabulary throughout the pair-sharing activity, extending vocabulary use into peer communication.
Evaluation for 5.4c
Students apply academic mathematical vocabulary within discourse through embedded prompts and educator guidance woven throughout the activities of a given lesson. During the warm-up, the Fraction Pieces widget prompts students to explain why they cannot simply add numerators when solving 3/10 + 7/100, embedding terms such as common denominator, equivalent fraction, and tenths versus hundredths directly into the discussion. The Teacher Guide directs educators to revoice students’ responses using these precise terms before students record equations, thus reinforcing accurate language at the point of use. In activity 1.2, students extend this practice by articulating to their peers why 12 is the preferred common denominator using precise fraction language. Together, these supports help students move from recognizing isolated vocabulary to applying mathematical language accurately within discourse.
Activity 1 embeds a prompt that asks students to explain why there are no other possible rectangle arrangements for 13 squares, requiring students to apply factor, prime number, and exactly two factors in oral discourse. The Teacher Guide instructs educators to have students justify why 1 is excluded, using the definition that prime numbers must have exactly two distinct factors. The discussion on the Sieve of Eratosthenes then requires students to apply composite, divisible, and multiple in a class discussion about crossed-out numbers.
Evaluation for 5.4d
Students hear and refine precise mathematical language through embedded discourse guidance involving educators as well as peers across lesson components. During the warm-up, the Teacher Guide directs educators to revoice students’ responses using posted terms such as common denominator and partial product, giving students repeated access to accurate fraction language in context. Activity 1.1 then extends this by directing partners to explain why 3/10 and 7/100 cannot be added by simply combining the numerators, requiring students to move beyond informal phrasing toward precise mathematical language through peer exchanges. The Teacher Guide further supports this by prompting educators to ask, “Could you explain why we can’t just add the numerators?” This question positions students to hear, refine, and use accurate fraction vocabulary with their peers, rather than relying on imprecise descriptions.
Activities 1 and 2 are structured as pair work, with students collaboratively drawing and discussing rectangles with fractional sides and sharing their reasoning about area with a partner before the class discussion. Activity 3 then asks pairs of students to order three multiplicative frames from least to greatest result without solving, requiring mathematical conversation to justify predictions before verifying. The Teacher Guide concludes by directing pairs of students to discuss what they notice about the results, thus facilitating peer exchange of mathematical language around scaling up and scaling down.
Evaluation for 5.4e
Educators receive support through anticipated student responses and guidance on embedded redirection that allow them to address misconceptions and deliver targeted feedback during instruction. During the warm-up, the Teacher Guide anticipates that students may add numerators and denominators directly, redirecting educators to prompt students to “read the operation aloud as 3 tenths and 7 hundredths,” thus surfacing the size-of-pieces mismatch before it becomes a persistent error. Activity 1.1 provides an exemplar demonstrating that students must convert 3/10 to 30/100 before combining it with 7/100, giving educators a concrete reference point for correct reasoning. If students continue to propose adding across denominators, the guide instructs educators to use the Fraction Pieces widget to make the differences in piece size visible. This layered guidance helps educators recognize inaccurate responses, redirect students’ thinking, and assist them in developing their conceptual understanding in real time.
The Teacher Guide anticipates that students may think a 13 × 1 rectangle is different from a 1 × 13 rectangle and redirects students toward understanding that, from a geometric perspective, the figure does not change—even when rotated. The guide also anticipates that students may incorrectly classify 1 as prime, noting that prime numbers must have exactly two distinct factors, while 1 has only one. When students claim that a composite number such as 57 is prime, the guide redirects them by suggesting that educators ask for its factors, thus exposing the 3 × 19 relationship.
Evaluation for 5.5a
Students apply TEKS mathematical process standards through tasks that integrate estimation, number sense, and real-world reasoning across the lesson sequence. In the “Planteamiento,” process standard 1C is tagged as students select estimation and number sense as techniques for placing fractions on a number line using benchmarks of 0, 1/2, and 1, reasoning about fractional magnitude rather than computing exact positions. Activity 2 then integrates process standard 1A as students apply this reasoning to a real-world context, deciding whether half a 5-gallon tank suffices for Mei’s garden without performing an exact calculation. Both process standards are tagged in labeled sidebars that connect each standard directly to the instructional task, making the integration visible and purposeful rather than incidental. This explicit tagging ensures that educators can identify where and how process standards are embedded, thus supporting consistent and intentional implementation across the lesson.
The Math Journeys grade 5 Spanish program contains a labeled sidebar that tags process standard 1B, which requires students to analyze the given information, formulate a strategy by finding a common denominator, determine that the missing part is 1/6, and justify their solution. Activity 1.3 extends process standard 1F as students analyze the mathematical relationship between dividing by a whole number and multiplying by 1/a. Both standards are embedded within content tasks rather than presented as isolated exercises, showing that process standards are integrated appropriately into the materials.
Evaluation for 5.5b
Educators receive support to understand how process standards are incorporated and connected throughout the learning pathways through explicit documentation in the Guía de instrucciones del journey D6. This guide identifies which process standards are present in each lesson of the journey, providing educators with a clear map of where and how process standards appear across the broader learning pathway. The horizontal rationale within the guide explains how the standards are connected throughout the general learning pathway, while the session alignment details how the standards build on and work off of each other across lessons. Together, these three layers of documentation—lesson-level identification, the horizontal rationale, and session alignment—ensure that educators understand not only which process standards are present but also how they function together to support student learning across the journey.
The curriculum describes how process standards 1F and 1G are incorporated throughout the broader learning pathway, explaining that 1F connects common-denominator reasoning to equivalence work from D2 and D3, while 1G supports precise justification of fraction operations. The guide explicitly connects these process standards across lessons D4.1 through D4.16, showing how same-denominator reasoning, unlike-denominator strategies, and estimation are linked by recurring standards. This rationale demonstrates how process standards form a coherent thread across the entire journey involving additive fractions.
Evaluation for 5.5c
Educators receive support with a clear overview of the TEKS mathematical process standards incorporated into each lesson through explicit tagging in the session header. The session header identifies process standards 1F and 1G alongside TEKS 5.3.H before instruction begins, giving educators an at-a-glance reference for which process standards are embedded within a given lesson. Activity 1.1 addresses these tagged standards as students justify why numerators cannot simply be combined (applying process standard 1G) and analyze the relationship between denominators to find a common denominator (applying process standard 1F). This per-lesson tagging allows educators to anticipate where discourse and relational reasoning are expected, thus supporting intentional, informed lesson delivery before starting instruction.
In grade 5, the session header lists process standards 1F and 1G directly alongside TEKS 5.4.A, providing a lesson-level overview of which process standards are incorporated before any activity begins. The 1G block instructs educators to ask why there are no other possible rectangle arrangements for 13 squares, while the 1F block targets the Sieve of Eratosthenes pattern. Educators can use this overview to plan discourse moves tied to each labeled standard, supporting a clear, per-lesson view of how process standards are incorporated into instruction.
5.1 Development of Conceptual Understanding
5.1a
Questions and tasks provide opportunities for students to interpret, analyze, and evaluate models and representations for mathematical concepts and situations.
Questions and tasks provide opportunities for students to interpret, analyze, and evaluate models and representations for mathematical concepts and 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 models and representations for mathematical concepts and situations.
3 out of 3 points
The Math Journeys grade 5 Spanish program contains questions and tasks that require students to interpret, analyze, and evaluate models and representations for mathematical concepts and situations. Students interpret models and representations as they make sense of visual and contextual models, including groups, area representations, and fraction pieces, to understand multiplication of a whole number by a fraction. They analyze models and representations by comparing equivalent representations, decomposing fractions, and connecting visual models to multiplicative equations. Students also evaluate models and representations as they justify whether representations are equivalent or appropriate, determine which contexts correctly match a given multiplication, and defend their reasoning using visual and contextual evidence.
5.1b
Questions and tasks provide opportunities for students to create concrete models and pictorial representations to represent mathematical situations.
Questions and tasks provide opportunities for students to create concrete models and pictorial representations to represent 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 pictorial representations to represent mathematical situations.
2 out of 2 points
The Math Journeys grade 5 Spanish program contains questions and tasks that provide students with opportunities to create concrete models and pictorial representations in order to represent mathematical situations. Students create concrete models using fraction pieces and manipulatives to represent and combine fractions, making their understanding of denominators and equivalent fractions visible. Students also create pictorial representations, such as shaded figures and visual fraction models, to justify why common denominators are needed and how fractions are combined.
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
The Math Journeys grade 5 Spanish program contains questions and tasks that provide students with opportunities to apply their conceptual understanding to new problem situations and contexts. For example, in development activity 1, students encounter a word problem about plant growth that requires them to apply fraction addition in a new measurement context. Students transfer the “Jumping along the Number Line” strategy from abstract practice to a real-world situation by determining the total height of a sprout that measured 3/8 inch and grew 4/8 inches more. The lesson guide supports this transfer by prompting students to consider how 3/8 + 4/8 helps them answer the question about how tall the plant is now.
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
The Math Journeys grade 5 Spanish program provides students with opportunities to develop and demonstrate procedural fluency. For example, in applet 147, students solve multi-operation equations by applying the correct order of operations, building fluency and automaticity through repeated practice. The activity reinforces the importance of procedural accuracy by allowing students to observe how significantly a result changes when they do not follow the correct order of operations. This task provides the fluency needed to complete grade-level mathematical tasks by requiring students to automatically identify and apply the order of operations, thus supporting greater accuracy and efficiency in solving complex expressions.
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.
3 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.
3 out of 3 points
The Math Journeys grade 5 Spanish program provides students with opportunities to develop and demonstrate flexibility in procedural competency. For example, activity 1.2 surfaces two solution paths for 2 ÷ 1/5—repeated grouping with the Fraction Pieces widget and recognizing the multiplication pattern—and asks students to evaluate which approach is more efficient. Activity 1.3 extends the same comparison to 2 ÷ 1/3, requiring students to evaluate accuracy by checking their results against the multiplicative frame. Activity 2 deepens this flexibility by asking students to assess whether multiplying by the denominator is always a valid strategy. This requires evaluating a generalized procedure for accuracy and reinforces the importance of both strategic efficiency and procedural reliability across division tasks.
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
The Math Journeys grade 5 Spanish program provides students with opportunities to evaluate the reasonableness of their results and the efficiency of their procedures. For example, activity 1.2 surfaces two solution paths for 2 ÷ 1/5—repeated grouping with the Fraction Pieces widget and recognizing the multiplication pattern—and asks students to evaluate which approach yields the most reasonable and efficient outcome. Activity 1.3 extends the same comparison to 2 ÷ 1/3, requiring students to evaluate the accuracy of their results by checking them against the multiplicative frame. Activity 2 reinforces this by asking students to assess whether multiplying by the denominator is always a valid strategy. This requires students to evaluate a generalized procedure for reasonableness and accuracy across division tasks.
5.2d
Materials contain guidance to support students in selecting increasingly efficient approaches to solve mathematics problems.
Materials contain guidance to support students in selecting increasingly efficient approaches to solve mathematics problems.
1 out of 1 points
Evaluation for 5.2d
Evaluation for 5.2d
Materials contain guidance to support students in selecting increasingly efficient approaches to solve mathematics problems.
1 out of 1 points
The Math Journeys grade 5 Spanish program provides students with opportunities to apply procedural fluency by selecting and using the most efficient strategy for a given problem. For example, activity 1.2 guides students from using the Fraction Pieces widget toward recognizing that each liter fills five glasses, thus supporting the selection of multiplication by the denominator as the more efficient approach. Activity 2 then presents the statement “to divide a whole number by a unit fraction, multiply by the denominator” and asks students to evaluate whether it is always true, guiding them to internalize an efficient general strategy and reinforcing the importance of selecting and applying the most effective procedure based on the structure of the problem.
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.
2 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.
2 out of 2 points
The Math Journeys grade 5 Spanish program explains how the conceptual and procedural emphases of the TEKS are addressed. For example, the lesson addresses the conceptual emphasis by helping students develop their understanding of multiplying decimals through the area model and connections to place value, highlighting the reasoning behind the operation by interpreting decimal multiplication as area and scaling. The lesson simultaneously addresses the procedural emphasis by guiding students to compute products of decimals using models, estimation, and the algorithm. By connecting a conceptual understanding through area models and reasoning with procedural skills through accurate calculation and application, the curriculum clearly communicates both components of the TEKS emphases within the lesson.
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
The Math Journeys grade 5 Spanish program gives students consistent opportunities to use concrete models, pictorial representations, and abstract models as required by the TEKS. For example, students engage with concrete models by using fraction pieces to physically combine and transform fractions when they find common denominators. Students then connect these hands-on experiences to pictorial representations by visualizing fractions with fraction circles and models to compare, decompose, and represent equivalent fractions. Next, students link these concrete and pictorial experiences to abstract models through symbolic work with equivalent fractions, common denominators, and fraction equations. By consistently integrating and connecting all three representations throughout the lesson, the curriculum provides students with a coherent progression from concrete to pictorial to abstract understanding.
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
The Math Journeys grade 5 Spanish curriculum contains explicit, structured opportunities for students to connect, create, define, and explain both concrete and representational models leading to abstract concepts, as required by the TEKS. For example, students connect concrete models, such as fraction pieces and manipulatives, and representational models, such as visual fraction diagrams, to abstract fraction operations by linking models to equivalent fractions and common denominators. Students create models by building and manipulating fraction pieces and visual representations to transform and combine fractions, developing a hands-on foundation for abstract understanding. The lesson further helps students define and clarify their reasoning by requiring them to justify why fractions must share a common denominator, explain equivalence through multiplying by one, and connect these ideas to symbolic procedures. By consistently engaging students in connecting, creating, and explaining across all three representations throughout a given lesson, the curriculum fully addresses all components of the indicator.
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
Activity 1 asks students to develop academic mathematical language by using manipulatives to represent all possible rectangles with 13 squares on the grid section of their Magic Pads, anchoring the terms factor and prime number to a visual arrangement. The Teacher Guide then directs educators to connect each rectangle to factor pairs before formally naming prime numbers, tying vocabulary to the physical model. “Video 30,” about the Sieve of Eratosthenes, reinforces these same terms through a visual elimination strategy across a 1–100 chart.
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
In grade 5, the “Development” segment includes a dedicated Math Learning Routine (MLR) Sentence Frames sidebar that directs educators to scaffold students’ use of terms such as inverse, dividing, and multiplying through the tiered frames of “emerging,” “expanding,” and “bridging” in the context of verbally justifying why dividing by a whole number equals multiplying by its inverse. The Teacher Guide also directs educators to recast students’ language with precise mathematical vocabulary throughout the pair-sharing activity, extending vocabulary use into peer communication.
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
Activity 1 embeds a prompt that asks students to explain why there are no other possible rectangle arrangements for 13 squares, requiring students to apply factor, prime number, and exactly two factors in oral discourse. The Teacher Guide instructs educators to have students justify why 1 is excluded, using the definition that prime numbers must have exactly two distinct factors. The discussion on the Sieve of Eratosthenes then requires students to apply composite, divisible, and multiple in a class discussion about crossed-out numbers.
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
Activities 1 and 2 are structured as pair work, with students collaboratively drawing and discussing rectangles with fractional sides and sharing their reasoning about area with a partner before the class discussion. Activity 3 then asks pairs of students to order three multiplicative frames from least to greatest result without solving, requiring mathematical conversation to justify predictions before verifying. The Teacher Guide concludes by directing pairs of students to discuss what they notice about the results, thus facilitating peer exchange of mathematical language around scaling up and scaling down.
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
The Teacher Guide anticipates that students may think a 13 × 1 rectangle is different from a 1 × 13 rectangle and redirects students toward understanding that, from a geometric perspective, the figure does not change—even when rotated. The guide also anticipates that students may incorrectly classify 1 as prime, noting that prime numbers must have exactly two distinct factors, while 1 has only one. When students claim that a composite number such as 57 is prime, the guide redirects them by suggesting that educators ask for its factors, thus exposing the 3 × 19 relationship.
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
The Math Journeys grade 5 Spanish program contains a labeled sidebar that tags process standard 1B, which requires students to analyze the given information, formulate a strategy by finding a common denominator, determine that the missing part is 1/6, and justify their solution. Activity 1.3 extends process standard 1F as students analyze the mathematical relationship between dividing by a whole number and multiplying by 1/a. Both standards are embedded within content tasks rather than presented as isolated exercises, showing that process standards are integrated appropriately into the materials.
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 curriculum describes how process standards 1F and 1G are incorporated throughout the broader learning pathway, explaining that 1F connects common-denominator reasoning to equivalence work from D2 and D3, while 1G supports precise justification of fraction operations. The guide explicitly connects these process standards across lessons D4.1 through D4.16, showing how same-denominator reasoning, unlike-denominator strategies, and estimation are linked by recurring standards. This rationale demonstrates how process standards form a coherent thread across the entire journey involving additive fractions.
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 grade 5, the session header lists process standards 1F and 1G directly alongside TEKS 5.4.A, providing a lesson-level overview of which process standards are incorporated before any activity begins. The 1G block instructs educators to ask why there are no other possible rectangle arrangements for 13 squares, while the 1F block targets the Sieve of Eratosthenes pattern. Educators can use this overview to plan discourse moves tied to each labeled standard, supporting a clear, per-lesson view of how process standards are incorporated into instruction.
Rubric Section 6
Productive Struggle
Materials support students in applying disciplinary practices to productive problem-solving, including explaining and revising their thinking.
Total
100% (19 out of 19 points)
Evaluation for 6.1a
Students think mathematically, persevere through solving problems, and make sense of math through fraction tasks that prioritize reasoning over computation. During the warm-up, students estimate where fractions fall on a number line using benchmark reference points of 0, 1/2, and 1, which requires genuine mathematical thinking before performing any calculations. Activity 1C builds on this by directing educators to have students select estimation and number sense as techniques rather than computing exact answers, ensuring that they persevere in the absence of a direct solution path. “Number Talk 2” then grounds this reasoning in a real water-tank scenario where students must judge the reasonableness of fraction magnitude in an everyday context, making sense of math beyond abstract procedure. Together, these tasks position students to think flexibly about fractions, sustain effort through non-computational tasks, and connect mathematical reasoning to real-world meaning.
Activity 1 asks students to think mathematically by representing all possible rectangles for 13 squares. This requires students to reason about why only one arrangement exists. The guide encourages students to persevere rather than stop after a single attempt, instructing educators to “emphasize the difference between not finding more solutions and there not being any more solutions.” Students then make sense of primality as a structural property of numbers by watching the video on the Sieve of Eratosthenes and listing all 25 primes, thus connecting the earlier rectangle task to a broader mathematical idea. Together, these tasks require students to reason, persevere through unresolved questions, and construct meaning about number structure rather than simply follow a procedure.
Evaluation for 6.1b
Students understand, explain, and justify that there are multiple valid ways to solve problems through fraction tasks, which require both strategy and mathematical reasoning. In activity 1, students create addition equations using fraction cards and identify the two combinations with the greatest results, building an understanding that multiple valid fraction combinations exist within the same task. Students then explain which result is greater and why, using a common denominator as evidence—moving beyond computation to articulate the mathematical reasoning behind their comparison. The extension deepens this by asking students to find two subtraction equations with the same outcome. This directly requires students to justify that different fraction combinations can yield identical outcomes. Across these tasks, students are not simply solving for a correct answer but are actively constructing, comparing, and defending multiple solution paths.
Activity 2 further supports this understanding by presenting two word problems with identical numbers but different contexts, with the Teacher Guide directing educators to ask students to “solve one of the situations” using either repeated-addition or commutative-property reasoning. Students explain how both approaches—1/3 of 6 versus 6 × 1/3—yield the same product, and justify which representation best fits each context. The guide instructs educators to ensure that “both interpretations appear” on the board, confirming for students that multiple solution paths can lead to the same valid outcome.
Evaluation for 6.1c
Students make sense of fraction decomposition by doing, writing, and discussing math across a connected sequence of tasks. In small groups, students use fraction-circle pieces to physically build all decompositions of 4/12, recording each as an addition equation on Magic Pads. Groups then transition to their log books to write the multiplication expression connecting repeated addition to n times 1/b, producing a written record that requires students to make sense of the relationship between the two representations. The wrap-up then asks students to share and discuss which decompositions can be expressed as multiplication, consolidating reasoning through peer discourse and requiring students to defend their thinking beyond what they recorded in writing. By moving students from hands-on construction to written representation to structured discussion in a single lesson sequence, the curriculum ensures that all three modes of sense-making are embedded and mutually reinforcing.
The warm-up has students do math together as a class by physically using the Fraction Pieces widget to compare 1/3 and 1/4 before transitioning to paired card tasks. Students then write about their thinking individually by recording two addition equations with different results in their log books and circling the greater sum. Pairs of students discuss which strategy yields the greatest or smallest results, requiring students to engage in mathematical discourse to justify their choices to a peer. Together, these tasks help students move through doing, writing, and discussing math with both the whole class and a partner in a single session.
Evaluation for 6.2a
Educators have opportunities to guide grade 5 students to share and reflect on their problem-solving approaches, including explanations, arguments, and justifications. To encourage students to share both their strategy and its justification by explaining their reasoning about factor selection, during activity 1, the Teacher Guide directs educators to ask, “Could you explain why 4 and 5 are the only valid factors?” and “Have you checked if your answer gives the greatest result?” The Teacher Guide further directs pairs of students to compare two addition equations and argue which produces the larger sum. This requires students to construct and share a mathematical argument grounded in numerical reasoning. The “Desenlace” then prompts students to reflect by asking them to consider whether a different card arrangement could improve their outcome. This requires them to revisit and reconsider their own reasoning rather than simply confirm a correct answer. By guiding educators to press for explanations, require arguments, and prompt students to reflect on and refine their justifications across multiple activities, the curriculum supports both the sharing and reflecting dimensions required by the criterion.
Activity 1 instructs educators to ask students why a result is incorrect without calculating, requiring them to share explanations grounded in benchmark fractions. The guide directs educators to encourage students to argue that fractions close to 1 cannot sum to less than 1, constructing a mathematical argument from relational reasoning rather than computation. Development activity 2 then prompts students to reflect by asking them when one might use estimation versus exact calculations, guiding students to evaluate their own problem-solving approaches and the conditions under which each strategy is appropriate. By requiring students to explain their reasoning, construct an argument grounded in benchmark relationships, and reflect on the strategy they chose, the curriculum helps students share and reflect on their problem-solving approaches as required by the criterion.
Evaluation for 6.2b
The curriculum provides prompts and guidance that help educators provide explanatory feedback based on anticipated misconceptions and student responses. In activity 1, the Teacher Guide anticipates that students will accept incorrect equations without calculating and provides a specific feedback prompt: “How can you tell this is incorrect without calculating?” This gives educators an explicit redirect tied directly to an anticipated struggle, rather than simply confirming the error. The guide further anticipates the misconception that two fractions greater than 1/2 could sum to less than 1, supplying a model explanatory response that educators can use to correct that specific error with mathematical reasoning grounded in fraction magnitude. In activity 2, the curriculum anticipates that students will oversimplify by rounding both addends to 1, directing educators to acknowledge the contribution of that approach while redirecting students toward a more precise estimation strategy. Across all three instances, the anticipated misconceptions are paired with specific educator prompts or model responses embedded within the session flow. This shows that the curriculum contains both the prompts and guidance needed to help educators provide explanatory feedback based on students’ responses and anticipated misconceptions.
To elicit students’ justifications and surface incomplete reasoning before it goes unaddressed, activity 1 includes the prompt, “Could you explain why there aren’t any other possible rectangle arrangements for 13 squares?” The guide also anticipates that students will incorrectly identify 1 as prime, directing educators to contrast one with 13 by asking, “How many factors does each number have?” This guidance specifies that prime numbers must have exactly two distinct factors, giving educators precise language to redirect the common one-factor misconception rather than simply flagging it as incorrect.
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
Activity 1 asks students to think mathematically by representing all possible rectangles for 13 squares. This requires students to reason about why only one arrangement exists. The guide encourages students to persevere rather than stop after a single attempt, instructing educators to “emphasize the difference between not finding more solutions and there not being any more solutions.” Students then make sense of primality as a structural property of numbers by watching the video on the Sieve of Eratosthenes and listing all 25 primes, thus connecting the earlier rectangle task to a broader mathematical idea. Together, these tasks require students to reason, persevere through unresolved questions, and construct meaning about number structure rather than simply follow a procedure.
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
Activity 2 further supports this understanding by presenting two word problems with identical numbers but different contexts, with the Teacher Guide directing educators to ask students to “solve one of the situations” using either repeated-addition or commutative-property reasoning. Students explain how both approaches—1/3 of 6 versus 6 × 1/3—yield the same product, and justify which representation best fits each context. The guide instructs educators to ensure that “both interpretations appear” on the board, confirming for students that multiple solution paths can lead to the same valid outcome.
6.1c
Materials are designed to require students to make sense of mathematics through multiple opportunities for students to do, write about, and discuss math with peers and/or educators.
Materials are designed to require students to make sense of mathematics through multiple opportunities for students to do, write about, and discuss math with peers and/or educators.
3 out of 3 points
Evaluation for 6.1c
Evaluation for 6.1c
Materials are designed to require students to make sense of mathematics through multiple opportunities for students to do, write about, and discuss math with peers and/or educators.
3 out of 3 points
The warm-up has students do math together as a class by physically using the Fraction Pieces widget to compare 1/3 and 1/4 before transitioning to paired card tasks. Students then write about their thinking individually by recording two addition equations with different results in their log books and circling the greater sum. Pairs of students discuss which strategy yields the greatest or smallest results, requiring students to engage in mathematical discourse to justify their choices to a peer. Together, these tasks help students move through doing, writing, and discussing math with both the whole class and a partner in a single session.
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, and justifications.
Materials support educators in guiding students to share and reflect on their problem-solving approaches, including explanations, arguments, and justifications.
6 out of 6 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, and justifications.
6 out of 6 points
Activity 1 instructs educators to ask students why a result is incorrect without calculating, requiring them to share explanations grounded in benchmark fractions. The guide directs educators to encourage students to argue that fractions close to 1 cannot sum to less than 1, constructing a mathematical argument from relational reasoning rather than computation. Development activity 2 then prompts students to reflect by asking them when one might use estimation versus exact calculations, guiding students to evaluate their own problem-solving approaches and the conditions under which each strategy is appropriate. By requiring students to explain their reasoning, construct an argument grounded in benchmark relationships, and reflect on the strategy they chose, the curriculum helps students share and reflect on their problem-solving approaches as required by the criterion.
6.2b
Materials include prompts and guidance to support educators in providing explanatory feedback based on student responses and anticipated misconceptions.
Materials include prompts and guidance to support educators in providing explanatory feedback based on student responses and anticipated misconceptions.
4 out of 4 points
Evaluation for 6.2b
Evaluation for 6.2b
Materials include prompts and guidance to support educators in providing explanatory feedback based on student responses and anticipated misconceptions.
4 out of 4 points
To elicit students’ justifications and surface incomplete reasoning before it goes unaddressed, activity 1 includes the prompt, “Could you explain why there aren’t any other possible rectangle arrangements for 13 squares?” The guide also anticipates that students will incorrectly identify 1 as prime, directing educators to contrast one with 13 by asking, “How many factors does each number have?” This guidance specifies that prime numbers must have exactly two distinct factors, giving educators precise language to redirect the common one-factor misconception rather than simply flagging it as incorrect.