Program Information
- ISBN
- 9791370378097
- 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 4 (Spanish)
Supplemental Math (Spanish) Grade 4
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 4 | 100% | N/A |
Criteria for Quality
Rubric Section 1
Intentional Instructional Design
Materials support educators in effective implementation through intentional course, unit, and lesson-level design.
Total
100% (23 out of 23 points)
Evaluation for 1.1a
The TEKS Correlation Guide of the Math Journeys grade 4 program outlines the TEKS corresponding to each of the lessons, including both content and process standards for educators. The scope and sequence document is organized into sections called “Journeys” and identifies the TEKS and ELPS addressed in each. The Journey Instructional Guide provides a detailed rationale for each journey. For example, section 2 of the guide explains the vertical rationale for how the current journey builds on the previous one and how it prepares students for subsequent concepts. The guide notes that the current journey, which focuses on identifying numbers and counting from 1–100, extends students’ understanding of counting, comparing, ordering, and estimating, skills developed in the previous journey, which involves numbers 1–20. Section 3 further describes how learning progresses from concrete experiences to representational models and ultimately to abstract understandings of number sense.
Each Math Journeys Spanish Instructional Guide clearly explains both the vertical and horizontal alignment for every journey. The vertical rationale describes why a journey is strategically positioned within the materials and how the learning connects across grade levels, ensuring that prior knowledge is extended and future learning is supported. The horizontal rationale illustrates how lessons within a journey build upon one another by demonstrating the intentional sequencing and interconnectedness of concepts within the same grade level, reinforcing and deepening students’ mathematical understanding.
Evaluation for 1.1b
The Math Journeys grade 4 Spanish Program Guide provides comprehensive instruction for implementation, including the three-step framework of “build,” “consolidate,” and “practice.” Each lesson starts with an educator-led, small-group lesson, followed by logsheets for students to complete independently with educator feedback and then further optional practice on Atlas Math, an adaptive digital platform. Additionally, the “Lesson Internalization and Planning” section explains how to plan for learner variability, including explanations for multiple entry points, just-in-time supports, extensions, and multiple representations and modes of expression.
The Math Journeys grade 4 Spanish program provides specific instructions and activities for enrichment and small-group instruction within each journey. Educators receive guidance on using manipulatives to help students solve problems, offering a concrete, hands-on approach to instruction. These strategies help educators adapt instruction to meet the diverse needs of students across multiple instructional contexts, including enrichment for students who have shown mastery and targeted, small-group support for students who need additional practice.
Evaluation for 1.1c
The TEKS Correlation Guide recommends skill entry points by connecting lessons and activities within each journey to specific TEKS content and process standards. In addition, a digital diagnostic assessment and placement report identifies appropriate instructional starting points based on student performance data. After students complete the diagnostic assessment, a report is generated that suggests specific journeys and skill entry points to assign. These recommendations support targeted instruction, differentiated learning opportunities, and instructional decision-making by helping educators identify appropriate entry points and interventions based on individual students’ needs.
The placement test report sample for grade 4 students illustrates how educators can use diagnostic assessment results 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 skill entry point for each group. In addition, the report provides a page for the individual student that offers a snapshot of the student’s current understanding and a recommended starting point tailored to 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 4 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 helping educators 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. Additionally, 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 help educators 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 4 Spanish program contains protocols with corresponding guidance for internalizing lessons. The “Lesson Internalization and Planning” section of the Program Guide includes guidance for internalizing each lesson component. The sections “Preparing for a Building Session,” “Preparing for a Consolidating Session,” and “Preparing for an Additional Practice Session” help educators internalize the lesson’s components, ensuring they are well prepared to deliver effective, responsive instruction that meets the needs of all students.
Evaluation for 1.1e
Resources within the Math Journeys grade 4 Spanish program give instructional leaders some support during program implementation. Specifically, the “Hands on Partnership” section of the Program Guide describes ways that a math success manager can collaborate with and provide guidance to instructional leaders throughout implementation. While this section offers examples of partnership and support, instructional leaders have access to additional embedded guidance and dedicated implementation resources designed specifically for them.
The training materials include on-demand videos that provide guidance 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 for both educators and leaders 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, ensuring that the materials are used as intended.
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 identifies assessment resources aligned with the TEKS. Formative assessments embedded throughout the lesson overviews clearly identify the aligned TEKS. End-of-journey assessments are also aligned with the TEKS. The answer key lists the corresponding TEKS for each assessment. Because the Math Journeys grade 4 Spanish program is a Spanish-language math curriculum, ELPS alignment does not apply and is therefore not referenced in the assessment materials.
Evaluation for 1.2b
The Math Journeys grade 4 Spanish program contains detailed lesson overviews that identify TEKS-aligned learning objectives, student materials, educator resources, and lesson components. Each lesson overview contains key vocabulary and cognates to support language development. The “Inside a Journey” section of the Program Guide suggests timeframes for lesson components, allowing educators to plan and pace instruction according to students’ needs.
Each lesson overview contains assessment resources that are aligned with the TEKS. Formative assessments embedded throughout the lesson overviews clearly identify the aligned TEKS, allowing educators to make direct connections between instructional activities and the standards being assessed. End-of-journey assessments are also aligned with the TEKS, and the answer key lists the corresponding aligned TEKS. Because the Math Journeys grade 4 Spanish program is a Spanish-language math curriculum, alignment with the ELPS does not apply. Thus, ELPS alignment is not referenced within 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 4 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 clearly explains both the vertical and horizontal alignment for every journey. The vertical rationale describes why a journey is strategically positioned within the materials and how the learning connects across grade levels, ensuring that prior knowledge is extended and future learning is supported. The horizontal rationale illustrates how lessons within a journey build upon one another by demonstrating the intentional sequencing and interconnectedness of concepts within the same grade level, reinforcing and deepening students’ mathematical understanding.
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
The Math Journeys grade 4 Spanish program provides specific instructions and activities for enrichment and small-group instruction within each journey. Educators receive guidance on using manipulatives to help students solve problems, offering a concrete, hands-on approach to instruction. These strategies help educators adapt instruction to meet the diverse needs of students across multiple instructional contexts, including enrichment for students who have shown mastery and targeted, small-group support for students who need 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 4 students illustrates how educators can use diagnostic assessment results 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 skill entry point for each group. In addition, the report provides a page for the individual student that offers a snapshot of the student’s current understanding and a recommended starting point tailored to 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 4 Spanish program contains protocols with corresponding guidance for internalizing lessons. The “Lesson Internalization and Planning” section of the Program Guide includes guidance for internalizing each lesson component. The sections “Preparing for a Building Session,” “Preparing for a Consolidating Session,” and “Preparing for an Additional Practice Session” help educators internalize the lesson’s components, ensuring they are well prepared to deliver effective, responsive instruction that meets 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
The training materials include on-demand videos that provide guidance 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 for both educators and leaders 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, ensuring that the materials are used as intended.
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 identifies assessment resources aligned with the TEKS. Formative assessments embedded throughout the lesson overviews clearly identify the aligned TEKS. End-of-journey assessments are also aligned with the TEKS. The answer key lists the corresponding TEKS for each assessment. Because the Math Journeys grade 4 Spanish program is a Spanish-language math curriculum, ELPS alignment does not apply and is therefore not referenced in the assessment materials.
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 contains assessment resources that are aligned with the TEKS. Formative assessments embedded throughout the lesson overviews clearly identify the aligned TEKS, allowing educators to make direct connections between instructional activities and the standards being assessed. End-of-journey assessments are also aligned with the TEKS, and the answer key lists the corresponding aligned TEKS. Because the Math Journeys grade 4 Spanish program is a Spanish-language math curriculum, alignment with the ELPS does not apply. Thus, ELPS alignment is not referenced within 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 4 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
The “Evaluación y monitoreo del progreso” section of the Program Guide defines and explains the purposes of diagnostic, formative, and summative assessment. The guidance describes how each assessment type is intended to be used throughout the program and helps educators plan lessons, deliver instruction, monitor students’ progress, and make data-informed instructional decisions across the school year.
A comprehensive assessment system is embedded throughout the Math Journeys grade 4 Spanish program and clearly defines the purposes of diagnostic, formative, and summative assessment. Diagnostic assessments are administered at the beginning of the year as well as throughout it to establish a baseline understanding and monitor ongoing progress. Daily formative assessments are embedded within classroom activities, enabling educators to continuously monitor students’ understanding during instruction. Summative assessments are administered 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 students’ progress and informing instructional decisions throughout the school year.
Evaluation for 2.1b
The Placement Test Implementation Guide provides clear, detailed steps for educators to administer the diagnostic assessment consistently and accurately. The guide mentions the estimated testing time, the instructor’s role during administration, and suggested materials. For example, the “Administration Guidance” section 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 4 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 guidance for administering the assessment. It is organized into three clear 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 accuracy in administration across classrooms.
Evaluation for 2.1c
The Math Journeys grade 4 Spanish program provides printable versions of digital assessments throughout the curriculum to allow for flexible administration options as well as increased 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 assessments can be administered 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 within the digital assessment platform, including text-to-speech functionality, but calculators and content language supports are not available. Additionally, the option to select a testing language does not constitute content language support because content 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 Math Journeys grade 4 Spanish program provides students with a diagnostic placement test through the Atlas Math app. The test 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 assessment can be adjusted to capture each student’s level of understanding.
The diagnostic placement test contains a variety of interactive question types, allowing students to show their understanding in multiple ways. The test includes more than two unique interactive item types, such as multiple-choice, graphing, inline choice, hot spot, drag-and-drop, and fraction models. This variety of interactive item types ensures that students have multiple opportunities to show their understanding across different question formats while also 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 provides 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, illustrating that the formative assessments include more than two unique item formats and varying levels of cognitive demand. These assessment opportunities allow students to show their understanding in multiple ways while providing educators with meaningful evidence of learning 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 individual student 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’s placement test report provides detailed scoring information and guidance for interpreting performance. The report displays scores based on the 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 the results of diagnostic assessment to understand trends in student performance and determine appropriate instructional next steps. The guide mentions practical administration details, including the estimated testing time, the educator’s role during administration, and the recommended materials for implementation. By establishing consistent administration procedures and expectations, the guide helps educators interpret assessment data, make decisions about instructional placement, and identify targeted supports for individual students and groups.
The placement test report sample helps educators use assessment results to plan purposeful tasks and activities aligned with the appropriate TEKS. The report includes a chart displaying the assessed TEKS, the process standard targeted, the class percentage of correct responses, and the percentage 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 allows educators to respond directly to assessment data by assigning targeted tasks and activities that address the specific learning needs of individual groups of students.
Evaluation for 2.2c
The Math Journeys grade 4 Spanish program offers tools to help educators track students’ progress and growth. The Teacher Guide outlines the use of diagnostic, formative, and summative assessments to monitor students’ progress throughout the program. The tools provided allow educators to identify students’ strengths, address areas of need, and make informed instructional decisions. In addition, the guide states, “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 4 Spanish program provides some progress monitoring tools through the digital platform. The platform enables educators to track students’ progress and growth through a general overview as students complete activities on the app. Students receive immediate feedback on their performance as they complete activities. However, the platform lacks a log or tracker that allows students to revisit and monitor their 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
Activities 1 and 2 help educators conduct frequent checks for 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 progressing to new learning.
Each lesson in the Math Journeys grade 4 Spanish program contains support to help educators frequently check students’ understanding. 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 recommends manipulatives and instructional strategies that help clarify concepts for students who need additional support. Together, these resources enable educators to monitor students’ understanding at key points during instruction and make responsive instructional adjustments as needed.
Evaluation for 2.2e
Educators frequently check students’ understanding throughout lessons and activities through embedded opportunities for formative assessment as well as immediate feedback during digital practice. Within lesson activities, educators encounter strategically placed questions for monitoring students’ understanding and have opportunities to determine whether students are ready to progress to new content. During applet activities, students receive immediate feedback based on their responses, and the sequence of follow-up activities is adjusted based on educator pacing and student performance.
The Math Journeys grade 4 Spanish program does not contain adaptive checks for understanding within an activity. Although the sequence of follow-up applet activities may change based on students’ performance, the current activity does not adjust the level of rigor, modify question types, or provide additional instructional supports in response to individual students’ answers. Thus, the materials enable educators to frequently check students’ understanding but do not provide adaptive checks that allow 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
A comprehensive assessment system is embedded throughout the Math Journeys grade 4 Spanish program and clearly defines the purposes of diagnostic, formative, and summative assessment. Diagnostic assessments are administered at the beginning of the year as well as throughout it to establish a baseline understanding and monitor ongoing progress. Daily formative assessments are embedded within classroom activities, enabling educators to continuously monitor students’ understanding during instruction. Summative assessments are administered 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 students’ 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 4 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 guidance for administering the assessment. It is organized into three clear 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 accuracy in administration across classrooms.
2.1c
Digital assessments include printable versions and accommodations, including text-to-speech, content and language supports, and calculators, that educators can enable or disable to support individual students.
Digital assessments include printable versions and accommodations, including text-to-speech, content and language supports, and calculators, that educators can enable or disable to support individual students.
1 out of 2 points
Evaluation for 2.1c
Evaluation for 2.1c
Digital assessments include printable versions and accommodations, including text-to-speech, content and language supports, and calculators, that educators can enable or disable to support individual students.
1 out of 2 points
The “Accommodations in Assessment” section of the Program Guide identifies accommodations embedded within the digital assessment platform, including text-to-speech functionality, but calculators and content language supports are not available. Additionally, the option to select a testing language does not constitute content language support because content 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
The diagnostic placement test contains a variety of interactive question types, allowing students to show their understanding in multiple ways. The test includes more than two unique interactive item types, such as multiple-choice, graphing, inline choice, hot spot, drag-and-drop, and fraction models. This variety of interactive item types ensures that students have multiple opportunities to show their understanding across different question formats while also 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 provides 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, illustrating that the formative assessments include more than two unique item formats and varying levels of cognitive demand. These assessment opportunities allow students to show their understanding in multiple ways while providing educators with meaningful evidence of learning 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’s placement test report provides detailed scoring information and guidance for interpreting performance. The report displays scores based on the 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 includes a chart displaying the assessed TEKS, the process standard targeted, the class percentage of correct responses, and the percentage 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 allows educators to respond directly to assessment data by assigning targeted tasks and activities that address the specific learning needs of individual groups of students.
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 4 Spanish program provides some progress monitoring tools through the digital platform. The platform enables educators to track students’ progress and growth through a general overview as students complete activities on the app. Students receive immediate feedback on their performance as they complete activities. However, the platform lacks a log or tracker that allows students to revisit and monitor their 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
Each lesson in the Math Journeys grade 4 Spanish program contains support to help educators frequently check students’ understanding. 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 recommends manipulatives and instructional strategies that help clarify concepts for students who need additional support. Together, these resources enable educators to 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 Math Journeys grade 4 Spanish program does not contain adaptive checks for understanding within an activity. Although the sequence of follow-up applet activities may change based on students’ performance, the current activity does not adjust the level of rigor, modify question types, or provide additional instructional supports in response to individual students’ answers. Thus, the materials enable educators to frequently check students’ understanding but do not provide adaptive checks that allow 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
Each lesson of the Math Journeys grade 4 Spanish program provides educators with explicit guidance to help students who have not yet reached proficiency in prerequisite or grade-level concepts and skills. Educators can print and distribute the “Material de apoyo” resources located in the right-hand panel of each lesson to students who require additional scaffolding and support. These printable resources provide foundational support that enables students to access grade-level content while allowing educators to differentiate instruction based on individual students’ needs.
Each lesson in the Math Journeys grade 4 Spanish program contains additional supports for students who have not yet reached proficiency. The “Desenlace” section includes a worksheet version of the lesson with embedded supports that provides an accessible entry point for students who need additional scaffolding. Furthermore, the “Apoyo” section at the end of each lesson suggests specific manipulatives and instructional strategies to clarify concepts and address learning needs. Together, these embedded supports help educators clearly identify and respond to students who have not yet shown proficiency in grade-level content and skills.
Evaluation for 3.1b
Language supports embedded throughout the Math Journeys grade 4 Spanish curriculum help students develop their academic vocabulary and access grade-level mathematical content. In the “Adaptaciones lingüísticas” section, educators can access the “Guía bilingüe/ESL” resource, which provides language scaffolds and guidance to support students’ language development during instruction. Lesson overviews also incorporate key vocabulary and cognates to promote academic language development and reduce linguistic barriers to content. The materials provide explicit guidance for pre-teaching unfamiliar references in the text.
Each lesson in the Math Journeys grade 4 Spanish program contains dedicated support for emergent bilingual (EB) students and identifies intentional opportunities to reinforce key terms. For example, in activity 1.1, sentence stems help students explain their mathematical thinking through oral discourse. The materials also recommend using gestures and visual representations to reinforce vocabulary development and comprehension. These embedded supports provide meaningful guidance for building students’ academic vocabulary and increasing their comprehension.
Evaluation for 3.1c
Enrichment and extension opportunities are embedded within the Math Journeys grade 4 Spanish program for students who have shown proficiency in grade-level content and skills. In the “Desenlace” section of each lesson, the dedicated “Ampliación” component contains extension activities and questions that challenge students to apply and extend their understanding beyond the core lesson objectives. For example, one “Ampliación” activity asks students to solve an additional problem not addressed during the lesson. These activities provide opportunities for deeper learning and continued engagement. The program clearly explains how to implement enrichment and extension activities for students who have demonstrated proficiency in above grade-level content and skills. In addition, the program offers general suggestions such as “For advanced learners, provide more challenging problems” or “Encourage students to explore topics further on their own.”
Within the “Recursos” section of each lesson, a printable worksheet titled “Ampliación” extends learning by asking students to use different numbers than those presented during the lesson and identify patterns and relationships. Additionally, this worksheet provides students with opportunities to extend their thinking beyond the lesson objectives and includes explicit guidance for educators to effectively implement or facilitate these extension activities. Thus, the materials provide enrichment resources for students who have shown above grade-level proficiency in the content and skills taught.
Evaluation for 3.1d
The digital components of the Math Journeys grade 4 Spanish program do not meet the requirements of this indicator. Specifically, the materials do not provide text-to-speech functionality, content and language supports that educators can enable or disable, or calculators to meet individual students’ needs. As a result, the materials do not contain the embedded features of digital accessibility required by this indicator.
The digital materials do not provide text-to-speech functionality, content and language supports, or calculators.
Evaluation for 3.1e
The Math Journeys grade 4 Spanish program provides students with multiple opportunities to express their understanding of mathematical concepts. For example, in journey C1, lesson 14, activity 1, pictures help students connect to the story’s context and provide a concrete visual representation of the mathematical concept before transitioning to an equation. This progression from visual representation to symbolic notation allows students to show their understanding in different ways by moving from concrete pictorial understanding to abstract mathematical expression. These embedded supports help educators offer students multiple entry points to access and demonstrate their understanding of mathematical content.
The Math Journeys grade 4 Spanish program helps educators provide varied opportunities for students to demonstrate mathematical understanding. In a lesson focused on multiplying numbers between one and 1,000 by single-digit numbers, students first discuss a problem and explain their mathematical thinking through oral discourse. They then use manipulatives and multiplicative frames to represent problems concretely and visually before independently representing and solving problems using an area model. Together, these opportunities to express, represent, and perform mathematical thinking help educators offer students multiple and varied ways to show their understanding of mathematical concepts throughout the lesson.
Evaluation for 3.2a
Prompts embedded throughout the Math Journeys grade 4 Spanish program help educators build students’ knowledge by activating their prior knowledge, highlighting patterns and relationships, and connecting mathematical ideas through multiple representations. In grade 4, students compare and order sums without calculating, explain their strategies using place-value reasoning, and analyze incorrect solutions using number lines and equations. Educators pose questions that help students justify the relationships between numbers and operations while making connections among symbolic expressions, visual models, and verbal reasoning. The embedded prompts and supports equip educators to help students make meaningful connections between mathematical concepts and representations throughout each lesson.
The Math Journeys grade 4 Spanish program contains numerous opportunities to activate students’ prior knowledge, anchor big ideas, and connect relationships through multiple representations. In the activities, students analyze and compare mathematical relationships, explain their reasoning using conceptual understanding, and evaluate solution strategies through visual models, equations, and other representations. The materials also help educators 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 support educators in helping students develop a deep, connected understanding of mathematical concepts throughout each lesson.
Evaluation for 3.2b
The Math Journeys grade 4 Spanish program helps educators effectively deliver and facilitate lessons through a variety of instructional approaches. The lessons incorporate whole-group instruction, collaborative learning 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 provide step-by-step facilitation guidance, questioning prompts, and differentiated supports. Together, these instructional approaches enable educators to deliver engaging lessons that address the diverse learning needs of grade 4 students.
The Math Journeys grade 4 Spanish program clearly explains how to effectively deliver and facilitate lessons through multiple instructional approaches. In a lesson focused on multiplying numbers between one and 1,000 by single-digit numbers, students first discuss a given problem, promoting mathematical discourse and collaborative learning. Students then use manipulatives and multiplicative frames to represent problems, engaging in hands-on and visual learning experiences. Finally, students represent and solve problems using an area model, transitioning from concrete and visual representations to more abstract mathematical thinking. Thus, the curriculum enables educators to facilitate lessons using multiple instructional methods throughout each lesson.
Evaluation for 3.2c
The Math Journeys grade 4 Spanish program contains multi-tiered intervention methods, varied practice structures, and guidance for educators to effectively implement the lessons. The lessons incorporate multiple types of practice, including collaborative partner work and whole-group discussions, throughout the activities. Students also engage in independent practice through individualized activities assigned during “Sesión completada,” providing self-paced opportunities aligned with individual learning needs. Additionally, the embedded “Apoyo” and “Ampliación” sections provide differentiated guidance to scaffold instruction for students who need further support and to extend learning for students who have demonstrated mastery. Together, these supports help educators address diverse learning needs through multiple tiers of support.
The Math Journeys grade 4 Spanish program contains multi-tiered intervention methods involving a variety of instructional practices and structures to address diverse learning needs. The program provides opportunities for guided, collaborative, independent, and educator-facilitated practice across whole-group, partner, and individual settings. Implementation supports include questioning strategies, manipulatives, models, and visual representations that facilitate effective instruction across multiple levels of support. Furthermore, the embedded “Apoyo” and “Ampliación” sections provide differentiated supports for students who need additional scaffolding as well as extension opportunities for students who have shown mastery. Together, these varied instructional practices and differentiated supports help educators implement multi-tiered intervention methods throughout the lessons.
Evaluation for 3.2d
The Math Journeys grade 4 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, provide differentiated supports that allow educators to extend or scaffold learning based on individual student readiness and performance. The lessons also clearly explain how to effectively implement the activities through questioning prompts, manipulatives, number lines, partner discussions, visual models, and opportunities for independent practice. For example, students solve problems using multiple strategies, calculate distances on number lines, compare solution methods, and justify their mathematical reasoning through whole-group, partner, and individual activities. These scaffolded supports and enrichment opportunities equip educators with the tools needed to differentiate instruction for grade 4 students while keeping students meaningfully engaged with grade-level mathematical concepts and skills.
The Math Journeys grade 4 Spanish program provides educators with explicit guidance on enrichment and extension activities that support various forms of engagement for students who have demonstrated proficiency in the content and skills. Within the “Desenlace” of each lesson, a dedicated “Ampliación” section provides specific guidance on how to offer extension activities and questions to students who have mastered the content. For example, in one lesson, the “Ampliación” extension activity directs educators to ask students to explain what would happen if the initial number were different from the previous example. This challenges students to apply their understanding by reasoning through a new scenario and extend their mathematical thinking beyond the core lesson objectives. This embedded guidance ensures that educators have the specific, actionable tools they need to keep students engaged and deepen learning for students who have shown mastery of the content and skills taught.
Evaluation for 3.2e
Throughout the Math Journeys grade 4 Spanish program, embedded prompts and instructional guidance help educators provide timely feedback during lesson delivery. Within each lesson overview, a dedicated section accompanying the activities contains specific prompts and educator guidance to use during instruction. The embedded prompts encourage educators to pause at key moments to monitor students’ understanding, identify misconceptions, and provide immediate, meaningful feedback. Additionally, the lessons provide multiple ways for students to show their understanding, including using manipulatives such as cubes and cloths, verbal explanations, drawings, and written equations. These varied opportunities for students to respond allow educators to observe their thinking in real time and provide responsive feedback that helps students progress toward the lesson objectives. Together, these embedded prompts and demonstration opportunities equip educators with the guidance they need to provide timely feedback throughout lesson delivery.
Discussion opportunities embedded throughout the Math Journeys grade 4 Spanish program provide educators with prompts and guidance for delivering timely feedback during lessons. Educators intentionally prompt students to explain their mathematical thinking and verify their understanding based on their responses. Specific guidance identifies what educators should expect to see and hear when students demonstrate understanding, creating intentional checkpoints for monitoring progress and addressing misconceptions in real time. Additionally, the lessons provide students with multiple ways to show their understanding, including physical participation through a game using hoops, verbal discussion, and written and drawn representations. These varied opportunities enable educators to observe students’ thinking through multiple modalities and provide immediate, responsive feedback that supports their understanding and advances their learning throughout a given lesson.
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
Educators can access guidance on providing lesson-level language support through the “Gestor de aula.” By navigating to the “Adaptaciones lingüísticas” tab in the left-side panel, educators can access documents for lesson-level language support within each journey. For example, the “Lesson-Level ELPS Companion” is available in the “Documentación” section of journey D6. Although the document references the ELPS, it appears to contain a direct translation of the English version. In Texas, the ELPS are designed for EB students developing English proficiency and do not apply to Spanish-language math instruction. Thus, this guidance does not provide linguistically appropriate supports designed specifically for Spanish-language instruction.
The Math Journeys grade 4 Spanish program contains implementation guidance to help educators use the materials effectively in state-approved bilingual programs. The ESL/Bilingual Implementation Guide provides detailed instruction on language support for each journey, highlighting specific routines, strategies, and activities designed to facilitate effective teaching within models for state-approved bilingual programs. This guide ensures that educators have the targeted, actionable guidance they need to effectively implement the Math Journeys grade 4 Spanish program within the context of state-approved bilingual programs, supporting both language development and mathematical understanding for EB students.
Evaluation for 3.3d
Supports embedded throughout the Math Journeys grade 4 Spanish program 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 presents key academic terms along with definitions and visual representations that support the development of mathematical language in Spanish. The “Antes de empezar” section enables educators to help students activate and build their background knowledge before introducing new content, preparing them to engage with grade-level mathematical concepts. Throughout lesson activities, discussion prompts and partner conversations provide opportunities for students to develop and use academic language during oral discourse. Additionally, printable log books engage students in written discourse by requiring them to record and explain their mathematical thinking in writing. Furthermore, the lesson vocabulary contains cognates to support cross-linguistic connections between Spanish and English mathematical terms. Together, these embedded supports provide educators with guidance for helping EB students develop their language and content knowledge.
Each lesson in the Math Journeys grade 4 Spanish program provides EB students with dedicated support and educators with specific guidance for developing academic vocabulary as well as fostering cross-linguistic connections through oral and written discourse. These supports identify intentional opportunities throughout the lesson to reinforce key vocabulary in meaningful, targeted ways. For example, activity 1.3 encourages educators to record students’ statements using key vocabulary words, supporting students as they develop and apply academic language through oral and written discourse. Additionally, educators highlight cognates in Spanish to reinforce the meaning of key vocabulary and help students make connections between Spanish and English mathematical terms. Together, these embedded supports provide educators with explicit guidance to support EB students’ language development while strengthening their conceptual understanding of mathematical content.
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
Each lesson in the Math Journeys grade 4 Spanish program contains additional supports for students who have not yet reached proficiency. The “Desenlace” section includes a worksheet version of the lesson with embedded supports that provides an accessible entry point for students who need additional scaffolding. Furthermore, the “Apoyo” section at the end of each lesson suggests specific manipulatives and instructional strategies to clarify concepts and address learning needs. Together, these embedded supports help educators clearly identify and respond to students who have not yet shown 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 in the Math Journeys grade 4 Spanish program contains dedicated support for emergent bilingual (EB) students and identifies intentional opportunities to reinforce key terms. For example, in activity 1.1, sentence stems help students explain their mathematical thinking through oral discourse. The materials also recommend using gestures and visual representations to reinforce vocabulary development and comprehension. These embedded supports provide meaningful guidance for building students’ academic vocabulary and increasing their comprehension.
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
Within the “Recursos” section of each lesson, a printable worksheet titled “Ampliación” extends learning by asking students to use different numbers than those presented during the lesson and identify patterns and relationships. Additionally, this worksheet provides students with opportunities to extend their thinking beyond the lesson objectives and includes explicit guidance for educators to effectively implement or facilitate these extension activities. Thus, the materials provide enrichment resources for students who have shown above grade-level proficiency in the content and skills taught.
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 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 4 Spanish program helps educators provide varied opportunities for students to demonstrate mathematical understanding. In a lesson focused on multiplying numbers between one and 1,000 by single-digit numbers, students first discuss a problem and explain their mathematical thinking through oral discourse. They then use manipulatives and multiplicative frames to represent problems concretely and visually before independently representing and solving problems using an area model. Together, these opportunities to express, represent, and perform mathematical thinking help educators offer students multiple and varied ways to show their understanding of mathematical concepts throughout the lesson.
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 4 Spanish program contains numerous opportunities to activate students’ prior knowledge, anchor big ideas, and connect relationships through multiple representations. In the activities, students analyze and compare mathematical relationships, explain their reasoning using conceptual understanding, and evaluate solution strategies through visual models, equations, and other representations. The materials also help educators 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 support educators in helping students develop 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 4 Spanish program clearly explains how to effectively deliver and facilitate lessons through multiple instructional approaches. In a lesson focused on multiplying numbers between one and 1,000 by single-digit numbers, students first discuss a given problem, promoting mathematical discourse and collaborative learning. Students then use manipulatives and multiplicative frames to represent problems, engaging in hands-on and visual learning experiences. Finally, students represent and solve problems using an area model, transitioning from concrete and visual representations to more abstract mathematical thinking. Thus, the curriculum enables educators to facilitate lessons using multiple instructional methods 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 4 Spanish program contains multi-tiered intervention methods involving a variety of instructional practices and structures to address diverse learning needs. The program provides opportunities for guided, collaborative, independent, and educator-facilitated practice across whole-group, partner, and individual settings. Implementation supports include questioning strategies, manipulatives, models, and visual representations that facilitate effective instruction across multiple levels of support. Furthermore, the embedded “Apoyo” and “Ampliación” sections provide differentiated supports for students who need additional scaffolding as well as extension opportunities for students who have shown mastery. Together, these varied instructional practices and differentiated supports help educators implement multi-tiered intervention methods throughout the lessons.
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 4 Spanish program provides educators with explicit guidance on enrichment and extension activities that support various forms of engagement for students who have demonstrated proficiency in the content and skills. Within the “Desenlace” of each lesson, a dedicated “Ampliación” section provides specific guidance on how to offer extension activities and questions to students who have mastered the content. For example, in one lesson, the “Ampliación” extension activity directs educators to ask students to explain what would happen if the initial number were different from the previous example. This challenges students to apply their understanding by reasoning through a new scenario and extend their mathematical thinking beyond the core lesson objectives. This embedded guidance ensures that educators have the specific, actionable tools they need to keep students engaged and deepen learning for students who have shown 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
Discussion opportunities embedded throughout the Math Journeys grade 4 Spanish program provide educators with prompts and guidance for delivering timely feedback during lessons. Educators intentionally prompt students to explain their mathematical thinking and verify their understanding based on their responses. Specific guidance identifies what educators should expect to see and hear when students demonstrate understanding, creating intentional checkpoints for monitoring progress and addressing misconceptions in real time. Additionally, the lessons provide students with multiple ways to show their understanding, including physical participation through a game using hoops, verbal discussion, and written and drawn representations. These varied opportunities enable educators to observe students’ thinking through multiple modalities and provide immediate, responsive feedback that supports their understanding and advances their learning throughout a given lesson.
3.3 Support for Emergent Bilingual Students
3.3a
If designed to be static, materials include educator guidance on providing and incorporating linguistic accommodations for all levels of language proficiency [as defined by the English Language Proficiency Standards (ELPS)], which are designed to engage students in using increasingly more academic language.
If designed to be static, materials include educator guidance on providing and incorporating linguistic accommodations for all levels of language proficiency [as defined by the English Language Proficiency Standards (ELPS)], which are designed to engage students in using increasingly more academic language.
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 4 Spanish program contains implementation guidance to help educators use the materials effectively in state-approved bilingual programs. The ESL/Bilingual Implementation Guide provides detailed instruction on language support for each journey, highlighting specific routines, strategies, and activities designed to facilitate effective teaching within models for state-approved bilingual programs. This guide ensures that educators have the targeted, actionable guidance they need to effectively implement the Math Journeys grade 4 Spanish program within the context of state-approved bilingual programs, 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 in the Math Journeys grade 4 Spanish program provides EB students with dedicated support and educators with specific guidance for developing academic vocabulary as well as fostering cross-linguistic connections through oral and written discourse. These supports identify intentional opportunities throughout the lesson to reinforce key vocabulary in meaningful, targeted ways. For example, activity 1.3 encourages educators to record students’ statements using key vocabulary words, supporting students as they develop and apply academic language through oral and written discourse. Additionally, educators highlight cognates in Spanish to reinforce the meaning of key vocabulary and help students make connections between Spanish and English mathematical terms. Together, these embedded supports provide educators with explicit guidance to support EB students’ language development while strengthening their conceptual understanding of mathematical content.
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 4, a lesson on connecting multiplication to the area model within journey C3 provides practice opportunities that require students to demonstrate a depth of understanding aligned with the TEKS. During the “Planteamiento,” students color squares on a multiplication chart using a factor of 3 without numbers, engaging in a concrete, visual exploration of the concept. In activity 1, students connect the concept of area with decomposing numbers to multiply using the area model, bridging concrete and representational thinking. Activity 2 and the “Desenlace” extend this progression through an applet activity that asks students to practice and apply their understanding in a new format, transitioning from representational to abstract mathematical thinking. This structured movement across concrete, representational, and abstract levels within a single lesson shows that practice opportunities in the Math Journeys grade 4 Spanish program are aligned with the full rigor of the TEKS.
The Math Journeys grade 4 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 and interpreting integers in multiple real-world contexts and applying number-line reasoning to solve problems. The lessons also contain instructional assessments that require students to show a depth of understanding aligned with the TEKS, including individual tasks, group work, and contextual problem-solving in which students must justify and apply their understanding of integers.
Evaluation for 4.1b
The Math Journeys grade 4 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 and the “Desenlace.” This structured progression ensures that students are consistently challenged at increasing levels of rigor as they move through each lesson. In addition, the “Ampliación” section, embedded within the “Desenlace,” provides extension activities that further 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 4 Spanish program provides students with opportunities to build upon their prior knowledge as lessons increase in rigor. For example, in journey D3, lesson 8, students start by practicing comparing whole numbers before building on that knowledge by applying it to their understanding of money and decimals. The lesson progresses from students placing a decimal point to creating their own numbers. The “Apoyo” and “Ampliación” sections further extend learning by guiding educators to extend questioning and prompting students to find different ways to obtain the same outcome.
Evaluation for 4.2a
In grade 4, a lesson on division within pathway C4, “Mastering Division: Bridging Strategies and Algorithms,” demonstrates horizontal coherence by connecting patterns, big ideas, and relationships between multiplication and division. During the “Planteamiento,” students analyze images to identify how distinct multiplication equations produce identical products, recognizing patterns within number sets. The development activity then links multiplication to division by presenting division as the operational inverse of equal groups, connecting concrete representations to abstract partial quotients. By threading multiplication patterns and division relationships through a single lesson, the materials help students recognize these operations as interconnected ideas rather than isolated skills, demonstrating coherence across concepts horizontally within the grade level.
The Math Journeys grade 4 Spanish program demonstrates horizontal coherence within the grade level. The “Vista general de tramo” outlines the progression of concepts across previous, current, and future learning clusters within a given topic. For example, the cluster C document, “Pensamiento multiplicativo,” explains that students previously moved away from counting by ones toward thinking in groups and have mastered the idea that totals can be broken down and rearranged. In the current cluster, students build upon that foundation by working with equal groups using strategies such as arrays and equal jumps on the number line. The following cluster then extends this understanding by focusing on partitioning, sharing, and working with larger numbers and more complex grouping, showing a coherent progression that builds from previous concepts toward more complex mathematical ideas.
Evaluation for 4.2b
The Math Journeys grade 4 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 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 a set of isolated skills.
The Math Journeys grade 4 Spanish program demonstrates coherence vertically across grade levels. For example, in lesson 4 of journey D3, students develop their understanding of fraction comparison and conversion by first finding all factors of 24 to learn how to identify common factors. Students then create pictorial models of fractions to aid in comparison before applying multiplication or division to find common factors and accurately compare fractions. This lesson deepens students’ understanding of finding common denominators, a skill rooted in prior knowledge of multiplication and division that supports fraction comparison. This skill will be essential for adding and subtracting fractions with unlike denominators in future grades. Thus, the materials show coherence vertically across grade levels by connecting previously learned concepts to current understanding, laying the foundation for more complex fraction work ahead.
Evaluation for 4.2c
Educators receive guidance to connect students’ prior knowledge of concepts and procedures to current and future mathematical learning. In pathway C1, lesson 1, students explore doubling two-digit numbers using base 10 blocks, with educator notes explicitly connecting the lesson to students’ prior understanding of odd and even numbers, using the doubling activity as an opportunity to revisit the concept. The materials further connect prior knowledge of place-value composition by guiding students to see that doubling a two-digit number requires doubling the tens and ones separately. To enable students to analyze relationships across place-value concepts and apply that understanding to new numbers, the educator uses prompts such as “¿Podrías explicar qué ocurre con las decenas y las unidades cuando haces el doble de 24?” and “¿Cómo te ayuda esa relación a encontrar el doble de un número diferente, como 37?” This progression builds the foundation for multi-digit multiplication strategies in future grade levels, demonstrating coherence across lessons by connecting prior knowledge of both concepts and procedures to current and future mathematical learning.
The Math Journeys grade 4 Spanish program shows coherence vertically across grade bands through the progression of concepts outlined in the “Vista general de tramo.” For example, the cluster C document, “Pensamiento multiplicativo,” explains that students previously moved away from counting by ones toward thinking in groups and have mastered the idea that totals can be broken down and rearranged. In the current cluster, students build upon that foundation by working with equal groups using strategies such as arrays and equal jumps on the number line. The following cluster then extends this understanding by focusing on partitioning, sharing, and working with larger numbers as well as more complex grouping, demonstrating a coherent vertical progression that builds from previous concepts toward more complex mathematical ideas.
Evaluation for 4.3a
The Math Journeys grade 4 Spanish program provides opportunities for spaced retrieval with 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 learning for the current lesson. This consistent structure focuses on introducing new concepts and having students practice them within the lesson while also providing intentional opportunities for students to retrieve skills and concepts from earlier pathways at a later point in time. Thus, the materials provide opportunities for spaced retrieval of previously learned skills and concepts across the learning pathways.
The Math Journeys grade 4 Spanish program provides opportunities for spaced retrieval with previously learned skills and concepts across learning pathways. For example, lessons revisit students’ prior understanding of number lines and whole numbers by having them locate integers on the number line before extending to decimals, such as comparing 3.5 and 4.8 and rewriting 6.2 as 6.20. These repeated activities across multiple segments support retrieval of previously learned skills, such as ordering numbers and interpreting place value. The materials also reinforce previously learned concepts like place value and the structure of decimals by connecting representations across contexts, such as measurement, money, number lines, and applying them to rounding, such as rounding 3.14 to the nearest whole number or tenth using proximity on the number line. These opportunities throughout the lesson sequence support spaced retrieval of prior learning and promote deeper conceptual understanding.
Evaluation for 4.3b
As an adaptive curriculum, the Math Journeys grade 4 Spanish program mixes previously learned skills and concepts within practice sessions based on student performance and progress, providing opportunities for interleaved practice across the learning pathways. During the reviewed lessons, the materials interleave multiplication and division concepts across the pathways. In pathway C1, lesson 1, students connect doubling concepts to place-value skills, and in pathway C2, lesson 2, they practice multiplicative comparison alongside additive reasoning. In pathway C3, lesson 14 and pathway C4, lesson 6, the materials continue to interleave prior multiplication concepts with area models and division strategies, requiring students to draw on skills from earlier pathways to engage with the new content. This adaptive design ensures that students encounter previously learned skills and concepts alongside new information, rather than in isolation.
The Math Journeys grade 4 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 ÷ 5 and 70 ÷ 7, to deduce unknown results, such as 99 ÷ 6 and 74 ÷ 7, thus strengthening their fluency with quotients and remainders. The lessons also deepen students’ conceptual understanding by connecting division to equal groups, multiplication relationships, and decomposition, 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 4 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 and interpreting integers in multiple real-world contexts and applying number-line reasoning to solve problems. The lessons also contain instructional assessments that require students to show a depth of understanding aligned with the TEKS, including individual tasks, group work, and contextual problem-solving in which students must justify and apply their understanding of integers.
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 4 Spanish program provides students with opportunities to build upon their prior knowledge as lessons increase in rigor. For example, in journey D3, lesson 8, students start by practicing comparing whole numbers before building on that knowledge by applying it to their understanding of money and decimals. The lesson progresses from students placing a decimal point to creating their own numbers. The “Apoyo” and “Ampliación” sections further extend learning by guiding educators to extend questioning and 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 4 Spanish program demonstrates horizontal coherence within the grade level. The “Vista general de tramo” outlines the progression of concepts across previous, current, and future learning clusters within a given topic. For example, the cluster C document, “Pensamiento multiplicativo,” explains that students previously moved away from counting by ones toward thinking in groups and have mastered the idea that totals can be broken down and rearranged. In the current cluster, students build upon that foundation by working with equal groups using strategies such as arrays and equal jumps on the number line. The following cluster then extends this understanding by focusing on partitioning, sharing, and working with larger numbers and more complex grouping, showing a coherent progression that builds 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 4 Spanish program demonstrates coherence vertically across grade levels. For example, in lesson 4 of journey D3, students develop their understanding of fraction comparison and conversion by first finding all factors of 24 to learn how to identify common factors. Students then create pictorial models of fractions to aid in comparison before applying multiplication or division to find common factors and accurately compare fractions. This lesson deepens students’ understanding of finding common denominators, a skill rooted in prior knowledge of multiplication and division that supports fraction comparison. This skill will be essential for adding and subtracting fractions with unlike denominators in future grades. Thus, the materials show coherence vertically across grade levels by connecting previously learned concepts to current understanding, laying the foundation for more complex fraction work ahead.
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 4 Spanish program shows coherence vertically across grade bands through the progression of concepts outlined in the “Vista general de tramo.” For example, the cluster C document, “Pensamiento multiplicativo,” explains that students previously moved away from counting by ones toward thinking in groups and have mastered the idea that totals can be broken down and rearranged. In the current cluster, students build upon that foundation by working with equal groups using strategies such as arrays and equal jumps on the number line. The following cluster then extends this understanding by focusing on partitioning, sharing, and working with larger numbers as well as more complex grouping, demonstrating a coherent vertical progression that builds from previous concepts toward more complex mathematical ideas.
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 4 Spanish program provides opportunities for spaced retrieval with previously learned skills and concepts across learning pathways. For example, lessons revisit students’ prior understanding of number lines and whole numbers by having them locate integers on the number line before extending to decimals, such as comparing 3.5 and 4.8 and rewriting 6.2 as 6.20. These repeated activities across multiple segments support retrieval of previously learned skills, such as ordering numbers and interpreting place value. The materials also reinforce previously learned concepts like place value and the structure of decimals by connecting representations across contexts, such as measurement, money, number lines, and applying them to rounding, such as rounding 3.14 to the nearest whole number or tenth using proximity on the number line. These opportunities throughout the lesson sequence support spaced retrieval of prior learning and promote 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 4 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 ÷ 5 and 70 ÷ 7, to deduce unknown results, such as 99 ÷ 6 and 74 ÷ 7, thus strengthening their fluency with quotients and remainders. The lessons also deepen students’ conceptual understanding by connecting division to equal groups, multiplication relationships, and decomposition, 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
In grade 4, questions and tasks require students to interpret, analyze, and evaluate models and representations for mathematical concepts and situations. Students interpret models and representations by using visual fraction models and manipulatives to understand subtraction as removing equal parts from a whole. Students analyze models and representations by connecting concrete representations to equations and identifying patterns, such as the role of a common denominator when subtracting fractions. Students also evaluate models and representations by determining when they can compare or operate on fractions based on the unit and justifying the validity of their representations using mathematical reasoning. This progression from interpreting to analyzing to evaluating models and representations shows that the Math Journeys grade 4 Spanish program provides students with opportunities to engage with fraction concepts at increasing levels of cognitive demand.
The Math Journeys grade 4 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 pattern blocks and visual area models to identify fractional parts of a whole and understand how the unit affects the value of each piece. They then analyze models and representations by composing and decomposing fractions into sums of unit fractions, comparing equivalent representations, and identifying relationships between the parts and the whole. Finally, students evaluate models and representations as they justify why their representations are valid, explain equivalence, and defend their reasoning when multiple decompositions or representations are possible.
Evaluation for 5.1b
The Math Journeys grade 4 Spanish program provides opportunities for students to create concrete models and pictorial representations of mathematical situations. Students create concrete models as they construct number lines using paper strips and fraction pieces, iterating units to build and extend the line and represent fractional quantities and equivalences. Students also create pictorial representations by drawing number lines and representing fractions, equivalent fractions, and movements along the number line, making their reasoning visible through visual models.
The Math Journeys grade 4 Spanish program provides opportunities for students to create concrete models and pictorial representations of mathematical situations. Students create concrete models as they use fraction pieces to build a fraction wall, physically aligning and comparing lengths to represent equivalent fractions and multiplicative relationships. Students also create pictorial representations by recording, drawing, and explaining fraction relationships and equivalences, using visual models to justify how fractions represent the same quantity.
Evaluation for 5.1c
Activity 1.1 presents students with a word problem about a plant’s growth over time. Students apply their conceptual understanding of adding fractions using the “Jumping along the Number Line” strategy to a new context. They do so by determining the total height of a plant that started at 3/8 inches tall and grew 4/8 inches more.
In the warm-up activity, students apply their conceptual understanding that a fraction’s value depends on the unit it references to a new real-world situation. Students are presented with a claim that three glasses, each containing 1/3 juice, are combined to fill exactly one whole glass. Students must transfer their understanding that fractions depend on the unit’s size to determine why the claim is false when the glasses are different sizes.
Evaluation for 5.2a
The Math Journeys grade 4 Spanish program gives students opportunities to develop and demonstrate procedural fluency. For example, the applet presents tasks involving fraction addition across seven denominator families—halves, thirds, fourths, sixths, eighths, tenths, and twelfths—providing the volume of targeted practice needed to build automaticity with like-denominator addition at grade level. Cycling through all seven denominator families enables students to develop fluency across the full range of denominators they encounter at this grade level, rather than isolating a single number type. The consistent addend structure supports procedural internalization through repetition, while the varied denominators prevent rote recall without understanding, ensuring that students build both efficiency and flexibility with fraction addition.
The Math Journeys grade 4 Spanish curriculum gives students opportunities to develop and demonstrate procedural fluency. For example, in applet 350, students build automaticity by converting given fractions to decimals expressed in tenths or hundredths. This activity helps students develop the fluency they need to complete grade-level tasks by supporting their understanding not only of fractions and decimals but also of pictorial models, number lines, and comparison and calculation problems. Thus, the materials reinforce the foundational skills required for accurate and efficient performance across a range of grade-level tasks.
Evaluation for 5.2b
The Math Journeys grade 4 Spanish program gives students opportunities to develop and demonstrate flexibility in procedural competency. For example, in lesson 3 of journey D3, a dropdown box explicitly labeled “Process Standard 1C” requires students to select the technique that makes comparing 3/4 and 5/8 most efficient, prompting them to evaluate and choose among common-denominator, common-numerator, and benchmark strategies. The Teacher Guide further builds flexible application by asking students how the same-denominator rule applies to fractions with unlike denominators, extending procedural flexibility across multiple strategy types. Activity 1 then reinforces accurate application by having students apply their chosen procedure across multiple fraction pairs using <, >, and = notation.
The Math Journeys grade 4 Spanish program provides students with opportunities to develop and demonstrate flexibility in procedural competency. For example, in activity 1.1, pairs of students create a number line divided into fifths by iterating a 1/5 fraction bar. They then verify their diagram against applet A271, evaluating their physical model for accuracy. Next, students discover that every fifth aligns with an even-numerator tenth, evaluating two representational systems (fifths and tenths) for equivalence and accuracy. The class discussion requires students to explain why they think certain fractions are equivalent, assessing their reasoning against the visible alignment on both the paper strip and the applet. Thus, the materials reinforce flexibility in representation as well as precision in evaluating procedural accuracy.
Evaluation for 5.2c
The Math Journeys grade 4 Spanish program provides students with opportunities to evaluate the reasonableness of their results and the efficiency of their procedures. For example, the “Planteamiento” asks students to determine what fraction each pattern block color represents, evaluating whether the proposed representation of six triangles out of 12 is equivalent to 1/2 by reasoning about the relationship between the numerator and denominator. The Teacher Guide instructs educators to have students verify this equivalence using pattern blocks, requiring students to evaluate a pictorial representation against a concrete model for accuracy. Activity 1.1 extends this by asking students to compare and evaluate multiple decompositions of the same fraction, assessing whether each representation names the same value and reinforcing the importance of evaluating reasonableness across multiple representations.
The Math Journeys grade 4 Spanish program gives students opportunities to evaluate the reasonableness of their results and the efficiency of their procedures. For example, in activity 1.1, pairs of students create a number line divided into fifths by iterating a 1/5 fraction bar. They then verify their diagram against applet A271, evaluating their physical model for accuracy. Next, students discover that every fifth aligns with an even-numerator tenth, evaluating two representational systems (fifths and tenths) for equivalence and reasonableness. The class discussion requires students to explain why they think certain fractions are equivalent, assessing their reasoning against the visible alignment on both the paper strip and the applet to confirm accuracy across multiple representations.
Evaluation for 5.2d
The Math Journeys grade 4 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 1.1 provides scaffolding that helps students move from using snap cubes in groups of 10 to deriving nearby facts mentally. To guide students toward more efficient approaches, the Teacher Guide directs the educator to ask, “Are there numbers close to 17 that can be divided evenly by 5?” Activity 1.2 then builds upon known facts such as 70 ÷ 7 = 10 to solve 72 ÷ 7 without manipulatives, reinforcing the use of known relationships to increase efficiency. The Teacher Guide further supports this progression by explicitly instructing educators to encourage students to find the optimal quotient as they advance, steering them toward increasingly efficient strategies across division tasks.
The Math Journeys grade 4 Spanish program provides students with opportunities to apply procedural fluency by selecting and using the most efficient strategy for a given problem. For example, in lesson 7 of journey C3, students begin by interpreting an area model to determine the product of a two-by-two-digit multiplication problem, analyzing the model to evaluate how to solve the problem most efficiently. Students discover that although counting every individual square would yield a correct result, it is not the most efficient strategy. Through this reasoning, students develop the more efficient approach of decomposing factors into tens and ones, finding the area of each individual section of the rectangle, and adding all four parts together to determine the product.
Evaluation for 5.3a
The Math Journeys grade 4 Spanish program clearly explains how the conceptual and procedural emphases of the TEKS are addressed. For example, lesson 7, “Representar decimales: contextos de medición,” explicitly connects conceptual understanding of decimals to a real-world measurement context by having students select classroom objects with lengths between 50 centimeters and 3 meters, such as the width of a door and the height of a chair. Students receive a metric tape measure to find the length of selected objects and record the results on the board using meters as the unit of measure. The lesson shows the conceptual emphasis through the use of familiar measurement contexts to help students understand how decimal notation represents and connects to real-world quantities, connecting concrete measurement experiences to abstract decimal representations.
The Math Journeys grade 4 Spanish program clarifies how the conceptual and procedural emphases of the TEKS are addressed. For example, the lesson reflects the conceptual emphasis by enabling students to develop the understanding that fractions must share a common unit and can be combined as equal-sized parts of a whole through models and reasoning. The lesson simultaneously addresses the procedural emphasis by having students compute sums of fractions with common denominators, represent the results, including mixed numbers, and apply strategies in contextual problems. By explicitly integrating conceptual understanding through meaning and models with procedural fluency through calculation and application, the materials explain both components of the TEKS emphases within a given lesson.
Evaluation for 5.3b
In “División mediante reparto,” students physically manipulate fichas on a tray, distributing them equally among four students to build a concrete understanding of division as equal sharing. The lesson then connects this hands-on experience to pictorial representations by projecting images of equal groups through resource 1, prompting students to analyze and defend both the similarities and differences between the two images. This progression helps students connect their concrete experience with equal sharing to a visual representation of the same concept.
Students engage with concrete models by using money, such as pennies and dimes, and completing interactive tasks with grids, allowing them to physically and contextually represent fractional parts of a whole. Students then connect their hands-on experiences to pictorial representations by shading 10×10 grids and visual models to represent hundredths and tenths, helping them visualize equivalence and the composition of fractions and decimals. They also link these concrete and pictorial experiences to abstract models through fraction notation and decimal expressions, such as 20/100 = 0.20 = 0.2, as well as symbolic equations. By intentionally integrating and connecting all three representations throughout the lesson, students move from concrete to pictorial to abstract understanding via a coherent progression.
Evaluation for 5.3c
During the warm-up, students manipulate physical rectangular fraction pieces to analyze equivalence by aligning different denominators to a fixed length, recognizing that four-sixths and eight-twelfths are equivalent to two-thirds because they align at the same endpoint. The development activity uses process standard 1F to prompt students to explain the relationship between multiplication and equivalent fractions through prompts such as “Could you find a rule that provides you a shortcut to create equivalent fractions?” and “What relationship do you see between the numerators and denominators of two-thirds, four-sixths, and eight-twelfths?” The lesson further supports EB students through the discussion supports in Mathematical Language Routine (MLR) 8, providing tiered sentence stems to explain equivalent fractions. Students then transition from using concrete tools to representational models by partitioning and shading blank fraction models. Finally, students connect these pictorial experiences to abstract notation through written numerical equations, creating a direct bridge between the physical, visual, and symbolic representations.
Students connect concrete models, such as pattern blocks and manipulatives, with pictorial representations, including colored diagrams and partitioned figures, and then relate both to abstract fraction notation, such as 4/5. Students create both physical and visual models to represent unit fractions and their decompositions, building a hands-on foundation for abstract understanding. In addition, students must define and explain their reasoning by justifying how the parts relate to the whole and expressing fractions as repeated addition and symbolic equations.
Evaluation for 5.4a
The Math Journeys grade 4 Spanish program provides clear instruction on mathematical vocabulary and academic language. For example, the “Vista general de tramo—B: pensamiento aditivo” explicitly introduces and defines terms such as tens, units, and values, providing students with the foundational vocabulary to engage with additive thinking concepts. Linguistic supports introduce students to identifying and interpreting mathematical symbols, ensuring that they develop the academic language and symbolic literacy required to access and communicate mathematical ideas throughout the broader learning pathway.
In activity 1.1, students develop their academic mathematical language using manipulatives as they iterate a 1/5 fraction-bar piece along a paper strip, physically building a number line while naming each mark with fraction notation. The Teacher Guide instructs educators to ask how many fifths reach 1, connecting the manipulative action to denominator vocabulary. Students then label equivalent tenths using terms such as equivalent, numerator, and denominator through the visual number-line artifact.
Evaluation for 5.4b
The Math Journeys grade 4 Spanish program provides scaffolding to support and extend students’ use of academic mathematical vocabulary through dedicated Journey Language Banks housed in the “Adaptaciones bilingües” documents. For example, the B2 Journey Language Bank provides educators with instructions for using the bank, multiple instructional routines, and a guide for discussion and writing. This combination of routines and discourse guidance 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.
Lesson 10 in journey C4 provides students with opportunities to develop academic mathematical language at multiple points within the lesson. Students encounter key vocabulary at the start of the lesson, introducing terms they will use throughout the lesson. In activity 2, a dropdown box titled “Estudiantes bilingües emergentes” offers educators a language strategy to scaffold and support vocabulary use for EB students. The lesson also includes “Apoyos para la conversación” discussion supports, which are tailored to each language proficiency level from beginner to advanced-high. Students utilize the word bank to extend their use of academic vocabulary when communicating with their peers and the educator.
Evaluation for 5.4c
The Math Journeys grade 4 Spanish program provides educators with embedded guidance and students with opportunities to apply academic mathematical vocabulary in discourse through structured routines. The tip on EB students incorporates the MLR6 “Three Reads” routine, which guides students through three structured readings and prompts them to name quantities and predict operations using academic language before solving the problem. To encourage students to use terms such as forward, backward, and fraction in spoken responses, the Teacher Guide directs educators to ask, “Could you explain how the jumps on the number line diagram show the plant’s growth?” Support notes further instruct educators to encourage the use of precise terms such as addend, jump, and mixed number throughout partner and whole-class discourse.
Lesson 10 in journey C4 helps students apply appropriate mathematical language and academic vocabulary in discourse at multiple points throughout the lesson. Students encounter key vocabulary at the beginning of the lesson, establishing the terms they will use as they engage in discourse. In activity 2, a dropdown box titled “Estudiantes bilingües emergentes” explains a language strategy for educators to help students use this vocabulary in conversation. The lesson further includes “Apoyos para la conversación” discussion supports, which are tailored to language proficiency levels ranging from beginner to advanced-high and include a word bank to help students apply appropriate mathematical vocabulary during discussions.
Evaluation for 5.4d
The note on EB students provides leveled sentence frames, such as “To solve the equation…I first…because…,” so that students hear academic subtraction language modeled by their peers before producing it independently. To enable students to refine everyday phrases into precise mathematical language using terms such as numerator, denominator, and same denominator, the Teacher Guide directs educators to ask, “Can you explain your reasoning about why these images are the same or different?” In activity 1.2, pairs of students share and compare written subtraction equations, giving them a structured second opportunity to use the refined vocabulary in peer discourse.
Students encounter key vocabulary at the beginning of the lesson, giving them a shared language to draw upon during peer conversation. In activity 2, a dropdown box titled “Estudiantes bilingües emergentes” explains a language strategy for educators to use in facilitating these conversations. The lesson further includes “Apoyos para la conversación” discussion supports for language proficiency levels ranging from beginner to advanced-high, providing a word bank that helps students hear, refine, and use mathematical language with their peers during discourse.
Evaluation for 5.4e
In D3.6, “Introducir los decimales y las fracciones decimales,” the Teacher Guide anticipates a variety of student answers by directing educators to “expect all possible answers using all the coins students know.” The guide then provides a specific exemplar: “Expect students to use the grid to observe that, since there are 10 columns in total, you can also use the fraction 1/10.” When students use informal language, an embedded language redirect guides educators to affirm and recast. For example, when a student says “one point five,” the educator responds, “We say one and five tenths.” For inaccurate fraction reasoning, the guide instructs educators to ask students to look at the array representation, steering them back to the concrete model to rebuild understanding.
Activity 1 anticipates multiple solution paths students may use by embedding two exemplar strategies: one directing students to start at the green flag and jump forward 7/10, and another suggesting that students add 7/10 + 7/10 directly, then express the result as the mixed number 1 4/10. Activity 1 also provides an exemplar justification, modeling that students should justify the distance between 0 and 7/10 as 7/10. This gives educators clear language for the reasoning expected of students. The guide further redirects inaccurate thinking by noting that students should recognize that no fraction with a denominator of 10 can be placed between 2/10 and 3/10, helping educators connect the correction to students’ prior learning rather than simply flagging the error.
Evaluation for 5.5a
Students in the Math Journeys grade 4 Spanish program apply the TEKS mathematical process standards through tasks that integrate real-world problem-solving and analysis of mathematical relationships within the same lesson sequence. Process standard 1A is integrated as students apply fraction addition to a real-world context of plant growth, using forward jumps on the number line to find the new height of a sprout that grew 4/8 inches. Here, students translate a concrete situation into a mathematical model and interpret the result in context. Process standard 1F is simultaneously embedded as students analyze the relationship between decomposing a jump and passing through a whole unit, connecting fractional distances to addition and subtraction. To encourage students to articulate the connection between their mathematical reasoning and the real-world situation, the Teacher Guide reinforces both process standards by directing educators to ask, “How does finding 3/8 + 4/8 on the number line help you answer the question?” Together, these integrated process standards ensure that students not only compute with fractions but also reason about mathematical relationships and apply them meaningfully to everyday contexts.
Process standard 1C is explicitly labeled with integration guidance, noting that students engage in this standard when they select the technique that makes comparing 3/4 and 5/8 most efficient. Strategy selection is embedded directly into activity 2 rather than being treated as an add-on. Process standard 1G is also clearly labeled, with guidance stating that students engage in this standard when they explain and justify the correct fraction comparison using precise mathematical language, integrating oral justification as a required component of the main activity. Both standards appear as embedded instructional notes within the session rather than as optional extensions.
Evaluation for 5.5b
Educators can reference the Guía de instrucciones for journey C4 to identify how process standards connect across the learning pathway. This document 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 pathway. A horizontal rationale within the Guía de instrucciones explains how the process standards are connected throughout the broader learning pathway, while the session alignment details how the standards build on and function together across lessons.
The D4 Instructional Guide describes how recurring actions (representing, renaming, comparing, justifying, and interpreting) connect process standards across all D4 lessons into a coherent pathway. D4.7 tags process standards 1A and 1F, and the guide explicitly links forward-jump language from this session to the common-denominator and word-problem work in D4.10 and D4.13. The horizontal rationale further explains that these process standards deliberately revisit the same big ideas across new representations throughout the journey, demonstrating how the standards connect across lessons.
Evaluation for 5.5c
The Guía de instrucciones del journey D4 describes how recurring actions, such as representing, renaming, comparing, justifying, and interpreting, connect the process standards across all D4 lessons into a coherent pathway. Lesson D4.7 tags process standards 1A and 1F, and the guide explicitly links the forward-jump language from that session to the common-denominator and word-problem work in D4.10 and D4.13, making the cross-lesson connections visible to educators before starting instruction. The horizontal rationale states that these process standards “deliberately revisit the same big ideas” across new representations throughout the journey, ensuring that educators understand how each lesson contributes to a larger arc of mathematical reasoning.
In grade 4, the materials include a dedicated overview panel of process standards that lists two standards with integration descriptions. The panel notes that students engage in process standard 1G when they explain and justify the correct fraction comparison using precise mathematical language, and that students engage in process standard 1C when they select the technique that makes comparing 3/4 and 5/8 most efficient. Each description links the listed standard to a specific moment during the lesson, allowing the overview to function as a navigational tool for educators.
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 4 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 pattern blocks and visual area models to identify fractional parts of a whole and understand how the unit affects the value of each piece. They then analyze models and representations by composing and decomposing fractions into sums of unit fractions, comparing equivalent representations, and identifying relationships between the parts and the whole. Finally, students evaluate models and representations as they justify why their representations are valid, explain equivalence, and defend their reasoning when multiple decompositions or representations are possible.
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 4 Spanish program provides opportunities for students to create concrete models and pictorial representations of mathematical situations. Students create concrete models as they use fraction pieces to build a fraction wall, physically aligning and comparing lengths to represent equivalent fractions and multiplicative relationships. Students also create pictorial representations by recording, drawing, and explaining fraction relationships and equivalences, using visual models to justify how fractions represent the same quantity.
5.1c
Questions and tasks provide opportunities for students to apply conceptual understanding to new problem situations and contexts.
Questions and tasks provide opportunities for students to apply conceptual understanding to new problem situations and contexts.
1 out of 1 points
Evaluation for 5.1c
Evaluation for 5.1c
Questions and tasks provide opportunities for students to apply conceptual understanding to new problem situations and contexts.
1 out of 1 points
In the warm-up activity, students apply their conceptual understanding that a fraction’s value depends on the unit it references to a new real-world situation. Students are presented with a claim that three glasses, each containing 1/3 juice, are combined to fill exactly one whole glass. Students must transfer their understanding that fractions depend on the unit’s size to determine why the claim is false when the glasses are different sizes.
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 4 Spanish curriculum gives students opportunities to develop and demonstrate procedural fluency. For example, in applet 350, students build automaticity by converting given fractions to decimals expressed in tenths or hundredths. This activity helps students develop the fluency they need to complete grade-level tasks by supporting their understanding not only of fractions and decimals but also of pictorial models, number lines, and comparison and calculation problems. Thus, the materials reinforce the foundational skills required for accurate and efficient performance across a range of grade-level tasks.
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 4 Spanish program provides students with opportunities to develop and demonstrate flexibility in procedural competency. For example, in activity 1.1, pairs of students create a number line divided into fifths by iterating a 1/5 fraction bar. They then verify their diagram against applet A271, evaluating their physical model for accuracy. Next, students discover that every fifth aligns with an even-numerator tenth, evaluating two representational systems (fifths and tenths) for equivalence and accuracy. The class discussion requires students to explain why they think certain fractions are equivalent, assessing their reasoning against the visible alignment on both the paper strip and the applet. Thus, the materials reinforce flexibility in representation as well as precision in evaluating procedural accuracy.
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 4 Spanish program gives students opportunities to evaluate the reasonableness of their results and the efficiency of their procedures. For example, in activity 1.1, pairs of students create a number line divided into fifths by iterating a 1/5 fraction bar. They then verify their diagram against applet A271, evaluating their physical model for accuracy. Next, students discover that every fifth aligns with an even-numerator tenth, evaluating two representational systems (fifths and tenths) for equivalence and reasonableness. The class discussion requires students to explain why they think certain fractions are equivalent, assessing their reasoning against the visible alignment on both the paper strip and the applet to confirm accuracy across multiple representations.
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 4 Spanish program provides students with opportunities to apply procedural fluency by selecting and using the most efficient strategy for a given problem. For example, in lesson 7 of journey C3, students begin by interpreting an area model to determine the product of a two-by-two-digit multiplication problem, analyzing the model to evaluate how to solve the problem most efficiently. Students discover that although counting every individual square would yield a correct result, it is not the most efficient strategy. Through this reasoning, students develop the more efficient approach of decomposing factors into tens and ones, finding the area of each individual section of the rectangle, and adding all four parts together to determine the product.
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 4 Spanish program clarifies how the conceptual and procedural emphases of the TEKS are addressed. For example, the lesson reflects the conceptual emphasis by enabling students to develop the understanding that fractions must share a common unit and can be combined as equal-sized parts of a whole through models and reasoning. The lesson simultaneously addresses the procedural emphasis by having students compute sums of fractions with common denominators, represent the results, including mixed numbers, and apply strategies in contextual problems. By explicitly integrating conceptual understanding through meaning and models with procedural fluency through calculation and application, the materials explain both components of the TEKS emphases within a given 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
Students engage with concrete models by using money, such as pennies and dimes, and completing interactive tasks with grids, allowing them to physically and contextually represent fractional parts of a whole. Students then connect their hands-on experiences to pictorial representations by shading 10×10 grids and visual models to represent hundredths and tenths, helping them visualize equivalence and the composition of fractions and decimals. They also link these concrete and pictorial experiences to abstract models through fraction notation and decimal expressions, such as 20/100 = 0.20 = 0.2, as well as symbolic equations. By intentionally integrating and connecting all three representations throughout the lesson, students move from concrete to pictorial to abstract understanding via a coherent progression.
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
Students connect concrete models, such as pattern blocks and manipulatives, with pictorial representations, including colored diagrams and partitioned figures, and then relate both to abstract fraction notation, such as 4/5. Students create both physical and visual models to represent unit fractions and their decompositions, building a hands-on foundation for abstract understanding. In addition, students must define and explain their reasoning by justifying how the parts relate to the whole and expressing fractions as repeated addition and symbolic equations.
5.4 Development of Academic Mathematical Language
5.4a
Materials provide opportunities for students to develop academic mathematical language using visuals, manipulatives, or other language development strategies.
Materials provide opportunities for students to develop academic mathematical language using visuals, manipulatives, or other language development strategies.
1 out of 1 points
Evaluation for 5.4a
Evaluation for 5.4a
Materials provide opportunities for students to develop academic mathematical language using visuals, manipulatives, or other language development strategies.
1 out of 1 points
In activity 1.1, students develop their academic mathematical language using manipulatives as they iterate a 1/5 fraction-bar piece along a paper strip, physically building a number line while naming each mark with fraction notation. The Teacher Guide instructs educators to ask how many fifths reach 1, connecting the manipulative action to denominator vocabulary. Students then label equivalent tenths using terms such as equivalent, numerator, and denominator through the visual number-line artifact.
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
Lesson 10 in journey C4 provides students with opportunities to develop academic mathematical language at multiple points within the lesson. Students encounter key vocabulary at the start of the lesson, introducing terms they will use throughout the lesson. In activity 2, a dropdown box titled “Estudiantes bilingües emergentes” offers educators a language strategy to scaffold and support vocabulary use for EB students. The lesson also includes “Apoyos para la conversación” discussion supports, which are tailored to each language proficiency level from beginner to advanced-high. Students utilize the word bank to extend their use of academic vocabulary when communicating with their peers and the educator.
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
Lesson 10 in journey C4 helps students apply appropriate mathematical language and academic vocabulary in discourse at multiple points throughout the lesson. Students encounter key vocabulary at the beginning of the lesson, establishing the terms they will use as they engage in discourse. In activity 2, a dropdown box titled “Estudiantes bilingües emergentes” explains a language strategy for educators to help students use this vocabulary in conversation. The lesson further includes “Apoyos para la conversación” discussion supports, which are tailored to language proficiency levels ranging from beginner to advanced-high and include a word bank to help students apply appropriate mathematical vocabulary during discussions.
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
Students encounter key vocabulary at the beginning of the lesson, giving them a shared language to draw upon during peer conversation. In activity 2, a dropdown box titled “Estudiantes bilingües emergentes” explains a language strategy for educators to use in facilitating these conversations. The lesson further includes “Apoyos para la conversación” discussion supports for language proficiency levels ranging from beginner to advanced-high, providing a word bank that helps students hear, refine, and use mathematical language with their peers during discourse.
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
Activity 1 anticipates multiple solution paths students may use by embedding two exemplar strategies: one directing students to start at the green flag and jump forward 7/10, and another suggesting that students add 7/10 + 7/10 directly, then express the result as the mixed number 1 4/10. Activity 1 also provides an exemplar justification, modeling that students should justify the distance between 0 and 7/10 as 7/10. This gives educators clear language for the reasoning expected of students. The guide further redirects inaccurate thinking by noting that students should recognize that no fraction with a denominator of 10 can be placed between 2/10 and 3/10, helping educators connect the correction to students’ prior learning rather than simply flagging the error.
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
Process standard 1C is explicitly labeled with integration guidance, noting that students engage in this standard when they select the technique that makes comparing 3/4 and 5/8 most efficient. Strategy selection is embedded directly into activity 2 rather than being treated as an add-on. Process standard 1G is also clearly labeled, with guidance stating that students engage in this standard when they explain and justify the correct fraction comparison using precise mathematical language, integrating oral justification as a required component of the main activity. Both standards appear as embedded instructional notes within the session rather than as optional extensions.
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 D4 Instructional Guide describes how recurring actions (representing, renaming, comparing, justifying, and interpreting) connect process standards across all D4 lessons into a coherent pathway. D4.7 tags process standards 1A and 1F, and the guide explicitly links forward-jump language from this session to the common-denominator and word-problem work in D4.10 and D4.13. The horizontal rationale further explains that these process standards deliberately revisit the same big ideas across new representations throughout the journey, demonstrating how the standards connect across lessons.
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 4, the materials include a dedicated overview panel of process standards that lists two standards with integration descriptions. The panel notes that students engage in process standard 1G when they explain and justify the correct fraction comparison using precise mathematical language, and that students engage in process standard 1C when they select the technique that makes comparing 3/4 and 5/8 most efficient. Each description links the listed standard to a specific moment during the lesson, allowing the overview to function as a navigational tool for educators.
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
In activity 1.1, students reason about 100 ÷ 6 using groups of 10 and then deduce related facts such as 99 ÷ 6 and 98 ÷ 6 without starting over. This requires sustained mathematical thinking rather than rote computation. Activity 1.2 extends this by asking students to use known facts like 70 ÷ 7 = 10 to derive 72 ÷ 7 and 78 ÷ 7, persevering through the additional step of adjusting when remainders exceed the divisor. “Number Talk 2” then embeds a word problem that requires students to make sense of why 60 ÷ 3 and 18 ÷ 3 can be combined to solve 78 ÷ 3 = 26, helping them connect decomposition to a meaningful context. Across these tasks, students are not simply executing procedures—they are reasoning about mathematical relationships, adjusting strategies, and building a conceptual understanding of division.
In grade 4, a lesson on additive part-part-whole relationships within a unit on fraction operations opens with a warm-up that presents a challenging task, asking students to identify which fraction piece fills an empty space in the Fraction Pieces widget. This requires students to think mathematically before receiving any formal instruction. Students must then persevere through the challenge of seeing a single additive part-part-whole frame as two different operations, making sense of how one representation can simultaneously encode both addition and subtraction. The Teacher Guide supports this sense-making by explicitly modeling that “3/8 + 5/8 = 8/8” and “8/8 − 5/8 = 3/8” are hidden within the same frame, guiding students to construct this relationship rather than follow a stated procedure.
Evaluation for 6.1b
Process standard 1C is explicitly embedded as students choose among the common-denominator, common-numerator, and benchmark strategies for comparing 3/4 and 5/8. The Teacher Guide states that students “select the technique that makes comparing most efficient,” establishing from the outset that no single strategy is required. Activity 2 extends this by inviting students to consider multiple solution strategies, with the educator asking students to share different approaches before the class discusses which is the most efficient. This requires students to explain their reasoning beyond simply arriving at a correct answer. The “Two Truths, One Lie” activity then requires students to identify which expression is false and defend their reasoning, with the materials clearly validating multiple reasoning paths as long as the justification is mathematically sound.
Activity 1 further supports understanding by explicitly presenting two valid solution paths for the same flag problem, offering students the strategy to “start at the green flag and jump forward 7/10” alongside the option to “add 7/10 + 7/10 directly, then express the result as a mixed number.” Students explain their reasoning by recording their chosen strategy in log books and are prompted to “share the strategies they used,” creating a structured opportunity to compare methods with peers. The class discussion then allows students to justify the equivalence of the two approaches by showing that both paths produce the same outcome, reinforcing the idea that students can reach a correct answer through more than one legitimate strategy.
Evaluation for 6.1c
Students independently solve two addition equations in their log books before sharing strategies in a whole-class discussion, moving through all three modes in a single instructional sequence. The Teacher Guide instructs educators to ask, “Which strategy required fewer steps?” during the share-out, prompting students to compare jumping methods with peers rather than simply reporting their answers. Students also produce labeled number-line diagrams with matching equations in their log books, creating a written record that anchors the subsequent group discussion and gives students a concrete artifact to reference when justifying their reasoning. By requiring students to solve problems independently, document their thinking in writing, and engage in structured peer comparison, activity 1.2 ensures that doing, writing, and discussing math are all embedded in one coherent task.
The session guide further supports this work by explicitly recommending “visibly random pairs and groups with VNPS” (visible non-permanent surfaces), structuring collaborative work as students persevere through flag-placement problems with their peers. Students write about their mathematical thinking by recording fraction answers and solution strategies in log books, with the guide directing educators to “ask students to write the fraction in their log books and share the strategies they used.” This creates a written record that anchors subsequent discourse. The warm-up and activity 1 each conclude with a whole-class share-out, providing opportunities in a single session for students to discuss their mathematical reasoning with their peers and the educator.
Evaluation for 6.2a
During activity 1, after students solve 100 ÷ 6, the Teacher Guide directs educators to encourage students to explain their partial quotient strategy by asking, “Could you explain why you chose to start with groups of 10?” The development activity extends this by instructing educators to record both partial equations on the board and ask students to justify why combining 60 ÷ 3 and 18 ÷ 3 yields the correct total quotient. This requires students to construct and share mathematical justifications grounded in decomposition. The “Desenlace” then prompts students to reflect by connecting each distribution choice back to the final quotient. This requires students to explain the relationship between partial quotients and the whole and revisit the reasoning behind their procedural choices.
To encourage students to clearly explain and justify their reasoning within the context of pizza, the Teacher Guide directs educators to ask, “Could you explain why we can’t compare the pieces just by looking?” and instructs them to “Ask students to state what fraction of pizza Carlos has left.” Following discussion, the Teacher Guide facilitates structured reflection immediately after students share their thinking by instructing educators to “use this moment to reinforce that the value of a fraction depends on the unit it refers to.” Process standard 1G is clearly identified alongside these prompts, reinforcing the idea that students’ justification and explanation of their reasoning are intentional design features rather than incidental outcomes. By embedding explicit discussion prompts and setting aside time for structured reflection tied to a labeled process standard, the materials help students share and reflect on their problem-solving approaches as required by the criterion.
Evaluation for 6.2b
A supporting note in the lesson anticipates a specific student struggle with expressing pennies and dimes as fractions of a dollar, providing educators with a concrete redirect prompt: “If students have difficulty expressing pennies and dimes as fractions of a dollar, ask them to look at the array representation and ask: How many pennies can we put in each row?” This ties the corrective feedback directly to the visual model that students are already using, rather than redirecting them to an entirely new strategy. The Teacher Guide further scripts explanatory feedback for a language-based error, directing educators to affirm and recast when a student says “one point five” by responding, “We say one and five tenths.” This shows educators how to acknowledge and correct inaccurate mathematical language without dismissing the student’s thinking. Both prompts are embedded in the session flow, positioning them as anticipated responses that require prepared educator feedback rather than improvised correction.
Two additional anticipated misconceptions in this session come with explicit, scripted educator responses rather than a general description of the error, equipping educators with the precise corrective language to use in real time. In the warm-up, when students struggle to locate a fraction on the number line, the Teacher Guide directs educators to explain that “the denominator shows how many equal parts make up the unit (the space between 0 and 1), and the numerator shows how many of those parts to count.” The guide provides a worked example showing that “to place 3/4, divide the unit into 4 equal parts and count 3 of these parts starting from 0.” In activity 2, when students only propose fractions with a denominator of six, the guide instructs educators to redirect students “to find other fractions that satisfy the conditions using different denominators.”
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
In grade 4, a lesson on additive part-part-whole relationships within a unit on fraction operations opens with a warm-up that presents a challenging task, asking students to identify which fraction piece fills an empty space in the Fraction Pieces widget. This requires students to think mathematically before receiving any formal instruction. Students must then persevere through the challenge of seeing a single additive part-part-whole frame as two different operations, making sense of how one representation can simultaneously encode both addition and subtraction. The Teacher Guide supports this sense-making by explicitly modeling that “3/8 + 5/8 = 8/8” and “8/8 − 5/8 = 3/8” are hidden within the same frame, guiding students to construct this relationship rather than follow a stated 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 1 further supports understanding by explicitly presenting two valid solution paths for the same flag problem, offering students the strategy to “start at the green flag and jump forward 7/10” alongside the option to “add 7/10 + 7/10 directly, then express the result as a mixed number.” Students explain their reasoning by recording their chosen strategy in log books and are prompted to “share the strategies they used,” creating a structured opportunity to compare methods with peers. The class discussion then allows students to justify the equivalence of the two approaches by showing that both paths produce the same outcome, reinforcing the idea that students can reach a correct answer through more than one legitimate strategy.
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 session guide further supports this work by explicitly recommending “visibly random pairs and groups with VNPS” (visible non-permanent surfaces), structuring collaborative work as students persevere through flag-placement problems with their peers. Students write about their mathematical thinking by recording fraction answers and solution strategies in log books, with the guide directing educators to “ask students to write the fraction in their log books and share the strategies they used.” This creates a written record that anchors subsequent discourse. The warm-up and activity 1 each conclude with a whole-class share-out, providing opportunities in a single session for students to discuss their mathematical reasoning with their peers and the educator.
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
To encourage students to clearly explain and justify their reasoning within the context of pizza, the Teacher Guide directs educators to ask, “Could you explain why we can’t compare the pieces just by looking?” and instructs them to “Ask students to state what fraction of pizza Carlos has left.” Following discussion, the Teacher Guide facilitates structured reflection immediately after students share their thinking by instructing educators to “use this moment to reinforce that the value of a fraction depends on the unit it refers to.” Process standard 1G is clearly identified alongside these prompts, reinforcing the idea that students’ justification and explanation of their reasoning are intentional design features rather than incidental outcomes. By embedding explicit discussion prompts and setting aside time for structured reflection tied to a labeled process standard, the materials help 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
Two additional anticipated misconceptions in this session come with explicit, scripted educator responses rather than a general description of the error, equipping educators with the precise corrective language to use in real time. In the warm-up, when students struggle to locate a fraction on the number line, the Teacher Guide directs educators to explain that “the denominator shows how many equal parts make up the unit (the space between 0 and 1), and the numerator shows how many of those parts to count.” The guide provides a worked example showing that “to place 3/4, divide the unit into 4 equal parts and count 3 of these parts starting from 0.” In activity 2, when students only propose fractions with a denominator of six, the guide instructs educators to redirect students “to find other fractions that satisfy the conditions using different denominators.”