Program Information
- ISBN
- 9781483880051
- Technical Specifications: Checklist
- Tech Specs: Checklist (pdf 564.73 KB)
- Technical Specifications: Professional Development
- Tech Specs: Professional Development (pdf 174 KB)
Takeoff by IXL, Texas Edition: Grade 4 Math
Math (English) Grade 4
IMRA 2026
Publisher: IXL Learning, Inc.
Copyright: 2026
Series includes:
Rubric: Mathematics K–12 (English) | 2025 (Download Not Available)
* Some programs submit evidence for only part of a standard, while others submit all sections. A 100% score means this program met all the expectations it submitted.
Quality Review
Standards Alignment
Rubric Section
| Grade | TEKS % | ELPS % |
|---|---|---|
| Grade 4 | 100% | 100% |
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% (24 out of 24 points)
Evaluation for 1.1a
The materials provide a yearlong scope and sequence outlining the grade 4 Texas Essential Knowledge and Skills (TEKS), English Language Proficiency Standards (ELPS), and concepts taught throughout the course. For example,“Fourth Grade At-a-Glance: Planning and Materials” provides an overview of each unit and the concepts taught, including the aligned grade 4 TEKS and ELPS.
In addition, each unit provides a “Daily Planner” that outlines the grade 4 TEKS, ELPS, and concepts taught throughout the unit. For example, in unit 2 students add and subtract multi-digit numbers using the standard algorithm. Students use strip models and equations to represent and solve multistep word problems and estimate to assess the reasonableness of their solutions. These concepts align with grade 4 standards 4.4A, 4.4G, and 4.5A.
Evaluation for 1.1b
The materials provide suggested pacing to support effective implementation for various instructional calendars. The “Pacing Calendars” section includes 165-, 180-, and 210-day calendars that provide pacing guidance for different numbers of instructional days. Each calendar assigns instructional activities to specific days so educators can adjust implementation to the length of the school year.
“Fourth Grade At-a-Glance: Planning and Materials” includes a “Unit and Lesson Outline” that sequences units and lessons and identifies the suggested number of instructional days. Educators can compare the time allotted to a unit with the day-by-day calendar to plan instruction.
Evaluation for 1.1c
The materials provide a rationale for the unit order and explain how concepts connect throughout the course. In “Fourth Grade At-a-Glance: Planning and Materials,” the “Unit-by-Unit Overview” identifies the mathematical concepts that each unit addresses and shows how the course is organized across the instructional year. For example, in unit 2 students build fluency with multi-digit addition and subtraction. Students begin by using place value reasoning to add and subtract numbers in expanded form and then connect this thinking to the standard algorithm as an efficient and accurate way to find sums and differences. Students extend this understanding when they add and subtract decimals in unit 11.
The materials also explain how concepts connect across the course at the unit level. The “Instructional Context” tab on the unit outline page connects the current unit to prior learning and upcoming content. For example, the unit 6 “Look Back” section explains that in grade 3 students learned multiplication facts through 10 × 10 and the related division facts. Students also used equal groups, arrays, strip diagrams, and the relationship between multiplication and division to solve division problems. In earlier units, students learned to multiply multi-digit factors by decomposing them into smaller numbers that were easier to use.
Evaluation for 1.1d
The educator resource Discover Takeoff by IXL: Inside a Takeoff Unit explains the unit structure and identifies key information that educators review before instruction, including the unit outline, instructional context, objectives, lesson sequence, and additional resources. Lessons include learning activities for one instructional day, ranging from introducing new concepts to opportunities for independent practice. Review days provide written and online activities for cumulative practice before the unit test. Each unit also includes additional resources and assessments.
The materials also provide lesson planning guidance to help educators prepare for implementation. Discover Takeoff by IXL: Comprehensive Lesson Plans explains how lesson components are organized and how educators can use the lesson structure to understand the purpose, flow, and instructional supports within each lesson. For example, the lesson components include goals, instructional context, materials, and additional supports. Lessons follow a consistent structure of warm-up, instruction, guided practice, and independent practice so students know what to expect.
Evaluation for 1.1e
Instructional leaders use an administrative account to access a classroom walkthrough checklist and guiding questions for collaborative conversations. The checklist helps leaders observe how the materials are implemented, including whether the educator follows the sequence and structure of the lesson, uses the lesson components and materials, and checks for understanding throughout the lesson.
Questions for collaborative conversations provide guidance for educator planning and reflection. The guiding questions are a reference point for discussions with and among educators about learning goals, student data, and built-in instructional guidance and tools. The questions help educators plan, reflect, and make instructional decisions, supporting responsive teaching that meets the needs of all learners.
Evaluation for 1.2a
The materials include comprehensive unit overviews that provide the background content knowledge and academic vocabulary necessary to teach the concepts in the unit. The program dashboard provides educators with unit outline pages and lesson plan pages that review the lesson focus, objectives, and instructional supports.
The materials also include unit-level supports that help educators prepare for instruction. Unit outline pages include an “Additional Resources” section and “Instructional Context” information that provide background content knowledge and academic vocabulary connected to the unit concepts. These resources support educators by identifying key concepts, vocabulary, and contextual information before instruction.
Evaluation for 1.2b
The materials contain supports for families in both English and Spanish for each unit, with suggestions on supporting student progress. In the program dashboard, educators can find “Additional Resources” in the unit outline and access the “Family Letter” section. These letters explain what students are learning and provide suggestions for how families can support learning at home.
The materials also include guidance for using family-facing resources beyond classroom instruction. The educator guide resource Discover Takeoff by IXL: Additional Resources—Takeoff Beyond the Classroom explains how program resources extend support outside of the classroom.
Evaluation for 1.3a
Lesson plans include a lesson overview, materials, instructional activities, practice opportunities, and checks for understanding aligned to the lesson content. The structure of lesson 3.5 in the dashboard and unit outline supports educators in presenting the objective, modeling the concept, and monitoring student understanding during practice.
The Discover Takeoff by IXL: Comprehensive Lesson Plans guide explains how the lesson components work together. The guide describes instruction, guided practice, independent practice, and additional supports. Educators use this guidance to understand how the lesson should move from educator modeling to student application.
Lesson plans include questions, student tasks, and assessment opportunities aligned with the TEKS and ELPS. Educator notes provide prompts for instruction and discussion, while practice tasks allow students to apply the lesson objective. “Additional Supports” provide language and instructional scaffolds educators can use to support emergent bilingual (EB) students and students who need additional help.
Evaluation for 1.3b
The unit 14 “Daily Planner” identifies the educator and student materials needed for instruction in geometry. For example, lesson 14.1 “Parallel and Perpendicular Lines,” identifies student workbook resources, independent practice resources, the “Lines in the Neighborhood” activity, and rulers. Lesson 14.2 “Sides and Angles in Polygons,” identifies student materials, colored pencils, paper clips, and pencils. These examples show that the materials identify student-facing resources, physical supplies, and tools needed for instruction.
The unit 8 “Daily Planner” provides additional examples of lesson materials. In the equivalent fractions and comparing unit, lesson 8.1 “Fractions Greater Than One,” identifies colored pencils and note cards or equal-sized pieces of paper. Lesson 8.2 “Use Models to Find Equivalent Fractions,” identifies blank sheets of paper. These materials support visual modeling, student practice, and hands-on representation of fraction concepts.
The Discover Takeoff by IXL: Comprehensive Lesson Plans guide provides suggested timing for the daily lesson structure. Each lesson includes a five-minute warm-up, 15–20 minutes of instruction, 10–15 minutes of guided practice, and 15–20 minutes of independent practice. This pacing guidance helps educators understand the intended lesson length and how the lesson divides time across prior knowledge activation, instruction, supported practice, and independent application.
Evaluation for 1.3c
Discover Takeoff by IXL: Comprehensive Lesson Plans explains how educators use lesson materials for extended practice. For example, students may complete independent practice pages at school or bring them home for homework or reinforcement. The front side of the independent practice page provides targeted practice on the lesson’s key concept, while the back side provides spiral review so students revisit and apply skills from previous units.
Unit 11 provides lesson-level guidance for extended practice and enrichment. In lesson 11.8 students complete a puzzle by finding missing numbers in a decimal operation pattern. The “Idea for Extension” gives educators a specific follow-up task where students make their own puzzles and trade with a partner. This extension asks students to apply the same decimal reasoning in a new way by creating a puzzle, checking mathematical relationships, and solving a peer-created task.
The materials also provide additional practice options after instruction. Discover Takeoff by IXL: Comprehensive Lesson Plans explains that each lesson pairs with online skills for continued practice, including practice skills for on-target independent practice and support skills for additional scaffolding. The independent practice pages also include a challenge problem that asks students to apply learning in a new way, select an efficient strategy, and persevere to find a solution.
1.1 Course-Level Design
1.1a
Materials include a scope and sequence outlining the TEKS, ELPS, and concepts taught in the course.
Materials include a scope and sequence outlining the TEKS, ELPS, and concepts taught in the course.
3 out of 3 points
Evaluation for 1.1a
Evaluation for 1.1a
Materials include a scope and sequence outlining the TEKS, ELPS, and concepts taught in the course.
3 out of 3 points
In addition, each unit provides a “Daily Planner” that outlines the grade 4 TEKS, ELPS, and concepts taught throughout the unit. For example, in unit 2 students add and subtract multi-digit numbers using the standard algorithm. Students use strip models and equations to represent and solve multistep word problems and estimate to assess the reasonableness of their solutions. These concepts align with grade 4 standards 4.4A, 4.4G, and 4.5A.
1.1b
Materials include suggested pacing (pacing guide/calendar) to support effective implementation for various instructional calendars (e.g., varying numbers of instructional days - 165, 180, 210).
Materials include suggested pacing (pacing guide/calendar) to support effective implementation for various instructional calendars (e.g., varying numbers of instructional days - 165, 180, 210).
2 out of 2 points
Evaluation for 1.1b
Evaluation for 1.1b
Materials include suggested pacing (pacing guide/calendar) to support effective implementation for various instructional calendars (e.g., varying numbers of instructional days - 165, 180, 210).
2 out of 2 points
“Fourth Grade At-a-Glance: Planning and Materials” includes a “Unit and Lesson Outline” that sequences units and lessons and identifies the suggested number of instructional days. Educators can compare the time allotted to a unit with the day-by-day calendar to plan instruction.
1.1c
Materials include an explanation for the rationale of unit order as well as how concepts to be learned connect throughout the course.
Materials include an explanation for the rationale of unit order as well as how concepts to be learned connect throughout the course.
2 out of 2 points
Evaluation for 1.1c
Evaluation for 1.1c
Materials include an explanation for the rationale of unit order as well as how concepts to be learned connect throughout the course.
2 out of 2 points
The materials also explain how concepts connect across the course at the unit level. The “Instructional Context” tab on the unit outline page connects the current unit to prior learning and upcoming content. For example, the unit 6 “Look Back” section explains that in grade 3 students learned multiplication facts through 10 × 10 and the related division facts. Students also used equal groups, arrays, strip diagrams, and the relationship between multiplication and division to solve division problems. In earlier units, students learned to multiply multi-digit factors by decomposing them into smaller numbers that were easier to use.
1.1d
Materials include protocols with corresponding guidance for unit and lesson internalization.
Materials include protocols with corresponding guidance for unit and lesson internalization.
2 out of 2 points
Evaluation for 1.1d
Evaluation for 1.1d
Materials include protocols with corresponding guidance for unit and lesson internalization.
2 out of 2 points
The materials also provide lesson planning guidance to help educators prepare for implementation. Discover Takeoff by IXL: Comprehensive Lesson Plans explains how lesson components are organized and how educators can use the lesson structure to understand the purpose, flow, and instructional supports within each lesson. For example, the lesson components include goals, instructional context, materials, and additional supports. Lessons follow a consistent structure of warm-up, instruction, guided practice, and independent practice so students know what to expect.
1.1e
Materials include resources and guidance for instructional leaders to support teachers with implementing the materials as designed.
Materials include resources and guidance for instructional leaders to support teachers 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 teachers with implementing the materials as designed.
2 out of 2 points
Questions for collaborative conversations provide guidance for educator planning and reflection. The guiding questions are a reference point for discussions with and among educators about learning goals, student data, and built-in instructional guidance and tools. The questions help educators plan, reflect, and make instructional decisions, supporting responsive teaching that meets the needs of all learners.
1.2 Unit-Level Design
1.2a
Materials include comprehensive unit overviews that provide the background content knowledge and academic vocabulary necessary to effectively teach the concepts in the unit.
Materials include comprehensive unit overviews that provide the background content knowledge and academic vocabulary necessary to effectively teach the concepts in the unit.
2 out of 2 points
Evaluation for 1.2a
Evaluation for 1.2a
Materials include comprehensive unit overviews that provide the background content knowledge and academic vocabulary necessary to effectively teach the concepts in the unit.
2 out of 2 points
The materials also include unit-level supports that help educators prepare for instruction. Unit outline pages include an “Additional Resources” section and “Instructional Context” information that provide background content knowledge and academic vocabulary connected to the unit concepts. These resources support educators by identifying key concepts, vocabulary, and contextual information before instruction.
1.2b
Materials contain supports for families in both Spanish and English for each unit with suggestions on supporting the progress of their student.
Materials contain supports for families in both Spanish and English for each unit with suggestions on supporting the progress of their student.
2 out of 2 points
Evaluation for 1.2b
Evaluation for 1.2b
Materials contain supports for families in both Spanish and English for each unit with suggestions on supporting the progress of their student.
2 out of 2 points
The materials also include guidance for using family-facing resources beyond classroom instruction. The educator guide resource Discover Takeoff by IXL: Additional Resources—Takeoff Beyond the Classroom explains how program resources extend support outside of the classroom.
1.3 Lesson-Level Design
1.3a
Materials include comprehensive, structured, detailed lesson plans that include daily objectives, questions, tasks, materials, and instructional assessments required to meet the content and language standards of the lesson (aligned with the TEKS and the ELPS).
Materials include comprehensive, structured, detailed lesson plans that include daily objectives, questions, tasks, materials, and instructional assessments required to meet the content and language standards of the lesson (aligned with the TEKS and the ELPS).
5 out of 5 points
Evaluation for 1.3a
Evaluation for 1.3a
Materials include comprehensive, structured, detailed lesson plans that include daily objectives, questions, tasks, materials, and instructional assessments required to meet the content and language standards of the lesson (aligned with the TEKS and the ELPS).
5 out of 5 points
The Discover Takeoff by IXL: Comprehensive Lesson Plans guide explains how the lesson components work together. The guide describes instruction, guided practice, independent practice, and additional supports. Educators use this guidance to understand how the lesson should move from educator modeling to student application.
Lesson plans include questions, student tasks, and assessment opportunities aligned with the TEKS and ELPS. Educator notes provide prompts for instruction and discussion, while practice tasks allow students to apply the lesson objective. “Additional Supports” provide language and instructional scaffolds educators can use to support emergent bilingual (EB) students and students who need additional help.
1.3b
Materials include a lesson overview listing the teacher and student materials necessary to effectively deliver the lesson, and the suggested timing for each lesson component.
Materials include a lesson overview listing the teacher and student materials necessary to effectively deliver the lesson, and the suggested timing for each lesson component.
3 out of 3 points
Evaluation for 1.3b
Evaluation for 1.3b
Materials include a lesson overview listing the teacher and student materials necessary to effectively deliver the lesson, and the suggested timing for each lesson component.
3 out of 3 points
The unit 8 “Daily Planner” provides additional examples of lesson materials. In the equivalent fractions and comparing unit, lesson 8.1 “Fractions Greater Than One,” identifies colored pencils and note cards or equal-sized pieces of paper. Lesson 8.2 “Use Models to Find Equivalent Fractions,” identifies blank sheets of paper. These materials support visual modeling, student practice, and hands-on representation of fraction concepts.
The Discover Takeoff by IXL: Comprehensive Lesson Plans guide provides suggested timing for the daily lesson structure. Each lesson includes a five-minute warm-up, 15–20 minutes of instruction, 10–15 minutes of guided practice, and 15–20 minutes of independent practice. This pacing guidance helps educators understand the intended lesson length and how the lesson divides time across prior knowledge activation, instruction, supported practice, and independent application.
1.3c
Materials include guidance on the effective use of lesson materials for extended practice (e.g., homework, extension, enrichment).
Materials include guidance on the effective use of lesson materials for extended practice (e.g., homework, extension, enrichment).
1 out of 1 points
Evaluation for 1.3c
Evaluation for 1.3c
Materials include guidance on the effective use of lesson materials for extended practice (e.g., homework, extension, enrichment).
1 out of 1 points
Unit 11 provides lesson-level guidance for extended practice and enrichment. In lesson 11.8 students complete a puzzle by finding missing numbers in a decimal operation pattern. The “Idea for Extension” gives educators a specific follow-up task where students make their own puzzles and trade with a partner. This extension asks students to apply the same decimal reasoning in a new way by creating a puzzle, checking mathematical relationships, and solving a peer-created task.
The materials also provide additional practice options after instruction. Discover Takeoff by IXL: Comprehensive Lesson Plans explains that each lesson pairs with online skills for continued practice, including practice skills for on-target independent practice and support skills for additional scaffolding. The independent practice pages also include a challenge problem that asks students to apply learning in a new way, select an efficient strategy, and persevere to find a solution.
Rubric Section 2
Progress Monitoring
Materials support educators in effective implementation through frequent, strategic opportunities to monitor and respond to student progress.
Total
100% (18 out of 18 points)
Evaluation for 2.1a
In the “Teacher Guides” section, under “Additional Resources,” the grade 4 Takeoff by IXL Assessment Overview identifies diagnostic, formative, and summative assessments throughout the course. The overview explains where educators find each assessment type and how assessment opportunities support progress monitoring. For example, educators use the “IXL LevelUp Diagnostic” to identify student readiness and use lesson and unit tests to monitor progress toward grade 4 objectives.
Lessons embed formative assessment opportunities in instruction, guided practice, and independent practice. Warm-ups, guided practice questions, independent practice items, and skill checks allow educators to monitor student understanding during instruction. These tasks vary by format and require students to demonstrate understanding through selected responses, written or entered responses, visual models, and skill-based practice.
End-of-unit tests provide summative assessment opportunities that align to unit objectives. For example, the unit 1 test includes a variety of item types, such as drag-and-drop, multiple-choice, and fill-in-the-blank. The student math diagnostic plan also breaks down student performance by strand and includes hyperlinked skills with item types such as inline-choice, multiple-choice, and open-ended questions.
Evaluation for 2.1b
The Takeoff by IXL Assessment Overview defines diagnostic, formative, and summative assessments and explains each type’s intended purpose. Diagnostic assessments identify what students know before or during instruction. Formative assessments monitor learning as students work through lessons. Summative assessments evaluate mastery after students complete a unit or set of lessons.
The Insightful Assessments guide explains how educators use unit assessment results. The guide describes how educators use unit assessment data and the “Student Score Chart” to group students by performance, identify learning needs, and plan instructional next steps. The guidance helps educators connect assessment results to reteaching, targeted practice, or enrichment.
The “Assessments on IXL” video provides additional information about the purpose of diagnostic, formative, and summative assessments. The video explains the diagnostic assessments and describes how educator-made quizzes can monitor progress or evaluate mastery. The unit 1 “Personalized Activities” section also shows how assessment results can group students and recommend skill practice.
Evaluation for 2.1c
The IXL LevelUp Diagnostics Guide for Teachers provides guidance for administering the diagnostic assessment. The guide includes educator scripts that support consistent and standardized administration so students receive the same directions. The guide helps educators administer the diagnostic assessment accurately across grade 4 classrooms.
The Insightful Assessments guide explains how educators administer unit-level assessments. The guide describes how educators assign a digital assessment, print an assessment, review objectives and point values, support students during assessment, and use post-assessment data. These steps help educators consistently administer quizzes and unit tests.
The LevelUp Math Teacher Guide for Benchmarks provides additional administration guidance for benchmark assessments. The guide includes a scripted protocol that supports reliable and valid benchmark results. Educators use this protocol with unit assessment guidance to maintain consistent administration before, during, and after assessment.
Evaluation for 2.1d
The “IXL LevelUp Diagnostic” connects diagnostic results to standards and grade-level expectations. The diagnostic identifies which grade 4 skills students know, partially know, or have not yet mastered. Educators also use standards-level data in the “Analytics” tab to identify which of the TEKS individual students or groups have not yet mastered before planning support.
Formative assessments align to the TEKS and objectives within each lesson. Warm-ups identify gaps before new instruction, while independent practice provides formative evidence aligned to the lesson’s TEKS and objectives. Lesson plan pages identify the TEKS and objectives so educators can confirm that the formative tasks measure the intended lesson outcomes.
Summative assessments align to the TEKS and unit objectives through end-of-unit tests. The unit tests identify the TEKS and objective for each question in the “Objectives” tab. The unit 3 test provides details for each question, including the connected TEKS and learning objective, so educators can interpret student performance in relation to the standards taught in the unit.
Evaluation for 2.1e
Unit tests include TEKS-aligned items with varied item types and levels of complexity. The online assessment bank includes technology-enhanced items, such as inline-choice, hotspot, drag-and-drop, multiple-choice, and fill-in-the-blank. These item types allow students to demonstrate understanding through selection, written response, visual interpretation, and application of a mathematical process.
Unit assessments require students to demonstrate understanding across multiple levels of complexity. For example, the unit 1 test asks students to show place value in multiple ways, answer multiple-selection questions, and explain their thinking. The unit 4 test on multiplication requires students to solve two-by-two multiplication problems, interpret word problems, and explain their reasoning.
Lesson-level formative assessments also vary in complexity. Lessons include multiple-choice, text-entry, and open-response items aligned to the TEKS and lesson objectives. Educators use the “LevelUp Diagnostic Standards Performance Report” with lesson and unit assessment results to monitor student mastery across TEKS-aligned items that vary by skill, task type, and complexity.
Evaluation for 2.2a
The “Quiz Analysis” report helps educators interpret grade 4 assessment results by question, objective, class performance, and individual student performance. The “Question Review” section breaks down how students performed on each assessment question and shows which questions or objectives were most difficult for the class. Educators use this information to determine whether students mastered the intended grade 4 objectives or need reteaching, targeted practice, or enrichment.
Assessment reports provide visual and item-level information that helps educators identify patterns in student understanding. For example, educators can review class performance, individual student scores, and performance by question on a quiz or unit test. Educators can use the unit 7 test answer key and “Personalization Day” objective breakdown to connect student performance to specific objectives and recommended student groupings.
In the “Diagnostic Resources” section, under the “My IXL” tab, “A Guide to Understanding the Diagnostic Action Plan” provides additional guidance for interpreting diagnostic assessment data. The guide explains how educators read student diagnostic results and use the information to plan instruction. The Insightful Assessments supplement also explains how educators administer and score assessments, supporting interpretation after quizzes and tests.
Evaluation for 2.2b
Each unit includes a “Personalization Day” that uses assessment data to recommend instructional next steps. The “Personalization Day” in unit 7 breaks down objectives, recommends student groupings based on unit test performance, identifies what the whole class needs to practice through “Group Jam,” and includes extension opportunities for students who demonstrate mastery.
The “Personalized Activities” report groups students by need and recommends targeted skills based on assessment performance. Educators use these recommended activities to provide reteaching, additional practice, or enrichment. Students who struggle with specific objectives receive targeted skill practice, while students who demonstrate understanding receive opportunities to extend learning.
The “IXL LevelUp Diagnostic Action Plan” provides additional guidance for responding to diagnostic assessment results. The action plan gives students tailored learning recommendations connected to specific skills. Lesson plan pages also provide educator notes, additional support guidance, and language supports that educators can use when students do not yet understand the lesson content.
Evaluation for 2.2c
In the “Analytics” tab, the “Progress and Growth” report allows educators to track student progress and growth over time. Educators use the report to monitor whole-class skill progress, review improvement, and identify skills that may need additional instruction. The report helps educators track whether students are progressing toward grade 4 expectations across the course.
Additional educator-facing reports provide more detailed information about individual student progress. For example, the “IXL Student Quick View” allows educators to review recent student practice, identify current skill progress, and determine which students may need additional attention. The “Student Diagnostic Growth” tab also helps educators monitor student mastery and growth by strand.
The materials also include student-facing tools for tracking progress and growth. For example, the “Student Reflection” resource includes self-assessment opportunities before and after each unit. The “Get Ready” section prompts students to reflect on prior knowledge and learning goals. The “Look Back” section asks students to evaluate their understanding, growth, and mastery of unit concepts.
2.1 Instructional Assessments
2.1a
Materials include a variety of instructional assessments at the unit and lesson level (including diagnostic, formative, and summative) that vary in types of tasks and questions.
Materials include a variety of instructional assessments at the unit and lesson level (including diagnostic, formative, and summative) that vary in types of tasks and questions.
3 out of 3 points
Evaluation for 2.1a
Evaluation for 2.1a
Materials include a variety of instructional assessments at the unit and lesson level (including diagnostic, formative, and summative) that vary in types of tasks and questions.
3 out of 3 points
Lessons embed formative assessment opportunities in instruction, guided practice, and independent practice. Warm-ups, guided practice questions, independent practice items, and skill checks allow educators to monitor student understanding during instruction. These tasks vary by format and require students to demonstrate understanding through selected responses, written or entered responses, visual models, and skill-based practice.
End-of-unit tests provide summative assessment opportunities that align to unit objectives. For example, the unit 1 test includes a variety of item types, such as drag-and-drop, multiple-choice, and fill-in-the-blank. The student math diagnostic plan also breaks down student performance by strand and includes hyperlinked skills with item types such as inline-choice, multiple-choice, and open-ended questions.
2.1b
Materials include the definition and intended purpose for the types of instructional assessments included.
Materials include the definition and intended purpose for the types of instructional assessments included.
1 out of 1 points
Evaluation for 2.1b
Evaluation for 2.1b
Materials include the definition and intended purpose for the types of instructional assessments included.
1 out of 1 points
The Insightful Assessments guide explains how educators use unit assessment results. The guide describes how educators use unit assessment data and the “Student Score Chart” to group students by performance, identify learning needs, and plan instructional next steps. The guidance helps educators connect assessment results to reteaching, targeted practice, or enrichment.
The “Assessments on IXL” video provides additional information about the purpose of diagnostic, formative, and summative assessments. The video explains the diagnostic assessments and describes how educator-made quizzes can monitor progress or evaluate mastery. The unit 1 “Personalized Activities” section also shows how assessment results can group students and recommend skill practice.
2.1c
Materials include teacher guidance to ensure consistent and accurate administration of instructional assessments.
Materials include teacher guidance to ensure consistent and accurate administration of instructional assessments.
1 out of 1 points
Evaluation for 2.1c
Evaluation for 2.1c
Materials include teacher guidance to ensure consistent and accurate administration of instructional assessments.
1 out of 1 points
The Insightful Assessments guide explains how educators administer unit-level assessments. The guide describes how educators assign a digital assessment, print an assessment, review objectives and point values, support students during assessment, and use post-assessment data. These steps help educators consistently administer quizzes and unit tests.
The LevelUp Math Teacher Guide for Benchmarks provides additional administration guidance for benchmark assessments. The guide includes a scripted protocol that supports reliable and valid benchmark results. Educators use this protocol with unit assessment guidance to maintain consistent administration before, during, and after assessment.
2.1d
Diagnostic, formative, and summative assessments are aligned to the TEKS and objectives of the course, unit, or lesson.
Diagnostic, formative, and summative assessments are aligned to the TEKS and objectives of the course, unit, or lesson.
6 out of 6 points
Evaluation for 2.1d
Evaluation for 2.1d
Diagnostic, formative, and summative assessments are aligned to the TEKS and objectives of the course, unit, or lesson.
6 out of 6 points
Formative assessments align to the TEKS and objectives within each lesson. Warm-ups identify gaps before new instruction, while independent practice provides formative evidence aligned to the lesson’s TEKS and objectives. Lesson plan pages identify the TEKS and objectives so educators can confirm that the formative tasks measure the intended lesson outcomes.
Summative assessments align to the TEKS and unit objectives through end-of-unit tests. The unit tests identify the TEKS and objective for each question in the “Objectives” tab. The unit 3 test provides details for each question, including the connected TEKS and learning objective, so educators can interpret student performance in relation to the standards taught in the unit.
2.1e
Instructional assessments include TEKS-aligned items at varying levels of complexity.
Instructional assessments include TEKS-aligned items at varying levels of complexity.
2 out of 2 points
Evaluation for 2.1e
Evaluation for 2.1e
Instructional assessments include TEKS-aligned items at varying levels of complexity.
2 out of 2 points
Unit assessments require students to demonstrate understanding across multiple levels of complexity. For example, the unit 1 test asks students to show place value in multiple ways, answer multiple-selection questions, and explain their thinking. The unit 4 test on multiplication requires students to solve two-by-two multiplication problems, interpret word problems, and explain their reasoning.
Lesson-level formative assessments also vary in complexity. Lessons include multiple-choice, text-entry, and open-response items aligned to the TEKS and lesson objectives. Educators use the “LevelUp Diagnostic Standards Performance Report” with lesson and unit assessment results to monitor student mastery across TEKS-aligned items that vary by skill, task type, and complexity.
2.2 Data Analysis and Progress Monitoring
2.2a
Instructional assessments and scoring information provide guidance for interpreting student performance.
Instructional assessments and scoring information provide guidance for interpreting student performance.
2 out of 2 points
Evaluation for 2.2a
Evaluation for 2.2a
Instructional assessments and scoring information provide guidance for interpreting student performance.
2 out of 2 points
Assessment reports provide visual and item-level information that helps educators identify patterns in student understanding. For example, educators can review class performance, individual student scores, and performance by question on a quiz or unit test. Educators can use the unit 7 test answer key and “Personalization Day” objective breakdown to connect student performance to specific objectives and recommended student groupings.
In the “Diagnostic Resources” section, under the “My IXL” tab, “A Guide to Understanding the Diagnostic Action Plan” provides additional guidance for interpreting diagnostic assessment data. The guide explains how educators read student diagnostic results and use the information to plan instruction. The Insightful Assessments supplement also explains how educators administer and score assessments, supporting interpretation after quizzes and tests.
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 “Personalized Activities” report groups students by need and recommends targeted skills based on assessment performance. Educators use these recommended activities to provide reteaching, additional practice, or enrichment. Students who struggle with specific objectives receive targeted skill practice, while students who demonstrate understanding receive opportunities to extend learning.
The “IXL LevelUp Diagnostic Action Plan” provides additional guidance for responding to diagnostic assessment results. The action plan gives students tailored learning recommendations connected to specific skills. Lesson plan pages also provide educator notes, additional support guidance, and language supports that educators can use when students do not yet understand the lesson content.
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.
2 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.
2 out of 2 points
Additional educator-facing reports provide more detailed information about individual student progress. For example, the “IXL Student Quick View” allows educators to review recent student practice, identify current skill progress, and determine which students may need additional attention. The “Student Diagnostic Growth” tab also helps educators monitor student mastery and growth by strand.
The materials also include student-facing tools for tracking progress and growth. For example, the “Student Reflection” resource includes self-assessment opportunities before and after each unit. The “Get Ready” section prompts students to reflect on prior knowledge and learning goals. The “Look Back” section asks students to evaluate their understanding, growth, and mastery of unit concepts.
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
100% (20 out of 20 points)
Evaluation for 3.1a
The materials include teacher guidance for differentiated instruction, activities, and scaffolded support for students who have not yet reached proficiency on grade-level content and skills. For example, the lesson plan pages include “Tips for Support” within each lesson. In unit 4, lesson 4.3, the “Tips for Support” provide on-the-spot strategies educators can use to identify students who are struggling and help them reconnect to the lesson content during instruction.
The lessons also include “Additional Supports” that help educators scaffold instruction for students who need support before or during grade-level learning. For example, the “Additional Supports” tab includes language supports differentiated for beginning, intermediate, advanced, and advanced high students, as well as tips and supports for individual questions. These embedded supports help educators adjust instruction, clarify concepts, and provide targeted assistance while students continue working toward grade-level expectations.
Program-level tools provide additional guidance for differentiated instruction for students who have not yet reached proficiency. For example, in the “Teacher Guides” section, under “Additional Resources,” “Unleashing the Power of IXL” explains how educators can use differentiated activities, “Group Jam,” and “Live Classroom” to identify what individual students are struggling with in real time. The “Personalization Day” in the unit 6 overview also provides specific practice problems matched to the TEKS that students missed on the unit test and groups students by need for targeted follow up.
Evaluation for 3.1b
Each unit outline includes a vocabulary list under “Additional Resources” that identifies the academic vocabulary in the unit and links to the student glossary. Educators can use this vocabulary list before instruction to preview key terms and prepare students for the language in lessons, activities, and assessments.
The materials also provide vocabulary support within lesson guidance. For example, unit 5 includes a vocabulary list under “Additional Resources.” Unit 5, lesson 5.1 embeds support for unfamiliar vocabulary—including factor, factor pair, and common factors—directly within the educator notes. Student glossaries in both English and Spanish accompany each term with a definition and an image to support student understanding.
Each lesson embeds language support strategies to help educators address unfamiliar vocabulary and references in the text. For example, the “Additional Supports” tab provides strategies for supporting EB students across proficiency levels and includes guidance for vocabulary that may be challenging for EB students. In lesson 5.1 the “Additional Supports” tab suggests creating a visual glossary of academic vocabulary for students to reference while working. Lesson 4.1 includes an educator guide callout for explaining word meanings for EB students.
Evaluation for 3.1c
Lessons embed “Ideas for Extension” that provide ready-made enrichment and real-world problem-solving activities for students who have already mastered core math concepts. In unit 5, lesson 5.1, the “Idea for Extension” appears before question 8 and provides educators with a concrete activity to extend learning for advanced students.
The materials also include unit-level guidance for enrichment and extension following assessment. For example, each unit includes a “Personalization Day” that uses assessment results to provide targeted learning paths. Students who have already mastered the unit objectives receive enrichment activities, projects, or extension opportunities, while students who need more practice receive targeted support. The unit 13 “Personalization Day” includes enrichment activities, practice problems, and projects for students who met grade-level expectations on the unit test.
Additional educator-facing resources explain how the program supports enrichment and extension for proficient students. For example, under the “View Additional Resources” section, the “Instructional Design” document explains that automatic differentiation is built into each assessment. Lesson plan pages also include an “Ideas for Extension” dropdown that gives students who have demonstrated understanding additional ways to practice or alternative ways to show their answers.
Evaluation for 3.2a
Lessons include educator notes that provide step-by-step guidance for modeling and explaining mathematical concepts. The notes help educators introduce the concept, ask questions, model strategies, and connect student responses to the lesson objective. The notes give educators a clear path for explaining the concept before students begin guided and independent practice.
In the unit 5, lesson 5.1 “Summary,” the educator notes provide guidance for explaining how students can use different ways to organize photos by finding pairs of numbers whose product is eight. The notes include a model educators can reference as students reason about factor pairs. The notes help educators make the mathematical idea visible before students apply the concept in practice.
The materials also include guidance for responsive modeling when students need additional support. For example, “Tips for Support” in the lesson notes help educators identify students who may be struggling and provide targeted strategies to address misconceptions. Lesson 12.1 includes think-aloud prompts and concrete steps for students who need additional support. Lesson 12.4 provides guiding questions for student discussion and guidance for how educators can respond to student answers.
Evaluation for 3.2b
Lessons provide guidance for effective lesson delivery through direct instruction, educator notes, “Tips for Support,” guided practice, collaborative activities, and independent practice. This structure helps educators use multiple instructional approaches within one lesson rather than relying on a single method of instruction.
In unit 5, lesson 5.2, the educator guidance supports student discourse, “Think and Talk” prompts, and written responses that ask students to explain their thinking. The educator notes provide structure for whole-group instruction and collaborative practice. This guidance helps educators facilitate mathematical discussion and student engagement before students complete independent work.
Under the “My IXL Implementation Guides” section, the “IXL for Daily Instruction” guide provides program-level guidance for lesson facilitation. The guide recommends direct instruction to introduce concepts, collaborative activities for practice, math stations to reinforce learning, and real-world applications to connect content to student’s lives. The “Think and Talk” and “Model and Talk” sections in lessons also guide students through concrete representations before moving toward abstract thinking.
Evaluation for 3.2c
Lesson plan pages provide clear routines for guided, independent, and collaborative practice. Lessons include headings for warm-up, instruction, guided practice, and independent practice. This structure supports implementation because educators can identify when students work as a whole group, work with educator support, and apply the concept independently.
Lesson 8.1 includes opportunities for guided practice, individual work, and partner work. These practice structures help educators provide support while students first apply the concept, then allow students to practice in pairs or individually. The structure supports students as they move from educator-supported learning to more independent application.
The unit 5 “Personalization Day” provides practice structures beyond the core lesson. The materials use student performance data from the unit test to provide individual practice for students who need support, enrichment opportunities for students who have mastered the objectives, and a “Group Jam” for whole-class practice. This guidance supports individual, small-group, and whole-group implementation based on student data.
Evaluation for 3.3a
Each lesson includes an “Additional Supports” tab with language support strategies differentiated across proficiency levels, including pre-production/beginning, intermediate, and high intermediate/advanced. In unit 5, lesson 5.2, the language supports include sentence stems, graphic organizers, and word banks that help students access the lesson content and participate in mathematical discourse.
Language supports help students use more precise academic language across proficiency levels. For example, lessons 4.1 and 14.2 provide sentence stems targeted at beginning, intermediate, and high intermediate/advanced EB students. Lessons also prompt educators to have students add math terms to vocabulary lists in both English and their home languages, supporting cross-linguistic connections and vocabulary development.
Evaluation for 3.3b
Under “Additional Resources,” the “Instructional Design: Empowering Language Learners in Math” document provides implementation strategies for supporting EB students in bilingual and ESL programs. The document explains how educators can help students engage with grade-level mathematics content while developing academic language.
The “Additional Supports” tab embeds implementation guidance within each lesson. For example, each tab includes a language objective and language support strategies with guidance for different proficiency levels. In unit 5, lesson 5.2, the “Additional Supports” tab gives educators proficiency-level guidance they can use during instruction to support vocabulary development, comprehension, and participation in mathematical discussion.
Educators use the program-level guidance and lesson-level supports together to integrate language development into mathematics instruction. The “Instructional Design: Empowering Language Learners in Math” document explains the program’s approach, while the lesson-specific “Additional Supports” guide educators during whole-group instruction, guided practice, partner discussion, and written-response tasks.
Evaluation for 3.3c
Lessons embed guidance for academic vocabulary development, background knowledge, and cross-linguistic connections. Each lesson’s “Additional Supports” tab includes a language objective and differentiated language strategies connected to the lesson content. For example, lesson 14.2 includes vocabulary to pre-teach and sentence stems that help beginning EB students use academic vocabulary in context.
The materials provide language supports that increase comprehension through structured discourse. For example, lesson 4.1 includes sentence stems that help students explain their thinking. Lesson 11.3 provides sentence stems at multiple proficiency levels to help students discuss the process of solving a word problem. These supports connect academic terms to students’ prior knowledge and everyday language.
Lessons support oral and written discourse for EB students. Lesson 4.1 includes a structured written-response activity with peer feedback. Lesson 14.2 includes a collaborative activity in which students provide written responses and offer feedback to each other. In the “Teacher Guides” section, under “Additional Resources,” “Unleashing the Power of IXL” provides program-level guidance for “empowering language learners in math.”
Evaluation for 3.3d
This guidance is not applicable because the program is not designed for dual language immersion (DLI) programs.
3.1 Differentiation and Scaffolds
3.1a
Materials include teacher guidance for differentiated instruction, activities, and paired (scaffolded) lessons for students who have not yet reached proficiency on grade-level content and skills.
Materials include teacher guidance for differentiated instruction, activities, and paired (scaffolded) lessons for students who have not yet reached proficiency on grade-level content and skills.
1 out of 1 points
Evaluation for 3.1a
Evaluation for 3.1a
Materials include teacher guidance for differentiated instruction, activities, and paired (scaffolded) lessons for students who have not yet reached proficiency on grade-level content and skills.
1 out of 1 points
The lessons also include “Additional Supports” that help educators scaffold instruction for students who need support before or during grade-level learning. For example, the “Additional Supports” tab includes language supports differentiated for beginning, intermediate, advanced, and advanced high students, as well as tips and supports for individual questions. These embedded supports help educators adjust instruction, clarify concepts, and provide targeted assistance while students continue working toward grade-level expectations.
Program-level tools provide additional guidance for differentiated instruction for students who have not yet reached proficiency. For example, in the “Teacher Guides” section, under “Additional Resources,” “Unleashing the Power of IXL” explains how educators can use differentiated activities, “Group Jam,” and “Live Classroom” to identify what individual students are struggling with in real time. The “Personalization Day” in the unit 6 overview also provides specific practice problems matched to the TEKS that students missed on the unit test and groups students by need for targeted follow up.
3.1b
Materials include pre-teaching or embedded supports for unfamiliar vocabulary and references in text (e.g., figurative language, idioms, academic language).
Materials include pre-teaching or embedded supports for unfamiliar vocabulary and references in text (e.g., figurative language, idioms, academic language).
2 out of 2 points
Evaluation for 3.1b
Evaluation for 3.1b
Materials include pre-teaching or embedded supports for unfamiliar vocabulary and references in text (e.g., figurative language, idioms, academic language).
2 out of 2 points
The materials also provide vocabulary support within lesson guidance. For example, unit 5 includes a vocabulary list under “Additional Resources.” Unit 5, lesson 5.1 embeds support for unfamiliar vocabulary—including factor, factor pair, and common factors—directly within the educator notes. Student glossaries in both English and Spanish accompany each term with a definition and an image to support student understanding.
Each lesson embeds language support strategies to help educators address unfamiliar vocabulary and references in the text. For example, the “Additional Supports” tab provides strategies for supporting EB students across proficiency levels and includes guidance for vocabulary that may be challenging for EB students. In lesson 5.1 the “Additional Supports” tab suggests creating a visual glossary of academic vocabulary for students to reference while working. Lesson 4.1 includes an educator guide callout for explaining word meanings for EB students.
3.1c
Materials include teacher guidance for differentiated instruction, enrichment, and extension activities for students who have demonstrated proficiency in grade-level content and skill.
Materials include teacher guidance for differentiated instruction, enrichment, and extension activities for students who have demonstrated proficiency in grade-level content and skill.
1 out of 1 points
Evaluation for 3.1c
Evaluation for 3.1c
Materials include teacher guidance for differentiated instruction, enrichment, and extension activities for students who have demonstrated proficiency in grade-level content and skill.
1 out of 1 points
The materials also include unit-level guidance for enrichment and extension following assessment. For example, each unit includes a “Personalization Day” that uses assessment results to provide targeted learning paths. Students who have already mastered the unit objectives receive enrichment activities, projects, or extension opportunities, while students who need more practice receive targeted support. The unit 13 “Personalization Day” includes enrichment activities, practice problems, and projects for students who met grade-level expectations on the unit test.
Additional educator-facing resources explain how the program supports enrichment and extension for proficient students. For example, under the “View Additional Resources” section, the “Instructional Design” document explains that automatic differentiation is built into each assessment. Lesson plan pages also include an “Ideas for Extension” dropdown that gives students who have demonstrated understanding additional ways to practice or alternative ways to show their answers.
3.2 Instructional Methods
3.2a
Materials include explicit (direct) prompts and guidance to support the teacher in modeling and explaining the concept(s) to be learned.
Materials include explicit (direct) prompts and guidance to support the teacher in modeling and explaining the concept(s) to be learned.
2 out of 2 points
Evaluation for 3.2a
Evaluation for 3.2a
Materials include explicit (direct) prompts and guidance to support the teacher in modeling and explaining the concept(s) to be learned.
2 out of 2 points
In the unit 5, lesson 5.1 “Summary,” the educator notes provide guidance for explaining how students can use different ways to organize photos by finding pairs of numbers whose product is eight. The notes include a model educators can reference as students reason about factor pairs. The notes help educators make the mathematical idea visible before students apply the concept in practice.
The materials also include guidance for responsive modeling when students need additional support. For example, “Tips for Support” in the lesson notes help educators identify students who may be struggling and provide targeted strategies to address misconceptions. Lesson 12.1 includes think-aloud prompts and concrete steps for students who need additional support. Lesson 12.4 provides guiding questions for student discussion and guidance for how educators can respond to student answers.
3.2b
Materials include teacher guidance and recommendations for effective lesson delivery and facilitation using a variety of instructional approaches.
Materials include teacher guidance and recommendations for effective lesson delivery and facilitation using a variety of instructional approaches.
1 out of 1 points
Evaluation for 3.2b
Evaluation for 3.2b
Materials include teacher guidance and recommendations for effective lesson delivery and facilitation using a variety of instructional approaches.
1 out of 1 points
In unit 5, lesson 5.2, the educator guidance supports student discourse, “Think and Talk” prompts, and written responses that ask students to explain their thinking. The educator notes provide structure for whole-group instruction and collaborative practice. This guidance helps educators facilitate mathematical discussion and student engagement before students complete independent work.
Under the “My IXL Implementation Guides” section, the “IXL for Daily Instruction” guide provides program-level guidance for lesson facilitation. The guide recommends direct instruction to introduce concepts, collaborative activities for practice, math stations to reinforce learning, and real-world applications to connect content to student’s lives. The “Think and Talk” and “Model and Talk” sections in lessons also guide students through concrete representations before moving toward abstract thinking.
3.2c
Materials support multiple types of practice (e.g., guided, independent, collaborative) and include guidance for teachers and recommended structures (e.g., whole group, small group, individual) to support effective implementation.
Materials support multiple types of practice (e.g., guided, independent, collaborative) and include guidance for teachers and recommended structures (e.g., whole group, small group, individual) to support effective implementation.
2 out of 2 points
Evaluation for 3.2c
Evaluation for 3.2c
Materials support multiple types of practice (e.g., guided, independent, collaborative) and include guidance for teachers and recommended structures (e.g., whole group, small group, individual) to support effective implementation.
2 out of 2 points
Lesson 8.1 includes opportunities for guided practice, individual work, and partner work. These practice structures help educators provide support while students first apply the concept, then allow students to practice in pairs or individually. The structure supports students as they move from educator-supported learning to more independent application.
The unit 5 “Personalization Day” provides practice structures beyond the core lesson. The materials use student performance data from the unit test to provide individual practice for students who need support, enrichment opportunities for students who have mastered the objectives, and a “Group Jam” for whole-class practice. This guidance supports individual, small-group, and whole-group implementation based on student data.
3.3 Support for Emergent Bilingual Students
3.3a
Materials include teacher guidance on providing linguistic accommodations for various 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.
Materials include teacher guidance on providing linguistic accommodations for various 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.
2 out of 2 points
Evaluation for 3.3a
Evaluation for 3.3a
Materials include teacher guidance on providing linguistic accommodations for various 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.
2 out of 2 points
Language supports help students use more precise academic language across proficiency levels. For example, lessons 4.1 and 14.2 provide sentence stems targeted at beginning, intermediate, and high intermediate/advanced EB students. Lessons also prompt educators to have students add math terms to vocabulary lists in both English and their home languages, supporting cross-linguistic connections and vocabulary development.
3.3b
Materials include implementation guidance to support teachers in effectively using the materials in state-approved bilingual/ESL programs.
Materials include implementation guidance to support teachers in effectively using the materials in state-approved bilingual/ESL programs.
1 out of 1 points
Evaluation for 3.3b
Evaluation for 3.3b
Materials include implementation guidance to support teachers in effectively using the materials in state-approved bilingual/ESL programs.
1 out of 1 points
The “Additional Supports” tab embeds implementation guidance within each lesson. For example, each tab includes a language objective and language support strategies with guidance for different proficiency levels. In unit 5, lesson 5.2, the “Additional Supports” tab gives educators proficiency-level guidance they can use during instruction to support vocabulary development, comprehension, and participation in mathematical discussion.
Educators use the program-level guidance and lesson-level supports together to integrate language development into mathematics instruction. The “Instructional Design: Empowering Language Learners in Math” document explains the program’s approach, while the lesson-specific “Additional Supports” guide educators during whole-group instruction, guided practice, partner discussion, and written-response tasks.
3.3c
Materials include embedded guidance for teachers 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 for teachers 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 3.3c
Evaluation for 3.3c
Materials include embedded guidance for teachers to support emergent bilingual students in developing academic vocabulary, increasing comprehension, building background knowledge, and making cross-linguistic connections through oral and written discourse.
8 out of 8 points
The materials provide language supports that increase comprehension through structured discourse. For example, lesson 4.1 includes sentence stems that help students explain their thinking. Lesson 11.3 provides sentence stems at multiple proficiency levels to help students discuss the process of solving a word problem. These supports connect academic terms to students’ prior knowledge and everyday language.
Lessons support oral and written discourse for EB students. Lesson 4.1 includes a structured written-response activity with peer feedback. Lesson 14.2 includes a collaborative activity in which students provide written responses and offer feedback to each other. In the “Teacher Guides” section, under “Additional Resources,” “Unleashing the Power of IXL” provides program-level guidance for “empowering language learners in math.”
3.3d
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 3.3d
Evaluation for 3.3d
If designed for dual language immersion (DLI) programs, materials include resources that outline opportunities to address metalinguistic transfer from English to the partner language.
Not applicable.
Rubric Section 4
Depth and Coherence of Key Concepts
Materials are designed to meet the rigor of the standards while connecting concepts within and across grade levels/courses.
Total
100% (19 out of 19 points)
Evaluation for 4.1a
In the unit 12 “Daily Planner” students demonstrate depth of understanding with data by representing and interpreting information in frequency tables, stem-and-leaf plots, and dot plots. Across the unit, students create and interpret frequency tables, create stem-and-leaf plots and use them to solve problems, create dot plots and use them to solve problems, and solve multistep problems involving data. These tasks require students to organize data, choose appropriate representations, interpret information, and solve problems using whole numbers, decimals, and fractions.
Instructional assessments also require students to demonstrate understanding aligned to the grade 4 data TEKS. In the unit 12 “Data” test, students use a frequency table about lap times to answer questions, complete a stem-and-leaf plot from popcorn sales data, interpret a stem-and-leaf plot about bike rides, complete a dot plot using fractional data, and explain the mistake in a stem-and-leaf plot about rainfall. These assessment tasks require students to represent data, interpret data displays, analyze errors, and solve problems using data in multiple forms.
Evaluation for 4.1b
The unit 12 “Daily Planner” organizes questions and tasks so students move from foundational understanding to more complex data analysis. Students begin by representing and interpreting data using frequency tables, then create stem-and-leaf plots, interpret stem-and-leaf plots to solve problems, create dot plots, and use dot plots to solve problems. The unit ends with multistep problems involving data represented in frequency tables, stem-and-leaf plots, and dot plots. This progression increases rigor by moving students from creating individual data displays to selecting, interpreting, and solving problems from multiple data representations.
The unit 12 review and test also show increasing complexity by requiring students to apply data skills in different contexts. In the unit 12 review students complete frequency tables, interpret stem-and-leaf plots, create dot plots, compare quantities, and solve problems using data displays. In the unit 12 test students answer questions from a frequency table, complete a stem-and-leaf plot, mark statements true or false based on a stem-and-leaf plot, complete a dot plot using fractional data, and explain an error in a data display. These tasks move students beyond reading a graph to creating, analyzing, and critiquing data representations.
Evaluation for 4.2a
In the unit 4 outline, the “Instructional Context” tab explicitly connects mathematical patterns, big ideas, and relationships across units. In unit 4 “Multiply by 2-Digit Numbers,” the “Look Back” section explains that students previously multiplied multi-digit numbers by one-digit numbers by breaking the multi-digit factors into smaller parts and recording their work with area models, partial products, and the standard algorithm. The “This Unit” section explains that students multiply two-digit numbers by breaking both factors into 10s and ones, and continue to record their work with area models, partial products, and the standard algorithm. This explanation connects prior multiplication strategies to more complex multiplication with two-digit factors.
The unit 4 “Instructional Context” tab also connects multiplication to future problem solving across the course. The “Look Forward” section explains that in later units students will continue to use multiplication to solve problems with number patterns, areas of rectangles, and measurement conversions. The section also explains that students will solve multistep problems involving all four operations. This explanation shows coherence among multiplication strategies, area, measurement, patterns, and multistep problem solving.
Evaluation for 4.2b
The “Instructional Context” tab connects grade 4 content to previous and future grade-level learning. In unit 14 “Geometry,” the “Look Back” section explains that in earlier grades students described attributes of polygons, including right angles, parallel sides, and equal sides, and used those attributes to recognize and sort quadrilaterals. The section also explains that students previously partitioned shapes into equal parts and, in unit 13, identified and drew points, lines, line segments, rays, and angles and classified angles as acute, right, or obtuse.
The unit 14 “Instructional Context” tab also shows future grade-level connections. The “This Unit” section explains that students identify parallel and perpendicular lines, classify triangles and quadrilaterals based on sides and angles, and identify and draw lines of symmetry in two-dimensional shapes. The “Look Forward” section explains that in grade 5 students will classify triangles, quadrilaterals, and other polygons in multiple ways and develop a hierarchy of special quadrilaterals. The section also connects line symmetry to later work with reflections and graphs of functions on the coordinate plane.
Evaluation for 4.2c
At the lesson and unit level, the “Instructional Context” tab connects students’ prior knowledge to new mathematical learning. In unit 2 “Add and Subtract Whole Numbers,” the “Look Back” section explains that in grade 3 students developed addition and subtraction strategies based on place value to fluently add and subtract numbers within 1,000. The section also explains that students represented one- and two-step problems using strip models, number lines, and equations.
In unit 2 the “This Unit” and “Look Forward” sections show how prior knowledge connects to current and future learning. The “This Unit” section explains that students build fluency with adding and subtracting larger multi-digit numbers and solve multistep problems using strip models and equations with a letter for the unknown. The section explains that students first use a separate model or equation for each step and later represent a multistep problem with a single strip model or equation. The “Look Forward” section explains that students will use addition and subtraction to develop strategies for multiplying and dividing multi-digit numbers and will extend their work to multistep problems involving all four operations.
Evaluation for 4.3a
The unit 12 “Daily Planner” provides spaced retrieval opportunities by revisiting previously learned skills while students work on current data objectives. In lesson 12.1 students represent and interpret frequency tables while completing spiral review with decimal representations. In lesson 12.2 students create stem-and-leaf plots while completing spiral review with adding and subtracting mixed numbers. In lesson 12.3 students interpret stem-and-leaf plots and solve data problems while completing spiral review with multi-digit multiplication word problems. These review opportunities revisit earlier concepts after time has passed.
The lesson 10.1 independent practice also provides spaced retrieval opportunities. Students work on converting metric units of length, such as centimeters to meters, meters to millimeters, kilometers to meters, and millimeters to centimeters. On the second page, students revisit equivalent fractions, compare multi-digit numbers in a real-world context, and complete place value relationship statements such as identifying a number that is 10 times as much as 6,500. These review tasks require students to retrieve previously learned fraction, place value, and computation skills while working on measurement conversion.
Evaluation for 4.3b
The lesson 7.1 independent practice provides interleaved practice by mixing current perimeter work with previously learned concepts. Students find the perimeter of rectangles and squares, determine missing side lengths, and solve a real-world perimeter comparison problem about custom picture frames. On the next page, students label fractions and identify equivalent fractions, identify quadrilaterals with four right angles, and complete multi-digit multiplication problems. These tasks mix current perimeter content with prior fraction, geometry, and multiplication skills.
The lesson 10.1 independent practice also provides interleaved practice by combining current measurement conversion skills with concepts from prior units. Students convert metric units, identify equivalent measurements, and solve real-world metric conversion problems. The same practice also includes equivalent fractions, multi-digit subtraction, and place value relationship problems. This structure requires students to continue applying previously learned fraction, place value, and computation skills while working on new measurement conversion content.
4.1 Depth of Key Concepts
4.1a
Practice opportunities over the course of a lesson and/or unit (including instructional assessments) require students to demonstrate depth of understanding aligned to the TEKS.
Practice opportunities over the course of a lesson and/or unit (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 over the course of a lesson and/or unit (including instructional assessments) require students to demonstrate depth of understanding aligned to the TEKS.
2 out of 2 points
Instructional assessments also require students to demonstrate understanding aligned to the grade 4 data TEKS. In the unit 12 “Data” test, students use a frequency table about lap times to answer questions, complete a stem-and-leaf plot from popcorn sales data, interpret a stem-and-leaf plot about bike rides, complete a dot plot using fractional data, and explain the mistake in a stem-and-leaf plot about rainfall. These assessment tasks require students to represent data, interpret data displays, analyze errors, and solve problems using data in multiple forms.
4.1b
Questions and tasks progressively increase in rigor and complexity, leading to grade-level proficiency in the mathematics TEKS.
Questions and tasks progressively increase in rigor and complexity, leading to grade-level proficiency in the mathematics TEKS.
1 out of 1 points
Evaluation for 4.1b
Evaluation for 4.1b
Questions and tasks progressively increase in rigor and complexity, leading to grade-level proficiency in the mathematics TEKS.
1 out of 1 points
The unit 12 review and test also show increasing complexity by requiring students to apply data skills in different contexts. In the unit 12 review students complete frequency tables, interpret stem-and-leaf plots, create dot plots, compare quantities, and solve problems using data displays. In the unit 12 test students answer questions from a frequency table, complete a stem-and-leaf plot, mark statements true or false based on a stem-and-leaf plot, complete a dot plot using fractional data, and explain an error in a data display. These tasks move students beyond reading a graph to creating, analyzing, and critiquing data representations.
4.2 Coherence of Key Concepts
4.2a
Materials demonstrate coherence across units by explicitly connecting patterns, big ideas, and relationships between mathematical concepts.
Materials demonstrate coherence across units by explicitly connecting patterns, big ideas, and relationships between mathematical concepts.
1 out of 1 points
Evaluation for 4.2a
Evaluation for 4.2a
Materials demonstrate coherence across units by explicitly connecting patterns, big ideas, and relationships between mathematical concepts.
1 out of 1 points
The unit 4 “Instructional Context” tab also connects multiplication to future problem solving across the course. The “Look Forward” section explains that in later units students will continue to use multiplication to solve problems with number patterns, areas of rectangles, and measurement conversions. The section also explains that students will solve multistep problems involving all four operations. This explanation shows coherence among multiplication strategies, area, measurement, patterns, and multistep problem solving.
4.2b
Materials demonstrate coherence across units by connecting the content and language learned in previous courses/grade levels and what will be learned in future courses/grade levels to the content to be learned in the current course/grade level.
Materials demonstrate coherence across units by connecting the content and language learned in previous courses/grade levels and what will be learned in future courses/grade levels to the content to be learned in the current course/grade level.
3 out of 3 points
Evaluation for 4.2b
Evaluation for 4.2b
Materials demonstrate coherence across units by connecting the content and language learned in previous courses/grade levels and what will be learned in future courses/grade levels to the content to be learned in the current course/grade level.
3 out of 3 points
The unit 14 “Instructional Context” tab also shows future grade-level connections. The “This Unit” section explains that students identify parallel and perpendicular lines, classify triangles and quadrilaterals based on sides and angles, and identify and draw lines of symmetry in two-dimensional shapes. The “Look Forward” section explains that in grade 5 students will classify triangles, quadrilaterals, and other polygons in multiple ways and develop a hierarchy of special quadrilaterals. The section also connects line symmetry to later work with reflections and graphs of functions on the coordinate plane.
4.2c
Materials demonstrate coherence at the lesson level by connecting students' prior knowledge of concepts and procedures from the current and prior grade level(s) to new mathematical knowledge and skills..
Materials demonstrate coherence at the lesson level by connecting students' prior knowledge of concepts and procedures from the current and prior grade level(s) to new mathematical knowledge and skills..
4 out of 4 points
Evaluation for 4.2c
Evaluation for 4.2c
Materials demonstrate coherence at the lesson level by connecting students' prior knowledge of concepts and procedures from the current and prior grade level(s) to new mathematical knowledge and skills..
4 out of 4 points
In unit 2 the “This Unit” and “Look Forward” sections show how prior knowledge connects to current and future learning. The “This Unit” section explains that students build fluency with adding and subtracting larger multi-digit numbers and solve multistep problems using strip models and equations with a letter for the unknown. The section explains that students first use a separate model or equation for each step and later represent a multistep problem with a single strip model or equation. The “Look Forward” section explains that students will use addition and subtraction to develop strategies for multiplying and dividing multi-digit numbers and will extend their work to multistep problems involving all four operations.
4.3 Spaced and Interleaved Practice
4.3a
Materials provide spaced retrieval opportunities with previously learned skills and concepts across lessons and units.
Materials provide spaced retrieval opportunities with previously learned skills and concepts across lessons and units.
4 out of 4 points
Evaluation for 4.3a
Evaluation for 4.3a
Materials provide spaced retrieval opportunities with previously learned skills and concepts across lessons and units.
4 out of 4 points
The lesson 10.1 independent practice also provides spaced retrieval opportunities. Students work on converting metric units of length, such as centimeters to meters, meters to millimeters, kilometers to meters, and millimeters to centimeters. On the second page, students revisit equivalent fractions, compare multi-digit numbers in a real-world context, and complete place value relationship statements such as identifying a number that is 10 times as much as 6,500. These review tasks require students to retrieve previously learned fraction, place value, and computation skills while working on measurement conversion.
4.3b
Materials provide interleaved practice opportunities with previously learned skills and concepts across lessons and units.
Materials provide interleaved practice opportunities with previously learned skills and concepts across lessons and units.
4 out of 4 points
Evaluation for 4.3b
Evaluation for 4.3b
Materials provide interleaved practice opportunities with previously learned skills and concepts across lessons and units.
4 out of 4 points
The lesson 10.1 independent practice also provides interleaved practice by combining current measurement conversion skills with concepts from prior units. Students convert metric units, identify equivalent measurements, and solve real-world metric conversion problems. The same practice also includes equivalent fractions, multi-digit subtraction, and place value relationship problems. This structure requires students to continue applying previously learned fraction, place value, and computation skills while working on new measurement conversion content.
Rubric Section 5
Balance of Conceptual and Procedural Understanding
Materials are designed to balance conceptual understanding, procedural skills, and fluency.
Total
100% (41 out of 41 points)
Evaluation for 5.1a
In unit 11, lesson 11.1 “Relate Fractions and Decimals,” students interpret and analyze models that connect fractions to decimals. The educator guidance asks students to use place value blocks and decimal grids to represent fractions with denominators of 10 or 100, then record the values in place value charts, decimal notation, and word form. Students analyze how one rod represents 1/10, how one cube represents 1/100, and how a fraction such as 25/100 can be represented with two rods and five cubes before writing the decimal. These tasks require students to interpret and analyze concrete and pictorial representations before connecting them to symbolic decimals.
In unit 12, lesson 12.2 “Create Stem-and-Leaf Plots,” students interpret and analyze data representations. The educator guidance explains how a stem-and-leaf plot organizes values by separating each number into a stem and a leaf, then asks students to use the plot to answer questions about the data. Students also analyze stem-and-leaf plots with decimal values by identifying how the stem represents the ones digit and the leaf represents the tenths digit. These tasks require students to interpret the structure of a data display and evaluate how the representation helps answer questions about the data.
Evaluation for 5.1b
In unit 1, lesson 1.3 “Read and Write Numbers to One Billion,” students create models to represent large whole numbers. The guidance instructs educators to provide place value disks and a place value mat and ask students to model numbers such as 215,342. Students place disks in the appropriate columns, record the number in standard form, and use the value of each digit to write the number in expanded notation and expanded form. This task requires students to create a mathematical model and connect the model to multiple written representations.
In unit 7, lesson 7.1 “Perimeter of Rectangles,” students create models to represent perimeter situations. The guidance instructs educators to provide grid paper and ask students to draw rectangles with sides along gridlines, trade rectangles with a partner, and find the perimeter of the partner’s rectangle. Students use their drawings to identify length and width, recognize equal opposite sides, and develop formulas for the perimeter of rectangles and squares. This task requires students to create models that represent mathematical situations and use those models to reason about perimeter.
Evaluation for 5.1c
In unit 7, lesson 7.1 “Perimeter of Rectangles,” students apply conceptual understanding of perimeter to new problem situations. Students begin by finding a perimeter by counting units around a figure and labeling side lengths. Students then use rectangle properties to develop formulas, apply the formulas to find the perimeter, and solve problems involving missing side lengths. This progression requires students to apply their understanding of perimeter to new rectangles, squares, and real-world measurement situations.
In unit 12, lesson 12.2 “Create Stem-and-Leaf Plots,” students apply conceptual understanding of data organization to new data sets. Students learn how to organize whole-number and decimal data in stem-and-leaf plots, interpret what each stem and leaf represents, and use the display to answer questions. Students also collect measurement data to the nearest quarter inch and organize the data in a stem-and-leaf plot. These tasks require students to apply data representation concepts to unfamiliar numerical and measurement contexts.
Evaluation for 5.2a
In unit 3, lesson 3.1, “Multiply by 10s, 100s, and 1,000s,” students build fluency with multiplication patterns using place value. The educator guidance asks students to use place value disks to represent related products such as 3 × 4, 3 × 40, 3 × 400, and 3 × 4,000. Students identify patterns in the models and equations, explain how the value of the disks changes, and use the patterns to multiply by multiples of 10, 100, and 1,000. These repeated opportunities build automaticity with place value-based multiplication strategies.
In unit 3, lesson 3.5 “Multiply Using the Standard Algorithm,” students build fluency with multi-digit multiplication. The lesson begins with partial products and then connects those partial products to the standard algorithm. Students compare two multiplication methods, practice regrouping, use the standard algorithm to multiply multi-digit numbers by one-digit numbers, and estimate products to check reasonableness. These tasks build fluency with an efficient grade-level multiplication procedure.
Evaluation for 5.2b
In unit 3, lesson 3.5 “Multiply Using the Standard Algorithm,” students practice efficient, flexible, and accurate multiplication procedures. The educator guidance asks students to compare partial products with the standard algorithm and notice that both methods use the same place value relationships. Students practice multiplying multi-digit numbers by one-digit numbers, regroup as needed, and use estimation to check whether products are reasonable. This practice supports both procedural accuracy and flexibility in method selection.
In unit 4, lesson 4.4 “The Standard Algorithm with 2-Digit Numbers,” students extend efficient multiplication procedures to two-digit factors. The educator guidance asks students to compare partial products with the standard algorithm, notice how the algorithm combines partial products, and explain why the second partial product has a zero in the ones place when multiplying by a tens digit. Students then practice multiplying two two-digit numbers using the standard algorithm and estimate to check whether their answers are reasonable.
Evaluation for 5.2c
In unit 2, lesson 2.4 “Estimate Sums and Differences,” students evaluate procedures for efficiency and accuracy. The educator guidance asks students to estimate sums and differences by rounding to different places and using compatible numbers. Students predict which estimate will be closer to the actual answer, compare the estimates, and discuss why rounding to a smaller place usually gives a closer estimate while still being easy to calculate mentally.
In unit 4, lesson 4.4 “The Standard Algorithm with 2-Digit Numbers,” students evaluate multiplication procedures and solutions. Students compare partial products methods with the standard algorithm, discuss why the product is the same when partial products are in a different order, and use estimation to determine whether products are reasonable. These opportunities require students to evaluate procedures and solutions for flexibility, efficiency, and accuracy.
Evaluation for 5.2d
In unit 2, lesson 2.4 “Estimate Sums and Differences,” embedded educator guidance supports students in moving toward increasingly efficient estimation strategies. Educators guide students to round to different places, compare the accuracy of estimates, use compatible numbers, and determine which approach gives an estimate that is both close to the actual answer and easy to calculate mentally. These prompts help educators guide students from basic rounding to more strategic estimation.
In unit 7, lesson 7.1 “Perimeter of Rectangles,” embedded educator guidance supports students to move from counting units to using formulas. Students first count side lengths and add to find perimeter. The educator then guides students to notice that opposite sides of rectangles are equal and that students can use this structure to develop perimeter formulas. Students compare counting with formula use and recognize that formulas are quicker and more efficient for larger rectangles.
Evaluation for 5.3a
The unit 1 “Instructional Context” tab explicitly describes how the materials address both conceptual and procedural expectations for place value. The “Look Back” section explains that students previously read and represented numbers up to 100,000 and used place value to compare, order, and round numbers. The “This Unit” section explains that students extend place value understanding to numbers up to 1 million, represent large numbers with place value disks, use models to determine digit values, and practice writing, comparing, ordering, and rounding multi-digit numbers. This section shows how conceptual understanding with models supports procedural work with number forms and comparisons.
Unit 1, lesson 1.3 “Read and Write Numbers to One Billion,” explicitly connects conceptual models to procedural representations. Students use place value disks and place value mats to model large numbers, then use the value of each digit to write numbers in standard form, expanded notation, expanded form, and word form. This sequence balances conceptual understanding of digit value with procedural fluency in representing numbers in different forms.
Evaluation for 5.3b
In unit 1, lesson 1.3 “Read and Write Numbers to One Billion,” students use concrete models and pictorial and abstract representations. Students model numbers with place value disks and sketch place value disks to represent numbers. Students then write the same numbers in standard form, expanded notation, expanded form, and word form. This sequence connects concrete manipulatives, drawings, and symbolic representations as required by the grade 4 place value TEKS.
In unit 11, lesson 11.1 “Relate Fractions and Decimals,” students use concrete, pictorial, and abstract representations to connect fractions and decimals. Students use place value blocks to represent tenths and hundredths, shade decimal grids, record values in place value charts, and write decimals in standard form and word form. The lesson also connects equivalent representations such as 7/10, 70/100, 0.7, and 0.70.
Evaluation for 5.3c
Unit 1, lesson 1.3 “Read and Write Numbers to One Billion,” supports students in connecting concrete and pictorial models to abstract representations. Students use place value disks to model each digit in a number, sketch the disks when manipulatives are not available, and explain how each digit’s place determines its value. Students then connect the model to standard form, expanded notation, expanded form, and word form.
Unit 11, lesson 11.1 “Relate Fractions and Decimals,” supports students in connecting models to symbolic decimal and fraction notation. Students use place value blocks and decimal grids to show tenths and hundredths, then record the values in place value charts and write them as decimals, fractions, and word form. Students also explain why equivalent decimals such as 0.7 and 0.70 represent the same quantity by connecting the model to equivalent fractional parts.
Evaluation for 5.4a
In unit 5, lesson 5.1 “Factors,” students develop academic mathematical language using visuals, number charts, and factor-pair representations. Students write multiplication equations with a product of 18, complete a table showing different ways to organize eight photos equally, and learn that the factors of a number are the numbers that can be multiplied to get that number. Students then complete a factor-pair rainbow for 28 and use a number chart to find factor pairs for 24. These tasks support students in developing and using academic vocabulary such as factor, factor pair, product, multiply, and common factors.
In unit 8, lesson 8.2 “Use Models to Find Equivalent Fractions,” students develop academic mathematical language using folded paper and visual fraction models. Students learn the term equivalent fractions as they fold paper into equal parts, shade a fraction, fold the paper again, and determine what equivalent fractions the paper shows. Students also use area models, circle models, and fraction notation to identify and write equivalent fractions. These tasks support students in connecting the term equivalent fractions to concrete models, visual representations, and symbolic fraction notation.
Evaluation for 5.4b
Unit 7, lesson 7.2 “Area of Rectangles,” scaffolds students’ development and use of academic mathematical vocabulary in context. Students use labeled rectangle and square diagrams to find area, write formulas such as A = l × w, and discuss how the area formula for a square is similar to and different from the area formula for a rectangle. Students also solve problems involving length, width, square units, and unknown dimensions. These tasks support students in using academic vocabulary such as area, formula, length, width, square, rectangle, and square units in context.
In unit 14, lesson 14.1 “Parallel and Perpendicular Lines,” students develop and use geometric vocabulary in context. Students complete sentences defining intersecting lines, parallel lines, and perpendicular lines, then use a diagram to identify each type of line. Students also determine whether statements about lines are true or false and explain how they know. These tasks scaffold students’ use of precise geometric vocabulary while they analyze diagrams and justify relationships among lines.
Evaluation for 5.4c
Unit 8, lesson 8.1 “Fractions Greater Than One,” includes support for students to apply mathematical language through vocabulary, syntax, and discourse. Students use paper-folding models, fraction models, mixed numbers, and number lines to represent fractions greater than one. In the “Think and Talk” task, students analyze Jayla and Kendrick’s statements about a point on a number line and explain what fraction the point represents and how they know. This task gives students opportunities to hear, refine, and use language such as fraction, whole, equal parts, fourths, mixed number, number line, less than one whole, and greater than one.
In unit 14, lesson 14.1 “Parallel and Perpendicular Lines,” students apply mathematical vocabulary, syntax, and discourse while describing line relationships. Students use diagrams to complete definitions of intersecting, parallel, and perpendicular lines, identify examples in diagrams, and explain whether statements are true or false. Students also respond to prompts such as whether all perpendicular lines are also intersecting lines and why. These tasks support mathematical conversations in which students use precise academic language to explain, justify, and refine their understanding of geometric relationships.
Evaluation for 5.5a
Unit 7, lesson 7.3 “Area of Compound Figures,” appropriately integrates the TEKS process standards as students solve real-world and mathematical problems involving area. Students compare two strategies for finding the area of the same compound figure, such as subtracting a missing section from a larger rectangle or adding three areas. Students then solve real-world area problems, including finding the area of a combined shed and garage space. These tasks require students to select strategies, analyze representations, communicate mathematical ideas, and justify solution methods.
Unit 4, lesson 4.5 “Multi-Step Problems with 2-Digit Numbers,” integrates the TEKS process standards as students solve real-world multistep multiplication problems. Students draw strip models, write equations for each step, use letters for unknown numbers, and solve problems about cookies, kelp growth, puzzle sales, coin collections, dog walks, donations, and weekly earnings. These tasks require students to analyze given information, formulate a solution plan, use equations and models, communicate reasoning, and solve problems that arise in everyday life and the workplace.
Evaluation for 5.5b
The “Instructional Design” document includes a “Mathematical Process Standards” section that describes how the TEKS process standards are incorporated and connected throughout the course. The document explains that the lesson plans and activities are designed to target the seven TEKS process standards and support students to make mathematical connections, communicate precisely, and solve complex problems in the classroom and everyday life.
The “Instructional Design” document provides course-level examples of how the process standards connect to grade-level content. The document describes how students use conceptual understanding, procedural fluency, and real-world applications across lessons, including using place value blocks and charts to understand decimal addition and subtraction before applying efficient procedures. This course-level guidance shows how mathematical reasoning, representation, communication, and problem solving are embedded throughout the course.
Evaluation for 5.5c
The unit 2 “Process Standards” tab provides a unit-level description of how the TEKS process standards are incorporated and connected throughout the unit. The materials explain that students add and subtract to solve problems drawn from the world around them, including apple orchards and food banks. The unit also describes how students use strip models and equations to represent one-step and multistep addition and subtraction problems, analyze what they know and what they need to find, and use estimation to evaluate reasonableness.
The unit 7 “Process Standards” tab provides a unit-level description of how process standards are connected throughout the perimeter and area unit. The materials explain that students solve real-world area and perimeter problems, develop formulas for rectangles, determine missing side lengths, and solve problems involving compound figures. The unit guidance also describes how students compare strategies, use diagrams and formulas, justify their approaches, and communicate mathematical ideas using precise language related to length, width, perimeter, area, and formulas.
Evaluation for 5.5d
“Fourth Grade At-a-Glance” provides an overview of the TEKS process standards incorporated into lessons across the grade level. A TEKS chart lists each mathematical process standard and identifies the lessons in which each standard appears. For example, process standard 4.1.A is connected to lessons 2.5, 2.6, 4.5, 7.1, 7.2, 7.3, 7.4, 10.1–10.9, 12.1–12.6, and additional lessons across the course.
“Fourth Grade At-a-Glance” also provides lesson-level alignment for additional process standards. A chart identifies lessons connected to process standards for using a problem-solving model, selecting tools and techniques, communicating mathematical ideas with multiple representations, creating and using representations, analyzing relationships, and explaining and justifying mathematical ideas. This standards chart functions as an overview of where the TEKS process standards are incorporated into individual lessons.
5.1 Development of Conceptual Understanding
5.1a
Questions and tasks require students to interpret, analyze, and evaluate models and representations for mathematical concepts and situations.
Questions and tasks require 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 require students to interpret, analyze, and evaluate models and representations for mathematical concepts and situations.
3 out of 3 points
In unit 12, lesson 12.2 “Create Stem-and-Leaf Plots,” students interpret and analyze data representations. The educator guidance explains how a stem-and-leaf plot organizes values by separating each number into a stem and a leaf, then asks students to use the plot to answer questions about the data. Students also analyze stem-and-leaf plots with decimal values by identifying how the stem represents the ones digit and the leaf represents the tenths digit. These tasks require students to interpret the structure of a data display and evaluate how the representation helps answer questions about the data.
5.1b
Questions and tasks require students to create models to represent mathematical situations.
Questions and tasks require students to create models to represent mathematical situations.
1 out of 1 points
Evaluation for 5.1b
Evaluation for 5.1b
Questions and tasks require students to create models to represent mathematical situations.
1 out of 1 points
In unit 7, lesson 7.1 “Perimeter of Rectangles,” students create models to represent perimeter situations. The guidance instructs educators to provide grid paper and ask students to draw rectangles with sides along gridlines, trade rectangles with a partner, and find the perimeter of the partner’s rectangle. Students use their drawings to identify length and width, recognize equal opposite sides, and develop formulas for the perimeter of rectangles and squares. This task requires students to create models that represent mathematical situations and use those models to reason about perimeter.
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 unit 12, lesson 12.2 “Create Stem-and-Leaf Plots,” students apply conceptual understanding of data organization to new data sets. Students learn how to organize whole-number and decimal data in stem-and-leaf plots, interpret what each stem and leaf represents, and use the display to answer questions. Students also collect measurement data to the nearest quarter inch and organize the data in a stem-and-leaf plot. These tasks require students to apply data representation concepts to unfamiliar numerical and measurement contexts.
5.2 Development of Fluency
5.2a
Materials provide tasks that are designed to build student automaticity and fluency necessary to complete grade-level tasks.
Materials provide tasks that are designed to build student automaticity and fluency necessary to complete grade-level 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 tasks.
2 out of 2 points
In unit 3, lesson 3.5 “Multiply Using the Standard Algorithm,” students build fluency with multi-digit multiplication. The lesson begins with partial products and then connects those partial products to the standard algorithm. Students compare two multiplication methods, practice regrouping, use the standard algorithm to multiply multi-digit numbers by one-digit numbers, and estimate products to check reasonableness. These tasks build fluency with an efficient grade-level multiplication procedure.
5.2b
Materials provide opportunities for students to practice the application of efficient, flexible, and accurate mathematical procedures within the lesson and/or throughout a unit.
Materials provide opportunities for students to practice the application of efficient, flexible, and accurate mathematical procedures within the lesson and/or throughout a unit.
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 within the lesson and/or throughout a unit.
3 out of 3 points
In unit 4, lesson 4.4 “The Standard Algorithm with 2-Digit Numbers,” students extend efficient multiplication procedures to two-digit factors. The educator guidance asks students to compare partial products with the standard algorithm, notice how the algorithm combines partial products, and explain why the second partial product has a zero in the ones place when multiplying by a tens digit. Students then practice multiplying two two-digit numbers using the standard algorithm and estimate to check whether their answers are reasonable.
5.2c
Materials provide opportunities for students to evaluate procedures, processes, and solutions for efficiency, flexibility, and accuracy within the lesson and throughout a unit.
Materials provide opportunities for students to evaluate procedures, processes, and solutions for efficiency, flexibility, and accuracy within the lesson and throughout a unit.
3 out of 3 points
Evaluation for 5.2c
Evaluation for 5.2c
Materials provide opportunities for students to evaluate procedures, processes, and solutions for efficiency, flexibility, and accuracy within the lesson and throughout a unit.
3 out of 3 points
In unit 4, lesson 4.4 “The Standard Algorithm with 2-Digit Numbers,” students evaluate multiplication procedures and solutions. Students compare partial products methods with the standard algorithm, discuss why the product is the same when partial products are in a different order, and use estimation to determine whether products are reasonable. These opportunities require students to evaluate procedures and solutions for flexibility, efficiency, and accuracy.
5.2d
Materials contain embedded supports for teachers to guide students toward increasingly efficient approaches.
Materials contain embedded supports for teachers to guide students toward increasingly efficient approaches.
1 out of 1 points
Evaluation for 5.2d
Evaluation for 5.2d
Materials contain embedded supports for teachers to guide students toward increasingly efficient approaches.
1 out of 1 points
In unit 7, lesson 7.1 “Perimeter of Rectangles,” embedded educator guidance supports students to move from counting units to using formulas. Students first count side lengths and add to find perimeter. The educator then guides students to notice that opposite sides of rectangles are equal and that students can use this structure to develop perimeter formulas. Students compare counting with formula use and recognize that formulas are quicker and more efficient for larger rectangles.
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
Unit 1, lesson 1.3 “Read and Write Numbers to One Billion,” explicitly connects conceptual models to procedural representations. Students use place value disks and place value mats to model large numbers, then use the value of each digit to write numbers in standard form, expanded notation, expanded form, and word form. This sequence balances conceptual understanding of digit value with procedural fluency in representing numbers in different forms.
5.3b
Questions and tasks include the use of concrete models and manipulatives, pictorial representations (figures/drawings), and abstract representations, as required by the TEKS.
Questions and tasks include the use of concrete models and manipulatives, pictorial representations (figures/drawings), and abstract representations, as required by the TEKS.
3 out of 3 points
Evaluation for 5.3b
Evaluation for 5.3b
Questions and tasks include the use of concrete models and manipulatives, pictorial representations (figures/drawings), and abstract representations, as required by the TEKS.
3 out of 3 points
In unit 11, lesson 11.1 “Relate Fractions and Decimals,” students use concrete, pictorial, and abstract representations to connect fractions and decimals. Students use place value blocks to represent tenths and hundredths, shade decimal grids, record values in place value charts, and write decimals in standard form and word form. The lesson also connects equivalent representations such as 7/10, 70/100, 0.7, and 0.70.
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
Unit 11, lesson 11.1 “Relate Fractions and Decimals,” supports students in connecting models to symbolic decimal and fraction notation. Students use place value blocks and decimal grids to show tenths and hundredths, then record the values in place value charts and write them as decimals, fractions, and word form. Students also explain why equivalent decimals such as 0.7 and 0.70 represent the same quantity by connecting the model to equivalent fractional parts.
5.4 Development of Academic Mathematical Language
5.4a
Materials provide opportunities for students to develop academic mathematical language using visuals, manipulatives, and other language development strategies.
Materials provide opportunities for students to develop academic mathematical language using visuals, manipulatives, and other language development strategies.
3 out of 3 points
Evaluation for 5.4a
Evaluation for 5.4a
Materials provide opportunities for students to develop academic mathematical language using visuals, manipulatives, and other language development strategies.
3 out of 3 points
In unit 8, lesson 8.2 “Use Models to Find Equivalent Fractions,” students develop academic mathematical language using folded paper and visual fraction models. Students learn the term equivalent fractions as they fold paper into equal parts, shade a fraction, fold the paper again, and determine what equivalent fractions the paper shows. Students also use area models, circle models, and fraction notation to identify and write equivalent fractions. These tasks support students in connecting the term equivalent fractions to concrete models, visual representations, and symbolic fraction notation.
5.4b
Materials include embedded teacher guidance to scaffold and support students' development and use of academic mathematical vocabulary in context.
Materials include embedded teacher guidance to scaffold and support students' development and use of academic mathematical vocabulary in context.
1 out of 1 points
Evaluation for 5.4b
Evaluation for 5.4b
Materials include embedded teacher guidance to scaffold and support students' development and use of academic mathematical vocabulary in context.
1 out of 1 points
In unit 14, lesson 14.1 “Parallel and Perpendicular Lines,” students develop and use geometric vocabulary in context. Students complete sentences defining intersecting lines, parallel lines, and perpendicular lines, then use a diagram to identify each type of line. Students also determine whether statements about lines are true or false and explain how they know. These tasks scaffold students’ use of precise geometric vocabulary while they analyze diagrams and justify relationships among lines.
5.4c
Materials include embedded teacher guidance to support the application of appropriate mathematical language to include vocabulary, syntax, and discourse to include guidance to support mathematical conversations that provide opportunities for students to hear, refine, and use math language with peers and develop their math language toolkit over time as well as guide teachers to support student responses using exemplar responses to questions and tasks.
Materials include embedded teacher guidance to support the application of appropriate mathematical language to include vocabulary, syntax, and discourse to include guidance to support mathematical conversations that provide opportunities for students to hear, refine, and use math language with peers and develop their math language toolkit over time as well as guide teachers to support student responses using exemplar responses to questions and tasks.
6 out of 6 points
Evaluation for 5.4c
Evaluation for 5.4c
Materials include embedded teacher guidance to support the application of appropriate mathematical language to include vocabulary, syntax, and discourse to include guidance to support mathematical conversations that provide opportunities for students to hear, refine, and use math language with peers and develop their math language toolkit over time as well as guide teachers to support student responses using exemplar responses to questions and tasks.
6 out of 6 points
In unit 14, lesson 14.1 “Parallel and Perpendicular Lines,” students apply mathematical vocabulary, syntax, and discourse while describing line relationships. Students use diagrams to complete definitions of intersecting, parallel, and perpendicular lines, identify examples in diagrams, and explain whether statements are true or false. Students also respond to prompts such as whether all perpendicular lines are also intersecting lines and why. These tasks support mathematical conversations in which students use precise academic language to explain, justify, and refine their understanding of geometric relationships.
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
Unit 4, lesson 4.5 “Multi-Step Problems with 2-Digit Numbers,” integrates the TEKS process standards as students solve real-world multistep multiplication problems. Students draw strip models, write equations for each step, use letters for unknown numbers, and solve problems about cookies, kelp growth, puzzle sales, coin collections, dog walks, donations, and weekly earnings. These tasks require students to analyze given information, formulate a solution plan, use equations and models, communicate reasoning, and solve problems that arise in everyday life and the workplace.
5.5b
Materials include a description of how TEKS process standards are incorporated and connected throughout the course.
Materials include a description of how TEKS process standards are incorporated and connected throughout the course.
2 out of 2 points
Evaluation for 5.5b
Evaluation for 5.5b
Materials include a description of how TEKS process standards are incorporated and connected throughout the course.
2 out of 2 points
The “Instructional Design” document provides course-level examples of how the process standards connect to grade-level content. The document describes how students use conceptual understanding, procedural fluency, and real-world applications across lessons, including using place value blocks and charts to understand decimal addition and subtraction before applying efficient procedures. This course-level guidance shows how mathematical reasoning, representation, communication, and problem solving are embedded throughout the course.
5.5c
Materials include a description for each unit of how TEKS process standards are incorporated and connected throughout the unit.
Materials include a description for each unit of how TEKS process standards are incorporated and connected throughout the unit.
2 out of 2 points
Evaluation for 5.5c
Evaluation for 5.5c
Materials include a description for each unit of how TEKS process standards are incorporated and connected throughout the unit.
2 out of 2 points
The unit 7 “Process Standards” tab provides a unit-level description of how process standards are connected throughout the perimeter and area unit. The materials explain that students solve real-world area and perimeter problems, develop formulas for rectangles, determine missing side lengths, and solve problems involving compound figures. The unit guidance also describes how students compare strategies, use diagrams and formulas, justify their approaches, and communicate mathematical ideas using precise language related to length, width, perimeter, area, and formulas.
5.5d
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 5.5d
Evaluation for 5.5d
Materials include an overview of the TEKS process standards incorporated into each lesson.
1 out of 1 points
“Fourth Grade At-a-Glance” also provides lesson-level alignment for additional process standards. A chart identifies lessons connected to process standards for using a problem-solving model, selecting tools and techniques, communicating mathematical ideas with multiple representations, creating and using representations, analyzing relationships, and explaining and justifying mathematical ideas. This standards chart functions as an overview of where the TEKS process standards are incorporated into individual lessons.
Rubric Section 6
Productive Struggle
Materials support students in applying disciplinary practices to productive problem-solving, including explaining and revising their thinking.
Total
100% (22 out of 22 points)
Evaluation for 6.1a
In unit 6, lesson 6.8, question 2, students think mathematically, persevere through problem solving, and make sense of mathematics as they solve a multistep division problem. The “Tip for Support” guides educators to help students identify the information they know, determine what they need to find, and recognize hidden questions before solving. Students represent the situation with strip diagrams, write equations for each step, and explain how each representation supports the solution. These instructional supports encourage students to make sense of the problem structure while persevering through complex problem solving.
In unit 10, lesson 10.9, question 4, students think mathematically and make sense of mathematics as they solve an elapsed-time problem using multiple strategies. Educators guide students to model the problem on an open number line before verifying the solution with vertical computation. Students compare representations, determine whether their answer is reasonable, and explain their reasoning. These opportunities encourage students to apply multiple strategies while solving real-world problems and evaluating the reasonableness of their solutions.
Evaluation for 6.1b
In unit 3, lesson 3.6, questions 3 and 4, students understand, explain, and justify that mathematical problems can be represented and solved in multiple ways. The “Compare and Talk” activity guides educators to ask students to analyze two different methods for solving the same multiplication problem, using an equation and a strip diagram. Students note the similarities and differences between the representations before creating two different solution methods for a new problem. These activities help students recognize that different representations and strategies can correctly model and solve the same mathematical situation.
In unit 3, lesson 3.2, students compare multiple strategies for estimating products. Educators guide students to estimate products using rounding before introducing compatible numbers during the “Think and Talk” discussion. Students compare both estimation methods, explain which strategy they prefer, and justify why one approach may be more efficient for a particular problem. These opportunities support students in evaluating, explaining, and justifying multiple solution strategies.
Evaluation for 6.1c
In unit 2, lesson 2.6, students make sense of mathematics through opportunities to do, discuss, and write about mathematics. The “Think and Talk” activity guides educators to ask students to evaluate whether a classmate’s solution strategy will correctly solve a multistep word problem. Students discuss their reasoning with peers before creating their own four-digit numbers to complete a related problem and recording their mathematical thinking in writing. These activities engage students in analyzing strategies, discussing mathematical reasoning, and writing about their solutions.
The “Instructional Design” document explains that lessons incorporate “Compare and Talk” and “Think and Talk” routines to promote meaningful mathematical discourse. Educators facilitate structured discussions that encourage students to compare strategies, justify solutions, and communicate mathematical reasoning orally and in writing. These routines provide ongoing opportunities for students to make sense of mathematics by doing, discussing, and writing about mathematical ideas throughout the program.
Evaluation for 6.2a
In unit 6, lesson 6.7, educator notes support students to share and reflect on problem-solving approaches as they interpret remainders in division word problems. Educators prompt students to explain whether the quotient, the remainder, or one more than the quotient is appropriate based on the context of the problem. Students compare interpretations, justify their reasoning, and explain how the remainder affects the solution. These discussions encourage students to reflect on and justify their mathematical thinking.
In unit 7, lesson 7.4, educator notes guide students to share and reflect on their approaches as they solve multistep area and perimeter problems. Educators prompt students to explain how they determined missing dimensions, compare alternative solution paths, and justify the efficiency of their strategies. Students share their mathematical reasoning, evaluate multiple approaches, and defend their solutions during classroom discussions. These opportunities support students in reflecting on problem-solving approaches through explanations and justifications.
Evaluation for 6.2b
Unit 9, lesson 9.5, includes prompts and guidance to support teachers in providing explanatory feedback based on anticipated misconceptions. Educator notes anticipate that students may have difficulty tracking fractional increments while subtracting fractions on a number line. The lesson guides educators to have students label each tick mark, count backward one interval at a time, and verbalize each fraction as they subtract. Students use the number line to monitor their thinking, explain each step of the subtraction process, and revise their work as needed.
Unit 13, lesson 13.4 includes prompts and guidance for educators to address common errors with angle measurement. The educator notes anticipate that students may incorrectly read a protractor because they use the wrong scale or fail to extend a ray. The lesson guides educators to have students re-measure the angle, extend the ray if necessary, and verify that they are reading the correct scale before calculating angle sums. Students revisit their measurements, explain their reasoning, and correct misconceptions using the educator guidance.
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 unit 10, lesson 10.9, question 4, students think mathematically and make sense of mathematics as they solve an elapsed-time problem using multiple strategies. Educators guide students to model the problem on an open number line before verifying the solution with vertical computation. Students compare representations, determine whether their answer is reasonable, and explain their reasoning. These opportunities encourage students to apply multiple strategies while solving real-world problems and evaluating the reasonableness of their solutions.
6.1b
Materials support students in understanding, explaining, and justifying that there can be multiple ways to represent and solve problems and complete tasks.
Materials support students in understanding, explaining, and justifying that there can be multiple ways to represent and solve problems and complete tasks.
6 out of 6 points
Evaluation for 6.1b
Evaluation for 6.1b
Materials support students in understanding, explaining, and justifying that there can be multiple ways to represent and solve problems and complete tasks.
6 out of 6 points
In unit 3, lesson 3.2, students compare multiple strategies for estimating products. Educators guide students to estimate products using rounding before introducing compatible numbers during the “Think and Talk” discussion. Students compare both estimation methods, explain which strategy they prefer, and justify why one approach may be more efficient for a particular problem. These opportunities support students in evaluating, explaining, and justifying multiple solution strategies.
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 teachers.
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 teachers.
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 teachers.
3 out of 3 points
The “Instructional Design” document explains that lessons incorporate “Compare and Talk” and “Think and Talk” routines to promote meaningful mathematical discourse. Educators facilitate structured discussions that encourage students to compare strategies, justify solutions, and communicate mathematical reasoning orally and in writing. These routines provide ongoing opportunities for students to make sense of mathematics by doing, discussing, and writing about mathematical ideas throughout the program.
6.2 Facilitating Productive Struggle
6.2a
Materials support teachers in guiding students to share and reflect on their problem-solving approaches, including explanations, arguments, and justifications.
Materials support teachers 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 teachers in guiding students to share and reflect on their problem-solving approaches, including explanations, arguments, and justifications.
6 out of 6 points
In unit 7, lesson 7.4, educator notes guide students to share and reflect on their approaches as they solve multistep area and perimeter problems. Educators prompt students to explain how they determined missing dimensions, compare alternative solution paths, and justify the efficiency of their strategies. Students share their mathematical reasoning, evaluate multiple approaches, and defend their solutions during classroom discussions. These opportunities support students in reflecting on problem-solving approaches through explanations and justifications.
6.2b
Materials include prompts and guidance to support teachers in providing explanatory feedback based on student responses and anticipated misconceptions.
Materials include prompts and guidance to support teachers 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 teachers in providing explanatory feedback based on student responses and anticipated misconceptions.
4 out of 4 points
Unit 13, lesson 13.4 includes prompts and guidance for educators to address common errors with angle measurement. The educator notes anticipate that students may incorrectly read a protractor because they use the wrong scale or fail to extend a ray. The lesson guides educators to have students re-measure the angle, extend the ray if necessary, and verify that they are reading the correct scale before calculating angle sums. Students revisit their measurements, explain their reasoning, and correct misconceptions using the educator guidance.