Program Information
- ISBN
- 9781483880068
- 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 5 Math
Math (English) Grade 5
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 5 | 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 5 Texas Essential Knowledge and Skills (TEKS), English Language Proficiency Standards (ELPS), and concepts taught throughout the course. For example, “Fifth Grade At-a-Glance: Planning and Materials” provides an overview of each unit and the concepts taught, including the aligned grade 5 TEKS and ELPS.
In addition, each unit provides a “Daily Planner” that outlines the grade 5 TEKS, ELPS, and concepts taught throughout the unit. For example, in unit 7 students multiply decimal numbers by whole numbers and other decimal numbers. Students use area models, partial products, the standard algorithm, and other strategies. These concepts align with grade 5 standards 5.3A, 5.3D, and 5.3E.
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.
“Fifth 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
In “Fifth 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, unit 6 extends students’ understanding of decimal place value and computation from grade 4 as they work with decimals through the thousandths place. Unit 6 prepares students for units 7 and 8, which introduce decimal multiplication and division, and supports later applications involving measurement and data.
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 4 “Look Back” section explains that in grade 4 students added and subtracted fractions and mixed numbers with like denominators. Students also learned to create equivalent fractions by multiplying or dividing the numerator and denominator by the same number.
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 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 unit overviews provide the background content knowledge and academic vocabulary necessary to effectively teach the grade 5 concepts. For example, in the unit 7 outline the “Instructional Context” includes a “Look Back” section that identifies students’ prior learning and explains how it connects to the concepts taught in the current unit.
The “Additional Resources” section of each unit identifies academic vocabulary educators can introduce before instruction. For example, the unit 11 overview provides a list of vocabulary connected to the unit concepts and guidance educators can use to prepare students for the mathematical language they encounter, such as bar graph, frequency table, dot plot (line plot), scatter plot, and stem-and-leaf plot.
Evaluation for 1.2b
The materials contain supports for families in both English and Spanish for each unit. For example, English and Spanish glossaries provide academic vocabulary, explanations, and learning supports that families can use to reinforce the concepts taught in the course.
The English and Spanish “Welcome Letters” provide families with information about the program and suggestions for supporting student progress. For example, the letters explain how families can access program resources and reinforce student learning outside the classroom.
Evaluation for 1.3a
Lesson plans include lesson objectives, TEKS and ELPS correlations, instructional tasks, educator questions, materials, and assessments. For example, lesson 3.1 includes “Instructional Context” that explains the lesson objective, the lesson content, and how the concepts connect to prior and future learning. The lesson also includes educator questions, guided practice, independent practice, and checks for understanding.
Lesson 3.2 outlines the content students learn, provides questions educators use during instruction, and includes guided and independent practice that allow students to apply the concepts. Educator notes support formative assessment by helping educators monitor student responses during instruction and practice.
The Student Workbook provides practice tasks that align with lesson objectives and instructional assessments. Students complete guided practice, independent practice, and problem-solving opportunities connected to the lesson concepts. These student-facing tasks support mastery of the content standards and provide educators with evidence of student understanding.
Evaluation for 1.3b
The unit 4 “Daily Planner” identifies educator and student materials needed for instruction in adding and subtracting fractions. For example, lesson 4.1 “Estimate Sums and Differences of Fractions,” identifies student workbook resources, independent practice resources, and fraction strips. Lesson 4.2 “Add Fractions with Models,” identifies student materials and online readiness skills connected to fraction strips and equivalent fractions. These examples show that the materials identify student-facing resources, physical manipulatives, and online skills needed for instruction and practice.
The unit 12 “Daily Planner” provides additional examples of materials. Lesson 12.1 “Classify Polygons,” identifies student resources, the “Polygon Sort” activity, and colored pencils. Lesson 12.2 “Classify Triangles,” identifies student materials and skills for classifying triangles. These resources support hands-on sorting, visual classification, student work, and independent practice.
The Discover Takeoff by IXL: Comprehensive Lesson Plans guide provides suggested timing for the lesson sequence. Lessons include 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 daily lesson length and how the lesson divides time across warm-up, educator-led instruction, guided practice, and independent practice.
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 4 provides lesson-level guidance for extended practice and enrichment in adding and subtracting fractions. In lesson 4.5 students determine whether fraction equations are true or false and correct false equations by changing one fraction to make the equation true. The “Idea for Extension” gives educators a specific follow-up task where students find a second way to correct problems 11 and 13. This extension asks students to revisit their work, generate another valid equivalent fraction or correction, and apply fraction reasoning in more than one way.
The unit 4 “Daily Planner” also identifies additional practice and support resources connected to fraction concepts. The planner includes student workbook resources, independent practice resources, fraction strips, readiness skills, practice skills, support skills, spiral review, the unit test, and “Personalization Day.” These resources give educators options for assigning homework-style practice, providing additional support, or extending learning after students complete the core lesson.
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 5 TEKS, ELPS, and concepts taught throughout the unit. For example, in unit 7 students multiply decimal numbers by whole numbers and other decimal numbers. Students use area models, partial products, the standard algorithm, and other strategies. These concepts align with grade 5 standards 5.3A, 5.3D, and 5.3E.
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
“Fifth 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 4 “Look Back” section explains that in grade 4 students added and subtracted fractions and mixed numbers with like denominators. Students also learned to create equivalent fractions by multiplying or dividing the numerator and denominator by the same number.
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 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 “Additional Resources” section of each unit identifies academic vocabulary educators can introduce before instruction. For example, the unit 11 overview provides a list of vocabulary connected to the unit concepts and guidance educators can use to prepare students for the mathematical language they encounter, such as bar graph, frequency table, dot plot (line plot), scatter plot, and stem-and-leaf plot.
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 English and Spanish “Welcome Letters” provide families with information about the program and suggestions for supporting student progress. For example, the letters explain how families can access program resources and reinforce student learning outside 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
Lesson 3.2 outlines the content students learn, provides questions educators use during instruction, and includes guided and independent practice that allow students to apply the concepts. Educator notes support formative assessment by helping educators monitor student responses during instruction and practice.
The Student Workbook provides practice tasks that align with lesson objectives and instructional assessments. Students complete guided practice, independent practice, and problem-solving opportunities connected to the lesson concepts. These student-facing tasks support mastery of the content standards and provide educators with evidence of student understanding.
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 12 “Daily Planner” provides additional examples of materials. Lesson 12.1 “Classify Polygons,” identifies student resources, the “Polygon Sort” activity, and colored pencils. Lesson 12.2 “Classify Triangles,” identifies student materials and skills for classifying triangles. These resources support hands-on sorting, visual classification, student work, and independent practice.
The Discover Takeoff by IXL: Comprehensive Lesson Plans guide provides suggested timing for the lesson sequence. Lessons include 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 daily lesson length and how the lesson divides time across warm-up, educator-led instruction, guided practice, and independent practice.
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 4 provides lesson-level guidance for extended practice and enrichment in adding and subtracting fractions. In lesson 4.5 students determine whether fraction equations are true or false and correct false equations by changing one fraction to make the equation true. The “Idea for Extension” gives educators a specific follow-up task where students find a second way to correct problems 11 and 13. This extension asks students to revisit their work, generate another valid equivalent fraction or correction, and apply fraction reasoning in more than one way.
The unit 4 “Daily Planner” also identifies additional practice and support resources connected to fraction concepts. The planner includes student workbook resources, independent practice resources, fraction strips, readiness skills, practice skills, support skills, spiral review, the unit test, and “Personalization Day.” These resources give educators options for assigning homework-style practice, providing additional support, or extending learning after students complete the core lesson.
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 5 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 assessments to monitor progress toward grade 5 objectives.
Lessons include formative assessment opportunities during instruction, guided practice, and independent practice. Warm-ups, guided practice questions, independent practice items, and skill checks allow educators to monitor student understanding as students work through the lesson. 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 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 student learning during lessons. Summative assessments evaluate student mastery after instruction.
The Insightful Assessments guide explains how educators use unit assessment results. The guide describes how educators use 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 are an option for monitoring progress or evaluating 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 5 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 procedures help educators consistently administer grade 5 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 the benchmark 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 5 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. The unit 8 outline includes lesson plan pages that identify the TEKS and lesson objectives. Warm-ups, guided practice, independent practice, and skill checks provide ongoing evidence of whether students are progressing toward 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 3 test asks students to show an answer in multiple ways, find volume without a visual, and explain their thinking. The unit 4 test on adding and subtracting fractions requires students to apply computation, classify fractions, 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 5 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 5 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. The unit 3 test answer key provides scoring information, while the “Personalization Day” objective breakdown connects assessment results to 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. “Personalization Day” 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. This information helps educators respond directly to trends in grade 5 assessment results.
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 5 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 include formative assessment opportunities during instruction, guided practice, and independent practice. Warm-ups, guided practice questions, independent practice items, and skill checks allow educators to monitor student understanding as students work through the lesson. 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 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 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 are an option for monitoring progress or evaluating 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 procedures help educators consistently administer grade 5 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 the benchmark 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. The unit 8 outline includes lesson plan pages that identify the TEKS and lesson objectives. Warm-ups, guided practice, independent practice, and skill checks provide ongoing evidence of whether students are progressing toward 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 3 test asks students to show an answer in multiple ways, find volume without a visual, and explain their thinking. The unit 4 test on adding and subtracting fractions requires students to apply computation, classify fractions, 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. The unit 3 test answer key provides scoring information, while the “Personalization Day” objective breakdown connects assessment results to 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 educator guidance for differentiated instruction, activities, and scaffolded support for students who have not yet reached proficiency with grade-level content and skills. For example, the lesson plan pages include “Tips for Support” within each lesson to scaffold instruction for students who need additional support. In unit 11, lesson 11.3, the “Tips for Support” help educators identify students who are struggling and provide on-the-spot strategies to address gaps 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 9 includes a vocabulary list under “Additional Resources.” Unit 9, lesson 9.4 embeds support for unfamiliar vocabulary—including leap day and leap year—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 emergent bilingual (EB) students across proficiency levels and includes guidance for vocabulary that may be challenging for EB students. In lesson 9.1 the “Additional Supports” tab suggests creating a picture dictionary of relevant academic vocabulary for the lesson. Lesson 9.2 includes a “Tip for Support” in which the educator demonstrates the concept using a visual.
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 9, lesson 9.4, the “Idea for Extension” appears before question 11 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 8 “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 unit 9, lesson 9.4, the guided practice educator notes instruct students to convert each measurement for questions 12–15. The notes suggest having students check one another’s answers, work together to correct mistakes, and point out abbreviations for time units on the reference sheet. The guidance helps educators model the concept while supporting students through the practice process.
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 10.2 includes think-aloud prompts and concrete steps for students who need additional support. Lesson 10.1 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 9, lesson 9.4 connects instruction to real-world problems and scenarios, such as movie length times. The educator notes provide structure for both collaborative and individual practice. Lessons also include written-response opportunities that ask students to justify their thinking and answers.
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 students’ 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 9 “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. For example, unit 9, lesson 9.4 includes a dedicated section for EB students with accommodations at each proficiency level to help students access lesson content and participate in mathematical discourse.
Language supports help students use more precise academic language across proficiency levels. For example, in unit 9, lesson 9.3, the language support strategies guide educators to use color-coded anchor charts and prefix discussions to help students at the pre-production through intermediate levels make visual connections between metric prefixes and their meanings. Lessons 5.1 and 12.3 include sentence stems targeted at beginning, intermediate, and high intermediate/advanced EB students.
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 9, lesson 9.3, 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 1.6 uses Spanish cognates to support understanding academic vocabulary. Lesson 13.1 asks students to define key vocabulary by creating picture dictionaries and annotating unfamiliar words in word problems before solving.
The materials provide language supports that increase comprehension through connections to prior knowledge, home languages, and everyday language. For example, lesson 1.10 provides educators with questions to monitor EB student comprehension of word problems. Other lesson guidance connects new academic terms to students’ prior knowledge and home languages, supporting background knowledge and cross-linguistic connections.
Lessons support oral and written discourse for EB students. Sentence stems, written-response tasks, partner discussion, and educator-guided questioning help students explain their thinking, use academic vocabulary, and communicate mathematical understanding. 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 9 includes a vocabulary list under “Additional Resources.” Unit 9, lesson 9.4 embeds support for unfamiliar vocabulary—including leap day and leap year—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 emergent bilingual (EB) students across proficiency levels and includes guidance for vocabulary that may be challenging for EB students. In lesson 9.1 the “Additional Supports” tab suggests creating a picture dictionary of relevant academic vocabulary for the lesson. Lesson 9.2 includes a “Tip for Support” in which the educator demonstrates the concept using a visual.
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 8 “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 unit 9, lesson 9.4, the guided practice educator notes instruct students to convert each measurement for questions 12–15. The notes suggest having students check one another’s answers, work together to correct mistakes, and point out abbreviations for time units on the reference sheet. The guidance helps educators model the concept while supporting students through the practice process.
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 10.2 includes think-aloud prompts and concrete steps for students who need additional support. Lesson 10.1 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 9, lesson 9.4 connects instruction to real-world problems and scenarios, such as movie length times. The educator notes provide structure for both collaborative and individual practice. Lessons also include written-response opportunities that ask students to justify their thinking and answers.
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 students’ 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 9 “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, in unit 9, lesson 9.3, the language support strategies guide educators to use color-coded anchor charts and prefix discussions to help students at the pre-production through intermediate levels make visual connections between metric prefixes and their meanings. Lessons 5.1 and 12.3 include sentence stems targeted at beginning, intermediate, and high intermediate/advanced EB students.
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 9, lesson 9.3, 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 connections to prior knowledge, home languages, and everyday language. For example, lesson 1.10 provides educators with questions to monitor EB student comprehension of word problems. Other lesson guidance connects new academic terms to students’ prior knowledge and home languages, supporting background knowledge and cross-linguistic connections.
Lessons support oral and written discourse for EB students. Sentence stems, written-response tasks, partner discussion, and educator-guided questioning help students explain their thinking, use academic vocabulary, and communicate mathematical understanding. 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 4 “Daily Planner” students demonstrate depth of understanding with adding and subtracting fractions by using equivalent fractions, models, and procedures across the unit. Students begin by estimating sums and differences of fractions using benchmarks, then add fractions with unlike denominators using models, add fractions without the support of visual models, subtract fractions with unlike denominators using models, and subtract fractions without models. Later lessons ask students to use least common denominators, add and subtract mixed numbers, regroup with mixed numbers, and solve multistep word problems involving fractions and mixed numbers. These practice opportunities require students to connect models, equivalent fractions, benchmark reasoning, and symbolic notation.
Instructional assessments also require students to demonstrate understanding aligned to grade 5 fraction TEKS. In the unit 4 “Add and Subtract Fractions” test, students add and subtract fractions with unlike denominators, simplify answers, use a visual model to interpret the sum of 2/5 and 3/10, and add and subtract mixed numbers. These assessment tasks require students to use equivalent fractions, interpret models, apply fraction operations, and demonstrate procedural fluency with fractions and mixed numbers.
Evaluation for 4.1b
The unit 4 “Daily Planner” organizes questions and tasks so students move from foundational understanding to more complex fraction operations. Students begin by estimating sums and differences using benchmarks, then add fractions with unlike denominators using models, then add fractions without visual models. The unit follows the same progression for subtraction by first using models and then moving to subtracting without models. This progression increases rigor by moving students from visual and benchmark reasoning to more abstract fraction computation.
The unit 4 sequence continues to increase in complexity as students move from fractions to mixed numbers and multistep problems. Students use least common denominators to add and subtract fractions, then add and subtract mixed numbers without regrouping, add mixed numbers with regrouping, subtract mixed numbers with regrouping, and solve multistep word problems involving fractions and mixed numbers. This progression supports grade-level proficiency by moving students from single-step fraction operations to multistep problem solving with rational numbers.
Evaluation for 4.2a
In the unit 6 outline the “Instructional Context” tab explicitly connects mathematical patterns, big ideas, and relationships across units. In unit 6 “Decimals,” the “Look Back” section explains that students previously explored place value with whole numbers and decimals to the hundredths place, and wrote decimals in standard form, expanded form, expanded notation, and word form. Students also previously compared and ordered decimals to the hundredths place and added and subtracted decimals using various strategies. The “This Unit” section explains that students extend decimal numbers to the thousandths place, write decimals in different forms, compare and round decimals, add and subtract decimal numbers fluently, and add and subtract fractions and decimals by writing them in the same form.
The unit 6 “Instructional Context” also connects decimal concepts to future mathematical work. The “Look Forward” section explains that in the next few units students will multiply and divide decimal numbers. The section also explains that later in the year students will add and subtract decimal numbers to solve problems involving measurement and data. This explanation shows coherence among decimal place value, decimal operations, fraction-decimal relationships, measurement, and data across the grade 5 course.
Evaluation for 4.2b
The “Instructional Context” tab connects grade 5 content to previous and future grade-level learning. In unit 2 “Factors, Multiples, Expressions, and Equations,” the “Look Back” section explains that in grade 4 students identified factors and multiples of whole numbers and represented and solved multistep problems involving all four operations with whole numbers. The section also explains that in the previous unit students developed fluency with adding, subtracting, multiplying, and dividing whole numbers.
The unit 2 “Instructional Context” tab also shows how current grade 5 learning prepares students for future mathematics. The “This Unit” section explains that students revisit factors and multiples, describe numbers as prime or composite, evaluate expressions with grouping symbols using the order of operations, translate between expressions and written descriptions, and use equations to represent and solve multistep problems. The “Look Forward” section explains that later in the year, students will use the order of operations to evaluate expressions with fractions and decimals. In future grades, students will write and interpret variable equations representing complex situations that cannot be broken down into individual steps.
Evaluation for 4.2c
At the lesson level, the “Instructional Context” tab connects students’ prior knowledge to new mathematical learning. In unit 6, lesson 6.1 “Relate Decimals and Fractions,” the “Look Back” section explains that in grade 4 students learned about decimal numbers to the hundredths place by relating them to fractions with denominators of 10 or 100. This section activates students’ prior understanding of fraction-decimal relationships before extending decimal work in grade 5.
In unit 6 the “This Lesson” and “Look Forward” sections show how prior knowledge connects to current and future learning. In “This Lesson” students review the relationship between decimal numbers and fractions with denominators of 10 or 100 and use this relationship to write fractions as decimals and decimals as fractions. The “Look Forward” section explains that in the next lesson students will explore place value with decimal numbers to the thousandths place, and later in the unit they will add and subtract fractions and decimal numbers.
Evaluation for 4.3a
The unit 4 “Daily Planner” provides spaced retrieval opportunities by revisiting previously learned skills while students work on current fraction objectives. In lesson 4.1 students estimate sums and differences of fractions while completing spiral review with prime and composite numbers. In lesson 4.2 students add fractions with unlike denominators using models while completing spiral review with evaluating numerical expressions with parentheses and brackets. In lesson 4.4 students subtract fractions with unlike denominators using models while completing spiral review with equations for multistep word problems.
The lesson 7.7 independent practice also provides spaced retrieval opportunities. Students estimate products with decimals in numerical and real-world problems, such as estimating the cost of dog treats and the length of a song after a scale factor is applied. On the second page, students also solve a fraction problem involving time spent vacuuming cars, order decimals from least to greatest, find the volume of a rectangular prism, and solve a volume challenge. These review tasks require students to retrieve previously learned fraction, decimal comparison, and volume skills while working on decimal multiplication estimation.
Evaluation for 4.3b
The lesson 11.3 independent practice provides interleaved practice by mixing current data work with previously learned concepts. Students create and interpret dot plots using fractional measurements, such as pipe sizes, vending machine prices, and hamster weights. On the next page, students use models to divide unit fractions, subtract mixed numbers in a rope swing context, and draw a quadrilateral with exactly one pair of parallel sides. These tasks mix current data representation with prior fraction division, mixed-number subtraction, and geometry skills.
The lesson 12.2 independent practice also provides interleaved practice by combining current geometry work with skills from prior units. Students classify triangles by their angles and sides, classify triangular sails, and draw triangles in a Venn diagram. On the second page, students convert measurements in feet, yards, pounds, and ounces. Students then solve a multistep decimal measurement problem about stacked storage bins and solve a money word problem. This structure requires students to continue applying previously learned measurement, decimal, and problem-solving skills while working on new geometry 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 grade 5 fraction TEKS. In the unit 4 “Add and Subtract Fractions” test, students add and subtract fractions with unlike denominators, simplify answers, use a visual model to interpret the sum of 2/5 and 3/10, and add and subtract mixed numbers. These assessment tasks require students to use equivalent fractions, interpret models, apply fraction operations, and demonstrate procedural fluency with fractions and mixed numbers.
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 4 sequence continues to increase in complexity as students move from fractions to mixed numbers and multistep problems. Students use least common denominators to add and subtract fractions, then add and subtract mixed numbers without regrouping, add mixed numbers with regrouping, subtract mixed numbers with regrouping, and solve multistep word problems involving fractions and mixed numbers. This progression supports grade-level proficiency by moving students from single-step fraction operations to multistep problem solving with rational numbers.
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 6 “Instructional Context” also connects decimal concepts to future mathematical work. The “Look Forward” section explains that in the next few units students will multiply and divide decimal numbers. The section also explains that later in the year students will add and subtract decimal numbers to solve problems involving measurement and data. This explanation shows coherence among decimal place value, decimal operations, fraction-decimal relationships, measurement, and data across the grade 5 course.
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 2 “Instructional Context” tab also shows how current grade 5 learning prepares students for future mathematics. The “This Unit” section explains that students revisit factors and multiples, describe numbers as prime or composite, evaluate expressions with grouping symbols using the order of operations, translate between expressions and written descriptions, and use equations to represent and solve multistep problems. The “Look Forward” section explains that later in the year, students will use the order of operations to evaluate expressions with fractions and decimals. In future grades, students will write and interpret variable equations representing complex situations that cannot be broken down into individual steps.
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 6 the “This Lesson” and “Look Forward” sections show how prior knowledge connects to current and future learning. In “This Lesson” students review the relationship between decimal numbers and fractions with denominators of 10 or 100 and use this relationship to write fractions as decimals and decimals as fractions. The “Look Forward” section explains that in the next lesson students will explore place value with decimal numbers to the thousandths place, and later in the unit they will add and subtract fractions and decimal numbers.
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 7.7 independent practice also provides spaced retrieval opportunities. Students estimate products with decimals in numerical and real-world problems, such as estimating the cost of dog treats and the length of a song after a scale factor is applied. On the second page, students also solve a fraction problem involving time spent vacuuming cars, order decimals from least to greatest, find the volume of a rectangular prism, and solve a volume challenge. These review tasks require students to retrieve previously learned fraction, decimal comparison, and volume skills while working on decimal multiplication estimation.
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 12.2 independent practice also provides interleaved practice by combining current geometry work with skills from prior units. Students classify triangles by their angles and sides, classify triangular sails, and draw triangles in a Venn diagram. On the second page, students convert measurements in feet, yards, pounds, and ounces. Students then solve a multistep decimal measurement problem about stacked storage bins and solve a money word problem. This structure requires students to continue applying previously learned measurement, decimal, and problem-solving skills while working on new geometry 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 4, lesson 4.4 “Subtract Fractions with Models,” students interpret and analyze fraction strip representations before subtracting fractions with unlike denominators. The educator guidance directs students to use fraction strips to show 1/2 and 1/3, identify that the pieces are not the same size, rename the fractions using equivalent fractions with a common denominator, and connect the model to the subtraction expression. Students evaluate how the fraction strip model and the drawing both show the difference, supporting conceptual understanding of subtraction with unlike denominators.
In unit 5, lesson 5.7 “Use Models to Divide by Whole Numbers,” students interpret area models representing division of unit fractions by whole numbers. The educator guidance asks students to fold and shade paper to model a soccer field that is a half acre and then divide the shaded area into three equal parts. Students analyze the double-shaded section, connect it to the quotient, and explain how the model represents 1/2 ÷ 3. These tasks require students to interpret and analyze a visual representation before connecting it to the division equation.
Evaluation for 5.1b
In unit 5, lesson 5.7 “Use Models to Divide by Whole Numbers,” students create area models to represent division of unit fractions by whole numbers. Students fold paper to represent the whole, shade half of the paper to represent the soccer field, divide the shaded portion into three equal parts, and identify the portion that represents one practice area. The task requires students to create a model, partition the model accurately, and connect the shaded part to the quotient.
In unit 5, lesson 5.8 “Use Models to Divide by Unit Fractions,” students create models to represent division of whole numbers by unit fractions. The guidance instructs educators to provide each student or small group with three pieces of paper to represent three yards of fabric. Students fold each piece in half to model how many half-yard pieces they can make. Students use the model to see that there are six halves in three wholes and connect the model to the equation 3 ÷ 1/2 = 6.
Evaluation for 5.1c
In unit 7, lesson 7.6 “Understand Decimal Multiplication,” students apply conceptual understanding of grid models to new decimal multiplication contexts. Students use a hundredths grid to represent 0.8 acres, shade 0.3 of the shaded area, and determine that the double-shaded region represents 0.24 acres. The lesson connects the model to the expression 0.3 × 0.8 and then asks students to apply the same reasoning to additional decimal multiplication problems.
In unit 3, lesson 3.4 “Use Volume Formulas,” students apply their conceptual understanding of unit cubes and base layers to new volume problems. Students first build rectangular prisms with inch cubes, analyze the number of cubes in each layer, and connect the number of cubes in a layer to the area of the base. Students then use this understanding to develop and apply the formulas V = l × w × h and V = B × h to find volume and missing edge lengths.
Evaluation for 5.2a
In unit 1, lesson 1.1 “Estimate Sums and Differences,” students build fluency with estimation strategies for multi-digit numbers. The educator guidance asks students to estimate sums and differences using rounding, front-end estimation, compatible numbers, and compensation. Students compare the strategies, discuss which estimates are easier to calculate mentally, and consider which strategies are more accurate. These repeated strategy comparisons support flexible and efficient estimation fluency.
In unit 1, lesson 1.6 “Division Patterns,” students build fluency with division by using place value patterns to extend basic division facts. The lesson guides students to divide multiples of 10, 100, and 1,000 by one-digit numbers and by multiples of 10 or 100. Students connect related multiplication and division equations, describe patterns in dividends and quotients, and use known facts to efficiently divide larger numbers.
Evaluation for 5.2b
In unit 7, lesson 7.4 “Multiply by Whole Numbers: Partial Products,” students practice applying accurate and flexible procedures for decimal multiplication. The lesson begins by reviewing area models for whole-number multiplication, then extends the same representation to multiplying decimal numbers by two-digit whole numbers. Students break apart factors by place value, complete area models, find partial products, add the partial products, and estimate to check whether their answers are reasonable.
In unit 7, lesson 7.6 “Understand Decimal Multiplication,” students practice flexible procedures by connecting grid models, decimal notation, and whole-number products. Students first model decimal multiplication with hundredths grids, then relate the product of decimals to a product of whole numbers. This task gives students opportunities to move from visual models to more efficient symbolic procedures while maintaining accuracy and conceptual understanding.
Evaluation for 5.2c
In unit 7, lesson 7.1 “Multiplication Patterns with Decimals,” students evaluate procedures for multiplying decimals by powers of 10. The educator guidance prompts students to compare strategies such as using place value patterns, moving digits, and moving the decimal point. Students discuss how the strategies are related and why multiplying by powers of 10 changes the value of the number. This task helps students evaluate efficiency, flexibility, and accuracy in decimal multiplication procedures.
In unit 1, lesson 1.1 “Estimate Sums and Differences,” students evaluate estimation strategies for efficiency and accuracy. The educator guidance asks students to compare rounding, front-end estimation, compatible numbers, and compensation. Students discuss that front-end estimation may be quick but less accurate, while rounding to smaller places or using compatible numbers may produce estimates closer to the actual value. This task supports students in selecting procedures that are both efficient and reasonable.
Evaluation for 5.2d
In unit 3, lesson 3.4 “Use Volume Formulas,” educator guidance supports students in moving toward increasingly efficient approaches for finding volume. Students begin by building a rectangular prism with inch cubes and counting cubes in each layer. The educator then guides students to connect the number of cubes in each layer to the area of the base and to multiply the base area by the height. This progression helps students move from counting individual cubes to using the formulas V = l × w × h and V = B × h.
In unit 7, lesson 7.4 “Multiply by Whole Numbers: Partial Products,” educator guidance supports students in moving from area models to partial products for decimal multiplication. Students first review how area models represent multiplication. Students then break apart decimal and whole-number factors by place value, multiply to find each partial product, and add the partial products. The lesson also asks students to estimate to check reasonableness, supporting more efficient and accurate multiplication strategies.
Evaluation for 5.3a
The unit 3 “Instructional Context” tab explains how the materials develop conceptual understanding before procedural fluency in the volume unit. The “Look Back” section connects volume to students’ prior understanding of area—the amount of space a two-dimensional figure takes up—and to finding area by counting unit squares or multiplying rows and columns. The “This Unit” section explains that students extend this understanding to volume by counting unit cubes, using multiplication to count cubes efficiently, and developing the formulas V = l × w × h, V = B × h, and V = s × s × s.
Unit 3, lesson 3.4 “Use Volume Formulas,” explicitly balances conceptual and procedural work. Students first use inch cubes to build a rectangular prism and analyze how the number of cubes in each layer relates to the area of the base. The educator guidance then connects this concrete understanding to symbolic formulas for volume. Students use both V = l × w × h and V = B × h, showing how the conceptual model supports the procedural formulas.
Evaluation for 5.3b
In unit 3, lesson 3.4 “Use Volume Formulas,” students use concrete models, pictorial reasoning, and abstract formulas as required by the TEKS. Students use inch cubes to build and analyze rectangular prisms. Students connect the cube layers to the area of the base and then represent the relationship with the formulas V = l × w × h and V = B × h. This progression connects concrete unit cubes, visual structure, and symbolic equations.
In unit 4, lesson 4.4 “Subtract Fractions with Models,” students use fraction strips, drawings, and equations to subtract fractions with unlike denominators. Students model fractions with strips, rename fractions with equivalent fractions that share a denominator, draw lines to show the renamed parts, and connect the model to the symbolic subtraction expression. This lesson supports students in moving from concrete and pictorial representations to abstract fraction computation.
Evaluation for 5.3c
Unit 4, lesson 4.4 “Subtract Fractions with Models,” supports students in connecting concrete and representational models to abstract fraction subtraction. Students use fraction strips to show why 1/2 and 1/3 cannot be subtracted in that format because the pieces are different sizes. Students then rename the fractions using equivalent fractions with a common denominator, represent the change in the model, and connect the model to the subtraction equation. This lesson helps students explain the relationship between visual models and symbolic procedures.
Unit 3, lesson 3.4 “Use Volume Formulas,” supports students in connecting concrete models to abstract formulas. Students build rectangular prisms with inch cubes, identify the number of cubes in each layer, connect that number to the area of the base, and then use letters to represent the relationships in formulas. Students explain why multiplying the three edge lengths and multiplying the base area by the height are equivalent approaches for finding volume.
Evaluation for 5.4a
In unit 3, lesson 3.1 “Understand Volume,” students develop academic mathematical language using visuals, concrete models, and hands-on language development strategies. Students use grid paper to build a box, fill the box with cubes, arrange the cubes as a solid figure, and compare the volume of the container and the solid figure. Students also complete definitions for volume, use a unit cube model, and count unit cubes to find the volume of solid figures. These tasks support students in developing and using academic vocabulary such as volume, unit cube, cubic unit, container, solid figure, and space.
In unit 12, lesson 12.1 “Classify Polygons,” students develop academic mathematical language using visual shape models, sorting tasks, and written descriptions. Students match shapes to names such as triangle, hexagon, pentagon, and quadrilateral, and identify which shape is not a polygon. Students also sort shape cards in different ways and draw examples of regular and irregular polygons. Students also classify polygons by the number of sides and attributes such as congruent, parallel, and perpendicular sides, and acute and obtuse angles. These tasks support students in using precise geometric vocabulary while connecting visual representations to formal polygon language.
Evaluation for 5.4b
Unit 3, lesson 3.1 “Understand Volume,” scaffolds students’ development and use of academic mathematical vocabulary in context. Students complete statements defining the volume of a container and the volume of a solid figure. Students then use a unit cube labeled with one-unit edges to complete statements about edge length and the volume of a unit cube. Students apply this vocabulary as they count unit cubes, compare figures, and explain the volume of boxes of sugar cubes measured in cubic centimeters.
In unit 3, lesson 3.2 “Volume of Rectangular Prisms,” students continue using academic mathematical vocabulary in context as they work with rectangular prisms made of unit cubes. Students find the volume of prisms by counting cubes in one layer and multiplying by the number of layers. Students also solve real-world problems involving cube-shaped candy, robot boxes, crate height, layers, and volume. These tasks support students in using vocabulary such as rectangular prism, unit cube, volume, layer, base, and cubic units while connecting visual models to multiplication.
Evaluation for 5.4c
Unit 1, lesson 1.1 “Estimate Sums and Differences,” includes embedded support for students to apply mathematical language through vocabulary, syntax, and discourse. Students estimate the total number of flowers on a Battle of the Flowers Parade float using rounding, front-end estimation, and compatible numbers. In the “Think and Talk” task, students compare estimation strategies, discuss how they are similar and different, and determine which strategy gives the most accurate estimate. Students also analyze David and Emmy’s estimation conversation and explain how to make an estimate more accurate. These tasks support students in hearing, refining, and using academic language such as estimate, rounding, front-end estimation, compatible numbers, accurate, reasonable, sum, and difference.
In unit 2, lesson 2.2 “Divisibility Rules,” students apply mathematical language through investigation, discussion, and explanation of number patterns. Students use a hundred chart to find numbers with factors of two, five, and 10, describe patterns they notice, and discuss Kimi’s observation about numbers with a factor of three. The lesson also asks students to complete statements explaining the relationship between a factor and divisibility, such as “If one number is a factor of another, then the second number is divisible by the factor.” These tasks provide structured opportunities for students to use and refine vocabulary such as factor, multiple, divisible, divisibility, pattern, and factor pair during mathematical discourse.
Evaluation for 5.5a
Unit 1, lessons 1.1 and 1.2, appropriately integrate the TEKS process standards as students apply estimation, addition, and subtraction to real-world contexts. In lesson 1.1, students estimate sums and differences using a Battle of the Flowers Parade context, evaluate which estimate is most accurate, and explain how to improve an estimate. In lesson 1.2 students use a road trip map from Dallas to national parks to add and subtract mileage, estimate to check reasonableness, and solve real-world problems involving distances, stadium tickets, Texas land and water area, and app downloads. These tasks integrate problem solving, mathematical reasoning, representation, communication, and real-world application.
Unit 3, lesson 3.4 “Use Volume Formulas,” integrates the TEKS process standards as students connect models, formulas, and reasoning to solve volume problems. Students use unit cubes to build a prism, compare the number of cubes in each layer to the area of the base, and derive formulas for volume, including V = B × h and V = l × w × h. Students also compare Kira’s strategy of multiplying length, width, and height and decide whether the method always works. Students also use formulas to solve problems involving rectangular prisms, cubes, missing dimensions, planters, and a container of homemade ice cream. These tasks require students to analyze relationships, select strategies, communicate reasoning, and justify formula use.
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 program is designed with mathematical reasoning, communication, representations, problem solving, and discourse across the grade level. The document provides a course-level description of how students use process standards to acquire and demonstrate mathematical understanding.
The “Instructional Design” document provides course-level examples of how process standards connect to grade-level content and mathematical rigor. The document describes how students use varied approaches and representations to develop conceptual understanding, procedural fluency, and real-world application with fraction multiplication, including shape models, number lines, arrays, and efficient procedures. This guidance shows how mathematical reasoning, representation, communication, and problem solving are embedded throughout the course.
Evaluation for 5.5c
The unit 3 “Process Standards” tab provides a unit-level description of how the TEKS process standards are incorporated and connected throughout the volume unit. The materials explain that students use volume to solve problems arising in life, society, and the workplace, including business contexts involving packaging candy, shipping toys, and packing shoeboxes. The unit guidance also describes how students use models, diagrams, formulas, and precise language to organize and communicate their understanding of volume, base area, length, width, height, and rectangular prisms.
The unit 6 “Process Standards” tab provides a unit-level description of how the TEKS process standards are incorporated throughout the decimals unit. The materials explain that students represent decimals using place value blocks, grid models, number lines, place value charts, word form, expanded form, expanded notation, and standard form. The unit guidance also describes how students solve real-world decimal problems involving money, measurements, and addition and subtraction, while using representations, estimation, standard algorithms, and precise mathematical language to communicate and justify their reasoning.
Evaluation for 5.5d
The “Fifth Grade At-a-Glance” standards document 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 5.1.A is connected to lessons including 1.1–1.7, 1.9, 1.10, 2.6, 2.7, 3.2, 3.5, 4.1, 4.7, 4.8, 5.1–5.12, 6.4–6.8, 7.2, 7.5–7.7, 8.2, 8.5, 8.6, 9.1–9.6, 10.2–10.6, 11.1–11.7, and 13.1–13.4.
The “Fifth Grade At-a-Glance” standards document provides lesson-level alignment for additional process standards. A chart identifies lessons connected to standards for using a problem-solving model, selecting tools and techniques, communicating mathematical ideas with 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 5, lesson 5.7 “Use Models to Divide by Whole Numbers,” students interpret area models representing division of unit fractions by whole numbers. The educator guidance asks students to fold and shade paper to model a soccer field that is a half acre and then divide the shaded area into three equal parts. Students analyze the double-shaded section, connect it to the quotient, and explain how the model represents 1/2 ÷ 3. These tasks require students to interpret and analyze a visual representation before connecting it to the division equation.
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 5, lesson 5.8 “Use Models to Divide by Unit Fractions,” students create models to represent division of whole numbers by unit fractions. The guidance instructs educators to provide each student or small group with three pieces of paper to represent three yards of fabric. Students fold each piece in half to model how many half-yard pieces they can make. Students use the model to see that there are six halves in three wholes and connect the model to the equation 3 ÷ 1/2 = 6.
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 3, lesson 3.4 “Use Volume Formulas,” students apply their conceptual understanding of unit cubes and base layers to new volume problems. Students first build rectangular prisms with inch cubes, analyze the number of cubes in each layer, and connect the number of cubes in a layer to the area of the base. Students then use this understanding to develop and apply the formulas V = l × w × h and V = B × h to find volume and missing edge lengths.
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 1, lesson 1.6 “Division Patterns,” students build fluency with division by using place value patterns to extend basic division facts. The lesson guides students to divide multiples of 10, 100, and 1,000 by one-digit numbers and by multiples of 10 or 100. Students connect related multiplication and division equations, describe patterns in dividends and quotients, and use known facts to efficiently divide larger numbers.
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 7, lesson 7.6 “Understand Decimal Multiplication,” students practice flexible procedures by connecting grid models, decimal notation, and whole-number products. Students first model decimal multiplication with hundredths grids, then relate the product of decimals to a product of whole numbers. This task gives students opportunities to move from visual models to more efficient symbolic procedures while maintaining accuracy and conceptual understanding.
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 1, lesson 1.1 “Estimate Sums and Differences,” students evaluate estimation strategies for efficiency and accuracy. The educator guidance asks students to compare rounding, front-end estimation, compatible numbers, and compensation. Students discuss that front-end estimation may be quick but less accurate, while rounding to smaller places or using compatible numbers may produce estimates closer to the actual value. This task supports students in selecting procedures that are both efficient and reasonable.
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 7.4 “Multiply by Whole Numbers: Partial Products,” educator guidance supports students in moving from area models to partial products for decimal multiplication. Students first review how area models represent multiplication. Students then break apart decimal and whole-number factors by place value, multiply to find each partial product, and add the partial products. The lesson also asks students to estimate to check reasonableness, supporting more efficient and accurate multiplication strategies.
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 3, lesson 3.4 “Use Volume Formulas,” explicitly balances conceptual and procedural work. Students first use inch cubes to build a rectangular prism and analyze how the number of cubes in each layer relates to the area of the base. The educator guidance then connects this concrete understanding to symbolic formulas for volume. Students use both V = l × w × h and V = B × h, showing how the conceptual model supports the procedural formulas.
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 4, lesson 4.4 “Subtract Fractions with Models,” students use fraction strips, drawings, and equations to subtract fractions with unlike denominators. Students model fractions with strips, rename fractions with equivalent fractions that share a denominator, draw lines to show the renamed parts, and connect the model to the symbolic subtraction expression. This lesson supports students in moving from concrete and pictorial representations to abstract fraction computation.
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 3, lesson 3.4 “Use Volume Formulas,” supports students in connecting concrete models to abstract formulas. Students build rectangular prisms with inch cubes, identify the number of cubes in each layer, connect that number to the area of the base, and then use letters to represent the relationships in formulas. Students explain why multiplying the three edge lengths and multiplying the base area by the height are equivalent approaches for finding volume.
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 12, lesson 12.1 “Classify Polygons,” students develop academic mathematical language using visual shape models, sorting tasks, and written descriptions. Students match shapes to names such as triangle, hexagon, pentagon, and quadrilateral, and identify which shape is not a polygon. Students also sort shape cards in different ways and draw examples of regular and irregular polygons. Students also classify polygons by the number of sides and attributes such as congruent, parallel, and perpendicular sides, and acute and obtuse angles. These tasks support students in using precise geometric vocabulary while connecting visual representations to formal polygon language.
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 3, lesson 3.2 “Volume of Rectangular Prisms,” students continue using academic mathematical vocabulary in context as they work with rectangular prisms made of unit cubes. Students find the volume of prisms by counting cubes in one layer and multiplying by the number of layers. Students also solve real-world problems involving cube-shaped candy, robot boxes, crate height, layers, and volume. These tasks support students in using vocabulary such as rectangular prism, unit cube, volume, layer, base, and cubic units while connecting visual models to multiplication.
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 2, lesson 2.2 “Divisibility Rules,” students apply mathematical language through investigation, discussion, and explanation of number patterns. Students use a hundred chart to find numbers with factors of two, five, and 10, describe patterns they notice, and discuss Kimi’s observation about numbers with a factor of three. The lesson also asks students to complete statements explaining the relationship between a factor and divisibility, such as “If one number is a factor of another, then the second number is divisible by the factor.” These tasks provide structured opportunities for students to use and refine vocabulary such as factor, multiple, divisible, divisibility, pattern, and factor pair during mathematical discourse.
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 3, lesson 3.4 “Use Volume Formulas,” integrates the TEKS process standards as students connect models, formulas, and reasoning to solve volume problems. Students use unit cubes to build a prism, compare the number of cubes in each layer to the area of the base, and derive formulas for volume, including V = B × h and V = l × w × h. Students also compare Kira’s strategy of multiplying length, width, and height and decide whether the method always works. Students also use formulas to solve problems involving rectangular prisms, cubes, missing dimensions, planters, and a container of homemade ice cream. These tasks require students to analyze relationships, select strategies, communicate reasoning, and justify formula use.
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 process standards connect to grade-level content and mathematical rigor. The document describes how students use varied approaches and representations to develop conceptual understanding, procedural fluency, and real-world application with fraction multiplication, including shape models, number lines, arrays, and efficient procedures. This 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 6 “Process Standards” tab provides a unit-level description of how the TEKS process standards are incorporated throughout the decimals unit. The materials explain that students represent decimals using place value blocks, grid models, number lines, place value charts, word form, expanded form, expanded notation, and standard form. The unit guidance also describes how students solve real-world decimal problems involving money, measurements, and addition and subtraction, while using representations, estimation, standard algorithms, and precise mathematical language to communicate and justify their reasoning.
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
The “Fifth Grade At-a-Glance” standards document provides lesson-level alignment for additional process standards. A chart identifies lessons connected to standards for using a problem-solving model, selecting tools and techniques, communicating mathematical ideas with 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 2, lesson 2.7, question 4, students think mathematically, persevere through multistep problem solving, and make sense of mathematics as they analyze two word problems that use the same numbers but require different operations. Educator notes guide students to identify known information, determine what needs to be found, apply the order of operations, and explain how each equation represents the problem context. Students compare the problems, solve each situation, and justify their reasoning, supporting mathematical sense-making through analysis and explanation.
In unit 10, lesson 10.4, students make sense of mathematics as they graph polygons on the coordinate plane, classify the figures, and compare solution strategies. Students graph ordered pairs, analyze geometric relationships, justify the most effective strategy, and explain how changing the coordinates affects the figure. These opportunities encourage students to think mathematically through reasoning, problem solving, and mathematical communication.
Evaluation for 6.1b
In unit 5, lesson 5.5, questions 3 and 4, students understand, explain, and justify that mathematical ideas can be represented and solved in multiple ways. Educator notes guide students to draw two different models to represent two groups of three-fourths, or 2 x 3/4. Students compare the representations during the “Write and Talk” activity, explaining how both models represent the same product and justifying why the different representations produce equivalent solutions.
In unit 7, lesson 7.8, question 4, students represent decimal multiplication using both an area model and partial products. Educators guide students to compare the representations, explain how each partial product corresponds to a section of the area model, and justify why both methods produce the same solution. These opportunities support students in explaining and justifying multiple representations of the same mathematical concept.
Evaluation for 6.1c
In unit 1, lesson 1.5, students make sense of mathematics through opportunities to discuss, write about, and analyze multiplication strategies. The “Think and Talk” activity guides students to compare Julian’s multiplication algorithm with their own solution strategies. Students discuss similarities and differences between the methods before writing an explanation describing how partial products can be combined to solve a multiplication problem. These tasks engage students in discussing, writing about, and making sense of mathematical procedures.
The “Instructional Design” document explains that the program embeds “Compare and Talk” and “Think and Talk” routines throughout to support meaningful mathematical discourse. Educators facilitate mathematical discussions that encourage students to compare solution strategies, justify reasoning, and communicate mathematical ideas through speaking and writing. These routines provide consistent opportunities for students to do, discuss, and write about mathematics throughout the course.
Evaluation for 6.2a
In unit 1, lesson 1.7, educator notes support students to share and reflect on problem-solving approaches as they estimate quotients using compatible numbers rather than standard rounding. Educators prompt students to compare estimation strategies, explain what makes an estimate reasonable, and justify why one set of compatible numbers is more appropriate than another. Students evaluate multiple estimation methods, defend their reasoning, and reflect on the advantages of different strategies.
In unit 5, lesson 5.10, educator notes guide students to discuss Destiny’s strategy for multiplying fractions and whole numbers. Educators prompt students to summarize Destiny’s method, explain why it works, compare it with drawing a model, and justify whether the strategy can be applied in other situations. Students explain, compare, and defend different solution methods while reflecting on the efficiency of each approach.
Evaluation for 6.2b
Unit 2, lesson 2.4, includes prompts and guidance to support educators in providing explanatory feedback based on anticipated misconceptions. Educator notes anticipate that students may incorrectly evaluate expressions from left to right without applying the order of operations. The lesson guides educators to compare different student solutions and explain why multiplication and division must be completed before addition and subtraction when appropriate. The educator then revisits the discussion after introducing the order of operations. Students analyze incorrect reasoning, explain why one solution is correct, and revise their thinking based on mathematical rules.
Unit 5, lesson 5.11, includes educator notes and a “Tip for Support” that address anticipated misconceptions in fraction division word problems. The guidance anticipates that students may confuse 12 ÷ 1/2 with 1/2 ÷ 12 or may incorrectly determine whether to multiply or divide. The lesson guides educators to ask targeted questions that help students identify the quantities in the problem, explain the meaning of each operation, and use number sense to evaluate whether a solution is reasonable. Students explain their reasoning, compare operations, and revise misconceptions through educator-guided questioning.
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 10.4, students make sense of mathematics as they graph polygons on the coordinate plane, classify the figures, and compare solution strategies. Students graph ordered pairs, analyze geometric relationships, justify the most effective strategy, and explain how changing the coordinates affects the figure. These opportunities encourage students to think mathematically through reasoning, problem solving, and mathematical communication.
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 7, lesson 7.8, question 4, students represent decimal multiplication using both an area model and partial products. Educators guide students to compare the representations, explain how each partial product corresponds to a section of the area model, and justify why both methods produce the same solution. These opportunities support students in explaining and justifying multiple representations of the same mathematical concept.
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 the program embeds “Compare and Talk” and “Think and Talk” routines throughout to support meaningful mathematical discourse. Educators facilitate mathematical discussions that encourage students to compare solution strategies, justify reasoning, and communicate mathematical ideas through speaking and writing. These routines provide consistent opportunities for students to do, discuss, and write about mathematics throughout the course.
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 5, lesson 5.10, educator notes guide students to discuss Destiny’s strategy for multiplying fractions and whole numbers. Educators prompt students to summarize Destiny’s method, explain why it works, compare it with drawing a model, and justify whether the strategy can be applied in other situations. Students explain, compare, and defend different solution methods while reflecting on the efficiency of each approach.
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 5, lesson 5.11, includes educator notes and a “Tip for Support” that address anticipated misconceptions in fraction division word problems. The guidance anticipates that students may confuse 12 ÷ 1/2 with 1/2 ÷ 12 or may incorrectly determine whether to multiply or divide. The lesson guides educators to ask targeted questions that help students identify the quantities in the problem, explain the meaning of each operation, and use number sense to evaluate whether a solution is reasonable. Students explain their reasoning, compare operations, and revise misconceptions through educator-guided questioning.