Program Information
- ISBN
- 9781483880044
- 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 3 Math
Math (English) Grade 3
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 3 | 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 3 Texas Essential Knowledge and Skills (TEKS), English Language Proficiency Standards (ELPS), and concepts taught throughout the course. For example, “Third Grade At-a-Glance: Planning and Materials” provides an overview of each unit and the concepts taught, including the aligned grade 3 TEKS and ELPS.
Each unit provides a “Daily Planner” that outlines the grade 3 TEKS, ELPS, and concepts taught throughout the unit. For example, in unit 5 students divide fluently with divisors and quotients up to 10. Students also use divisibility rules to identify even and odd numbers and solve word problems involving division situations. These concepts align with grade 3 standards 3.4F, 3.4I, 3.4J, 3.4K, 3.5B, and 3.5D.
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 suggested pacing for varying numbers of instructional days. Each calendar assigns instructional activities to specific days so educators can adjust implementation to the length of the school year.
“Third Grade At-a-Glance: Planning and Materials” includes a “Unit and Lesson Outline” that sequences units and lessons and identifies the suggested number of instructional days. Educators can compare the time allotted to a unit with the day-by-day calendar to plan instruction.
Evaluation for 1.1c
The materials provide a rationale for the unit order and explain how concepts connect throughout the course. In “Third Grade At-a-Glance: Planning and Materials,” the “Unit-by-Unit Overview” identifies the mathematical concepts each unit addresses and shows how the course is organized across the instructional year. For example, in unit 9, students learn that perimeter is the distance around a shape. Students begin finding perimeter by counting units in tiled figures and compare this work with their first explorations of area in unit 3.
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 8 “Look Back” section explains that students learned to multiply and divide fluently within 100 and solved one-step word problems involving both operations. In the previous unit, students also solved one- and two-step word problems involving addition and subtraction.
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. In Discover Takeoff by IXL: Comprehensive Lesson Plans, the materials explain 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
Through an administrator account, instructional leaders have access to the classroom walkthrough checklist and guiding questions for collaborative conversations. The classroom walkthrough checklist supports leaders in observing implementation of the materials, including whether the educator follows the sequence and structure of the lesson, uses the lesson components and materials, and checks for student understanding throughout the lesson.
Questions for collaborative conversations provide guidance for educator planning and reflection. The questions provide 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 3 concepts. For example, in the unit 1 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 that educators can introduce before instruction. For example, the unit 9 overview provides a list of vocabulary connected to the unit concepts and guidance that educators can use to prepare students for the mathematical language they will encounter, such as area, centimeter, compound figure, foot, inch, length, meter, perimeter, width, and yard.
Evaluation for 1.2b
The materials for each unit contain supports for families in both English and Spanish. For example, the English and Spanish glossaries provide academic vocabulary, explanations, and learning supports that families can use to reinforce unit concepts.
The English and Spanish “Welcome Letters” provide families with information about the program and guidance for supporting student progress. For example, the letters explain how families can access student learning information and reinforce the concepts students practice throughout the course.
Evaluation for 1.3a
Lesson plans include a lesson overview, lesson objectives, standards correlations, instructional questions, tasks, materials, student practice, and assessments. For example, in unit 6, lesson 3, the lesson structure gives educators the information needed to introduce the concept, guide students through practice, and check whether students understand the lesson objective.
Lesson plans provide educator-facing questions and student tasks that support content mastery. Students complete guided practice and independent practice aligned with the lesson objective, while educators use embedded questions and practice responses to monitor understanding. These components help educators determine whether students are ready for independent application or need additional support.
Lesson plans include supports for content and language development. “Additional Supports” provide strategies that educators can use to support emergent bilingual (EB) students and students who need scaffolding. These supports help educators address vocabulary, academic language, and access to grade-level mathematics during instruction.
Evaluation for 1.3b
The unit 9 “Daily Planner” identifies educator and student materials needed for the perimeter unit. For example, lesson 9.1 “Understand Perimeter,” identifies student workbook resources, independent practice resources, and dice. The lesson also identifies online readiness skills, practice skills, spiral review, and a game. This guidance helps educators prepare student-facing materials, physical materials, digital practice, and review activities before instruction begins.
The unit 2 “Daily Planner” provides additional examples of educator and student materials. In the multiplication fluency unit, the planner identifies student workbook resources, independent practice resources, colored pencils, paper clips, pencils, counters, online readiness skills, practice skills, support skills, spiral review, games, quizzes, tests, and “Personalization Day.” These materials support instruction, guided practice, independent practice, fluency development, and extended practice across the unit.
The Discover Takeoff by IXL: Comprehensive Lesson Plans guide provides suggested timing for each lesson. Lessons begin with a five-minute warm-up, continue with 15–20 minutes of instruction, move into 10–15 minutes of guided practice, and end with 15–20 minutes of independent practice. This timing guidance helps educators plan the daily lesson and understand how instructional time is divided across each component.
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 6 provides lesson-level guidance for extension and enrichment. In lesson 6.2 students study place value relationships by comparing places and periods in a place value chart. The “Idea for Extension” directs educators to ask whether students know what place or period is to the left of the hundred thousands place and then guides educators to highlight that the next period is the millions period. This extension asks students to extend the place value pattern beyond the lesson example by identifying the one millions, ten millions, and hundred millions places.
The lessons also provide guidance for using lesson materials during additional practice. In unit 6, lesson 6.2, educators provide each student or small group with a “Place Value Mat: Values of Digits.” Students place value disks on the mats to model numbers, record the number of disks in each place, and compare the values of digits. This activity gives students hands-on extended practice with the lesson concept and helps them apply place value reasoning beyond the initial instruction.
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
Each unit provides a “Daily Planner” that outlines the grade 3 TEKS, ELPS, and concepts taught throughout the unit. For example, in unit 5 students divide fluently with divisors and quotients up to 10. Students also use divisibility rules to identify even and odd numbers and solve word problems involving division situations. These concepts align with grade 3 standards 3.4F, 3.4I, 3.4J, 3.4K, 3.5B, and 3.5D.
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
“Third 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 8 “Look Back” section explains that students learned to multiply and divide fluently within 100 and solved one-step word problems involving both operations. In the previous unit, students also solved one- and two-step word problems involving addition and subtraction.
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. In Discover Takeoff by IXL: Comprehensive Lesson Plans, the materials explain 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 questions provide 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 that educators can introduce before instruction. For example, the unit 9 overview provides a list of vocabulary connected to the unit concepts and guidance that educators can use to prepare students for the mathematical language they will encounter, such as area, centimeter, compound figure, foot, inch, length, meter, perimeter, width, and yard.
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 guidance for supporting student progress. For example, the letters explain how families can access student learning information and reinforce the concepts students practice throughout the course.
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 plans provide educator-facing questions and student tasks that support content mastery. Students complete guided practice and independent practice aligned with the lesson objective, while educators use embedded questions and practice responses to monitor understanding. These components help educators determine whether students are ready for independent application or need additional support.
Lesson plans include supports for content and language development. “Additional Supports” provide strategies that educators can use to support emergent bilingual (EB) students and students who need scaffolding. These supports help educators address vocabulary, academic language, and access to grade-level mathematics during instruction.
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 2 “Daily Planner” provides additional examples of educator and student materials. In the multiplication fluency unit, the planner identifies student workbook resources, independent practice resources, colored pencils, paper clips, pencils, counters, online readiness skills, practice skills, support skills, spiral review, games, quizzes, tests, and “Personalization Day.” These materials support instruction, guided practice, independent practice, fluency development, and extended practice across the unit.
The Discover Takeoff by IXL: Comprehensive Lesson Plans guide provides suggested timing for each lesson. Lessons begin with a five-minute warm-up, continue with 15–20 minutes of instruction, move into 10–15 minutes of guided practice, and end with 15–20 minutes of independent practice. This timing guidance helps educators plan the daily lesson and understand how instructional time is divided across each component.
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 6 provides lesson-level guidance for extension and enrichment. In lesson 6.2 students study place value relationships by comparing places and periods in a place value chart. The “Idea for Extension” directs educators to ask whether students know what place or period is to the left of the hundred thousands place and then guides educators to highlight that the next period is the millions period. This extension asks students to extend the place value pattern beyond the lesson example by identifying the one millions, ten millions, and hundred millions places.
The lessons also provide guidance for using lesson materials during additional practice. In unit 6, lesson 6.2, educators provide each student or small group with a “Place Value Mat: Values of Digits.” Students place value disks on the mats to model numbers, record the number of disks in each place, and compare the values of digits. This activity gives students hands-on extended practice with the lesson concept and helps them apply place value reasoning beyond the initial instruction.
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 3 Takeoff by IXL Assessment Overview identifies diagnostic, formative, and summative assessments throughout the course. The overview describes 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 3 objectives.
Lessons include formative assessment opportunities during instruction, guided practice, and independent practice. Readiness skills, warm-ups, guided practice questions, independent practice items, and skill checks allow educators to monitor student understanding while instruction is happening. These tasks vary in format and require students to demonstrate understanding through selected responses, open responses, visual models, and skill-based practice.
End-of-unit tests provide summative assessment opportunities aligned to unit objectives. For example, the unit 1 test includes a variety of question types, such as drag-and-drop, inline-choice, multiple-choice, and fill-in-the-blank items. These tasks allow students to demonstrate mastery of the concepts and skills taught throughout the unit through more than one type of assessment item.
Evaluation for 2.1b
The Takeoff by IXL Assessment Overview defines diagnostic, formative, and summative assessments and explains the intended purpose of each type. Diagnostic assessments identify student readiness and learning gaps. Formative assessments monitor learning during instruction. Summative assessments evaluate student mastery after instruction.
The Insightful Assessments guide explains how educators use unit assessment data after students complete quizzes or tests. The guide describes how educators review assessment data and use the “Student Score Chart” to group students by performance, identify learning needs, and plan next instructional steps. This guidance gives educators a clear purpose for using unit assessment results beyond assigning a score.
The “Assessments on IXL” video provides additional guidance on how assessment types function within the program. The video explains the diagnostic assessment and describes options for formative and summative assessments, including educator-made quizzes. Educators use this guidance to select an assessment based on whether they need to identify readiness, monitor progress, or evaluate mastery.
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 scripts help educators administer the diagnostic assessment accurately across classrooms.
The Insightful Assessments guide provides step-by-step guidance for administering unit-level assessments. The guide explains 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 administer quizzes and unit tests consistently.
The assessment guidance also supports educators after administration. The Insightful Assessments guide explains how educators review assessment items, connect results to objectives, and interpret student performance after students complete an assessment. Educators use this guidance to determine which objectives need reteaching, additional practice, or enrichment.
Evaluation for 2.1d
The “IXL LevelUp Diagnostic” connects diagnostic results to standards and course expectations. The diagnostic identifies which grade 3 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 lesson objectives within each lesson. Lesson plan pages in the unit 12 outline identify the TEKS and lesson objectives. Warm-ups, guided practice, independent practice, and skill checks provide 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. Unit tests identify the TEKS and objective for each assessment question through the “Objectives” tab. Educators use this alignment to verify that test questions measure the standards and outcomes 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 items. These item types allow students to show understanding through selection, written response, visual interpretation, and application of a mathematical process.
The unit 14 test on data requires students to demonstrate understanding across multiple levels of complexity. Students create a graph, analyze a graph, answer multiple-selection questions, and explain their thinking. These tasks require students to apply procedural skill, conceptual understanding, and mathematical reasoning aligned to grade 3 data standards.
Lesson-level formative assessments also vary in complexity. Lessons include readiness skills, warm-ups, guided practice, independent practice, and open-response tasks aligned to the TEKS and lesson objectives. Educators use the “LevelUp Diagnostic Standards Performance Report” with these lesson and unit assessments 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 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 3 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 after students complete a quiz or unit test. This information allows educators to identify which concepts students understood, which concepts were challenging, and which students need additional support.
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. Educators use the diagnostic action plan with quiz and unit assessment reports to identify readiness, learning gaps, and next instructional steps.
Evaluation for 2.2b
Each unit includes a “Personalization Day” that uses assessment data to recommend instructional next steps. The “Personalization Day” breaks down objectives, recommends student groupings based on quiz or unit test performance, identifies what the whole class needs to practice through “Group Jam,” and includes extension opportunities for students who demonstrate mastery. This helps educators respond directly to trends in 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. Educators use these recommendations to address individual learning gaps, build on existing knowledge, and connect diagnostic data to targeted instructional tasks.
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 3 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. Readiness skills, warm-ups, guided practice questions, independent practice items, and skill checks allow educators to monitor student understanding while instruction is happening. These tasks vary in format and require students to demonstrate understanding through selected responses, open responses, visual models, and skill-based practice.
End-of-unit tests provide summative assessment opportunities aligned to unit objectives. For example, the unit 1 test includes a variety of question types, such as drag-and-drop, inline-choice, multiple-choice, and fill-in-the-blank items. These tasks allow students to demonstrate mastery of the concepts and skills taught throughout the unit through more than one type of assessment item.
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 data after students complete quizzes or tests. The guide describes how educators review assessment data and use the “Student Score Chart” to group students by performance, identify learning needs, and plan next instructional steps. This guidance gives educators a clear purpose for using unit assessment results beyond assigning a score.
The “Assessments on IXL” video provides additional guidance on how assessment types function within the program. The video explains the diagnostic assessment and describes options for formative and summative assessments, including educator-made quizzes. Educators use this guidance to select an assessment based on whether they need to identify readiness, monitor progress, or evaluate mastery.
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 provides step-by-step guidance for administering unit-level assessments. The guide explains 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 administer quizzes and unit tests consistently.
The assessment guidance also supports educators after administration. The Insightful Assessments guide explains how educators review assessment items, connect results to objectives, and interpret student performance after students complete an assessment. Educators use this guidance to determine which objectives need reteaching, additional practice, or enrichment.
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 lesson objectives within each lesson. Lesson plan pages in the unit 12 outline identify the TEKS and lesson objectives. Warm-ups, guided practice, independent practice, and skill checks provide 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. Unit tests identify the TEKS and objective for each assessment question through the “Objectives” tab. Educators use this alignment to verify that test questions measure the standards and outcomes 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
The unit 14 test on data requires students to demonstrate understanding across multiple levels of complexity. Students create a graph, analyze a graph, answer multiple-selection questions, and explain their thinking. These tasks require students to apply procedural skill, conceptual understanding, and mathematical reasoning aligned to grade 3 data standards.
Lesson-level formative assessments also vary in complexity. Lessons include readiness skills, warm-ups, guided practice, independent practice, and open-response tasks aligned to the TEKS and lesson objectives. Educators use the “LevelUp Diagnostic Standards Performance Report” with these lesson and unit assessments 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 after students complete a quiz or unit test. This information allows educators to identify which concepts students understood, which concepts were challenging, and which students need additional support.
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. Educators use the diagnostic action plan with quiz and unit assessment reports to identify readiness, learning gaps, and next instructional steps.
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. Educators use these recommendations to address individual learning gaps, build on existing knowledge, and connect diagnostic data to targeted instructional tasks.
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
Each lesson includes an “Additional Supports” tab that provides “Readiness Skills,” “Tips for Support,” “Support Skills,” and “Language Supports.” These supports help educators identify prerequisite skills, provide just-in-time scaffolds, and adjust instruction for students who need additional support before or during grade-level instruction.
The “Readiness Skills” and “Support Skills” provide targeted activities that help students access the lesson content. For example, when students have not yet demonstrated proficiency with a skill needed for the current lesson, educators can use the suggested readiness or support skill to review prerequisite understanding before students continue with the lesson task. This guidance gives educators a clear way to provide scaffolded instruction while keeping students connected to the grade-level learning objective.
The materials also include educator-facing tools for monitoring progress and growth. For example, in the “Analytics” tab, the “Progress and Growth” report tracks skill progress and improvement over time. The “IXL Student Quick View” allows educators to review recent student practice and identify students who may need additional attention.
Evaluation for 3.1b
Each unit includes academic vocabulary in the “Additional resources” section. Educators can use this vocabulary list before instruction to introduce key terms that students will encounter in the unit and prepare students for the mathematical language used in lessons, activities, and assessments.
The student glossaries provide additional vocabulary support in both English and Spanish. Each glossary entry includes the academic term, a definition, and a student-friendly image. These glossary supports help students understand unfamiliar vocabulary and provide educators with a resource for pre-teaching or reinforcing mathematical language throughout the unit.
The lesson guidance also embeds supports for vocabulary development and comprehension of the lesson content. For example, the “Additional Supports” tab includes “Language Supports” aligned to the ELPS, which provide teaching strategies for clarifying academic language, using visuals and models, supporting student discussion, and helping students access unfamiliar vocabulary during mathematics instruction.
Evaluation for 3.1c
Lessons include “Extension Ideas” with follow-up questions and enrichment activities for students who are ready to deepen or extend their learning. These supports help educators move proficient students beyond basic skill practice and provide opportunities for continued mathematical thinking.
The “Additional Supports” tab provides guidance that educators can use to differentiate instruction for students who have already demonstrated understanding. “Extension Activities” give educators specific ways to extend the lesson objective, ask additional questions, or provide more challenging applications of the grade-level content. These activities support students who have met lesson expectations by encouraging them to apply skills in new or more complex ways.
After each unit, the materials include a “Personalization Day” that provides targeted support based on each student’s assessment data and proficiency level. For example, students who need additional practice receive targeted skill assignments, while students who demonstrate proficiency receive enrichment or extension opportunities. This structure allows educators to respond to student performance after quizzes and tests by assigning tasks that match each student’s level of mastery, including challenge activities for students who are ready to extend their learning.
Evaluation for 3.2a
Lessons use a gradual-release structure that supports educator modeling before students work independently. During instruction, educator-facing notes and scripts guide educators in introducing the concept, explaining the mathematical thinking, and modeling the strategy students will use. The lesson then moves into guided practice and independent practice so students apply the concept with support and then on their own.
The lesson guidance includes visuals, questions, and step-by-step prompts that help educators explain concepts. For example, lesson plan pages in the unit 12 outline identify the lesson objectives and provide educator notes that support instruction, guided practice, and independent practice. Educators use these notes to model the concept, ask questions, and connect student responses to the lesson objective.
Guided practice continues to support educator modeling after the initial instruction. Educators use embedded questions and notes to clarify misconceptions, connect student thinking to the modeled examples, and support students as they solve practice problems. This guidance helps educators move students from direct instruction to shared practice and then to independent application.
Evaluation for 3.2b
Educator notes provide guidance for lesson delivery through a variety of instructional approaches. The notes include prompts for explaining concepts, asking questions, modeling strategies, and facilitating student discussion. These supports help educators use direct instruction, questioning, discourse, guided practice, and independent work within the lesson sequence.
Lessons include visual, hands-on, collaborative, digital, and paper-and-pencil practice opportunities. For example, students may use models during instruction, discuss strategies during guided practice, complete game-based practice, and then apply the concept independently. These approaches help students build understanding through concrete representations, conversation, and independent application.
Educator prompts support mathematical discourse and real-world connections. Students explain their thinking, discuss strategies with classmates, and apply lesson concepts to problem-solving situations. This guidance helps educators facilitate student reasoning and communication rather than relying only on direct explanation.
Evaluation for 3.2c
Lessons include whole-group instruction, guided practice, collaborative practice, and independent practice. The lesson cycle gives educators a clear structure for moving students from educator modeling to student application. Students learn concepts first through educator explanation, then practice with support before completing tasks independently.
Guided practice gives educators a structure for monitoring student understanding during the lesson. Educator notes include questions and prompts that educators use as students work through practice problems. These supports help educators check for understanding, provide feedback, and address misconceptions before students move into independent practice.
Collaborative and independent practice opportunities help students apply a lesson concept in multiple ways. For example, “Game Time” gives students opportunities to practice with classmates, while independent practice allows students to demonstrate understanding on their own. Educators use these structures for whole-group, small-group, partner, or individual practice based on student needs.
Evaluation for 3.3a
Lessons include language support guidance in the “Additional Supports” section. This guidance identifies supports for students at the beginning, intermediate, advanced, and advanced high levels so educators can adjust instruction based on language proficiency. These accommodations help students participate in grade-level mathematics while building academic language.
Linguistic supports help students use increasingly more academic language during instruction and practice. For example, the “Additional Supports” section provides guidance for adapting language expectations, supporting student responses, and helping students participate in lesson tasks using academic vocabulary. Students move from basic language use toward more precise oral and written explanations.
Evaluation for 3.3b
The “Instructional Design: Empowering Language Learners in Math” document provides implementation guidance for supporting EB students in mathematics. The document explains how educators support language development through vocabulary, discourse, and modeling strategies. This guidance helps educators use the materials in bilingual and ESL settings while keeping students engaged with grade-level mathematics.
Lessons embed language supports that educators can use during instruction and practice. For example, lesson guidance includes strategies for building vocabulary, using visual models, supporting oral language production, and encouraging student discussion. These supports help students develop academic language while learning the mathematics content.
Educators can apply language supports during whole-group instruction, guided practice, partner discussion, and independent practice. This structure helps educators support EB students throughout the lesson. Students use academic vocabulary and mathematical language as they explain thinking, respond to questions, and complete practice tasks.
Evaluation for 3.3c
Units include vocabulary support in the “Additional Resources” section, and student glossaries provide academic terms, definitions, and visuals in both English and Spanish. Educators use these resources to preview vocabulary, connect terms to prior knowledge, and support cross-linguistic connections between English, Spanish, and students’ home languages.
Lesson-level language supports provide guidance for increasing comprehension during mathematics instruction. The “Additional Supports” section includes strategies such as visuals, models, gestures, sentence frames, repeated exposure to key terms, and clarification of unfamiliar words or words with multiple meanings. These supports help students access problem situations, directions, and mathematical vocabulary.
Lessons support oral and written discourse through educator questions, partner discussion, and student explanations. “Think and Talk” activities prompt students to use academic vocabulary and explain mathematical ideas with a partner or group. Written-response tasks and guided practice give students additional opportunities to communicate mathematical understanding.
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 “Readiness Skills” and “Support Skills” provide targeted activities that help students access the lesson content. For example, when students have not yet demonstrated proficiency with a skill needed for the current lesson, educators can use the suggested readiness or support skill to review prerequisite understanding before students continue with the lesson task. This guidance gives educators a clear way to provide scaffolded instruction while keeping students connected to the grade-level learning objective.
The materials also include educator-facing tools for monitoring progress and growth. For example, in the “Analytics” tab, the “Progress and Growth” report tracks skill progress and improvement over time. The “IXL Student Quick View” allows educators to review recent student practice and identify students who may need additional attention.
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 student glossaries provide additional vocabulary support in both English and Spanish. Each glossary entry includes the academic term, a definition, and a student-friendly image. These glossary supports help students understand unfamiliar vocabulary and provide educators with a resource for pre-teaching or reinforcing mathematical language throughout the unit.
The lesson guidance also embeds supports for vocabulary development and comprehension of the lesson content. For example, the “Additional Supports” tab includes “Language Supports” aligned to the ELPS, which provide teaching strategies for clarifying academic language, using visuals and models, supporting student discussion, and helping students access unfamiliar vocabulary during mathematics instruction.
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 “Additional Supports” tab provides guidance that educators can use to differentiate instruction for students who have already demonstrated understanding. “Extension Activities” give educators specific ways to extend the lesson objective, ask additional questions, or provide more challenging applications of the grade-level content. These activities support students who have met lesson expectations by encouraging them to apply skills in new or more complex ways.
After each unit, the materials include a “Personalization Day” that provides targeted support based on each student’s assessment data and proficiency level. For example, students who need additional practice receive targeted skill assignments, while students who demonstrate proficiency receive enrichment or extension opportunities. This structure allows educators to respond to student performance after quizzes and tests by assigning tasks that match each student’s level of mastery, including challenge activities for students who are ready to extend their learning.
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
The lesson guidance includes visuals, questions, and step-by-step prompts that help educators explain concepts. For example, lesson plan pages in the unit 12 outline identify the lesson objectives and provide educator notes that support instruction, guided practice, and independent practice. Educators use these notes to model the concept, ask questions, and connect student responses to the lesson objective.
Guided practice continues to support educator modeling after the initial instruction. Educators use embedded questions and notes to clarify misconceptions, connect student thinking to the modeled examples, and support students as they solve practice problems. This guidance helps educators move students from direct instruction to shared practice and then to independent application.
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
Lessons include visual, hands-on, collaborative, digital, and paper-and-pencil practice opportunities. For example, students may use models during instruction, discuss strategies during guided practice, complete game-based practice, and then apply the concept independently. These approaches help students build understanding through concrete representations, conversation, and independent application.
Educator prompts support mathematical discourse and real-world connections. Students explain their thinking, discuss strategies with classmates, and apply lesson concepts to problem-solving situations. This guidance helps educators facilitate student reasoning and communication rather than relying only on direct explanation.
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
Guided practice gives educators a structure for monitoring student understanding during the lesson. Educator notes include questions and prompts that educators use as students work through practice problems. These supports help educators check for understanding, provide feedback, and address misconceptions before students move into independent practice.
Collaborative and independent practice opportunities help students apply a lesson concept in multiple ways. For example, “Game Time” gives students opportunities to practice with classmates, while independent practice allows students to demonstrate understanding on their own. Educators use these structures for whole-group, small-group, partner, or individual practice based on student needs.
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
Linguistic supports help students use increasingly more academic language during instruction and practice. For example, the “Additional Supports” section provides guidance for adapting language expectations, supporting student responses, and helping students participate in lesson tasks using academic vocabulary. Students move from basic language use toward more precise oral and written explanations.
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
Lessons embed language supports that educators can use during instruction and practice. For example, lesson guidance includes strategies for building vocabulary, using visual models, supporting oral language production, and encouraging student discussion. These supports help students develop academic language while learning the mathematics content.
Educators can apply language supports during whole-group instruction, guided practice, partner discussion, and independent practice. This structure helps educators support EB students throughout the lesson. Students use academic vocabulary and mathematical language as they explain thinking, respond to questions, and complete practice 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
Lesson-level language supports provide guidance for increasing comprehension during mathematics instruction. The “Additional Supports” section includes strategies such as visuals, models, gestures, sentence frames, repeated exposure to key terms, and clarification of unfamiliar words or words with multiple meanings. These supports help students access problem situations, directions, and mathematical vocabulary.
Lessons support oral and written discourse through educator questions, partner discussion, and student explanations. “Think and Talk” activities prompt students to use academic vocabulary and explain mathematical ideas with a partner or group. Written-response tasks and guided practice give students additional opportunities to communicate mathematical understanding.
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 unit 13, lesson 13.1, “Understand Equivalent Fractions,” students demonstrate depth of understanding by using models to determine whether two fractions are equivalent. Students partition and shade models to show fractions such as 1/4, 5/8, 2/4, and 1/2, compare the sizes of shaded parts, and explain that fractions are equivalent when they represent the same portion of a same-sized whole. The lesson also asks students to reason about why 1/8 of two different-sized pizzas may not represent the same amount, which requires them to connect fraction notation, models, same-sized wholes, and conceptual understanding of equivalence.
Instructional assessments also require students to demonstrate understanding aligned to the grade 3 TEKS. In the unit 9 “Perimeter” test, students find the perimeter of figures on grids, find the perimeter of rectangles and polygons with labeled side lengths, distinguish between area and perimeter in real-world contexts, and solve problems involving ribbon, paper, and rectangular figures. These assessment tasks require students to apply perimeter and area concepts in visual, numerical, and real-world situations rather than only recall a formula.
Evaluation for 4.1b
The unit 9 review and test show questions and tasks increasing in rigor and complexity across the perimeter unit. Students begin by finding the perimeter of shaded figures on grids and polygons with given side lengths, then find unknown side lengths when the perimeter is provided. Students also solve real-world problems involving rectangular property lines, tape around a stage, fabric, and area-versus-perimeter decisions. This progression moves students from concrete grid models to more complex problem-solving situations involving unknown measurements and real-world contexts.
The unit 13 “Daily Planner” also shows tasks increasing in rigor across the fraction unit. Students begin by understanding equivalent fractions with models, then find equivalent fractions using models and fraction strips, and later represent equivalent fractions on number lines. Students then compare fractions with the same denominator, compare fractions with the same numerator, and finally compare fractions using either the same numerator or the same denominator. This sequence moves students from visual models to number lines, comparison reasoning, and justification.
Evaluation for 4.2a
The “Instructional Context” tab in the unit 2 outline explicitly connects mathematical patterns, big ideas, and relationships across units. In unit 2 “Multiplication Fluency,” the “Look Back” section explains that students previously solved multiplication problems using equal groups, arrays, number lines, and strip diagrams. The “This Unit” section explains that students multiply fluently with factors up to 10, use skip counting, apply the distributive property, and use the commutative and associative properties. The materials connect earlier multiplication representations to fluency, strategy selection, and properties of multiplication.
The unit 2 “Instructional Context” tab also connects multiplication fluency to later mathematical ideas. The “Look Forward” section explains that students will connect multiplication to area in the next unit by relating the area of a rectangle made of unit squares to finding a product using an array. The section also explains that students will later use place value to multiply one-digit numbers by multiples of 10, develop division fluency, and solve two-step word problems involving all four operations. This explanation shows coherence among multiplication models, area, place value, division, and problem solving.
Evaluation for 4.2b
The “Instructional Context” tab connects grade 3 content to previous and future grade-level learning. In unit 12 “Understand Fractions,” the “Look Back” section explains that in grade 2 students made and identified halves, fourths, and eighths and described equal shares of a whole. The “This Unit” section explains that students extend this understanding to thirds and sixths, use fraction notation, identify fractions of a group, represent fractions on number lines, and write fractions as sums of unit fractions.
The unit 12 “Instructional Context” tab also shows future grade-level connections. The “Look Forward” section explains that in the next unit students will use models and number lines to compare fractions. The section also explains that in grade 4 students will represent and compare fractions with a wider range of denominators and work with fractions greater than one. The materials provide a clear vertical progression from equal shares in grade 2, to fraction notation and number line work in grade 3, and then to fraction comparison and fractions greater than one in grade 4.
Evaluation for 4.2c
At the lesson level, the “Instructional Context” tab connects students’ prior knowledge to new mathematical learning. In unit 4, lesson 4.1 “Understand Division,” the “Look Back” section explains that in grade 2 students used equal groups to represent division situations and used repeated addition to solve problems. The section also explains that earlier in grade 3 students related equal groups to multiplication, interpreted products as the total number of objects in equal groups, and learned to multiply with factors up to 10.
The same lesson’s “This Lesson” and “Look Forward” sections show how prior knowledge connects to current and future learning. In “This Lesson” students relate equal groups to division and are introduced to two types of division questions: “How many equal groups are there?” and “How many are in each group?” Students use counters to model both problem types. The “Look Forward” section explains that students will use drawings, arrays, strip models, and number lines to solve division problems and later explore the relationship between multiplication and division.
Evaluation for 4.3a
The unit 13 “Daily Planner” provides spaced retrieval opportunities by revisiting previously learned skills while students work on current fraction objectives. In lesson 13.1 students begin equivalent fractions while the planner includes spiral review with multiplication facts through the game “Four in a Row: Multiply with 2–10.” In lesson 13.3 students work with equivalent fractions on number lines while also reviewing how to graph fractions less than one on number lines. In lesson 13.5 students compare fractions with the same numerator while completing spiral review with interpreting bar graphs.
The unit 13, lesson 13.1 independent practice also provides spaced retrieval within the lesson. Students first identify and model equivalent fractions. Then, students solve a multi-digit addition problem, solve a multi-digit subtraction problem, and identify expressions that find the area of a rectangle. These review tasks require students to retrieve prior computation and area skills while learning new fraction content.
Evaluation for 4.3b
The lesson 13.1 independent practice provides interleaved practice by mixing current fraction work with previously learned concepts. Students show pairs of fractions such as 3/4 and 5/6 or 2/8 and 1/4, decide whether the fractions are equivalent, write fractions for shaded models, and draw models to compare 1/3 and 2/6 of the same book. On the next page, students solve addition and subtraction problems and circle expressions that could find the area of a rectangle. This practice mixes current equivalent fraction content with prior computation and area concepts.
The unit 13 “Daily Planner” also supports interleaved practice across the unit. While students learn equivalent fractions and compare fractions, the planner includes spiral review with multiplication facts, graphing fractions less than one on number lines, division, interpreting bar graphs, and addition, subtraction, multiplication, and division facts. This structure requires students to continue applying previously learned skills while working on new grade 3 fraction concepts.
4.1 Depth of Key Concepts
4.1a
Practice opportunities over the course of a lesson and/or unit (including instructional assessments) require students to demonstrate depth of understanding aligned to the TEKS.
Practice opportunities over the course of a lesson and/or unit (including instructional assessments) require students to demonstrate depth of understanding aligned to the TEKS.
2 out of 2 points
Evaluation for 4.1a
Evaluation for 4.1a
Practice opportunities over the course of a lesson and/or unit (including instructional assessments) require students to demonstrate depth of understanding aligned to the TEKS.
2 out of 2 points
Instructional assessments also require students to demonstrate understanding aligned to the grade 3 TEKS. In the unit 9 “Perimeter” test, students find the perimeter of figures on grids, find the perimeter of rectangles and polygons with labeled side lengths, distinguish between area and perimeter in real-world contexts, and solve problems involving ribbon, paper, and rectangular figures. These assessment tasks require students to apply perimeter and area concepts in visual, numerical, and real-world situations rather than only recall a formula.
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 13 “Daily Planner” also shows tasks increasing in rigor across the fraction unit. Students begin by understanding equivalent fractions with models, then find equivalent fractions using models and fraction strips, and later represent equivalent fractions on number lines. Students then compare fractions with the same denominator, compare fractions with the same numerator, and finally compare fractions using either the same numerator or the same denominator. This sequence moves students from visual models to number lines, comparison reasoning, and justification.
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 2 “Instructional Context” tab also connects multiplication fluency to later mathematical ideas. The “Look Forward” section explains that students will connect multiplication to area in the next unit by relating the area of a rectangle made of unit squares to finding a product using an array. The section also explains that students will later use place value to multiply one-digit numbers by multiples of 10, develop division fluency, and solve two-step word problems involving all four operations. This explanation shows coherence among multiplication models, area, place value, division, and problem solving.
4.2b
Materials demonstrate coherence across units by connecting the content and language learned in previous courses/grade levels and what will be learned in future courses/grade levels to the content to be learned in the current course/grade level.
Materials demonstrate coherence across units by connecting the content and language learned in previous courses/grade levels and what will be learned in future courses/grade levels to the content to be learned in the current course/grade level.
3 out of 3 points
Evaluation for 4.2b
Evaluation for 4.2b
Materials demonstrate coherence across units by connecting the content and language learned in previous courses/grade levels and what will be learned in future courses/grade levels to the content to be learned in the current course/grade level.
3 out of 3 points
The unit 12 “Instructional Context” tab also shows future grade-level connections. The “Look Forward” section explains that in the next unit students will use models and number lines to compare fractions. The section also explains that in grade 4 students will represent and compare fractions with a wider range of denominators and work with fractions greater than one. The materials provide a clear vertical progression from equal shares in grade 2, to fraction notation and number line work in grade 3, and then to fraction comparison and fractions greater than one in grade 4.
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
The same lesson’s “This Lesson” and “Look Forward” sections show how prior knowledge connects to current and future learning. In “This Lesson” students relate equal groups to division and are introduced to two types of division questions: “How many equal groups are there?” and “How many are in each group?” Students use counters to model both problem types. The “Look Forward” section explains that students will use drawings, arrays, strip models, and number lines to solve division problems and later explore the relationship between multiplication and division.
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 unit 13, lesson 13.1 independent practice also provides spaced retrieval within the lesson. Students first identify and model equivalent fractions. Then, students solve a multi-digit addition problem, solve a multi-digit subtraction problem, and identify expressions that find the area of a rectangle. These review tasks require students to retrieve prior computation and area skills while learning new fraction content.
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 unit 13 “Daily Planner” also supports interleaved practice across the unit. While students learn equivalent fractions and compare fractions, the planner includes spiral review with multiplication facts, graphing fractions less than one on number lines, division, interpreting bar graphs, and addition, subtraction, multiplication, and division facts. This structure requires students to continue applying previously learned skills while working on new grade 3 fraction concepts.
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 3, lesson 3.2 “Area and Multiplication,” students interpret and analyze grid models that represent the area of rectangles. The educator guidance asks students to first find area by counting unit squares, then connect the tiled rectangle to an array with equal rows and columns. Students analyze the number of rows and the number of unit squares in each row, then connect the model to multiplication expressions such as 8 × 10 and 10 × 8. These tasks require students to interpret visual representations and analyze how multiplication can be used to determine area.
In unit 12, lesson 12.2 “Understand Fractions,” students interpret and analyze fraction models representing equal parts of a whole. The educator guidance has students fold paper into halves and fourths, label each equal part with fraction notation, and discuss what the numerator and denominator represent. Students also use fraction notation to describe shaded parts and make fractions given in fraction notation. These tasks require students to analyze visual models and connect the representations to symbolic fraction notation.
Evaluation for 5.1b
In unit 1, lesson 1.4 “Use Arrays to Multiply,” students create models to represent multiplication situations. The guidance instructs educators to connect equal groups to arrays by treating the rows of an array as equal groups. Students use counters to build arrays, identify the number of rows and the number of objects in each row, and connect the array to a multiplication equation. These tasks require students to create visual models that represent multiplication situations.
In unit 12, lesson 12.3 “Fractions of a Group,” students create models to represent fraction situations. In the warm-up, students draw a model of a sandwich divided into four equal parts and shade three parts to show the pieces that Scott took. The educator guidance reinforces that the denominator tells how many equal parts are in the whole and the numerator tells how many parts are being counted. Students then extend this idea to fractions of a group, where the whole is a set of objects and the part is a subset of those objects.
Evaluation for 5.1c
In unit 8, lesson 8.3 “Solve Two-Step Word Problems (Part 1),” students apply conceptual understanding to new multistep problem situations. The educator guidance asks students to use strip models and equations to represent and solve two-step word problems involving all four operations. Students identify the two steps needed to solve a problem, represent both steps with a single strip model, and use symbols to represent unknown numbers. These tasks require students to apply their understanding of operations, models, and equations to unfamiliar problem contexts.
In unit 3, lesson 3.2 “Area and Multiplication,” students apply conceptual understanding of area to new rectangle problems. Students begin by counting unit squares, then connect tiled rectangles to arrays and multiplication. Later in the lesson, students find the areas of rectangles that are not fully tiled with unit squares by using the side lengths and multiplication. This requires students to transfer their conceptual understanding of area from visible unit squares to new area situations.
Evaluation for 5.2a
In unit 2, lesson 2.1 “Multiply with 2,” students build fluency with multiplication facts involving a factor of two. The educator guidance begins with repeated addition and multiplication equations for models with two equal groups, then connects those equations to doubles facts. Students use skip counting and adding doubles to find products and missing factors in multiplication equations. Students continue practicing through guided practice, independent practice, and “Game Time,” building automaticity with grade-level multiplication facts.
In unit 7, lesson 7.9 “Add Using the Standard Algorithm,” students build procedural fluency with multi-digit addition. The lesson begins by connecting partial sums in a place value chart to the standard algorithm. Students transition from adding 100s to 100s, 10s to 10s, and ones to ones into using the standard algorithm for addition. Guided practice and independent practice provide repeated opportunities to apply the algorithm accurately and efficiently.
Evaluation for 5.2b
In unit 2, lesson 2.4 “Multiply with 4,” students practice efficient, flexible, and accurate multiplication procedures. The lesson builds from previous skip counting work and introduces multiple strategies for multiplying by four, including skip counting and doubling twice. Students use these strategies to find products and missing factors in multiplication equations, then continue practicing during guided practice, independent practice, and “Game Time.” These opportunities allow students to apply different strategies while developing accuracy and efficiency with multiplication facts.
In unit 10, lesson 10.1 “Multiply with Multiples of 10,” students practice flexible multiplication procedures using place value models, sketches, and equations. The educator guidance asks students to use place value blocks to represent products involving one-digit numbers and multiples of 10, then transition to calculating products without models. Students look for patterns, connect the models to place value reasoning, and apply increasingly efficient procedures to solve multiplication problems.
Evaluation for 5.2c
In unit 2, lesson 2.1 “Multiply with 2,” students evaluate procedures for efficiency and accuracy. The educator guidance asks students to compare repeated addition and multiplication equations for models with two equal groups. Students discuss how they can use both doubles facts and skip counting to find products involving two, evaluate whether the strategies produce the same result, and consider which procedure is more efficient for multiplication facts.
In unit 7, lesson 7.2 “Use Compensation to Add or Subtract,” students evaluate addition and subtraction procedures. The educator guidance asks students to compare Bill’s open number line strategy, which breaks 28 into 20 and 8, with Meg’s compensation strategy, which adds 30 and then subtracts 2. Students discuss how both approaches produce the same sum and analyze why compensation can be an efficient strategy when working with friendly numbers.
Evaluation for 5.2d
In unit 2, lesson 2.4 “Multiply with 4,” embedded educator guidance supports students in moving toward increasingly efficient multiplication strategies. Students begin with skip counting by four, then learn to double and double again to multiply by four. The educator guidance has educators connect the strategy to prior work with doubles and encourage students to use more efficient methods instead of relying only on long skip counting lists.
In unit 5, lesson 5.1 “Use Multiplication to Divide,” embedded educator guidance helps students compare models and move toward more efficient division strategies. Students first solve a division problem using a model of their choice, then discuss the benefits and drawbacks of equal groups, arrays, and strip models. The educator guidance notes that equal groups and arrays provide visual support but may take longer to draw, while strip models require less drawing. This comparison helps students select more efficient representations before using related multiplication facts to divide.
Evaluation for 5.3a
The unit 6 “Instructional Context” tab explains how the materials address both conceptual and procedural expectations for place value. The “Look Back” section explains that students previously read and wrote numbers up to 1,200 in standard, expanded, and word form and compared and ordered numbers using place value. The “This Unit” section explains that students extend place value understanding to numbers up to 100,000 by using models to determine digit values, investigating how moving a digit one place to the left increases its value by a factor of 10, and writing numbers in expanded notation. This section shows how conceptual understanding with models supports procedural work with reading, writing, comparing, ordering, and rounding numbers.
Unit 6, lesson 6.3 “Compose and Decompose Numbers,” explicitly connects conceptual models to procedural representations. Students use place value disks and place value mats to model five-digit numbers, then use each digit’s value to write the number in standard form, expanded notation, and expanded form. The educator guidance also asks students to compare the three forms and understand that standard form shows the total value, expanded notation shows each digit multiplied by the value of its place, and expanded form shows the value of each individual digit.
Evaluation for 5.3b
In unit 6, lesson 6.3 “Compose and Decompose Numbers,” students use concrete models and pictorial and abstract representations. Students use place value disks to model five-digit numbers on a place value mat, sketch the models, and then write the numbers in standard form, expanded notation, and expanded form. This progression connects concrete manipulatives, visual models, and symbolic representations required by the grade 3 place value TEKS.
In unit 12, lesson 12.2 “Understand Fractions,” students use concrete, pictorial, and abstract representations to understand fractions. Students fold paper into halves and fourths, label equal parts with fraction notation, and use visual models to represent shaded parts of a whole. Students then connect the models to numerator and denominator meanings. This sequence supports students in moving from concrete paper folding and visual models to abstract fraction notation.
Evaluation for 5.3c
Unit 6, lesson 6.3 “Compose and Decompose Numbers,” supports students in connecting concrete and representational models to symbolic number forms. Students model 24,153 with place value disks, connect each disk to the value of the digit, and write the number in expanded notation and expanded form. The educator guidance explains that each product in expanded notation represents the value of that place, helping students connect the place value model to abstract numeric representations.
Unit 8, lesson 8.3 “Solve Two-Step Word Problems (Part 1),” supports students in connecting visual models to symbolic equations. Students use strip models to represent two-step word problems involving all four operations, then write equations with symbols to represent unknown numbers. The lesson guides students to represent both steps with a single strip model before connecting the model to equations used to solve the problem.
Evaluation for 5.4a
In unit 6, lesson 6.3 “Compose and Decompose Numbers,” students develop academic mathematical language using visuals, place value models, and written representations. Students match numbers written in words, expanded form, and standard form. Students also identify the value of a digit and use place value disks to represent numbers. Students then write numbers in expanded notation, expanded form, and standard form, supporting their development of academic vocabulary related to place value, value, standard form, expanded notation, and expanded form.
In unit 1, lesson 1.4 “Use Arrays to Multiply,” students develop academic mathematical language using counters, arrays, drawings, and multiplication equations. Students use counters to make arrays, describe rows and the number of dots in each row, and connect the array to a multiplication equation. Problems require students to draw arrays, identify rows and equal groups, and write multiplication equations, supporting use of academic vocabulary such as array, row, group, equal groups, multiplication, and product.
Evaluation for 5.4b
Unit 6, lesson 6.3 “Compose and Decompose Numbers,” scaffolds students’ development and use of academic mathematical vocabulary in context. Students use place value disks and a place value chart labeled “ten thousands, thousands, hundreds, tens, and ones” to represent a number. Students then write the same number in expanded notation, expanded form, and standard form. These tasks support students in using place value vocabulary while connecting models, numerical expressions, and written forms of numbers.
Unit 3, lesson 3.3 “Area of Compound Figures,” supports students’ use of academic vocabulary in the context of area. Students work with compound figures made of rectangles, break figures into smaller rectangles, and find the area of each figure. Students use vocabulary such as area, square units, rectangle, compound figure, multiply, and equation while connecting visual models to calculations. These tasks scaffold students’ use of precise mathematical language as they describe how to decompose figures and how to calculate area.
Evaluation for 5.4c
Unit 3, lesson 3.3 “Area of Compound Figures,” includes embedded support for students to apply mathematical language through vocabulary, syntax, and discourse. In the “Compare and Talk” task, students compare Edward and Victor’s work for finding the area of the same compound figure. Students analyze how Edward and Victor divided the figure, explain the similarities and differences between the strategies, and connect each representation to multiplication equations and a total area of 32 square units. These tasks support students in hearing, refining, and using academic language such as area, square units, rectangle, multiply, divide, and total area during mathematical discussion.
Unit 6, lesson 6.6 “Round Numbers Using a Number Line,” provides opportunities for students to apply appropriate mathematical language through discussion, reasoning, and written explanation. In the “Think and Talk” task, students discuss which rounded number is nearby, which number is easy to work with, and which number is both nearby and easy to work with. Students then use number lines to round numbers to the nearest 10, 100, 1,000, or 10,000 and explain whether they agree with a statement about a rounded amount in a real-world cookie money context. These tasks support mathematical conversations in which students use vocabulary such as round, nearest, nearby, halfway, estimate, number line, and benchmark.
Evaluation for 5.5a
Unit 8, lesson 8.3 “Solve Two-Step Word Problems (Part 1),” appropriately integrates the TEKS process standards as students solve real-world two-step problems using models and equations. Students draw strip models, identify unknown quantities, write equations for each step, and solve problems involving a book fair, candy bars, stickers, a treehouse, donations, and pizza sales. Students also compare Hugo’s strip model to their own, requiring them to analyze representations, communicate reasoning, and justify how the model represents the problem.
Unit 8, lesson 8.4 “Solve Two-Step Word Problems (Part 2),” integrates the TEKS process standards as students estimate, solve, and evaluate the reasonableness of solutions to multistep problems. Students estimate sums and differences, use a table of arcade tickets to decide whether friends have enough tickets for a prize, and write a two-step word problem from given equations. Students also solve problems involving necklaces, baseball cards, volleyball teams, class treats, camping groups, and knitted items. These tasks require students to apply mathematics to real-world situations, represent and solve problems, communicate mathematical ideas, and evaluate reasonableness.
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 materials state that the program’s step-by-step lesson plans and activities are designed to target the seven TEKS process standards and build students’ ability to make mathematical connections, communicate effectively and precisely, and solve complex problems in the classroom and in everyday life.
The same “Instructional Design” document provides course-level explanations and examples for individual process standards. For example, the section for applying mathematics to problems from everyday life, society, and the workplace describes students solving real-world area and perimeter problems, identifying fractions in familiar contexts, and reasoning about financial situations. The educator guidance also prompts educators to ask students how they can represent problems with models or show what is happening in a problem, connecting process standards across grade-level instruction.
Evaluation for 5.5c
The unit 1 “Process Standards” tab provides a unit-level description of how the TEKS process standards are incorporated and connected throughout the unit. The materials explain that students build an understanding of multiplication through everyday problem situations, including a lesson 1.2 problem about tripling a smoothie recipe. The tab also describes how students use multiple representations, such as equal groups, repeated addition, skip counting, multiplication equations, strip models, number lines, drawings, and language, to communicate and justify multiplication relationships across the unit.
Unit 3, “Daily Planner,” “Area,” provides a unit-level overview of the content and process standards incorporated throughout the unit. The unit summary explains that students find the area of a figure by tiling it with unit squares, relate area to multiplication and addition, and use those relationships to find the areas of rectangles and figures made of rectangles. The unit overview lists process standards 3.1.A, 3.1.B, 3.1.D, 3.1.E, 3.1.F, and 3.1.G, connecting the area work to real-world problem solving, representations, mathematical relationships, communication, and justification.
Evaluation for 5.5d
The “Third Grade At-a-Glance” standards document provides an overview of the TEKS process standards incorporated into lessons across the grade level. The TEKS chart lists each mathematical process standard and identifies the lessons in which each standard appears. For example, process standard 3.1.A is connected to lessons 1.1, 1.2, 1.3, 1.6, 3.1, 3.4, 8.1, 8.2, 8.3, 8.4, 9.1–9.4, 16.1–16.5, and other lessons across the course.
The same “Third Grade At-a-Glance” standards document provides lesson-level alignment for additional process standards. For example, the document identifies lessons connected to 3.1.B for using a problem-solving model and lessons connected to 3.1.C for selecting tools and techniques. The chart also includes process standards for communicating mathematical ideas, creating and using representations, analyzing relationships, and displaying, explaining, and justifying mathematical arguments. The document functions as an overview of the TEKS process standards incorporated into individual lessons.
5.1 Development of Conceptual Understanding
5.1a
Questions and tasks require students to interpret, analyze, and evaluate models and representations for mathematical concepts and situations.
Questions and tasks require students to interpret, analyze, and evaluate models and representations for mathematical concepts and situations.
3 out of 3 points
Evaluation for 5.1a
Evaluation for 5.1a
Questions and tasks require students to interpret, analyze, and evaluate models and representations for mathematical concepts and situations.
3 out of 3 points
In unit 12, lesson 12.2 “Understand Fractions,” students interpret and analyze fraction models representing equal parts of a whole. The educator guidance has students fold paper into halves and fourths, label each equal part with fraction notation, and discuss what the numerator and denominator represent. Students also use fraction notation to describe shaded parts and make fractions given in fraction notation. These tasks require students to analyze visual models and connect the representations to symbolic fraction notation.
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 12, lesson 12.3 “Fractions of a Group,” students create models to represent fraction situations. In the warm-up, students draw a model of a sandwich divided into four equal parts and shade three parts to show the pieces that Scott took. The educator guidance reinforces that the denominator tells how many equal parts are in the whole and the numerator tells how many parts are being counted. Students then extend this idea to fractions of a group, where the whole is a set of objects and the part is a subset of those objects.
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 3.2 “Area and Multiplication,” students apply conceptual understanding of area to new rectangle problems. Students begin by counting unit squares, then connect tiled rectangles to arrays and multiplication. Later in the lesson, students find the areas of rectangles that are not fully tiled with unit squares by using the side lengths and multiplication. This requires students to transfer their conceptual understanding of area from visible unit squares to new area situations.
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 7, lesson 7.9 “Add Using the Standard Algorithm,” students build procedural fluency with multi-digit addition. The lesson begins by connecting partial sums in a place value chart to the standard algorithm. Students transition from adding 100s to 100s, 10s to 10s, and ones to ones into using the standard algorithm for addition. Guided practice and independent practice provide repeated opportunities to apply the algorithm accurately and efficiently.
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 10, lesson 10.1 “Multiply with Multiples of 10,” students practice flexible multiplication procedures using place value models, sketches, and equations. The educator guidance asks students to use place value blocks to represent products involving one-digit numbers and multiples of 10, then transition to calculating products without models. Students look for patterns, connect the models to place value reasoning, and apply increasingly efficient procedures to solve multiplication problems.
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 7, lesson 7.2 “Use Compensation to Add or Subtract,” students evaluate addition and subtraction procedures. The educator guidance asks students to compare Bill’s open number line strategy, which breaks 28 into 20 and 8, with Meg’s compensation strategy, which adds 30 and then subtracts 2. Students discuss how both approaches produce the same sum and analyze why compensation can be an efficient strategy when working with friendly numbers.
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 5, lesson 5.1 “Use Multiplication to Divide,” embedded educator guidance helps students compare models and move toward more efficient division strategies. Students first solve a division problem using a model of their choice, then discuss the benefits and drawbacks of equal groups, arrays, and strip models. The educator guidance notes that equal groups and arrays provide visual support but may take longer to draw, while strip models require less drawing. This comparison helps students select more efficient representations before using related multiplication facts to divide.
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 6, lesson 6.3 “Compose and Decompose Numbers,” explicitly connects conceptual models to procedural representations. Students use place value disks and place value mats to model five-digit numbers, then use each digit’s value to write the number in standard form, expanded notation, and expanded form. The educator guidance also asks students to compare the three forms and understand that standard form shows the total value, expanded notation shows each digit multiplied by the value of its place, and expanded form shows the value of each individual digit.
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 12, lesson 12.2 “Understand Fractions,” students use concrete, pictorial, and abstract representations to understand fractions. Students fold paper into halves and fourths, label equal parts with fraction notation, and use visual models to represent shaded parts of a whole. Students then connect the models to numerator and denominator meanings. This sequence supports students in moving from concrete paper folding and visual models to abstract fraction notation.
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 8, lesson 8.3 “Solve Two-Step Word Problems (Part 1),” supports students in connecting visual models to symbolic equations. Students use strip models to represent two-step word problems involving all four operations, then write equations with symbols to represent unknown numbers. The lesson guides students to represent both steps with a single strip model before connecting the model to equations used to solve the problem.
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 1, lesson 1.4 “Use Arrays to Multiply,” students develop academic mathematical language using counters, arrays, drawings, and multiplication equations. Students use counters to make arrays, describe rows and the number of dots in each row, and connect the array to a multiplication equation. Problems require students to draw arrays, identify rows and equal groups, and write multiplication equations, supporting use of academic vocabulary such as array, row, group, equal groups, multiplication, and product.
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
Unit 3, lesson 3.3 “Area of Compound Figures,” supports students’ use of academic vocabulary in the context of area. Students work with compound figures made of rectangles, break figures into smaller rectangles, and find the area of each figure. Students use vocabulary such as area, square units, rectangle, compound figure, multiply, and equation while connecting visual models to calculations. These tasks scaffold students’ use of precise mathematical language as they describe how to decompose figures and how to calculate area.
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
Unit 6, lesson 6.6 “Round Numbers Using a Number Line,” provides opportunities for students to apply appropriate mathematical language through discussion, reasoning, and written explanation. In the “Think and Talk” task, students discuss which rounded number is nearby, which number is easy to work with, and which number is both nearby and easy to work with. Students then use number lines to round numbers to the nearest 10, 100, 1,000, or 10,000 and explain whether they agree with a statement about a rounded amount in a real-world cookie money context. These tasks support mathematical conversations in which students use vocabulary such as round, nearest, nearby, halfway, estimate, number line, and benchmark.
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 8, lesson 8.4 “Solve Two-Step Word Problems (Part 2),” integrates the TEKS process standards as students estimate, solve, and evaluate the reasonableness of solutions to multistep problems. Students estimate sums and differences, use a table of arcade tickets to decide whether friends have enough tickets for a prize, and write a two-step word problem from given equations. Students also solve problems involving necklaces, baseball cards, volleyball teams, class treats, camping groups, and knitted items. These tasks require students to apply mathematics to real-world situations, represent and solve problems, communicate mathematical ideas, and evaluate reasonableness.
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 same “Instructional Design” document provides course-level explanations and examples for individual process standards. For example, the section for applying mathematics to problems from everyday life, society, and the workplace describes students solving real-world area and perimeter problems, identifying fractions in familiar contexts, and reasoning about financial situations. The educator guidance also prompts educators to ask students how they can represent problems with models or show what is happening in a problem, connecting process standards across grade-level instruction.
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
Unit 3, “Daily Planner,” “Area,” provides a unit-level overview of the content and process standards incorporated throughout the unit. The unit summary explains that students find the area of a figure by tiling it with unit squares, relate area to multiplication and addition, and use those relationships to find the areas of rectangles and figures made of rectangles. The unit overview lists process standards 3.1.A, 3.1.B, 3.1.D, 3.1.E, 3.1.F, and 3.1.G, connecting the area work to real-world problem solving, representations, mathematical relationships, communication, and justification.
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 same “Third Grade At-a-Glance” standards document provides lesson-level alignment for additional process standards. For example, the document identifies lessons connected to 3.1.B for using a problem-solving model and lessons connected to 3.1.C for selecting tools and techniques. The chart also includes process standards for communicating mathematical ideas, creating and using representations, analyzing relationships, and displaying, explaining, and justifying mathematical arguments. The document functions as an overview of the TEKS process standards 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 8, lesson 8.4, questions 5–7, students think mathematically, persevere through problem solving, and make sense of mathematics as they analyze a two-step word problem. Educator notes guide students to examine Brenna’s solution, determine whether the answer is reasonable, estimate before finding an exact solution, and explain any errors in the work. Students revise their reasoning and justify how estimation supports problem solving. These tasks require students to analyze another student’s work, evaluate reasonableness, estimate, and solve using mathematical reasoning.
In unit 9, lesson 9.3, question 8, students think mathematically and persevere through a multistep perimeter task. Educator notes guide students to create a visual model that represents known and unknown measurements needed to determine perimeter. Students identify the relationship between the perimeter and missing side lengths before solving the problem. By constructing a model, analyzing relationships among measurements, solving the problem, and explaining how the visual representation supports their solution, students make sense of mathematical relationships in context.
Evaluation for 6.1b
In unit 2, lesson 2.9, questions 2 and 3, students develop an understanding that mathematical situations can be represented and solved in multiple ways. Educator notes guide students to model a situation using counters arranged in arrays and then represent the same situation with multiplication equations. During the “Compare and Talk” discussion, students explain how their work is similar to and different from another student’s representation. Students use concrete models, repeated addition, and multiplication equations while comparing and justifying multiple solution methods.
In unit 7, lesson 7.6, question 9, students explain and justify that there can be multiple ways to complete an estimation task. Educator notes guide students to estimate sums and differences using either rounding or compatible numbers. Students choose an estimation strategy, explain why they selected it, and share their reasoning with classmates while discussing the advantages of different approaches. These discussions help students recognize that multiple strategies can produce reasonable estimates and support students in justifying their mathematical decisions.
Evaluation for 6.1c
In unit 13, lesson 13.2, students make sense of mathematics through opportunities to do, discuss, and write about mathematics. Educator notes guide students to work collaboratively with fraction strips to model equivalent fractions before participating in a “Think and Talk” discussion about Caleb’s model. Students build fraction models, discuss why the fractions are equivalent, and later explain in writing a pattern that helps identify fractions equivalent to one-half. These tasks require students to connect hands-on models, mathematical discussion, and written explanation.
The “Instructional Design” document describes how lessons incorporate “Compare and Talk” and “Think and Talk” routines to engage students in mathematical conversations. These routines guide students to explain their reasoning, compare solution strategies, and communicate mathematical thinking orally and in writing. The embedded routines provide consistent opportunities for students to make sense of mathematics by doing, discussing, and writing about mathematical ideas throughout the program.
Evaluation for 6.2a
In unit 2, lesson 2.9, educator notes support students in sharing and reflecting on problem-solving approaches through explanations and justifications. Students compare their array models with Max’s strategy for multiplying three numbers. Educators guide students to explain what each value represents, discuss different ways to group the factors using properties of multiplication, and justify which grouping creates the most efficient path to the product. These opportunities support students in comparing multiple solution methods, explaining their reasoning, and defending strategy choices during classroom discussions.
In unit 7, lesson 7.13, educator notes guide students to share and reflect on their approaches as they solve one- and two-step word problems using strip models, number lines, and equations. Educators prompt students to compare different visual representations, explain why they selected a particular strategy, and justify the sequence of operations used to solve each problem. Students share approaches, compare solution strategies, and defend the reasonableness of their solutions, supporting reflection on mathematical reasoning.
Evaluation for 6.2b
Unit 3, lesson 3.2, includes prompts and guidance to support educators in providing explanatory feedback based on anticipated misconceptions. Educator notes anticipate that students may incorrectly count boundary tiles when determining the area of a shaded rectangle. The notes guide educators to explain that only the unit squares inside the shaded region contribute to the area and to have students extend grid lines to identify complete unit squares when needed. This support helps students revisit the model, correct their reasoning, and explain how the visual representation supports the correct area calculation.
Unit 13, lesson 13.6, includes guidance to support educators in addressing misconceptions about fraction equivalence. Educator notes anticipate that students may think 5/6 and 5/8 are equivalent because they have the same numerator. The notes guide educators to explain that when fractions have the same numerator, the fraction with the smaller denominator represents larger parts of the whole. Students compare visual models, explain how the size of the parts affects fraction values, and justify which fraction is greater. This guidance supports explanatory feedback that builds conceptual understanding of fraction comparison.
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 9, lesson 9.3, question 8, students think mathematically and persevere through a multistep perimeter task. Educator notes guide students to create a visual model that represents known and unknown measurements needed to determine perimeter. Students identify the relationship between the perimeter and missing side lengths before solving the problem. By constructing a model, analyzing relationships among measurements, solving the problem, and explaining how the visual representation supports their solution, students make sense of mathematical relationships in context.
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 7.6, question 9, students explain and justify that there can be multiple ways to complete an estimation task. Educator notes guide students to estimate sums and differences using either rounding or compatible numbers. Students choose an estimation strategy, explain why they selected it, and share their reasoning with classmates while discussing the advantages of different approaches. These discussions help students recognize that multiple strategies can produce reasonable estimates and support students in justifying their mathematical decisions.
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 describes how lessons incorporate “Compare and Talk” and “Think and Talk” routines to engage students in mathematical conversations. These routines guide students to explain their reasoning, compare solution strategies, and communicate mathematical thinking orally and in writing. The embedded routines provide consistent opportunities for students to make sense of mathematics by doing, discussing, and writing about mathematical ideas throughout the program.
6.2 Facilitating Productive Struggle
6.2a
Materials support teachers in guiding students to share and reflect on their problem-solving approaches, including explanations, arguments, and justifications.
Materials support teachers in guiding students to share and reflect on their problem-solving approaches, including explanations, arguments, and justifications.
6 out of 6 points
Evaluation for 6.2a
Evaluation for 6.2a
Materials support teachers in guiding students to share and reflect on their problem-solving approaches, including explanations, arguments, and justifications.
6 out of 6 points
In unit 7, lesson 7.13, educator notes guide students to share and reflect on their approaches as they solve one- and two-step word problems using strip models, number lines, and equations. Educators prompt students to compare different visual representations, explain why they selected a particular strategy, and justify the sequence of operations used to solve each problem. Students share approaches, compare solution strategies, and defend the reasonableness of their solutions, supporting reflection on mathematical reasoning.
6.2b
Materials include prompts and guidance to support teachers in providing explanatory feedback based on student responses and anticipated misconceptions.
Materials include prompts and guidance to support teachers in providing explanatory feedback based on student responses and anticipated misconceptions.
4 out of 4 points
Evaluation for 6.2b
Evaluation for 6.2b
Materials include prompts and guidance to support teachers in providing explanatory feedback based on student responses and anticipated misconceptions.
4 out of 4 points
Unit 13, lesson 13.6, includes guidance to support educators in addressing misconceptions about fraction equivalence. Educator notes anticipate that students may think 5/6 and 5/8 are equivalent because they have the same numerator. The notes guide educators to explain that when fractions have the same numerator, the fraction with the smaller denominator represents larger parts of the whole. Students compare visual models, explain how the size of the parts affects fraction values, and justify which fraction is greater. This guidance supports explanatory feedback that builds conceptual understanding of fraction comparison.