Program Information
- ISBN
- 9781483880037
- 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 2 Math
Math (English) Grade 2
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 2 | 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 2 Texas Essential Knowledge and Skills (TEKS), English Language Proficiency Standards (ELPS), and concepts taught throughout the course. For example, the “Second Grade At-a-Glance: Planning and Materials” resource provides an overview of each unit and the concepts taught, including the aligned grade 2 TEKS and ELPS.
In addition, each unit provides a “Daily Planner” that outlines the grade 2 TEKS, ELPS, and concepts taught throughout the unit. For example, in unit 6 students create and interpret picture graphs and bar graphs. Students also solve addition and subtraction word problems involving data. These concepts align with grade 2 standards 2.10A, 2.10B, 2.10C, and 2.10D.
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.
“Second 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 before planning instruction.
Evaluation for 1.1c
The materials provide a rationale for the unit order and explain how concepts connect throughout the course. In “Second 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, unit 3 mirrors unit 2 by teaching similar strategies for subtraction within 100. This parallel approach helps students understand addition and subtraction as related operations that use similar structures and reasoning. Together, units 2 and 3 develop computational skills that students apply in unit 4 when solving addition and subtraction word problems and later when adding and subtracting three-digit numbers.
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 7 “Look Back” section explains that in earlier grades students learned that numbers up to 120 are composed of 100s, 10s, and ones. Students also modeled, identified, and compared numbers up to 120. Earlier in the course, students developed place value strategies to add and subtract numbers up to 100.
Evaluation for 1.1d
The educator resource Discover Takeoff by IXL: Inside a Takeoff Unit explains the unit structure and identifies key information that educators review before instruction, including the unit outline, instructional context, objectives, lesson sequence, and additional resources. Lessons include learning activities for one instructional day, ranging from introducing new concepts to opportunities for independent practice. Review days provide written and online activities for cumulative practice before the unit test. Each unit also includes additional resources and assessments.
The materials also provide lesson planning guidance to help educators prepare for implementation. Discover Takeoff by IXL: Comprehensive Lesson Plans explains how lesson components are organized and how educators can use the lesson structure to understand the purpose, flow, and instructional supports within each lesson. For example, the components include goals, instructional context, materials, and additional supports. Lessons follow a consistent structure of warm-up, instruction, guided practice, and independent practice so students know what to expect.
Evaluation for 1.1e
Through an administrator account, instructional leaders have access to the classroom walkthrough checklist and guiding questions for collaborative conversations. The checklist helps leaders observe how the materials are implemented, including whether the educator follows the sequence and structure of the lesson, uses the lesson components and materials, and checks for understanding throughout the lesson.
Questions for collaborative conversations provide guidance for educator planning and reflection. The questions are reference points for collaborative conversations 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 2 concepts. For example, in the unit 4 outline the “Instructional Context” includes a “Look Back” section that identifies students’ prior learning and explains how it connects to the concepts taught in the current unit.
The “Additional Resources” section of each unit identifies academic vocabulary educators can introduce before instruction. For example, the grade 2, unit 10 overview provides a list of vocabulary connected to the unit concepts and guidance for educators to prepare students for the mathematical language they will encounter, such as angle, closed shape, edge, face, hexagon, octagon, polygon, quadrilateral, rhombus, and side.
Evaluation for 1.2b
The materials contain supports for families in both English and Spanish for each grade 2 unit. For example, educators can access the English and Spanish “Family Letter” through the unit’s “Additional Resources” section. The letter explains what students will learn and provides suggestions for supporting student progress at home.
The English and Spanish “Family Welcome Letters” provide additional program guidance. For example, the letters explain how families can view assigned skills, access the resources students use in class, review achievements, and identify areas for continued practice.
Evaluation for 1.3a
Grade 2 lesson plans include lesson goals, educator questions, instructional tasks, materials, guided practice, independent practice, and assessment opportunities. For example, in unit 1, lesson 6 “Subtract by Counting On” guides educators in modeling the counting on strategy and then provides structured opportunities for students to apply the strategy with educator support and independently.
The materials include instructional questions, problem-solving tasks, student practice, and checks for understanding aligned with the lesson content. For example, in unit 5, lesson 10 “Word Problems with Length,” students apply measurement concepts to word problems, while educators use questions and practice responses to monitor whether students understand how to select and use the correct operation or strategy.
The lesson plans include language and instructional supports aligned to the lesson goals. Additional supports provide strategies for students who need help accessing vocabulary, directions, or mathematical representations. These supports help educators address both the content expectations and language demands of the lesson.
Evaluation for 1.3b
The grade 2, unit 1, “Daily Planner,” identifies educator and student materials needed for instruction in the addition and subtraction within 20. For example, lesson 1.2 “Add by Making Ten,” identifies student workbook resources, independent practice resources, ten frames, and counters. Lesson 1.5 “Use Ten to Subtract,” also identifies ten frames and counters. These examples show that the materials identify student-facing resources and physical manipulatives needed for instruction and practice.
The grade 2, unit 6, “Daily Planner,” provides additional examples of educator and student materials in the data unit. For example, lesson 6.2, “Make and Interpret Bar Graphs,” identifies student workbook resources, independent practice resources, pattern blocks, and centimeter rulers. Lesson 6.3, “Make and Interpret Scaled Graphs,” identifies the “Wild Class Pets” activity and dice. These resources support hands-on data collection, graphing, student practice, and digital skill practice.
The Discover Takeoff by IXL: Comprehensive Lesson Plans guide provides suggested timing for each lesson component. Lessons include a five-minute warm-up, 15–20 minutes of instruction, 10–15 minutes of guided practice, and 15–20 minutes of independent practice. This pacing guidance helps educators understand how long the lesson takes and how instruction is divided across warm-up, instruction, guided practice, and independent practice.
Evaluation for 1.3c
Discover Takeoff by IXL: Comprehensive Lesson Plans explains how educators use lesson materials for extended practice. For example, students may complete independent practice pages at school or bring them home for homework or reinforcement. The front side of the independent practice page provides targeted practice on the lesson’s key concept, while the back side provides spiral review so students revisit and apply skills from previous units.
Unit 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
In addition, each unit provides a “Daily Planner” that outlines the grade 2 TEKS, ELPS, and concepts taught throughout the unit. For example, in unit 6 students create and interpret picture graphs and bar graphs. Students also solve addition and subtraction word problems involving data. These concepts align with grade 2 standards 2.10A, 2.10B, 2.10C, and 2.10D.
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
“Second 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 before planning 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 7 “Look Back” section explains that in earlier grades students learned that numbers up to 120 are composed of 100s, 10s, and ones. Students also modeled, identified, and compared numbers up to 120. Earlier in the course, students developed place value strategies to add and subtract numbers up to 100.
1.1d
Materials include protocols with corresponding guidance for unit and lesson internalization.
Materials include protocols with corresponding guidance for unit and lesson internalization.
2 out of 2 points
Evaluation for 1.1d
Evaluation for 1.1d
Materials include protocols with corresponding guidance for unit and lesson internalization.
2 out of 2 points
The materials also provide lesson planning guidance to help educators prepare for implementation. Discover Takeoff by IXL: Comprehensive Lesson Plans explains how lesson components are organized and how educators can use the lesson structure to understand the purpose, flow, and instructional supports within each lesson. For example, the components include goals, instructional context, materials, and additional supports. Lessons follow a consistent structure of warm-up, instruction, guided practice, and independent practice so students know what to expect.
1.1e
Materials include resources and guidance for instructional leaders to support teachers with implementing the materials as designed.
Materials include resources and guidance for instructional leaders to support teachers with implementing the materials as designed.
2 out of 2 points
Evaluation for 1.1e
Evaluation for 1.1e
Materials include resources and guidance for instructional leaders to support teachers with implementing the materials as designed.
2 out of 2 points
Questions for collaborative conversations provide guidance for educator planning and reflection. The questions are reference points for collaborative conversations with and among educators about learning goals, student data, and built-in instructional guidance and tools. The questions help educators plan, reflect, and make instructional decisions, supporting responsive teaching that meets the needs of all learners.
1.2 Unit-Level Design
1.2a
Materials include comprehensive unit overviews that provide the background content knowledge and academic vocabulary necessary to effectively teach the concepts in the unit.
Materials include comprehensive unit overviews that provide the background content knowledge and academic vocabulary necessary to effectively teach the concepts in the unit.
2 out of 2 points
Evaluation for 1.2a
Evaluation for 1.2a
Materials include comprehensive unit overviews that provide the background content knowledge and academic vocabulary necessary to effectively teach the concepts in the unit.
2 out of 2 points
The “Additional Resources” section of each unit identifies academic vocabulary educators can introduce before instruction. For example, the grade 2, unit 10 overview provides a list of vocabulary connected to the unit concepts and guidance for educators to prepare students for the mathematical language they will encounter, such as angle, closed shape, edge, face, hexagon, octagon, polygon, quadrilateral, rhombus, and side.
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 “Family Welcome Letters” provide additional program guidance. For example, the letters explain how families can view assigned skills, access the resources students use in class, review achievements, and identify areas for continued practice.
1.3 Lesson-Level Design
1.3a
Materials include comprehensive, structured, detailed lesson plans that include daily objectives, questions, tasks, materials, and instructional assessments required to meet the content and language standards of the lesson (aligned with the TEKS and the ELPS).
Materials include comprehensive, structured, detailed lesson plans that include daily objectives, questions, tasks, materials, and instructional assessments required to meet the content and language standards of the lesson (aligned with the TEKS and the ELPS).
5 out of 5 points
Evaluation for 1.3a
Evaluation for 1.3a
Materials include comprehensive, structured, detailed lesson plans that include daily objectives, questions, tasks, materials, and instructional assessments required to meet the content and language standards of the lesson (aligned with the TEKS and the ELPS).
5 out of 5 points
The materials include instructional questions, problem-solving tasks, student practice, and checks for understanding aligned with the lesson content. For example, in unit 5, lesson 10 “Word Problems with Length,” students apply measurement concepts to word problems, while educators use questions and practice responses to monitor whether students understand how to select and use the correct operation or strategy.
The lesson plans include language and instructional supports aligned to the lesson goals. Additional supports provide strategies for students who need help accessing vocabulary, directions, or mathematical representations. These supports help educators address both the content expectations and language demands of the lesson.
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 grade 2, unit 6, “Daily Planner,” provides additional examples of educator and student materials in the data unit. For example, lesson 6.2, “Make and Interpret Bar Graphs,” identifies student workbook resources, independent practice resources, pattern blocks, and centimeter rulers. Lesson 6.3, “Make and Interpret Scaled Graphs,” identifies the “Wild Class Pets” activity and dice. These resources support hands-on data collection, graphing, student practice, and digital skill practice.
The Discover Takeoff by IXL: Comprehensive Lesson Plans guide provides suggested timing for each lesson component. Lessons include a five-minute warm-up, 15–20 minutes of instruction, 10–15 minutes of guided practice, and 15–20 minutes of independent practice. This pacing guidance helps educators understand how long the lesson takes and how instruction is divided across warm-up, instruction, guided practice, and independent practice.
1.3c
Materials include guidance on the effective use of lesson materials for extended practice (e.g., homework, extension, enrichment).
Materials include guidance on the effective use of lesson materials for extended practice (e.g., homework, extension, enrichment).
1 out of 1 points
Evaluation for 1.3c
Evaluation for 1.3c
Materials include guidance on the effective use of lesson materials for extended practice (e.g., homework, extension, enrichment).
1 out of 1 points
Unit 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 2 Takeoff by IXL Assessment Overview identifies diagnostic, formative, and summative assessments throughout the course. The overview explains where educators find each assessment type and how assessment opportunities support progress monitoring. For example, educators use the “IXL LevelUp Diagnostic” to identify readiness and use lesson and unit assessments to monitor student progress toward grade 2 objectives.
Grade 2 lessons provide formative assessment opportunities throughout 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 during the lesson. These tasks vary in format and require students to demonstrate understanding through selected responses, written or entered answers, visual models, and skill-based practice.
The end-of-unit tests provide summative assessment opportunities aligned to unit objectives. For example, the unit 1 test includes questions that assess students’ mastery of the concepts and skills taught in the unit. Students respond to varied item types, such as multiple-choice, text-entry, inline-choice, hotspot, and multi-select, which allows educators to evaluate student understanding across different task formats.
Evaluation for 2.1b
The grade 2 Takeoff by IXL Assessment Overview defines diagnostic, formative, and summative assessments and explains the intended purpose of each type. Diagnostic assessments identify what students know before or during instruction. Formative assessments monitor learning while instruction is happening. Summative assessments evaluate mastery after instruction.
The LevelUp Guide for Administrators explains how assessment data can be used to monitor growth and respond to learning needs. The guide describes how diagnostic, formative, and summative assessment data help educators identify strengths, learning gaps, and next instructional steps. Educators and instructional leaders use this guidance to connect assessment results to planning and intervention.
The “Assessments on IXL” video provides additional guidance for educators in using the program’s assessments. The video describes the diagnostic assessment and explains how quizzes and educator-created assessments can be used to monitor progress or evaluate mastery. This guidance supports educators in selecting assessment options that match the purpose of the instructional moment.
Evaluation for 2.1c
The LevelUp Benchmark Guide provides administration procedures that support consistent and accurate benchmark testing. The guide includes suggested time allotments and scripts so educators can administer assessments with consistent directions and expectations. This guidance helps reduce variation in administering assessments across grade 2 classrooms.
The Insightful Assessments guide explains how educators administer unit-level assessments. This guide describes how to assign digital assessments, print assessments, review objectives and point values, support students during assessment, and use post-assessment data. These steps help educators administer grade 2 quizzes and unit tests accurately and consistently.
The assessment guidance also helps educators use results after administration. Educators review assessment reports, item-level data, and objective-level performance to determine which skills students mastered and which skills need additional instruction. This supports accurate interpretation of grade 2 assessment results after students complete quizzes or unit tests.
Evaluation for 2.1d
The “IXL LevelUp Diagnostic” connects diagnostic results to standards and grade-level expectations. The diagnostic identifies student performance by standard and shows which grade 2 skills students know, partially know, or have not yet mastered. Educators use this data to connect diagnostic results to the TEKS and identify gaps that may need attention before or during instruction.
Grade 2 formative assessments align to the TEKS and the lesson objectives. Each lesson’s “Goals” tab identifies the aligned TEKS and objectives. Readiness skills, warm-ups, guided practice, independent practice, and skill checks provide ongoing evidence of student progress toward the intended grade 2 lesson outcomes.
Grade 2 summative assessments align to the TEKS and unit objectives through end-of-unit tests. Grade 2 unit tests include assessment questions tagged with the corresponding TEKS and learning objective. Educators use the “Objectives” tab to review how each question connects to the unit outcomes and to interpret student mastery of the standards taught in the unit.
Evaluation for 2.1e
Grade 2 lessons include TEKS-aligned assessment tasks that vary in complexity. Readiness skills and warm-ups check prerequisite understanding, guided practice supports students as they apply the concepts, and independent practice asks students to demonstrate understanding on their own. This sequence allows educators to monitor student progress from readiness to application of the grade-level objective.
Grade 2 assessments include varied item types aligned to the TEKS and lesson objectives. Students respond to multiple-choice, text-entry, inline-choice, hotspot, and multi-select items. These tasks require students to demonstrate understanding in different ways, including choosing an answer, entering a response, using a visual, or applying a mathematical strategy.
The “LevelUp Diagnostic Standards Performance Report” provides additional evidence of TEKS-aligned complexity. The report shows which TEKS each student knows, partially knows, or does not yet know. Educators use this report with lesson and unit assessments to monitor student mastery across items that vary by skill, task type, and level of complexity.
Evaluation for 2.2a
The “Quiz Analysis” report helps educators interpret grade 2 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 2 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 grade 2 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 can 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 information helps educators respond directly to trends in grade 2 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 educators with 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 grade 2 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 2 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
Grade 2 lessons provide formative assessment opportunities throughout 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 during the lesson. These tasks vary in format and require students to demonstrate understanding through selected responses, written or entered answers, visual models, and skill-based practice.
The end-of-unit tests provide summative assessment opportunities aligned to unit objectives. For example, the unit 1 test includes questions that assess students’ mastery of the concepts and skills taught in the unit. Students respond to varied item types, such as multiple-choice, text-entry, inline-choice, hotspot, and multi-select, which allows educators to evaluate student understanding across different task formats.
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 LevelUp Guide for Administrators explains how assessment data can be used to monitor growth and respond to learning needs. The guide describes how diagnostic, formative, and summative assessment data help educators identify strengths, learning gaps, and next instructional steps. Educators and instructional leaders use this guidance to connect assessment results to planning and intervention.
The “Assessments on IXL” video provides additional guidance for educators in using the program’s assessments. The video describes the diagnostic assessment and explains how quizzes and educator-created assessments can be used to monitor progress or evaluate mastery. This guidance supports educators in selecting assessment options that match the purpose of the instructional moment.
2.1c
Materials include teacher guidance to ensure consistent and accurate administration of instructional assessments.
Materials include teacher guidance to ensure consistent and accurate administration of instructional assessments.
1 out of 1 points
Evaluation for 2.1c
Evaluation for 2.1c
Materials include teacher guidance to ensure consistent and accurate administration of instructional assessments.
1 out of 1 points
The Insightful Assessments guide explains how educators administer unit-level assessments. This guide describes how to assign digital assessments, print assessments, review objectives and point values, support students during assessment, and use post-assessment data. These steps help educators administer grade 2 quizzes and unit tests accurately and consistently.
The assessment guidance also helps educators use results after administration. Educators review assessment reports, item-level data, and objective-level performance to determine which skills students mastered and which skills need additional instruction. This supports accurate interpretation of grade 2 assessment results after students complete quizzes or unit tests.
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
Grade 2 formative assessments align to the TEKS and the lesson objectives. Each lesson’s “Goals” tab identifies the aligned TEKS and objectives. Readiness skills, warm-ups, guided practice, independent practice, and skill checks provide ongoing evidence of student progress toward the intended grade 2 lesson outcomes.
Grade 2 summative assessments align to the TEKS and unit objectives through end-of-unit tests. Grade 2 unit tests include assessment questions tagged with the corresponding TEKS and learning objective. Educators use the “Objectives” tab to review how each question connects to the unit outcomes and to interpret student mastery of the standards taught in the unit.
2.1e
Instructional assessments include TEKS-aligned items at varying levels of complexity.
Instructional assessments include TEKS-aligned items at varying levels of complexity.
2 out of 2 points
Evaluation for 2.1e
Evaluation for 2.1e
Instructional assessments include TEKS-aligned items at varying levels of complexity.
2 out of 2 points
Grade 2 assessments include varied item types aligned to the TEKS and lesson objectives. Students respond to multiple-choice, text-entry, inline-choice, hotspot, and multi-select items. These tasks require students to demonstrate understanding in different ways, including choosing an answer, entering a response, using a visual, or applying a mathematical strategy.
The “LevelUp Diagnostic Standards Performance Report” provides additional evidence of TEKS-aligned complexity. The report shows which TEKS each student knows, partially knows, or does not yet know. Educators use this report with lesson and unit assessments to monitor student mastery across items that vary by skill, task type, and level of 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 grade 2 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 can 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 educators with 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 grade 2 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 provide guidance for educators as they respond to students who struggle during instruction. For example, the “Tips for Support” resource embedded within lessons gives educators on-the-spot strategies for helping students reconnect to the lesson content. In addition, the “Instant Review” tool identifies class Trouble Spots and creates a review session focused on the concepts students are struggling with, allowing educators to reteach exact skills based on current student performance.
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 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 grade 2 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 also 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
Grade 2 lessons use a gradual-release structure that supports educator modeling before independent practice. 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 grade 2 concepts. For example, in unit 1, lesson 6 “Subtract by Counting On,” educators model the counting on strategy before students practice with support. Educator questions guide students in explaining the strategy and help educators check whether students understand how counting on can be used to subtract.
Guided practice continues to support educator modeling after the initial instruction. Educators use embedded questions and notes to clarify misconceptions, connect student responses to the lesson objective, and help students explain their thinking. This guidance supports students as they move from modeled examples to independent application.
Evaluation for 3.2b
Grade 2 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 application to problem-solving situations. For example, in unit 5, lesson 10 “Word Problems with Length,” students apply measurement concepts to word problems while educators use questions to support reasoning and strategy selection. This guidance helps educators facilitate discussion and connect lesson concepts to problem solving.
Evaluation for 3.2c
Grade 2 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 first learn the concept 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 the lesson concept in multiple ways. “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
Grade 2 lessons include language support guidance in the “Additional Supports” section. The 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, educators use sentence stems, visuals, vocabulary support, and discussion prompts to help students explain mathematical ideas. Students move from simple responses toward more complete oral and written explanations using lesson vocabulary.
Evaluation for 3.3b
The “Instructional Design: Empowering Language Learners in Math” document provides implementation guidance for supporting emergent bilingual (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 without separating language support from mathematics instruction.
Grade 2 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
Grade 2 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 grade 2 mathematics instruction. For example, 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.
Grade 2 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 materials also provide guidance for educators as they respond to students who struggle during instruction. For example, the “Tips for Support” resource embedded within lessons gives educators on-the-spot strategies for helping students reconnect to the lesson content. In addition, the “Instant Review” tool identifies class Trouble Spots and creates a review session focused on the concepts students are struggling with, allowing educators to reteach exact skills based on current student performance.
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 grade 2 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 also 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 grade 2 concepts. For example, in unit 1, lesson 6 “Subtract by Counting On,” educators model the counting on strategy before students practice with support. Educator questions guide students in explaining the strategy and help educators check whether students understand how counting on can be used to subtract.
Guided practice continues to support educator modeling after the initial instruction. Educators use embedded questions and notes to clarify misconceptions, connect student responses to the lesson objective, and help students explain their thinking. This guidance supports students as they move from modeled examples 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 application to problem-solving situations. For example, in unit 5, lesson 10 “Word Problems with Length,” students apply measurement concepts to word problems while educators use questions to support reasoning and strategy selection. This guidance helps educators facilitate discussion and connect lesson concepts to problem solving.
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 the lesson concept in multiple ways. “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, educators use sentence stems, visuals, vocabulary support, and discussion prompts to help students explain mathematical ideas. Students move from simple responses toward more complete oral and written explanations using lesson vocabulary.
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
Grade 2 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 grade 2 mathematics instruction. For example, 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.
Grade 2 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 6, lesson 6.2 “Make and Interpret Bar Graphs,” students demonstrate depth of understanding by creating and interpreting bar graphs with up to four categories. Students begin by using pattern blocks to make a picture graph, then compare the picture graph to a bar graph and discuss how both graphs show the same data. Students also collect class data with tally marks, create a bar graph, and answer questions that require them to add, compare, and subtract based on the data.
Instructional assessments also require students to demonstrate understanding aligned to the grade 2 data TEKS. In the unit 6 “Data” test, students interpret picture graphs and bar graphs, list categories from fewest to most, find totals, create bar graphs from tables, and answer comparison questions using information in data displays. For example, students use a picture graph about musical instruments to order the instruments by votes and find the total number of votes, then use bar graphs and data tables to create graphs and solve problems.
Evaluation for 4.1b
The unit 6 “Daily Planner” organizes questions and tasks so students move from foundational understanding to more complex data work. Students begin by making and interpreting picture graphs, then make and interpret bar graphs. Students then create scaled picture graphs and bar graphs with scales of two, five, and 10. Later in the unit, students draw conclusions and make predictions based on information in graphs. This progression increases rigor by moving students from reading simple data displays to creating scaled graphs and using data to reason.
The unit 2 “Daily Planner” also shows questions and tasks increasing in rigor across the unit. Students begin by adding a one-digit number to a two-digit number, then add 10s to two-digit numbers, break apart one addend, and use compensation to add. Later lessons ask students to use place value blocks, regroup when needed, record addition in place value charts, and choose a strategy to add within 100. This progression moves students from supported number line strategies to more flexible and efficient addition strategies aligned to the grade 2 TEKS.
Evaluation for 4.2a
The “Instructional Context” tab in the unit 6 outline explicitly connects mathematical patterns, big ideas, and relationships across units. In “Data,” the “Look Back” section explains that in grade 1 students collected, organized, and interpreted data in tally charts, picture graphs, and bar graphs and solved simple addition and subtraction problems involving data. The “This Unit” section explains that grade 2 students create and interpret tally charts, picture graphs, and bar graphs, sometimes using scales of two, five, and 10. The materials connect prior data work to the current unit’s work with more complex data displays.
The unit 6 “Instructional Context” tab also connects data representations to problem solving. The “This Unit” section explains that students solve addition and subtraction word problems involving data and draw conclusions and make predictions based on information in data displays. This explanation shows coherence between data representation, operations, and mathematical reasoning rather than treating graphing as an isolated skill.
Evaluation for 4.2b
The “Instructional Context” tab connects grade 2 content to previous and future grade-level learning. In unit 6 “Data,” the “Look Back” section explains that in grade 1 students collected, organized, and interpreted data in tally charts, picture graphs, and bar graphs. The “Look Forward” section explains that in grade 3 students will create and interpret scaled picture graphs, scaled bar graphs, frequency tables, and dot plots and solve multistep problems using those data displays.
The unit 9 “Instructional Context” tab also shows vertical coherence across grade levels. In “Time,” the “Look Back” section explains that in grade 1 students learned to tell and write time to the nearest hour or half hour and learned that an hour is 60 minutes and a half hour is 30 minutes. The “This Unit” section explains that grade 2 students learn to tell and write time to the nearest minute and use a.m. and p.m. appropriately. The “Look Forward” section explains that in grade 3 students will solve addition and subtraction problems involving time, including finding start and end times.
Evaluation for 4.2c
At the lesson level, the “Instructional Context” tab connects students’ prior knowledge to new mathematical learning. In unit 3, lesson 3.2 “Subtract Tens from 2-Digit Numbers,” the “Look Back” section explains that in the previous lesson students subtracted one-digit numbers from two-digit numbers by counting back and using 10. The section also explains that in the previous unit students learned to add within 100 using various strategies, and that in earlier grades students learned to skip count by 10s.
The same lesson’s “This Lesson” and “Look Forward” sections show how prior knowledge connects to current and future learning. In “This Lesson” students use open number lines to subtract tens from two-digit numbers. Students start by counting back by tens and then subtract using only the tens digits. The “Look Forward” section explains that students will next subtract two-digit numbers by breaking the subtrahend into tens and ones and will continue exploring other strategies for subtracting two-digit numbers throughout the unit.
Evaluation for 4.3a
The unit 6 “Daily Planner” provides spaced retrieval opportunities by revisiting previously learned skills while students work on current data objectives. In lesson 6.1 students make and interpret picture graphs while completing spiral review with addition and subtraction word problems. In lesson 6.3 students make and interpret scaled graphs while completing spiral review with measuring using an inch ruler. In lesson 6.4 students draw conclusions and make predictions from data while completing spiral review with attributes of three-dimensional shapes.
The unit 2 “Daily Planner” also shows spaced retrieval across lessons and units. While students work on addition within 100, the planner includes spiral review with addition and subtraction word problems within 20, comparing numbers up to 100, skip-counting by twos, and addition and subtraction within 20. These review opportunities help students retrieve previously learned skills after time has passed while learning new strategies for addition.
Evaluation for 4.3b
The unit 6 “Daily Planner” provides interleaved practice by mixing current data skills with previously learned concepts. While students focus on picture graphs, bar graphs, scaled graphs, conclusions, and predictions, the unit also includes spiral review with addition and subtraction word problems, measurement with an inch ruler, and three-dimensional shape attributes. The unit mixes current data content with previously learned operations, measurement, and geometry skills.
The unit 2 “Daily Planner” also provides interleaved practice by combining current addition-within-100 skills with prior skills from other units. While students learn to add using number lines, compensation, place value blocks, regrouping, place value charts, and strategy selection, the unit also includes spiral review with word problems, comparing numbers, skip counting, and addition and subtraction within 20. This structure requires students to continue applying previously learned concepts while working on new grade 2 addition strategies.
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 2 data TEKS. In the unit 6 “Data” test, students interpret picture graphs and bar graphs, list categories from fewest to most, find totals, create bar graphs from tables, and answer comparison questions using information in data displays. For example, students use a picture graph about musical instruments to order the instruments by votes and find the total number of votes, then use bar graphs and data tables to create graphs and solve problems.
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 2 “Daily Planner” also shows questions and tasks increasing in rigor across the unit. Students begin by adding a one-digit number to a two-digit number, then add 10s to two-digit numbers, break apart one addend, and use compensation to add. Later lessons ask students to use place value blocks, regroup when needed, record addition in place value charts, and choose a strategy to add within 100. This progression moves students from supported number line strategies to more flexible and efficient addition strategies aligned to the grade 2 TEKS.
4.2 Coherence of Key Concepts
4.2a
Materials demonstrate coherence across units by explicitly connecting patterns, big ideas, and relationships between mathematical concepts.
Materials demonstrate coherence across units by explicitly connecting patterns, big ideas, and relationships between mathematical concepts.
1 out of 1 points
Evaluation for 4.2a
Evaluation for 4.2a
Materials demonstrate coherence across units by explicitly connecting patterns, big ideas, and relationships between mathematical concepts.
1 out of 1 points
The unit 6 “Instructional Context” tab also connects data representations to problem solving. The “This Unit” section explains that students solve addition and subtraction word problems involving data and draw conclusions and make predictions based on information in data displays. This explanation shows coherence between data representation, operations, and mathematical reasoning rather than treating graphing as an isolated skill.
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 9 “Instructional Context” tab also shows vertical coherence across grade levels. In “Time,” the “Look Back” section explains that in grade 1 students learned to tell and write time to the nearest hour or half hour and learned that an hour is 60 minutes and a half hour is 30 minutes. The “This Unit” section explains that grade 2 students learn to tell and write time to the nearest minute and use a.m. and p.m. appropriately. The “Look Forward” section explains that in grade 3 students will solve addition and subtraction problems involving time, including finding start and end times.
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 use open number lines to subtract tens from two-digit numbers. Students start by counting back by tens and then subtract using only the tens digits. The “Look Forward” section explains that students will next subtract two-digit numbers by breaking the subtrahend into tens and ones and will continue exploring other strategies for subtracting two-digit numbers throughout the unit.
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 2 “Daily Planner” also shows spaced retrieval across lessons and units. While students work on addition within 100, the planner includes spiral review with addition and subtraction word problems within 20, comparing numbers up to 100, skip-counting by twos, and addition and subtraction within 20. These review opportunities help students retrieve previously learned skills after time has passed while learning new strategies for addition.
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 2 “Daily Planner” also provides interleaved practice by combining current addition-within-100 skills with prior skills from other units. While students learn to add using number lines, compensation, place value blocks, regrouping, place value charts, and strategy selection, the unit also includes spiral review with word problems, comparing numbers, skip counting, and addition and subtraction within 20. This structure requires students to continue applying previously learned concepts while working on new grade 2 addition strategies.
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 6, lesson 6.2 “Make and Interpret Bar Graphs,” students interpret, analyze, and evaluate models and representations for data. Students first make a picture graph using pattern block shapes and then compare the picture graph to a bar graph showing the same data. The “Compare and Talk” prompt asks students to explain what is similar and different about the two graphs. This task requires students to interpret both representations, analyze how the same data are shown in different ways, and evaluate the relationship between pictographs and bar graphs.
In unit 8, lesson 8.1 “Add Tens or Hundreds,” students analyze place value models and representations for addition. Students use place value blocks to find sums when adding 10 or 100 and then compare different representations of the same problem. In the “Compare and Talk” task students compare Shane and Carly’s work for finding 247 + 30 and explain the differences and similarities between their strategies. These tasks require students to analyze representations and evaluate how different models or strategies represent the same mathematical concept.
Evaluation for 5.1b
In unit 8, lesson 8.2 “Use Number Lines to Add,” students create models to represent mathematical situations. Students match number line models to addition equations and then use a number line to find 254 + 235 by breaking apart one addend. This task requires students to create and interpret jumps on a number line to represent addition within 1,000.
In the same lesson, students continue creating models by using number lines to represent two-digit and three-digit addition problems. Students show jumps for 10s, 100s, and ones, and then connect the model to an addition equation. These tasks require students to create visual representations that show how addends are decomposed and recombined to find a sum.
Evaluation for 5.1c
The materials include questions and tasks that provide opportunities for students to apply conceptual understanding to new problem situations and contexts. In lesson 8.3, students apply conceptual understanding of place value and addition by decomposing a three-digit number and using a number line to add 100s, 10s, and ones in separate jumps, demonstrating their ability to select and apply an appropriate strategy in a new and non-routine addition context.
In unit 12, lesson 12.4 “Solve Problems Involving Equal Groups,” students apply conceptual understanding to equal-groups problem situations. Students draw models to solve problems such as four bins with five animals in each bin and 10 superhero toys arranged in rows of five. Students also write their own equal-groups problem using apples. These tasks require students to apply conceptual understanding of equal groups, rows, and repeated groups in new contextual situations.
Evaluation for 5.2a
Unit 3 “Subtraction Within 100” provides tasks designed to build fluency with grade-level subtraction. The unit summary explains that students subtract within 100 using a variety of models and strategies, including subtracting a one-digit number from a two-digit number, subtracting 10s from two-digit numbers, subtracting with and without regrouping, and using multiple subtraction strategies. These repeated opportunities support fluency with subtraction within 100.
The unit 3 “Daily Planner” also includes fluency-focused practice and games across the unit. Students practice subtracting by breaking apart numbers, subtracting multiples of 10, subtracting two-digit numbers, and solving subtraction word problems. The planner also includes spiral review games such as “On a Roll: Add Within 100,” helping students continue retrieving and applying addition and subtraction skills while building fluency with grade-level computation.
Evaluation for 5.2b
In unit 3, lesson 3.10 “Choose a Way to Subtract,” students practice efficient, flexible, and accurate mathematical procedures. Students solve one subtraction problem using compensation and another using a place value chart. Students then solve additional subtraction problems using any method. These tasks give students opportunities to select, apply, and compare subtraction procedures based on the numbers in each problem.
In unit 8, lesson 8.3 “Record 3-Digit Addition Strategies,” students practice flexible and accurate addition procedures. Students use a number line, compensation, and numbers and symbols to solve three-digit addition problems. For example, students find 538 + 397 using compensation and show their work in two ways. These tasks give students practice applying efficient strategies while accurately recording their mathematical thinking.
Evaluation for 5.2c
In unit 8, lesson 8.3 “Record 3-Digit Addition Strategies,” students evaluate procedures, processes, and solutions for efficiency, flexibility, and accuracy. Students compare a number line strategy with Devon’s symbolic strategy for finding 526 + 272, and explain how the two methods are alike and different. Students also find sums using a number line and numbers and symbols, which requires them to compare representations and evaluate whether each strategy produces the correct sum.
In unit 3, lesson 3.10 “Choose a Way to Subtract,” students evaluate subtraction procedures by choosing among strategies. Students solve subtraction problems using compensation, a place value chart, or any method they select. This task requires students to determine which procedure is appropriate for each problem, apply the strategy accurately, and evaluate whether their method is efficient and produces a reasonable difference.
Evaluation for 5.2d
Grade 2 materials embed supports for educators to guide students toward increasingly efficient approaches. In unit 3, lesson 3.10 “Choose a Way to Subtract,” students first use specific strategies, such as compensation and a place value chart, before choosing any method to solve additional subtraction problems. This lesson structure supports educators in moving students from assigned strategies toward independent selection of efficient subtraction methods.
In unit 8, lesson 8.3 “Record 3-Digit Addition Strategies,” the materials guide students toward increasingly efficient addition approaches. Students begin with number-line models, then compare that work to a symbolic strategy that breaks apart addends by place value. Later tasks ask students to use a number line, compensation, and numbers and symbols to solve problems. This progression helps educators guide students from visual models toward more efficient symbolic addition strategies.
Evaluation for 5.3a
Unit 2, “Daily Planner,” “Addition Within 100,” explicitly states how the conceptual and procedural emphasis of the TEKS are addressed. The unit summary explains that students add within 100 using a variety of models and strategies. The major unit objectives include adding two numbers within 100 with and without regrouping and using and explaining a variety of addition strategies. The listed TEKS connect these strategies to place value, properties of operations, and algorithms.
Unit 3, “Daily Planner,” “Subtraction Within 100,” also explicitly states how conceptual and procedural emphasis of the TEKS are addressed. The unit summary explains that students subtract within 100 using a variety of models and strategies. The objectives include subtracting from two-digit numbers with and without regrouping and using and explaining a variety of subtraction strategies. The listed TEKS connect subtraction procedures to place value understanding, mental strategies, algorithms, and problem solving.
Evaluation for 5.3b
In unit 8, lesson 8.2 “Use Number Lines to Add,” students use pictorial and abstract representations as required by the TEKS. Students match number line models to addition equations, then use number lines to add within 1,000 by breaking apart one addend. Students connect the visual jumps on the number line to symbolic addition equations.
In unit 11, lesson 11.3 “Relate Halves, Fourths, and Eighths,” students use concrete and representational models to understand fractional parts. Students fold and cut paper to make halves and fourths, compare the size of one half and one fourth, and reason about what would happen if a whole were partitioned into eighths. Students then complete statements explaining that more equal parts make smaller parts and fewer equal parts make larger parts. These tasks connect concrete paper folding models, visual fraction representations, and abstract fraction language.
Evaluation for 5.3c
Unit 11, lesson 11.3 “Relate Halves, Fourths, and Eighths,” includes supports for students in connecting, creating, defining, and explaining concrete and representational models to abstract fraction concepts. Students create concrete fraction models by folding and cutting one paper into halves and another paper into fourths. Students compare a half to a fourth, define which part is larger, and explain what happens to the size of the parts when a whole is divided into more or fewer equal parts. Students then connect the concrete models to abstract fraction language by completing statements that more equal parts create smaller parts and fewer equal parts create larger parts.
Unit 12, lesson 12.4 “Solve Problems Involving Equal Groups,” includes supports for students in connecting, creating, defining, and explaining models to abstract equal-groups concepts. Students draw models to represent contextual problems, such as four bins with five animals in each bin or 10 superhero toys arranged in rows of five. Students define the number of groups, the number in each group, and the total or number of rows, then explain how the drawing represents the problem situation. These supports help students connect representational models to abstract equal-groups reasoning and early multiplication and division concepts.
Evaluation for 5.4a
In unit 1, lesson 1.8 “Solve Word Problems (Part 2),” students develop academic mathematical language using visual models and written representations. Students use strip models to represent addition and subtraction word problems, identify known and unknown quantities, and write number sentences to match each situation. Students also write a story problem to match an addition sentence, which gives them an opportunity to connect mathematical vocabulary, visual models, number sentences, and oral or written explanations.
In unit 10, lesson 10.1 “Identify 3D Shapes and Their Attributes,” students develop academic mathematical language through visual models of three-dimensional shapes. Students name and compare shapes such as cube, cylinder, cone, and sphere, then complete definitions for face, edge, vertex, and vertices. Students also count faces, edges, and vertices and match shapes to descriptions such as “has 1 vertex and 1 circular face,” “has 0 vertices and 0 faces,” and “has 2 circular faces.” These tasks support students in using formal geometric vocabulary in context.
Evaluation for 5.4b
Unit 10, lesson 10.1 “Identify 3D Shapes and Their Attributes,” scaffolds students’ development and use of academic mathematical vocabulary in context. Students complete definitions for key geometric terms, including face as a flat surface of a three-dimensional shape, edge as a line where two faces meet, vertex as a point where edges meet, and vertices as the plural form of vertex. Students then use this vocabulary to describe rectangular prisms, triangular prisms, cones, cylinders, and spheres.
In unit 10, lesson 10.2 “Sort 3D Shapes,” students continue using academic vocabulary in context as they sort three-dimensional shapes by attributes. Students sort shapes into categories such as rectangular prisms and not rectangular prisms, cylinders and cones, shapes with 12 edges and fewer than 12 edges, shapes with triangular faces and no triangular faces, and shapes with no vertices, one vertex, or more than one vertex. These tasks support students in applying formal vocabulary such as faces, edges, vertices, rectangular prisms, triangular prisms, cylinders, cones, and curved surfaces while explaining how shapes are classified.
Evaluation for 5.4c
Unit 10, lesson 10.2 “Sort 3D Shapes,” includes embedded support for students to apply appropriate mathematical language through vocabulary, syntax, and discourse. Students sort three-dimensional shapes in multiple ways and explain the groups they made, including rectangular prisms and not rectangular prisms, cylinders and cones, shapes with triangular faces and no triangular faces, and shapes with no vertices, one vertex, or more than one vertex. The lesson also includes a discussion task in which Emmy and Brandon disagree about whether a shape is a rectangular prism or a cube. Students must explain who is correct using precise geometric language and defining attributes.
In unit 2, lesson 2.5 “Record Addition Strategies,” students apply mathematical language through comparison, explanation, and discourse about addition strategies. In the “Compare and Talk” task, students compare Carmen and Adam’s work for finding 27 + 18, where one student uses a number line and the other uses numbers and symbols. Students explain the differences and similarities between the strategies, using language that connects representations, compensation, number lines, numbers, and symbols. The grade 2 “Instructional Design” document also identifies this lesson as an example of students communicating mathematical ideas using multiple representations and discussing how each representation shows compensation being used to add.
Evaluation for 5.5a
Unit 12, lesson 12.2 “Join Equal Groups,” appropriately integrates the TEKS process standards as students apply mathematics to real-world equal-groups situations. Students model stories about picture frames, popsicle sticks, stickers, marching band rows, returned library books, parking spaces, shelves of board games, relay teams, and bagels. Students draw models, complete sentences, write repeated addition equations, and explain how the equal groups represent each situation. These tasks connect problem solving, tool use, representations, mathematical relationships, and communication.
In unit 4, lesson 4.3, students solve one-step word problems using strip models and number sentences. Students select appropriate representations, use the strip model to organize the information in the problem, and explain why a number sentence matches the visual model. These tasks integrate the TEKS process standards by requiring students to apply mathematics to real-world situations, select tools and models, communicate mathematical ideas using representations and symbols, and justify their thinking.
Evaluation for 5.5b
The “Instructional Design” document includes a section titled “Mathematical Process Standards,” which describes how the TEKS process standards are incorporated and connected throughout the course. The document explains that the program’s step-by-step lesson plans and activities are specifically designed to target the seven TEKS process standards and help students make mathematical connections, communicate precisely, and solve complex problems in the classroom and in everyday life.
The same “Instructional Design” document describes how students engage with process standards through tools, representations, discourse, and justification across the course. For example, the document explains that students solve problems using physical objects and manipulatives, diagrams and visual representations, and different strategies. The document also explains that students communicate mathematical ideas using multiple representations, including symbols, diagrams, graphs, and language. This guidance provides a course-level description of how process standards are embedded throughout grade-level instruction.
Evaluation for 5.5c
Unit 10, “Daily Planner,” “Geometry,” provides a unit-level description of how the TEKS process standards are incorporated and connected throughout the unit. The unit summary explains that students classify, sort, and compose two- and three-dimensional shapes and decompose two-dimensional shapes. The unit overview lists process standards 2.1.B, 2.1.F, and 2.1.G, connecting the geometry work to problem solving, analyzing mathematical relationships, and explaining or justifying mathematical ideas using precise language.
The unit 10 “Daily Planner” also shows how the process standards connect across individual lessons in the unit. For example, lesson 10.1 focuses on classifying cubes, rectangular prisms, triangular prisms, spheres, cylinders, and cones based on their attributes and identifying faces, edges, and vertices. Lesson 10.2 extends that work by having students sort three-dimensional shapes based on geometric attributes. These unit-level descriptions show how process standards are incorporated across the unit through classification, comparison, analysis, and mathematical communication.
Evaluation for 5.5d
The “Second 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 specific lessons in which the standard appears. For example, process standard 2.1.A is connected to lessons 1.7, 1.8, 4.3, 4.4, 4.5, 12.1, 12.2, 12.3, and 12.4, showing where students apply mathematics to real-world situations.
The same “Second Grade At-a-Glance” standards document provides lesson-level alignment for additional process standards. A chart identifies lessons connected to 2.1.B for using a problem-solving model, 2.1.C for selecting tools and techniques, 2.1.D for communicating mathematical ideas using multiple representations, 2.1.E for creating and using representations, 2.1.F for analyzing mathematical relationships, and 2.1.G for explaining and justifying mathematical ideas. This standards chart functions as an overview showing how TEKS process standards are incorporated into individual lessons.
5.1 Development of Conceptual Understanding
5.1a
Questions and tasks require students to interpret, analyze, and evaluate models and representations for mathematical concepts and situations.
Questions and tasks require students to interpret, analyze, and evaluate models and representations for mathematical concepts and situations.
3 out of 3 points
Evaluation for 5.1a
Evaluation for 5.1a
Questions and tasks require students to interpret, analyze, and evaluate models and representations for mathematical concepts and situations.
3 out of 3 points
In unit 8, lesson 8.1 “Add Tens or Hundreds,” students analyze place value models and representations for addition. Students use place value blocks to find sums when adding 10 or 100 and then compare different representations of the same problem. In the “Compare and Talk” task students compare Shane and Carly’s work for finding 247 + 30 and explain the differences and similarities between their strategies. These tasks require students to analyze representations and evaluate how different models or strategies represent the same mathematical concept.
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 the same lesson, students continue creating models by using number lines to represent two-digit and three-digit addition problems. Students show jumps for 10s, 100s, and ones, and then connect the model to an addition equation. These tasks require students to create visual representations that show how addends are decomposed and recombined to find a sum.
5.1c
Questions and tasks provide opportunities for students to apply conceptual understanding to new problem situations and contexts.
Questions and tasks provide opportunities for students to apply conceptual understanding to new problem situations and contexts.
1 out of 1 points
Evaluation for 5.1c
Evaluation for 5.1c
Questions and tasks provide opportunities for students to apply conceptual understanding to new problem situations and contexts.
1 out of 1 points
In unit 12, lesson 12.4 “Solve Problems Involving Equal Groups,” students apply conceptual understanding to equal-groups problem situations. Students draw models to solve problems such as four bins with five animals in each bin and 10 superhero toys arranged in rows of five. Students also write their own equal-groups problem using apples. These tasks require students to apply conceptual understanding of equal groups, rows, and repeated groups in new contextual 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
The unit 3 “Daily Planner” also includes fluency-focused practice and games across the unit. Students practice subtracting by breaking apart numbers, subtracting multiples of 10, subtracting two-digit numbers, and solving subtraction word problems. The planner also includes spiral review games such as “On a Roll: Add Within 100,” helping students continue retrieving and applying addition and subtraction skills while building fluency with grade-level computation.
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 8, lesson 8.3 “Record 3-Digit Addition Strategies,” students practice flexible and accurate addition procedures. Students use a number line, compensation, and numbers and symbols to solve three-digit addition problems. For example, students find 538 + 397 using compensation and show their work in two ways. These tasks give students practice applying efficient strategies while accurately recording their mathematical thinking.
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 3, lesson 3.10 “Choose a Way to Subtract,” students evaluate subtraction procedures by choosing among strategies. Students solve subtraction problems using compensation, a place value chart, or any method they select. This task requires students to determine which procedure is appropriate for each problem, apply the strategy accurately, and evaluate whether their method is efficient and produces a reasonable difference.
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 8, lesson 8.3 “Record 3-Digit Addition Strategies,” the materials guide students toward increasingly efficient addition approaches. Students begin with number-line models, then compare that work to a symbolic strategy that breaks apart addends by place value. Later tasks ask students to use a number line, compensation, and numbers and symbols to solve problems. This progression helps educators guide students from visual models toward more efficient symbolic addition strategies.
5.3 Balance of Conceptual Understanding and Procedural Fluency
5.3a
Materials explicitly state how the conceptual and procedural emphasis of the TEKS are addressed.
Materials explicitly state how the conceptual and procedural emphasis of the TEKS are addressed.
2 out of 2 points
Evaluation for 5.3a
Evaluation for 5.3a
Materials explicitly state how the conceptual and procedural emphasis of the TEKS are addressed.
2 out of 2 points
Unit 3, “Daily Planner,” “Subtraction Within 100,” also explicitly states how conceptual and procedural emphasis of the TEKS are addressed. The unit summary explains that students subtract within 100 using a variety of models and strategies. The objectives include subtracting from two-digit numbers with and without regrouping and using and explaining a variety of subtraction strategies. The listed TEKS connect subtraction procedures to place value understanding, mental strategies, algorithms, and problem solving.
5.3b
Questions and tasks include the use of concrete models and manipulatives, pictorial representations (figures/drawings), and abstract representations, as required by the TEKS.
Questions and tasks include the use of concrete models and manipulatives, pictorial representations (figures/drawings), and abstract representations, as required by the TEKS.
3 out of 3 points
Evaluation for 5.3b
Evaluation for 5.3b
Questions and tasks include the use of concrete models and manipulatives, pictorial representations (figures/drawings), and abstract representations, as required by the TEKS.
3 out of 3 points
In unit 11, lesson 11.3 “Relate Halves, Fourths, and Eighths,” students use concrete and representational models to understand fractional parts. Students fold and cut paper to make halves and fourths, compare the size of one half and one fourth, and reason about what would happen if a whole were partitioned into eighths. Students then complete statements explaining that more equal parts make smaller parts and fewer equal parts make larger parts. These tasks connect concrete paper folding models, visual fraction representations, and abstract fraction language.
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 12, lesson 12.4 “Solve Problems Involving Equal Groups,” includes supports for students in connecting, creating, defining, and explaining models to abstract equal-groups concepts. Students draw models to represent contextual problems, such as four bins with five animals in each bin or 10 superhero toys arranged in rows of five. Students define the number of groups, the number in each group, and the total or number of rows, then explain how the drawing represents the problem situation. These supports help students connect representational models to abstract equal-groups reasoning and early multiplication and division concepts.
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 10, lesson 10.1 “Identify 3D Shapes and Their Attributes,” students develop academic mathematical language through visual models of three-dimensional shapes. Students name and compare shapes such as cube, cylinder, cone, and sphere, then complete definitions for face, edge, vertex, and vertices. Students also count faces, edges, and vertices and match shapes to descriptions such as “has 1 vertex and 1 circular face,” “has 0 vertices and 0 faces,” and “has 2 circular faces.” These tasks support students in using formal geometric vocabulary in context.
5.4b
Materials include embedded teacher guidance to scaffold and support students' development and use of academic mathematical vocabulary in context.
Materials include embedded teacher guidance to scaffold and support students' development and use of academic mathematical vocabulary in context.
1 out of 1 points
Evaluation for 5.4b
Evaluation for 5.4b
Materials include embedded teacher guidance to scaffold and support students' development and use of academic mathematical vocabulary in context.
1 out of 1 points
In unit 10, lesson 10.2 “Sort 3D Shapes,” students continue using academic vocabulary in context as they sort three-dimensional shapes by attributes. Students sort shapes into categories such as rectangular prisms and not rectangular prisms, cylinders and cones, shapes with 12 edges and fewer than 12 edges, shapes with triangular faces and no triangular faces, and shapes with no vertices, one vertex, or more than one vertex. These tasks support students in applying formal vocabulary such as faces, edges, vertices, rectangular prisms, triangular prisms, cylinders, cones, and curved surfaces while explaining how shapes are classified.
5.4c
Materials include embedded teacher guidance to support the application of appropriate mathematical language to include vocabulary, syntax, and discourse to include guidance to support mathematical conversations that provide opportunities for students to hear, refine, and use math language with peers and develop their math language toolkit over time as well as guide teachers to support student responses using exemplar responses to questions and tasks.
Materials include embedded teacher guidance to support the application of appropriate mathematical language to include vocabulary, syntax, and discourse to include guidance to support mathematical conversations that provide opportunities for students to hear, refine, and use math language with peers and develop their math language toolkit over time as well as guide teachers to support student responses using exemplar responses to questions and tasks.
6 out of 6 points
Evaluation for 5.4c
Evaluation for 5.4c
Materials include embedded teacher guidance to support the application of appropriate mathematical language to include vocabulary, syntax, and discourse to include guidance to support mathematical conversations that provide opportunities for students to hear, refine, and use math language with peers and develop their math language toolkit over time as well as guide teachers to support student responses using exemplar responses to questions and tasks.
6 out of 6 points
In unit 2, lesson 2.5 “Record Addition Strategies,” students apply mathematical language through comparison, explanation, and discourse about addition strategies. In the “Compare and Talk” task, students compare Carmen and Adam’s work for finding 27 + 18, where one student uses a number line and the other uses numbers and symbols. Students explain the differences and similarities between the strategies, using language that connects representations, compensation, number lines, numbers, and symbols. The grade 2 “Instructional Design” document also identifies this lesson as an example of students communicating mathematical ideas using multiple representations and discussing how each representation shows compensation being used to add.
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
In unit 4, lesson 4.3, students solve one-step word problems using strip models and number sentences. Students select appropriate representations, use the strip model to organize the information in the problem, and explain why a number sentence matches the visual model. These tasks integrate the TEKS process standards by requiring students to apply mathematics to real-world situations, select tools and models, communicate mathematical ideas using representations and symbols, and justify their thinking.
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 describes how students engage with process standards through tools, representations, discourse, and justification across the course. For example, the document explains that students solve problems using physical objects and manipulatives, diagrams and visual representations, and different strategies. The document also explains that students communicate mathematical ideas using multiple representations, including symbols, diagrams, graphs, and language. This guidance provides a course-level description of how process standards are embedded throughout 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
The unit 10 “Daily Planner” also shows how the process standards connect across individual lessons in the unit. For example, lesson 10.1 focuses on classifying cubes, rectangular prisms, triangular prisms, spheres, cylinders, and cones based on their attributes and identifying faces, edges, and vertices. Lesson 10.2 extends that work by having students sort three-dimensional shapes based on geometric attributes. These unit-level descriptions show how process standards are incorporated across the unit through classification, comparison, analysis, and mathematical communication.
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 “Second Grade At-a-Glance” standards document provides lesson-level alignment for additional process standards. A chart identifies lessons connected to 2.1.B for using a problem-solving model, 2.1.C for selecting tools and techniques, 2.1.D for communicating mathematical ideas using multiple representations, 2.1.E for creating and using representations, 2.1.F for analyzing mathematical relationships, and 2.1.G for explaining and justifying mathematical ideas. This standards chart functions as an overview showing how TEKS process standards are incorporated into individual lessons.
Rubric Section 6
Productive Struggle
Materials support students in applying disciplinary practices to productive problem-solving, including explaining and revising their thinking.
Total
100% (22 out of 22 points)
Evaluation for 6.1a
In unit 1, lesson 1.2, students think mathematically and make sense of mathematics as they use ten frames and counters to solve addition problems. Students represent seven on one ten frame and five on another ten frame, then make 10 by moving three counters from the second frame to fill the first frame. Educator guidance explains that breaking five into three and two supports students in seeing why 7 + 3 and then 10 + 2 is more efficient than counting on from seven. This task supports students in reasoning about number relationships, decomposing addends, and making sense of addition strategies.
In unit 6, lesson 6.6, students think mathematically, persevere through solving problems, and make sense of mathematics during independent practice with real-world measurement and subtraction situations. Students interpret measurement contexts, determine appropriate operations, and represent their thinking with number sentences, diagrams, and measurements. Then students evaluate whether proposed solutions are reasonable. In questions 1–8, students compare lengths and apply mathematical reasoning to determine whether boards can be cut into specified pieces, supporting perseverance and sense-making in contextual problem solving.
Evaluation for 6.1b
In unit 3, lesson 3.3, students understand that problems can be represented and solved in multiple ways as they share and compare subtraction strategies. Students examine classmates’ approaches, discuss how each strategy represents the subtraction situation, and recognize that different methods can accurately lead to the same solution. These tasks support students in understanding, explaining, and justifying that subtraction problems can be represented and solved in more than one way.
In unit 3, lesson 3.10, students solve subtraction problems using a strategy of their choice and compare multiple solution methods. Students determine which strategies are most efficient based on the numbers and the context of the problem. By explaining their selected strategies and comparing them with other methods, students develop flexible problem-solving skills and justify that more than one approach can be used to solve the same mathematical task.
Evaluation for 6.1c
In unit 3, lesson 3.2, students make sense of mathematics through opportunities to do, write about, and discuss subtraction strategies. Students use number lines, counting strategies, and written solutions to represent how subtraction methods work. Students record and analyze their reasoning as they apply strategies and correct errors in mathematical work. These tasks require students to connect representations, written explanations, and mathematical reasoning.
In unit 1, lesson 1.2, students make sense of mathematics by identifying an error and writing about how to correct it. In question 16, students identify Brett’s error and explain how to fix it. This task requires students to analyze mathematical reasoning, write about the correction process, and communicate why the revised strategy or solution makes sense.
Evaluation for 6.2a
Unit 2, lesson 2.4, supports educators in guiding students to share and reflect on their problem-solving approaches. Students evaluate different strategies, explain which method they prefer and why, and consider how listening to classmates’ ideas may influence their own thinking. These prompts support students in reflecting on the efficiency and usefulness of different strategies and justifying their choices based on mathematical understanding.
Unit 3, lesson 3.7, guides students to discuss and explain the strategy they used to solve subtraction problems. Students compare two different strategies and discuss similarities and differences between the methods. These opportunities support students in sharing, explaining, and reflecting on their problem-solving approaches while using mathematical reasoning to justify their thinking.
Evaluation for 6.2b
Unit 9, lesson 9.3, includes prompts and guidance to support educators in providing explanatory feedback as students tell time to the minute. The educator notes above questions 8 and 16 provide guidance to support students’ understanding of how the hour hand and minute hand work together. The “Tip for Support” recommends using a clock manipulative so students can see how the hour hand moves as the minute hand moves. This support helps educators respond to student misconceptions with a concrete model and explanatory feedback.
Unit 12, lesson 12.1, guides educators in providing explanatory feedback as students identify even and odd numbers. The “Tip for Support” recommends that educators guide students in creating pairs of items to determine whether all items have a pair or whether one item is left over. This guidance helps educators address student misunderstandings by connecting the concept of even and odd numbers to a concrete pairing model.
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 6, lesson 6.6, students think mathematically, persevere through solving problems, and make sense of mathematics during independent practice with real-world measurement and subtraction situations. Students interpret measurement contexts, determine appropriate operations, and represent their thinking with number sentences, diagrams, and measurements. Then students evaluate whether proposed solutions are reasonable. In questions 1–8, students compare lengths and apply mathematical reasoning to determine whether boards can be cut into specified pieces, supporting perseverance and sense-making in contextual problem solving.
6.1b
Materials support students in understanding, explaining, and justifying that there can be multiple ways to represent and solve problems and complete tasks.
Materials support students in understanding, explaining, and justifying that there can be multiple ways to represent and solve problems and complete tasks.
6 out of 6 points
Evaluation for 6.1b
Evaluation for 6.1b
Materials support students in understanding, explaining, and justifying that there can be multiple ways to represent and solve problems and complete tasks.
6 out of 6 points
In unit 3, lesson 3.10, students solve subtraction problems using a strategy of their choice and compare multiple solution methods. Students determine which strategies are most efficient based on the numbers and the context of the problem. By explaining their selected strategies and comparing them with other methods, students develop flexible problem-solving skills and justify that more than one approach can be used to solve the same mathematical task.
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
In unit 1, lesson 1.2, students make sense of mathematics by identifying an error and writing about how to correct it. In question 16, students identify Brett’s error and explain how to fix it. This task requires students to analyze mathematical reasoning, write about the correction process, and communicate why the revised strategy or solution makes sense.
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
Unit 3, lesson 3.7, guides students to discuss and explain the strategy they used to solve subtraction problems. Students compare two different strategies and discuss similarities and differences between the methods. These opportunities support students in sharing, explaining, and reflecting on their problem-solving approaches while using mathematical reasoning to justify their thinking.
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 12, lesson 12.1, guides educators in providing explanatory feedback as students identify even and odd numbers. The “Tip for Support” recommends that educators guide students in creating pairs of items to determine whether all items have a pair or whether one item is left over. This guidance helps educators address student misunderstandings by connecting the concept of even and odd numbers to a concrete pairing model.