Program Information
- ISBN
- 9798213463149
- Technical Specifications: Checklist
- Tech Specs: Checklist (pdf 517.36 KB)
- Technical Specifications: Professional Development
- Tech Specs: Professional Development (pdf 516.5 KB)
ENVISION+ TEXAS MATHEMATICS 2027 (PRINT + DIGITAL), GRADE 4
Math (English) Grade 4
SBOE Approved | IMRA 2025
Commissioner Recommended
Publisher: Savvas Learning Company LLC
Copyright: 2027
Series includes:
Rubric: Mathematics K–12 (English) | 2025 (Download Not Available)
* Some programs submit evidence for only part of a standard, while others submit all sections. A 100% score means this program met all the expectations it submitted.
Quality Review
Standards Alignment
Rubric Section
| Grade | TEKS % | ELPS % |
|---|---|---|
| Grade 4 | 100% | 100% |
Criteria for Quality
Rubric Section 1
Implementation Quality
Materials support educators in effective implementation through intentional course, unit, and lesson-level design.
Total
100% (28 out of 28 points)
Evaluation for 1.1a
The grade 4 materials demonstrate complete alignment with the Texas Essential Knowledge and Skills (TEKS) and English Language Proficiency Standards (ELPS) through comprehensive "Scope and Sequence" documents for the grade level. The grade 4 materials include itemized math TEKS, ELPS, and concepts taught, and often revisited, throughout the curriculum in the "Scope and Sequence" pages. The grade 4 materials include the vertical "K–5 Scope and Sequence" which aligns the TEKS statements to enVision Plus Texas Mathematics Topics.
Evaluation for 1.1b
The grade 4 materials include three options for using the materials in the "Scope and Sequence Pacing Guide Document(s)," with clear and flexible usage recommendations. enVision Plus Mathematics Grade 4 "Scope and Sequence Pacing Guides" provide three implementation options. For example, the "165-Day Scope and Sequence," "180-Day Scope and Sequence," and "210-Day Scope and Sequence" options align with a variety of district instructional calendars. The grade 4 materials include suggested pacing for various instructional calendars. For example, the "180-Day Scope and Sequence" for Topic 5: "Divide by 1-Digit Numbers" indicates that the topic contains 17 days for instruction, differentiation, review, and assessment. The "210-day Pacing Guide" provides 20 days divided among these different lesson purposes. Each day is 45–70 minutes across all scope and sequence options.
Evaluation for 1.1c
enVision Plus Mathematics Grade 4 Program Overview materials explain each unit and its sequence within the grade level and the grade band, connecting content to prior and future learning. The materials provide an explanation for the mathematical concepts and instructional strategies in the program design. The grade 4 materials provide a thorough rationale for the content and instructional strategies underlying the program design. The "Grade 4 Content Organization Rationale" states, "groups of one or more topics are organized around a key concept that supports coherence and connections in that group." For example, Topics 3–5 focus on "the properties of operations." The grade 4 materials explain how concepts connect throughout the course. For example, the "Math Background" section at the start of each topic describes the key concepts addressed in the topic, while the "Coherence" section explains how the concepts connect across previous grades, within the current grade, and in future grades in the "Look Back," "In This Topic," and "Look Forward" sections.
Evaluation for 1.1d
The grade 4 materials include protocols with corresponding guidance for unit and lesson internalization. For example, the "Additional Support for Successful Implementation" page in the Program Overview details the protocols and guidance available. The grade 4 materials include protocols with corresponding guidance for unit internalization. For example, the "Teacher's Topic Internalization Protocol" guides teachers to internalize the unit and topics to understand key standards, unit objectives, and vocabulary. The grade 4 materials include protocols with corresponding guidance for unit internalization. For example, the "Teacher's Lesson Internalization Protocol" includes processes for teachers to internalize the goals, transitions, support, and materials.
Evaluation for 1.1e
The grade 4 materials include resources designed to support instructional leaders in effectively implementing the program. For example, the enVision Plus Texas Mathematics Program Overview outlines the program's structure, philosophy, and instructional strategies. This overview helps instructional leaders understand the program's key components, such as problem-based learning, visual learning, and differentiated instruction. The grade 4 materials include guidance for instructional leaders in effectively implementing the program. For example, the Instructional Leaders Topic Internalization Protocol contains the questions in the Teacher's Lesson Internalization Protocol, as well as "Rationale," "Implementation," and "Extension" prompts for leaders to guide the internalization process.
Evaluation for 1.2a
The grade 4 materials include comprehensive unit overviews that provide the background content knowledge necessary to effectively teach the concepts in the unit. For instance, the "Math Background, Key Concepts" pages at the start of each topic in the Teacher's Edition describe key concepts for groups of one or more lessons in the topic and guide teachers to "direct students' attention to, and make explicit, the important concepts students need to understand in a lesson." The grade 4 materials include comprehensive unit overviews that provide the academic vocabulary necessary to effectively teach the concepts in the unit. For example, Topic 4: "Multiply by 2-Digit Numbers," includes a "Linguistic Accommodations" section that includes 14 words under the "Topic Vocabulary Support" enabling the effective teaching of the concepts in the unit.
Evaluation for 1.2b
The grade 4 materials supports families in Spanish for each unit, with suggestions on supporting the progress of their student. For example, the Family Engagement Resource includes information about the objectives of each topic and lesson's content, sample problems worked, and related home activities that can be printed or accessed digitally by families. The grade 4 materials contain supports for families in English for each unit, with suggestions on supporting the student's progress. For example, the digital Family Engagement interface offers digital resources designed to help families support their students' progress. Components include additional practice exercises, visual learning animations, videos, digital manipulatives, digital and analog games, a digital glossary, and academic vocabulary.
Evaluation for 1.3a
The grade 4 materials include comprehensive, structured, detailed lesson plans required to meet content and language standards of the lesson. For example, Lesson 6-10: "Understand Mixed Numbers," includes a "Language Objective" to "use comparative language. . ." and both "Language Routine" and "Targeted ELPS Support" sections to meet the standard. The grade 4 materials include the 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). For example, Lesson 10-7: "Equivalence with Metric Units of Capacity and Mass," includes two objectives, two pages of whole-group practice and discussion, four pages of independent work, an exit ticket, and an intervention activity to meet the lesson standards.
Evaluation for 1.3b
The grade 4 materials include a Topic Planner, which presents an overview of all the lessons within a topic and include the list of materials necessary to deliver the lesson. The grade 4 materials provide Lesson Plans including detailed information such as lists of materials, student and teacher resources, manipulatives, and activity pages or templates required to deliver each lesson effectively. The grade 4 materials provide Lesson Plans with timing suggestions for each part of the lesson. For instance, lessons are divided into "Steps," and each step has a suggested timing in the top margin represented by a clock.
Evaluation for 1.3c
The grade 4 materials guide teachers in understanding how lesson materials can also serve as extended practice, allowing students to complete them independently at their own pace during school or as homework. For example, the "Differentiation Library" Teacher's Guide provides guidance and materials for teachers to use in whole-class, small-group, individual activities, or centers and stations. It provides six different types of materials for extended practice, such as "Pick a Project," "Math and Literacy," "Amazing Contributions," "Stand Up and Think," "Hands-On Games," and "Fluency Practice." The grade 4 materials guide teachers in understanding how lesson materials can also serve as extended practice. For example, each lesson provides an Additional Practice Workbook to extend practice for each lesson.
1.1 Course-Level Design
1.1a
Materials include a scope and sequence outlining the TEKS, ELPS, and concepts taught in the course.
Materials include a scope and sequence outlining the TEKS, ELPS, and concepts taught in the course.
4 out of 4 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.
4 out of 4 points
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
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
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
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
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
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
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).
8 out of 8 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).
8 out of 8 points
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
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
Rubric Section 2
Progress Monitoring
Materials support educators in effective implementation through frequent, strategic opportunities to monitor and respond to student progress.
Total
100% (26 out of 26 points)
Evaluation for 2.1a
The grade 4 materials include a variety of assessments, including diagnostic, formative, and summative. The Program Overview describes the progress monitoring, diagnostic, formative, and summative assessments available in the program. Furthermore, item types are also described, including all item types found on the STAAR assessments. The grade 4 materials include multiple comprehensive diagnostic assessments with vocabulary, short answer, multiple-choice, diagram, and open-ended questions. The diagnostic assessment includes a variety of tasks with questions assessing multiple levels of understanding (Depth of Knowledge). The grade 4 materials include formative assessments, such as "Review What You Know," and summative assessments, such as "Topic Assessments" and "Unit Assessments," which vary in the types of tasks and questions.
Evaluation for 2.1b
The Grade 4 Assessment Sourcebook includes an "Assessment Guide" that defines each program assessment, including the intended purpose for each type. The "Assessment Guide" provides a table titled "Why and When to Assess" that defines diagnostic assessment, progress monitoring assessment, formative assessment, and summative assessment. It also shows why to use the assessment, when to use it, and the purpose of the results. The materials clearly explain the use of differing assessments and provide guidance, including addressing misconceptions, within the explanations.
Evaluation for 2.1c
The grade 4 materials include clear, specific, and actionable guidance for consistent administration of instructional assessments. For example, the Assessment Sourcebook contains the "Assessment Guide: How to Administer Assessments" document, which is easily readable with sections on "preparing for" and "monitoring" instructional assessments that ensure consistent and accurate administration. The grade 4 materials include guidance to support accurate administration of assessments. The "Assessment Guide" section of the Assessment Sourcebook includes a "What to Assess" section and a "How to Assess" section, which describe procedures for each assessment type. The "Assessment Data" section contains answer keys to align teacher understanding with assessment expectations.
Evaluation for 2.1d
The enVision Plus Mathematics Grade 4 assessments are designed to assess the TEKS and objectives of the course, unit, and lessons. For example, the Assessment Sourcebook includes an overview of the diagnostic, formative, and summative assessments used throughout the program. The grade 4 materials include Item analysis charts in the Assessment Sourcebook, demonstrating the alignment to the TEKS for each assessed item on the progress monitoring, diagnostic, and summative assessments. The grade 4 materials include lesson-level exit tickets used to assess "students' understanding of the lesson content."
Evaluation for 2.1e
EnVision Plus Mathematics Grade 4 is designed to assess course content using a variety of item types with appropriate cognitive complexity. The Assessment Sourcebook includes "Item Analysis Charts" that align each item on program progress monitoring, diagnostic, and summative assessments with a Depth of Knowledge (DOK) level. EnVision Plus Mathematics Grade 4 instructional assessments include TEKS-aligned items at varying levels of complexity. For example, instructional assessment incorporates TEKS-aligned items that assess different levels of complexity, such as procedural tasks, application of multiple skills to problems and tasks, and open-ended questions. EnVision Plus Mathematics Grade 4 instructional assessments include TEKS-aligned items at varying levels of complexity. For example, the materials include the option of digital assessments with technology-enhanced features such as drag-and-drop, hot spot, inline choice, and equation editor which vary in complexity.
Evaluation for 2.2a
EnVision Plus Mathematics Grade 4 instructional assessments provide consistent guides for teachers to interpret student performance located in the Assessment Sourcebook, such as interpreting scoring information to determine students' strengths, weaknesses, and/or gaps. For example, "Exit Tickets," "Quick Checks," and "Performance Tasks" provide TEKS alignment documents, scoring rubrics, and item analysis charts with correlations to intervention activities, as needed. EnVision Plus Mathematics Grade 4 scoring information provides guidance for interpreting student performance. For example, the Assessment Data Resource in the online assessments include a variety of class and individual reports that show results for an item, an assessment, or a group of assessments.
Evaluation for 2.2b
The grade 4 materials provide guidance for the use of included tasks and activities to respond to student trends in performance on assessments. For example, the "Scoring Guide" for the Topics 1–9, "Cumulative/Benchmark Assessment," provides an "Item Analysis Chart" correlating errors on item 16 to Intervention Lesson H32. The grade 4 materials provide guidance for the use of included tasks and activities to respond to student trends in performance on assessments. For example, the "Exit Ticket support" in the Teacher's Edition provides suggested strategies and follow-up activities to enhance responses. The grade 4 materials provide guidance for the use of included tasks and activities to respond to student trends in performance on assessments. For example, the "Quick Check" support section of each lesson provides recommended use of Differentiation Library lesson resources to respond to student performance on lesson quick checks.
Evaluation for 2.2c
The grade 4 materials include a "Student Progress and Growth Teacher Tool" for teachers to monitor students individually for each topic. The tracker is divided into the TEKS and has the corresponding lessons listed next to the TEKS and before the columns labeled before, during, and end of topic. The grade 4 materials include a "Student Progress and Growth Tracker Tool" where students record their scores on exit tickets. For example, the exit ticket for Lesson 3-6 asks students to use emoji faces to rank how they feel about meeting their math goal ("I can use area models and partial products to multiply") by selecting "I can," "With help," or "Not yet."
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.
9 out of 9 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.
9 out of 9 points
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.
2 out of 2 points
Evaluation for 2.1b
Evaluation for 2.1b
Materials include the definition and intended purpose for the types of instructional assessments included.
2 out of 2 points
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.
2 out of 2 points
Evaluation for 2.1c
Evaluation for 2.1c
Materials include teacher guidance to ensure consistent and accurate administration of instructional assessments.
2 out of 2 points
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
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
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
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
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
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% (27 out of 27 points)
Evaluation for 3.1a
The grade 4 materials include teacher guidance for differentiated instruction for students who have not yet reached proficiency on grade-level content and skills. For example, in Lesson 3-6: "Use Area Models and Partial Products to Multiply," a reteaching opportunity is provided with specific teacher guidance and example discussion questions to lead students through utilizing ten-dollar and one-dollar bills to model partial products. The grade 4 materials include teacher guidance for differentiated activities for students who have not yet reached proficiency on grade-level content and skills. For example, in Lesson 6-3: "Equivalent Fractions with Area Models," teachers are provided guidance on preventing student misconceptions related to fractions and two worksheets to practice this skill. The grade 4 materials include paired (scaffolded) lessons for students who have not reached mastery on a concept. For example, Lesson 5-6: "Partial Quotients to Divide" provides an option for either "Reteach to Build Understanding" practice page with step-by-step practice or "Intervention Activity" with concrete and pictorial division to address deficiencies.
Evaluation for 3.1b
The grade 4 materials include pre-teaching or embedded supports for unfamiliar vocabulary in text. For example, Topic 1: "Place-Value Understandings," includes both a "Vocabulary Activity" for small-group student discussion of place value vocabulary and an "Academic Vocabulary" mini-lesson for teachers to directly instruct content vocabulary. The grade 4 materials include pre-teaching or embedded supports for unfamiliar references in text. For example, in Lesson 10-6: "Equivalence with Metric Units of Length," teachers are given explicit guidance for leading a class discussion on measurement unit vocabulary with differentiated ELPS supports, followed by a student think-pair-share utilizing this new language.
Evaluation for 3.1c
The grade 4 materials include differentiated instruction, such as an "Early Finishers" component with each lesson to continue building depth of knowledge within the grade level. For instance, Lesson 8-8: "Estimate Sums and Differences of Decimals," has "Early Finishers" prompts utilizing additional decimal addends. The grade 4 materials include enrichment through topic-wide projects and lesson-specific Enrichment pages for each lesson within the curriculum, designed for students who have demonstrated proficiency in the grade-level content. For instance, Topic 4: "Multiply by 2-Digit Numbers," provides four STEAM-based projects, and Lesson 4-5: "Use Area Models and Partial Products to Multiply 2-Digit Numbers," offers an "Enrichment 4–5" practice page. The grade 4 materials include sidebar notes with differentiated extension questions and/or activities. For example, in Lesson 10-4: "A Pint's a Pound," teachers are provided notes to support students' different needs when they create their own real-world water problems from previous work.
Evaluation for 3.2a
The grade 4 materials include explicit prompts to support the teacher in modeling the concept(s) to be learned. For example, in Lesson 2-6: "Add Multi-Digit Numbers Visual Learning," the teacher is provided explicit prompts to lead the "Classroom Conversation" to explain the concepts of adding large numbers. The grade 4 materials include explicit prompts to support the teacher in explaining the concept(s) to be learned. For example, in Lesson 10-2: "Equivalence with Customary Units of Capacity Guided Practice," the teacher is given prompts to lead the student through a discussion of converting units of measure. The grade 4 materials include explicit guidance to support the teacher in modeling the concept(s) to be learned. For instance, in Topic 3: "Math Background, Key Concepts, Multiply by one-Digit Numbers," teachers are given visual and written examples of each strategy used for multiplication in the unit. The grade 4 materials include explicit guidance to support the teacher in explaining the concept(s) to be learned. For example, in Topic 10: "Divide by One-Digit Numbers," the "Build G.R.I.T" section includes a sample classroom conversation, giving teachers language to explain connecting multiplication patterns to division to a student.
Evaluation for 3.2b
The grade 4 materials provide explicit directions for effective lesson delivery by including detailed lesson plans with step-by-step instructions, suggested pacing, and differentiation strategies for each lesson. For example, Lesson 10-3: "Equivalence with Customary Units of Weight," has detailed directions for the four components of the lesson, "Investigate," "Connect," "Practice and Problem Solving," and "Assess and Differentiate," totaling approximately one hour. The grade 4 materials include teacher guidance for effective lesson facilitation and delivery using more than two instructional approaches. For example, in Lesson 12-3: "Ways to Save," students turn and talk in pairs about mystery numbers of coins, transition between whole-group, small-group, and independent activities, engage in class conversations to define, analyze, and explain advantages and disadvantages of saving methods, and then apply this math to real-world simple budgets.
Evaluation for 3.2c
The grade 4 materials provide a variety of practice types and opportunities designed to support effective implementation. The Program Overview organizes these practice opportunities by format (whole-group, small-group, or individual), and specifies whether each practice is guided, independent, or collaborative. The grade 4 materials include guidance for teachers to support effective implementation. For example, every "Let's Build" lesson provides teachers with guidance on structuring and implementing guided practice, independent work, small-group instruction, and problem solving practice. EnVision Plus Mathematics Grade 4 "Differentiation Library" includes a collection of hands-on games aligned to each topic for collaborative pair or small-group play, as well as activities where students work together to solve engaging problems. For example, the Topic 2, "Differentiation Library" provides a math-based story, two small-group "Stand Up and Think" problem-solving activities, two partner games, and an independent fluency practice page on the concept of addition and subtraction.
Evaluation for 3.3a
EnVision Plus Mathematics Grade 4 Teacher's Edition includes a "Linguistic Accommodations" section for every topic, which details the upcoming vocabulary in the unit and includes academic vocabulary to teach at different lessons corresponding with the ELPS. EnVision Plus Mathematics Grade 4 Teacher's Edition includes "Targeted ELPS Support" in each daily lesson plan to support various levels of language proficiency—as defined by the ELPS. For example, Lesson 4-2: "Estimate Products of 2-Digit Factors," provides guidance for teachers for language support for each level of teaching rounding to the nearest 10, pre-production points to numbers and beginning draws and labels numbers on a number line, intermediate draws and labels number lines and then rounds numbers to the nearest 10, high-intermediate explains what it means to round numbers to the nearest 10, and advanced explain how rounding numbers can be useful. The grade 4 materials detail ways teachers can build academic vocabulary as the unit progresses, such as definitions, sentence stems, and conversation guides. For example, the word evaluate is a frequently occurring academic vocabulary word that has an online "Academic Vocabulary Activity" and "Academic Vocabulary Teacher Guide, Notes" for teachers to explicitly instruct the word's pronunciation, definition, sentence stem, and a brief task that uses the word in context.
Evaluation for 3.3b
The grade 4 materials include implementation guidance to support teachers in effectively using the materials in state-approved bilingual/ESL programs by integrating the "English Language Proficiency Standards (ELPS) Correlations" and the "Linguistic Accommodations" into any state-approved bilingual/ESL program. EnVision Plus Mathematics Grade 4 Language Support Handbook provides clear implementation strategies to effectively support emergent bilingual students. For example, the "Language Demands in Mathematical Lessons Tool" contains a table and corresponding guidance that enumerates the ways the Reading, Writing, Listening, Speaking, and Representing ELPS strands are supported in the "Problem-Based Learning," "Visual Learning," and "Assess and Differentiate" lesson phases.
Evaluation for 3.3c
The grade 4 materials include embedded guidance for teachers to support emergent bilingual students in developing academic vocabulary and comprehension through oral discourse. For example, Lesson 8-3: "More Place-Value Relationships Visual Learning," provides "Targeted ELPS Support" for students to orally compare the values of numbers in different place values. Sentence stems are provided to beginner and intermediate students; high intermediate students are asked to identify and compare the values. In contrast, the advanced students are asked to identify and explain why the values are different. The grade 4 materials include embedded guidance for teachers to support emergent bilingual students in building background knowledge and making cross-linguistic connections through oral discourse. For example, the Topic 1, "Place-Value Understandings, Linguistic Accommodations" pages list cognates, false cognates, transferable and non-transferrable cross-linguistic connections, as well as important multiple-meaning words with both their math and non-math related meanings. The grade 4 materials include embedded guidance for teachers to support emergent bilingual students' academic vocabulary and comprehension through written discourse. For example, the grade 4 "Differentiation Library Teacher's Guide" in Topic 8 contains "Pick A Project, Part of a Pie" activity for students to write and perform a skit about fraction equivalents in small groups. The grade 4 materials include embedded guidance for teachers to support emergent bilingual students in building background knowledge and making cross-linguistic connections through written discourse. For example, in Lesson 2-1: "Targeted ELPS Support," students use scaffolded discussions and connections to personal experiences to write multiplication problems.
Evaluation for 3.3d
This guidance is not applicable to the product.
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.
3 out of 3 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.
3 out of 3 points
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
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.
2 out of 2 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.
2 out of 2 points
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.
4 out of 4 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.
4 out of 4 points
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.
2 out of 2 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.
2 out of 2 points
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.
3 out of 3 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.
3 out of 3 points
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
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
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
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 scored
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.
0 out of 0 points
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
EnVision Plus Mathematics Grade 4 provides students with practice opportunities to demonstrate depth of knowledge through the inclusion of activities with increasingly complex demands. In grade 4, students learn division through concrete representation using mental math and estimation. They progress through partial quotients and place value blocks before dividing numbers by one-digit divisors with remainders using the standard algorithm. EnVision Plus Mathematics Grade 4 assessment reviews and instructional assessments provide a variety of questions and tasks that match the depth of understanding aligned to the TEKS. For example, Topic 7, "Add and Subtract Fractions and Mixed Numbers Topic Review," includes a review of TEKS 4.3e, "represent and solve addition and subtraction of fractions. . ." with specific language and practice to reinforce this skill.
Evaluation for 4.1b
EnVision Plus Mathematics Grade 4 questions and tasks progressively increase in rigor and complexity, leading to grade-level proficiency in the mathematics TEKS. The materials demonstrate coherence across units by explicitly connecting patterns, big ideas, and relationships between mathematical concepts. For example, in Topic 1, "Place Value Understandings," students begin with concrete work in place value blocks, progress to representational understandings with place value charts, and move to abstract work with standard form numbers to compare large numbers as enumerated in the TEKS. EnVision Plus Mathematics Grade 4 questions and tasks progressively increase in rigor and complexity, leading to grade-level proficiency in the mathematics TEKS. For example, in Lesson 11-7: "Determine Measures of Angles," students complete "Practice and Problem Solving," progressing from solving missing angle equations to scenarios that students must read to determine the math and the answer, to solving a "Higher Order Thinking Question" before finally looking at STAAR Assessment Practice questions.
Evaluation for 4.2a
The grade 4 materials demonstrate coherence across units by explicitly connecting patterns, big ideas, and relationships between mathematical concepts. For example, Topic 5: "Divide by 1-Digit Numbers," includes a "Math Background Coherence" explanation of prior grade 4 studies in place value and multiplication, current unit lessons on estimation, models, the standard algorithm, and problem solving, as well as upcoming units' use of division in equivalent fractions and general problem solving. The grade 4 materials demonstrate coherence across units by explicitly connecting patterns, big ideas, and relationships between mathematical concepts. For example, Topic 8: "Represent, Compare, Add, and Subtract Decimals," includes a "Math Background Coherence" explanation of prior grade 4 studies in fractions as a basis for decimal understanding, the current unit focus on fraction and decimal equivalence, decimal comparison and addition and subtraction operations, as well as upcoming connections to decimals in financial literacy.
Evaluation for 4.2b
The grade 4 materials demonstrate coherence across units by explicitly connecting patterns, big ideas, and relationships between mathematical concepts. For example, Topic 10: "Measurement, Units and Conversions," includes a "Math Background, Coherence" connecting concepts with lessons in grade 3 and earlier lessons in grade 4. The grade 4 materials include a list of previously learned terms, terms for the current grade level, and upcoming terms to support language connections across time in the section "Linguistic Accommodations." The grade 4 materials demonstrate coherence across units by connecting what will be learned in future grade levels to the content learned in the current grade level. For example, the Topic 1, "Math Background, Coherence" includes a section titled "Look Ahead" that explains how the current learning connects to learning in grade 5.
Evaluation for 4.2c
EnVision Plus Mathematics Grade 4 connects concepts and procedures across the current grade level. For example, the materials include a consistent method for approaching real-world problems through understanding, planning, solving, and justifying solutions. The grade 4 materials include a Problem-Solving Handbook and Teacher's Guide that are consistent across the grade band to ensure students use the same problem-solving strategies from year to year. EnVision Plus Mathematics Grade 4 Teacher's Edition contains a "coherence" section for each topic that ties the lesson to prior and future learning. For example, in Lesson 9-3: "Multiply a Whole Number by a Fraction," teachers are reminded that the current topic, dot plots with fractions, builds off prior learning on ways to display data and connects to creating dot plots from data sets in future lessons.
Evaluation for 4.3a
The grade 4 materials provide spaced retrieval opportunities with previously learned concepts across lessons. For example, in the "Math Talk" portion of Lesson 2-6: "Add Multi-Digit Numbers," students discuss what a number could be based on the information provided, requiring students to use their knowledge of rounding, odd numbers, and the concept of less than. The grade 4 materials provide practice opportunities with previously learned skills across units. Every practice contains a fluency practice; for instance, Topic 8: "Represent, Compare, Add, and Subtract Decimals," has students building fluency in division by finding matches based on division clues with a partner.
Evaluation for 4.3b
The grade 4 materials provide interleaved practice opportunities with previously learned skills across lessons and units. For example, in the "Review What You Know" in Topic 5, "Divide by One-Digit Numbers," students review vocabulary, find the quotient to division problems, round numbers to the nearest hundred, and solve a word problem about division. The grade 4 materials provide interleaved practice opportunities with previously learned concepts across lessons and units. For example, in the "Topic Review" for Topic 7, "Add and Subtract Fractions and Mixed Numbers," students work through the concepts learned in each lesson of the current topic, reinforcing fraction terminology from Topic 6 and estimating sum and difference reasonableness from Topic 2.
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
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
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
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
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
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
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
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
The grade 4 materials require students to interpret models and representations for mathematical concepts and situations. For example, in Lesson 8-3: "Visual Learning," students interpret a dollar as a whole base (flat) block, a dime as one-tenth of a base block, and a penny as one-hundredth of a base block (flat). The grade 4 materials require students to analyze models and representations of mathematical concepts and situations. For example, in Lesson 4-3: "Investigate," students analyze methods for dividing area models and calculating the composite area. The grade 4 materials require students to evaluate mathematical models to represent situations. For example, in "Act Two" of each "Three Act Task," students develop a plan and solve a real-world math issue. In "Act Three," the answer is revealed, and students evaluate their models, solutions, and possible variability of responses.
Evaluation for 5.1b
The grade 4 materials require student-created mathematical models and representations throughout the program. For example, each "Let's Investigate" lesson prompts students to develop models and representations in step one of the lesson, "Investigate." Students refine their models as they analyze and evaluate representations in step two of the lesson, "Connect." The grade 4 materials require student-created mathematical models and representations throughout the curriculum. For example, the "Let's Model in 3 Acts Lessons" requires students to watch a video and work as a class to determine a question they would like to answer about the video, gather information and data, develop models to answer the question, and finally analyze and refine their models as needed.
Evaluation for 5.1c
The grade 4 materials provide opportunities for students to apply conceptual understanding to new problem situations and contexts. For example, in Lessons 8-1 through 8–8, students learn to represent decimals using models and in Lesson 8-9, use this concept to represent addition and subtraction of decimal numbers. EnVision Plus Mathematics Grade 4 "Math Talks" provide opportunities at the start of each "Let's Build" lesson to apply previous understandings to a variety of situations and contexts. Varied "Math Talk" types, for example, open-ended questions, which one does not belong, deductive reasoning, and mathematical argumentation prompt mathematical reasoning and discourse that spiral and strengthen understanding.
Evaluation for 5.2a
The grade 4 materials provide repeated, focused exercises to build automaticity with core numerical strategies. For example, the Topic 3 "Differentiation Library", provides one independent activity and one partner game to practice basic one-digit by four-digit multiplication. The grade 4 materials provide a "Fluency Practice" with each topic to help students develop fluency in recognizing and using relationships between numbers. For example, the Topic 3, "Build Fluency," requires students to make connections between multiplication problems, their products, and place value.
Evaluation for 5.2b
The grade 4 materials provide opportunities for students to practice applying efficient mathematical procedures throughout a unit. For example, in Lesson 1-2: "Place Value," students efficiently connect the ten times greater relationship in our number system beyond visual representations of earlier grades in the "Practice and Problem Solving" section. The grade 4 materials provide opportunities for students to practice flexible mathematical procedures within the lesson. For example, in Lesson 9-8: "It is a Fine Line," students solve a data-related application problem, and specific teacher guidance is provided for sharing various solution methods encouraging flexible thinking. The grade 4 materials provide opportunities for students to practice accurate mathematical procedures throughout a unit. For example, in Lesson 10-8: "Solve Perimeter Problems," a small-group "Intervention Activity" utilizes toothpicks to verify possible side lengths of a shape with a given perimeter.
Evaluation for 5.2c
The grade 4 materials require students to evaluate procedures, processes, and solutions for efficiency. For example, Lesson 8-13: "Reflect on Thinking," includes reflection after solving an application problem, asking students to "analyze and evaluate the efficiency" of the solution they chose. The grade 4 materials require students to evaluate procedures, processes, and solutions for flexibility. For example, the Lesson 8-9 "Math Talk" requires students to discuss their flexible strategies after subitizing the sum of two decimal visual representations. The grade 4 materials require students to evaluate procedures, processes, and solutions for accuracy. For example, the Lesson 7-9 "Classroom Conversations" requires students to analyze multiple solutions to a problem and determine if all methods have the exact total.
Evaluation for 5.2d
The grade 4 materials contain embedded supports for teachers to guide students toward increasingly efficient approaches. For example, :-2, "Dot Plots," includes sample teacher questioning for each part of the lesson with responses in blue to guide students toward efficient approaches. The grade 4 materials contain embedded supports for teachers to guide students toward increasingly efficient approaches. For example, during Lesson 8-4: "Comparing and Ordering Decimals," assessing and advancing questions such as "How did you get that answer?" guide teachers to help students utilize efficient approaches. The grade 4 materials contain support and guidance throughout the curriculum in the "Let's Investigate" section of each lesson. For example, Lesson 7-5: "Adding and Subtracting Mixed Numbers" includes examples and guidance for starting with a visual in for one student, on a number line for another student, or by writing equations for another student to guide them all toward increasingly efficient approaches.
Evaluation for 5.3a
The grade 4 materials begin each topic with a "Math Background, Balance" section that explicitly outlines the conceptual overview of the unit and its correlation to the TEKS. For example, Topic 3: "Multiply by 1-Digit Numbers," contains a "Conceptual Understanding" subheading explaining the connection between partial products, the distributive property, and their connections to the standard algorithm. The grade 4 materials explicitly state the procedural emphasis of the TEKS. For example, in Lesson 6-1: "Fraction and Unit Fractions," the "Procedural Skill" subheading explains that this lesson develops fraction representation on the number line, listing 4.3A and C as focus TEKS for the work.
Evaluation for 5.3b
The grade 4 materials include using concrete models and manipulatives, as required by the TEKS. For example, in Lesson 6-2: "Equivalent Fractions," students use manipulatives to build fraction garden pavers to support TEKS 4.3(C), "determine if two given fractions are equivalent using a variety of methods." EnVision Plus Mathematics Grade 4 questions and tasks include the use of pictorial representations (figures/drawings), as required by the TEKS. For example, Lesson 9-2: "Analyzing Quadrilaterals" contains a table to illustrate drawings and descriptions of various quadrilaterals as described in TEKS 3.6D, "use attributes to. . .draw examples of quadrilaterals that do not belong to any of these [special quadrilateral] subcategories." EnVision Plus Mathematics Grade 4 questions and tasks include using abstract representations, as required by the TEKS. For example, in Lesson 11-7: "Determine Measures of Angles," students complete the "Practice and Problem Solving" by solving for angles using equations and definitions required in TEKS 4.7(E), "determine the measure of an unknown angle formed by two non‐overlapping adjacent angles."
Evaluation for 5.3c
The grade 4 materials include supports for students in connecting and creating concrete models to abstract mathematical concepts, as required by the TEKS. For example, in Lesson 6-9:"Understand Mixed Numbers," students create and connect fraction number line representations and fraction strips to deepen their understandings required in TEKS 4.1C, "select tools, including real objects, manipulatives, paper and pencil. . .as appropriate, to solve problems." The grade 4 materials include supports for students in connecting and creating representational models to abstract (symbolic/numeric/algorithmic) concepts, as required by the TEKS. For example, Lesson 7-1: "Decompose Fractions" connects area models, number lines, and algorithmic representations of decomposing fractions, as required by TEKS 4.3B, "decompose a fraction in more than one way. . .using concrete and pictorial models and recording results with symbolic representations." The grade 4 materials include supports for students in defining and explaining concrete models to abstract (symbolic/numeric/algorithmic) concepts, as required by the TEKS. For example, in Lesson 8-1: "Ways to Think About Subtraction Represent Fractions as Decimals," students use decimal grids and coins to build their understanding of representing fractions as decimals, as required in TEKS 4.2E, "represent decimals, including tenths and hundredths, using concrete and visual models and money." The grade 4 materials include supports for students in defining and explaining representational models to abstract (symbolic/numeric/algorithmic) concepts, as required by the TEKS. For example, in Lesson 4-3: "Strategies for Multiplying 2-Digit Numbers," students solve problems with an emphasis on arrays and area models to understand the relationship between square units and total product, as required in TEKS 4.4(C) represent the product of two‐digit numbers using arrays, area models, or equations, including perfect squares through 15 by 15."
Evaluation for 5.4a
The grade 4 materials provide opportunities for students to develop their academic mathematical language using visuals. For example, Lesson 3-6: "Use Area Models and Partial Products to Multiply by 1-Digit Numbers," contains a "Visual Learning" image of an area model and a connecting explanation of the distributive property. The grade 4 materials provide opportunities for students to develop their academic mathematical language using manipulatives. For example, the "Language Support" and "Visual Learning" sections of Lesson 10-6: "Equivalence with Metric Units of Length," utilize a ruler to help understand the relative sizes and use of centimeters and millimeters. The grade 4 materials provide opportunities for students to develop their academic mathematical language using other language development strategies. For example, in the Topic 4: "Multiply by 2-Digit Numbers," "Review What You Know Vocabulary Activity," students use a Frayer Model (graphic organizer) to analyze the words reviewed in the topic.
Evaluation for 5.4b
The grade 4 materials include embedded teacher guidance to scaffold and support students' development and use of academic mathematical vocabulary in context. For example, the Topic 2: "Add and Subtract Multi-Digit Whole Numbers" "Topic Review" includes a page of important vocabulary, with teacher guidance for a pre-activity game and a post-activity to write in partners utilizing the words. The grade 4 materials include embedded teacher guidance to scaffold and support students' development and use of academic mathematical vocabulary in context. For example, Lesson 5-5: "Strategies for Division" provides explicit instructions in the "Language Routines" section on how to read the passage and question students to ensure appropriate academic language is modeled and understood. The grade 4 materials include embedded teacher guidance to scaffold and support students' development and use of academic mathematical vocabulary in context. For example, Lesson 3-8: "Use a Standard Algorithm to Multiply by 1-Digit Numbers" integrates "Language Support" guidance, prompts, and sample answers for teachers to help students be more precise in their mathematical language.
Evaluation for 5.4c
The grade 4 materials include embedded teacher guidance to support the application of appropriate mathematical language to include vocabulary, syntax, and discourse to support mathematical conversations. For example, in Lesson 3-2: "Use Mental Math to Multiply," students progress from pointing to cards that can be used to show the distributive property, filling in sentence stems using those terms, describing a problem that has used the distributive property, explaining how the distributive property works, and finally writing their problems and explaining how to solve them. The grade 4 materials include embedded teacher guidance to support the application of appropriate mathematical language 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. For example, Lesson 2-5: "Adding and Subtracting Whole Numbers," includes "Assessing, Advancing, and Early Finisher," which provides questioning guidance for teachers to support student listening, deepening, and utilizing math language such as mental math, regroup, and sums. The grade 4 materials include embedded teacher guidance to support student responses using exemplar responses to questions and tasks. For example, Lesson 7-5: "Adding and Subtracting Mixed Numbers," includes four examples of student work and guided questions for teachers to use, explicit assessing and advancing questions, and guided reflection.
Evaluation for 5.5a
The grade 4 materials integrate TEKS process standards appropriately by including a Program Overview that describes how the standards are integrated throughout the lesson instruction, practice and problem solving, and program assessments components of the curriculum. The grade 4 materials integrate TEKS process standards appropriately; for example, Topic 2: "Add and Subtract Multi-Digit Whole Numbers" highlights two process standards throughout the unit and provides a "TEKS Mathematical Process Standards" page with specific teacher guidance and questioning strategies for students to become proficient with TEKS 4.1E and TEKS 4.1G throughout the lessons. Additionally, both the Teacher Edition and Student Edition highlight the process standards explicitly by listing the highlighted TEKS process standards on each lesson opener page. Process standards are highlighted in teal-colored text through callouts and practice items to help teachers and students recognize opportunities to engage with these standards while acquiring and demonstrating understanding.
Evaluation for 5.5b
The grade 4 materials include a description of how TEKS process standards are incorporated throughout the course. For example, the Table of Contents includes an overview of how all TEKS process standards are incorporated across all the topics throughout the curriculum. The grade 4 materials incorporate and connect the TEKS process standards in all problems. For example, "All math tasks evoke the selection, use, and management of multiple process standards. Specific process standards are highlighted in teal for some problems." Additionally, assessments incorporate the TEKS process standards. For example, the "Topic Performance Tasks" provide opportunities to assess students' proficiency with process standards. The digital Problem-Solving Handbook includes a problem-solving model students can use as a resource to support their thinking and assist them in becoming proficient with the TEKS process standards. For example, strip diagrams are provided to engage students with TEKS 4.1A, 4.1D, 4.1E, and 4.1F.
Evaluation for 5.5c
The grade 4 materials include a description for each unit of how TEKS process standards are incorporated throughout the unit. For example, the Table of Contents includes an overview list of all the TEKS and process standards that are incorporated and connected in each unit and lesson. For example, Topic 1, which covers place value, incorporates process TEKS such as 4.1A, 4.1D, and 4.1F. The grade 4 materials include a Topic Planner for each topic, which also lists the process standards that will be taught per lesson. For example, Topic 3, Lesson 3-1, which focuses on multiplying ten by one hundred, incorporates process standards 4.1A, 3.1F, and 4.1G. Additionally, each topic includes a "Mathematical Process Standards" section, which provides a table that illustrates student behaviors for demonstrating proficiency on these standards during topic-specific instruction. For example, in Topic 8: "Represent, Compare, Add, and Subtract Decimals," a table highlights 4.1A and 4.1D as focus process standards and enumerates with bullets the skills aligned to those standards.
Evaluation for 5.5d
The grade 4 materials include an overview of the TEKS process standards incorporated into each lesson. The Teacher's Edition includes the TEKS process standards listed at the bottom of each introductory lesson page. The grade 4 materials include an overview of the TEKS process standards incorporated into each lesson. For example, the Topic 11 "Process Standards" section highlights 4.1D and 4.1F as focus process TEKS, and the table under the "Practice and Problem Solving" page highlights the questions that support those process standards in Lessons 1-5, "Metric Units." The TEKS process standards are incorporated into each lesson in the Student Edition. For example, teal-colored process standard text in callouts and practice items helps students recognize opportunities to engage in the math processes as they acquire and demonstrate understanding. For instance, in Lesson 4-2, the callout encourages students to estimate an answer because an exact answer is not always necessary.
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
The grade 4 materials provide opportunities for students to think mathematically and encourage deeper engagement with mathematical concepts through open-ended tasks with challenging questions. For example, in Lesson 8-4: "Comparing and Ordering Decimals," students use problem-solving strategies to determine possible lengths of small creatures. Students choose a strategy and explain how they determined solutions. Four examples of student work and teacher questioning guidance are provided for teachers to ask how students got their answers, how they could determine if answers are correct, and to explain relationships between decimals and fractions. The grade 4 materials provide opportunities for students to persevere through solving problems. For example, in Lesson 5-3: "Interpret Remainders," students are asked what the word remain means and how that connects to remainder. Additionally, prompts such as why the remainder can sometimes be ignored, why problems sometimes do and do not require the remainder, why the remainder can never be larger than the divisor, and how to determine when one must be added to the quotient are provided. Students are asked what other numbers could be used to estimate, how place value blocks show decomposing, how decomposing one addend and adding the parts is different from decomposing both, and how this task could be shown with a strip diagram. In addition, earlier in Topic 5, "Build G.R.I.T., Divide by 1-Digit Numbers," teachers are given guidance to support student perseverance with sample "Classroom Conversations" to scaffold learning while leaving students in control of their learning. The grade 4 materials provide opportunities for students to make sense of mathematics. For example, in Lesson 10-11: "Solve Measurement Problems," the lesson progresses from mathematical argumentation about the area of rectangles on grids, to simple measurement unit conversion, to real-world application of surface area, including unit conversion to a variety of measurement application problems, allowing teachers to scaffold and challenge students' mathematical sense-making.
Evaluation for 6.1b
The grade 4 materials support students in understanding that there can be multiple ways to represent and solve problems and complete tasks. For example, Lesson 11-1: "Lines, Rays, and Angles," begins with the "Investigate" section, where students are encouraged to represent their solutions in multiple ways, connect their understanding to real-life scenarios, and provide teachers with both "Assessing" and "Advancing" questions to delve further into multiple representations. The grade 4 materials support students in explaining that there can be multiple ways to represent and solve problems and complete tasks. For example, in Lesson 7-10: "Let's Model in 3 Acts Just Add Water," students evaluate the fraction of each liquid in a container. "Act 1" requires students to make and discuss their predictions, "Act 2" has students develop a model and share solution strategies, and "Act 3" has students validate conclusions and reflect on their thinking to determine how their work would be changed if needed, in both whole-class and small-group explanations. The grade 4 materials support students in justifying that there can be multiple ways to represent and solve problems and complete tasks. For example, in "1–6, Let's Model In 3 Acts Page Through," students are tasked with modeling and solving a task to determine the relative size of books based upon number sense. Students develop a model, share solution strategies, validate conclusions, and then reflect on their thinking by explaining how they used math to represent the situation, justifying whether they agree with the final decision, and analyzing and evaluating the efficiency of the strategy they chose.
Evaluation for 6.1c
The grade 4 materials require students to make sense of mathematics through multiple opportunities to do math with peers and teachers. For example, in Lesson 10-6: "Equivalence with Metric Units of Length," students solve, discuss, and think-pair-share while doing math as both whole and small-groups. The grade 4 materials are designed to require students to make sense of mathematics through multiple opportunities to write about math with peers and teachers. For example, Topic 6, "Differentiation Library", allows students to choose one of the following activities: create a "math walk" (open ended); "Indianapolis Motor Speedway" (create a fraction game, explain and play with peers); "All the World's a Stage" (design a set and label dimensions); "Tailor Made" (create a fraction game, explain and play with peers); a "Math and Literacy" activity about space travel; and an "Amazing Contributions" article about a famous mathematician's contributions to the field. All these options include writing about math independently, with peers, and with their teacher. The grade 4 materials are designed to make sense of mathematics through multiple opportunities for students to discuss math with peers and teachers to enhance comprehension, allowing them to refine their thinking, consider different perspectives, and build communication skills. For example, Lesson 8-13: "Let's Model In 3 Acts Buzz In," provides framework and questioning to lead class discussions through all sections: "Brainstorm Questions," "Make Predictions," "Identify Important Information," "Share Solution Strategies," "Validate Conclusions," and "Reflecting on Thinking."
Evaluation for 6.2a
The grade 4 materials support teachers in guiding students to share their problem-solving approaches, including explanations, arguments, and justifications. Each topic includes a "Let's Model in 3 Acts Lesson" where students solve real-world problems with teacher guidance of problem-solving methods. For example, in "9–8, It's a Fine Line," students utilize data to determine if a child is keeping his New Year's Resolution. In the activity, students share their predictions, solution strategies, and justifications for their conclusions related to multiplying multi-digit numbers. The grade 4 materials support teachers in guiding students to reflect on their problem-solving approaches, including explanations, arguments, and justifications in multiple routines throughout each topic. For example, Lesson 6-4: "Equivalent Fractions on a Number Line," begins with "Math Talk" discussing, explaining, and justifying which fraction does not belong within an activity with multiple correct answers. It then progresses to "Explore and Share," where students visually and verbally justify equivalent fractions on a ruler, focusing on multiple fraction equivalences. The next section, "Visual Learning," includes "Classroom Conversation," "Talk About Math Ideas," and "Language Support" to encourage further conversations with justification of solutions and reasoning.
Evaluation for 6.2b
The grade 4 materials offer prompts to support teachers in providing explanatory feedback based on student responses and anticipated misconceptions. For example, Lesson 10-8: "Solve Perimeter Problems," offers a "Prevent Misconceptions" guiding teachers to watch for students making errors and remind them to use estimation to check if the value of the perimeter is reasonable. It also includes Exit Ticket feedback to support student understanding of formulas for solving perimeter questions and an "Intervention Activity" to reteach and give explanatory feedback related to the meaning of perimeter. The grade 4 materials offer guidance to support teachers in providing explanatory feedback based on student responses and anticipated misconceptions. For example, Lesson 4-4: "Use Arrays and Partial Products to Multiply 2-Digit Numbers," includes guidance and prompts for teachers to watch for students who are having a hard time splitting up the array and to remind them to decompose using place value, as well as "Guided Practice Error Intervention" item three guidance regarding algorithm steps and efficient strategies.
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
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
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
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
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