Program Information
- ISBN
- 9798213463163
- 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 5
Math (English) Grade 5
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 5 | 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
EnVision Plus Mathematics Grade 5 materials demonstrate strong alignment with the Texas Essential Knowledge and Skills (TEKS) and English Language Proficiency Standards (ELPS) through clearly organized and accessible "Scope and Sequence" documents for the grade level. The materials include a specific order of math TEKS, ELPS, and concepts taught throughout the instructional year listed at the top of the "Scope and Sequence" pages. The 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 materials include multiple iterations of "Scope and Sequence Pacing Guide Document(s)," with clear and flexible usage recommendations. enVision Plus Mathematics Grade 5 "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 materials include suggested pacing for various instructional calendars. For example, the "180-Day Scope and Sequence" for "Topic 5: Proficiently Divide Whole Numbers" indicates the topic contains 16 days divided among instruction, differentiation review, and assessment. The "210-Day Pacing Guide" provides 18 days divided among these different learning opportunities. Each day is 45–70 minutes across all scope and sequence options.
Evaluation for 1.1c
enVision Plus Mathematics Grade 5 Program Overview materials describe the intentional purpose of each unit and its sequence both within the grade level and within the grade band, explaining how concepts connect to prior and future learning within the course. A thorough rationale is provided for the content and instructional strategies underlying the program design. The materials provide a thorough rationale for the content and instructional strategies underlying the program design. The "Grade 5 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 1–6" focus on "patterns and relationships—between whole numbers and decimals." The materials include an explanation for how concepts connect throughout the course. For example, the "Math Background" section describes the key concepts addressed at the start of each topic. 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 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 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 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 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 materials include guidance designed to support 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 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 materials include comprehensive unit overviews that provide the academic vocabulary necessary to effectively teach the concepts in the unit. For example, Topic 2: "Fluently Add and Subtract Whole Numbers and Decimals," includes a "Linguistic Accommodations" section that includes 19 words under the "Topic Vocabulary Support" enabling the effective teaching of the concepts in the unit.
Evaluation for 1.2b
The materials support 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 materials contain supports for families in English for each unit, with suggestions on supporting the progress of their student. 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 materials include comprehensive, structured, detailed lesson plans required to meet content and language standards of the lesson. For example, Lesson 7-7: "Make Stem-and-Leaf Plots," includes a "Language Objective" to ". . .explain how data is represented" and both "Language Supports" and "Targeted ELPS Support" sections to meet the standard. The 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 5-1: "Use Patterns and Mental Math to Divide," 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 standards of the lesson.
Evaluation for 1.3b
The materials include "Topic Planners," which present an overview of all the lessons within a topic and include the list of materials necessary to deliver the lesson. The 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 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 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 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 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 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 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
enVision Plus Mathematics Grade 5 Assessment Sourcebook includes an "Assessment Guide" that defines each program assessment, including the intended purpose for each type of assessment. 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, in the explanations and guidance.
Evaluation for 2.1c
The 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" assessments that ensure consistent and accurate administration of instructional assessments. The 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, describing procedures for each assessment type. The "Assessment Data" section contains answer keys to align teacher understanding with assessment expectations.
Evaluation for 2.1d
enVision Plus Mathematics Grade 5 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 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 materials include lesson level exit tickets used to assess "students' understanding of the lesson content."
Evaluation for 2.1e
enVision Plus Mathematics Grade 5 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 5 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 5 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 5 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 5 scoring information provides guidance for interpreting student performance. For example, the "Assessment Data Resources" 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 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 1–13 Cumulative/Benchmark Assessment" provides an "Item Analysis Chart" correlating errors on number eight to Intervention Lesson H67. The 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 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 materials include "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 materials include a "Student Progress and Growth Tracker Tool" where students record their scores on exit tickets. For example, the exit ticket for Lesson 5-2 asks students to use emoji faces to rank how they feel about meeting their math goal ("I can estimate quotients.") 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 materials include teacher guidance for differentiated instruction for students who have not yet reached proficiency on grade-level content and skills. Lesson 4-3: "Use Number Sense to Multiply Decimals," includes an intervention activity that guides teachers' remediation of number sense for multiplying numbers with decimals. The materials include teacher guidance for differentiated activities for students who have not yet reached proficiency on grade-level content and skills. For example, in Lessons 1-2, "Decimal Place Value," teachers are provided guidance on preventing student misconceptions related to representing in expanded notation, and two worksheets to practice this skill. The materials include paired (scaffolded) lessons for students who have not reached mastery on a concept. For example, Lesson 10-4: "Solve Equations with Letters for Unknowns," provides an option for either "Reteach to Build Understanding" practice page with scaffolded practice or "Intervention Activity" with concrete objects as unknowns to address deficiencies.
Evaluation for 3.1b
The materials include pre-teaching or embedded supports for unfamiliar vocabulary in text. For example, Topic 13: "Personal Financial Literacy," includes both a "Vocabulary Activity" for small-group student discussion of personal financial literacy vocabulary and an "Academic Vocabulary" mini-lesson for teachers to directly instruct content vocabulary. The materials include pre-teaching or embedded supports for unfamiliar references in text. For example, in Lesson 11-9: "Solve Problems by Converting Units of Time," teachers are given explicit guidance for leading a class discussion on time-related vocabulary with differentiated ELPS supports, followed by a student think-pair-share utilizing this new language.
Evaluation for 3.1c
The 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 4-4: "Multiply a Decimal and a Whole Number," has "Early Finishers" prompts requiring pattern identification within decimal multiplication problems. The 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 5: "Proficiently Divide Whole Numbers," provides four STEAM-based projects, and Lesson 5-3: "Connect Models and Symbols" offers an "Enrichment 5-3" practice page. The materials include sidebar notes with differentiated extension questions and/or activities. For example, in "Let's Eat Pizza!," when students create their own real-world pizza problems from previous work, teachers are provided notes to support students' different needs.
Evaluation for 3.2a
The materials include explicit prompts to support the teacher in modeling the concept(s) to be learned. For example, in Lesson 3-3: "Multiply 3-Digit by 2-Digit Numbers," the teacher is provided with explicit prompts to lead the "Classroom Conversation" to explain the concepts of multiplying three-digit numbers by two-digit numbers. The materials include explicit prompts to support the teacher in explaining the concept(s) to be learned. For example, in Lesson 11-6: "Convert Metric Units of Capacity," the teacher is given prompts to lead the student through a discussion of converting metric units of measure. The materials include explicit guidance to support the teacher in modeling the concept(s) to be learned. For instance, in Topic 9: "Understand Multiplication and Division with Fractions," teachers are given visual and written examples of each strategy used for fraction multiplication and division in the unit. The materials include explicit guidance to support the teacher in explaining the concept(s) to be learned. For example, in Topic 5: "Build G.R.I.T: Divide by 1-Digit Numbers," a sample classroom conversation is modeled, giving teachers language to explain connecting whole number division and decimal division to a sample student.
Evaluation for 3.2b
The 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 7-3: "Make Dot Plots," 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 materials include teacher guidance for effective lesson facilitation and delivery using more than two instructional approaches. For example, in Lesson 5-1: "Use Patterns and Mental Math to Divide," students turn and talk in pairs about the math relationship between missing boxes of muffins, transition between whole-group, small-group, and independent activities, engage in class conversations to connect place value blocks in division representation, and then apply this math to write additional real-world math problems with division.
Evaluation for 3.2c
The 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 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 5 "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, "Differentiation Library: Topic 3" 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 multiplying multi-digit whole numbers.
Evaluation for 3.3a
enVision Plus Mathematics Grade 5 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 5 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, in Lesson 6-4: "Divide by a 1-Digit Whole Number," guidance is provided for teachers for language support for each level of teaching division with strip diagrams: pre-production identifies divisor, dividend, and quotient in a problem; beginning identifies numbers in the strip diagrams; intermediate writes problems based on strip diagrams; high-intermediate describes each part of the strip diagram; and advanced describes how each part of a division problem is represented in a strip diagram. The materials detail ways teachers can build academic vocabulary as the unit progresses, such as definitions, sentence stems, and conversation guides. For example, the word relationship 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 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 5 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 materials include embedded guidance for teachers to support emergent bilingual students in developing academic vocabulary and comprehension through oral discourse. For example, Lesson 7-7: "Make Stem-and-Leaf Plots: Visual Learning," provides "Targeted ELPS Support" for students to speak using content area vocabulary. Pre-production students only have to provide an answer to the questions; beginning students are to use sentence stems, intermediate students analyze the graph and use the words they have learned, high intermediate students explain data in their own words, and advanced students explain stem-and-leaf plots with their partners. The 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 2: "Fluently Add and Subtract Whole Numbers and Decimals: 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 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 11-1: "Targeted ELPS Support," students use scaffolded discussions and connections to personal experiences to write unit conversion problems. The materials include embedded guidance for teachers to support emergent bilingual students' academic vocabulary and comprehension through written discourse. For example, the grade 5 "Differentiation Library Teacher's Guide Topic 9" contains "Pick A Project: Pizza and Fractions" activity for students to write and perform a skit about fraction operations in small groups.
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 5 provides students with practice opportunities to demonstrate depth of knowledge through the inclusion of activities with increasingly complex demands. In grade 5, students learn to multiply decimals by using models and pictorial representations before progressing to partial products and properties. Students end by multiplying decimal numbers using strategies and algorithms. enVision Plus Mathematics Grade 5 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 10: "Algebra, Patterns, and the Coordinate Plane Topic Review" includes a review of TEKS 5.4e, "describe the meaning of parentheses and brackets" with specific language and practice to reinforce this skill.
Evaluation for 4.1b
enVision Plus Mathematics Grade 5 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. Teachers are guided to support depth of understanding with guiding questions and sample answers. For instance, in "Topic 2: Fluently Add and Subtract Whole Numbers and Decimals," the concept of compatible numbers is revisited from prior years, where novice and veteran teachers alike are provided sample estimation strategies, conversation starters, and misconceptions to develop deep, mathematically sound learning. enVision Plus Mathematics Grade 5 questions and tasks progressively increase in rigor and complexity, leading to grade-level proficiency in the mathematics TEKS. For example, in Lesson 12-2: "Classify Quadrilaterals," students complete "Practice and Problem Solving," progressing from identifying polygons pictured to explaining mathematical ideas to a "Higher Order Thinking Question" before finally reason question before finally answering "STAAR Assessment Practice" questions.
Evaluation for 4.2a
The materials demonstrate coherence across units by explicitly connecting patterns, big ideas, and relationships between mathematical concepts. For example, Topic 7: "Collect, Organize, Display, and Interpret Data," includes a "Math Background Coherence" explanation of prior grade 5 studies of place value that support the unit, current unit lessons on types of data, representing data, and analyzing data as well as upcoming units on the coordinate plane and numerical patterns. The materials demonstrate coherence across units by explicitly connecting patterns, big ideas, and relationships between mathematical concepts. For example, Topic 11: "Measurement Units and Measurement Conversions," includes a "Math Background Coherence" explanation of prior grade 5 studies in operations and patterns, current lessons on converting units and measurement problem solving as well as upcoming units on analyzing patterns and relationships.
Evaluation for 4.2b
The materials demonstrate coherence across units by explicitly connecting patterns, big ideas, and relationships between mathematical concepts. For example, the Teacher's Edition, Topic 12: "Math Background, Coherence," contains a section titled "Look Back," which connects lessons with grade 4 and earlier lessons in grade 5. The materials include a list of previously learned terms alongside terms for the current grade level and upcoming terms to support language connections across time in the section "Linguistic Accommodations." The 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, in Topic 3, the "Math Background: Coherence" includes a section titled "Look Ahead" that explains how the current learning connects to learning in grade 6.
Evaluation for 4.2c
enVision Plus Mathematics Grade 5 connects concepts and procedures across the current grade level. For example, the materials include a consistent procedure for approaching real-world problems through understanding, planning, solving, and justifying their solutions. The grade 5 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 5 Teacher's Edition contains a "coherence" section for each topic that ties the lesson to prior and future learning. For example, in Lesson 12-4: "Solve Perimeter and Area Problems," teachers are reminded that the current topic, perimeter and area with missing dimensions, will build off prior learning (perimeter and area with given dimensions), and will be connected to discovering the formula for volume in future lessons.
Evaluation for 4.3a
The materials provide spaced retrieval opportunities with previously learned concepts across lessons. For example, in the "Math Talk" portion of Lesson 3-5: "Multiply Whole Numbers with Zeros," students collect data and make a list of answers from least to greatest, comparing quantities and using statements to describe results to practice the concepts of estimation and comparisons. The materials provide practice opportunities with previously learned skills across units. Every practice contains a fluency practice; for instance, in Topic 9: "Understand Multiplication and Division with Fractions," students practice multiplication of three-digit numbers by two-digit numbers by working with a partner to match the clues to the problems.
Evaluation for 4.3b
The materials provide interleaved practice opportunities with previously learned skills across lessons and units. For example, in the "Review What You Know" in Topic 6: "Use Models and Strategies to Divide Decimals," students review vocabulary words, practice a variety of whole number operations, round decimals, respond to word problems regarding decimals, and solve operations with decimals. The materials provide interleaved practice opportunities with previously learned concepts across lessons and units. For example, in the "Topic Review" for Topic 12: "Measure Shapes and Solids," students work through the concepts learned throughout each lesson of the current topic, as well as reinforcing measurement terminology from Topic 11 and algebraic reasoning from Topics 5, 10, and 11.
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 materials require students to interpret models and representations for mathematical concepts and situations. For example, in Lesson 7-8: "Practice and Problem Solving," students practice interpreting scatter plots to answer questions. The materials require students to analyze models and representations for mathematical concepts and situations. For example, in Lesson 5-4: "Investigate," students analyze a math-based decision from data in a table and explain their thinking using division. The 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. Then, in "Act Three," the answer is revealed, and students evaluate their models, solutions, and possible variability of responses.
Evaluation for 5.1b
The materials require student-created mathematical models and representations throughout the curriculum. For example, each "Let's Investigate" lesson prompts students to develop models and representations of previously learned concepts. The 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, then gather information and data, and develop models to answer the question, and finally analyze and refine their models as needed.
Evaluation for 5.1c
The materials provide opportunities for students to apply conceptual understanding to new problem situations and contexts. For example, students learn different models and strategies to divide decimals in Lessons 6-1 through 6–7, then, in Lesson 6-8, students apply those concepts to real-world problem solving involving decimal division. enVision Plus Mathematics Grade 5 "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 materials provide repeated, focused exercises to build automaticity with core numerical strategies. For example, the "Differentiation Library: Topic 6" provides two partner games to build automaticity with decimal division. The materials provide a "Fluency Practice" with each topic to help students develop fluency in recognizing and using relationships between numbers. For example, the Topic 8 "Build Fluency" requires students to use front-end estimation to strategize when choosing factors in a multiplication game, and use division to check their work for accuracy.
Evaluation for 5.2b
The materials provide opportunities for students to practice the application of efficient mathematical procedures throughout a unit. For example, in Lesson 5-5: "Use Partial Quotients to Divide," students efficiently connect strip diagrams, estimation, and the standard algorithm to understand the interrelated importance of these skills in the "Explore and Share and Visual Learning" sections. The materials provide opportunities for students to practice flexible mathematical procedures within the lesson. For example, in Lesson 10-8: "Speed Stacks," students solve an algebraic thinking application problem, and specific teacher guidance is provided for various solution methods to encourage flexible thinking. The materials provide opportunities for students to practice accurate mathematical procedures throughout a unit. For example, in Lesson 2-5: "Use Strategies to Add Decimal," a small-group "Intervention Activity" utilizes grid paper to add decimal numbers as a follow-up to a whole-group lesson utilizing the algorithm and developing a method for checking the accuracy of solutions.
Evaluation for 5.2c
The materials require students to evaluate procedures, processes, and solutions for efficiency. For example, Lesson 8-11: "The Gif Recipe," includes student reflection after solving an application problem, asking students to "analyze and evaluate the efficiency" of the solution they chose. The materials require students to evaluate procedures, processes, and solutions for flexibility. For example, Lesson 9-7: "Divide a Unit Fraction by a Non-Zero Whole Number," requires students to discuss their flexible strategies after subitizing the quotient of a fraction division problem. The materials require students to evaluate procedures, processes, and solutions for accuracy. For example, Lesson 3-6: "Choose a Strategy to Multiply Multi-Digit Whole Numbers," includes "Classroom Conversations" requiring students to analyze multiple problem-solving methods to determine their effectiveness, accuracy, and application.
Evaluation for 5.2d
The materials contain embedded supports for teachers to guide students toward increasingly efficient approaches. For example, Lesson 9-1: "Multiplying with Fractions," includes sample teacher questioning for each part of the lesson with responses in blue to guide students toward efficient approaches. The materials contain support and guidance throughout the curriculum in the "Let's Investigate" section of each lesson. For example, Lesson 8-2: "Common Denominators," includes "Assessing and Advancing Questions" such as, "Which regions are the smallest?" and "How can you divide the larger regions into smaller regions?" to support student sense making during independent work. The materials contain guidance for developing understanding and efficient approaches. For example, during Lesson 3-5: "Multiply Whole Numbers with Zeros," students are solving 3-digit by 2-digit multiplication problems as the teacher materials provide guidance for students needing help with partial products to ask, "How can you break apart the number 103?," connecting to simpler multiplication problems earlier in the curriculum, partial products, the standard algorithm, and strip diagram work in other parts of the lesson to support learners' understanding and analysis of efficient strategies in math.
Evaluation for 5.3a
-enVision Plus Texas Mathematics 2027 Grade 3 Teacher’s Edition includes “Targeted ELPS Support” in each daily lesson plan to support various levels of language proficiency [as defined by the English Language Proficiency Standards (ELPS)]. For example, in lesson 2-3 guidance is provided for teachers for language support for teaching multiplication properties: pre-production uses hand signals, beginning fills in the blank in provided sentence stems, intermediate instructs student partners to say properties and give examples, high-intermediate writes definitions on notecards for partners to identify the identity and advanced uses examples and definitions to explain each property. -enVision Plus Texas Mathematics 2027 Grade 3 materials detail ways that the teacher can build academic vocabulary as the unit progresses, such as definitions, sentence stems, and conversation guides. For example, the word ‘demonstrate’ is a frequently occurring academic vocabulary which 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 5.3b
The materials include the use of concrete models and manipulatives, as required by the TEKS. For example, in Lesson 12-6: "Model Volume," students use manipulatives to build rectangular prisms from place value blocks to support TEKS 5.4G, "use concrete objects and pictorial models to develop the formulas for the volume of a rectangular prism." enVision Plus Mathematics Grade 5 questions and tasks include the use of pictorial representations (figures/drawings), as required by the TEKS. For example, Lesson 8-2: "Common Denominators," demonstrates the utilization of common denominators for addition as described in TEKS 5.3H, "represent and solve addition and subtraction of fractions with unequal denominators referring to the same whole using objects and pictorial models and properties of operations."
Evaluation for 5.3c
The materials include supports for students in connecting and creating concrete models to abstract mathematical concepts, as required by the TEKS. For example, in Lesson 9-6: "Connect Multiplication to Area," students build models of rectangles with unit squares and then solve additional problems using the formula for area, as required in TEKS 3.6D, "determine the area of rectangles . . .using multiplication related to the number of rows times the number of unit squares in each row formulas for area." The 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 4-7: "Multiply Decimals Using Partial Products," students use arrays, area models, and the multiplication algorithm to solve problems, as required by TEKS 5.3D, "represent multiplication of decimals with products to the hundredths using objects and pictorial models, including area models." The 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 9-1: "Multiplying with Fractions" the student solves problems with an emphasis option to use counters or fraction strips, as well as tables to fully understand the concept of multiplying fractions, as required in TEKS 5.3I, "represent and solve multiplication of a whole number and a fraction that refers to the same whole using objects and pictorial models, including area models." The 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 6-5: "Dividing Decimals," students solve problems with grid paper, area models, and calculations to understand decimal division, as required in TEKS 5.3F and G, "represent quotients of decimals. . .using objects and pictorial model," and "solve for quotients of decimals using strategies and algorithms."
Evaluation for 5.4a
The materials provide opportunities for students to develop their academic mathematical language using visuals. For example, the Lesson 4-5: "Use Models to Multiply a Decimal and a Decimal Language Support," encourages the use of a visual that gives students the practice of identifying overlaps and the understanding of the word overlap in order to better understand the concepts of using area models for decimal multiplication. The materials provide opportunities for students to develop their academic mathematical language using manipulatives. For example, in Lesson 11-1: "Convert Customary Units of Length Language Support," students are given yardsticks and work on finding equivalents and relative measurements while completing the "Visual Learning Box A" that displays a table with equivalent measurements for feet, inches, yards, and miles. The materials provide opportunities for students to develop their academic mathematical language using other language development strategies. For example, in Topic 5: "Proficiently Divide Whole Numbers" in the "Review What You Know Vocabulary Activity," students use Frayer Models (graphic organizer) to review the terms used in the topic.
Evaluation for 5.4b
The materials include embedded teacher guidance to scaffold and support students' development and use of academic mathematical vocabulary in context. For example, Topic 8: "Fluently Add and Subtract Fractions and Mixed Numbers," includes a page of important vocabulary, with teacher guidance for a pre-activity game to recall these words and a post-activity to write in partners utilizing the words. The materials include embedded teacher guidance to scaffold and support students' development and use of academic mathematical vocabulary in context. For example, "Lesson 8-2: Common Denominators," provides explicit instructions and modeling in the "Language Routines" section on how to read the passage and question students to ensure appropriate academic language is modeled and understood. The materials include embedded teacher guidance to scaffold and support students' development and use of academic mathematical vocabulary in context. For example, Lesson 6-2: "Estimate Decimal Quotients," integrates "Language Support" provides guidance on connecting to students' prior experiences to review the two meanings of estimate in the context of math lessons.
Evaluation for 5.4c
The 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 6-4: Divide by a 1-Digit Whole Number," the "Targeted ELPS Support" provides teacher guidance to help students progress from naming the terms that can be used to label numbers in division problems, using those terms to label a strip diagram, writing an equation to represent a strip diagram, and finally describing each part of a strip diagram using correct vocabulary and describing the first step to solve it. The 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 7-1: "Collecting, Representing, and Analyzing Data," includes "Assessing, Advancing, and Early Finisher" questioning guidance for teachers to support student listening, deepening, and utilizing math language such as data, categories, and format. The materials include embedded teacher guidance to support student responses using exemplar responses to questions and tasks. For example, Lesson 8-2: "Common Denominators," includes four exemplars of student work and specific examples for clarifying student understanding as well as deepening their understanding of equivalent fraction concepts.
Evaluation for 5.5a
The 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 assessment components of the curriculum. The materials integrate TEKS process standards appropriately. For example, Topic 2: "Fluently Add and Subtract Whole Numbers and Decimals," 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 5.1 C and F throughout all lessons. Additionally, both the Teacher's 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 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 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 5.1A, 5.1D, 5.1E, and 5.1F.
Evaluation for 5.5c
The 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 9, which covers multiplying fractions, incorporates process TEKS such as 5.1D, 5.1G, and 5.1F. The materials include a "Topic Planner" for each topic, which also lists the process standards that will be taught per lesson. For example, Topic 11, Lesson 11-1, which focuses on converting customary units of length, incorporates process standards 5.1A, 5.1C, and 5.1F. 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 4, the lessons include behaviors of students who are proficient in TEKS 5.1A (the student is expected to apply mathematical problems arising in everyday life, society) by recognizing that sums of money can be represented as decimals that can be multiplied by whole numbers or other numbers.
Evaluation for 5.5d
The materials include an overview of the TEKS process standards incorporated into each lesson.
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 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 2-4: "Adding and Subtracting Decimals," students use problem-solving strategies to determine what they can purchase for $10 from a food truck based on the given menu. Students choose a strategy and explain how they came up with solutions. Guidance is provided for teachers to ask how students got their answers, how they could determine if answers are correct, and what is the least amount of money they could use on a lunch that includes one item, one side, and one drink. The materials provide opportunities for students to persevere through solving problems. For example, in Lesson 6-4: "Divide by a 1-Digit Whole Number," students are asked how a strip diagram shows division, how does estimating help dividing, how can you write the remainder in the quotient, and when is it more accurate to show the quotient as a decimal number or as a whole number with a remainder. In addition, earlier in Topic 6: "Build G.R.I.T.: Use Models and Strategies to Divide Decimals," teachers are given guidance to support student perseverance with sample "Classroom Conversations" scaffold learning while leaving students in control of their learning. The materials provide opportunities for students to make sense of mathematics. For example, in Lesson 11-5: "Convert Metric Units of Length," the lesson progresses from mathematical argumentation about data and units of measure to students comparing the lengths of parts of the playground related to unit conversion and explaining their thinking. Then, to integrate their understanding of unit conversion with fraction and decimal number sense, teachers should scaffold and challenge students' mathematical sense-making throughout the lesson.
Evaluation for 6.1b
The materials support students in understanding that there can be multiple ways to represent and solve problems and complete tasks. For example, Lesson 12-5: "Let's Investigate Volume," begins with the "Investigate" section where students are encouraged to represent their solutions in multiple ways, connect their understanding to real-life scenarios, and provides teachers with both "Assessing" and "Advancing" questions to delve further into multiple representations. The materials support students in explaining that there can be multiple ways to represent problems, solve problems, and complete tasks. For example, in Lesson 11-8: "Let's Model in 3 Acts: Space Explorer's Challenge," students explain their problem-solving at multiple points. "Act 1" requires students to make and discuss their predictions, "Act 2" has students develop a model and share solutions and strategies, and "Act 3" has students validate conclusions and reflect on thinking to determine how their work would be changed if needed, in both whole-class and small groups. The materials support students in justifying that there can be multiple ways to represent problems, solve problems, and complete tasks. For example, in Lesson 2-9: "Let's Model In 3 Acts The Grocery Store," students are tasked with determining cost and change related to a shopping experience, including adding and subtracting decimals. 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, justify whether they agree with the final decision, and analyze and evaluate the efficiency of the strategy that they chose.
Evaluation for 6.1c
The materials are designed to require students to make sense of mathematics through multiple opportunities to do math with peers and teachers. For example, in Lesson 7-9: "Make Scatterplots" in "Step 2 Visual Learning," students solve, discuss, and think-pair-share while doing math in both whole and small groups. The materials are designed to require students to make sense of mathematics through multiple opportunities for students to write about math with peers and teachers. For example, Topic 3, "Differentiation Library" allows students to choose one of the following activities: create a "math walk" (open ended), "Bouncy Balls" (create and present a business plan), "Oldest Fort" (research, build, and create a table of supplies), and "Fabulous Ferries" (create and test a prototype), a "Math and Literacy" activity about structural engineers, 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 materials are designed to make sense of mathematics through multiple opportunities for students to discuss math with peers and teachers to enhance comprehension, allowing students to refine their thinking, consider different perspectives, and build communication skills. For example, Lesson 5-11: "Let's Model In 3 Acts Blueberry Bonanza" provides a 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 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 Lesson 5-11: "Blueberry Bonanza," students determine how many blueberries will be placed in each dish based upon a fruit harvesting scenario. In the activity, students share their predictions and solution strategies and share their justifications for their conclusions related to dividing multi-digit numbers. The 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 8-10: "Model and Solve One-Step and Multi-Step Problems with Fractions" begins with "Math Talk," where students discuss, explain, and justify the solution to an algebraic thinking fraction problem. It then progresses to "Explore and Share," where students visually and verbally justify the comparison of two mixed-number fractions. The following 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 materials offer prompts to support teachers in providing explanatory feedback based on student responses and anticipated misconceptions. For example, Lesson 11-6: "Convert Metric Units of Mass," includes "Prevent Misconceptions" guidance to watch for students who are uncertain about the meanings of math prefixes such as milli, to intervene immediately and guide them to a better understanding as they work. It also includes "Exit Ticket" feedback to support student understanding of unit conversion and an "Intervention Activity" to reteach and give explicit steps for converting units of measure in the metric system. The materials offer guidance to support teachers in providing explanatory feedback based on student responses and anticipated misconceptions. For example, Lesson 6-3: "Use Models to Divide a Decimal by a 1-Digit Whole Number" contains four exemplar student work samples along with specific questions to clarify understanding, point out potential misconceptions, and guidance to probe into incorrect answers with open-ended questions to diagnose needed remediation.
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