Program Information
- ISBN
- 9798213463323
- 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 7
Math (English) Grade 7
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 7 | 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 7 Teacher's Edition includes a scope and sequence outlining the Texas Essential Knowledge and Skills (TEKS), English Language Proficiency Standards (ELPS), and mathematical concepts taught in the course, along with vertical alignment for secondary mathematics courses. Relevant TEKS, ELPS, and concepts are also presented at the start of each unit and each lesson. ELPS are found in the "Scope and Sequence," "Pacing Guide," "Unit Overview," and lessons. The "End Matter" of the Teacher's Edition has an "ELPS Correlation List" with ELPS cross-referenced to each unit for teacher reference.
Evaluation for 1.1b
Materials include suggested pacing for 165, 180, and 210 days to support effective implementation for various instructional calendars. Each topic/unit specifies the number of instructional, assessment, and differentiation days. The pacing guide is in the Grade 7 Teacher's Edition in the "End Matter."
Evaluation for 1.1c
Materials include an explanation for the rationale of unit order in the "Math Background: Coherence" section of the Grade 7 Teacher's Edition, explaining connections within each topic from previous content taught and future lessons. For example, in the Grade 7 Teacher's Edition, Topic 4, "Math Background: Coherence," the following prompts are asked and answered: "How does Topic 4 connect to what students learned earlier?" "How is content connected within Topic 4?" and "How does Topic 4 connect to what students will learn later?" Materials include an explanation for the rationale of the sequencing of all topics connecting to key concepts and the connections made to other concepts in the course, and include a graphic outlining the progression of content in each topic in the Grade 7 Teacher's Edition, "Program Overview Grades 6–8." The "Grade 7 Content Organization Rationale" provides a detailed description of the key concepts and connections to explain the course's sequencing further.
Evaluation for 1.1d
Materials include protocols with corresponding guidance for unit and lesson internalization in the "Grade 7 Instructional Leader Topic Internalization Protocol" in the Lesson Implementation Guide. The guidance section includes rationale, implementation, and extensions for instructional leaders to utilize when guiding teachers through the internalization process. The "Grade 7 Instructional Leader Topic Internalization Protocol" includes protocols with corresponding guidance for unit and lesson internalization. The lessons are broken down by objectives, essential understanding, sequencing, and instructional strategies. Materials in the "Grade 7 Instructional Leader Topic Internalization Protocol" also include protocols with guidance for lesson internalization with lesson presentation sequence recommendations, engagement strategies, questions to ask, and examples of possible student work errors.
Evaluation for 1.1e
Materials include resources and guidance for instructional leaders to support teachers in implementing instructional materials. The "Grade 7 Instructional Leader Topic Internalization Protocol" in the Lesson Implementation Guide provides administrators with guidance segments to assist teachers with implementation under each sub-topic of the protocol, including rationale, implementation, and extensions for instructional leaders to utilize when guiding teachers through the internalization process. A "Classroom Observation and Analysis Tool" includes guidance for instructional leaders to support teachers with targeted feedback on indicators during observed instruction. Instructional leaders record "Yes," "Partially," or "No" to various tasks or look-fors in the lesson. A "Post-Visit Action Plan" allows instructional leaders to collaborate with teachers to better implement the curriculum after observation.
Evaluation for 1.2a
The Topic 3, "Math Background: Coherence" section of the Grade 7 Teacher's Edition includes comprehensive unit overviews that provide the background content knowledge necessary to effectively teach the concepts in the unit. The "Look Back" describes content learned by the student, both in previous lessons and the prior grade level, by unit and topic. At the beginning of each unit in the Grade 7 Teacher's Guide, a "Topic Planner" includes a comprehensive unit overview with background content knowledge and academic vocabulary necessary to effectively teach the concepts in the unit. The Grade 7 Teacher's Edition provides detailed academic vocabulary for each unit; for example, in Topic 3, "Linguistic Accommodations," the section "Topic Vocabulary Support" is broken down into "Topic Vocabulary," "Prior Terms," "Upcoming Terms," "Vocabulary in Context," and "Context Setting Vocabulary," describing the vocabulary necessary to effectively teach the concepts in the unit/topic.
Evaluation for 1.2b
The materials contain supports for families in both Spanish and English in the Family/Caregiver Guide. The digital resource includes Spanish and English options for each unit with additional supports to use at home in areas such as "Online Practice and Problem Solving," "Responsive Feedback," and "Question Help." The Family/Caregiver Guide provides resources for each unit through home connections, questions to ask, and how to help students with their homework. For example, Topic 3 on "Analyze and Solve Percent Problems" provides families with "Connect the Math" to describe the content in a real-world context of coupons, tips, and commissions. The materials include a "Spanish and English Glossary" for families to access outside of school. Each unit has a "Linguistic Accommodations" section citing ELPS and transferable/non-transferable skills for Spanish.
Evaluation for 1.3a
Materials include comprehensive, structured, detailed lesson plans that include daily objectives, questions, tasks, materials, and instructional assessments aligned with the TEKS and ELPS. For example, in the Grade 7 Teacher's Edition, the "3–2 Lesson Plan" is "Connect Percent and Proportion" and lists the TEKS, ELPS, mathematics, and language objectives aligned with the concept of percents aligned with TEKS 7.4D. The aligned ELPS is Speaking 2B, which states students are expected to explain, orally and in writing, how to use proportions to solve percent problems. The lesson plan includes a list of materials necessary to implement the lesson successfully. Within the lesson, a think-pair-share activity with a series of questions is described to allow students an opportunity to speak using content language and math terms. Throughout the lesson plan, multiple questions are listed to check for student understanding. Multiple tasks like "Try It!," "Do you Understand?," and "Do You know How?" are all evidence of tasks promoting mastery of the content. Step 4 of Lesson Plan 3-2 is titled "Assess and Differentiate," with various resources for student assessments. Materials include detailed lessons that address the TEKS listed for each lesson. The Grade 7 Teacher's Edition Lesson 2-6 uses graphs in proportional and nonproportional relationships to address TEKS 7.4A, 7.4C, and 7.7A. All are part of the lesson. The ELPS named for the lesson are met within the lesson plan.
Evaluation for 1.3b
In the Grade 7 Teacher's Edition, Lesson Plan 5-5, the lesson overview lists student and teacher materials necessary to effectively deliver the lesson. The "Topic Planner" includes a list of needed lesson materials. The materials list does not clearly identify which materials are teacher items and which are student items. Materials include suggested timing for each lesson component. For example, in the Grade 7 Teacher's Edition, Lesson Plan 5-5, the lesson is broken into four parts with a timeframe for implementing each part. For example, Step 1: "Explore and Share" is allotted 15–20 minutes, and Step 2: "Visual Learning" is allotted 40–45 minutes. In Lesson Plan 5-1, Step 1: "Investigate" is recommended to take 30–35 minutes.
Evaluation for 1.3c
Materials include guidance on the effective use of lesson materials for extended practice through the Differentiation Guide in the "Differentiation Library." For example, Lesson 2-4, Step 4: "Assess and Differentiate" of the "Differentiation Library" provides guidance for extension practice based on Quick Check results. Guidance for extended practice prompts the teacher on getting started, during the task, and for extra-challenge activities.
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
Materials include a variety of instructional assessments at the unit and lesson level (including diagnostic, formative, and summative) that vary in tasks and questions. For example, in the Grade 7 Teacher's Edition, each topic includes a "Topic Readiness Assessment, Exit Ticket, Quick Check, two Mid-Topic Assessments or Mid-topic Performance Tasks, a Topic Assessment, and a Topic Performance Task. Each assessment ranges in types of questions and tasks, such as ordering values, multiple-choice, and fill-in-the-blank questions. Some questions may involve multiple steps that require students to complete tasks before arriving at the solution. In the Grade 7 Assessment Sourcebook, the "Progress Monitoring Assessment Form A" has question number 26 as a three-part question where students are required to compare the costs of a product with different coupons (15% off and $50), before assessing the potential savings and choosing the option to save the most money. The Grade 7 Teacher's Edition, Quick Check 4-6 includes a summative assessment designed to be administered at the end of Lesson 4-6. The assessment consists of question types, including multiple-choice, multi-select, and graphing on a number line.
Evaluation for 2.1b
Materials include the definition and intended purpose for the types of instructional assessments included. A table in the Grade 7 Assessment Sourcebook describes the three types of assessment (diagnostic, formative, and summative) with reasons for administration and the best time to administer each type. The table states that "Diagnostic Assessment" is used to diagnose a student's readiness for learning by assessing prerequisite content before instruction. The "Formative Assessment" section of the table in the Grade 7 Assessment Sourcebook states that the assessment should be given during a lesson. The section also provides various types of formative assessments within the lesson under the areas of "Try It" and Exit Ticket. The Exit Ticket is intended to "assess students' understanding of critical lesson concepts and skills." The "Front Matter" has an "Assessment Resources" page that includes the definition and intended purpose for the types of instructional assessments, categorizing and identifying which types would be considered diagnostic, formative, or summative, and when to administer them.
Evaluation for 2.1c
Materials include teacher guidance to ensure accurate administration of instructional assessments. The Grade 7 Assessment Sourcebook outlines the purpose of each assessment type and provides directions on duration and how to monitor and administer assessments. These guidelines help support accuracy in test delivery across classrooms. An "Assessment Guide" in the Grade 7 Assessment Sourcebook is included to assist teachers. It is divided into three sections: "Why and When to Assess," "What to Assess," and "How to Assess," providing structured guidance for accurate assessment practices. Materials include clear, specific, and actionable guidance for the consistent administration of instructional assessments. For example, the Assessment Guide: How to Administer Assessments includes sections "Preparing for Assessments" and "Monitoring Assessments" that provide guidance for timing, preparing the testing environment, test directions, and active monitoring.
Evaluation for 2.1d
Diagnostic, formative, and summative assessments are aligned to the TEKS and objectives of the course, unit, or lesson. For example, in the Grade 7 Teacher's Edition, Lesson 3-3 has an objective of representing and solving percent problems, which aligns to TEKS 7.4D. The five questions in the "Item Analysis" for Quick Check 3-3 are aligned to TEKS 7.4D. In the Grade 7 Assessment Sourcebook, the "Readiness Test" is a diagnostic assessment aligned to TEKS from prior grades, which sets the foundation for Grade 7 TEKS. Another example from the Grade 7 Assessment Sourcebook, Quick Check 2-8, requires students to identify non-proportional representations through graphs, situations, and equations. The Exit Ticket for 2–8 also aligns to the non-proportional expectations, asking students, "How do you know that the linear relationship that describes the cost of an art class is or is not proportional?" with an answer of "The y-intercept is not (0, 0)."
Evaluation for 2.1e
Instructional assessments include TEKS-aligned items at varying levels of complexity. For example, in the Grade 7 Assessment Sourcebook, Quick Check 4-6 is aligned with TEKS 7.11A and has varying levels of complexity that include open response, a hot spot on a number line, and a multi-select question. Lesson 4-6 in the Grade 7 Teacher's Edition, the section "Do You Understand?/Do You Know How?" has questions aligned to 7.11A and includes items at varying levels of complexity. Question 1 is a multi-part question with a constructed response, and Question 4 is a hotspot question using a number line. Instructional assessments include TEKS-aligned items at varying levels of complexity according to the Depth of Knowledge (DOK) concept listed within "Item Analysis Charts" throughout the Grade 7 Assessment Sourcebook in the "Scoring Guide."
Evaluation for 2.2a
The results of the Quick Check assessments in the "Differentiation Library" of the Grade 7 Teacher's Edition provide guidance for interpreting student performance to provide targeted supports. For example, in Quick Check 2-2, students scoring 0–3 are provided with reteaching resources, and students scoring 4–5 are assigned enrichment activities. Online instructional assessments and scoring information, described in the Grade 7 Assessment Sourcebook "Assessment Data," provide guidance for interpreting student performance through class and individual reports on specific items, whole assessments, and groups of assessments. Using the "Item Analysis Chart" in the Grade 7 Assessment Sourcebook, teachers can see patterns in the TEKS and the DOK of student performance. Corresponding intervention lessons are provided for each missed item. For example, if a student misses question 1, intervention activities are L18 and L19. The Grade 7 Assessment Sourcebook, "Instructional Outcomes Informed by Assessment Results," provides guidance for interpreting student performance based on different types of tests. For example, the guide suggests that for specific diagnostic results, the teacher may need to "develop individual study plans, make grouping decisions, prescribe specific activities to fill in gaps in understanding all prerequisite content."
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, per the Assessment Sourcebook, online assessments in the SavvasRealize program automatically provide differentiation tasks to target specific skills toward mastery. In the Grade 7 Assessment Sourcebook, students scoring 0–3 on the Quick Check 3-5 are provided with reteaching resources, and students scoring 4–5 have recommended enrichment activities. Additionally, there is a suggestion for emergent bilingual students to perform the "Build Mathematical Literacy Activity." Using the "Item Analysis Chart" in the Grade 7 Assessment Sourcebook, teachers can see patterns in the TEKS and the DOK of student performance. Corresponding intervention lessons are provided for each missed item in the Grades 6–8 Intervention System.
Evaluation for 2.2c
Materials include tools for students to track their own progress and growth; for example, in the Seventh Grade Progress Monitoring Guide, the "Student Progress and Growth Tracker" allows students to record their progress before, during, and after each lesson. Students identify their progress and growth as the lesson advances through a math goals column stating, "I can. . .With help. . .Not yet." The materials include tools for teachers to track student progress and growth; for example, the "Student Progress and Growth Teacher Tool," aligned to grade-level TEKS, allows teachers to track student progress before, during, and after the topic. There are three indicators used: working on it, almost there, and got it. Additionally, in the Grade 7 Online Resources, there are tools for both students and teachers to track progress and growth for each topic, allowing students to reflect on math goals before, during, and after a topic, and teachers to track student growth before, during, and after a topic.
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
Materials include teacher guidance for differentiated instruction for students who have not yet reached proficiency on grade-level content and skills. The Grade 7 Teacher's Edition, Lesson 2-8, provides guidance for students who "may need to review how values in the table relate to the graph of the linear relationship." In "Support Student Understanding," teachers are provided guidance questions to assist in students' lack of understanding of the concept. Materials include teacher guidance for differentiated activities for students who have not yet reached proficiency on grade-level content. The Grade 7 Teacher's Edition, Lesson 2-8, provides guidance for teachers to use "Braining Camp," digital manipulatives marked by a specific icon, to support students who have not yet reached proficiency on proportional and non-proportional relationships. Materials include teacher guidance for paired lessons for students who have not yet reached proficiency on grade-level content and skills. For example, paired lessons with scaffolded questions and tasks are provided in the Grades 6–8 Intervention System. Intervention Lesson N86 guides teachers to support students in connecting fractions and percent equivalence to determine probability.
Evaluation for 3.1b
Materials include embedded supports for unfamiliar vocabulary and references in text. In the Grade 7 Teacher's Edition, Lesson 1-3, there is an embedded support called "Language Support," where teachers are guided to help students understand that dividing integer representations in Example 2 are associated with the science term gravity, which means pull down and correlates with the math term negative, and the science term thrusts, which means pushes up and correlates with the math term positive. Another example is the "Additional Vocabulary Support" section in each topic, which provides a resource that can be used as a pre-teach or a re-teach tool. "Topic 7 Resources" provides students with terms such as quadrilateral and rectangle with mathematical definitions and has them create a visual representation of the terms. Materials include pre-teaching supports for vocabulary and references in text. In "Topic 6 Topic Opener-Probability," the "Math Walk" video introduces students to probability in real-world situations by focusing on the chances of succeeding at probability games and tricks. More pre-teaching and embedded supports for unfamiliar vocabulary are found in the "Metalinguistic Transfer to Spanish" section, where teachers are informed of transferable and non-transferable skills, such as both English and Spanish languages use abbreviations, e.g., for health terms: recommend daily allowance (RDA) ingesta diaria recomendada (IDR) and providing a list of cognates such as coupon and cupon. The recommended terms to emphasize are modify and relate.
Evaluation for 3.1c
Materials include teacher guidance for differentiated instruction for students who have demonstrated proficiency in grade-level content and skill. In the Grade 7 Teacher's Edition, the section "Advancing Questions" includes teacher guidance on how to ask "questions to help students think more deeply," which includes questions like, "When will fractions with denominators of 3, 6, 7, and 9 become terminating decimals?" and "Which method of converting fractions do you prefer, and how might this help you convert other fractions?" Materials include teacher guidance for differentiated enrichment for students who have demonstrated proficiency in grade-level content and skill. In the "Program Overview" of the Grade 7 Teacher's Edition, teachers are provided guidance for a series of enrichment activities in response to student performance on assessments. The table provided in "Differentiated Instruction" lists various enrichment activities, including but not limited to, "Digital Games," "Hands-On Games," and "Pick a Project." Materials include teacher guidance for differentiated extension activities for students who have demonstrated proficiency in grade-level content and skill. In Lesson 7-2, teachers are provided guidance to "Extend Student Thinking" with an activity challenging students to draw a specific triangle, with given conditions, then explain why different triangles may be drawn.
Evaluation for 3.2a
Materials include explicit (direct) prompts to support the teacher in modeling and explaining the concept(s) to be learned. In the Grade 7 Teacher's Edition, Lesson 2-1 includes guided support for the teacher with questions to be asked, such as "How are the equivalent ratios generated?" This connects the model to the concept of setting up and solving a proportion. Another example is in Lesson 1-3, where the teacher is provided with explicit (direct) prompts and guidance for modeling and explaining how to add and subtract rational numbers. In Lesson 2-1, Example 1 includes explicit (direct) prompts that model the concept of unit rate by first using a model to illustrate the connections of the units, then translating the model into a proportion. This guidance supports the teacher by using representational and abstract models to teach the lesson. Within Lesson 6-2, the section "Math Talk" and its text include explicit (direct) prompts and guidance to support the teacher in modeling and explaining the concept(s) to be learned, prompting the teacher to ask the students specific questions involving spinners for this probability lesson. It also guides the teacher in how to respond and what to say if students ask questions about the spinners, like if the sizes of the sections in each spinner are the same size.
Evaluation for 3.2b
Materials include teacher guidance and recommendations for effective lesson delivery and facilitation using a variety of instructional approaches. In the Grade 7 Teacher's Edition, Lesson 2-6: "Explore and Share," there are teacher recommendations for effective lesson delivery and facilitation for whole-group instruction, small-groups, and early finishers. Teachers are provided with a variety of recommended instructional approaches for effective lesson delivery and facilitation on each topic. In Lesson 5-2, the "Math Talk" topic is "Data Literacy," with students analyzing data samples. The Exit Ticket provides teachers with guidance on possible student errors, such as selecting a biased sample. Each topic begins with a section titled "Math Background: Key Concepts" that provides the teacher with professional development videos, including a "Topic Overview" and "Listen and Look For" within a lesson; additionally, question previews, TEKS previews, and advanced concepts previews for teachers all prepare the teacher for effective lesson delivery.
Evaluation for 3.2c
Within the Program Overview Grades 6–8, guidance and recommendations for teachers are outlined with an overview of the multiple types of practice (e.g., guided, independent, collaborative) explained, along with definitions and symbols for recommended structures (e.g., whole-group, small-group, individual). This section includes a table exhibiting various parts of the lessons and indicating which parts have specific practices and structures. The "Practice and Problem Solving" parts of each lesson include guided, independent, and collaborative practices, as well as whole-group, small-group, and individual structures. In the Grade 7 Teacher's Edition, Lesson 3-1 includes teacher guidance on how to effectively implement collaborative and independent practices for the group work task for the "Choose a Problem" portion of lessons, which is followed by "Practice and Problem Solving" for independent practice and guidance on effective implementation. In the Topic 4 "Review What You Know," the materials guide teachers to multiple types of practice, such as having students collaboratively work with a partner to list as many vocabulary words or concepts they know, a review game, or writing a math question using one of the review vocabulary words, like inequality. For further review, the materials suggest using the online platform and going to "Academic Review Activities."
Evaluation for 3.3a
The Grade 7 Teacher's Edition, Lesson 4-3, teacher guidance includes "Targeted ELPS Support," where teachers are provided tasks and questions to assist students from each level of language proficiency, specifically ELPS 3G. The various levels of language proficiency in this lesson include beginning, intermediate, high intermediate, and advanced. Teacher guidance for students on the beginning level states, "Encourage students to use text features to identify key information." Students are asked to "explain vocabulary in their own words," and teacher guidance for students on the high intermediate level states, "Encourage students to use text features to distinguish key information and clarify unfamiliar terms." Lesson 6-2 provides teacher guidance for students working at pre-production to advanced levels of language proficiency. Teacher guidance for students working at the pre-production level encourages students to use gestures to explain theoretical concepts and predictions, while students at the intermediate level use dictionaries to define theoretical concepts and predictions. Another example is found in Topic 8 as students are learning about geometric figures. In Example 1, students calculate surface area, and the materials provide teacher guidance on how to navigate various levels of language proficiency. For pre-production students, teachers should read Example 1 aloud while students point to the triangles within the prism, and advanced students should read Example 1 in groups of three, then explain the difference between lateral and total surface area.
Evaluation for 3.3b
The Grade 7 Teacher's Edition includes implementation guidance to support teachers in effectively using the materials in state-approved ESL programs. In Lesson 4-6: "Solve Inequalities Using Addition or Subtraction," there is implementation guidance with "Language Support" located in the lesson overview. "Language Support" suggests an activity to "support reviewing language to describe inequalities." There is a detailed description of how to implement the activity within the lesson, along with guidance questions. More implementation guidance is found in Lesson 4-6: "Solve Inequalities Using Addition or Subtraction," which encourages the use of the online resource "Build Mathematical Literacy Activity," specifically suggested for emergent bilingual students after completing the Quick Check" assessment. The task is recommended for additional practice with academic language. Another example is found in Lesson 1-4, where the material provides teacher guidance to assist emergent bilingual students in using topic vocabulary to explain the errors in the problem shown.
Evaluation for 3.3c
In the Grade 7 Teacher's Edition, all topics have a "Linguistic Accommodations" section, where teachers are provided a detailed description of vocabulary terms associated with the topic. The topic's academic vocabulary is listed along with background knowledge students should be familiar with from other lessons, and a section called "Metalinguistic Transfer to Spanish" focuses on skills that can be transferred from English to Spanish. In Topic 1, cross-linguistic connections are made with the use of prepositions, like between and entre. Additionally, Topic 1 includes cognates and false cognates for the topic, increasing comprehension, building background knowledge, and making cross-linguistic connections. For instance, rational correlates with racional, and false cognates listed reduce confusion between integers and integro or scuba and cuba. Lessons also have "Language Support" activities that include embedded guidance for teachers to support emergent bilingual students. The activity in Lesson 1-3 is suggested to "Support understanding of physical science terms in Example 2. Teacher guidance states, "Encourage students to explain the terms [gravity and thrust] orally, providing examples and using gestures if necessary," which develops academic vocabulary, increases comprehension, builds background knowledge, and makes cross-linguistic connections through oral discourse.
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
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. For example, in the Grade 7 Teacher's Edition, Lesson 4-6, Step 3: "Practice and Problem-Solving," students demonstrate understanding of 7.11A by first solving and graphing solutions through numeric problems, then applying the same concept to real-world situations. Finally, students demonstrate depth of understanding and use critical thinking to analyze a diagram to determine the solution. The Grade 7 Teacher's Edition, Quick Check 1-1, demonstrates the depth of understanding by assessing various levels of rigor. Students begin by identifying examples of 'terminates' and 'repeats', then differentiate between 'repeating decimals' and 'terminating decimals.' Next, students apply knowledge by calculating and then analyzing a real-world situation, and end by evaluating by comparing the solution and justifying their answer.
Evaluation for 4.1b
Questions and tasks progressively increase in rigor and complexity, leading to grade-level proficiency in the mathematics TEKS. For example, in the Grade 7 Teacher's Edition, Lesson 6-2 focuses on TEKS 7.6D, where students make predictions and determine solutions using theoretical probability. Example 1 progresses from concrete/representational to abstract by utilizing a spinner and a formula with teacher-guided questions, including "How is the theoretical probability formula shown related to what is shown on the spinner?" demonstrating the increase in rigor from representational to abstract. Another example in Lesson 4-3, aligned with TEKS 7.10B, is students representing solutions for equations on number lines, transitioning from representational models using number lines to abstract models using standard algorithms. The guiding question, "What are the two steps you use to solve the equation?" can be justified by the representational and abstract models leading to grade-level proficiency. Questions and tasks in Lesson 1-4 progressively increase in rigor and complexity as students start with visual learning and progress to understand the concepts of multiplying rational numbers, and then move to multiplying a range of combinations of rational numbers.
Evaluation for 4.2a
The materials demonstrate coherence across units by explicitly connecting patterns, big ideas, and relationships between mathematical concepts. For example, the "Topic 3 Math Background: Coherence" section of the Teacher's Edition highlights explicit connections between previous and future topics. Topic 2 develops students' understanding of ratios and rates through unit rates, which Topic 3 then extends into percent and proportional reasoning. This progression leads into Topic 4, where students apply these concepts to write and solve equations, deepening their understanding of relationships between variables. The "Lesson Overview" for Lesson 4-3 demonstrates coherence by linking to Topic 2, where students learn to write and evaluate linear algebraic expressions. This foundation prepares them for Topic 5, where they use those expressions to solve two-step equations and compare algebraic solutions. These connections strengthen student understanding and demonstrate coherence across units by explicitly connecting patterns, big ideas, and relationships between mathematical concepts.
Evaluation for 4.2b
Materials demonstrate coherence across units by connecting the content and language learned in prior 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. For example, in Topic 4 of the Grade 7 Teacher's Edition, students solve two-step equations using models and mathematical algorithms, building on their grade 6 experience with writing and solving equations and inequalities using properties of equality. These foundational concepts extend into grade 8, where students apply them to solve equations in slope-intercept form involving two variables. This progression shows clear coherence across grade levels in developing algebraic reasoning. The Grade 7 Teacher's Edition supports coherence by including "Math Background: Coherence" sections in each topic. These sections explicitly connect grade 7 content to prior learning and future applications. For example, Topic 1 links to grade 6 use of number lines for decimal and fraction operations and prepares students for solving equations in grade 8. In Topic 9, the "Look Back" section references students' grade 6 learning of percent concepts and financial vocabulary, as well as earlier grade 7 work with percent and interest. Students then apply this knowledge to new concepts, such as budgeting, net worth, and incentives. The "Look Ahead" section connects this learning to grade 8 topics like loans, saving for the future, and paying for college, demonstrating a coherent progression in financial literacy.
Evaluation for 4.2c
In the Grade 7 Teacher's Edition, Lesson 6-2 on theoretical probability builds on students' prior knowledge of ratios and percents to make predictions. It connects to Lesson 2-1, where students learn to find equivalent ratios, demonstrating 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. Another example of 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 is in Lesson 9-1, which focuses on calculating income tax using the percent equation connected to Lesson 3-3, where students previously applied the percent equation to solve percent problems. Lesson 4-1 on understanding equations with two operations demonstrates coherence by referencing prior learning from Topic 4, where students generated equivalent expressions and used properties of operations to simplify them. Building on this foundation, students use bar diagrams and properties of equality to solve two-step equations, preparing them to write and solve multi-step inequalities later in the unit.
Evaluation for 4.3a
Lesson resources in the digital platform Savvas Realize provide spaced retrieval opportunities with previously learned skills and concepts across lessons and units in the "Differentiation Library." "Spiral Reviews" address a mixed review of concepts previously taught in both the grade 7 lessons and topics. The Grade 7 Teacher's Edition, Topic 9, "Review What You Know," provides spaced retrieval opportunities by revisiting percent problems, proportional reasoning, and operations with rational numbers. Percent problems that require students to determine part, whole, or percent are a previously learned skill and connect to Topic 3 and Topic 4, writing proportional equations. Another example is in Lesson 4-3 on solving two-step equations and comparing algebraic and arithmetic solutions. Later in Topic 4, students will solve equations using the distributive property and simplify inequalities. Previously learned skills and concepts from Topic 2 connect to the unit, writing and evaluating linear algebraic expressions, and solving problems with a variable.
Evaluation for 4.3b
Interleaved practice opportunities are found within the digital platform Savvas Realize in the "Differentiation Library" and include "Spiral Reviews," where the student completes a mixed review of previously learned skills and concepts across learning pathways in grade 7 lessons and topics. Lesson 4-8: "Practice and Problem Solving," found in the Grade 7 Teacher's Edition, demonstrates opportunities for interleaved practice across the lesson by requiring the student to write, solve, and represent inequalities on a number line, and asks questions of varying DOK. The concept of using the Properties of Equality is revisited throughout the topic; however, verbal representations are practiced, as well. Another example of interleaved practice opportunities with previously learned skills and concepts across units is in the "Fluency Practice" in Topic 9, which revisits TEKS 7.3A, adding, subtracting, and multiplying rational numbers. Topic 9 covers financial math, TEKS 7.13ABCDEF, and 7.1B, and uses numbers in different formats, like 5% or $45.67, interleaving the concepts across units.
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
Tasks require students to interpret models and representations for mathematical concepts and situations. In the Grade 7 Teacher's Edition, Lesson 7-2: "Practice and Problem Solving," Item 15 challenges students to interpret three triangle models and select the correct triangle for the given conditions. Questions require students to analyze and evaluate models for mathematical concepts and situations. In Lesson 3-2, the student is asked to interpret and analyze the diagram (the model) to determine the percent. Teacher-guided questions include "Divide the red bar into four parts. How many shots does each part represent?" and "On the bar diagram, what percent does each of the four parts represent?" These questions require students to analyze their model and evaluate their reasoning using the model. Another example is in each topic with "Let's Model in 3 Acts" lessons, requiring students to create, analyze, and evaluate models to represent mathematical concepts and situations. In Lesson 8-5: "That's A Wrap," "Act 1" has students analyze the situation by answering questions; "Act 2" has students create representations for the situations; and "Act 3" has students evaluate their answers for reasonableness.
Evaluation for 5.1b
All topics in the Grade 7 Teacher's Edition have a "Let's Model in 3 Acts" lesson requiring students to create, analyze, and evaluate models to represent mathematical situations. In Lesson 8-5: "That's A Wrap," "Act 1" requires students to analyze the situation by answering questions. In "Act 2," students create representations for the situation, and "Act 3" evaluates the representations for reasonableness. Another example is found in Lesson 4-1 on Item 1, where students are challenged to draw a bar diagram to represent the equation, creating a model to represent a mathematical situation. In Lesson 3-5, Know How, students create a model as a table to represent a mathematical situation in the sample space for Item 4.
Evaluation for 5.1c
Questions provide opportunities for students to apply conceptual understanding to new problem situations and contexts. In Lesson 6-7 of the Grade 7 Teacher's Edition, the section "Explore and Share" provides the teacher with the question, "How could you model each possibility?" which provides an opportunity for students to use a diagram or table to illustrate their understanding of sample space. At the beginning of each lesson, there is a "Conceptual Understanding" section, and Lesson 5-1 mentions that students learn that a representative sample can be selected randomly and includes members from all parts of the population in question. This is then demonstrated in the "Investigate" part of the lesson, titled "Good Samples Aren't Simple." Tasks provide opportunities for students to apply conceptual understanding to new problem situations. The "Explore and Share" in Lesson 9-1 prompts students to use a mathematical model to find the new price, using the conceptual understanding of percents and proportional reasoning to lead into the lesson about sales tax.
Evaluation for 5.2a
In the Grade 7 Teacher's Edition, Topic 2, "Fluency Practice" provides an activity where students practice adding, subtracting, multiplying, and dividing integers. This activity supports automaticity for grade-level tasks, focusing on solving equations and inequalities. The "Fluency Practice" allows students to build the computation and fluency skills necessary to evaluate equations and inequalities. Another example is at the end of each topic, where the materials provide additional fluency practice related to previous grade-level or foundational TEKS. In Topic 8, the fluency practice revisits using the percent equation to solve problems, which supports the grade-level tasks of solving problems involving three-dimensional geometry. Within the Grade 7 Differentiation Library, tasks are provided for students designed to build the automaticity and fluency necessary to complete grade-level tasks. These tasks are different from other activities within the materials. In Topic 5, the "Fluency Practice" task provided contains problems for students to practice adding, subtracting, multiplying, and dividing rational numbers.
Evaluation for 5.2b
In the Grade 7 Teacher's Edition, Lesson 3-7, "Explore and Share," students are given a scenario and asked to draw a representation of the situation. The teacher guidance provides sample responses where students may choose to create a bar diagram, or use algebraic expressions. This promotes efficient, flexible, and accurate mathematical procedures by allowing the student to choose procedures for problem solving within the lesson. The "Explore and Share" section of lessons encourages students to access a variety of processes to solve and represent mathematical procedures. In Lesson 2-5, students select a procedure to determine if a child's rate will allow them to break a record. Lesson 8-2: "Assess and Differentiate" provides opportunities for students to practice the application of efficient, flexible, and accurate mathematical procedures within the lesson. "Additional Practice" is provided for students to practice the mathematical procedures of Lesson 8-1, which solves problems involving surface area. Students have the opportunity to practice the application of drawing nets to find the surface area and to practice the application of analyzing math relationships through written expression about the surface area of a prism.
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. In each unit of the Grade 7 Teacher's Edition, there is a lesson titled "Let's Model in 3 Acts," and Lesson 3-4: "The Smart Shopper" utilizes this model; in "Act 2," the student develops procedures, processes, and solutions to model the problem using various tools, and in "Act 3," students evaluate their model for efficiency, flexibility, and accuracy and adjust where necessary. Teacher-guided questions include, "How useful was your model at predicting the answer?" and "How could your model better represent the situation?" In Lesson 2-7: "Talk About Math Ideas," students are prompted to evaluate the advantages of using different procedures, processes, and solutions to represent proportional reasoning, such as a ratio table, a bar diagram, a graph, and an equation. Within the teacher's guidance, the teacher is to partner students in completing a think-pair-share about their descriptions to evaluate solutions for efficiency, flexibility, and accuracy. At the beginning of each unit in the Grade 7 Student's Edition are the "Pick-A-Project" options that provide opportunities for students to evaluate procedures, processes, and solutions for efficiency, flexibility, and accuracy throughout the unit. In Topic 7, students have four options to evaluate procedures, processes, and solutions for efficiency, flexibility, and accuracy throughout the unit. They choose the best representation of their understanding of circles, diameters, and circumference.
Evaluation for 5.2d
In the Grade 7 Teacher's Edition, Lesson 4-3 starts with an "Explore and Share" activity to introduce multi-step equations using shapes, then encourages the attempt to solve the puzzles using logic. In Example 1, students use a number line to model the equation, and Example 2 focuses on the standard algorithm using properties of equality to determine the solution. Teacher guidance toward the increasingly efficient approach of the standard algorithm includes asking, "What steps did you take to isolate the variable?" Another example of embedded supports for teachers to guide students toward increasingly efficient approaches is in Lesson 7-9, when students first use a double number line in scale drawings, progress into using proportions, and are then introduced to a scale factor to implement algebraic expressions. Teacher guidance is provided throughout the lesson to make necessary connections between each transition of approaches, including questions such as, "How does the double number line represent the solution?" and "What is the constant of proportionality in the problem? Explain." Materials contain embedded supports for teachers to guide students toward increasingly efficient approaches. In Lesson 1-4, under "Visual Learning," the teacher guides the students with the utilization of strip diagrams, benchmark fractions, and benchmark percents before the learning and practice progress toward the student using mental math and line segments to determine percentages.
Evaluation for 5.3a
The Grade 7 Teacher's Edition includes Lesson 2-2, which has a section in the "Lesson Overview" that explicitly states how the lesson will address the TEKS conceptually and procedurally. The "Conceptual Understanding" states, "Students relate the use of a table of equivalent ratios to the procedure of dividing by a second term of a ratio, or multiplying by its reciprocal, to find the associated unit rate," and the "Application" section states, "Students extend their understanding and skills with unit rates and fraction operations as they solve problems involving ratios of fractions." These two sections of the "Lesson Overview" correlate with the TEKS and the learning objectives for the lesson. The beginning of each lesson provides a "Balance" section that provides the teacher with explicit conceptual and procedural information. Lesson 2-1 explicitly states that students will develop understanding and apply knowledge to calculate unit rates and equivalent ratios, aligned with TEKS 7.4A and 7.4B. In Topic 3, the section "Mathematical Process Standards" explicitly states how the conceptual and procedural emphasis of the TEKS are addressed while teaching analysis and solving percent problems, to communicate mathematical ideas, reasoning, and their implications using multiple representations, including symbols, diagrams, graphs, and language as appropriate (TEKS 7.1D). The guidance explicitly states, "As students solve percent and proportional reasoning problems, look for these behaviors to assess and identify students who demonstrate proficiency with mathematical reasoning and explaining," and TEKS 7.1D is the focus of a chart on this page listing various math concepts to be learned during this unit, including using properties of operations (procedural) to perform operations with the percent equation (conceptual).
Evaluation for 5.3b
The Grade 7 Teacher's Edition, Lesson 6-3: "Understand Experimental Probability," uses concrete models and manipulatives, pictorial representations, and abstract representations in Example 1. The example first uses a spinner (manipulative) located in the digital resource to determine the fraction and percent of one-eighth; then, students read a table illustrating a representational model of fractions; students finally use the standard algorithm (abstract representation) to convert fractions to percents, showing how experimental probability compares to theoretical probability of the spinner. In Lesson 1-3: "Add and Subtract Rational Numbers," students are tasked to determine the sum of numbers with different signs. Students first use a number line to determine the solution, with the option of using the online digital resource manipulatives to demonstrate the use of a concrete model and pictorial representation; and students next use the standard algorithm to subtract numbers and take the sign of the larger number to demonstrate an abstract representation. In the Grade 7 Student's Edition, the "Explore and Share" activity in Lesson 5-3 has students cast their votes on the paint color of the cafeteria walls. Students create a bar graph representing each color and how many students voted for it before evaluating the bar graph and answering questions such as "Which colors get the same amount of votes?" and "How does the voter for the color blue compare with the number of votes for the color red?" Based on the data represented in the given concrete and pictorial representations, students conclude how the rest of the school will vote.
Evaluation for 5.3c
In the Grade 7 Teacher's Edition, Lesson 1-3: "Add and Subtract Rational Numbers" supports students by connecting concrete and representational models of utilizing a number line to the abstract model of adding numbers with different signs. The question, "Why is the first number of the addition statement -4 1/2?" helps make the connection to the abstract model, focusing on the standard algorithm. The rational number is negative because, when compared to the number line, moving left represents negative integers. Students are asked to explain the relationships between the concrete/representational models and abstract models. Lesson 2-5: "Describe Proportional Relationships: Constant of Proportionality," supports students in connecting and explaining concrete models to abstract concepts using a ruler to demonstrate constant of proportionality by stating 2.54 centimeters is approximately 1 inch, illustrated by the ruler to confirm the constant of proportionality. The guidance question, "Could you use another mark on the ruler to determine the ratio of inches to centimeters? Explain," is used to illustrate the connection between concrete and abstract concepts. Additionally, Lesson 4-9 includes the activity "Checking A Bag," where students use manipulatives, create models, and solve using algorithms to solve two-step equations, and explain how the concrete and representational concepts connect to abstract concepts.
Evaluation for 5.4a
In the Grade 7 Teacher's Edition, Topic 2 introduces students to "Analyzing and Using Proportional Relationships" by viewing a "Math Walk" video about scale models. The students view the questions that coordinate with the video for a whole-class and partner discussion with questions such as, "What math do you already know that can help you answer the question?" and "What math questions do you have about what you saw in the video?" Students develop academic mathematical language by using the video subject-matter to discuss the mathematical concept of proportional relationships, with questions prompted by the teacher. In Step 1 of "Let's Build" in Lesson 4-2, students talk and work through a problem that displays two bar diagrams. Students compare the diagrams to develop mathematical language about two-step equations using visuals with questions such as, "How are the bar diagrams alike? How are they different?" This provides opportunities for students to develop academic mathematical language using visuals, written expression, and verbal discourse. "Additional Vocabulary Support" in Lesson 7-1 provides students with the name of a 2D shape and either the description or image. Students then have to complete the portion not given to them in the digital resource, Braining Camp Manipulatives.
Evaluation for 5.4b
In the Grade 7 Teacher's Edition, Lesson 2-3 has embedded teacher guidance to scaffold students' development of the vocabulary terms proportional relationship and proportion. In the activity, "Choose a Problem," students select one of the four problems to solve, and are then grouped by problem to discuss their solution strategies, utilizing mathematical vocabulary in context. Teacher guidance suggests discussions should be prioritized about ratios and proportional relationships, and encourages students to use vocabulary terms such as equivalent ratios, proportions, and proportional relationships. Additionally, in Lesson 9-1, the teacher guides student discussion and written expression through the use of sentence stems to scaffold and support student development and use of academic mathematical vocabulary in context connected to the topic of income tax. One of the sentence stems is "You only pay a higher rate on __________ of your income." In Lesson 6-2, the "Language Routine: Stronger and Clearer Each Time" provides teachers a prompt to instruct the students to solve the "Try It" independently before explaining to a partner how they solved it. The teacher is then guided to instruct the students and their partners to create a step-by-step graphic organizer, including important clues and phrases. This activity provides teacher guidance to support students' development and use of academic mathematical language through written expression, discourse, and creation of a thinking map.
Evaluation for 5.4c
The Grade 7 Teacher's Edition, Lesson 6-3, includes an activity in "Language Support" where students work with a peer to write sentences for the terms: relative frequency, theoretical probability, expected results, experimental probability, actual results, and guarantee. Partners then read their sentences aloud to the rest of the class, and misconceptions are corrected as a whole group, allowing students to use math language and develop their math vocabulary, syntax, and discourse. Exemplars for student responses to the "Explore and Share" task provide teachers with guidance to support students in proportional reasoning. Lesson 2-1, "Talk About Math Ideas," provides the teacher with guidance to have students hear and refine the use of math language with peers while discussing proportional and non-proportional relationships. Teacher guidance is provided to support students in mathematical language in vocabulary, syntax, and discourse as students are discussing proportional and non-proportional relationships. The vocabulary term for Lesson 6-9 is simulation, and the "Language Support" used in Example 1 supports the understanding of the term. Teacher guidance instructs teachers to give the definition of the term, then encourage students to discuss their familiarity with the term. Students are paired with peers to discuss an exemplar of simulation and how it is helpful with this problem: A simulation of a building during an earthquake can show what damage might occur, helping engineers make buildings actually safer, and students use the sentence frame, "A simulation of ______ can show _______," which provides opportunity for students to hear, refine, and use math language with peers.
Evaluation for 5.5a
In the Grade 7 Teacher's Edition, the process standards are integrated into multiple tasks and questions, and are identified with a teal-colored font. Lesson 6-4 has a section titled "Explore and Share," and under "Analyze Math Relationships," students analyze the relationship between Leah's and Luke's probability of being chosen as captain of a team, integrating with TEKS 7.1F. Process standard TEKS 7.1B is integrated in Example 1, where students use a problem-solving method to solve the problems. Also in Topic 5, the TEKS process standards integrated within the lesson are listed on the first page of Lesson 5-2, with one process standard listed is TEKS 7.1F, "analyze mathematical relationships to connect and communicate mathematical ideas," which is integrated when students solve problems related to investigating the relationship between populations and samples in order to connect and communicate mathematical ideas. Additionally, in the "End Matter," there is a "Correlation to TEKS" page listing every mathematical process standard aligned to the lessons, incorporating each process standard. For example, process standard TEKS 7.1E "create and use representations to organize, record, and communicate mathematical ideas" is integrated into Lessons 1-1, 7-2, and 9-7.
Evaluation for 5.5b
The Program Overview Grades 6–8 contains the "From the Authors: Grade 7 Content Organization Rationale," which details the relationship between topics throughout the course. Within the rationale for each topic, there is a section called "Connections" that begins with the statement, "Students apply mathematical process standards. . . y" This introductory statement implies that by using mathematical process standards, students are able to achieve mastery of the objectives provided in the section. The "From the Authors: Mathematical Process Standards" section describes how the process standards are incorporated and connected throughout each lesson. The following color-coded labels throughout the course correlate with a process standard and instruct the teacher/student that the activity connects with a process standard: "Apply Math" incorporates TEKS 1A, "Plan" and "Check" incorporate TEKS 1B, "Select Tools" incorporates TEKS 1C, "Communicate" and "Reason" incorporate TEKS 1D, "Represent" incorporates TEKS 1E, "Analyze" and "Connect" incorporate TEKS 1F, and "Explain" and "Justify" incorporate TEKS 1G. Additionally, in the "Front Matter" of the Grade 7 Teacher's Edition, a section titled "Mathematical Process Standards" contains a subheading titled "Process Standards and the Problem-Solving Handbook." This subheading describes how the "Problem-Solving Handbook," embedded within the materials, supports content and process standards by presenting a problem-solving model to the students along with a problem-solving recording sheet where students show their thinking. For example, process standard TEKS 1B expects the students to use a problem-solving model to analyze, formulate, justify, and evaluate the problem-solving process in addition to finding the solution.
Evaluation for 5.5c
In the Grade 7 Teacher's Edition, the Topic 8 "Topic Planner" provides a detailed overview of the lessons throughout the topic, including how TEKS process standards are incorporated and connected throughout the unit. The process standards for Topic 8 are listed in the TEKS section of the overview, and the "Mathematics Objective" includes verbs associated with the process standards of the lesson and topic. For example, Lesson 8-3 incorporates process standards TEKS 7.1B, 7.1F, and 7.1G in the lesson, and Lesson 8-4 incorporates TEKS 7.1A, 7.1B, 7.1C, 7.1D, and 7.1E. Another example is found in the "Topic Planner" for Topic 4, where each process standard featured in the topic is categorized by which lesson(s) it is incorporated and connected to throughout the unit. For example, process standard TEKS 7.1D is incorporated in Lessons 4-2, 4-3, 4-4, 4-7, 4-8, and 4-9. The materials also link TEKS 7.1D to a specific lesson, with page numbers to the question(s) and/or activity. Additionally, the "Mathematical Process Standards" section in Topic 9 suggests two process standards to focus on throughout the topic: TEKS 7.1A and 7.1G. A table is provided with mathematical objectives incorporated and connected throughout Topic 9 and relates them to the capabilities of a proficient student. For example, under the TEKS 7.1G column, mathematically proficient students can "communicate which monetary incentives are most valuable and justify their spending."
Evaluation for 5.5d
In the Grade 7 Teacher's Edition, each lesson overview provides the process standards covered within the lesson. In Lesson 7-1, the process standards are TEKS 7.1C and 7.1D, and these standards are demonstrated in various questions and tasks throughout the lesson. TEKS 7.1C is indicated in Example 1 with "Select Tools," where students are encouraged to select between a ruler and a protractor to construct precise drawings. In Lesson 4-1, the process standards TEKS 7.1C and 7.1E are demonstrated in various questions and tasks throughout the lesson. TEKS 7.1E is indicated in Items 1–2 of "Practice and Problem Solving" with "Represent Math Ideas," where students create a bar diagram to represent the given equation. Additionally, in the "End Matter," the "Correlation to TEKS" lists every mathematical process standard numerically and details which lessons and units contain the standard. For example, TEKS 7.1A is incorporated in lessons and units from Topics 1–9, with a heavier incorporation in Topic 4: "Solve Equations and Inequalities" and Topic 9: "Financial Math."
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
In the Grade 7 Teacher's Edition, Topic 2, "Topic Opener: Integers and the Coordinate Plane," students watch a "Math Talk" video that uses bargain shopping to relate to concepts involving percents. This activity allows students to think mathematically by later referencing the video to compare what they learn about markup and markdown problems to bargain shopping discussed in the video. A guidance question encouraging problem-solving perseverance asks, "What math did you learn that could help you answer the question or find the answer differently?" In Lesson 3-1, students investigate a real-world situation where three receipts are given with a specific tip amount presented as a fraction, a decimal, and a percent. Students use the given information and choose a strategy to determine the dollar amount of each tip and decide the best value. A prompt listed in the activity states, "What different methods can you use to find the percent of a number?" which requires students to persevere through solving problems and making sense of the math as they work toward a solution. Each lesson in the Grade 7 Student's Edition has a practice and problem-solving section that gives students the opportunity to persevere through solving problems. In Lesson 3-1, one question has students find the sales tax to complete the given table and to persevere in calculating the total cost, price, and sales tax. More specifically, students must calculate 4% of $40, and then get the total, which gives students the chance to think mathematically and make sense of the math.
Evaluation for 6.1b
In the Grade 7 Teacher's Edition, Lesson 2-4 has a "Try It" task where students select a technique provided in Example 1 to solve the problem. The techniques include writing a proportion, or using the unit rate. Students understand there are various ways to represent and solve the problem. Lesson 2-9 provides students the task of determining how many drops to put in a solution with the capacity of a cooler instead of a glass. Question 7 of the task asks, "What tools will you use to solve the problem? Explain how you will use them strategically," illustrating there are multiple ways to represent this problem. Question 8 of the task states, "Represent the situation using mathematics," which is completed through small-group discussions with students explaining and later justifying their representations in Question 13. In the Grade 7 Student's Edition, Lesson 1-3 Example 1 explains how to either add -2.75 and 5.5, or subtract 5.5 -2.75 to get the same answer, using two different operations and two different methods. The example explains and justifies that the task can use a number line to represent the distances, or the absolute value can be taken, and the operation used would be subtraction; next, the example shows that addition could occur by doing -2.75 + 5.5, and the sign with the greater (absolute value) addend will be used. The methods show there are multiple ways to represent and solve problems and complete tasks.
Evaluation for 6.1c
In the Grade 7 Teacher's Edition, Lesson 9-1 asks students to complete the "Explore and Share" activity, where students collaborate to determine the new price after a percent off the original price. As students work, materials suggest that teachers ask questions based on observations to guide student understanding with discussion questions, such as, "How can you use a mathematical model to find a new price?" This question provides opportunities for students to discuss math with both their teachers and peers. Lesson 8-2, Step 2: "Visual Learning," provides opportunities for students to collaborate to complete various tasks requiring them to solve problems, determine lateral and total surface area, write explanations about how to find the surface area of a pyramid or prism, and engage in a Think-Pair-Share during the section "Talk About Math Ideas." The Grade 7 Student's Edition includes Lesson 8-3 on finding the volume of prisms and pyramids, which has a section for students to "Talk About Math Ideas" with their peers by discussing, "How does the relationship between surface area and volume connect to their formulas?" Teachers are encouraged to guide students in discussing the question with each other, either in group or partner settings, and listen for key terms to create a teacher-to-student dialogue that enhances the student-to-student dialogue.
Evaluation for 6.2a
In the Grade 7 Teacher's Edition, in the Lesson 9-2 "Choose a Problem" activity, students select from four different problems and solve the selected problem individually; the teacher then groups students based on their selected problem to share their solution strategies. The groups present their findings to the class, and other groups ask questions and comment on the problem-solving approaches. Teacher guidance provides questions that center discussions around using the percent equation; for instance, "What parts of the equation can be filled in?" In Lesson 9-5 students participate in a collaborative task to develop a model to solve a given problem. During the collaboration, students explain and justify their reasoning, and after the teacher reveals the answer, students reflect on their model. Student prompts that promote reflection include "Would you change your model now that you know the answer? Explain," and "Explain how you used a mathematical model to represent the situation? How did the model help you answer the main question?" The Lesson 2-9 activity "Mixin' It Up" supports teachers in guiding students to share and reflect on their problem-solving approaches by asking students to watch a video to make the liquid in a water glass and the liquid in a large water cooler have the same flavor and having teachers take advantage of student reactions while watching the video with questions such as, "What did you notice? What did you wonder?" Students then answer brainstorming questions, and teachers are guided to have students share their thoughts on problem solving, before asking the main question, "How many drops are needed for the water in the cooler to have the same flavor as the water in the glass?"
Evaluation for 6.2b
In the Grade 7 Teacher's Edition, Lesson 1-4 guides teachers to anticipate student misconceptions regarding positive and negative numbers. If the student has difficulty with debits and credits, the materials suggest teachers ask the following questions: "Do you use a positive or a negative number to show a change in account balance after money is taken out?" or "What about after money is added?" The Lesson 3-6 Exit Ticket guides teachers if students answered a question about percent markup incorrectly, indicating the student may have misconceptions related to distinguishing between markup/markdown and percent markup/markdown, or connecting these ideas to the percent equation. The materials suggest preventing this misconception by pausing and drawing students' attention to the part = percent x whole equation before they complete practice problems on this topic. Questions provided for the teacher to ask include: "In this problem, do we know the whole?" "Do we know the part?" "Do we know the percent markup/markdown?" In Lesson 3-6 the materials include prompts and guidance on how to provide explanatory feedback by stating students need fluency in converting between percents and decimals, as they work through Examples 2 and 3. There is teacher guidance on how to walk students through converting 0.55, 0.1, and 0.025 to percents: "Move the decimal point to the right two places and add a percent symbol." There is also guidance on how to convert 35%, 70%, and 17.5% to a decimal: "Move the decimal point to the left two places and remove the percent symbol."
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