Cosenza Math – Grade 7 Advanced

Evaluation for 1.1a
Materials include a scope and sequence outlining the TEKS, ELPS, and concepts taught in the course.

The materials include a scope and sequence outlining the Texas Essential Knowledge and Skills (TEKS), English Language Proficiency Standards (ELPS), and course concepts. This scope and sequence can be found under the Course Level Documents titled Grade 7 Advanced Mathematics Scope and Sequence. The scope and sequence includes two correlation tables. The first is a unit-to-TEKS/ELPS correlation table that allows the educator to identify the standards in a specific unit. Additionally, TEKS/ELPS-to-unit correlation tables include the full language of the standards and allow the educator to locate units for a specific standard.

The Grade 7 Advanced Mathematics Scope and Sequence document includes a bulleted list of concepts titled “Concepts & Knowledge to Be Learned in Grade 7 Advanced Mathematics.” For example, the list includes “Dilations result in similar figures,” “Even if data is only approximately linear, a line can be used to estimate the data to make inferences and predictions,” and “Interest earned increases in value over time.”

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).

The materials include suggested pacing to support effective implementation for various instructional calendars. This pacing guide is available under the Course Level Documents. The guide includes 150-, 165-, and 180-day calendars. Each calendar includes columns for the instructional day, unit, lesson number, topic, TEKS, and ELPS.

At the end of each instructional calendar, the materials provide guidance for time adjustments that do not disrupt the instructional sequence or content coherence. For example, at the end of the 165-day calendar, a bulleted list outlines how the calendar may be adjusted: “The instructional day(s) spent on Enrich/Extend lessons designated at the end of each of Units 1, 2, 3, 4, 5, 6, 7, 8, and/or 9 can be reduced or skipped to recapture up to ten instructional days.” The length of the instructional calendar provides a variety of options for adjustment, with the longest calendar offering the most.

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.

The materials explain the rationale for the unit order and how the concepts connect throughout the course. The explanation is under the Course Level Documents heading within the Scope and Sequence, following the ELPS table. The page, titled Rationale for Unit Progression, contains the rationale for unit order and how the concepts connect throughout the course.

For Grade 7 Advanced Mathematics, the Rationale for Unit Progression provides detailed connections to both the Texas Response to the Curriculum Focal Points (TxRCFP) and to the TEKS process standards. An example from the rationale states, “In Unit 2, students calculate and interpret data with a single variable using visual and symbolic representations. Unit 3 focuses on symbolic manipulation of equations and inequalities to solve for a single variable. Unit 4 builds from the single-variable concepts and skills students have learned in previous grade levels and honed in the first three units of the course to begin to develop the idea of slope as a constant rate of change in linear relationships and the meaning of both x- and y-intercepts of linear functions.”

Evaluation for 1.1d
Materials include protocols with corresponding guidance for unit and lesson internalization.

The materials include protocols with corresponding guidance for unit and lesson internalization. This guidance is in the Course Level Documents section and includes a Unit Internalization Protocol and a Lesson Internalization Protocol for educators. Each protocol is a checklist to help educators internalize the content. The Unit Internalization Protocol guides educators through three main actions: “Read through the digital unit pages and make notes for your ‘three weeks from now’ self,” “Connect unit learning to culminating tasks,” and “Anticipate where students may need support.” Under each action are deeper-level tasks, such as “Begin with the end in mind by unpacking the unit assessments.” Finally, the materials provide questions for the educator to consider during unit internalization and prompts to support connections to student outcomes, such as “Think about what you have read before these resources as well as the additional information they provide. What will you do when students already know what you will be teaching?”

The Lesson Internalization Protocol presents the same educator guidance, but at the lesson level. It guides educators through three main actions: “Read through the digital lesson pages and make notes for your ‘three weeks from now’ self,” “Connect lessons to culminating tasks,” and “Anticipate where students may need support.” Under each action are deeper-level tasks, such as “Begin with the end in mind by unpacking the lesson assessments.” Finally, the materials prompt educators with questions to support continued lesson internalization and connections to student outcomes, such as “As you read through the lesson overview and detailed lesson plans, how does learning build and connect throughout the lesson?”

Evaluation for 1.1e
Materials include resources and guidance for instructional leaders to support teachers with implementing the materials as designed.

The materials include resources and guidance to help instructional leaders support educators in implementing the materials. The Implementation Guide under Course Level Documents includes these resources and guidance. The guide includes various resources to help instructional leaders support educators. For example, Teacher Conversations to Support Implementation includes a short paragraph describing the “plan-do-study-act” and a table detailing how to accomplish it. The table columns include Design, Facilitate, Analyze, and Improve. Each column further breaks down what each step entails: Lesson Planning, Teaching and Learning, Student Learning Evidence, and Evaluate Outcomes. Each column also includes timing for each step and offers questions instructional leaders can ask their educators.

The Implementation Guide also provides an Observation Protocol and Checklist page for instructional leaders, including observational support for “Prior to the Lesson,” “During the Lesson,” and “After the Lesson.” Each category includes checklist criteria. In the Prior to the Lesson section, the checklist prompts leaders to check that educators complete certain tasks, such as their daily lesson plan, and provides conversation starters to support leader conversations with educators. In During the Lesson, the checklist prompts the leader to look for various things, such as student placement in random groups and student engagement in mathematical discourse. In After the Lesson, the checklist prompts leaders to continue conversations with their educators, such as sharing “glows,” providing feedback, and discussing “grows.”

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.

The materials include comprehensive unit overviews that provide the background knowledge and academic vocabulary needed to teach the unit’s concepts effectively. Each unit begins with a page titled, for example, “Unit 1: Rational Number Operations and Real Numbers” that lists the unit, the lessons within the unit, the TEKS and ELPS covered, a unit introduction, a unit overview, and prior learning supports. The Unit Overview page provides the background knowledge needed to teach the unit’s concepts effectively.

For example, in the Prior Learning Supports section, a column provides previous years’ TEKS, the full language of the standards, and how they connect to the current grade’s TEKS. At the bottom of the page, under Resources, is a 7AM Unit 1 Document that provides the academic vocabulary needed to teach the unit’s concepts effectively.

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.

The materials include English supports for families in each unit, with suggestions to support their student’s progress. For example, at the bottom of the Unit Overview page for Unit 2, “Probability & One-Variable Statistics,” is a 7AM Unit 2 English Letter. The document includes suggestions for how families can support their students’ progress in that unit, such as involving their students in real-world applications and asking them to explain something they have learned.

The materials include Spanish supports for families for each unit, with suggestions to support their student’s progress. For example, at the bottom of the Unit Overview page for Unit 2, “Probability & One-Variable Statistics,” is a 7AM Unit 2 Spanish Letter. The document includes suggestions for how families can support their students’ progress in that unit, such as involving their students in real-world applications and asking them to explain something they have learned. This letter is in Spanish.

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).

Each unit’s Overview page includes comprehensive, structured, detailed lesson plans that specify daily objectives, questions, tasks, materials, and instructional assessments required to meet the content and language standards for the lesson. For example, in unit 8, lesson 1, “Pi, Circumference, and Diameter,” the Learning Outcomes subsection provides lesson objectives as “I can…” statements, such as “I can directly measure the circumference and diameter of a circle.” Within the same subsection, a table provides the TEKS and ELPS correlations with full indicator language for each.

The materials within the same Unit Overview page also contain questions aligned to the lesson objective in a subsection titled Lesson Overview. This is written as a Focusing Question, for example, “What are the relationships among the diameter of a circle, the circumference of a circle and [pi]?” Tasks within the lesson are found in the Lesson Plan subsection and contain three tasks: exploration, explanation, and the performance task. Each task provides educator guidance on implementation.

Finally, the lesson plan includes an instructional assessment in the form of one or more performance tasks. The Lesson Overview page includes the educator version of the performance task(s), with four levels based on student mastery.

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.

The materials include a lesson overview listing the educator and student materials needed to deliver the lesson effectively, along with the suggested timing for each lesson component. On each Lesson Overview page, near the center, a subsection titled Pacing Guide provides the suggested timing for each lesson component. The suggested timing for each lesson component is located here. Near the bottom of the Lesson Overview page are two subsections that include the necessary materials: Teacher Materials and Student Materials.

For example, in unit 6, lesson 1, “Translations, Reflections, and Rotations,” the Pacing Guide suggests the Exploration portion takes 20–25 minutes, the Explanation and Practice portion takes 40–45 minutes, and the performance task takes 30–35 minutes. Further down the page, the Teacher Materials section lists graphing technology, patty paper, cardboard, and pushpins as necessary for educators. The Student Materials section lists pencil, paper, and colored pencils, as well as optional patty paper.

Evaluation for 1.3c
Materials include guidance on the effective use of lesson materials for extended practice (e.g., homework, extension, enrichment).

The materials include guidance on effectively using lesson materials for extended practice through performance tasks. Within each lesson’s Overview page, under the Lesson Components table, a column provides one or more performance tasks. When an educator clicks the hyperlink, it opens and details the task’s various components. Each task has four versions, depending on the student’s proficiency level, and the lesson’s Overview page provides educator guidance on effective use of the performance task.

For example, in unit 5, lesson 4, “Writing Equations for Linear Relationships,” the Lesson Overview page includes a subsection titled Lesson Plan. At the end of this plan is a bullet point for the performance task, with sub-bullets that guide educators on how and when to use it. Examples of sub-bullets include “As a formative assessment, use the performance task to determine what students know about the topic,” “Performance tasks have four versions: on-level, simplified, enriched, and scaffolded,” and “If there are multiple performance tasks, select one or encourage self-differentiation by allowing students to select a task based on their interests and comfort levels.”

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.

The materials include a variety of instructional assessments at the unit and lesson level (including diagnostic, formative, and summative) that vary in task and question types. In Grade 7 Advanced Mathematics, each unit provides a diagnostic assessment at the beginning, followed by lesson-level formative assessments, and concludes with a unit summative assessment. For example, unit 7 begins with a diagnostic assessment split into two parts. Problems 1–8 in section 7A contain previous-grade-level TEKS, and problems 1–7 in section 7B contain current-grade-level TEKS. Both parts include various task and question types, such as open-ended and multiple-choice.

Each lesson contains various formative assessments. For example, in unit 7, lesson 2, “Solving Problems with the Pythagorean Theorem and Its Converse,” materials provide two assessment options for educators. The Explanation portion of the lesson includes the first formative assessment and instructs educators to provide students with the practice problems from specific workbook pages. When students arrive at those pages, they see open-ended and multiple-choice questions. A second option for lesson-level formative assessment is the performance tasks at the end of each topic. Unit 7, lesson 2 contains two task options: Laptop Stand or Sails. Both tasks use open-ended questions, and each has four performance levels. The levels include simplified, scaffolded, on-level, and enriching tasks, and educators assign them based on students’ mastery level.

The materials provide a summative assessment at the end of each unit, such as the unit 7 Test. Educators can print the assessment or assign it digitally. In the Unit 7 Test, the main question types are multiple-choice and open-ended.

Evaluation for 2.1b
Materials include the definition and intended purpose for the types of instructional assessments included.

The materials include definitions and intended purposes for the instructional assessment types included. For example, the Grade 7 Advanced Mathematics Assessment Guide, available on the Course Level Documents page, includes a table listing the three assessment types: lesson-level formative, unit-level diagnostic, and unit-level summative. The table includes the definitions, purposes, administration guidance, and examples/formats for each instructional assessment.

For example, the lesson-level formative assessment row defines it as “Assessment during the lesson (consistently during the lesson).” The purpose states, “Provide teachers with feedback to make instructional decisions for the remainder of the lesson and/or next lesson.” The unit-level diagnostic assessment row defines it as “Assessment at the beginning of the unit of instruction (once per unit)” and states the purpose as “Uncover misconceptions prior to instruction.” The unit-level summative also states the definition and purpose.

Evaluation for 2.1c
Materials include teacher guidance to ensure consistent and accurate administration of instructional assessments.

The materials include educator guidance to ensure consistent and accurate administration of instructional assessments. For example, under the Grade 7 Advanced Mathematics Course Level Documents is a Performance Task Rubric and Scoring Guide. The document opens with a rubric for all course lesson-level performance tasks. It contains three main scoring sections: procedural, conceptual, and communication, with each section contributing zero, one, or two points each for a total of six points possible for each performance task. Breaking down the rubric further, the zero-, one-, or two-point columns have three options for the procedural, conceptual, and communication sections.

For example, in the procedural section, the zero-point column breaks down into three options. An example of a statement in this column is “Little to no evidence of mathematical reasoning is present or the reasoning is scattered and incomplete.” The one-point column includes three options. An example of a statement in this column is “Uses a strategy that leads to a solution of the problem. Some errors in the procedure may result in an incorrect solution, but the errors are minor and the procedures are appropriate.” The two-point column breaks down into three options. An example of a statement in this column is “Uses a very efficient and organized strategy leading to a solution.” The conceptual and communication sections are also broken down into three options each for the zero-, one-, and two-point columns.

Evaluation for 2.1d
Diagnostic, formative, and summative assessments are aligned to the TEKS and objectives of the course, unit, or lesson.

The materials include diagnostic assessments aligned to the TEKS and objectives of the course, unit, or lesson. For example, in Grade 7 Advanced Mathematics, each unit begins with a diagnostic assessment, such as the Unit 7 Diagnostic Assessment. The Grade 7 Advanced Mathematics Test Answer Key & Diagnostic Guide provides educators with the diagnostic assessment answer key and includes the item number, TEKS, correct answer, and diagnostic information. For example, the diagnostic assessment for unit 7, problem number 3 under section 7B, shows a triangle with two given interior angles, one missing interior angle, and its adjacent missing exterior angle. The problem states, “What do you think is the measure of the exterior angle? Justify your reasoning.” This question aligns with one of the unit 7, lesson 3 objectives, which states, “I can establish and apply facts about the relationships among the measures of interior and exterior angles of a triangle.”

The materials include formative assessments aligned to the TEKS and objectives of the course, unit, or lesson. For example, the unit 7, lesson 3 performance task is a formative assessment aligned with the TEKS and the lesson objective. In the educator edition of the task, the first page lists the TEKS the task assesses. The objective for unit 7, lesson 3 states, “I can establish and apply facts about the relationships among the measures of interior and exterior angles of a triangle,” and the task provides students with an image of streets that cross to make a right triangle with various streets parallel to the base of the triangle forming smaller right triangles within. The problem reads, “Several streets in Halton City, Texas, intersect as shown in the diagram. East Belknap Street and NE 28th Street intersect such that the acute angle at their intersection is 43.5 [degrees]. NE 28th Street is perpendicular to the parallel streets of North Beach Street, Higgins Lane, and Haltom Road. Determine the measurements of [angle] KLN, [angle] MNL, and [angle] MNQ. Justify your reasoning.”

The materials include summative assessments aligned to the TEKS and objectives of the course, unit, or lesson. At the end of each unit, educators can assign a summative assessment called the unit test. In the test answer key, educators are provided a table with columns such as the item number, reporting category, readiness or supporting, content student expectation (TEKS), process student expectation (also TEKS), and the correct answer. For example, in the unit 7 Test Answer Key, educators are able to see each of the TEKS the test is aligned to. When viewing the printable test, for example, problem 4 reads, “A 39-foot ladder leans against a building. The bottom of the ladder is 15 feet from the base of the building. How far up the side of the building does the ladder reach?” This question aligns with an objective from unit 7, lesson 2, which states, “I can use the Pythagorean Theorem to solve problems.”

Evaluation for 2.1e
Instructional assessments include TEKS-aligned items at varying levels of complexity.

Instructional assessments include TEKS-aligned items evaluating varying levels of complexity. In Grade 7 Advanced Mathematics, instructional assessments include three types: diagnostic, formative, and summative. Each assessment includes items of varying complexity. For example, in unit 7, the diagnostic assessment is split into two sections. The first section covers TEKS-aligned items from previous grade levels, while the second section covers current-grade-level TEKS. Within each section, questions vary in complexity, ranging from listing items to making predictions. Each lesson includes two formative assessments: the performance task and practice problems from the book. Teachers can assign the task based on students’ level of mastery, and it can vary in complexity, with options such as an enriched, scaffolded, on-level, or simplified task. The practice problems in the book also offer a range of complexity levels. Finally, the unit summative assessment, called the unit test, provides varying levels of complexity, and the questions are based on similar problems students encounter in the book, practice problems, the performance task, and the grade-level section of the diagnostic test.

Instructional assessments also include a variety of TEKS-aligned item types. For example, in unit 7, the diagnostic assessment contains open-ended and multiple-choice item types. The performance task contains only open-ended questions, but the practice questions in the book include both open-ended and multiple-choice item types. The unit test includes multiple-choice and open-ended items.

Evaluation for 2.2a
Instructional assessments and scoring information provide guidance for interpreting student performance.

The materials include scoring information to ensure accurate scoring of instructional assessments. For example, in Grade 7 Advanced Mathematics under the Course Level Documents, a Performance Task Rubric and Scoring Guide provides a rubric for all course lesson-level performance tasks. The rubric contains three main scoring sections: procedural, conceptual, and communication, with each section contributing 0, 1, or 2 points for a total of 6 points possible for each task. The 0, 1, or 2-point columns have three options for the procedural, conceptual, and communication sections. For example, in the procedural section, the 0-point column lists three options. An example of a statement in this column is “Little to no evidence of mathematical reasoning is present or the reasoning is scattered and incomplete.” The 1-point column includes three options. An example of a statement in this column is, “Uses a strategy that leads to a solution of the problem. Some errors in the procedure may result in an incorrect solution, but the errors are minor and the procedures are appropriate.” The 2-point column breaks down into three options. An example of a statement in this column is “Uses a very efficient and organized strategy leading to a solution.” The conceptual and communication sections break down into three options each for the 0-, 1-, and 2-point columns.

The materials include guidance for interpreting student performance on instructional assessments. In Grade 7 Advanced Mathematics, under Course Level Documents, a document titled Grade 7 Advanced Mathematics Assessment Guide includes a section titled Guidance for Interpreting Student Assessment Performance. This section explains how to interpret student performance across different assessments and outlines steps educators can take. For example, one paragraph in this section states, “For assessment scoring and its relationship to student progress, consider the aggregate of all questions related to the same TEKS. Did the student master this TEKS by answering the vast majority of questions aligned to the TEKS correctly? What pattern(s) do you see in their incorrect answers? (e.g. a student answers all computation questions that provide a decimal are answered correctly but items that provide a fraction are answered incorrectly).”

Evaluation for 2.2b
Materials provide guidance for the use of included tasks and activities to respond to student trends in performance on assessments.

The materials provide educators with guidance on using the included tasks and activities to respond to student performance trends on assessments. In Grade 7 Advanced Mathematics, each unit contains one or more performance tasks as a formative assessment option. For example, unit 3, lesson 1, “Model and Solve One-Variable Equations” contains two different tasks titled Flowerbeds and Snacks. Each task contains four levels of complexity: simplified, scaffolded, on-level, and enriching. The performance task in unit 3, lesson 1 guides educators on assigning tasks at each level and to “Differentiate tasks based on instructional assessments in the previous portions of the lesson,” such as the Exploration and Explanation portions.

The Unit 3 Diagnostic Assessment answer key also provides guidance. When opened, the Grade 7 Advanced Mathematics Test Answer Key & Diagnostic Guide is set up in a table format, with two sections as the document’s main focus. The first section covers “assessment of prerequisite content knowledge,” while the second covers “assessment of preconceptions & misconceptions.” Within each section, the table is further broken down into item number, content TEKS, correct answer (with work shown), and diagnostic information. The diagnostic information column guides educators in responding to student performance trends. An example explanation in the diagnostic column is, “Item 1 addresses prerequisite knowledge about representing multistep problems involving operations. Review is recommended prior to teaching Lesson 2 in Unit 3 for students scoring 50% or less on this item.”

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.

The materials include tools for educators to track student progress and growth. For example, in Grade 7 Advanced Mathematics, Course Level Documents include a guide titled Grade 7 Advanced Mathematics Teacher Tracking Document. The document is divided into five main columns, with the last further divided into six sub-columns. The first column is for educators to enter student names; the second lists student strengths; the third notes what students are working on now; and the fourth lists the student’s next goal(s). The last column contains each grade-level TEKS, broken down into five assignment sub-columns and an overall progress column.

The materials include tools that help students track their own progress and growth. For example, in Grade 7 Advanced Mathematics, under Course Level Documents, the Grade 7 Advanced Mathematics Assessment Guide includes the Printable Student Progress Tracking Tool, followed by a paragraph that explains how to use it. The tracking tool is a table with multiple columns. The first column lists the TEKS in the course with full standards language. Students use the next five columns to list any assignments that cover that specific TEKS within the course. Students use the final column to enter their overall progress for that TEKS. After the TEKS table, students list their Strengths, their “What I am Working On Now,” and “What My Next Goal Will Be.”

Another example of an available tool that lets students track their progress is on each unit’s Overview page. For example, in Grade 7 Advanced Mathematics, on the unit 2 Overview page, the 7AM Unit 2 English Letter describes the content taught in unit 2 and how guardians can support their students’ progress. Finally, a table at the bottom of the letter allows guardians and students to track student progress within the unit. The table has three columns: unit activity, assignments, and grades earned. Students and guardians can track students’ progress within each lesson.

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.

The materials include educator guidance for differentiated instruction, activities, and paired (scaffolded) lessons for students who have not yet reached proficiency on grade-level content and skills. For example, in Grade 7 Advanced Mathematics, on the unit 3, lesson 1 Overview page, a section titled Paired (Scaffolded) Lessons & Guidance for Small Group Instruction contains a short worksheet and answer key for students who have not yet reached proficiency. The section states, “For students who have not yet reached proficiency on grade-level content and skills, use the paired (scaffolded) lesson below during the Explanation lesson phase and follow the educator guidance below the table that contains the paired lesson activity. Convene a small group of students based on information from the Unit Diagnostic Assessment and Exploration activity for you to work with while the remainder of the class is working on the Explanation activity.” The worksheet and answer key include explicit educator guidance on using the activity sheet to best support students.

The materials include educator guidance for differentiated activities that support students who have not yet reached proficiency in grade-level content and skills. For example, in Grade 7 Advanced Mathematics, each lesson provides one or more performance tasks as formative assessments. Each task offers four levels of complexity: a simplified task for students who have not yet reached proficiency, a scaffolded task for students who are somewhat proficient, an on-level task for students who are proficient, and an enriching task for students who are highly proficient. The Performance Task Overview page gives educators guidance on how to distribute each task.

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).

The materials include pre-teaching of unfamiliar vocabulary and in-text references. In Grade 7 Advanced Mathematics, each unit and lesson includes a vocabulary list for educators at the bottom of the page, along with guidance on supporting students’ acquisition of new vocabulary terms. For example, unit 2, lesson 2 lists the vocabulary terms to preteach as complement and probability. The description above these terms states, “One way to support students’ acquisition of new vocabulary terms is to preteach the vocabulary terms using a strategy such as a Frayer model.”

The materials also include educator guidance under Course Level Documents in the Grade 7 Advanced Mathematics Teacher’s Guide, which provides educators with a six-step process for building academic vocabulary: “1. Introduce the new term(s) by providing a student-friendly example, description, and/or explanation. 2. Students restate the example, description, and/or explanation in their own words. 3. Students create a non-linguistic representation of the term(s) (pictures, graphic, symbol, etc). 4. Engage students periodically in activities that deepen their understanding of the term(s). 5. Periodically involve students in discourse during which they discuss the term(s) with one another. 6. Involve students periodically in games that allow them to play with the term(s).”

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.

The materials include educator guidance for differentiated instruction, enrichment, and extension activities for students who have demonstrated proficiency in grade-level content and skills. For example, in Grade 7 Advanced Mathematics on the unit 3, lesson 1 Overview page, a section titled Paired (Differentiated) Lessons & Guidance for Small Group Enrichment contains a short worksheet and answer key for students who have not yet reached proficiency. The section states, “For students who have demonstrated proficiency on grade-level content and skills, use the differentiated lesson below during the Explanation lesson phase and follow the educator guidance below the table that contains the paired lesson activity. Gather any students who have already demonstrated proficiency on the Unit Diagnostic Assessment and excelled during the Exploration activity.” The worksheet and answer key include explicit educator guidance on how to use the activity sheet to best support students.

The materials include educator guidance for differentiated extension activities for students who have demonstrated proficiency in grade-level content and skills. In Grade 7 Advanced Mathematics, each lesson within each unit includes one or more performance tasks assigned to students based on mastery of the lesson’s content. For example, unit 4, lesson 1 provides the tasks Election and Property, with four levels for each task. These levels are a simplified task for students who are not yet proficient, a scaffolded task for somewhat proficient students, an on-level task for proficient students, and an enriching task for highly proficient students. The Teacher Notes for Task prompts educators to “Differentiate tasks based on instructional assessment in the previous portions of the lesson.” The materials do not include educator guidance for differentiated instruction and paired (scaffolded) lessons for students who have demonstrated proficiency in grade-level content and skills.

The materials also include educator guidance for students who have demonstrated proficiency in grade-level content and skills in the Explanation section. For example, in unit 8, lesson 3, “Area of Composite Figures,” the Instructional Hints state, “Some students may intuitively think of subtracting the area of a figure that is the negative space of a composite figure. Encourage them to compare process and results with a student who chose to divide up and add together the areas of several figures within the positive space of a composite figure.”

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.

The materials include explicit prompts to help the educator model and explain the concepts to be learned. For example, in Grade 7 Advanced Mathematics on the unit 6, lesson 3 Overview page, there is a subsection titled Teaching Hints. This section provides the educator with a visual example and the direct prompt, “Use a graphic organizer such as a 2x2 box to organize key pieces of information.” A second example is on the unit 2, lesson 4 Overview page in the Teaching Hints subsection. This section provides the educator with an example and the direct prompt, “An event with replacement resets the situation to its original conditions each time. An event without replacement reduces the number of possible outcomes and the number of favorable outcomes each time.”

The materials include guidance to help the educator model and explain the concepts to be learned. For example, in Grade 7 Advanced Mathematics on the unit 6, lesson 3 Overview page, there is a subsection titled Teaching Hints that provides the educator with guidance such as “Have students draw a picture of what the problem describes. Students may better visualize the relationships from pictures rather than words.” A second example is on the unit 2, lesson 4 Overview page, where the Teaching Hints for the educator state, “Continue to emphasize differences between probabilities of simple events and probabilities of compound events. For simple events, the ratio of favorable outcomes to possible outcomes is sufficient to determine probabilities. For compound events, students will often need to find probabilities of two or more simple events and use an operation to combine them.”

Evaluation for 3.2b
Materials include teacher guidance and recommendations for effective lesson delivery and facilitation using a variety of instructional approaches.

The materials include educator guidance and recommendations for effectively delivering and facilitating lessons using a variety of instructional approaches. For example, in the Grade 7 Advanced Mathematics course, all lessons follow the same structure. Each lesson features an Exploration section, an Explanation section, and one or more performance tasks. During the Exploration portion, guidance directs educators to group students in a visibly random way and have these groups watch a short video. Students then collaborate within their groups on an activity while the educator applies provided Questioning Strategies such as, “When you say ___________, what do you mean?” and “How do you know your answer is correct?” This section also offers educators instructional hints and specific supports for emergent bilingual students.

After students complete the Exploration section, they move on to the Explanation section. Here, educator guidance instructs students to read specific sections of a book, then independently solve the “You try it!” problem. Educators support reasoning and productive struggle by using Questioning Strategies provided in this section. Educators also bring students back together as a whole group to discuss their answers before having students complete practice problems independently. This section provides educators with more instructional hints, Questioning Strategies, and ideas for formative assessments.

Lastly, educators review the results from formative assessments in previous sections and assign a performance task to students. Each task contains four levels, and the guidance helps educators determine which level to assign based on students’ content mastery. For example, educators assign the simplified task to students who are not yet proficient, the scaffolded task to students who are somewhat proficient, the on-level task to students who are proficient, and the enriching task to students who are highly proficient.

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.

The materials support multiple types of practice and include guidance for educators and recommended structures to support effective implementation. The Grade 7 Advanced Mathematics unit 1, lesson 3 Exploration subsection provides educators with recommended structures and types of practice. For example, “Group students in a visibly random way (e.g., playing cards, drawing straws, spinner, etc.) into groups no larger than three students per group,” followed by collaborative activities. Following this are Instructional Hints, which state, “While students are in their groups, support collaborative learning strategies by assigning roles to each student within the group.”

Another example is found on the unit 1, lesson 1 Overview page. In the Lesson Plan subsection, educator guidance states, “Guide students through the activity,” “Assign students the ePub to provide direct instruction on the content along with guided practice through examples and a set of practice questions,” and “Allow students to work in pairs or small groups if desired.”

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.

The materials include educator guidance on providing linguistic accommodations for various levels of language proficiency as defined by the ELPS. Support for Emergent Bilinguals provides prompts, accommodation recommendations, scaffolding, and Questioning Strategies for educators to implement. For example, in unit 8, lesson 1, under Exploration, the materials in Support for Emergent Bilinguals guide the educator to “Provide students with an opportunity to write to describe the relationships between parts of circles with supporting details from the exploration video and activity using appropriate style (word choice [informal vocabulary v. academic vocabulary], syntax [word order in sentences], voice, tone) to inform their peers about their current level of understanding of the relationships among radius, diameter, and circumference of a circle.” The materials provide scaffolding prompts for Pre-Production, Beginning, Intermediate, High-Intermediate, and Advanced proficiency levels. The prompt for the Beginning level states, “Use the visual of a circle on the top of the third page of the exploration activity to connect the Spanish-English cognates in the table to a visual representation. Then ask the student to use each academic vocabulary term as they point to each part of the circle.”

The unit 8, lesson 1, Support for Emergent Bilinguals provides a table with Spanish-English cognates to “facilitate comprehension of students’ mathematical discourse and written classroom materials.” For example, “circle/circulo, circumference/circunferencia, and radius/radio.” Lastly, the materials include questioning strategies to support productive struggle and reasoning through questions. For example, in unit 3, lesson 1, “Clarifying Question: When you say __________, what do you mean?” or “Advancing Question(s) [ask and walk away] Are there any like terms? How can you isolate the variable term?”

Evaluation for 3.3b
Materials include implementation guidance to support teachers in effectively using the materials in state-approved bilingual/ESL programs.

The materials include implementation guidance to help educators use the materials effectively in state-approved bilingual/ESL programs. The Grade 7 Advanced Mathematics Teacher’s Guide, Guiding Principles to Support Emergent Bilinguals, states, “Planning multimodal lessons that grow students’ listening, speaking, reading, and writing skills as they acquire more complex English language is recommended. Each lesson is aligned to at least one ELPS, and many suggestions for supporting emergent bilinguals can be found in lesson plans.” The materials provide a “six-step process for building academic vocabulary” that can be “used with the vocabulary terms listed in each Lesson Overview.” Each Lesson Overview contains Frayer models that support the six-step process via hyperlinked vocabulary terms. Additionally, Guidance for Teachers to Provide Linguistic Accommodations and Support Emergent Bilinguals provides a table that “outlines examples of teacher actions that support emergent bilingual students at any level of English language proficiency to make cross-linguistic connections through oral and written discourse.” For example, in the cross-curricular language acquisition domain of Reading and at the Pre-Production level of language proficiency, the educator’s actions are “Demonstrate gestures & provide pictures/concrete objects related to academic vocabulary.”

The unit 6, lesson 1, Exploration and Support for Emergent Bilinguals includes implementation guidance. For example, “Support students’ development of basic sight vocabulary in written classroom materials. Sight words are words students read so often that they recognize them on sight instead of sounding them out or analyzing root words. Include sight words in your classroom, such as: Add, equal, less than, greater than, number, and, some, use, every.” Additional guidance states, “Support students’ acquisition of English and academic vocabulary through a strategy such as a word wall. Display vocabulary words used in each unit of study. As you progress through the unit, add new words.”

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.

The materials include embedded guidance for educators to support emergent bilingual students in developing academic vocabulary and increasing comprehension through oral and written discourse. For example, in the unit 6, lesson 1 Exploration, the materials in Support for Emergent Bilinguals state, “Teach students the Latin root words for the various congruence transformations: Reflection: reflectere (meaning ‘to bend back’), Rotation: rotare (meaning ‘to turn or revolve’), Translation: translatio (meaning ‘carry or bring’).” Then, “Ask students to use these root word meanings (word analysis) to determine what sort of transformation is suggested by each English word either by drawing or pointing to a picture, making a gesture, giving an oral response, or writing.”

The materials include embedded guidance for educators to support emergent bilingual students in developing academic vocabulary, building background knowledge, and making cross-linguistic connections through oral and written discourse. In unit 2, lesson 2’s Instructional Hints, the materials provide guidance and prompts for educators such as “Probability is a new concept for grade 7. Ensure that students have ample exposure to and repetition of the new vocabulary that comes along with new content. One potential point of confusion is that students may have heard the word ‘complement’ before in a mathematical context involving angles. Engage students with this confusion by leading a class discussion exploring how the two uses of the word are similar and different: Two angles that are complements of one another add up to 90 degrees. Two probabilities that are complements of one another add up to 1.” The materials direct educators to “Use Spanish-English cognates to foster student cross-linguistic connections in oral and written mathematical discourse and increase comprehension.” For example, in unit 8, lesson 1, diameter/diametro and circle/circulo.

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.

This guidance is not applicable because the program is not designed for dual language immersion (DLI) programs.

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.

The materials provide practice opportunities throughout a lesson and/or unit (including instructional assessments) that require students to demonstrate depth of understanding aligned with the TEKS. Exploration activities frequently scaffold from mathematical contexts to real-world applications. For example, in TEKS 7AM.8A, unit 5, lesson 1, Constant of Proportionality, the Blackline Master (Student Pages) exploration document develops the concept of a constant of proportionality through patterns and relationships in tables. In the Explanation phase of the lesson, the ePub gives students the opportunity to respond to a “You Try It!” prompt and practice questions that continue to require them to develop and demonstrate a depth of understanding aligned with the TEKS. Finally, the performance task provides differentiated opportunities for students to demonstrate their depth of understanding of the TEKS.

The materials provide practice opportunities throughout a lesson to demonstrate depth of understanding aligned with TEKS. For example, in unit 7, lesson 2, Solving Problems with the Pythagorean Theorem (TEKS 7AM.11F), the Exploration component gives students practice using the Pythagorean Theorem or its converse to solve problems. A sample of questions includes, “A tree is staked to provide strength so that it will grow straight. A diagram of a staked tree is shown below. A ring has been placed on the tree 6 feet from the ground, and a rope is tied to the ring and attached to the stake. Approximately how far away from the tree will the stake need to be placed to provide maximum support?” and “Explain how you know the lengths 8 inches, 10 inches, and 13 inches do not form the sides of a right triangle?”

Instructional assessments require students to demonstrate depth of understanding aligned to the TEKS over the course of a unit. For example, in alignment with TEKS cluster 7AM.8, unit 5, Proportional and Non-Proportional Situations, in the Diagnostic Assessment, section 5B, question 1 asks, “An ocean diver falls backwards into the water from a platform on a boat that is 8 feet above sea level. The diver descends at a rate of 9 feet per second. Write an equation to represent the situation. Use the numbers and operations provided. Not all numbers and operations will be used.” In unit 5, lesson 2, the TEKS 7AM.8C Performance Task—Shipping (formative assessment) states, “Mrs. Mancini is starting a small business where she will ship her product directly to customers. She wants to make sure her shipping and handling charges are proportional to the amount of the customer’s purchase. Mrs. Mancini is trying to select between 2 different shipping plans: Plan A - charge a flat rate of $10 plus 5% of the order subtotal. Plan B - charge 15% of the order subtotal for shipping regardless of order size. Which plan(s) meet(s) her needs? Justify your reasoning.” The unit 5 Test requires students to demonstrate depth of understanding aligned to the TEKS. For example, an open-ended question asks, “Scoops Ice Cream Shop boasts that they can scoop 12 cups of ice cream every 4 minutes. If Scoops continues at this rate, which equation can be used to find c, the number of cups of ice cream they can scoop in 45 minutes?”

Evaluation for 4.1b
Questions and tasks progressively increase in rigor and complexity, leading to grade-level proficiency in the mathematics TEKS.

The materials provide questions and tasks that progressively increase in rigor and complexity, leading to grade-level proficiency in the mathematics TEKS. The Diagnostic Assessment, the performance task for each lesson, and the Unit Test include questions and tasks that demonstrate this progression. For example, in the unit 7 Diagnostic Assessment, a question states, “The area of a triangle is 32.5 square inches. The base of the triangle is 13 inches long. What is the height of the triangle in inches?” (TEKS 6AM.8.D) The final question increases in rigor and states, “A ladder 25 feet long leans against a building. The bottom of the ladder is 7 feet from the building. How far up the building do you think this ladder reaches?” (TEKS 7AM.11G). In unit 7, “Relationships Involving Angles and Triangles,” under 7AM.11F Performance Task—Laptop Stand, the task description states, “Doug has a laptop stand with a fan inside to keep the laptop cool when it is on his desk. The laptop fits perfectly on the top of the stand. The side of the stand forms a right angle as shown below. The stand is 1.5 inches high, putting the laptop on a slight incline. The laptop is 9.5 inches long from top to bottom. About how deep from front to back is the bottom of the laptop stand that sits along the desk’s surface? Justify your reasoning.” Lastly, the TEKS-aligned, summative Unit Assessment allows students to demonstrate mastery of learning objectives. For example, the unit 3, test 1, Variable Equations and Inequalities questions demonstrate progressive rigor and complexity. A multiple-choice question states, “What is the solution to the inequality 4x - 3 < 70?” The final question states, “South Plains Wireless charges a user fee of $35 each month and $9.95 per gigabyte used. Tumbleweed Cellular charges a user fee of $15 each month and $13.95 per gigabyte of data used. What number of gigabytes will make the charge the same for both companies in one month?”

The Explanation component of each lesson demonstrates questions and tasks that progressively increase in rigor and complexity, leading to grade-level proficiency in the mathematics TEKS. For example, in unit 8, lesson 3, “Area of Composite Figures,” the Explanation component links to the ePub: Area of Composite Figures. The first set of questions asks students to find the area of a composite figure. As questions continue, they progress in rigor. A later multiple-choice question states, “Daniela drew a model of her backyard with quarter-circular gardens in two different corners. She will install grass in the shaded area since her house is brand new. A diagram of her backyard is shown below. How much of the yard is available for her to install grass?”

Evaluation for 4.2a
Materials demonstrate coherence across units by explicitly connecting patterns, big ideas, and relationships between mathematical concepts.

The materials demonstrate coherence across units by explicitly connecting patterns, big ideas, and relationships between mathematical concepts. The Grade 7 Advanced Mathematics Scope and Sequence, Rationale for Unit Progression, explains that the materials directly correlate with the Texas Response to the Curriculum Focal Points (TxRCFP) “to create TEKS-aligned instructional materials in a logical progression,” and that the course incorporates process standards throughout. For example, to demonstrate a strategic sequence, the rationale states, “Unit 1 equips students with the tools they will need to work with real numbers that are a TxRCFP grade-level connection to rational numbers from previous grade levels, but for the first time, including irrational numbers that are needed for application of the Pythagorean Theorem. In Unit 2, students calculate and interpret data with a single variable using visual and symbolic representations. Unit 3 focuses on symbolic manipulation of equations and inequalities to solve for a single variable. Unit 4 builds from the single-variable concepts and skills students have learned in previous grade levels and honed in the first three units of the course to begin to develop the idea of slope as a constant rate of change in linear relationships and the meaning of both x- and y-intercepts of linear functions.”

The materials demonstrate coherence across units by explicitly connecting patterns, Big Ideas, and relationships among mathematical concepts in the Unit Introduction and Unit Overview. For example, in unit 4, “Problem Solving with Multiple Representations,” the Unit Introduction states, “Advanced Math-Grade 7 Unit 4 bridges between numeracy and proportionality. Students use what they know about rates and ratios to solve problems and then use multiple representations to determine and interpret the slope and intercepts of a linear function.” The connection of relationships among mathematical concepts is further demonstrated in the Unit Overview, which states, “In 7th grade advanced math, students are introduced to the concept of constant rate of change in the linear function. Students are also introduced to the intercepts and slope as key attributes of a linear function and determine and interpret the slope and intercepts of a linear function in a variety of representations.”

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.

The materials demonstrate coherence across units by connecting content learned in previous courses/grade levels to content to be learned in the current course/grade level on each Lesson Overview page. For example, on the Grade 7 Advanced Mathematics, unit 8, lesson 2 Overview page, a Prior Learning Supports section connects the current unit to 6th-grade expectations. An example provided from the 6th-grade expectations states, “In 6th grade, students used a decomposed and rearranged a rectangle to model and write area formulas for polygons such as triangles, parallelograms, and trapezoids,” and in 7th grade, “Students will build on their 6th grade experiences to model and write the area formula for a circle.”

The materials demonstrate coherence across units by connecting the language learned in previous courses/grade levels to the content learned in the current course/grade level on each Lesson Overview page. For example, the Grade 7 Advanced Mathematics, unit 8, lesson 2 Overview page features a Vocabulary section that introduces new terms and encourages students to engage with them using a Frayer model template. In unit 8, lesson 2, students encounter and connect the terms area, circle, circumference, diameter, and radius.

The materials demonstrate coherence across units by connecting what students will learn in future courses/grade levels to the content in the current course/grade level within each Lesson Overview page. For example, on the Grade 7 Advanced Mathematics, unit 8, lesson 2 Overview page, a Prior Learning Supports section connects the 7th-grade topic to Geometry topics. An example provided from 7th grade states, “In this lesson, students will build on their 6th grade experiences to model and write the area formula for a circle. In the next lesson of 7th grade advanced mathematics, students will determine the areas of composite figures that include circles, semicircles, and quarter circles. Later in the unit, students will determine the surface area and volume of cylinders, the volumes of cones, and the volume of spheres. In Geometry, students will determine the surface area and volume of composite 3-dimensional figures that may include cylinders, cones, and/or portions of spheres.”

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..

The materials demonstrate coherence at the lesson level by connecting students’ prior knowledge of concepts and procedures from the current grade level to new mathematical knowledge and skills within each lesson’s Overview page. For example, in Grade 7 Advanced Mathematics, the unit 8, lesson 4 Overview page features a Prior Learning Supports section that highlights connections within 7th-grade advanced math. This section states, “In lesson 3 of this unit, students determined the area of composite figures. In this lesson, students represent a 3-dimensional pyramid or prism with a 2-dimensional net.” Unit 8, lesson 4 covers surface area and nets.

The materials demonstrate coherence at the lesson level by connecting students’ prior knowledge of concepts and procedures from the prior grade levels to new mathematical knowledge and skills within each lesson’s Overview page. For example, in Grade 7 Advanced Mathematics, the unit 8, lesson 4 Overview page features a Prior Learning Supports section that highlights connections from 4th grade and 6th grade advanced math to 7th grade advanced math. Unit 8, lesson 4 covers surface area and nets. The 4th-grade connection says, “In 4th grade, students determined the area of rectangles using simple formulas such as A = lxw or A = sxs for squares.” The 6th grade advanced mathematics connection says, “In 6th grade advanced math, students used models to derive formulas for the area of triangles and other quadrilaterals.” In this lesson, “Students represent a 3-dimensional pyramid or prism with a 2-dimensional net. From the net, students build on their experiences with composite figures to determine the area of the net as a composite figure made up of rectangles and triangles.”

Evaluation for 4.3a
Materials provide spaced retrieval opportunities with previously learned skills and concepts across lessons and units.

The materials provide spaced retrieval opportunities with previously learned skills and concepts across lessons and units. For example, in Grade 7 Advanced Mathematics, most units contain one or more Spiral Reviews. These reviews provide educators with information on which units, lessons, and TEKS are spiraled through the review. The unit 2 Spiral Review 3 states, “This spaced retrieval and interleaved practice opportunity across lessons and units addresses the following TEKS from previous instruction,” and follows with a list of units, lessons, and TEKS. The examples provided from this unit spiral review include unit 1, lesson 6: 7AM.2A; unit 6, lesson 2: 7AM.6E; unit 6, lessons 3 and 6: 7AM.6C; unit 6, lesson 3: 7AM.6F; and unit 6, lessons 4 and 6: 7AM.6G. The Spiral Review is a whole-class (large-group) activity in which students are divided into two teams. The review contains various question types, such as open-ended, write-a-statement, and choose-the-correct-answer.

Another example can be seen in the unit 8 Spiral Review 4, which states, “This spaced retrieval and interleaved practice opportunity across lessons and units addresses the following TEKS from previous instruction:” and then lists the units, lessons, and TEKS. The examples provided from this Spiral Review include unit 6, lesson 1: 7AM.12C; unit 6, lessons 4 and 6: 7AM.5E; unit 7, lesson 2: 7AM.11F; unit 8, lessons 5 and 6: 7AM.11C; and unit 8, lessons 6, 9, and 10: 7AM.11E.

Evaluation for 4.3b
Materials provide interleaved practice opportunities with previously learned skills and concepts across lessons and units.

The materials provide interleaved practice opportunities with previously learned skills and concepts across lessons and units. For example, in Grade 7 Advanced Mathematics, most units contain one or more Spiral Reviews. These Spiral Reviews provide educators with information on which units, lessons, and TEKS are spiraled through the review. The unit 6 Spiral Review 2 states, “This spaced retrieval and interleaved practice opportunity across lessons and units addresses the following TEKS from previous instruction,” and is followed by a list of units, lessons, and TEKS. The examples provided from this unit Spiral Review include unit 6, lesson 1: 7AM.12C; unit 7, lessons 1 and 4: 7AM.12A; unit 7, lessons 4 and 6: 7AM.5E; and unit 7, lesson 6: 7AM.12D.

Another example is found in the unit 8 Spiral Review 3, which states, “This spaced retrieval and interleaved practice opportunity across lessons and units addresses the following TEKS from previous instruction” and is followed by a list of units, lessons, and TEKS. The examples provided from this unit Spiral Review include Grade 6 Advanced Math, unit 4, lesson 5: 6AM.6C; unit 6, lessons 2 and 3: 7AM.5C; unit 8, lessons 2 and 3: 7AM.11A; unit 8, lesson 3: 7AM.11B; and unit 8, lessons 7 and 8: 7AM.11D.

Evaluation for 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 models and representations for mathematical concepts in Exploration: unit 8, lesson 2 of the Grade 7 Advanced Mathematics course. For example, the Exploration section provides educators with an activity sheet for students to fold and cut a paper plate into eighths, cut along the folds, and arrange the pieces in an alternating pattern. From here, students will use the area of a parallelogram to discover the area of a circle. Students will then use the formula for the area of a circle to find the area of half of the paper plate (a semicircle) and a quarter of the paper plate.

Questions and tasks require students to analyze and evaluate models and representations for mathematical concepts and situations in Exploration: unit 3, lesson 1 of the Grade 7 Advanced Mathematics course. For example, the Exploration section includes an activity sheet for students to complete. In this activity, students are given a problem that asks them to use algebra tiles to solve an algebraic equation. The activity sheet contains four columns: Symbolic (this is where the equation is written), Tiles (where students sketch the algebra tiles they use to represent the situation), Verbal Description (where students write out, in words, what their algebra tile representation means), and a column for Property of Equality. One example is already provided, with all areas of the table completed for reference. The next three problems are blank, where students will complete the tables on their own.

Evaluation for 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 in Exploration: unit 2, lesson 6 of the Grade 7 Advanced Mathematics course. In the Exploration section, educators are provided instructions to pass out a simple events activity sheet to students. Students are instructed to “Roll two dice, find the sum, and complete the table. Then compile the data on a frequency chart on the following page. Finally, answer the questions below.” The first table directs students to write the number they got on cube 1 and cube 2 for each trial, and the last column shows the sum of the cubes. Students use this data to fill out the next table, which contains the sum in one column and a space for the frequency in a second column. Students use this frequency table to answer questions. Later in the activity, students compile class data in a table. The first column contains the sum, then the frequency, and lastly the experimental probability. Again, students use this data table to answer questions.

Questions and tasks require students to create models to represent mathematical situations in performance task: unit 6, lesson 3 of the Grade 7 Advanced Mathematics course titled “Building a Greenhouse.” This task states, “Mrs. Patton wants to build a new greenhouse for her farm. The greenhouse will be shaped like a rectangular prism with a roof shaped like an isosceles triangular prism. The blueprints Mrs. Patton bought online are printed on centimeter grid paper and have dimensions marked by a scale of 1/2 cm to 1 1/2 feet.” More information about the greenhouse is provided. The task asks students to sketch the greenhouse and then label the known blueprint dimensions.

Evaluation for 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 in the enriched performance task: unit 5, lesson 3 in the Grade 7 Advanced Mathematics course. Each lesson includes one or more performance tasks, and educators assign tasks at different levels based on students’ understanding and ability. The “Plumbing” task covers linear relationships and states, “Ricardo is a plumber. He charges $65 per hour for a service call plus the cost of materials for each job. Ricardo has three jobs this week and has purchased the materials for each job. The information about this week’s jobs is shown in the table below.” Students are given a table that is split into two columns: Job name and cost of materials. The problem then states, “Ricardo wants to use an equation to represent the total amount of money he will earn this week based on the hours each job will take.” The problem asks students questions about the situation, such as, “How much of Ricardo’s earnings are gross income?”

Questions and tasks provide opportunities for students to apply conceptual understanding to new problem situations and contexts in the unit 7, lesson 3 Explanation in the Grade 7 Advanced Mathematics course. Educators assign students practice problems from the student’s course workbook. The first assignment covers triangles, and one problem shows a triangle with each angle labeled and marked with a congruence arc. All angles are marked with different congruence markers, and the question states, “A triangle is shown in the diagram. Which angle labels can be placed in the blank spaces to make a true equation?” The blank spaces are m< _____ + m< ______ = m< ________. The idea is for students to add the remote interior angles and set their sum equal to the exterior angle. Another example comes from the second practice assignment. Two sets of parallel lines cross to make a tic-tac-toe shape. Some angles contain expressions or variables. One question states, “How does the value of z relate to the value of y?” Another question states, “How can the value of z be determined?”

Evaluation for 5.2a
Materials provide tasks that are designed to build student automaticity and fluency necessary to complete grade-level tasks.

The materials provide tasks designed to build the student’s automaticity and fluency needed to complete grade-level tasks. In Grade 7 Advanced Mathematics, students participate in Spiral Reviews for each unit. Some units have more than one Spiral Review. These Reviews indicate which units and TEKS are present in the specific Spiral Review, and then assign a task. For example, the unit 2 Spiral Review 1 states, “This spaced retrieval and interleaved practice opportunity across lessons and units addresses the following TEKS from previous instruction: ‘Unit 2, Lesson 1: 7AM.6A’, ‘Unit 2, Lesson 2: 7AM.6E’, ‘Unit 2, Lesson 3: 7AM.6F’, and ‘Unit 2, Lesson 4: 7AM.6D and 7AM.6G’.” The activity in the Spiral Review has students practice prior skills using simple probability. Another example comes from the unit 5 Spiral Review 2, which states, “This spaced retrieval and interleaved practice opportunity across lessons and units addresses the following TEKS from previous instruction: ‘Grade 6 Adv Math, Unit 5, Lessons 7, 9, and 12: 6AM.8E’, ‘Grade 6 Adv Math, Unit 6, Lessons 5 and 6: 6AM.10A’, ‘Unit 1, Lesson 3: 7AM.3B’, ‘Unit 4, Lesson 1: 7AM.4A’, and ‘Unit 5, Lesson 3: 7AM.9A’.” The activity provided in this Spiral Review has students practice previous skills with one-variable, two-step equations and inequalities.

The materials provide tasks that are designed to build student automaticity and fluency necessary to complete grade-level tasks on the Grade 7 Advanced Mathematics, unit 6, lesson 1 Overview page. The Overview page for this unit and lesson provides educators with a Prior Learning Supports section and states, “Transformations (translations, reflections, rotations, and dilations) are new to 7th grade advanced math but have their roots in other geometric concepts in earlier grades. In 4th grade, students classified 2-dimensional figures based on attributes including parallel or perpendicular lines and when classifying quadrilaterals, students may have encountered congruent sides within a figure. However, the notion of congruent figures is new to 8th grade and the notion of transforming a figure by translating it, reflecting it, or rotating it while preserving its congruence, if not its orientation, is new to 7th grade advanced math students. Translations and reflections have implications for functions in high school algebra. Students will apply these transformations, along with dilations, to linear and quadratic functions in Algebra 1, and to additional functions in Algebraic Reasoning or Algebra 2.” The first task to build fluency and automaticity is in the Exploration section of this Overview page. Students are given an activity sheet on translations, reflections, and rotations. Students move on to the Explanation section, which includes information about their coursework and again covers practice with rotations, reflections, and translations. Finally, students complete a performance task on logo designs.

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.

The materials give students opportunities to practice applying efficient, flexible, and accurate mathematical procedures within the lesson and/or throughout a unit. For example, in Grade 7 Advanced Mathematics, the unit 2, lesson 1 Overview page contains an activity sheet for students on simple events, specifically, representing sample spaces. Students are to “Represent the sample space for the situation using the method(s) indicated or use the given sample space to create a situation.” The first question asks students to create a tree diagram. The second question asks students to create a list. The third question asks students to create both a tree diagram and a list. The fourth question asks students to create a tree diagram or a list. The last question states, “Draw a bag of marbles that could have the sample space shown: {red, blue, white, black}.” The “Pizza” performance task can also be assigned within this same unit and lesson and states, “Zyana and Rayna are ordering pizza for dinner. The sisters have to agree on a crust type, meat, topping, and a vegetable topping to use a coupon. They listed choices of toppings and crusts they each like in a table.” A table of crusts, meat toppings, and vegetable toppings follows. The problem continues, “Zyana does not like the cheese-stuffed crust and Rayna does not like the hand-tossed crust. Zyana does not like any green vegetables on her pizza, and Rayna does not like onions on her pizza. Neither sister is in the mood to eat a pork product. (pepperoni, bacon, or sausage).” Students then answer four questions: “If the sisters choose only 1 option from each list to create a pizza, how many different pizza combinations are possible?,” “Based on their preferences, how many pizza combinations can be eliminated?,” “If they ordered one combination at random, what is the percent chance of getting a pizza they both like?,” and “What pizza combinations might they order?” Students must then justify their reasoning.

The materials give students opportunities to practice applying efficient, flexible, and accurate mathematical procedures within the lesson and/or throughout a unit. For example, in Grade 7 Advanced Mathematics, the unit 2, lesson 5 Exploration provides educators with an activity sheet for students to complete on technological simulations of compound events. The activity sheet states, “At a pop-up ice cream shop, there are two possible containers: a sugar cone or a waffle cone, six different ice cream flavors, and four different toppings.” Problem 1 says, “Decide which online tools your group will use to simulate the ice cream cone choices of 50 people if each person can choose one option each for the cone, ice cream flavor, and topping, and options for each item are equally likely to be chosen.” A table follows with links to online tools, such as a virtual coin flip and cube roller, and space for students to write down the tool they used and their answers. A second table is provided for recording their answers after each simulation. Students then answer questions such as, “How do your simulation results compare with theoretical probabilities?” and “Would the combined results of the simulations of the different groups in your class better approximate the theoretical probability? Why or why not?”

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.

The materials provide opportunities for students to evaluate procedures, processes, and solutions for efficiency, flexibility, and accuracy within the lesson and throughout a unit in the unit 6 Spiral Review 2. Educators give students an activity sheet on congruence transformations and dilations. Students work in pairs to complete the activity sheet. Once the time is up, an activity called “Four Corners” begins. Students stay with their partner and move to the corner of the room that contains their answer. Educators then ask students questions about how many students are in each corner of the room, such as: “If all four locations have students, ask the groups of students to hold a discussion about how they know their answer is correct. This allows you to work with any/each of the three incorrect groups to ask questions designed to push their thinking”; “If three locations have students, ask groups to convince other groups to join them. Begin with an incorrect group with a common misconception first and then the correct group second. Members of any group can move during these arguments if they choose”; and “If two locations have students, hold a class debate to determine which solution is correct.”

The materials provide opportunities for students to evaluate procedures, processes, and solutions for efficiency, flexibility, and accuracy within the lesson and throughout a unit in the Explanation: unit 6, lesson 5. Educators assign students to practice from their student course book on similar triangles. At the beginning of this assignment, a section titled “TELL ME MORE…” states, “In order for two triangles to be similar, each pair of corresponding angles must be congruent, and each pair of corresponding side lengths must be proportional.” The page shows two triangles with all sides and angles labeled with measurements, plus a few fill-in-the-blank questions about what is congruent within the triangles. At the bottom of this “TELL ME MORE…” section is a box titled “ANGLE-ANGLE CRITERION,” which states, “To show that two triangles are similar, is it enough to know that two angles are congruent? Explain how you know.”

Evaluation for 5.2d
Materials contain embedded supports for teachers to guide students toward increasingly efficient approaches.

The materials include embedded supports for educators to guide students toward increasingly efficient approaches in various lessons of unit 8 of the Grade 7 Advanced Mathematics course. For example, each Lesson Overview page features a section titled Overview of Process Standards that explains how the lesson incorporates certain process standards. On the unit 8, lesson 4 Overview page, this section states, “In this lesson, students will solve problems involving the surface area of prisms or pyramids from their nets. Students may: Use visual models to approach the area of the net like the area of a composite figure. Use area formulas as a strategy for determining the area of each part of the net. Use estimation or compatible numbers as a method of evaluating the reasonableness of a solution. Use the area of a larger or smaller figure (such as a rectangle) to estimate the area of the composite figure as they evaluate the reasonableness of a solution.” Another section in each lesson, Prior Learning Supports, describes how the lesson builds on similar content from previous lessons and grade levels. The example from unit 8, lesson 4 states, “In 4th grade, students determined the area of rectangles using simple formulas such as A = l × w or A = s × s for squares. In 6th grade advanced math, students used models to derive formulas for the area of triangles and other quadrilaterals. In Lesson 3 of this unit, students determined the area of composite figures. In this lesson, students represent a 3-dimensional pyramid or prism with a 2-dimensional net. From the net, students build on their experiences with composite figures to determine the area of the net as a composite figure made up of rectangles and triangles.” A third section on each Lesson Overview page, Teaching Hints, gives educators hints and information to assist students. In this lesson, the hints state, “Many students struggle with the concept of surface area as a two-dimensional measure of a three-dimensional object. Use prism and pyramid solid models for students’ reference during this lesson so they may visualize how surface area relates to the solid itself...”

The materials include embedded supports for educators to guide students toward increasingly efficient approaches in various lessons of unit 8 of the Grade 7 Advanced Mathematics course. For example, each Lesson Overview page features a section titled Overview of Process Standards that explains how the lesson incorporates certain process standards. On the unit 8, lesson 6 Overview page, this section states, “In this lesson, students use a problem-solving model to solve problems involving the lateral and total surface area of cylinders and the volume of cylinders. Students employ these processes to master content in the following ways: Formulate a plan or strategy such as using a surface area or volume formula, using a visual diagram, or creating a net of the cylinder. Using a visual model to analyze the given information. Use strategies such as rounding or compatible numbers to evaluate the reasonableness of the solution.” Another section in each lesson, Prior Learning Supports, describes how the lesson builds on similar content from previous lessons and grade levels. The example from unit 8, lesson 6 states, “In 6th grade advanced math, students determined area formulas for rectangles, parallelograms, trapezoids, and triangles. Earlier in this unit, students determined area formulas for circles and then extended their prior knowledge to determining the area of composite figures made up of these shapes, including semicircles and quarter circles. Students also applied their knowledge of determining the area of a composite figure to determining the surface area of a rectangular prism, pyramid, or triangular prism or pyramid from the shape’s net. In 7th grade advanced math, students extend their prior learning experiences to developing surface area formulas for rectangular and triangular prisms and cylinders. Surface area is thought of in terms of the area of the parallel, congruent bases of the prisms and cylinders and the area(s) of the lateral surfaces or faces.” A third section in each Lesson Overview page, Teaching Hints, gives educators hints and information to assist students. In this lesson, the hints state, “Clarify your expectations with students regarding pi in the surface area and volume of cylinders. Will you: require students to use the pi key on the graphing technology available to students, require students to substitute 3.14 for pi in any estimated solutions, or require students to leave pi in their final, exact answers?”

Evaluation for 5.3a
Materials explicitly state how the conceptual and procedural emphasis of the TEKS are addressed.

The materials explicitly state how the lesson addresses the conceptual and procedural emphasis of the TEKS. The lesson components, including a Lesson Overview, Learning Outcomes, Overview of the Process Standards, and Teaching Hints, describe how the lesson addresses the conceptual and procedural emphasis of the TEKS. For example, in unit 8, lesson 8, Volume of Triangular Prisms and Pyramids, the Lesson Overview - Focusing Question states, “How can I solve problems involving the volume of triangular prisms and pyramids? “ The Learning Outcomes state that students will “show the relationship between the volume of a triangular prism and the volume of a triangular pyramid with the same base and height, determine the volume of a triangular prism or pyramid, and solve problems involving the volume of triangular prisms and pyramids.” The materials address the procedural emphasis of the TEKS in the Overview of the Process Standards. The overview states that students will “use visual models to analyze and make sense of the given information in the problem, use strategies such as drawing a diagram or using volume formulas to solve problems, and use estimation or compatible numbers as a method of evaluating the reasonableness of a solution.”

In unit 4, lesson 1, “Solving Problems with Rates, Ratios, and Percents,” the Learning Outcomes state the conceptual emphasis of the TEKS in student-friendly statements: “I can solve problems involving rates or ratios,” and “I can solve problems involving percents, including percent increase or percent decrease.” The Overview of Process Standards section states the procedural emphasis of the TEKS. For example, students will use visual models, such as a percent bar, and use strategies such as estimation or compatible numbers to check solutions for reasonableness.

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.

Questions and tasks include the use of concrete models and manipulatives as required by the TEKS. For example, in unit 2, lesson 5, “Using Simulations for Simple and Compound Events,” the Blackline Master: Technological Simulations of Compound Events directs students to select online tools to simulate the ice cream cone choices of 50 people. The online tools include a virtual coin flip, a random number generator, a two-sectioned spinner, and an online number cube roller. Questions and tasks include pictorial representations (figures/drawings) and abstract representations, as required by the TEKS. The 7AM.6B Performance Task—Predicting Defects states, “Students may create a simulation using a random number generator using any form and may use any way to organize the information for 8,000 trials.”

Questions and tasks include the use of concrete models, pictorial representations (figures/drawings), and abstract representations, as required by the TEKS. For example, in unit 6, lesson 1, “Translations, Reflections, and Rotations,” the Exploration section directs students to “Use patty (tracing) paper, mental math, and/or paper and pencil to perform each transformation of pentagon ABCDE.” The Debriefing Questions for the Exploration activity direct the students to “Classify each statement as always, sometimes, or never true.” Students must justify their response and “provide an algebraic expression when words are given.” Finally, in the 7AM.12A Performance Task—Logos, the directions explain that students can use “a variety of strategies, including the use of graph paper and/or a graphing device.”

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.

The 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. In unit 3, lesson 1, “Model and Solve One-Variable Equations,” the Overview of Process Standard(s) defines how students will “select tools, such as pencil and paper, manipulatives (e.g., algebra tiles), or technology to solve one-variable equations with variables on both sides of the equal sign. Students also select techniques, including mental math and properties of operations, to solve equations.” The materials encourage students to “Select a tool such as algebra tiles or graphing technology to solve a one-variable equation with variables on both sides of the equal sign. Select a technique, such as estimation (rounding or compatible numbers), to evaluate the reasonableness of a solution. Select a technique, such as properties of operations or mental math, to solve equations.” In the Explanation lesson component, 7AM unit 3, lesson 1, “Solving One-Variable Equations,” the materials direct students to “solve an equation using one of many different strategies,” including “use models to represent the equation. Then, you can use the properties of algebra to manipulate the model until you determine the value of the object that represents the variable.”

The materials provide further opportunities for the students to connect, create, define, and explain concrete and representational models to abstract (symbolic/numeric/algorithmic) concepts, as required by the TEKS. For example, in the Exploration component in unit 8, lesson 2, “Circumference and Area of Circles,” the instructions direct students to “Fold a paper plate into eighths, cut along the folds, and arrange the pieces in an alternating fashion. Use the formula for the area of a parallelogram to discover the formula for the area of a circle.” The Exploration’s Debriefing Questions allow students to define and explain. For example, a question asks, “How can you determine the radius of a circle when given the circumference?” and “How can you determine the diameter of a circle when you are given the area?”

Evaluation for 5.4a
Materials provide opportunities for students to develop academic mathematical language using visuals, manipulatives, and other language development strategies.

The materials provide opportunities for students to develop academic mathematical language using visuals, manipulatives, and other language-development strategies on the Grade 7 Advanced Mathematics Lesson Overview page. For example, the unit 6, lesson 1 Overview page contains Teaching Hints that state, “For rotations, it may be helpful to paste a blank coordinate plane on a piece of cardboard and provide student groups with this cardboard coordinate plane and a pushpin. They can trace the figure (preimage) and coordinate axes on a piece of patty paper and then lay it on top of the cardboard coordinate plane, lining up the axes. Push the pushpin into the origin. Rotate the patty paper the desired distance and direction about the origin and record the new coordinates of the rotated figure (image).” Further into the Overview page is a section titled Vocabulary that states, “One way to support students’ acquisition of new vocabulary terms is to preteach the vocabulary terms using a strategy such as a Frayer model. For these key terms, we provide partially completed Frayer models to which students should add as they move through the lesson and develop a deeper understanding of the vocabulary term. Click on the term to see the Frayer model.” Students receive a Frayer model template along with a list of important vocabulary terms. Students complete an activity sheet on translations, reflections, and rotations. The directions state, “Use patty (tracing) paper, mental math, and/or paper and pencil to perform each transformation of pentagon ABCDE.”

The materials provide opportunities for students to develop academic mathematical language using visuals, manipulatives, and other language-development strategies on the Grade 7 Advanced Mathematics Lesson Overview page. For example, the unit 2, lesson 1 Overview page contains Teaching Hints that state, “For some situations involving spinners or number cubes, provide students with actual spinners or actual number cubes so they may see and then count the potential outcomes of spinning the spinner or rolling a number cube. Connect tree diagrams with lists to show how they can both represent the same sample space.” Further into the Overview page is a section titled Vocabulary that states, “One way to support students’ acquisition of new vocabulary terms is to preteach the vocabulary terms using a strategy such as a Frayer model. For these key terms, we provide partially completed Frayer models to which students should add as they move through the lesson and develop a deeper understanding of the vocabulary term. Click on the term to see the Frayer model.” Students receive a Frayer model template along with a list of important vocabulary terms.

Evaluation for 5.4b
Materials include embedded teacher guidance to scaffold and support students' development and use of academic mathematical vocabulary in context.

The materials include embedded educator guidance to scaffold and support students’ development and use of academic mathematical vocabulary in context. For example, in Grade 7 Advanced Mathematics, educators can access a Teacher’s Guide on the Course Overview page. The Guide’s section on scaffolds states, “Clarifying and focusing questions are included in multiple portions of each lesson to support educators in scaffolding student learning. Supports for emergent bilinguals are provided throughout the course to scaffold listening and speaking during mathematical discourse, as well as reading and writing to acquire and express understanding, including academic and classroom vocabulary. Prior learning supports are included for each lesson to connect prior learning that may be essential for understanding the new learning taking place in the classroom.” A little more than halfway through the educator’s guide is a section on building vocabulary using a six-step process: “1. Introduce the new term(s) by providing a student-friendly example, description, and/or explanation. 2. Students restate the example, description, and/or explanation in their own words. 3. Students create a non-linguistic representation of the term(s) (picture, graphic, symbol, etc.). 5. Periodically involve students in discourse during which they discuss the term(s) with one another. 6. Involve students periodically in games that allow them to play with the term(s).”

The materials include embedded educator guidance to scaffold and support students’ development and use of academic mathematical vocabulary in context in the Grade 7 Advanced Mathematics course under the Exploration section of unit 7, lesson 1. A section is labeled for emergent bilingual students, but these scaffolds can be used for all students. This section states, “Create structures that empower students to use support from you and their peers to read grade-appropriate mathematics text. For example, use a SQPRR structure (Seidlitz & Avila, 2010). Survey—students scan the visuals, headings, and other text features. Question—students write a list of questions they might find answers to while reading. Predict—Students write predictions about what they will learn. Read—Students read the text. Respond—Students revisit their questions and think through responses to reading.” Another section on Questioning Strategies states, “As needed, support student reasoning and productive struggle through questioning. When you say __________, what do you mean? How do you know if a triangle is a right triangle? How are the side lengths of a right triangle related to one another?”

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.

The materials include embedded educator guidance to support the application of appropriate mathematical language, including vocabulary, syntax, and discourse. The materials provide guidance to support mathematical conversations that give students opportunities to hear, refine, and use math language with peers, develop their math language toolkit over time, and guide educators in supporting student responses using exemplar responses to questions and tasks. Under Exploration, the Support for Emerging Bilinguals provides educator guidance and prompts to support vocabulary development and mathematical discourse. For example, under Exploration in unit 8, lesson 4, “Surface Area and Nets,” the Support for Emerging Bilinguals materials guide educators to “Support students’ speaking skills by providing opportunities for them to learn about and use prefixes, suffixes, and root words that describe different three-dimensional figures. Before students complete the exploration activity, engage them in a discussion and activity regarding the language structures of vocabulary in this lesson.” The materials further guide the educator to use questions to monitor students’ oral language production. Sample question prompts include, “What I hear you say is...,” “Please say that again,” “What is the plural of that word?” and “How do you pronounce this?”

The Spiral Review leverages an instructional strategy designed to support student mathematical discourse. For example, in the unit 3 Spiral Review: Equations and Inequalities with Rational Coefficients, the students work together collaboratively to solve spaced retrieval and interleaved practice questions. The materials provide educator guidance that states, “Provide supports for emergent bilingual students to use transition words as they describe (by speaking or in writing) the relationships among representations and parts of equations and inequalities.” Additionally, the Lesson Overview’s Vocabulary section provides the following educator guidance: “One way to support students’ acquisition of new vocabulary terms is to preteach the vocabulary terms using a strategy such as a Frayer model. For these key terms, we provide partially completed Frayer models to which students should add as they move through the lesson and develop a deeper understanding of the vocabulary term.” The Frayer model is a graphic organizer that asks students to define the vocabulary word in their own words and list facts, characteristics, examples, and non-examples. The Frayer model helps students build their math language toolkit over time.

Evaluation for 5.5a
TEKS process standards are integrated appropriately into the materials.

The TEKS process standards are integrated appropriately into the materials. In Grade 7 Advanced Mathematics, each lesson includes an Overview page with a learning outcomes section that lists the lesson TEKS and indicates whether they are process standards, along with an overview of the lesson’s process standards. For example, on the unit 3, lesson 1 Model and Solve One-Variable Equations Overview page, the learning outcome TEKS states, “7AM.1C Mathematical process standards. The student uses mathematical processes to acquire and demonstrate mathematical understanding. The student is expected to select tools, including real objects, manipulatives, paper and pencil, and technology as appropriate, and techniques, including mental math, estimation, and number sense as appropriate, to solve problems.” The Overview of Process Standards section states, “In this lesson, students select tools, such as pencil and paper, manipulatives (e.g., algebra tiles), or technology to solve one-variable equations with variables on both sides of the equal sign. Students also select techniques, including mental math and properties of operations, to solve equations. Students may: Select a tool such as algebra tiles or graphing technology to solve a one-variable equation with variables on both sides of the equal sign. Select a technique, such as estimation (rounding or compatible numbers), to evaluate a solution for reasonableness. Select a technique such as properties of operations or mental math to solve equations.”

The Exploration section of unit 3, lesson 1 directs students to model and solve one-variable equations. The directions state, “Use algebra tiles to solve the following equations. Sketch the tiles at each step, write the verbal description of the actions you made with the tiles, and identify the property of equality that justifies those actions. The equation 2x – 4 = 4x + 4 is solved using algebra tiles below as an example.” The table comprises four columns: symbolic (where the equation is given), tiles (where students draw the algebra tiles used to represent the problem), verbal description, and property of equality. Further into the worksheet, the materials provide students with a new problem that states, “The area and perimeter of a certain rectangle have the same numerical value. The length of the rectangle is 6 units. What is the width of the rectangle in units? Select tools such as color tiles, a ruler, and ribbon to model the rectangle. Draw a picture of the iterations of your model you use to solve the problem in the provided table below.” As students work collaboratively to determine the solution, they will apply the TEKS process standards 7AM.1C.

Evaluation for 5.5b
Materials include a description of how TEKS process standards are incorporated and connected throughout the course.

The materials include a description of how the TEKS process standards are incorporated and connected throughout the course in the Grade 7 Advanced Mathematics Scope and Sequence document on the Course Overview page. The description of this document states, “The scope and sequence document provides information concerning alignment to the Texas Essential Knowledge and Skills (TEKS) for Grade 7 Advanced Mathematics and the English Language Proficiency Standards (ELPS), along with a rationale for the order of units of instruction, including the knowledge and concepts to be learned during the course.” The scope and sequence document includes a table at the beginning that lists each unit in the course. Under each unit is a list of the TEKS found within that unit, including the process standards. For example, under unit 1, “Rational Number Operations & Real Numbers,” the TEKS list includes “7AM.1A, 7AM.1B, 7AM.1C, 7AM.1E, 7AM.2A, 7AM.2B, 7AM.2C, 7AM.2D, 7AM.3A, and 7AM.3B” and the process TEKS within that list are 7AM.1A, 7AM.1B, 7AM.1C, and 7AM.1E. Those same process standards are found in unit 2 (7AM.1A, 7AM.1B, 7AM.1C, and 7AM.1E), unit 3 (7AM.1A, and 7AM.1C), unit 4 (7AM.1B), unit 5 (7AM.1E), unit 6 (7AM.1B and 7AM.1E), unit 7 (7AM.1B), unit 8 (7AM.1A and 7AM.1B), and unit 9 (7AM.1A and 7AM.1C).

The materials include a description of how the TEKS process standards are incorporated and connected throughout the course in the Grade 7 Advanced Mathematics Scope and Sequence document found in the Course Overview page. The description of this document states, “The scope and sequence document provides information concerning alignment to the Texas Essential Knowledge and Skills (TEKS) for Grade 7 Advanced Mathematics and the English Language Proficiency Standards (ELPS) along with a rationale for the order of units of instruction, including the knowledge and concepts to be learned during the course.” The document includes a table listing all 7th-grade advanced math TEKS in full and indicating whether each is a process standard. Next to each TEKS are the units in the course, and if the TEKS is found in that unit, an “x” is placed in the box under the unit, next to the TEKS. This chart helps the user see which TEKS are found in which unit, and which units overlap TEKS throughout the course.

Evaluation for 5.5c
Materials include a description for each unit of how TEKS process standards are incorporated and connected throughout the unit.

The materials include a description for each unit of how the TEKS process standards are incorporated and connected throughout the unit. The Unit Overview’s Resources section includes a document with a TEKS and ELPS Alignment table. The table notes the mathematical process standards, the knowledge and skills student expectations, and the ELPS student expectations. Additionally, the document lists Objectives that include “I can” statements and describe what students will know and be able to do across the unit. For example, in unit 6, “Geometric Transformations and Similarity,” the 7AM Unit 6 Document includes the process standards 7AM.1B, 7AM.1D, 7AM.1E, 7AM.1F, and 7AM.1G. An example of the alignment between the TEKS process standards and the Objectives includes “7AM.1G—The student is expected to display, explain, and justify mathematical ideas and arguments using precise mathematical language in written or oral communication.” The Objective states, “I can explain the properties of orientation and congruence of rotations, reflections, and translations.”

The Course Level Documents include a scope and sequence and an Implementation Guide. Each document includes a description of how the TEKS process standards are incorporated and connected throughout the unit. For example, the Grade 7 Advanced Mathematics Scope and Sequence provides a year-at-a-glance table that shows the distribution of TEKS, including the TEKS process standards, across two semesters. A separate chart demonstrates the distribution of TEKS process standards by unit. For example, unit 1 includes TEKS process standards 7AM.1A, 7AM.1B, 7AM.1C, and 6AM.1E. Unit 2 includes 7AM.1A, 7AM.1B, 7AM.1C, 7AM.1D, 7AM.1E, 7AM.1F, and 7AM.1G. Unit 3 includes 7AM.1A and 7AM.1C. This table allows educators and administrators to determine where the TEKS process standards are addressed and whether they are adequately addressed. The Implementation Guide’s Embedded Process Standards section provides the following teaching guidance: “Each Lesson Overview page in our online system includes an overview paragraph and bullet points that describe how the process standards specifically connect to the content standards of the lesson… For more details regarding which process standards are highlighted in each lesson, please refer to the Lesson Overview pages in the online platform or the Pacing Guide document.”

Evaluation for 5.5d
Materials include an overview of the TEKS process standards incorporated into each lesson.

The materials include an overview of the TEKS process standards incorporated into each lesson. The Lesson Overview includes a table of the TEKS process standards aligned to the lesson. Each Lesson Overview also includes an Overview of Process Standard(s) that describes how the TEKS process standards are incorporated. For example, in unit 2, lesson 7, “Mean Absolute Deviation,” the Overview of Process Standard(s) states, “In this lesson, students calculate and interpret mean absolute deviation from real-world data arising in everyday life, society, and the workplace. Students also analyze mathematical relationships to connect and communicate mathematical ideas.” In unit 3, lesson 4, “Writing Real World Problems from Equations and Inequalities,” the Overview of Process Standard(s) states, “In this lesson, students apply mathematics, particularly writing equations or inequalities, to represent problems arising from everyday life, society, and the workplace.”

The lesson components Exploration and Performance Task incorporate the TEKS process standards. For example, in the unit 2, lesson 7 Exploration, “Blackline Master: Mean Absolute Deviation (AK),” the materials ask the student, “Compare Vivienne’s performance in the first week of practice to her performance in the second week of practice. Did her skills improve? Justify your response. Speak with your partner about how you know” (TEKS 7AM.1F). The 7AM.13D Performance Task—Food Drive demonstrates alignment with the TEKS process standard 7AM.1E in the Mathematically Speaking section. The materials state, “In this task, students are asked to use a table of data to calculate the mean absolute deviation for the set of data and determine the data point whose difference from the mean is closest to the mean absolute deviation for the set of all data points.”

Evaluation for 6.1a
Materials provide opportunities for students to think mathematically, persevere through solving problems, and to make sense of mathematics.

The Exploration component of each lesson gives students the opportunity to think mathematically, persevere through problem-solving, and make sense of mathematics. The materials direct educators to randomly group students into groups of no more than three. Students watch an instructional video and work collaboratively to complete the Exploration assignment while the educator monitors to “facilitate student group exploration and reflection.” The materials provide Instructional Hints to guide educators with suggested scaffolding and instructional strategies. For example, in unit 7, lesson 3, “Angles in Triangles and Angles Formed by Parallel Lines and Transversals,” the Instructional Hints state, “This exploration makes use of a set of examples to guide students to understand three different generalizable relationships. Consider asking students to create a non-example for each relationship and explain it to you and/or a partner to check their understanding.” The materials provide Questioning Strategies” to support student reasoning and productive struggle through questioning.” For example, a Clarifying Question asks, “When you say __________, what do you mean?” An Advancing Question [ask and walk away] asks, “What relationship(s) do you see among the angles?” The activity sheet “6AMU3L4 Blackline Master, Angles in Triangles, Angles Formed by Parallel Lines & Transversals” directs students to consider the relationship of interior angles of a triangle, the exterior angles of a triangle, determine the measure of missing angles in a triangle, and lastly, write a paragraph to describe the relationships between angles created by parallel lines and a transversal. The answer key provides multiple possible responses for the educator to reference and support productive struggle.

The performance task component of each lesson offers multiple task levels, allowing educators to differentiate based on student performance in earlier components. This differentiation ensures that students have the opportunity to think mathematically, persevere through problem solving, and make sense of mathematics at a level that allows for productive struggle. The materials provide Teacher Notes for Task that “provide additional educator guidance for scaffolding and opportunities to extend student thinking. For example, in unit 4, lesson 2, “Multiple Representations of Proportional Relationships,” the 7AM.9A Performance Task—Candy Bar notes state, “The Music Downloads Task assesses the ability to find slope and y-intercept in a real-world context from a table of data. Typing for Money and Candy Bar Sales offers a straightforward assessment of producing multiple representations of a linear situation that may or may not be proportional. If time is a constraint, consider whether you will only assign two of the tasks, choosing between Typing for Money and Candy Bar Sales as the second task.” The materials provide educators with question prompts to “support student reasoning and productive struggle through questioning.” For example, a Clarifying Question asks, “Can you rephrase what the problem is asking?” A Focusing Question asks, “What representations are called for in this situation?” And an Assessing Question asks, “What evidence from the problem/task supports your answer?”

The Teacher Guide’s Providing Students Effective Feedback section provides educator guidance to ensure students have the opportunity to think mathematically, persevere through solving problems, and to make sense of mathematics through effective educator feedback. The materials state, “The focus of feedback should be to support students’ productive struggle—not to remove it. Effective feedback leads students to recognize their next step(s) and how to take them to achieve the learning objective(s).” The materials explain that educators should create a classroom environment that fosters students’ belief in their own self-efficacy. The guidance states, “If feedback needs to be extensive, it should be chunked into smaller pieces so that students can digest each one and work toward improvement… ”

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.

The materials support students in understanding that there can be multiple ways to represent and solve problems and complete tasks. The Teacher Materials include a Unit Introduction and a Unit Overview. Both resources describe the vertical coherence between grade levels, within a course, and within a unit. This coherence shows how skills and concepts build on each other and gives students the opportunity to understand that there are multiple ways to represent and solve problems and tasks. For example, in unit 4, “Problem Solving with Multiple Representations,” the Teacher Materials Unit Introduction explains, “Advanced Math-Grade 7, Unit 4 bridges between numeracy and proportionality. Students use what they know about rates and ratios to solve problems and then use multiple representations to determine and interpret the slope and intercepts of a linear function.” The Unit Overview explains, “In 6th grade advanced math, students worked with unit rate and connected unit rate with the constant of proportionality in a proportional relationship of the form y = kx. In 7th grade advanced math, students are introduced to the concept of constant rate of change in the linear function.” The Teacher Materials provide a Unit Document that includes all Objectives as “I can” statements. The Objectives also demonstrate how students will understand multiple representations to solve problems and complete tasks. For example, “I can use data from a table or graph of a proportional relationship to determine the rate of change (slope) and y-intercept in a real-world problem,” and “I can use data from a table or graph of a linear relationship to determine the rate of change (slope) and y-intercept in a real-world problem.”

The Spiral Review gives students the opportunity to explain that there are multiple ways to represent and solve problems and complete tasks. For example, in unit 6, “Triangles and Similarity,” the Teacher Directions state, “This spiral review utilizes an instructional strategy designed to foster student mathematical discourse.” Students work in pairs. The directions state, “Pairs of students discuss and sort the cards into the correct placement in the table on the first page.”

The Exploration and Performance Task lesson components support students in justifying that there can be multiple ways to represent and solve problems and complete tasks. For example, in unit 9, lesson 1, “Interest” under Exploration, a question states, “Who earned more interest, Sybilla or Whitney? Why do you think that is the case?” In the 7AM.4B Performance Task—Investments, the task directions state, “Of the total withdrawal, about what percent of Bertram’s money came from each account? Justify your reasoning.” Within the educator’s guidance, a section titled Look For states, “Look for student justification of choices of solution strategy.”

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.

The materials are designed to help students make sense of mathematics through multiple opportunities to do, write about, and discuss math with peers and educators. For example, in Grade 7 Advanced Mathematics, in the Exploration section of unit 8, lesson 1, students work in pairs or groups. First, students watch a video on pi, circumference, and diameter in their pairs. The video directs students to find a circular object in the room and measure the distance around it, the distance across it, and the distance from the center to the edge, recording their measurements in their math journals. Students share their findings with another pair. Questions at the end of the video ask students to complete the problems in their math journals and then check their answers against the ones in the video. After the video, pairs complete an activity sheet on pi, circumference, and diameter. As pairs work, educators can use the Questioning Strategies section within the exploration to help students write about and discuss math. Some questions include, “When you say __________, what do you mean?” and “How are the radius and diameter of a circle related to one another?”

The materials are designed to help students make sense of mathematics through multiple opportunities to do, write about, and discuss math with peers and educators. For example, in Grade 7 Advanced Mathematics, in the Explanation section of unit 9, lesson 3, students read the “Tell Me More…” section in their student course book and try a problem on their own. As students work, the educator will “Ask all students to write to justify their responses, including showing their work to calculate the percentages, to a partner with supporting evidence from the content of the worked-out Example 1 and You Try It problem statement. Have partners read their written responses to one another and discuss similarities and differences in the way they showed their work. As needed, support student reasoning and productive struggle through questioning (see below). Bring students back together as a whole group to debrief the content and examples.” Some questions from the Questioning Strategies are “Is this a fixed expense or a variable expense?” and “Is it necessary to have a circle graph of a budget? Why or why not?”

Evaluation for 6.2a
Materials support teachers in guiding students to share and reflect on their problem-solving approaches, including explanations, arguments, and justifications.

The materials support educators in guiding students to share and reflect on their problem-solving approaches, including explanations, arguments, and justifications. For example, in Grade 7 Advanced Mathematics, the materials provide educators with embedded guidance on Questioning Strategies in the Exploration and Explanation sections of each lesson. The Questioning Strategies found in unit 8, lesson 3, “Areas of Composite Figures” include: “How much does the strategy you use to find composite area matter? Justify your response with examples from the exploration activity.” “If you know the areas of these parts, how can you find the area of the composite figure?” “How did you solve the problem?” and “How does your strategy compare to someone else’s strategy? Does it matter which strategy you choose? Why or why not?” In the Explanation section of the lesson, educators can use the instructional hints, which state, “Encourage students to draw dashed lines to divide up the composite figure into other figures and then make a plan for how they will find the area of each part and what operation(s) they will perform on those parts to find the area of the composite figure.” and “Some students may intuitively think of subtracting the area of a figure that is the negative space of a composite figure. Encourage them to compare process and results with a student who chose to divide up and add together the areas of several figures within the positive space of a composite figure.”

The materials support educators in guiding students to share and reflect on their problem-solving approaches, including explanations, arguments, and justifications. For example, in Grade 7 Advanced Mathematics, educators have embedded guidance on Questioning Strategies in the exploration and explanation section of each lesson. The Questioning Strategies found in unit 1, lesson 3, “Applying Rational Numbers” include: “What form (fraction or decimal) should the rational numbers all be in so that you can work with them?”, “How do you know your solution is reasonable?,” “If you know the action in the problem, how can you determine the operation to use?,” and “Does your answer make sense in the context of the problem? Explain how you know.” In the Explanation section of the lesson, educators can use the Instructional Hints, which state, “If necessary, use problem-solving template narrative to provide students with heuristics they may use to guide themselves through the problem-solving process.”

Evaluation for 6.2b
Materials include prompts and guidance to support teachers in providing explanatory feedback based on student responses and anticipated misconceptions.

The materials include prompts and guidance to help educators provide explanatory feedback based on student responses and anticipated misconceptions. For example, in unit 8, Spiral Review 3: Measurement Conversions, in the four corners activity Teacher Directions, the materials include guidance to support educators in providing explanatory feedback based on student responses and anticipated misconceptions, such as “Pair students. Provide all students with a copy of the STAAR™ Reference Materials.” The guidance states, “For each question, provide pairs of students with time to determine a solution. Recommended times are: Question 1: 3 minutes, Question 2: 5 minutes, Question 3: 6 minutes, Question 4: 6 minutes, Question 5: 10 minutes. After each question’s time limit, display the next slide. Pairs of students then move to the corner of the room that matches their answer choice. If all four locations have students, ask the groups to discuss how they know their answer is correct. This allows you to work with any/each of the three incorrect groups to ask questions designed to push their thinking. If three locations have students, ask groups to convince other groups to join them. Begin with an incorrect group with a common misconception, then the correct group. Members of any group can move during these arguments if they choose. If two locations have students, hold a class debate to determine which solution is correct. If only one location has students and it is incorrect, provide direct instruction. If only one location has students and is correct, ask a student to justify their stance before students return to their seats. Repeat for each question.”

The materials include prompts and guidance to help educators provide explanatory feedback based on student responses and anticipated misconceptions. For example, in unit 8, Spiral Review 3, the Teacher Directions section provides guidance on responding to student thinking, instructing educators to “work with any/each of the three incorrect groups to ask questions designed to push their thinking.” The materials also direct educators to begin discussions with “an incorrect group with a common misconception first and then the correct group second,” allowing educators to address errors and guide students toward deeper understanding.