Cosenza Math – Grade 6 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 6 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 instructor 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 instructor to locate units for a specific standard.

The Grade 6 Advanced Mathematics Scope and Sequence document includes a bulleted list of “Concepts & Knowledge to Be Learned” in Grade 6 Advanced Mathematics. For example, the list includes the statements “A function is composed of independent and dependent quantities in relationship with one another,” “All integers are rational numbers,” and “Some representations of data allow you to visually see a numeric summary of the data, such as the median in a box plot.”

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-, 180-, and 210-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, such as “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 adjustment options, 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 include an explanation of the rationale for the unit order as well as how the concepts connect throughout the course. The explanation is under the Course Level Documents within the scope and sequence following the ELPS table. The page is titled Rationale for Unit Progression and contains the rationale for unit order and how the concepts connect throughout the course.

For 6 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, “Units 1 and 3 explore the range of applicable number types that are encountered in the remainder of the Grade 6 Advanced Mathematics course and both connect to TxRCFP: using operations with integers and positive rational numbers to solve problems. Unit 4 builds from equivalent fractions to equivalent ratios and rates to introduce proportional reasoning.”

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 instructors. Each protocol is a checklist to help instructors internalize the content. The Unit Internalization Protocol guides instructors 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 instructor 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 instructor guidance but at the lesson level. The Lesson Internalization Protocol guides instructors 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 instructors 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 instructors in implementing the materials. The Implementation Guide includes these resources and guidance under Course Level Documents. The guide includes various resources to help instructional leaders support instructors. 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. Within each column, the document further breaks down each step into 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 instructors.

The Implementation Guide also provides an Observation Protocol and Checklist page for instructional leaders. This page gives leaders an instructor observation checklist and includes 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 instructors complete certain tasks, such as their daily lesson plan, and provides conversation starters to support leader conversations with instructors. In the During the Lesson portion, the checklist prompts the leader to “look” for various things, such as student placement in random groups and student engagement in mathematical discourse. In the After the Lesson section, the checklist prompts leaders to continue conversations with their instructors, 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. At the beginning of each unit in the course, a page titled, for example, Unit 1: Numeracy and Integer Operations 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 1 Overview page provides the background knowledge needed to teach the unit’s concepts effectively.

For example, the Prior Learning Supports section includes a column with previous years’ TEKS, the full language of the standards, and how they connect to the TEKS in the current grade. At the bottom of the page, under Resources, a 6AM Unit 1 Document 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 4, “Rates and Ratios,” a 6AM Unit 4 English Letter 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 4, “Rates and Ratios,” a 6AM Unit 4 Spanish Letter 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).

The materials include 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, as outlined in the lesson Overview page. For example, in unit 3, lesson 1, “Fraction Multiplication,” the subsection Learning Outcomes provides the lesson objectives as “I can…” statements, such as “I can use visual models to represent fraction multiplication.” Within the same subsection, a table includes 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 and, in this example, is stated as “How do I solve a problem involving the multiplication of two or more fractions?” The Lesson Plan subsection includes three tasks: exploration, explanation, and the performance task. Each task provides instructor guidance on implementation.

Finally, the lesson plan includes an instructional assessment in the form of a performance task or multiple performance tasks. The lesson Overview page contains the instructor version of the performance task(s) and includes four levels of the performance task(s), which depend on student mastery in the lesson.

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 instructor and student materials needed to deliver the lesson effectively, along with suggested timing for each lesson component. Each Lesson Overview page includes a subsection near the center titled Pacing Guide. 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 1, lesson 4, “Integer Addition and Subtraction,” the Pacing Guide suggests that the Exploration portion of the lesson takes 20–25 minutes, the Explanation and Practice portion takes 20–25 minutes, and the Performance Task takes 30–35 minutes. Further down the page, the Teacher Materials section lists two-color counters and number-line models as necessary materials for instructors. The Student Materials section lists pencil, paper, two-color counters, and number-line models as necessary materials.

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, is a column that provides one or more performance tasks. When an instructor clicks the performance task hyperlink, the instructor’s version opens and details the task’s components. Each performance task has four versions, depending on the student’s proficiency level, and the lesson’s Overview page provides instructor guidance on effectively using the performance task.

For example, in unit 8, lesson 2, “Represent and Interpret Data in Histograms and Box Plots,” 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. These sub-bullets guide instructors on how and when to use the performance task. Some examples of the 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 6 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 6 begins with a diagnostic assessment split into two parts. Problems 1-7 in section 6A contain previous-grade-level TEKS, and problems 1-12 in section 6B contain current-grade-level TEKS. Both parts include various task types and questions, such as fill-in-the-table, open-ended, drag-and-drop, graphing, multiple-choice, and matching.

Each lesson contains various formative assessments. For example, in unit 6, lesson 4, “Additive and Multiplicative Relationships,” materials provide two assessment options for instructors. The Explanation portion of the lesson includes the first formative assessment and instructs instructors to give students practice problems from specific workbook pages. When students arrive at those pages, they see open-ended, graphing, fill-in-the-table, and multiple-choice questions. A second option for formative assessments at the lesson level is the performance tasks at the end of each topic. Unit 6, lesson 4 includes two performance task options: “Carnival” or “Company Picnic.” Both performance tasks use open-ended questions, and each task has four performance levels. The levels include simplified, scaffolded, on-level, and enriching tasks, and instructors assign based on mastery level.

The materials provide a summative assessment at the end of each unit, such as the Unit 6 Test. Instructors can print the assessment or assign it digitally. In the Unit 6 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 types of instructional assessments included. For example, the Grade 6 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 instructor guidance to ensure consistent and accurate administration of instructional assessments. For example, under the Grade 6 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. The rubric contains three main scoring sections: procedural, conceptual, and communication, with each section contributing 0, 1, or 2 points each for a total of 6 points possible for each performance task. Breaking down the rubric further, 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 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 1-point column breaks down into 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.

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 6 Advanced Mathematics, each unit begins with a diagnostic assessment, such as the Unit 2 Diagnostic Assessment. The Grade 6 Advanced Mathematics Test Answer Key & Diagnostic Guide provides instructors with the diagnostic assessment answer key and includes the item number, TEKS, correct answer, and diagnostic information. The diagnostic assessment for unit 2, problem number 1 under section 2B, for example, shows a shaded model and states, “This shaded model represents 100%. Which model do you think represents 66 2/3%?” followed by multiple choices with various shaded models. This question is aligned to one of the unit 2, lesson 1 objectives, which states, “I can represent a percent using a concrete model, fraction, or decimal.”

The materials include formative assessments aligned to the TEKS and objectives of the course, unit, or lesson. For example, the unit 2, lesson 5 performance task is a formative assessment aligned with the TEKS and the lesson objective. In the instructor edition of the performance task, the first page lists the TEKS the task assesses. The objective for unit 2, lesson 5 states, “I can solve a real-world problem involving percents using concrete examples,” and the performance task provides students with a table comparing the color of milk chocolate candies to the total number of candies. The problem reads, “Josh was curious about the color of the candy coating in a bag of milk chocolate candies. He decided to do an experiment by buying 48 bags of the candies and noting their colors. The results are shown in the table.” After the table, the problem changes depending on the level of performance task assigned to the student, but the example for the Simplified Task continues with “On the company website, Josh found the percent of each color that is produced in each batch of the candies. They state that they make 13% brown, 20% orange, 14% yellow, 16% green, 24% blue, and 13% red candies in each batch. Which color is the closest to the expected percent stated by the company? 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, instructors can assign a summative assessment called the unit test. When instructors view the test answer key, they 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, when viewing the Unit 2 Test Answer Key, instructors can see each TEKS the test aligns to. In the printable test, for example, problem 3 shows a circle cut into five equal pieces, with four shaded, and asks, “What percent of the model is shaded?” This question aligns with an objective from unit 2, lesson 1, which states, “I can represent a percent using a concrete model, fraction, or decimal.”

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. Grade 6 Advanced Mathematics, includes three types of instructional assessments: diagnostic, formative, and summative. Each assessment includes varying levels of complexity. For example, in unit 2, 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, such as finding equivalent forms and creating word problems based on given information. Each lesson includes two formative assessments: the performance task and practice problems from the book. The performance task can be given based on students’ level of mastery and 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 2, the diagnostic assessment contains open-ended, drag-and-drop, choose-all-that-apply, 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 contains multiple-choice, open-ended, and drawing item types.

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 6 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 performance task. The 0-, 1-, and 2-point columns include 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 has 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 6 Advanced Mathematics under the Course Level Documents, there is a document titled Grade 6 Advanced Mathematics Assessment Guide, and within this document is 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 instructor guidance to use the included tasks and activities to respond to student performance trends on assessments. In Grade 6 Advanced Mathematics, each unit contains one or more performance tasks as a formative assessment option. For example, unit 3, lesson 1, “Fraction Multiplication” contains three different performance tasks titled “Carnival,” “Food,” and “Mums.” Each performance task includes four complexity levels: simplified, scaffolded, on-level, and enriching. The page “Performance Task: Unit 3, Lesson 1” guides instructors 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 6 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 instructors in responding to student performance trends. An example explanation in the diagnostic column is, “Item 1 addresses using the relationship between multiplication and division to solve division problems. Review is recommended prior to teaching Lesson 3 in Unit 3 for students answers less than 75% correct 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 that help educators track student progress and growth. For example, in Grade 6 Advanced Mathematics, Course Level Documents include a guide titled Grade 6 Advanced Mathematics Teacher Tracking Document. The document has five main columns, with the last column 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 6 Advanced Mathematics, Course Level Documents, the Grade 6 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 table of TEKS, 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, on the Grade 6 Advanced Mathematics, unit 1 Overview page, the 6AM Unit 1 English Letter describes the content taught in unit 1, how families can support their students’ progress, and, finally, a table at the bottom of the letter allows families to track student progress within the unit. The table has three columns: unit activity, assignments, and grades earned. Students and their families 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 6 Advanced Mathematics under the unit 5, lesson 7 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 teacher 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 6 Advanced Mathematics, each lesson provides one or more performance tasks as formative assessments. Each performance 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 6 Advanced Mathematics, each unit and lesson includes a vocabulary list for educators at the bottom of the page, along with guidance on how to support students’ acquisition of new vocabulary terms. For example, unit 7, lesson 6 lists the vocabulary terms to preteach as base of a prism, height of a prism, and triangular prism. 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 in the Course Level Documents titled Grade 6 Advanced Mathematics Teacher’s Guide. This guide provides educators with a six-step process for building academic vocabulary. The process states the six steps as: “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 6 Advanced Mathematics under the unit 5, lesson 7 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.

Materials include educator guidance for differentiated extension activities for students who have demonstrated proficiency in grade-level content and skills. In Grade 6 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 1, lesson 4, provides the performance task Golfer Rankings, with four levels of the same 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 include educator guidance in each unit’s lesson Overview page. For example, unit 8, lesson 2: Represent and Interpret Data in Histograms and Box Plots contains a Teaching Hints section and mentions, “As an extension, encourage students to search online to find data sets about sports statistics, weather data, or other numeric data sets that align with their interests.”

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 6 Advanced Mathematics in the Exploration: unit 3, lesson 1 section, there is a subsection titled Instructional Hints. This section provides the educator with a visual example and the direct prompt, “Connect the models and multiplication sentences back to one meaning of multiplication. For example, 1/5 X 2/3 means ‘one fifth of two thirds,’ which can be visualized by shading 2/3 of a square in one direction and 1/5 of the square in the other. The overlap of the shaded regions represents 1/5 of 2/3, which is 2/15.” A second example is on the unit 7, lesson 1 Overview page in the Teaching Hints subsection. This section provides the educator with the direct prompt, “Trace a triangle onto paper. Color each angle a different color. Tear the corners of the triangle off and lay them end to end with their vertices touching in a non-overlapping way. Describe the resulting figure as a straight line (180 [degrees]).”

The materials include guidance to help the educator model and explain the concepts to be learned. For example, in Grade 6 Advanced Mathematics in the Exploration: unit 3, lesson 1 section is a subsection titled Instructional Hints. This section provides the educator with guidance such as “Provide models like patty paper for students to fold into fractions and visualize the multiplication.” A second example is on the unit 7, lesson 1 Overview page in the Teaching Hints subsection. Guidance for the educator states, “Use a protractor to measure each angle in a triangle. Determine the sum of the angle measures. Repeat for several triangles and see if there is a pattern.”

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 6 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 emerging 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 performance 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. In the Grade 6 Advanced Mathematics unit 1, lesson 3 Exploration section, the Instructional Hints subsection provides educators with recommended structures and types of practice; for example, “Use an interactive or human number line to help students compare and order integers and rational numbers as a whole class.” Unit 9, lesson 1’s Exploration is another example. Guidance prompts educators to “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 learning through a video and a group worksheet.

Another example of instructor guidance on recommended structures is found in the unit 9, lesson 1 Exploration section, under the Support for Emergent Bilinguals subsection. This subsection states, “Use structured conversation protocols. Pair students and give them a topic to discuss. Allow 2 minutes for Student A to speak while Student B listens. Allow Student B 1 minute to summarize. Allow 2 minutes for Student B to speak while Student A listens. Allow Student A 1 minute to summarize.”

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 English Language Proficiency Standards (ELPS). Support for Emergent Bilinguals provides prompts, accommodation recommendations, scaffolding, and questioning strategies for educators to implement. For example, in the unit 4, lesson 5 Exploration, Support for Emergent Bilinguals, the materials guide the educator to “Provide students with an opportunity to write to explain their understanding about unit conversions between measurement systems 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 educator about their current level of understanding as more English is acquired.” The materials provide scaffolding prompts for Pre-Production, Beginning, Intermediate, High-Intermediate, and Advanced proficiency levels. The prompt for the Beginning level states, “Ask students to draw their response and connect their drawings to written vocabulary as they respond in writing to a reflective journal entry prompt such as the one described above.”

Additionally, unit 4, lesson 5, Support for Emergent Bilinguals, provides a table with Spanish-English cognates to “foster student cross-linguistic connections in oral and written mathematical discourse and increase comprehension of metric and customary measurement systems.” For example, “liter/litro, millimeter/mililitro, and pint/pinta.” Lastly, the materials include Questioning Strategies to support productive struggle and reasoning through questions. For example, in unit 7, lesson 2, “Clarifying Question: When you say __________, what do you mean?” or “Advancing Question(s) [ask and walk away]: If you know two angles are supplementary, how can you determine one of their measures? If you know two angles are congruent, what do you know about their measures?”

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 6 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.”

Unit 9, lesson 1’s Exploration and Support for Emergent Bilinguals sections include implementation guidance. For example, “Provide linguistic support to enhance and confirm students’ understanding of increasingly complex and elaborated spoken language. Use structured conversation protocols. Pair students and give them a topic to discuss. Allow 2 minutes for Student A to speak while Student B listens. Allow Student B 1 minute to summarize. Allow 2 minutes for Student B to speak while Student A listens. Allow Student A 1 minute to summarize.” Finally, the materials guide educators to “Provide students with sentence stems to complete as they watch the video and listen to the spoken language in the video.” Such as “The balance column keeps track of ____” and “Mr. Phillips records the dollars and cents of his paycheck in the _____ column.”

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. The Spiral Review, a “spaced retrieval and interleaved practice opportunity across lessons and units,” allows students to develop academic vocabulary and increase comprehension through oral discourse. For example, in the unit 4 Spiral Review activity Card Sort, students match solutions to problems through collaboration and discourse. The educator directions state, “Ask students to restate information in their own words during formal classroom interactions using prompts like: Please tell us in your own words what ___ means.” and “Would you tell a partner what you just heard in your own words?” The materials include additional opportunities in the Explanation portion of each lesson. For example, unit 9, lesson 4, Student Centered Learning, directs students to try the “You Try It” and “Make a Note” problems. To complete the Make a Note problem, students “write to explain their reasoning regarding the financial responsibility of Bernardo’s choice with supporting evidence from the Tell Me More section using appropriate style (word choice, syntax, voice, tone)” and then “present their reasoning to a small group of peers.” The materials guide educators to direct students to “gather in groups of no more than 3 students to read what they wrote and then discuss what they reasoned about the relative financial responsibility of Bernardo’s decision.”

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. The Lesson Overview’s Vocabulary section 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.” For example, in unit 9, lesson 3, students complete a Frayer model for the term Credit Report. The template provides the “definition in your own words” as “a credit report is a summary of information about a person’s credit.” Students complete the Facts/Characteristics, Examples, and Non-examples sections. 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 4, lesson 5, quart/cuarto and kiloliter/kilolitro.

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 the Blackline Master (Student Pages) exploration document in unit 7, lesson 5, Volume of Right Rectangular Prisms, in alignment with TEKS 6AM.6C, 11B, 12C, and 1B, the questions begin with the volume of a rectangular prism in a mathematical context and increase in depth and complexity as mathematical process standards are interwoven to solve problems arising from society, the workplace, and everyday life. 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 6, lesson 1, Graphing Points in all Four Quadrants (TEKS 6AM.2H), the Exploration component gives students practice graphing a point on a two-dimensional coordinate plane. The first set of questions asks students to name the coordinates of the points shown on the grid. The next set of questions directs students to graph a point on a two-dimensional coordinate plane. Then, questions instruct students to “Use the grid below to answer questions,” such as “Which of the points satisfies the conditions X > 1 and Y < -3?” Lastly, the directions for the final set of questions state, “The shaded sections represent all the points located inside both overlapping geometric figures.” The questions include “What are integer coordinates located in both triangles?” and “What are coordinates located in both the rectangle and the 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 6AM.3B, unit 3, Working With Rational Numbers, in the Diagnostic Assessment, section 3B, question 2 asks the student to “Evaluate each statement below. If the statement is true, explain why. If the statement is false, provide an example that disproves the statement. Statement 1: Multiplication makes bigger. Statement 2: Division makes smaller.” In unit 3, lesson 1, 6AM.3B Performance Task—Carnival (formative assessment), one question states, “McMath Middle School is hosting a math carnival family night. Through each game, students can win tickets to trade for various donated prizes. Josiah is playing a game where he can spin a wheel and multiply his tickets by the number shown on the wheel. If the amount comes out as a decimal, tickets are rounded to the whole number of tickets.” Questions for the task include, “What percent of the time will Josiah’s spin land on a space that will decrease his number of tickets? Justify your reasoning.” and “How many tickets will he have after he spins and lands on the worst space on the wheel? Justify your reasoning.” The Unit 3 Test requires students to demonstrate depth of understanding aligned to the TEKS. For example, an open-ended question asks, “Jackson lost 1/10 of his supply of golf balls the last time he played a round of golf. If Jackson had 120 golf balls before he played, how many does he have now?”

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, TEKS 6AM.12.C, a question states, “The dimensions of a rectangular prism are 2.5 yards by 1.5 yards by 3 yards. What do you think is the volume of the rectangular prism in cubic yards?” Next, a question states, “A package in the shape of a rectangular prism has a volume of 360 cubic centimeters. The base of the package is a rectangle with an area of 150 square centimeters. What is the height in centimeters of the package?” In unit 8, lesson 1, Represent and Interpret Data in Dot Plots and Stem and Leaf Plots, 6AM.13B Performance Task—Pets, the task description states, “The Pet Place keeps data on the size of dogs that owners bring in so that they can plan for future space needs. The data below shows the weights of the dogs regularly in the pet daycare this week. The Pet Place manager wants to present information about the dog sizes to the owner that helps them visualize the important pieces of information, such as mean size, median size, and range of sizes, including small and large dogs. What graphical representations could the manager use for this data set? Draw one of the possible data sets that will show the information needed for the owner.” Lastly, the TEKS-aligned, summative Unit Assessment allows students to demonstrate mastery of learning objectives. For example, in the unit 8 Test, Representing and Analyzing Data, the questions demonstrate progressive rigor and complexity. A multiple-choice question states, “The graph shows the average test scores in math, science, and social studies for girls and boys. Which table best corresponds to this graph?” An additional question states, “The stem-and-leaf plot below shows the ages of recent recipients of a best actor award. What is the spread of the data represented in the graph?”

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 6, lesson 5: Rates of Change, the Explanation component links to the ePub: Constant Rate of Change. The first set of questions asks students to determine the rate of change from a graph or table. As the questions continue, they progress in rigor. For example, “The student council held a fundraiser to raise money for a new flagpole for the school. They decided to sell sandwiches after school. The table below shows the total amount of money they collected, y, after selling x number of sandwiches. What is the rate of change in the table?” and “What does the rate of change represent in the scenario?”

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 6 Advanced Mathematics scope and sequence, Rationale for Unit Progression, explains that the materials are directly correlated with the Texas Response to the Curriculum Focal Points (TxRCFP) “to create TEKS-aligned instructional materials in a logical progression,” and the process standards are incorporated throughout the course. For example, to demonstrate a strategic sequence, the rationale states, “Unit 2 equips students with the tools they will need to work with rational numbers and reason proportionally. Units 1 and 3 explore the range of applicable number types that are encountered in the remainder of the Grade 6 Advanced Mathematics course, and both connect to TxRCFP: using operations with integers and positive rational numbers to solve problems.” Unit 4 continues with Ratios and Rates, followed by unit 5: Algebraic Expressions, Equations, and Inequalities, unit 7: Geometry and Measurement, unit 6: Algebraic Reasoning, unit 8: Representing and Analyzing Data, and lastly, unit 9: Personal Finance Literacy.

The materials demonstrate coherence across units by explicitly connecting patterns, Big Ideas, and relationships among mathematical concepts in the unit 6 Overview page. Within the Unit Overview section, the materials state, “In 5th grade, students were introduced to the coordinate plane as an intersection of two perpendicular number lines with a focus on Quadrant I since 5th grade mathematics is restricted to whole numbers and positive rational numbers. Students also identified number patterns in additive (y = x + a) and multiplicative (y = ax) relationships from an equation and a graph. In 6th grade advanced math, students were introduced to integers and negative rational numbers in unit 1. In this unit, students extend their prior knowledge to a coordinate system with all four quadrants, including integers and negative rational numbers. As well, since students are now familiar with integers and negative rational numbers, students may now represent additive and multiplicative relationships using graphs in all four quadrants as well as verbal descriptions, tables, and equations. In 6th grade advanced math, students are introduced to the notion of dependency relationships (independent and dependent variables) and begin writing equations to represent these relationships when given a table of data.”

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, in the Grade 6 Advanced Mathematics unit 6, lesson 5 Overview page, a Prior Learning Supports section connects the current unit to 5th-grade expectations. An example provided from the 5th-grade expectations states, “5.4D The student is expected to recognize the difference between additive and multiplicative numerical patterns given a table or graph,” and in 6th grade, “6AM.9D The student is expected to compare two rules verbally, numerically, graphically, and symbolically in the form of y = ax or y = x+a in order to differentiate between additive and multiplicative relationships.”

The materials demonstrate coherence across units by connecting the language learned in previous courses/grade levels to the content to be learned in the current course/grade level within each lesson Overview page. For example, in Grade 6 Advanced Mathematics, the unit 6, lesson 5 Overview page features a Vocabulary section that introduces new terms and encourages students to engage with them using a Frayer model template. In unit 6, lesson 5, students encounter and connect the terms rate of change and ratio.

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 on each lesson Overview page. For example, in the Grade 6 Advanced Mathematics, unit 6, lesson 5 Overview page, a Prior Learning Supports section connects the 6th-grade topic to 7th-grade, 8th-grade, and Algebra 1 topics. An example provided from 6th grade states, “6AM.9D The student is expected to compare two rules verbally, numerically, graphically, and symbolically in the form y = ax or y = x+a in order to differentiate between additive and multiplicative relationships.” In 7th grade, “Multiplicative relationships will be formalized as proportional relationships with constant rates of change and a constant of proportionality.” In 8th grade/Algebra 1, “These relationships will be recognized as direct variation.”

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 6 Advanced Mathematics, the unit 1, lesson 1 Overview page features a Prior Learning Supports section that highlights connections within 6th-grade advanced math. This section states, “In 6th-grade advanced math, students locate, compare, and order integers on a number line. Students also use a number line to better understand how the sign of an integer represents the number’s direction from zero (negative sign is to the left of zero and positive sign is to the right of zero).” Unit 1, lesson 1 introduces integers.

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 6 Advanced Mathematics, the unit 1, lesson 1 Overview page features a Prior Learning Supports section that highlights connections from 2nd, 3rd, and 4th grade to 6th-grade advanced math. Unit 1, lesson 1 introduces integers. The 2nd-grade connection says, “In 2nd grade, students were introduced to number lines by locating whole numbers.” The 3rd-grade connection states, “In 3rd grade, students represented fractions between 0 and 1 on a number line,” and the 4th-grade connection explains, “In 4th grade, students represented fractions and decimals (0.1 and 0.01) as distances from zero on a number line.” In 6th-grade advanced math, “students locate, compare, and order integers on a number line.”

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 6 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 2 Spiral Review 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, lessons 2 and 3: 6AM.2A, 6AM.2D, 6AM.2F, and 6AM.2G, and unit 2, lessons 3 and 4: 6AM.2D. The spiral review is a group activity where students are put into pairs and go through the review together, with each question requiring a set amount of time, such as one or two minutes.

Another example can be seen in unit 6, Spiral Review 2, 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 1, lessons 4 and 5: 6AM.3E; unit 4, lesson 6: 6:AM.4A; unit 4, lessons 7 and 8: 6AM.6A; unit 5, lessons 6 and 8: 6AM.8D; and unit 6, lesson 4: 6AM.9C. The review contains various question types, such as open-ended, write-a-statement, and choose-the-correct-answer.

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 6 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 7 Spiral Review 1 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 3, lessons 1 and 3: 6AM.3F; unit 6, lesson 1: 6AM.2H; unit 7, lesson 1: 6AM.12C; and unit 7, Lessons 2 and 3: 6AM.11A, 6AM.11B, 6AM.12B.

Another example is found in the second spiral review in unit 7. Unit 7, 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 3, lessons 1 and 3: 6AM.3F; unit 4, lessons 3 and 4: 6AM.6C; “unit 6, lesson 1: 6AM.2H; and “unit 7, lessons 3, 4 and 5: 6AM.12B.

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 Explanation: unit 2, lesson 1 of the Grade 6 Advanced Mathematics course. This section guides educators to direct students to their course book to work through problems tied to the lesson. The unit 2, lesson 1 topic covers ratios and percents and allows students to practice problems covering these topics in their course book. For example, questions in this topic require students to interpret various models with shaded and unshaded portions. Students read the real-world application problem and then write the fraction, percent, or ratio of the shaded or nonshaded portion.

Questions and tasks require students to analyze and evaluate models and representations for mathematical concepts and situations in Exploration: unit 4, lesson 6 of the Grade 6 Advanced Mathematics course. This section provides educators with an activity sheet for students to complete. In this activity, students read a few real-world application problems involving percentages. The first few questions direct students to label a completed percent bar graph that represents the problem, use the completed and labeled percent bar graph to label a proportion, and then solve the proportion. The next question builds on the previous two and directs students to read a real-world problem, shade an incomplete percent bar graph, set up a proportion on their own, and then solve the proportion. Students then describe what the answer means in terms of the situation.

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 Explanation: unit 1, lesson 4 of the Grade 6 Advanced Mathematics course. In this section, the materials provide educators with instructions to direct students to work in their course book. In this topic, students add and subtract integers. The first few practice problems state, “Use two-color counters to determine the sum or difference.” The next set of problems states, “Use a number line to determine the sum or difference.”

Questions and tasks require students to create models to represent mathematical situations in Exploration: unit 6, lesson 6 of the Grade 6 Advanced Mathematics course. In this section, the materials provide an activity sheet for students to create an equation and a graph from a verbal description and a table. The first question states, “The Texas State Rodeo begins at noon with a parade through downtown, ending at the courthouse. The parade is led by a group of rodeo horses. The table shows how far the horses are from the starting point since the parade started.” A table follows with time in minutes and blocks from the starting point. Students then create an equation and a table that represents the situation.

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 1 in the Grade 6 Advanced Mathematics course. Each lesson includes one or more performance tasks, and educators assign students different levels of tasks based on their understanding and ability. The performance task, Tickets, covers expressions and equations and states, “Students in Mr. Jeffree’s class are given reward tickets in class that they can later use to make purchases. On Friday, students will have an opportunity to use their tickets. Mr. Jeffree posted the ticket price for each prize on a poster outside his classroom door. The table shows the ticket prices as the product of prime factors.” Students are given a table that is split into two columns: Prize (such as “Listen to music while working” and “No homework pass”) and Tickets Required (represented as “3^2 x 7” and “2^4 x 5”). The problem then states, “Joaquin has 105 tickets. Mr. Jeffree said he would give 10 extra tickets to the first person to tell how many tickets it takes to buy all of the items on the list using prime factorization and Joaquin won the extra tickets.” The problem asks students questions about the situation, such as “What possible items or combinations of items can Joaquin purchase using his quantity of tickets?”

Questions and tasks provide opportunities for students to apply conceptual understanding to new problem situations and contexts in the on-level Performance Task: unit 8, lesson 3, in the Grade 6 Advanced Mathematics course. Each lesson includes one or more performance tasks, and educators assign students different levels of tasks based on their understanding and ability. The performance task, Sales, covers statistics and data and states, “Mr. Carmichael owns a specialty store that sells kitchen products. The most popular product in the store has mean sales of $9,650, median sales of $9,600, a range of $2,000 in monthly sales, and low variability. Mr. Carmichael is concerned about the sales of a certain product in his store’s inventory. To investigate his concerns, he asked the sales manager to compile the monthly sales income from the product for the last year of sales.” A table follows, split into four columns: two for the month and two for sales. The problem then asks students questions such as, “How is the data shaped? What does that tell about the mean and median data?” and “How do the measures of center and spread compare to the more successful product?”

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 that are designed to build student automaticity and fluency necessary to complete grade-level tasks. In Grade 6 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 states, “This spaced retrieval and interleaved practice opportunity across lessons and units addresses the following TEKS from previous instruction: ‘Unit 1, Lessons 2 and 3: 6AM.2A, 6AM.2D, 6AM.2F, and 6AM.2G’ and ‘Unit 2, Lessons 3 and 4: 6AM.2D.’” The activity provided in the spiral review has students practice previous skills with whole numbers, integers, and rational numbers. Another example comes from the unit 5 Spiral Review 2. The spiral review states, “This spaced retrieval and interleaved practice opportunity across lessons and units addresses the following TEKS from previous instruction: ‘Unit 1, Lessons 4 and 5: 6AM.3E’, ‘Unit 3, Lessons 1 and 3: 6AM.3F’, ‘Unit 4, Lesson 6: 6AM.4A’, ‘Unit 4, Lessons 7 and 8: 6AM.6A’, and ‘Unit 5, Lessons 6 and 8: 6AM.8D’.” The activity provided in this spiral review has students practice previous skills with ratios and rates.

The materials provide tasks that are designed to build student automaticity and fluency necessary to complete grade-level tasks in the Grade 6 Advanced Mathematics, unit 7, lesson 3 Overview page. The Overview page for this unit and lesson provides educators with a Prior Learning Supports section and states, “In 4th grade, students used models to determine formulas for the perimeter and area of a rectangle and then used those formulas to solve problems. In 6th grade advanced math, students use the area of a rectangle to model and derive formulas for the area of a parallelogram, trapezoid, and triangle. In 7th grade advanced math, students determine the area of circles and composite figures as well as the lateral and total surface areas for rectangular prisms and pyramids and triangular prisms and pyramids from their nets and use surface area formulas to solve problems involving rectangular prisms, triangular prisms, and cylinders.” The first task that builds fluency and automaticity is found in the Exploration section of this Overview page. Students are given an activity sheet on the area and perimeter of rectangles and parallelograms. Students move on to the Explanation section, which includes information about the students’ coursework, again covering practice with rectangles and parallelograms. Finally, students complete a performance task over swimming pools. The performance task states, “A swimming pool is in the shape of a rectangle and has an island in the middle for sunbathing. The island is in the shape of a parallelogram.” Questions follow that ask about the area of the water surface with and without the island.

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 provide opportunities for students to practice the application of efficient, flexible, and accurate mathematical procedures within the lesson and/or throughout a unit. For example, in Grade 6 Advanced Mathematics, Exploration: unit 4, lesson 4 contains an activity sheet for students on measurement conversions. The first portion of the activity sheet states, “Use a proportion to solve questions 1–3. Question 1 is done for you as an example.” An example from this section states, “The length of a football field is 360 feet from goalpost to goalpost. How long is a football field in yards?” The next set of directions states, “Use a unit rate to solve questions 4–6.” An example from the section states, “Mr. Garcia’s new truck has a 12,700-pound towing capability. How many tons can Mr. Garcia tow with his new truck?” The last section of the activity sheet states, “Use a method of your choice to solve questions 7–10.” An example from this section states, “Greta picked 4.5 cups of blackberries. How many pints of blackberries did Greta pick?”

The materials provide opportunities for students to practice applying efficient, flexible, and accurate mathematical procedures within the lesson and/or throughout a unit. For example, in Grade 6 Advanced Mathematics, the Explanation: unit 6, lesson 3 Overview page prompts educators to assign questions from the student’s course book. One question asks, “Which of these statements represents an additive relationship?” and provides two examples. The first states, “Jeanie’s age is Pablo’s age plus 6 years,” and the second example states, “Marla’s age is twice Pablo’s age.” A different question states, “Steven has 8 more baseball cards in his collection than his best friend Matt. Each boy represented the relationship between Steven’s cards, y, and Matt’s cards, x.” Below this problem are Steven’s equation, written as y = 8x, and Matt’s table, with x-values of 10, 15, 24, 31, and y-values of 18, 23, 32, 39. Two questions follow: “What type of pattern is this situation?” and “Which person correctly represented the situation? How do you know?”

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 8, lesson 6 performance task, Languages. For example, in the educator notes for the task, there is a Mathematically Speaking section that states, “Students may use the information in any order and perform operations using any appropriate form of a rational number and using any appropriate operation. When computing percent, students may use proportions, ratio tables, diagrams, percent proportions, operations, and other appropriate methods to solve problems and answer questions … The focus of the task is for students to apply proportional reasoning to solve problems involving data.” A different section in the educator’s notes, “Look For,” provides items for educators to look for in student answers, such as “student justification of choices of solution strategy.” The performance task itself has four levels of difficulty, and educators assign a level based on the student’s previous ability within the unit. The on-level version of the performance task states, “At Jones City High School, students speak several languages. While 2/3 of the 1,272 students in the school speak English as their primary language, about 85% of those who speak a language other than English at home speak Spanish. The remaining students are represented in the graph below, showing their primary home language.” A bar graph contains the languages Vietnamese, Chinese, German, and Hindi. Three questions follow: “What percent of students in the school speak each language?,” “How many students in the school have their primary language as Spanish?,” and “Of the students speaking a language at home other than English, what is the ratio of Spanish speakers to all other languages?” Students then justify their reasoning.

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 Exploration: unit 1, lesson 5. Educators give students an activity sheet on integer multiplication and division. The directions state, “Use two color counters and the provided number lines to represent the given multiplication and division of integers.” Each question provides students with a multiplication or division problem and a table. The table is separated into three boxes: two color counters, quotient/product, and a blank number line. Further down is a large table with positive and negative integers written vertically and horizontally (like a coordinate grid), and students are asked to “Complete the multiplication table shown below. Use a colored pencil to shade positive products in yellow and negative products in red.” Random boxes are completed for students and colored appropriately. Debriefing questions are last and ask, “In general, when two integers with the same sign are multiplied, what will be the sign of the product? Explain to a partner how you know.”

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

The materials contain embedded supports for educators to guide students toward increasingly efficient approaches in various lessons of unit 2 of the Grade 6 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. In the unit 2, lesson 1 Overview page, this section states, “In this lesson, students will create and use representations to organize, record, and communicate mathematical ideas. Students can use and connect various representations in the following ways: Describe connections among the ways a ratio is represented with concrete models, fractions, and decimals. Describe connections among the ways a percent is represented with concrete models, fractions, and decimals. Use several representations to explain what a percent is and interpret that percent in the context of a problem.” Another section in each lesson, Prior Learning Supports, describes how the lesson extends from similar content in previous lessons and grade levels. The example from “unit 2, lesson 1 states, “Ratios and percents are topics that are new to 6th grade advanced math. However, students previously used visual models to represent fractions and decimals. 3.3A expects the student to represent fractions greater than zero and less than or equal to one with denominators of 2, 3, 4, 6, and 8 using concrete objects and pictorial models, including strip diagrams and number lines. 4.2F expects students to compare and order decimals to the hundredths using concrete and visual models. Students often represent fractions using strip diagrams and decimals using hundreds grids. Both models represent parts of a whole and show equivalence among fractions, decimals, and percents. Students may also use these models to compare part-to-part ratios within a whole.” A third section in each lesson Overview page, Teaching Hints, gives educators hints and information to assist students. In this lesson, the hints for the educator state, “Ratios and percents are new to 6th grade advanced math students. Anchor this content in students’ prior knowledge about equivalent fractions. Manipulatives such as proportionality rods (e.g., Cuisenaire® rods) can help students visualize ratios and how different quantities relate to one another. Visual models such as hundreds grids allow students to see the relationships between percents and decimals.”

The materials contain embedded supports for educators to guide students toward increasingly efficient approaches in various lessons of unit 2 of the Grade 6 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. In the unit 2, lesson 3 Overview page, this section states, “In this lesson, students will communicate mathematical ideas, reasoning, and their implications using multiple representations. Students can communicate in the following ways: Use visual models to show how a fraction, decimal, and percent represent the same quantity. Describe, using words, how they know a fraction, decimal, and percent are equivalent.” Another section in each lesson, Prior Learning Supports, describes how the lesson extends from similar content in previous lessons and grade levels. The example from unit 2, lesson 3 states, “Percents are new to 6th grade advanced math. However, students previously used visual models to represent equivalent fractions (Grade 3 and Grade 4) and related decimals to fractions (Grade 4). Percents were introduced in Grade 6 Advanced Mathematics, Unit 2 Lesson 1. 4.2G The student is expected to relate decimals to fractions that name tenths and hundredths. 4.3C The student is expected to determine if two given fractions are equivalent using a variety of methods. 4.3D The student is expected to compare two fractions with different numerators and different denominators and represent the comparison using the symbols >, =, or <. 3.3F The student is expected to represent equivalent fractions with denominators of 2, 3, 4, 6, and 8 using a variety of objects and pictorial models, including number lines. In 3rd grade, students used number lines and pictorial models to represent equivalent fractions with denominators of 2, 3, 4, 6, and 8.” A third section in each lesson Overview page, Teaching Hints, gives educators hints and information to assist students. In this lesson, the hints for the educator state, “Visual models are helpful for students to understand how a number between 0 and 1 can be represented in different ways. When making comparisons between models, remind students that parts can only be compared if the regions representing the whole have equal areas.”

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

The materials explicitly state how the conceptual and procedural emphasis of the TEKS are addressed. 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 5, lesson 1, Prime Factorization, the Lesson Overview - Focusing Question states, “How can I represent a number as a product of its prime factors?” The Learning Outcomes state that students will “determine the prime factors of a composite whole number” and “determine if two expressions, including one written in prime factorization, are equivalent.” The materials address the procedural emphasis of the TEKS in the Overview of the Process Standards. The overview states, “Students will create and use representations to show equivalent expressions, including prime factors of whole numbers. Students may create and use diagrams such as factor trees to organize and record the partial factors and prime factors of a composite whole number,” and “create and use expressions such as prime factorization to communicate mathematical ideas of decomposing a composite whole number into a product of its prime factors.”

In unit 4, lesson 1, “Rates and Ratios,” the Learning Outcomes state the conceptual emphasis of the TEKS in student-friendly statements: “I can describe a ratio as a comparison of two quantities that describe the same attribute,” and “I can describe a rate as a comparison of two quantities that have different attributes.” The Overview of Process Standards section states the procedural emphasis of the TEKS. For example, students will use visual models and ratio tables to show rates and ratios.

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. The materials include a Blackline Master for Concrete Models and an answer key that provides a manipulative exemplar. For example, in unit 2, lesson 5, “Percents with Concrete Objects,” the Blackline Master Concrete Models and Part, Whole, or Percent directs students to “Use concrete models to determine the missing part, whole, or percent in each real-world problem.” Questions and tasks include pictorial representations (figures/drawings) and abstract representations, as required by the TEKS. The 6AM.4A Performance Task—Candy Colors states, “Students may use a variety of strategies to compute percents, including equations, proportions, equivalent fractions, models, and other appropriate strategies.”

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 8, lesson 9, Problem Solving Using Data from Circle Graphs, the materials direct students to “construct a circle graph to represent categorical data, and interpret data from a circle graph and use it to solve problems.” The Teaching Hints suggest that the educator can “Consider connecting bar graphs to circle graphs at the beginning of this exploration by taking an already constructed bar graph, cutting its differently colored bars out, taping them together end to end, and then taping both ends of the bars together to create a circle, noting how the bars denote the arcs of the sectors in a circle graph.” Finally, in the 6AM.14D Performance Task—Budget, the directions state, “When working with percents and in computing the percents based on the degrees in the circle, students may use proportions, ratio tables, diagrams, percent proportions, operations, and other appropriate methods to solve problems and answer questions.”

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 1, lesson 5, “Integer Multiplication and Division,” the Overview of Process Standard(s) defines how students will “display, explain, and justify mathematical ideas and arguments.” The materials encourage students to “communicate their thinking in a variety of ways,” including: “Explain, verbally or in writing, how the concrete models used to add or subtract integers connect to the procedures that we use to add or subtract integers. Justify how the sign of the sum or difference relates to the signs of the addends or subtrahend and minuend. Explain, verbally or in writing, how the solution to a problem seems reasonable.” In the Explanation lesson component, 6AM unit 1, lesson 5 Multiplying and Dividing Integers, the student is expected to “represent integer operations with concrete models and connect the actions with the models to standardized algorithms.”

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 unit 5, lesson 7, “Modeling and Solving One-Variable, Two-Step Equations and Representing Solutions on Number Lines,” the instructions to the Exploration section direct students to “Write an equation you can use to solve the problem. Use cups and counters to solve the equation. Represent the solution on a number line and use substitution to verify your solution.” The Exploration Debriefing Questions allow students to define and explain. For example, a question asks, “How did you use the model to represent each expression?” and “For equations with a sum or difference, how did you determine the value of x?”

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 6 Advanced Mathematics Lesson Overview page. For example, the unit 4, lesson 1 Overview page contains Teaching Hints that state, “A concrete model such as Cuisenaire or proportionality rods allows students to physically compare two different quantities with similar attributes (length of the rod) and visualize ratios between those two quantities. If physical proportionality rods are not available, consider using a paper model that students may cut out and use.” The paper model mentioned links to a sheet of paper with Cuisenaire rods that students can cut out if needed. 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.” A Frayer model template is provided to students along with the list of important vocabulary terms. In the lesson Overview page, educators can assign students practice problems from their students’ course book. A worked-out problem in this book provides students with an example involving two differently colored shirts and asks them to explain how the ratio shows a multiplicative comparison. The example provides students with a visual: a table with nine purple squares and 12 green squares. The question asks students to “Use a part-to-part ratio to describe the shirts.” In the book’s practice problems, a question provides students with a visual of squares and triangles and asks them to find the ratio of squares to triangles.

The materials provide opportunities for students to develop academic mathematical language using visuals, manipulatives, and other language-development strategies on the Grade 6 Advanced Mathematics Lesson Overview page. For example, the unit 2, lesson 4 Overview page contains Teaching Hints that state, “Provide scaffolding tools such as number lines, hundreds grids, or fraction strips if students need additional support. For word problems, provide students with a problem-solving model template as needed.” 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 for students to add to as they move through the lesson and develop a deeper understanding of the vocabulary term. Click on the term to see the Frayer model.” A Frayer model template is provided to students along with the list of important vocabulary terms. In the lesson Overview page, educators can assign students practice problems from their students’ course book. These practice problems are on generating equivalent rational numbers, and students see a hundred grid with 62 squares colored in. Students read about how those 62 out of 100 squares can be written as a fraction, decimal, and percent.

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 6 Advanced Mathematics, educators can access a Teacher’s Guide on the course Overview page. Within this document is a section on scaffolds which 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. Those steps are “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 unit 6 Advanced Mathematics course under the Exploration section of unit 8, lesson 1. A section is labeled for emergent bilingual students, but these scaffolds can be used for all students. This section states, “Make sure that students record their thoughts in response to the Debriefing Questions.” Ask students, “The last question describes data as a ‘variable.’ What does it mean for data to be variable? How is this use of the term ‘variable’ similar to and different from what we have done in this class previously? Ensure students use context to distinguish between the multiple meanings of ‘variable’ as a noun (in describing parts of algebraic expressions) and as an adjective (in describing variance in data and in describing the different values that a letter can stand for in an algebraic expression). In student groups, make sure that each emergent bilingual student speaks using grade-level content and real vocabulary in context to internalize new English words, including data representation, range, and variability, and build academic language proficiency. Use sentence stems such as: Which ____ best represents ___? Which ____ can be used to determine ___? Which ____ appears to be ___?”

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, and 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 educators to support student responses using exemplar responses to questions and tasks. The Exploration section Support for Emerging Bilinguals provides educator guidance and prompts to support vocabulary development and mathematical discourse. For example, in unit 7, lesson 4, “Area of Triangles and Trapezoids,” the Support for Emerging Bilinguals materials in the Exploration section guide educators to “Support students’ speaking skills by providing opportunities for them to learn about and use prefixes and root words that describe different polynomials.” The materials further guide the educator to assign students a writing prompt supporting vocabulary, syntax, and discourse by directing students to “use appropriate writing conventions (spelling of units, punctuation, spacing, etc.) and mathematical conventions (appropriate use of operations, equations, etc.) for the purpose of informing a partner.” A final educator prompt allows students the opportunity to hear, refine, and use math language with peers. The guidance states, “Each partner provides feedback regarding how effectively they felt informed by the details provided in their partner’s work.”

The Exploration lesson component includes a Blackline Master answer key to support vocabulary development during students’ independent practice. The answer key includes an ELPS Strategy prompt and exemplar answer for educators. For example, in unit 1, lesson 3, Comparing and Ordering Numbers, the prompt states, “Explain to a partner how you selected the symbol <, =, or >.” The possible exemplar response demonstrates the application of appropriate mathematical language and states, “I located both integers on the number line. If the first integer was to the left of the second integer, I used <. If the first integer was to the right of the second integer, I used >.” Additionally, the Vocabulary section of the Lesson Overview 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 instructs students to define the vocabulary word in their own words, 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 6 Advanced Mathematics, each lesson includes an Overview page with a learning outcomes section that lists the TEKS in the lesson and indicates whether they are process standards, along with an overview of the lesson’s process standards. For example, on the unit 1, lesson 1, “Introduction to Integers” Overview page, the learning outcome TEKS states, “6AM.1D Mathematical process standards. The student uses mathematical processes to acquire and demonstrate mathematical understanding. The student is expected to communicate mathematical ideas, reasoning, and their implications using multiple representations, including symbols, diagrams, graphs, and language as appropriate.” The overview of process standards sections states, “In this lesson, students will use multiple representations, including absolute value symbols and number lines, to describe and interpret the value of a number, its absolute value, and its opposite. Students can use and connect various representations in the following ways: Represent a number on a number line and explain that its absolute value is that number’s distance from 0. Use a number line to show that a number and its opposite are the same distance from 0 but in opposite directions.”

The performance task for unit 1, lesson 1, 6AM.2B Performance Task—Absolutely Puzzling Temperature Values, allows students to use their understanding of the absolute value of a number to determine the possible high and low temperatures of a Swedish city. The task states, “On a January day, the high and low temperatures were recorded for a city in Sweden. The product of the absolute values of two temperatures was 24. The sum of the absolute values of the two temperatures was 10. What are all of the possible temperature pairs that could have been recorded for the two cities? What is the difference in the absolute values of the two temperatures that day? What is the quotient of the absolute values of the two temperatures? Justify your reasoning.” As students work collaboratively to determine the solution, they will apply the TEKS process standards, 6AM.1A, 6AM.1B, and 6AM.1C.

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

The materials describe how TEKS process standards are incorporated and connected throughout the course in the Grade 6 Advanced Mathematics scope and sequence document on the course Overview page. The scope and sequence document states, “The scope and sequence document provides information concerning alignment to the TEKS for Grade 6 Advanced Mathematics and the 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: Numeracy and Integer Operations, the TEKS list includes 6AM.1D, 6AM.1E, 6AM.1G, 6AM.2A, 6AM.2B, 6AM.2D, 6AM.2F, 6AM.3D, and 6AM.3E. The process TEKS within that list are 6AM.1D, 6AM.1E, and 6AM.1G. Those same process standards are found in unit 2 (6AM.1D and 6AM.1G), unit 5 (6AM.1E and 6AM.1G), unit 6 (6AM.1D and 6AM.1G), unit 8 (6AM.1E and 6AM.1G), and unit 9 (6AM.1E and 6AM.1G).

The materials describe how TEKS process standards are incorporated and connected throughout the course in the Grade 6 Advanced Mathematics scope and sequence document on the course Overview page. The scope and sequence description states, “The scope and sequence document provides information concerning alignment to the TEKS for Grade 6 Advanced Mathematics and the 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 that lists all 6th-grade advanced math TEKS in full and indicates 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 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 9, “Personal Financial Literacy,” the 6AM Unit 9 Document includes the process standards 6AM.1A, 6AM.1E, 6AM.1F, and 6AM.1G. An example of the alignment between the TEKS process standards and the Objectives includes “6AM.1A - The student is expected to apply mathematics to problems arising in everyday life, society, and the workplace.” The Objective states, “I can apply operations on decimals and rational numbers to balance a check register.”

The Course Level Documents titled Course Resources include a scope and sequence and implementation guide. Each document includes a description for each unit of how the TEKS process standards are incorporated and connected throughout the unit. For example, the Grade 6 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 6AM.1A, 6AM.1D, and 6AM.1E. Unit 2 includes 6AM.1C and 6AM.1F. Unit 3 includes 6AM.1D, 6AM.1E, and 6AM.1G. 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), which describes how the TEKS process standards are incorporated. For example, in unit 8, lesson 5: Relative Frequency Tables and Percent Bar Graphs, the Overview of Process Standard(s) states, “In this lesson, students will analyze relationships in categorical data sets and use those relationships to connect and communicate important mathematical ideas about frequency and distribution of data within the data set.” In unit 4, lesson 2, “Unit Rates,” the Overview of Process Standard(s) states, “In this lesson, students will analyze mathematical relationships in order to connect and communicate ideas about unit rates.”

The lesson components Exploration and Performance Task incorporate the TEKS process standards. For example, in unit 8, lesson 5, Exploration, Blackline Master: Relative Frequency Tables (AK), the materials ask the student, “According to the relative frequency table, what is the mode cell phone company among the people Andre surveyed? Explain how you know” (TEKS 6AM.1G). The 6AM.14F Performance Task - Library demonstrates alignment with the TEKS process standard 6AM.1E in the Mathematically Speaking section. The materials state, “In this task, students are given a percent bar graph representing the 1,200 visitors to the city library last week. Using the bar graph, students will find the mode, the number of visitors per day, so they can be ordered numerically, and answer questions about the visitors per day, including interpreting the mean number.”

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 the educator to randomly group students into groups no larger 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 3, lesson 4, “Adding and Subtracting Rational Numbers,” the Instructional Hints state, “Use diagrams such as a strip diagram to help students understand how the numbers fit together in the problem. From there, students may deduce which operation to use.” 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, “Is this true in every case?” The activity sheet Adding and Subtracting Rational Numbers directs students to use number tiles to make true equations, using each digit only once. The materials encourage students to see how many different true equations they can create. 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 levels of tasks that allow educators to differentiate based on student performance in previous components of the lesson. 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 8, lesson 6: Problem Solving Using Data from Bar Graphs and Dot Plots, in the 6AM.14D Performance Task – Languages, the notes state, “Students write the content-area text of their responses and justification for those responses using appropriate mathematical proportions and in complete sentences as much as possible using a variety of transition words. Support emergent bilinguals’ writing skills by providing sentence stems focused on transition words.” 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 might you use?,” while an Assessing question asks, “What evidence from the problem/task supports your answer?”

The Teacher’s 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 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, “Rates and Ratios,” the Unit Introduction to the Teacher Materials explains, “Before Advanced Math—Grade 6 Unit 4, much of what students learn about mathematics is numerical in nature. Students used arithmetic operations on whole numbers and rational numbers (fractions, integers, and decimals) to solve problems. In 6th grade advanced math, beginning with this unit, the focus of students’ mathematical study shifts toward proportional thinking and reasoning.” The Unit Overview explains, “In 5th grade, students solved problems involving conversions within a measurement system (customary or metric) using a scaling strategy where they multiplied or divided the given quantity by a conversion factor to obtain the same quantity with new measurement units (e.g., 3 feet × 12 inches per foot = 36 inches). In 6th grade advanced math, students are introduced to rates and ratios and then use rates to convert measurements within and between measurement systems.” 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 a variety of strategies to solve a problem using percents.”

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 the unit 3 section Integer and Rational Number Operations, the Teacher Directions state, “This spiral review utilizes an instructional strategy designed to foster student mathematical discourse.” Students work in small groups at each station. The directions for Station 1 state, “Support students’ speaking skills as they work collaboratively before recording their answers by providing sentence stems to encourage speaking with a variety of sentence lengths during group discussions during exploration activities.” The materials provide sentence stems to support student discourse. For example, “The answer is positive/zero/negative because… ” and “The expression is the same as the model in that ___ and ___ mean the same thing.”

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 3, lesson 3, Fraction Division, under Exploration, the directions state, “Carry out each indicated operation. Justify your answers.” In the 6AM.3A Performance Task—Cutting Wood, the task directions state, “Which length creates the least amount of leftover scrap wood wasted after cutting the sections? Justify your reasoning.” The 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 require students to make sense of mathematics through multiple opportunities to do, write about, and discuss math with peers and educators. For example, in Grade 6 Advanced Mathematics, in the Exploration section of unit 3, lesson 3, students work in pairs or groups. First, students watch a video on dividing fractions with models in their pairs. The video directs students to fold and color paper to model fractions, then refold it to show the division. At the end of the video, students complete the problem in their math journals and check their answers against the video. After the video, pairs complete an activity sheet on dividing fractions and justify their answers. 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 “If you know the divisor, how do you determine the quotient?”

The materials are designed to require students to make sense of mathematics through multiple opportunities to do, write about, and discuss math with peers and educators. For example, in Grade 6 Advanced Mathematics, in the Explanation section of unit 7, lesson 5, students read the Tell Me More… section in their student course book and try a problem on their own. As students work, educators can use questioning strategies, including questions such as “Which faces are the bases of the prism?” and “How did you solve this problem?” Once students complete the problem on their own, the educator brings students back together to discuss and debrief.

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 6 Advanced Mathematics, the materials provide educators with embedded guidance on questioning strategies in the Exploration and Explanation sections of each lesson. The questioning strategies in unit 7, lesson 5, “Volume of Right Rectangular Prisms” include “How do you know your solution is reasonable?” “If you know the volume formula, how can you determine the volume?” “Does your answer make sense in the context of the problem? Explain how you know” and “If you know the bases of a prism, how can you determine the prism’s height?” In the explanation section of the lesson, educators can use the instructional hints, which state, “Provide students with a problem-solving template to guide them through the problem-solving process. Analyze the given information, formulate a plan or strategy, implement the plan or strategy, evaluate the solution for reasonableness, and evaluate the problem-solving process.”

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 6 Advanced Mathematics, educators have embedded guidance on questioning strategies in the exploration and explanation section of each lesson. The questioning strategies found in unit 4, lesson 8, “Rates in the Real World” include “How do you know your answer is correct?” “If you know one rate, how can you determine the next rate?” “How might you use a ratio table to identify several possible ratios for this given situation?,” 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, “When students calculate an answer, ask them to explain how they know their answer is reasonable in the context of the problem.”

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 6, Spiral Review 2: Additive and Multiplicative Relationships, 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 “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: 2 minutes, Question 2: 5 minutes, Question 3: 5 minutes, Question 4: 6 minutes, Question 5: 2 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, unit 4, lesson 2, “Unit Rates” provides educators with specific questioning strategies to respond to student thinking, including clarifying, focusing, advancing, and assessing questions. Examples include “What does the problem ask?” “What do you know?” “What do you want to find out?” “If you know two quantities in a rate, how can you determine the unit rate?” and “How did you solve the problem?” The materials also instruct educators to “support student reasoning and productive struggle through questioning” and use student responses to “gauge their proficiency with the content.” These questions appear under the Student Centered Learning Option, Questioning Strategies, and Assessment Strategies sections.