enVision+ Texas Mathematics, Adv 08

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

The Scope and Sequence tab, located under the “Browse” heading in the Navigation Guide, includes four files for school years of varying lengths (135, 165, 180, and 210 days). Each file includes Topics (concepts) taught in the course, broken into individual lessons, and indicates that the Texas Essential Knowledge and Skills (TEKS) and the English Language Proficiency Standards (ELPS) are addressed. For example, enVision+ Texas Mathematics 2028 Advanced Grade 6 Scope and Sequence: 165 Days details “Topic 1: Solving Equations and Inequalities” as a 13.5-day lesson that teaches TEKS 8AM.5A, 8AM.5B, and 8AM.12F, using ELPS 1C, 1E, 1F, 3E, 3G, 4D, 4E, and 4F. This same topic spans 12.5 days, 14.5 days, and 16 days in the respective 135-day, 180-day, and 210-day Scope and Sequence files.

Additionally, the “Scope and Sequence” tab in the End Matter section of the enVision+ Texas Mathematics 2028 Advanced Grade 8 Teacher’s Edition provides a vertical scope and sequence, including Advanced Grades 6-8, Geometry, and Algebra II. It states, “The statements in the Scope and Sequence are from the TEKS. The chart is organized to show progressions across similar strands.” For example, the scope and sequence chart contains 17 strands, such as Numbers and Operations and Circles, that highlight the strands taught in each course, demonstrating that six of the 17 strands are taught in Advanced Grade 8.

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).

In the Pacing Guides tab under the “Browse” heading, four separate files include pacing guides for school years of varying lengths (135, 165, 180, and 210 days). This information includes the topics, the number of days each topic should take to teach, and which TEKS are covered. The number of days allocated to each topic varies depending on the length of the instructional calendar. Specifically, topic 7, “Quadratic Functions,” requires 24 days under the 180-day instructional calendar and 22 days under the 165-day instructional calendar.

Under the “Browse” heading, four Scope and Sequence Documents files cover school years of varying lengths (135, 165, 180, and 210 days). This information includes the suggested number of days allocated to each topic for each school-year length. For example, the guide for topic 1, “Solving Equations and Inequalities,” suggests 12.5 instructional days and 2.5 assessment days for the 135-day calendar and 16 instructional days and four assessment days for the 210-day calendar.

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 article titled “Advanced Grade 8 Content Organization Rationale” states that “Topics are sequenced to support mathematics progressions that connect new content to prior knowledge,” and explains that the TEKS recur in multiple lessons within and across topics to reinforce more connections.

In the “Advanced Grade 8 Program Overview” section of the Teacher’s Edition, a graphic organizer provides rationale for the content grouping and how it builds mathematical connections. It states that topics 1 (Solving Equations and Inequalities), 2 (Linear Equations), 3 (Linear Functions), and 4 (Systems of Linear Equations and Inequalities) are grouped because “Students apply mathematical process standards to extend their understanding of solving linear equations to include multi-step equations and inequalities with real coefficients. Students build on writing equations in the form y = mx + b to write linear two-variable equations and inequalities in different forms. Students graph, interpret features, and determine the domain and range of linear functions in real-world situations.”

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

In Internalization Protocols and Observational Tools, a document titled “Teacher’s Topic Internalization Protocol” guides educators through the steps to internalize each unit and lesson by providing a four-part protocol with detailed steps for “Scope & Sequence and Pacing,” “Preparing to Teach the Topic,” “Assessing the Topic,” and “Gather and Prepare Materials.” For example, in the “Scope & Sequence and Pacing” section, step 1 guides educators to “Consult your scope and sequence to place this topic in the context of the year-long curriculum.” Step 3 of the “Preparing to Teach the Topic” section guides educators to “Identify relationships between lessons and how they build toward successful TEKS coverage.”

The Teacher’s Edition provides a “Math Background” section for each topic. Specifically, “Topic 1: Solving Equations and Inequalities” guides educators through key concepts, balance and coherence, process standards, and linguistic accommodations for the unit. Furthermore, the Teacher’s Edition provides side-by-side guidance for lesson internalization for each page of the lesson that corresponds to the Student Edition.

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

In the Internalization Protocols and Observational Tools section, several links provide resources for instructional leaders to help educators implement the materials as designed, including internalizing topics and lessons, with step-by-step guidance on topic and lesson internalization. For example, the “Instructional Leaders’ Lesson Internalization Protocol” resource document includes a Guidance section broken into three parts. One of these sections, called “Implementation,” guides educators to “...facilitate discussions about fundamental concepts and skills addressed in the lesson and how these are assessed through the lesson’s practice and the Exit Tickets.”

Furthermore, the Internalization Protocols and Observational Tools section provides an “Instructional Leaders’ Student Work Analysis Protocol” document with step-by-step guidance on analyzing students’ work. Specifically, it provides guidance for implementation to coach educators to “identify not just which TEKS are addressed, but which specific breakout of the TEKS” so educators can “Sort and Categorize Student Work” to “create meaningful categories based on solution strategies, common misconceptions, levels of reasoning, [and] completeness of solution.”

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 Teacher’s Edition provides a “Math Background” section at the beginning of “Topic 2: Linear Equations.” It includes guidance on key concepts such as “Relationships among Quantities” and “Different Forms of Linear Eq,” plus academic vocabulary and linguistic accommodations for terms such as direct variation, slope, and y-intercept. For example, the guidance states that the Vocabulary in Context includes “Rule,” with a “Math Meaning” of “a statement of what is possible” and other meanings, such as “Control; the government of a country.”

The “Math Background: Coherence” section explains how concepts connect to what students in grade A6 learned previously, such as “Solving Linear Equations” and “Literal Equations” in Topic 1. It also specifies how concepts such as “Direct Variation” and “Writing Equations in Different Forms” in topic 2 lead to concepts such as “Lines of Fit” in topic 3 and “Solving Systems of Equations by Graphing” in topic 4.

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.

In the online platform, a “Family Engagement” section for each topic gives families access to the concepts in each lesson within the unit. For example, in lesson 1-5, “Compound Inequalities,” families have access to two tutorial videos and are directed to key vocabulary, including the term “compound inequalities.” Families can change the language from English to Spanish by toggling the language selection at the top right of the window.

Additionally, in the Family Engagement tab, the “Overview of Resources” section of the menu lists “Independent Resources” students can use at home with their family’s support. For example, the Question Help resource details a “Help Me Solve This” feature that “explains each step of the question,” a View and Example feature that “shows a similar question,” and a “Videos” feature that “offers students tutorials on related concepts.”

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).

In the enVision+ Texas Advanced Grade 8 Lesson Plan, “Lesson 1-1: Solving Linear Equations” correlates with TEKS 8AM.5A and ELPS 3E and 4D for the Mathematics Objectives to “Explain that each step in solving a linear equation follows from the equality in the previous step” and “Model and solve linear equations with one variable using the properties of equality,” plus the Language Objective to “Verbally justify each step in creating and solving a linear equation using precise mathematical language and terms.” The lesson includes questions such as “How do you find the cost of renting a kayak for x hours?” and uses a Quick Check from the Assessment Sourcebook as an instructional assessment that aligns with the objectives.

Additionally, lesson 6-3, “Multiplying Special Cases” includes determining the square of a binomial and finding the product of a sum and difference of two squares, and reading and explaining how to multiply monomials and binomials as daily objectives, which correlate with TEKS 8AM.10B and ELPS 2B. In the lesson, students use algebra tiles and game boards as materials to meet the objectives and complete tasks, including “Explain how to use the square of a binomial to find the product of (–16) squared.” An Exit Ticket assessing students’ ability to determine the square of a binomial prompts them to select the correct expanded form of (3x – 10) squared from four choices, aligning with the objective.

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.

In the document titled “Texas Advanced Grade 8 Lesson Plans,” lesson plans are provided for all lessons in the course. These plans provide the number of days allocated for each lesson, then break them into detailed steps with the number of minutes for each step. The document also includes educator and student materials necessary for each lesson. For example, the plan for lesson 1-2, “Solving Equations with a Variable on Both Sides” indicates the lesson should take two days and lists four steps, each broken down into minutes. It also lists necessary materials as a Vocabulary Builder for educators and algebra tiles and game boards for students.

Similarly, each topic begins with a “Topic Overview” section that presents a chart about the lessons. It cites the objectives, the materials educators and students need to deliver each lesson effectively, and the number of days allocated for each lesson within the topic. For example, “Topic 2 Overview, Linear Equations” states that “2-4, Point-Slope Form” should take two days and indicates that a list of materials for the lesson is available on the digital platform.

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

Step 4 in most lessons in the Teacher’s Edition includes a Lesson Quick Check formative assessment; it provides guidance for educators on extended practice based on student performance, including suggested resources. For example, if a student scores 0–3 points, the educator is prompted to use the Reteach to Build Understanding Activity or Additional Practice as an extension. If a student scores 4-5 points, the educator should use the Enrichment Activity as an extension.

Moreover, a document titled “Texas Advanced Grade 8 Lesson Plans” includes the lesson plans for all lessons in the course. This document includes a blue plus-sign symbol as educator guidance to indicate opportunities for extended practice in each step of the lesson. For example, in lesson 1-3, “Literal Equations and Formulas,” “Step 2: Understand and Apply” on Day 2, a blue plus sign labeled “Extend Student Thinking” challenges students to relate the Kelvin temperature scale to degrees Fahrenheit.

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 grade A8 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 the Assessment Sourcebook. For example, the Mid-Topic Performance Task serves as a formative assessment for each topic, and the Topic Assessment serves as a summative assessment, exhibiting question types such as multiple-choice, open-ended, fill-in-the-blank, and graphing. Similarly, a Readiness Assessment, which serves as a diagnostic assessment at the beginning of each topic, varies in task and question types, such as multiple-choice, open-ended, fill-in-the-blank, and multiple-select.

Specifically, “Topic 3: Linear Functions” provides formative assessment opportunities embedded in the lessons, such as “Try It!,” “Exit Ticket,” “Do You Understand?,” “Do You Know How?,” and “Quick Check,” which contain a variety of tasks and questions. This topic also includes a Mid-Topic Assessment and a Mid-Topic Performance Task to monitor student progress and support instructional adjustments throughout the topic. Summative assessment opportunities include a Topic Assessment (Forms A and B) and a Topic Performance Task (Forms A and B), which allow students to demonstrate mastery of topic content through both assessment questions and performance-based application tasks. Finally, before moving into the next topic, students should take a diagnostic Topic 4 Readiness Assessment.

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

The Assessment Guide in the Assessment Sourcebook includes the definitions and intended purposes for diagnostic, formative, and summative assessments in a chart that indicates the “Why” and “When” for each type of assessment. For example, it states the following for diagnostic assessment: “Why: Diagnose students’ readiness for learning by assessing prerequisite content. When: Before instruction.” Then, the chart describes the goals of Instructional Outcomes Informed by Assessment Results as “develop[ing] individual study plans, [making] grouping decisions, and [prescribing] specific activities to fill gaps in understanding of prerequisite content.”

Furthermore, the Assessment Guide clearly defines assessment types and organizes them by category. For example, formative assessments are embedded during and at the end of lessons, including “Try It!,” “Exit Ticket,” “Do You Understand?,” “Do You Know How?,” and “Quick Check.” These assessments evaluate students’ conceptual understanding and procedural fluency and can be used to modify or inform instruction.

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

The grade A8 materials provide an Assessment Guide that includes guidance for educators to ensure consistent and accurate administration of instructional assessments. For example, the “How to Administer Assessments” section guides educators to “Prepare for Assessments” by understanding and scheduling time for the assessment, ensuring a proper testing environment, and “Monitor[ing] Assessments” actively, including making accommodations for emergent bilingual students.

In the Teacher’s Edition, lesson 3-1, “Understanding Relations and Functions,” the materials include guidance on administering and using the Exit Ticket. Specifically, educators are prompted to use it any time after Example 1 and to use the results to inform instructional decisions. In a section titled “Instructional Implications,” educators are supported in interpreting student responses and addressing common errors and misconceptions. For example, the guidance states that students who selected incorrect answer choices likely understood that a function requires an output for every input but failed to recognize that a single input cannot map to multiple different outputs, or that the students were distracted by the numbers themselves rather than the relationship between the input and output sets. The materials then provide specific corrective actions that the educator can implement.

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

The Assessment Sourcebook provides answer keys for all assessment types throughout the course and indicates the TEKS aligned to each question, as well as the objectives for each unit and lesson. For example, each topic begins with a Readiness Assessment that educators can use as a diagnostic tool for the specific TEKS and objectives that students will learn during that unit. Throughout the topic, formative assessments such as a Quick Check and an Exit Ticket gauge students’ achievement of the TEKS and objectives and align with the unit’s individual lessons. Finally, a Topic Assessment and a Topic Performance Task serve as summative assessments that align with all of the unit’s TEKS and objectives.

Specifically, in the Teacher’s Edition, lesson 5-3, “Exponential Functions” aligns the Exit Ticket with TEKS 8AM.9B and includes a DOK level-2 question asking whether a relation represented by an input-output chart is a function. The student can choose between two “Yes” responses with qualifiers and two “No” responses with qualifiers; the correct answer is “No, because the input –1 has two corresponding outputs.”

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

In the Assessment Sourcebook, each assessment includes an answer key that shows the DOK level and the TEKS for each item-type question. For example, the “Topic 1 Assessment” includes 17 questions (one DOK-1, 14 DOK-2, and three DOK-3); some are multiple-choice, while others are graphing or open-ended.

Additionally, lesson 8-3, “Solving Quadratic Functions and Square Roots,” uses a Quick Check to assess students’ understanding of the lesson concepts and includes five items aligned to TEKS 8AM.8A at varying DOK levels. For example, items 1, 3, and 4 are at DOK level 1, and items 2 and 5 are at DOK level 2.

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

In step 4 of each lesson, students should answer five questions in an online Quick Check that is automatically scored; based on student performance, educators can assign appropriate differentiated practice. For example, the scoring interpretation guides educators to use sections titled “Reteach to Build Understanding,” “Mathematical Literacy and Vocabulary,” and “Lesson Student Tutorial videos” for students who score 0–3 points. Educators can use “Additional Practice” and “Enrichment” sections for students who score 4–5 points.

Furthermore, in the Teacher’s Edition, lesson 2-2, “Slope and y-Intercept of a Line” includes an “Item Analysis” table with Differentiated Resources for the Quick Check. These resources give educators clear guidance for interpreting students’ results and responding instructionally, so the next steps are informed by assessment data.

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

In the Teacher’s Edition, each lesson includes a Quick Check with an answer key that ties to an Intervention Lesson to support students in that concept. For example, if a student answers questions in the Quick Check for lesson 1-3 incorrectly, the educator is prompted to use Intervention Lesson A08 for that student.

Additionally, “Lesson 7-8: Linear, Exponential, and Quadratic Models” includes an “Instructional Implications” section for the Exit Ticket in the Teacher’s Edition. This section provides educators with specific, actionable guidance for responding to student performance trends. For example, it states, “If students chose answer choices A or C, then they did not correctly interpret the difference between subsequent weeks.” The section then guides the educator to “Review the difference between linear, quadratic, and exponential functions” and to “Use Do You Know How item 4 or 5, if needed.”

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 grade A8 materials include charts for educators to track student progress and growth and charts for students to track their own progress and growth. For example, the Student Progress and Growth Teacher Tool allows educators to mark a student’s progress and growth according to the TEKS for each lesson, using symbols such as “x” for “working on it,” “–” for “almost there,” and “+” for “got it.” Likewise, students can track their own progress and growth “Before Topic,” “During Topic,” and “After Topic” using the “Student Progress and Growth Tracker” for each lesson objective, with options like “I Can,” “With Help,” and “Not Yet.”

Furthermore, each lesson includes an Exit Ticket with one question that assesses the objective and a section that lets students track their progress and growth in a Self-Assessment. For example, the Exit Ticket for the lesson 1-2, “Solving Equations With a Variable on Both Sides” self-assessment includes a Math Goal statement that reads, “I can write and solve equations with a variable on both sides to solve problems.” Students can select one of three responses—either “Got it,” “Need help,” or “Working on it.”

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 grade A8 materials include guidance in the Teacher’s Edition for differentiated instruction, activities, and paired (scaffolded) lessons for students who have not yet reached proficiency on grade-level content and skills. For example, the “Support Student Understanding” section that follows example 1 in lesson 3-4, “Transforming Linear Functions,” prompts the educator to use an “activity to simplify the example into incremental steps” by writing both equations from the example in slope-intercept form. The educator can then ask students questions like “What do the equations have in common?” and “How are the equations different?”

Additionally, in lesson 5-4, “Exponential Growth and Decay,” educators are prompted to use the Quick Check assessment data to identify students who have not yet reached proficiency with an “Item Analysis” table that aligns each item to a specific DOK level and TEKS standard (8AM.9B, 8AM.9C, 8AM.9D, or 8AM.9E). This guidance helps educators pinpoint where students need additional support. For students who score 0–3 points, educators are prompted to assign the Reteach to Build Understanding resource, which provides scaffolded reteaching of key lesson concepts. They can also assign “Mathematical Literacy and Vocabulary” activities to support emergent bilingual students as they develop understanding of key terms and “Lesson Student Tutorial” videos for additional instructional support.

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 grade A8 materials include pre-teaching and embedded supports for unfamiliar vocabulary and references within the text in the “Linguistic Accommodations” section at the beginning of each topic in the Teacher’s Edition. For example, in the “Context Setting Vocabulary” section of “Topic 3: Linear Functions,” pre-teaching supports state, “Students will encounter the following terms in this topic; be sure they understand their meaning to make sense of the problem situation.” It continues with terms for each lesson, such as gauge and profit in lesson 3-2. Item 29 in the “Practice and Problem-Solving” section includes an image of a river with a measuring tool. The book says, “A staff gauge measures the height of the water level in a river. At one gauge, the river is 1 ft below its average water level of 10 ft. It begins to rise by a constant rate of 1.5 ft per hour.” Then the book asks students to graph the linear function that represents the situation. Likewise, the “Vocabulary in Context” section of Linguistic Accommodations provides different meanings of the word “function,” including the Math Meaning—“When each input has one output”—and Other Meanings—“The purpose of something.”

Additionally, the Linguistic Accommodations in “Topic 1: Solving Equations and Inequalities” offer multiple layers of vocabulary support, including a “Topic Vocabulary Support” table that pre-identifies key vocabulary terms such as variable, equality, absolute value, identity, formula, literal equation, and compound inequality before instruction begins. Educators are prompted to support students with Vocabulary in Context, which presents math-specific terms alongside their everyday meanings. This vocabulary section can help students distinguish between the mathematical and common uses of words such as formula, inequalities, and irrational. Additionally, context-setting vocabulary is pre-identified lesson by lesson, alerting educators to unfamiliar references that students might encounter in problem situations within each lesson, such as nonrefundable, nitrogen, and fertilizer. For emergent bilingual students, the materials provide Metalinguistic Transfer to Spanish guidance that identifies cognates such as real/real and linear/lineal, as well as false cognates such as sets and setos. This guidance helps educators proactively address potential points of confusion before students encounter those terms in texts.

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 grade A8 materials include educator guidance for differentiated instruction for each lesson, including instructional support and activities in the Teacher’s Edition. For example, lesson 2-3, “Slope-Intercept Form,” includes educator guidance “For Early Finishers” with notes in “Step 1: Explore & Share” that challenge students who master the objectives quickly to “Change one or more of the values in the image and draw a representation using the different constraints.” In “Step 2: Understand & Apply,” the “Extend Student Thinking” section provides a challenging problem for students who demonstrated proficiency with grade-level content and skills. These students are asked to determine Joel’s monthly allowance and a one-time birthday gift using two points on a graph that represent his account balance at two and five months, aligning with the lesson examples.

Furthermore, in the Teacher’s Edition, lesson 6-1, “Adding and Subtracting Polynomials,” prompts educators to use Quick Check assessment data to identify students who demonstrated proficiency in grade-level content and skills. For students who scored 4–5 points, educators are prompted to assign the Additional Practice resource, which provides extra practice for each lesson. Educators can also assign the Enrichment resource, which presents addition and subtraction of polynomials and asks students to “Locate and draw a circle around each result in the search grid,” which resembles a word search and extends the lesson concepts. Additionally, educators are prompted to assign the STEAMQuest resource during or after the lesson as a further extension activity that lets students apply math concepts and skills from the lesson in real-world contexts.

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 grade A8 materials include lessons with explicit prompts and guidance in the Teacher’s Edition to support the educator as they model and explain each lesson’s concepts. For example, “Step 1: Explore and Share” of lesson 8-4, “Completing the Square,” includes several guiding questions to use before, during, and after the activity. It also includes a “Process Standards Connection” section, which prompts the educator to “Explain how the properties of equality are used to solve equations. [The properties of equality allow addition, subtraction, and multiplication/division of values without changing the equality between expressions.]” Also, in the Teacher’s Edition, “Step 2: Understand & Apply” includes specific questions the educator can ask while working through each example, ensuring students build accurate conceptual understanding.

Additionally, in lesson 5-3, “Exponential Functions,” educators receive structured, step-by-step instructions across each phase of the lesson. In “Step 1: Explore,” an “Explore and Share” section includes explicit instructional focus guidance for questions to ask before, during, and after the activity, with sample responses. This section also includes prompts to facilitate meaningful mathematical discourse; educators are guided to ask students questions like “What kind of function represents the accordion-style folding?” and “How can you determine the type of function that would represent each method?” In “Step 2: Understand & Apply,” educators are guided through each example to “Pose Purposeful Questions.” Suggested questions and sample answers help educators model mathematical reasoning for students. For example, in Example 1, educators are prompted to ask students, “What key features can be identified from the graph of an exponential function?” This example provides educators with guidance on possible responses that identify the y-intercept, asymptote, domain, and range.

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

The grade A8 Teacher’s Edition provides educator guidance and recommendations for effective lesson delivery and facilitation by integrating various instructional approaches. Each lesson follows a consistent four-step instructional design (Explore, Understand & Apply, Practice & Problem Solving, and Assess & Differentiate) that integrates exploration through a combination of problem-based learning and explicit instruction pedagogy. For example, in lesson 6-4, “Factoring Polynomials,” “Step 1: Explore & Share,” educators prompt students to consider how their favorite lunch is served so they can visualize how to factor a polynomial. Then, the educator can use the “Step 2: Understand & Apply” section to guide students through specific problem-solving methods for factoring polynomials. Finally, students can use their understanding of the “Practice & Problem Solving” and “Assess & Differentiate” sections to factor polynomials in various ways.

Similarly, lesson 1-3, “Literal Equations and Formulas” guides educators to facilitate instruction through multiple approaches across the lesson. In the first step, educators are prompted to begin with a whole-class Explore & Share activity that activates prior knowledge through a real-world situation, followed by small-group work. In the second step, educators “Introduce the Essential Questions” using guided examples, including two examples that “Build Procedural Fluency From Conceptual Understanding,” with guidance to “Remind students that there are key features and characteristics of the graphs of exponential functions that help distinguish them from other functions.” The guidance continues in the third example, which includes a “Try It!” component for students to “Use and Connect Mathematical Representations.” The educator is told in a “Common Error” section that “some students may think the b value is 3. Once students write an equation, have them substitute x- and y-values into the equation to check their work.”

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 grade A8 materials include the “Advanced Grade 8 Program Overview,” which provides a chart that organizes a variety of practice types and opportunities by format (whole group, small group, or individual) to support effective implementation. This overview also specifies whether each practice is guided, independent, or collaborative. For example, the recommended structures for Math Talks are whole-group and small-group, using guided or collaborative practice, and Topic Review is recommended for whole-group, small-group, or individual structures, using guided, collaborative, or independent practice.

Furthermore, the Teacher’s Edition explicitly guides educators on how to structure practice across multiple formats throughout the lesson, like in lesson 1-3, “Literal Equations and Formulas,” “Step 1: Explore & Share.” The materials prompt educators to facilitate a specific collaborative activity, recommended in a whole-group structure—to write an equation representing the perimeter of a rectangle. Then, the materials recommend a small-group structure for guided learning to “Support Productive Struggle in Learning Mathematics,” and they provide suggested discussion questions and sample responses. “Step 2: Understand & Apply” guides educators through guided practice with “Try It!” problems embedded after each example. Provided answers allow educators to check for understanding before moving forward. Next, the materials include Support Student Understanding and Extend Student Thinking sections tied to specific examples, offering additional guided and extension practice structures for individual students who need further support or challenge. Finally, the “Do You Understand?” and “Do You Know How?” sections provide a structured transition from guided to independent practice for individual students at the end of the lesson.

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 grade A8 Teacher’s Edition includes a “Linguistic Accommodations” section that provides guidance and support for topic vocabulary. A chart on the second page of the section identifies the specific ELPS targeted by each lesson’s components, meeting the needs of all five language proficiency levels and aligning the ELPS modalities to the lesson content. For example, the ELPS chart in “Topic 5: Exponents and Exponential Functions” indicates the targeted ELPS in each lesson, including Listening 1E in lesson 1, Speaking 2F and Writing 4B in lesson 2, and Reading 3G in lesson 4. These targeted ELPS are designed to engage students in using increasingly more academic language. Specifically, in “Lesson 5-2: Exponential Functions,” the “Targeted ELPS Support” section aligned to Speaking 2F prompts the educator to “Explain that ‘plot’ has more than one meaning in English.” The educator is then guided to explain three different meanings of the word and “Read the first sentence of the example text aloud. Have [pre-production-level] students raise one, two, or three fingers to indicate which definition of ‘plot’ is used in the sentence.” The section also prompts educators to “Read aloud the text in Example 3. Point out the terms ‘radius,’ ‘slant,’ and ‘slant height.’ Discuss the meaning of these terms as a class and have [intermediate-level] students record them in their journals” and then ask, “What is a radius?”

Similarly, “Targeted ELPS Support” sections are directly embedded within each lesson. Instruction at five differentiated language proficiency levels is provided, guiding educators on how to scaffold language access and engage students in using increasingly academic language. In lesson 3-3, “Key Features of a Linear Function,” “Targeted ELPS Support” is aligned to Listening 1F and prompts educators to support pre-production-level students by using gestures and graphs to convey the meaning of positive and negative slope. Beginning students are asked to respond with thumbs-up or thumbs-down to “yes” or “no” questions; intermediate students are asked to identify and calculate slopes and discuss their predictions; and advanced students are asked to independently identify the line with a positive slope, calculate the line’s slope, and explain how the graph would change if the slope increased. Later, in lesson 3-4, “Transforming Linear Functions,” “Targeted ELPS Support” aligned to Writing 4E prompts educators to scaffold these academic vocabulary terms: stretch, compression, and scale. Students should progress from giving thumbs-up responses at the pre-production level to independently writing a paragraph using vocabulary terms to summarize the text at the advanced level.

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

In the Teacher’s Edition, the “Linguistic Accommodations” section at the start of each topic provides an extensive array of linguistic strategies and resources that can be integrated with any state-approved bilingual/ESL program. For example, the “Linguistic Accommodations” section in “Topic 5: Exponents and Exponential Functions” states, “Activities in this topic offer diverse and engaging experiences with math vocabulary to build confidence and support for all, but particularly for emergent bilingual (EB) students in developing both their academic and language skills.” The section includes resources like “Topic Vocabulary Support,” “Metalinguistic Transfer to Spanish,” and “Cognates,” plus an ELPS chart that helps educators use the materials effectively in state-approved bilingual/ESL programs.

Specifically, in “Topic 8: Solving Quadratic Equations,” the “Linguistic Accommodations” section offers educators explicit implementation guidance that is aligned to the ELPS. This guidance includes a “Metalinguistic Transfer to Spanish” section that identifies transferable skills, non-transferable skills, cognates such as formula/fórmula and variable/variable, and false cognates such as notice and noticia. It provides educators with specific cross-linguistic guidance for teaching Spanish-speaking emergent bilingual students. Additionally, the materials include an ELPS alignment chart that maps specific listening, speaking, reading, and writing standards in each lesson across the topic and gives educators a clear roadmap for implementation.

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 grade A8 materials include Linguistic Accommodations for each topic in the Teacher’s Edition. Guidance helps educators support emergent bilingual students in oral and written discourse and develop academic vocabulary by reinforcing previously learned terms, defining current concept vocabulary, and previewing upcoming vocabulary. These resources provide background knowledge, cross-linguistic connections, and guidance on Spanish transfer (including transferable terms, non-transferable terms, and cognates) to increase comprehension throughout the topic. For example, the “Linguistic Accommodations” section for “Topic 5: Exponents and Exponential Functions” includes a “Topic Vocabulary Support” resource that builds academic vocabulary to increase comprehension while strengthening background knowledge. It also prompts the educator to “be sure [students] understand [context-setting vocabulary] meaning to make sense of the problem situation,” highlighting the use of the word “exponent” for the topic, plus terms for individual lessons, like perfect square factor in lesson 2. Guidance also covers cognates—for example, exponent/exponente is a cross-linguistic connection students can use in oral and written discourse, versus false cognates like integer and integro. Finally, each topic includes an ELPS chart that is broken down by lesson to help educators use the ELPS, particularly for oral and written discourse. For example, lesson 2, “Targeted ELPS Support: Speaking 2F” guides the educator during Example 2. Later, a different “Targeted ELPS Support: Writing 4B” section gives the educator ways to engage students in written discourse for the “Pick a Project” activity. Specifically, the educator is prompted to “Read the first question aloud. Say, ‘Words like “snowflakes” follow the conventional spelling rule of adding s to make the singular word plural. “Galaxies” follows the conventional spelling rule of changing y into ies when transforming to a plural word.’ Have students practice these conventional spelling rules by writing a sentence about fractals incorporating both rules. For example, ‘Repeated branching patterns are one of the properties of many fractals.’”

Furthermore, the materials include Targeted ELPS Support sections embedded directly within lesson instruction that guide educators in supporting emergent bilingual students across oral and written discourse. In lesson 3-3, the embedded “Targeted ELPS Support” section that is aligned to Listening 1F prompts educators to build background knowledge and increase comprehension by using visual representations of linear functions and gestures to make the meaning of “slope” concrete and accessible. Educators are also prompted to help students develop academic vocabulary through oral discourse and to progressively guide advanced students to explain how increasing the slope affects the graph. The section also aligns with Speaking 2C and prompts educators to increase comprehension and develop academic vocabulary by using mapping diagrams as visual tools to clarify the meanings of the terms relation, function, and one-to-one. Students are expected to progress from giving gesture-based responses at the pre-production level to independently describing all three terms and drawing their own mapping diagram using oral discourse at the advanced level. Later, in lesson 3-4, the“Targeted ELPS Support aligned to Writing 4E prompts educators to support emergent bilingual students as they develop academic vocabulary through both oral and written discourse by scaffolding the terms stretch, compression, vertical, and horizontal. Students are expected to first give thumbs-up responses to educator-led reading at the pre-production level. Then, they should be able to independently read the text at the advanced level, discuss vocabulary meanings with a partner using a dictionary for support, and write a paragraph, making cross-linguistic connections to summarize what they read.

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.

Each topic includes lessons with a “Practice and Problem Solving” section that challenges students’ depth of understanding by solving problems aligned to the TEKS for the lesson’s concept(s). Each “Practice and Problem Solving” section ends with a Topic Assessment that uses scaffolded DOK-leveled questions aligned to the topic’s TEKS to assess students’ learning. For example, lesson 2-4, “Point-Slope Form,” uses a variety of questions aligned to TEKS 8AM.2B in the “Practice and Problem Solving” section. These questions require students to use a point and a slope to write the equation of a line, match a real-world situation to data in a table, and demonstrate depth of understanding by comparing point-slope and slope-intercept forms and explaining how the different forms relate to real-world situations. The Assessment Sourcebook provides a “Topic Assessment” section for topic 2, which includes questions that ask students to demonstrate depth of understanding to use points, slopes, and graphs to write equations and solve a real-world evaluation aligned to 8AM.2B and 8AM.2C. This section also requires students to use points and slopes to evaluate equations of parallel lines and demonstrate depth of understanding of TEKS 8AM.2E.

Additionally, lesson 3-1, “Understanding Relations and Functions” opens with “Step 1: Explore and Share,” which lets students explore different ways to organize desks in a study hall and explain the relationship between the number of rows and desks. Students should consider what a reasonable domain looks like, whether a line can represent the relationship, and what other representations, such as a bar graph or a table, could display the data. During “Step 2: Understand and Apply,” students work through six sequenced examples that increase in complexity, starting with identifying functions using mapping diagrams in a real-world shipping context and ordered pairs, then extending their understanding by classifying relations as functions and determining whether they are one-to-one. Next, students recognize domain and range from tables and ordered pairs, analyze reasonable domains and ranges, and distinguish between continuous and discrete functions in real-world contexts. The embedded “Try It!” prompts require students to justify their thinking by explaining why a relation is not a function when a single input maps to two different outputs and to use inequality notation to write the domain and range of a continuous function. The “Concept Summary” and “Do You Understand/Do You Know How” sections require students to articulate why domain and range are important in defining a function, analyze errors, and communicate reasoning about relations and functions across multiple representations, including words, tables, numbers, diagrams, and graphs, demonstrating depth of understanding aligned to TEKS 8AM.2A, 8AM.12A, and 8AM.12B.

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

Lesson 6-6, “Factoring ax[squared] + bx + c” uses scaffolded steps, including “Explore & Share” and “Visual Learning,” that prompt educators to use a variety of strategies and visual models as guided examples. Students can find the area of a TV using sides that are represented by binomials with a variable to activate prior knowledge about binomials. Students can also factor out the trinomial’s common terms and variables and find the area of a quilt made from squares and rectangles that represent the terms within the trinomial, so they understand the connection between the factors of the trinomial and its original terms. Next, students work through guided practice to communicate, reason, and justify the steps in factoring a trinomial. The “Practice and Problem Solving” questions progressively increase in rigor and complexity from determining the factors of trinomials to applying the concept to real-world situations, leading to proficiency in TEKS 8AM.10E.

Additionally, the materials include a progression of questions and tasks that move students from classifying numbers using supported representations that increase in rigor and complexity to justifying classifications and analyzing relationships among number sets. For example, “Lesson 5-1: LET’S BUILD Classify Numbers” first introduces students to the characteristics of whole numbers, integers, and rational numbers through visual supports and vocabulary development in the “Language Support” section. Then, the lesson increases rigor by requiring more demanding reasoning in the Math Talk section, where students compare and contrast number classifications and determine how a number can belong to multiple sets simultaneously. Finally, the Exit Ticket demonstrates increased complexity by requiring students to independently classify numbers using a Venn diagram and justify their placement based on the relationships among the number sets, leading to grade-level proficiency in the mathematics TEKS.

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

The “Advanced Grade 8 Content Organization Rationale” section of the Program Overview explains how the organization supports students as they develop a coherent understanding of mathematics as concepts become increasingly sophisticated. For example, topics 6 to 8 focus on building, analyzing, and solving quadratic functions and equations. This learning builds on the foundational concepts introduced in topics 1 to 4, which help students understand linear functions and learn to solve and graph linear equations. As students progress through the course, they can apply their understanding of function relationships and graphing to increasingly complex situations involving quadratic functions.

Additionally, each topic begins with guiding pages in the Teacher’s Edition that prepare educators to teach its concepts. These resources include the “Math Background: Coherence” page, which connects the topic’s concepts to patterns, big ideas, and relationships that students previously learned in grade A8. This page also explains how the topics connect to concepts that students will learn later in grade A8. For example, the “Looking Back” section of the “Math Background: Coherence” page in “Topic 6: Polynomials and Factoring” explains that students learned about multiplication properties of exponents and solved exponential equations, which connects to topic 6 because “students apply the properties of exponents when multiplying polynomials and finding products of binomials.” Students also learn about factoring polynomials in this topic and demonstrate coherence in the section titled “Looking Ahead.” This section explains that “in topic 6, students recognize that a quadratic trinomial in the form ax^2 + bx + c is factored by finding a factor pair of ac that has a sum of b... Then, in topic 8, students will solve quadratic equations using tables, graphs, and factoring.”

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 grade A8 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 at the beginning of each topic in the Teacher’s Edition. For example, “Topic 5: Exponents and Exponential Functions” begins with several pages that prepare educators to teach the topic’s lessons, including “Math Background: Coherence” and “Linguistic Accommodations.” The “Linguistic Accommodations” page demonstrates coherence across units by connecting mathematical language students learned in grades A6 and A7 to terms they learned in grade A8, such as exponent, power, and radical. The “Math Background: Coherence” page is separated into three columns titled “Looking Back,” “In This Topic,” and “Looking Ahead.” The “Looking Back” section connects content learned in grade A7 and earlier in grade A8 to content students learn in Topic 5, demonstrating the mathematical language that connects concepts like solving and graphing linear equations. The “In This Topic” section uses mathematical terms like “Understanding Exponential Functions” and “Modeling With Exponential Functions” as headings that describe the content students will learn throughout the lessons in topic 11, connecting the content students learned in grades A6 and A7. Finally, the “Looking Ahead” section explains how the content and language students will learn in topic 5 connect to Algebra 2, stating that “students will apply their knowledge of radical expressions to identify key features and graph radical functions.”

Additionally, the “Math Background: Coherence” and “Linguistic Accommodations” sections in “Topic 1: Solving Equations and Inequalities” demonstrate coherence by connecting content and language from previous grade levels to grade A8 content and to future grade levels. For example, the “Math Background: Coherence” section includes “Looking Back” to Advanced Grade 7. It connects content and language that students already learned, including developing fluency with rational number operations, using properties of equality, and solving problems with inequalities. The “Linguistic Accommodations” section highlights terms that students learned in previous grade levels, such as equality, formula, and identity. To connect the content to future courses/grade levels, topic 2 and “Looking Ahead” on the “Math Background: Coherence” page indicate that students will work with equations by writing and solving equations, literal equations, and inequalities. This work connects to Algebra 2, where students use properties of equality to solve non-linear equations.

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 grade A8 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, as outlined in the “Coherence” section on the first page of each lesson in the Teacher’s Edition. For example, the first page of lesson 4-1, “Solving Systems of Equations by Graphing” prompts the educator to use the Skills Review & Practice resource titled “A04: Equations with Variables on Both Sides,” which connects prior knowledge of solving equations with variables. The “Coherence” section also notes that students will “create and graph systems of linear equations to find exact and approximate solutions,” which connects to later in the topic when students “solve systems of linear equations algebraically to find exact solutions.”

Additionally, the Let’s Build lessons demonstrate coherence through “Step 1: Explore and Share,” which lets students connect with prior knowledge of concepts and procedures from current and prior grade levels and prepare for new mathematical knowledge and skills in “Step 2: Visual Learning.” For example, in step 1 of lesson 3-1, “Understanding Relations and Functions,” students learn to differentiate between additive and multiplicative relationships; this work lays the foundation for determining whether a relationship is additive or multiplicative by analyzing a table of data points.

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

The grade A8 materials provide spaced retrieval opportunities with previously learned skills and concepts across lessons and units, as demonstrated in a Venn diagram on the “Space and Interleaved Practice in enVision+ Texas Mathematics” page in the Program Overview. This diagram compares sections within the materials that offer spaced and interleaved practice and shows that Math Talks and Skills Review & Practice both provide spaced retrieval opportunities. For example, the “Skills Review & Practice, A04: Equations with Variables on Both Sides” page recommended for use with lesson 7-1, “Key Features of a Quadratic Function,” in the Teacher’s Edition provides spaced retrieval for students to solve equations with variables on both sides, which are skills and concepts that were previously learned in grade A7. The topic ends with a Topic Review that provides spaced retrieval practice for the concepts and skills associated with the key features of quadratic functions, which students learned throughout the topic.

Additionally, the “Coherence” section of lesson 1-6, “Absolute Value Equations and Inequalities” in the Teacher’s Edition identifies previously learned content, stating that students have “written and solved equations and inequalities in one variable” and “written and solved compound inequalities and interpreted the solutions in context.” The Math Talk section at the beginning of the lesson gives students an opportunity to revisit compound inequalities by analyzing a graphed solution and discussing how compound inequalities with “and” and “or” are represented on a number line. Also, the “Skills Review & Practice” section directs educators to “present or assign to reactivate prior knowledge,” requiring students to retrieve previously learned skills and concepts related to equations, inequalities, and compound inequalities before extending their learning to absolute value equations and inequalities.

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

The grade A8 materials provide interleaved practice opportunities with previously learned skills and concepts across lessons in “Practice and Problem Solving” and units in “Review What You Know.” For example, the “Practice and Problem Solving” section of lesson 5-2, “Radical Expressions,” provides interleaved practice with previously learned skills and concepts across lessons for calculating and factoring square roots and radicals. The “Spiral Review” provides interleaved practice of previously learned skills and concepts across topics, including solving systems of equations and determining a sphere’s diameter from its volume.

Additionally, the materials include a cumulative Topic Review that intermixes skills and concepts from all lessons in “Topic 8: Solving Quadratic Functions,” including quadratic graphs, roots, factoring, square roots, discriminants, and systems of equations in a mixed set of questions. The review also provides interleaved practice of previously learned skills across units, including interpreting graphs, solving equations, manipulating algebra, and analyzing functions—skills they developed in earlier topics. Finally, the review provides interleaved practice of previously learned concepts across units by integrating concepts from prior units, including linear equations, systems of equations, functions, and graphing, which includes determining the roots of a function, solving quadratic equations algebraically, and analyzing a system containing both a linear and quadratic relationship.

Evaluation for 5.1a
Questions and tasks require students to interpret, analyze, and evaluate models and representations for mathematical concepts and situations.

The “Math Modeling in 3 Acts” lessons in each topic in the Teacher’s Edition require students to create models to solve problems involving mathematical concepts and situations and to interpret, analyze, and evaluate their models to find efficient solutions. For example, “Topic 4: Math Modeling in 3 Acts: Get Up There!” provides students with a 34-second video about employees taking two elevators, one express and the other regular, to a rooftop party. After students watch the video, they write a question they can solve using a model. The educator can guide students by saying, “After watching the video, what is the first question that comes to mind? Write down the main question you will answer about what you saw in the video. Make an initial conjecture that answers this main question. Explain how you arrived at your conjecture.” The Teacher’s Edition prompts the educator to ask students to use what they learned in that topic about systems of linear equations and inequalities “to make a mathematical model that represents the relationship between time and floor number for each elevator.” In the second part of the lesson, students receive the detailed information they need to solve the problem, including each elevator’s speed, the number of floors in the building, and the floor each employee started on. Then, students use that information to interpret how their model can determine which employee will reach the rooftop first and how long it will take. In the third part of the lesson, students analyze and evaluate their model for its efficiency and accuracy in solving the problem using question 7, which asks, “Does your refined conjecture match the answer exactly? If not, what might explain the difference?”

Additionally, in the Student Edition, lesson 5-6, “Translations of Exponential Functions,” “Step 1: Explore” and “Step 2: Understand & Apply,” questions and tasks require students to work with tables, graphs, and equations to understand and compare vertical translations of exponential functions. Students should interpret models and representations by examining the graph, table, and equation for “B and A” and “B and B” and identify what the representations show about fan growth over time. Then, students can analyze models and representations by comparing multiple representations of exponential functions and determining how changes to parameters affect the graph, including the initial value, growth rate, y-intercept, and vertical translations. Students also evaluate models and representations by justifying conclusions about whether a graph correctly represents a situation and explaining how modifications to an equation affect the accuracy and characteristics of the resulting graph.

Evaluation for 5.1b
Questions and tasks require students to create models to represent mathematical situations.

The grade A8 materials include questions and tasks that require students to create models that represent mathematical situations in the “Math Modeling in 3 Acts” lessons in each topic of the Teacher’s Edition. For example, “Topic 3: Linear Equations” includes a section titled “Topic 3 Math Modeling in 3 Acts: The Express Lane,” which provides students with a 27-second video that depicts a customer with a small number of items. This customer is deciding whether to use the express lane, which has eight customers with small baskets of items, or the regular lane, which has three customers with large carts of items. After students watch the video, they are asked to write a question they can solve using a model. The educator can guide students by saying, “After watching the video, what is the first question that comes to mind? Write down the main question you will answer about what you saw in the video. Make an initial conjecture that answers this main question. Explain how you arrived at your conjecture.” The Teacher’s Edition prompts the educator to ask students which variables they think affect how long it takes to get through the grocery store line and to rank them by importance. The second part of the lesson gives students the number of items each customer is purchasing in both lanes. The Student Edition asks students to “Develop a Model: Use the information you have learned about in this topic to refine your conjecture.” Then, students can create a model that represents the mathematical situation to determine which lane will take less time.

Additionally, in the Teacher’s Edition, lesson 3-1, “Understanding Relations and Functions,” educator guidance consistently directs students to create multiple representations, including mapping diagrams, tables, graphs, and sets of ordered pairs, to model relations and functions in both mathematical and real-world contexts. In “Step 1: Explore & Share,” students create organizational models that represent the relationship between rows and desks in a study hall. The educator’s guidance includes questions like “How can you organize your findings?” and prompts students to create a table listing different numbers of rows alongside the total number of desks. This work requires students to construct a representation before introducing the formal definition of a function. The “Process Standards Connection” section asks students to select and describe an additional representation, such as a bar graph, to display the same information. In “Step 2: Understand and Apply,” the first example directs students to create a mapping diagram to represent a shipping cost function, connecting inputs to outputs to evaluate whether the relation is a function. The educator is prompted to ask, “What other representations could you use to help determine whether a relation is a function?” and to require students to analyze and create alternative models. In example 5, students create a bar graph and a written inequality to model the reasonable domain and range values for real-world situations like a bowling game and a jogger’s distance. In “Step 3: Practice and Problem Solving,” item 28 prompts students to create a table that models the relationship between a train’s travel time and speed; item 31 asks students to create a table that represents bicycle rental costs for specific time intervals, then determine whether the relationship is a function.

Evaluation for 5.1c
Questions and tasks provide opportunities for students to apply conceptual understanding to new problem situations and contexts.

The grade A8 materials include questions and tasks that give students opportunities to apply conceptual understanding to new problem situations and contexts in the “Practice & Problem Solving” portion of lessons across topics. For example, in the Student Edition, lesson 5-2, “Radical Expressions,” students learn to rewrite radical expressions so that no perfect squares remain under the radicand through five guided examples and develop a conceptual understanding of how to simplify radical expressions. Next, students work through the “Practice & Problem Solving” part of the lesson, which moves from “Understand” problems that solidify conceptual understanding to “Practice” problems that refine their skills with that concept. Finally, “Apply” problems give students opportunities to apply conceptual understanding to new problem situations and contexts, such as real-world situations that require students to rewrite radical expressions to determine measurements in space, on a baseball diamond, and the dimensions of a television.

Additionally, in the Student Edition, lesson 2-2, “Slope and y-Intercept of a Line,” “Step 3: Practice & Problem Solving,” the “Apply” section asks students to analyze a real-world situation involving resting heart rate. Students are prompted to answer the question “Is the relationship proportional or non-proportional?” and “Write an equation to describe the relationship. Interpret the slope and y-intercept.” The lesson culminates in “Performance Task 26,” which lets students apply their understanding in a real-world context involving a roof, using this information: “The roof’s pitch is 8:12, meaning for every 12 inches of horizontal distance, the roof rises 8 inches” and “the vertical height of the roof is 9.”

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

The grade A8 materials provide tasks designed to build the student automaticity and fluency needed to complete grade-level tasks, such as the lessons in the “Skills and Review” section of the Resources tab in the “Savvas Realize” digital program. The Teacher’s Edition provides specific “Skills and Review” practice designed to build student automaticity and fluency, corresponding to each lesson’s concepts on the first page. For example, the Teacher’s Edition recommends using “Skills and Review: R03 Points on the Coordinate Plane” to reactivate prior knowledge for lesson 2-1, “Direct Variation,” which builds automaticity and fluency in locating points from given coordinates, plotting coordinates, and moving x units to the left or right and y units up or down in the coordinate plane, which students use throughout grade-level tasks in linear equations and functions.

Additionally, in the “Practice and Problem Solving” section of lesson 3-3, “Key Features of a Linear Function,” in the Teacher’s Edition, materials include a dedicated practice section that builds fluency with identifying and interpreting key features of linear functions across multiple problem types and contexts. The practice section builds automaticity through scaffolded sets of parallel problems, in which students find the slope of linear functions, then the x- and y-intercepts, and finally the zeros of each linear function. This practice targets a specific skill with increasing complexity in coefficients and constants, building fluency through focused repetition before students move to application.

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 grade A8 materials provide opportunities for students to practice the application of efficient, flexible, and accurate mathematical procedures within lesson 4-3, “Solving Systems of Equations by Elimination.” For example, in the Teacher’s Edition, “Step 2: Understand & Apply: Introduce the Essential Question” prompts the educator to explain to students that multiple ways exist to solve systems of equations, and the most efficient method may change depending on the equations in the system. Then, through examples, students can practice applying flexible and accurate mathematical procedures to identify the characteristics of the equations in a system and determine which method to use. These procedures include using the Properties of Equality to manipulate equations, adding equations, multiplying one equation by a constant, and interpreting what the variables in the equations represent in a real-world situation. Finally, students practice applying flexible mathematical procedures to accurately identify the characteristics of equations and determine the most efficient method for solving the system of equations through elimination.

Additionally, in the Student Edition, lesson 6-3, “Multiplying Special Cases,” “Step 1: Explore” and “Step 2: Understand & Apply” provide opportunities for students to practice the application of efficient, flexible, and accurate mathematical procedures for multiplying binomials and determining squares of binomials through pattern recognition, algebraic reasoning, and application of polynomial multiplication. The lesson supports efficient mathematical procedures by prompting students to identify and apply the general pattern (x+y)^2 = x^2 + 2xy + y^2, enabling them to compute binomial squares without repeatedly expanding each expression. The lesson supports flexible mathematical procedures by asking students to examine numerical examples, tables, algebraic expressions, and symbolic generalizations, and by connecting patterns discovered in the “Explore & Share” activity to formal algebraic procedures in example 1. Finally, the lesson supports accurate mathematical procedures through guided examples, “Try It!” problems, and prompts that require students to apply polynomial multiplication correctly, identify middle terms, and verify resulting expressions.

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 grade A8 materials provide opportunities for students to evaluate procedures, processes, and solutions for efficiency, flexibility, and accuracy within the “Math Modeling in 3 Acts” lessons in each topic of the Teacher’s Edition. For example, “Topic 7: Quadratic Functions” includes “Topic 3: Math Modeling in 3 Acts: The Long Shot,” which provides students with a 49-second video that depicts a person throwing a basketball from several distances. However, each throw is shown as a series of still images of the basketball that stop just after the ball reaches its highest point. After students watch the video, they are asked to write a question they can solve using a model. Students are guided by questions like, “After watching the video, what is the first question that comes to mind? Write down the main question you will answer about what you saw in the video. Make an initial conjecture that answers this main question. Explain how you arrived at your conjecture.” In the second part of the lesson, students use a digital tool to adjust the width, maximum height, and intercepts of the parabola formed by the ball’s trajectory for each throw, helping them determine which throws will make it into the basket. The Teacher’s Edition prompts the educator to let students discuss and update their conjectures before revealing the solution in the next part of the lesson. Then, the educator reveals the solution, and students compare and evaluate their procedures, processes, and solutions for efficiency, flexibility, and accuracy, including possible errors, in a whole-class “post-game” analysis.

Additionally, in the Student Edition, lesson 3-1, “Understanding Relations and Functions,” students evaluate strategies, representations, and solutions. In “Step 1: Explore & Share,” the “Process Standards Connection” section asks students to evaluate which representation (a table, a bar graph, or an equation) best displays the relationship between rows and student desks and to explain the advantages of each. Students can evaluate how accurate a line graph is for showing their results. In “Step 2: Understand & Apply,” the “Process Standards Connection” section in Examples 3 and 4 asks students to evaluate the efficiency of using mapping diagrams versus graphs for analyzing functions. In example 6, students evaluate whether a continuous or discrete domain is the more accurate procedure for a given real-world situation. In “Topic 3: Linear Functions,” lesson 3-7, “Analyzing Lines of Fit” asks students to evaluate the efficiency, flexibility, and accuracy of procedures and models for fitting and interpreting linear data. In “Step 1: Explore & Share,” students compare two linear functions graphed on the same scatter plot and evaluate which best fits the given data.

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

The grade A8 materials include embedded supports to guide educators as they lead students toward increasingly efficient approaches in “Step 1: Explore & Share” and “Step 2: Visual Learning” of the “Let’s Build” lessons. For example, in the Teacher’s Edition, lesson 3-6, “Scatter Plots and Lines of Fit,” “Step 1: Explore & Share” prompts the educator to help students use scatter plots by comparing the screen size and price of different televisions. Students discuss the relationship between a table and a graph comparing the size and cost of various televisions before moving to “Step 2: Understand & Apply.” Then, students can use six examples to show increasingly efficient approaches in constructing, understanding, analyzing, interpreting, and evaluating scatter plots. The embedded supports in the “Process Standards Connection” section prompt the educator to ask, “What features of two datasets can help you determine whether the datasets have a negative, a positive, or no association?” This work helps students efficiently determine the association of datasets. Next, students use the examples to write, interpret, and make predictions of a line of fit in a scatter plot. Before students move on to individual practice, the “Concept Summary” section prompts the educator to ask, “How can you tell what type of association two datasets have?” and guide students toward the most efficient approach to create the line of fit in a scatter plot.

Additionally, in the Teacher’s Edition, lesson 2-1, “Direct Variation,” “Step 2: Understand & Apply” provides embedded questioning to help students connect representations and apply direct variation. Educators are prompted to ask, “How can you use the table to solve this problem?” In example 2, students must determine whether two real-world situations, including a company making blankets and a pool toy that moves from the water’s surface to the pool’s bottom, represent a direct variation. Embedded supporting questions for educators include, “How do you know from the problem description...that you can model the total cost using the equation y = 3x?” and “How can you use the information in part B to write a model for the situation?” Finally, in example 4, supporting questions in the “Elicit and Use Evidence of Student Thinking” section guide students toward increasingly efficient approaches. These questions include “Which variable is replaced by k in the equation?” and “Why is it useful to first find the constant of proportionality?”

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

The grade A8 materials explicitly state how the conceptual and procedural emphasis of the TEKS are addressed in the Math Background pages at the beginning of each topic in the Teacher’s Edition. For example, the Math Background: Balance page in “Topic 3: Linear Functions” explicitly states the conceptual emphasis in the “Conceptual Understanding” section titled “Linear Functions.” The book says, “Students understand that a function is a relationship between sets of values in which each element of the domain (x-value) is assigned to exactly one element in the range (y-value). (8AM.2A).” In the “Procedural Skill” section, “Function Notation” explicitly states, “Students use their ability to write and solve linear equations when writing rules of linear functions in function notation. (8AM.2C).”

Additionally, in the Teacher’s Edition, lesson 3-2, “Understanding Linear Functions,” the “Essential Understanding” section establishes the conceptual foundation as, “Linear functions can be represented in multiple ways, using words, tables, graphs, and rules. Function notation is a way to write the rule for a function.” The “Balance” section highlights that this lesson incorporates a blend of procedural skill, fluency, and application and specifies, “Students write the rule of a linear function using function notation and evaluate functions in function notation,” while also applying conceptual understanding by “relating the domain of a function to the quantitative relationship that it describes” in context. The TEKS section reinforces this with TEKS 8AM.3F, which targets procedural fluency for graphing linear functions and identifying key features, including x-intercept, y-intercept, zeros, and slope, in mathematical and real-world problems, centered on the conceptual understanding of multiple representations of linear functions.

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.

The Advanced Grade 8 Program Overview describes the progression of concrete to pictorial (representational) to abstract in an article titled “Concrete, Representational, Abstract (CRA) Instructional Model.” It details, “During the Explore & Share [section] in each lesson, students solve a problem that embeds new ideas any way they choose. Students might use concrete materials (counters, geoboards, anglegs, algebra tiles) [or] pictorial representations (number lines, arrays, grids, strip diagrams). Students interact with the ‘Desmos’ [digital] program to access concrete models and manipulatives, as well as pictorial representations. They move through the examples within lessons to use concrete models and manipulatives, pictorial representations, and abstract representations, as required by the TEKS.”

Additionally, the Student Edition includes lesson 8-4, “Completing the Square,” which uses algebra tiles as concrete models and manipulatives in Example 1 to model the quadratic expression, rearrange tiles to form a square, determine the missing area needed to complete the square, and connect the model to the algebraic procedure for solving quadratic equations. The lesson includes pictorial representations like diagrams of algebra-tile arrangements, area models, geometric square models, and coordinate graphs of quadratic functions. Examples 1 to 5 also include visual representations that students can analyze to understand completing the square, identifying vertex form, and interpreting quadratic functions. Finally, the lesson includes abstract representations like symbolic quadratic equations, algebraic expressions, formulas, and vertex-form equations that let students solve equations in the form of x^2 + bx + c = 0, rewrite quadratic functions in vertex form, determine solutions, and justify algebraic procedures using symbolic notation.

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 Advanced Grade 8 Program Overview describes the progression of concrete to pictorial (representational) to abstract in an article titled “Concrete, Representational, Abstract (CRA) Instructional Model.” It details, “During the Explore & Share [section] in each lesson, students solve a problem that embeds new ideas any way they choose. Students might use concrete materials (counters, geoboards, anglegs, algebra tiles) [or] pictorial representations (number lines, arrays, grids, strip diagrams).... When students share and discuss solutions, rich conversations deepen conceptual understanding of connections between concrete, pictorial, and abstract.” The article explains in the “Visual Learning” section that “Lesson Examples provide explicit instruction that connects students’ work in the Explore and Share [section] to new ideas taught and shows pictures of concrete materials, drawings of concrete materials, diagrams, or some combination of those to represent math concepts. Example instruction connects these representations to abstract numbers, symbols, and procedures.” Students receive access to digital manipulatives through the Savvas Realize digital program embedded in the materials. These manipulatives serve as concrete models that students can connect to abstract concepts. The Brainingcamp Live feature allows educators to view each student’s work with the digital manipulatives in real time. Furthermore, the Desmos digital program offers representational models that students can create to connect to abstract concepts. In each lesson, the progression from “Explore & Share” to “Understand & Apply” supports students as they connect andconcrete and representational models to tract concepts. Then, in the final guided examples, students discuss how to define and explain the abstract concepts they connected to the concrete and representational models.

Additionally, in lesson 6-2, “Multiplying Polynomials,” the materials support students as they connect concrete and representational models to abstract polynomial multiplication across multiple examples. In “Step 1: Explore & Share,” students use the area formula for a rectangle as a concrete organizational model, find the area of each rectangular section in a painting, and add them together. In the Teacher’s Edition, the “After: Facilitate Meaningful Mathematical Discourse” section prompts educators to ask students how they can use the area formula for a rectangle to create concrete models of area when side lengths are represented by variable expressions. This work connects the concrete and representational area model to the abstract process of multiplying polynomials. In “Step 2, Understand & Apply,” example 2 uses a color-coded table and area diagram to help students connect the visual representation of rectangular sections to the abstract symbolic process of multiplying binomials using the distributive property. The educator is prompted to ask students how the table model is related to the area model and the distributive property. The “Process Standards Connection” section for examples 1 to 3 asks students to evaluate whether an area model can represent products with subtracted terms. This work requires students to explain concrete and representational models and justify why they need to connect to the abstract algebraic approach.

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

The grade A8 materials provide opportunities for students to develop academic mathematical language using visuals, manipulatives, and other language development strategies within lessons, like in the “Language Routine: Compare and Connect” section in lesson 5-6, “Translations of Exponential Functions,” in the Teacher’s Edition. For example, students can use visuals and digital manipulatives, including tables and graphs, to discuss with a partner how to compare the functions that result in vertical and horizontal translations. The Teacher’s Edition guides the educator to “Help students develop precise communication as they discuss the Process Standards Connection question.” Then, the educator is prompted to “Invite student pairs to analyze and compare their solutions in the Try It! and with the Example. Provide these prompts to encourage precise math language in their responses: How are the equations related? How do they differ? What will be your visual clue for whether the translation is horizontal or vertical?”

Additionally, the Teacher’s Edition Vocabulary Game in “Topic 1: Solving Equations and Inequalities” gives students opportunities to develop academic mathematical language. This game presents mathematical vocabulary in an interactive visual format that helps students connect terms to mathematical concepts. The “Hands-on Game: Stack Tactics” in topic 1 is an interactive digital activity that lets students use on-screen manipulatives to reinforce mathematical concepts and vocabulary. Students can develop academic mathematical language using other language development strategies through multiple vocabulary-rich learning experiences, including activities like the “Vocabulary Game,” “Amazing Contributions: Al-Khwarizmi,” “Pick a Project,” and “STEAMQuest: Get in the Zone,” which engage students in using and applying mathematical vocabulary in varied instructional contexts.

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

The grade A8 materials include embedded educator guidance, such as “Co-Craft Questions,” to scaffold and support students’ development and use of academic mathematical vocabulary in context. These activities appear in the “Language Routines” section embedded within examples of certain lessons throughout the materials. For example, in the Teacher’s Edition, the “Language Routines: Co-Craft Questions and Problems” section contains embedded educator guidance in lesson 5-1, “Rational Exponents and Properties of Exponents.” This guidance directs educators to “Help students develop precise communication as they discuss the Process Standards Connection question. Invite students to read through Part B of the example, then work in pairs to create a similar problem. Provide these prompts to encourage student creativity. Q: What key information will you need to write the first exponential expression? Q: What strategies can you apply to find another expression that is equivalent? Q: How can you combine your expressions to write a similar problem?”

Additionally, in the Teacher’s Edition, lesson 2-2, “Slope and y-Intercept of a Line,” the “Language Routine: Three Reads” section provides embedded guidance. This guidance directs educators to “Pair students with a partner and have the students read the problem three times. During the first read, have students focus on what the problem is about. During the second read, have students identify key numbers that they need to solve the problem. During the last read, ask students to think about how they would solve the problem. After each read, have the partners discuss with each other what they learned from the reading.” The routine also gives educators prompts that students can respond to, like “What is the problem trying to solve?,” “What numbers are important for solving the problem?,” and “What strategy will you use to solve the problem?” These questions give students structured opportunities to use academic mathematical vocabulary while discussing slope, unit rate, and proportional relationships.

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 grade A8 materials include embedded educator guidance within “Language Routine: Stronger and Clearer Each Time” sections in lessons that support the application of appropriate mathematical vocabulary, syntax, and discourse that support mathematical conversations and provide opportunities for students to hear, refine, and use math language with peers and develop their math language toolkit over time. “Concept Summary” sections help educators support student responses using exemplar responses to questions and tasks. For example, in the Teacher’s Edition, lesson 1-1, “Solving Linear Equations” includes a “Language Routine: Stronger and Clearer Each Time” section with guidance that educators can use after reading example 5. The educator is prompted to “present to students the prompt and graphic. Individually, have students complete step 1. With a partner, have students share their equations, providing opportunities for students to ask clarifying questions. Lastly, have students independently revise their work if necessary.” This guidance supports student discourse using appropriate academic vocabulary and syntax and gives students opportunities to hear, refine, and use math language with peers. Students also can develop their math language toolkit over time. The “Concept Summary” section includes questions for educators to ask, such as “How can you use equations to help you solve problems?” This question has an example response: “You write equations to represent a real-world situation and then use the properties of equality to solve the equation.” In the “Talk About Math Ideas” section within the “Concept Summary,” the guidance prompts educators to “Listen for students to talk about identifying one variable and arriving at an expression for that variable. The expression can be a number for a solution to a linear equation, while the expression for the literal equations will be a variable expression.” Then, the educator is prompted to ask, “How would you solve the Explore & Share problem with linear equations?” The example response for this question is, “I can solve the equation 15x + 25 = 50.”

Additionally, in the Teacher’s Edition, lesson 3-1, “Understanding Relations and Functions” guides educators to use the Math Talk activity titled “Which One Doesn’t Belong?” before instruction begins. Educators are directed to “look for students who recognize that three of the relations follow a pattern, where every x has a unique y, and the bottom right table is the outlier because –3 has two different y values.” This work builds vocabulary terms like domain, range, continuous, and discrete as students justify which relation does not belong. The “Skills and Review Practice” section includes “R03: Points of the Coordinate Plane,” which supports appropriate syntax through fill-in-the-blank sentences about coordinate locations and the coordinate plane. The “Language Routine: Compare and Connect” section prompts educators to pair students so they can analyze and compare their solutions for the “Try It!” problem and example 5. The educator guidance notes that this helps “students develop precise communication” and provides prompts like “How are the domain and range values similar and different for each situation?” and “How do your responses differ from someone else’s?” This work gives students structured opportunities to hear a partner’s reasoning, refine their own explanation, and practice using precise mathematical language in peer discourse. The materials also embed exemplar responses that model the depth and precision expected of students. In example 1, the sample response to “Communicate Math Ideas” reads, “This relation is a function because each input value is assigned exactly one output value.” In example 5, the sample response to “Connect Math Ideas” explains, “The parameters of each situation regulate the domain of the function that describes it,” guiding educators in coaching students toward complete and precise mathematical explanations.

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

The grade A8 materials appropriately integrate the TEKS process standards, as discussed in the “Mathematical Process Standards” section in the Front Matter of the Teacher’s Edition. For example, this article explains how the TEKS process standards are integrated into the materials through instruction, problems, and assessments in six sections with specific information. The guidance notes that “All math tasks evoke the selection, use, and management of multiple math processes” and explains that some problems have specific math processes highlighted in red that “lend themselves to a discussion of a specific Math Process.” The guidance also notes that “Items that assess content can also engage students in using math processes. The Topic Performance Task is an especially good opportunity to assess students’ proficiency with Math Processes.”

Additionally, the Teacher’s Edition explicitly identifies where the Mathematical Process Standards are incorporated within lesson instruction, guided and independent practice, problem-solving activities, and assessments. For example, the first page of lesson 8-6, “Solving Systems of Linear and Quadratic Equations,” identifies the TEKS Mathematical Process Standards that are addressed, including 8AM.1E and 8AM.1F. These standards emphasize creating and using representations to communicate mathematical ideas and analyzing mathematical relationships to connect mathematical ideas. The lesson also includes a “Process Standards Connection” section that lets students communicate their reasoning by explaining why a solution to a linear-quadratic system of equations might not be included in a problem’s solution. The materials support educators as they intentionally integrate the process standards throughout daily instruction, ensuring that students consistently engage in mathematical reasoning, problem-solving, communication, representation, and analysis while developing grade-level mathematical content knowledge.

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

The grade A8 materials include a description of how the TEKS process standards are incorporated and connected throughout the course, as discussed in the “Mathematical Process Standards” section in the Front Matter of the Teacher’s Edition. For example, this article explains how the TEKS process standards are incorporated throughout the course in instruction, problems, and assessments in six sections with specific information. The guidance notes that “A Mathematical Process Standards page at the beginning of every topic provides suggestions for giving special emphasis on two Process Standards in the topic” and “Core Instruction Driven by a Marriage of Content and Math Processes: Math Processes are infused and explicitly highlighted in lesson instruction. Look for boxes with ‘read’ heads throughout the lesson that model the thinking that these processes embody.”

Additionally, in the Teacher’s Edition, an article titled “A Program Paced for Success” explicitly states that “TEKS Mathematical Process Standards are integrated throughout every Topic: 8AM.1A, 8AM.1B, 8AM.1C, 8AM.1D, 8AM.1E, 8AM.1F, [and] 8AM.1G.” The pacing guide identifies these process standards across all eight topics, lists the TEKS addressed within each topic, and recommends the required number of instructional days. The guide demonstrates that the mathematical process standards are intentionally connected and integrated throughout the grade 8 course rather than taught as isolated skills. The Topic Content pages in the Front Matter of the Teacher’s Edition corroborate this by listing, in bold, the process standards for each lesson across the topics.

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

The grade A8 materials include a description for each unit about how the TEKS process standards are incorporated and connected throughout each topic on the Mathematical Process Standards page at the beginning of the topic in the Teacher’s Edition. For example, “Topic 1: Solving Equations and Inequalities” uses a “Mathematical Process Standards” page to describe how 8AM.1E is incorporated and connected throughout the topic. The guidance notes that “Mathematically proficient students use equations, inequalities, tables, number lines, and diagrams and understand the limitations of each, check their solutions by substituting the value into the original equation or inequality to see if the appropriate tool was used and the solution holds true, and choose to use tools, such as algebra tiles, to help them when writing and solving equations and determining the number of solutions an equation has.” The page details that 8AM.1C is incorporated and connected throughout the topic because “Mathematically proficient students identify important quantities and look at relationships in real-world situations in order to write expressions and to determine when two expressions can be set equal to each other, determine whether an equation or inequality best represents a given situation, and reflect on whether the results of an equation or inequality make sense within the situation and revise the model if necessary.”

Additionally, the beginning of each topic in the Teacher’s Edition includes a section titled “Mathematical Process Standards,” which identifies particular TEKS process standards that will be covered. For example, “Topic 7: Quadratic Functions” highlights standards 8AM.1E and 8AM.1F throughout its lessons. Standard 8AM.1E is embedded as students create and use representations to organize, record, and communicate mathematical ideas, using quadratic functions to model the trajectory of projectiles, writing a quadratic function to represent vertical motion problems, choosing an appropriate form of an equation to suit a particular purpose, and using trends in data to decide the best type of equation to represent the data through regression. Standard 8AM.1F is developed as students analyze mathematical relationships to connect and communicate ideas, seeing the standard form of a quadratic function as composed of the values of a, b, and c that determine the intercepts, axis of symmetry, and vertex of the parabola, analyzing the effect of changes to h and k in vertex form on the graph, applying what they have learned about the structure of linear and absolute value functions to the structure of quadratic functions, and relating the vertical motion model to the standard form of a quadratic equation.

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

The grade A8 materials include an overview of the TEKS process standards incorporated into each lesson of the Teacher’s Edition in the Item Analysis answer key in the “Practice & Problem Solving” section. For example, in lesson 4-3, “Solving Systems of Equations by Elimination,” the Item Analysis answer key provides an overview showing that 8AM.1BG is integrated into Examples 1 and 4 and Items 14 and 32; 8AM.1F is integrated into Examples 2 and 4 and Items 10 and 11; and Example 3 incorporates TEKS process standards 8AM.1A and 1C, which are also integrated in Items 34 and 12, respectively.

Additionally, the first page of each lesson in the Teacher’s Edition lists the TEKS content standards and the “Mathematical Process Standards” addressed in the lesson. For example, lesson 7-3, “Quadratic Functions in Standard Form,” identifies that Mathematical Process Standard 8.1E (create and use representations to organize, record, and communicate mathematical ideas) is incorporated throughout the lesson, supporting students in acquiring and demonstrating mathematical understanding as they engage with the lesson content and enabling educators to easily identify the TEKS mathematical process standards incorporated in the lesson.

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

The grade A8 materials give students opportunities to think mathematically, persevere through problem-solving, and make sense of mathematics in lessons such as lesson 5-4, “Exponential Growth and Decay,” in the Teacher’s Edition. For example, in “Step 1: Explore & Share,” students think mathematically by using a chart that shows a vehicle’s value when it is purchased and each year thereafter, illustrating how the car’s value decreases over time. Students persevere through problem-solving to determine which type of function could explain the pattern and make sense of mathematics in a small-group setting before discussing as a whole class what growth and decay would mean in terms of an exponential function.

Additionally, each topic in the Teacher’s Edition includes a “Build G.R.I.T.” section that gives educators concrete talking points for cultivating a growth mindset, resilience, self-efficacy, and time management as students work through multi-step, real-world math tasks. In “Topic 4: Systems of Linear Equations and Inequalities,” the “Build G.R.I.T.” section provides opportunities for students to think mathematically about systems of linear equations and inequalities and to understand why mistakes led to incorrect solutions, so they can make sense of mathematics. It offers ways for educators to support students as they build confidence, like helping them stay open-minded to their classmates’ different approaches during the “Math Modeling” lesson, building resilience to persevere through solving problems by encouraging students to verify their graphed solutions rather than assuming the intersection point is exact, and developing self-efficacy by reminding students that they can try multiple methods if one approach is unsuccessful.

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 grade A8 materials include the Advanced Grade 8 Program Overview, which provides an article titled “Productive Struggle” and a section titled “Productive Struggle in Lessons” that detail how students can use the “Explore and Share” task in each lesson to “complete the task any way they choose.” These materials help students understand that there are multiple ways to represent and solve problems and complete tasks. They prompt educators to select solutions for students to present and note that “teachers use sample student work from the class or from the Teacher’s Edition to orchestrate an in-depth class discussion that connects different student-created methods and representations to the new ideas.” This guidance supports students in explaining and justifying multiple ways they can represent and solve problems and complete tasks.

Additionally, in lesson 8-4, “Completing the Square,” the Math Talk routine begins the lesson to help students compare different methods for solving quadratic equations. Each Math Talk routine begins as a whole-class activity, and students are frequently asked to elaborate on their solutions with peers or in small groups. These discussions illustrate that there are multiple ways to represent and solve problems. In the Teacher’s Edition, “Step 1: Explore” supports students in understanding that there can be multiple ways to represent and solve problems and complete tasks during a small-group lesson by asking, “What method of solving the quadratic equation is Enrique using?” Students are given time and the opportunity to collaborate to determine that factoring is the most appropriate method for Enrique’s solution. Educators then extend students’ thinking by asking, “What method of solving the quadratic equation is Nadine using?” Students can identify a different solution method—extracting roots—and compare the two approaches. These discussions allow students to explain and justify their reasoning while recognizing that quadratic equations can be solved using multiple valid methods.

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 grade A8 materials include a Math Talk section in every lesson that gives students multiple opportunities to make sense of mathematics and discuss it with peers and educators. For example, in the Teacher’s Edition, lesson 7-1, “Key Features of a Quadratic Function” includes a “Math Talk: Every Picture Tells a Story” activity that shows a graph of a parabola and asks students to “Describe a scenario that matches the graph.” This work requires students to make sense of mathematics and discuss what core shapes are part of each figure in a small group of peers and with the educator. Examples 2 and 3 model how the shape of a parabola changes depending on the leading coefficient of x, giving students the opportunity to do and write about math with their peers and their educator.

Additionally, in lesson 8-1, “Solving Quadratic Equations Using Graphs and Tables,” students do math with their peers and their educator during the “Explore & Share” activity, examining the path of a golf ball and relating its height and distance to the graph of a quadratic function. Then, students use graphing calculators and tables to solve equations in examples 1 through 3. Students write about math with their peers and their educator in “Explore & Share” in response to a prompt analyzing how the ball’s height and distance are related, and complete “Try It!” problems that ask them to justify their reasoning. Students discuss math with their peers through the small-group “Support Productive Struggle” segment of “Explore & Share” and through the “Talk About Math Ideas” discussions that compare the two solution methods. Students discuss math with their educator, as the Teacher’s Edition provides prompts in the “Pose Purposeful Questions” section for the whole class during “Step 2: Understand & Apply.” This section includes questions like “How does the number of real solutions of the quadratic equation relate to the graph?” to guide a whole-class discussion after “Explore & Share,” connecting the ball’s path to key features of a parabola.

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 grade A8 materials include a Problem-Solving Model in the Savvas Realize digital program that uses guiding questions and a graphic organizer to help educators guide students to share and reflect on their problem-solving approaches. For example, reflection questions include “What operations are needed?” and “Does my solution answer the question?” These questions are broken into categories—such as “Analyze Given Information,” “Determine a Solution,” and “Justify the Solution and Evaluate Its Reasonableness”—to support explanations, arguments, and justifications. The “Problem-Solving Model Recording Sheet” tool gives students space to share their problem-solving approaches. The recording sheet includes sections that correspond to the guiding questions on the previous page plus a box in which to write the problem, an “Analyze Given Information” section divided into “Need to Find” and “Given,” and spaces to share students’ explanations and arguments in the “Formulate a Plan” section. The latter section provides sample ways to represent problems and math tools to use to “Determine a Solution.” The “Justify the Solution and Evaluate Its Reasonableness” and “Evaluate the Process” sections allow students to share their justifications.

Additionally, in lesson 8-1, “Solving Quadratic Equations Using Graphs and Tables,” students examine a golf ball’s path during the “Explore & Share” activity. The Teacher’s Edition prompts a discussion with questions like “How does the path of the ball relate to key features of a parabola?” and “How could the shape of the parabola that models the path of the ball change?” to assist students in explaining the connection between the graph and the real-world context. In the “Understand & Apply” section, a “Language Routine: Compare and Connect” activity asks students to pair up. Each partner is assigned a different method, graphing versus tables from examples 1 and 2, so they can argue what is similar and what is different about the two methods. Guiding prompts like “Will the two methods produce the same answers?” and “What are the advantages and disadvantages of each approach?” are provided. Students can also justify their reasoning in the “Analyze Math Relationships” prompts, such as explaining when it is easier to solve a quadratic equation by graphing versus using a table. In example 3, students justify how the graph of an absolute-value function relates to the graph of a quadratic function.

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

The grade 8 materials include a “Pose Purposeful Questions” section and a “Common Error” section for some of the examples. The materials also include “Try It!” practice problems in “Step 2: Understand & Apply” in every lesson, supporting educators with prompts and guidance for providing explanatory feedback based on student responses and anticipated misconceptions. For example, in lesson 6-5, “Factoring x^2 + bx + c,” the Teacher’s Edition provides prompts for Example 3: “Factor x^2 + bx + c, when c < 0.” These prompts include “Why do the factors have opposite signs? [because c is negative]” and “Why are 1 and -6 not the correct factor pair of x^2 + 5x – 6? [Although 1 and –6 is a factor pair of -6, it is not a sum of 5 since 1 + (–6) = –5.]” The “Common Error” box that accompanies the “Try It!” section for example 3: “Factor x^2 + bx + c, when c < 0” notes, “Since b and c are negative, some students may think the factors of the trinomial are both negative. The factors actually have opposite signs. Instead of students trying to memorize which sign the factors have, encourage the students to ask which factor pairs have a product of c and a sum of b.”

Additionally, in the Teacher’s Edition, lesson 1-1, “Solving Linear Equations,” the “Support Productive Struggle in Learning Mathematics” section of “Step 2: Understand & Apply” provides educators with questions and sample responses to monitor students’ understanding. These questions include “When writing an equation to represent a real-world problem situation, how do you determine what the variable will represent?” and “How are the properties of equality useful when solving the equation?” The materials also include a section titled “Elicit and Use Evidence of Student Thinking,” which asks, “Before solving, would you expect the price per ticket to be close to the price per ticket in the example?” The sample response is “Yes; the total cost is a little more than 2 times higher, but it is divided by twice the number of tickets.” The “Common Error” box anticipates a misconception by explaining that “Students may write the equation as 8t – 5 because they don’t understand how to translate $5 off each ticket algebraically.” The materials guide educators to provide explanatory feedback by reminding students to “put parentheses to show that the $5 is subtracted from each ticket.”