HMH Into Math Texas, Grade 8

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

The materials include yearlong scope and sequence documents within the Program Overview and the Implementation Guide that clearly outline the Texas Essential Knowledge and Skills (TEKS), the English Language Proficiency Standards (ELPS), and concepts taught throughout the course.

The scope and sequence charts identify the concepts taught throughout the instructional year and align each module and lesson to the TEKS and ELPS. The “Discover” tab under the program dropdown in the scope and sequence supports instructional planning and pacing by outlining the course TEKS, ELPS, and lesson concepts. The “Correlations by Lesson” documents also provide information about TEKS and ELPS alignment.

Evaluation for 1.1b
Materials include suggested pacing (pacing guide/calendar) to support effective implementation for various instructional calendars (e.g., varying numbers of instructional days - 165, 180, 210).

The materials provide a “Scope and Sequence with Yearly Pacing” for 165-day and 210-day instructional calendars. The guidance provided in the calendar “moves step by step through each module and shows how each module covers the instructional sequence and standards, and then lists each Module Review and Module Test.” These options support effective implementation while remaining aligned with the TEKS, ELPS, and course concepts.

The materials provide guidance on extending the 165-day pacing calendar to 180 days by adding “one extra day to each lesson where a Readiness Standard is first taught.” Educators can use the extra day to provide targeted reinforcement, practice, or challenges based on formative assessments, “Quick Checks,” and observations.

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 Teacher’s Guide provides a rationale for the module order and explains how concepts progress across modules. For example, the guide shows how students will apply knowledge of real numbers to dilations and similarity, progress from proportional and non-proportional relationships to functions, and transition from equations to systems of equations.

The materials show educators how mathematical concepts connect throughout the course. This helps educators internalize these concepts and then assist students in making connections. For example, “Students develop conceptual knowledge of real numbers in module 1 before using them in module 2 when exploring dilations and similarity.”

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

The program materials include comprehensive planning supports, structured instructional routines, and embedded guidance to support educators with unit and lesson internalization. The Teacher’s Guide planning support reviews the standards, outlines what students will learn in each module, explains the module flow, identifies the TEKS and ELPS, and includes background information to support instructional preparation and lesson internalization.

The materials also include resources that help educators understand the sequence of learning within each module and prepare for daily instruction. The “Before You Teach” sections outline the mathematical understanding needed for each lesson and explain what students will learn. Planning tools such as the “Editable Lesson Plan,” pacing guidance, module flow charts, and lesson sequencing explanations also support educator preparation.

Additionally, the “Step Through a Module” section of the Implementation Guide provides guidance for internalizing module and lesson components. The “Teacher Background” sections include mathematical rationale, examples, summaries, and explanations of the importance of concepts to deepen educator understanding before instruction. “Internalization Tools” use guiding questions to support both lesson and unit internalization. Examples include “What do the lesson and language objectives expect from students?” and “What concepts, strategies, or procedures will students learn?” Educators can use the tools to internalize lessons and units, either individually or in a group.

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

The Professional Learning and Coaching Guide includes instructional support, implementation guidance, pacing recommendations, and professional learning resources to assist leaders in supporting effective program use.

The materials also include tools that support classroom observations, reflection, and coaching conversations. For example, the Look-Fors and Reflection Guide provides classroom observation indicators, implementation expectations, reflection questions, and suggested discussion topics to help instructional leaders monitor instruction and support educator planning.

Additionally, the materials include look-for checklists designed for the first 30 days of instruction, along with reflection tools and guiding questions to support classroom visits, targeted feedback, and ongoing instructional implementation conversations with educators.

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 Guide includes a “What should I understand about the math in this module?” section that provides a comprehensive overview and background knowledge for each TEKS standard covered within the module. For example, this section in module 4 states, “Representing proportional relationships and identifying the constant of proportionality from the table, graph, and equation prepares students to represent other linear relationships.”

The materials include academic vocabulary support within lesson and module planning materials, including a vocabulary list embedded in lesson overviews, mathematical language supports, and ELPS-aligned language development guidance to support effective instruction of unit concepts.

The materials also provide an educator’s glossary to help educators understand and teach the mathematical concepts. The glossary includes not only definitions but also pictorial examples when appropriate.

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.

Each module includes family resources in English and Spanish, delivered through a “Family Letter” that explains module objectives, academic vocabulary, and online supports aligned to each lesson. The letters help foster family involvement in supporting students’ progress outside the classroom.

Each “Family Letter” also includes a home activity families can complete together to further reinforce learning. For example, module 6 suggests families roll a rectangular sheet of paper to create a cylinder and work together to estimate its radius and volume.

Evaluation for 1.3a
Materials include comprehensive, structured, detailed lesson plans that include daily objectives, questions, tasks, materials, and instructional assessments required to meet the content and language standards of the lesson (aligned with the TEKS and the ELPS).

The lesson plans and overviews in the Teacher’s Guide clearly define lesson objectives and correlations to the TEKS and ELPS. For example, in module 9, lesson 1 aligns with TEKS 8.9.A, and it has students “solve a system of two linear equations by graphing” through a series of three tasks.

Each lesson plan includes tasks, assessments, and practice sets aligned with the learning and language objectives, which directly correlate to the TEKS and the ELPS. The materials include instructional assessments and tools such as “Spark Your Learning,” task routines, “Quick Check,” and “Differentiation and Practice” sections.

Evaluation for 1.3b
Materials include a lesson overview listing the teacher and student materials necessary to effectively deliver the lesson, and the suggested timing for each lesson component.

The Teacher’s Guide includes detailed lesson plans that outline the manipulatives and materials for each lesson. For example, the “Spark Your Learning” activity in module 7, lesson 7 requires a ruler per student and a Safe-T compass and tape measure per group. During this activity, students use these materials to determine whether a label will wrap a cylindrical metal bottle.

In addition, the Teacher’s Guide includes guidance and recommendations for the timing of each lesson component. The “What does this look like in my classroom?” section illustrates how to structure the lesson over two 45-minute sessions. Each component of the lesson also includes a suggested timing. For example, module 9, lesson 3, task 2 should take approximately 15 minutes.

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

The materials include guidance on using lesson materials in “Differentiation and Practice,” “Homework,” “Extension,” “Collaborative Groups,” and “Teacher-Led Small-Group Activities” sections for extended practice. Educators can use student performance data to assign additional practice, enrichment, intervention, and adaptive learning opportunities.

The Teacher’s Guide includes guidance on effectively using “Almost There,” “On Track,” and “Ready for More” differentiation and practice activities. Educators may assign one of these three activities based on student assessment performance. Students work through one to three rotations per lesson, focusing on independent practice, collaborative groups, and educator-led small-group activities.

Additionally, the materials support using the lesson materials effectively through ongoing, leveled practice on Waggle, an adaptive digital learning platform. “HMH Waggle supports instruction with auto-assigned, skill-based practice tailored by its AI engine.” When educators actively use the guidance report, they learn how to use student data to meet the needs of all learners.

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.

Each module includes a variety of formative assessments, including “Quick Checks” and “Are You Ready?” tasks, “Mid-Module Checks,” and Module Reviews. These assessments include multiple item types such as procedural fluency, reasoning, application, modeling, and open-response tasks.

Each module provides a variety of summative assessments to determine “whether students have mastered skills taught in each module.” The assessments include a Module Test available in digital and printable options. The Module Test offers a variety of item types; for example, the module 8 test includes numerical response, multiple-choice, and matching item types. In addition, students complete a Module Project that requires them to “apply and extend the mathematics found within the modules.”

The materials use “Benchmark Assessments” and other diagnostic assessments to “determine progress at strategic points in the school year.” The materials include three “Benchmark Assessments.” Each includes questions in various formats, such as drag-and-drop, graphing, multiple-select, and multiple-choice. This type of assessment helps gauge mastery of the skills taught during the year.

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

The Implementation Guide gives educators a clear understanding of the purpose and types of instructional assessments that support data-driven instructional decisions throughout the year. The materials define each type of assessment, assign a specific use, and allocate a time limit.

The Program Assessments at a Glance chart explains how each assessment can help determine student readiness, monitor progress, inform instruction, and measure mastery. For example, the “Quick Check” provides educators with “data that helps them identify students who need support, are ready to practice the relevant skill, or could benefit from a challenge.”

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

The Implementation Guide provides guidance to ensure consistent, accurate administration across all assessment types by outlining what the assessment measures, why it is important, and how to administer it. For example, the Module Test measures “how well your students have understood the TEKS and Process Standards covered in the module.”

The materials include guidance on consistently administering assessments to ensure that all students receive the same test instructions. For example, guidance for the Module Project states, “students can work on the project after whole-group instruction, or you can devote a specific instructional day to completing the project.” At the same time, the included rubrics ensure that outcomes accurately reflect student learning.

The materials also include suggested timing for each assessment to help maintain consistent administration across classrooms. For example, the “Quick Checks” should be used daily, with a suggested duration of five to ten minutes.

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

Formative assessments in the course include “Quick Check,” “Practice on Your Own,” and “Are You Ready?” tasks. These assessments align with the lesson TEKS and the daily learning objectives identified within the lesson-planning materials. For example, the “Practice on Your Own” answer key identifies the TEKS alignment and the related task for each question.

Summative assessments such as the Module Test include answer keys that identify the TEKS alignment and lesson source for each question. For example, module 6, question 9 requires students to relate a cylinder’s volume to a cone’s volume of the same radius and height, which aligns with TEKS 8.6.B and lesson 3, “Relate the Volume Formulas for a Cylinder and a Cone.”

Diagnostic assessments such as the “Benchmark Assessments” include answer keys with a TEKS correlation table that identifies the TEKS alignment and the related lesson for each question.

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

The materials include TEKS-aligned formative and summative assessment tasks of varying complexity, including procedural tasks, open-response questions, mathematical modeling tasks, multistep application problems, and performance-based activities.

All module tests include TEKS-aligned questions that vary in item type and complexity. The Module Test answer key identifies the TEKS alignment and Depth of Knowledge (DOK) level for each item. For example, the module 1 test includes multiple-choice, free-response, ordering, and matching questions that vary in complexity from DOK 1 to 2.

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

The materials include formative assessment opportunities such as “Practice on Your Own” tasks that provide scoring information, sample answers, and educator guidance for evaluating student responses. The materials also reference “Assessment Reports on Ed,” which support educators in interpreting student performance and identifying strengths, misconceptions, and instructional needs.

Each Module Review provides guidance for scoring correct responses and a “Data-Driven Support” table with intervention activities to address skill gaps. For example, in module 4, students who miss item 6 would benefit from a reteach activity on solving problems involving direct variation.

Additionally, Module Projects include scoring rubrics and exemplar responses for interpreting student performance. Guidance also suggests that educators “Have students use the project rubric to set a goal for how they will perform on the activity.”

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

The “Differentiation and Practice” sections for each lesson includes “Almost There,” “On Track,” and “Ready for More” activities that educators assign based on students’ performance on the “Quick Check” assessments. These small-group, educator-led activities address the learning needs and misconceptions for students at different levels of understanding. In addition, the materials provide multiple levels of independent practice activities to meet the needs of learners who do not participate in educator-led small-group activities.

Each module includes “Data-Driven Supports” to respond to student trends on the “Prerequisite Check” and Module Review. Guidance includes recommended reteaching resources based on various skills available on HMH Ed™. Waggle provides adaptive skill development and uses a skill-driven AI engine to provide targeted support to students.

Evaluation for 2.2c
Materials include tools for teachers to track student progress and growth, and tools for students to track their own progress and growth.

The materials include tools for educators to track student progress and growth through assessment reports, progress-monitoring resources, and data-analysis supports connected to lesson and module assessments. Educators can use a printable “Whole Class Proficiency and Growth Tracker” and digital reports to monitor student proficiency and progress throughout the school year.

The materials include student-facing progress-monitoring opportunities such as self-check routines, progress checks, and reflection opportunities embedded within lesson and assessment structures. The materials also include a printable tracker to help students “set goals and track their scores for Module Tests throughout the year.”

Each lesson incorporates a “Learning Goal” routine for students to “assess their content knowledge based on the I Can statement” at the beginning and end of the lesson. This allows both students and educators to track student growth. For example, the learning goal for module 5, lesson 2 is “I can use a trend line of the form y = kx to approximate a linear relationship between bivariate sets of data and make predictions.” Students can rate themselves as “I don’t understand,” “I need more practice,” or “I’ve got 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.

Each lesson includes educator guidance for differentiated instruction and scaffolded small-group activities for students who have not yet reached proficiency based on the “Quick Check.” The “Almost There” educator-led, small-group activity provides explicit reteaching guidance, guided questioning, visual models, and structured practice to help students master grade-level content and skills. For example, in module 11, lesson 1, the activity provides specific guidance to help students create scatterplots, such as “Have students write the data in the table as ordered pairs.”

Additionally, the materials include guidance within the “Data-Driven Report” to “address specific learning gaps identified in the Prerequisite Check.” The materials provide intervention activities on 29 skills, including “Simplify Ratios,” “Inverse Operations,” and “Finding Perimeter,” to prepare students for grade-level content.

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 “Words to Learn (WTL)” routine and WTL vocabulary cards provide pre-teaching supports for unfamiliar academic and mathematical vocabulary. These supports guide educators to introduce key mathematical terms using strategies such as “Say it” and “Define it” before students engage with lesson content. Guidance states, “This routine provides each student with an opportunity to practice and internalize each new term.”

The “Three Reads,” “Turn and Talk,” and “Collect and Display” sections include embedded vocabulary and language supports to help students understand unfamiliar academic language and references in text. For example, in module 4, lesson 1, the “Collect and Display” routine states, “During pair/group work, circulate and listen to student discussion. Write common or important words, phrases, sketches, or diagrams such as origin, unit rate, slope, y = kx, and constant of proportionality on a visual display for students to see.”

The “ELPS Teaching Strategies” section includes embedded support to help educators address unfamiliar references and contextual language that students will encounter during mathematical tasks. For example, module 4, lesson 6 states, “As students study functions, they will encounter several words that have meanings outside of the mathematical definitions provided in these lessons. Help students use contexts to construct a mathematical understanding of words with multiple meanings.”

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.

Each lesson provides differentiated instruction, including enrichment and extension activities, for students who have demonstrated grade-level proficiency based on the “Quick Check” assessment. Students who are ready for a challenge will benefit from the “Ready for More” small-group activity. For example, in the module 9, lesson 1 “Ready for More” activity, students create systems of equations, graph solutions, verify results, and apply mathematical reasoning in new contexts.

Additionally, each module provides leveled practice, including challenge activities for students who have demonstrated proficiency in grade-level content. For example, in the “Is It Growing or Shrinking?” challenge activity in module 2, students apply their understanding of perimeter and dilations to solve an application problem.

The materials also include a module project that “engages students in Depth of Knowledge (DOK) Level 4 tasks that apply and extend the mathematics found within the modules.” For example, in the “Boxing a Mobile Masterpiece” project, students will design cell phone packaging by applying the Pythagorean theorem to determine the length and width of a cell phone screen given a diagonal screen size, among other characteristics needed for packaging design.

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 Teacher’s Guide provides explicit prompts to support the educator in modeling and explaining the mathematical concepts, such as a series of “Ask” prompts for each lesson task. For example, in module 12, lesson 1, task 1, students use an online calculator to calculate the total repayment of a loan for different time periods. The materials state, “ASK: Why does the monthly payment decrease when the length of the loan period increases?” and “ASK: How might this affect the decision someone makes when getting a loan?” along with exemplary responses to guide instruction.

In addition, the materials provide guidance for modeling and explaining concepts through mathematical modeling supports and mathematical language routines. For example, in module 12, lesson 1, task 1 guidance states, “Have students use the Turn & Talk routine. For students who need support, have them verify one vertex with the rule on the grid, then generalize to the rest.”

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

The Teacher’s Guide provides detailed lesson plans for effective lesson delivery and facilitation using a variety of instructional approaches. Each lesson begins with a “Spark Your Learning” activity to engage students and encourage discussion of mathematical concepts. The materials provide whole-group instruction through a series of tasks with a variety of instruction strategies such as “Turn and Talk,” hands-on manipulatives, and real-world connections. Teaching strategies throughout each lesson address the needs of all learners, including “ELPS Support” and common error correction.

The Universal Design for Learning (UDL) strategies in the Teacher’s Guide guide educators on how to use multiple instructional approaches—including visual, verbal, collaborative, and hands-on learning opportunities—for effective lesson delivery. For example, in module 2, lesson 2, task 1, the UDL Support states, “Provide a table for the coordinates of the vertex points on each triangle. Color-code the coordinates in the table and the points on the graph.”

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.

Each lesson provides multiple types of practice to support implementation within the “Differentiation and Practice” section. The materials include independent practice, educator-led small-group activities, and collaborative group activities tailored to students’ needs. Guidance suggests that students complete collaborative group activities in pairs. In addition, a variety of independent practices allow students to work individually to reinforce concepts and skills from the lesson.

The materials support implementation by providing guidance for a range of recommended instructional structures, including whole-group instruction, small-group intervention, partner work, and independent learning opportunities. For example, each lesson has a “What does this look like in my classroom?” section, which includes guidance on presenting the lesson tasks to the whole group and differentiating instruction using one to three small-group rotations.

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 “Spark Your Learning” opening activity for each lesson includes teaching strategies for Emergent Bilingual (EB) students at varying language proficiency levels. For example, in module 5, lesson 3, guidance suggests students can “create their own vocabulary cards to support them in explaining how to use trend lines to justify a linear relationship between two variables.” Pre-production and beginner-level students draw a picture on their cards, while advanced students include a full definition.

The materials also include embedded educator guidance for linguistic accommodations aligned with the ELPS, including sentence stems, academic vocabulary supports, discussion routines, and scaffolded language-development activities. For example, module 7, lesson 6 includes an ELPS teaching strategy that states, “To support students’ speaking skills, explain that evaluating a response means giving your judgment or opinion about something and explaining the opinion clearly and with examples and details. Allow for opportunities for students to revise and reshare their written work to build fluency.”

The “Mathematical Language & Emergent Bilingual” page at the beginning of each module provides the educator with tools to plan for language development in the upcoming lessons. Guidance includes vocabulary support and mathematical language routines. This page highlights one of Dr. Kate Kinsella’s seven key routines that “support teachers and students with best practices for language development, such as ‘Building Fluency,’ ‘Partnering,’ ‘Assigning Discussion Tasks,’ ‘Eliciting Responses,’ ‘Using Response Scaffolds,’ ‘Words to Learn,’ and ‘Vocabulary Quick Teach.’”

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

The “Language Growth for All Learners” section of the Implementation Guide describes how each lesson aligns with the ELPS, includes observable and measurable language objectives, and provides teaching strategies that support mathematical communication. This section helps educators effectively use the program with emergent bilingual students in bilingual and ESL instructional settings. Guidance states, “You’ll find that Into Math® Texas provides you with opportunities to help your students develop their command of mathematical language and content simultaneously.”

In addition, the materials include a Language Development Resource Guide designed to “offer a structured approach to supporting students’ language development through professional development for teachers.” The guide provides math language routines, teaching strategies, student support resources for academic vocabulary and cognate support, and a description of the UDL principles. The guide helps ensure students receive targeted support that promotes language development.

Evaluation for 3.3c
Materials include embedded guidance for teachers to support emergent bilingual students in developing academic vocabulary, increasing comprehension, building background knowledge, and making cross-linguistic connections through oral and written discourse.

The materials include a variety of “Mathematical Language Routines” to support emergent bilingual students in developing academic vocabulary, increasing comprehension, and building background knowledge through oral and written discourse. For example, the “Words to Learn (WTL)” routine supports students as they learn and internalize the academic vocabulary introduced in lessons. The routine involves saying, defining, discussing, and using the new academic vocabulary. In module 2, lesson 1, task 1, the guidance suggests using the routine for the academic words: transformation, preimage, image, dilation, scale factor, and center of dilation.

The materials also include embedded “Emergent Bilingual” and “ELPS” teaching strategies to further increase comprehension and build background knowledge. For example, in module 3, lesson 1, the guidance states, “To support students’ writing skills, have them write the definition of slope in their own words and then compare with a partner.”

In addition, the materials include embedded guidance to help students make cross-linguistic connections through oral and written discourse, connecting their home language to English. For example, in module 8, lesson 1, task 1 guidance states, “Model the explanation with algebra tiles: point to the 2x tiles on both sides, remove them together, and say in English (and allow quick home-language rehearsal first), ‘Remove the same 2x from both sides to keep the equation balanced.’ This helps students connect mathematical language to visual meaning.”

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.

Lesson practice provides opportunities for students to demonstrate depth of understanding aligned with the TEKS by solving, representing, and interpreting equations; exploring linear relationships and functions; and applying geometric formulas. For example, the lesson 2.1 “Quick Check” requires students to apply the concept of dilations using coordinate geometry and determine image coordinates from a given scale factor and center of dilation. Students also analyze attributes preserved under dilation, compare preimages and images, and distinguish between scale factors using graphical representations. The “Quick Check” gives students an opportunity to reason about geometric transformations, proportional relationships, and invariant properties, rather than perform calculations. Successful completion of the assessment requires conceptual understanding of how dilations affect side lengths while preserving angle measures and orientation, a concept that aligns with the depth of understanding required by TEKS 8.3B.

Instructional assessments over the course of a module, such as Module Reviews and Module Tests, assess the same grade-level concepts and require students to apply procedural skill, conceptual understanding, and mathematical reasoning as required by the TEKS. Both assessments include educator guidance that directly correlates each question with the TEKS.

Additionally, each module includes a Module Project that requires the application of mathematical concepts in a real-world context. Guidance states, “Through real-life explorations, students synthesize concepts and apply understanding to complex tasks.” The DOK level 4 task asks students to analyze information, select an appropriate strategy, solve the problem, and explain or justify their reasoning using mathematical representations and written responses as required by the process standards.

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

Each lesson provides a series of tasks that progressively increase in rigor and complexity, leading to grade-level proficiency. For example, in module 6, lesson 3, students model the relationship between the volume of a cylinder and a cone with the same base. The lesson begins by exploring a real-world problem involving filling a cylindrical rain gauge with a cone-shaped measuring cup to help students determine how many cones fit inside a cylinder with the same base. The task requires students to use the volume of a cone to determine the volume of a cylinder and vice versa.

Each task uses guiding questions that increase in complexity and rigor. These questions lead to grade-level proficiency by providing access points for students to build on prior knowledge and deepen their mathematical understanding. In task 2 of 6.1, students explain the Pythagorean theorem. The task begins with direct questions, such as “Find the area of each leg’s square,” using a visual representation. Then progresses to “Explain why finding c requires taking the square root of c². Use complete sentences in your explanation.”

Additionally, Module Tests use a variety of question types to progress from procedural fluency to application and mathematical reasoning. This progression allows students to answer questions of increasing rigor and complexity. For example, the module 3 test begins with calculating and interpreting slope and unit rates. The test progresses to comparing relationships, analyzing proportional situations, and applying concepts across graphs, tables, equations, and geometric contexts.

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

The materials include module-level and course-level rationales that explicitly connect mathematical ideas across lessons and modules. For example, the rationale for module 3 states, “It begins with foundational knowledge of how similar right triangles can be used to determine the rate of change or slope of a line. Students then apply this understanding to graph proportional relationships and understand that the unit rate is the slope of the line. With these skills in place, they are equipped to find the slope and y-intercept of a line when given a table or graph.”

The lessons include “Turn and Talk” routines designed to connect to prior learning by explicitly connecting big ideas, patterns, and relationships between mathematical concepts. For example, lesson 7.3 asks, “Think back to previous learning about the Triangle Inequality Theorem. If two sides of a triangle measure 5 and 12, what values could the third side be so that the three lengths form a triangle?” The materials explicitly connect to the student’s prior learning of the Pythagorean theorem and geometric problems related to determining distance on the coordinate plane. Students extend previously learned concepts about right triangles and distances to a new context by using the Pythagorean theorem to calculate distances between points. This activity demonstrates coherence across lessons and mathematical representations.

Additionally, the “Turn and Talk” routine in task 4 of lesson 4.3 states, “Apply what you know about linear equations and slope to explain which points you can use to calculate the slope of a line.” Students connect what they already know about slope to justify using any two points on the line.

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 Teacher’s Guide for each module includes a “What will students learn in this module?” section that connects the current content to prior learning and future connections. For example, in module 4, students look at proportional and non-proportional relationships. Previously, students have “understood ratios and unit rates and related them to multiplicative comparisons.” In the future, students will “model and solve multistep problems involving proportions, including the use of function notation in their relationships.”

Additionally, each lesson explicitly connects the content and language learned in previous grade levels to the current lesson and how it extends to future learning. For example, lesson 3.3 connects concepts of proportional relationships, unit rates, and slope developed in earlier lessons and grades to the identification and interpretation of slope and the y-intercept from tables and graphs in mathematical and real-world contexts. The lesson also establishes future connections to writing and interpreting linear equations, analyzing similar figures, and solving more advanced algebraic relationships, demonstrating a clear progression of mathematical concepts and academic language across grade levels.

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..

Each lesson begins with a “Spark Your Learning” activity designed to connect students’ prior knowledge of concepts and procedures to the new mathematical skills. Educator guidance states, “Resist the temptation to teach the content needed to solve the Spark problem; instead, let students use their prior knowledge.” For example, module 5, lesson 3 begins with students investigating a given data set to determine whether a student can reach their fundraiser goal if the pattern continues. Students apply previously learned concepts of rate of change before fitting a linear model to given data sets in the lesson.

The materials also include a “Prerequisite Check” for each module to connect prior concepts and procedures from current and previous grades to new learning. For example, module 6 activates prior knowledge of the order of operations, estimations of square roots, and the area of circles to connect to the investigation of geometric formulas. The “Data-Driven Support” table helps educators identify intervention activities to help prepare students for the upcoming lessons.

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

The independent practice handout for each lesson includes a “Train Your Memory” section that offers spaced retrieval opportunities for previously learned skills and concepts across lessons and units. For example, in module 12, lesson 5, the section includes three review questions from modules 7, 9, and 11. Students review skills used for solving systems of equations, such as graphing, identifying associations in scatterplots, and using the Pythagorean theorem to identify a right triangle.

Additionally, each module begins with a “Prerequisite Check” on previously learned skills and concepts, providing “insight into students’ mastery of prerequisite concepts that are required to succeed with the new learning in the module.” For example, module 9 provides opportunities for spaced retrieval practice focused on verifying solutions to linear equations, identifying special solutions, and graphing linear functions. This practice prepares students for solving systems of equations in the upcoming lessons.

The materials also include a Module Project that offers opportunities for students to apply previously learned skills and concepts. “Each Module Project gives students essential and extended opportunities to practice engaging with content within the modules, and to do so at a Depth of Knowledge level 4.”

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

The “Train Your Memory” section of the independent practice provides interleaved practice by requiring students to apply previously learned skills and concepts. For example, in module 9, lesson 3, students revisit content from earlier lessons and units, including solving equations (lesson 8.3), applying the Pythagorean Theorem and classifying right triangles (lesson 7.3), analyzing direct variation and proportional relationships (lesson 4.2), and integer operations fluency. The program mixes these previously learned concepts and procedures with current learning on systems of linear equations, requiring students to select appropriate strategies across multiple mathematical domains. This interleaving of algebra, geometry, proportional reasoning, and numerical operations promotes flexible thinking and reinforces learning across lessons and units.

The materials include a variety of practice- and application-based tasks that require students to use previously learned skills and concepts within the same problem set, such as multiple representations, calculations, mathematical reasoning, and real-world interpretation. For example, the “Practice on Your Own” section provides a mixed set of problems on the lesson concepts, giving students a choice in how to solve. The questions align with the lesson tasks in random order, which promotes flexible thinking as students learn to switch between different types of problems and strategies.

Additionally, each module provides a Module Review that provides interleaved practice opportunities with previously learned skills and concepts across lessons. The review allows students to practice and review the TEKS taught in the module and includes a variety of questions that promote flexible thinking to solve different types of problems.

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

Lesson tasks regularly require students to interpret, analyze, and evaluate representations for mathematical concepts and situations. These tasks enable students to select appropriate methods for finding solutions in unfamiliar contexts and to develop flexible thinking skills. For example, in lesson 10.5, task 3, students must first interpret transformation notation for a bike logo on a coordinate plane and evaluate the transformations. Students then participate in a “Turn and Talk” activity to discuss whether the transformations could have been performed in a different order.

Additionally, in module 6, lesson 3, students use visual models to compare the volumes of a cylinder and a cone with the same base and height, analyze the models, and interpret the relationship between the formulas.

The materials also provide low-floor, high-ceiling “Spark Your Learning” activities to help students interpret, analyze, and evaluate representations. These activities enhance students’ critical thinking skills and enable them to transfer their learning to new contexts. For example, in lesson 7.2, students use the Pythagorean theorem to find new points for (o, a) and (b, 0) to form a right triangle. Next, they analyze the points they found to justify that they do make a right triangle.

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

Throughout the materials, students use and create mathematical models to represent and solve real-world situations. For example, in module 3, lesson 3, task 1, students analyze diagrams of two rectangles and create a table of their attributes. Students then use the table to determine whether the rectangles are similar. These models, figures, and drawings equip students to respond to the prompt “Are the rectangles similar? Explain how you know.”

Additionally, in module 2, lesson 2.1, task 2, students create their own geometric models by constructing the image of a rectangle on the coordinate plane after applying a dilation with a scale factor of 3 from the origin. They graph the transformed figure, develop and explain the algebraic rule governing the dilation, verify the model using an alternate method, and determine whether the resulting figure is an enlargement or a reduction. Rather than interpreting a completed model, students generate a mathematical representation that models the given situation.

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

Each lesson uses lesson tasks and structured language routines such as “Turn and Talk.” to provide opportunities for students to apply conceptual understanding to new problem situations and contexts. For example, in lesson 3.3, task 1, students identify y-intercepts from graphs and tables. The materials state, “Why is looking at x = 0 the fastest way to find the y-intercept?” Through discussions, students go beyond definitions to develop a conceptual understanding of what a y-intercept represents algebraically.

The materials also include “Practice on Your Own” assessments that provide students with opportunities to apply their conceptual understanding to new contexts.  For example, in lesson 5.3, students apply conceptual understanding of linear functions to answer questions related to the real-world problem on social media. Questions include “What is the value of y in the point (0, y) on your trend line? What connection does this have when writing an equation of the form y = mx + b?”

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

Throughout the materials, students engage in repeated practice that builds automaticity and fluency with grade-level mathematical concepts before applying these skills to more complex tasks. The Implementation Guide lists independent practice resources such as “Practice Plus,” “Practice on Your Own,” and Waggle and explains that independent practice reinforces skills and helps develop automaticity.

The “Practice on Your Own” is designed to build the automaticity and fluency necessary to complete grade-level tasks. For example, in module 8, lesson 1, students begin solving equations using algebra tiles and progress to algorithms. Lastly, students create their own equations, solve them, and justify their answers. Once the process of solving equations becomes automatic, students become fluent in setting up and solving problems without the tiles.

Additionally, the materials provide fluency practice on a variety of concepts within the “Differentiation and Practice” portion of the lesson. Educator guidance states, “Give students Fluency practice as it is available to help promote automaticity.” The grade 8 fluency practice includes skills such as decimal operations and solving two-step equations.

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 lesson tasks provide opportunities for students to apply flexible and accurate mathematical procedures. For example, in lesson 10.3, task 3, students rotate a rectangle on the coordinate plane 270 degrees counterclockwise and label the new vertices. The materials prompt students to “Explain another way to transform Rectangle ABCD to create Rectangle A′B′C′D′.” The materials demonstrate flexibility among transformations that end in the same image, while maintaining accuracy.

Additionally, in the “On Track” activity for lesson 8.1, the materials state, “Have students work with a partner to solve the equation in two different ways. One student can solve the equation by eliminating the fractions first, while the other student subtracts the fractions. Ask students to explain each method and discuss if they prefer one method and why.” The activity provides students with the opportunity to practice flexible problem-solving approaches, which lead to a discussion of efficiency and accuracy.

The materials also provide continued opportunities to apply the efficient, flexible, and accurate procedures independently after the lesson through practice, such as “Practice on Your Own,” “Practice Plus,” and Waggle. For example, in lesson 9.1, students develop efficient procedures by repeatedly solving systems of linear equations through graphing. Students use flexible procedures by analyzing different types of systems and interpreting graphical representations to determine solutions. They also practice accurate procedures through multiple application problems that require them to graph, identify intersection points, verify solutions, and solve increasingly complex systems.

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 problem-solving model used throughout the materials provides students with opportunities to evaluate their processes for efficiency, flexibility, and accuracy. For example, in module 5, lesson 3, students write a trend line for a given data set to make predictions. Questions such as “Does the predicted day that Raena reaches her goal make sense based on the data? Explain” require students to evaluate the accuracy of their answer. The “Spark Review” asks students to consider efficiency and flexibility by answering questions such as “Think about how you solved the Spark Your Learning at the beginning of the first session. Is there anything new that you are now able to interpret from the data set? How does your understanding of using trend lines make the data easier to interpret?”

Additionally, in lesson 7.6, task 2, students calculate the surface area for a rectangular prism using the formula. The materials ask students to “Compare the method used in this Task to using a net of six rectangles. Which is more efficient for this donation box, and why?” The materials demonstrate flexibility in calculating surface area but highlight that the formula is the most efficient and maintains accuracy.

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

Embedded educator guidance provides instructional prompts, questioning strategies, and scaffolds that help students refine solution methods and develop increasingly efficient mathematical approaches. For example, in module 8, the “Teacher Background” explains how “Mathematical and real-world problems can often be solved most efficiently by modeling the problem with an equation and then finding its solution.” During task 5, students evaluate their processes and discuss how writing an equation is more efficient compared to building a table.

Additionally, in lesson 7.6, the Teacher’s Guide includes instructional supports that help educators guide students from visual models and nets to a more efficient use of formulas to determine the surface area of cylinders. Educator prompts encourage students to justify why formulas provide a more efficient solution method while maintaining conceptual understanding.

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

The “Teacher Background” in each module explicitly states how the materials balance conceptual understanding with procedural fluency required by the TEKS. For example, in module 3, guidance states, “Conceptually, students will understand the slope of a line. They will learn why the slope of a line is constant.” Then students learn how to determine the slope of a line from two points, graph proportional relationships, and interpret slope in context.

Additionally, in module 8, the “Teacher Background” explicitly identifies the conceptual emphasis as it develops understanding of geometric relationships among surface area, volume, and the Pythagorean theorem. The procedural emphasis describes how students use formulas, nets, and mathematical reasoning to solve problems involving prisms, cylinders, cones, spheres, and coordinate geometry.

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 questions and tasks incorporate concrete models and representations alongside standard algorithms to help students build connections. For example, in task 2 of lesson 8.1, the materials guide students to use algebra tiles to model solving multistep equations. After solving with algebra tiles, students compare two algebraic representations to determine whether both are valid approaches. In module 10, lesson 2, students use graphing and reflection models to connect transformations to coordinate rules. The materials provide opportunities for students to explore hands-on solving to build connections with the algebraic process.

Additionally, the “Teacher Background” emphasizes the importance of using concrete models and manipulatives, pictorial representations, and abstract representations to meet the standards. For example, module 6 states, “Using models to derive the formula for the Pythagorean Theorem helps students to develop a conceptual understanding of the formula. Students will continue to use the Pythagorean Theorem to find missing sides of right triangles. Later, they will apply the theorem to finding the distance between two points on a coordinate plane and to develop the equation of a circle graphed on the coordinate plane.” The materials ensure that students engage in meaningful mathematics, not just memorizing rules and procedures, by actively constructing their own understanding through various representations. 

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 tasks include support to help students create and connect concrete models to abstract concepts. For example, in lesson 8.1, task 2 requires students to model equations using algebra tiles, connect the concrete model to symbolic equations, create and manipulate representations while maintaining equality, and explain why each algebraic step is valid. Students justify multiple solution paths, strengthening connections between concrete, representational, and abstract reasoning.

The materials also support students in creating, defining, connecting, and explaining representational models to abstract concepts.  For example, in lesson 10.2, task 1, students create a graph of two roads and an art panel to solve a real-world problem. Students work hands-on, folding their model and reflecting the image to help make connections between the coordinates of the image and the preimage, leading to an algebraic rule. The materials ask students to explain “How do you know that the orientation of the art panel changes from ABCD to A′B′C′D′? How do you know that the size and shape remain the same?”

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

The materials intentionally develop students’ academic mathematical language by integrating multiple visual representations, hands-on manipulatives, and structured language routines. For example, in module 2, lesson 3, students connect academic language to a visual coordinate-plane representation by graphing multiple images and explaining relationships among the representations. The materials state, “Graph △A′B′C′ and △A′′B′′C′′ on the same coordinate plane as △ABC” and “How is the scale factor of dilation related to the scale factor of the corresponding side lengths?” Guidance also suggests using the “Compare and Connect” language routine to “compare the algebraic dilation rules and the coordinate graphs.” The task develops terms, such as dilation and scale factor, through a visual model and a written mathematical explanation.

Additionally, in lesson 10.3, students use a grid and tracing paper to develop the academic vocabulary related to rotations. Guidance states, “Provide a transparent sheet or tracing paper and have students color-code the axes. This reduces spatial-visual load and helps students align their explanations to what they see on the coordinate plane.” The visuals help students understand the algebraic rule for rotations. The materials also suggest using the “Discussion Supports” routine to “model the use of precise mathematical language when explaining their thinking about 90 degrees.”

The materials also provide educator guidance through the Implementation Guide, which explains how educators support students’ development of academic mathematical language through intentional instructional routines and language supports. For example, the “Language Growth for All Learners” section describes instructional strategies that help educators build mathematical vocabulary, scaffold academic conversations, and provide multiple opportunities for students to explain and justify their mathematical thinking using precise mathematical language during instruction.

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

The materials include embedded educator guidance during activities to support the implementation and development of academic vocabulary throughout the lessons. For example, in lesson 4.2, the “Turn and Talk” routine guidance states, “For students who may need extra support, encourage them to describe how they have analyzed graphs in the past and how points can be shown with different representations.”

Additionally, in module 2, lesson 1, the embedded language routine directs educators to build precise transformation vocabulary from students’ contextual observations. The materials state, “Listen for students who use language such as ‘turned,’ ‘flipped,’ or ‘slid.’” The guidance then supports connecting students’ informal descriptions to the academic terms rotation, reflection, and translation, scaffolding development of mathematical vocabulary within the transformation task.

The materials also include a Language Development Resource Guide that provides scaffolding and supports students’ development of academic mathematical language. The materials state, “Deliberately teaching academic vocabulary plays a crucial role in fostering student success both in the classroom and in life. Here are some key advantages of building and reinforcing academic vocabulary: enhanced comprehension, critical thinking, improved communication, academic achievement, lifelong learning, and confidence building.” The guide provides strategies for teaching academic vocabulary and for using the “Words to Learn (WTL)” routine, high-utility words, and vocabulary cards.

Evaluation for 5.4c
Materials include embedded teacher guidance to support the application of appropriate mathematical language to include vocabulary, syntax, and discourse to include guidance to support mathematical conversations that provide opportunities for students to hear, refine, and use math language with peers and develop their math language toolkit over time as well as guide teachers to support student responses using exemplar responses to questions and tasks.

The materials include educator guidance to support students’ application of mathematical language throughout instruction. Each lesson incorporates multiple “Mathematical Language Routines” (MLRs) to structure mathematical discourse. Guidance provides scripted questions, anticipated student responses, and discussion prompts that encourage students to explain their reasoning using precise mathematical vocabulary. Students listen to classmates’ explanations, compare mathematical representations, refine their thinking through peer discussions, and communicate mathematical ideas using appropriate vocabulary and syntax. The materials also provide educator guidance for addressing misconceptions and extending students’ responses, helping students strengthen their mathematical language over time.

The materials embed language supports in the Teacher’s Guide for each lesson. For example, in module 4, lesson 2, guidance includes “Support understanding of vocabulary by providing students with a visual diagram showing a graph and equation of a direct variation labeled with ‘proportional relationship, linear equation, direct variation, constant of proportionality, slope, constant of variation.’” This guidance supports students in developing precise vocabulary for problems involving direct variations. The materials also provide sentence stems to support students in communicating their thinking and multiple opportunities for peer-to-peer discussions.

Additionally, each module incorporates a “Stronger and Clearer Each Time” language routine that allows students to use, hear, and refine mathematical language. The routine asks students to share their thoughts with a partner, ask thoughtful questions, and revise their response. The materials include embedded educator guidance to support the routine. For example, in lesson 5.2, guidance prompts educators to “Remind students to ask questions that focus on describing each other’s thinking about how using different ratios affects each model’s accuracy, and to use insights from the discussion to refine their models and predictions.” The materials also include exemplar responses to all guiding questions.

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

Lesson materials integrate the TEKS process standards by embedding problem-solving, mathematical communication, reasoning, representation, and tool selection throughout instruction and student tasks. For example, in lesson 2.1, students engage in problem-solving, construct and analyze geometric representations, communicate mathematical reasoning during structured discussions, and justify conclusions using appropriate mathematical language. The “Three Reads,” “Compare and Connect,” and “Turn and Talk” activities integrate the process standards into authentic mathematical learning experiences.

Additionally, each “Practice on Your Own” assessment integrates the process standards by identifying questions labeled “PS.” For example, in lesson 8.6, questions require students to “justify” when determining whether two angles are same-side exterior or alternate exterior angles and “use precise language” when explaining how to find the measure of two same-side interior angles formed by parallel lines and a transversal.

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

The course-level “Mathematical Connections” guidance explicitly describes the role of process standards across grade 8. The guidance states, “Into Math Texas intentionally make[s] mathematical connections across the grade level to help drive the scope and sequence.” The program also “uses these connections, supported by the Texas Mathematical Process Standards, to build deeper understanding, promote transfer of learning, support coherence across topics, and strengthen problem-solving and reasoning.” The accompanying coursewide table then describes process-standard connections across modules, such as “in modules 2-4, 7 and 9-10 students communicate mathematical ideas using multiple representations of relationships, including graphically and algebraically” and “in modules 6-9, students use precise mathematical language to justify steps for applying the Pythagorean theorem, solving problems involving volume and surface area, and solving equations and inequalities.”

Additionally, the Implementation Guide provides a “Correlation by Standard” table that directly identifies where the course incorporates each process standard. For example, lessons 1.1, 1.4, 3.1, 4.1, 6.2, 8.7, and 9.2 incorporate process standard 8.1.F.

The materials also include course-level “Process Standards Anchor Charts” guidance that describes how students use the process standards throughout instruction. For example, the guidance suggests, “To support students’ understanding of the TEKS Process Standards, have them use the anchor charts in the front of the Student Edition as they work through the lessons.” The student-facing chart operationalizes the standards through recurring prompts, including “What situation does the problem describe?” “What plan or strategy will you use?” “How do you know the solution answers the question?” and “How reasonable is the solution?”

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

The Teacher’s Guide includes a dedicated “Module Planning” section that explains how the materials incorporate grade 8 TEKS process standards throughout each module and how concepts connect across the unit. For example, module 2 explains that students develop a problem-solving model throughout the unit, culminating in lesson 3, when students apply all steps of the process together to solve a similarity problem. The description also identifies the lessons that align to individual process standards. For example, lesson 1 emphasizes using mathematical representations (process standard 8.1.E), and lesson 2 focuses on communicating mathematical ideas (process standard 8.1.D) and using precise mathematical language (process standard 8.1.G). During lesson 2, students write algebraic rules for dilations and explain relationships among representations. The materials intentionally connect the process standards across multiple lessons within the unit.

The planning pages for module 3 describe how multiple process standards connect to content across lessons. Lesson 1 has students analyze relationships (process standard 1.F) and use precise language (process standard 1.G) “to explain how the legs of a right triangle are connected to the rise and run of the line.” Lesson 2 has students use representations (process standard 1.E) and communicate ideas (process standard 1.D) as they “represent a proportional relationship with a table and a graph.” The guidance explicitly maps analysis, precise language, representation, and communication to the mathematical content developed across the unit.

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

At the beginning of each lesson, the Teacher’s Guide provides a comprehensive lesson overview that identifies the mathematical content standards, learning objective, language objective, prior learning, future connections, and the specific TEKS process standards incorporated into the lesson. For example, in module 8, lesson 3, the overview explicitly identifies process standard 8.1.F (analyze mathematical relationships to connect and communicate mathematical ideas) and process standard 8.1.G (display, explain, and justify mathematical ideas using precise mathematical language) as aligned standards. The overview also describes how students will engage in mathematical reasoning and communication while developing an understanding of slope using similar right triangles.

Additionally, throughout each lesson, a “PS” appears next to specific items where the process standards apply. For example, in lesson 4.1, task 2 requires students to use representations to describe proportional relationships, as required by process standard 8.1.E.

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

Each lesson opens with a “Spark Your Learning” activity before formal instruction. The activity presents an authentic scenario and asks students to identify multiple ways to represent and solve the problem. For example, lesson 4.1 asks students to determine the unit cost of blueberries using only two price points. Students show their thinking and then participate in a “Turn and Talk” to discuss what the graph of the relationship might look like. Rather than provide a procedure, the lesson requires students to reason through the proportional relationship, explore possible solution strategies, and communicate their mathematical thinking. This design promotes productive struggle by allowing students to construct understanding before educators introduce formal concepts such as the constant of proportionality.

The materials also incorporate a problem-solving model throughout each module, providing opportunities for students to think mathematically, persevere, and make sense of mathematics in real-world contexts. For example, in lesson 8.1, students write and solve an equation to determine when two runners will have the same weekly mileage. Students analyze the problem, create a plan, solve the problem, and justify their work. Educator guidance includes prompts such as “ASK: Why is it important to perform the same operations on both sides of the equation?” to help students persevere through the solving process. The “Turn and Talk” activity asks students, “How did the structure of the two expressions help you decide how to write the equation and which operations to use when solving?” These questions allow students to make sense of the mathematics.

Evaluation for 6.1b
Materials support students in understanding, explaining, and justifying that there can be multiple ways to represent and solve problems and complete tasks.

The materials provide additional support to help students understand, explain, and justify how to use more than one method to solve mathematical problems. For example, in module 7, lesson 6, students compare alternative methods for representing and solving a surface-area problem and justify which approach is more efficient. After students work with an algebraic surface-area expression, the lesson says, “Compare the method used in this Task to using a net of six rectangles. Which is more efficient for this donation box, and why?” Students must understand two different approaches, explain their comparison, and justify the relative efficiency of the methods.

Additionally, the materials incorporate “Show Another Way” questions that help students understand and explain that there are multiple ways to represent and solve problems. For example, in module 10, lesson 3, students rotate a rectangle on the coordinate plane 270 degrees. The task states, “Explain another way to transform Rectangle ABCD to create Rectangle A′B′C′D′.” The “Turn and Talk” activity asks, “What is one way to verify the rule for rotating 270° counterclockwise around the origin using other rules?” This question supports students in justifying the use of multiple approaches.

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.

Each lesson follows a series of tasks that allow students to make sense of mathematics. Students complete tasks that provide opportunities to explore, write, and discuss mathematical concepts with peers and educators. For example, in lesson 7.1, students complete four tasks using the Pythagorean theorem to solve problems. All four tasks provide real-world problems to help students make sense of the mathematics. Students discuss the math through “Turn and Talk” routines and justify their answers through written discourse.

The materials provide additional opportunities for students to communicate mathematical understanding through writing and discussion. For example, in module 4, lesson 2, task 4, students explain their reasoning in writing, compare multiple solution methods with classmates, and justify mathematical conclusions using evidence from the task. Educators guide students through purposeful questioning that promotes mathematical communication and reflection throughout the lesson.

The materials also provide prompts and guidance for educators to help students share and reflect on their problem-solving methods through justifications, explanations, and arguments. For example, in lesson 9.1, task 1, the educator guidance states, “Encourage students to share their thinking. Students may need additional support, so consider having them sketch a line. Then have students attempt to sketch a second line that intersects the first line exactly twice.”

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 8 materials provide many activities and educator supports to help guide students to share and reflect on their problem-solving approaches. For example, in lesson 1.4, the materials guide educators to use a variety of language routines and direct questioning prompts to help students share and reflect. In task 1, students explain how multiplying by 103 changes the place value. The educator guidance states, “Student justifications should include evidence and reasoning to support their claim.” In task 3, students critique and make a claim. The supporting guidance prompts educators to “have students argue whether the conversion is correct as they reflect on their problem-solving approach.” The “Review: Spark Your Learning” section asks students to “Think about how you solved the Spark Your Learning at the start of this lesson. What might you do differently to solve the problem now? Explain.”

The materials provide additional opportunities for educators to support students in reflecting on mathematical reasoning. For example, in lesson 4.2, task 4, students explain and justify their solution strategies, compare mathematical representations, and evaluate their classmates’ reasoning. Educators guide discussion before independent practice by asking students to defend their mathematical arguments with evidence, critique alternative approaches, and reflect on how different strategies lead to equivalent solutions.

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

The Teacher’s Guide provides explicit guidance for educators to monitor student understanding throughout the lesson using the “Learning Goal” routine, “Quick Checks,” and real-time student responses. Educators begin the lesson by assessing students’ confidence with the learning objective and reviewing student responses to determine instructional needs. At the conclusion of the lesson, educators revisit the learning goal and use student evidence to determine next instructional steps. This ongoing cycle supports responsive instruction by encouraging educators to offer and adjust support during the lesson based on demonstrated understanding.

The materials direct educators to monitor student responses and provide targeted explanatory feedback throughout each lesson. For example, module 2, lesson 1 states, “Students may incorrectly subtract the measurements to make their comparisons” when comparing similar figures and directs educators to “Use the scripting to provide support for this error.” The materials prompt educators to redirect students toward multiplicative reasoning: “What common relationship do you see when you compare the lengths of corresponding sides of each figure?” and “What common relationship do you see when you compare corresponding angles of each figure?” This supports feedback that addresses the identified misconception by guiding students to recognize proportional side lengths and the corresponding congruent angles.

Additionally, the Teacher’s Guide provides prompts and guidance throughout each lesson to address common errors. For example, in lesson 7.3, students use the converse of the Pythagorean theorem to determine which set of side lengths forms a right triangle. The materials identify a common error: misidentifying the hypotenuse. Guidance tells educators to remind students that c is the longest side in a right triangle and suggests having students circle the longest length provided.