HMH Into Math Texas, Algebra 1

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

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

The scope and sequence charts include an alignment to the TEKS and ELPS for each module and lesson and identify the concepts taught throughout the instructional year. Additional program materials further support this alignment through the TEKS and ELPS correlations, as well as “Correlations by Lesson” documents that break down concepts by module. Within the “Discover” tab under the program dropdown, the scope and sequence also outlines the TEKS, ELPS, and lesson concepts to support instructional planning and pacing.

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. Students progress from linear equations and functions to quadratic and exponential functions, and from operations with polynomials to operations with radical expressions and equations.

The materials support educators in understanding how concepts connect throughout the course. This guidance helps educators internalize concepts and make connections. For example, in modules 5–7, “Students build on their understanding of linear functions and equations by studying quadratic functions and equations.”

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

The program materials provide unit and lesson internalization through comprehensive planning supports, structured instructional routines, and embedded educator guidance. The Teacher’s Guide reviews the standards and outlines what students will learn in each module. The guide also 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 students need 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 support educator preparation.

Additionally, the “Step Through a Module” section of the Implementation Guide provides guidance for internalizing module and lesson components, while “Teacher Background” sections include mathematical rationale, examples, summaries, and explanations to deepen educators’ understanding of the concepts before instruction. The materials also include “Internalization Tools” to support both lesson and unit internalization through guiding questions such as “What do the lesson and language objectives expect from students?” and “What concepts, strategies, or procedures will students learn?”

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 provides 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, reflection tools, and guiding questions. Look-for checklists provide guidance to educators for the first 30 days of instruction. Reflection tools and guiding questions 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 “What should I understand about the math in this module?” section in the Teacher’s Guide provides a comprehensive overview and background knowledge of the TEKS standards in the module. For example, module 4 states, “Solving a system of equations algebraically is more accurate when the solutions are not integers, which can be more challenging to identify on a graph.”

The materials include academic vocabulary supports within lesson- and module-planning materials to promote effective instruction of unit concepts. Examples of these supports include vocabulary lists embedded in lesson overviews, mathematical language supports, and ELPS-aligned language development guidance.

The materials also provide an educator’s glossary to help educators teach the mathematical concepts effectively. 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 the student’s progress outside the classroom.

Each “Family Letter” also includes a home activity families can complete together to reinforce learning. For example, module 8 provides a real-life example of dropping a ball and measuring its bounce height to reinforce the concept of exponential functions.

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 Teacher’s Guide includes lesson plans with clearly defined lesson objectives and correlations to the TEKS and ELPS. For example, module 9, lesson 4, aligns with TEKS A.10. B, which expects students to “multiply polynomials using the distributive property and combine like terms” through a series of four tasks.

Each lesson plan includes tasks, quick checks, and practice sets aligned with the learning and language objectives and the TEKS and ELPS. The materials include many instructional assessments and tools using “Spark Your Learning,” task routines, “Quick Check,” and “Differentiation and Practice” sections of the lesson.

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

The Teacher’s Guide includes detailed lesson plans that include the manipulatives and materials needed for each lesson. For example, module 5, lesson 2 requires students to use foam algebra tiles in task 1 to expand the product of two binomials.

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 1, lesson 2, task 1 should take approximately 20 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 the effective use of lesson materials for extended practice through the “Differentiation and Practice,” “Homework,” “Extension,” “Collaborative Groups,” and “Teacher-Led Small-Group Activities” sections. The resources support educators in assigning additional practice, enrichment, intervention, and adaptive learning opportunities based on student performance data.

The Teacher’s Guide provides guidance for educators on how to effectively use “Differentiation and Practice” activities, including “Almost There,” “On Track,” and “Ready for More.” 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 effective use of the lesson materials through ongoing, leveled practice on Waggle, an adaptive digital learning platform. The materials note, “HMH Waggle supports instruction with auto-assigned, skill-based practice tailored by its AI engine.” The guidance report shows educators 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 contains a variety of formative assessments, including “Quick Checks” and “Are You Ready?” tasks, “Mid-Module Checks,” and Module Reviews. These formative 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, as well as a module project that requires students to “apply and extend the mathematics found within the modules.” The module test offers a variety of item types. For example, the module 9 test includes open-ended, multiple-choice, and matching item types.

The materials use diagnostic assessments to “determine progress at strategic points in the school year.” The materials include three benchmark assessments with a variety of question formats on each test, including drag-and-drop, graphing, multiple-select, and multiple-choice. These diagnostic assessments help 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, helping them make 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 inform instruction and help educators determine student readiness, monitor student progress, and measure student 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 each 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 to help educators administer assessments consistently, ensuring that all students receive the same instructions. For example, guidance for the Module Project states that “students can work on the project after whole-group instruction, or you can devote a specific instructional day to completing the project.” 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, educators should use the “Quick Checks” 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, including “Quick Checks,” “Practice on Your Own,” and “Are You Ready?” tasks align to the lesson TEKS and daily learning objectives identified within lesson-planning materials. For example, the “Practice on Your Own” answer key describes how each question aligns to the tasks and the TEKS.

Summative assessments, such as the Module Test, include answer keys that align questions with the TEKS and the corresponding lesson source. For example, module 10, question 4 requires students to simplify an expression containing rational exponents by applying the power rule. This task aligns with TEKS A.11.B and lesson 3, “Apply the Laws of Exponents.”

Diagnostic assessments, such as the “Benchmark Assessments,” have tables within their answer keys that show how each test item aligns to the TEKS and individual lessons.

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 indicates the TEKS alignment and DOK level for each item. For example, the module 3 test includes multiple-choice, free-response, drag-and-drop, and match table 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 help them to identify 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, the table indicates that in module 6, students who miss items 1A, 1B, and 1C will benefit from a reteach activity on graphing quadratic functions in vertex form.

Additionally, Module Projects include scoring rubrics and exemplar responses for interpreting student performance. Guidance also suggests, “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.

Every lesson includes a “Differentiation and Practice” section that suggests how to respond to student trends in their “Quick Check” performance. The materials provide guidance on how to use the “Almost There,” “On Track,” and “Ready for More” activities. These small-group, educator-led activities address each student’s learning needs and misconceptions based on their performance on the assessments. To meet the needs of all learners, the materials also provide multiple levels of independent practice activities for students who are not currently participating in educator-led, small-group activities

Each module includes “Data-Driven Supports” to respond to student trends on the “Prerequisite Check” and Module Review. Educators can find recommended reteaching resources for various skills on HMH Ed. Waggle’s skill-driven AI engine provides targeted support for students and guidance for adaptive skill development.

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 the 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 time embedded within lesson and assessment structures. The materials also include a printable student tracker to “help them 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 routine allows students and educators to track growth. For example, the learning goal for module 2, lesson 2 is “I can graph linear functions in slope-intercept form by using the slope and y-intercept, and identify the x-intercept and zero of a function from the graph or equation.” Students can assess their knowledge in one of three ways: “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 6, lesson 3, the activity provides students with a graphic organizer to help them graph quadratic functions in intercept form. The graphic organizer helps them identify key attributes so that they can better understand the problem. The materials provide guiding questions for each attribute to help students make connections, such as “How can you use the line of symmetry to plot another point? Have students plot the point, helping them count over to the point if needed.”

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 24 skills, including Constant Rate of Change, Exponents, and Multistep Equations, 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 materials include pre-teaching supports for unfamiliar academic and mathematical vocabulary. For example, the “Words to Learn (WTL)” routine and WTL vocabulary cards 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 materials also include embedded vocabulary and language supports to help students understand unfamiliar academic language and references in text, through language routines such as “Three Reads,” “Turn and Talk,” and “Collect and Discuss.” For example, in module 6, lesson 3, the “Collect and Display” routine suggests, “During pair work, collect and display vocabulary and sketches: zeros, intercepts, axis x = 2, vertex, minimum. Show small diagrams linking factors to zeros and the midpoint formula.”

The ELPS Teaching Strategies include embedded educator support to help students understand unfamiliar references and contextual language they will encounter during mathematical tasks. For example, module 7, lesson 3 states, “Read student explanations about the figurative language in the passage. Focus on their understanding of the phrase in the given context.”

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 their “Quick Check” results. Students who are ready for a challenge will benefit from the “Ready for More” small-group activity. For example, in the module 5, lesson 2 activity, students model real-world situations with quadratic functions, analyze relationships, and apply concepts beyond the lesson objective.

Additionally, each module provides leveled practice, including “Challenge” activities for students who have demonstrated proficiency in grade-level content. For example, in the module 3 “Fit Linear Functions to Data with Technology” challenge activity, students develop a deeper understanding of the correlation coefficient and its relationship to the slope of the regression line.

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 “Fore!” project, students examine and use quadratic equations to design one aspect of a golf course.

Evaluation for 3.2a
Materials include explicit (direct) prompts and guidance to support the teacher in modeling and explaining the concept(s) to be learned.

The materials provide explicit prompts to support educators in modeling and explaining mathematical concepts. The Teacher’s Guide includes a series of “Ask” prompts for each lesson task. For example, in module 3, lesson 3, task 2, students compare association and causation in real-world situations. The materials state, “ASK: What pattern do you notice in the table as both variables change?” and “ASK: How can you tell there is or is not an association between the two variables?” 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, the module 6, lesson 1, task 2 guidance states, “Have students use the Compare and Connect routine to discuss their thinking. Have pairs compare Task 1 and Task 2 graphs, describe how the sign and magnitude of a affect opening and ‘width,’ and decide which changes they prefer for making a ‘steeper’ or ‘wider’ curve, citing points.”

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, including “Turn and Talk,” hands-on manipulatives, and real-world connections. Teaching strategies embedded throughout each lesson address the needs of all learners, including “ELPS Support” and common error correction.

The Teacher’s Guide also provides educator guidance and recommendations for Universal Design for Learning (UDL) strategies. These strategies promote effective lesson delivery through multiple instructional approaches, including visual, verbal, collaborative, and hands-on learning opportunities. For example, in module 8, lesson 2, task 1, UDL support states, “Display a small anchor chart stating, Initial value: f(0) = a; Growth factor: b = f(1) ÷ f(0).”

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” sections. 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. Independent practices give students the opportunity to work individually to reinforce concepts and skills from the lesson.

The materials include guidance and recommended structures, such as whole-group instruction, small-group intervention, partner work, and independent learning opportunities to support effective implementation. For example, each lesson has a “What does this look like in my classroom?” section, which includes guidance on whole-group instruction and differentiating instruction with 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 Bilinguals (EB) at varying language proficiency levels. For example, module 3, lesson 2 provides EB teaching strategies to help students fit linear functions to data. Pre-production and beginner-level students receive highly structured frames with visuals such as “The line goes ______” with a visual of an up/down arrow. Advanced students receive a word bank including terms such as independent variable, dependent variable, increase, and decrease to help them use more academic language.

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 9, lesson 4 includes an ELPS teaching strategy that states, “Explain that when speaking with classmates, it is acceptable to use informal language to describe math terms and situations; however, with teachers and other school personnel, a more formal style is appropriate.”

Additionally, at the beginning of each module, there is a “Mathematical Language & Emergent Bilingual” page that provides educators with tools to plan for language development in the upcoming lessons. Guidance includes vocabulary support and mathematical language routines. The 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 and includes observable and measurable language objectives. This section also provides teaching strategies that support mathematical communication, helping educators effectively use the program with EB students in bilingual and ESL instructional settings. The materials state, “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 cognates, 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 EB students in developing academic vocabulary, increasing comprehension, and building background knowledge through oral and written discourse. For example, the “Words to Learn” routine supports students as they learn and internalize the academic vocabulary introduced in lessons. The routine involves saying, defining, discussing, and using new academic vocabulary. In module 1, lesson 2, task 1, the guidance suggests using the routine for the academic words function, linear function, independent variable, dependent variable, function notation, domain, and range.

The materials also include embedded “Emergent Bilingual” and “ELPS” teaching strategies to increase comprehension and build background knowledge. For example, in module 9, lesson 2, task 4 the guidance states, “Offer a quick write scaffold: students draft a sentence first in their home language, then in English. Encourage underlining math words (linear, constant, difference). This supports precise academic writing about structure.”

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, the guidance in module 3, lesson 3, task 1 states, “Students can mark any parts of association and causation that look familiar, say the words aloud to hear similarities to their first language, and then connect meaning they know from the cognate to the English math term.” The guidance for module 6, lesson 2, task 3 asks students to “write a two-sentence explanation in their home language first and in English second, describing how lowering the value of h_0 changes the graph and time.”

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 through modeling, comparing, explaining, and applying algebraic concepts such as functions, linear relationships, systems, quadratics, and the rules of exponents. For example, the lesson 1.5 “Quick Check” requires students to write and solve equations involving direct variation, interpret relationships between variables, and apply algebraic reasoning in contextual situations. Students analyze proportional relationships, determine constants of variation, represent relationships using equations, tables, and verbal descriptions, and justify solutions within real-world contexts as required by TEKS 2.D.

Instructional assessments over the course of a module, such as Module Reviews and Module Tests, assess 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 assessed 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 4, lesson 1, students solve multistep linear equations algebraically. Task 1 begins with a single-variable equation, whereas tasks 2 and 3 progress to equations with variables on both sides. Task 4 provides examples of equations with special solutions. Tasks 5 and 6 involve multistep equations with fractions and decimals. The lesson ends with task 7, in which students solve a real-world problem comparing two streaming services.

Each task uses guiding questions that increase in complexity and rigor, leading to grade-level proficiency by providing access points for students to build on prior knowledge and deepen their mathematical understanding. In task 3 of lesson 6.1, students graph quadratics in vertex form for a real-world problem. The task begins with direct questions, such as “Estimate the zeros, which are the x-intercepts of the graph, using your graphing calculator.” It progresses to “Are both zeros valid in this situation? Justify your answer with specific details about the key attributes of the function.”

Additionally, Module Tests progress from procedural fluency to application and mathematical reasoning through a variety of question types. For example, the module 2 test progresses from identifying and interpreting linear functions to analyzing systems of equations and inequalities, transformations, rates of change, and real-world modeling situations, requiring increasingly sophisticated algebraic reasoning and application aligned to the Algebra I TEKS.

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 course-level rationale explains how solving equations and graphing linear functions support later work with systems, quadratics, exponentials, polynomials, radicals, and sequences.

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 2.1 asks, “How does using the slope formula help keep subtraction consistent while calculating slope?” The materials explicitly connect prior learning about calculating slope using two points to new Algebra I learning involving rate of change and linear relationships. Students recall and apply the slope formula from previous coursework and then extend their understanding to more advanced representations and interpretations of linear functions, demonstrating coherence across grades and mathematical topics.

Additionally, the “Turn and Talk” routine in lesson 1.2, task 5 states, “Is the function for the cost per print job continuous or discrete? Use what you know about continuous and discrete functions to explain.” Students must apply previously learned concepts in a new context, helping build connections.

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 section “What will students learn in this module?” in the Teacher’s Guide for each module connects the current content to prior learning and future connections. For example, in module 1, students look at writing linear equations and inequalities. Previously, students “used equations to represent relationships between two variables,” and in the future, students will “solve linear equations and linear inequalities by graphing.”

Additionally, each lesson connects the content and language learned in previous grade levels to the current lesson and extends it to future learning. For example, lesson 3.3 connects students’ prior understanding of representing relationships with tables, graphs, equations, and linear models to new content requiring students to analyze data sets and distinguish between association and causation in real-world contexts. This learning prepares students for future work involving statistical models, data analysis, correlation, trend interpretation, and informed decision-making using quantitative evidence. The lesson explicitly connects previously learned linear modeling concepts to more advanced statistical reasoning and application.

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 7, lesson 6 begins with students investigating a real-world problem to determine how long it takes for a projectile to hit the water. Students must apply previously learned skills by completing the square before introducing the quadratic formula.

The materials also include a “Prerequisite Check” for each module to connect concepts and procedures from current and previous grades to new learning. For example, module 9 activates students’ prior knowledge of the distributive property and the simplification of expressions with exponents and connects these concepts to operations with polynomials. 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.

Each lesson includes a “Train your Memory” section on the independent practice handout that offers spaced retrieval opportunities for previously learned skills and concepts across lessons and units. In module 11, lesson 4, practice includes three review questions from modules 6, 8, and 9. Students review polynomial division skills and concepts related to attributes of quadratic and exponential functions.

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 6 provides opportunities for spaced retrieval practice focused on identifying intercepts of linear functions, writing quadratic equations given the vertex and a point, and graphing linear functions. These practices prepare students for graphing quadratic functions 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 7, lesson 1, students revisit prior content from earlier lessons and units, including graphing and analyzing linear equations (lesson 2.4), writing equations of parallel lines (lesson 1.6), solving one-step equations, and applying statistical concepts from grade 8 such as mean absolute deviation. These problems intentionally blend current quadratic reasoning, requiring students to select and apply multiple strategies across algebra, statistics, and equation-solving contexts. This interleaved structure reinforces prior learning across lessons and units while supporting flexible mathematical thinking.

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, letting students choose how to solve them. 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 Review provides interleaved practice opportunities with previously learned skills and concepts across lessons. The review is designed to allow 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 3.2, task 2, students interpret a line of best fit for data presented in tables and continue to evaluate their process, including the benefits of using technology versus drawing the line by hand. Lastly, the students analyze the r value, interpret its meaning, and consider the challenges of calculating it by hand or with technology.

Additionally, in module 6, students interpret key attributes of quadratic functions in different forms and analyze how transformations change the graph and the function’s contextual meaning.

The materials also provide low-floor, high-ceiling “Spark Your Learning” activities to help students interpret, analyze, and evaluate representations, enhancing their critical-thinking skills and enabling them to transfer their learning to new contexts. For example, in lesson 9.2, students use algebra tiles to represent polynomial expressions and must interpret their meaning. Students then analyze the meaning of the variables and numbers using the algebra tile representation.

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

Throughout the materials, students create mathematical models to represent and solve real-world situations by constructing visual representations, equations, tables, and diagrams that model mathematical relationships. For example, in module 2, lesson 2, students create tables and graphs to represent linear functions and analyze their key attributes. Guided tasks, such as “Encourage students to reflect on how they found the x-intercept and the zero of the function and to make connections to a y-value of 0” help students connect the graph to the algebraic features. The questions within the task require students to generate and explain their own mathematical representation to aid in the solving process.

The materials also provide students with opportunities to create tangible representations, figures, or drawings to aid in the problem-solving process. For example, in module 9, lesson 4, students use algebra tiles and area representations to model multiplication of binomials before moving to symbolic polynomial multiplication.

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

Lesson tasks and structured language routines, such as “Turn and Talk,” provides opportunities for students to apply conceptual understanding to new problem situations and contexts. For example, lesson 6.1, task 2 states, “Compare and contrast the graphs from Task 1 and Task 2. How does changing the value of a from positive to negative modify the graph?” Through discussions, students move beyond identifying attributes of quadratic graphs to developing a conceptual understanding of how the coefficients in the equations affect the graphs.


The materials also include “Practice on Your Own” assessments that provide opportunities for students to apply conceptual understanding to new contexts. For example, in lesson 4.4, students solve a multistep linear equation with fractional coefficients using algebraic reasoning and the properties of equality. They determine the least common denominator, clear fractions, isolate the variable through equivalent transformations, and verify the solution. The task requires students to demonstrate procedural fluency while connecting multiple algebraic concepts, including equivalent equations, inverse operations, and solution verification, rather than simply apply a single computational step.

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. The guide also explains that independent practice reinforces skills and helps develop automaticity.

The “Practice on Your Own” section builds the automaticity and fluency students need to complete grade-level tasks. For example, in module 4, lesson 4, students begin by solving systems of equations using substitution. Once they have developed automaticity, students create their own equations and then solve them to determine whether a specific point is a solution to the system. The repeated tasks strengthen automaticity, and applying a small new idea to each preceding problem supports fluency.

Additionally, the materials provide fluency practice on a variety of concepts within the “Differentiate and Practice” portion of the lesson. Educator guidance states, “Give students Fluency practice as it is available to help promote automaticity.” Algebra 1 fluency practice includes skills such as decimal and fraction operations and solving one- and 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 7.6, task 1, students calculate the lateral surface area in two different ways, demonstrating flexibility while maintaining accuracy. The materials also prompt students to discuss “How does using the perimeter of the base help find the lateral surface area efficiently?”

In the “On Track” activity for lesson 5.1, students write quadratic equations in vertex form from two random points. The materials give students opportunities to verify their equation by calculating where a third point (the reflected point) should go and making a graph to see if the three points form a “U” shape. This activity provides opportunities to practice accurate mathematical procedures.

The materials also provide continued opportunities for students to apply the efficient, flexible, and accurate procedures independently after the lesson through practice activities, such as “Practice on Your Own,” “Practice Plus,” and Waggle. For example, in lesson 7.5, students are encouraged to select a variety of tools to complete the square. The activity states, “Show using a diagram, algebra tiles, a table, or other representation why Jun’s solution is incorrect.” The materials reinforce flexibility by allowing students to choose their own tool and to focus on accuracy as they correct a mathematical error.

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 opportunities for students to evaluate their processes for efficiency, flexibility, and accuracy. For example, in module 1, lesson 9, students write and solve a linear model to determine the amounts saved after 15 weeks. Activities such as “Explain why your answer in part C makes sense” require students to evaluate the accuracy of their solution. Questions such as “How effective was your strategy? What might you do differently?” require students to evaluate their process for efficiency and flexibility.

Lesson 3.2, task 2 asks, “How is using a graphing calculator or other technology to generate a line of best fit different from drawing a line of fit by hand on a scatterplot? Explain what feels more straightforward or more challenging about each method and why.” This question requires students to compare multiple methods for generating a line of best fit, demonstrate flexibility, and reflect on the accuracy and efficiency of each method.

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 lesson 3.2, students first use a scatterplot to make a prediction by hand, drawing and writing a trend line. The lesson tasks introduce linear regression methods using technology. In the “Spark your Learning Review” activity at the end of the lesson, students revisit the opening problem and make another prediction using technology. Students answer the question “What changes when you use technology to estimate the 2-mile time?” This question encourages students to think about how technology provides a more efficient and accurate prediction.

Additionally, in lesson 7.2, the Teacher’s Guide contains embedded supports that help educators guide students from earlier solution methods toward choosing the most efficient strategy (completing the square). Discussion prompts, questioning strategies, and educator facilitation notes encourage students to compare multiple methods and determine the most effective approach based on the structure of the quadratic equation.

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 10, guidance states, “Conceptually, students will understand that expressions with radicals and exponents can be rewritten in equivalent forms. They will learn why recognizing perfect squares and quotients under a root, and applying the laws of exponents, makes simplifying valid and efficient.” To strengthen their conceptual understanding, students learn to simplify radical expressions and algebraic expressions involving exponents.

Additionally, in module 10, the Teacher’s Guide states, “Conceptually, students will understand that expressions with radicals and exponents can be rewritten in equivalent forms. They will learn why recognizing perfect squares and quotients under a root, and applying the laws of exponents, makes simplifying valid and efficient.” To strengthen their conceptual understanding, students learn to simplify radical expressions and algebraic expressions involving exponents.

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, module 2, lesson 6, task 4 requires students to graph a system of equations using technology to estimate the solution to a real-world problem. The task tells students, “Verify that the solution from your graph is correct using the equations,” connecting the model’s intersection to the algebraic representations.

Additionally, in lesson 9.4, task 1 encourages students to use algebra tiles to expand binomials. Task 2 encourages students to use horizontal and vertical formats to organize their work when multiplying polynomials of degrees one and two. The progression of the tasks helps students develop a connection between the manipulative and the algebraic 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 9.14, students organize polynomial expressions using algebra tiles, create symbolic models using visual organization methods, and define relationships among like terms. Students also explain how representational methods support the abstract algorithms used to perform polynomial operations. Discussion prompts and written explanations, such as “Which expressions could be expanded faster by recognizing a pattern, and which are better with distribution?” require students to justify the abstract connections they make.

The materials also support students in creating, defining, and connecting representational models to abstract concepts. For example, in lesson 3.1, task 3, students record their own data and create a scatterplot to make connections between the number of cups stacked and the stack’s height. Students use their model to fit a line to their data and make predictions. The materials say, “Explain how you used your line of fit to make your estimate and prediction.” During the “Turn and Talk,” students make connections between the models and abstract concepts through the following prompt: “How do your table, scatterplot, line of fit, and equation all show the same relationship? Explain what each representation helped you see.”

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 1, lesson 1, students use a graph to develop precise language for discrete functions, domain, and range. The lesson explains, “When a function consists of a set of discrete values, however, it is often easier to explicitly show the values using set notation,” and then it asks students to determine whether the graphed function is “continuous or discrete” and write its domain and range using set notation. The task connects a visual representation to academic mathematical terminology and symbolic notation. Guidance also suggests using the “Collect and Display” language routine to “Display and reference examples of how the terms are used to support precise language.”

Additionally, in lesson 9.2, students use algebra tiles to model the subtraction of polynomial expressions. The manipulatives help students visualize the concept of like terms. The “Turn and Talk” routine asks, “How does using a model like algebra tiles help you combine different variables and numbers?” This question reinforces vocabulary development through concrete models and student-led discussion.

The materials also provide educator guidance through the Implementation Guide, which explains how to 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 to support the implementation and development of academic vocabulary through the language routines. For example, in lesson 5.1, the “Turn and Talk” routine includes guidance that states, “Encourage students to describe the differences by comparing the equations and graphs for linear functions and quadratic functions. Remind students of point-intercept form and point-slope form, and point them towards the shapes of their graphs.”

Additionally, in module 4, lesson 4, the educator guidance scaffolds students from everyday language to precise mathematical terminology. The materials state, “Write the word substitute on the board. Have students describe examples of when something is substituted for something else.” The guidance then advances students toward contextual mathematical use: “Have pairs of students explain to each other how to use substitution to solve a system of equations when one equation is already solved for a variable.” The guidance explicitly supports the transition from familiar meaning to precise use of substitution while solving systems of equations.

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” 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” to structure mathematical discourse. Guidance includes 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 student 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 5, lesson 2, the materials scaffold mathematical vocabulary and syntax at multiple levels through the use of sentence frames, such as “I see _____. This part is _____. The total is _____.” and “First, I find…, Next, I add…, Then, I write….,” along with a word bank containing partial product, sum, expression, and expand. Guidance states that educators should “Provide time for revising with peer feedback” and record “key phrases and visuals” for students to reference as they explain their reasoning. The lesson embeds vocabulary, syntax, discourse, peer feedback, and revision within the mathematical task.

Additionally, each module incorporates the “Stronger and Clearer Each Time” language routine, which allows students to use, hear, and refine mathematical language. The routine has students share thoughts with a partner, ask thoughtful questions, and revise their response. The materials include embedded educator guidance to support the routine. For example, guidance from lesson 9.1 states, “Remind students to ask questions of each other that focus on describing their thinking, especially related to like terms and substitution, and to then use insights from the discussion to refine their answers or reasoning.” 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 1.4, students apply the process standards as they analyze multiple representations, communicate mathematical reasoning, justify solution strategies, and write linear equations from points, graphs, tables, and verbal descriptions. Guidance specifically addresses the process standards, telling educators to “Have students make a table to help organize their mathematical ideas, listing four solutions for their equations that are reasonable in the context of the situation” when using representations.

Additionally, each “Practice on Your Own” assessment integrates the process standards by identifying questions labeled “PS.” For example, in lesson 7.4, questions require students to “communicate ideas” by solving a quadratic equation to determine how long it takes a ball to reach the bottom of the ramp and to “use precise language” when describing and correcting a mathematical error.

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 Algebra 1: “Into Math Texas intentionally make[s] mathematical connections across the grade level to help drive the scope and sequence.” It clarifies that the course “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 describes process-standard connections across modules, such as “students select tools, including technology, to fit linear, quadratic, and exponential functions to data in modules 3, 7 and 8” and “in modules 4, 7 and 11 students use precise language to justify steps for solving linear equations and inequalities, quadratic equations and literal equations.”

Additionally, the Implementation Guide provides a “Correlation by Standard” table that directly identifies where each process standard is incorporated throughout the course. For example, lessons 2.7, 11.3, and 11.4 incorporate process standard A.1.F.

The materials also include course-level “Process Standards Anchor Charts” guidance that describes how students use the process standards throughout instruction. Sample guidance includes “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 Edition includes a dedicated “Module Planning” section that describes how the Algebra 1 TEKS process standards are incorporated throughout each module and how these standards connect across the unit. For example, module 1 explains how students develop and apply the process standards throughout the unit as they write linear equations, model direct variation, write systems of equations, and represent linear inequalities. The description identifies how students repeatedly engage in mathematical problem-solving, analyze relationships among multiple representations, communicate mathematical reasoning, select appropriate tools, and justify conclusions as concepts build from lesson to lesson. The materials intentionally integrate the process standards throughout the module’s instructional sequence.

The planning pages for module 5 describe how process standards are incorporated and how they connect to the quadratic-function content across the unit. The planning pages state, “Throughout Module 5, students learn the steps of the problem-solving model (PS 1.B), and then they use all the steps together in lesson 2 to solve a problem related to writing the equation for a quadratic function in standard form and determining the domain and range in context.” The materials further explain that students “communicate ideas (PS 1.D)” about the vertex and its contextual meaning, “select tools (PS 1.C)” when rewriting quadratic functions, and communicate how graphs and inequalities represent domain and range.

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 Edition 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 1, lesson 4, the overview explicitly identifies PS A.1.E, which students will use throughout the lesson when writing linear equations from points, graphs, tables, and verbal descriptions. By presenting the process standards alongside the lesson objectives and instructional context, the materials prepare educators to integrate the mathematical practices intentionally throughout instruction.

Additionally, throughout each lesson, a “PS” appears next to specific items where the process standards are applicable. For example, in lesson 9.4, task 1 requires students to select tools to expand binomial products, as required by A.1.C.

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 that presents an authentic scenario before formal instruction and asks students to identify multiple ways to represent and solve the problem. For example, in module 4, lesson 1, students first compare two delivery plans for produce and determine when the two plans have the same cost. Students then learn formal procedures for solving multistep linear equations. They revisit the problem in the “Show your thinking” and discuss different ways to represent the situation with a partner. Rather than immediately teaching an algorithm, the lesson positions students to make sense of the mathematics through exploration, informal reasoning, and mathematical discourse before formalizing the solution process.

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 5.2, students use the problem-solving model to write a quadratic equation describing the soccer ball’s trajectory. Students analyze the problem, create a plan, solve the problem, and justify their work. Educator guidance includes prompts such as “ASK: How can you find the distance where the ball landed by using the graph?” to help students persevere through the solving process. The “Turn and Talk” activity states, “If the team increases the velocity and adjusts the angle at which the ball launches so the vertex becomes (14, 20), would a be affected? How would the domain and range be affected?” This question allows students to make sense of the mathematics related to the real-world problem.

Additionally, students have repeated opportunities to refine their mathematical thinking rather than stop at an initial response. In lesson 9.1, the educator guidance states, “Remind students to ask questions of each other that focus on describing their thinking, especially related to like terms and substitution, and to then use insights from the discussion to refine their answers or reasoning.” This supports productive perseverance by requiring students to examine their reasoning, respond to peers’ questions, apply new insights, and revise their mathematical thinking as they make sense of algebraic relationships.

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

The materials support students in understanding, explaining, and justifying that there can be multiple ways to solve mathematical problems. For example, in module 4, lesson 1, task 1, students solve a multistep linear equation using properties of equality. They justify their solution through substitution and then complete a “Show Another Way” activity in which they solve the same equation without using the distributive property. The accompanying “Turn and Talk” prompt asks students to explain to a classmate what an equivalent equation is. These opportunities require students to compare solution methods, explain their mathematical reasoning, and justify why different approaches produce the same solution.

Additionally, in module 8, lesson 1, students evaluate expressions with rational exponents in two different ways. The “Turn and Talk,” which asks, “Which way was more efficient for evaluating 9^3/2, and how do you know both ways get the same result?” supports students in explaining and justifying why both methods work.

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 do, write, and discuss mathematical concepts with peers and educators. For example, in lesson 6.1, students complete three tasks involving graphing quadratic functions written in vertex form. In tasks 1 and 2, students identify and graph the key attributes of a parabola and discuss with a partner how the function compares with the parent function. Task 3 requires students to apply their knowledge in a real-world context, helping them make sense of the mathematics. The materials ask students to provide details “to explain what the x-intercepts represent in this context” through written explanations.

The materials provide additional opportunities for students to communicate mathematical understanding through writing and discussion. For example, in module 2, lesson 4, task 3, students explain their algebraic reasoning in writing, justify conclusions using mathematical evidence, and engage in collaborative discussions that compare different solution methods. Educators support mathematical discourse by encouraging students to question, defend, and evaluate mathematical arguments while using precise academic language.

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 6.1, task 3, the educator guidance states, “To support students’ speaking skills, have them pair up and share their justifications orally. Listen for specific features of the graph. Students can revise their justifications to be more specific and then share with another partner.”

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

The materials help educators guide students to share and reflect on their problem-solving approaches. For example, in module 1, lesson 9, task 1, students explain and justify their algebraic reasoning, compare different solution methods, and evaluate the efficiency of multiple approaches. Educators ask questions that prompt students to defend mathematical arguments, critique peers’ reasoning, and reflect on how their thinking has changed throughout the task before students complete independent practice.

Additionally, in lesson 11.4, the guidance encourages educators to use a variety of language routines and direct questioning prompts to help students share and reflect. Task 2 suggests the “Discussion Support” routine: “Provide time for students within groups to check in with one another to ensure everyone can explain or justify their approach to calculating the value of ℓ for each situation. Then call on a variety of students from each group so students become comfortable with preparing to share their thinking.” Later, in task 4, students provide an argument to a statement: “A classmate claims that there are two formulas for voltage because they must take square roots to solve. Why might your classmate be correct?” At the end of the lesson, students reflect on how their original approach may have changed. The materials state, “Think about how you solved the Spark Your Learning at the beginning of the first session. How would you describe the way you would write an equation to model the situation now? Explain how your understanding of literal equations helps you answer the question in the problem.”

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

The Teacher’s Edition 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 adjust support based on demonstrated understanding rather than wait until the end of instruction.

The materials direct educators to monitor student responses and provide targeted explanatory feedback throughout each lesson. For example, module 2, lesson 1 states, “As students solve the problem, monitor their responses and use the ‘Spark Discussions’ table to provide common-error support.” The guidance notes, “Students might incorrectly swap the independent and dependent variable and divide minutes by miles.” Guidance directs educators to respond by helping students “compare changes between equal time intervals and keep units consistent” and pointing out the independent and dependent variables in the table. This provides explicit feedback guidance tied to an anticipated incorrect student response.

Additionally, the Teacher’s Guide provides prompts and guidance throughout each lesson to address common errors. For example, in lesson 8.1, students evaluate zero and negative exponents. The materials highlight a common error: mistaking 3-2 for -9. Guidance provides the direct questioning prompt “What operation happens as exponents decrease?” and suggests, “Have them show two-color counters grouped and divided by 3, then restate: ‘It’s (1/3)2, not negative 9.’”