Progress Learning Precalculus (TEKS)

Evaluation for 1.1a
Materials include an alignment guide outlining the TEKS, ELPS, and concepts covered, with a rationale for learning paths across grade levels (vertical alignment) and within the same grade level (horizontal alignment) as designed in the materials.

The materials include a Precalculus Scope and Sequence that provides a chart outlining the Texas Essential Knowledge and Skills (TEKS) for each lesson. In each lesson, the “Standards” section lists the TEKS covered and the English Language Proficiency Standards (ELPS) supported in that lesson.

The Precalculus Scope and Sequence includes a “Precalculus Sequence Rationale” section that explains how each lesson connects to prior and future learning. For example, this section explains that lesson 1 “Composition of Functions” “establishes the operational foundation for decomposing complex mathematical models, which is a critical skill for understanding how different function families interact later in the course.”

Each lesson includes a “Looking Back” section that lists the aligned TEKS from Algebra I and II. For example, the “Looking Back” section of lesson 2 “Even and Odd Functions and Inverses of Functions” states that students will build on skills, such as graphing quadratic functions on the coordinate plane, which aligns with TEKS A.7A, and writing the inverse of a function using notation (e.g., f – 1(x)), which aligns with TEKS 2A.2B. The “Looking Ahead” section of the same lesson states that students will use the skills developed in this lesson in calculus when determining continuity.

Evaluation for 1.1b
Materials include an implementation guide with usage recommendations and strategies for effective educator use, such as just-in-time supports, advanced learning, or as a course.

The materials include a High School Math Implementation Guide that provides clear usage recommendations and instructional strategies for educators. The lesson materials offer multiple delivery options, such as using videos paired with cooperative learning strategies (e.g., think-pair-share) and assigning independent practice with follow-up discussion. These supports demonstrate flexibility in instructional approaches and guidance for use in various contexts, including whole-group instruction and independent learning.

The materials include a Cooperative Learning Strategy Guide with Embedded Support for ELLs document that outlines all the cooperative learning strategies included in the materials and provides grouping suggestions for different math proficiency and emergent bilingual (EB) levels.

The materials also include recommendations for adapting instruction to meet varied student needs. The lesson plans provide intervention and enrichment activities for struggling and advanced learners through additional videos and scaffolded practice opportunities. In addition, the materials provide just-in-time support by identifying common misconceptions and guiding educators on addressing them with students. For example, in lesson 5 “Polynomial Functions,” the materials advise educators to project a problem with which students are struggling and model a mistake in the problem-solving process. Through error analysis, students identify multiple approaches to the problem and justify their answers.

Evaluation for 1.1c
Materials include a TEKS correlation guide with recommended skill entry points based on diagnostic assessment results.

The materials include a Precalculus Scope and Sequence document that provides a chart outlining the TEKS for each lesson, which serves as a TEKS correlation guide. The scope and sequence paired with the “Student Diagnostic Strengths and Weaknesses Report” provide educators with recommended skill entry points based on diagnostic assessment results, which enables them to make instructional decisions aligned with student readiness.

For students who demonstrate mastery, the “Student Diagnostic Strengths and Weaknesses Report” directs educators to assign enrichment opportunities. These data-informed recommendations support flexible grouping, such as small-group instruction for intervention or enrichment, and help educators connect prerequisite skills to new content.

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

The materials include a High School Math Implementation Guide that supports lesson internalization. The “Explore” section of each lesson includes clearly labeled subsections, such as “Objective,” “Materials,” “Supports,” and “Implementation,” which guide educators in understanding lesson expectations, planning instruction, and anticipating student needs. Additional components outlined in the lesson plan, such as standards alignment, key vocabulary, and assessment guidance, provide further structure to support educator preparation and delivery.

In addition, each Teacher Guide provides protocols with corresponding guidance for unit and lesson internalization. For example, the Teacher Guide for lesson 5 “Polynomial Functions” provides lesson objectives, guiding questions, implementation strategies (including cooperative and collaborative learning strategies), and a “Guidance for Teacher” section.

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

The materials include implementation checklists that leaders can use to monitor and support educator use of the program. For example, instructional leaders can use these checklists to ensure that educators consistently administer diagnostic assessments, review “Student Strengths and Weaknesses Reports,” and group students appropriately for intervention or enrichment. The checklists can also guide leaders in observing whether educators are implementing lesson components, such as small-group instruction, TEKS-aligned tasks, and recommended program strategies.

The materials include guidance that supports leaders in planning professional development by identifying key practices, such as using diagnostic data to assign targeted skills and facilitating cooperative learning activities. This structured support allows administrators and instructional coaches to provide consistent feedback, model effective practices, and ensure fidelity of implementation.

The materials include leader-specific resources, such as training modules, webinars, and supporting documents, to guide campus and district leaders in implementing the program with fidelity. These resources provide clear guidance for onboarding new educators and supporting ongoing professional development, which ensures consistent use of the materials across classrooms. Additionally, the resources allow administrators and instructional coaches to model effective practices and support educators in applying strategies, such as differentiated instruction and data-driven planning.

Evaluation for 1.2a
If designed to be static, materials include detailed lesson plans with learning objectives, teacher and student materials, lesson components with suggested timeframes, and assessment resources aligned with the TEKS and ELPS.

The materials include detailed lesson plans that have clearly stated learning objectives at the beginning of each lesson, educator and student materials, and structured lesson components using the 5E Instructional Model (Engage, Explore, Explain, Elaborate, Evaluate). For example, the “Exponential and Logarithmic Equations” lesson gives specific pacing of approximately 5 minutes for the “Engage” section, 27 minutes for the “Explore” section, 20 minutes for the “Explain” section, 18 minutes for the “Elaborate” section, and 10 minutes for the “Evaluate” section of an 80-minute lesson. The Precalculus Scope and Sequence also provides a course-level pacing chart that has an estimated number of minutes for each 5E component across all 27 lessons.

Although each lesson plan states the TEKS and ELPS, the assessment components do not clearly align with the ELPS because the assessments primarily measure content understanding and do not require explicit evidence of language development expectations. The materials include an assessment builder that allows educators to select questions aligned with the TEKS. However, the assessment builder does not provide options to align questions with the ELPS, which limits educators’ opportunities to intentionally incorporate language development objectives.

Evaluation for 1.2b
If designed to be adaptive, materials include detailed lesson overviews with learning objectives, lesson components with suggested timeframes, and assessment resources aligned with the TEKS and ELPS.

This guidance is not applicable because the program is not designed to be adaptive.

Evaluation for 1.2c
Materials contain support for families in Spanish and English for each unit, with suggestions on supporting the progress of their student(s).

The materials include family support resources in both English and Spanish for each lesson, which ensures equitable access to instructional information. The resources provide families access to lesson slideshows and suggestions for supporting their children’s progress at home. For example, the lesson 3 “Exponential and Logarithmic Functions” “Family Support” section invites families to challenge students by finding a real-world example of exponential growth, such as compound interest and a rapidly spreading rumor.

The materials include “Welcome Letters” in both English and Spanish and a “5 Things Every Family Member Should Know about PL (English and Spanish)” resource that answers questions, such as “How can I motivate my child to reach their best?”

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

The High School Math Implementation Guide includes an “Assessment Types and Implementation Guidance” section that defines and explains the purpose of formative Learning Snapshots, Assessment Reflection Tools, Study Plan practice, pre- and post-diagnostic assessments, and summative state practice assessments. For example, Learning Snapshots are described as formative assessments that evaluate student learning of the TEKS taught in each lesson and include item rationales to inform reteach opportunities or small-group instruction.

The materials include the definitions and intended purposes for the types of instructional assessments. For example, the How-To Guides article “What types of diagnostic tests are available in Progress Learning?” mentions “State Practice Assessments,” the “Question Quick Pick” option, “Summative Tests (Teacher-Assigned),” “Summative Tests (Student Dashboard)”, and “Pre- and Post-Tests.” The article provides definitions and guidance for the use of each diagnostic test type.

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

The materials include guidance to ensure consistent and accurate administration of instructional assessments. For example, in the High School Math Implementation Guide, the Learning Snapshot guidance says “Administer either the print or digital assessment during the Evaluate phase of each lesson” and “Refer to the suggested assessment time listed in the Evaluate section of each lesson.”

The lesson plan for lesson 3 “Exponential and Logarithmic Equations” provides course-specific administration guidance. The “Evaluate” section identifies the assessment as “Learning Snapshot: Exponential and Logarithmic Equations” and provides an approximately 10-minute administration window. Educators can administer the assessment in two formats: a printable version or a digital version.

Evaluation for 2.1c
Digital assessments include printable versions and accommodations, including text-to-speech, content and language supports, and calculators, that educators can enable or disable to support individual students.

In the High School Math Implementation Guide, the “Evaluate” section explains that educators can “locate and print the Learning Snapshots from within each lesson plan file or assign a digital version from the assignment center.” The printable and digital versions share the same name, items, and answer choices.

The materials provide an online platform that allows educators to enable/disable text-to-speech for individual students. This feature is available for both the diagnostic pre- and post-tests, as well as any educator-created assessments.

Evaluation for 2.1d
Materials include diagnostic assessments with TEKS-aligned tasks or questions, including interactive item types with varying complexity levels.

The materials provide an Assessment Bank that includes pre- and post-diagnostic tests that include questions aligned with the TEKS and at varying depths of knowledge. The materials include a “Precalculus (TEKS) Diagnostic Pre-Test” that has TEKS-aligned questions across a range of cognitive demands. For example, students compute or identify answers in questions involving inverse functions, trigonometric values, and sequence terms; analyze graphs of polynomial functions to determine degree and end behavior; interpret rational functions and discontinuities; solve logarithmic, polynomial, rational, and trigonometric equations; and apply trigonometry, vectors, parametric equations, and real-world modeling contexts.

The materials also include more than two unique interactive item types. The pre-assessment item types includes multiple-choice, text-entry response boxes, graphing/plotting, multiselect, matching/table-style equivalency choices, and drag-and-drop style answer selections. In addition, the technology-enhanced question item types description indicates additional interactive formats, including bar graph, classification, constructed response, dot plot, drag-and-drop, drawing, equation editor, graphing, histogram, hot text, hotspot, inline choice, inline text entry, and label-image item types.

Evaluation for 2.1e
Materials include a variety of formative assessments with TEKS-aligned tasks or questions, including interactive item types with varying complexity levels.

The materials include an assessment builder that allows educators to build formative assessments that have multiple interactive items and varying question levels. For instance, the How-To Guides article titled, “What types of Technology Enhanced Items (TEIs) are available?” lists the following options: match table grid, drag & drop, inline text entry, inline choice, and label image with drag & drop. One of the questions is labeled “[2.F] Graph Functions 2 - Skill/Concept Which of the following graphs best represents the function?” and another question is labeled “[2.I] Key Features of Functions 3 - Strategic Thinking Analyze the graph of the polynomial function below to determine the possible degree.”

The materials include a Study Plan feature aligned with the standards taught in each lesson that provides immediate feedback when students answer incorrectly. The materials describe the Learning Snapshots in the “Evaluate” section as formative assessments aligned with lesson standards that mirror the rigor, language, and cognitive complexity of State of Texas Assessments of Academic Readiness End-of-Course assessment items.

Evaluation for 2.2a
Instructional assessments include scoring information and guidance for interpreting student performance, including rationale for each correct and incorrect response.

In the High School Math Implementation Guide, an answer key for a Learning Snapshot includes item rationales for each item in the assessment, which help create small- or whole-group reteach. Each item rationale addresses both correct and incorrect responses to support reteaching decisions.

The “Teacher Progress Report” allows educators to filter assessment data by subject, class, dates, assessment tags, and sources, then view class and individual student performance by standard using “Dot Rank” color categories. The report identifies performance bands by using colors, including pink for scores less than 65 percent, yellow for 65 to 79 percent, and green for 80 percent or greater, and allows educators to assign remediation to students performing below 80 percent.

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 High School Math Implementation Guide provides educators guidance on additional activities for students who might be struggling (interventions) and for those who have mastered the lesson concepts (enrichments). The guide provides suggested intervention and enrichment activities after each lesson, noting that “the teacher may organize students into small groups based on their needs.”

The “Quick-Click Remediation” guidance shows educators how to respond to assessment trends by selecting standards requiring additional support, choosing students, setting start and end dates, and assigning targeted remediation. Using the “Teacher Progress Report,” educators can select standards requiring additional support from the “Class Dot Rank” or “Student Dot Rank” views and assign remediation to students who need additional support.

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. Educators can view assessment results through the Results Report, including the overall assessment average, class-level filters, “Student Dot Rank” view, “Completion Status” tab, “Item Analysis” tab, “Assignment Mastery” tab, and “Student Attempts” tab. The “Item Analysis” tab shows class performance by individual question. In contrast, individual student reports identify areas of needed practice by domain or standard and provide videos and practice questions for areas of weakness. Educators can also assign remediation for students who scored 80 percent or lower on a standard.

The materials include tools to help students track their own progress and growth. The Precalculus TEKS tracker allows students to record their beginning-of-year score, the number of practice attempts, and whether they achieved a ribbon or green dot for each Precalculus TEKS. In addition, the student “Graded Work Report” allows students to view their overall scores and review performance by domain and standard. The platform also suggests additional practice based on individual performance.

Evaluation for 2.2d
If designed to be static, materials provide prompts and guidance to support educators in conducting frequent checks for understanding at key points throughout each lesson or activity.

The materials provide prompts for educators to conduct checks for understanding at key points throughout the lessons. For example, in the lesson plan for the “Exponential and Logarithmic Equations” lesson, students engage with multiple embedded prompts across the 5E Instructional Model, including a “Two Truths and a Lie” activity during the “Engage” section, think-pair-share prompts on slides 5–8 and 11–12, “Sage and Scribe” prompts on slides 9–10, “Discuss and Do” prompts on slides 13–14, video questions during the “Explain” section, platform practice during the “Elaborate” section, and a Learning Snapshot during the “Evaluate” section. The lesson also includes a “3-2-1 Reflection” activity that asks students to name three things discussed, two new or interesting things, and one remaining question. Together, these features provide both prompts for checking understanding and guidance for educators on how to use student responses during instruction.

Using the 5-E Instructional Model, all lesson plans include frequent checks for understanding throughout the lessons and guidance for educators. For example, quick write or draw activities help students recall prior knowledge and include an “Instructions for Teacher” section with guidance on administration.

Evaluation for 2.2e
If designed to be adaptive, materials provide frequent checks for understanding at key points throughout each lesson or activity.

This guidance is not applicable because the program is not designed to be adaptive.

Evaluation for 3.1a
Materials include explicit educator guidance for lessons or activities scaffolded for students who have not yet reached proficiency in prerequisite or grade-level concepts and skills.

The High School Math Implementation Guide includes explicit educator guidance for lessons or activities scaffolded for students who have not yet reached proficiency in prerequisite or grade-level concepts and skills. The guide states that intervention videos—which may come from below-grade-level or on-grade-level resources—include two or three questions for students to work through to reinforce key concepts and promote discussion. For example, in lesson 7 “Polynomial Equations and Inequalities,” the educator can assign the Algebra II videos on “Quadratic Inequalities” and “Solving Quadratic Equations” for struggling learners. The materials direct educators to organize students into small groups based on their needs to complete the appropriate set of activities.

Each lesson has an “Evaluate” section that includes a Learning Snapshot and an optional Snapshot Reflection Tool, which asks students to describe their confidence level on the topic discussed and the types of problems they did well on and the types they struggled with. These questions allow the educator to track trends and provide additional support and extensions tailored to students’ needs. The materials offer support and extensions in the form of videos.

Evaluation for 3.1b
Materials include explicit educator guidance for language supports, including pre-teaching and embedded supports for developing academic vocabulary and unfamiliar references in text.

The High School Math Implementation Guide includes embedded supports for developing academic vocabulary and unfamiliar references in text. The guide provides strategies to scaffold, support, and extend academic vocabulary, including vocabulary scavenger hunts, structured student talk routines, tiered vocabulary scaffolds, peer vocabulary exchanges, extension prompts, cognate callouts, and multilingual word walls or anchor charts.

The “Engage” section of each lesson uses the Accessing Prior Knowledge (APK) strategy as embedded support for developing academic vocabulary and supporting comprehension of unfamiliar references. The materials provide explicit guidance on grouping strategies, question prompts to probe student thinking, directions for students working in groups, and linguistic accommodations, including sentence starters differentiated by language proficiency level. For example, in lesson 2 “Even and Odd Functions and Inverses of Functions,” the APK strategy is a think-pair-share routine. The strategy guides educators to provide independent think time, during which students answer a question and reflect on how to explain their problem-solving process and verify their answers. Then, students form cooperative pairs in which they take turns discussing their answers and problem-solving processes. Finally, pairs of students share what they discussed with the whole class. However, the materials do not include explicit educator guidance on pre-teaching to develop academic vocabulary.

Evaluation for 3.1c
Materials include explicit educator guidance for enrichment and extension activities for students who have demonstrated proficiency in grade-level and above grade-level content and skills.

The High School Math Implementation Guide includes explicit educator guidance for enrichment and extension activities for students who have demonstrated proficiency in grade-level and above-grade-level content and skills. The guide states that each lesson includes videos with two or three questions for students to work through to reinforce key concepts and promote discussion. For example, educators can assign the AP calculus video titled “Instantaneous Velocity” to advanced learners. Educators can organize students into small groups based on their needs to complete the appropriate intervention or enrichment activities.

In the lesson on “Exponential and Logarithmic Equations,” the “Additional Activities for Intervention and Enrichment” section identifies an advanced learner activity titled “Solving Logarithmic Equations Graphically.” The lesson also guides educators to extend student thinking by asking students to explain how they solved problems, consider alternate approaches, justify their reasoning, and share multiple solution methods.

Evaluation for 3.1d
Digital materials include accommodations, including text-to-speech, content and language supports, and calculators that educators can enable or disable to support individual students.

The How-To Guides article “What accommodations are available in Progress Learning?” states that the materials include text-to-speech supports that educators can enable or disable to support individual students. The materials show that educators can set individual student language supports to English Default, Spanish Default, or English Only. The materials also provide Spanish translation options, Spanish video transcripts, and accessibility tools, such as color contrast, font size, zoom, highlighting, response masking, drawing tools, sticky notes, and line reader. However, the materials do not provide the ability to turn on content and language supports for students.

The materials also include a section on calculator accessibility that educators can enable or disable for individual students during assessments. Educators can select one of three types of calculators (four-function, scientific, and graphing) that are powered by Desmos to include with an assessment. However, the materials do not provide the ability to turn on content and language supports for students.

Evaluation for 3.1e
Materials include educator guidance on offering options and supports for students to demonstrate understanding of mathematical concepts in various ways, such as perform, express, and represent.

The High School Math Implementation Guide provides educators guidance on various types of exploration activities that require students to demonstrate understanding of mathematical concepts in different ways. For example, some activities instruct students to engage in academic discourse in “Discuss and Do” activities, to show their problem-solving strategies step-by-step in “Show What You Know!” activities, and to make comparisons using diagrams in “Alike and Different” activities. Additionally, the High School Math Implementation Guide says, “The Implementation section of the Explore Teacher Guide includes a step-by-step guide that directly correlates to the sequence and content of the Slides presentation. It includes important cues for when to pass out specified materials, which cooperative learning strategies to use, and identifies key moments in the lesson for when to listen and check for student understanding.”

The lessons include multiple opportunities for students to demonstrate understanding through discussion, written work, technology-based practice, reflection, and mathematical representation. Students use think-pair-share routines, “Sage and Scribe” activities, and “Discuss and Do” activities to write and solve exponential and logarithmic equations, explain solution processes, compare approaches, and justify their reasoning.

Evaluation for 3.2a
Materials include explicit (direct) prompts and guidance for educators to build knowledge by activating prior knowledge, anchoring big ideas, and highlighting and connecting key patterns, features, and relationships through multiple means of representation.

The “Engage” section of each lesson includes explicit prompts and guidance for educators to build knowledge by activating prior knowledge and anchoring big ideas. The High School Math Implementation Guide states that the “Engage” phase is when educators “activate and gain an understanding of their students’ prior knowledge.” The “Engage” section includes questions that are vertically aligned with prior-grade-level standards. For example, the “Rational Functions” lesson directs educators to “Activate prior knowledge of 2A.6.G using the specified APK structure” through a “Two Truths and a Lie” activity. The lesson also provides educator steps, potential student questions, and suggested feedback to help students connect prior work to transformations of rational functions. The Teacher Guide then anchors the lesson’s big ideas through guiding questions, such as “How do transformations that use multiplication change the graph of a rational function? Transformations that use addition?” and “How can you determine if a rational function has a horizontal asymptote, an oblique asymptote, or a hole?”

In Lesson 5: Polynomial Functions, the 'Engage' section has an application problem and graphing technology to highlight and connect key features through multiple representations. In Lesson 7: Polynomial Equations and Inequalities, the 'Engage' section prompts students to compare and contrast a quadratic equation with a quadratic inequality. Educators use a “Brain Dump” activity to identify different ways to solve polynomial equations, such as factoring, division, and technology, before applying the same methods to solve higher-order polynomial equations. Together, these examples demonstrate educator prompts and guidance for activating prior knowledge, anchoring big ideas, and highlighting and connecting key patterns, features, and relationships through multiple means of representation.

Evaluation for 3.2b
If designed to be static, materials include educator guidance for effective lesson delivery and facilitation using various instructional approaches.

The “Implementation” section of each lesson plan includes educator guidance to support effective lesson delivery and facilitation using various instructional approaches. The “Explain” section directs educators to use cooperative learning strategies, such as think-pair-share, when discussing video content and to use sentence stems to support academic vocabulary development.

The lessons include educator guidance for more than two instructional approaches. For example, the lessons direct educators to facilitate multiple cooperative learning structures, including “Odd One Out,” think-pair-share, “Rally Round/Rally Robin,” “Discuss and Do,” and “Finger Vote.” The lessons also include educator-led modeling, student discussion, independent practice, digital platform assignments, videos with questions, real-world application problems, and reflection using a 3-2-1 tool. The Teacher Guide gives step-by-step facilitation notes, including when to display questions, provide discussion time, have students justify responses, clarify misconceptions, and model problem-solving strategies. For example, the lessons direct educators to use think-pair-share routines for video questions and academic vocabulary sentence stems, then use practice problems in the platform, circulate during student work, ask reflection questions, identify common mistakes, and model corrections.

Evaluation for 3.2c
Materials include multi-tiered intervention methods for various types of practice and structures and educator guidance to support effective implementation.

The High School Math Implementation Guide provides intervention methods for multiple practice types. Students can receive support through intervention videos with accompanying questions, Study Plan practice, educator-created assignments, Learning Snapshots reflection, and reteach opportunities based on item rationales. The guide states that intervention videos may come from below-grade or on-grade-level resources and include questions for students to work through. The guide also notes that educators can gather and analyze student data as students engage with the content.

The “Additional Activities for Intervention and Enrichment” section of lesson 14 identifies a specific intervention video for struggling learners: “Precalculus Video: Graphs of Basic Trig Functions.” The lesson also includes Study Plan practice, educator-selected assignments, a Learning Snapshots assessment, Snapshot Rationales, and an optional reflection tool to help students identify areas needing more practice.

Evaluation for 3.2d
Materials include enrichment and extension methods that support various forms of engagement, and guidance to support educators in effective implementation.

The High School Math Implementation Guide provides guidance on implementing enrichment and extension methods effectively. The lesson-specific Teacher Guides provide directions for assigning enrichment activities, organizing students, facilitating cooperative learning structures, using reflection tools, asking probing questions, and addressing misconceptions through suggested educator responses.

The Teacher Guide for lesson 14 “Inverse Trigonometric Functions” contains directions for several cooperative learning strategies to support on-level and advanced students. For example, educators group students and use the SPARK strategy at the end of each section of the lesson to help students process and practice that section’s content before moving on. SPARK stands for “Solve-Pass-Agree-Repeat-Keep Going.” These components provide opportunities for individual reflection and work, analysis of other students’ solution steps and answers, possible error identification, and explanations or justifications using informal and academic language.

Evaluation for 3.2e
Materials include prompts and guidance to support educators in providing timely feedback during lesson delivery.

The High School Math Implementation Guide includes prompts and guidance to help educators provide timely feedback during lesson delivery. The guide explains that when students miss items in their Study Plans, the platform provides immediate text-based feedback to guide students through the problem-solving process.

The lesson plans provide lesson-specific prompts and guidance to help educators give timely feedback during lesson delivery. For example, lesson 4 “Exponential and Logarithmic Equations” provides educators potential student questions and feedback responses, such as how to start the exponential decay problem and how to clarify the misuse of the quotient rule. During the “Explore” and “Elaborate” sections, the lesson directs educators to ask students questions, such as “How did you solve this problem?” “Can you think of any other ways to approach the problem?” and “What is something you could say or provide to convince the class that your approach is valid?” The lesson also directs educators to identify common mistakes, project a problem students are struggling with, model a mistake, and have students identify and correct it.

Evaluation for 3.3a
If designed to be static, materials include educator guidance on providing and incorporating linguistic accommodations for all 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 Cooperative Learning Strategy Guide with Embedded Support for ELLs outlines all the cooperative learning strategies used in the program, explains their purposes, offers grouping suggestions for different math proficiency and EB levels, and provides instructions and guidance for educators. The guide also includes directions for students and linguistic accommodations for the five EB proficiency levels as defined by the ELPS. The “Linguistic Accommodations for Language Proficiency Levels” section gives guidance and prompts for Pre-Production, Beginning, Intermediate, High Intermediate, and Advanced students.

The materials include educator guidance for incorporating linguistic accommodations across ELPS proficiency levels in the lessons. The “Inverse Trigonometric Functions” lesson includes ELPS-aligned language objectives that require students to speak using content-area vocabulary and to narrate, describe, explain, justify, discuss, elaborate, or evaluate orally with increasing specificity and detail. The lesson directs educators to use embedded cooperative learning strategies, including think-pair-share, “Discuss and Do,” and SPARK, and identifies educator guidance for implementing the strategies in the appendices.

Evaluation for 3.3b
If designed to be adaptive, materials include embedded linguistic accommodations for all 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.

This guidance is not applicable to the program because it is not designed to be adaptive.

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

The Cooperative Learning Strategy Guide with Embedded Support for ELLs outlines all cooperative learning strategies included in the materials. Each strategy description featured in the guide includes the strategy’s purpose, grouping suggestions for different mathematics proficiency and EB levels, educator and student directions, and linguistic accommodations aligned with the five EB proficiency levels. For example, the “IQ Slapdown” activity suggests grouping a Pre-Production level student with a High Intermediate level buddy and then pairing that pair with non-EB students. The linguistic accommodations for this activity include allowing Pre-Production level students to point to the answer in each round as their partner explains the answer. The materials provide increasingly more-complex sentence stems for Beginning, Intermediate, High Intermediate, and Advanced level students.

Furthermore, each lesson begins with an APK activity. The materials include an appendix that explains each APK activity, each activity’s intended purpose, grouping suggestions for different mathematics proficiency and EB levels, educator and student directions, and linguistic accommodations aligned with the five EB proficiency levels. For example, lesson 6 “Binomial Theorem” uses the APK structure for a think-pair-share activity. The appendix also suggests grouping a Pre-Production level student with a High Intermediate level student or a non-EB student who speaks the EB student’s native language. The linguistic accommodations for this activity include allowing Pre-Production level students to use visual cues and point to images or models and asking a group member to explain their reasoning. The materials provide increasingly more-complex sentence stems for Beginning, Intermediate, High Intermediate, and Advanced level students.

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

Each lesson in the materials includes language objectives requiring students to use content-area vocabulary and to explain, justify, discuss, elaborate, respond orally, and write with supporting details and evidence. Each lesson also identifies lesson vocabulary, such as arccos(x), arcsin(x), arctan(x), and inverse trigonometric functions. The lesson embeds think-pair-share, “Discuss and Do,” SPARK, and 3-2-1 reflection opportunities, including sentence stems for academic vocabulary development and written reflection prompts. Additionally, the Cooperative Learning Strategy Guide with Embedded Support for ELLs document provides EB-specific supports, such as word banks, sentence frames, completed/narrated examples, visual cues, partner discussion, and written recording on handouts.

Lesson 2: “Even and Odd Functions and Inverses of Functions” includes embedded guidance to support emergent bilingual students in building background knowledge through oral and written discourse. Students participate in a think-pair-share activity in which they activate prior knowledge of 2A.2(B). However, the materials do not include guidance for cross-linguistic connections through either oral or written discourse.

Evaluation for 3.3e
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 throughout learning pathways (including instructional assessments) require students to demonstrate depth of understanding aligned to the TEKS.

As outlined in the High School Math Implementation Guide, the materials structure each lesson around the 5E Instructional Model, which provides opportunities for students to practice throughout the lesson and demonstrate their understanding. For example, in the “Explore” section, students complete correlating activities aligned with the instructional slides that require students to “Show What You Know,” which are open-ended tasks requiring students to show their work. Additionally, each lesson includes assessments in the “Elaborate” and “Evaluate” sections. During the “Elaborate” phase, students “apply what they’ve learned and develop a deeper understanding. This phase allows students to solidify their knowledge before being assessed.”

The materials include instructional assessments throughout the learning pathway that require students to demonstrate depth of understanding aligned with the TEKS. For example, the “Inverse Trigonometric Functions” lesson includes an “Evaluate” section with an “Inverse Trigonometric Functions Learning Snapshot,” which is available as a printable or digital assessment, and an optional Learning Snapshot Reflection. These assessments support the instructional assessment part of the guidance because the assessments are tied to the same TEKS-aligned lesson objectives and require students to show understanding of inverse trigonometric functions, key features, domain limitations, and discontinuities.

Evaluation for 4.1b
Questions and tasks, including enrichment and extension materials, increase in rigor and complexity, leading to grade-level and above grade-level proficiency in the mathematics TEKS.

The materials include questions and tasks that increase in rigor and complexity, leading to grade-level proficiency in the mathematics TEKS. For example, in unit 8 “Rational Functions,” students begin by graphing rational functions and transformations, then analyze the graphs to identify key features, such as domain, range, intercepts, asymptotes, end behavior, and intervals of increase or decrease. Students also examine rational functions around discontinuities by determining the type of discontinuity and describing the left-sided and right-sided behavior of the graph. In the “Elaborate” sections of the lessons, students explain their problem-solving process, compare alternate solution methods, justify their reasoning, identify common errors, and correct mistakes. The lesson plans show above-grade-level concepts in “Looking Ahead” sections, such as graphing rational functions and their transformations and analyzing key features and end behavior that may be encountered in calculus.

The materials include enrichment and extension materials that increase in rigor and complexity, leading to above-grade-level proficiency in the mathematics TEKS. In unit 8 “Rational Functions,” the materials explicitly include an “Additional Activities for Intervention and Enrichment section.” The materials direct advanced students to an AP calculus AB video on limits and asymptotes, which extends students’ work with rational functions beyond grade-level precalculus expectations. This enrichment activity builds on students’ grade-level analysis of rational functions, asymptotes, discontinuities, and end behavior by connecting those concepts to above-grade-level calculus content.

Evaluation for 4.2a
Materials demonstrate coherence across concepts horizontally within the grade level by connecting patterns, big ideas, and relationships.

In the Precalculus Scope and Sequence, the “Precalculus Sequence Rationale” section explains how the materials demonstrate coherence across concepts horizontally within the grade level by connecting patterns, big ideas, and relationships. Lesson 1 begins with the critical skill of decomposing complex mathematical models before moving on to mastering inverses. By lesson 3, students algebraically manipulate different functions after understanding their growth and boundaries. Lesson 1 is a prerequisite for verifying inverses, which lesson 3 then extends to domain and range constraints.

Lesson 3: “Exponential and Logarithmic Functions” reinforces key concepts, including function behavior, transformations, inverses, rates of change, and mathematical modeling. Students examine how to use exponential and logarithmic functions to represent and solve real-world problems involving population growth, compound interest, radioactive decay, and other applications. By exploring these relationships across multiple representations, students deepen their understanding of how different function types are connected and how changes in one representation affect another. As a result, students are better prepared to make connections among algebraic, graphical, and analytical concepts throughout the course.

Evaluation for 4.2b
Materials demonstrate coherence vertically across concepts and grade bands, including connections from grades 3–12, by connecting patterns, big ideas, and relationships.

The “Vertical Alignment” section in each lesson demonstrates coherence vertically across concepts and grade bands by connecting patterns, big ideas, and relationships. For example, lesson 5 “Polynomial Functions” builds on Algebra I skills of determining the domain and range of quadratic functions and representing them using inequalities. These experiences extend students’ understanding of domain and range and prepare students for advanced study of function behavior in calculus, in which students examine limits, continuity, instantaneous rates of change, and optimization problems involving polynomial functions.

Lesson 10 demonstrates coherence vertically across concepts and grade bands by connecting patterns, big ideas, and relationships. The lesson states that students “graph power functions and their transformations” and analyze “the key features and end behavior of power functions.” The “Looking Back” section refers to graphing and transforming quadratic functions in Algebra I and Algebra II, and the “Looking Ahead” section connects to calculus by studying integration symmetry or root-finding through analysis of the key features of power functions.

Evaluation for 4.2c
Materials demonstrate coherence across lessons or activities by connecting students’ prior knowledge of concepts and procedures to the mathematical concepts to be learned in the current grade level and future grade levels.

The APK activities and “Vertical Alignment” sections demonstrate coherence across lessons by connecting concepts and procedures from prior learning to the current grade level. For example, in lesson 3 “Exponential and Logarithmic Functions,” the APK activity requires students to compare and contrast similar graphs (i.e., linear relationships) to support students’ current conceptual and procedural knowledge of exponential and logarithmic functions and key attributes. Then, the “Vertical Alignment” section connects these concepts and procedures to analyze exponential and logarithmic functions in calculus.

In the “Exponential and Logarithmic Functions” lesson, the “Vertical Alignment” section identifies prior learning from Algebra I and Algebra II, including graphing exponential functions; identifying key features, such as y-intercepts and asymptotes; describing inverse relationships between exponential and logarithmic functions; and analyzing transformations of exponential and logarithmic functions. The lesson then uses those prior concepts and procedures in the current lesson as students graph exponential and logarithmic functions, analyze transformations, and determine key features and end behavior. The same lesson also connects current learning to future learning by noting that exponential and logarithmic functions may be encountered in calculus when students move from solving for x to analyzing rates of change.

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

The assessments and assignments provide spaced retrieval opportunities with previously learned skills and concepts across learning pathways. The features allow educators to create assessments by handpicking each question. Additionally, educators can use the “Question Quick Pick” feature or create an assessment by standards.

The materials provide spaced retrieval opportunities with previously learned skills. Lesson 15 “Trigonometric Equations” reviews student expectation G.9(A), for which students must “determine the lengths of sides and measures of angles in a right triangle by applying the trigonometric ratios sine, cosine, and tangent to solve problems.” These skills and concepts are essential for solving trigonometric problems in precalculus, as outlined in student expectation P.5(N): “Generate and solve trigonometric equations in mathematical and real-world problems.” The lesson then continues with “Explore” activities, videos, platform practice, and a Learning Snapshot, which provide students multiple opportunities to retrieve and apply those skills throughout the lesson pathway.

The materials provide spaced retrieval opportunities with previously learned concepts. Lesson 3: Exponential and Logarithmic Functions also retrieves previously learned concepts. The “Vertical Alignment” section identifies prior conceptual knowledge about exponential functions, logarithmic/exponential inverse relationships, and exponential/logarithmic models from earlier courses. Students revisit those concepts in the APK activity by solving exponential and logarithmic problems and then extend those concepts to current work on properties of logarithms and exponential/logarithmic equations.

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

The materials provide interleaved practice opportunities with previously learned skills and concepts across learning pathways in the main lesson plan guidance. For example, using the Assessments and Assignments features, educators can create assessments and assignments on previously learned skills and concepts.

The lesson plans include APK activities, current lesson practice, Learning Snapshots, and reflection tools, which shows mixed practice that combines prior and current concepts across learning pathways. For example, Lesson 2 “Even and Odd Functions and Inverses of Functions” practices prior skills of graphing, analyzing the graphs, and transformations of different functions—linear, quadratic, square root, and their inverses—It then moves to the current content on determining whether the function is odd or even.

Evaluation for 5.1a
Questions and tasks provide opportunities for students to interpret, analyze, and evaluate mathematical concepts and complex, real-world situations.

The materials provide opportunities for students to interpret mathematical concepts and complex, real-world situations. In lesson 3 “Exponential and Logarithmic Functions,” students work with real-world scenarios involving bacterial growth, air freshener release, tournament rounds, factory processing, cloud storage, and cybersecurity protocols. Students must connect each scenario to an appropriate exponential or logarithmic function or transformation, which requires interpreting the mathematical meaning of the situation.

Lesson 3 also provides opportunities for students to analyze mathematical concepts and complex, real-world situations. In this lesson, students analyze the end behavior of exponential functions using infinity notation, and the lesson objectives include graphing exponential and logarithmic functions and analyzing key features and end behavior.

Additionally, lesson 3 provides opportunities for students to evaluate mathematical concepts and complex, real-world situations. The lesson asks students to select the graph and function that match a given real-world scenario, which requires students to evaluate multiple function representations and determine which one best models the situation.

Evaluation for 5.1b
Questions and tasks provide opportunities for students to create concrete models and representations of mathematical situations.

The materials include questions and tasks that provide opportunities for students to create representations of mathematical situations. For example, lesson 25 “Conics” shows pictures of three-dimensional double-napped models as stimuli for students to describe the different types of conics. Students identify the conics represented by images of real-world objects, such as architectural structures, satellites, and flashlights. Students represent the different types of conics graphically and symbolically. However, the materials do not ask students to create concrete models of mathematical situations.

Additionally, lesson 5 “Polynomial Functions” focuses mainly on having students compare different types of polynomial functions and how their attributes change during transformations. The lesson prompts students to graph various polynomial functions and analyze situations that they could model. However, there are no prompts or tasks in which students create concrete models. The “Explore” section provides students a real-world scenario about a company designing storage cubes. However, the section does not task students with creating a concrete model of the mathematical situation. Instead, students describe the end behavior of the function that represents the volume of the storage space.

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

Lesson 12 “Piecewise/Step Functions” has questions and tasks that provide opportunities for students to apply conceptual understanding to new problem situations and contexts. For example, students graph and discuss the key features of linear, quadratic, and absolute value functions. Next, students graph piecewise functions and discuss key features, such as slope, x- and y-intercepts, domain, and range. Students show their conceptual understanding when asked, “Is it possible for a piecewise function or a step function to have a domain of all real numbers? Justify your reasoning.”

During guided instruction, the materials provide opportunities for students to apply their conceptual understanding to new problem situations and contexts. For example, in the educator slideshow for Lesson 3 “Exponential and Logarithmic Functions,” students read different scenarios, such as “Scientists studying an unknown substance discovered on the moon whose culture doubles every hour” and “The number of milliliters of air freshener released from a dispenser now doubles every twenty minutes instead of every hour,” to which they must apply the characteristics and graphs of exponentials functions.

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

The lesson plans include repeated grade-level practice opportunities through platform-based practice problems in the Study Plan feature. For example, the “Exponential and Logarithmic Equations” lesson directs students to complete practice problems aligned with P.5(G), P.5(H), and P.5(I), including logarithmic expressions, logarithmic equations, and exponential equations. The “Rational Functions” and “Inverse Trigonometric Functions” lessons similarly include platform practice aligned with grade-level function skills and provide Learning Snapshots to assess student performance.

The “Think or Swim” activity provides opportunities for students to build automaticity and fluency with grade-level standards in a competitive setting. Educators select questions aligned with the TEKS, and students take turns answering the revealed questions in a timed setting. The timed format of “Think or Swim” builds automaticity by requiring students to retrieve facts quickly under time pressure, and the repeated Study Plan practice across lessons builds broader fluency with grade-level procedures.

Evaluation for 5.2b
Materials provide opportunities for students to practice the application of efficient, flexible, and accurate mathematical procedures throughout learning pathways.

The materials provide opportunities for students to practice efficient procedures through structured tasks that ask them to identify patterns and apply those procedures. In Lesson 3: Exponential and Logarithmic Functions, students work with transformations of exponential and logarithmic functions, compare function formats, identify patterns, and use those patterns to determine vertical stretches, horizontal compressions, and translations.

The materials provide opportunities for flexible procedural practice across the learning pathway. The Precalculus Scope and Sequence shows that later lessons require students to apply previously learned procedures in new settings, such as using algebraic solving techniques from earlier exponential/logarithmic and polynomial lessons when solving trigonometric equations and using identities to transform complex trigonometric equations into simpler forms.


Additionally, the materials provide opportunities for students to practice accurate mathematical procedures throughout learning pathways. In the “Explain” section of Lesson 16 “Sinusoidal Functions,” students complete a video-based quiz on modeling real-world cycles with sinusoidal functions. After students complete the quiz, educators review the questions and answers. Students complete Study Plan questions in the platform during the “Elaborate” section. While students are working, educators identify questions for discussion and/or review.

Evaluation for 5.2c
Materials provide opportunities for students to evaluate mathematical representations, models, strategies, and solutions for efficiency, flexibility, and accuracy throughout learning pathways.

The materials provide opportunities for students to evaluate the accuracy of mathematical representations, models, strategies, and solutions throughout learning pathways. Students justify their approaches, provide evidence that answers are valid, identify common mistakes, and correct errors in the problem-solving process. In the “Exponential and Logarithmic Equations” lesson, students determine which statements are true or false, explain why a logarithmic property is applied incorrectly, and verify correct answers during discussion.

The materials provide opportunities for students to evaluate mathematical representations, models, strategies, and solutions for flexibility throughout learning pathways. Students move between graphical, algebraic, and contextual representations of functions, including exponential, logarithmic, polynomial, rational, and power functions. In the “Rational Functions” lesson, students analyze transformations, key features, asymptotes, discontinuities, and left- and right-sided behavior, which supports flexible evaluation of functions across equations, graphs, and written descriptions.

Lesson 22 “Vectors” provides an opportunity for students to evaluate mathematical representations, models, strategies, and solutions for efficiency throughout learning pathways. For instance, in the “Elaborate” section, students work in groups and discuss their problem-solving processes. With their group members, students answer the following questions: “How did you solve this problem? Can you think of any other ways to approach the problem? What is something you could say or provide to convince the class that your approach is valid?”

Evaluation for 5.2d
Materials contain guidance to support students in selecting the most efficient approaches when solving mathematics problems.

Lesson 18 “Trigonometric Identities” guides students in selecting increasingly efficient approaches to solving mathematical problems. For instance, the “Elaborate” section guides educators to “identify and discuss common mistakes that arise. Project one problem that students are struggling with and model a mistake in the problem-solving process. Ask students to identify the mistake and how to correct it. Encourage students to share multiple ways to approach the problem and to justify their approach.” In a “Brain Dump” activity, students begin by simplifying trigonometric identities and create a chart to assist them in simplifying expressions. Educators ask, “Why are all of these identities equations?” “How can you tell when a cofunction identity or an even/odd identity will help you simplify an expression?” and “What are some strategies you can use to help you simplify expressions containing trigonometric functions?”

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

The Precalculus Scope and Sequence includes a rationale for each lesson that addresses how the materials address the conceptual and procedural emphasis of the TEKS. For example, in lesson 2 “Even and Odd Functions and Inverses of Functions,” students determine an inverse function, use multiple representations of the inverse, and describe the symmetry of the graphs of even and odd functions. Students use tables to write the inverse function by interchanging the x and y values. Students then plot the points from the table to graph both functions. Students use graphs of different functions to determine whether they are odd, even, or neither based on their attributes, which connects the graphical representation to the conceptual property of symmetry. During the Odd One Out activity, students took turns choosing a function and explaining why it is the odd one out.

The materials explicitly state how they address the conceptual and procedural emphasis of the TEKS in the Teacher Guide for each lesson. For example, in lesson 27 “The nth Term of a Series,” the learning objectives for students are to calculate the nth term and the nth partial sum of an arithmetic series in problems and to calculate the nth term of a geometric series, the nth partial sum of a geometric series, and the sum of an infinite geometric series when it exists, which are the exact verbiage of the TEKS P.5(C) and P.5(E). Students use formulas to calculate the nth term and partial sum of arithmetic and geometric series, then apply these skills to real-world applications. To determine whether a geometric series can be infinite, students first check whether the absolute value of the common ratio is less than 1. Once the value is identified, the formula is used to perform the calculation.

Evaluation for 5.3b
Questions and tasks provide opportunities for students to use concrete models, pictorial representations, and abstract models as required by the TEKS.

In lesson 3 “Exponential and Logarithmic Functions,” students graph exponential and logarithmic functions and their transformations; analyze key features, such as domain, range, intercepts, and asymptotes; and describe end behavior. This graph-based work with parent functions and their transformations gives students the opportunity to represent mathematical relationships visually, which addresses the TEKS expectation for pictorial representations.

The lesson also requires students to use function notation, equations, inequalities, interval notation, set notation, and logarithmic and exponential expressions to model and solve real-world problems. By translating situations into symbolic form, these tasks support the TEKS expectation that students use abstract models to represent and solve mathematical problems. However, the materials do not provide opportunities for students to use concrete models.

Evaluation for 5.3c
Materials include supports for students in connecting, creating, defining, and explaining concrete and representational models to abstract (symbolic/numeric/algorithmic) concepts, as required by the TEKS.

The materials include supports for students to connect, create, define, and explain representational models to abstract (symbolic/numeric/algorithmic) concepts, as required by the TEKS. In lesson 16 “Sinusoidal Functions,” students analyze graphs; identify amplitude, period, phase shift, and vertical shift; and use these characteristics to develop sinusoidal equations. The video “Modeling Real-World Cycles with Sinusoidal Functions” in the lesson effectively connects representational models to abstract concepts. For instance, example 2 shows ocean tides, how they would be represented on a graph, and the steps to solve the problem.

In various lessons, the materials support students in creating representational models when they graph functions and transformations, develop and use sinusoidal functions to model periodic situations, graph inverse trigonometric functions, graph parametric and polar equations, and use vectors to model magnitude and direction. These representations connect visual models to symbolic equations and numeric values.

In lessons 8 and 14, the materials support students in defining and explaining representational models by asking students to analyze key features of graphs, describe end behavior, identify asymptotes and discontinuities, describe left- and right-sided behavior, and explain domain limitations for inverse trigonometric functions. However, the materials do not provide supports for connecting concrete models to abstract concepts, and the materials do not provide supports for creating, defining, and explaining concrete models.

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

The 5E Instructional Model design incorporates a variety of cooperative learning strategies, such as think-pair-share, “Discuss and Do,” and SPARK, which allow students to work independently and share their problem-solving process with other students by using their academic mathematical language. For example, in the “Explore” section of lesson 17 “Applications of the Unit Circle,” educators use think-pair-share to discuss the relationship between degrees and radians. Afterward, educators transition the cooperative grouping to “Rally Round,” in which educators group students into teams of four to promote discourse and “reinforce understanding of mathematical concepts by hearing, seeing, and/or building on peer responses.” During this “Rally Round,” each student on each team takes a turn matching a rotation description to the correct angle. Students examine graphical representations of angle rotation to distinguish reference angles from the standard position of angles.

The materials provide opportunities for students to develop academic mathematical language through graph-based representations and language supports. In the “Rational Functions” lesson, students describe rational functions graphically and algebraically while using terms, such as rational function, asymptote, discontinuity, domain, range, and key features. Sentence stems and discussion routines help students connect academic vocabulary to the graphical behavior of rational functions.

Evaluation for 5.4b
Materials include embedded educator guidance to scaffold, support, and extend students’ use of academic mathematical vocabulary in context when communicating with peers and educators.

The materials provide embedded educator guidance to scaffold and support students’ use of academic vocabulary in context when communicating with peers and educators. For example, lesson 3 “Exponential and Logarithmic Functions” directs educators to have students use think-pair-share to answer video questions and complete sentence stems, such as “Some important key features of exponential and logarithmic functions include _____” and “The end behavior of functions refers to _____,” which extends students’ vocabulary use through peer discussion and whole-class review. The materials include language expectations for students to “speak using content-area vocabulary” and to “narrate, describe, explain, justify, discuss, elaborate, or evaluate” in academic discourse. The lesson also identifies vocabulary terms, such as asymptote, intercepts, range, domain, parent function, and transformations.

In the 'Explore' portion of lesson 3, educators guide students in “Rally Robin” to analyze the key features of a logarithmic function. Educators pair students and ask each member to “take turns stating answers, discuss if needed, and record the answers.” Next, educators use real-world application problems to have students identify the correct function for each scenario using a “Finger Vote” strategy. Then, educators extend students’ vocabulary use by asking students to “analyze the end behavior of the functions, then describe it with their partner.”

Evaluation for 5.4c
Materials include embedded guidance to support student application of appropriate mathematical language and academic vocabulary in discourse.

The materials include embedded guidance to support student application of appropriate mathematical language and academic vocabulary in discourse. In the “Exponential and Logarithmic Equations” lesson, students use the think-pair-share and “Discuss and Do” cooperative learning strategies. The educator guidance includes time for discussion, possible responses, and justifications. The lesson also provides academic sentence stems, such as “The three properties of logarithms are _____” and “Logarithms help me to solve exponential equations by _____,” which support students in using lesson vocabulary during mathematical discourse.

In the “Rational Functions” lesson, students use think-pair-share to answer video questions and complete sentence stems, such as “Rational functions are identified as equations by _____ and graphically by _____” and “Important key features of rational functions include _____.” The lesson further directs educators to ask students how they solved a problem, what other approaches are possible, and what they could say to convince the class that their approach is valid.

Evaluation for 5.4d
Materials include embedded guidance to facilitate mathematical conversations allowing students to hear, refine, and use math language with peers.

The materials include embedded guidance to facilitate mathematical conversations that allow students to hear mathematical language with peers. In the lesson “Exponential and Logarithmic Functions,” the “Explore” section includes multiple cooperative learning strategies, including think-pair-share, “Rally Round,” “Discuss and Do,” and “Rally Robin,” across vocabulary review, graphing, transformations, key features, and real-world applications.

In lesson 17 “Applications of the Unit Circle,” the educator lesson slideshow asks students to define and identify reference angles and to identify the quadrant in which a given angle lies and the process for determining the reference angle. Educators use a cooperative learning structure, think-pair-share, allow students to think about the problem or situation individually, explain their thinking to their partner, and share their conclusions with the whole class. Educators guide students to record their responses on their student handouts.

Evaluation for 5.4e
Materials include embedded guidance to anticipate a variety of student answers including exemplar responses to questions and tasks, including guidance to support and/or redirect inaccurate student responses.

The Teacher Guide for each lesson includes a “Common Misconceptions and Suggestions of Teacher Responses” section that provides guidance for educators to anticipate and respond to a variety of student answers. For example, in lesson 13 “Trigonometric Functions,” the Teacher Guide cautions that “Students may think that multiplication transformations change the graph vertically and addition transformations change the graph horizontally, or vice versa. Suggested Teacher Response: Multiplication or addition outside the function, such as af(x) or f(x) + d, transform f(x) vertically. Multiplication or addition inside the function, such as f(bx) or f(x − c), transforms f(x) horizontally.”

The “Explore” section of each lesson provides students lesson handouts, for which an answer key is also available that provides exemplar responses to the questions and tasks on the handouts. For example, lesson 1 “Composition of Functions” provides students several sections of questions and tasks to complete, including section IV, in which students decompose functions. Problem #8 is “Given ℎ(𝑥) = 8𝑥^4 + 5, rewrite h(x) as a composition of two or more functions.” The key provides several exemplar answers: 𝑔(𝑥) = 𝑥^4 and 𝑓(𝑢) = 8𝑢 + 5; 𝑔(𝑥) = 𝑥^2 and 𝑓(𝑢) = 8𝑢^2 + 5; and 𝑔(𝑥) = 8𝑥^4 and 𝑓(𝑢) = 𝑢 + 5.

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

The materials appropriately integrate the TEKS process standards using APK through Learning Snapshot activities. Students apply mathematics to everyday problems, which aligns with P.1(A); use representations to organize mathematical ideas, which aligns with P.1(F); and explain or justify arguments using mathematical language in written or oral communication, which aligns with P.1(G). For example, the Learning Snapshot Reflection activity for lesson 1 “Composition of Functions,” instructs students to “Choose one problem you solved correctly. Explain your problem-solving approach. How could you demonstrate that your solution is valid to someone who approached the problem in a different way?”

In addition, students apply mathematics to everyday problems, which aligns with P.1(A); use representations to organize mathematical ideas, which aligns with P.1(F); and explain or justify arguments using mathematical language in written or oral communication, which aligns with P.1(G). For example, in the student handout for lesson 8 “Rational Functions,” students must graph and analyze various rational functions to determine key attributes, including vertical, horizontal, and oblique asymptotes; holes (points of discontinuity); and end behavior.

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

The Teacher Guides describe how each lesson incorporates the process standards and connects the process standards to previous and future lessons. For example, in lesson 8 “Rational Functions,” three of the seven process standards listed for the lesson are P.1(E) Create and use representations to organize, record, and communicate mathematical ideas; P.1(D) Communicate mathematical ideas, reasoning, and their implications using multiple representations, including symbols, diagrams, graphs, and language as appropriate; and P.1(F) Analyze mathematical relationships to connect and communicate mathematical ideas. The guide also informs that “Graphing rational functions and their transformations may be encountered in conjunction with analyzing key features and end behavior in calculus as limits at infinity and slant or oblique asymptotes to describe ‘linear growth with a delay.’”

The materials describe how they connect the process standards throughout the learning pathways by explaining how each lesson builds toward later mathematical work and by connecting process standards to specific content tasks. For example, the sequence moves from composition of functions to inverse functions, exponential/logarithmic functions, polynomial equations, rational functions, and trigonometric functions. Lesson activities require students to analyze relationships, which aligns with P.1(F), and communicate mathematical ideas and use multiple representations, which aligns with P.1(D), by connecting prior learning to new content.

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

The Precalculus Scope and Sequence provides a course-level overview of the lesson sequence and includes a standards-alignment table that identifies which process standards are incorporated across the lessons. This table helps educators see how the materials address the TEKS process standards.

In addition, each lesson plan includes a “Standards” section that lists the content, process, and language standards for the lesson separately. For example, the “Exponential and Logarithmic Equations” lesson identifies process standards, such as applying mathematics to real-world problems, using a problem-solving model, selecting appropriate tools and techniques, communicating mathematical ideas, and analyzing mathematical relationships.

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

The materials provide opportunities for students to persevere through solving problems. For example, in lesson 14 “Inverse Trigonometric Functions,” students solve multistep real-world modeling problems, compare solution strategies, justify their reasoning, identify errors in sample solutions, and explain why their approach is valid. Educator prompts ask, “How did you solve this problem?” and “Can you think of any other ways to approach the problem?” to encourage persistence rather than procedural completion.

In Lesson 11 “Modeling Situations with Functions,” students demonstrate mathematical thinking by completing the think-pair-share and “Discuss and Do” activities. During these exercises, students analyze authentic scenarios (logarithmic retention, box optimization, power, rational, and exponential models) and determine which function best represents each situation before solving.

In addition, the materials provide opportunities for students to make sense of mathematics. For example, in Lesson 11 “Modeling Situations with Functions,” students make sense of mathematics by interpreting solutions in the context of a problem, such as determining the feasible domain of a box, explaining the meaning of a horizontal asymptote, and interpreting depreciation over time, which requires students to connect mathematical results to real-world situations.

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

The materials support students in understanding, explaining, and justifying that there can be multiple ways to solve problems and complete tasks. For example, in Lesson 2 “Even and Odd Functions and Inverses of Functions,” students learn that there is more than one way to represent a function’s inverse. The materials guide educators to emphasize that inverses of functions can be represented as tables, graphs, and equations. The “Discuss and Do” activity asks students to identify different ways to represent function inverses. Then, the “Sage & Scribe” activity asks students to justify their preferred method of finding the inverse of a function.

Materials support students in understanding, explaining, and justifying that there can be multiple ways to solve problems and complete tasks. For example, in Lesson 25: Conics, during the "Explore" section, students analyze different conic sections using multiple representations, including equations and graphs. In the " Explain" section, students compare methods for identifying conic characteristics and communicate their reasoning with partners through cooperative learning structures. During "Elaborate", students defend the method they selected for writing equations and identifying key features, recognizing that more than one solution strategy can lead to a correct conclusion. This lesson requires students to understand, explain, and justify multiple mathematical 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/or educators.

The materials require students to make sense of mathematics through multiple opportunities for students to do, write about, and discuss mathematics with peers and educators. For example, in the “Explore” section of Lesson 19 “Angles and the Concept of Rotation,” students do mathematics by solving problems involving angle rotation, angular velocity, and linear velocity. In the “Explain” section, students write about mathematics by recording and comparing mathematical reasoning using multiple representations, including diagrams and equations. In the “Elaborate” section, cooperative learning structures require students to discuss mathematics by explaining solution strategies, comparing approaches, and responding to educator questioning.

Additionally, in the “Explore” section of Lesson 27 “The nth Term of a Series,” students do mathematics by determining the nth term and partial sums of arithmetic and geometric series when solving application problems. In the “Explain” section, students write recursive and explicit representations and justify how the formulas relate to the series. In the “Elaborate” section, students participate in collaborative discussions comparing finite and infinite series and defend their reasoning using mathematical evidence.

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

The materials support educators in guiding students to share their problem-solving approaches, including explanations, arguments, and justifications. The Cooperative Learning Strategy Guide with Embedded Support for ELLs document includes routines, such as “Rally Coach and Player,” think-pair-share, “Discuss and Do,” “Rally Round,” “Rally Robin,” “Sage & Scribe,” and “Two Truths and a Lie,” which require students to discuss solution processes with partners or groups, explain their reasoning, present arguments when disagreements arise, and justify their answers during whole-class discussion. For example, Lesson 22 “Vectors” uses cooperative learning structures, such as “Rally Coach and Player” and “Discuss and Do,” that ask students to explain how they determine a vector’s magnitude and direction and to share the process they used to solve the problem.

In addition, the Cooperative Learning Strategy Guide with Embedded Support for ELLs document provides guidance on helping students reflect on their problem-solving approaches. The educator guidance prompts educators to ask questions, such as “Did someone else use an approach to solve the problem that was different from the approach that you chose to use?” “What argument did you give to support your viewpoint?” “What evidence do you have to support your answer?” and “How could you justify your problem-solving process to someone who disagrees?”

The materials give educators options for multiple points of student entry, including different situations, varied levels of rigor, scaffolded questions, different information in the question stem, verbal descriptions, diagrams, grid paper, and other tools. For example, in Lesson 27 “The nth Term of a Series,” the students find the nth term and nth partial sum of a series using formulas and making predictions while in cooperative learning groups. The “Cooperative Learning Strategies” section of the Lesson plan suggests that educators use the “Discuss and Do” activity in the “Explore” section to find the nth term and nth partial sum of a series. The Lesson provides multiple points of entry, such as different situations with varied levels of rigor or with scaffolded questions and different information in the question stem.

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

The materials include prompts and guidance to support educators in providing explanatory feedback based on student responses. The Teacher Guides direct educators to display questions and possible responses, verify correct answers, and clarify student questions during instruction. For example, lesson 5 “Polynomial Functions” prompts students to discuss the transformations by analyzing the graphs of four polynomial functions and asks, “Are there patterns? Are there any clues to help you remember the effects of different transformations?” The lesson guides educators to think aloud about what they notice, such as putting an additive operation with a creates a translation, whereas putting a multiplicative operation with a creates a stretch or compression.


The materials include prompts and guidance to support educators in providing explanatory feedback based on student responses and anticipated misconceptions. For example, the Teacher Guide for lesson 20 “Problem Solving with Trigonometric Ratios” provides common misconceptions and suggested responses to address errors involving angle measures, trigonometric ratios, and directional bearings. The “Discuss and Do” activity provides educators with questioning prompts that ask students to explain their reasoning, identify errors, and revise their solution strategies. This guidance supports educators in providing immediate explanatory feedback based on anticipated misconceptions rather than simply correcting answers. For example, the materials state, “Guidance for Teachers, Reflect (guiding question): What are the three types of directional bearings? Identify (misconception): Students may confuse the different types of bearings. Clarify (feedback response): a. Consider using slide 18 to make an anchor chart to post for student use, etc.”