Financial Algebra: Advanced Algebra with Financial Applications, Enhanced Package

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 an alignment guide outlining the Texas Essential Knowledge and Skills (TEKS), English Language Proficiency Standards (ELPS), and concepts covered. The Financial Algebra: Scope and Sequence with Pacing contains a chart that identifies the TEKS, the ELPS, topics taught in each chapter, and the suggested number of instructional days required for each section.

The “Explore and Explain” section of each lesson plan references skills previously taught and/or skills yet to be taught. For example, the “Skills and Strategies” of chapter 11’s lesson plan reminds educators that students encountered rational functions in chapters 2 and 9, which is foundational learning for the content in chapter 11. However, the materials do not include a rationale for learning paths across grade levels or within the same grade level.

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 Annotated Instructor’s Edition includes usage recommendations for adapting the material to meet various students’ needs. For example, the chapter opener asks students to reflect on their current wants and needs, as well as the wants and needs they anticipate having 10 years in the future. The materials suggest, “It might be more difficult to answer for their future selves. Provide examples of financial needs and wants of adults that you know.”

The Annotated Instructor’s Edition also includes differentiated instructional strategies and educator guidance for supporting varied student needs. For example, the “Class Discussion” and “Skills and Strategies” sections for chapter 11 direct educators to use collaborative grouping activities, scaffold conceptual understanding, clarify misconceptions, and connect spreadsheets to algebraic representations. Examples include grouping students into categories, such as full-time workers, military personnel, and higher education students, and providing guidance for interpreting measures of central tendency and sigma notation. In addition, the materials include a “Reality Check” section at the end of each chapter that provides alternate assessment options and activities to extend and enrich learning for advanced learners.

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

The Financial Algebra: Scope and Sequence with Pacing includes a correlation guide that aligns chapters, sections, TEKS student expectations, ELPS, and pacing information for the course. The materials include daily warm-ups that educators can use as a formative assessment to drive instruction. However, the materials do not include a diagnostic assessment, nor do the materials include recommendations on skill entry points based on district diagnostic assessment results.

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

The materials do not provide clear steps or expectations for how educators should internalize units and lessons. Instead, the materials offer general resources, such as pacing recommendations, learning objectives, key terms, warm-up activities, discussion prompts, formative checks, and instructional notes for examples and applications. These resources help educators with instruction but do not provide guidance to ensure consistent instructional practices across classrooms.

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

The Annotated Instructor’s Edition does not include resources for instructional leaders to support educators with implementing the materials. Each chapter in the Annotated Instructor’s Edition includes a pacing guide, section durations, objectives, key terms, warm-ups, class discussion prompts, “Skills and Strategies” notes, formative checks, and section application guidance, but these resources are educator-facing resources. There are no resources for instructional leaders to enhance their ability to support educators with curriculum implementation.

In addition, the materials do not provide guidance for instructional leaders on how to support educators with implementing the course materials as designed. The lesson plan shows educator-facing directions, such as asking students questions about creditworthiness, highlighting differences between lending institutions, guiding calculator use and parentheses, researching current loan rates, distributing a credit calendar, and walking around during partner or small-group work to listen for misconceptions. These directions are instructional supports for educators during lesson delivery, but the materials do not provide leader-specific resources or guidance.

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.

Although the Financial Algebra: Scope and Sequence with Pacing document lists the TEKS and ELPS addressed in each chapter, the materials do not list the TEKS and ELPS addressed in each lesson. The materials include lesson plans for each chapter that break down the learning objectives and key terms for each section. Each lesson plan also provides pacing guidance at the section level. For example, the lesson plan for chapter 1 states that section 1.1, “Discretionary and Essential Expenses” should take approximately three to five days, depending on the length of the math class. Both the educator and student editions include various assessment options, including “Check Your Understanding,” “Applications,” and “Reality Check” activities and projects. However, the assessment resources do not align with the TEKS or the ELPS.

Educator materials include the Annotated Teacher’s Edition, which provides chapter outlines that organize activities and assessments by chapter and topic. The educator materials also include PowerPoints with suggested discussion questions and supplemental activities. Student materials include a student textbook and workbook with practice problems for each section.

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 do not include communication with families. The materials help students make real-life connections. The “Really? Really!” section engages students through real-life examples that relate to chapter concepts. However, these activities are student-facing and focus on content relevance. The materials do not provide family-facing supports in Spanish or English, nor do the materials include unit-specific activities, questions, vocabulary, progress supports, or guidance that families can use to support student learning at home.

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

The materials define “Check Your Understanding” as an embedded assessment within the “Skills and Strategies” section. For example, students review a worked financial problem, such as calculating biweekly pay from an annual salary, and then complete a related “Check Your Understanding” item using new data to practice and demonstrate understanding of the concept.


The Annotated Instructor’s Edition includes a section on comprehensive assessments, defining them and their purpose. The section states, “Check Your Understanding: The Skills and Strategies sections are the heart of each chapter, teaching math concepts through detailed step-by-step examples and real-life applications. Prompts for each step are detailed in the example to demonstrate how the solution was derived.”

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

The materials include a variety of assessment options, such as projects, reports, and oral presentations, but do not provide guidance to ensure consistent and accurate administration of these assessments. The “Reality Check” projects include teaching tips, instructional strategies, and grading criteria that support evaluation of student work rather than consistent administration.

Although the materials provide a Solution and Answer Guide with solutions and answers to all the activities and assessments appearing in the student edition and Practice Problems for Financial Algebra, this guide does not provide educator-facing administration procedures, such as timing guidance, standardized directions, testing conditions, scripts, or recommendations for administering assessments consistently across classrooms.

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.

The materials provide a Cognero Test Generator platform that enables educators to generate assessment items that they can assign as digital or printed tests. For example, the chapter 2 final quiz in the digital platform includes a print option in the educator view, indicating that educators can print the digital assessment for students.

In addition, the online platform allows students to access course content digitally, including “Concept Checks,” “Lesson Applications,” and chapter quizzes. Through the digital platform, students have access to various accessibility features, such as adjusting the color scheme and font size and using a zoom feature. The platform also provides a calculator, but educators cannot toggle this feature on or off for individual students. Despite these features, the materials do not include digital assessments that allow educators to enable or disable accommodations for individual students, including text-to-speech, content and language supports, and calculators.

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

The materials do not include diagnostic assessments with TEKS-aligned tasks or questions. Problems throughout each chapter in the textbook vary in complexity but include only non-interactive problem types, such as multiple-choice warm-up problems, open-ended “Check Your Understanding” problems, and critical thinking application problems. The Explore digital learning platform includes concept checks for each section that feature questions with interactive item types, such as drag-and-drop and inline choice. However, the tasks and questions from the textbook and the online platform serve a formative purpose and do not function as diagnostic assessments designed to identify skill entry points before instruction begins.

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 a variety of formative assessment opportunities with TEKS-aligned tasks or questions. The student edition includes “Check Your Understanding,” “Extend Your Understanding,” “Applications,” “Lesson Applications,” “Concept Checks,” and “Reality Check” assessments that assess student understanding during and after the lesson at various levels of complexity. For example, the included warm-up questions and “Check Your Understanding” vary in complexity from multiple-choice questions at the recall and understand level to “Extend Your Understanding” and “Reality Check” assessments that ask students to analyze, create, and evaluate.

The materials provide TEKS-aligned tasks that allow students to demonstrate understanding using a variety of item types. For example, the section 1.1 exercises require students to calculate markup, discounts, and sales tax; convert yearly rates to monthly rates; and calculate measures of center from a real-world data set. The digital “Concept Check” includes dropdown and fill-in response formats.

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

The materials include scoring information, such as project grading sheets that assign 1–10 points per category and convert the results to a percentage, but the materials do not provide guidance for interpreting student performance, such as proficiency descriptors, performance levels, or instructional next steps.

The materials include a solution and answer guide for the test bank, but this guide contains only answer keys and does not provide rationales for correct or incorrect responses.

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 Activity Performance Report and Standards Performance Report can be generated to monitor student progress, but there is no explicit guidance on using these reports to address student trends. In addition, there are some teacher notes that address student difficulty during instruction, such as pausing before moving to the next example if students struggle, but the materials do not provide systematic guidance for analyzing assessment results, identifying class trends, grouping students, or assigning targeted intervention or enrichment based on performance data.

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 growth. For example, educators use the Cognero Test Generator platform to generate reports that track student progress, including grade book, progress, assignment results, question item analysis, prescription, and proficiency. There are also reports to compare classes and rosters.


The student view displays completed and in-progress assignments but does not include tools for students to monitor their own progress or growth.

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 include prompts to support educators in conducting frequent checks for understanding at key points throughout each lesson or activity. For instance, chapter 1, “Discretionary Expenses,” highlights each “Check Your Understanding.” The chapter provides these checks frequently throughout the lessons.


The materials include a variety of formative assessments that educators can use to monitor and adjust their instruction. Educators can use “Do Now” activities as a diagnostic assessment to determine the level of understanding necessary for subsequent work on a topic. The materials also include “Warm-Ups,” which are short, formative assessment questions that determine whether or not students have met the prerequisite material necessary for success in the upcoming lesson. In addition, “Ticket to Leave” activities are ungraded activities that allow students to demonstrate their level of understanding of the content of the day’s lesson. The educator can review the “Ticket to Leave” responses and adjust the following day’s lesson accordingly.

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 materials include a scope and sequence with suggested pacing, as well as an instructor manual with chapter objectives, activity outlines, and additional resources. Lesson plans provide whole-group instructional suggestions for delivering grade-level content. However, these resources are for all students and do not specifically support students who have not yet reached proficiency in prerequisite or grade-level concepts and skills.

The materials do not differentiate instructional approaches based on student proficiency level. For example, lesson plans provide whole-group instructional suggestions but do not include guidance for scaffolding lessons, providing alternative instructional methods, or supporting students who have not yet met grade-level proficiency in concepts or skills.

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.

Each lesson begins with “Key Terms” and includes pre-teaching supports for developing academic vocabulary. For example, the lesson plans for lesson 2 lists financial and academic vocabulary before instruction, such as checking account, electronic funds transfer, overdraft protection, check register, debits, and credits. The educator guidance also states that new terminology “must be introduced to students” and suggests using a word wall so that terms can be referenced throughout the lesson. In addition, the Financial Algebra Emergent Bilingual Support Guide acknowledges that most of the course assumes familiarity with U.S. financial institutions, stating that a student who has never seen a checking account statement or who arrived from a country with a different banking system is “missing the schema rather than the mathematics.” The guide provides suggestions on how to pre-teach unfamiliar references in text so that students can focus on mathematics. For example, the guide suggests educators explain unknown terms before engaging in arithmetic. Educators should introduce what Social Security is and who pays into it before engaging in the mathematics in section 5.5. The guide goes on to suggest the educator “invites comparison, rather than assuming absence” by asking how banking, credit, taxation, or retirement works in a country the student knows.

The lessons also include embedded supports for developing academic vocabulary and unfamiliar financial references. The lesson guidance directs educators to discuss checking and debit accounts, overdraft protection, mobile payment apps, and check registers. The lesson guidance also notes that many students may never have heard of mobile payment apps or seen a check register, then provides support such as researching examples, using a blank check register from the Financial Algebra Third Edition Instructor Companion site, and walking through the register line by line.

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 materials include project-based activities and student-designed projects that provide enrichment and extension opportunities for students who have demonstrated proficiency in grade-level content and skills. Some of the activities included are chapter projects, project templates, student-designed projects, and “You Write the Story!” activities. For example, the “Reality Check” projects allow students to conduct research, collect and analyze data, prepare presentations, and design their own project assignment with educator approval. Educator margin notes also explain that projects may be used as alternative assessments, presented to the class, offered for extra credit, or supported with project templates at the class or individual level. The “Reality Check Project Templates and Instructional Strategies” resource provides additional guidance for educators to support enrichment and extension activities for differentiated instruction. However, the materials do not have additional activities for students who have demonstrated proficiency in above grade-level content and skills.

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 materials do not allow educators to enable or disable text-to-speech, content and language supports, or calculators for individual students. The digital materials include student-facing accessibility features, such as read aloud, text highlighting, reading speed and voice adjustments, color scheme, font size, zoom, and calculator access.

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 Annotated Instructor’s Edition provides educators with guidance on offering students options to demonstrate understanding of mathematical concepts in various ways. This edition includes opportunities for performing, expressing, and representing, such as “You Write the Story!”, class discussions, and projects, which allow students to demonstrate understanding through written explanations, discussion, research, posters, presentations, data collection, and real-world applications. The Annotated Instructor’s Edition describes these projects as an “alternative assessment” that gives students an additional avenue to show what they have learned.

The Annotated Instructor’s Edition provides educators with guidance on supporting students in demonstrating understanding in various ways. The edition includes TEACH margin notes that provide guidance in facilitating class discussions, prompting students to explain reasoning, and supporting students as they complete projects. The project guidance also references project proposal forms and templates that help students organize and complete their work, supporting students in demonstrating understanding through formats such as posters, presentations, written reports, and visual representations.

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 sidebars on the Annotated Instructor’s Edition provide educators with explicit prompts to activate prior knowledge and anchor big ideas. Lesson 5.2, “Pay Periods and Hourly Rates,” instructs educators to reference students’ part-time paychecks and provide information on labor laws on pay rates, hours, overtime, breaks, and job safety. The class discussion sidebar instructs educators to focus on key ideas during the lesson, such as the differences between semi-monthly and biweekly pay periods and the advantages of direct deposits.

While the chapter 8 lesson plan includes educator actions such as warm-ups, class discussion prompts, and directions to guide students through stock trend graphs, stock bar charts, and candlestick charts, the guidance primarily focuses on lesson delivery and task completion. The materials do not include explicit (direct) prompts and guidance for educators to build knowledge by 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 chapter 8 lesson plan includes educator guidance for effective lesson delivery and facilitation using at least two instructional approaches. The lesson plan also includes direct instruction and guided facilitation through “Skills and Strategies” notes, such as reviewing percent-to-decimal conversions, reteaching how to convert fractions to percents and decimals, and guiding students to use proportions or equations to solve percent problems. The lesson includes class discussion prompts, warm-ups, section quotes, and “Check Your Understanding” formative opportunities to support whole-group discussion, educator modeling, and guided practice.

The lesson plans guide educators to use class discussions, real-world financial scenarios, direct instruction, guided practice, student explanation, technology/spreadsheet formulas, graphing, and application problems. For example, section 8.3 directs educators to support students with graph paper and rulers, guide students in interpreting stock trend graphs, identify high and low prices, compare different graph units, construct stock bar charts, and interpret candlestick charts. Section 8.7 also includes guidance for addressing common student struggles with fractional percentages, using equivalent expressions, and having students compare different equivalent forms on the board.

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 lesson plans and “Teaching Guide” sections of the materials provide general educator guidance for lesson delivery, including warm-ups, class discussions, examples, formative checks, section applications, chapter applications, and practice problems. While these components support general lesson delivery, they do not constitute multi-tiered intervention methods, such as guided, independent, or collaborative practice, nor do the components provide multi-tiered intervention methods for various instructional structures, such as whole-group, small-group, or individual support. For example, the chapter 9 lesson plan includes general teaching suggestions and practice opportunities but does not provide explicit intervention tiers, criteria for assigning students to intervention supports, or educator guidance for implementing multi-tiered interventions based on student needs.

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

“Extend Your Understanding” problems and related applications move students beyond routine practice with various forms of engagement. For instance, the problems engage students in real-world financial contexts, mathematical reasoning, graphing, algebraic methods, technology-supported calculations, spreadsheet use, student-created scenarios, discussion, and peer explanation. These methods provide opportunities for cognitive, contextual, visual/representational, technological, and collaborative engagement.

The “Reality Check” section at the end of each chapter provides enrichment and extension opportunities by asking students to apply financial mathematics in broader, real-world project contexts beyond routine practice. These projects support varied engagement through application, analysis, decision-making, and mathematical modeling. The Financial Algebra Third Edition Instructor Companion site offers support material for educators who assign these projects. The site includes teaching tips, instructional strategies, and grading criteria. The materials also include project templates that can be used to differentiate and guide students who need extra support in organizing and completing the projects.

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

The Annotated Instructor’s Edition includes prompts to support educators in providing timely feedback during lesson delivery. For example, in chapter 1, section 5, the TEACH note prompts educators to ask students whether a situation is an example of interpolation or extrapolation and why before attempting the solution. In addition, the class discussion prompts students to examine a graph, describe a situation with only one breakeven point, explain what that means for production and sales, and identify prices that would yield small, medium, and large profits. These prompts give educators opportunities to check student reasoning during instruction and respond to student understanding in the moment.

The materials also include educator notes related to the examples worked in the textbook. Some of these notes identify common misconceptions so that educators can proactively address these concepts. For example, the note for chapter 2, section 2, example 1, identifies that transposition of numbers is a common error when reconciling a check register. The note explains that transposition errors often result in a difference divisible by nine and directs educators to have students make a transposition error, then ask how knowing that the difference is a multiple of nine can help fix the error. Other educator notes provide corrective instructional guidance, such as reminding students to convert percents to decimals before substituting into the simple interest formula. These notes encourage step-by-step note-taking and student questions when solving with logarithms. The guidance also reminds students that a medical deduction applies only if the result is greater than zero. These notes in the margin provide guidance to support educators in providing timely feedback during lesson delivery.

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 materials include a Financial Algebra Emergent Bilingual Support Guide that includes educator guidance on what each ELPS proficiency level looks like in the Financial Algebra course. The guide states that a student at the pre-production level can match a labeled pay stub to its parts, sort expenses into essential and discretionary piles, or point to the interest line on a credit card statement.

In addition, the guide provides linguistic accommodations by proficiency level for each of the ELPS domains. For example, in the Listening domain, an educator would support a pre-production student by pairing every spoken direction with a gesture, a written word, or an image, such as holding up a labeled check and pointing to each field name when introducing checking accounts. In the Speaking domain, an educator would support a high intermediate student by providing discussion stems that invite justification and comparison, such as “I would choose the _____ loan because _____, even though the _____ loan has a lower _____.”

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 materials include implementation guidance to support educators in effectively using the materials in state-approved bilingual and English as a Second Language (ESL) programs. The Financial Algebra Emergent Bilingual Support Guide includes a section that describes each of the six state-approved program models used in Texas, as well as suggestions of how to implement the program in each of the models. For example, the guide states that ESL content-based and ESL pull-out are the two most commonly used models in high schools. The materials suggest that, in an ESL content-based model, the educator delivers the vocabulary, comprehension, and discourse supports in the guide during regular instruction. However, in an ESL pull-out model, the guide recommends sharing the “Key Terms” list and the lesson quotation with the ESL educator in advance so that pre-teaching occurs before the mathematics lesson rather than after the lesson.

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.

The Financial Algebra Emergent Bilingual Support Guide provides embedded guidance to support emergent bilingual (EB) students in developing academic vocabulary through oral and written discourse. Part 5 of the guide separates each of the academic vocabulary terms into four distinct categories, each requiring a different instructional approach. In addition, the guide provides a vocabulary routine for each lesson so that educators can prioritize five of the most important terms and pre-teach and continually reinforce them throughout instruction. Part 9 of the guide describes a discourse routine that provides all students the opportunity to increase comprehension through oral and written discourse. In this routine, students engage in one minute of individual writing before engaging in a pair exchange in which each partner restates the other’s reasoning before responding. This routine provides students with the opportunity to refine their mathematical language after listening to their peers. Then, the educator selects and sequences two contrasting responses so that the class can compare the responses with a focus on the reasoning involved rather than the answer. Finally, students close the discussion with a written response. Sentence frames specific to each course phase support EB students as they engage with the language.

Part 6 of the Financial Algebra Emergent Bilingual Support Guide provides embedded guidance for educators to support EB students in building background knowledge through oral and written discourse. The materials provide a chart that lists common barriers, the course location for each barrier, and a remedy for each barrier. For example, the course contains many numeric and date conventions that differ internationally. The “Remedy” section reminds educators that many students have learned a decimal comma and a day-month-year order that differs from ours. Students may read dates incorrectly, which makes it look like they have made a computational error when they have not. Educators should check with students to ensure they are familiar with standard conventions in the United States.

Part 8 of the Financial Algebra Emergent Bilingual Support Guide supports students in making cross-curricular connections through oral and written discourse. The materials provide a chart with English financial terms alongside their Spanish cognates, as well as a “False Friends” chart that lists common English financial terms and their false cognates. Students engage with these terms by using sentence stems to talk and write about their meaning application to everyday life.

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.

The problems in each lesson increase in rigor and complexity throughout the lesson. For example, unit 8, “Rational Functions,” begins with graphing rational functions and transformations, then moves to analyzing key features, end behavior, asymptotes, discontinuities, and left- and right-sided behavior. The “Elaborate” section provides TEKS-aligned practice problems for P.2(F), P.2(G), P.2(I), P.2(J), P.2(K), P.2(L), and P.2(M). Students reflect on their problem-solving, identify alternate approaches, justify their thinking, and correct errors.

The materials include numerous formative assessments and end-of-chapter assessments that require students to demonstrate depth of understanding aligned to the TEKS. For example, the lesson plan for lesson 1,”Discretionary and Essential Expenses,” walks the educator through the lesson objectives, provides examples, and a formative assessment (“Check Your Understanding”) after each skill is practiced. The end of the chapter recommends practice problems from the student workbook for additional practice and a summative assessment.

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 contain questions and tasks that increase in rigor and complexity toward grade-level proficiency. For example, in the chapter 9, section 9.7 lesson plan, the student tasks begin with determining the profit equation and finding the maximum profit. Then, students graph the revenue, expense, and profit functions and “interpret the situation modeled at each point.” Lastly, the students determined the price that maximizes profit algebraically.

In addition, each lesson in the materials contains worked examples, “Check Your Understanding,” “Extend Your Understanding,” and section and chapter “Applications” that increase in complexity and lead to grade-level proficiency. For example, in the “Reality Check” section of chapter 2, students work through questions and tasks that increase in detail and complexity, from opening a bank account and keeping track of debit and credit transactions to the types of accounts and various types of interest calculations. Students also determine which offer a person should take and justify their response using a time value of money analysis.

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

Throughout the course, the materials begin by reviewing simple mathematical computations, followed by problem-solving drawn from real-life scenarios in which students analyze tables, construct graphs, formulate models, and predict values to understand patterns, big ideas, and relationships. For example, in section 6.2, “Modeling Tax Schedules,” students formulate piecewise functions to represent tax tables as bounded equations and then use them to compute taxes for a specific income level. This question explicitly makes the connection in example 2, “How does the piecewise function relate to the tax computation worksheet?”

In chapter 1, section 1.5, “Personal Expenses,” the materials connect financial decision-making to bivariate data, scatter plots, trends, correlation, linear regression, interpolation, extrapolation, and prediction. The educator’s guidance explains that the question “How Can Past Trends Predict Future Occurrences?” sets the stage for using statistical prediction tools, and the discussion connects univariate expense data to paired bivariate data over time. This approach supports horizontal coherence because students connect financial contexts, graphical representations, rates of change, correlation, and prediction within the same 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.

Problems in the student edition demonstrate coherence vertically across concepts and grade bands by revisiting connected skills from previous grade levels that are foundational for the mathematical skills being taught. For instance, the “Linear Regression Analysis” refers to the slope-intercept form, in which m is the slope, b is the y-intercept, and x and y are the independent and dependent variables, which were learned in earlier grade levels.

The materials also connect current financial mathematics concepts to prior and future mathematics learning. The educator notes in the Annotated Instructor’s Edition guide instruction based on previously studied systems of equations and connect introductory hypothesis testing to more rigorous future statistics coursework. This connection is supported by the chapter 9 lesson plan, which explains that students apply systems of equations to find the intersection of boundary lines. The plan states that the course introduces the logic of hypothesis testing, with a more rigorous treatment occurring in a future statistics course.

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 student edition demonstrates coherence across activities by connecting students’ prior knowledge of concepts and procedures to the mathematical concepts to be learned in the current grade level. Each “Warm-Up” exercise reviews basic math concepts that serve as a foundation for those introduced in the chapter. For instance, in section 2.10, the warm-up gives three different expressions. Students simplify “each of the following expressions where r = 0.036, n = 4, and a = 2. Round to the nearest thousandth.” Also, in section 2.10, students review a formula for periodic deposit investment used in sections 2.7 and 2.8. The educator’s notes say, “Review the formulas for finding compound interest and for finding the present value of a periodic investment. Have students find those formulas in their notes or in their textbook and transcribe them to the beginning of their notes for this new lesson. As a review, ask students to offer some situations where the formulas might be used.”

The Course Overview resources provide guidance for educators to 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. For example, section 9.1 includes topics normally found in the AP Statistics curriculum, such as undercoverage, descriptive statistics, inferential statistics, and the central limit theorem. Also, in section 9.1, “students determine via sampling with hypothetical populations which measures of central tendency are unbiased estimators.”

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

The materials provide spaced retrieval opportunities by requiring students to reference and apply mathematical concepts learned in previous chapters. Throughout the course, the materials provide application problems and projects to students, enabling them to retrieve and practice the concepts they have learned. For example, the “Applications” problem set at the end of each section starts by asking students to revisit and explain the quotes at the start of each section, following the “Warm-Ups.” The problem set also revisits the “Really? Really?” real-world scenarios and applies them to problem-solving. For example, in the “Really? Really? Revisited,” students use their previously learned concept to “determine the linear, quadratic, and cubic regression equations for the Tax Freedom Day data.”

Piecewise functions are first used in chapter 4, “Automobile Ownership.” In lesson 5.1, “Looking for Employment,” students review their knowledge of piecewise functions through the “Warm-Up” activity, apply the same concept in the lessons throughout the chapter, and review the concept again in lesson 6. Students review and practice the concepts and skills for applying piecewise functions over several lessons across the learning pathways.

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

The materials often require students to practice previously learned mathematical skills within the context of new financial topics. For example, students must use logarithms from chapter 2 to solve loan problems in chapter 3, and students apply linear regression from chapter 1 to analyze rentals in chapter 7. For example, students first solve simple interest problems, then compare those results with compound interest models, and later extend their understanding to continuous compounding and exponential functions. This sequence requires students to retrieve and apply previously learned skills while developing new mathematical understanding. The lessons also connect algebra, financial literacy, statistics, and modeling concepts, creating multiple pathways for students to practice and reinforce learning over time.

In section 7.3, “Mortgage Application Process,” students recall and use the loan monthly payment formula to calculate the monthly mortgage payment. Students then move on to analyzing a table that details a home’s square footage and additional features to calculate property taxes. Throughout the course, each section presents guided examples in which students practice problems of increasing complexity and across varied contexts, requiring students to apply previously learned skills.

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 support opportunities for students to interpret mathematical concepts and complex, real-world situations. In chapter 1, students interpret financial data in the context of spending and expenses, including comparing expenses with coworkers, interpreting measures of center, reading frequency distributions, and later interpreting patterns and trends in bivariate financial data. One section specifically includes objectives for students to “interpret patterns and trends based on data,” “find and interpret the correlation coefficient,” and describe how linear regression supports interpreting financial data.


The materials also support opportunities for students to analyze mathematical concepts and complex, real-world situations. In chapter 9, students analyze sampling methods, bias, experimental design, observational studies, and the logic of hypothesis testing in business and invention contexts. The educator’s guidance notes that flawed survey data may be unreliable because manipulation of the data is possible. Students work through examples involving question-wording bias, representative samples, fair tests, matched-pairs designs, observational studies, and normal-distribution outcomes.

The materials support opportunities for students to evaluate mathematical concepts and complex, real-world situations. In chapter 9, students use linear programming to evaluate optimal outcomes, including maximizing profit and minimizing costs. Students construct feasible regions, write objective functions, and test endpoints to determine the best financial decision. The materials also include business modeling tasks in which students use multiple sources of information, functions, and methodologies to model a startup business.

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

The materials provide opportunities for students to create concrete models of mathematical situations. For example, in chapter 1, students use candies to model relative frequency and make predictions. In chapter 7, students construct and use a clinometer to model angle-of-elevation relationships and indirect measurement. In chapter 9, students use labeled ping pong balls to create a random-number model and investigate experimental variability.

In addition, the materials provide opportunities for students to create mathematical representations. In chapter 1, section 1.5, the lesson objectives include “Graph bivariate data,” “Construct a scatter plot,” “Fit a linear regression equation to a scatter plot,” and “Make predictions based on lines of best fit.” The educator’s guidance also notes that the section begins the process of linear regression “graphically rather than algebraically,” and students identify patterns and trends in ordered pairs from the scatter plot before finding the regression equation.

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

The materials provide opportunities for students to apply conceptual understanding to new problem situations and contexts. In chapter 1, section 1.5, “Personal Expenses,” students apply their understanding of bivariate data, scatter plots, trends, correlation, and linear regression to financial contexts. The section objectives include graphing bivariate data, interpreting patterns and trends, fitting a linear regression equation, making predictions based on lines of best fit, and describing how linear regression analysis can assist in interpreting financial data. The educator’s guidance also connects the lesson to real-world financial examples, such as monthly income and monthly discretionary expenses.

The materials provide additional opportunities for students to apply conceptual understanding in new business-related contexts. In chapter 9, section 9.4, “Fixed and Variable Expenses,” students define fixed and variable expenses, create expense equations, explain revenue, and determine breakeven points. The educator’s guidance asks students to connect variables and constants to fixed and variable expenses, express revenue in terms of price, and interpret breakeven points graphically and algebraically in the context of manufacturing and business decisions.

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

At the beginning of each section, “Warm-Up” exercises provide opportunities for students to build automaticity and fluency. For example, the “Warm-Up” exercises for section 2.5 provide students with an opportunity to factor trinomial expressions, a skill students should do fluently.

The Cognero Test Generator contains multiple-choice and true/false questions that provide students with opportunities to build fluency and automaticity. For example, questions such as “The dimension of a [given] matrix is 2x3” (true or false) and “The zeros of a quadratic function can be found by which of the following methods” (multiple choice) are simple tasks that build automaticity and fluency.

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 guide students toward more efficient mathematical procedures. For example, in chapter 1, students use spreadsheets to organize and calculate with large data sets, and the educator’s guidance explicitly notes that spreadsheet formulas help generate answers. Students connect extended sum formulas to compact sum formulas and consider why the compact version may be preferable.

The materials provide opportunities to use and compare multiple methods. Chapter 1 directs educators to show students two methods for working with percents and to explain why both methods yield the same answer. Students also learn a physical matching strategy as a backup method for finding the median before applying procedures in later examples and applications. In chapter 9, the materials encourage students to solve problems in two ways—graphically and algebraically—and students work with multiple sources of information, functions, and methodologies to model a new business.

The materials provide repeated procedural practice through examples, “Check Your Understanding,” “Extend Your Understanding,” section and chapter “Applications,” and accompanying “Practice Problems.” The guidance also reminds educators to have students check data entries before applying formulas because incorrect entries can lead to incorrect answers. This guidance supports accurate use of procedures across the learning pathway.

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 flexibility of math content across learning pathways. Chapter 1, example 1 presents two valid methods for percent calculations involving markup, discount, and sales tax. Because percentages are used throughout the course, the educator guidance recommends showing both methods and explaining why each works, thereby supporting flexible use of strategies.

In chapter 2.2, “Reconcile a Bank Statement,” students examine a check register to evaluate its mathematical content by identifying errors. In chapter 3.2, “Loans,” an application problem requires students to analyze calculator errors and describe the error and how to fix it to ensure accuracy. The materials contain “Linking Concepts: Writing Projects” at the end of each chapter that provide a multitude of opportunities for students to evaluate models, strategies, and solutions for efficiency throughout the learning pathways. For example, in chapter 6, problem 2, students evaluate the efficiency of the formula for the binomial probability distribution compared with using a binomial table.

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

The materials contain guidance to support students in selecting increasingly efficient approaches to solve mathematics problems. In chapter 1, section 1.2, the educator shows the students how to use a spreadsheet to organize and make sense of data. Example 3 asks students to write a formula to find the sum of the relative frequencies and gives two different ways to write the formulas. The first is the extended formula, while the other is the compact formula. Educators ask, “Why might the latter be a better choice?”

In addition, chapter 2, section 2.10, example 3 guides educators to review the formula for calculating the future value of a periodic deposit investment. Students discuss with their partners why this formula is appropriate for the situation. Each partner chooses one method for solving the problem. After solving the problem with their assigned method, students explain the steps to their partner and validate that both students arrive at the same solution.

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

The materials include both conceptual and procedural learning opportunities. However, the materials do not explicitly identify how the course addresses the conceptual and procedural emphasis of the TEKS. The materials do not include explicit statements, instructional guidance, lesson annotations, or educator supports that clearly identify how the course addresses the conceptual and procedural emphasis of the TEKS.

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.

Questions and tasks in the student edition provide opportunities for students to use concrete and abstract models as required by the TEKS. For example, chapter 9, section 9.9, introduces students to linear programming. Students model the objective program with a pencil, which they slide across the feasible region to determine the optimal outcomes. In example 3, students create and use the profit objective functions to “test all of the endpoints for the maximum value.”

In addition, students use pictorial representations, such as graphs and diagrams, to analyze data as required by the TEKS. For example, students use scatter plots to represent bivariate data. In Section 4.4, “Probability: the Basis of Insurance,” students solve example 5 using a Venn diagram to illustrate how people use probability in random selection. Students use a diagram or clinometer representation in a trigonometry context. Also, students use graphs to model relationships and interpret circle graphs or pie charts. These visual models support students in communicating mathematical ideas through graphs, diagrams, and other visual 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 materials help students connect representational models to abstract concepts. Students use scatter plots, floor plan drawings, normal curve graphs, and budget charts to derive equations, calculate costs, interpret probabilities, and convert information into matrices. The lesson plans also support this connection through section 1.5, in which students construct scatter plots, fit linear regression equations, determine regression equations, and interpret correlation coefficients.

The materials support students in creating representational models connected to abstract concepts. In section 1.5, students graph bivariate data, construct scatter plots, fit a linear regression equation, and make predictions based on lines of best fit. These tasks align with the TEKS that require students to collect bivariate numerical data to create a scatter plot, select a model, justify the selection, interpret the results, and make predictions.

The materials include support for students explaining representational models. In chapter 9, the educator guidance asks students to discuss what mathematical models are, compare models such as equations and graphs to models used in earlier grades, and recognize that equations, graphs, and manipulatives can all function as models. Also, chapter 1, “Reality Check” 6, students use candies to concretely model relative frequency and show how to use it to make predictions. However, the materials do not include support for students in 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.

In the Annotated Instructor’s Edition, the materials provide opportunities for students to develop academic mathematical language through visuals, manipulatives, and other language-development strategies. For example, chapter 4, section 4.1, example 5 introduces the word cusp with its definition, the graph of the piecewise function in “Figure 4-1”, and the following real-world example: “it resembles the sharp cusp on a tooth.”

The student textbook provides visual aids and mathematical representations to support the development of academic mathematical language in context. For example, in lesson 4.9, as students learn about accident investigation data, they encounter the terms accident reconstructionist and skid mark. The textbook shows a real-life picture of a skid mark while defining the two words and explaining how the words relate to each other.

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 Annotated Instructor’s Edition provides TEACH and class discussion notes in the margin of the pages. These notes help the educator scaffold and support their students’ use of academic mathematical vocabulary in context when communicating with peers and educators. For example, in lesson 8.1, as students learn about business organizations, they learn vocabulary such as partnership, corporation, limited liability, and others. Educators facilitate a class discussion that supports the development of understanding what these words mean with the following prompts: “What are everyday products that you think sell millions each year? In which type of business do you think an owner’s personal possessions may potentially be taken in the event of a lawsuit or financial crisis? If you owned shares of stock in a public corporation, what profit would you earn, and what would be your personal liability?”

In addition, the Financial Algebra Emergent Bilingual Support Guide provides a discourse routine that scaffolds, supports, and extends students’ use of academic vocabulary in context when communicating with peers and educators. In this routine, students engage in one minute of individual writing before engaging in a pair exchange in which each partner restates the other’s reasoning before responding. Then, the educator selects and sequences two contrasting responses so that the class can compare the responses with a focus on the reasoning involved rather than the answer. Finally, students close the discussion with a written response. Sentence frames specific to each course phase support EB students as they engage with the language.

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. For example, in section 4.5, the “Class Discussion” guides educators through discussing real-world items that “depreciate” and “appreciate”. Then, educators should explain that “straight line depreciation” is just a model and that the IRS uses this mathematical model for depreciation. Lastly, educators should review slope-intercept form and discuss “the slope, the intercepts, and the fact that all points on the line must satisfy the equation.”

The Annotated Instructor’s Edition provides guidance in the margin to help educators apply appropriate mathematical language and academic vocabulary in discourse. For example, as students conclude their lessons on employment basics, they apply the learning in the “Really? Really! Revisited” activity. The educator facilitates academic discourse with students by first discussing the fastest-growing occupations from 2022 to 2032. Then, the educator asks, “How do the data presented in the table contribute to the sorting formula?” and “You may need to suggest that the solution lies in setting up ratios.”

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

The Annotated Instructor’s Edition provides guidance to facilitate mathematical conversations, allowing students to hear and use math language with peers. For example, as students learn about purchasing a home in lesson 7.4, there is the following guidance to facilitate conversation during the class discussion: “Before addressing the opening questions in the text, ask students to come up with some questions of their own that they believe need to be answered before buying a home. Ask students to identify some recurring and nonrecurring costs that they are responsible for now. Why is it important for a prospective buyer to have a title search? Ask students for other financial responsibilities that, like interest, are paid in arrears (e.g., credit card balances).”

Furthermore, the Financial Algebra Emergent Bilingual Support Guide provides an oral and written discourse routine that provides all students the opportunity to practice listening, speaking, and writing about the course content. In this routine, students engage in one minute of individual writing before engaging in a pair exchange in which each partner restates the other’s reasoning before responding. This exchange provides students with the opportunity to refine their mathematical language after listening to their peers. Then, the educator selects and sequences two contrasting responses so that the class can compare the responses with a focus on the reasoning involved rather than the answer. Finally, students close the discussion with a written response. Sentence frames specific to each course phase support EB students as they engage with the language.

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.

There are exemplar responses throughout the textbook that guide students’ understanding of how to solve problems and their solutions. For example, in the lesson on automobile depreciation, students write “the straight-line depreciation equation for the situation discussed in Examples 1 and 2. Then draw the graph of the equation.” In addition to the worked-out example, the Annotated Instructor’s Edition provides the following additional guidance to support student responses: “Some students may want to express the slope as a fraction with 1 in the denominator. Indicate that it is not necessary to do so, and eliminating the 1 makes the equation easier to interpret.”

The materials provide embedded support to redirect inaccurate student responses. For example, in section 1.1 of the chapter 1 lesson plan, the educator guidance anticipates a specific student error when calculating the mean from a frequency distribution. The guidance notes that students may incorrectly divide by the number of entries in the product column rather than by the total number of data values and directs educators to ensure that students divide by the correct total.

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

The materials integrate the TEKS process standards appropriately. For example, in lesson 7.4, “Purchasing a Home,” students apply mathematics to an authentic financial decision by analyzing mortgage options, comparing costs, and interpreting payment information. Throughout the lesson, students represent information using formulas and spreadsheets, justify financial decisions, and communicate the reasonableness of their solutions. The lesson applications, worked examples, and end-of-section exercises integrate the TEKS process standards for problem-solving (P.1(B)), communicating mathematical reasoning (P.1(D)), and representation (P.1(E)).

Additionally, in lesson 11.3, “Charting a Budget,” students organize financial data into charts and graphs, analyze spending patterns, and develop a budget based on real-world constraints. The lesson integrates the process standards by requiring students to represent data (P.1(E)) visually, analyze relationships (P.1(F)), justify budgeting decisions, and communicate mathematical conclusions (P.1(D)) through application problems and spreadsheet activities.

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

The materials include a description of how process standards are incorporated throughout the learning pathways. For example, in chapter 8, “The Stock Market,” the chapter learning pathway begins with interpreting stock tables and investment data; progresses through calculating gains, losses, and rates of return; and culminates in applying these concepts to investment decision-making. Worked examples model mathematical reasoning from P.1(D), while the “Section Exercises” and “Chapter Review” require students to analyze financial information from P.1(F), justify investment choices from P.1(B), and communicate conclusions using multiple mathematical representations from P.1(E). The progression intentionally connects problem-solving, reasoning, representation, and communication throughout the chapter. However, the materials do not include a description of how process standards are connected throughout the learning pathways.

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

The materials do not include an overview of the TEKS process standards incorporated into each lesson. While the student edition includes lesson objectives, and the Lesson Plans and Teaching Guide provide instructional components, such as warm-ups, discussions, examples, formative checks, and applications, the materials do not identify the TEKS process standards by lesson or explain how those process standards are incorporated into each lesson.

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 think mathematically. In chapter 1, students work with scatter plots and determine the types of correlation represented by the data. In section 1.5’s “Application” problems, students must determine the type of correlation a scatter plot will show based on the amount of money left in a discretionary fund after paying bills. The students determine if it is a positive or negative correlation and explain their reasoning.

In chapter 9, linear programming tasks require students to organize information, construct a polygonal region, determine vertices, write an objective function, and test endpoints to maximize profit or minimize cost. The guidance notes that students need to organize a “great deal of information” before solving, which supports perseverance through complex problem-solving.

Additionally, chapter 9, “Mathematically Modeling a Business Start-Up,” asks students to make sense of mathematics by reasoning about production, supply, and demand; fixed and variable expenses; revenue; and breakeven points. These contexts require students to interpret mathematical results as business decisions rather than treating the math as disconnected computation.

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

Educator guidance supports students in understanding that there can be multiple ways to solve problems and complete tasks. For example, in lesson 8.1, “Business Organizations,” students learn that there is more than one way to determine how many shares of stock an individual owns. The educator explains to students that they can use a proportion or an equation to solve the guided example presented. However, the materials do not provide opportunities for students to justify multiple ways to solve problems and complete tasks.

When appropriate, the materials contain problems that can be solved with or without technology (i.e., a calculator or a spreadsheet). During lesson 10.5, “Investment Diversification,” students explain how they can compute the sum of a table of values. Educator guidance in the margin of the Annotated Instructor’s Edition helps students understand and explain the different ways to solve the problem. Example 7 states, “You can use the tables feature in your calculator, or a spreadsheet, to substitute for i, and then use the tables menu or spreadsheet commands to find the sum of the results.”

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 provide repeated opportunities for students to engage in mathematical tasks through “Check Your Understanding,” “Extend Your Understanding,” section and chapter “Applications,” and project-based tasks that involve working with peers and/or educators. For example, the 9.1 “Check for Understanding” states, “The Long-Last Light Company designed a new type of bulb, and they are testing it for defects. They need to pick 60 bulbs from the first lot of 500 bulbs to see if the bulbs last 2,000 hours as they claim. If they number the bulbs 001-500, and start at line 3 on the random number table, what are the numbers of the first five bulbs that will be tested for defects?” Also, an “Extend Your Understanding” to the previous problem states, “If the Long-Last Light Company from the Check Your Understanding problem in Example 2 selects the 60 bulbs, and the mean life of the bulbs is 1,665 hours with a standard deviation of 30 hours, do you think they should claim their bulbs last 2,000 hours on the package?”

Also, “You Write the Story!” activities require students to communicate mathematical ideas in writing. These activities ask students to “examine a graph or chart and write a story or article, helping students to sharpen their interpretation skills.” For instance, in chapter 9, students analyze a scatter plot that shows product failure over time. After analyzing the graphs, students write “a short news-type article centered on the data in this graph, based on a hypothetical situation you create.”

The Annotated Instructor’s Edition guidance includes repeated prompts for “Class Discussion” to discuss mathematics. For example, chapter 1 directs students to work in groups to create need/want lists and then “share and compare their findings with the class,” supporting discussion with peers and the educator. Chapter 9 includes discussion prompts asking students to define optimal cost and optimal profit, explain feasible outcomes, and share organizational approaches before solving.

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.

TEACH notes in the margin of the Annotated Instructor’s Edition support educators in guiding students to reflect on their problem-solving approaches and multiple points of entry. For example, lesson 9.8, “Mathematically Modeling a Business,” example 1 guides students in determining an item’s production cost given its price. The educator models two methods for solving the problem. The first method uses the given price to find the quantity demanded, which can then be substituted into the expense equation. The second method substitutes q in terms of p into the expense function and then uses the given price to compute the expense. The TEACH notes for example 1 further guide the educator to “work through both methods with students so that they can see the nature of mathematical dependency in this situation.”

Class discussion prompts also support educators as they encourage students to share and reflect on their problem-solving approaches and explanations. For example, lesson 11.4, “Cash Flow and Budgeting,” begins with the educator asking students if they have monthly expenses. Students explain how they will pay for those expenses each month. The educator and students discuss saving money, and the educator asks the students to explain why they might save money.

In addition, the Financial Algebra Emergent Bilingual Support Guide provides a discourse routine that gives students the opportunity to share and reflect on their problem-solving approaches, including arguments and justifications. In this routine, students engage in one minute of individual writing before listening to and restating a peer’s reasoning. In the next phase, students compare different problem-solving approaches and engage in a conversation in which they justify why their approach is reasonable and argue about which approach is the most efficient or makes the most sense. Finally, students synthesize what they learned during the exchange and write a conclusion. Sentence frames specific to each course phase support EB students as they engage with the language. ‘

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

In Lesson 2.3, “Savings Accounts,” worked-out examples and educator notes include prompts and guidance to support educators in providing explanatory feedback based on anticipated misconceptions. For example, while learning about arithmetic sequences and applying them to savings accounts, students must compare three local banks and one online bank to determine which bank pays the highest interest on a two-year certificate of deposit (CD). The educator asks, “Which bank pays the highest interest for this two-year CD?” Students may enter division problems in the calculator in the incorrect order. Educators then give “students practice in entering division problems on the calculator, when they are given with the dividend/divisor notation or the divisor/dividend notation.“ Also, educators remind students that filling “in the extra zeroes on the right makes it easier to compare the numbers because they will have the same number of decimal places and the decimal points can be lined up.”

In addition, the materials include educator prompts and guidance to support educators in providing explanatory feedback based on student responses. For example, in chapter 3, educators ask, “How would you decide which type of institution from which to borrow?” The materials inform educators that “banks” are the most popular student response. Possible feedback from educators could be pawnshops because of “the popularity of some cable TV pawnshop shows.”