Kiddom Texas: Algebra 1 (Second Edition)

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

The Algebra 1 Scope and Sequence consists of a table with columns for each unit, section title, lesson number, lesson title, learning target, the TEKS, and ELPS. The learning target outlines the concepts taught in the course. For example, one of the unit 1 concepts is “Use words and graphs to represent relationships that are functions, including identifying the independent and dependent variables.” The materials list the TEKS to address the learning target as ALGI.1B, ALGI.1A, ALGI.1D, and ALGI.12A.

The materials include a scope and sequence with ELPS alignments identified throughout the course year. The scope and sequence provides a table with the following headings: “Location in Program,” “Lesson Title,” and “ELPS.” For the nine units, it includes the name of each lesson title and corresponding ELPS. For example, the ELPS for unit 2, lesson 1 are 1.F, 2.D, 4.A, 4.B, and 4.E.

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

Kiddom Texas Algebra 1 provides 165-, 180-, and 210-day calendars that outline recommended pacing for the instructional year. The organization of pacing is by unit and includes lessons, assessment days, flex days, total days, and suggested activities for flex days. For example, in the 165-day calendar, unit 1 includes 17 lessons and two days allocated for check-ins, a mid-unit assessment, and other assessments. The unit also includes four flex days for a total of 23 instructional days. Suggested flex day activities include beginning-of-the-year routines, diagnostics, and norms.

The materials provide pacing calendars for 165-, 180-, and 210-day schedules, outlining the suggested time for each unit and major concept. They also include flex days for review, reteaching, assessments, lesson extensions, and transitions between units. Kiddom Texas Algebra 1 includes a pacing guide for a 31-week instructional year that does not account for student or staff holidays. The guide also outlines pacing for Algebra II and Geometry, suggesting potential vertical alignment across courses and specifying the number of days and weeks for each unit. For example, in unit 1, the total duration is 18 days, with a duration of four weeks.

Evaluation for 1.1c
Materials include an explanation for the rationale of unit order as well as how concepts to be learned connect throughout the course.

The Algebra 1 materials include a course narrative that shows how learning connects throughout the course. Students develop understanding of functions, linear equations and inequalities, statistics, exponential relationships, and quadratic equations through problem-solving, graphing, and real-world modeling. For example, in “Lesson 7.1: Exponential Situations as Functions,” students build on prior knowledge of exponential relationships by defining independent and dependent variables and using function language and notation. They also begin representing real-world situations as functions to describe exponential change.

The materials include an anchor graphic that explains the rationale for the sequence of units and demonstrates how mathematical concepts connect throughout the course. The graphic illustrates a coherent progression of learning, showing how concepts introduced in earlier units support the development of new understandings in later units. For example, the graphic shows learning progression at the unit, lesson, and activity levels, helping educators and students understand how knowledge developed in one unit supports learning in subsequent units. By highlighting these connections, the materials communicate both the purpose of the unit order and the progression of concepts across the course.

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

The Kiddom Texas materials include processes to support educators in understanding and preparing to teach each unit through internalization protocols. These processes include reviewing lesson objectives, key vocabulary, and success criteria. Each unit overview includes learning goals and a narrative that describes what students will learn and the instructional intent. For example, in unit 1, one learning goal states, “Analyze and interpret various function types (linear and exponential) through graphs, equations, and contextual situations.” The instructional intent emphasizes developing students’ ability to connect visual representations with verbal descriptions.

The lesson overview provides guidance that supports lesson internalization by explaining the purpose of the lesson, reviewing prerequisite knowledge, highlighting key concepts, and describing connections to future learning. For example, unit 1, lesson 1 includes guidance that helps educators understand the instructional focus before teaching the lesson. The overview identifies the lesson learning goals and includes “I can” statements that clarify the expected student outcomes. This information supports educators in preparing for instruction by understanding the lesson objectives, mathematical focus, and intended learning progression.

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

The materials provide comprehensive implementation supports that enable instructional leaders to guide and monitor the effective use of the curriculum. The course guide outlines coaching practices and campus-level implementation guidelines, and includes an implementation reflection tool to help leaders support educators in refining instructional practices and improving student learning outcomes. The materials also provide implementation checklists and rubrics that enable leaders to monitor progress and offer targeted feedback. For example, the organization of the rubric is by categories such as implementing, developing, and organizing, and includes indicators such as “Instructional leaders have set the purpose for and scheduled ongoing collaboration time for educators,” providing clear guidance for supporting successful implementation of the materials.

The Implementation Support for Leaders provides articles and resources focused on effective mathematics instruction and curriculum implementation. For example, the article “From Struggles to Success” shares a math coach’s reflections and experiences implementing the curriculum, offering practical guidance that instructional leaders can use to support educators. The article also includes links to additional implementation resources that promote ongoing professional learning and help ensure consistent implementation of the materials.

Evaluation for 1.2a
Materials include comprehensive unit overviews that provide the background content knowledge and academic vocabulary necessary to effectively teach the concepts in the unit.

The materials include a unit overview with learning goals, instructional narratives, and background content knowledge. Each unit begins with a “Check Your Readiness” activity that assesses students’ prior knowledge. For example, students demonstrate understanding of functions without the use of graphing technology. The “Unit Narrative” also explains what students will learn and the instructional intent. For instance, in unit 1, one learning goal states, “Analyze and interpret various function types (linear and exponential) through graphs, equations, and contextual situations.”

Within the unit overviews, the materials identify and embed the academic vocabulary necessary to teach the unit, for example, vocabulary such as function, function notation, and domain. In addition, the materials include a course and lesson glossary that introduces key terms as they come up in the lessons. In unit 1, lesson 1, students work with terms such as dependent variable, independent variable, and function, giving educators language to introduce these ideas and help students talk about relationships in graphs and real-world situations.

Evaluation for 1.2b
Materials contain supports for families in both Spanish and English for each unit with suggestions on supporting the progress of their student.

The materials provide strategies and activities in English and Spanish for families to support student learning at home for each unit. For example, “Álgebra 1, unidad 1: Cantidades relaciones preguntas frecuentes” provides information on unit skills and main ideas, explains how the content connects to real-world contexts, and describes how it prepares students for college and career. It also offers suggestions for how families can support student learning with practical ideas related to the math concept they are currently learning in school. Some practical suggestions to the question, “What can I do to support my student at home?” include “Encouraging discussion about real-world relationships: Talk about situations in which quantities change in relation to each other such as how the distance traveled depends on time and speed, or how the balance in a savings account might grow over time.”


Unit 2 includes two frequently-asked-questions documents, one in English and one in Spanish, that explain the unit content and provide at-home support strategies for families. One suggestion in the “English FAQ for Sequences” encourages families to “identify patterns in everyday life such as the number of steps in a staircase, the arrangement of tiles, or even simple growth patterns. Encourage them to describe the pattern they see and try to predict what comes next.”

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

The materials provide well-organized and coherent lesson plans that include clearly sequenced instructional components such as warm-ups, hands-on activities, synthesis activities, and cool-down assessments. Each lesson includes identifiable daily objectives, structured student tasks, guiding questions, instructional materials, and embedded formative assessments that support mastery of TEKS-aligned mathematical concepts. ELPS alignment is evident through structured discourse routines, intentional opportunities for partner talk, and scaffolds that support academic language development during mathematical reasoning. The lesson flow integrates instructional assessments, allowing educators to continuously monitor student understanding and adjust instruction based on student responses and discourse.

In the “Describing and Graphing Situations” lesson, the materials present a clearly sequenced instructional progression aligned with TEKS expectations for identifying and analyzing functions in real-world contexts. The lesson begins with a “Bagel Shop” warm-up, which activates prior knowledge by situating students in a familiar context involving pricing relationships. The “Bagel Shop” activity also demonstrates ELPS integration through structured peer discussion tasks and intentional development of academic language around functions.

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

Each activity includes required materials to support effective lesson delivery. For example, in unit 1, lesson 9, activity 9.2, students use pre-printed cards from a blackline master to decide which input values make sense for different functions. The card materials make the sorting and discussion concrete, helping students justify their thinking. As students work, educators listen for explanations that show understanding of valid inputs, using those moments to guide the class discussion toward the idea of domain.

The materials include a lesson overview with suggested timing for each lesson component to support effective lesson delivery. For example, unit 2, lesson 4 allots 10 minutes for the warm-up. The next portion of the lesson includes 10 minutes for an “Optional Activity” in which students “generate terms of geometric and arithmetic sequences using a spreadsheet.”

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

The lesson materials include an extension opportunity through the “Are You Ready for More?” sections that provide additional enrichment for students ready to deepen their understanding of lesson content. For example, in unit 1, lesson 4, activity 4.3, the “Are You Ready for More?” activity presents an additional challenge in which students analyze a new set of exponential functions and respond to the question “Which function would you choose? Does your choice depend on x?” Unlike the core lesson, which focuses on how the parameters a and affect the graphs of exponential functions, this extension requires students to compare equivalent exponential expressions and reason about whether one function is always greater than another regardless of the input value. Educator notes and sample responses support the effective implementation of this enrichment opportunity by providing guidance for facilitating student reasoning and evaluating responses.

The materials provide guidance for educators on using optional extension activities to extend student learning. Unit 7, lesson 10, activity 10.4 guides educators to introduce the rule of 72, a method for estimating the doubling time of a quantity that grows exponentially. The optional activity guidance states, “If desired, this may be an opportunity to introduce the Rule of 72, a method for estimating the doubling time of a quantity that grows exponentially. In an earlier lesson, when comparing the graphs of the owed amounts at 12%, 24%, and 30% interest rates, students made estimates of when each loan would double. If the Rule of 72 is introduced, consider referring back to that activity to test the rule.” This guidance supports educators in using the optional activity as an extension opportunity by connecting new learning to previously explored exponential relationships and providing students with an opportunity to apply and deepen their understanding of exponential growth.

Evaluation for 2.1a
Materials include a variety of instructional assessments at the unit and lesson level (including diagnostic, formative, and summative) that vary in types of tasks and questions.

In the Kiddom materials, each unit begins with “Check Your Readiness,” a diagnostic assessment that evaluates students’ prior knowledge of key concepts and skills. For example, in unit 1, the “Check Your Readiness” assessment measures students’ understanding of functions and related concepts. Students respond to a range of item types, including text-entry and multiple-choice questions, as well as tasks that require them to draw graphs.

The materials include a cumulative set of problems at the end of unit 1, lesson 1, which serves as a summative assessment and includes multiple-choice, draw, and fill-in-the-blank questions, as well as text-entry/open-ended free response. This lesson also includes a warm-up, which serves as a diagnostic assessment and includes written response inference problems. An example of a text-entry/open-ended free response prompt is “Explain why the relationship between the side lengths is linear.”

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

The “Kiddom Math High School Teacher Resource Guide” defines the instructional assessments used in the curriculum and explains their intended purposes, including formative, summative, and diagnostic assessments, as well as cool-downs, “Checkpoints,” and end-of-unit assessments. For example, it defines cool-downs as brief formative assessments at the end of each lesson designed to gauge students’ understanding of a key mathematical concept from the day’s instruction. Their intended purpose is to inform ongoing instruction by identifying student understanding and misconceptions in real time.

Additionally, the educator resource guide explains that formative assessments, such as “Check Your Readiness,” identify students’ prerequisite knowledge before a unit begins. Within the materials, summative assessments, including mid-unit and end-of-unit assessments, have a purpose of measuring mastery of course standards after instruction. The “Kiddom Math High School Teacher Resource Guide” also explains that the end-of-unit assessments gauge students’ understanding of the key concepts of the unit.

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

The “Kiddom Math High School Teacher Resource Guide” provides information on the consistent and accurate administration of instructional assessments, including clear guidance on when to administer assessments. For example, it explains how to administer the diagnostic “Check Your Readiness” assessment at the beginning of each unit to evaluate prior knowledge. It also provides guidance for supporting students who are below grade level such as revisiting prerequisite skills during the warm-up to reinforce understanding before new instruction begins.

The “Kiddom Math High School Teacher Resource Guide” provides guidance on the administration of assessments, including suggested time allocations and recommendations for pacing extended assessments across multiple class periods when appropriate. For example, unit 3, lesson 1.5 allots approximately five minutes for the completion of the cool-down. The guide also outlines instructional next steps when students struggle with a cool-down, such as modifying a “Launch” to address common errors identified in student responses.

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

The materials include a scope and sequence that outlines unit and lesson titles, the aligned TEKS, and learning targets for each lesson. The scope and sequence identifies where lessons embed formative assessments. This alignment supports progress monitoring by clearly connecting formative assessments to lesson learning targets and the Algebra I TEKS, allowing educators to gauge student understanding of course objectives throughout instruction.

Unit 2, lesson 1 identifies the TEKS at the beginning of the lesson, and the embedded assessments align with these standards throughout instruction. The TEKS addressed in this lesson include 111.39.c.1.G, 111.39.c.1.B, 111.39.c.12.D, and 111.39.c.12.C, which focus on writing formulas for the nth term and identifying terms of arithmetic and geometric sequences using precise mathematical language and a structured problem-solving model. The cool-down asks students to write rules for both an arithmetic and a geometric sequence and determine the next three terms of each.

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

The instructional assessments include TEKS-aligned items with varying item types and levels of complexity, including multiple-choice, multi-select, open-ended responses, and text-entry. These items require students to engage in different cognitive processes, ranging from recalling and selecting information to constructing explanations and representing relationships visually. For example, in unit 2, algebra 1.2, the “Check Your Readiness” assessment includes fill-in-the-blank, text-entry, sketch-a-graph, multi-select, and written-response items, reflecting a range of task complexity within a single assessment.

The “Kiddom Math Middle School Teacher Resource Guide” describes task complexity as requiring careful attention to the complexity of contexts, numbers, and computations, as well as students’ familiarity with given contexts and representations. In unit 8, lesson 1, activity 1.2, students have a concrete experience with a quadratic relationship in a familiar geometric context. The materials provide students with an image of a real-world garden with a fixed perimeter, and students experiment with how changes to one side of the rectangle affect its area. The questions vary in levels of complexity by first asking students to draw possible diagrams of the garden and label the length and width, which they can do tabularly. Questions then progress to finding the length and width to produce the largest possible area and having students explain or show why they think the particular length and width pairing they determined gives the possible largest area.

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

The course guide includes rubrics for evaluating restricted, constructed, and extended response items to support accurate scoring and interpretation of student performance. In the rubric for restricted constructed responses, a tier one response indicates work that is complete and correct, a tier two response reflects general conceptual understanding with some errors, and a tier three response demonstrates limited or no conceptual understanding or mastery.

The materials provide guidance for scoring instructional assessments and interpreting student performance through evaluator notes that accompany assessment items. These notes include sample responses and instructional guidance intended to help educators address common misconceptions. For example, in unit 4, “Check Your Readiness,” question 3 asks students to write an equation representing the amount of dog food remaining after Jada removes 0.25 kilograms per day from a five-kilogram bag. The “Note for Evaluating Responses” advises that if most students struggle with the item, educators should revisit lesson 16, activity 1, in which students write equations for linear functions, and also reference lessons 4 and 5 to support equation writing through the use of tables.

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

Formative assessments such as “Check Your Readiness” and cool-downs provide guidance for using included tasks and activities to respond to student trends in assessment performance. The “Notes for Evaluating Responses” and “Responding to Student Thinking” sections provide targeted recommendations based on patterns in student responses, including specific guidance for where and how educators can support students’ development of essential skills. For example, in unit 7, algebra 1.7, “Check Your Readiness” states, “If most students struggle with this item, plan to use Lesson 3 and write the number of bacteria in expanded form to show students how the exponent changes the way the expression is calculated. Help make it explicit how the expanded form is the same as substituting a value and evaluating the expression. Practice Problems in Lesson 1 can be used for extra practice with evaluating expressions.” This guidance connects assessment results to specific misconceptions and directs educators to use included lessons and practice problems to address student needs.

The “Check Your Readiness” assessments provide educators with guidance for using included instructional activities to respond to trends in student performance. For example, in unit 9, algebra 1.9, “Check Your Readiness,” students determine the zeros of quadratic functions. The educator guidance includes targeted instructional actions based on assessment results, stating, “If most students struggle with this item, plan to incorporate a review of the connections between the zeros of a function and the x-intercepts of the graph after the warm-up. Consider displaying a chart that details these connections, and keep it posted during this lesson.” This guidance helps educators respond to class-wide trends in performance by incorporating an included instructional review and visual support to reinforce the identified concept.

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 provide educators with tools to monitor student progress and growth over time. Educators can access multiple reporting features, including the “Assignment View,” “Scoreboard,” “Scorecard,” “Question View,” and “Standards View,” which offer data on both individual student performance and class-wide achievement across assignments, assessment items, and standards. For example, the resource “What Do My Reports Mean?” provides explicit guidance for interpreting and using key reporting tools, including the “Class Grade Average” line graph, “Mastery Groups” pie chart, “Class Standard Mastery” tracker, and “Student Standard Progress” reports. These features allow educators to analyze changes in student performance over time, monitor mastery of specific standards, group students according to performance levels, and track individual growth toward learning goals.

The materials include student-facing tools that allow learners to monitor their own progress and growth. A student dashboard enables students to review their performance through visual charts on a report page or by downloading individualized reports. These reports display performance aligned to specific standards, helping students understand what they have mastered and identify areas in which they need additional learning to guide their next steps.

Evaluation for 3.1a
Materials include teacher guidance for differentiated instruction, activities, and paired (scaffolded) lessons for students who have not yet reached proficiency on grade-level content and skills.

In unit 2, lesson 5, activity 5.3, students write recursive definitions using function notation. The materials guide educators to support students by having them revisit prior examples, describe relationships in words before writing symbolic representations, and compare different correct forms of recursive definitions. Partner discussions provide additional opportunities for students to check their work, clarify their thinking, and develop understanding of equivalent representations. These scaffolds and instructional supports help students who need additional assistance access and master the grade-level content.

The materials provide some educator guidance for supporting students who have not yet reached proficiency on grade-level content. For example, in unit 4, lesson 6, activity 6.3, educator guidance includes suggestions for helping students make connections between numerical calculations and algebraic representations. The “Advancing Student Thinking” section provides scaffolding for students who struggle to write expressions using variables, stating, “For students who struggle to write expressions for p liters and v liters, encourage them to revisit their previous three calculations. Some students may need to write out their work more carefully before noticing that they could perform the same steps using, or in place of, a number.”

Evaluation for 3.1b
Materials include pre-teaching or embedded supports for unfamiliar vocabulary and references in text (e.g., figurative language, idioms, academic language).

In unit 2, lesson 9, activity 9.2, students develop understanding of academic vocabulary such as domain, geometric sequence, and exponential function through contextual explanations, discussion prompts, and repeated use throughout the lesson. The materials also support comprehension of the problem context by helping students interpret phrases such as “Each person takes a fraction of what is left” and connect this language to diagrams, tables, and other mathematical representations. Additionally, the “Co-Craft Questions” routine encourages students to engage with and clarify the language of the task before beginning problem-solving, supporting their understanding of both the vocabulary and the situation described in the problem.

The educator guide includes sentence frames aligned to each unit’s problem-solving tasks along with a sample educator talk that models how to introduce and use the frames to support academic language during math discussions. For example, in unit 7, lesson 1, activity 1.3, the support for emergent bilingual (EB) students and the mathematical language routine (MLR) include sentence frames such as “I agree because . . .” or “I disagree because . . .” to help students respond. Materials also include sample educator modeling talk such as “If necessary, revoice student ideas to demonstrate mathematical language use by restating a statement as a question to clarify, apply appropriate language, and involve more students.”

Evaluation for 3.1c
Materials include teacher guidance for differentiated instruction, enrichment, and extension activities for students who have demonstrated proficiency in grade-level content and skill.

The materials include guidance for enrichment activities such as project-based learning activities, research projects, and creative projects that synthesize content and student learning for students who have demonstrated proficiency in grade-level content and skills. For example, the “Further Reading” section contains articles, projects, and lessons that extend beyond the grade level with complex open-ended problems that require applying grade-level math concepts to real-world scenarios. For example, the “A Thread Through Units 5–7, Exponential and Quadratic Functions, Critically Examining the National Debt” series has students respond to the questioning prompts and analyze the United States debt data for the past 30 years, graph it determining the best fit model (linear or exponential), and make predictions based on the model of best fit.

According to the “Kiddom Math High School Teacher Resource Guide,” optional activities “address a concept or a skill that goes beyond the requirements of a standard,” and their aim is to act as enrichment opportunities when time allows. For example, in unit 8, lesson 12, activity 12.3, students engage in an optional extension activity in which they evaluate quadratic expressions with varying coefficients and constant terms and analyze how these changes affect the corresponding graphs. Students record their observations in a table or use a spreadsheet tool to compare patterns and relationships.

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

In unit 2, lesson 1, activity 1.2, the “Activity Synthesis” provides a direct script for educators to introduce the concept by asking, “How many moves does it take to complete the puzzle with one disc?” and to guide students to recognize that the puzzle requires only one move. The “Launch” instructs educators to have students solve the puzzle with two discs and then facilitate a demonstration showing why the puzzle requires three moves. These explicit prompts support educators in modeling and explaining the recursive pattern in the sequence of moves, helping students build an understanding of the underlying mathematical concept.

The materials include explicit prompts and guidance to support the educator in modeling and explaining the concept of quadratic functions. For example, in unit 8, lesson 12, activity 12.2, students use graphs to observe how the value of the constant affects the graph. As students discuss their observations, the materials explicitly direct the educator to “tell students that people often describe the shape when a is positive as a parabola that ‘opens upward’ and the shape when a is negative as a parabola that ‘opens downward.’” This direct instructional prompt provides educators with precise language to explain the mathematical concept and supports consistent modeling of the relationship between the coefficient and the graph of a quadratic function.

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

In unit 2, lesson 3, activity 8.2, students explore connections between representations of arithmetic and geometric sequences by revisiting a paper-cutting context and analyzing tables, visual models, recursive definitions, and explicit formulas. The materials encourage a mix of instructional approaches, including whole-class discussion, partner talk, hands-on drawing or paper modeling, and the optional use of technology to support reasoning. It also prompts educators to highlight key ideas such as constant rate of change, growth factor, and how the starting term affects a sequence while addressing common misconceptions about domain and interpretation.

The materials provide educator guidance and recommendations for effective lesson facilitation using a variety of instructional strategies, including entry/exit tickets, think-pair-share routines, conceptual explorations, and structured problem-solving routines that support student reasoning and sense-making. Unit 4, lesson 8, activity 8.1 begins with a warm-up entry ticket to activate prior knowledge, followed by a “Launch” in which students work in pairs to engage in structured exploration. Students then move through quiet work time, partner discussions, and a whole-class synthesis of ideas. The instructional routine follows a think-pair-share structure, during which students investigate slope and tables to develop and connect their understanding of the concept.

Evaluation for 3.2c
Materials support multiple types of practice (e.g., guided, independent, collaborative) and include guidance for teachers and recommended structures (e.g., whole group, small group, individual) to support effective implementation.

The materials support multiple types of practice and provide varied opportunities for students to practice and apply mathematical concepts within a structured lesson flow. In unit 2, lesson 11, activity 11.3, students explore patterns in a geometric construction involving equilateral triangles, beginning with an educator launch in which the educator draws a figure and prompts students to describe how the creation of the second triangle and to identify how many sides steps 0 and 1 contain. Students then engage in collaborative group work in groups of four, followed by independent work time before returning to whole-class discussion. The lesson concludes with a collaborative synthesis in which students explain what it means to sum the terms in a sequence from zero to three and contrast this with finding the total number of triangles at step 3 of T.

The materials provide a variety of opportunities for students to practice and apply the concepts they learn, including individual, whole-group, and small-group opportunities. For example, in unit 4, lesson 5, activity 5.2, the students do a think-pair-share during the “Launch,” in which they work independently for a few minutes and then pair and share their responses with their partner in small groups.

Evaluation for 3.3a
Materials include teacher guidance on providing linguistic accommodations for various levels of language proficiency [as defined by the English Language Proficiency Standards (ELPS)], which are designed to engage students in using increasingly more academic language.

The materials include generic tips for EB students and do not address multiple levels of language proficiency. Units, lessons, and directions use the same sentence stems. For example, in unit 1, lesson 1, activity 1.3, the linguistic accommodations for EB students state, “Display the following sentence frames for all to see: ‘_____ is the input or output because . . .,’ ‘I noticed _____, so . . .,’ or ‘To determine a scale on the graph, I . . .’” However, the materials do not offer explicit guidance on providing linguistic accommodations and multiple levels of language support for pre-production, beginning, intermediate, high intermediate, and advanced EB students.

Although the materials include opportunities for building academic vocabulary over time such as through anchor charts and ongoing discussion, they do not provide specific guidance for accommodations based on varying levels of English language proficiency. For example, in unit 5, lesson 3, activity 3.3, the support for EB students includes a general prompt in which educators invite students to create a visual display showing the two inequalities they selected to solve, encouraging them to consider how to present their work so that others can interpret it and to add notes or details to communicate their thinking. However, the materials frame these supports broadly and do not differentiate instruction or accommodations across proficiency levels, nor do they provide tiered language supports aligned to varying stages of language development.

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

“Kiddom’s Approach to English Language Proficiency in Texas Math” provides a general overview of the MLRs with the supporting ELPS. For example, MLR1 connects to ELPS 1.E.iv, 5.B.i, 5.F.iii, and 5.G.iii. In unit 1, lesson 3, activity 3.3, the implementation guidance helps educators support EB students through MLR8, which states, “Use this routine to support whole-class discussion. After each student shares, provide the class with the following sentence frames to help them respond: ‘I agree because . . .’ or ‘I disagree because . . .’ If necessary, re-voice students’ ideas by restating their statements as questions.” This embedded guidance provides educators with explicit strategies for facilitating mathematical discussions, encouraging student engagement, and supporting the development of academic language aligned to the ELPS.

The materials include “Algebra 1 ELPS Alignment” that identifies where the course embeds English Language Proficiency Standards, and it offers suggestions for supporting students with language needs. This alignment helps educators understand how lessons incorporate language expectations so they can plan appropriate instructional support in bilingual and ESL settings. For example, unit 1, lesson 1 aligns with ELPS 1A, 3B, 3C, and 3G, illustrating how mathematical instruction incorporates specific language development standards.

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

Within the materials, supports for EB students appear in program components such as the “Launch,” “Activity Narrative,” “Support for English Learners,” “Activity Synthesis,” and “Advancing Student Thinking” sections. For example, unit 1, lesson 2, activity 2.2 includes prompts that build academic vocabulary, increase comprehension, and support structured discussion and written explanation. However, the materials do not provide explicit guidance for helping students make cross‑linguistic connections through oral and written discourse such as identifying cognates, analyzing language structures, or leveraging the home language to support mathematical understanding.

The materials include embedded guidance for educators to support EB students in developing academic vocabulary, increasing comprehension, and building background knowledge through oral and written discourse; however, they do not provide explicit support for making cross-linguistic connections. In unit 4, lesson 7, activity 7.3, students participate in partner and whole-class discussions to explain their thinking, interpret mathematical situations, and compare solution strategies. These activities support vocabulary development and comprehension through instructional routines such as MLR7: Compare and Connect and MLR6: Three Reads, which guide students in discussing key mathematical ideas, identifying important information in word problems, and communicating their reasoning. Students also strengthen understanding by connecting mathematical ideas to real-world contexts and by explaining their solutions in writing.

Evaluation for 3.3d
If designed for dual language immersion (DLI) programs, materials include resources that outline opportunities to address metalinguistic transfer from English to the partner language.

This guidance is not applicable because the program is not designed for dual language immersion (DLI) programs.

Evaluation for 4.1a
Practice opportunities over the course of a lesson and/or unit (including instructional assessments) require students to demonstrate depth of understanding aligned to the TEKS.

In the unit 1, algebra 1.1 mid-unit assessment, students demonstrate their understanding of functions by representing and interpreting relationships in multiple ways, including verbal descriptions, equations, graphs, tables, and symbolic representations. The assessment also requires students to analyze key features of functions such as identifying and describing the domain and range. These tasks require students to make connections among multiple representations of functions rather than applying a single procedure, supporting conceptual understanding and mathematical reasoning aligned with the TEKS.

In unit 8, lesson 3, activity 3.2, students move between visual patterns, equations, and functions to analyze quadratic relationships. Students connect features of growing geometric patterns to components of quadratic expressions, explain how each part of an equation represents aspects of the pattern, and use equations to predict values for later steps. Students also create visual patterns from given equations and justify whether the relationships represent functions. These tasks require students to interpret, represent, and explain quadratic relationships across multiple forms, demonstrating conceptual understanding beyond simply writing or solving equations.

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

Unit 6, lesson 4, activity 4.2 increases in complexity as students progress from interpreting and graphing equations to creating and analyzing equivalent equations. The activity gives students two equations that represent school supplies purchased by the educator during two different trips. They graph the equations to determine the cost of measuring tapes and calculators based on the given relationships. The complexity increases when students add the two equations to create a third equation and analyze how all three equations produce the same solution when graphed. The unit 6 “Section Level Planning Guide” explains that students “create new, equivalent equations that maintain the same solution,” which extends their understanding of equivalent relationships and systems of equations. This progression requires students to analyze structure, make connections among representations, and justify why different equations can represent the same solution.

In unit 9, the tasks progressively increase in complexity, leading students toward grade-level proficiency in the TEKS. The unit begins with students solving quadratic equations by factoring and explaining the relationship between a quadratic function and its graph in a given context. Students then extend their understanding by converting quadratic functions from standard form to vertex form using the process of completing the square. They identify key features such as the vertex and maximum or minimum values to solve problems and interpret quadratic relationships. Students then apply the quadratic formula to solve increasingly complex real-world problems. In the final lesson of the unit, students integrate multiple strategies for working with quadratic functions to solve a real-world problem involving the height of a diver.

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

The materials demonstrate coherence across units by connecting mathematical concepts and showing how relationships among ideas develop over time. For example, in unit 5, lesson 2, activity 2.2, students analyze a real-world situation to determine which orchard trip would be cheaper. Students identify the boundary value (n = 17) where two options have the same cost, and investigate values on either side of the boundary value to determine when each option is more cost-effective. Unit 5, lesson 4, activity 4.2 extends this understanding with students solving linear inequalities in two variables. Students connect the boundary line of a linear inequality to the related linear equation and reason that one side of the boundary line represents the solutions to the inequality.

Unit 8, lesson 4, activity 4.2 demonstrates coherence across units by connecting patterns, relationships, and mathematical concepts related to the big idea of functions. In this lesson, students compare and contrast quantities that grow exponentially and quadratically within a geometric context by analyzing patterns of growth in two situations. Students build on their prior learning of exponential functions from unit 7 and quadratic functions from unit 8 as they use pictorial representations, graphical representations, tables, and function notation to analyze and compare the two types of functions. This lesson reinforces the connection among different representations of functions and helps students understand how to analyze functions based on patterns of change and growth.

Evaluation for 4.2b
Materials demonstrate coherence across units by connecting the content and language learned in previous courses/grade levels and what will be learned in future courses/grade levels to the content to be learned in the current course/grade level.

Unit 1, lesson 1, activity 1.2 demonstrates coherence across units by connecting the content and mathematical language learned in previous courses to new learning in the current course. Students recall the meaning of functions, a concept introduced in the previous grade, and begin using more formal language to describe and analyze functions. The “Lesson Narrative” explains the progression of learning by stating, “The work here prepares students to describe and talk about functions more formally in upcoming lessons.” This foundation supports students as they continue studying additional types of functions throughout Algebra I, including exponential and quadratic functions, and prepares them for future coursework in Algebra II, where they will extend their understanding to functions such as rational, logarithmic, and radical functions.

In unit 3, lesson 1, activity 1.2, students investigate data relating the number of oranges to the weight of the oranges and determine a line of best fit for the data. The “Lesson Narrative” explains that this lesson connects to previous grade-level learning because “students investigated patterns of associations in bivariate data in eighth grade.” This connection builds on students’ prior experience analyzing relationships between two variables and extends their understanding to modeling data with linear relationships. Students will continue developing their understanding of patterns of association in future coursework, including Algebra II.

Evaluation for 4.2c
Materials demonstrate coherence at the lesson level by connecting students' prior knowledge of concepts and procedures from the current and prior grade level(s) to new mathematical knowledge and skills..

Unit 2, lesson 2, activity 2.2 demonstrates coherence at the lesson level by connecting students’ prior knowledge of concepts and procedures from current and prior grade levels to new mathematical knowledge and skills. Students build on their previous understanding of ratios and exponential functions as they explore the relationship between exponential growth and geometric sequences. Through the “Paper Slicing” activity, students generate exponential functions and analyze the growth pattern created by repeatedly slicing paper. By identifying the growth factor and connecting it to the common ratio of a geometric sequence, students extend their understanding of exponential relationships to a new mathematical representation. This lesson strengthens connections between prior function concepts and new skills involving geometric sequences.

Additionally, unit 4, lesson 1, activity 1.3 demonstrates coherence at the lesson level by connecting students’ prior knowledge of equations and inequalities to new learning about constraints. Students build on their previous experience writing equations and inequalities to represent information from real-world situations and apply this understanding to a class pizza party context. In this activity, students extend their knowledge by writing constraints using relational symbols such as <, >, and = to describe the conditions of the situation. This connection reinforces how to represent and interpret mathematical relationships, providing a foundation for understanding how constraints influence functions and modeling in future learning.

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

In unit 6, lesson 4, questions 1–7 focus on the current lesson’s content related to solving systems of equations by elimination, while question 8 (parts A–F) includes review problems from previous units. These review problems provide students with opportunities to retrieve previously learned information from long-term memory and apply prior knowledge in new contexts.

In unit 8, lesson 3, activity 3.2, students write a quadratic equation to describe a visual pattern without creating a table. Students retrieve and apply previously learned skills from an earlier unit in which they wrote expressions to describe visual patterns by creating tables and analyzing how the pattern changes at each step. Unit 2, lesson 2, activity 2.2 develops this prior learning with students using visual patterns to identify structure and write equations representing the relationship. By applying these previously learned strategies to quadratic patterns, students strengthen connections between visual representations, patterns, and algebraic equations.

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

In unit 1, lesson 8, students engage in interleaved practice opportunities by applying previously learned skills and concepts across lessons and units. Students do not encounter graph interpretation for the first time; instead, they build on prior understanding of functions, graphs, variables, units, rates, and equations by applying these concepts in a new context involving flag raising. Students interpret graphs, analyze function behavior, label axes, and connect equations to graphical representations using skills developed in earlier lessons. The lesson introduction reinforces this progression by stating, “Prior to this point, students have had multiple opportunities to interpret graphs of functions in terms of a situation.” During the activity, students apply their prior knowledge when prompted, “For each graph assigned to you, explain what it tells us about the flag.” This requires students to move beyond identifying graph features and explain how those features represent real-world behavior.

Unit 8 includes 17 lessons, and each lesson contains a “Cumulative Practice Problem Activity.” These practice sets provide students with opportunities to review concepts from the current unit through a variety of problem types while also revisiting skills from previous units. Each practice set includes at least one problem, and often multiple problems, connected to prior learning. This structure allows students to mix and apply different mathematical concepts, supporting flexible problem-solving and strengthening connections among skills rather than practicing concepts in isolation.

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

Unit 3, lesson 1, activity 1.3 gives students a graph showing the relationship between the sales price of food and the cost of ingredients. Students use the graph to interpret values and determine approximate outputs when given input values for ingredient cost. Students analyze the linear model by estimating the slope and y-intercept and evaluating how well the graph represents the relationship between cost and sales price. Students then evaluate the meaning of the slope and y-intercept in context. For example, it asks students a question regarding why a food item with free ingredients would still cost $0.76, requiring them to evaluate what the y-intercept represents in the real-world situation.

In unit 6, lesson 9, activity 9.2, students use a nutrition table, inequalities, graphs, and contextual information to analyze trail mix constraints. Within this task, students interpret the meaning of variables and solution regions, analyze relationships among the table, inequalities, and graphs, and evaluate which ingredients and constraints each model represents. Students justify their reasoning using evidence from multiple representations.

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

In unit 2, lesson 2, activity 2.2, students generate geometric sequences from a paper-cutting activity and create representations of the sequences using tables and graphs. Students complete a structured model of the situation based on an 8-by-10-inch sheet of paper, including the table “Number of Cuts/Number of Pieces/Area in Square Inches of Each Piece,” recording the number of pieces and the area of each piece after successive cuts. In this model, students observe that the number of pieces doubles with each cut and the area of each piece halves with each cut, representing exponential change. Students then “sketch a graph of the number of pieces as a function of the number of cuts” and “sketch a graph of the area of each piece as a function of the number of cuts.” Through this process, students build and use mathematical models of a real-world process by connecting tables and graphs to patterns of repeated cutting and using these representations to analyze exponential relationships.

In unit 3, lesson 3, activity 3.2, students use data about the weight of boxes of oranges to create a scatter plot representing the relationship between the number of oranges and the total weight. Students then construct a line of best fit to model the relationship between the variables. They also calculate and plot residuals to represent the differences between actual data values and the values predicted by the model. Students use these student-created models to analyze the data and determine how well the linear model fits the situation and represents the relationship.

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

In unit 1, lesson 1, activity 1.2, students reason about the relationship between time and distance in a real-world scenario involving a dog tied to a post. They sketch graphs to represent the dog’s movement, interpret points on the graph, and decide whether the relationship qualifies as a function. By connecting the abstract ideas of independent and dependent variables to a tangible situation, students show how to apply conceptual understanding of functions in new and meaningful ways.

In unit 3, lesson 7, activity 7.2, students collect, summarize, interpret, and draw conclusions from bivariate data using scatter plots, best fit lines, residuals, and correlation coefficients. Students apply their knowledge of the correlation coefficient in a real-world context. One of the questions asks students, “Is there a relationship between the number of penalties a team gets in a season and the number of wins in that season? Show any mathematical work that leads to your answer. If needed, snip a screenshot of your work and paste it below.” To answer this, students collect their own data and determine the correlation coefficient and the meaning of the correlation coefficient.

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

In unit 6, lesson 3, students repeatedly practice solving systems of linear equations using the elimination method. The sequence of questions moves from guided steps such as combining like terms through addition or subtraction to more independent problem-solving where students determine whether addition or subtraction is most appropriate and then solve systems without scaffolds such as graphing. Students also practice writing systems from verbal descriptions and identifying the slope and y-intercept across different forms of linear equations. This repeated and structured practice supports students in increasing accuracy and efficiency with the elimination process, building automaticity and procedural fluency for solving systems of equations.

In unit 9, lesson 13, activity 13.1, students engage in targeted review of simplifying radical expressions such as √288 prior to working with more complex expressions involving variables. The warm-up provides repeated practice with foundational procedures, so students can complete more complex grade-level tasks such as simplifying √2x²y with greater accuracy and efficiency. By reinforcing core skills through practice, the materials support the development of automaticity and procedural fluency with radical expressions.

Evaluation for 5.2b
Materials provide opportunities for students to practice the application of efficient, flexible, and accurate mathematical procedures within the lesson and/or throughout a unit.

In unit 7, lesson 4, activity 4.2, students model the relationship between successive tennis ball bounce heights and determine whether an exponential or linear function best represents the data. Students determine the growth factor using multiple strategies, including estimating from data patterns, using ratios of successive values, selecting initial data points, and using graphing technology to generate regression models. Students choose among these methods and compare results, allowing them to apply procedures flexibly while maintaining accuracy and selecting more efficient approaches based on the structure of the data.

In unit 9, lesson 13, students simplify radical expressions using strategies such as identifying perfect-square factors, applying prime factorization, and using properties of square roots. Students compare these approaches, select efficient methods for simplifying expressions, and justify why equivalent forms are valid. Across practice problems and the cool-down, students consistently apply procedures while demonstrating flexibility in strategy selection and improving efficiency as they recognize more direct simplification methods.

Evaluation for 5.2c
Materials provide opportunities for students to evaluate procedures, processes, and solutions for efficiency, flexibility, and accuracy within the lesson and throughout a unit.

Unit 5, lesson 3 provides opportunities for students to evaluate procedures, processes, and solutions for efficiency, flexibility, and accuracy within the lesson and throughout a unit. Students compare multiple solution strategies for inequalities, including Andre’s strategy of testing values on either side of a boundary and Priya’s strategy of reasoning structurally about the inequality. Students evaluate which method is more efficient and generalizable across different problems and explain why. Students also demonstrate flexibility by solving inequalities using both strategies and applying different methods across multiple problems. To support accuracy, students verify their solution sets using substitution and confirm that both approaches produce the same correct solution set, allowing them to evaluate the reliability of each method.

Unit 9, lesson 8 introduces students to the idea that they cannot always solve quadratic equations by factoring. For example, the summary states, “What is even trickier is that most quadratic expressions can’t be written in factored form!” Students examine how to use graphing to determine solutions and later compare this approach with completing the square and using the quadratic formula. As students progress through the unit, they evaluate which methods are most efficient or appropriate for different types of quadratic equations and consider the accuracy and usefulness of each approach when determining solutions. This ongoing comparison of solution methods supports students in evaluating procedures for efficiency, flexibility, and accuracy across the unit.

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

In unit 6, lesson 3, activity 3.2, the materials provide embedded prompts to guide instruction on using elimination to solve systems of linear equations. The materials prompt educators to ask questions such as “Why does adding the equations work for solving the system with 2x + y = 4 and x – y = 11, but doesn’t work for 8x + 11y = 37 and 8x + y = 7?” These supports help students recognize that elimination is an efficient method when they can remove one variable through addition or subtraction, and that in some cases the structure of the system requires a more strategic approach to make elimination effective.

In unit 6, lesson 4, activity 4.3, the guidance includes prompts such as “What happens if we add or subtract the equations?” and emphasizes that “no variables are eliminated, so it doesn’t help with solving.” It also guides educators to facilitate comparisons across systems, helping students identify why elimination works efficiently in some cases but not others. These embedded supports guide students toward recognizing when elimination is an efficient strategy and when to use an alternative approach, strengthening their ability to select more efficient solution methods.

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

The unit 6 overview describes how students first develop a conceptual understanding of systems of equations by interpreting two linear equations simultaneously and recognizing that the point of intersection represents a solution that satisfies both equations. Students then build procedural fluency by using multiple methods for solving systems, including graphing, substitution, and elimination. The materials explicitly connect this progression by moving students from conceptual-understanding-of-solution meaning to procedural-application-of-solution methods, and then to applying both conceptual and procedural understanding in real-world modeling situations involving systems of equations and inequalities.

Unit 8, lesson 8, activity 8.2 explicitly connects conceptual understanding to procedural skills through the use of algebra tiles. Students develop a conceptual understanding of the distributive property by manipulating tiles to represent expressions visually. The materials then connect this conceptual model to procedural skill by having students write the corresponding expanded algebraic expression. As stated in the narrative, “By manipulating the tiles, students create a visual model of the expression, which helps solidify the meaning of distribution. After constructing the model, the corresponding expanded expression is displayed below, allowing students to compare the model with the symbolic representation and self-check their work.”

Evaluation for 5.3b
Questions and tasks include the use of concrete models and manipulatives, pictorial representations (figures/drawings), and abstract representations, as required by the TEKS.

In unit 8, lesson 2, activity 2.3, students use a growing square pattern as a concrete model to represent the structure of the pattern. Students then create and analyze pictorial representations by drawing the growing square figures and identifying how the pattern develops visually. Finally, students connect these representations to abstract representations by writing quadratic expressions that describe the pattern. Students compare the drawings and algebraic expressions and explain how the symbolic expressions represent the structure shown in the diagram. This progression supports students in moving between concrete, pictorial, and abstract representations within the same task.

In unit 8, lesson 3, activity 3.2, students analyze a growing square pattern that serves as a concrete model of the relationship they are studying. Students use pictorial representations by examining the visual pattern, sketching additional steps, and creating their own pattern from a given equation. Students also use abstract representations by writing equations, applying function notation, connecting variables to quantities in the pattern, and generalizing the relationship as a quadratic function. Throughout the activity, students move between physical/visual models and symbolic representations to build connections across all three 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.

In unit 1, lessons 14 and 15, students connect real-world exponential decay situations to tables, graphs, and equations to develop an understanding of exponential expressions. Students build tables and graphs from contextual situations and use these representations to identify and define key features such as the initial amount and decay factor. They explain how repeated multiplication represents decreasing quantities in context and connect this pattern to exponential expressions. The lessons provide support for students to move between contextual situations, visual representations, and symbolic notation, strengthening their understanding of how to abstractly represent concrete situations using exponential functions.

In unit 4, lesson 2, activity 2.2, students examine concrete geometric figures such as a tetrahedron, cube, and dodecahedron and determine quantities, including the number of faces, vertices, and edges. Students use this concrete and representational information to make observations about relationships among the quantities. They then move toward abstract representation by using letters to represent the quantities and creating an equation that models the relationship such as V + F – 2 = E. The activity supports students in explicitly connecting a concrete geometric context to symbolic representations by having them explain how the equation represents the relationships they observed in the figures.

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

The materials provide opportunities for students to develop academic mathematical language using visuals and manipulatives. In unit 2, lesson 1, activity 1.3, students use manipulatives or the GeoGebra applet to model and analyze patterns while solving a problem involving the minimum number of moves needed to complete the puzzle. Students describe their solutions using academic vocabulary related to sequences, including sequence and term. The use of concrete models and visual representations supports students in connecting their observations to formal mathematical language.

The materials provide opportunities for students to develop academic mathematical language using visuals, manipulatives, and multiple representations. In unit 7, lesson 2, activity 2.3, students investigate exponential functions by modeling repeated folds of paper and analyzing the resulting thickness and area. Students use mathematical vocabulary such as discrete graph, table, equation, domain, range, initial measurement, and growth factor to describe relationships represented through different models. Educator guidance supports language development by directing educators to identify student strategies using tables, graphs, or equations and provide opportunities for students to share their reasoning. This activity connects visual and concrete representations to the academic language of exponential functions.

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

In unit 3, lesson 3, activity 3.2, students develop their understanding of the term residual as they graph and analyze residuals from a previous scatter plot investigation. Students connect the vocabulary terms residual, line of best fit, and vertical distance to the relationship between actual and predicted values. The “Activity Synthesis” provides educator guidance and prompts such as “Find the residual that has the furthest vertical distance from the horizontal axis” and “What does this mean in the context of the scatter plot and the line of best fit?” These prompts support students in applying academic vocabulary while interpreting mathematical relationships.
All in all, this is an example of how the materials include embedded educator guidance to scaffold students’ development and use of academic mathematical vocabulary in context.

The unit 8, lesson 14 “Lesson Synthesis” provides educators with guidance on connecting a new function representing revenue and ticket price to the previous context of projectile motion. The guidance supports students in applying vocabulary terms such as vertical intercept, horizontal intercept, and vertex to interpret features of graphs. Educator prompts, including “What information does the horizontal intercept, the vertical intercept, and the vertex of the graph give us?” guide students in explaining mathematical relationships using precise academic language. All in all, this is an example of how the materials include embedded educator guidance to scaffold students’ development and use of academic mathematical vocabulary in context.

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

Students have opportunities to hear, refine, and use mathematical language with peers through structured discussion routines. For example, in unit 8, lesson 14, activity 14.4, students apply their understanding of key characteristics of quadratic functions to solve contextual problems. Each pair of students receives a data card and a problem card and must ask questions, share information, and explain their reasoning to solve the problem. Through multiple rounds of discussion, students use academic vocabulary related to quadratic functions, including vertex, x-intercepts, and maximum height. The materials provide exemplar responses that model precise mathematical explanations such as explaining that the rocket’s maximum height occurs at the vertex because it is halfway between the x-intercepts. These supports help students develop and refine mathematical language during peer conversations.

In unit 9, lesson 18, activity 18.4, students write expressions that define quadratic functions with specific graphical features. Students work with partners using data cards and problem cards, asking questions and explaining information needed to write an expression. Through multiple rounds of discussion, students hear, refine, and use mathematical language with peers. Students apply academic vocabulary including vertex, vertex form, factored form, standard form, x-intercepts, zeros, and function as they describe and compare quadratic representations. The “Activity Synthesis” provides educator guidance to support mathematical conversations by helping students analyze which form of a quadratic equation is most useful in different situations. These supports help students develop and refine mathematical language during conversations.

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

In unit 1, lesson 1, activity 1.2, students analyze a real-world situation involving a dog tied to a post and create a graph to represent the relationship between time and distance. Students explain how their graph represents the situation, determine whether the relationship is a function, and justify their reasoning. This activity shows how materials integrate TEKS process standards through opportunities for students to discuss and compare representations, communicate mathematical ideas, and connect graphical representations to a real-world context.

Materials integrate TEKS process standards into lessons through opportunities for students to analyze, represent, and communicate mathematical ideas. For example, in unit 1, lesson 1, activity 1.3, students analyze relationships between quantities in a real-world situation and identify independent and dependent variables. Students create and interpret graphs, use function language to describe relationships, and explain their reasoning with a partner. The activity provides opportunities for students to represent relationships in multiple ways, communicate mathematical ideas, and connect representations to the context of the problem.

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

The “Kiddom Math High School Teacher Resource Guide” provides a description of how the materials incorporate and connect TEKS process standards throughout the course. The guide describes classroom structures that support students in engaging in mathematical discourse, solving problems, reasoning, constructing arguments, modeling with mathematics, using tools strategically, and communicating mathematical ideas. The materials state, “The curriculum materials include classroom structures that support students in taking risks, engaging in mathematical discourse, productively struggling through problems, and participating in ways that make their ideas visible.” The guide also describes that “doing mathematics” means “learning mathematical concepts and procedures while engaging in the mathematical practices, making sense of problems, reasoning abstractly and quantitatively, constructing arguments and critiquing the reasoning of others, modeling with mathematics, using appropriate tools strategically, attending to precision in their use of language, looking for and making use of structure, and expressing regularity in repeated reasoning.”

The Algebra 1 Scope and Sequence and “Course Narratives” describe how the materials incorporate and connect TEKS process standards throughout the course. The scope and sequence identifies the TEKS addressed across the course, including process standards, while the “Course Narrative” describes how students represent, interpret, and communicate mathematical ideas as they develop understanding of functions. For example, the materials state that students “deepen their understanding of functions and deepen their ability to represent, interpret, and communicate about them—using function notation, domain and range, average rate of change, and features of graphs.” The materials also describe how students analyze mathematical structures and express relationships through different representations. These descriptions demonstrate how TEKS process standards connect to mathematical content throughout the course.

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

The “Section Level Planning Guide” for unit 7 provides a description of how the unit regularly incorporates and connects TEKS process standards. The guide identifies opportunities for students to apply exponential modeling techniques to real-world situations by selecting appropriate models, analyzing and interpreting exponential functions through graphs, function notation, and rate of change calculations, and applying exponential models to financial contexts involving interest rates and compounding intervals. These descriptions demonstrate how the unit regularly embeds TEKS process standards as students represent, analyze, model, and communicate mathematical relationships.

The unit 8 overview describes how the unit regularly incorporates and connects TEKS process standards. Students explore quadratic relationships using multiple representations, including graphs, tables, and equations, and connect visual models to algebraic representations. As students compare quadratic and linear functions and analyze standard, factored, and vertex forms, they develop strategies for interpreting key features of functions. The unit overview also describes how students apply quadratic models to real-world situations, create equations to represent contexts, and interpret solutions.

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

The materials regularly integrate TEKS process standards throughout lessons, including warm-ups, instructional activities, and supports for EB students. For example, in unit 4, lesson 1, activity 1.2, students create expressions to represent quantities and relationships in a situation, engage in mathematical modeling, make assumptions and estimates, perform calculations, and revise their models as they gather additional information. Students compare strategies, justify their plans, represent changing quantities with variables, and explain what their expressions represent, demonstrating how the lesson incorporates mathematical modeling, reasoning, representation, and communication.


Lessons in the materials incorporate TEKS process standards through lesson-level expectations and activities. For example, in unit 8, lesson 2, the top of the lesson codes the TEKS process standards. Students compare visual patterns that represent quadratic relationships with patterns that represent linear and exponential relationships. The “Learning Goals” include expectations for students to communicate mathematical ideas, including “Describe (orally and in writing) a pattern of change associated with a quadratic relationship” and “Determine and explain (orally and in writing) whether a visual pattern represents a linear, exponential, or quadratic relationship.”

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

Unit 6, lesson 4, activity 4.2 provides opportunities for students to think mathematically, persevere through solving problems, and make sense of mathematics by developing an understanding of how adding two equations in a system creates a new equation with the same solution. Students engage in mathematical reasoning through educator-guided open-ended questions that encourage them to justify their thinking and explain their strategies. For example, materials prompt the educator to ask students, “In general, why does it make sense for a third equation that is the sum of the two equations in a system to share a common solution with the other two?” The activity also includes multipart tasks that require students to interpret the meaning of each equation, solve the system, explain what each equation represents in the context of the situation, and compare the resulting equation to the original system. The lesson regularly embeds opportunities to persevere when it gives students quiet time to think, followed by partner discussions and whole-class sharing before reaching conclusions. The tasks increase in complexity by moving from interpreting solutions to solving systems, writing systems from real-world situations, and evaluating the reasonableness of solutions by explaining how many solutions make sense in context.

Unit 8, lesson 3, activity 3 provides opportunities for students to think mathematically, persevere through solving problems, and make sense of mathematics by emphasizing reasoning, justification, and connections among multiple representations of quadratic expressions. In the activity, students analyze a growing pattern, determine whether the relationship is linear or quadratic, critique mathematical reasoning, and compare equivalent algebraic expressions using both visual and symbolic representations. For example, students sketch the next stage of a growing pattern, determine whether the growth is linear, evaluate Kiran’s claim, and determine whether Diego and Jada’s equations correctly represent the pattern. The activity requires students to work through multiple reasoning tasks that involve identifying patterns, constructing mathematical arguments, addressing misconceptions, and justifying their conclusions, including recognizing that increasing dimensions do not necessarily indicate linear growth. Students also connect visual patterns, area models, and algebraic expressions to explain why the growth is quadratic and why different algebraic expressions can represent the same function.

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

Unit 2, lesson 10, activity 10.3 supports students in understanding, explaining, and justifying that there are multiple ways to represent and solve mathematical problems. Students investigate square patterns by representing the situation with a diagram, a definition, or an equation and determine whether the pattern represents an arithmetic or geometric sequence. The activity asks students to share and justify the strategy they used to identify the type of sequence. During the “Activity Synthesis,” educator guidance states, “As students share, ask them to justify their solution methods. Display any representations used for all to see during the explanations.” The practice problems provide additional opportunities for students to solve problems involving arithmetic and geometric sequences using multiple representations and solution strategies, reinforcing that different approaches can lead to valid solutions.

Unit 9, lesson 2 supports students in understanding, explaining, and justifying multiple ways to represent and solve mathematical problems by connecting symbolic and geometric representations of polynomial multiplication. Students interpret polynomial multiplication as finding the area of a rectangle whose side lengths are polynomial expressions, demonstrating how an area model represents the same mathematical process as symbolic multiplication. Educator discussion prompts encourage students to explain and justify their reasoning such as “How did the distributive property help you multiply polynomials?” Students also compare multiplying a linear expression by a quadratic expression with multiplying two quadratic expressions and discuss the similarities and differences between the procedures. These experiences help students recognize they can use multiple representations and solution methods to solve the same problem while strengthening their conceptual understanding of polynomial multiplication.

Evaluation for 6.1c
Materials are designed to require students to make sense of mathematics through multiple opportunities for students to do, write about, and discuss math with peers and teachers.

The “Kiddom Math High School Teacher Resource Guide: Problem-Based Teaching and Learning” establishes an instructional framework that engages students in solving problems, writing about their mathematical thinking, and discussing ideas with peers and educators as part of daily instruction. The guide describes how students learn mathematics by “doing mathematics” and explains that classroom structures support students in “taking risks, engaging in mathematical discourse, productively struggling through problems, and participating in ways that make their ideas visible.” The guide also states that students have opportunities to “express their mathematical ideas and discuss them with others,” while educators facilitate learning by asking questions, listening to student thinking, “orchestrating discussions,” and helping students share and synthesize their mathematical reasoning. This framework supports consistent opportunities for students to actively engage in mathematical problem-solving, communicate their thinking, and learn from the ideas of others.

Unit 3, lesson 1, activity 1.4 provides a concrete example of this instructional framework in practice. Students solve mathematical problems, write about their reasoning, and engage in discussions with peers and the educator as they interpret the slope and vertical intercept of a line of best fit in the context of a given data set by analyzing scatter plots with independent and dependent variables. Students first describe the meaning of the slope and vertical intercept with a partner before sharing their interpretations with the whole class. Suggested questions, including “How do you interpret the slope for each equation?” and “How could Elena compare the decrease in fuel economy as mass increases for hybrid cars to the decrease in fuel economy as mass increases for new cars? Explain your reasoning,” prompt students to explain and justify their mathematical thinking.

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

Unit 3, lesson 7, activity 7.2 supports educators in guiding students to share and reflect on their problem-solving approaches through explanations, arguments, and justifications. Students examine the relationship between the number of penalties and the number of wins for a sports team by creating a scatter plot and determining a correlation coefficient from a given data set. The “Activity Synthesis” provides educator guidance to facilitate discussions about students’ reasoning and solution strategies. For example, the “Activity Synthesis” encourages educators to voice prompts such as “If there is a negative correlation, do you think the penalties would cause fewer wins?” and “How did you conclude? Explain your reasoning.” These prompts encourage students to explain how they interpreted the data, justify whether the correlation is positive or negative, and construct arguments about whether the number of penalties may influence the number of wins for a sports team.

Unit 8, lesson 1, activity 1.3 supports educators in facilitating opportunities for students to share and reflect on their mathematical thinking. Students use a table of values from the previous lesson, which includes possible lengths, widths, and areas of rectangles with a perimeter of 50 meters, to plot points and investigate a new type of function. The “Activity Synthesis” provides educators with questions to guide student reflection such as “Is the graph linear? Is it exponential?” and “Can we tell if a point represents the length and area of the garden simply by plotting it on the graph?” As students respond to these prompts, they explain their observations, justify their interpretations of the graph, and reflect on the meaning of plotted points, symmetry, and patterns. The “Lesson Synthesis” further supports reflection by asking students to “reflect on how the relationship between the side lengths and the area of a rectangle differs from other relationships they’ve seen,” providing additional opportunities for students to share and refine their mathematical reasoning.

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

Unit 7, lesson 10, activity 10.3 includes prompts and guidance to support educators in providing explanatory feedback based on student responses and anticipated misconceptions. Students build mathematical models to compare two investment options using exponential growth in a real-world context. The “Advancing Student Thinking” section prepares educators to address potential misconceptions, including when students are unsure how to proceed because they don’t have the length of time for the investment. The educator guidance states, “Students may be unsure about what to do because the length of time of the investment is not given. Encourage them to try out different time frames, or prompt them to choose different time frames for different cases. They should still support any decisions with mathematical reasoning.” As students share their investment choices and reasoning, the “Activity Synthesis” provides questions that help educators respond to student thinking and provide feedback such as “What is the nominal annual interest rate for each option?” “Do they have the same effective annual rate? Why or why not?” and “How does the length of investments influence your calculations and investment choice?”

Unit 9, lesson 15, activity 15.2 provides educators with guidance for anticipating misconceptions and providing explanatory feedback as students transition from solving quadratic equations by graphing to solving them algebraically. The “Advancing Student Thinking” section identifies possible errors and provides guidance for addressing student understanding, including the prompt “Watch for students who incorrectly substitute 40 for and evaluate h(40), or who write g(t) = 8 instead of evaluating g(8). These students may be having trouble distinguishing between the input and output.” The “Activity Synthesis” supports educators with questions that allow them to respond to student strategies and deepen understanding, including, “Once you have the equations, how did you find the solutions when the equation has a 0 on one side?” “What about when the equation has a non-zero number on one side?” and “How many solutions did you get?”