Kiddom Texas: Grade 7, Middle School Advanced Mathematics

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

The organization of the scope and sequence consists of a table with columns that name and outline the unit, section title, lesson number, lesson title, learning target, TEKS, and ELPS. The learning target outlines the concepts taught in the course. For example, one of the concepts taught in unit 1 is “Create and describe (in writing) graphs that show measurements of circles.” The TEKS to address the learning target include 7AM.1.D, 7AM.1.E, 7AM.5.A, and 7AM.10.A. The corresponding ELPS is 1.C.


The Grade 7 materials include a scope and sequence with ELPS alignments identified throughout the course year. The scope and sequence consists of a table with the following headings, “Location in Program,” “Lesson Title,” and “ELPS.” It includes units 1–12 along with the name of each lesson title and the corresponding ELPS. For example, unit 1, lesson 3 identifies ELPS 4.C, 4.D, and 4.E as the standards addressed.

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

The materials include three instructional calendars to support effective pacing for the implementation of the materials. The program provides 165-, 180-, and 210-day calendars outlining recommended pacing for the instructional year. The program organizes pacing by unit, lessons, assessment days, flex days, and total days. For example, in the 165-day calendar, “Unit 1: Circles” includes nine lessons, with one day allocated for a check-in, mid-unit assessment, and end-of-unit assessment. This unit includes zero flex days, for a total of 10 instructional days.

The materials provide pacing calendars for 165-, 180-, and 210-day schedules, showing the suggested time for each unit and major concept while also including flex days for review, reteaching, assessments, lesson extensions, and transitions between units. For example, the 180-day calendar includes a column for the total number of suggested days for each unit to support effective implementation. Unit 2 includes 12 lessons with a total of 13 days.

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 materials include a “Course Narrative” that shows how learning connects throughout the course. Students build understanding through work with circles, proportional relationships, personal finance, transformations, rational numbers, equations, statistics, and geometry. Throughout the course, students apply math to real-world situations and strengthen problem-solving and reasoning skills. For example, in unit 1, lesson 7, students connect their earlier estimates about circle area to the formula for the area of a circle by cutting and rearranging circles into familiar shapes. They see how the circumference contributes to the formula, leading to the relationship A = πr².

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 materials include processes that support educators in understanding and preparing to teach a unit. These resources include lesson objectives, key vocabulary, success criteria, and a unit overview. Each unit overview contains learning narratives that describe the mathematical concepts students will learn and the instructional intent of the unit. For example, unit 1 includes the “Learning Narrative” that students will “develop understanding of pi (π) as a constant of proportionality between circle measurements, exploring relationships between diameter, circumference, and area through measurement, visualization, and mathematical reasoning.” The unit overview also provides an explanation of how students will engage with the content and progress toward the unit objectives. For example, it states that students explore circles by investigating the relationship between diameter and circumference, discover pi (π) through hands-on measurements, and learn its approximate value of 3.14.

Unit 11, lesson 3 explains how students build on previous work with samples to estimate population proportions and use those estimates to make inferences about a population. The overview identifies the lesson objectives, lists the materials needed for instruction, highlights an optional activity that deepens students’ understanding of sampling variability, and includes an “I can” statement that clarifies the expected student learning. This guidance supports educators in understanding the lesson focus and preparing for instruction.

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

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 consists of 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.

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 provide a unit overview that includes the unit learning goals, narratives, and background content knowledge. The “Check Your Readiness” activity at the beginning of each unit also assesses students’ background knowledge. For example, there is an activity to test students’ background knowledge on understanding the perimeter and area of shapes. The “Unit Narrative” also includes an explanation of what students will learn in the unit and the instructional intent. For example, one of the unit learning goals and narratives for “Unit 1: Circles” is to “develop understanding of pi (π) as a constant of proportionality between circle measurements, exploring relationships between diameter, circumference, and area through measurement, visualization, and mathematical reasoning.”

The materials identify and embed the academic vocabulary necessary to teach the unit, such as area, area of a circle, and circle. In addition, the materials include course and lesson glossaries that define key academic terms as they are introduced. For example, in unit 1, lesson 1, the glossary defines terms such as circle, circumference, diameter, pi, and radius. This supports educators in introducing concepts clearly and helps students use precise mathematical language to understand relationships within circles.

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 for families in English and Spanish to use at home to support students’ learning and development for each unit. Each unit contains a family support material in both English and Spanish. For example, the document Grado 7, unidad 1: Círculos preguntas frecuentes provides suggestions for how families can support their children, information about key skills and main ideas, connections to the real world, and explanations of how the content prepares students for college and career.


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 encourages families to “discuss real-world examples of percentages they may encounter in real life such as sales at stores, tips at restaurants, or interest rates on savings accounts.”

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 and synthesis activities, and cool-down assessments. Each lesson includes clearly defined 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 regularly integrates instructional assessments, allowing educators to continuously monitor student understanding and adjust instruction based on student responses and discourse.

Unit 1, lesson 1 presents a clearly structured instructional sequence aligned to TEKS expectations for understanding circle measurements and the relationship between circumference and diameter. The lesson begins with a warm-up to activate prior knowledge and engage students in mathematical thinking. It also includes guided questions and activities that encourage exploration; identifies lesson materials; and provides built-in opportunities for formative assessment throughout the lesson. For example, during the “Activity Synthesis,” students compare the height of a toilet paper tube to the distance around the tube and discuss questions such as “What was important to you when making your decision?” and “What information would help you make a better decision?”

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

The materials include a lesson overview that identifies the educator and student materials needed for instruction. For example, unit 1, lesson 7 lists required materials for both students and educators. Materials needed for this lesson are blank paper, cylindrical household items, glue, markers, and scissors. The lesson overview also identifies necessary educator preparation, such as gathering cylindrical household items prior to instruction.

The materials include a lesson overview with suggested timing for each lesson component to support effective instruction. For example, unit 2, lesson 1 allots five minutes for the warm-up. It allots 15 minutes for the next section, stating, “The purpose of this task is to introduce students to the idea of a proportional relationship.”

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

The materials provide explicit guidance for educators on implementing optional extension activities and identifying student thinking to support deeper learning. For example, in unit 6, lesson 11, activity 11.3, the optional extension activity asks students to determine which triangles in a given set are similar. The educator guidance identifies specific strategies to monitor for, including students who determine triangle similarity by “determining if the corresponding sides have the same scale factor or checking that two (or three) corresponding angles are congruent.” It also directs educators to select students who use these methods and invite them to share their reasoning during the discussion.

In unit 3, lesson 3, activity 3.2, students engage in an enrichment problem following the primary activity. The enrichment problems challenge students to reason about the composition of transformations by responding to the question, “Can you find a simple description of reflecting across the x-axis followed by reflecting across the y-axis?” This extension builds beyond the core lesson objective by requiring students to generalize the effect of composing two transformations into a single transformation and describe the resulting relationship. The “Are You Ready for More?” activity provides an opportunity for students who are ready for additional challenge to extend their learning through deeper mathematical reasoning and application of transformation concepts.

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

Each unit begins with a “Check Your Readiness” diagnostic assessment, which evaluates students’ prior knowledge of key concepts and skills. For example, in unit 1, the “Check Your Readiness” assessment measures students’ understanding of the area and perimeter of shapes such as squares, triangles, and circles, helping to identify and address misconceptions before new instruction begins. This assessment varies in types of tasks and questions, as some items are text-entry, some are multiple-choice, and some require students to draw, write, or upload responses.

At the end of unit 1, lesson 1 is a cumulative set of problems that functions as a summative assessment and includes multiple-choice, fill-in-the-blank, and text-entry/free-response items. The lesson also includes a warm-up that serves as a diagnostic assessment and requires students to respond in writing to inference-based questions. An example of a text-entry/free-response is “Lin measured the diameter of a circle in two different directions. Measuring vertically, she got 3.5 cm, and measuring horizontally, she got 3.6 cm. Explain some possible reasons why these measurements differ.”

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

The “Kiddom Math Middle School Teacher Resource Guide” defines the instructional assessments such as cool-downs, “Checkpoints,” and end-of-unit assessments and their intended purpose. 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 “Kiddom Math Middle School Teacher Resource Guide” explains that formative assessments such as “Check Your Readiness” function as diagnostic assessments used to determine what students already know about upcoming concepts. The resource guide also provides examples of how to use various formative assessments, including the “Lesson Narrative,” “Activity Narrative,” “Lesson Synthesis,” and “Activity Synthesis,” to support instructional decision-making.

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

The “Kiddom Math Middle 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 Middle School Teacher Resource Guide” includes suggested time allocations and recommendations for pacing extended assessments across multiple class periods when needed. For example, unit 3, lesson 3.3 allots five minutes for the cool-down. The guide also outlines instructional next steps when students struggle with a cool-down such as modifying the time spent on 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, aligned TEKS, and lesson-level learning targets. The scope and sequence identifies where units and lessons embed formative assessments and demonstrates alignment between these assessments, the TEKS, and the lesson objectives. This clear alignment supports ongoing progress monitoring by connecting formative assessment tasks directly to intended learning outcomes. It ensures that formative assessments consistently measure student understanding and progress toward mastery of the Grade 7 math TEKS throughout instruction.

In unit 2, lesson 1, the beginning of the lesson identifies the TEKS, and the embedded assessments align with these standards throughout instruction. The TEKS addressed in this lesson include 111.27.b.1.G and 111.27.b.4.C, which focus on determining the constant of proportionality. In the cool-down, students define the constant of proportionality, explain its meaning in context, and determine it within a real-world scenario.

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, including multiple-choice, multi-select, open-ended, and text-entry responses. These items also vary in levels of complexity and cognitive demand, requiring students to engage in tasks ranging from recalling and selecting information to explaining reasoning and solving problems. For example, unit 3, “7.3 Check Your Readiness (A)” includes fill-in-the-blank, text-entry, multi-select, and written-response items, reflecting a range of 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. For example, in unit 3, lesson 3, students determine and request the information needed to perform a transformation in the coordinate plane using problem cards and progress to more complex tasks. One of the complex tasks asks students, “Can you find a simple description of reflecting across the x-axis, followed by reflecting across the y-axis?” The task provides students with a verbal description of the transformation, followed by the question.

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

The materials include 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 to help educators address common misconceptions and understand acceptable variations in student reasoning. For example, unit 1, “Check Your Readiness A,” question 2, part B provides sample responses, including “Sample response 1: Priya may have rounded her measurements of each side of the square to the nearest cm, while Noah may have rounded to the nearest mm.”

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 identify common student approaches and misconceptions and provide targeted instructional recommendations based on patterns in student responses. For example, unit 2, “Check Your Readiness A” explains that the assessment item aims to reveal students’ understanding of two types of percentage problems, finding a whole given a part and a percentage and finding a percentage of a given value. The guidance states, “If most students struggle with this item, plan to use lesson 1 and the lessons that follow to study these two types of percentage problems. In lesson 1, activity 2 students will begin thinking about percent increase and percent decrease situations.” This guidance explicitly connects assessment results to specific follow-up lessons and activities, enabling educators to address misconceptions and support students in developing essential percentage concepts.

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 10, “Check Your Readiness A,” students complete prerequisite skill questions on decimals, fractions, percents, and their relationships before beginning the study of probability. The educator guidance provides a targeted instructional response based on assessment results, stating, “If most students struggle with this item, plan to take extra time for the launch of Activity 4. Display a blank number line and call on students to place benchmark fractions, decimals, and percents on the number line. Ask students to share their strategies for making the placement. Connect this to the questions ‘Which is closer to 1?’ and ‘Which has the largest value?’” This guidance helps educators respond to class-wide trends in performance by modifying the launch of an included instructional activity to reinforce prerequisite concepts before students begin new learning.

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 1, lesson 1, activity 4.3, the “Anticipated Misconceptions” section guides educators in assisting students who struggle with the conversion between inches and miles. Educators can “remind students that there are 5,280 feet in a mile. Ask students how many inches are in 1 foot. Make sure students arrive at a final answer of 63,360 inches in one mile before calculating the number of rotations made by each wheel.”

In unit 1, lesson 7, activity 7.5, there is a task in which students reason about the relationship between a circle’s circumference and diameter. The “Response to Student Thinking” section guides educators in supporting students who struggle to find the area of a circle by revisiting the concept in later lessons, such as inviting multiple students in lesson 9 to share their reasoning about finding the area. The “Anticipated Misconceptions” section also prompts educators to check that students correctly determine the diameter and, if needed, remind them that since circumference is a little more than three times the diameter, the diameter is slightly less than one-third of the circumference.

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).

Unit 4, lesson 2, activity 2.3 introduces terms such as interest rate and compound interest in context, and it offers those terms repeatedly as students work through savings scenarios. The activity guides educators to walk through an example first and then move students into practice with a worksheet, so the meaning of the terms is clear before independent work. The discussion questions also help students connect the language in the problem to what is happening mathematically such as how money grows over time and why the “growth of savings” depends on both rate and time.

The educator guide provides sentence frames aligned to each unit’s problem-solving tasks, along with sample educator talk that models how to introduce and use these frames to support academic language during math discussions. For example, in unit 5, lesson 3, activity 3.3, the mathematical language routine (MLR) includes sentence frames to help students respond such as “First, I _____ because . . .” and “I noticed _____ so I . . .” The guidance also encourages opportunities for turn and talk, noting that some students may benefit from rehearsing their responses with a partner before sharing with the whole class.

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 “Further Reading” section provides articles, projects, and lessons that extend beyond grade-level expectations through complex, open-ended problems requiring application of mathematical concepts to real-world scenarios. One example is the “Why Is a Negative Times a Negative a Positive?” lesson. This lesson engages students in higher-order thinking tasks such as finding equivalent ratios using real-world contexts such as recipes with varying quantities and concentrations, analyzing visual representations, and determining equivalent ratios of geometric figures on a coordinate plane. It also prompts students to explain their reasoning, describe mathematical relationships, and even invent their own situations that demonstrate the concept.

According to the “Kiddom Math Middle School Teacher Resource Guide,” optional activities “address a concept or a skill that goes beyond the requirements of a standard” with the intention of acting as enrichment opportunities when time allows. For example, in the optional extension activity in unit 8, lesson 8, activity 8.3, students “compare the structure of equations that have no solution, one solution, and infinitely many solutions.” The materials state the activity is “particularly useful for students needing more practice identifying which equations will have each of these types of solutions before attempting to solve.”

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.

Unit 1, lesson 5, activity 5.3 includes guidance to support educators in explaining mathematical concepts, particularly when there is a student misconception. The “Advance Student Thinking” section prompts educators to address a common error in which students decompose the shape into a rectangle and triangle, but incorrectly use 270 miles as a side length instead of calculating the difference between 490 miles and 270 miles. The guidance instructs educators to have students check their work with a partner and revisit their calculations, supporting accurate reasoning and reinforcing the mathematical concept.

The materials include questioning strategies and discussion prompts to guide educators in explaining mathematical concepts. Each activity embeds these prompts and questions, including in the “Launch,” “Activity Synthesis,” and “Advancing Student Thinking” sections. For example, in unit 5, lesson 1, activity 1.2, the “Activity Synthesis” includes prompts such as asking students how they would describe a quantity “greater than zero” on the number line and discussing the use of “+” and “–” as symbols for positive and negative numbers. The materials include the following prompt, “Discuss the use of + and – as symbols to denote positive and negative numbers.”

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

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, concept explorations, and structured problem-solving and reasoning routines that support student sense-making. The educator’s guide also provides suggested pacing for each lesson. For example, unit 4, lesson 3, activity 3.1 begins with a warm-up (entry ticket), followed by a “Launch” with two minutes of quiet think time and a whole-class discussion. The instructional routine uses a notice-and-wonder structure as students examine household budgets from different cities in Texas, with students exploring patterns and identifying factors that influence financial decision-making.

The materials include guidance for lesson delivery and facilitation such as organizing students in pairs, using hands-on sampling with physical slips, and structuring time for partner work followed by whole-class discussion. The materials also support educators in introducing key statistical concepts, including defining proportions and connecting them to real data through concrete examples. Discussion questions guide facilitation by prompting students to compare results across groups, interpret variability in samples, and refine their estimates based on class data. It offers multiple instructional strategies, including collaborative learning, manipulatives, visual displays of results, guided questioning, and structured reflection. For example, in unit 11, lesson 3, activity 3.2, students sample reaction times and use class comparisons to evaluate the accuracy of their estimates.

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 provide guidance for educators on implementing instructional routines and structures that support effective practice and keep students focused on the content throughout the lesson. For example, in unit 2, lesson 2, activity 2.2, the educator launches the activity by organizing students into pairs, followed by five minutes of independent quiet work time, then partner collaboration, and finally whole-class discussion. Lesson 2 also concludes with an independent activity, 2.5, in which students work independently for five minutes to demonstrate understanding.

The materials provide a variety of opportunities for students to practice and apply the concepts they learn across these different grouping formats. For example, unit 6, lesson 7, activity 7.2 entails students arranged in pairs to work independently for two to three minutes before sharing responses with a partner in a brief small-group discussion. Guidance also supports multiple participation structures. For example, it prompts educators to provide two minutes of quiet think time for students to evaluate statements, followed by partner discussion and then whole-class sharing with two to three selected students.

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 emergent bilingual (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 1, lesson 5, activity 5.3, the “Support for English Language Learners” guides educators to “use this routine when students present their strategy for finding the area of Nevada. Ask students to consider what is the same and what is different about each approach. Draw students’ attention to the language used to describe the different ways the area can be calculated (decompose, rearrange, enclose, area, etc.). These exchanges can strengthen students’ mathematical language use.” 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, MLR 1 associates with ELPS 1.E.iv, 5.B.i, 5.F.iii, and 5.G.iii. In unit 2, lesson 1, activity 1.4, the implementation guidance helps educators support EB students through MLR8, which states, “To provide a support students in precision of language when describing proportional relationships from a table, provide sentence frames for students to use, such as: ‘_____ is equal in value to _____, because . . .’” This embedded guidance provides educators with explicit strategies for supporting students’ mathematical language development through sentence frames and discussion supports aligned to the ELPS.

The materials include “Grade 7 ELPS Alignment,” which identifies where the course embeds English Language Proficiency Standards and offers suggestions for supporting students with language needs. This alignment helps educators understand how lessons integrate language expectations, so educators can plan appropriate instructional support in bilingual and ESL settings. For example, unit 1, lesson 3 connects to ELPS 4C, 4D, and 4E, 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.

In unit 8, lesson 8, activity 8.2, students develop academic vocabulary and comprehension through structured discussions, visual representations, sentence frames, and written explanations. The statistics activity uses MLR7 to support the discussion of concepts such as samples, populations, and proportions, while the equations activity uses MLR8 to encourage the use of mathematical terms such as variable, coefficient, and constant term. Students explain their reasoning both orally and in writing, supporting both language development and conceptual understanding of the mathematics. The activities also build background knowledge through problem-solving tasks and mathematical discussions.

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, in unit 2, lesson 3, activity 3.2, the lesson components work together to strengthen students’ comprehension, develop academic vocabulary, and build conceptual understanding through structured oral and written discourse. 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.

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 Grade 7, practice opportunities throughout lessons and units require students to demonstrate depth of understanding aligned with the TEKS by developing increasingly complex strategies and applying concepts in varied contexts. In unit 1, lesson 8, activity 8.2, students compare the areas of regions involving different-sized circles and analyze multiple strategies for solving the problems. Students begin by using subtraction to determine the area of a region around the outside of a circle, then progress to more complex figures that require them to reason about fractional parts of circles and use division to determine areas. These tasks require students to move beyond applying a formula, and instead analyze the structure of the figures, select appropriate strategies, and justify their mathematical reasoning.

In unit 4, lesson 9, activity 9.3, students develop a savings plan for their first year of college by analyzing timelines, calculating monthly savings amounts, and evaluating strategies for reaching a financial goal. Students explain how the number of months available impacts the amount needed to save each month, identify possible challenges, and revise their plans based on factors such as income, family contributions, and financial aid. These tasks require students to demonstrate depth of understanding aligned with the TEKS by applying proportional reasoning, interpreting financial information, and justifying their choices as they compare different approaches to create realistic and achievable savings plans.

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

In unit 1, the tasks increase in complexity throughout the unit, leading students toward grade-level proficiency in the mathematics TEKS. The unit begins with students determining the circumference of circles, then extends to finding the area of circles. In unit 1, lesson 10, activity 10.1, students demonstrate their understanding by solving a multi-step problem that requires them to apply both circumference and area formulas in a real-world context. In this final lesson of the unit, students determine the cost of a stained glass window containing fractional parts of circles within the design. They calculate the area of glass needed and the cost of the materials, and they use the circumference formula to determine the amount and cost of material required to connect the glass pieces along the seams.

In unit 2, lesson 11, the tasks increase in complexity across the lesson, leading students toward grade-level proficiency. Students begin by calculating earnings for an account that accrues simple interest. They then extend their understanding by calculating earnings for the same account using compound interest and comparing the two outcomes to determine which account earns more and by how much. In activity 11.3, students engage in more complex reasoning by changing one variable at a time in the compound interest formula and analyzing how those changes impact total earnings.

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

In unit 6, lesson 12, activity 12.2, students use ratios and proportions to represent the relationship between corresponding side lengths of similar triangles. Students build an understanding that equivalent ratios can describe proportional relationships and use this reasoning to analyze geometric figures. This learning connects to future work in unit 7, lesson 4, activity 4.3, in which students extend their understanding of proportional relationships beyond geometry to real-world contexts such as the relationship between elapsed time and distance traveled.

Unit 7, lesson 7, activity 7.2 demonstrates coherence across the unit by connecting the mathematical concept of a single proportional relationship to the comparison of two proportional relationships. In the previous lessons of the unit, students developed their understanding of representing and interpreting a single proportional relationship. In this lesson, students extend that understanding by representing two different proportional relationships using multiple representations and comparing the relationships in context. For example, students compare who would earn more money stuffing envelopes when working for different companies by analyzing proportional relationships. This progression continues the development of the broader pattern of linear relationships within the unit and connects to unit 7, lesson 16, activity 16.2, in which students compare five different savings account balances and describe how to determine the balances through graphical representations, linear equations, and verbal descriptions.

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.

In unit 7, lesson 7, activity 7.3, students build on prior learning about savings accounts and financial contexts as they extend their understanding to calculating compound interest. The activity connects familiar concepts about money and savings to new mathematical ideas involving exponential growth and repeated multiplication. The “Activity Narrative” explains the progression of learning by stating, “In future lessons, students will continue to investigate the effects of compounding interest in the long term.”

Within the materials, each unit begins with a warm-up that activates students’ prior knowledge and prepares them to engage with new learning. For example, in unit 8, lesson 5, activity 5.1, students revisit their understanding of solving equations for x and engage in discussion about integer operations and the role of a negative coefficient with a variable. This activity bridges prior learning with new concepts by encouraging students to use familiar reasoning strategies to analyze more complex equations. In addition, as explained in the “Further Reading” section, the website Illustrative Mathematics highlights the progression from Grades 6–8 to Algebra I by explaining that reasoning about equations builds on earlier understandings of maintaining equality in equations with one variable and solving equations in simpler forms such as px + q = r.

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..

The materials demonstrate coherence by connecting students’ prior knowledge of personal financial literacy and savings accounts from previous grade levels to new procedures for calculating compound interest in the current course. For example, in unit 2, lesson 2, activity 2.3, students build on their understanding of saving money over time and interest rates as they analyze how compound interest affects account growth. The lesson connects familiar financial concepts to new mathematical procedures and helps students understand the relationship between compound interest, growth over time, and exponential functions. This learning supports students’ continued development of financial literacy and prepares them to apply exponential reasoning in future mathematical contexts.

Unit 12, lesson 1, activity 1.2 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 previously determined the volume of rectangular prisms and, in this activity, apply that understanding to explore how to find volume for prisms with bases that are not necessarily rectangles. The lesson extends students’ understanding by emphasizing that students can multiply the area of the base by the height of the prism, regardless of the shape of the base, to determine volume. This connection strengthens students’ understanding of volume as a relationship between the base area and height and prepares them to apply these ideas to additional geometric figures 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 7, questions 1–3 focus on the current lesson content, while question 4 includes a review item from a previous unit. This review problem provides students with an opportunity to retrieve previously learned knowledge and apply it in a new context.

The materials provide spaced retrieval opportunities by requiring students to revisit and apply previously learned skills and concepts across lessons and units. For example, in unit 12, lesson 8, activity 8.2, students apply their prior understanding of surface area and volume to solve a new real-world problem involving a three-dimensional structure. Students also retrieve and apply proportional reasoning skills from a previous unit to determine the cost of the vinyl needed for the structure. By integrating previously learned concepts with current learning, the activity strengthens connections among mathematical ideas and supports the long-term retention and transfer of skills.

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

In unit 3, lesson 21, students focus primarily on applying scale factor while also revisiting previously learned concepts related to finding the dimensions, perimeter, and area of two-dimensional figures, including triangles, rectangles, circles, and hexagons. These practice problems require students to draw upon their understanding of measurement concepts from earlier units while applying new reasoning related to proportional relationships and scale. The problems encourage students to connect multiple mathematical ideas by analyzing how changes in scale affect linear measurements and the resulting perimeter and area of figures.

Unit 10 includes 11 lessons, and each lesson provides a variety of problem types within the lesson practice. Of the 11 lessons, eight include review problems from previous units in the “Practice Problems” sections. These practice sets require students to apply current learning while also retrieving and using previously learned concepts, supporting flexible application of skills and strengthening connections across units. In this way, the materials provide interleaved practice opportunities with previously learned skills and concepts across lessons and units.

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

In unit 7, lesson 6, activity 6.2, students work with descriptions, tables, graphs, and equations representing proportional relationships. Students interpret the constant of proportionality in each representation, analyze how the representations connect, and evaluate whether all representations describe the same situation. Students also justify their reasoning and discuss which representations make the constant of proportionality most easily identifiable.

In unit 9, lesson 20, activity 20.1, students use a blackline master containing computer hardware specifications over time to interpret and compare real-world data related to storage, processing speed, and memory, including values expressed in scientific notation and decimal form. Students analyze the data by comparing technological changes over time and evaluate how different representations of numerical data support accurate comparisons across contexts. Students also answer questions and select and interpret representations that best support meaningful comparison between historical and modern computer systems while developing understanding of scientific notation.

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

In unit 10, lesson 8, activity 8.2, students model real-world situations using simulations to determine whether Alpine Zoom will make money based on weather conditions. Students choose a chance experiment to create a model of the situation, such as rolling a number cube, drawing slips of paper from a bag, using a paper clip spinner, flipping a coin, or another method they create. One prompt provides explicit choices, stating, “Describe two different chance experiments that you could use to simulate whether it will snow at least 4 out of 10 days of spring break. Choose from options such as rolling a number cube, drawing slips of paper from a bag, using a paper clip spinner, flipping a coin, or another method you create.” Students also have the opportunity to use a digital simulation applet to create and test their models.

Unit 3, lesson 4 requires students to create mathematical models of transformations on the coordinate plane. Students construct reflected images of polygons using the x-axis as the line of reflection and generate coordinate pairs for the image. By plotting and labeling the transformed figure, students create a mathematical model that represents the transformation rule on a coordinate grid. For example, the task states, “Using the x-axis as the line of reflection, plot the image of each polygon” and “Label the image of each polygon with its coordinates.” Through this process, students create and represent a transformation model using both a geometric figure and its corresponding coordinate notation.

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

In unit 4, lesson 9, activity 9.2, students estimate the total cost of attending their first year of college and determine how much they need to save. Students will analyze data such as tuition rates and living expenses, identify potential financial aid or family contributions, and calculate how much they need to save each month. One of the prompts asks students to “research or use provided data to estimate the total cost of attendance, including tuition, housing, books, and other expenses for one year.” Students use these real-world financial literacy strategies to apply mathematical reasoning about accumulation over time and the impact of consistent savings.

In unit 9, lesson 16, activity 16.2, students determine the distance between two points on a coordinate grid. In the previous lesson, students developed understanding of the Pythagorean Theorem. In this new context, students apply that conceptual understanding by constructing a right triangle between the two points, identifying the lengths of the legs using the coordinate grid, and then using the Pythagorean Theorem to calculate the length of the hypotenuse. Through this task, students apply prior conceptual understanding of right triangles and distance to solve a new type of problem in coordinate geometry.

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

In unit 1, lesson 5, activity 5.1, students add 599 + 87 without writing anything down or using a calculator. The task encourages students to use a compensation strategy by adjusting numbers to make the computation more efficient, such as rewriting the problem as 600 + 86. This repeated use of mental strategies supports students in developing accuracy and efficiency with addition, building fluency for later work involving area calculations in the lesson.

In unit 2, lesson 7, activity 7.2, students find the percentages from dollar amounts, including commission, tip, and markdown. One of the questions provides a visual representation, including the steps to make a Koch snowflake, with the aim of students representing the steps and the percentage increase of the perimeter in tabular format. The question asks, “By what percentage does the perimeter increase at step 2? Step 3? Step 10?” Students represent this in tabular format. These questions build fluency and automaticity through the repetitive testing of the skill of percentage increase, including percentages from dollar amounts such as commission, tip, and markdown.

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 5, lesson 3, activity 3.3, students add rational numbers using multiple strategies, including grouping terms, rewriting fractions with common denominators, and combining decimals by place value. Students apply structure, use properties of operations, and compare strategies to determine which methods are most efficient in different situations. Students also discuss which strategies support more accurate and efficient computation, particularly when working with fractions.

Unit 8, lesson 12 provides opportunities for students to practice the application of efficient, flexible, and accurate mathematical procedures within the lesson and across the unit. For example, students model a real-world situation by writing, solving, and interpreting an inequality representing the maximum number of boxes that an elevator can safely carry. Students apply flexible procedures by identifying relevant information, representing the situation with an inequality, graphing the solution, and interpreting the results in context. The lesson supports efficiency by guiding students to use an inequality as a direct mathematical model rather than relying on guess-and-check methods to determine the maximum number of boxes. It supports accuracy by requiring students to correctly solve the inequality, represent the solution on a number line, and justify the final answer, including accounting for real-world constraints such as whole-number solutions and rounding down to avoid exceeding the weight limit.

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 8, lesson 1, activity 1.3 provides an opportunity for students to create a multi-step puzzle and develop two representations to show how they solved it. Students then share their puzzles with peers and compare representations, evaluating which methods are most efficient for solving the puzzle. Students also discuss the flexibility of different solution strategies and consider the accuracy of each representation in clearly and correctly showing their reasoning, allowing them to evaluate multiple approaches to the same problem.

In unit 12, lesson 16, activity 16.2, students determine the radius of a sphere when its volume is known. Students use multiple strategies, including reasoning from the structure of the volume formula, isolating variables by dividing both sides by pi, or substituting values to solve the equation. During the whole-class discussion, students compare approaches using guiding questions such as “If the final step in your solution was solving for r when r³ = 216, how did you solve? If you found that r³ was a different number, how did you solve?” Students evaluate the efficiency and accuracy of different solution methods based on these comparisons.

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

In unit 2, lesson 7, activity 7.2, students solve multi-step percent problems involving dollar amounts such as commission, tips, and markdowns. Educator prompts guide students to first determine the base amount through addition or subtraction, then use that value to calculate the percent. The activity also prompts educators to emphasize that multi-step reasoning is essential when working with rates and percent change. This emphasis supports students in applying a consistent and efficient problem-solving structure across similar problems.

In unit 3, lesson 4, activity 4.3, students use tracing paper, index cards, and the coordinate grid to perform 90-degree rotations. Educator guidance directs instructors to “highlight these strategies,” and notes that using the coordinate grid is “the most accurate because it does not require any technology,” emphasizing reliance on mathematical structure rather than physical tools. This guidance helps educators move students from concrete representations toward more efficient, structure-based reasoning using the coordinate plane.

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

“Unit 5: Operating with Rational Numbers” explicitly states how the unit addresses the conceptual and procedural emphasis of the TEKS. Students begin by developing a conceptual understanding of signed numbers using contexts such as temperature and elevation. They interpret positive and negative values on number lines, compare rational numbers, and represent signed numbers as movement in opposite directions. Students use number lines and plotting to build conceptual understanding of rational numbers before extending this understanding to operations. They then connect this conceptual foundation to procedural skills by adding, subtracting, multiplying, and generalizing operations with signed numbers, including understanding subtraction as addition of the opposite and identifying patterns in products of positive and negative numbers.

In unit 12, lesson 13, activity 13.2, students first develop conceptual understanding of the relationship between the volume of a cylinder and a cone with congruent bases and the same height by analyzing a video demonstration. Students understand that the volume of a cone is 1/3 the volume of a cylinder. In the subsequent section (13.3), students apply this conceptual understanding using a formula-based procedure to calculate the volumes of cones related to cylinders with the same base and height. This clearly connects conceptual understanding to procedural application.

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 10, lesson 8, activity 8.2, students model real-world situations using simulations to estimate probability and make predictions about whether a business will make money based on weather outcomes. Students select and use concrete models such as rolling a number cube, drawing slips of paper, using a spinner, or flipping a coin. They also use a digital simulation applet to generate and compare outcomes. Students connect these concrete simulations to pictorial representations of results shown in the applet and to abstract representations by analyzing probabilities and making predictions based on repeated trials. One question asks, “How could this chance experiment be used to determine whether Alpine Zoom will make money?”, requiring students to link the simulation model to the real-world situation.

In unit 10, lesson 8, activity 8.3, students use blocks, slips of paper, coins, spinners, and a game board to model a compound probability situation. They use pictorial representations through the game board and simulation setups and abstract representations when estimating probabilities, analyzing simulation results, and explaining how changes to the game affect the probability of winning. Through this process, students connect hands-on models, visual representations, and mathematical reasoning to represent compound events.

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 3, lesson 4, activity 4.2, students review multiple examples of points reflected across the x-axis using the coordinate plane as a representational model. Students explain how to determine the reflection of a point given an axis of reflection and then generalize the rule for reflections, connecting specific coordinate grid representations to an abstract rule for how to transform any point. In the warm-up, students focus on studying translations using a coordinate grid, building prior understanding of transformations as visual representations. Through class discussions, students explain how to find the reflection of a point and connect visual changes on the graph to coordinate rules. In the next lesson, students will study 90-degree rotations on a coordinate grid, extending their understanding of transformations and further developing connections between representational models and abstract rules.

In unit 7, lesson 13, activity 13.3, students create coordinate-plane designs based on information communicated by a partner. Partners use mathematical language such as x- and y-intercepts and slope to describe line locations. Students interpret these verbal and representational cues to construct a concrete design on the coordinate plane, then translate that design into abstract representations using linear equations. Students also create their own designs and communicate them to a partner using algebraic language, reinforcing the connection between concrete visual models and abstract symbolic representations.

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

In unit 1, lesson 4, activity 4.2, students use rulers, receipt tape, and cylindrical objects to measure the diameter and circumference of circular objects. Students record measurements in a table and use visual representations of the relationship between circumference and diameter to describe their observations. Through discussion of their data, students use mathematical language related to circles and measurement to explain the relationship between circumference and diameter.

In unit 3, lesson 1, activity 1.2, students develop academic mathematical vocabulary related to transformations through visuals, manipulatives, and language supports. Students observe and describe the movement of a triangle during a dance sequence using terms such as clockwise, counterclockwise, left, right, up, and down. Educator guidance supports vocabulary development by directing educators, “On a display, record language students use to describe the movement of shapes to later be grouped and connected to more formal language such as ‘rotation’ and ‘translation.’” This guidance supports students in connecting informal descriptions of movement to formal transformation vocabulary.

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 7, lesson 6, activity 6.3, students investigate relationships among the amounts of honey, salt, and flour in a recipe. Students use “Problem Cards” and “Data Cards” to gather information from partners and solve the problem. During the “Activity Synthesis,” embedded educator guidance includes questions that prompt students to explain their graphs and describe how they selected the scale for the axes. These questions support students’ use of academic mathematical vocabulary related to the lesson, including axis, cups, grams, scale, and proportional.

In unit 10, lesson 3, activity 3.2, students develop and use academic vocabulary related to probability, including probability, sample space, experimental probability, and theoretical probability. Students create sample spaces to determine theoretical probability and conduct experiments to collect data for experimental probability. During the “Activity Synthesis,” educator questions, including “How many outcomes are in the sample space?” and “What is the theoretical probability of rolling a 3? Explain your reasoning,” prompt students to use academic vocabulary while explaining mathematical reasoning.

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.

In unit 2, lesson 6, activity 6.4, students use vocabulary related to percentages, including sales tax, gratuity, interest, markup, discount, and commission. Students work with partners to match vocabulary cards with descriptive cards, providing opportunities to hear, refine, and use mathematical language while discussing the meaning of terms. The materials provide a reference chart of these terms for students to use in future lessons. During the “Activity Synthesis,” educator guidance includes discussion questions such as “How does a coupon act as a monetary incentive, and why might one coupon be a better deal than another?” to support students in explaining and comparing mathematical ideas using precise language.

In unit 11, lesson 3, activity 3.2, students collect sample data, calculate proportions, and discuss estimates of a population based on their results. Students work collaboratively and respond to prompts such as “Using the class’s data, how accurate do you think your group’s estimate is? Explain or show your reasoning.” Students create visual displays of their work and discuss their reasoning with classmates. Educator guidance supports mathematical conversations by prompting students to compare samples and proportions, providing opportunities for students to hear, explain, and refine mathematical ideas using academic language.

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

In unit 1, lesson 4, activity 4.2, students select and use tools, including real objects, to solve a measurement problem. The Grade 7 Advanced Math Scope and Sequence identifies TEKS 7AM.1.C as a process standard addressed in this lesson. Students use receipt tape and rulers to measure the circumference and diameter of circular objects, record measurements, and analyze the relationship between circumference and diameter. The lesson incorporates the process standard through students’ selection of tools and use of measurements to investigate a mathematical relationship.

In unit 12, lesson 8, activity 8.3, students apply mathematics to a real-world problem involving volume. The scope and sequence identifies TEKS 7AM.1.A as a process standard addressed in this lesson. Students use information about two hexagonal prisms, including base areas and depth, to determine the volume of sand needed to fill each sandbox. The lesson incorporates the process standard as students apply mathematical concepts to solve a problem arising in an everyday context.

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

The “Kiddom Math Middle School Teacher Resource 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 resource guide states, “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 resource guide also explains 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 Grade 7 Advanced Math Scope and Sequence identifies the TEKS process standards addressed across the course, and the “Course Narrative” includes descriptions of how students engage in reasoning, estimation, problem-solving, representation, and mathematical communication. For example, the materials state, “Students use multiple representations, tables, graphs, diagrams, and equations, to analyze and solve problems involving scaling, recipes, speed, and financial scenarios.” The “Course Narrative” also describes how students analyze transformations and develop precise language to describe mathematical relationships. These descriptions show how 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 unit 6 overview describes how the unit regularly incorporates and connects TEKS process standards. Students explore scaled copies and similarity by identifying corresponding parts, analyzing measurements, and using mathematical language such as scale factor and corresponding parts. Students create and analyze scaled copies, justify their strategies, and explain relationships between similar figures. The unit connects these ideas to slope and linear equations by relating similar triangles on a coordinate grid to the slope of a line. Throughout the unit, students represent, analyze, justify, and communicate mathematical relationships in geometric and real-world contexts, demonstrating the integration of TEKS process standards across the unit.

The unit 10 “Section Level Planning Guide” provides a description of how TEKS process standards are incorporated and connected throughout the unit. The guide identifies opportunities for students to evaluate and communicate relationships between theoretical and experimental probability, create and interpret multiple representations, and apply mathematical understanding to real-world scenarios through simulations. These descriptions demonstrate how the unit progression regularly embeds TEKS process standards as students reason, represent, communicate, and apply mathematical ideas.

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

The materials provide lesson-level descriptions of how the instruction incorporates TEKS process standards. In unit 1, lesson 3, activity 3.4, students compare different strategies for decomposing the figure, justify their solution methods, and connect the perimeter of the wire frame to the circumference of a circle. The lesson overview also identifies opportunities for students to share multiple strategies, explain their use of the circumference formula, and work backward to determine a circle’s radius.

In unit 1, lesson 4, the “Lesson Narrative” describes how students engage in TEKS process standards by stating, “Students make use of the structure of a proportional relationship as they work toward describing the relationship between the number of rotations of a wheel and the distance the wheel travels with an equation.” The “Learning Goals” further identify opportunities for students to analyze and communicate mathematical ideas, including comparing wheels of different sizes and explaining orally why a larger wheel requires fewer rotations to travel the same distance.

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

In unit 1, lesson 5, activity 5.2, students calculate the area of an irregular shape presented in a scale drawing by composing and decomposing triangles and parallelograms. The materials provide visual support through the floor plan of a house and approximate wall lengths. The materials encourage students to think mathematically by requiring them to determine multiple ways to decompose and compose the figure to find its area. The materials also promote perseverance by providing four to five minutes of quiet work time before a whole-class discussion, allowing students time to develop their own solution strategies. In addition, the materials support students who struggle by suggesting, “If students struggle getting started finding the area of the floor plan, consider suggesting that they use composition and decomposition to break the floor plan up into familiar shapes whose area can be calculated.” Students then share and justify their reasoning for the different approaches used to decompose and compose the floor plan, helping them make sense of the mathematics through mathematical discourse.

In unit 6, lesson 2, activity 2.3, rather than relying on measurement, students use parallel lines and angle relationships to explain why the interior angles of a triangle sum to 180°. They show that angles “make a line,” use alternate interior angles to justify congruent angle pairs, and explain why the same argument works for any triangle by drawing a line parallel to one side through the opposite vertex. Rather than applying a memorized formula, students construct and justify a mathematical argument, allowing them to make sense of the underlying geometric relationships. The activity concludes by extending this reasoning to exterior angles and quadrilaterals, giving students opportunities to apply and generalize their mathematical thinking.

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.

In unit 6, lesson 12, activity 12.2, students build on their understanding that corresponding side lengths of similar triangles have a scale factor relationship. The materials support multiple ways for students to represent and solve problems involving similar triangles: through diagrams, tables, scale factors, and proportions. The “Activity Narrative” guides educators to support students in explaining and justifying their reasoning through the prompt, “Watch for students who look to explain why the internal ratios of corresponding side lengths of similar triangles are equivalent and invite them to share their thinking during the discussion.” This guidance encourages students to move beyond finding an answer and explain why their method works. Students then apply these representations and strategies in the “Practice Problems” section.

In unit 8, lesson 3, activity 3.3, students investigate multiple methods for solving equations by comparing the strategies used by two students. Students determine which method they agree with and recognize that both approaches are valid, demonstrating that they can solve equations in more than one way. The “Activity Synthesis” includes educator questions that support students in explaining and justifying their reasoning, including “What are the advantages of choosing to distribute first? To divide first?” and “Is one path more ‘right’ than another?” The “Practice Problems” provide additional opportunities for students to solve equations using multiple representations and strategies, including the hanger model and algebraic properties.

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.

In unit 2, lesson 5, activity 5.2, students apply their understanding of percent rates to determine the percentage of appetizers, entrees, and desserts delivered by a waiter. The materials use the Co-Craft Questions math language routine, which asks students to generate mathematical questions about a context before solving the given problem. Students write about the mathematics, compare and discuss their questions with a partner, and share their thoughts during a whole-class discussion. After solving the problem, students engage in further mathematical discussion through questions such as “What do the percentages add up to?”

In unit 11, lesson 5, activity 5.2, students analyze sample data to determine whether there is a meaningful difference between two populations. The collaborative activity requires students to work in groups of two to construct informal arguments explaining whether the samples represent meaningfully different populations. Students use visual representations, including dot plots, and respond to prompts such as “The mean weight of this sample of tenth-grade backpacks is 14.8 pounds. Do you think there is a meaningful difference between the weight of all seventh-grade and tenth-grade students’ backpacks? Explain or show your reasoning.” Students discuss and justify their mathematical thinking through educator-facilitated questions, including “Is the overlap of the data more important when you only have a sample or when you have data from the population? Explain your reasoning.”

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 4, lesson 4 provides students with opportunities to explain their thinking, defend their choices, listen to classmates’ reasoning, and reflect on different approaches. The lesson prompts students, stating, “Record your findings and explain how you arrived at your answer.” The educator then facilitates discussion by asking students to “share the hourly wage they estimated and explain how it relates to the costs of living in their city.” Students justify their calculations by connecting their mathematical reasoning to city-specific expenses. For example, a sample response explains, “The cost of living in our city is higher because housing costs are greater. A higher hourly wage is needed to meet these expenses.” The educator further supports reflection by summarizing how changes in expenses may require adjustments to pay, prompting students to reconsider and refine their justifications.

In unit 8, lesson 4, students analyze Clare and Lin’s solutions and explain how their problem-solving approaches are similar and different. The lesson instructs the educator to prompt students to use precise mathematical language when describing how each student used the distributive property. Students discuss whether both solutions are valid by responding to the question, “Are both of their solutions correct?” and sharing which approach they prefer. The educator guides students to recognize that different strategies can lead to the same solution and supports students in justifying their conclusions with mathematical evidence. The educator also asks, “How do you know when a solution to an equation is correct?” and encourages students to verify solutions by substituting values back into the original equation.

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

Unit 10, lesson 5, activity 5.2 provides educators with questions that encourage students to explain and evaluate their reasoning such as “How does the probability you calculated from the sample space compare to the outcomes you observed in your trials?” and “Why might two different simulation tools . . . give slightly different results?” The materials anticipate a common misconception that experimental probability should always match theoretical probability, and guide educators to address this misunderstanding by emphasizing the difference between theoretical and experimental probability. The activity supports educators in explaining that variation may occur because of simulation design or an insufficient number of trials, and that increasing the number of trials generally produces results closer to the expected probability.

In unit 12, lesson 8, activity 8.2 provides educators with additional guidance for responding to student misconceptions in the “Advancing Students’ Thinking” section. For example, the materials identify the potential misconception that students may confuse “0.8¢” with “$0.80,” and they prompt the educator to remind students of their previous work with fractional percentages and the relationship between cents and dollars. The “Activity Synthesis” provides educators with questions to guide explanatory feedback based on student responses, including “Are there other ways to calculate the area of the base?”, “How did you know if you had to calculate surface area or volume for this problem?”, and “If Kiran decides not to cover the bottom of the structure with vinyl, how much would he save?” These prompts help educators address misconceptions, press students to explain their reasoning, and provide feedback that advances student understanding.