Kiddom Texas: Grade 6, 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 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, in the scope and sequence, unit 1, lesson 1 aligns with TEKS 6AM.2.G and 6AM.2.C.

The materials include a scope and sequence with ELPS alignment identified throughout the course year. The scope and sequence is a table with the headings “Location in Program,” “Lesson Title,” and “ELPS.” It includes units 1–13 along with the name of each lesson title and corresponding ELPS. For example, in the scope and sequence, unit 1, lesson 3 identifies ELPS 2.D and 3.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 pacing for effective implementation of the materials. The materials provide 165-, 180-, and 210-day calendars outlining recommended pacing for the instructional year. The organization of the pacing is by unit, lessons, assessment days, flex days, and total days. For example, in the 165-day calendar, unit 1 includes nine lessons, with one day allocated for check-in assessments, mid-unit assessments, and end-of-unit assessments. 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 21 lessons with a total of 23 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 concepts connect between units throughout the course. Students develop their understanding of functions, linear equations and inequalities, statistics, exponential relationships, and quadratic equations through problem-solving and modeling activities. Throughout the course, students apply mathematics in real-world contexts and engage in modeling tasks that support deeper understanding. For example, in unit 1, lesson 1, students connect concrete division situations to division expressions by reasoning about the relationship between the dividend, divisor, and quotient. They begin to understand how the relative sizes of the numbers help predict whether the quotient will be greater than one, close to one, or close to zero.

The materials include an anchor graphic that explains the rationale for the sequence of units to demonstrate 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.

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

The materials include “Unit Narratives” and “Section Narratives” that guide educators through unit internalization. Within units, students build understanding from foundational concepts to more advanced mathematical ideas. For example, unit 3 offers support for internalizing ratio reasoning through visual models, tables, diagrams, equations, and real-world situations. Unit activities and discussions encourage students to connect multiple representations, deepen their understanding of proportional relationships, and clearly explain their mathematical thinking.

The lesson overview provides guidance that supports lesson internalization by explaining the purpose of the lesson, connecting new learning to prior concepts, and identifying key instructional expectations. For example, unit 11, lesson 6 explains how students build on previous learning about education expenses, money management, and financial planning as they investigate how education and vocational training influence lifetime earnings. The overview identifies lesson goals, materials, educator preparation needed before instruction, and “I can” statements that clarify the instructional focus and expected student learning. This guidance supports educators in understanding the lesson objectives 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 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 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, “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 “Unit Narratives” include an explanation of background knowledge needed in the unit, along with the learning and instructional intent. For example, the background knowledge in the narrative for “Unit 1: Positive Rational Numbers” is to “develop and demonstrate comprehensive understanding of division relationships through multiple representations, including visual models, equations, and verbal explanations.”

The materials identify or embed the academic vocabulary, such as reciprocal and strip diagram, necessary to teach a unit within the unit overviews. In addition, the materials include a course glossary that defines key academic terms as they first appear. For example, in unit 1, lesson 9, the glossary defines important terms such as reciprocal, which helps educators introduce the idea clearly and support students in using it correctly when dividing fractions.

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 comprehensive family supports in English and Spanish that explain unit content, instructional approaches, and practical strategies families can use to support student learning at home. The family resource outlines the major mathematical understandings of the unit, including division with whole numbers and fractions, the meaning of quotients, and the development of the reciprocal algorithm. It explains the instructional progression from visual models to abstract reasoning and describes the representations students will use such as tape diagrams, equations, symbolic notation, and verbal explanations. This guidance helps families understand the conceptual focus of the unit and how students should think about mathematics.

The materials provide support for families in both English and Spanish that includes explicit suggestions for how families can support student progress at home. The family resource encourages caregivers to ask students to explain their reasoning; review vocabulary, such as dividend, divisor, and reciprocal; and discuss real-world division scenarios while comparing different problem-solving strategies. Additionally, the guide explains how mathematics connects to everyday life, college readiness, and future careers, helping families reinforce the relevance and importance of the learning.

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.

In unit 4, lesson 2, the organization of the instructional sequence clearly supports conceptual understanding of functions as relationships between inputs and outputs, which aligns with TEKS expectations for function reasoning. The lesson begins with a warm-up that activates prior knowledge by having students analyze how squaring numbers can produce identical outputs from different inputs. The “Using Function Language” and related activities demonstrate strong ELPS alignment through structured opportunities for academic discourse and language development.

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 listing the educator and student materials necessary to effectively deliver the lesson. For example, unit 5, lesson 1 outlines required materials; in this case, rulers, for both students and the educator. The lesson further explains that students will use rulers as a tool to create number lines in the “High Places, Low Places” activity.

The materials include a lesson overview with suggested timing for each lesson component to support effective instruction. For example, unit 2, lesson 1 allots 10 minutes for the warm-up. It allots 25 minutes for the next section, the “Activity Narrative,” during which time “students [will] compare the amounts of the plane covered by tiling patterns.”

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

The materials include an enrichment opportunity through the “Are You Ready for More?” section that extends students’ reasoning about area relationships and multiple solutions. Unit 6, lesson 3, activity 3.3 asks students to “find the lengths w, x, y, and z, and the area A. All values are whole numbers.” The activity then includes an open-ended extension, asking, “Can you find another set of lengths that will work? How many possibilities are there?” This enrichment opportunity extends student thinking beyond determining area expressions by requiring them to analyze relationships among dimensions, explore multiple solutions, and generalize patterns.

The materials include optional extension activities with embedded educator guidance that supports effective implementation. For example, unit 13, lesson 6, activity 6.3 guides educators to have students analyze voting data from different student clubs and model how to represent groups’ preferences. The educator guidance includes specific facilitation directions such as “Tell them, ‘There are four clubs in this other class, and everyone in each club agrees to vote exactly the same way, as shown in the table.’ Have each group of four act out the voting for this class: each person is the president of a club, and delivers the votes for all the club members.” The guidance further supports educators in modeling the activity by demonstrating how students represent and communicate the votes for each club.

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.

The materials include a “Check Your Readiness” diagnostic assessment at the beginning of each unit that assesses students’ background knowledge of the concepts or skills. For example, in “Unit 1: Positive Rational Numbers,” “Check Your Readiness” assesses students’ prior knowledge on the concepts that support the division of fractions. This assessment varies in types of tasks and questions: Some items are text-entry, some are multiple-choice, and some require students to draw their response.

The materials include a summative assessment, called an end-of-unit assessment, at the end of each unit, which students complete individually. The questions vary in types of tasks, as some questions are text-entry, some are multiple-choice, and some require students to draw their response. For example, one of the questions in the “Unit 1: End-of-Unit Assessment” that requires text-entry states, “Tyler used 11/4 gallons of paint to paint 5/7 of a fence. How many gallons will it take to paint the whole fence? Write a multiplication equation or a division equation to represent this question, then find the answer. Show your reasoning.”

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 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.

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 Grade 6 Advanced Math Course Guide provides information on the consistent and accurate administration of instructional assessments, including guidance on when to administer each assessment. For example, it recommends giving the “Check Your Readiness” diagnostic assessment at the beginning of each unit to evaluate prior knowledge. It also provides directions for supporting students who are below grade level, such as revisiting prerequisite skills during the warm-up to reinforce understanding before introducing new content.

The Grade 6 Advanced Math Course 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 4, lesson 8.4 allots approximately five minutes for the cool-down. The course 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, aligned TEKS, and lesson-level learning targets. The scope and sequence identifies where lessons embed formative assessments and demonstrates alignment of those assessments with both the TEKS and the lesson objectives. This alignment supports progress monitoring by connecting formative assessments to lesson learning targets and the TEKS. This ensures that formative assessments measure student progress toward both standards and lesson objectives throughout instruction.

Unit 2, lesson 1 identifies the TEKS it addresses at the beginning, and the embedded assessments align with those standards throughout instruction. The TEKS addressed in this lesson include 11.26.b.1.C and 111.26.b.8.B. The cool-down, which functions as a formative assessment, asks students to write their own definition of area, demonstrating their conceptual understanding of the topic.

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 explaining reasoning and solving problems. For example, unit 2, grade 6.2, “Check Your Readiness (A),” includes fill-in-the-blank, text-entry, 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. For example, in unit 2, lesson 2, warm-up 2.1 “What Is Area?”, students begin by determining area through covering a region completely with square units without gaps or overlaps using concrete representations. Students later progress to more complex and abstract tasks such as writing the definition of area and including all the information students think is important to know about the concept.

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 evaluator notes that accompany assessment items that support scoring. These notes include sample responses and instructional guidance to help educators address common misconceptions and understand acceptable variation in student reasoning. For example, in unit 3, “Check Your Readiness (A),” question 2, part D, the “Note for Evaluating Responses” states, “Explanations vary.” The guidance further explains that lesson 4 first introduces the assessed content, color mixtures, and emphasizes that students should demonstrate understanding of how multiplication and division relate, as well as how to multiply and divide integers and fractions.

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

In their “Notes for Evaluating Responses” and “Responding to Student Thinking” sections, formative assessments such as “Check Your Readiness” and cool-downs provide recommendations for targeted support based on student performance. These recommendations guide educators in using particular lessons and instructional activities to address student needs. For example, unit 2, “Check Your Readiness (A),” identifies the connection between the assessment item and lesson 1. The guidance states, “The content in this problem is first addressed in Lesson 1: Tiling the Plane. Students have studied the area of rectangles in both Grade 3 and Grade 5. If students struggle with this problem, consider spending additional time during the synthesis of Lesson 1 discussing what area is and how it is calculated for rectangles.” This guidance connects student performance on the assessment to targeted support within the included lesson sequence and directs educators to revisit key concepts during the “Lesson Synthesis” to address misconceptions and strengthen understanding.

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 11, “Check Your Readiness (B),” students complete a prerequisite skill assessment involving decimal operations while balancing a check register. The educator guidance connects student performance to subsequent instruction, stating, “The content in this problem is first encountered in Lesson 3: Balancing a Check Register: Deposits, Withdrawals, and Transfers. This problem will allow students to practice adding decimals. If students struggle with this concept, plan to spend some time reviewing decimal operations.” This guidance helps educators respond to patterns in assessment results by revisiting the prerequisite concept through an included instructional focus before students continue with the unit.

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 3, lesson 3, activity 3.4, the “Response to Student Thinking” section guides educators in scaffolding instruction for students who have not mastered the mathematical concept of divisors. The materials state, “If students struggle with coming up with a correct divisor in the cool-down, plan to find a correct divisor when opportunities arise over the next several lessons. For example, practice problems 2 and 3 in lesson 5 give students opportunities to practice this idea in the context of determining equivalent ratios.”

In unit 3, lesson 11, activity 11.2, the “Advance Student Thinking” section supports educators in differentiating instruction for students who have not yet mastered the concept of equivalent ratios. For students who have not yet reached proficiency with this skill, the materials guide educators to reinforce foundational understanding by reminding them that to create equivalent ratios, they multiply both terms by the same number. Educators may also direct students to a posted or previously learned definition of equivalent ratios or encourage them to revisit simpler cases such as examining the relationship between 4:5 and 36:45.

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

The 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 3, lesson 2, activity 2.1, mathematical language routines (MLRs) include 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.

In unit 3, lesson 8, activity 8.2, students work with terms such as unit price and per, which a real shopping context introduces and reinforces for students before they begin solving problems. The materials guide the educator to explicitly explain what cost per one means, and to connect it to division and representations such as double number lines. The “Co-Craft Questions” routine also supports students in making sense of the situation by focusing on the language of the problem before answering, helping them understand how the context and wording relate to the mathematics they are doing.

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, research projects, or creative tasks that synthesize content for students who have demonstrated proficiency in grade-level content and skills. For example, the “Further Reading” section includes articles with linked projects, activities, and lessons that extend beyond grade level through complex open-ended problems that require applying mathematical concepts to real-world scenarios. In the resources, the article “Why Is 3 – 5 = 3 + (–5)?” includes a hyperlink to Illustrative Mathematics that leads to curriculum materials for Grades 6–8. The unit 2 activities addressing ratios asks students to represent ratios in recipes using diagrams and to analyze nutritional drinks based on quantities and ratios.

The materials include guidance for extension activities through optional tasks designed to extend student thinking beyond grade-level requirements. 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.” Their intention is to act as enrichment opportunities for educators to use when time allows. For example, in the unit 4, lesson 11 optional extension activity, students explore “percentages that describe parts of a whole” and explain their reasoning using a choice of different representations such as the number line, table, or the strip diagram.

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 3, lesson 7 directs educators to emphasize key ideas about equivalent ratios using double number lines, including why ratios involving one unit are useful and how to interpret “per” as “for every.” The materials provide specific language for educators, anticipated student responses, and discussion questions to support students’ understanding of the concept. The materials also guide educators to highlight student strategies such as using division to find unit rates and multiplication to generate equivalent ratios while using visual representations like double number lines to model relationships between equivalent ratios.

The materials include questioning strategies and discussion prompts that guide educators in explicitly explaining concepts. The activity regularly embeds such prompts, for example, in the “Launch,” “Activity Synthesis,” and “Advancing Student Thinking” sections. The materials enforce students’ understanding of natural restrictions of certain questions to natural numbers only. For example, in unit 5, lesson 1, activity 1.2, an “Activity Synthesis” prompt states, “Ask students how they would describe a quantity that is greater than zero on the number line” and “Discuss the use of + and − as symbols to denote positive and negative numbers.” The end of the introductory discussion for this activity guides educators to introduce the term negative as a way to represent a quantity less than zero. This direct prompt provides the educator with explicit guidance to use when explaining new concepts in the lesson.

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 and exit tickets, think-pair-share routines, conceptual explorations, and structured approaches to support student problem-solving, reasoning, and sense-making. For example, unit 1, lesson 3, activity 3.3 begins with a “Launch” that includes a period of independent work followed by partner discussion. The instructional routine is a think-pair-share, and students “investigate division problems in context, think of them in terms of equal-size groups, and represent them using diagrams and equations.”

Unit 3, lesson 7, activity 7.2 provides guidance on structuring the lesson through partner work, independent thinking time, and whole-class discussion. It guides educators to monitor student strategies during work time, such as noticing when students use division or multiplication with double number lines, and to use these strategies to inform the class discussion. The materials also include prompts that help educators emphasize key ideas such as “for every 1 ml” and support connections among representations, reasoning, and language during the debrief. In addition, the activity incorporates multiple instructional approaches, including visual models (double number lines), collaborative learning, structured discussion, and MRLs.

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, including guided, independent, and collaborative work, and provide varied opportunities for students to practice and apply new concepts. The materials also offer guided instruction to help educators implement instructional routines and structures that support effective practice and keep students focused on the content throughout the lesson. For example, in unit 2, lesson 3, activity 3.2, the educator begins the activity by modeling how to find the area of a figure on a grid. Independent work time follows during which students have access to geometry toolkits, and then there is collaborative work in pairs where students share and discuss their responses. The lesson concludes with a cool-down, in which students independently demonstrate their understanding.

The materials provide a variety of opportunities for students to practice and apply concepts, including independent work, small-group collaboration, and whole-class discussion. For example, in unit 4, lesson 7, activity 7.1, students engage in a think-pair-share during the launch, beginning with independent work. After that, the activity guides educators to allow students to have a partner discussion and, later, to conclude the lesson with a whole-class discussion.

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 3, lesson 1, activity 1.3, the support for EB students includes educators recording “ideas and displays for all to see. Examples of these types of details or annotations include: the order in which representations are organized on the display, attaching written notes or details to certain representations, using specific vocabulary or phrases, or using color or arrows to show connections between representations.” 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 8, lesson 5, activity 5.1, the implementation guidance helps educators support EB students through MLR8, which states, “Display sentence frames to support students when they explain their strategy. For example, ‘First, I _____ because . . .’ or ‘I noticed _____ so I . . . .’ Some students may benefit from the opportunity to rehearse what they will say with a partner before they share with the whole class.” 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 provide “Grade 6 ELPS Alignment” that 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 2, lesson 1 connects to ELPS 1B and 2C, 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.

Materials include embedded guidance for educators to support EB students but not in cross-linguistic connections. In unit 2, lesson 4, activity 4.2 and in unit 3, lesson 7, activity 7.2, students engage in partner and whole-class discussions supported by visual models, contextual problems, and educator questioning to make sense of ideas such as area, decomposition, ratios, and double number lines. These routines help students build academic vocabulary and comprehension as they explain reasoning orally and document their thinking in written responses connected to diagrams and problem situations. The tasks also support background knowledge through real-world and geometric contexts.

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 4, activity 4.2, the “Launch,” instructional questions, and supports for EB students strengthen comprehension, develop academic vocabulary, and build conceptual understanding through structured 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.

The materials provide practice opportunities throughout lessons and units that require students to demonstrate depth of understanding aligned to the TEKS through multiple representations, reasoning, and application of mathematical strategies. For example, in unit 1, lesson 9, activity 9.3, students divide non-unit fractions using strip diagrams, and compare their visual reasoning with another strategy that involves multiplying by the denominator and dividing by the numerator. Students then generalize the process into an algorithm and apply this method to additional fraction division problems. These tasks require students to connect representations, explain relationships, and develop procedural fluency grounded in conceptual understanding rather than relying on a single procedure.

Practice opportunities throughout the lesson require students to demonstrate depth of understanding aligned to the TEKS by engaging in meaningful application, reasoning, and justification. In unit 4, lesson 14, activity 14.3, students find 80 percent of several values, identify a general process for finding a percent of any quantity, and explain why their method works. Students use multiple representations, including tables, diagrams, expressions, and written explanations, to justify their reasoning and make connections between strategies. The activity extends beyond computation by requiring students to recognize patterns, generalize their thinking, and connect mathematical representations to explain the underlying concepts.

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

Unit 5, lesson 19, activity 19.3 increases in complexity of tasks by requiring students to move from solving a provided real-world estimation problem to independently creating and investigating their own Fermi problem. For example, the first task in activity 19.2 asks students, “How many times does your heart beat in a year?” In activity 19.3, students extend this reasoning by developing their own questions involving ratios and large-scale estimation such as “How much would it cost to replace all the windows on all the buildings in the United States?” Students determine the information needed to solve the problem, make reasonable assumptions, estimate quantities, and perform calculations to justify their solutions. This progression requires students to apply mathematical reasoning, make strategic decisions, and model real-world situations.

Unit 9, lesson 1, activity 1.2 increases in complexity by guiding students through multiple representations that build toward grade-level proficiency in the TEKS. Students begin by exploring a real-world ratio situation in which they create a shade of paint using three parts yellow for every two parts red. They represent possible combinations of red and yellow paint on a graph, and the activity introduces students to the vocabulary of independent and dependent variables. Students then organize the relationship in a table and extend their reasoning by writing an equation to model the situation. As the task progresses, students move from a concrete context to graphical, tabular, and algebraic representations, requiring them to analyze relationships among variables and demonstrate deeper understanding of proportional relationships.

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

Unit 2, lesson 3, activity 3.2 demonstrates coherence across units by connecting the mathematical idea that students can compose, decompose, and rearrange figures to determine area while preserving the same measurement. Students begin by analyzing figures that they can divide into rectangles to find the area and develop an understanding that rearranging parts of a figure does not change its total area. Throughout the unit, students extend this pattern of reasoning by applying composition, decomposition, and rearrangement strategies to determine the areas of parallelograms, triangles, and trapezoids. This progression strengthens students’ understanding of part-whole relationships and supports their development of area formulas through visual reasoning and mathematical connections.

Unit 5, lesson 16, activity 16.2 demonstrates coherence across units by connecting mathematical concepts and extending students’ understanding of geometry through different representations. In this lesson, students use the coordinate plane to plot polygons and analyze geometric figures using numerical representations. The “Activity Synthesis” states, “Complete the connection by explaining to students that the coordinate plane allows us to describe shapes and geometry in terms of numbers. This is how computers can create two- and three-dimensional images even though they can only interpret numbers.” This connects to prior learning from unit 2, lesson 9, activity 9.2 in which students used grids to analyze and determine the area of triangular shapes.

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 9, activity 9.2 demonstrates coherence by connecting the mathematical content and language from previous courses to the content students are learning in the current course and will learn in future courses. Students build on prior understanding of dividing fractions by using strip diagrams to represent and explain fraction division. The lesson then connects this visual model to the formal algorithm for dividing fractions, helping students understand the relationship between representations, mathematical language, and procedures. This progression strengthens students’ conceptual understanding of fraction division and prepares them for future learning in Algebra I, where they will apply fraction reasoning when simplifying rational expressions.

Unit 5, lesson 15, activity 15.2 demonstrates coherence across units by connecting mathematical concepts learned in previous grades to current learning and future applications. In this activity, students build on their understanding of the coordinate plane by finding distances through counting units on a grid and interpreting the location of points using positive and negative numbers. The “Lesson Narrative” explains how this learning progresses to future courses, stating, “Students will use these skills in grade 7 to find distances on maps. In grade 8, they will use these skills to draw slope triangles in the coordinate plane and find the lengths of their sides.” This progression demonstrates how students’ understanding of coordinate relationships and distance develops across grade levels and supports future geometric and algebraic reasoning.

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 1, lesson 7, activity 7.2 demonstrates coherence at the lesson level by connecting students’ prior knowledge and procedures from current and previous grade levels to new mathematical learning. Students build on their understanding of multiplication and division with whole numbers as they begin exploring division with fractions. Because students have not yet learned the formal algorithm for dividing fractions, they rely on their understanding of the context and use visual representations, including images and strip diagrams, to represent the situation and write an equation. This approach allows students to develop conceptual understanding of fraction division by connecting familiar strategies to new mathematical ideas.

Unit 2, lesson 4, activity 4.2 demonstrates coherence at the lesson level by connecting students’ prior knowledge from current and previous grade levels to new mathematical thinking. Students build on their previous understanding of finding the area of rectangles and their knowledge of the attributes of parallelograms to explore how to determine the area of a parallelogram. This lesson focuses on developing conceptual understanding as students analyze the relationship between shapes and area rather than immediately applying a formula. Because later lessons introduce the formal procedure for finding the area of a parallelogram, this activity allows students to first build a strong foundation through reasoning and visual connections.

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

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 6, lesson 2, activity 2.3, students apply the distributive property using numerical expressions while connecting their understanding of area from previous lessons and units. In the “Advanced Student Thinking” section, students can use rectangle models to represent expressions with sums in parentheses by partitioning a rectangle into smaller sections and interpreting the sum as the combined areas of those sections.

Unit 6, lesson 7 provides spaced retrieval opportunities by integrating previously learned skills and concepts alongside the current lesson’s content. Questions 1–3 focus on applying new learning related to expressions with exponents, while Questions 4–7 include review items from previous units that require students to revisit and apply prior mathematical knowledge. These review problems allow students to retrieve previously learned concepts from long-term memory and make connections between current algebraic reasoning and foundational skills developed earlier in the course.

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

In grade 6, students practice representing ratios using multiple strategies, including concrete models, tables, and fractions, allowing them to develop flexibility in their mathematical thinking. Later units reinforce this understanding of ratios through increasingly complex applications that require students to apply ratio reasoning to real-world situations. In unit 3, lesson 5, activity 5.2, students explore equivalent ratios within the context of adjusting a recipe. Students apply multiplication and division strategies to the original recipe to create equivalent ratios that represent double, half, five times, and one-fifth of the original amount. They then analyze given ratios of ingredients to determine how many batches of the recipe each represents. In this way, the materials provide interleaved practice opportunities by incorporating previously learned skills and concepts alongside current lesson content across units.

In unit 4, lesson 10, students apply their current learning related to percentages and double number lines while also revisiting concepts from earlier units. Problems 4 and 5 include review tasks from unit 3, requiring students to determine which previously learned strategies apply in new contexts. Problem 4 reviews determining rates at which vehicles are traveling, connecting to unit 3, lesson 14, activity 14.3 in which students analyzed reading rates. Problem 5 reviews determining ratios between the amount of potatoes needed and the quantity of mashed potatoes produced, connecting to unit 3, lesson 3, activity 3.3 in which students investigated ratios in a cookie recipe context. By mixing concepts from multiple units within the same practice set, students strengthen their ability to transfer knowledge and apply strategies flexibly, and at the same time, students receive interleaved practice opportunities.

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

In unit 2, lesson 9, activity 9.2, students use visual models of triangles embedded in rectangles and parallelograms to reason that they can represent the area of a triangle as 1/2bh. Within this task, students interpret how the diagrams represent area relationships and analyze why the area of a triangle is half the area of a rectangle or parallelogram. Students also evaluate the validity of their reasoning by responding to questions such as “Can you explain why this expression is true for any triangle?” and by selecting a diagram to justify why 1/2bh works for all triangles.

In unit 7, lesson 8, activity 8.2, students interpret inequalities in the context of a basketball scoring situation and represent solutions on number lines. Students analyze solution sets by examining how to represent values graphically and determine which values satisfy one or both inequalities. They evaluate whether specific values make sense in context, including identifying when negative or unrealistic values are not valid solutions, demonstrating the use of mathematical reasoning to interpret and evaluate representations.

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

In unit 2, lesson 8, activity 8.2, students create models to represent mathematical situations involving area relationships. Students construct visual models using rectangles and parallelograms to represent triangles with the same base and height, including drawing rectangles over triangles to decompose them into two right triangles. Students use these created models to determine the area of the rectangle, and then reason that the area of the triangle is half of that value before formalizing the area formula. In the final task, students create a new model by decomposing a triangle into a trapezoid and a smaller triangle and rearranging it into a parallelogram model to determine the area of the original triangle.

In unit 3, lesson 15, activity 15.2, students determine whether sequences are additive or multiplicative and create equations and graphs to represent the patterns. They use these models to show how the sequences grow and compare the relationships. One of the discussion prompts asks, “What do you notice about how the sequences generated by addition change compared to those generated by multiplication?” Students also create their own sequences and write rules to represent them.

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

In unit 2, lesson 2, activity 2.2, students use tangram pieces to compose and decompose shapes, reasoning that rearranged or overlapping figures can have equivalent area. Students determine the area of non-rectangular shapes by combining triangles and a square unit into different configurations, using the square as a unit of measure. They apply their conceptual understanding of area conservation to a hands-on problem-solving situation by justifying why different arrangements maintain the same area. A question asks, “Notice that you can put together two small triangles to make a square. What is the area of the square composed of two small triangles? Explain your reasoning.”

In unit 7, lesson 4, activity 4.2, students apply their conceptual understanding of equality and equation-solving to a new practice context in which they solve equations using multiple strategies, including balanced hanger models from prior learning, substitution, and informal reasoning such as “2 times what number is 18?” As the equations increase in complexity, students determine when more formal algebraic methods are more efficient. Students then graph solutions on a number line, applying their understanding of equations to a new representational context. One task states, “Solve the equations in one column. Your partner will work on the other column. When you find each solution, graph it on a number line.” In these ways, the materials provide opportunities for students to apply conceptual understanding to new problem situations and contexts.

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

In unit 5, lesson 4, activity 4.2, students classify rational numbers using Venn diagrams. The activity provides a list of 17 numbers, including decimals, negative numbers, and whole numbers, such as 3.00, 0.00, −5.00, 0.50, 3.14, −2.50, and 2. Students use a Venn diagram template to sort each number into the categories of whole numbers, integers, and rational numbers. Through repeated classification of multiple values, students develop automaticity and fluency in identifying number types accurately and efficiently.

In unit 6, lesson 6, activity 6.2, students explore a coin-doubling scenario to connect repeated multiplication with exponent notation. Students repeatedly calculate powers of two across multiple scenarios, building automaticity in evaluating exponential expressions. Through repeated practice, students develop fluency in recognizing and computing exponential growth patterns efficiently and accurately.

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 4, lesson 3, students use tables, double number lines, unit rates, multiplication, and division to convert measurements and compare different solution methods. The lesson explains that finding “how much per 1” is an efficient strategy while continuing to connect it to familiar representations. Students also explain their reasoning, compare approaches, analyze an incorrect solution, and decide whether to multiply or divide based on the situation, strengthening their ability to choose accurate and efficient procedures when converting units.


In unit 7, lesson 3, activity 3.2, students match hanger diagrams to equations and use both representations to solve equations. Students apply flexible and accurate procedures by translating between visual models and symbolic equations to find solutions. Later, in unit 7, activity 4.2, students solve equations of increasing complexity. The “Activity Narrative” states, “As students progress through the activity, the equations become more difficult to solve by strategies other than ‘do the same thing to each side.’” This progression supports students in selecting more efficient algebraic procedures as less efficient strategies become less effective, reinforcing procedural fluency in solving equations.

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.

In unit 2, lesson 3, activity 3.2, students evaluate procedures, processes, and solutions for efficiency, flexibility, and accuracy. Students find areas of regions using multiple strategies, including decomposing, rearranging, subtracting, and enclosing. Students compare these approaches by identifying similarities and differences and explaining how each strategy works to determine area. They also evaluate which strategies are more efficient or effective in different situations and justify their reasoning. Students choose which strategy to use, while educators may support students who do not independently select a method.

In unit 13, lesson 1, activity 1.3, students estimate the total number of tiles needed to cover the Washington Monument. Students determine what information they need, select a method to organize their work, and choose strategies to estimate a solution. Students then create a visual display of their solution and compare approaches across groups. The educator supports students in evaluating efficiency by prompting them to consider ways to “simplify the situation” and improve their calculations. Through this process, students evaluate the efficiency and reasonableness of their chosen methods and refine their approaches based on comparison with other solutions.

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

In unit 2, lesson 10, activity 10.2, the embedded prompts for educators support students in developing an accurate and consistent method for identifying triangle height. Educators guide students to understand that they must draw the height perpendicular to the base and that the base does not need to be horizontal. Students use an index card to help align the base and identify the perpendicular height. Educators support students in extending the base when needed to locate the opposite vertex. Educator questions such as “For which triangles was it easy to find the corresponding height for the given base?” and “For which triangles was it harder?” help students reflect on the efficiency and ease of different approaches, guiding them toward more reliable methods.

Unit 2, lesson 11, activity 11.3 includes embedded educator guidance that explicitly directs students toward more efficient solution methods. The activity prompts educators to highlight that “some strategies are more direct or efficient than others” and to ask students to revisit their plans and consider the “pros and cons of their original plan.” Educators also remind students to “keep in mind the merits of the different strategies” as they solve problems. These supports help educators guide students to compare approaches and recognize more efficient methods while still valuing multiple valid strategies.

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

“Unit 6: Expressions” explicitly states how the unit addresses the conceptual and procedural emphasis of the TEKS. Students first develop conceptual understanding of equivalent expressions using multiple representations, including diagrams, verbal explanations, and algebraic notation. They use area models to build and justify conceptual understanding of the distributive property by connecting visual and algebraic reasoning. Students then connect this conceptual understanding to procedural skills by creating, interpreting, and simplifying equivalent expressions, including in real-world contexts in which they apply and communicate their reasoning.

In addition, the materials explicitly state how unit 7, lesson 3, activity 3.3 addresses the conceptual and procedural emphasis of the TEKS. Students use the hanger model to develop conceptual understanding of equality, then connect this model to procedural methods for solving equations. For example, the “Activity Narrative” states, “Students notice the structure of equations and diagrams and find correspondences between them and between solution strategies.” This explicitly shows how students move from conceptual understanding of representations to procedural strategies for solving equations.

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 2, lesson 9, activity 9.3, students use concrete triangle models and pictorial diagrams to identify base-height pairs and determine area. Students analyze labeled geometric figures as pictorial representations to select appropriate measurements and then move to abstract representations by writing equations and applying the area formula, A = 1/2bh. Students also generalize their reasoning using the formula to represent all triangles, connecting concrete models, visual representations, and symbolic expressions.

Unit 7, lesson 3, activity 3.2 includes questions that encourage the use of pictorial diagrams to make connections to equations. Students analyze correspondences between hanger diagrams and equations to find unknown values, interpreting these values as solutions to equations. A prompt states, “Use the hangers to explain what each solution means.” Students then transition to abstract representations by writing equations based on the balanced hanger models and using algebraic reasoning to solve them. In the following lesson, students further extend this understanding by moving from diagrams to equations, strengthening connections between pictorial models and abstract symbolic 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 3, lesson 7, activity 7.3, students create their own double number line to represent a real-world ratio situation in which they create a recipe for art paste. For example, the recipe calls for two pints of water for every eight cups of flour. Students determine how to label the representation and use it to answer questions about the relationship. Students then explain how they used the model to find missing values, including how they determined the unit rate, supporting the connection between the visual model and abstract reasoning about ratios.

In unit 9, lesson 4, activity 4.2, students connect a symbolic equation from a previous activity to its real-world context. For example, the previous activity gave students equations such as “S – 2 = T” in which S is the number of sides on a polygon and T is the number of triangles they can draw from one vertex without overlapping. Students interpret the variables and values in terms of the situation. Questions support and guide students to move between representations. They rewrite the equation in words, organize the information in a table, explain the meaning of key values in context, and create a graph to represent the relationship between the variables. One prompt states, “In the previous activity, you matched equations and tables. Copy the values from the table that matched your assigned equation into the first 3 rows of this table. Make sure to label what each column represents and which variable is the independent and dependent variable. Use your equation to find the values that complete the last 2 rows of the table.”

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

In unit 2, lesson 2, activity 2.2, students develop academic mathematical language using visuals, manipulatives, and language development strategies while exploring the area of non-rectangular shapes. Students use physical tangram pieces and visual representations to compose, decompose, arrange, and rearrange figures. The materials support vocabulary development by connecting informal student language to academic mathematical terms. The educator guidance states, “Demonstrate the use of the word ‘compose’ by repeating students’ everyday language use and then recast using the formal terms here.” This strategy supports students in using precise mathematical vocabulary to describe their geometric reasoning.

In unit 4, lesson 1, activity 1.3, students develop academic mathematical language using visuals, manipulatives, and collaborative discussion while exploring measurement concepts. Students sort cards based on length, volume, weight, or mass while using vocabulary such as quart, gallon, ton, milliliter, and kilogram. The educator provides visual and concrete supports, including household items, a quart-sized bottle, meter sticks, and rulers, to connect measurement vocabulary to real-world objects. After sorting the cards, students discuss their classifications with peers and explain their reasoning using the academic language of the lesson.

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 5, activity 5.2, the “Launch” includes guidance that reads, “Explain to students that in this task, they will think about the ratios of ingredients for a tuna casserole and how to adjust them for making different numbers of batches.” The “Activity Synthesis” provides embedded educator guidance for facilitating discussion by displaying student responses, asking students to explain their reasoning, and prompting students to analyze how ratios change when the number of batches changes. Academic vocabulary in this lesson includes one-half, one-fifth, twice, ounces, and cups. These supports provide opportunities for students to hear, discuss, and use mathematical language in context.

In unit 12, lesson 8, activity 8.2, students develop and use academic vocabulary related to analyzing data distributions. Students analyze dot plots to describe the center and spread of a distribution that is not symmetric. The “Activity Synthesis” provides embedded educator guidance to support mathematical discussions through prompts such as “What would you consider the center for the two dot plots shown in this activity?” and “Ask students how they thought about the spread of the data.” Students share descriptions of the data sets and use vocabulary related to the lesson, including center, spread, distribution, and dot plot. This guidance supports educators in facilitating conversations in which students interpret data representations and communicate their mathematical ideas using appropriate academic language.

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 6, lesson 1, activity 1.2, students use diagrams to represent expressions and equations and determine when expressions are equivalent or equal for a specific value of a variable. The materials provide graph paper and prompt students to create diagrams that represent expressions, distinguish between expressions and equations, and explain their reasoning with a partner before whole-class discussion. Students use sentence stems such as “I know these expressions are equal (or not equal) when ______ because ______.” The educator guide includes exemplar responses and discussion guidance that highlights how diagrams connect to the expressions students are analyzing. These supports provide opportunities for students to use mathematical vocabulary, explain relationships between representations, and communicate their reasoning during mathematical conversations.

Materials provide educator guidance that supports students’ use of mathematical vocabulary, notation, and discourse while providing opportunities to hear, refine, and use mathematical language with peers. For example, in unit 7, lesson 6, activity 6.2, students use exponential notation to represent repeated multiplication and explain whether the value of the magical coins will exceed one million dollars. The lesson includes Math Language Routine 1: Stronger and Clearer Each Time, which guides students to share an initial explanation with multiple partners, receive feedback through prompts such as “Can you explain how . . .?” and “You should expand on . . .,” and revise their responses using more precise mathematical language. The materials also provide sample responses that support educators in guiding students’ explanations and mathematical communication.

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

Materials integrate TEKS process standards into lessons. For example, in unit 3, lesson 6, activity 6.2, students use a double number line as a representation to investigate equivalent ratios. Students use discrete diagrams and double number lines to represent equivalent ratios and explain how the representations are alike and different. The process standard aligned with this lesson, as given in the scope and sequence, is 6AM.1.D, which focuses on communicating mathematical ideas using multiple representations. Students respond to questions such as “How can we tell that 4:1 and 12:3 are equivalent ratios?” as they explain the relationship between different representations of equivalent ratios.

In unit 6, lesson 8, activity 8.2, students use the context of surface area to extend their understanding of the order of operations to include exponents. The process standard aligned with this lesson, as given in the scope and sequence, is 6AM.1.G, which focuses on displaying, explaining, and justifying mathematical ideas. Students evaluate solutions from two students and explain why 6 × 10² is equivalent to 600 square inches. Through analyzing solutions and justifying their reasoning, students engage in the TEKS process standard integrated in the lesson.

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” 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 course guide also explains that “doing mathematics” means learning mathematical concepts and procedures while engaging in mathematical practices such as 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 language, looking for and making use of structure, and expressing regularity in repeated reasoning. In this way, the materials describe how they incorporate and connect TEKS process standards throughout the course.

The Grade 6 Advanced Math Scope and Sequence lists the TEKS process standards, showing their incorporation throughout the course. The “Course Narrative” also includes descriptions of mathematical learning that connect to process standards such as students developing “logical thinking and problem-solving strategies that will serve them in academics and life.” Additionally, the materials describe how the course “continues a focus on graphing points on the coordinate plane, recognizing patterns, and interpreting relationships through graphs, tables, and equations.”

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 8 overview describes how the unit incorporates and connects the TEKS process standards as students explore algebraic relationships through multiple representations. Students connect verbal descriptions to mathematical representations by using strip diagrams to represent unknown quantities, writing equations, and explaining their reasoning. The unit overview describes how students solve equations such as (px + q = r) and (p(x + q) = r), determine boundary points, graph solution sets, and interpret inequalities in real-world contexts. Throughout the unit, students use representations, analyze relationships, justify solutions, and communicate mathematical reasoning while developing understanding of equations and inequalities.

In unit 12, the “Section Level Planning Guide” provides a description of how the unit incorporates TEKS process standards. The guide describes how students make connections between survey questions and data sets, justify their reasoning in oral and written forms, and analyze and communicate characteristics of data distributions, including the center, spread, shape, and other key features, using statistical vocabulary. Students evaluate appropriate statistical measures for different data distributions and communicate their reasoning throughout the unit.

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

Unit 2, lesson 9 codes the process standards at the top of the lesson. The “Lesson Narrative” provides a description of how students engage with process standards during the lesson. The “Learning Goal” states that students will “compare, contrast, and critique (orally) different strategies for determining the area of a triangle.” The “Learning Target” states, “I can write and explain the formula for the area of a triangle.” These lesson components describe opportunities for students to communicate mathematical ideas, explain reasoning, and critique strategies.

Unit 7, lesson 6 codes the process standards at the top of the lesson. The “Lesson Narrative” describes how students apply mathematical reasoning during the lesson, stating, “After writing inequality statements to represent situations, students test values to see if they make the statement true.” The “Learning Goal” states that students will “critique (orally and in writing) possible values given for a situation with a constraint, including determining whether the boundary value is included and making sense of situations with discrete quantities.”

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

In unit 10, lesson 12, students have opportunities to think mathematically about which uses more water, a bath or a shower. Students persevere through solving the problem by making reasonable estimates of variables such as time, volume, and rate, determining what information they need, and converting rates, from either a website or information provided by the educator, into more usable units for their calculations. The open-ended nature of the task encourages students to make sense of the mathematics by analyzing their results, creating a display (graph or table) to communicate their solution, and justifying their reasoning by responding to questions such as “Do you agree or disagree? Why?”

In unit 13, lesson 1, activity 1.3, students estimate the total number of tiles needed to cover the Washington Monument. The open-ended task provides opportunities for students to think mathematically as they determine what information they need, develop solution strategies, and justify their estimates. Students persevere through solving the problem by brainstorming the information they need, requesting it from the educator or using internet-enabled devices to research it, and refining their approaches. The materials support students in making sense of mathematics through viewing visual representations of the monument’s dimensions, engaging in educator-guided discussion, creating visual displays, conducting a gallery walk, and explaining why different estimates are reasonable in response to the question “How many tiles would it take to cover the Washington Monument?”

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 3, lesson 10, activity 10.2 instructs students that they may compare rates using a double number line, multiply or divide to create equivalent ratios, or find the unit price. During the “Three Reads” routine, students discuss possible approaches before solving the problem and respond to prompts such as “Can you think of a different way to solve it?” and “What strategy or method would you try first?” Students then explain and justify their methods with classmates, and the lesson concludes with students comparing different solution strategies. This activity example emphasizes that students can use each method to determine whether Diego and Andre paid the same rate.

In unit 9, lesson 1, activity 1.2, students have opportunities to represent and solve problems using multiple representations, including graphs, tables, verbal descriptions, and equations, to describe the relationship between two quantities using the terms independent and dependent variables. During the “Activity Synthesis,” the materials guide the educator to emphasize the connections among representations by stating, “The discussion should focus on how all the representations (tables, equations, graphs) capture the same information but look at it in a different way.” Students further demonstrate their understanding by explaining and justifying their solutions in the “Practice Problems” section using multiple representations, reinforcing that students can represent and solve mathematical relationships in more than one valid way.

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 Middle School Teacher Resource Guide” states, “Students learn mathematics by doing mathematics, rather than by watching someone else do mathematics or getting told what to do.” The resource guide also states, “In a math community, all students have the opportunity to express their mathematical ideas and discuss them with others.” Additionally, the guide explains, “Writing is a useful catalyst in learning mathematics because [it supplies] students with an opportunity to describe their feelings, thinking, and ideas clearly.” This philosophy is evident in Kiddom lessons as well. For example, in unit 11, lesson 8, activity 8.2, students deepen their understanding of financial assets and liabilities by doing mathematics, writing about their mathematical thinking, and discussing their reasoning with both peers and the educator.

In unit 12, lesson 4, students make sense of mathematics through multiple opportunities to do, write about, and discuss mathematics with peers and the educator as they investigate sampling and measures of center. Students actively do mathematics by calculating either the mean or the median for multiple samples and for the full population of painting prices. They write about mathematics by completing written-response tasks, including calculating measures of center for three different samples and comparing how closely the sample measures matched the population measure. Students then discuss mathematics by comparing their responses with a partner, analyzing similarities and differences in their results, and participating in structured whole-class discussions to explain their reasoning and make sense of sampling and measures of center.

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

In unit 9, lesson 1, activity 1.1 “Warm-Up—Which One Would You Choose?” students determine which is the better deal for purchasing honey. As students share their solutions, the materials support educators in guiding students to explain their reasoning, construct arguments, critique the reasoning of classmates, and justify their conclusions. The “Activity Synthesis” provides educator prompts that encourage students to reflect on and discuss problem-solving approaches, including, “Who can restate ___’s reasoning in a different way?” “Does anyone want to add on to _____’s reasoning?” and “Do you agree or disagree? Why?” These prompts support educators in facilitating discussions in which students share, reflect on, and justify their mathematical thinking.

In unit 11, lesson 6, students explore various occupations, including required education, possible salary, and total lifetime earnings. The materials support educators in guiding students to share and reflect on their reasoning by providing discussion questions such as “How might the level of education or vocational training impact an individual’s ability to obtain a career?” “How might these findings influence your future career decisions?” and “What other factors might influence your career choice beyond annual salary?” As students reflect on their occupational choices and the associated financial implications, they respond to the prompt, “Does this map look the way you expected? Are there requirements or financial implications that affect your overall personal and financial goals?” Students explain, justify, and support their conclusions while reflecting on the reasoning behind their decisions.

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

In unit 12, lesson 10, activity 10.2, students use measurements for the lengths of 25 earthworms to create a histogram. The materials provide prompts and guidance that support educators in anticipating misconceptions and providing explanatory feedback based on student responses. The “Advancing Student Thinking” section informs educators that “when determining frequencies of data values, students might lose track of their counting. Suggest that they use tally marks to keep track of the number of occurrences for each bin.” The materials also anticipate that “when drawing the histogram, students might mistakenly use bar graphs as a reference and leave spaces between the bars. Ask them to look at the bars in other histograms they have seen so far and to think about what the gaps might mean, considering that the bars are built on a number line.” The “Activity Synthesis” provides educators with prompts such as “In a histogram, are we able to see clusters of values in the distribution?” “Can we see the largest and smallest values? Can we tell the overall spread?” and “How do we identify the center of a distribution?” to provide explanatory feedback and deepen students’ understanding based on their responses.

Unit 13, lesson 2 provides prompts and guidance that support educators in providing explanatory feedback based on student responses and anticipated misconceptions. During class discussions, the materials prompts educators to probe students’ reasoning, suggesting, “Ask students if the ratio for the world population is equivalent to the population for people in the class.” The lesson anticipates that “students may not recognize that the ratio of people from Africa to the world population is only approximately equal to the ratio of students in the class from Africa to the total number of students.” To address this misconception, the materials prompts educators to ask about how many people they think live in Africa, helping students recognize the role of approximation in proportional reasoning. The lesson further guides educators in explaining that the ratios are not exactly equivalent because 7.4 billion is an approximate population. The lesson emphasizes that students should look for a ratio close to 5 out of 30 rather than a ratio exactly equivalent to it, and reminds educators to reinforce 12 out of 30, or 40 percent, as a benchmark percentage.