Kiddom Texas: Mathematics, Grade 6 (Second Edition)

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

The scope and sequence states that unit 1, lesson 1 aligns with TEKS 6.7A. The learning targets for lesson 1 are to explain (orally) how to create and solve an equation that represents a situation with an unknown amount and to write an expression with a variable to generalize the relationship between quantities in a situation. Unit 1, lesson 1 also aligns with ELPS 2.D, 3.D, and 2.A.

The materials include a year-long scope and sequence of concepts for instruction. For example, the course includes “Unit 1: Factors and Multiples,” “Unit 2: Positive Rational Numbers,” “Unit 3: Shapes and Solids,” “Unit 4: Decimals,” “Unit 5: Ratios,” “Unit 6: Percents, Unit Rates, and Conversions,” “Unit 7: Signed Numbers, Integers, and the Four Quadrants,” “Unit 8: Expressions,” “Unit 9: Equations and Inequalities,” “Unit 10: Graphing Quantitative Relationships,” “Unit 11: Financial Literacy: Accounts, Credits, and Careers,” “Unit 12: The Statistical Process and Numerical Data,” and “Unit 13: End-of-Course Topics.”

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 a suggested pacing to support three instructional calendars for 165, 180, and 210 days. The document providing calendar options includes lessons and activities for a full year of instruction. The implementation of units aligns with the time constraints of a school year. In the 165-day calendar, unit 1 includes five lessons scheduled over seven days. In the 180-day calendar, unit 1 includes five lessons scheduled over nine days. In the 210-day calendar, unit 1 includes five lessons scheduled over 10 days.

The materials include a document with suggested pacing that outlines the concepts in each unit and the recommended pacing for each unit. For example, the “Program Pacing Guide” indicates educators should teach unit 1 during weeks 1–2 of the school year. The pacing guide specifies teaching unit 2 during weeks 3–4 of the school year.

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 an anchor graphic illustrating the progression of learning, which serves as a reference for educators to support their understanding and internalization of concept connections across units. For example, the materials include an anchor graphic that provides a visual representation of the overarching design structure of each unit in the course. The graphic shows that each unit begins with an invitation to the mathematics, in which the first few lessons provide an accessible entry point for all students and offer opportunities for educators to observe students’ prior understandings. It also illustrates that each lesson begins with a warm-up designed to activate prior knowledge and prepare students for the learning of the day.

The materials include a rationale for unit order that helps educators understand how the sequence of units supports the development of concepts throughout the course, along with an explanation of how concepts connect across the course. For example, in the Kiddom Math Middle School Course Guide for Teachers, “Principles of Kiddom Math Curriculum Design” section, the course overview states, “Every unit, lesson, and activity has the same overarching design structure: The learning begins with an invitation to the mathematics, is followed by a deep study of concepts and procedures, and concludes with an opportunity to consolidate understanding of mathematical ideas.”

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

The materials include protocols with corresponding guidance for unit internalization through previewing the unit to understand key standards, unit objectives, vocabulary, and assessments. For example, the unit 3 “Section Level Planning Guide” organizes the unit into six sections: “Section A, Reasoning to Find Area”; “Section B, Parallelograms”; “Section C, Triangles and Other Polygons”; “Section D, Polygons with Given Conditions”; “Section E, Fractions in Lengths, Areas, and Volume”; and “Section F, Putting It All Together for Real-World Applications.” Each section outlines the concepts, objectives, and key standards that students will learn throughout the unit.

The materials include guidance that supports lesson internalization by explaining the purpose, mathematical focus, and progression of learning within each lesson. In unit 12, lesson 4, the “Lesson Narrative” explains that students learn to choose appropriate visual representations for numerical data and interpret data distributions in context. The guidance describes how students engage in higher-order thinking by analyzing, interpreting, and reasoning with data distribution tables. It explains that students continue developing their ability to choose representations for categorical and numerical data, reason abstractly and quantitatively by interpreting displays, and describe features of data distributions. The narrative also identifies how the unit introduces informal understandings of concepts, such as typical, center, and spread, as foundations for future formal learning.

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

The course overview includes the “Implementation Support for Leaders” document. One example of guidance the document provides to school leaders states, “Most of us get a great deal of pleasure out of telling others how to solve their problems. But effective coaches know they need to refrain from fixing people and focus on creating conditions where people unlock their own potential. This means that coaches should only share their expertise when it is clearly needed.”

The materials provide resources to guide instructional leaders in facilitating team meetings and addressing instructional challenges with implementation. The materials include a curated collection of research-based articles designed to support campus-level coaching and implementation of the curriculum. These resources provide guidance for coaching and leading implementation, adult-level explanations of mathematical concepts and learning progressions, examples of how concepts develop beyond the grade level, and series-level and course-specific articles that support coherent implementation.

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 unit 6 “Section Level Planning Guide” provides background content knowledge to teach units of measurement and unit conversion. The materials state, “In this section, students explore measurement units across length, volume, weight, and mass. They start by comparing standard units like inches and kilograms . . . Students learn to estimate by associating objects with units, understanding that smaller units mean larger quantities for the same measurement.”

In unit 1, the “Unit Narrative” provides embedded support for developing the academic vocabulary necessary for students to understand and engage with the mathematical concepts in the unit. The “Key Terms” section explicitly identifies important vocabulary, including greatest common factor and least common multiple, and provides definitions and examples to clarify their meaning and use. For example, the materials define greatest common factor as “the largest number that divides evenly into both numbers” and explain, “Sometimes we call this the GCF.” Similarly, the materials define least common multiple as “the smallest product you can get by multiplying each of the two numbers by some whole number,” followed by the statement, “Sometimes we call this the LCM.” By explicitly identifying, defining, and providing examples of these key mathematical terms, the materials support students in developing and using the academic vocabulary needed to access the unit content.

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 both English and Spanish to support student learning and development at home for each unit. These supports include activities that reinforce in-class learning, questions families can ask about classroom learning, and strategies to strengthen new learning. For example, the family support materials for each unit include a section titled “What Can I Do to Support My Student at Home?” that provides guidance and suggestions for supporting student success.

In a unit about shapes, the materials encourage families to explore shapes and their properties in everyday objects, discuss area using real-world surfaces, and use building blocks or drawings to decompose and recompose shapes. The materials also encourage families to ask students to explain their reasoning and strategies, discuss real-world applications of geometry, review fraction operations, and use academic vocabulary such as base, height, and perpendicular while fostering a positive attitude toward mathematics.

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).

Unit 6, lesson 3, activity 3.3 provides a detailed lesson plan in which students learn to convert units of measurement between pounds and kilograms. The narrative explains the lesson objective is for students to apply insights from a previous activity, with some using unit rates and others reasoning with representations of equivalent ratios. This lesson’s “Launch” introduces the prompt “Ask students to recall which is heavier, a pound or a kilogram?” Students meet the language standard of the lesson as they think quietly and share their explanation with a partner.

The lesson plans include tasks and questions designed to support the development of language aligned to the ELPS through discussion, collaboration, and written explanations. For example, in the Mathematical Language Routine (MLR) section “Representing, Listening, Speaking: MLR7 Compare and Connect,” students display their approaches to determine whether “Elena’s mom was speeding.” As students share their work, they explain the meaning of each quantity used in their reasoning, including conversions between miles per hour and kilometers per hour. Educators prompt students to connect representations such as tables and double number lines to other strategies and to explain how these methods support reasoning about equivalent ratios and unit conversions. The design principles include cultivating conversation and maximizing meta-awareness.

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 list of educator and student materials, such as manipulatives and activity pages or templates, in each lesson overview, along with guidance on how and when the materials support student learning. For example, in unit 3, lesson 3, the required materials include a geometry toolkit and instructional routines such as MLR3: Clarify, Critique, Correct and think-pair-share. The activity engages students in finding the area of shapes using multiple strategies, including counting squares, decomposing rectangles, and subtracting missing regions.

The materials include guidance and recommendations for the suggested timing of lesson components such as inquiry and exploration, direct instruction, guided practice, collaborative work, and independent work. For example, unit 3, activity 6.2 recommends 25 minutes for the “Activity Narrative.” During this time, students practice finding and reasoning about the area of parallelograms on and off a grid by identifying appropriate base and height measurements and recognizing that parallelograms with the same base-height product have the same area.

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

In unit 3, lesson 3, the “Lesson Narrative” provides guidance for using an optional activity as extended practice to deepen students’ understanding of fractions and greatest common factors. The materials explain that the activities build on one another and provide students with opportunities to connect the greatest common factor of two numbers to related fractions through repeated reasoning. The guidance states, “The activities in this lesson build on each other, providing students an opportunity to express the relationship between the greatest common factor of two numbers and related fractions through repeated reasoning. Thus, the activities should be done in order.” The materials also provide pacing guidance, noting that completing all activities may require multiple class periods and that educators can determine how much time to spend based on instructional needs. The guidance explains that the lesson is an optional opportunity for students to explore concepts more deeply and make connections across mathematical domains.

Unit 12, lesson 17 provides guidance for using lesson activities as extended practice to deepen students’ understanding of statistical processes and numerical summaries of data. In activity 2, students extend their learning of box plots by connecting features of box plots to the five-number summary, including the interquartile range (IQR), range, median, minimum, and maximum values across multiple data sets. The materials provide educators with guidance for using MLR4: Information Gap to support students in explaining their reasoning and identifying the information needed to interpret box plots. For example, the materials guide educators to “give students a purpose for discussing information necessary to connect features of a box plot to information about the five-number summary and provide question starters such as ‘Can you tell me . . . (specific piece of information)?’ and ‘Why do you need to know . . . (that piece of information)?’” This guidance supports educators in using the activity as extended practice by engaging students in mathematical communication, reasoning, and application of statistical 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.

The materials include diagnostic assessments with a variety of question types including problem-solving tasks, conceptual reasoning prompts, and real-world application questions to determine students’ readiness for new mathematical concepts. For example, in unit 9, “Check Your Readiness” assesses students’ incoming knowledge about concepts that support their understanding of expressions and equations. An example of one of the short-constructed response prompts from the diagnostic assessment is “Describe what you would do to find the missing value in each equation. ? + 59 5/8 = 82 2/3.”

The “6.2 Check Your Readiness (A)” assessment functions as a diagnostic assessment that measures students’ prerequisite knowledge for fraction division. The assessment evaluates skills ranging from fraction comparison and number sense to interpreting multiplication and division situations. It includes a variety of task types such as multiple-select questions, written responses, computations, and diagrams. For example, question 1 is a multiple-select problem worth four points in which students select all fractions greater than 1/2. Question 5 asks students to draw a diagram to explain how they know the answer to 3 ÷ 4.

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

The materials define the purpose of each assessment type and explain how to use the results. The intention of formative assessments such as cool-downs and “Section Checks” is to monitor student understanding and inform instructional decisions. The aim of summative assessments, such as unit assessments and the end-of-course assessment, is to measure students’ mastery of grade-level standards and learning objectives. The assessment guide provides specific guidance for interpreting student performance and planning next steps for instruction. For example, the materials state the cool-down is “a brief check to determine whether students understand the main concepts of the lesson” and to use it “as a formative assessment to plan future instruction.”

The materials provide definitions and intended purposes for the instructional assessments included. The materials also offer examples of how to implement various formative assessments such as quick checks, warm-ups, think-pair-share activities, and exit tickets. For example, in unit 6, lesson 4.1, the warm-up includes a description of its purpose, which is to prompt students to reason about the meaning of division by closely examining the dividend and divisor. The materials further explain that the intention of the selection of expressions is to encourage more precise reasoning rather than simple estimation. One warm-up question asks students to determine whether the value of each expression is closer to 1/2, 1, 1 1/2, or 9/20, demonstrating how the activity develops students’ understanding of division concepts while preparing them for the lesson’s learning goals and instructional purpose.

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

The materials include guidance for educators to administer the assessments consistently such as reminders or tips that suggest the time allotted to complete the assessment. For example, in unit 12, lesson 5, the cool-down provides a suggested time allotment of five minutes to complete the assessment. The materials also provide additional guidance on the administration of the assessment by stating, “Students will have more opportunities to understand the mathematical ideas in this cool-down, so there is no need to slow down or add additional work to the next lessons.”


The materials provide overviews of assessments, outline the time to administer each task, and give step-by-step guidance for administering each component of assessments, including information to support the educator in understanding the assessments, ensuring consistency and standardized administration across examiners. For example, in the Kiddom Math Middle School Course Guide for Teachers, “The Assessment Guide” section provides educators guidance on administering each component of assessment within each unit to ensure consistency and standardized administration across examiners. Educators should use diagnostic assessments to ensure consistent and accurate administration, and the materials state, “Use the diagnostic assessments to pace or tune instruction.”

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 diagnostic assessments that align with the TEKS. For example, “Grade 6.10 Check Your Readiness (A)” serves as a diagnostic assessment aligned with the TEKS and with unit objectives for expressions, equations, and coordinate relationships. Students demonstrate prerequisite skills by interpreting and plotting points on a coordinate plane and identifying variables as x- and y-coordinates in ordered pairs. The diagnostic assessment aligns with TEKS 111.26.b.6.A, which states that students will identify independent and dependent quantities from tables and graphs.

The materials include assessment items that align with practice questions within a lesson or unit, demonstrating consistency with instructional goals. For example, unit 11 includes the “Grade 6.11 End of Unit Assessment (A).” One of the objectives of this unit is to investigate career paths and calculate long-term financial outcomes to understand the relationship between education and lifetime earnings. One of the questions from the summative assessment that aligns to this lesson objective is “A Computer Engineer requires a Bachelor’s Degree and makes $105,000 per year. A High School Math Teacher requires a Bachelor’s Degree and makes $60,000 per year. How much more will the Computer Engineer earn over 40 years compared to the High School Teacher?”

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

The materials include instructional assessments with TEKS-aligned items that assess student understanding at varying levels of complexity, including procedural tasks, the application of multiple skills to solve problems, and open-ended questions. For example, in unit 8, the “Grade 6.8 End of Unit Assessment (A)” includes items that require students to demonstrate conceptual understanding and apply mathematical reasoning. One item asks students to “write an expression involving whole number exponents that represents the prime factorization of the number 8,” requiring students to connect their knowledge of prime factorization and exponents to construct a correct mathematical expression.

The “Grade 6.7 End of Unit Assessment (A)” includes items aligned to the TEKS that assess students’ knowledge of rational numbers, inequalities, absolute value, coordinate planes, and the classification of real numbers. The assessment incorporates multiple-choice, multiple-select, short-answer, written-response, graphing, and drawing tasks, requiring students to demonstrate both procedural fluency and conceptual understanding. Students engage in increasingly complex tasks, progressing from comparing and ordering numbers to interpreting coordinate graphs, solving real-world problems, and explaining their mathematical reasoning.

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

The materials guide educators on how to interpret student performance on assessments and reflect on levels of understanding and/or proficiency. In unit 5, the “Grade 6.5 End of Unit Assessment (B)” provides educators with guidance on how to interpret the student level of understanding based on their responses. For example, the question “A bag contains 150 marbles. Some are blue, and the rest are white. There are 21 blue marbles for every 4 white marbles. How many blue marbles are in the bag?” cites a tier three response as “significant errors in work demonstrate lack of conceptual understanding or mastery.” The evidence additionally provides sample errors in student responses. The guidance for incorrect answers states, “Work does not show evidence of an understanding of equivalent ratios; incorrect answer with no work shown.”

The materials provide guidance on interpreting scoring information to determine students’ strengths, weaknesses and/or gaps, as well as common misconceptions. In unit 1, the “Grade 6.1 End of Unit Assessment (A)” provides educators with guidance on interpreting scoring information to determine students’ gaps in learning that have led to common misconceptions. For example, one question states, “Diego is selling raffle tickets for $1.75 per ticket. Complete the table to show how much money he would earn if he sold each number of tickets. How many tickets would Diego need to sell to earn $140?” The materials provide educator guidance on interpreting students’ weaknesses and misconceptions by stating, “Work shows a developing but incomplete conceptual understanding, with significant errors. Sample errors: The table reflects a lack of understanding of the multiplicative relationship, which affects the equation in part B. Work involves a misinterpretation of the situation that affects all or most problem parts, but work does show understanding of writing equations to represent situations and interpreting solutions to equations.”

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 the unit 6 “Check Your Readiness (B) Diagnostic,” the materials provide guidance for using included tasks and activities to respond to student trends in assessment performance. The diagnostic identifies prerequisite knowledge and connects assessment results to specific lessons and activities for targeted intervention. Educator guidance explains which concepts each assessment item measures, identifies common misconceptions, and recommends instructional responses based on patterns of student performance. For example, when students demonstrate difficulty dividing to produce decimal quotients, the materials direct educators to revisit practice problems from lessons 1–3; use lesson 4, activity 3 for additional contextual practice; and incorporate estimation warm-ups to support students in evaluating the reasonableness of their answers. Similarly, when students struggle with converting fractions to decimals, materials direct educators to lesson 7, activity 1 to strengthen fraction-decimal connections before students apply these concepts to unit rates and scale.

In their “Notes for Evaluating Responses” and “Responding to Student Thinking” sections, formative assessments such as “Check Your Readiness” and cool-downs include recommendations for targeted support based on student performance. These recommendations provide specific guidance for where and how educators can use included lessons and activities to support students’ development of essential course skills. For example, in unit 2, “Check Your Readiness (A)” states, “If most students struggle with this item, plan to use Lesson 2 to support students in representing and reasoning about multiplication and division situations. After sharing their responses from Activity 1, ask students to think of a story for this expression and check it against the shared responses.”

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.

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.

Students have access to reports that display class grade averages, standards mastery, assignment performance, and progress trends over weekly or monthly periods. For example, students can view “Class Standard Mastery” reports that present color-coded mastery levels, allowing them to track their progress over time. Students can also select specific standards to access related assignments, grades, and educator feedback. These features support students in actively tracking their learning, reflecting on their performance, and understanding their progress across standards and assignments.

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.

Unit 6, lesson 5 provides educators with support for students who are developing their understanding of how to use unit rates to solve word problems. The materials suggest, “If students are not sure how to use the unit rates they found for each situation to answer the second half of the task, remind them of how the oatmeal problem was solved. Suggest that this problem is similar because they can scale up from a unit rate to answer the questions.” This guidance helps educators support students in making connections between prior examples and new problems by using scaling strategies with unit rates to solve word problems.

In unit 8, lesson 1, the cool-down includes differentiated instruction for students who are not on grade level. This cool-down states, “If students struggle with determining if expressions are equivalent in the cool-down, plan to focus on this idea when opportunities arise over the next several lessons. For example, in the practice problem sets for Lessons 8 and 9, consider inviting students to reflect on the reasoning they go through in prompt 3 Lesson 8 practice and prompt 5 Lesson 9 practice.”

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

In unit 1, lesson 3, the warm-up includes embedded support for academic vocabulary by explicitly introducing and defining the mathematical term factor within the lesson. Educator guidance directs instructors to ask scaffolded questions such as “2 and 3 are both factors of 6. How is this reflected in the diagram?” and “2 is a factor of both 6 and 10. How is this reflected in the diagram?” to help students connect the vocabulary to visual representations. The lesson further supports comprehension by having educators record and display student observations, so students can build understanding of mathematical language through discussion and concrete examples. At the conclusion of the activity, the educator formally defines factor as “one of two or more numbers that, when multiplied together, result in a given product” and connects the term to the context of rectangle dimensions and area, reinforcing academic language in a meaningful setting.

The materials embed supports such as the use of tools, including fraction boards, place value charts, and number lines, alongside academic vocabulary to build concrete understanding of abstract terms. For example, in unit 6, lesson 2, students engage in hands-on measurement activities designed to support the understanding of unfamiliar vocabulary related to measurement and unit conversion. The materials state, “In groups, students rotate through five different stations, where they measure one or more quantities using different units, and answer a series of summary questions afterward,” including stations for measuring the volume of a box in cubic inches and cubic centimeters and its length in meters and feet; the volume of water in gallons, quarts, and liters; weights and masses in ounces, pounds, grams, and kilograms; and the volume of salt in milliliters and teaspoons.

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 provide enrichment opportunities such as project-based learning, research tasks, or creative activities that require students to synthesize mathematical concepts. For example, unit 6, lesson 12 guides educators to extend learning by having students work with benchmark percentages in multistep contextual problems. The materials state, “In this activity, students find C (where A% of B is C), given benchmark percentages and a single value in the context of telling time.” These enrichment tasks guide students to apply percents, unit rates, and conversions together to solve problems that require integrating multiple mathematical concepts.

The materials provide students at the proficiency level with complex, open-ended extended practice problems that require applying grade-level math concepts to real-world scenarios such as designing a budget for a community project. For example, unit 7, lesson 3 guides educators to provide tasks that extend students’ understanding of signed numbers in context. The materials explain, “The purpose of the task is for students to compare signed numbers in a real-world context and then use inequality signs accurately with negative numbers. The context should help students understand ‘less than’ or ‘greater than’ language.” These tasks support students in applying number sense with positive and negative values while using mathematical language to justify comparisons.

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.

Exemplar models that educators use during direct instruction support instruction. For example, in unit 7, lesson 3, educators use a number line model to help students understand rational numbers. The guidance in the lesson states, “The key takeaway from the discussion is that now that we have numbers on both sides of 0, distance from 0 isn’t enough to compare two numbers. Instead, we call numbers farther to the left on the number line ‘less’ and numbers farther to the right ‘greater.’ Display the following number line for all to see.” This guidance directs educators to use the number line to illustrate how a number’s position relative to zero determines comparisons between rational numbers.

In unit 7, lesson 4, educators use a Venn diagram to support students in classifying and comparing rational numbers. The materials state, “In this activity, have students use a Venn diagram to classify a set of rational numbers into their appropriate subsets (whole, integer, and rational numbers). Students will share their comparisons with a partner. The primary purpose of this activity is to help students understand the characteristics of whole numbers, integers, and rational numbers. This task encourages students to think about numbers independently, and then share their answers with a partner to collaborate and provide an opportunity to deepen their understanding of how to classify real numbers.” This guidance supports educators in using visual representations and structured partner discussion to strengthen students’ understanding of number classification.

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

The materials include a variety of instructional approaches that support problem-solving, reasoning, and sense-making. For example, in unit 6, lesson 8, educators implement routines that support students in sharing and comparing strategies for solving rate problems. The materials state, “Select 2–3 students who used different but effective strategies to share their thinking with the class. Encourage students to listen to others’ reasoning. Record the different strategies in one place and display them for all to see. Highlight any similarities and differences.” This guidance supports educators in facilitating whole-class discussion in which students compare solution methods, analyze reasoning, and identify connections between different approaches to rate problems.

The materials include educator guidance and recommendations for effective lesson delivery and facilitation using a variety of instructional approaches, including opportunities for student discourse. For example, in unit 7, lesson 1, educators facilitate discussions in which students share observations and respond to one another’s thinking about real-world contexts involving temperature. The materials state, “Ask students to share the things they noticed and wondered. Record and display their responses for all to see . . . After each response, ask the class if they agree or disagree and to explain alternative ways of thinking.” This guidance supports educators in structuring discourse so students share ideas, evaluate peer reasoning, and connect their thinking to temperature contexts involving positive and negative numbers.

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.

In unit 2, lesson 6, the warm-up includes independent thinking, partner collaboration, and whole-group discussion within a single activity. Students first engage in individual think time, and then participate in a think-pair-share routine to compare tape diagrams representing division with fractions. The materials guide educators to facilitate a whole-class discussion after partner work, using prompts to check for understanding and elicit reasoning, followed by a class poll to support collective sense-making. This structure supports a progression from individual reasoning to collaborative discussion and finally to whole-group synthesis, with explicit educator guidance at each stage.

The materials include modeling, structured partner work, and whole-class discussion to support effective lesson implementation. For example, in unit 6, lesson 13, educators model a problem-solving strategy for percentage contexts and then guide students through structured partner and whole-class discussions. The materials state, “Arrange students in groups of 2. In each group, distribute the first problem card to one student and a data card to the other student. After debriefing on the first problem, distribute the cards for the second problem, in which students switch roles. Select students with different strategies to share their approaches to the first question, starting with less efficient methods and ending with more efficient methods. Then, ask the class to predict how the same strategies might be used to solve the second question, and how the second problem could be solved more quickly.” This guidance supports a progression from educator modeling to partner work and whole-class discussion, in which students compare strategies, make predictions, and justify their reasoning when solving percentage problems.

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 provide general supports for emergent bilingual (EB) students without distinguishing between proficiency levels or specifying supports for pre-production, beginning, intermediate, high-intermediate, or advanced learners. For example, in unit 6, lesson 12, there is a section titled “Support for English Language Learners,” which offers general guidance but does not identify targeted language domains or differentiate instruction based on students’ English proficiency levels.

Supports for EB students are general and do not differentiate across proficiency levels. For example, unit 2, lesson 1, activity 1.2 prompts students to discuss estimates for how many objects they need to reach a five-foot stack and explain their reasoning using terms such as divisor, dividend, and quotient. The lesson includes MLR8: Discussion Supports to encourage students to share ideas and use academic vocabulary during discussion; however, all students receive the same prompts and structures regardless of language proficiency. There are no leveled scaffolds such as sentence frames, targeted ELPS-aligned supports, or differentiated language tasks to support students at different stages of English language development.

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

The materials provide educators with strategies to support EB students’ linguistic and academic development while maintaining alignment with state standards. For example, unit 6, lesson 1 uses the mathematical language routine MLR2: Collect and Display to support academic language development. The materials state, “During small-group discussion, listen for and collect the vocabulary and phrases students use to describe how to find the values of the table and how the expression represents the situation.” This guidance helps educators support students in using shared academic language to describe relationships between quantities in expressions and tables during discussion.

Unit 7, lesson 1 uses MLR6: Three Reads to support comprehension of temperature word problems. The materials state, “Use this routine to support students’ comprehension of the temperature changes for the first situation. In the first read, students read the situation with the goal of comprehending the text . . . In the second read, ask students to analyze the text to understand the quantities . . . In the third read, direct students’ attention to the question and ask students to brainstorm possible mathematical solution strategies.” This routine guides educators in structuring repeated readings that help students understand the context, identify relevant quantities, and determine appropriate strategies for solving the problem.

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.

The materials include embedded educator guidance to support EB students in developing academic vocabulary and increasing comprehension through written discourse. For example, unit 6, lesson 1, activity 1 incorporates the strategies like representing, listening, and conversing through MLR3: Clarify, Critique, Correct. In this activity, the materials state, “After secondary groups finish analyzing their initial matches, present a common conceptual error to the whole class such as incorrectly matching 1 pound to 1 kilogram or 1 gallon to 1 liter, and have students work in pairs to identify the mismatch, analyze the mistake, and write a justification using correct units of measure. Sharing these written justifications with the class helps solidify students’ understanding of the distinct differences between standard units of length, volume, weight, and mass.”

While the materials include cross-linguistic connections within the “Texas English Language Proficiency Support” tables, the tables align with the former four-level proficiency level descriptors and do not meet the advanced cognitive rigor demanded by the current five-level proficiency level descriptors. For example, unit 8, lesson 3, activity 2 states, “Have students explain why área/area and expresión/expression transfer while largo/length and ancho/width do not.” According to the table in this activity, this strategy supports cross-linguistic connections for “advanced-high” students. The activity chart also includes additional strategies for students within outdated and obsolete proficiency level descriptor headings. The cross-linguistic connections embedded to support EB students do not align with the new updated English language proficiency descriptors—pre-production, beginner, intermediate, high intermediate, and advanced—and do not include support through written discourse.

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 unit 10, lesson 4, students demonstrate their understanding of the TEKS related to representing proportional and linear relationships. The cumulative practice addresses skills such as writing equations that represent relationships between independent and dependent quantities from tables, representing situations using verbal descriptions, tables, graphs, and equations in the forms y = kx or y = x + b, and identifying independent and dependent quantities from tables and graphs. The practice set includes a variety of question types, including selected response, short answer, and written response, allowing students to demonstrate understanding in multiple ways. For example, in question 1, part A, students analyze a situation in which Tyler buys four ounces of vegetable seeds for $10 and complete a table showing costs for different amounts of seeds. This task requires students to recognize the relationship between the amount of seeds and the cost, identify the constant rate of change, and understand that multiplying the number of ounces by 2.5 determines the total cost.

In the unit 12 “End of Unit Assessment (A),” students apply statistical concepts by analyzing data displays, interpreting distributions, and justifying their reasoning. In question 7, students analyze a box plot and histogram through the task, “Jada asked some students at her school how many hours they spent watching television last week, to the nearest hour. Here are a box plot and a histogram for the data she collected. About how many students did Jada ask? Is the mean or the median a more appropriate measure of center for this data set? Can Jada use these data displays to find the exact median? Can Jada use these data displays to find the exact mean?” Students demonstrate understanding by interpreting distributions, identifying measures of center and variability, and explaining their reasoning rather than relying on procedural recall. Another assessment task requires students to create box plots for two data sets and determine which group shows greater variability, requiring application of statistical reasoning. These practice opportunities align with TEKS 111.26.b.12.C by requiring students to summarize numerical data using measures of center and spread and describe characteristics of data distributions.

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, lesson 3, the questions and tasks progressively increase in rigor and complexity by moving students from identifying patterns to explaining and justifying their mathematical reasoning. Students begin by analyzing a dot image, and the task encourages them to identify efficient strategies rather than count individual dots. For example, students determine that the image contains 72 dots by viewing it as equal groups or decomposing the arrangement into smaller rectangular arrays. They then explain how their strategy demonstrates the properties of multiplication and compare their reasoning with that of their classmates. These tasks require students to recognize mathematical structure, apply prior knowledge of multiplication, and justify their thinking using precise mathematical language. This lesson aligns with TEKS 111.26.b.1.G, which requires students to display, explain, and justify mathematical ideas and arguments using precise mathematical language in written or oral communication.

The materials provide questions and tasks that increase in rigor and complexity by requiring students to independently formulate, solve, and justify solutions to open-ended problems. For example, in unit 5, lesson 19, students develop their own questions and determine strategies for solving problems without a predetermined solution path. The activity prompts students to “brainstorm at least five Fermi problems that you want to research and solve.” Students apply prior knowledge, make estimates, gather relevant information, perform calculations, and evaluate the reasonableness of their solutions. The materials also guide students to use tools such as tables and double number line diagrams and to organize their thinking in a visual display. These tasks increase in complexity by requiring students to make strategic decisions, refine assumptions, and communicate their reasoning. This lesson aligns with TEKS 111.26.b.1.B by engaging students in a problem-solving process that includes analyzing information, developing a strategy, determining and justifying a solution, and evaluating the reasonableness of their results.

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

Unit 1, lesson 3 demonstrates coherence by connecting mathematical patterns and relationships among factors, multiples, and divisibility concepts developed throughout the unit. Students build on prior understanding of multiplication and factor pairs as they explore common factors and the greatest common factor (GCF) of two whole numbers in real-world contexts. For example, in the “Diego’s Bake Sale” activity, students use snap cubes to model groups of 48 and 64 items and determine the greatest number of equal-sized groups that they can create, reinforcing connections between factors and problem-solving strategies. These experiences support future learning with common multiples, least common multiples, ratios, and proportional reasoning by helping students recognize relationships and recurring mathematical structures across concepts.

Unit 9, lesson 1 demonstrates coherence by connecting mathematical relationships and representations across concepts. The “Lesson Narrative” explains how students apply their understanding of operations and relationships to interpret equations with variables. The materials state, “In this first activity on tape diagram representations of equations with variables, students use what they know about relationships between operations to identify multiple equations that match a given diagram. Ask students to explain how these equations match the parts of the tape diagram.” Students use tape diagrams as visual models to connect known relationships among operations to symbolic equations, helping them recognize patterns between representations.

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 1, the end of unit assessment demonstrates coherence across units by connecting prior learning of factors, multiples, properties of operations, and proportional relationships to future algebraic reasoning and linear representations. Students build on earlier grade-level experiences with multiplication, division, and number sense as they apply concepts such as common factors and multiples in real-world contexts like cutting a 24-inch ribbon into equal parts. For example, students determine possible whole-number lengths (1, 2, 3, 4, 6, 8, 12) by linking factor knowledge to division situations and later use multiplicative reasoning in contexts such as ticket sales modeled by 1.75r = 140, which connects directly to future work with equations and functions.

In unit 7, lesson 11, students build on familiar financial vocabulary such as deposits and withdrawals to extend their understanding to positive and negative numbers represented on a coordinate plane. The lesson guides students to interpret coordinate points within a real-world context, connecting numerical values to their meaning in situations involving account balances. For example, question 1 asks students to analyze a graph showing a bank account balance over 14 days. It states, “The graph shows the balance in a bank account over a period of 14 days. The axis labeled B represents account balance in dollars. The axis labeled D represents the day. Estimate the greatest account balance. On which day did it occur?” Students use coordinate representations and mathematical language to interpret changes in quantity and position. This work builds toward future algebraic reasoning by preparing students to interpret relationships represented through graphs and linear equations.

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 3, lesson 2 demonstrates coherence at the lesson level by connecting students’ prior understanding of area from earlier grades to new learning about finding the area of complex shapes. Students build on their knowledge of decomposing rectangles and extend their reasoning by using the mathematical language of compose, decompose, and rearrange to analyze how to preserve area when shapes transform. The lesson supports students in recognizing that they can break complex figures into smaller parts or rearrange them to determine area, strengthening connections between visual models and geometric reasoning. For example, students use an applet with squares and right triangles to create a new shape with an area of two square units, applying decomposition and rearrangement strategies to justify their thinking. This lesson aligns with TEKS 111.26.b.8.B by having students model area formulas for parallelograms, trapezoids, and triangles through decomposing and rearranging parts of shapes.

Unit 10, lesson 10 demonstrates coherence at the lesson level by connecting students’ prior knowledge of unit fractions, tape diagrams, and division from earlier grades to new learning about dividing by non-unit fractions. Students extend their understanding of fraction models and whole-number division by using tape diagrams to represent how to partition a whole into equal parts and how those parts form groups based on the numerator and denominator. For example, students model expressions such as 6 ÷ 3/4 by dividing each whole into fourths and grouping three-fourths at a time to determine the number of groups, connecting visual representations to the relationship between division and multiplication by the reciprocal. Through representations, discussion, and analysis of strategies such as Elena’s method, students connect conceptual understanding to procedural reasoning and develop skills that support future work with fraction and rational number operations.

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 revisiting previously learned concepts such as properties of operations, equivalent expressions, and algebraic reasoning from earlier lessons and Grade 5 foundations. For example, in unit 2, lesson 2, students recall and apply the identity, inverse, commutative, associative, and distributive properties across multiple tasks, reinforcing prior understanding while extending these concepts to expressions involving variables. Students transform expressions such as (2 x b) x 5 into 2 x (b x 5) using the associative property and simplify (1/3 x 3) x x to x using the inverse and identity properties. These tasks require students to retrieve and apply prior knowledge of operations and relationships while working with new algebraic representations. Through repeated practice with varied expression types, students strengthen their understanding of equivalence and connect earlier number concepts to current algebraic reasoning.

In unit 3, lesson 3, students retrieve prior understanding of finding area by counting unit squares and connect that strategy to more grade-level approaches for determining area. The materials guide educators to begin with a familiar strategy, stating, “Tell students that they will find the areas of various figures on a grid. To encourage students to use a more grade-appropriate strategy for finding areas, show them a strategy from earlier grades, like counting squares on a grid.” Students then revisit and apply strategies such as decomposing, rearranging, enclosing and subtracting, and comparing methods to find the area of new figures. The lesson also prompts students to discuss similarities and differences among strategies, using sentence starters to explain their reasoning. These repeated applications of area concepts and mathematical language reinforce retention while supporting students in developing flexible problem-solving strategies aligned with TEKS 111.26.b.G.1.

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

Unit 2, lesson 2 provides interleaved practice opportunities by combining previously learned skills such as decomposing and recomposing shapes, area models, multiplication, and problem-solving with new applications across varied geometric contexts. Students revisit and connect concepts from earlier lessons, including area reasoning and rectangle area formulas, while applying fraction-based composition and multistep spatial reasoning within the same set of tasks. For example, students decompose a rectangle along a diagonal and recombine the parts into a new shape while explaining why the area remains unchanged, solve for missing dimensions using area relationships such as 78 ÷ 13 = 6, and justify how irregular shapes can have measurable area by decomposing them into simpler figures. By integrating concepts such as area conservation, multiplication, and composite figures, the practice requires students to apply multiple strategies and mathematical relationships rather than focus on a single skill in isolation.

Unit 2, lesson 8 provides interleaved practice opportunities by integrating the previously learned concepts of multiplication, division, fractions, tape diagrams, and proportional reasoning across multiple real-world contexts. Students apply and compare strategies in water-container and highway-length situations, requiring them to connect whole-number division and fraction division while interpreting visual models and equations. For example, students use tape diagrams to determine the size of one group when 15 cups of water fill fractional numbers of containers and when fractional lengths of highway represent portions of a larger section. These tasks require students to revisit relationships among multiplication, division, and fractions while switching between representations and problem types.

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

In unit 1, lesson 1, students analyze algebraic expressions by substituting a given value for a variable and evaluating the resulting expressions. The task in lesson 1 requires students to interpret symbolic representations and explain the reasoning behind each solution rather than simply compute answers. For example, when students determine that x² = 36 when x = 6, they interpret the notation as “6 multiplied by itself” and explain why the expression represents multiplication rather than doubling. Embedded discussion prompts and MLR8: Sentence Frames support students in evaluating different strategies, restating classmates’ reasoning, and critiquing mathematical explanations, deepening their understanding of algebraic concepts and symbolic representation.

Unit 5, lesson 19 provides questions and tasks that require students to interpret, analyze, and evaluate mathematical models and representations connected to real-world situations. In activity 3, students complete an open-ended task that requires them to generate questions, make assumptions, and construct solutions. For example, the activity prompts students to “brainstorm at least five Fermi problems that you want to research and solve. If you get stuck, consider starting with ‘How much would it cost to . . .?’ or ‘How long would it take to . . .?’” Students interpret real-world situations, analyze mathematical models developed from their assumptions, and evaluate the reasonableness of their estimates and solutions. Through estimation, modeling, and explanation, students use multiple representations to develop and communicate their mathematical understanding.

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

In unit 1, lesson 2, students work in groups to analyze scenario cards and create algebraic expressions that model each situation. Students identify relevant quantities, choose variables, and determine how constants and rates should be represented symbolically. For example, in the car rental scenario, students create the expression 30d + 0.25m to model a cost of $30 per day plus $0.25 per mile driven. Through group discussion, whiteboard work, and explanations of their reasoning, students connect real-world contexts to algebraic models and justify why specific expression forms best represent each situation.

The materials require students to create mathematical models to represent and solve meaningful situations involving fractions and division. In unit 2, lesson 4, students use concrete pattern blocks to model multiplication and division situations involving fractions, strengthening their conceptual understanding of fraction operations. Students create visual models by composing and decomposing hexagons, triangles, rhombuses, and trapezoids to represent fractional quantities and determine relationships between parts and wholes. For example, students use pattern blocks to model the question “How many one-halves are in 4?” by constructing four hexagons and representing each one-half with trapezoids, ultimately determining that there are eight one-half groups in four.

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 11, students revisit multiplication expressions involving fractions and mixed numbers and apply their conceptual understanding to new problem situations involving fraction division. The lesson prompts students to explain their reasoning, compare strategies, and critique alternative solutions, encouraging them to transfer prior knowledge of fraction multiplication to unfamiliar division tasks. Educator guidance emphasizes efficient procedures such as dividing common factors before multiplying and interpreting “canceling” conceptually as dividing by one, helping students connect mathematical procedures to underlying concepts. By applying familiar fraction concepts to new mathematical situations, students extend their conceptual understanding to increasingly complex problems.

Unit 12, lesson 17 provides educators with guidance for using questions and tasks that require students to apply their conceptual understanding of statistical measures to new data analysis situations. In activity 3, students create box plots from data sets, determine five-number summaries and interquartile ranges, and compare distributions that have the same median but different interquartile ranges. For example, students analyze data collected from three paper airplanes by calculating the five-number summary for each data set, determining the interquartile range, constructing box plots, and using those representations to answer questions about the data. By applying their understanding of statistical concepts to interpret and compare new data sets, students extend their learning to meaningful mathematical 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 3, educators facilitate a hands-on taste test and demonstration in which students compare mixtures containing different amounts of water and drink mix, allowing them to reason about flavor intensity through direct experience. The lesson then guides students to recognize that multiplying both quantities by the same factor preserves the taste, helping them transition from informal comparisons to more efficient ratio reasoning using diagrams, scaling, and proportions. Embedded educator prompts such as “How can we make Mixture A taste like Mixture B?” and “How would the taste of Mixture C compare?” encourage students to refine their strategies while developing fluency with equivalent ratios. By progressing from concrete experiences to increasingly efficient mathematical methods, students build the automaticity and flexibility needed to solve grade-level ratio problems in a variety of contexts.

The materials provide tasks specifically designed to build student automaticity and fluency by engaging students in repeated analysis and interpretation of statistical representations across multiple contexts. In unit 12, lesson 17, students repeatedly interpret box plots, compare distributions, analyze measures of center and variability, and justify conclusions using data from professional sports, emergency response times, pineapple weights, and television viewership. For example, students determine which sports have the most similar height distributions and identify which data sets show the greatest or least variability, requiring them to efficiently interpret medians, ranges, and interquartile ranges. The cumulative nature of these tasks reinforces previously learned statistical concepts and provides repeated opportunities to apply data analysis skills in a variety of contexts.

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 1, lesson 3, students determine all factors of pairs of numbers, such as 21 and 6 or 28 and 12, and accurately identify the greatest common factor, reinforcing procedural fluency with factorization. The lesson promotes flexibility by asking students to explain the meaning of “greatest common factor,” compare strategies with partners, and use graph paper or rectangular arrays to visualize factors when needed. Students then apply these procedures in a geometric context by determining the largest possible square tile that can cover a 12-inch-by-27-inch bulletin board without gaps or overlaps, connecting numerical procedures to a real-world problem. Throughout the lesson, embedded educator supports, structured mathematical discussions, and opportunities to refine explanations strengthen students’ ability to apply efficient, flexible, and accurate mathematical procedures.

The materials provide opportunities for students to practice efficient, flexible, and accurate mathematical procedures by engaging them in multiple representations of equivalent relationships. In unit 9, lesson 3, students analyze hanger diagrams and match them to corresponding equations, requiring them to flexibly connect visual models with symbolic representations. Students practice efficient procedures for solving equations by reasoning about balanced hangers, grouping objects, and removing equal quantities from both sides while maintaining equality. For example, students determine that the balanced hanger represented by 3x = 6 has the solution x = 2 and explain that each circle represents two unit weights, reinforcing procedural accuracy through visual verification. Throughout the activity, educator prompts encourage students to compare strategies, recognize that equations such as y + 3 = 6 and 6 = y + 3 represent the same relationship, and develop increasingly flexible and precise approaches to 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.

Unit 5, lesson 3 provides educators with guidance on providing opportunities to students to evaluate procedures, processes, and solutions for efficiency, flexibility, and accuracy within the unit on ratios. In activity 2, the guidance supports students in selecting efficient strategies for generating equivalent ratios. For example, “Use the diagrams to complete each statement: Mixture B uses ______ cups of water and ______ teaspoons of drink mix. The ratio of cups of water to teaspoons of drink mix in Mixture B is ________. Mixture C uses ______ cups of water and ______ teaspoons of drink mix. The ratio of cups of water to teaspoons of drink mix in Mixture C is ________.” Educator prompts and the structured comparison of mixtures guide students to recognize that multiplying both quantities by the same factor is a more efficient and reliable method than adjusting one quantity at a time.

In unit 12, lesson 1, activity 1, students evaluate their own reasoning across multiple scenarios. The materials state, “Poll students on their responses to each scenario presented in the first question and ask a few students to explain their reasoning for each. After each student shares their explanation, ask the class if they agree or disagree and why.” Students compare reasoning methods and justify agreement or disagreement, supporting evaluation of different approaches and solutions.

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

In unit 5, lesson 3 provides embedded supports that guide educators in helping students use increasingly efficient approaches when working with ratios. Activity 3 directs educators to support students in recognizing that doubling each ingredient is an equivalent ratio to a single batch. For example, the “Launch” section states, “A double batch of a recipe doubling each ingredient is an equivalent ratio to a single batch.” Students use this understanding to compare approaches for scaling recipes and identify that multiplying each quantity by the same factor is an efficient method for generating equivalent ratios.

In unit 10, lesson 4 provides educators with guidance for supporting students in using increasingly efficient approaches when analyzing quantitative relationships. In activity 1, students match equations and tables that represent the same relationship without knowing the associated real-world contexts. Students use structure to narrow down possible matches, including identifying whether dependent values are greater than or less than independent values based on the operations in each equation. Students eliminate incorrect matches and refine their reasoning when identifying corresponding representations.

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

The materials explicitly state how they address the conceptual and procedural emphasis of the TEKS through students representing and solving fraction division situations using multiple mathematical representations. Unit 2, lesson 8 describes a context in which $240 represents two-fifths of a total trip cost, and students use a tape diagram to represent the relationship. The materials include tasks in which students write multiplication and division equations to represent the relationship and determine the total cost of the trip. The lesson connects fraction bar diagrams with symbolic equations to support understanding of why division by a fraction produces the solution. Educator guidance includes continued use of tape diagrams in later instruction to support representation of fractional division situations.

In unit 5, lesson 16, the materials provide educators with guidance describing how they address the conceptual and procedural emphasis of the TEKS related to ratios and equations. The “Lesson Narrative” and learning goals describe students interpreting relationships between quantities and understanding how equations represent real-world situations. Students construct equations, organize data in tables, and analyze representations to model situations. For example, students engage with activities that develop their understanding of real-world situations represented using additive and multiplicative relationships. Students use equations in the form y = ax or y = x + a to represent real-world scenarios involving sequential addition or multiplication. The lesson connects abstract algebraic representations to concrete contexts using prior knowledge from earlier lessons to extend understanding.

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 1, lesson 5, the materials include questions and tasks in which students use tables to organize and compare the value of the digit 6 in different numbers, providing a representational model of place value relationships. Students use written equations and numerical comparisons to express relationships between values using multiplication and division. For example, students determine that the value of 6 in 7,600,000 (600,000) is 10 times the value of 6 in 7,060,000 (60,000) and represent this relationship symbolically with equations such as 600,000 ÷ 10 = 60,000 or 60,000 x 10 = 600,000. Structured peer discussions and revisions support students in interpreting and explaining these representations.

Unit 5, lesson 3 includes questions and tasks that use concrete models, pictorial representations, and abstract representations to represent ratios. In activity 2, students move from concrete and pictorial representations to abstract reasoning. Students begin with a real-world mixture context and represent relationships using tables, diagrams, and numerical patterns. For example, “A recipe for one batch of cookies calls for 5 cups of flour and 2 teaspoons of vanilla. Draw a diagram that shows the amount of flour and vanilla needed for two batches of cookies. How many batches can you make with 15 cups of flour and 6 teaspoons of vanilla? Show the additional batches by adding more ingredients to your diagram. Whether the ratio of cups of flour to teaspoons of vanilla is 5:2, 10:4, or 15:6, the recipes would make cookies that taste the same. We call these equivalent ratios.” Students use diagrams and numerical ratios such as 5:2, 10:4, and 15:6 to represent equivalent relationships.

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.

Unit 2, lesson 6 provides support for educators so students can connect concrete and representational models to abstract concepts for positive rational numbers. Students create and interpret tape diagrams to represent fraction division situations, strengthening their understanding of division as finding the number of groups. The lesson connects representational and abstract thinking by asking students to write both multiplication and division equations that represent the same situation. For example, students determine how many 3/4 units are in 2 by drawing a tape diagram partitioned into fourths and representing the relationship with corresponding multiplication and division equations. These connected representations support students in explaining their reasoning and recognizing the relationship between multiplication and division.

Unit 5, lesson 4 provides supports for students in connecting, creating, defining, and explaining concrete and representational models to abstract concepts of ratios. In activity 3, students move from concrete and pictorial representations to abstract reasoning. Students begin with a real-world mixture context and represent relationships using tables and numerical patterns. For example, “Students revisit color mixing this time by producing purple-colored water to further understand equivalent ratios. They recall that doubling, tripling, or halving a recipe for colored water yields the same resulting color, and that equivalent ratios can represent different numbers of batches of the same recipe.” Students use these representations to reason about equivalent ratios and multiplicative relationships.

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

In the unit 3 lesson activity, students use tiling patterns, geometry toolkits, tracing paper, pattern blocks, and digital applets to compare polygons and reason about area relationships while developing vocabulary such as triangle, rhombus, trapezoid, and area. The lesson incorporates MLR2: Collect and Display, in which the educator records and displays students’ words, phrases, drawings, and comparisons, creating a shared mathematical language resource that students revisit throughout the lesson and unit. Think-pair-share discussions and educator prompts such as “How does the area of the trapezoid compare to the area of the triangle?” encourage students to explain, justify, and refine their mathematical thinking using precise mathematical language.

Unit 3, lesson 1, activity 2 incorporates MLR2: Collect and Display, in which the educator records students’ words, phrases, and drawings and displays them for the class to reference throughout the lesson and unit. The materials state, “In this routine, the educator circulates and listens to students talk while writing down the words, phrases, or drawings students produce. The language collected is displayed visually for the whole class to use throughout the lesson and unit.” Students use visual representations and manipulatives to describe relationships among geometric figures while refining informal language into precise mathematical vocabulary, supporting the development of academic mathematical language.

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

Unit 6, lesson 4, activity 2 includes embedded educator guidance so educators can scaffold and support students’ development of vocabulary related to time, distance, speed, ratios, and unit rates through discussion and problem-solving. The materials state, “Encourage students to use ‘per 1’ and ‘for each’ language throughout, as this language supports the development of the concept of unit rate.” Educator prompts ask students to justify comparisons using precise mathematical language and units as they discuss unit rates.

In unit 11, lesson 3, the materials include embedded educator guidance to support students’ development and use of academic mathematical vocabulary in context as they explore debit and credit cards. Unit 11, lesson 3 directs educators to gather a variety of credit and debit card images and statements describing key terms, including balances, interest rates, rewards, and fees, to support vocabulary development through comparison and discussion. The materials state, “Gather a variety of credit and debit card images for students to compare, along with statements that describe the key aspects of card usage such as balances, interest rates, rewards, and fees. Prepare scenarios that students will use to determine when a debit or credit card is the better choice. Provide each group with 3–4 different credit card offers to calculate the amount owed on a $500 balance after 30 days.”

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 10, lesson 4, activity 1 includes embedded educator guidance to support students to hear, refine, and use mathematical language with peers as one partner identifies a matching representation and explains the reasoning. Students explain and justify their thinking using terms such as variable, relationship, independent variable, and dependent variable. The materials state, “Much of the discussion will take place between partners. Invite students to share how they identified tables and equations that match.” The lesson also includes educator guidance and exemplar student responses to support discussion and responses to questions and tasks.

In unit 1, “Check Your Readiness (A),” the materials include embedded educator guidance to support students in using mathematical language as they identify fractions and decimals on a number line, simplify algebraic expressions by combining like terms, and explain how they determined the factors of a number. The educator guidance includes exemplar responses such as explaining that “factors of 20 are numbers that divide evenly into 20,” modeling appropriate mathematical vocabulary and syntax for student responses. The guidance also identifies common errors, including incorrect denominators and misconceptions about factors, and directs educators to use this information to plan additional instruction and mathematical discussions. The embedded educator guidance includes exemplar responses and instructional follow-up to support students’ development and use of mathematical language.

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

Unit 9, lesson 9 integrates TEKS process standards through opportunities for students to communicate mathematical ideas, justify reasoning, and use mathematical language while working with equations and inequalities. In activity 2, the “Information Gap” routine provides embedded guidance for students to ask clarifying questions, communicate precisely, and listen to peers to complete the task. The materials guide educators to facilitate discussion after students complete their work by asking students to explain the process of writing and solving a one-variable, one-step inequality. Discussion questions include “How did you decide which inequality symbol to use when writing your inequality?” “What does the variable represent in this situation?” “What single operation did you use to solve the inequality?” and “How can you check whether a number is a solution by substituting it back into the original inequality?” These activities integrate TEKS process standards by requiring students to communicate mathematical ideas, explain reasoning, and use representations and mathematical language to solve problems.

The materials integrate TEKS process standards by engaging students in problem-solving, mathematical reasoning, communication, and the use of representations throughout instruction. In unit 2, lesson 6, students solve contextual division problems by writing multiplication and division equations, explaining their reasoning, and selecting representations such as tape diagrams, fraction bar diagrams, or equations to represent and justify their solutions. Educator guidance prompts students to verify answers using multiplication, compare solution strategies, and explain how they interpret division expressions. The embedded MLR1: Stronger and Clearer Each Time provides structured opportunities for students to share explanations with partners, receive feedback, revise their mathematical language, and strengthen written and oral responses using prompts such as “Can you describe that a different way?” and “Can you use both a tape diagram and multiplication equation to explain this?” The activity includes exemplar responses and reflection prompts that support student discourse and demonstrate the integration of TEKS process standards through reasoning, communication, representation, and justification.

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

In unit 10, lesson 3, students use graphs, tables, and equations to represent the same relationship and make connections among representations. The lesson connects new concepts involving constant area, constant volume, and inverse relationships to prior learning about exponents and patterns. During the “Lesson Synthesis,” students share and compare representations orally and in writing, explaining their reasoning and connections among mathematical ideas. The materials regularly include TEKS process standards through mathematical modeling, representation, communication, and problem-solving across the course progression.

Across the course, students engage in activities that require them to analyze mathematical relationships, justify solutions, and communicate their thinking using mathematical language. For example, in unit 1, lesson 5, students apply their understanding of factors and multiples in a game-based activity while explaining their reasoning, identifying patterns, and using mathematical vocabulary to justify their selections. The lesson includes embedded supports such as MLR8: Discussion Supports, sentence frames, and educator-facilitated discussions to guide students in communicating mathematical ideas and responding to the reasoning of others. This demonstrates how the materials regularly incorporate and connect TEKS process standards throughout the course through mathematical communication, reasoning, problem solving, and representation.

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

In unit 7, the “Section Level Planning Guide” describes opportunities for students to represent mathematical relationships, justify reasoning, analyze constraints, communicate mathematical ideas, model real-world situations, and evaluate solutions using multiple representations. In section A, the guide states, “Students explore positive and negative numbers using real-world contexts like temperature and elevation. They learn to interpret negative numbers and plot them on number lines, understanding concepts like opposite numbers and using terms like positive and negative.” In section B, the guide states, “Students analyze geometric shapes and real-world scenarios on the coordinate plane, plotting polygons and calculating distances. They connect abstract coordinates to practical applications, like tracking changes in temperature or finances, showcasing the coordinate plane’s utility in problem-solving.” These unit descriptions demonstrate how the unit progression regularly incorporates and connects TEKS process standards.

The unit 9 “Section Level Planning Guide” provides a description of how this unit about equations in one variable regularly incorporates and connects TEKS process standards. In section A, students explore linear equations using tape diagrams and balanced hanger diagrams to represent relationships in equations such as x + p = q and px = q. Students connect visual representations to algebraic symbols, identify variables as unknown quantities, solve equations using models, and verify solutions through substitution. The materials describe opportunities for students to communicate their reasoning, justify solutions using mathematical terms, and apply equation-solving strategies to real-world scenarios, including writing and solving equations involving percentages. Throughout the section, students use representations, problem-solving, reasoning, and mathematical communication as they develop strategies for solving and explaining equations.

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

In the Kiddom Math Middle School Course Guide for Teachers, the “What Is in a Kiddom Lesson?” section provides an overview of how the course regularly incorporates and connects TEKS process standards. The lesson structure describes opportunities for students to engage in mathematical practices such as making sense of problems, reasoning, constructing arguments, modeling, using tools, and communicating mathematical ideas. The lesson components include a warm-up, instructional activities, a “Lesson Synthesis,” and a cool-down, with each phase providing opportunities for students to explore concepts, represent ideas, discuss strategies, and explain their reasoning. The course guide describes how lessons include these practices through instructional routines, mathematical discussions, and problem-solving activities.

The unit 4 “Section Level Planning Guide” provides an overview of how instruction regularly incorporates the TEKS process standards. It explains that students develop problem-solving, mathematical reasoning, communication, and representation skills while determining place value through multiplication and division. It describes how students use visuals and manipulatives to build conceptual understanding, compare solution methods, explain their reasoning using precise mathematical language, apply decimal multiplication to real-world situations, justify their selected strategies, and verify results using multiple techniques.

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

Unit 3, lesson 19 provides opportunities for students to think mathematically, persevere through solving problems, and make sense of mathematics while working with geometric shapes and solids. In unit 3, lesson 19, activity 19.2, students solve a problem involving the best way to ship jewelry boxes using different USPS flat-rate boxes. Students select a box size, determine the best orientation for the jewelry boxes, calculate shipping costs, and apply mathematical strategies to find a solution. As students work through the task, they collaborate with classmates and use lesson vocabulary to explain their thinking. Educator guidance encourages students to consider multiple approaches, including using drawings or physical models to visualize the problem and determine helpful calculations. The materials state, “Notice groups using different strategies for division with fractions. Ask students to think about the different ways they have used fractions in calculations. If they are stuck, remind students that drawing the boxes, or making them from paper, might help them to visualize what calculations would be most helpful in finding a solution for the task at hand.”

Unit 12, lesson 7 provides opportunities for students to think mathematically, persevere through problem-solving, and make sense of mathematics while analyzing data and numerical summaries. In unit 12, lesson 7, activity 2, students engage in an open-ended task that requires them to determine what information they need, make assumptions, and select strategies without following a prescribed solution path. Students create and interpret histograms, describe data distributions, and explain their reasoning. Educator guidance includes opportunities for students to share completed histograms and explain their responses. An example of that educator guidance is “Ask one or two students to display their completed histograms for all to see and briefly describe the overall distribution. Then, select a few other previously identified students to share their responses and explanations for the last two questions.”

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 3, lesson 2 supports students in understanding, explaining, and justifying that there can be multiple ways to represent and solve problems involving geometric shapes and solids. In unit 3, lesson 2, activity 2, students use tangram pieces to explore different ways to compose, decompose, rearrange, subtract, and enclose shapes to determine the area of complex figures. Students develop mathematical vocabulary to explain their reasoning, compare strategies with peers, and analyze similarities and differences between approaches. The materials state, “Give each group of 2 students a set of tangram pieces. Give students 2-3 minutes of quiet think time for the first three questions. Ask them to pause afterwards and compare their solutions to their partner’s. If they created the same shape for each question, ask them to create a different shape that has the same given area before moving on. Then, ask them to work together to answer the remaining questions.” The materials provide multiple sample solution methods and highlight that different strategies can result in the same area, requiring students to explain and justify their approaches.

In unit 6, lesson 8 supports students in understanding, explaining, and justifying that there can be multiple ways to represent and solve problems involving percents, unit rates, and conversions. In unit 6, lesson 8, activity 8.2, students analyze price comparisons, determine whether offers represent a good deal, and use different strategies to justify their conclusions. Students first solve problems independently and then compare their approaches with peers. Educator guidance supports students in sharing and evaluating multiple methods, stating “Select 2–3 students who used different but effective strategies to share their thinking with the class. Encourage students to listen to others’ reasoning. Record the different strategies in one place and display them for all to see. Highlight any similarities and differences (e.g., whether a unit rate was used, whether students compare the original unit rate to the new quantity or the other way around, etc.).” These supports provide opportunities for students to explain their reasoning, compare representations and strategies, and justify different valid approaches to solving the same problem.

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.

Unit 2, lesson 4, activity 3 allows students to make sense of mathematics through multiple opportunities to do, write about, and discuss mathematical ideas. In this activity, students analyze a real-world scenario involving common multiples and least common multiples, record their reasoning in written responses, and use strategies such as skip counting, listing multiples, or marking multiples with different colors or symbols to determine which customers receive one or more prizes. MLR6: Three Reads supports students in understanding the context, identifying important quantities, and representing the situation before solving. Throughout the activity, students explain and compare their reasoning with partners, while educators facilitate discussions in which students share, sequence, and connect solution strategies using mathematical language such as common multiple and least common multiple.

In the warm-up for unit 10, lesson 4, activity 1, students analyze equations and tables, identify matching representations, and record their reasoning for how they determined each match. Students explain their thinking about dependent and independent variables and the structure of each relationship. The “Take Turns” routine supports structured mathematical discourse by requiring one partner to explain the reasoning behind each match while the other partner listens, asks questions, and collaborates to reach an agreement before switching roles. Educator prompts such as “What characteristics of the equation or table helped you narrow down the potential matches?” and “Were there any matches you and your partner disagreed about? How did you reach an agreement?” support students in explaining, comparing, and refining their mathematical thinking. Through analysis of representations, written reasoning, and partner discussions, students engage in multiple ways to make sense of mathematical relationships.

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 3, lesson 3, activity 3.2, students explore multiple strategies for finding area, including decomposing, rearranging, subtracting, and enclosing. Educator guidance supports discussion by directing educators to record student strategies, discuss additional methods, and identify similarities and differences among approaches. The materials state, “Discussion should center around how different strategies—decomposing, rearranging, subtracting, and enclosing—are used to find area. For each figure, select two students with different strategies to share their work, if possible. Sequence students’ presentations so that, for each figure, a subtracting strategy comes last, as that is typically the most challenging. Before sharing begins, explain to students that they should notice similarities and differences in the strategies shared and be ready to explain them.” These supports help educators facilitate mathematical discussions in which students explain and justify their reasoning.

In unit 6, lesson 8, activity 2, students first solve pricing scenarios independently, then explain their reasoning to a partner, compare alternative approaches, and discuss their decisions. Educator guidance supports selecting students with different solution strategies, such as comparing unit rates, scaling equivalent ratios, or using proportional tables to share their thinking and highlight similarities and differences among approaches. Through MLR2: Collect and Display, educators record students’ mathematical language and strategies using terms such as unit rate, equal, and cost for the same number of items to support clearer explanations. By facilitating opportunities for students to justify whether each offer is a good deal, compare reasoning, and refine their conclusions, the materials support educators in guiding students to communicate and reflect on their mathematical approaches.

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

Unit 3, lesson 3, activity 2 anticipates that some students may count complete and partial grid squares without considering strategies such as decomposing and rearranging shapes. Educator guidance states, “Some students may count both complete and partial grid squares instead of looking for ways to decompose and rearrange larger shapes. Ask them if they can find a way to find the area by decomposing and rearranging larger pieces. The discussion at the end, during which everyone sees a variety of strategies, is especially important for these students.” These supports help educators identify student misconceptions, use questioning to guide students toward more efficient reasoning strategies, and provide feedback that strengthens understanding of area concepts.

Unit 9, lesson 9 anticipates that students may incorrectly conclude that it is necessary to round 13.86 sandwiches to 14 and guides educators to address this misconception by asking students to calculate the cost of 14 sandwiches and compare it to the budget of $83. The lesson prompts educators to poll the class, ask students to explain why statements are true or false, and record student reasoning to clarify the meaning of the inequality and its solution within the context. The materials identify key ideas students should include such as recognizing that while 13.86 satisfies the inequality mathematically, a sandwich shop cannot sell fractional sandwiches, making 13 sandwiches the greatest whole-number solution. These embedded supports help educators respond to student thinking with explanatory feedback that addresses misconceptions and connects mathematical solutions to real-world situations.