Program Information
- ISBN
- 9798901105405
- Technical Specifications: Checklist
- Tech Specs: Checklist (pdf 516.34 KB)
- Technical Specifications: Professional Development
- Tech Specs: Professional Development (pdf 174.13 KB)
Kiddom Texas: Grade 8, Middle School Advanced Mathematics, Algebra 1
Math (English) Grade 8
IMRA 2026
Publisher: Kiddom, Inc.
Copyright: 2026
Series includes:
Rubric: Mathematics K–12 (English) | 2025 (Download Not Available)
* Some programs submit evidence for only part of a standard, while others submit all sections. A 100% score means this program met all the expectations it submitted.
Quality Review
Standards Alignment
Rubric Section
| Grade | TEKS % | ELPS % |
|---|---|---|
| Grade 8 | 100% | 100% |
Criteria for Quality
Rubric Section 1
Intentional Instructional Design
Materials support educators in effective implementation through intentional course, unit, and lesson-level design.
Total
100% (24 out of 24 points)
Evaluation for 1.1a
The organization of the scope and sequence consists of a table with columns that name and outline the unit, section title, lesson number, lesson title, learning target, TEKS, and ELPS. The learning target outlines the concepts taught in the course. For example, one of the concepts taught in unit 1 is “Describe (orally and in writing) a context using function language, e.g., ‘the [output] is a function of the [input],’ or ‘the [output] depends on the [input].’” The TEKS that address the learning target is 8AM.12.A and the corresponding ELPS are 2.D, 2.F, 2.B, and 3.F.
The materials include a scope and sequence with ELPS alignments identified throughout the course year. The scope and sequence consists of a table with the following headings, “Location in Program,” “Lesson Title,” and “ELPS.” It includes units 1–9 along with the name of each lesson title and corresponding ELPS. For example, unit 1, lesson 1 identifies ELPS 2.D, 2.F, 2.B, and 3.F as the standards addressed.
Evaluation for 1.1b
The materials include three instructional calendars to support effective pacing for the implementation of the materials. The program provides 165-, 180-, and 210-day calendars outlining recommended pacing for the instructional year. The program organizes pacing by unit, lessons, assessment days, flex days, and total days. For example, in the 165-day calendar, “Unit 1: Functions and Function Types” includes 17 lessons with three days allocated for check-ins, a mid-unit assessment, and an end-of-unit assessment. This unit also includes six flex days for a total of 26 instructional days.
The materials provide pacing calendars for 165-, 180-, and 210-day schedules, showing the suggested time for each unit and major concept while also including flex days for review, reteaching, assessments, lesson extensions, and transitions between units. For example, the 180-day calendar includes a column for the total number of suggested days for each unit to support effective implementation. Unit 3 includes seven lessons with a total of 12 days.
Evaluation for 1.1c
The materials include a “Course Narrative” that shows how learning connects throughout the course. Students move from functions and linear relationships to statistics, exponential relationships, and quadratic equations, applying their learning through problem-solving and real-world modeling activities. For example, in unit 1, students connect functions to their prior understanding of independent and dependent variables by recognizing that one input produces exactly one output. They also explore how different rules can represent the same function when the input-output pairs remain consistent.
The materials include an anchor graphic that explains the rationale for the sequence of units and demonstrates how mathematical concepts connect throughout the course. The graphic illustrates a coherent progression of learning, showing how concepts introduced in earlier units support the development of new understandings in later units. For example, the graphic shows learning progression at the unit, lesson, and activity levels, helping educators and students understand how knowledge developed in one unit supports learning in subsequent units. By highlighting these connections, the materials communicate both the purpose of the unit order and the progression of concepts across the course.
Evaluation for 1.1d
The materials include “Unit Narratives” and “Section Narratives” that help illustrate how students build understanding from foundational concepts to more complex ideas. For example, the unit 5 overview supports the development of understanding of equations and inequalities through multiple representations, real-world applications, and structured problem-solving. Lesson activities and discussions help students connect graphs, equations, and verbal descriptions while strengthening reasoning and interpretation of solutions in context.
Unit 8, lesson 4 explains how the lesson builds on students’ previous work comparing linear and exponential growth before introducing comparisons between quadratic and exponential functions. The lesson overview includes the lesson goal, technology recommendations, and an “I can” statement that clarify the intended learning outcomes and instructional focus. This guidance helps educators understand the mathematical purpose of the lesson and prepare for instruction.
Evaluation for 1.1e
The “Course Guide” outlines coaching practices and campus-level implementation guidelines, and includes an implementation reflection tool to help leaders support educators in refining instructional practices and improving student learning outcomes. The materials also provide implementation checklists and rubrics that enable leaders to monitor progress and offer targeted feedback. For example, the organization consists of categories such as “implementing,” “developing,” and “organizing,” and includes indicators such as “Instructional leaders have set the purpose for and scheduled ongoing collaboration time for educators,” providing clear guidance for supporting successful implementation of the materials.
Implementation Support for Leaders provides articles and resources focused on effective mathematics instruction and curriculum implementation. For example, the article “From Struggles to Success” shares a math coach’s reflections and experiences implementing the curriculum, offering practical guidance that instructional leaders can use to support educators. The article also includes links to additional implementation resources that promote ongoing professional learning and help ensure consistent implementation of the materials.
Evaluation for 1.2a
The materials provide a unit overview that includes the unit learning goals, narratives, and background content knowledge. The “Check Your Readiness” activity at the beginning of each unit also assesses students’ prior knowledge. For example, one “Check Your Readiness” activity asks students to demonstrate understanding of functions without using graphing technology. The “Unit Narrative” also outlines what students will learn and the instructional intent. For instance, in unit 1, the background knowledge to effectively teach the concepts in the lesson states, “Analyze and interpret various function types (linear and exponential) through graphs, equations, and contextual situations.”
The materials identify and embed the academic vocabulary necessary to teach the unit within the unit overviews. For example, unit 1 includes academic vocabulary such as function, function notation, and domain. In addition, the materials include an extensive glossary that defines critical mathematical terminology, connects vocabulary to conceptual understanding, and provides examples, visual representations, and contextual explanations that support educator content knowledge. The glossary supports instructional planning by clarifying the mathematical language students will encounter throughout the course and reinforcing conceptual progression across algebraic, functional, and statistical topics.
Evaluation for 1.2b
The materials provide family supports in English and Spanish that explain unit content, instructional approaches, and practical strategies families can use to support student learning at home. The family resource outlines the major mathematical understandings of the unit, including the concept of functions and how they represent relationships between quantities. For example, in unit 1, the frequently asked questions outline ways parents can support their children at home, such as “Encouraging discussion about real-world relationships: Talk about situations where quantities change in relation to each other such as how the distance traveled depends on time and speed, or how the balance in a savings account might grow over time.”
Each unit includes family support materials in both English and Spanish. For example, the document “Algebra 1 Unit 1: Quantities and Relationships Frequently Asked Questions” provides suggestions for how families can support their children, outlines key skills and main ideas, and explains how the content connects to real-world applications. One suggestion is to “encourage discussions about real-world relationships.”
Evaluation for 1.3a
The materials provide well-organized and coherent lesson plans that include clearly sequenced instructional components such as warm-ups, hands-on and synthesis activities, and cool-down assessments. Each lesson includes clearly defined daily objectives, structured student tasks, guiding questions, instructional materials, and embedded formative assessments that support mastery of TEKS-aligned mathematical concepts. ELPS alignment is evident through structured discourse routines, intentional opportunities for partner talk, and scaffolds that support academic language development during mathematical reasoning. The lesson flow regularly integrates instructional assessments, allowing educators to continuously monitor student understanding and adjust instruction based on student responses and discourse.
The materials include detailed lesson plans with daily objectives, activities, questions, materials, and assessments aligned to the lesson standards. For example, unit 1, lesson 3 focuses on writing and interpreting functions, identifying independent and dependent variables, and explaining reasoning orally and in writing. The lesson includes five activities and cumulative practice problems. For example, one of the questions in the cumulative practice set for equations for functions is “Can you graph a system of linear equations with no solutions?”
Evaluation for 1.3b
Each activity includes required materials to support effective lesson delivery. For example, in unit 1, lesson 9, activity 9.2, students use pre-printed cards from a blackline master to decide which input values make sense for different functions. The card materials make the sorting and discussion concrete, helping students justify their thinking. As they work, educators listen for explanations that show understanding of valid inputs, using those moments to guide the class discussion toward the idea of domain.
The materials include a lesson overview with suggested timing for each lesson component to support effective instruction. For example, unit 7, lesson 3.1 allots five minutes for the warm-up. It allots 15 minutes for the next section, the “Activity Narrative,” stating that its purpose is for students to contrast three types of sequences and to introduce the term arithmetic sequence. It also includes opportunities for the educator to monitor students’ precise language.
Evaluation for 1.3c
The lesson materials include extension opportunities through the “Are You Ready for More?” sections, which provide additional enrichment for students ready to deepen their understanding of the lesson content. For example, in unit 1, lesson 4, activity 4.3, the “Are You Ready for More?” activity presents an additional challenge in which students analyze a new set of exponential functions and respond to the question, “Which function would you choose? Does your choice depend on x?” Unlike the core lesson, which focuses on how the parameters a and b affect the graphs of exponential functions, this extension requires students to compare equivalent exponential expressions and reason about whether one function is always greater than another regardless of the input value. Educator notes and sample responses support the effective implementation of this enrichment opportunity by providing guidance for facilitating student reasoning and evaluating responses.
The materials include optional extension activities with educator guidance for supporting students who are ready to explore more advanced concepts. For example, in unit 7, lesson 8, activity 8.4, the educator guidance explains, “If desired, this may be an opportunity to introduce the Rule of 72, a method for estimating the doubling time of a quantity that grows exponentially. In an earlier lesson, when comparing the graphs of the owed amounts at 12%, 24%, and 30% interest rates, students made estimates of when each loan would double. If the Rule of 72 is introduced, consider referring back to that activity to test the rule.”
1.1 Course-Level Design
1.1a
Materials include a scope and sequence outlining the TEKS, ELPS, and concepts taught in the course.
Materials include a scope and sequence outlining the TEKS, ELPS, and concepts taught in the course.
3 out of 3 points
Evaluation for 1.1a
Evaluation for 1.1a
Materials include a scope and sequence outlining the TEKS, ELPS, and concepts taught in the course.
3 out of 3 points
The materials include a scope and sequence with ELPS alignments identified throughout the course year. The scope and sequence consists of a table with the following headings, “Location in Program,” “Lesson Title,” and “ELPS.” It includes units 1–9 along with the name of each lesson title and corresponding ELPS. For example, unit 1, lesson 1 identifies ELPS 2.D, 2.F, 2.B, and 3.F as the standards addressed.
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).
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).
2 out of 2 points
Evaluation for 1.1b
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).
2 out of 2 points
The materials provide pacing calendars for 165-, 180-, and 210-day schedules, showing the suggested time for each unit and major concept while also including flex days for review, reteaching, assessments, lesson extensions, and transitions between units. For example, the 180-day calendar includes a column for the total number of suggested days for each unit to support effective implementation. Unit 3 includes seven lessons with a total of 12 days.
1.1c
Materials include an explanation for the rationale of unit order as well as how concepts to be learned connect throughout the course.
Materials include an explanation for the rationale of unit order as well as how concepts to be learned connect throughout the course.
2 out of 2 points
Evaluation for 1.1c
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.
2 out of 2 points
The materials include an anchor graphic that explains the rationale for the sequence of units and demonstrates how mathematical concepts connect throughout the course. The graphic illustrates a coherent progression of learning, showing how concepts introduced in earlier units support the development of new understandings in later units. For example, the graphic shows learning progression at the unit, lesson, and activity levels, helping educators and students understand how knowledge developed in one unit supports learning in subsequent units. By highlighting these connections, the materials communicate both the purpose of the unit order and the progression of concepts across the course.
1.1d
Materials include protocols with corresponding guidance for unit and lesson internalization.
Materials include protocols with corresponding guidance for unit and lesson internalization.
2 out of 2 points
Evaluation for 1.1d
Evaluation for 1.1d
Materials include protocols with corresponding guidance for unit and lesson internalization.
2 out of 2 points
Unit 8, lesson 4 explains how the lesson builds on students’ previous work comparing linear and exponential growth before introducing comparisons between quadratic and exponential functions. The lesson overview includes the lesson goal, technology recommendations, and an “I can” statement that clarify the intended learning outcomes and instructional focus. This guidance helps educators understand the mathematical purpose of the lesson and prepare for instruction.
1.1e
Materials include resources and guidance for instructional leaders to support teachers with implementing the materials as designed.
Materials include resources and guidance for instructional leaders to support teachers with implementing the materials as designed.
2 out of 2 points
Evaluation for 1.1e
Evaluation for 1.1e
Materials include resources and guidance for instructional leaders to support teachers with implementing the materials as designed.
2 out of 2 points
Implementation Support for Leaders provides articles and resources focused on effective mathematics instruction and curriculum implementation. For example, the article “From Struggles to Success” shares a math coach’s reflections and experiences implementing the curriculum, offering practical guidance that instructional leaders can use to support educators. The article also includes links to additional implementation resources that promote ongoing professional learning and help ensure consistent implementation of the materials.
1.2 Unit-Level Design
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.
Materials include comprehensive unit overviews that provide the background content knowledge and academic vocabulary necessary to effectively teach the concepts in the unit.
2 out of 2 points
Evaluation for 1.2a
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.
2 out of 2 points
The materials identify and embed the academic vocabulary necessary to teach the unit within the unit overviews. For example, unit 1 includes academic vocabulary such as function, function notation, and domain. In addition, the materials include an extensive glossary that defines critical mathematical terminology, connects vocabulary to conceptual understanding, and provides examples, visual representations, and contextual explanations that support educator content knowledge. The glossary supports instructional planning by clarifying the mathematical language students will encounter throughout the course and reinforcing conceptual progression across algebraic, functional, and statistical topics.
1.2b
Materials contain supports for families in both Spanish and English for each unit with suggestions on supporting the progress of their student.
Materials contain supports for families in both Spanish and English for each unit with suggestions on supporting the progress of their student.
2 out of 2 points
Evaluation for 1.2b
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.
2 out of 2 points
Each unit includes family support materials in both English and Spanish. For example, the document “Algebra 1 Unit 1: Quantities and Relationships Frequently Asked Questions” provides suggestions for how families can support their children, outlines key skills and main ideas, and explains how the content connects to real-world applications. One suggestion is to “encourage discussions about real-world relationships.”
1.3 Lesson-Level Design
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).
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).
5 out of 5 points
Evaluation for 1.3a
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).
5 out of 5 points
The materials include detailed lesson plans with daily objectives, activities, questions, materials, and assessments aligned to the lesson standards. For example, unit 1, lesson 3 focuses on writing and interpreting functions, identifying independent and dependent variables, and explaining reasoning orally and in writing. The lesson includes five activities and cumulative practice problems. For example, one of the questions in the cumulative practice set for equations for functions is “Can you graph a system of linear equations with no solutions?”
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.
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.
3 out of 3 points
Evaluation for 1.3b
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.
3 out of 3 points
The materials include a lesson overview with suggested timing for each lesson component to support effective instruction. For example, unit 7, lesson 3.1 allots five minutes for the warm-up. It allots 15 minutes for the next section, the “Activity Narrative,” stating that its purpose is for students to contrast three types of sequences and to introduce the term arithmetic sequence. It also includes opportunities for the educator to monitor students’ precise language.
1.3c
Materials include guidance on the effective use of lesson materials for extended practice (e.g., homework, extension, enrichment).
Materials include guidance on the effective use of lesson materials for extended practice (e.g., homework, extension, enrichment).
1 out of 1 points
Evaluation for 1.3c
Evaluation for 1.3c
Materials include guidance on the effective use of lesson materials for extended practice (e.g., homework, extension, enrichment).
1 out of 1 points
The materials include optional extension activities with educator guidance for supporting students who are ready to explore more advanced concepts. For example, in unit 7, lesson 8, activity 8.4, the educator guidance explains, “If desired, this may be an opportunity to introduce the Rule of 72, a method for estimating the doubling time of a quantity that grows exponentially. In an earlier lesson, when comparing the graphs of the owed amounts at 12%, 24%, and 30% interest rates, students made estimates of when each loan would double. If the Rule of 72 is introduced, consider referring back to that activity to test the rule.”
Rubric Section 2
Progress Monitoring
Materials support educators in effective implementation through frequent, strategic opportunities to monitor and respond to student progress.
Total
100% (18 out of 18 points)
Evaluation for 2.1a
Each unit begins with a diagnostic assessment called “Check Your Readiness,” which evaluates students’ prior knowledge of key concepts and skills. For example, in unit 1, the “Check Your Readiness” assessment measures students’ understanding of foundational function concepts, helping to identify and address misconceptions before new instruction begins. The assessment includes multiple formats such as text-entry responses, multiple-choice questions, and tasks that require students to graph functions.
The materials include a summative assessment at the end of each unit, which students complete individually. The questions vary in types of tasks, as some questions are text-entry, some are multiple-choice, and some require students to draw a graph. For example, one of the questions in the end-of-unit assessment for unit 1 states, “A new online music service has a collection of 1,500 songs. It expects to triple the number of songs each year for the next few years. Write an equation representing the relationship, where x is time in years, and y is the number of songs available.”
Evaluation for 2.1b
The “Kiddom Math Middle School Teacher Resource Guide” defines the instructional assessments such as cool-downs, “Checkpoints,” and end-of-unit assessments and their intended purpose. For example, it defines cool-downs as brief formative assessments at the end of each lesson designed to gauge students’ understanding of a key mathematical concept from the day’s instruction. Their intended purpose is to inform ongoing instruction by identifying student understanding and misconceptions in real time.
The “Course Guide” describes the “Check Your Readiness” assessment as a diagnostic formative assessment designed to determine what students already know about upcoming concepts and to identify any misconceptions prior to instruction. The “Kiddom Math High School Teacher Resource Guide” further supports this by providing definitions and guidance for the effective use of formative assessments, including “Lesson Narratives,” “Activity Narratives,” “Lesson Synthesis” tasks, and “Activity Synthesis” tasks. These components illustrate how to use and integrate formative assessments into instruction to monitor student understanding and inform teaching.
Evaluation for 2.1c
The “Course Guide” provides information on the consistent and accurate administration of instructional assessments, including clear guidance on when to administer assessments. For example, it explains how to administer the diagnostic “Check Your Readiness” assessment at the beginning of each unit to evaluate prior knowledge. It also provides guidance for supporting students who are below grade level, such as revisiting prerequisite skills during the warm-up to reinforce understanding before new instruction begins.
The “Course Guide” provides guidance on the administration of assessments, including suggested time allocations and recommendations for pacing extended assessments across multiple class periods when appropriate. For example, unit 3, lesson 1.5 allots five minutes for the completion of the cool-down.
Evaluation for 2.1d
The materials include diagnostic assessments that align with the TEKS and the learning objectives of the course. For example, one objective in unit 1 is for students to analyze and interpret various function types, including linear and exponential functions, using graphs, equations, and contextual situations. The “Check Your Readiness” diagnostic assessment evaluates students’ prior understanding of functions in relation to these expectations.
In unit 1, lesson 2, one objective is to “interpret descriptions and graphs of functions in context,” which aligns to TEKS 111.39.c.1.A. The “Lesson Narrative” includes opportunities for students to analyze and sketch graphs of functions, allowing the educator to check for understanding as students demonstrate their ability to interpret real‑world situations through graphical representations.
Evaluation for 2.1e
The instructional assessments include TEKS-aligned items with varying item types, including multiple-choice, multi-select, open-ended, and text-entry responses. These items also vary in levels of complexity and cognitive demand, ranging from selecting correct answers to generating written explanations and constructing graphs. For example, in unit 5, algebra 1.5, “Check Your Readiness” includes fill-in-the-blank, text-entry, multi-select, graphing solution sets, and written-response items, reflecting a range of cognitive demand and problem-solving complexity within a single assessment.
The course overview describes the intentionality behind the design of task complexity and how assessments support task complexity. The overview explains that the materials give attention to the complexity of contexts, numbers, and required computations, as well as to students’ potential familiarity with given contexts and representations. For example, in the unit 8, lesson 1 warm-up, students analyze and compare patterns of change, identifying a new quadratic relationship by contrasting it with previously learned linear and exponential patterns. This progression supports students in engaging with increasing levels of conceptual complexity before transitioning to more abstract tasks.
Evaluation for 2.2a
The materials include rubrics for evaluating restricted, constructed, and extended response items to support accurate scoring and interpretation of student performance. In the rubric for restricted constructed responses, a tier one response indicates work that is complete and correct, a tier two response reflects general conceptual understanding with some errors, and a tier three response demonstrates limited or no conceptual understanding or mastery.
The materials provide guidance for scoring instructional assessments and interpreting student performance through evaluator notes that accompany assessment items. These notes include sample responses and instructional guidance to help educators address common misconceptions and understand acceptable variations in student reasoning. For example, in unit 4, in “Check Your Readiness,” question 3 asks students to write an equation representing the amount of dog food remaining after Jada removes 0.25 kg per day from a five kg bag. The accompanying “Notes for Evaluating Responses” advises that if most students struggle with the item, educators should allocate additional time to the first part of lesson 16, activity 1, in which students write equations for linear functions, and revisit lessons 4 and 5 for examples of using tables to support equation writing.
Evaluation for 2.2b
Formative assessments such as “Check Your Readiness” and cool-downs provide guidance for using included tasks and activities to respond to student trends in assessment performance. The “Notes for Evaluating Responses” and “Responding to Student Thinking” sections identify common student approaches and misconceptions and provide targeted instructional recommendations based on patterns in student responses. For example, in unit 7, the guidance for the “Check Your Readiness” pre-assessment states, “If most students struggle with this item, plan to use Lesson 3 and write the number of bacteria in expanded form to show students how the exponent changes the way the expression is calculated. Help make it explicit how the expanded form is the same as substituting a value and evaluating the expression. Practice Problems in Lesson 1 can be used for extra practice with evaluating expressions.” This guidance connects assessment results to specific misconceptions and directs educators to use included lessons and practice problems to provide targeted support for students who need additional instruction with evaluating expressions and understanding exponents.
The “Check Your Readiness” assessments provide educators with guidance for using included instructional activities to respond to trends in student performance. For example, in unit 9, in “Check Your Readiness,” students determine the zeros of quadratic functions and make connections between the zeros of a function and the x-intercepts of its graph. The educator guidance provides a specific response based on student performance, stating, “If most students struggle with this item, plan to incorporate a review of the connections between the zeros of a function and the x-intercepts of the graph after the warm-up. Consider displaying a chart that details these connections, and keep it posted during this lesson.” This guidance supports educators in responding to class-wide trends by incorporating targeted review and instructional supports within the lesson to address identified areas of need.
Evaluation for 2.2c
The materials provide educators with tools to monitor student progress and growth over time. Educators can access multiple reporting features, including the “Assignment View,” “Scoreboard,” “Scorecard,” “Question View,” and “Standards View,” which offer data on both individual student performance and class-wide achievement across assignments, assessment items, and standards. For example, the resource “What Do My Reports Mean?” provides explicit guidance for interpreting and using key reporting tools, including the “Class Grade Average” line graph, “Mastery Groups” pie chart, “Class Standard Mastery” tracker, and “Student Standard Progress” reports. These features allow educators to analyze changes in student performance over time, monitor mastery of specific standards, group students according to performance levels, and track individual growth toward learning goals.
The materials include student-facing tools that allow learners to monitor their own progress and growth. A student dashboard enables students to review their performance through visual charts on a report page or by downloading individualized reports. These reports display performance aligned to specific standards, helping students understand what they have mastered and identify areas in which they need additional learning to guide their next steps.
2.1 Instructional Assessments
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.
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.
3 out of 3 points
Evaluation for 2.1a
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.
3 out of 3 points
The materials include a summative assessment at the end of each unit, which students complete individually. The questions vary in types of tasks, as some questions are text-entry, some are multiple-choice, and some require students to draw a graph. For example, one of the questions in the end-of-unit assessment for unit 1 states, “A new online music service has a collection of 1,500 songs. It expects to triple the number of songs each year for the next few years. Write an equation representing the relationship, where x is time in years, and y is the number of songs available.”
2.1b
Materials include the definition and intended purpose for the types of instructional assessments included.
Materials include the definition and intended purpose for the types of instructional assessments included.
1 out of 1 points
Evaluation for 2.1b
Evaluation for 2.1b
Materials include the definition and intended purpose for the types of instructional assessments included.
1 out of 1 points
The “Course Guide” describes the “Check Your Readiness” assessment as a diagnostic formative assessment designed to determine what students already know about upcoming concepts and to identify any misconceptions prior to instruction. The “Kiddom Math High School Teacher Resource Guide” further supports this by providing definitions and guidance for the effective use of formative assessments, including “Lesson Narratives,” “Activity Narratives,” “Lesson Synthesis” tasks, and “Activity Synthesis” tasks. These components illustrate how to use and integrate formative assessments into instruction to monitor student understanding and inform teaching.
2.1c
Materials include teacher guidance to ensure consistent and accurate administration of instructional assessments.
Materials include teacher guidance to ensure consistent and accurate administration of instructional assessments.
1 out of 1 points
Evaluation for 2.1c
Evaluation for 2.1c
Materials include teacher guidance to ensure consistent and accurate administration of instructional assessments.
1 out of 1 points
The “Course Guide” provides guidance on the administration of assessments, including suggested time allocations and recommendations for pacing extended assessments across multiple class periods when appropriate. For example, unit 3, lesson 1.5 allots five minutes for the completion of the cool-down.
2.1d
Diagnostic, formative, and summative assessments are aligned to the TEKS and objectives of the course, unit, or lesson.
Diagnostic, formative, and summative assessments are aligned to the TEKS and objectives of the course, unit, or lesson.
6 out of 6 points
Evaluation for 2.1d
Evaluation for 2.1d
Diagnostic, formative, and summative assessments are aligned to the TEKS and objectives of the course, unit, or lesson.
6 out of 6 points
In unit 1, lesson 2, one objective is to “interpret descriptions and graphs of functions in context,” which aligns to TEKS 111.39.c.1.A. The “Lesson Narrative” includes opportunities for students to analyze and sketch graphs of functions, allowing the educator to check for understanding as students demonstrate their ability to interpret real‑world situations through graphical representations.
2.1e
Instructional assessments include TEKS-aligned items at varying levels of complexity.
Instructional assessments include TEKS-aligned items at varying levels of complexity.
2 out of 2 points
Evaluation for 2.1e
Evaluation for 2.1e
Instructional assessments include TEKS-aligned items at varying levels of complexity.
2 out of 2 points
The course overview describes the intentionality behind the design of task complexity and how assessments support task complexity. The overview explains that the materials give attention to the complexity of contexts, numbers, and required computations, as well as to students’ potential familiarity with given contexts and representations. For example, in the unit 8, lesson 1 warm-up, students analyze and compare patterns of change, identifying a new quadratic relationship by contrasting it with previously learned linear and exponential patterns. This progression supports students in engaging with increasing levels of conceptual complexity before transitioning to more abstract tasks.
2.2 Data Analysis and Progress Monitoring
2.2a
Instructional assessments and scoring information provide guidance for interpreting student performance.
Instructional assessments and scoring information provide guidance for interpreting student performance.
2 out of 2 points
Evaluation for 2.2a
Evaluation for 2.2a
Instructional assessments and scoring information provide guidance for interpreting student performance.
2 out of 2 points
The materials provide guidance for scoring instructional assessments and interpreting student performance through evaluator notes that accompany assessment items. These notes include sample responses and instructional guidance to help educators address common misconceptions and understand acceptable variations in student reasoning. For example, in unit 4, in “Check Your Readiness,” question 3 asks students to write an equation representing the amount of dog food remaining after Jada removes 0.25 kg per day from a five kg bag. The accompanying “Notes for Evaluating Responses” advises that if most students struggle with the item, educators should allocate additional time to the first part of lesson 16, activity 1, in which students write equations for linear functions, and revisit lessons 4 and 5 for examples of using tables to support equation writing.
2.2b
Materials provide guidance for the use of included tasks and activities to respond to student trends in performance on assessments.
Materials provide guidance for the use of included tasks and activities to respond to student trends in performance on assessments.
1 out of 1 points
Evaluation for 2.2b
Evaluation for 2.2b
Materials provide guidance for the use of included tasks and activities to respond to student trends in performance on assessments.
1 out of 1 points
The “Check Your Readiness” assessments provide educators with guidance for using included instructional activities to respond to trends in student performance. For example, in unit 9, in “Check Your Readiness,” students determine the zeros of quadratic functions and make connections between the zeros of a function and the x-intercepts of its graph. The educator guidance provides a specific response based on student performance, stating, “If most students struggle with this item, plan to incorporate a review of the connections between the zeros of a function and the x-intercepts of the graph after the warm-up. Consider displaying a chart that details these connections, and keep it posted during this lesson.” This guidance supports educators in responding to class-wide trends by incorporating targeted review and instructional supports within the lesson to address identified areas of need.
2.2c
Materials include tools for teachers to track student progress and growth, and tools for students to track their own progress and growth.
Materials include tools for teachers to track student progress and growth, and tools for students to track their own progress and growth.
2 out of 2 points
Evaluation for 2.2c
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.
2 out of 2 points
The materials include student-facing tools that allow learners to monitor their own progress and growth. A student dashboard enables students to review their performance through visual charts on a report page or by downloading individualized reports. These reports display performance aligned to specific standards, helping students understand what they have mastered and identify areas in which they need additional learning to guide their next steps.
Rubric Section 3
Supports for All Learners
Materials support educators in reaching all learners through design focused on engagement, representation, and action/expression for learner variability.
Total
80% (16 out of 20 points)
Evaluation for 3.1a
The materials provide educator guidance for supporting students who have not yet reached proficiency with grade-level content with activities for support. For example, in unit 3, lesson 3.5. the “Response to Student Thinking” section supports educators in addressing difficulties with linear models in scatter plots, noting, “If students struggle with this cool-down, and possibly previous, related cool-downs, working with linear models in scatter plots, make time to revisit the work of unit 6: section B.”
In unit 4, lesson 6.3, the “Advanced Student Thinking” section provides scaffolds for students who may not know how to begin the activity by suggesting they solve two to three systems and notice whether there is a point in the process where they can determine the number of solutions or anticipate what the graphs of the equations would look like. It also encourages educators to prompt students to look for similarities in the structure of the equations and consider how structure relates to the number of solutions. The support for emergent bilingual (EB) students further provides guidance through sentence stems to support small-group discussion and encourage students to challenge one another such as “This system has _____ solutions because . . .”
Evaluation for 3.1b
The educator guide provides sentence frames aligned to each unit’s problem-solving tasks, along with sample educator talk that models how to introduce and use these frames to support academic language during math discussions. For example, in unit 7, lesson 1, activity 1.3, the mathematical language routine (MLR) includes sentence frames to help students respond, such as “I agree because . . .” and “I disagree because . . .” The materials also include sample educator modeling talk, such as “If necessary, revoice student ideas to demonstrate mathematical language use by restating a statement as a question to clarify, apply appropriate language, and involve more students.”
The materials provide a glossary of academic terms with embedded teaching suggestions and integrating vocabulary supports throughout lesson activities and presentation slides. For example, unit 7, lesson 1 includes ongoing references to exponential functions across the lesson, including an “Activity Synthesis” question that asks, “How are exponential functions here alike or different from linear functions we saw earlier in the course?” In addition, the materials include background knowledge supports, questions, and rephrasing strategies to help students understand unfamiliar references in text. For example, a vocabulary launch at the beginning of activity 1.3 reviews students’ prior knowledge of functions through sentence frames and prompts such as writing a sentence in the form of “______ is a function of ______” and identifying the independent and dependent variables.
Evaluation for 3.1c
The “Further Reading” section provides articles, projects, and lessons that extend beyond grade-level expectations through complex, open-ended problems requiring application of mathematical concepts to real-world scenarios. One example is the series “A Thread Through Algebra 1, Units 5–7: Exponential and Quadratic Functions, Critically Examining the National Debt,” in which students respond to guiding questions, analyze United States debt data over the past 30 years, create graphs, determine the best-fit model (linear or exponential), and make predictions based on their chosen model.
According to the “Kiddom Math High School Teacher Resource Guide,” optional activities “address a concept or a skill that goes beyond the requirements of a standard” with the intention of acting as enrichment opportunities when time allows. For example, in the optional extension activity for unit 8, lesson 12, activity 12.3, students evaluate quadratic expressions with different coefficients and constant terms and compare the effects to the graphs. Students record their observations on a table or use a spreadsheet tool.
Evaluation for 3.2a
The materials include questioning strategies and discussion prompts to guide educators in explaining mathematical concepts. Each activity embeds these prompts and questions, including the “Launch,” “Activity Synthesis,” and “Advancing Student Thinking” sections. For example, in unit 2, lesson 1, activity 1.2, the “Activity Synthesis” provides a direct prompt for facilitating whole-class discussion. The prompt states, “Begin the discussion by asking students, ‘How many moves does it take to complete the puzzle with 1 disc?’ (Just 1, since the puzzle specifies the discs have to end up on a different peg.)” The “Launch” instructs educators to ask students to read the rules of the puzzle and attempt to solve it with two discs, followed by a prompt to have a student demonstrate why it takes three moves to complete the task.
Unit 8, lesson 12, activity 12.b provides graphs to help students observe how the constant term changes the graph. As students discuss their observations, the activity guides the educator to “tell students that people often describe the shape when a is positive as a parabola that ‘opens upward’ and the shape when a is negative as a parabola that ‘opens downward.’” This direct educator prompt provides explicit guidance for explaining the relationship between the value of the constant term and the resulting shape of a quadratic graph.
Evaluation for 3.2b
Unit 4, lesson 7, activity 7.3 guides educators to introduce a real-world budgeting context, support students in defining variables, and help them write and interpret equations that represent the situation. It also prompts educators to use questioning to check for understanding, have students explain equivalent forms of equations, and extend thinking with additional questions when appropriate. The activity incorporates multiple instructional approaches, including contextual problem-solving, guided discussion, structured questioning, and optional use of technology such as spreadsheets. It also includes scaffolds and accommodations to support a range of learners. Together, these elements provide clear direction for effective lesson facilitation in multiple ways.
The materials provide educator guidance and recommendations for effective lesson facilitation using a variety of instructional strategies, including entry/exit tickets, think-pair-share routines, concept explorations, and structured problem-solving and reasoning routines that support student sense-making. The educator’s guide also provides suggested pacing for each lesson. For example, unit 4, lesson 8, activity 8.1 begins with a warm-up (an entry ticket) followed by a “Launch” that includes independent thinking, partner discussion, and whole-class discussion. The instructional routine is a think-pair-share, and students “explore the relationship between points on a line and the slope of the line.”
Evaluation for 3.2c
The materials provide guidance for educators on implementing instructional routines and structures that support effective practice and keep students focused on the content throughout the lesson. For example, in unit 2, lesson 11, activity 11.3, the educator launches the activity by having students analyze an equilateral triangle pattern, describe the construction of the second triangle, and compare the number of sides in different steps. Students then engage in independent work followed by collaborative discussion in groups. The lesson concludes with students explaining and contrasting different ways of interpreting sequence sums and pattern growth, supporting deeper conceptual understanding of sequences and structure.
In unit 4, lesson 5, activity 5.2, students engage in a think-pair-share routine, beginning with independent work followed by partner discussion to compare and share their responses. Some of the discussions include “Discuss questions such as: ‘What does the point mean in this situation?’ (Claire purchased 10 pounds of almonds and 3 pounds of figs.).”
Evaluation for 3.3a
The materials include generic tips for EB students and do not address multiple levels of language proficiency. Units, lessons, and directions use the same sentence stems. For example, in unit 1, lesson 2, activity 2.3, the linguistic accommodations for EB students state, “Display the following sentence frames for all to see: ‘_____ is the input or output because . . .,’ ‘I noticed _____, so . . .,’ or ‘To determine a scale on the graph, I . . .’” However, the materials do not offer explicit guidance on providing linguistic accommodations and multiple levels of language support for pre-production, beginning, intermediate, high intermediate, and advanced EB students.
Although the materials include opportunities for building academic vocabulary over time such as through anchor charts and ongoing discussion, they do not provide specific guidance for accommodations based on varying levels of English language proficiency. For example, in unit 5, lesson 3, activity 3.3, the “Support for English Language Learners” suggests inviting students to create a visual display showing the two inequalities they selected to solve and encouraging them to consider how to present their work so another student can interpret it. It also prompts students to add notes or details to communicate their thinking. However, the materials frame these supports broadly and do not differentiate instruction or accommodations across proficiency levels, nor do they provide tiered language supports aligned to varying stages of language development.
Evaluation for 3.3b
“Kiddom’s Approach to English Language Proficiency in Texas Math” provides a general overview of the MLRs with the supporting ELPS. For example, MLR1 associates with ELPS 1.E.iv, 5.B.i, 5.F.iii, and 5.G.iii. In unit 1, lesson 1, activity 1.2, the implementation guidance helps educators support EB students through MLR8, which states, “To provide a support to students in precision of language when describing proportional relationships from a table, provide sentence frames for students to use, such as: ‘_____ is equal in value to _____, because . . .’” This embedded guidance provides educators with explicit strategies for supporting students’ mathematical language development through sentence frames and discussion supports aligned to the ELPS.
The materials include “Grade 8 ELPS Alignment” that identifies where the course embeds English Language Proficiency Standards and offers suggestions for supporting students with language needs. This alignment helps educators understand how lessons integrate language expectations, so educators can plan appropriate instructional support in bilingual and ESL settings. For example, unit 1, lesson 1 aligns with ELPS 1A, 3B, 3C, and 3G, illustrating how mathematical instruction incorporates specific language development standards.
Evaluation for 3.3c
In unit 4, lesson 7, activity 7.3 and unit 6, lesson 1, activity 1.3, students use partner and whole-group discussions, including MLRs, to explain their thinking and build understanding through real-world contexts. Students also write equations and justify their solutions, supporting mathematical communication. However, language supports are mostly indirect, with limited use of tools such as word banks or sentence frames. Overall, the materials support discussion and written reasoning but lack consistent ELPS-aligned language scaffolds and cross-linguistic supports across lessons.
Within the materials, supports for EB students appear in program components such as the “Launch,” “Activity Narrative,” “Support for English Learners,” “Activity Synthesis,” and “Advancing Student Thinking” sections. For example, unit 1, lesson 2, activity 2.2 includes questions and prompts that help increase comprehension, develop academic vocabulary, and build background knowledge through structured discussion and written explanation. However, the materials do not include references to or explicit support for cross-linguistic connections.
Evaluation for 3.3d
This guidance is not applicable because the program is not designed for dual language immersion (DLI) programs.
3.1 Differentiation and Scaffolds
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.
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.
1 out of 1 points
Evaluation for 3.1a
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.
1 out of 1 points
In unit 4, lesson 6.3, the “Advanced Student Thinking” section provides scaffolds for students who may not know how to begin the activity by suggesting they solve two to three systems and notice whether there is a point in the process where they can determine the number of solutions or anticipate what the graphs of the equations would look like. It also encourages educators to prompt students to look for similarities in the structure of the equations and consider how structure relates to the number of solutions. The support for emergent bilingual (EB) students further provides guidance through sentence stems to support small-group discussion and encourage students to challenge one another such as “This system has _____ solutions because . . .”
3.1b
Materials include pre-teaching or embedded supports for unfamiliar vocabulary and references in text (e.g., figurative language, idioms, academic language).
Materials include pre-teaching or embedded supports for unfamiliar vocabulary and references in text (e.g., figurative language, idioms, academic language).
2 out of 2 points
Evaluation for 3.1b
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).
2 out of 2 points
The materials provide a glossary of academic terms with embedded teaching suggestions and integrating vocabulary supports throughout lesson activities and presentation slides. For example, unit 7, lesson 1 includes ongoing references to exponential functions across the lesson, including an “Activity Synthesis” question that asks, “How are exponential functions here alike or different from linear functions we saw earlier in the course?” In addition, the materials include background knowledge supports, questions, and rephrasing strategies to help students understand unfamiliar references in text. For example, a vocabulary launch at the beginning of activity 1.3 reviews students’ prior knowledge of functions through sentence frames and prompts such as writing a sentence in the form of “______ is a function of ______” and identifying the independent and dependent variables.
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.
Materials include teacher guidance for differentiated instruction, enrichment, and extension activities for students who have demonstrated proficiency in grade-level content and skill.
1 out of 1 points
Evaluation for 3.1c
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.
1 out of 1 points
According to the “Kiddom Math High School Teacher Resource Guide,” optional activities “address a concept or a skill that goes beyond the requirements of a standard” with the intention of acting as enrichment opportunities when time allows. For example, in the optional extension activity for unit 8, lesson 12, activity 12.3, students evaluate quadratic expressions with different coefficients and constant terms and compare the effects to the graphs. Students record their observations on a table or use a spreadsheet tool.
3.2 Instructional Methods
3.2a
Materials include explicit (direct) prompts and guidance to support the teacher in modeling and explaining the concept(s) to be learned.
Materials include explicit (direct) prompts and guidance to support the teacher in modeling and explaining the concept(s) to be learned.
2 out of 2 points
Evaluation for 3.2a
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.
2 out of 2 points
Unit 8, lesson 12, activity 12.b provides graphs to help students observe how the constant term changes the graph. As students discuss their observations, the activity guides the educator to “tell students that people often describe the shape when a is positive as a parabola that ‘opens upward’ and the shape when a is negative as a parabola that ‘opens downward.’” This direct educator prompt provides explicit guidance for explaining the relationship between the value of the constant term and the resulting shape of a quadratic graph.
3.2b
Materials include teacher guidance and recommendations for effective lesson delivery and facilitation using a variety of instructional approaches.
Materials include teacher guidance and recommendations for effective lesson delivery and facilitation using a variety of instructional approaches.
1 out of 1 points
Evaluation for 3.2b
Evaluation for 3.2b
Materials include teacher guidance and recommendations for effective lesson delivery and facilitation using a variety of instructional approaches.
1 out of 1 points
The materials provide educator guidance and recommendations for effective lesson facilitation using a variety of instructional strategies, including entry/exit tickets, think-pair-share routines, concept explorations, and structured problem-solving and reasoning routines that support student sense-making. The educator’s guide also provides suggested pacing for each lesson. For example, unit 4, lesson 8, activity 8.1 begins with a warm-up (an entry ticket) followed by a “Launch” that includes independent thinking, partner discussion, and whole-class discussion. The instructional routine is a think-pair-share, and students “explore the relationship between points on a line and the slope of the line.”
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.
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.
2 out of 2 points
Evaluation for 3.2c
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.
2 out of 2 points
In unit 4, lesson 5, activity 5.2, students engage in a think-pair-share routine, beginning with independent work followed by partner discussion to compare and share their responses. Some of the discussions include “Discuss questions such as: ‘What does the point mean in this situation?’ (Claire purchased 10 pounds of almonds and 3 pounds of figs.).”
3.3 Support for Emergent Bilingual Students
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.
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.
0 out of 2 points
Evaluation for 3.3a
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.
0 out of 2 points
Although the materials include opportunities for building academic vocabulary over time such as through anchor charts and ongoing discussion, they do not provide specific guidance for accommodations based on varying levels of English language proficiency. For example, in unit 5, lesson 3, activity 3.3, the “Support for English Language Learners” suggests inviting students to create a visual display showing the two inequalities they selected to solve and encouraging them to consider how to present their work so another student can interpret it. It also prompts students to add notes or details to communicate their thinking. However, the materials frame these supports broadly and do not differentiate instruction or accommodations across proficiency levels, nor do they provide tiered language supports aligned to varying stages of language development.
3.3b
Materials include implementation guidance to support teachers in effectively using the materials in state-approved bilingual/ESL programs.
Materials include implementation guidance to support teachers in effectively using the materials in state-approved bilingual/ESL programs.
1 out of 1 points
Evaluation for 3.3b
Evaluation for 3.3b
Materials include implementation guidance to support teachers in effectively using the materials in state-approved bilingual/ESL programs.
1 out of 1 points
The materials include “Grade 8 ELPS Alignment” that identifies where the course embeds English Language Proficiency Standards and offers suggestions for supporting students with language needs. This alignment helps educators understand how lessons integrate language expectations, so educators can plan appropriate instructional support in bilingual and ESL settings. For example, unit 1, lesson 1 aligns with ELPS 1A, 3B, 3C, and 3G, illustrating how mathematical instruction incorporates specific language development standards.
3.3c
Materials include embedded guidance for teachers to support emergent bilingual students in developing academic vocabulary, increasing comprehension, building background knowledge, and making cross-linguistic connections through oral and written discourse.
Materials include embedded guidance for 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.
6 out of 8 points
Evaluation for 3.3c
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.
6 out of 8 points
Within the materials, supports for EB students appear in program components such as the “Launch,” “Activity Narrative,” “Support for English Learners,” “Activity Synthesis,” and “Advancing Student Thinking” sections. For example, unit 1, lesson 2, activity 2.2 includes questions and prompts that help increase comprehension, develop academic vocabulary, and build background knowledge through structured discussion and written explanation. However, the materials do not include references to or explicit support for cross-linguistic connections.
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.
If designed for dual language immersion (DLI) programs, materials include resources that outline opportunities to address metalinguistic transfer from English to the partner language.
Not applicable.
Evaluation for 3.3d
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.
Not applicable.
Rubric Section 4
Depth and Coherence of Key Concepts
Materials are designed to meet the rigor of the standards while connecting concepts within and across grade levels/courses.
Total
100% (19 out of 19 points)
Evaluation for 4.1a
Unit 1 provides multiple practice opportunities for students to develop and demonstrate understanding of functions. For example, the mid-unit assessment gives students an opportunity to demonstrate depth of understanding of the TEKS expectations for unit 1. Students practice identifying whether a relation represents a function through multiple representations, including verbal descriptions, graphs, tables, and algebraic representations, and they demonstrate their ability to write functions using function notation. Additionally, unit 1, lesson 7 provides continued opportunities for students to practice determining the average rate of change using various representations, including tables, graphs, and verbal descriptions.
Additionally, unit 9 provides multiple practice opportunities for students to develop and demonstrate their understanding of quadratic equations. The algebra 1.9 end-of-unit assessment allows students to demonstrate depth of understanding aligned with the TEKS expectations for unit 9. Throughout the unit, students practice solving quadratic equations using multiple methods, including factoring, completing the square, and applying the quadratic formula. Students also build fluency by writing quadratic equations when given two points and rewriting equations from vertex form to standard form. These varied practice opportunities allow students to apply their understanding of quadratic relationships across different representations.
Evaluation for 4.1b
In unit 6, lesson 4, activity 4.2, the questions and tasks progressively increase in rigor and complexity by moving students from graphing a system of equations to creating and analyzing equivalent systems. Students first graph two equations representing the cost of classroom supplies purchased on two separate shopping trips to determine the cost of measuring tapes and calculators. The task then increases in complexity as students add the two equations to create a third equation and graph all three equations, recognizing that each equation represents the same solution. The “Section Level Planning Guide” for unit 6 explains that students “create new, equivalent equations that maintain the same solution,” requiring them to reason about the structure of systems of equations rather than simply solve them procedurally.
Students begin unit 9 by solving quadratic equations through factoring and explaining the relationship between a quadratic function and its graph. The tasks then increase in complexity as students convert quadratic functions from standard form to vertex form by completing the square and identifying key features such as the vertex and maximum or minimum values to solve contextual problems. Later lessons require students to apply the quadratic formula to solve real-world situations. In the final lesson, students select and apply the most appropriate method — factoring, completing the square, or the quadratic formula — to solve a real-world problem involving the height of a diver, demonstrating conceptual understanding, strategic decision-making, and mathematical reasoning.
Evaluation for 4.2a
In unit 5, lesson 2, activity 2.2, students analyze a real-world situation by comparing two orchard trip options and determining the boundary value (n = 17) where the costs are equivalent. Students then investigate values on either side of the boundary value to determine when each option is more cost-effective. This mathematical pattern extends to unit 5, lesson 4, activity 4.2, in which students apply their understanding of boundary values to solve linear inequalities in two variables. Students recognize that the boundary line represents the related linear equation and that one side of the boundary line contains the solutions to the inequality. These lessons demonstrate coherence by connecting the pattern of solutions and boundaries in linear relationships, extending students’ understanding from linear inequalities in one variable to linear inequalities in two variables through multiple representations and reasoning strategies.
Unit 8, lesson 4, activity 4.2 demonstrates coherence across units by connecting patterns, big ideas, and relationships among mathematical concepts. The activity develops the big idea of functions as students compare and contrast quantities that grow exponentially and quadratically within a geometric context. Students build on their prior learning of exponential functions from unit 7 and quadratic functions from unit 8 as they analyze growth patterns across different situations. The task connects multiple representations, including pictorial models, graphs, tables, and function notation, to help students interpret and compare exponential and quadratic relationships.
Evaluation for 4.2b
In unit 1, lesson 2, activity 2.2, students revisit the meaning of functions, a concept introduced in earlier grades, and apply this understanding as they analyze relationships between quantities. The “Lesson Narrative” states, “This activity further refreshes students’ understanding of functions.” By reinforcing the language and structure of functions, students build a foundation for future learning in Algebra I, in which they will extend this understanding to additional function types, including exponential and quadratic functions, and in Algebra II, in which they will study rational, logarithmic, and radical functions. This progression supports students in developing increasingly sophisticated understanding of functions across grade levels.
Unit 3, lesson 1, activity 1.2 demonstrates coherence across units by connecting content and language learned in previous grades. In this activity, students investigate the relationship between the number of oranges and the weight of the oranges by analyzing bivariate data and determining a line of best fit. The “Lesson Narrative” explains that this lesson builds on prior learning because “students investigated patterns of associations in bivariate data in eighth grade.” Students apply familiar concepts and vocabulary related to data relationships while extending their understanding through linear modeling. Although the materials do not explicitly describe connections to future courses, students will continue developing their understanding of patterns of association and relationships between variables in Algebra II.
Evaluation for 4.2c
In unit 2, lesson 2, activity 2.2, students build on their previous understanding of ratios and exponential functions as they explore the relationship between exponential growth and geometric sequences. In the activity, students generate exponential functions and analyze the growth pattern created by repeatedly slicing paper. By identifying the growth factor and connecting it to the common ratio of a geometric sequence, students extend their understanding of exponential relationships to a new mathematical representation. This lesson strengthens connections between prior function concepts and new skills involving geometric sequences.
Additionally, in unit 4, lesson 1, activity 1.3, students build on their previous experience writing equations and inequalities to represent information from real-world situations and apply this understanding to a class pizza party context. In this activity, students extend their knowledge by writing constraints using inequality symbols, such as <, >, and =, to describe the conditions of the situation. This connection reinforces the representation and interpretation of mathematical relationships, providing a foundation for understanding how constraints influence functions and modeling in future learning.
Evaluation for 4.3a
In unit 8, lesson 3, activity 3.2, students write a quadratic equation to describe a visual pattern without creating a table. This task requires students to retrieve prior strategies for identifying patterns and writing expressions from visual representations. Students build on skills developed in the earlier unit 2, lesson 2, activity 2.2, in which they created tables, analyzed how patterns changed over incremental steps, and used structure to represent relationships with equations. By applying these previously learned strategies to a new quadratic context, students strengthen their ability to recognize patterns, generalize relationships, and connect visual models to algebraic representations.
In unit 6, lesson 6, activity 6.3, students use previous knowledge of slope, intercepts, and equivalent equations to analyze the structure of systems rather than solving each system directly. They apply skills such as rewriting equations and comparing coefficients, then extend this reasoning to justify the number of solutions and modify constants to create different solution types. Earlier in unit 6, lesson 4 provides additional retrieval practice as students review solving systems by elimination and determining solutions. Questions 1–7 align with the lesson’s focus, while question 8 (parts A–F) revisits concepts from previous units.
Evaluation for 4.3b
The materials provide interleaved practice opportunities by requiring students to apply previously learned skills and concepts across lessons and units. The glossary explains that “interleaved practice involves mixing different topics or types of problems with a single study session.” In unit 6, lesson 4, questions 1–7, students complete problems involving systems of equations, which include a variety of problem types requiring students to apply different strategies. Question 8 (parts A–F) extends the practice by revisiting concepts from unit 4. In this task, students analyze the relationship between cricket chirps and outdoor temperature and apply multiple skills, including identifying slope, y-intercept, constraints, equations, and graphs.
Within the materials, unit 8 includes 17 lessons, each containing a “Cumulative Practice Problem Activity” that requires students to revisit and apply concepts from the current unit through a variety of problem types. These practice sets also provide opportunities to review previously learned skills from earlier units, with each set including at least one problem, and often multiple problems, connected to prior learning. This structure supports interleaved practice by requiring students to mix and apply different mathematical concepts, recognize which strategies are appropriate for each problem, and build connections among skills rather than practicing concepts in isolation.
4.1 Depth of Key Concepts
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.
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.
2 out of 2 points
Evaluation for 4.1a
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.
2 out of 2 points
Additionally, unit 9 provides multiple practice opportunities for students to develop and demonstrate their understanding of quadratic equations. The algebra 1.9 end-of-unit assessment allows students to demonstrate depth of understanding aligned with the TEKS expectations for unit 9. Throughout the unit, students practice solving quadratic equations using multiple methods, including factoring, completing the square, and applying the quadratic formula. Students also build fluency by writing quadratic equations when given two points and rewriting equations from vertex form to standard form. These varied practice opportunities allow students to apply their understanding of quadratic relationships across different representations.
4.1b
Questions and tasks progressively increase in rigor and complexity, leading to grade-level proficiency in the mathematics TEKS.
Questions and tasks progressively increase in rigor and complexity, leading to grade-level proficiency in the mathematics TEKS.
1 out of 1 points
Evaluation for 4.1b
Evaluation for 4.1b
Questions and tasks progressively increase in rigor and complexity, leading to grade-level proficiency in the mathematics TEKS.
1 out of 1 points
Students begin unit 9 by solving quadratic equations through factoring and explaining the relationship between a quadratic function and its graph. The tasks then increase in complexity as students convert quadratic functions from standard form to vertex form by completing the square and identifying key features such as the vertex and maximum or minimum values to solve contextual problems. Later lessons require students to apply the quadratic formula to solve real-world situations. In the final lesson, students select and apply the most appropriate method — factoring, completing the square, or the quadratic formula — to solve a real-world problem involving the height of a diver, demonstrating conceptual understanding, strategic decision-making, and mathematical reasoning.
4.2 Coherence of Key Concepts
4.2a
Materials demonstrate coherence across units by explicitly connecting patterns, big ideas, and relationships between mathematical concepts.
Materials demonstrate coherence across units by explicitly connecting patterns, big ideas, and relationships between mathematical concepts.
1 out of 1 points
Evaluation for 4.2a
Evaluation for 4.2a
Materials demonstrate coherence across units by explicitly connecting patterns, big ideas, and relationships between mathematical concepts.
1 out of 1 points
Unit 8, lesson 4, activity 4.2 demonstrates coherence across units by connecting patterns, big ideas, and relationships among mathematical concepts. The activity develops the big idea of functions as students compare and contrast quantities that grow exponentially and quadratically within a geometric context. Students build on their prior learning of exponential functions from unit 7 and quadratic functions from unit 8 as they analyze growth patterns across different situations. The task connects multiple representations, including pictorial models, graphs, tables, and function notation, to help students interpret and compare exponential and quadratic relationships.
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.
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.
3 out of 3 points
Evaluation for 4.2b
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.
3 out of 3 points
Unit 3, lesson 1, activity 1.2 demonstrates coherence across units by connecting content and language learned in previous grades. In this activity, students investigate the relationship between the number of oranges and the weight of the oranges by analyzing bivariate data and determining a line of best fit. The “Lesson Narrative” explains that this lesson builds on prior learning because “students investigated patterns of associations in bivariate data in eighth grade.” Students apply familiar concepts and vocabulary related to data relationships while extending their understanding through linear modeling. Although the materials do not explicitly describe connections to future courses, students will continue developing their understanding of patterns of association and relationships between variables in Algebra II.
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..
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..
4 out of 4 points
Evaluation for 4.2c
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..
4 out of 4 points
Additionally, in unit 4, lesson 1, activity 1.3, students build on their previous experience writing equations and inequalities to represent information from real-world situations and apply this understanding to a class pizza party context. In this activity, students extend their knowledge by writing constraints using inequality symbols, such as <, >, and =, to describe the conditions of the situation. This connection reinforces the representation and interpretation of mathematical relationships, providing a foundation for understanding how constraints influence functions and modeling in future learning.
4.3 Spaced and Interleaved Practice
4.3a
Materials provide spaced retrieval opportunities with previously learned skills and concepts across lessons and units.
Materials provide spaced retrieval opportunities with previously learned skills and concepts across lessons and units.
4 out of 4 points
Evaluation for 4.3a
Evaluation for 4.3a
Materials provide spaced retrieval opportunities with previously learned skills and concepts across lessons and units.
4 out of 4 points
In unit 6, lesson 6, activity 6.3, students use previous knowledge of slope, intercepts, and equivalent equations to analyze the structure of systems rather than solving each system directly. They apply skills such as rewriting equations and comparing coefficients, then extend this reasoning to justify the number of solutions and modify constants to create different solution types. Earlier in unit 6, lesson 4 provides additional retrieval practice as students review solving systems by elimination and determining solutions. Questions 1–7 align with the lesson’s focus, while question 8 (parts A–F) revisits concepts from previous units.
4.3b
Materials provide interleaved practice opportunities with previously learned skills and concepts across lessons and units.
Materials provide interleaved practice opportunities with previously learned skills and concepts across lessons and units.
4 out of 4 points
Evaluation for 4.3b
Evaluation for 4.3b
Materials provide interleaved practice opportunities with previously learned skills and concepts across lessons and units.
4 out of 4 points
Within the materials, unit 8 includes 17 lessons, each containing a “Cumulative Practice Problem Activity” that requires students to revisit and apply concepts from the current unit through a variety of problem types. These practice sets also provide opportunities to review previously learned skills from earlier units, with each set including at least one problem, and often multiple problems, connected to prior learning. This structure supports interleaved practice by requiring students to mix and apply different mathematical concepts, recognize which strategies are appropriate for each problem, and build connections among skills rather than practicing concepts in isolation.
Rubric Section 5
Balance of Conceptual and Procedural Understanding
Materials are designed to balance conceptual understanding, procedural skills, and fluency.
Total
100% (41 out of 41 points)
Evaluation for 5.1a
In unit 3, lesson 1, activity 1.3, students analyze a graph that represents the relationship between the cost of ingredients and the sales price of food. Students interpret values from the graph to determine approximate outputs for given inputs and analyze the structure of the linear relationship to estimate the slope and y-intercept. Students evaluate how the graph represents the relationship between cost and price and explain the meaning of the slope and y-intercept in context. For example, students respond to the question “Why would a food item with free ingredients still cost $0.76?” by interpreting the y-intercept as a fixed cost represented in the model. In this way, students interpret, analyze, and evaluate models and representations for mathematical concepts and situations.
In unit 8, lesson 3, activity 3.3, students interpret and analyze a visual pattern of growing squares to understand how the structure changes at each step. Students evaluate how the pattern supports the expression n(n + 2) and connect the visual model to the expanded form n² + 2n. As students examine the structure of the pattern, they analyze how growth changes across steps and evaluate why the relationship is not linear. Educators support students in justifying the equivalence of n(n + 2) and n² + 2n using diagrams and symbolic representations.
Evaluation for 5.1b
In unit 2, lesson 2, activity 2.2, students generate geometric sequences from a paper-cutting activity and create representations of those sequences using tables and graphs. Students complete a table using an original 8-inch-by-10-inch piece of paper and, after making cuts, record the number of pieces and the area (in square inches) of each piece. Students also describe how to use results after five cuts to determine results after six cuts and sketch a graph showing the number of pieces as a function of the number of cuts.
In unit 7, lesson 4, activity 4.2, students analyze data showing the height of a tennis ball after successive bounces and create an exponential model to represent the relationship. Students examine the pattern in a table, determine the growth factor, write an exponential equation that models the situation, and use the equation to make predictions such as determining when the ball’s height will fall below a given value. Through constructing and applying the equation, students create a mathematical model that represents a real-world situation and use it to answer contextual questions.
Evaluation for 5.1c
In unit 1, lesson 19, students apply their understanding of exponential growth, exponential decay, and function modeling in a real-world context involving cell phone depreciation. Students analyze graphs, tables, equations, and contextual information to compare how the value of two phones changes over time. For example, students reason that “Phone A loses a fraction of its value each year while Phone B loses a different fraction” and compare growth factors to explain differences in the rates of depreciation rather than relying on arithmetic differences.
In unit 3, lesson 11, activity 11.2, students apply their understanding of bivariate data and correlation to investigate a real-world question about the relationship between penalties and wins in sports. Students construct and interpret scatter plots, determine a line of best fit and a correlation coefficient, and explain what the correlation means in context. For example, students respond to the question, “Is there a relationship between the number of penalties a team gets in a season and the number of wins in that season? Show any mathematical work that leads to your answer,” using data analysis to justify their conclusions.
Evaluation for 5.2a
In the unit 6, lesson 3, part 1 cumulative practice set for solving systems by elimination, students complete a sequence of tasks that builds automaticity and fluency with solving systems of linear equations. Students repeatedly determine whether addition or subtraction is the appropriate elimination strategy, solve systems without graphing, and write systems of equations from verbal descriptions. The progression of tasks reinforces efficient procedures while requiring students to apply elimination across multiple equation forms. Students also identify slope and y-intercept from different forms of linear equations, providing additional practice with prerequisite skills needed for grade-level algebra tasks.
In unit 7, lesson 5, activity 5.3, students repeatedly represent percent increase and decrease using multiplication-only expressions. Across multiple scenarios, students convert percent changes into multiplication factors, compare equivalent expressions, and explain why the expressions represent the same relationship. Students then connect these representations to exponential growth and decay, reinforcing efficient procedures while developing fluency with applying multiplication factors to model percent change.
Evaluation for 5.2b
In unit 2, lesson 8, students write recursive and explicit equations for arithmetic and geometric sequences, calculate sequence terms, and represent sequences using tables, equations, and visual patterns. Students compare equivalent equations, determine the appropriate domain for each sequence, and explain how different procedures represent the same relationship. These tasks provide repeated opportunities to practice accurate procedures while developing flexibility in representing and analyzing sequences.
In unit 7, lesson 4, activity 4.2, students analyze the rebound heights of a tennis ball and determine whether a linear or an exponential function best models the relationship. Students determine the growth factor using multiple strategies, including estimating from the data, calculating successive quotients, averaging the quotients, or using graphing technology to generate a regression equation. By selecting and comparing different solution methods while verifying that each produces a reasonable model, students practice efficient, flexible, and accurate mathematical procedures.
Evaluation for 5.2c
In unit 4, lesson 3, activity 3.2, students compare multiple strategies for converting measurement units, including double number lines, tables, and unit rates. Students evaluate the advantages and limitations of each approach by determining which strategy is most appropriate for different conversion situations. They justify their conversions, compare the results produced by different methods, and explain how the representations support accurate solutions in context.
In unit 7, lesson 5, activity 5.2, students solve percent increase and decrease problems using a variety of calculation strategies. Students create visual displays of their own solution methods and analyze the strategies presented by classmates, comparing similarities, differences, advantages, and disadvantages. Through these discussions, students evaluate the efficiency, flexibility, and accuracy of multiple procedures and justify which approaches are most appropriate for different situations.
Evaluation for 5.2d
In unit 6, lesson 3, activity 3.2, the guidance prompts educators to help students determine when adding or subtracting equations is the most effective strategy for solving a system of linear equations. During the “Activity Synthesis,” educators ask questions such as “Why does adding the equations work for solving the system with 2x + y = 4 and x – y = 11, but doesn’t work for 8x + 11y = 37 and 8x + y = 7?” The guidance also directs educators, instructing them, “Point out that there is nothing wrong about adding the equations in the last system. It simply doesn’t get us anywhere closer to the solution and is therefore unproductive.” These prompts support educators in guiding students toward selecting more efficient solution methods.
In unit 9, lesson 9, activity 9.2, the guidance prompts educators to highlight students who simplify fractions by dividing out common factors. Within the activity, the educator asks, “How can we tell if a polynomial is easily factorable?” The guidance tells educators to “highlight any students who say they simplified the fractions by dividing out any common factors.” Educators also facilitate discussion about what happens when the divisor is not factorable, guiding students to recognize when factoring is an efficient strategy and when a different approach would be more appropriate.
Evaluation for 5.3a
The “Unit 6 Systems of Equations and Inequalities Overview” explicitly states how the unit addresses the conceptual and procedural emphasis of the TEKS. The materials describe how students develop conceptual understanding before applying procedural methods for solving systems of equations. Students begin by interpreting graphs of two linear equations and recognizing that the point of intersection represents a solution that satisfies both equations. The overview then explains how students extend this conceptual understanding by learning and applying graphing, substitution, and elimination methods to solve systems of equations and model real-world situations with systems of equations and inequalities.
In unit 8, lesson 8, activity 8.2, the “Lesson Narrative” explicitly describes how conceptual understanding connects to procedural fluency. The materials state, “By manipulating the tiles, students create a visual model of the expression, which helps solidify the meaning of distribution. After constructing the model, the corresponding expanded expression is displayed below, allowing students to compare the model with the symbolic representation and self-check their work.” The “Lesson Narrative” explicitly connects students’ conceptual understanding of the distributive property with the symbolic procedures for multiplying algebraic expressions.
Evaluation for 5.3b
In unit 2, lesson 11, activity 11.2, students use paper and scissors as concrete manipulatives to model a paper-sharing situation. They organize the results using tables and visual representations of the paper pieces, then connect those models to fractions, sequences, and symbolic equations that describe the pattern. Throughout the activity, students move between concrete, pictorial, and abstract representations to generalize the mathematical relationship.
In unit 8, lesson 3, activity 3.2, students analyze a growing pattern made of small squares as a visual model of the relationship they are studying. Students use pictorial representations by examining the diagram of the pattern, sketching additional steps, and constructing their own representations from a given equation. Students also use abstract representations by writing equations, using function notation, connecting variables to quantities in the pattern, and generalizing the relationship as a quadratic function. In the activity, students move between visual models and symbolic expressions, making connections across multiple representations.
Evaluation for 5.3c
In unit 2, lesson 11, students analyze a representational model of the Koch snowflake using diagrams of step 0, step 1, and subsequent iterations. The lesson supports students in connecting these visual representations to recursive and symbolic relationships by guiding them to define and express a function f(n) that represents the number of sides at step n. Students also explain how the pattern grows from step to step and use this structure to represent cumulative quantities such as determining the total number of triangles used at a given stage by summing across iterations.
Unit 4, lesson 2, activity 2.2 provides students with an opportunity to “examine multiple quantities and relationships in a geometric context, and to use letters to represent quantities.” Students determine the number of faces, vertices, and edges for a tetrahedron, a cube, and a dodecahedron. Students make observations about the number of faces, vertices, and edges in the geometric figures and any relationships they observe. Then students create an equation that models this relationship (e.g., V + F – 2 = E). This activity gives students an opportunity to connect concrete and abstract concepts in a geometric context.
Evaluation for 5.4a
Unit 2, lesson 1, activity 1.3 guides the educator with the instruction, “This activity works best when each student has access to manipulatives or devices that can run the GeoGebra applet, because students will benefit from seeing the relationship in a dynamic way.” Students use manipulatives and visual models to determine the smallest number of moves needed to move each checker to the opposite side while following the puzzle rules. As they describe their solutions, students use academic vocabulary such as sequence and term to explain the patterns they observe.
In unit 7, lesson 2, activity 2.3, students develop academic mathematical language using visuals, manipulatives, and language development strategies while investigating exponential functions. Students fold paper to explore changes in thickness and area and use mathematical vocabulary such as discrete graph, table, equation, domain, range, initial measurement, and growth factor to describe the relationships. Educator guidance states, “Look for the different ways students use to find out how many folds are needed to reach a certain thickness. Identify students who used a table, a graph, or an equation so they can share later.” This activity provides opportunities for students to connect visual models and multiple representations to academic mathematical language through classroom discussion.
Evaluation for 5.4b
In unit 3, lesson 3, activity 3.2, students graph residuals and develop an understanding of the term residual as the difference between the actual and expected y-values. Educator guidance incorporates vocabulary such as line of best fit and vertical distance through questions in the “Activity Synthesis,” including, “Find the residual that has the furthest vertical distance from the horizontal axis. What does this mean in the context of the scatter plot and the line of best fit?” These prompts support students in using mathematical vocabulary in the context of analyzing data.
In unit 8, lesson 14, the “Lesson Synthesis” guides the educator to connect a new function representing revenue and ticket prices to the previous lesson on projectile motion while reinforcing vocabulary such as vertical intercept, horizontal intercepts, and vertex. Educator prompts include, “Here is the graph representing the same function. What information do the horizontal intercepts, the vertical intercept, and the vertex of the graph give us?” This guidance supports students in applying academic mathematical vocabulary in a new mathematical context.
Evaluation for 5.4c
In unit 1, lesson 2, students use academic vocabulary including function, independent variable, dependent variable, input, output, graph, scale, relationship, and coordinate plane while discussing representations and relationships. Educator guidance supports mathematical syntax by prompting students to use sentence structures such as “___ is a function of ___” and introducing the alternate phrasing “depends on.” Students participate in take-turns, think-pair-shares, partner discussions, whole-class discussions, and justification of reasoning, providing opportunities to hear, refine, and use mathematical language with peers. The lesson also includes exemplar responses to support educators in guiding student discussions and responses.
In Grade 8, unit 9, lesson 18, activity 18.4, students work with a partner to ask questions, exchange information, and write quadratic equations that match specified graph features. Students use academic vocabulary including vertex, vertex form, factored form, standard form, x-intercepts, zeros, and function while explaining their reasoning and interpreting mathematical representations. During the “Activity Synthesis,” the educator supports discussion by prompting students to determine which form of a quadratic equation is most useful in different situations, providing opportunities for students to hear, refine, and use mathematical language with peers.
Evaluation for 5.5a
In unit 1, lesson 2, activity 2.2, students analyze a situation involving a dog’s movement while attached to a post, sketch a distance-versus-time graph, and determine whether the graph represents a function. Students develop and justify solution strategies while evaluating the reasonableness of their conclusions, which exemplifies how the materials integrate TEKS process standards throughout the activity.
In unit 5, lesson 6, activity 6.3, students sort and match verbal, symbolic, and graphical representations of inequalities and explain how the representations relate to one another. As students justify their matches and discuss relationships among the representations, they engage in mathematical communication, reasoning, and representation, which exemplifies how the materials integrate TEKS process standards throughout the activity.
Evaluation for 5.5b
The “Kiddom Math High School Teacher Resource Guide” describes how the course regularly incorporates and connects TEKS process standards. The guide explains that warm-up routines provide opportunities for students to communicate mathematical ideas, ask questions, justify their reasoning, and critique the reasoning of others. The guide also describes how instructional routines, including MLRs, engage students in mathematical discourse and collaborative conversations that support problem-solving, reasoning, communication, and representation throughout the course.
The Grade 8 Advanced Math Scope and Sequence identifies the TEKS process standards addressed across the course. The “Course Narrative” explains that students deepen their understanding of functions while developing their ability to represent, interpret, and communicate mathematical ideas using function notation, domain and range, average rate of change, and graph features. It also explains that students investigate real-world and mathematical contexts, analyze the structural attributes of functions, and connect those attributes across multiple representations. These descriptions demonstrate how the course intentionally integrates and develops TEKS process standards.
Evaluation for 5.5c
In unit 7, the “Section Level Planning Guide” describes how the unit regularly incorporates and connects TEKS process standards as students investigate exponential functions through modeling, reasoning, representation, and communication. The guide explains that students apply exponential models to real-world situations by selecting appropriate models, analyzing exponential functions using graphs, function notation, and rate of change, and applying their understanding to financial contexts such as comparing investment options with different interest rates and compounding intervals. These unit descriptions identify opportunities for students to represent mathematical relationships, analyze information, solve problems, and communicate mathematical reasoning throughout the learning progression.
In unit 8, the materials describe how the unit regularly incorporates and connects TEKS process standards as students develop their understanding of quadratic equations through problem-solving, multiple representations, reasoning, and mathematical communication. The unit overview explains that students explore quadratic relationships using graphs, tables, and equations while connecting visual representations to algebraic notation. Students compare quadratic and linear functions, analyze standard, factored, and vertex forms to identify key features of quadratic functions, and apply quadratic models to real-world situations. These descriptions show how students use representations, analyze relationships, interpret solutions in context, and communicate mathematical reasoning throughout the unit.
Evaluation for 5.5d
In unit 2, lesson 2, activity 2.2, students create tables and graphs, identify patterns, explain relationships between the number of pieces and area after each cut, and determine the growth factor. The lesson overview describes opportunities for students to compare representations, discuss observations, and connect geometric sequences to exponential functions, demonstrating how lesson activities incorporate TEKS process standards.
In unit 6, lesson 2, students solve systems algebraically, analyze substitution strategies, determine which variable or expression to substitute, and justify solutions by substituting answers back into the original equations. Additionally, the Grade 8 Advanced Math Scope and Sequence identifies the process and content standards addressed in each unit and lesson, including process standards 8AM.1.D and 8AM.1.G in unit 6, lesson 2.
5.1 Development of Conceptual Understanding
5.1a
Questions and tasks require students to interpret, analyze, and evaluate models and representations for mathematical concepts and situations.
Questions and tasks require students to interpret, analyze, and evaluate models and representations for mathematical concepts and situations.
3 out of 3 points
Evaluation for 5.1a
Evaluation for 5.1a
Questions and tasks require students to interpret, analyze, and evaluate models and representations for mathematical concepts and situations.
3 out of 3 points
In unit 8, lesson 3, activity 3.3, students interpret and analyze a visual pattern of growing squares to understand how the structure changes at each step. Students evaluate how the pattern supports the expression n(n + 2) and connect the visual model to the expanded form n² + 2n. As students examine the structure of the pattern, they analyze how growth changes across steps and evaluate why the relationship is not linear. Educators support students in justifying the equivalence of n(n + 2) and n² + 2n using diagrams and symbolic representations.
5.1b
Questions and tasks require students to create models to represent mathematical situations.
Questions and tasks require students to create models to represent mathematical situations.
1 out of 1 points
Evaluation for 5.1b
Evaluation for 5.1b
Questions and tasks require students to create models to represent mathematical situations.
1 out of 1 points
In unit 7, lesson 4, activity 4.2, students analyze data showing the height of a tennis ball after successive bounces and create an exponential model to represent the relationship. Students examine the pattern in a table, determine the growth factor, write an exponential equation that models the situation, and use the equation to make predictions such as determining when the ball’s height will fall below a given value. Through constructing and applying the equation, students create a mathematical model that represents a real-world situation and use it to answer contextual questions.
5.1c
Questions and tasks provide opportunities for students to apply conceptual understanding to new problem situations and contexts.
Questions and tasks provide opportunities for students to apply conceptual understanding to new problem situations and contexts.
1 out of 1 points
Evaluation for 5.1c
Evaluation for 5.1c
Questions and tasks provide opportunities for students to apply conceptual understanding to new problem situations and contexts.
1 out of 1 points
In unit 3, lesson 11, activity 11.2, students apply their understanding of bivariate data and correlation to investigate a real-world question about the relationship between penalties and wins in sports. Students construct and interpret scatter plots, determine a line of best fit and a correlation coefficient, and explain what the correlation means in context. For example, students respond to the question, “Is there a relationship between the number of penalties a team gets in a season and the number of wins in that season? Show any mathematical work that leads to your answer,” using data analysis to justify their conclusions.
5.2 Development of Fluency
5.2a
Materials provide tasks that are designed to build student automaticity and fluency necessary to complete grade-level tasks.
Materials provide tasks that are designed to build student automaticity and fluency necessary to complete grade-level tasks.
2 out of 2 points
Evaluation for 5.2a
Evaluation for 5.2a
Materials provide tasks that are designed to build student automaticity and fluency necessary to complete grade-level tasks.
2 out of 2 points
In unit 7, lesson 5, activity 5.3, students repeatedly represent percent increase and decrease using multiplication-only expressions. Across multiple scenarios, students convert percent changes into multiplication factors, compare equivalent expressions, and explain why the expressions represent the same relationship. Students then connect these representations to exponential growth and decay, reinforcing efficient procedures while developing fluency with applying multiplication factors to model percent change.
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.
Materials provide opportunities for students to practice the application of efficient, flexible, and accurate mathematical procedures within the lesson and/or throughout a unit.
3 out of 3 points
Evaluation for 5.2b
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.
3 out of 3 points
In unit 7, lesson 4, activity 4.2, students analyze the rebound heights of a tennis ball and determine whether a linear or an exponential function best models the relationship. Students determine the growth factor using multiple strategies, including estimating from the data, calculating successive quotients, averaging the quotients, or using graphing technology to generate a regression equation. By selecting and comparing different solution methods while verifying that each produces a reasonable model, students practice efficient, flexible, and accurate mathematical procedures.
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.
Materials provide opportunities for students to evaluate procedures, processes, and solutions for efficiency, flexibility, and accuracy within the lesson and throughout a unit.
3 out of 3 points
Evaluation for 5.2c
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.
3 out of 3 points
In unit 7, lesson 5, activity 5.2, students solve percent increase and decrease problems using a variety of calculation strategies. Students create visual displays of their own solution methods and analyze the strategies presented by classmates, comparing similarities, differences, advantages, and disadvantages. Through these discussions, students evaluate the efficiency, flexibility, and accuracy of multiple procedures and justify which approaches are most appropriate for different situations.
5.2d
Materials contain embedded supports for teachers to guide students toward increasingly efficient approaches.
Materials contain embedded supports for teachers to guide students toward increasingly efficient approaches.
1 out of 1 points
Evaluation for 5.2d
Evaluation for 5.2d
Materials contain embedded supports for teachers to guide students toward increasingly efficient approaches.
1 out of 1 points
In unit 9, lesson 9, activity 9.2, the guidance prompts educators to highlight students who simplify fractions by dividing out common factors. Within the activity, the educator asks, “How can we tell if a polynomial is easily factorable?” The guidance tells educators to “highlight any students who say they simplified the fractions by dividing out any common factors.” Educators also facilitate discussion about what happens when the divisor is not factorable, guiding students to recognize when factoring is an efficient strategy and when a different approach would be more appropriate.
5.3 Balance of Conceptual Understanding and Procedural Fluency
5.3a
Materials explicitly state how the conceptual and procedural emphasis of the TEKS are addressed.
Materials explicitly state how the conceptual and procedural emphasis of the TEKS are addressed.
2 out of 2 points
Evaluation for 5.3a
Evaluation for 5.3a
Materials explicitly state how the conceptual and procedural emphasis of the TEKS are addressed.
2 out of 2 points
In unit 8, lesson 8, activity 8.2, the “Lesson Narrative” explicitly describes how conceptual understanding connects to procedural fluency. The materials state, “By manipulating the tiles, students create a visual model of the expression, which helps solidify the meaning of distribution. After constructing the model, the corresponding expanded expression is displayed below, allowing students to compare the model with the symbolic representation and self-check their work.” The “Lesson Narrative” explicitly connects students’ conceptual understanding of the distributive property with the symbolic procedures for multiplying algebraic expressions.
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.
Questions and tasks include the use of concrete models and manipulatives, pictorial representations (figures/drawings), and abstract representations, as required by the TEKS.
3 out of 3 points
Evaluation for 5.3b
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.
3 out of 3 points
In unit 8, lesson 3, activity 3.2, students analyze a growing pattern made of small squares as a visual model of the relationship they are studying. Students use pictorial representations by examining the diagram of the pattern, sketching additional steps, and constructing their own representations from a given equation. Students also use abstract representations by writing equations, using function notation, connecting variables to quantities in the pattern, and generalizing the relationship as a quadratic function. In the activity, students move between visual models and symbolic expressions, making connections across multiple representations.
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.
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.
6 out of 6 points
Evaluation for 5.3c
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.
6 out of 6 points
Unit 4, lesson 2, activity 2.2 provides students with an opportunity to “examine multiple quantities and relationships in a geometric context, and to use letters to represent quantities.” Students determine the number of faces, vertices, and edges for a tetrahedron, a cube, and a dodecahedron. Students make observations about the number of faces, vertices, and edges in the geometric figures and any relationships they observe. Then students create an equation that models this relationship (e.g., V + F – 2 = E). This activity gives students an opportunity to connect concrete and abstract concepts in a geometric context.
5.4 Development of Academic Mathematical Language
5.4a
Materials provide opportunities for students to develop academic mathematical language using visuals, manipulatives, and other language development strategies.
Materials provide opportunities for students to develop academic mathematical language using visuals, manipulatives, and other language development strategies.
3 out of 3 points
Evaluation for 5.4a
Evaluation for 5.4a
Materials provide opportunities for students to develop academic mathematical language using visuals, manipulatives, and other language development strategies.
3 out of 3 points
In unit 7, lesson 2, activity 2.3, students develop academic mathematical language using visuals, manipulatives, and language development strategies while investigating exponential functions. Students fold paper to explore changes in thickness and area and use mathematical vocabulary such as discrete graph, table, equation, domain, range, initial measurement, and growth factor to describe the relationships. Educator guidance states, “Look for the different ways students use to find out how many folds are needed to reach a certain thickness. Identify students who used a table, a graph, or an equation so they can share later.” This activity provides opportunities for students to connect visual models and multiple representations to academic mathematical language through classroom discussion.
5.4b
Materials include embedded teacher guidance to scaffold and support students' development and use of academic mathematical vocabulary in context.
Materials include embedded teacher guidance to scaffold and support students' development and use of academic mathematical vocabulary in context.
1 out of 1 points
Evaluation for 5.4b
Evaluation for 5.4b
Materials include embedded teacher guidance to scaffold and support students' development and use of academic mathematical vocabulary in context.
1 out of 1 points
In unit 8, lesson 14, the “Lesson Synthesis” guides the educator to connect a new function representing revenue and ticket prices to the previous lesson on projectile motion while reinforcing vocabulary such as vertical intercept, horizontal intercepts, and vertex. Educator prompts include, “Here is the graph representing the same function. What information do the horizontal intercepts, the vertical intercept, and the vertex of the graph give us?” This guidance supports students in applying academic mathematical vocabulary in a new mathematical context.
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.
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.
6 out of 6 points
Evaluation for 5.4c
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.
6 out of 6 points
In Grade 8, unit 9, lesson 18, activity 18.4, students work with a partner to ask questions, exchange information, and write quadratic equations that match specified graph features. Students use academic vocabulary including vertex, vertex form, factored form, standard form, x-intercepts, zeros, and function while explaining their reasoning and interpreting mathematical representations. During the “Activity Synthesis,” the educator supports discussion by prompting students to determine which form of a quadratic equation is most useful in different situations, providing opportunities for students to hear, refine, and use mathematical language with peers.
5.5 Process Standards Connections
5.5a
TEKS process standards are integrated appropriately into the materials.
TEKS process standards are integrated appropriately into the materials.
1 out of 1 points
Evaluation for 5.5a
Evaluation for 5.5a
TEKS process standards are integrated appropriately into the materials.
1 out of 1 points
In unit 5, lesson 6, activity 6.3, students sort and match verbal, symbolic, and graphical representations of inequalities and explain how the representations relate to one another. As students justify their matches and discuss relationships among the representations, they engage in mathematical communication, reasoning, and representation, which exemplifies how the materials integrate TEKS process standards throughout the activity.
5.5b
Materials include a description of how TEKS process standards are incorporated and connected throughout the course.
Materials include a description of how TEKS process standards are incorporated and connected throughout the course.
2 out of 2 points
Evaluation for 5.5b
Evaluation for 5.5b
Materials include a description of how TEKS process standards are incorporated and connected throughout the course.
2 out of 2 points
The Grade 8 Advanced Math Scope and Sequence identifies the TEKS process standards addressed across the course. The “Course Narrative” explains that students deepen their understanding of functions while developing their ability to represent, interpret, and communicate mathematical ideas using function notation, domain and range, average rate of change, and graph features. It also explains that students investigate real-world and mathematical contexts, analyze the structural attributes of functions, and connect those attributes across multiple representations. These descriptions demonstrate how the course intentionally integrates and develops TEKS process standards.
5.5c
Materials include a description for each unit of how TEKS process standards are incorporated and connected throughout the unit.
Materials include a description for each unit of how TEKS process standards are incorporated and connected throughout the unit.
2 out of 2 points
Evaluation for 5.5c
Evaluation for 5.5c
Materials include a description for each unit of how TEKS process standards are incorporated and connected throughout the unit.
2 out of 2 points
In unit 8, the materials describe how the unit regularly incorporates and connects TEKS process standards as students develop their understanding of quadratic equations through problem-solving, multiple representations, reasoning, and mathematical communication. The unit overview explains that students explore quadratic relationships using graphs, tables, and equations while connecting visual representations to algebraic notation. Students compare quadratic and linear functions, analyze standard, factored, and vertex forms to identify key features of quadratic functions, and apply quadratic models to real-world situations. These descriptions show how students use representations, analyze relationships, interpret solutions in context, and communicate mathematical reasoning throughout the unit.
5.5d
Materials include an overview of the TEKS process standards incorporated into each lesson.
Materials include an overview of the TEKS process standards incorporated into each lesson.
1 out of 1 points
Evaluation for 5.5d
Evaluation for 5.5d
Materials include an overview of the TEKS process standards incorporated into each lesson.
1 out of 1 points
In unit 6, lesson 2, students solve systems algebraically, analyze substitution strategies, determine which variable or expression to substitute, and justify solutions by substituting answers back into the original equations. Additionally, the Grade 8 Advanced Math Scope and Sequence identifies the process and content standards addressed in each unit and lesson, including process standards 8AM.1.D and 8AM.1.G in unit 6, lesson 2.
Rubric Section 6
Productive Struggle
Materials support students in applying disciplinary practices to productive problem-solving, including explaining and revising their thinking.
Total
100% (22 out of 22 points)
Evaluation for 6.1a
In unit 6, lesson 4, activity 4.2, students engage in mathematical reasoning through educator-guided, open-ended questions that encourage them to justify their thinking and explain their strategies. For example, the activity asks students, “In general, why does it make sense for a third equation that is the sum of the two equations in a system to share a common solution with the other two?” The activity also includes multipart tasks that require students to interpret the meaning of each equation, solve the system, explain what each equation represents in the context of the situation, and compare the resulting equation to the original system. The lesson includes opportunities for students to persevere when it recommends they engage in quiet think time, followed by partner discussions and whole-class sharing before reaching conclusions. The tasks increase in complexity by moving from interpreting solutions to solving systems, writing systems from real-world situations, and evaluating the reasonableness of solutions by explaining how many solutions make sense in context.
In unit 8, lesson 3, activity 3, students analyze a growing pattern, determine whether the relationship is linear or quadratic, critique mathematical reasoning, and compare equivalent algebraic expressions using both visual and symbolic representations. For example, students sketch the next stage of a growing pattern, determine whether the growth is linear, evaluate Kiran’s claim, and determine whether Diego and Jada’s equations correctly represent the pattern. The activity requires students to work through multiple reasoning tasks that involve identifying patterns, constructing mathematical arguments, addressing misconceptions, and justifying their conclusions, including recognizing that increasing dimensions do not necessarily indicate linear growth. Students also connect visual patterns, area models, and algebraic expressions to explain why the growth is quadratic and why different algebraic expressions can represent the same function.
Evaluation for 6.1b
In unit 5, lesson 2, activity 2.2, students represent the orchard situation using an equation, an inequality, a number line, and the real-world context, then explain what each representation means and how it relates to the situation. Students use multiple strategies to determine the solution set, including testing values, solving a related equation, reasoning about the costs, and solving the inequality algebraically. During the discussion, students share and justify their solution methods, explain why the related equation identifies the boundary value, and discuss why using a strategy they understand and can explain is more reliable than relying solely on a memorized rule.
In unit 9, lesson 2, students interpret polynomial multiplication as finding the area of a rectangle whose side lengths are polynomial expressions, demonstrating how an area model represents the same mathematical process as symbolic multiplication. Educator discussion prompts encourage students to explain and justify their reasoning, such as asking, “How did the distributive property help you multiply polynomials?” Students also compare multiplying a linear expression by a quadratic expression with multiplying two quadratic expressions, and discuss the similarities and differences between the procedures.
Evaluation for 6.1c
In unit 2, lesson 11, activity 11.2, students represent “a situation where it makes sense to add terms of a sequence together” by acting out the situation in groups of four. After modeling the situation, students determine their solution by representing it in either a table or an equation. The lesson incorporates the “Discussion Supports” strategy to strengthen mathematical discourse by directing students to “make sure that everyone in their group can explain their solutions and the relationships between the quantities represented. Invite groups to rehearse what they will say when they share with the whole class.” Students then share and discuss their solutions during a whole-class discussion.
Unit 3, lesson 1, activity 1.4 engages students in analyzing data and interpreting mathematical relationships through structured opportunities to write about and discuss their thinking. Students interpret the slope and vertical intercept of a line of best fit in the context of a given data set by analyzing scatter plots with independent and dependent variables. Students first discuss the meaning of the slope and vertical intercept with a partner before sharing their interpretations with the whole class. Educator prompts such as “How do you interpret the slope for each equation?” and “How could Elena compare the decrease in fuel economy as mass increases for hybrid cars to the decrease in fuel economy as mass increases for new cars? Explain your reasoning” require students to explain and justify their mathematical thinking.
Evaluation for 6.2a
In unit 3, lesson 7, activity 7.2, students create a scatter plot and determine the correlation between the number of penalties and the number of wins for a sports team. Next, the “Activity Synthesis” provides educator prompts that encourage students to explain and defend their reasoning. Suggested questions include “If there is a negative correlation, do you think the penalties would cause fewer wins?” and “How did you reach a conclusion? Explain your reasoning.” These prompts encourage students to justify whether they believe the correlation is positive or negative and to support their claims with evidence from the data while reflecting on how they reached their conclusions.
In unit 8, lesson 1, activity 1.3, using a table of values created in the previous lesson, students plot points representing the relationship between the dimensions of a rectangle with a perimeter of 50 meters and its area, then investigate the resulting graph. The “Activity Synthesis” provides the educator with discussion prompts such as “Is the graph linear? Is it exponential?” and “Can we tell if a point represents the length and area of the garden simply by plotting it on the graph?” These questions prompt students to explain their observations, justify their conclusions about the graph, and reflect on patterns such as symmetry and the meaning of the plotted points. The “Lesson Synthesis” further supports reflection by asking students to “reflect on how the relationship between the side lengths and the area of a rectangle differs from other relationships they’ve seen,” reinforcing opportunities for students to share, justify, and refine their mathematical reasoning.
Evaluation for 6.2b
In unit 7, lesson 8, activity 8.3, students build mathematical models to compare two investment options using exponential growth. The “Advancing Students’ Thinking” section prepares educators for likely misconceptions. For example, the guidance states, “Students may be unsure about what to do because the length of time of the investment is not given. Encourage them to try out different time frames, or prompt them to choose different time frames for different cases. They should still support any decisions with mathematical reasoning.” The “Activity Synthesis” provides educators with questions such as “What is the nominal annual interest rate for each option?” “Do they have the same effective annual rate? Why or why not?” and “How does the length of investments influence your calculations and investment choice?”
Unit 9, lesson 15, activity 15.2 provides educators with guidance for anticipating misconceptions and delivering explanatory feedback as students transition from solving quadratic equations by graphing to solving them algebraically. The “Advancing Students’ Thinking” section identifies common misconceptions and includes guidance such as “Watch for students who incorrectly substitute 40 for t and evaluate h(40), or who write g(t) = 8 instead of evaluating g(8). These students may be having trouble distinguishing between the input and output.” The “Activity Synthesis” also provides discussion prompts that help educators respond to student thinking, including “Once you have the equations, how did you find the solutions when the equation has a 0 on one side?”, “What about when the equation has a non-zero number on one side?”, and “How many solutions did you get?”
6.1 Student Self-Efficacy
6.1a
Materials provide opportunities for students to think mathematically, persevere through solving problems, and to make sense of mathematics.
Materials provide opportunities for students to think mathematically, persevere through solving problems, and to make sense of mathematics.
3 out of 3 points
Evaluation for 6.1a
Evaluation for 6.1a
Materials provide opportunities for students to think mathematically, persevere through solving problems, and to make sense of mathematics.
3 out of 3 points
In unit 8, lesson 3, activity 3, students analyze a growing pattern, determine whether the relationship is linear or quadratic, critique mathematical reasoning, and compare equivalent algebraic expressions using both visual and symbolic representations. For example, students sketch the next stage of a growing pattern, determine whether the growth is linear, evaluate Kiran’s claim, and determine whether Diego and Jada’s equations correctly represent the pattern. The activity requires students to work through multiple reasoning tasks that involve identifying patterns, constructing mathematical arguments, addressing misconceptions, and justifying their conclusions, including recognizing that increasing dimensions do not necessarily indicate linear growth. Students also connect visual patterns, area models, and algebraic expressions to explain why the growth is quadratic and why different algebraic expressions can represent the same function.
6.1b
Materials support students in understanding, explaining, and justifying that there can be multiple ways to represent and solve problems and complete tasks.
Materials support students in understanding, explaining, and justifying that there can be multiple ways to represent and solve problems and complete tasks.
6 out of 6 points
Evaluation for 6.1b
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.
6 out of 6 points
In unit 9, lesson 2, students interpret polynomial multiplication as finding the area of a rectangle whose side lengths are polynomial expressions, demonstrating how an area model represents the same mathematical process as symbolic multiplication. Educator discussion prompts encourage students to explain and justify their reasoning, such as asking, “How did the distributive property help you multiply polynomials?” Students also compare multiplying a linear expression by a quadratic expression with multiplying two quadratic expressions, and discuss the similarities and differences between the procedures.
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.
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.
3 out of 3 points
Evaluation for 6.1c
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.
3 out of 3 points
Unit 3, lesson 1, activity 1.4 engages students in analyzing data and interpreting mathematical relationships through structured opportunities to write about and discuss their thinking. Students interpret the slope and vertical intercept of a line of best fit in the context of a given data set by analyzing scatter plots with independent and dependent variables. Students first discuss the meaning of the slope and vertical intercept with a partner before sharing their interpretations with the whole class. Educator prompts such as “How do you interpret the slope for each equation?” and “How could Elena compare the decrease in fuel economy as mass increases for hybrid cars to the decrease in fuel economy as mass increases for new cars? Explain your reasoning” require students to explain and justify their mathematical thinking.
6.2 Facilitating Productive Struggle
6.2a
Materials support teachers in guiding students to share and reflect on their problem-solving approaches, including explanations, arguments, and justifications.
Materials support teachers in guiding students to share and reflect on their problem-solving approaches, including explanations, arguments, and justifications.
6 out of 6 points
Evaluation for 6.2a
Evaluation for 6.2a
Materials support teachers in guiding students to share and reflect on their problem-solving approaches, including explanations, arguments, and justifications.
6 out of 6 points
In unit 8, lesson 1, activity 1.3, using a table of values created in the previous lesson, students plot points representing the relationship between the dimensions of a rectangle with a perimeter of 50 meters and its area, then investigate the resulting graph. The “Activity Synthesis” provides the educator with discussion prompts such as “Is the graph linear? Is it exponential?” and “Can we tell if a point represents the length and area of the garden simply by plotting it on the graph?” These questions prompt students to explain their observations, justify their conclusions about the graph, and reflect on patterns such as symmetry and the meaning of the plotted points. The “Lesson Synthesis” further supports reflection by asking students to “reflect on how the relationship between the side lengths and the area of a rectangle differs from other relationships they’ve seen,” reinforcing opportunities for students to share, justify, and refine their mathematical reasoning.
6.2b
Materials include prompts and guidance to support teachers in providing explanatory feedback based on student responses and anticipated misconceptions.
Materials include prompts and guidance to support teachers in providing explanatory feedback based on student responses and anticipated misconceptions.
4 out of 4 points
Evaluation for 6.2b
Evaluation for 6.2b
Materials include prompts and guidance to support teachers in providing explanatory feedback based on student responses and anticipated misconceptions.
4 out of 4 points
Unit 9, lesson 15, activity 15.2 provides educators with guidance for anticipating misconceptions and delivering explanatory feedback as students transition from solving quadratic equations by graphing to solving them algebraically. The “Advancing Students’ Thinking” section identifies common misconceptions and includes guidance such as “Watch for students who incorrectly substitute 40 for t and evaluate h(40), or who write g(t) = 8 instead of evaluating g(8). These students may be having trouble distinguishing between the input and output.” The “Activity Synthesis” also provides discussion prompts that help educators respond to student thinking, including “Once you have the equations, how did you find the solutions when the equation has a 0 on one side?”, “What about when the equation has a non-zero number on one side?”, and “How many solutions did you get?”