Program Information
Hands-On Standards Mini-Lessons - Algebra I
Supplemental Math (English) Grade 9
IMRA 2025
Commissioner Recommended
Publisher: hand2mind, Inc.
Copyright: 2022
Series includes:
Quality Review
Standards Alignment
Rubric Section
| Grade | TEKS Student % | TEKS Teacher % | ELPS Student % | ELPS Teacher % |
|---|---|---|---|---|
| Grade 9 | 100% | N/A | N/A | N/A |
Criteria for Quality
Rubric Section 1
Intentional Instructional Design
Materials support educators in effective implementation through intentional course, unit, and lesson-level design.
Total
78% (18 out of 23 points)
Evaluation for 1.1a
The "Strand Overviews" within the Supplemental Guide provide an individual overview of each of the five strands: Expressions and Equations, Linear and Exponential Relationships, Descriptive Statistics, Quadratic Functions and Modeling, and Polynomials. Each overview outlines concepts covered within the strand summary, along with alignment to the Texas Essential Knowledge and Skills (TEKS) and English Language Proficiency Standards (ELPS). The "Implementation Guide" within the Supplemental Guide provides a Scope and Sequence that outlines the content TEKS for each strand, along with a Learning Path that explains the rationale for the strand, identifying the horizontal alignment within the materials. The materials do not include a rationale for learning paths across grade levels (vertical alignment).
Evaluation for 1.1b
The "Implementation Guide" within the Supplemental Guide outlines instructional methods and supports for all learners. By design, "tasks include multiple entry points, and additional guidance is available for various proficiency levels." The materials support and meet diverse learning needs by providing effective strategies that ensure students receive timely and appropriate intervention. The "Look Out!" section highlights misconceptions or undeveloped understandings for students who have not yet reached proficiency. The "More Ideas" section can be used to extend thinking for students who have demonstrated grade-level proficiency.
Evaluation for 1.1c
The "Strand Overviews" within the Supplemental Guide provide a TEKS Correlation Guide for each lesson within the strand. For example, the "Descriptive Statistics Strand's" second lesson on Lines of Best Fit covers content standards A.4B and A.4C. The "Assessments & Project Tracking Sheets" within the Supplemental Guide provide a 10-question diagnostic assessment for each of the five strands, along with an Assessment Student Progress Report that recommends skill entry points based on accuracy for each question. The guidance states, "For each item missed, a lesson is recommended to strengthen the student's understanding."
Evaluation for 1.1d
The "Strand Overviews" within the Supplemental Guide provide a summary of the unit, specific student expectations, potential misconceptions, academic mathematical language, and language supports. The "Strand Overview" is designed to provide "a broader perspective to support effective lesson planning." The "Implementation Guide" within the Supplemental Guide outlines the structure of the guidance provided for each lesson. Each lesson "includes many features, including background information, objectives, pacing and grouping suggestions, and ideas for further activities, all in addition to the step-by-step, hands-on activity instruction."
Evaluation for 1.1e
Materials do not provide resources for instructional leaders to aid in the implementation of the materials.
Evaluation for 1.2a
Each lesson includes the TEKS- and ELPS-aligned learning objectives, located at the top left side of the page, to ensure alignment with the Texas Education Agency's standards. These items identify what students will learn and master. Student and teacher materials are listed just below the objectives on the left side of the first page of the lesson. Formative assessment resources are identified at the bottom right-hand side of the last page of the lesson. The "Strands Overviews" within the Supplemental Guide include a suggested timeframe for each strand and lesson. For example, the "Expressions and Equations" strand's suggested timeframe is 12–15 days, while the second lesson is suggested to be one to two days.
Evaluation for 1.2b
This guidance is not applicable because the program is not designed to be adaptive.
Evaluation for 1.2c
The materials do not contain support for families in Spanish and English for each unit, with suggestions on supporting the progress of their students.
1.1 Course-Level Design
1.1a
Materials include an alignment guide outlining the TEKS, ELPS, and concepts covered, with a rationale for learning paths across grade levels (vertical alignment) and within the same grade level (horizontal alignment) as designed in the materials.
Materials include an alignment guide outlining the TEKS, ELPS, and concepts covered, with a rationale for learning paths across grade levels (vertical alignment) and within the same grade level (horizontal alignment) as designed in the materials.
4 out of 5 points
Evaluation for 1.1a
Evaluation for 1.1a
Materials include an alignment guide outlining the TEKS, ELPS, and concepts covered, with a rationale for learning paths across grade levels (vertical alignment) and within the same grade level (horizontal alignment) as designed in the materials.
4 out of 5 points
1.1b
Materials include an implementation guide with usage recommendations and strategies for effective educator use, such as just-in-time supports, advanced learning, or as a course.
Materials include an implementation guide with usage recommendations and strategies for effective educator use, such as just-in-time supports, advanced learning, or as a course.
3 out of 3 points
Evaluation for 1.1b
Evaluation for 1.1b
Materials include an implementation guide with usage recommendations and strategies for effective educator use, such as just-in-time supports, advanced learning, or as a course.
3 out of 3 points
1.1c
Materials include a TEKS correlation guide with recommended skill entry points based on diagnostic assessment results.
Materials include a TEKS correlation guide with recommended skill entry points based on diagnostic assessment results.
2 out of 2 points
Evaluation for 1.1c
Evaluation for 1.1c
Materials include a TEKS correlation guide with recommended skill entry points based on diagnostic assessment results.
2 out of 2 points
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
1.1e
Materials include resources and guidance for instructional leaders to support educators with implementing the materials as designed.
Materials include resources and guidance for instructional leaders to support educators with implementing the materials as designed.
0 out of 2 points
Evaluation for 1.1e
Evaluation for 1.1e
Materials include resources and guidance for instructional leaders to support educators with implementing the materials as designed.
0 out of 2 points
1.2 Lesson-Level Design
1.2a
If designed to be static, materials include detailed lesson plans with learning objectives, teacher and student materials, lesson components with suggested timeframes, and assessment resources aligned with the TEKS and ELPS.
If designed to be static, materials include detailed lesson plans with learning objectives, teacher and student materials, lesson components with suggested timeframes, and assessment resources aligned with the TEKS and ELPS.
7 out of 7 points
Evaluation for 1.2a
Evaluation for 1.2a
If designed to be static, materials include detailed lesson plans with learning objectives, teacher and student materials, lesson components with suggested timeframes, and assessment resources aligned with the TEKS and ELPS.
7 out of 7 points
1.2b
If designed to be adaptive, materials include detailed lesson overviews with learning objectives, lesson components with suggested timeframes, and assessment resources aligned with the TEKS and ELPS.
If designed to be adaptive, materials include detailed lesson overviews with learning objectives, lesson components with suggested timeframes, and assessment resources aligned with the TEKS and ELPS.
Not scored
Evaluation for 1.2b
Evaluation for 1.2b
If designed to be adaptive, materials include detailed lesson overviews with learning objectives, lesson components with suggested timeframes, and assessment resources aligned with the TEKS and ELPS.
0 out of 0 points
1.2c
Materials contain support for families in Spanish and English for each unit, with suggestions on supporting the progress of their student(s).
Materials contain support for families in Spanish and English for each unit, with suggestions on supporting the progress of their student(s).
0 out of 2 points
Evaluation for 1.2c
Evaluation for 1.2c
Materials contain support for families in Spanish and English for each unit, with suggestions on supporting the progress of their student(s).
0 out of 2 points
Rubric Section 2
Progress Monitoring
Materials support educators in effective implementation through frequent, strategic opportunities to monitor and respond to student progress.
Total
75% (18 out of 24 points)
Evaluation for 2.1a
The "Implementation Guide" within the Supplemental Guide provides guidance on progress monitoring, which "leverages a diverse range of assessments that vary in complexity throughout each lesson and strand to provide a holistic picture of a student's understanding of a mathematical concept." Guidance is provided on the different types of assessments included; for example, formative assessments can be found throughout each lesson within "Try It!," "Talk About It," "Formative Assessment," and "More Ideas." The "Implementation Guide" within the Math-Mini Lessons Supplemental Guide includes the definition and intended purpose of instructional assessments, including diagnostic, formative, and summative assessments. For example, the guidance states that diagnostic assessments "help teachers identify strengths, weaknesses, and misconceptions to select the appropriate lesson and tools to use to support student learning."
Evaluation for 2.1b
Each lesson provides guidance for teachers to administer the formative assessment efficiently, ensuring all students receive the same instructions with consistent formative assessment tools, such as "Try It!," "Talk About It," and "Solve It." The guidance includes scripts for questioning and suggestions for implementation, including pacing and grouping guidelines. The "Implementation Guide" within the Supplemental Guide provides guidance for progress monitoring, outlining consistent and accurate administration of diagnostic, formative, and summative assessments. For example, the guidance states, "when administering summative assessments, students may work in small groups for the exercise portion of the page but should complete the standards-based math practice and challenge independently to ascertain their progress."
Evaluation for 2.1c
The materials do not include digital modalities or interfaces for assessments; however, they do provide printable versions of formative assessments. The materials show no evidence of text-to-speech, content, language supports, or calculators for student use. The materials are not designed for student-facing digital use. While housed in a digital platform for educators, assessments are provided only in print and do not include digital accommodations.
Evaluation for 2.1d
The Supplemental Guide includes printable diagnostic assessments for each strand, which feature TEKS-aligned tasks or questions with varying complexity levels. For example, the assessment for "Expressions and Equations" asks students to write an expression for "3 more than 8 times a number" as an open-ended response and graph a line "y=2/3x - 3" on a coordinate plane, as well as solve a system of equations given their equations with a graphing approach. The printable diagnostic assessment includes interactive item types with varying complexity levels in paper-based formats such as short constructed responses, multipart questions, and graphing item types.
Evaluation for 2.1e
The "Implementation Guide—Progress Monitoring" within the Supplemental Guide states, "Formative assessments are included throughout the lesson in the 'Try It!' activity, 'Talk About It,' 'Formative Assessment,' and 'More Ideas.'" The items vary in complexity level; for example, some questions can be solved hands-on using manipulatives, while others require an algebraic approach, and still others ask students to analyze the problem. "Expressions and Equations," Lesson 2 asks students to answer the question: "The second side of a triangle is 2 times the length of the first. The third side is 3 units long. The perimeter of the triangle is 9. What is the length of the first side of the triangle?" Students use manipulatives to help model the scenario and solve the problem aligned with A.5A. "Linear and Exponential Equations," Lesson 2 presents students with the task: "A bathtub has up to 6 inches of water in it. The water is draining at a rate of 0.5 inches per minute. How much water, y, is left after x minutes? Write and graph an inequality." Students use a geoboard to graph the line and represent the shaded region with more rubber bands aligned with A.3D.
Evaluation for 2.2a
The material offers an answer key for assessments and an "Assessment Student Progress Report" for scoring information, but does not include rationales for correct and incorrect answers. The answer key only provides the correct answer without any explanation. The "Implementation Guide—Progress Monitoring" within the Supplemental Guide provides guidance on how to utilize the provided "Assessment Student Progress Report" to interpret student performance on the diagnostic assessment, formative assessments, and the student pages. For example, guidance suggests that if a student answers the "Exercise" portion correctly but does not meet the "Standards-Based Math Practice" standards, the student needs more help in translating concrete to abstract representations.
Evaluation for 2.2b
The "Assessment Student Progress Report" within the Supplemental Guide correlates each lesson to an assessment item, allowing teachers to assign or focus attention on specific lessons based on student performance on the diagnostic assessment. Materials include a "More Ideas" section, which provides "suggestions for additional practice with the skill or an extension of the lesson," based on student trends.
Evaluation for 2.2c
The "Assessments & Project Tracking Sheets" within the Supplemental Guide provide both teachers and students with printable resources to track student progress and growth for each strand. The "Assessment Student Progress Report" for teachers provides detailed tracking by concept, directly correlated to specific lessons within each strand, with three opportunities for mastery. The "Student Lesson Tracking Report" enables self-reflection on each lesson.
Evaluation for 2.2d
The materials include a "Solve It" section that provides guidance on conducting a check for understanding following the "Try It!" section. For example, "Descriptive Statistics," Lesson 1, suggests that students create a histogram or box plot to display the same data and discuss the similarities and differences in their representations. Materials include a "Talk About It" section that provides prompts to support educators in conducting frequent checks for understanding. For example, "Polynomials," Lesson 4 states, "Ask: Why do you think we call this special pattern the difference of two squares?"
Evaluation for 2.2e
This guidance is not applicable because the program is not designed to be adaptive.
2.1 Instructional Assessments
2.1a
Materials include the definition and intended purpose for the types of instructional assessments.
Materials include the definition and intended purpose for the types of instructional assessments.
2 out of 2 points
Evaluation for 2.1a
Evaluation for 2.1a
Materials include the definition and intended purpose for the types of instructional assessments.
2 out of 2 points
2.1b
Materials include guidance to ensure consistent and accurate administration of instructional assessments.
Materials include guidance to ensure consistent and accurate administration of instructional assessments.
2 out of 2 points
Evaluation for 2.1b
Evaluation for 2.1b
Materials include guidance to ensure consistent and accurate administration of instructional assessments.
2 out of 2 points
2.1c
Digital assessments include printable versions and accommodations, including text-to-speech, content and language supports, and calculators, that educators can enable or disable to support individual students.
Digital assessments include printable versions and accommodations, including text-to-speech, content and language supports, and calculators, that educators can enable or disable to support individual students.
0 out of 4 points
Evaluation for 2.1c
Evaluation for 2.1c
Digital assessments include printable versions and accommodations, including text-to-speech, content and language supports, and calculators, that educators can enable or disable to support individual students.
0 out of 4 points
2.1d
Materials include diagnostic assessments with TEKS-aligned tasks or questions, including interactive item types with varying complexity levels.
Materials include diagnostic assessments with TEKS-aligned tasks or questions, including interactive item types with varying complexity levels.
4 out of 4 points
Evaluation for 2.1d
Evaluation for 2.1d
Materials include diagnostic assessments with TEKS-aligned tasks or questions, including interactive item types with varying complexity levels.
4 out of 4 points
2.1e
Materials include a variety of formative assessments with TEKS-aligned tasks or questions, including interactive item types with varying complexity levels.
Materials include a variety of formative assessments with TEKS-aligned tasks or questions, including interactive item types with varying complexity levels.
4 out of 4 points
Evaluation for 2.1e
Evaluation for 2.1e
Materials include a variety of formative assessments with TEKS-aligned tasks or questions, including interactive item types with varying complexity levels.
4 out of 4 points
2.2 Data Analysis and Progress Monitoring
2.2a
Instructional assessments include scoring information and guidance for interpreting student performance, including rationale for each correct and incorrect response.
Instructional assessments include scoring information and guidance for interpreting student performance, including rationale for each correct and incorrect response.
1 out of 3 points
Evaluation for 2.2a
Evaluation for 2.2a
Instructional assessments include scoring information and guidance for interpreting student performance, including rationale for each correct and incorrect response.
1 out of 3 points
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
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
2.2d
If designed to be static, materials provide prompts and guidance to support educators in conducting frequent checks for understanding at key points throughout each lesson or activity.
If designed to be static, materials provide prompts and guidance to support educators in conducting frequent checks for understanding at key points throughout each lesson or activity.
2 out of 2 points
Evaluation for 2.2d
Evaluation for 2.2d
If designed to be static, materials provide prompts and guidance to support educators in conducting frequent checks for understanding at key points throughout each lesson or activity.
2 out of 2 points
2.2e
If designed to be adaptive, materials provide frequent checks for understanding at key points throughout each lesson or activity.
If designed to be adaptive, materials provide frequent checks for understanding at key points throughout each lesson or activity.
Not scored
Evaluation for 2.2e
Evaluation for 2.2e
If designed to be adaptive, materials provide frequent checks for understanding at key points throughout each lesson or activity.
0 out of 0 points
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
92% (36 out of 39 points)
Evaluation for 3.1a
The "Implementation Guide—Instructional Methods and Support for All Learners" within the Supplemental Guide states, "students who have not yet reached proficiency may have misconceptions or underdeveloped understandings of mathematical concepts. These are highlighted in the 'Look Out!' section of the lesson." For example, in "Expressions and Equations," Lesson 4, explicit guidance is provided in the "Look Out!" section for students who change the direction of the inequality when adding and subtracting on both sides of the equation. Guidance suggests demonstrating with simple numerical examples to see when the inequality holds true. The "Talk About It" section of the lesson prompts students to draw on prior knowledge and provides a script to help clarify their thinking. For example, in "Linear and Exponential Relationships," Lesson 3, students revisit the concept of using the vertical line test to determine whether a relation represents a function. If students struggle with identifying functions given a rule, the use of a pegboard is encouraged to help students plot the points and show the relation, and then apply the vertical line test.
Evaluation for 3.1b
The "EL Support" section provides pre-teaching guidance to review key vocabulary and unfamiliar references. For example, "Linear and Exponential Relationships," Lesson 3, gives teachers explicit guidance to "review vocabulary: domain, function, range, relation, sequence. Remind students that the root of relation is relate, and explain that a relation is a description of how two sets of numbers are related. Encourage students to explain the meaning of relation in their own words." The "EL Support" section provides explicit guidance for the use of embedded sentence frames for language supports. For example, the "Descriptive Statistics," Lesson 2, provides teachers with the sentence frame "A line of best fit often has _____ numbers of points on either side of the _____." Teachers can use these frames during the "Talk About It" section to support the development of academic vocabulary and unfamiliar references. In the materials, the "Talk About It" section "supports language development through academic discourse, and the challenge portion of the student pages often requires students to explain their connections, reasoning, or justification in writing, further developing their speaking, listening, and written language." For example, the challenge for "Polynomials," Lesson 2 requires students to find the product of two polynomials and explain their process, providing support for developing academic language.
Evaluation for 3.1c
In the materials, the "More Ideas" section of the lesson provides teachers with guidance on enrichment and extension activities for students who have demonstrated proficiency at or above grade level. For example, in "Expressions and Equations," Lesson 5, students use the XY Coordinate Pegboard to graph different types of equations, including exponential (at the grade level) and rational equations (above grade level), by first creating a table of values and then graphing on the pegboard. In the materials, the "More Ideas" section "provides additional activities and suggestions for teaching about the lesson concept using a variety of manipulatives. These ideas might be suggestions for additional practice with the skill or an extension of the lesson." For example, in the "Linear and Exponential Relationships," Lesson 3, guidance suggests providing a sequence of numbers, such as the Fibonacci sequence, for students to build a table, graph the sequence, and determine if the sequence represents a function. This enrichment activity requires students to apply their knowledge of functions in a new context, with sequences for enrichment in grade-level and above-grade-level content, dependent on the type of sequence provided.
Evaluation for 3.1d
The materials do not include digital accommodations; by design, all assessments and student pages are printable only and therefore do not include text-to-speech, content and language supports, nor calculator accommodations.
Evaluation for 3.1e
In the materials, the "More Ideas" section of the lesson provides teachers with guidance on various ways students can demonstrate an understanding of the concept. For example, the "Descriptive Statistics," Lesson 2, provides three options for additional practice on lines of best fit, including creating a grid on the floor using masking tape and a string to calculate the line of best fit for graphs created by the students. Materials provide educators with guidance to support students in demonstrating understanding in various ways, such as offering sentence frames to help students express their mathematical reasoning (in the EL Support margin of the lessons), prompts to facilitate mathematical discourse, and suggesting manipulatives that students can use to represent and solve problems within every lesson.
Evaluation for 3.2a
Each lesson includes explicit prompts and guidance in the "Talk About It" section to activate prior knowledge and anchor big ideas. For example, in "Quadratic Functions and Modeling," Lesson 1, students explore key features of quadratic functions represented tabularly and graphically. To activate prior knowledge, guidance suggests asking, "Ask: Is this a linear relationship?" before introducing quadratic functions. To anchor big ideas, guidance states, "Say: The graph of a quadratic function is called a parabola. Discuss the features of a parabola, such as the shape of the curve, its symmetry, and the highest or lowest point called the vertex." Each lesson includes explicit prompts and guidance in the "Solve It" section, providing students with the opportunity to demonstrate what they have learned by highlighting and connecting key patterns, features, and relationships through multiple means of representation. For example, in "Linear and Exponential Relationships," Lesson 1, students solve systems of equations first algebraically using Algeblocks, while the "Solve It" sections require students to solve the same problem graphically. Prompts include "Ask: How does the intersection of the two lines tell you the cost of each juice and sandwich?" This question helps connect the relationship between the algebraic solution and the graphical representation. Each lesson includes explicit prompts and guidance in the "Try It!" section to help students connect key patterns, features, and relationships through multiple representations. For example, in "Linear and Exponential Relationships," Lesson 4, students construct tables, plot data, and write an exponential function for the thickness of a folded paperboard after x folds. Prompts include "Ask: How can you describe the pattern of the function's value?" and "Ask: How can you write an equation to represent repeated multiplication?" to help connect patterns, features, and relationships between the table, graph, and equation.
Evaluation for 3.2b
Each lesson includes educator guidance with step-by-step instructions and visuals for the hands-on "Try It!" activity. For example, "Polynomials," Lesson 1 provides four steps to solve the real-world "Try It!" activity by subtracting polynomials using Algeblocks. Each step includes specific prompts, such as "What is the first term you will subtract?" and guidance on manipulating the blocks at each step, such as "Subtract 2 by removing two blocks from the positive side of the mat." Each lesson includes a "Solve It" section that provides educators with guidance on ways students can demonstrate what they have learned by summarizing the lesson concept or extending the skill through a new variation of the "Try It!" activity problem. For example, the "Solve It" guidance for "Descriptive Statistics," Lesson 1, suggests that students create histograms or boxplots to represent the same data previously shown with dot plots, and then compare the similarities and differences in their displays of the same data. Each lesson includes a "More Ideas" section that provides educator guidance on additional activities and suggestions for teaching the lesson concept. For example, the "More Ideas" section of "Expressions and Equations," Lesson 2, guidance suggests students work in groups of three, where one student creates a real-world scenario, another student models the equation with Algebra Tiles. The third student solves the model, repeating the process with alternating roles.
Evaluation for 3.2c
Each lesson includes various types of multi-tiered intervention practice opportunities and structures to support the implementation of the materials. The "Try It!" activity offers opportunities for collaborative practice through small-group activities. The "Talk About It" portion of the lesson offers whole-group guided instruction to facilitate discussion on the key concepts presented. The "Student Pages" provide independent, structured practice to assess progress. Each section includes direct guidance from the educator for implementation. The diagnostic assessment for each strand provides educator guidance to help teachers "identify strengths, weaknesses, and misconceptions to select the appropriate lessons and tools to use to support student learning." For example, students who miss questions 9 and 10 on the Unit 4 diagnostic assessment would benefit from completing Lesson 2, which focuses on analyzing quadratic functions.
Evaluation for 3.2d
The materials identify enrichment and extension activities in the "More Ideas" section of the lesson. Each activity provides teacher guidance for effective implementation. For example, "Quadratics Functions and Modeling," Lesson 2, provides an extension option for analyzing quadratic functions that states: "provide students with a few quadratic functions, and have them graph each on graph paper to see the shape of the curve and analyze their features . . . be sure to include at least one that opens up, one that opens down, and one with no x-intercept." The "More Ideas" section of the lesson offers suggested activities for enrichment or extension of the lesson content. For example, in "Linear and Exponential Relationships," Lesson 1 includes guidance on extending solving systems of equations by having students work in pairs to create their own problems to solve. Guidance states, "Have each partner choose a value for x and y and then write two equations using those values for x and y. Then have them read the equations to their partner, who will solve the system." This activity can be repeated, switching roles each time.
Evaluation for 3.2e
Materials provide prompts and guidance to support educators in offering timely feedback during lessons. For example, "Quadratics Functions and Modeling," Lesson 2 guides teachers to: "Say: Make a table of values for the equation given in the problem. Ask: What is the y-intercept? What are the x-intercepts? . . . Guide students to observe that the vertex is at a maximum and that the values are symmetrical around it." Prompts for questions like this are regularly embedded throughout every lesson. In the materials, the "Look Out!" section provides guidance on common misconceptions and offers troubleshooting suggestions. For example, in "Descriptive Statistics," Lesson 3, guidance suggests, "Watch for students who think that the line of best fit has to start and end at points on the line. Point out that the line of best fit is an estimate that is closest to the points overall, but it does not necessarily pass through any points on the line."
Evaluation for 3.3a
Each lesson within the materials provides "EL Support," which includes strategies for all proficiency levels in listening, reading, writing, and speaking. For example, guidance such as "use gestures and visuals to make content comprehensible, such as drawing a number line on the board" is provided to support listening skills for beginner students.
Evaluation for 3.3b
This guidance is not applicable to the program because it is not designed to be adaptive.
Evaluation for 3.3c
In the materials, "EL Support" is provided for each lesson. For example, "Expressions and Equations," Lesson 2, includes guidance to: "Review vocabulary: equation. Note the root of the word that is the same as in equal and equality. Tell students that an equation relates two expressions that have the same value," and "as students justify the steps of solving equations, prompt them to use accurate language." The "Strand Overviews" within the Supplemental Guide provide language development and support specific to each of the five strands, along with a description of how the ELPS are integrated into each lesson. For example, in the "Polynomials Strand Overview," guidance states, "Remind students that the prefix bi- means two, like in bicycle, which is a cycle that has two wheels, and biweekly, which describes things that happen every two weeks, like a paycheck."
Evaluation for 3.3d
The materials incorporate embedded oral language development strategies in each lesson. For example, in "Expressions and Equations," Lesson 2, there is guidance to: "Review vocabulary: equation. Note the root of the word that is the same as in equal and equality. Tell students that an equation relates two expressions that have the same value," allowing students to make cross-linguistic connections and develop academic vocabulary through oral discourse. Other guidance includes opportunities to increase comprehension and build background with supports like: "Discuss the concept of opposites like up and down, left and right. Extend this discussion to using opposites in solving equations. Subtraction and addition are opposite operations. Multiplication and division are opposite operations." The "Strand Overviews" within the Supplemental Guide provide embedded guidance to facilitate oral discourse for language development. For example, in the "Quadratic Functions and Modeling Strand Overview," guidance states, "Discuss the term parent function with students. Relate this idea to a family tree to show what a set of functions has in common," supporting the development of academic vocabulary and cross-linguistic connections. Materials provide teacher guidance throughout the "Talk About" and "Try It!" activities to support the development of written language for emergent bilingual (EB) students. For example, guidance to encourage written discourse, such as "Describe your steps to evaluate this expression," includes sentence stems and a graphic organizer to support writing development.
Evaluation for 3.3e
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 explicit educator guidance for lessons or activities scaffolded for students who have not yet reached proficiency in prerequisite or grade-level concepts and skills.
Materials include explicit educator guidance for lessons or activities scaffolded for students who have not yet reached proficiency in prerequisite or grade-level concepts and skills.
1 out of 1 points
Evaluation for 3.1a
Evaluation for 3.1a
Materials include explicit educator guidance for lessons or activities scaffolded for students who have not yet reached proficiency in prerequisite or grade-level concepts and skills.
1 out of 1 points
3.1b
Materials include explicit educator guidance for language supports, including pre-teaching and embedded supports for developing academic vocabulary and unfamiliar references in text.
Materials include explicit educator guidance for language supports, including pre-teaching and embedded supports for developing academic vocabulary and unfamiliar references in text.
4 out of 4 points
Evaluation for 3.1b
Evaluation for 3.1b
Materials include explicit educator guidance for language supports, including pre-teaching and embedded supports for developing academic vocabulary and unfamiliar references in text.
4 out of 4 points
3.1c
Materials include explicit educator guidance for enrichment and extension activities for students who have demonstrated proficiency in grade-level and above grade-level content and skills.
Materials include explicit educator guidance for enrichment and extension activities for students who have demonstrated proficiency in grade-level and above grade-level content and skills.
2 out of 2 points
Evaluation for 3.1c
Evaluation for 3.1c
Materials include explicit educator guidance for enrichment and extension activities for students who have demonstrated proficiency in grade-level and above grade-level content and skills.
2 out of 2 points
3.1d
Digital materials include accommodations, including text-to-speech, content and language supports, and calculators that educators can enable or disable to support individual students.
Digital materials include accommodations, including text-to-speech, content and language supports, and calculators that educators can enable or disable to support individual students.
0 out of 3 points
Evaluation for 3.1d
Evaluation for 3.1d
Digital materials include accommodations, including text-to-speech, content and language supports, and calculators that educators can enable or disable to support individual students.
0 out of 3 points
3.1e
Materials include educator guidance on offering options and supports for students to demonstrate understanding of mathematical concepts in various ways, such as perform, express, and represent.
Materials include educator guidance on offering options and supports for students to demonstrate understanding of mathematical concepts in various ways, such as perform, express, and represent.
2 out of 2 points
Evaluation for 3.1e
Evaluation for 3.1e
Materials include educator guidance on offering options and supports for students to demonstrate understanding of mathematical concepts in various ways, such as perform, express, and represent.
2 out of 2 points
3.2 Instructional Methods
3.2a
Materials include explicit (direct) prompts and guidance for educators to build knowledge by activating prior knowledge, anchoring big ideas, and highlighting and connecting key patterns, features, and relationships through multiple means of representation.
Materials include explicit (direct) prompts and guidance for educators to build knowledge by activating prior knowledge, anchoring big ideas, and highlighting and connecting key patterns, features, and relationships through multiple means of representation.
5 out of 5 points
Evaluation for 3.2a
Evaluation for 3.2a
Materials include explicit (direct) prompts and guidance for educators to build knowledge by activating prior knowledge, anchoring big ideas, and highlighting and connecting key patterns, features, and relationships through multiple means of representation.
5 out of 5 points
3.2b
If designed to be static, materials include educator guidance for effective lesson delivery and facilitation using various instructional approaches.
If designed to be static, materials include educator guidance for effective lesson delivery and facilitation using various instructional approaches.
2 out of 2 points
Evaluation for 3.2b
Evaluation for 3.2b
If designed to be static, materials include educator guidance for effective lesson delivery and facilitation using various instructional approaches.
2 out of 2 points
3.2c
Materials include multi-tiered intervention methods for various types of practice and structures and educator guidance to support effective implementation.
Materials include multi-tiered intervention methods for various types of practice and structures and educator guidance to support effective implementation.
3 out of 3 points
Evaluation for 3.2c
Evaluation for 3.2c
Materials include multi-tiered intervention methods for various types of practice and structures and educator guidance to support effective implementation.
3 out of 3 points
3.2d
Materials include enrichment and extension methods that support various forms of engagement, and guidance to support educators in effective implementation.
Materials include enrichment and extension methods that support various forms of engagement, and guidance to support educators in effective implementation.
2 out of 2 points
Evaluation for 3.2d
Evaluation for 3.2d
Materials include enrichment and extension methods that support various forms of engagement, and guidance to support educators in effective implementation.
2 out of 2 points
3.2e
Materials include prompts and guidance to support educators in providing timely feedback during lesson delivery.
Materials include prompts and guidance to support educators in providing timely feedback during lesson delivery.
2 out of 2 points
Evaluation for 3.2e
Evaluation for 3.2e
Materials include prompts and guidance to support educators in providing timely feedback during lesson delivery.
2 out of 2 points
3.3 Support for Emergent Bilingual Students
3.3a
If designed to be static, materials include educator guidance on providing and incorporating linguistic accommodations for all 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.
If designed to be static, materials include educator guidance on providing and incorporating linguistic accommodations for all 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.
4 out of 4 points
Evaluation for 3.3a
Evaluation for 3.3a
If designed to be static, materials include educator guidance on providing and incorporating linguistic accommodations for all 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.
4 out of 4 points
3.3b
If designed to be adaptive, materials include embedded linguistic accommodations for all 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.
If designed to be adaptive, materials include embedded linguistic accommodations for all 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.
Not scored
Evaluation for 3.3b
Evaluation for 3.3b
If designed to be adaptive, materials include embedded linguistic accommodations for all 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 0 points
3.3c
Materials include implementation guidance to support educators in effectively using the materials in state-approved bilingual/ESL programs.
Materials include implementation guidance to support educators in effectively using the materials in state-approved bilingual/ESL programs.
1 out of 1 points
Evaluation for 3.3c
Evaluation for 3.3c
Materials include implementation guidance to support educators in effectively using the materials in state-approved bilingual/ESL programs.
1 out of 1 points
3.3d
Materials include embedded guidance 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 to support emergent bilingual students in developing academic vocabulary, increasing comprehension, building background knowledge, and making cross-linguistic connections through oral and written discourse.
8 out of 8 points
Evaluation for 3.3d
Evaluation for 3.3d
Materials include embedded guidance to support emergent bilingual students in developing academic vocabulary, increasing comprehension, building background knowledge, and making cross-linguistic connections through oral and written discourse.
8 out of 8 points
3.3e
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 scored
Evaluation for 3.3e
Evaluation for 3.3e
If designed for dual language immersion (DLI) programs, materials include resources that outline opportunities to address metalinguistic transfer from English to the partner language.
0 out of 0 points
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% (16 out of 16 points)
Evaluation for 4.1a
The "Implementation Guide" within the Supplemental Guide states, "Each strand and lesson is carefully crafted to provide opportunities for students to practice and demonstrate their understanding of key concepts while balancing conceptual understanding and procedural fluency." All practice and assessments align with the depth of knowledge required by the TEKS. Each lesson within the materials includes student pages designed to "take the student from the concrete to the abstract, completing the instructional cycle." Each page offers concrete and representational exercises that utilize pictorial representations and manipulatives, as well as abstract exercises that provide standards-based math practice, and extended-response exercises featuring open-ended constructed responses. The variety of practice opportunities helps students demonstrate a depth of understanding aligned with the TEKS. "Expressions and Equations," Lesson 3, asks the students: "Susan charges a $7 fee plus $2 per hour for babysitting. Joan charges a $3 fee plus $4 per hour. When will their babysitting fees be the same?" Students use Algebra Tiles to model the scenario on the "Algebra Tiles Equations Mat" while writing the equivalent mathematical expression. Then, they simplify the expression by physically rearranging the tiles and combining like terms in the mathematical expression. Lastly, students solve the equation by creating equal groups on each side of the mat while dividing with the mathematical expression. Students simultaneously work with concrete Algebra Tiles while working with abstract mathematical equations, as the teacher asks guiding questions to connect the two representations.
Evaluation for 4.1b
In the materials, questions and tasks increase in rigor and complexity, leading to grade-level proficiency in math and above-grade-level proficiency. The student pages begin with concrete representations, progress to standards-based math practice questions, and extend to open-ended constructed responses that are beyond grade level. For example, "Equations & Expressions," Lesson 3, asks students to use Algebra Tiles to help solve equations with variables on both sides, including the distributive property. They then progress to representing the process pictorially and connecting the concrete and pictorial models to standard algorithms. The "Implementation Guide—Instructional Methods & Supports for All Learners" within the Supplemental Guide states, "students who have demonstrated grade-level proficiency can extend their learning using the 'More Ideas' section of the lesson, completing the Challenge portion of the student pages." For example, the "Quadratic Functions and Modeling," Lesson 1 challenge activity asks students to graph the possible surface areas of a cylindrical can, given constraints for the height and radius, which extends above grade level.
Evaluation for 4.2a
The "Program Overview—Depth and Coherence of Key Mathematical Concepts" section of the Supplemental Guide describes each lesson as including an introduction that "shows how these concepts and skills fit into the larger context of students' mathematical development, including . . . horizontally throughout grade level." The materials are sequenced in a way that allows students to build on prior big ideas. For example, the "Linear and Exponential," Lesson 2 states, "Students have graphed linear equations and systems of linear equations. Students will extend their understanding of these concepts by transitioning to linear inequalities."
Evaluation for 4.2b
The "Program Overview—Depth and Coherence of Key Mathematical Concepts" section of the Supplemental Guide describes each lesson as including an introduction that "shows how these concepts and skills fit into the larger context of students' mathematical development, including vertically across grade levels . . ." Each lesson within the materials begins with an introduction that explores how the concepts learned build to future course expectations. For example, the "Expressions and Equations," Lesson 6, describes how solving systems of two linear equations will expand to "other types of equations and equations in three dimensions" in future courses.
Evaluation for 4.2c
Each lesson includes an introduction that "explores the background of the concepts and skills covered in each lesson" by connecting prior knowledge to current and future concepts. The introduction "shows how [the concepts] fit into the larger context of students' mathematical development." In "Linear and Exponential Relationships," Lesson 2, students extend their understanding of graphing linear equations to linear inequalities. During the lesson, students are encouraged to test points to determine which region to shade. This approach prepares students for future lessons on graphing systems of linear inequalities and future courses that explore nonlinear inequalities. In "Polynomials," Lesson 5, students explore the pattern for perfect square trinomials through a hands-on exploration, building upon prior knowledge of multiplying binomials. The guidance states, "Recognizing patterns of perfect square trinomials will enable students to simplify rational expressions, factor trinomials, and solve rational equations more efficiently."
Evaluation for 4.3a
Each lesson includes a "Talk About It" section that integrates spaced retrieval opportunities with prior learning to reinforce concepts. For example, in "Descriptive Statistics," Lesson 2, students create a scatterplot and sketch a trend line to revisit previous learning and connect it to the current lesson on lines of best fit. The "Strands Overviews" within the Supplemental Guide include prior learning standards to guide teachers to understand what builds upon each skill. For example, "Descriptive Statistics," Lesson 2, builds directly on TEKS 8.5C and 8.5D.
Evaluation for 4.3b
The conclusion of each strand provides interleaved practice opportunities by combining items from each lesson, requiring students to discern which concept is being addressed and how best to approach it. The "Implementation Guide" within the Supplemental Guide provides guidance on revisiting prior "More Ideas" tasks in subsequent lessons, thereby creating opportunities for interleaved practice.
4.1 Depth of Key Concepts
4.1a
Practice opportunities throughout learning pathways (including instructional assessments) require students to demonstrate depth of understanding aligned to the TEKS.
Practice opportunities throughout learning pathways (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 throughout learning pathways (including instructional assessments) require students to demonstrate depth of understanding aligned to the TEKS.
2 out of 2 points
4.1b
Questions and tasks, including enrichment and extension materials, increase in rigor and complexity, leading to grade-level and above grade-level proficiency in the mathematics TEKS.
Questions and tasks, including enrichment and extension materials, increase in rigor and complexity, leading to grade-level and above grade-level proficiency in the mathematics TEKS.
4 out of 4 points
Evaluation for 4.1b
Evaluation for 4.1b
Questions and tasks, including enrichment and extension materials, increase in rigor and complexity, leading to grade-level and above grade-level proficiency in the mathematics TEKS.
4 out of 4 points
4.2 Coherence of Key Concepts
4.2a
Materials demonstrate coherence across concepts horizontally within the grade level by connecting patterns, big ideas, and relationships.
Materials demonstrate coherence across concepts horizontally within the grade level by connecting patterns, big ideas, and relationships.
1 out of 1 points
Evaluation for 4.2a
Evaluation for 4.2a
Materials demonstrate coherence across concepts horizontally within the grade level by connecting patterns, big ideas, and relationships.
1 out of 1 points
4.2b
Materials demonstrate coherence vertically across concepts and grade bands, including connections from grades 3–12, by connecting patterns, big ideas, and relationships.
Materials demonstrate coherence vertically across concepts and grade bands, including connections from grades 3–12, by connecting patterns, big ideas, and relationships.
1 out of 1 points
Evaluation for 4.2b
Evaluation for 4.2b
Materials demonstrate coherence vertically across concepts and grade bands, including connections from grades 3–12, by connecting patterns, big ideas, and relationships.
1 out of 1 points
4.2c
Materials demonstrate coherence across lessons or activities by connecting students’ prior knowledge of concepts and procedures to the mathematical concepts to be learned in the current grade level and future grade levels.
Materials demonstrate coherence across lessons or activities by connecting students’ prior knowledge of concepts and procedures to the mathematical concepts to be learned in the current grade level and future grade levels.
4 out of 4 points
Evaluation for 4.2c
Evaluation for 4.2c
Materials demonstrate coherence across lessons or activities by connecting students’ prior knowledge of concepts and procedures to the mathematical concepts to be learned in the current grade level and future grade levels.
4 out of 4 points
4.3 Coherence and Variety of Practice
4.3a
Materials provide spaced retrieval opportunities with previously learned skills and concepts across learning pathways.
Materials provide spaced retrieval opportunities with previously learned skills and concepts across learning pathways.
2 out of 2 points
Evaluation for 4.3a
Evaluation for 4.3a
Materials provide spaced retrieval opportunities with previously learned skills and concepts across learning pathways.
2 out of 2 points
4.3b
Materials provide interleaved practice opportunities with previously learned skills and concepts across learning pathways.
Materials provide interleaved practice opportunities with previously learned skills and concepts across learning pathways.
2 out of 2 points
Evaluation for 4.3b
Evaluation for 4.3b
Materials provide interleaved practice opportunities with previously learned skills and concepts across learning pathways.
2 out of 2 points
Rubric Section 5
Balance of Conceptual and Procedural Understanding
Materials are designed to balance conceptual understanding, procedural skills, and fluency.
Total
95% (36 out of 38 points)
Evaluation for 5.1a
Each lesson includes a "Try It!" section that provides "a hands-on activity for students to explore the mathematical concepts using a real-world problem." The tasks offer students opportunities to interpret, analyze, and evaluate mathematical concepts. For example, in "Descriptive Statistics," Lesson 2, students work to determine a line of best fit to model a real-world problem. Students must evaluate different models using pegboards to determine the qualities required for a line of best fit, enabling them to make accurate predictions. For more practice, each lesson includes a student page that provides questions for students to interpret, analyze, and evaluate mathematical concepts. The "Expressions and Equations," Lesson 1 student page provides questions for students to interpret the contextual meaning of values within an algebraic expression. The challenge question states, "The cost for one person to bowl for x hours is 3x + 5 dollars. What does 3 represent? What might 5 represent?" In the materials, students can find more opportunities to interpret, analyze, and evaluate mathematics concepts and real-world applications in the "More Ideas" section. For example, the "Quadratic Functions and Modeling," Lesson 2 suggests that students graph multiple quadratic functions and analyze their key features.
Evaluation for 5.1b
The "Program Overview" within the Supplemental Guide states each lesson "begins with instruction and practice at the concrete state, progresses to the pictorial or representation stage, and ends with an abstract representation by the end of the lesson." The materials provide students with opportunities to create concrete models and representations of mathematical situations. For example, "Expressions and Equations," Lesson 2, asks students to answer the question: "The second side of a triangle is two times the length of the first. The third side is three units long. The perimeter of the triangle is nine. What is the length of the first side of the triangle?" Students first use Algebra Tiles to help model the scenario to solve the problem, and later "sketch a model and record their work."
Evaluation for 5.1c
Materials provide questions and tasks that offer opportunities for students to apply their conceptual understanding to new problem situations and contexts. For example, the "Expressions and Equations," Lesson 3 states, "By understanding how to isolate the variables on one side of the equation, students will be able to solve real-world problems in algebra that involve variables on both sides of the equation." Students are tasked with applying their knowledge of isolating a variable to a real-world problem to determine when two different babysitting fees will be the same. In the "Polynomials" strand, students use Algebra Tiles to multiply polynomials using an area model in Lessons 2 and 3. In future lessons on factoring, students revisit the area model and apply their conceptual understanding of the model in a new context to find the dimensions of the rectangle that represents the trinomial.
Evaluation for 5.2a
The materials provide 42 "Problem Strings" and "Problem Talks" routines designed to increase the automaticity and fluency necessary to complete grade-level tasks. For example, one "Problem String" focuses on solution-preserving moves, helping students improve fluency when solving equations.
Evaluation for 5.2b
The "Program Overview" within the Supplemental Guide states, "students evaluate different representations, models, and strategies to determine which yield solutions that are efficient, flexible, and accurate." For instance, in "Expressions and Equations," Lesson 2, the use of Algebra Tiles models solving equations as students build efficiency with the procedures algebraically. Students write the corresponding equation to each step when using the Algebra Tiles Equations Mat to reinforce procedural accuracy. The "Student Pages" for each lesson offer students opportunities to practice efficient, flexible, and accurate mathematical procedures. For example, each student page begins with solving using a pictorial representation, then builds to abstract questions to show flexibility and efficiency in the solving approach.
Evaluation for 5.2c
The materials encourage students to model problems using math manipulatives. As students practice using the models while writing the corresponding algebraic expressions, they evaluate the representations, models, and solutions for efficiency. Students also appreciate the flexibility of different representations, models, and strategies in various contexts, recognizing how Algebra Tiles can be applied to solve a wide range of problems. Students can see that different representations, models, and strategies can all lead to accurate solutions. In the materials, the "Talk About It" section provides students with opportunities to evaluate mathematical strategies for efficiency and flexibility. For example, in "Linear and Exponential Relationships," Lesson 2, guidance highlighting flexibility states, "Discuss how to choose which variable to solve for when solving a system of equations." Meanwhile, prompts such as "What would make it easier to solve for x instead of y?" are included to highlight efficiency. The "Talk About It" section also offers students the opportunity to evaluate mathematical solutions for accuracy. For example, "Polynomials," Lesson 1, gives direct guidance to ask, "How can you check your answer? If students do not suggest it, note that addition and subtraction are inverse operations, so they can add their result to the cost and see if they get the total sales."
Evaluation for 5.2d
Materials include teacher guidance to support students in selecting increasingly efficient approaches. For example, in "Expressions and Equations," Lesson 3, the guidance states, "What other ways could we have determined when their fees are the same? Which was the most efficient? When might we want to use a less efficient method?"
Evaluation for 5.3a
The "Program Overview" within the Supplemental Guide addresses the conceptual and procedural emphasis of the TEKS. Each lesson addresses conceptual emphasis through "an application problem that allows students to interpret, analyze, and evaluate the mathematical or real-world situation." While "students solidify their understanding of the mathematical concept, they use those relationships to fluently complete the grade level tasks by applying efficient, flexible, and accurate procedures to various contexts." The "Strand Overview" within the Supplemental Guide explicitly states how the conceptual and procedural emphasis of the TEKS is addressed. For example, the "Strand Summary" for "Expressions and Equations" specifies the conceptual emphasis as students should "understand the meaning of equivalent forms of expressions, equations, and relations." It also emphasizes the procedural emphasis as students should "write equivalent forms of equations and solve them with fluency. Solve a System of equations graphically." The materials address the conceptual and procedural elements of the standards. For example, the "Linear and Exponential Strand," Lesson 5, asks students to graph a linear and an exponential function on the same coordinate grid, given a verbal description of each function, and "describe and compare the rates of change for each block of cheese." The activity addresses the conceptual understanding of the rate of change and the procedure for graphing the scenario to visually represent the decrease in the amount of cheese left.
Evaluation for 5.3b
In the materials, "the mathematics concept begins with instruction and practice at the concrete stage, progresses to the pictorial or representation stage, and ends with an abstract representation by the end of the lesson." Each lesson demonstrates this by using math manipulatives, such as Algebra Tiles, to represent the math concept concretely and pictorially, then moving to the abstract algebraic equations at the end of the lesson. Each lesson includes "Student Pages" for additional practice and review. The practice provides opportunities for the students to "begin by using manipulatives, move to creating visual representations, and then complete the cycle by working with abstract mathematical symbols." In the materials, questions and tasks incorporate concrete, pictorial, and abstract models. For example, in "Polynomials," Lesson 5, students multiply binomials to find a perfect square trinomial using Algeblocks, model sketches, and algebraic representations.
Evaluation for 5.3c
The materials incorporate Algebra Tiles into lessons, enabling students to create, connect, and explain concrete models of associated abstract concepts with guidance to support step-by-step implementation. For example, in "Expressions and Equations," Lesson 2, guidance includes solving the equation with the tiles and recording the algebraic process. Prompts such as "How can we isolate the variable?" allow students to explain how the concrete models translate to the abstract representation. The materials provide guidance to support students in creating, connecting, and explaining representational models to abstract concepts. For example, in the "Solve It" section of "Linear and Exponential Relationships," Lesson 1, students create a graph to represent a system of equations and locate the intersection. Prompts state "Ask: How does the intersection of the two lines tell you the cost of each juice and sandwich?," helping connect models to algebraic representation.
Evaluation for 5.4a
Each "Strand Overview" within the Supplemental Guide includes language development and support for all students. For example, the "Quadratic Functions and Modeling Strand Overview" encourages students to use sentence stems to develop their academic mathematical language during the "Try It!" section and utilize word walls to provide visuals for words such as coefficient and constant. The materials provide students with opportunities to develop academic language using visuals and manipulatives. For example, in "Expressions and Equations," Lesson 5, students graph a linear equation (and a quadratic equation) on an XY Coordinate Pegboard, and the teacher guidance states, "point out that in linear, there is the word line, which is why the graph of a linear equation is a line."
Evaluation for 5.4b
Materials include guidance to scaffold, support, and extend students' use of academic vocabulary in context when communicating with peers and educators. For example, "Expressions and Equations," Lesson 3, encourages teachers to review vocabulary, remind students that the root of relation is related, and explain that a relation describes how two sets of numbers are related. To extend their use of vocabulary, guidance encourages students to explain the meaning of relation in their own words. Also, to scaffold materials encourage teachers to "write the following sentence frame to be used during the 'Try It!': In a ___, each element of the ___ is paired with exactly one element of the ___." Each "Strand Overview" within the Supplemental Guide includes language development guidance to scaffold, support, and extend students' use of academic vocabulary when communicating. For example, the "Expressions and Equations Strand Overview" provides guidance on using sentence stems during the "Try It!" sections to scaffold language development, stating, "as students justify the step of solving equations, prompt them to use accurate language."
Evaluation for 5.4c
The "Talk About It" section of each lesson provides guidance to support student discourse using appropriate mathematical language and vocabulary. For example, "Expressions and Equations," Lesson 1, includes embedded guidance to lead the discussion, such as, "Have students identify coefficients in the expression. Ask: What do these mean in the context of the problem?" Materials embed guidance to support student application of appropriate mathematical language and vocabulary in discourse. For example, "Expression and Equations," Lesson 3, encourages teachers to "write the following sentence frame to be used during the 'Try It!': In a ___, each element of the ___ is paired with exactly one element of the ___." Students then practice using that sentence frame when working collaboratively with a partner to solve a problem. The "Try It!" sections provide direct guidance to support student application of appropriate mathematical language. For example, in "Linear and Exponential Relationships," Lesson 5, guidance includes the statement, "Describe the rate of change for the amount of cheese left. Have students write their description."
Evaluation for 5.4d
The materials provide guidance to facilitate mathematical conversations, enabling students to hear and use math language with their peers. For example, in "Descriptive Statistics," Lesson 2, guidance states, "Discuss with students their ideas, including which qualities they think are more important for the line to best fit the data." The materials include sentence frames for discussion in the "Talk About It" section, such as "A line of best fit often has _ number of points on either side of the _." Each lesson includes a "Talk About It" section that provides embedded guidance to facilitate mathematical conversations, enabling students to hear math language in conversation with their peers. For example, "Polynomials," Lesson 9, offers guiding questions to facilitate conversations, such as "How does the coefficient of the squared term affect the model?", "What strategy can you use to build the trinomial rectangle?", and "How can you check your answer?" The materials do not provide prompts for students to critique and refine math language with peers.
Evaluation for 5.4e
Each lesson includes a "Look Out!" section to support and redirect students who provide inaccurate responses. For example, in "Linear and Exponential," Lesson 1, guidance states, "Watch out for students who solve for one variable and not the other. Remind them that the solution to a system of equations must have a value for each variable. Remind them that the solution to this system can be represented by a point on the xy-coordinate plane. The point must have both an x-coordinate and a y-coordinate." The materials do not include embedded guidance to anticipate a variety of student answers, including exemplar responses to questions and tasks.
Evaluation for 5.5a
The "Program Overview" within the Supplemental Guide states that the process standards are incorporated throughout each lesson: "Students apply mathematics to problems, use a problem-solving model, and select tools (manipulatives) with each 'Try It!' activity. As students progress through the step-by-step procedure and answer questions in the 'Talk About It' section, they communicate their ideas and reasoning by creating and using representations, analyzing relationships for connections, and display, explain, and justify their mathematical ideas using precise mathematical language." The materials embed real-world problem-solving scenarios in each lesson to integrate the TEKS process standards. Students solve the problem using multiple representations and communicate their ideas and procedures. For example, in "Descriptive Statistics," Lesson 1, students use high temperatures from two cities to represent and summarize data sets. Students create multiple representations of data and communicate the similarities and differences in their displays.
Evaluation for 5.5b
The "Program Overview" within the Supplemental Guide includes a description of how process standards are incorporated and connected throughout the materials: "Students apply mathematics to problems, use a problem-solving model, and select tools (manipulatives) with each 'Try It!' activity. As students progress through the step-by-step procedure and answer questions in the 'Talk About It' section, they communicate their ideas and reasoning by creating and using representations, analyzing relationships for connections, and display, explain, and justify their mathematical ideas using precise mathematical language." The "Strand Overview" within the Supplemental Guide describes how process standards are incorporated and connected throughout the learning pathways for each strand. For example, in the "Linear and Exponential Strand Overview," guidance states: "Students explore linear and exponential functions to understand relationships and patterns, learning to transform functions and distinguish between them. They develop skills to identify functions, compare properties of linear and exponential relationships, solve systems of equations symbolically, and work with linear inequalities. Hands-on activities provide concrete experiences to support comprehension, emphasizing problem-solving, representation, communication, and connections between algebraic relationships."
Evaluation for 5.5c
Each "Strand Overview" within the Supplemental Guide includes a table that contains the content and process standards covered in each lesson. Every lesson has A1.A-G listed in the process standard column, stating that all standards are covered in each lesson. Guidance states, "Hands-On Standards Math Mini Lessons provides lessons that foster collaboration and communication with and between students. Each lesson engages students to apply their knowledge of problem-solving to real-world situations, as required by the process standards." The "Strand Overview" within the Supplemental Guide includes an overview of how the process standards are incorporated throughout the unit. For example, the "Expressions and Equations Strand Overview" states, "This strand helps students transition from written descriptions to concrete, pictorial, and abstract representations, emphasizing problem-solving, reasoning, and communication . . . Students select appropriate tools and communicate reasoning through symbols, diagrams, graphs, and language."
5.1 Development of Conceptual Understanding
5.1a
Questions and tasks provide opportunities for students to interpret, analyze, and evaluate mathematical concepts and complex, real-world situations.
Questions and tasks provide opportunities for students to interpret, analyze, and evaluate mathematical concepts and complex, real-world situations.
3 out of 3 points
Evaluation for 5.1a
Evaluation for 5.1a
Questions and tasks provide opportunities for students to interpret, analyze, and evaluate mathematical concepts and complex, real-world situations.
3 out of 3 points
5.1b
Questions and tasks provide opportunities for students to create concrete models and representations of mathematical situations.
Questions and tasks provide opportunities for students to create concrete models and representations of mathematical situations.
2 out of 2 points
Evaluation for 5.1b
Evaluation for 5.1b
Questions and tasks provide opportunities for students to create concrete models and representations of mathematical situations.
2 out of 2 points
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
5.2 Development of Fluency
5.2a
Materials provide tasks that are designed to build student automaticity and fluency necessary to complete grade-level mathematical tasks.
Materials provide tasks that are designed to build student automaticity and fluency necessary to complete grade-level mathematical 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 mathematical tasks.
2 out of 2 points
5.2b
Materials provide opportunities for students to practice the application of efficient, flexible, and accurate mathematical procedures throughout learning pathways.
Materials provide opportunities for students to practice the application of efficient, flexible, and accurate mathematical procedures throughout learning pathways.
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 throughout learning pathways.
3 out of 3 points
5.2c
Materials provide opportunities for students to evaluate mathematical representations, models, strategies, and solutions for efficiency, flexibility, and accuracy throughout learning pathways.
Materials provide opportunities for students to evaluate mathematical representations, models, strategies, and solutions for efficiency, flexibility, and accuracy throughout learning pathways.
3 out of 3 points
Evaluation for 5.2c
Evaluation for 5.2c
Materials provide opportunities for students to evaluate mathematical representations, models, strategies, and solutions for efficiency, flexibility, and accuracy throughout learning pathways.
3 out of 3 points
5.2d
Materials contain guidance to support students in selecting the most efficient approaches when solving mathematics problems.
Materials contain guidance to support students in selecting the most efficient approaches when solving mathematics problems.
1 out of 1 points
Evaluation for 5.2d
Evaluation for 5.2d
Materials contain guidance to support students in selecting the most efficient approaches when solving mathematics problems.
1 out of 1 points
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
5.3b
Questions and tasks provide opportunities for students to use concrete models, pictorial representations, and abstract models as required by the TEKS.
Questions and tasks provide opportunities for students to use concrete models, pictorial representations, and abstract models as required by the TEKS.
3 out of 3 points
Evaluation for 5.3b
Evaluation for 5.3b
Questions and tasks provide opportunities for students to use concrete models, pictorial representations, and abstract models as required by the TEKS.
3 out of 3 points
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
5.4 Development of Academic Mathematical Language
5.4a
Materials provide opportunities for students to develop academic mathematical language using visuals, manipulatives, or other language development strategies.
Materials provide opportunities for students to develop academic mathematical language using visuals, manipulatives, or other language development strategies.
1 out of 1 points
Evaluation for 5.4a
Evaluation for 5.4a
Materials provide opportunities for students to develop academic mathematical language using visuals, manipulatives, or other language development strategies.
1 out of 1 points
5.4b
Materials include embedded educator guidance to scaffold, support, and extend students’ use of academic mathematical vocabulary in context when communicating with peers and educators.
Materials include embedded educator guidance to scaffold, support, and extend students’ use of academic mathematical vocabulary in context when communicating with peers and educators.
2 out of 2 points
Evaluation for 5.4b
Evaluation for 5.4b
Materials include embedded educator guidance to scaffold, support, and extend students’ use of academic mathematical vocabulary in context when communicating with peers and educators.
2 out of 2 points
5.4c
Materials include embedded guidance to support student application of appropriate mathematical language and academic vocabulary in discourse.
Materials include embedded guidance to support student application of appropriate mathematical language and academic vocabulary in discourse.
1 out of 1 points
Evaluation for 5.4c
Evaluation for 5.4c
Materials include embedded guidance to support student application of appropriate mathematical language and academic vocabulary in discourse.
1 out of 1 points
5.4d
Materials include embedded guidance to facilitate mathematical conversations allowing students to hear, refine, and use math language with peers.
Materials include embedded guidance to facilitate mathematical conversations allowing students to hear, refine, and use math language with peers.
1 out of 2 points
Evaluation for 5.4d
Evaluation for 5.4d
Materials include embedded guidance to facilitate mathematical conversations allowing students to hear, refine, and use math language with peers.
1 out of 2 points
5.4e
Materials include embedded guidance to anticipate a variety of student answers including exemplar responses to questions and tasks, including guidance to support and/or redirect inaccurate student responses.
Materials include embedded guidance to anticipate a variety of student answers including exemplar responses to questions and tasks, including guidance to support and/or redirect inaccurate student responses.
1 out of 2 points
Evaluation for 5.4e
Evaluation for 5.4e
Materials include embedded guidance to anticipate a variety of student answers including exemplar responses to questions and tasks, including guidance to support and/or redirect inaccurate student responses.
1 out of 2 points
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
5.5b
Materials include a description of how process standards are incorporated and connected throughout the learning pathways.
Materials include a description of how process standards are incorporated and connected throughout the learning pathways.
2 out of 2 points
Evaluation for 5.5b
Evaluation for 5.5b
Materials include a description of how process standards are incorporated and connected throughout the learning pathways.
2 out of 2 points
5.5c
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 5.5c
Evaluation for 5.5c
Materials include an overview of the TEKS process standards incorporated into each lesson.
1 out of 1 points
Rubric Section 6
Productive Struggle
Materials support students in applying disciplinary practices to productive problem-solving, including explaining and revising their thinking.
Total
71% (15 out of 21 points)
Evaluation for 6.1a
Each lesson includes a "Try It!" section designed to allow students to develop conceptual understanding through a real-world problem. The "Program Overview" states, "Students are challenged to think mathematically about a given situation, and they are able to use manipulatives to persevere as they problem solve and make sense of the mathematics." Materials require students to think mathematically, persevere, and make sense of mathematics through multiple opportunities for students to do and discuss math with peers and/or educators. For example, in "Expressions and Equations," Lesson 5, the "More Ideas" section includes guidance: "Have students work in pairs, where one student describes a scenario and the other writes an equation to match it. Together, they make a table of values and graph the equation on graph paper with labeled axes." Each lesson includes "Student Pages" where students solve problems that require manipulatives (Part 1), pictorial representations (Part 2), and algebraic representations (Part 3), which require them to make sense of the mathematics. Each "Student Page" also includes "Challenge!" questions designed to extend their thinking and persevere.
Evaluation for 6.1b
Each lesson incorporates hands-on manipulatives to support students in understanding, explaining, and justifying that there can be multiple ways to solve problems. For example, in "Expressions and Equations," Lesson 3, students solve equations by manipulating Algebra Tiles on an equation mat and transition to solving algebraically, demonstrating an understanding that there can be multiple ways to solve problems. The "Talk About It" section provides questions for the teacher to guide students in explaining different solving approaches, such as "Does it matter on which side of the equation we decide to collect the terms with the variables? Explain." Each lesson incorporates guiding questions to support students in explaining and justifying multiple ways to solve problems. For example, in "Linear and Exponential Relationships," Lesson 1, prompts such as, "Which equation should you use to find the value of the second variable? Does using a different equation affect your answer? How do you know?" support students in understanding, explaining, and justifying multiple ways to solve for the unknown variable. Materials support students in understanding that there can be multiple ways to solve problems and complete tasks. For example, in "Polynomials," Lesson 3, the "Solve It" section of the lesson states: "Multiply the binomials. Ask students to show their work by creating a model with Algeblocks. Then have students sketch the model and record their work." Students must demonstrate an understanding of how to solve the problem both algebraically and by modeling it using manipulatives.
Evaluation for 6.1c
Each lesson's "More Ideas" section provides additional activities to help students make sense of mathematics through opportunities to engage in, write about, and discuss math with their peers. For example, "Expressions and Equations," Lesson 2, provides a group activity where one student writes a scenario to form an algebraic equation, similar to the one in the "Try It!" activity. Another partner models the equation using Algebra Tiles, and the third partner solves the equation using the Algebra Tiles. Students then switch roles and repeat, providing opportunities for each student to write, do, and discuss math. Each lesson includes a "Try It!" activity that requires students to make sense of the mathematics through multiple opportunities to do, write about, and discuss math with peers and educators. For example, in "Quadratic Functions and Modeling," Lesson 3, students work to compare two quadratic functions using different representations through a hands-on exploration using pegboards. Guiding questions facilitate conversation with specific details to "have students write their observations on a sheet of paper."
Evaluation for 6.2a
Materials support educators in guiding students to share their problem-solving approaches, including explanations, arguments, justifications, and multiple points of entry (e.g., "Solve Inequalities," Lesson 4, encourages students to use Algebra Tiles to model a linear inequality representing a real-world scenario, while simultaneously solving the inequality using algebraic methods, which allows multiple points of entry to the content). The suggested teacher questions throughout the "Try It!" activity provide students opportunities to explain, "What inequality symbol should you use to compare the two services?" and justify, "How did you know how many green tiles and yellow tiles to use?" their thinking. Educators guide students in using mathematical reasoning to make an argument when asking the following question: "How should Anita decide which streaming service to use?" The "Talk About It" and "Solve It" sections support educators in guiding students to share their problem-solving approaches by providing questions for teachers to ask students, thereby developing an understanding of the concept, and then having students demonstrate what they have learned. Students may summarize the lesson concept through representation or writing, or extend the skill through a new variation on the problem. For example, in "Polynomials," Lesson 9, guiding questions to provide explanations and justifications state, "How does the squared term coefficient affect the model? What strategy can you use to build the trinomial rectangle? How can you check your answer?" Then, in the "Solve It" section, teachers are to reread the problem, have students factor the trinomial, show their work, create a model, sketch it, and record it. The materials do not include questions or prompts that educators can use to guide students in reflecting on their problem-solving approaches.
Evaluation for 6.2b
Each lesson includes a "Look Out!" section that includes prompts and guidance to support educators in providing explanatory feedback based on anticipated misconceptions. For example, in "Polynomials," Lesson 9 states, "Students may have difficulty understanding that the rectangle formed can be oriented one of two ways. Have students model a problem using Algeblocks and the Algeblock Quadrant Mat. Have students rotate the mat to see that the orientation does not change the answer. Review the commutative property with whole numbers so that students remember that the factors can be written in either order." The materials do not provide prompts or questions for offering explanatory feedback based on specific student responses; instead, only general misconceptions are addressed.
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
6.1b
Materials support students in understanding, explaining, and justifying that there can be multiple ways to solve problems and complete tasks.
Materials support students in understanding, explaining, and justifying that there can be multiple ways to solve problems and complete tasks.
3 out of 3 points
Evaluation for 6.1b
Evaluation for 6.1b
Materials support students in understanding, explaining, and justifying that there can be multiple ways to solve problems and complete tasks.
3 out of 3 points
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/or educators.
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/or educators.
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/or educators.
3 out of 3 points
6.2 Facilitating Productive Struggle
6.2a
Materials support educators in guiding students to share and reflect on their problem-solving approaches, including explanations, arguments, justifications, and multiple points of entry.
Materials support educators in guiding students to share and reflect on their problem-solving approaches, including explanations, arguments, justifications, and multiple points of entry.
4 out of 8 points
Evaluation for 6.2a
Evaluation for 6.2a
Materials support educators in guiding students to share and reflect on their problem-solving approaches, including explanations, arguments, justifications, and multiple points of entry.
4 out of 8 points
6.2b
Materials include prompts and guidance to support educators in providing explanatory feedback based on student responses and anticipated misconceptions.
Materials include prompts and guidance to support educators in providing explanatory feedback based on student responses and anticipated misconceptions.
2 out of 4 points
Evaluation for 6.2b
Evaluation for 6.2b
Materials include prompts and guidance to support educators in providing explanatory feedback based on student responses and anticipated misconceptions.
2 out of 4 points