Progressions by Alba Math Grade 2

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

The "Snapshot" table functions as a scope and sequence. This table includes a "Content Standards" section, which details the Texas Essential Knowledge and Skills (TEKS) that each unit covers, thus fulfilling the requirement that the scope and sequence outlines the TEKS taught in the course. Additionally, each unit's "Snapshot" table provides a "Suggested Instructional Days" section. This section offers teachers guidance on instructional pacing to ensure that they cover all content within the instructional year. The "Program Unit Map" resource functions as a scope and sequence by providing an overview of each unit's topics and yearly progression. The map details how the materials introduce topics such as addition and subtraction, as well as how such concepts build upon grade 1 material. The map also details the sequence of concepts such as place value, geometry, and fractions during the instructional year. The "Unit Overview" resource functions as a detailed scope and sequence for each unit. The "Content Summary" section of the overview outlines each unit's TEKS and English Language Proficiency Standards (ELPS). This section also details each unit's content, providing a clear sequence of instruction.

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

The materials include a "Snapshot" table at the beginning of each unit. This table features a "Suggested Instructional Days" section that outlines each unit's suggested pacing. For example, the materials suggest spending 18–20 days on Unit 1: Addition and Subtraction, Part 1 and 33–37 days on Unit 3: Place Value. These pacing suggestions allow teachers to effectively implement the materials and allocate appropriate time for each unit. While the document does not explicitly provide pacing for various instructional calendars, it advises teachers to "consider the number of days on your instructional calendar, and adjust as needed," indicating an awareness of the need for flexibility. The "Program Unit Map" gives teachers an overview of the units throughout the year and the suggested number of days for each unit. This overview helps teachers plan their instruction by visualizing the progression of content, ensuring that they cover all necessary material within the school year. This overview advises teachers to adjust their schedules based on their specific instructional calendar. The materials suggest spending 18–22 instructional days on "Addition and Subtraction, Part 1," and 33–42 days on "Place Value." The materials thus provide teachers with an overview of the entire year and a suggested timeframe for each unit, supporting effective implementation.

Evaluation for 1.1c
Materials include an explanation for the rationale of unit order as well as how concepts to be learned connect throughout the course.

The "Program Unit Map" document explains the rationale for unit order and how concepts connect throughout the year. For example, the document states that Unit 1: Addition and Subtraction, Part 1 begins with addition and subtraction concepts. In this unit, students first focus on math facts and then add and subtract within 120, bridging grade 1 concepts to grade 2 materials. The document also states that "combining equal groups helps set the stage for Unit 3: Place Value." The document further explains that the materials treat each grade level's math concepts as interconnected, rather than approaching concepts as isolated. Unit 1: Addition and Subtraction, Part 1 includes a "Content Summary" section, which provides a rationale for the unit order and an explanation of how concepts to be learned connect throughout the course. For example, in grade 1, students work on applying basic fact strategies. By the end of grade 2, students are expected to know their addition and subtraction facts within 20 with automaticity. Students build this skill from the application and generalization of fact strategies. For example, students look for patterns when adding or subtracting ten from a number. Once students look for patterns and make generalizations, they play fluency games to practice these strategies, eventually developing automaticity. While this unit largely focuses on individual math facts, students continue working towards automaticity in Unit 6: Addition and Subtraction, Part 2. The "Program Unit Map" explains how units are sequenced to build upon one another. For example, the "Place Value Progression—Grade 2 Activity Map" explains that the activities in the "Concept Development" section are numbered to show their suggested teaching order. This order ensures that students progress through the content in a sequence that is research-based and that builds students' conceptual understanding over time.

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

Each unit in the materials features a custom "Unit-at-a-Glance" template that can be used for mapping out each unit's central ideas, recording historical data, and analyzing instructional implications. The materials provide protocols with corresponding guidance for unit and lesson internalization. The materials provide a "Lesson Internalization" template that teachers can use while planning individual lessons. The materials suggest pairing this template with the "Suggested Lesson Component Timing" section, which allows teachers to plan lessons in conjunction with timing suggestions. Such resources demonstrate a structured approach to lesson planning and preparation. The materials include a "Unit Overview" section within each unit, which provides a deeper look into the content that the unit addresses. This section helps teachers plan their lessons. The overview lists the standards aligned to the "Scaffold Forward" lessons and highlights each unit's academic vocabulary.

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

The materials include guidance for district mathematics leaders, instructional coaches, and teachers on using the "Year-at-a-Glance," "Unit-at-a-Glance," and "Lesson Internalization" templates. The materials include recommendations for leaders to utilize a "Goal-Action Planning Template" as a resource for addressing action steps, possible obstacles, and methods for overcoming obstacles. Leaders can reference an "Instructional Look Fors Observation Form," which helps ensure the materials are faithfully implemented. Leaders can integrate the materials in a professional learning community. Leaders can also set SMART goals, which observations and reflections can help support. For example, the "Instructional Look Fors Observation Form" allows for an initial observation in which instructional leaders can help determine a teacher's area of focus.

Evaluation for 1.2a
Materials include comprehensive unit overviews that provide the background content knowledge and academic vocabulary necessary to effectively teach the concepts in the unit.

The "Grade 2 Content Map" in Unit 1: Addition and Subtraction, Part 1 provides an overview of the unit (including its central goal), which helps students work toward automaticity concerning addition and subtraction facts. While the document includes a "Vocabulary/Academic Language" section, it does not provide a comprehensive overview of academic vocabulary at the beginning of the unit. Instead, the unit lists terms that appear in the standards and suggests creating a word wall. Unit 1: Addition and Subtraction, Part 1 includes "Content Summary" and "Vocabulary/Academic Language" sections, which provide the background content knowledge necessary to effectively teach the unit's concepts. For example, in the "Content Summary" section, teachers can note that students in grade 1 worked on applying basic math fact strategies. In order to learn their addition and subtraction facts with automaticity in grade 2, students will need to develop and build upon the skills they learned in grade 1. In Unit 2: Multiplication and Division, the materials provide a "Content Map" for each unit, which provides a "Responding to Student Performance" table. This resource includes a pre-assessment that teachers can use to assess what students already know about the unit's standards based on real-life experiences. Students will continue to develop these skills throughout the unit.

Evaluation for 1.2b
Materials contain supports for families in both Spanish and English for each unit with suggestions on supporting the progress of their student.

Unit 1: Addition and Subtraction, Part 1 includes a "Family Letter" resource, which provides an overview of the unit and suggests activities that students can practice at home, such as using crayons to solve problems and playing a "Subtraction Bump" game. The "Family Support" tab includes a "Family Letter" in English and Spanish. The letter provides suggestions to families on supporting the progress of their child. These letters are available for each unit of the teacher guide, ensuring that families are supported in their child's learning throughout the school year. The "Family Letters" provide identical information and suggestions in Spanish, ensuring support for Spanish-speaking families.

Evaluation for 1.3a
Materials include comprehensive, structured, detailed lesson plans that include daily objectives, questions, tasks, materials, and instructional assessments required to meet the content and language standards of the lesson (aligned with the TEKS and the ELPS).

Unit 3: Place Value includes a lesson titled "Small Ten Frames, Part 1." The lesson's objective reads, "Students will represent numbers up to 120 using pictorial models and expanded and standard forms." The lesson aligns with TEKS 1.2(C) and 1.3(A), as well as ELPS standards 1(A) and 1(E). The lesson includes a list of required materials and an example of a question to check for student understanding. The materials direct the teacher to engage students in a think-pair-share routine by asking them how they know they represented the number 71. The "Lesson Suggestions" section helps students distinguish sound patterns when saying number names. For example, the section emphasizes that students repeat "30" for all numbers between 30 and 40. This emphasis allows students to focus on the difference between saying "30" and "13," supporting the ELPS language standards that the lesson addresses. The "Small Ten Frames" exit ticket prompts students to fill in the blanks for each number sentence. While students complete this work, teachers look for students who are still confusing the value of each digit. Unit 4: Geometry includes a "My Target Shape" lesson. The objective of this lesson reads, "Students will explore a variety of 2D shapes and explain their similarities and differences." This lesson lists TEKS 2.8(C), which requires students to classify and sort polygons with 12 or fewer sides, including identifying the number of sides and vertices. The lesson also lists ELPS 1(B): "Demonstrate an understanding of content-area vocabulary when heard during formal and informal classroom interactions by responding with gestures, images, orally, or in writing." Finally, the lesson lists ELPS 2(B): "Speak using content-area vocabulary during formal and informal classroom interactions to demonstrate acquisition of new words and high frequency words." The lesson's required materials include a book titled Tangled and one set of two-dimensional shape cutouts per group of students. To promote the use of language to meet language objectives, the teacher attaches formal vocabulary to the descriptions that students generate. For example, a student says, "This triangle has a big corner." The teacher responds by saying, "Yes, this angle is larger than the others." The lesson also includes questions to check for student understanding. For example, the teacher asks students to explain how certain shapes look like their target shape. The lesson does not explain how student mastery of the content will be assessed.

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

The "Grasshopper Races" lesson in Unit 1 lists the teacher and student materials necessary to deliver the lesson, which include "sticky notes" and "index cards." The "Overview" section of Unit 1: Addition and Subtraction, Part 1 lists each lesson's suggested instructional days. Teachers should allow approximately 18–20 days for this unit. In Unit 3: Place Value, a lesson on introducing base ten blocks lists the teacher and student materials necessary to effectively deliver the lesson. In grade 2, the "Implementation Support" section provides recommendations for the suggesting timing of each lesson component.

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

The materials provide a "Content Map" resource that includes a "Scaffold Back" section. The activities in this section are intended to fill in knowledge gaps before the materials cover new content. Unit pre-assessments help determine these student needs. For example, Unit 5: Fractions includes a lesson titled "Cut It in Half: Pizza Fractions," which is a "Scaffold Back" lesson. Students partition circles into halves, describing the parts using words. Students describe what the shape looked like as a whole. The materials introduce the concept of "half" using examples and non-examples of pizza slices or parts. Teachers can differentiate instruction by selecting appropriate materials and activities for students who need additional practice. Among other units, Unit 9: Measurement provides "Scaffold Forward" content maps. Such resources include activities and ideas for extending content for students who are ready. For example, in the "Scaffold Forward" activity titled "Centimeters Versus Meters," students progress from concrete to representational to abstract concepts. The activities in the "Scaffold Forward" section help streamline the lesson planning process for teachers, reducing their guesswork concerning enrichment tasks and offering students extended practice opportunities. The materials also provide "Responding to Student Performance" suggestions, which guide teachers on selecting lessons for students who struggle with specific areas that unit assessments evaluate.

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

The unit assessment for grade 2, Unit 1 is a pretest that responds to student performance. The materials demonstrate varied assessment tasks through activities such as Unit 5's "Fraction Sort," in which students identify examples and non-examples of halves, fourths, and eighths. This activity moves beyond simple recall, requiring students' classification and reasoning. Teachers can access the "Program Overview" tab within the digital teacher guide and locate the "Program Components" section, which describes the materials (including evaluations) in each unit. These evaluations vary in type and complexity level, working together to provide a complete picture of a student's learning. The materials position diagnostic assessments before instruction to determine students' existing knowledge, skills, and abilities.

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

Unit 1 includes prompts that are aligned to assessed standards. These prompts help teachers check for understanding, providing students with a descriptive score based on their performance. The materials also including a recording sheet, which encourages teachers to ask students questions as well as track student progress, responses, and data. The materials guide educators to the "Program Components" section, which includes the definition and intended purpose of each of the unit's instructional assessments. For example, the "Program Components" section in the "Program Overview" includes diagnostic, formative, and summative assessments. The section also provides examples of how to utilize these assessment types. Diagnostic assessments include unit pre-assessments. Formative assessments include exit tickets, recording sheets, and teacher observations. Summative assessments include unit and end-of-year fluency assessments. At the end of each unit, the materials include the definition of summative assessments and their purpose of evaluating learning, skill acquisition, and achievement. Shorter units culminate in a unit assessment, while longer units contain multiple unit assessments. These assessments include prompts that are aligned to the content that students learn within the unit. The materials provide a rubric to guide teachers in scoring student responses to each prompt. Teachers can find assessments at designated points throughout each unit, which focus on the skills students have learned up until that point.

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

Unit 5: Fractions includes an "Overview" section, which suggests spending approximately 9–12 days on the unit. The "Content Table" resource also includes a "Suggested Days" section, which offers teachers clear pacing guidance for each lesson. The pre-assessment for Unit 3: Place Value provides insight into students' knowledge and skills. The materials include an "Assessment Instructions" section, which provides steps that the teacher follows to conduct the assessment. The "Responding to Student Performance" section indicates that if students struggle with the first four prompts, then teachers should assign them the lesson titled "Vacation Time." The unit assessment for Unit 8: Time lists the assessed standards, materials needed, and three prompts that teachers should give to students. These prompts ensure the assessment's consistent and accurate administration.

Evaluation for 2.1d
Diagnostic, formative, and summative assessments are aligned to the TEKS and objectives of the course, unit, or lesson.

Summative assessments, such as the "End-of-Year Fluency Assessment" in the grade 2 teacher guide, provide data to the educator regarding students' mastery of skills and content in order to evaluate their learning. Such assessments include the assessed standard next to each prompt, thus aligning with the rubric. A table in Unit 5: Fractions clearly maps each lesson. The unit assessment and pre-assessment for this unit align with the TEKS, demonstrating consistent alignment across all assessment types and instructional objectives. Diagnostic assessments, such as the pre-assessment for Unit 1: Addition and Subtraction, Part 1, include an "Assessed Standards" section, which identifies the TEKS covered in the unit. The materials list the TEKS number next to the prompt.

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

Unit 5: Fractions includes a "Content Map" section, which outlines a clear learning sequence. The unit progresses from foundational partitioning skills (1.6C, 1.6G) to identifying fractional parts (1.6H). The unit then progresses to abstract concepts such as the relationship between parts and the whole. Activities such as "Counting Beyond a Whole" require students to use concrete models to count fractional parts beyond the whole. This activity represents a higher level of complexity than simple identification, building towards a deeper understanding of fractions. Grade 2, Unit 2: Multiplication and Division includes a summative assessment. In Prompt 1, which aligns with TEKS 2.6(A), students must model a problem, correctly answer it, and describe a situation using a sentence stem. To apply Bloom's taxonomy, students must understand what the story problem is asking and apply the correct strategy (as indicated in the rubric). The pre-assessment for Unit 3: Place Value assesses standards that will be reviewed in the unit. The pre-assessment also includes teacher prompts to assess students at different levels of complexity.

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

Units include a pre-assessment and post-assessment with corresponding student and class trackers. Such assessments provide structured tools and guidance for interpreting student performance and identifying instructional needs, fully aligning with rubric expectations for detailed scoring and interpretation support. In grade 2, the materials include a "Program Overview" tab. Here, teachers can access the "Unit Assessments" section to learn about instructional assessments and scoring information. For example, unit pre-assessments include prompts that introduce the performance task to students and provide guidance to teachers in the form of a scoring rubric with proficiency levels. The materials also provide guidance helping teachers determine each student's proficiency level based on their performance. In Unit 2, the materials direct teachers to the unit pre-assessment and provide a class tracker for each prompt. This tracker allows the teacher to interpret student data through an item analysis to examine student performance on specific skills. An example includes Prompt 1: Model and Solve Multiplication Situations 2.6(A) in the pre-assessment for Unit 2.

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

Units provide explicit guidance for reteaching content based on assessment results. For example, in Unit 7, teachers can link specific prompts to targeted lessons such as "Slice Into Data" and "Cap-tivating Graphs" (see the "Responding to Student Performance" section of Unit 7). The materials thus align with rubric expectations for responsive instructional planning. Teachers can reference the "Program Overview" tab of the teacher guide to access the "Lesson Plans and Progress Checks" section. The "Fractions Unit Pre-Assessment" visual contains class tracker instructions, which explain that teachers can use the class tracker to inform small group decisions. The "Responding to Student Performance" suggestions recommend activities that teachers can use to fill in student knowledge gaps that assessments have revealed. The progress-monitoring tools in Unit 4: Geometry include a unit pre-assessment, which provides class tracker instructions and a "Responding to Student Performance" section. Such resources allow teachers to group students based on assessment results. They also provide targeted activities to address specific skills. For example, if students struggle with Prompt 1, teachers can assign them the lessons titled "Circles and Triangles" and "Rectangles, Rhombuses, and Squares."

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.

Unit 3: Place Value includes a class tracker for assessments, which allows the teacher to track class progress from student to student. This tracker includes various descriptors to assess student performance. Units include a student-facing tracker and a teacher-facing class tracker, enabling both students and teachers to monitor progress and growth over time. The materials thus align with rubric expectations for dual tracking tools. In grade 2, Unit 4: Geometry, the materials include a student tracker, which allows students to track their progress and growth on the pre-assessment and unit assessment. The tracker thus allows students to take ownership of their learning journey. In Unit 4: Geometry, the unit assessment includes a class tracker that allows teachers to monitor the progress and growth of individual students and the whole class. Teachers enter student names in either the "Proficient," "Developing," or "Emerging" category for each prompt of the unit assessment.

Evaluation for 3.1a
Materials include teacher guidance for differentiated instruction, activities, and paired (scaffolded) lessons for students who have not yet reached proficiency on grade-level content and skills.

Grade 2, Unit 3 includes a pre-unit assessment titled "Place Value." The materials include language indicating that if students struggle with Prompt 2, "Representing Numbers," they should engage with the lesson "Small Ten Frames, Part 1." Grade 2, Unit 1: Addition and Subtraction, Part 1 includes a pre-unit assessment. Lessons include "Scaffold Back" opportunities that differentiate students' needs. For example, if students struggle with Prompt 7 of the pre-assessment, "Representing Numbers Using Standard Form," the materials recommend that students engage with the lesson "Filling in the 100 Chart." In grade 2, the "Program Overview" includes a "Learning Progressions" section, which explains that "Scaffold Back" lessons allow teachers to differentiate students' needs. Teachers can use these lessons to fill in student knowledge gaps that the pre-assessment revealed.

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

In Unit 4: Geometry, the "Vocabulary/Academic Language" section repeatedly uses anchor charts across lessons such as "Classifying Polygons" and "Spheres, Cones, and Cylinders; Oh My!" The materials provide embedded supports for unfamiliar academic language using student-friendly definitions, visual aids, and structured opportunities to use content-specific vocabulary in context. Grade 2, Unit 5: Fractions includes a "Vocabulary/Academic Language" section, which highlights how using vocabulary words bridges students' understanding from informal to formal language. The materials guide educators to create word walls containing the vocabulary words. Each word wall entry includes a student-friendly definition and a picture. Grade 2, Unit 7: Data Analysis contains a "Sentence Stems for Language Development" section. This section includes sentence stems that allow students to use "routine language for classroom communication to expand and internalize vocabulary associated with math concepts."

Evaluation for 3.1c
Materials include teacher guidance for differentiated instruction, enrichment, and extension activities for students who have demonstrated proficiency in grade-level content and skill.

In Unit 4: Geometry, "Scaffold Forward" lessons such as "Composing Polygons" and "Wrapping Presents" offer enrichment and extension opportunities for students who have demonstrated proficiency. The lessons guide teachers to extend learning via more complex tasks and deeper conceptual exploration. In Unit 10, "Scaffold Forward" lessons such as "Dollar Store Dilemma" and "Producing Lemonade" provide enrichment and extension opportunities for proficient students. These lessons guide students to apply financial concepts in real-world simulations that require deeper reasoning and decision-making. In the "Learning Progressions" section of the "Program Overview," the materials explain that the "Scaffold Forward" lessons provide opportunities for extending students' skills. The "Scaffold Forward" section includes activities and ideas for extending content for students who are ready.

Evaluation for 3.2a
Materials include explicit (direct) prompts and guidance to support the teacher in modeling and explaining the concept(s) to be learned.

Grade 2, Unit 2: Multiplication and Division includes a a lesson titled "Going to the Market." The lesson includes prompts to support the teacher in explaining the concepts that students will learn. Teachers model the lesson's concepts by using sentence stems from the "Lesson Suggestions" section. For example, in Prompt 8 of the lesson's facilitation, teachers model strategies such as repeated addition and skip counting. Prompt 3 of the lesson's facilitation also supports teachers. In this prompt, teachers demonstrate how to engage in the "Five-to-Jive" protocol with a volunteer. In Unit 4: Geometry, lessons such as "Rectangles, Rhombuses, and Squares" and "What Is a Cylinder?" include explicit teacher prompts, anchor chart models, and think-aloud routines that guide teachers in modeling and explaining geometric concepts. Such materials satisfy Guidance 3.2a by providing structured support for concept development and vocabulary acquisition. In the Unit 10 lesson "Penny’s Prices," the materials prompt the teacher to model coin counting using a work mat. The teacher explains the use of cent and dollar notation with visual anchor charts. This inclusion aligns with Guidance 3.2a by providing explicit modeling and scripted explanations that support student understanding of monetary values.

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

In Unit 10, lessons such as "Borrowing, Lending, and Learning" and "PFL Four Corners" incorporate read-alouds, anchor charts, partner discussions, and movement-based activities. Such inclusions align with Guidance 3.2b by guiding teachers to use multiple instructional approaches, including direct instruction, collaborative learning, and real-world applications. In Unit 4: Geometry, lessons such as "The Shape Shop" and "Geometry Circuit" incorporate direct instruction, hands-on exploration, collaborative learning, and real-world connections. Such inclusions align with Guidance 3.2b by offering teachers guidance on delivering lessons through multiple instructional approaches that support diverse learners. Unit 4: Geometry also includes a lesson titled "Shape Sorting." This lesson includes collaborative group work in which students sort shapes and explain their reasoning for sorting the shapes. The lesson utilizes a think-pair-share routine to determine if Shape 13 should be categorized as a polygon. Teachers use chart paper to create an anchor chart for the vocabulary word polygons. Students complete a "Shape Sorting" exit ticket at the end of the lesson.

Evaluation for 3.2c
Materials support multiple types of practice (e.g., guided, independent, collaborative) and include guidance for teachers and recommended structures (e.g., whole group, small group, individual) to support effective implementation.

Unit 1: Addition and Subtraction, Part 1 includes a lesson titled "Four in a Row," which provides various materials to support the lesson's implementation. Step 1 of the lesson's facilitation provides teachers with guidance on modeling oral directions to a game. The lesson includes collaborative practice, as Player A and Player B take turns determining the sum or difference of various numbers. Bullet 2 of the "Lesson Suggestions" section includes guidance for teachers on recommended structures. Bullet 1 ensures that teachers support the lesson's effective implementation by "providing students with basic facts practice." In grade 2, Unit 8, a lesson titled "Rolling Minutes" supports guided, collaborative, and independent practice. The materials include workstation instructions for problem-solving practice, ensuring the lesson's effective implementation. In Unit 10, lessons such as "Money Circuit" and "Great Coin Count Off" provide guided, independent, and collaborative practice. These lessons provide clear teacher facilitation notes and structures for whole group, small group, and partner work.

Evaluation for 3.3a
Materials include teacher guidance on providing linguistic accommodations for various levels of language proficiency [as defined by the English Language Proficiency Standards (ELPS)], which are designed to engage students in using increasingly more academic language.

In the "Multilingual Supports" section, the program provides leveled sentence stems in both English and Spanish for beginner, intermediate, and advanced students across all units. The materials thus offer differentiated linguistic accommodations for speaking and writing that are aligned to students’ language proficiency levels. In Unit 9: Measurement, the lesson "Inch Upon Inch" includes sentence stems such as "To measure the ___, first we ___" and "I predict the ___ will equal ___ inch tiles because ___." Such sentence stems support students at various levels of English proficiency in expressing mathematical thinking, both orally and in writing. In grade 2, the materials provide "Multilingual Supports" and "Unit Planning" documents. These documents help teachers plan accommodations and supports based on class and student needs for each unit. The documents provide an opportunity to reflect on students' individual needs at the beginner, intermediate, and advanced levels of language proficiency. The documents also help teachers plan accommodations for speaking, writing, reading, and listening, ultimately developing students' language proficiency.

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

The "ELPS Connections" section states that students will use visual, contextual, and linguistic supports that will enhance their understanding of multiplication and division. The section also states that students will read and comprehend story problems requiring multiplication and division, such as in the "Going to the Market, Part 1" lesson. The "Multilingual Supports" section includes guidance for bilingual and dual language programs. Such guidance includes strategies such as using read-alouds in both languages, leveraging cognates, and planning metalinguistic transfer, providing clear and actionable implementation support for bilingual and ESL instructional models. Unit 9: Measurement includes a "Unit Overview" section. This section includes ELPS-aligned objectives and structured opportunities for oral language development, providing clear guidance for implementation in bilingual and ESL instructional settings. The materials include an "Additional Suggested Program-Level Supports" section within the "Multilingual Supports" resource. This section includes information for addressing both bilingual and dual language program implementation. For example, in grade 2, the "Linguistic Considerations" section of each unit provides items that teachers should consider when engaging students in the unit's lessons. This resource provides teachers with guidance for effective implementation and practical tips for scaffolding instruction.

Evaluation for 3.3c
Materials include embedded guidance for teachers to support emergent bilingual students in developing academic vocabulary, increasing comprehension, building background knowledge, and making cross-linguistic connections through oral and written discourse.

The "Multilingual Supports" section embeds academic language development through vocabulary cards that include visuals, gestures, student-friendly definitions, structured sentence stems, and explicit linguistic considerations for each unit. The materials thus support students' oral and written discourse and comprehension. Unit 9: Measurement includes the lesson "What’s My Area?" This lesson includes a "Vocabulary" section, which provides sentence stems that support students' use of academic language. Such stems allow teachers to explicitly teach math-specific terms such as area, length, and unit. The stems prompt students to use these terms in context through structured discourse and writing. Unit 4: Geometry includes a lesson on classifying 2D and 3D figures. The materials focus multilingual students’ attention on the cognates on each "Geometry Circuit" poster, enhancing cross-linguistic connections. The materials encourage students to "use the anchor charts from previous lessons to help with shape identification and classification when reading the name of each shape on each poster." The materials also note that "writing the attributes or drawing a picture supports multilingual students when reading and writing about the shapes and solids." In Step 1 of the lesson's facilitation, students complete a geometry circuit to review previous shapes and solids from the unit. Step 2 guides students to practice new vocabulary, engaging them in a think-pair-share routine by asking the following: "What is your favorite shape or solid we learned about during this unit, and why?" This question helps develop students' comprehension and oral discourse. It also requires students to use their background knowledge about 2D and 3D shapes.

Evaluation for 3.3d
If designed for dual language immersion (DLI) programs, materials include resources that outline opportunities to address metalinguistic transfer from English to the partner language.

This guidance is not applicable to the product.

Evaluation for 4.1a
Practice opportunities over the course of a lesson and/or unit (including instructional assessments) require students to demonstrate depth of understanding aligned to the TEKS.

In grade 2, Unit 2: Multiplication and Division, the "Content Map" resource states that the unit assesses student mastery of the following TEKS: 2.4(B), 2.6(A), 2.6(B), and 2.7(A). The assessment for Unit 2 includes a variety of questions to promote students' deeper thinking. The unit's question contexts and stories enable creating an array as a model. The materials require students to describe multiplication situations. The "Activity Map" for Unit 2: Multiplication and Division includes a "Sentence Stems for Language Development" section. This section informs the educator that using sentence stems allows students to use routine language for classroom communication, thus enabling students to expand and internalize the vocabulary associated with complex math concepts.

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

The "Fractions Content Map" outlines a clear increase in rigor throughout the unit. Students progress from partitioning 2D figures (1.6C) to identifying halves and fourths (1.6H) to explaining foundational fraction concepts (2.3B, 2.3C). This progression systematically leads to students' grade-level proficiency. The unit's design scaffolds learning from concrete partitioning activities to more abstract explorations of fraction concepts, ensuring that questions and tasks progressively increase in complexity. In a Unit 3 lesson titled "What Do You See, Part 2," students represent quantities using base ten blocks, expanded form, and standard form, explaining how these models are related to one another. Students utilize pictorial models to interpret the value of the base ten blocks, represent numbers in word form, and utilize expanded and standard forms. These tasks progressively increase in rigor. In Unit 1: Addition and Subtraction, Part 1, the "Boxes and Crates, Part 2" lesson requires students to solve change-unknown problems and part-part-whole problems. Students explain and write about how they solved the problems. Students then compare and contrast how the scenarios in the lesson are similar and different. The learning progression focuses on relationships between different numbers and why certain strategies are more efficient than others.

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

The "Content Summary" section of the "Unit Overview" describes how students use grade 1 graphing skills to interpret pictographs and bar graphs with intervals. The materials thus explicitly connect foundational data concepts to more complex representations, aligning with rubric expectations for conceptual coherence. Grade 2, Unit 4: Geometry includes a lesson on sorting solids. The lesson includes a "Lesson Suggestions" section that describes connections to previous learning. This section helps students understand connections between concepts. For example, Bullet 5 states that teachers should use the lesson "as a formative assessment to determine students' knowledge about the solids from throughout the unit." The materials include a "Program Overview" tab, which provides a "Unit Rationale Map." The second paragraph of this document describes how Unit 4: Geometry and Unit 5: Fractions connect to reinforce learning and introduce new topics: "Students examine Unit 4: Geometry, then move to Unit 5: Fractions, where they use their spatial reasoning to partition 2D figures." In grade 2, the materials include daily energizers that feature daily prompts. According to the materials, these resources "can be used to keep students thinking creatively about the math concepts they are learning." The resources can also be used as a "method of spiraling back or using spaced retrieval for previously learned concepts." The energizers and prompts are designed to engage students in brief conversations, allowing students to share ideas and learn from one other. The "Overview" document explains how to facilitate these conversations in the classroom.

Evaluation for 4.2b
Materials demonstrate coherence across units by connecting the content and language learned in previous courses/grade levels and what will be learned in future courses/grade levels to the content to be learned in the current course/grade level.

In grade 2, Unit 2's "Scaffold Back" lesson, students use their prior knowledge of the grade 1 TEKS in relation to coin identification. Students share what they know about coins. Each student's prior knowledge of coins allows them to improve their understanding of money concepts in grade 2. Teachers can reference the "Content Map" resource to understand how the content to be learned in future grade levels connects to the content to be learned in the current grade level. For example, the goal of Unit 6 is for "students to become fluent with their addition and subtraction facts within 20. Students also represent and solve problems of all types, along with multistep problems, within 1,000." The materials further state that "the goal of grade 2 is to develop strategies that use place value and properties of operations, while representing and solving contextual problems. The work students do in grade 2 prepares them for solving similar problems with fluency in grade 3." For example, in grade 2, the "Vocabulary/Academic Language" section of the "Addition and Subtraction, Part 2" document indicates that vocabulary terms in the materials also appear in the standards. The materials state that teachers should use this vocabulary during instruction to help "bridge students' understanding from informal to formal language."

Evaluation for 4.2c
Materials demonstrate coherence at the lesson level by connecting students' prior knowledge of concepts and procedures from the current and prior grade level(s) to new mathematical knowledge and skills..

Lessons such as "Vacation Time," "Slice Into Data," and "Walk-a-Thon Laps" build on students' prior knowledge of tally marks and picture graphs as they learn to interpret bar graphs with intervals. The materials use consistent routines and sentence stems to connect current and prior grade-level concepts and procedures, aligning with rubric expectations for lesson-level coherence. In a Unit 8 lesson on time, students learn to distinguish between ante meridiem (a.m.) and post meridiem (p.m.). Students share what they have learned so far about clocks and time, connecting their new math knowledge of time to different parts of the day. In a grade 2, Unit 8 lesson on approximating time on an analog clock, students make observations concerning the number that an analog clock's hour hand represents. Students then observe the hour hand's placement halfway between two numbers. Students discuss and make predictions on telling time to the half hour. Meanwhile, teachers provide scaffolding questions such as "How do you read the time on Card C?" and "How can you use the hour hand to approximate the time?" In grade 2, Unit 8, the "Content Summary" section lists concepts that students were introduced to in grade 1, such as clocks and their function. Grade 2 extends students' knowledge by focusing on reading and writing time. Students use the strategy of skip counting by fives and then ones to determine the minutes that the clock displays.

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

The grade 2, Unit 5 "Scaffold Back" lesson allows students to apply their knowledge of equal parts and partitioning figures to identify halves, fourths, and eighths in grade 2. The unit incorporates spiraled review through prior unit workstations, fluency-building activities, and daily energizers (spiral and interleaved practice opportunities). Such inclusions provide students with repeated exposure to previously learned skills and concepts across lessons and units, as required by the rubric. In grade 2, Unit 8, students participate in a lesson titled "Clock Riddles." The students engage in a think-pair-share routine to discuss what they have learned so far about the concept of time. The lesson contains the key "W," which indicates that "the lesson can be transitioned into a workstation that allows for spiraled review and practice throughout the year." Grade 2, Unit 10: Money and Personal Finance includes a lesson on determining the total value of coins. The materials provide students with retrieval opportunities through previously learned concepts, such as counting coins while playing a game called "Lemonade Sales Spin." Previously, the lesson "What's in My Piggy Bank?" required students to identify coins and share their observations. Now, students revisit the concept of coins by writing the names of coins. This practice allows students to see the "whole picture" of identifying, counting, and writing about coins. The "Money and Personal Financial Literacy Overview" document includes a "Spiral and Interleaved Practice Opportunities" section, which explains that "the daily energizers serve as a spiraled review or spaced retrieval opportunity throughout the program."

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

Activities such as "Data Detectives" and "Same Data, Different Representations" include interleaved practice. These activities require students to apply multiple data analysis skills in varied contexts, aligning with rubric expectations for interleaved practice across lessons and units. For example, the "Money and Personal Financial Literacy Overview" document includes a "Spiral and Interleaved Practice Opportunities" section, which states that "all workstations from prior units can be utilized as a spiraled review throughout this unit. The 'Fluency-Building' activities should be prioritized. Additionally, students can complete the 'Money and Personal Financial Literacy' interleaved practice found at the end of the unit." In grade 2, the "Program Overview" tab includes a section titled "Program Components." This section details the formative assessments that monitor student learning. The formative assessments include interleaved practice opportunities to engage with concepts.

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

In Unit 4: Geometry, lessons such as "Pattern Block Puzzles" and "Decomposing Snippets" require students to interpret and analyze geometric models by composing and decomposing shapes. These tasks engage students in evaluating visual representations to understand shape attributes and relationships. In Unit 10, lessons such as "Lemonade Sales Spin" and "Money Circuit" require students to interpret and analyze coin models and monetary representations. These lessons align with Guidance 5.1a by engaging students in evaluating visual collections of coins and comparing values using both cent and dollar notations. Unit 3 includes a lesson on representing quantities in tens and ones. The lesson includes questions and tasks that require students to interpret, analyze, and evaluate mathematical concepts. For example, students work in pairs to share how they solved the problem "300 + 60 + 7." The teacher asks students how the number sentence (or expression) represents the problem. Teachers also ask students to compare problems. For example, Step 16 of the lesson's facilitation states the following: "Problem A only had 40 plus nine more cupcakes, while Problem B had 400 plus nine more cupcakes. Problem B had more cupcakes because there are 400 instead of 40."

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

Unit 4: Geometry includes lessons titled "String Shapes" and "The Shape Shop." These lessons prompt students to physically construct models of polygons based on given attributes. The lessons thus align with Guidance 5.1b by requiring students to create tangible representations that demonstrate their understanding of sides and vertices. In Unit 10, lessons such as "Savings Plan" and "Producing Lemonade" prompt students to create models of savings goals and production costs. These lessons require students to construct visual and written representations of financial scenarios using real or simulated currency. Grade 2 includes a lesson on measurement. Students build an inch ruler to compare inches and feet and describe how the ruler can be used to measure the length of items. In order to share their prior knowledge, students discuss what they know about inches and feet. For example, the lesson indicates that students might say, "Inches are shorter than feet, so it takes more of them to equal the length of an item." At the end of the lesson, the materials provide students with an exit ticket to write about the process they used to measure items on the "Building a Ruler" task card.

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

Unit 10 includes the lessons "PFL Four Corners" and "Borrowing, Lending, and Learning." In these lessons, students apply financial concepts to novel scenarios. The materials prompt students to evaluate real-life decisions involving saving, spending, borrowing, and lending through contextualized role-play and discussion. The grade 2 teacher guide provides a "Research" section within the "Program Overview" tab. The "Concept Exploration and Productive Struggle" section states the following: "Productive struggle means allowing students to wrestle with a task or question within their cognitive reach to build their problem-solving ability. As students are working, the role of the teacher is to ask clarifying questions." Questions and tasks enable students to develop flexible thinking and target critical thinking skills. Daily energizers provide math prompts to promote students' critical thinking, allowing them to make connections across mathematical concepts. Such resources enable the real-world application of problems and solutions. For example, in Week 1, Section 2.002 of the Facilitation Guide, the teacher asks a guiding question to students. Students then share their solution and their strategy for solving the question. For example, the materials require students to solve a "puzzling problem" and answer the question, "How many more to ten?"

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

The materials in grade 2 include a "Content Map" resource that offers guidance on teaching and learning. This resource includes questions and tasks that help students interpret, analyze, and evaluate models and representations of mathematical concepts and situations. In Unit 4: Geometry, repeated classification tasks in "Two-Dimensional Shape Bump" and "Geometry Circuit" build students' fluency and automaticity in identifying and naming polygons and solids. The materials thus align with Guidance 5.2a by reinforcing foundational geometric vocabulary and recognition through structured, engaging practice. Unit 6: Addition and Subtraction, Part 2 includes a lesson titled "Choral Counting, Part 3." This lesson provides tasks that are designed to build student automaticity. For example, students rote count by tens (one ten, two tens, three tens, etc.) as the teacher records the numbers that students count on the board. This routine continues throughout the year with variations on the starting and ending numbers, as well as the numbers that students count by. Such automaticity develops students' fluency and supports their understanding of the place-value system, a grade-level task.

Evaluation for 5.2b
Materials provide opportunities for students to practice the application of efficient, flexible, and accurate mathematical procedures within the lesson and/or throughout a unit.

Unit 2: Multiplication and Division includes a lesson titled "Going to the Market, Part 1." This lesson provides opportunities for students to practice the application of efficient, flexible, and accurate mathematical procedures. For example, Step 5 of the lesson's facilitation requires pairs of students to share the strategies they used to determine and solve the number of vegetables that Pablo sold at the market. Efficient strategies include repeated addition and skip counting. Guiding questions include "How are the problems similar and how are they different?" and "Create another story that might be solved using the same process." Unit 4: Geometry includes the lessons "Composing Polygons" and "Decomposing Snippets." These lessons prompt students to apply multiple strategies to build and break down shapes, allowing students to practice the flexible, efficient, and accurate use of geometric procedures and reasoning. In Unit 10, lessons such as "Dollar Store Dilemma" and "Producing Lemonade" prompt students to build different coin combinations and compare strategies for reaching one dollar. The lessons encourage the efficient, flexible, and accurate application of monetary procedures.

Evaluation for 5.2c
Materials provide opportunities for students to evaluate procedures, processes, and solutions for efficiency, flexibility, and accuracy within the lesson and throughout a unit.

In Unit 4: Geometry, lessons such as "Space Prisms" and "Wrapping Presents" engage students in evaluating how nets and solids relate to each other, prompting students to reflect on the accuracy and efficiency of their classification and geometric strategies. Unit 4: Geometry also includes a lesson titled "Composing Polygons," which contains a "Composing Polygons Recording Sheet." This document is available for students to use as a progress check or to evaluate their procedures, processes, and solutions. Unit 5: Fractions includes a "Responding to Student Performance" section. This section provides students with opportunities to engage in a lesson that allows them to cut a pizza into halves and fourths, as well as evaluate each of these processes. Unit 10: Money and Personal Financial Literacy includes a lesson titled "Money Circuit." This lesson provides a self-check as a means for students to evaluate their own efficiency and accuracy within the lesson and/or unit. Unit 10 also includes the "PFL Four Corners" and "Savings Plan" lessons, which prompt students to evaluate financial decisions and justify their reasoning. These lessons require students to reflect on the efficiency and accuracy of saving, spending, and borrowing strategies in real-world contexts.

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

Unit 1: Addition and Subtraction, Part 1 includes a "Counting Collections" lesson. The "Lesson Suggestions" section states the following: "Encourage students to see a full ten frame as one ten. Learning to unitize a group of ten objects prepares students for a deeper understanding of the place-value system." This guidance encourages students to adopt a more efficient counting strategy. Unit 4: Geometry includes the lessons "Pattern Block Prisms" and "Prisms, Prisms, Everywhere!" In these lessons, the teacher prompts and guides students toward recognizing efficient classification strategies based on base shapes and their individual attributes. These lessons include embedded supports that promote students' strategic thinking and efficient problem-solving strategies. In Unit 5: Fractions, the lesson "Sharing a Cake" includes lesson suggestions. Teachers suggest to students that there are various ways to cut a cake into fourths to achieve equal-sized portions. This guidance encourages students to adopt an efficient approach while understanding fractions as parts of a whole. In Unit 10: Money and Personal Financial Literacy, lessons such as "Producing Lemonade" include teacher prompts and anchor charts. These resources require students to select cost-effective ingredients and calculate production costs to ensure that their expenses are below $1.00. This lesson highlights embedded supports that lead students to increasingly efficient problem-solving approaches. The "Lesson Facilitation" section states: "Look for students who are selecting more than one cup or whose cup of lemonade or limeade costs more than $1.00. Help these students determine which items are essential for their cup of lemonade or limeade." This prompt encourages students to use the most efficient strategies.

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

In Unit 9: Measurement, lessons such as "Building a Ruler" and "What’s My Area?" embed tasks that require students to use concrete manipulatives (e.g., inch tiles, sentence strips), visual models (e.g., task cards), and symbolic representations (e.g., number lines and rulers) to explore measurement concepts. As students complete problems on the "Sharing Cookies" task cards, they build their conceptual understanding of multiplication and division. The "Program Overview" resource includes a "Spiral and Interleaved Practice Opportunities" section. This section provides a list of fluency-building activities.

Evaluation for 5.3b
Questions and tasks include the use of concrete models and manipulatives, pictorial representations (figures/drawings), and abstract representations, as required by the TEKS.

The "Multilingual Supports" section includes lessons such as "What’s My Area?" and "Inch Upon Inch," which prompt each student to use manipulatives, visuals, and sentence stems to describe their measurement process. Such lessons require students to translate between physical models, visual representations, and verbal or written explanations. In Unit 9: Measurement, the lesson "Anticipating Distance" requires students to use rulers to measure distances on number lines and record their findings numerically. This work prompts students to translate between visual, concrete, and symbolic representations. In grade 2, a unit on addition and subtraction provides questions and tasks that include concrete, pictorial, and abstract representations, as required by the TEKS. The "Activity Map" document includes lessons labeled with a "C," "R," or "A" accordingly.

Evaluation for 5.3c
Materials include supports for students in connecting, creating, defining, and explaining concrete and representational models to abstract (symbolic/numeric/algorithmic) concepts, as required by the TEKS.

In grade 2, the "Content Map" resource shows how the "Scaffold Back" lessons use hands-on manipulatives and pictures to teach lesson concepts. The "Concept Development" lessons enhance this work by expanding what students have learned to different types of practice. The "Scaffold Forward" lessons then challenge students to engage in abstract thinking to apply what they have learned. In Unit 9: Measurement, the lesson "What’s My Area?" prompts students to justify their answers using sentence stems such as "To find the area of a rectangle, I ___." This stem requires students to explain their reasoning using visual models and written language. For example, Bullet 3 of the "Lesson Suggestions" section states the following: "Make the connection between time and fractions throughout the unit. The time 2:15 can also be called 'a quarter past 2.' The time 2:45 can be called 'a quarter till (to) 3.'" Teachers can explain this concept with the help of "Hour Hand Clock, Part 1" cards, a "Digital Clock" work mat, and dry-erase markers. Students share their ideas and explain what they notice about terms such as hour hand, arrow, and middle or halfway between.

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

Unit 2: Multiplication and Division includes a lesson titled "Going to the Market." Prompt 5 of the "Lesson Facilitation" section provides prompts and sentence stems to support the teacher in explaining the concepts to be learned. Prompt 3 of the "Lesson Facilitation" section supports the teacher in modeling the lesson's concepts. For example, the teacher demonstrates with a volunteer how to engage in the "Five-to-Jive" protocol. The "Implementation Support" document provides opportunities for students to develop academic mathematical language. For example, this document directs teachers to connect vocabulary to visuals and manipulatives in the "Unit-at-a-Glance" and "Lesson Internalization" templates, including anchor charts, models, and vocabulary integration strategies. The "Multilingual Supports" document provides visuals, manipulatives, and language strategies such as vocabulary cards with pictures and gestures, anchor charts, and sentence stems in English and Spanish. These resources support students in developing academic mathematical language.

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

Teacher guidance in the "Multilingual Supports" section includes strategies such as using read-alouds in both languages, leveraging cognates, and planning metalinguistic transfer. Such strategies provide clear and actionable implementation support for bilingual and ESL instructional models. Furthermore, the materials embed teacher guidance through unit-level linguistic considerations and planning documents, which scaffold vocabulary development in context using pre-teaching, cognates, and sentence stems. The "Unit Internalization" template in the "Implementation Support" document embeds teacher guidance that prompts reflections on vocabulary, misconceptions, and differentiation strategies. The materials use "Scaffold Back" and "Scaffold Forward" lessons to support students' vocabulary development in context. For example, Unit 2 frequently employs the terms rows and groups. The teacher models reading and writing these terms using sentence stems. Lessons embed cognates that enable quicker associations between English and Spanish, improving students' understanding of mathematical concepts. Examples include multiplication/multiplicación, multiply/multiplicar, group/el grupo, and equal/igual. Each vocabulary card contains the English word, the Spanish word, a visual, and an action (allowing students to connect the word to a physical action). For example, on one vocabulary card, the Spanish word igual appears next to the English word equal. The card also includes a definition ("is the same as") and an action ("holding one hand above the other"). Finally, the cards include a visual of the academic vocabulary word.

Evaluation for 5.4c
Materials include embedded teacher guidance to support the application of appropriate mathematical language to include vocabulary, syntax, and discourse to include guidance to support mathematical conversations that provide opportunities for students to hear, refine, and use math language with peers and develop their math language toolkit over time as well as guide teachers to support student responses using exemplar responses to questions and tasks.

The "Implementation Support" document includes "Lesson Internalization" prompts and an "Instructional Look Fors" section. Such resources guide teachers to anticipate misconceptions, use sentence stems, and facilitate structured discourse, helping students refine and apply mathematical language over time. The "Multilingual Supports" document includes embedded teacher guidance for supporting vocabulary, syntax, and discourse. Such supports include leveled sentence stems, think-pair-share routines, and multilingual scaffolds that promote peer conversations and enable students to refine their language over time. Teachers can access the "Lesson Suggestions" section of the "Addition and Subtraction: Four in a Row" lesson. This section includes guidance on listening to and modeling the use of vocabulary words such as doubles, making ten, and adding ten. Step 1 of the "Lesson Facilitation" section notes that, as pairs of students play a game in the lesson, the teacher should model oral directions during each player's turn, periodically checking for understanding. During each turn, the teacher encourages students to justify why they chose to determine the sum or difference, supporting students' syntax and discourse during mathematical conversations. According to the materials, "having pairs work together helps students hear math language with peers and develop (as well as refine) their math language toolkit over time." The materials guide teachers to extend student conversations by asking questions such as "What number will come next?" and "How do you know?"

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

The "Implementation Support" document integrates the TEKS process standards through the "Lesson Internalization" process, which requires teachers to unpack and align the TEKS and ELPS to lesson objectives. This process ensures that process standards are embedded in instruction. The "Multilingual Supports" document integrates the TEKS process standards by including opportunities for students to communicate mathematical ideas using visuals, manipulatives, and structured language supports across all units. Teachers can refer to the "Process Standards Connections" section at the beginning of each unit. For example, Unit 6: Addition and Subtraction, Part 2 states the following: "Students are given opportunities to use a problem-solving model throughout the unit, which includes selecting tools to help solve problems. Students create multiple representations when solving problems and make connections between representations. Work mats, pictorial representations, and number sentences are also utilized. Students communicate their reasoning and solution process with peers." Unit 6: Addition and Subtraction, Part 2 includes a lesson on solving change-unknown and part-part-whole (part-unknown) problems. Engaging in a think-pair-share routine, students use a problem-solving model to explain how many cupcakes Bonnie has baked so far and how many more cupcakes she needs to bake. Students use small ten-frame cards and work mats as tools to help solve the problems. Students also use number sentences to connect the number of crates and the number of cupcakes. Teachers then ask students to explain how the problems in the lesson were the same or different.

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

Students first interact with a unit on addition and subtraction in Unit 1, then circle back to this concept in Unit 6. Students engage with questions and tasks that explore concrete, pictorial, and abstract representations in alignment with the TEKS. The "Activity Map" resource labels lessons with a "C," "R," or "A," which correspond to concrete, representational, and abstract approaches. The materials thus make learning fun and effective and incorporate the TEKS process standards. The "Implementation Supports" document includes "Year-at-a-Glance" and "Unit-at-a-Glance" templates. These templates provide details on instructional pacing and content alignment with the TEKS process standards. The "Lesson Internalization Overview" document instructs educators on which approaches are applicable based on whether the content is new or a continuation of previous content. This resource highlights the embedded patterns or routines within the program, ensuring that the materials incorporate and connect the TEKS process standards throughout the course. Teachers can refer to the "Process Standards Connections" section at the beginning of each unit. For example, Unit 6: Addition and Subtraction, Part 2 states that "students are given opportunities to use a problem-solving model throughout the unit, which includes selecting tools to help solve problems. Students create multiple representations when solving problems and make connections between representations. Work mats, pictorial representations, and number sentences are also utilized. Students communicate their reasoning and solutions process with peers." The "Program Overview" includes a "Process Standards Unit Map," which explains how the process standards are embedded within the materials and spiraled throughout the year. Each unit in the materials includes one of these maps.

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

The "Implementation Support" document includes a "Unit-at-a-Glance" section for each unit. This section includes vocabulary, manipulatives, and "big ideas" aligned with student expectations, demonstrating how the materials incorporate and connect process standards throughout each unit. The beginning of each unit includes a "Process Standards Connections" section. In Unit 6: Addition and Subtraction, Part 2, students create multiple representations when solving problems and make connections between representations. Students use work mats, pictorial representations, and number sentences, communicating their reasoning and solution processes with peers. The "Unit Overview" section notes each lesson's process standards. Each lesson and its corresponding lesson facilitation steps provide further details concerning these standards. The "Process Standards Connections" section at the beginning of Unit 9: Measurement states the following: "Throughout this unit, students use mental math to estimate the length of different objects, then they use different measurement units to explore the linear nature of measuring length. Next, students problem-solve when using formal measuring tools. They also analyze the relationship between the size of the unit and the number of units that equal the length of an object. Students will communicate their findings using both written and verbal communication. Students also determine the area of different rectangles by problem-solving and selecting tools to solve problems." These details demonstrate how the materials incorporate and connect process standards within each unit.

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

Unit 4: Geometry includes an "Activity Map" that details lesson titles, content standards, process skills, ELPS, and suggested days for instruction, providing a clear overview of how these standards are embedded in instruction. The "Process Standards Connections" section states the following: "Students use a problem-solving model to determine how to classify and sort both 2D and 3D figures. They analyze relationships to make connections and generalizations about the figures. The teacher and students engage in shared writing to display, explain, and justify mathematical ideas." In Unit 8: Time, the "Process Standards" section states the following: "Students are expected to analyze relationships between different clocks and are provided opportunities to create and analyze the connection between multiple representations. They solve real-world problems and communicate their mathematical ideas with their peers." All Unit 8 lessons require students to use skills that align with the TEKS process standards. In Unit 10: Money and Personal Financial Literacy, the "Process Standards" section states the following: "Students are expected to make connections between coins, their values, and how to record the value of coins." Students also use a problem-solving model to count a collection of coins and record the value using different methods. Last, students solve real-world problems when analyzing concepts such as lending, borrowing, spending, and saving. Students use their process skills to solve real-world problems by exploring the difference between producers and consumers and calculating the cost to manufacture a simple product.

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

Grade 2, Unit 2: Multiplication and Division includes a lesson titled "Going to the Market." Prompt 5 of the "Lesson Facilitation" section includes prompts to support the teacher in explaining the concepts to be learned. The materials support the teacher in modeling lesson concepts by using sentence stems from the "Lesson Suggestions" sections. Prompt 3 of the "Lesson Facilitation" section supports the teacher in modeling lesson concepts as well. For example, the teacher demonstrates with a volunteer how to engage in the "Five-to-Jive" protocol. The "Multilingual Supports" document provides opportunities for students to think mathematically and make sense of math through scaffolded vocabulary, manipulatives, and sentence stems that support problem-solving and conceptual understanding. In grade 2, the teacher guide includes a "Program Overview" section. This section states that "productive struggle means allowing students to wrestle with a task or question within their cognitive reach to build their problem-solving ability. As students progress, they will need conceptual understanding as a foundation for content learned. Concept exploration involves concrete objects for students to manipulate and associate with relevant context that is accessible to them. Teachers ask clarifying questions to 'pull out the math' from students' actions. Exploration provides opportunities to attach formal vocabulary to mathematical processes and address common misconceptions." In a grade 2 lesson on solving joining problems within ten, students solve Task 4.A, which reads as follows: "Your animal has five apples up on top. He stacks four more apples up on top. How many apples does he have up on top?" This task results in "5 + 4 = 9," a "joining result unknown" problem. The example gradually increases in complexity. The teacher asks students how the tasks relate to the current problem.

Evaluation for 6.1b
Materials support students in understanding, explaining, and justifying that there can be multiple ways to represent and solve problems and complete tasks.

The "Multilingual Supports" document includes guidance for bilingual and dual language programs, which includes strategies such as using read-alouds in both languages, leveraging cognates, and planning metalinguistic transfer. The materials thus provide clear and actionable implementation support for bilingual and ESL instructional models. The "Implementation Support" document includes lesson-level questions and unit reflections that prompt teachers to engage students in comparing strategies and justifying their reasoning, supporting multiple representations and solution paths. Unit 1: Addition and Subtraction, Part 1 includes a lesson on using concrete objects to represent part-part-whole problems within ten. Students solve for the number of fireflies outside a jar and the number of fireflies inside the jar. Teachers give students time to model the problem on the "Glass Jar" work mat and discuss the total number of fireflies. Teachers then ask students to make observations about the number sentences. Students can use multiple strategies in this lesson, helping them understand that there are multiple ways to represent, solve, and complete part-part-whole problems. These strategies include counting all the fireflies or recognizing the "one more/one less" relationship. Unit 1: Addition and Subtraction, Part 1 includes a lesson on solving change-unknown problems with a total of up to 20. Students explain their models as they "bake" cupcakes. Students engage in a think-pair-share routine to share ideas on how many strawberry cupcakes they will need to bake a total of 20 cupcakes. The lesson reads as follows: "You bake a total of 20 cupcakes. You bake five lemon cupcakes. How many strawberry cupcakes will you bake?" The teacher asks guiding questions, such as, "How do you know you baked 15 cupcakes?" Students practice by playing the "20 Cupcakes" game.

Evaluation for 6.1c
Materials are designed to require students to make sense of mathematics through multiple opportunities for students to do, write about, and discuss math with peers and teachers.

In Unit 4: Geometry, the lessons "The Shape Shop" and "Snippets" require students to create shapes with a variety of materials. Students explain the reasoning of their shape design. In the latter lesson, students create polygons, use them to compose other shapes, then describe the attributes they create. The "Implementation Support" document includes "Lesson Internalization" prompts and an "Instructional Look Fors" section. Such resources guide teachers to anticipate misconceptions, use sentence stems, and facilitate structured discourse, helping students refine and apply mathematical language over time and discuss math with peers and teachers. The "Multilingual Supports" document requires students to do, write about, and discuss math through structured routines such as think-pair-shares, sentence stems, and writing prompts. Such routines promote peer interaction and language-rich mathematical discourse. Unit 1: Addition and Subtraction, Part 1 includes a lesson on solving problems that involve adding ten to a number within 20. Students use animal cards to solve each problem. Students then determine which number sentence represents each situation. For example, the lesson reads, "There were five feet on the beach. A crab joins. How many feet are there now? (5 + 10 = 15)" Using its corresponding game board, students practice this concept by playing a game titled "Plus Ten Connect Four." Students engage in a think-pair-share routine with peers and write about math using the "Feet on the Beach: Plus Ten" exit ticket. Unit 1: Addition and Subtraction, Part 1 includes a lesson on solving problems that involve doubling numbers, looking for patterns, and explaining one's reasoning. Teachers provide the problems to students one at a time. Students use their counters and a "Doubling Pot" work mat to solve each problem (either horizontally, vertically, or diagonally). Students discuss the problems with their peers in a think-pair-share routine. They also write about math using the "Feet on the Beach: Subtract Ten" exit ticket. This lesson allows students to complete math problems with both peers and the teacher during whole group instruction.

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

Materials support teachers in guiding students to share and reflect on their problem-solving approaches, including explanations, arguments, and justifications. The "Multilingual Supports" document ensures that teachers guide students to share and reflect on problem-solving approaches, embedding routines such as think-pair-shares and the "Three Reads" protocol into lessons. The materials also honor native languages for initial thinking and provide prompts for teachers to extend student thinking. Unit 3: Place Value includes a lesson on counting objects and sharing ideas for organizing objects with a group. The materials support teachers in guiding students to share and reflect on their problem-solving approaches. For example, the materials include prompts in which students engage in a think-pair-share routine concerning their observations about the quantity of a given toy. Students estimate the number of toys based on groups of twos, fives, or tens. The materials include guiding questions to support students, such as "How many dinosaurs are there? How do you know?" and "How are they able to prove the number of objects in the collection?" Students explain their strategy for counting (by ones, twos, fives, or tens). Unit 3: Place Value includes a lesson on counting a set of objects and representing a number as a certain number of tens and ones. Students explain how they counted a set of objects by engaging in a think-pair-share routine. The teacher guides students to share their predictions, explaining why they made a particular prediction. The teacher poses questions to students, such as, "Is there a faster way to count?" Such questions encourage students to think about their problem-solving approaches to counting (by ones, twos, fives, or tens). Unit 3: Place Value includes a lesson on representing quantities. The materials support teachers in guiding students to share and reflect on their problem-solving approaches. For example, teachers ask students the following questions: "How many more cupcakes does Robin need to fill another box? How many cupcakes will Robin have if he fills another box? How does the numeral 87 represent this situation?"

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

Unit 4: Geometry includes the lessons "Composing Polygons" and "Pattern Block Puzzles." In these lessons, the teacher guidance states that the teacher reads students a book and then stops to discuss the animals on the book's various pages. Students then compose different shapes and animals using tangrams. Next, students participate in a think-pair-share routine with a partner. In grade 2, the "Program Overview" resource contains a "Learning Progressions" section. This section addresses how formative assessments are "conducted through the instructional process to monitor student learning and provide ongoing feedback." This process includes exit tickets, recording sheets, interleaved practice, daily energizers, student projects, and teacher observations. According to the materials, "the program provides opportunities for teachers to check for understanding through questioning and observing how students engage with math concepts." Unit 5: Fractions includes a lesson on identifying examples and non-examples of halves, fourths, and eighths. The materials offer guidance to support teachers in providing explanatory feedback. For example, in Step 9 of the "Lesson Facilitation" section, the guidance states to "debrief" by asking students to identify a "Fraction Sort" card cutout that is a non-example of halves. Students should then explain how they know it is a non-example. Students respond using the sentence stem "Card ____ represents ____. I know this because...." The lesson suggestions direct the teacher to avoid telling students the correct answers, which encourages students to discuss their ideas with a peer and the class. This lesson assesses students' prior knowledge from grade 1 to determine if students can use what they know about halves and fourths to uncover a new fractional amount (eighths). If students struggle to identify examples and non-examples of halves and fourths during the lesson, teachers give them the opportunity to engage in the "Scaffold Back" lesson "Cut It in Half: Pizza Fractions and Pattern Block Fractions." Unit 5: Fractions includes a lesson on fourths. The lesson materials provide prompts and guidance to support teachers in providing explanatory feedback based on student responses and anticipated questions. For example, in Step 4 of the "Lesson Facilitation" section, the teacher engages students in a think-pair-share routine by asking if they would prefer one slice of cake over another, and why. After a few students share their responses, the teacher allows students to agree or respectfully disagree with one other. Students explain their thinking using sentence stems. The teacher then prompts students to use scissors to prove their predictions about each of the fourths that they discussed.