Step Up to the TEKS 4th Math Full Program

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

The 4th Grade Math Implementation Guide includes a scope and sequence that outlines the Texas Essential Knowledge and Skills (TEKS) and concepts taught in the course. It provides a suggested timeline per unit and allows educators to ensure that lessons align with the state standards and cover all required content, promoting consistency and completeness.

The scope and sequence does not include the ELPS. The ELPS are instead listed in a separate table of contents chart.

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 4th Grade Math Implementation Guide includes suggested pacing calendars to support effective implementation for various instructional calendars, including 165, 180, and 210 instructional days.

The materials do include a suggested pacing guide for schools or districts that run for 165 days, 180 days, and 210 days. For example, the data analysis unit is to be taught in 10 days if educators are in school for 165 days, 11 days if educators are in school for 180 days, and 13 days if educators are in school for 210 days.

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

The 4th Grade Math Implementation Guide provides each unit with a unit rationale, Big Ideas, and background knowledge. The unit rationale includes connections with other concepts and background knowledge from prior grade levels.

The materials include how concepts learned are connected throughout the course. For example, in the 4th Grade Math Assessment Teacher Edition, “Unit 4: Addition and Subtraction,” the unit rationale states, “This unit strengthens students’ fluency and reasoning with addition and subtraction of whole numbers. Students connect place-value understanding to standard algorithms, use estimation to assess reasonableness, and apply strategies to solve real-world problems. These skills support later work with multiplication, division, and multi-step problem solving. Throughout the unit, students apply the mathematical process standards by analyzing relationships, representing problems with models and equations, and communicating mathematical reasoning.”

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

The beginning of the lesson provides a conceptual learning goal. There are also explicit instructions on how an educator can best run a lesson. For example, unit 11, lesson 1 says to “ask for volunteers to share things they remember about working with dot plots. Keep in mind that they may have worked previously with dot plots that were primarily labeled with categories. Explain that dot plots labeled numerically will be used often to represent data. Have two or three examples ready to display and briefly go over what data is represented.” The unit also gives the educator misconceptions to look for, such as, “Students may not understand why there are multiple ways of representing data. Data are used for many purposes, and different ways of representing data are helpful in specific situations.” This allows educators to thoroughly understand and prepare to teach lessons.

Each unit includes “Unit Rationale,” “Big Ideas,” “Background Knowledge,” “Instructional Notes,” “Key Academic Vocabulary,” “Required Materials,” and “Unit Assessment Overview” sections to help educators internalize the unit. The “Unit Rationale” section includes connections with other concepts and background knowledge with prior grade levels.

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

The materials provide guidance such as look-fors, implementation pitfalls, and coaching questions. The 4th Grade Math Implementation Guide includes a “Leadership Lens” at the unit level that provides guidance to instructional leaders on supporting educators in implementing the materials as designed. The “Leadership Lens” includes “Implementation Priorities,” “Classroom Look-Fors,” “Common Implementation Pitfalls,” “Coaching Questions,” and “Evidence to Review” sections for guidance.

However, the materials do not include resources for instructional leaders to support educators in implementing them as designed. The materials do not provide a framework or tools to assist instructional leaders to monitor implementation or specific resources to help instructional leaders build their capacity to support educators, such as exemplar responses to the coaching questions.

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.

Materials include unit overviews in the 4th Grade Math Implementation Guide that address background content knowledge and academic vocabulary. For example, the unit 4 overview states, “Background Knowledge for Students (Prior-Grade TEKS Alignment) Students should already understand: Adding and subtracting within 1,000 using place-value strategies (Grade 3 TEKS 3.4A, 3.4B), Using number lines and models to represent addition and subtraction (Grade 3 TEKS 3.4C), Estimating sums and differences (Grade 3 TEKS 3.4D).” Additionally, the materials include a vocabulary chart with key words, definitions, and cognates.

The unit overview within the 4th Grade Math Implementation Guide provides educators with key academic vocabulary, which includes terms, definitions, and Spanish cognates. “Unit 11: Data Analysis” contains six key terms. For example, category, which is defined as “a group of data” and whose Spanish cognate is categoría.

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

The family letter describes in both English and Spanish the concepts the students will learn based on the topic. The letter also provides strategies to reinforce TEKS-aligned content and support student progress.

In the 4th Grade Math Implementation Guide, family letters inform families in both English and Spanish about what students are learning, why it is important, and how families can support their students. For the data analysis unit, families are informed that students will be representing data and solving problems using data with explanations on what that will look like, such as using dot plots to then solve one- and two-step problems. The letter further elaborates that the unit is important because it will help students “understand and interpret data,” “enhance problem-solving abilities,” and “prepare for real-world applications.” Families are informed that they can help support their child’s learning by “Exploring Everyday Data: Look for examples of data in everyday life, such as sports statistics, weather forecasts, or survey results, and discuss what the numbers mean.”

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

The materials include aligned activities, math talks, reflections, journal writing, vocabulary activities, and formative assessments. The “Background Information,” “General Information,” and “Teacher Notes” pages include the ELPS. The materials also include directions, components and pages to be used, facilitating Questions, blackline masters, and formative assessment answer keys. The 4th Grade Math Implementation Guide contains “Lesson-at-a-Glance” components that include daily objectives and TEKS.

The materials include structured lesson plans aligned to TEKS 4.2B that incorporate TEKS, ELPS, daily objectives, educator questioning, instructional tasks, and embedded assessments. Each lesson follows a clear progression from direct instruction (“teach lesson”) to guided practice, collaborative partner practice, and independent practice. This structure ensures that students develop conceptual understanding before applying skills independently and provides educators with all components necessary to deliver TEKS-aligned instruction.

Lessons in the 4th Grade Math Implementation Guide contain TEKS, lesson objectives in plain language for student understanding, and the “Lesson-at-a-Glance” section. For example, the first lesson of the data analysis unit teaches TEKS 4.9A: “collect, organize, and represent data using tables and charts.” The student objective is, “I can collect and organize data to answer a question.” The two offered pathways for educators each have a “Lesson-at-a-Glance” section that includes how long each component should take and if the component should be taught individually, to the whole class, in small groups, or in pairs. The suggested assessment aligned to the lesson objectives is for students to journal and “explain how [their] table organizes data.”

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.

In the 4th Grade Math Implementation Guide, the “Lesson-at-a-Glance” section gives suggested time frames for each portion of the lesson. For unit 11, lesson 1, educators who use the Practice Book pathway are spending five minutes on the warm-up, 10 minutes on the “I-Do: Explicit Instruction,” seven minutes on the “We Do: Guided Practice,” eight minutes on the “Partner Practice,” 10 minutes on the “Independent Practice,” and 10 minutes on the “Exit Ticket,” for a total of 50 minutes.

The “Lesson-at-a-Glance” section in the 4th Grade Math Implementation Guide provides materials and timing. While a materials list is provided, it is not clearly differentiated by educator or student materials. For example, unit 7, lesson 2 includes the following: “Materials & Notes: Problem of the Day - Warm-Up 4.6B, Practice SE (Eng/Span) - TEKS Lesson 4.6B, Practice SE (Eng/Span) - Guided Practice 4.6B, Practice SE (Eng/Span) - Partner Practice 4.6B, Practice SE (Eng/Span) -Independent Practice 4.6B, Journal: Explain how one shape fits into two categories.”

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

The materials include a generic list of practice activities for students but do not provide guidance on how to use these materials, such as determining assignments based on student performance or academic needs.

At the end of each lesson, suggested extended practices are provided for students to complete. The suggestions for lesson 2 of the data analysis unit are “Homework: Practice SE (Eng/Span) - Independent Practice 4.9B (creating pictographs and bar graphs), Enrichment: Collect data from classmates (e.g., favorite snack or color) and create both a pictograph and a bar graph; compare which representation is more effective and explain why, Intervention: TEKS-tivity - Activity 4.9B with educator support, focusing on organizing data and correctly labelling graphs.” However, there is no specific guidance on how to use the materials that align with a student’s performance, whether they need review and additional practice or require extensions and enrichment activities.

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

The materials include a variety of formative instructional assessments embedded within each book. The practice books include “Guided Practice,” “Partner Practice,” and “Independent Practice” sections. The TEKS-tivity books include daily activities, “Math Talks,” reflection questions, journaling, and Exit Tickets. The “Problem of the Day Journal” has initialization questions, including vertically and horizontally aligned items for entry into the lesson, along with activities.

The materials include a variety of instructional assessments at the unit and lesson levels, including summative assessments that vary in types of tasks/questions. In the 4th Grade Math TEKS-tivity Book Student Edition, students can complete activities. For example, they answer questions like, “How do you solve problems from a dot plot representing whole numbers?” or answering STAAR-style questions.

Additionally, the materials include diagnostic assessments that vary in the types of tasks/questions. Diagnostics are provided for use at the beginning of each unit within the TEKSnology digital platform.

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

In the 4th Grade Math Practice Book Teacher Edition, the “Purpose of Instructional Assessments” section explains the key instructional features such as hands-on activities, STAAR-style questions, and collaborative learning. The purpose of each is to “allow students to practice and apply concepts while providing educators with opportunities to assess understanding and adjust instruction,” “solidify understanding,” and “foster discussion and collaboration...extensive exercises, readiness, and supporting standards ensure individual mastery.”

The materials include the definitions and purpose of the included assessments. For example, the introduction to the book states, “Formative Assessment: Each lesson includes a short formative assessment designed to help educators monitor student understanding and identify misconceptions. These checks provide actionable information to support instructional decisions, differentiation, and targeted intervention as needed.”

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

The 4th Grade Math Assessment Teacher Edition provides “Teacher Guidance for Consistent and Accurate Administration of Instructional Assessments,” which tells educators to “Create Uniform Instructions,” “Maintain Testing Conditions,” “Use Approved Tools”, “Provide Accommodations,” and “Give Language Support.” This ensures the administration of included assessments is consistent and standardized across examiners.

The materials provide a standardized assessment format that supports consistent administration across classrooms. The benchmark includes clear directions, uniform item structure, and embedded reference materials, ensuring that all students are assessed under consistent conditions

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

The 4th Grade Math TEKS-tivity Book Teacher Edition includes formative assessments that are aligned to the TEKS and unit objectives. Each unit includes formal and informal formative assessments in the form of activities, Math Talks, reflections, journal writings, vocabulary development, and a formative unit assessment. Each piece is aligned to the proper TEKS and objective of the unit. Activities also include facilitating questions that educators can use to assess students’ learning throughout the activity.

The summative assessments are aligned to the TEKS of the course and the objectives of the unit. For example, the unit 11 assessment labels each question item with correlating TEKS. For example, question 1 is aligned with TEKS 4.9A, which is to represent data on a frequency table, dot plot, or stem-and-leaf plot marked with whole numbers and fractions. Question 1 asks students to complete a dot plot based on the given data, which is aligned to the TEKS.

Additionally, each unit includes a diagnostic aligned with the TEKS and the unit objectives. Diagnostic assessments are included in the TEKSnology digital platform, and educator guidance for using the diagnostic is included in the 4th Grade Math Implementation Guide.

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

The formative and summative assessments within the materials are aligned to the TEKS. At the beginning of the unit, the TEKS are outlined. Then, for each activity, reflection, and/or assessment, there is a TEKS label. For example, activity 1 for data analysis and personal financial literacy is labeled with TEKS 4.9A.

Instructional assessment includes various TEKS-aligned item types throughout the materials. For example, “Benchmark A” in the 4th Grade Math Assessment Teacher Edition includes questions with multiple-choice, multi-select, drag-and-drop, and text entry.

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

The materials include an online assessment scoring through their TEKSnology digital platform. This platform automatically grades most items and provides a gradebook view for educators to review the grading or make changes. Reports are generated so educators can view the results by course, strand, or reporting category. A visual is provided so educators have consistent information when interpreting student performance.

The TEKSnology digital platform provides instructional assessment reports and educator guidance for interpreting student assessment performance and using assessment data to inform instruction. TEKSnology.com automatically generates multiple report types, including “Item Analysis Reports,” “TEKS Mastery Reports,” “Question Analysis Reports,” and “Class Achievement Reports.” These reports allow educators to analyze student performance from multiple perspectives. “Item Analysis Reports” identify student performance on specific skills, “Question Analysis Reports” reveal trends in student responses, “TEKS Mastery Reports” display progress toward standards mastery, and “Class Achievement Reports” compare individual and class performance. “Standards Reports” can be viewed by reporting category or strand and include class percentages and mastery color-coding to help educators identify strengths and areas of need. Selecting “Details” provides student-level performance data, allowing educators to interpret individual progress. Similarly, the “Course Report” displays class averages for each assessment with access to individual student reports, and Assignments > Gradebook includes both details and standards views for reviewing assessment results. Collectively, these reports provide guidance for interpreting student performance and support data-informed instructional and curricular decisions.

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

The materials provide guidance on how to use tasks and activities in response to students’ needs based on assessments. The 4th Grade Math Assessment Teacher Edition provides educators with a flow of the lesson. The materials indicate educators are to make a “data-informed decision” after students take an Exit Ticket (formative assessment). Based on the data, educators then do extensions, enrichments, reteach, or power review found in the 4th Grade Math Implementation Guide.

When students complete their Exit Tickets, educators decide whether students receive an “Extend / Enrich” activity or a “Reteach / Power Review” activity based on Exit Ticket data. For example, in unit 11 “Data Analysis,” lesson 2 “Representing Data with Graphs,” students who need enrichment should “collect data from classmates and create both a pictograph and a bar graph; compare which representation is more effective and explain why.” For students who need Intervention complete “TEKS-tivity - Activity 4.9B with educator support, focusing on organizing data and correctly labeling graphs.” When educators go to the specified activity, there are directions, materials, and facilitating questions to guide them.

Evaluation for 2.2c
Materials include tools for teachers to track student progress and growth, and tools for students to track their own progress and growth.

The materials include tools for students to track their own progress and growth. For example, at the end of each “Benchmark” assessment, students have a “My STAAR Chart” that they use to “chart [their] progress by coloring in each star that [they] got correct on the Benchmark. The “My STAAR Chart” allows students to visualize and monitor their own progress.

The materials include tools for educators to track student progress and growth. For example, the TEKSnology digital platform has reports that educators can use to track student progress and growth with assessments and assignments. The data shows if students are at Does Not Meet, Approaching, Meets, and/or Masters on assessments and assignments by clicking “Details” to see how students are doing individually.

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.

The 4th Grade Math Practice Book Teacher Edition includes educator guidance for students who have not yet reached proficiency. For example, the “Misconceptions” section embedded into the TEKS 4.4E lesson states, “Students may not understand how to use a model to represent a division problem. Ask students to model a multiplication problem using base tens and record the division problem that is also being represented. This helps them relate the area of the model to the quotient.”

In the 4th Grade Math Implementation Guide, educators are directed to activities within the TEKS-tivity book should students need intervention. For example, students who require intervention in unit 11 “Data Analysis,” lesson 1 “Collecting and Organizing Data” are to complete “TEKS-tivity - activity 4.9A with structured templates.” When educators navigate to that activity in the 4th Grade Math Practice Book Teacher Edition, there are facilitating questions with sample answers. For example, “How do you create a stem-and-leaf plot?”

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

The materials provide educator guidance that highlights key academic terms in each lesson and provide guidance for addressing common language misunderstandings, utilizing visuals to reinforce learning. For example, within the TEKS-tivity pathway, every lesson begins with a “Math Talk,” which can serve as a pre-teach for students who are unfamiliar with the vocabulary. These questions facilitate discussions that encourage further understanding of new terms and the lesson’s content.

Within the Practice Book pathway, lessons preview vocabulary with students for unfamiliar vocabulary and/or references in text. For example, in the “Personal Financial Literacy” unit, key vocabulary terms, such as profit, sales, and expenses, are defined. Students work through a problem with educator guidance and are then asked, “How much profit did Adam make?”

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

The materials include embedded educator guidance for differentiation for students who have demonstrated proficiency throughout the 4th Grade Math Practice Book Teacher Edition. For example, the “Extension Learning Opportunity” section embedded into the TEKS 4.4A lesson states, “Have students plan a pretend shopping trip using prices with decimals. They must calculate total costs, change, and savings using the standard algorithm and show all their work clearly labeled.”

The “Lesson-at-a-Glance” section of the 4th Grade Math Implementation Guide includes an activity the educator can use for enrichment for each lesson. For example, unit 5, lesson 2 guidance states, “Enrichment: Create two different arrays for the same product and explain how they are the same.”

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.

The “TEKS Lesson” component provides explicit instruction through direct teaching of grade-level concepts before student practice. This structure ensures that educators model new learning aligned to TEKS before students engage in guided and independent work. In the 4th Grade Math Practice Book Teacher Edition, there are explicit prompts. For example, “ask students to sit in groups of three or four to discuss the questions at the top of the page. Allow members of each group to share thoughts with the whole class. Emphasize that in order to analyze data and use it to solve problems, familiarity with different parts of the graph is very important.” Lessons also include an “Important Concepts” section that outlines what students need to understand.

The materials include facilitating questions throughout the 4th Grade Math Practice Book Teacher Edition that provide guidance to support the educator during “Guided Practice.” Questions and sample student responses are included to support the educator in explaining the concepts students are learning. For example, 4.4E lesson includes, “Facilitating Questions: Ask the students these questions as they are working the problems (Answers will vary, sample answers are provided.) How do models help represent division of numbers? (Models are used to represent division to show the equal parts a number can be broken into) How do equations help to represent division of numbers? (Equations can be used to represent division of numbers by showing what number is getting broken into equal parts.)”

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

The materials include a variety of instructional approaches with educator guidance and recommendations throughout the 4th Grade Math TEKS-tivity Book Teacher Edition. The introduction of the book explains, “TEKS-tivity resources are designed to help students deepen conceptual understanding, strengthen reasoning, and build confidence with grade-level TEKS through structured learning routines that promote engagement and meaningful thinking. Rather than focusing primarily on repetitive practice, the lessons in this book emphasize: Hands-on and discussion-based learning, Productive struggle and sense-making, Multiple representations and strategies, Student reflection and metacognition, [and] Ongoing formative assessment.”

The materials support differentiation through multiple instructional pathways, including direct instruction and hands-on TEKS-tivity activities. These options allow educators to adjust instruction based on student readiness and learning preferences, ensuring that all students can access TEKS-aligned content. The 4th Grade Math Teacher Guide includes a description of the two-pathway instructional model. It states, “The Two-Pathway Model reflects research demonstrating that no single instructional approach sufficiently addresses the range of student needs in elementary mathematics. Instead, effective instruction blends explicit modeling, guided practice, conceptual exploration, and structured discourse.”

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.

Lessons are created to facilitate a gradual release model through the Practice Book pathway. The “Lesson-at-a-Glance” provides time stamps on how long each component and activity should take and what the component and activity are for each lesson. For example, unit 8 “Data Analysis,” lesson 1 “Collection and Organizing Data” has the suggested time stamps for the following components and activities: “five minutes, Warm-Up/Spiral; 10 minutes, I Do: Explicit Instruction; seven minutes, We Do: Guided Practice; eight minutes, Partner Practice; 10 min, Independent Practice; 10 min, Exit Ticket.” By providing the “Lesson-at-a-Glance,” educators can effectively deliver lessons with diverse practice opportunities with active engagement from students.

The 4th Grade Math Teacher Guide has detailed lesson plans with step-by-step instructions, suggested pacing, and differentiation strategies for each lesson. For example, unit 6 of the 4th Grade Math TEKS-tivity Book Teacher Edition includes “Math Talks,” tickets out the door, journal and vocabulary activities, and formative assessments. Each component has guidance for implementation as an independent or collaborative activity. “Math Talks” include instructions to “place students in pairs. Have the students spend three to five minutes discussing each of the prompts provided in their student books.” Part 1 of the directions for activity 1 says, “Students should work independently on this activity.” In contrast, part 1 of the steps for activity 2 says, “Students may work in pairs or independently on this activity.” Facilitating questions are included with each activity to help educators guide students during the lesson component and monitor understanding. The “Reflection,” “Ticket Out The Door,” “Journal,” and “Vocabulary sections and the formative assessment are independent activities.

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

The materials include educator guidance on providing linguistic accommodations for various levels of language proficiency for each lesson in the 4th Grade Math Implementation Guide. The “Emergent Bilingual Oral and Written Discourse Support” is provided for each lesson and includes guidance for “Embedded Oral Discourse Guidance,” “Embedded Written Discourse Guidance,” and “ELPS Sentence Stem.”

Additionally, the “ELPS Sentence Stem” section includes the five levels of language proficiency, with sentence stems that increase in academic language as students progress through the levels.

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

The materials include “Guiding Principles to Support Emergent Bilinguals in Mathematics” in the 4th Grade Math Teacher Guide to support educators in better using the materials within bilingual/ESL programs. Implementation guidance includes 10 different ways educators can effectively differentiate the material to fit the needs of emergent bilingual (EB) students.

For example, the 4th Grade Math Teacher Guide states, “Create Opportunities for Meaningful Interaction. Collaborative Learning: Use pair and group activities where students engage in mathematical discussions. Encourage Talk: Provide opportunities for emergent bilinguals to verbalize their thinking, both in English and their home languages. Use Turn-and-Talk: Structure peer interactions to allow processing and verbal rehearsal of mathematical ideas.”

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

The materials include embedded guidance for educators to develop vocabulary and increase comprehension through oral discourse using “Math Talks” and working in pairs to complete activities. The “Reflection,” “Ticket Out The Door,” and “Journal” sections allow students to use vocabulary and improve comprehension through written discourse of the math concept using prompts like, “How can a table be used to represent the numbers in a sequence and their position in the sequence?”

The 4th Grade Math Implementation Guide includes “Emergent Bilingual Oral and Written Discourse Support” at the lesson level. The chart provides examples of connections, guidance on embedded oral discourse, guidance on embedded written discourse, and ELPS sentence stems. The embedded oral and written discourse guidance includes sections that address vocabulary, comprehension, background knowledge, and cross-linguistic connections for each lesson.

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

This guidance is not applicable because the program is not designed for dual language immersion (DLI) programs.

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

The materials include practice opportunities throughout a lesson that require students to demonstrate depth of understanding aligned with the TEKS. For example, in the TEKS 4.5D lesson within the 4th Grade Math Practice Book Student Edition, students must use a variety of strategies to solve area and perimeter problems. Practice includes situations where the area or perimeter is given, requiring students to determine a missing side. Practice also includes situations where students must apply their knowledge of area and perimeter to determine which one applies to the given real-world situation before solving the problem.

Instructional assessments throughout the course include practice opportunities that require students to demonstrate depth of understanding aligned to the TEKS. Throughout the unit 9 assessment, included in the 4th Grade Math TEKS-tivity Book, students apply their understanding of area and perimeter to real-world situations. For example, item 2 states, “Mr. Kind walks around the perimeter of a rectangular playground every day for exercise. The perimeter is 90 yards. The short sides of the playground are 15 yards each. What is the length of the longest side in yards? (4.5D, RS, RC3)” Educators can use the assessments to collect data on the TEKS and make informed decisions based on student needs.

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

The materials include questions and tasks that progressively increase in rigor and complexity throughout the lesson cycle presented in the 4th Grade Math Practice Book Student Edition. Lessons move from educator modeling during the mini-lesson to “Guided Practice,” “Partner Practice,” and “Independent Practice,” gradually requiring students to demonstrate greater independence and deeper understanding aligned to the TEKS.

For example, the TEKS 4.6D lesson begins with an educator-modeled activity focused on vocabulary terms for lines and angles. Students then work in pairs/groups to match given shapes to vocabulary terms. Students then complete the engaging activity in the appendix, which gives students a polygon to label the lines and angles and then provides an attribute and has them match the correct shape. Students then work through guided and partner multiple-choice questions, some of which no longer provide a model of the shape. The independent practice questions continue to increase in rigor and complexity, with multi-select items and several questions no longer providing a model of the shape.

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

The 4th Grade Math Implementation Guide connects mathematical concepts across units through a coherent instructional progression that builds from foundational number relationships to algebraic reasoning, geometry, measurement, and real-world application. The “Sequence Rationale” states, “The sequence ensures a logical progression, moving from foundational skills to more complex applications, while connections between units reinforce learning and support long-term retention. Each unit builds on prior knowledge, deepens conceptual understanding, and prepares students for the next stage of learning. This coherent progression fosters mathematical fluency, problem-solving ability, and confidence in mathematics.”

For example, in the 4th Grade Math Implementation Guide, the “Sequence Rationale” explains that unit 6 “Algebraic Reasoning” occurs after students master operations because “this builds on prior knowledge of multiplication and division, preparing them for more abstract mathematical concepts in later grades.” This demonstrates coherence, as students will use knowledge of operations from previous units to identify patterns and relationships in this unit.

The materials explicitly connect patterns and relationships between math concepts at the lesson level in the 4th Grade Math Practice Book Teacher Edition. For example, the following educator guidance is provided when introducing grade 4 students to conversions: “Provide students with copies of the STAAR Reference Materials and make sure they all can locate the measurement equivalents on the page. Remind students that they have solved many problems using a ratio table and that these tables are also helpful when finding equivalent measures. Ask, ‘Who can find a relationship between feet and inches on your reference materials?’ Call on a volunteer to verify that one foot equals twelve inches. Ask this question for students to discuss in a small group: ‘How is this relationship shown in the table at the top of the page?’ Ask a volunteer to share how the table shows the relationship. Encourage students to write the process used in the middle of the table.” This guidance ensures that the educator connects the previously taught skill of ratio tables to the new learning of measurement conversions, helping students make meaningful math connections between concepts.

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.

The materials demonstrate coherence across units by connecting content and language learned in previous grade levels, the current grade level, and what will be learned in future grade levels, as outlined in the 4th Grade Math Implementation Guide. The materials connect prior-grade knowledge to current grade-level learning by explicitly identifying prerequisite skills and foundational understandings necessary for new mathematical concepts. The “Unit Sequence Rationale” demonstrates how students extend their prior learning and connect it to the next unit’s concept. The “Background Knowledge for Students” lists the TEKS and concepts that students should already understand prior to the unit. The “Key Academic Vocabulary” section pulls vocabulary words directly from the unit’s TEKS, allowing the TEKS to provide a natural coherence of language.

The 4th Grade Math TEKS Checklist includes a vertical alignment component that connects current grade-level standards to prior and future learning. For example, grade 4 TEKS 4.9A “represent data on a frequency table, dot plot, or stem-and-leaf plot marked with whole numbers and fractions,” is aligned to grade 3 TEKS 3.8A, grade 5 TEKS 5.9A, and grade 6 TEKS 6.12A. These standards progressively extend students’ data representation skills using more complex numerical data. The vertical alignment component demonstrates coherence across grade levels and supports the progression of mathematical concepts and academic vocabulary.

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..

The materials demonstrate coherence at the lesson level by connecting students’ prior knowledge of concepts and procedures from both previous and current grade levels to new mathematical knowledge and skills. For example, educator guidance for TEKS lesson 4.2B states, “Point out that the expanded notation of digits in a number is a review from grade 3, but at this level will extend to the one-billions place, as well as to the tenths and hundredths decimal places.”

The “Problem of the Day Journal” activities provide coherence by systematically spiraling prior and current grade-level concepts and procedures. These activities use diverse methods to support vertical alignment and ensure that students consistently build on foundational knowledge for future success.

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

The “Problem of the Day Journal” within the Practice Book pathway provides spaced retrieval opportunities with previously learned skills and concepts across lessons and units. “The ‘Problem of the Day Journal’ incorporates research-based instructional practices shown to strengthen retention and transfer of learning: Spaced Retrieval to reinforce long-term retention of essential concepts.” Additionally, the framework of question design follows “Instructional Structure: Monday-Thursday. Students complete five problems per day: Problems 1-2: Spiral Review. Prior grade-level standards that support readiness and previously taught grade 4 concepts. Problems 3-5: New Learning Current grade 4 TEKS focus. This intentional balance promotes retention of prerequisite skills while building depth in grade-level standards.”

For example, during the data analysis unit, “Problem of the Day” questions range from comparing fractions to multistep problems involving fractions and multiplication. All questions were introduced in previous units. These activities bridge learning across lessons and units to ensure that students maintain proficiency and achieve long-term mastery.

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

The materials provide interleaved practice opportunities with previously learned skills and concepts across lessons within the “Problem of the Day Journal.” Daily problem sets include five problems that are designed for “interleaved practice to develop flexible thinking across mathematical domains.” For example, in the data analysis unit, students are given a pictograph and asked to “write and solve an equation to find the fraction of all the balls that are basketballs or footballs,” requiring them to apply concepts from both the fractions and addition units. These activities provide interleaved practice opportunities that connect previously learned concepts across units.

The 4th Grade Math Practice Book Teacher Edition instructs educators to have students solve multiple problems using different methods. This practice strengthens mathematical proficiency and aligns with interleaved practice opportunities for previously learned skills and concepts across lessons and units. This approach encourages students to shift between varied strategies, fostering the cognitive flexibility necessary to integrate new knowledge with past learning. For example, lesson 4.4C presents students with a graphic organizer that asks students to represent multiplication products in a variety of ways using arrays, area models, or mental math. The “Guided Practice,” “Partner Practice”, and “Independent Practice” activities present a mixture of opportunities to use a variety of strategies. Some of these same strategies can be found in later lessons. For example, area models in 4.4D represent multiplication and arrays, and area models in 4.4E represent division problems. Students would later need to use multiplication and division skills to solve perimeter and area problems in the 4.5D lesson. This demonstrates skills and concepts being used across lessons and units. By consistently applying these interleaved techniques, the curriculum ensures that students not only solve individual problems but also develop a deeper, more cohesive understanding of mathematical concepts over time.

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

The materials include opportunities for students to interpret, analyze, and evaluate mathematical reasoning and representations. In the 4th Grade Math TEKS-tivity Book of the TEKS-tivity pathway, students analyze two graphs and respond to the prompt, “Who solved the problem correctly? Explain the mistake that was made.” This requires students to interpret data, analyze errors in mathematical reasoning, and evaluate the accuracy of each solution.

In the 4th Grade TEKS-tivity Book Teacher Edition, unit 5, activity 2 provides a task where students interpret and analyze a collection of arrays, area models, and equations. Students determine which equation is represented and to match a set of three cards for each question. Then, students can make connections between the representations, and upon evaluating the models, they can determine the mathematical situation to pair with an equation.

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

Questions and tasks require students to create models to represent math situations. For example, the “Vocabulary” activity in the 4th Grade Math TEKS-tivity Book unit 2, activity 5 has students “draw a model to represent 2 3/10” and “draw a number line and label the point 7/10.”

In the Practice Book pathway of the 4th Grade Math Practice Book Student Edition, students are directed to draw an area model to represent a division equation and an array to represent another. This occurs after students have had opportunities to analyze and evaluate models provided throughout the lesson, making connections between division models and equations representing quotients.

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

The materials include questions and tasks that provide students with opportunities to apply conceptual understanding to new problem situations and concepts. For example, the TEKS lesson 4.7C in the 4th Grade Math Practice Book Student Edition included in the Practice Book pathway starts with students using a circle handout to fold and cut, demonstrating 90- and 45-degree angles. After the paper-folding activity, students are introduced to the protractor and use what they learned about paper angles to estimate angles before measuring them with a protractor. During guided practice, students deepen their understanding by identifying angles marked on a printed protractor and determining their measures. Students then apply what they have learned during independent practice, in which they must determine the measures of a variety of new angles printed on the protractor. This progression supports students in applying their conceptual understanding of volume to new mathematical situations and contexts.

Additionally, in the 4th Grade Math Practice Book Student Edition, the TEKS lesson “Converting Measurements” has students answering questions such as “Based on this information in the table, how many feet are in 84 inches?” In the next lesson, “Solving Measurement Problems,” students begin answering questions such as, “Madi has 8 feet of ribbon to make bracelets. She needs 4 inches of ribbon to make each bracelet. How many bracelets can she make with the amount of ribbon she has?” This progression supports students in applying their conceptual understanding of measurement conversion to new mathematical situations and contexts.

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

The materials support automaticity and fluency through repeated opportunities for cumulative practice, retrieval, and ongoing application of previously learned mathematical concepts and procedures using the “Problem of the Day Journal” in the Practice Book pathway. Monday through Thursday, students complete five problems per day, each designed to take only five to seven minutes as a structured warm-up or instructional launch. The first two questions are a spiral review, and the last three questions focus on new learning. For example, the “Week 18 Problem of the Day” practice set on Tuesday includes spiral practice of expanded notation and decimal models, as well as multiplication and division word problems from the current unit. This daily routine builds the automaticity and fluency needed to complete grade-level tasks by reinforcing concepts during the first five to seven minutes of class each day.

In the 4th Grade Math TEKS-tivity Book within the TEKS-tivity pathway, students develop procedural fluency by solving perimeter and area problems involving rectangles and squares, including finding missing side lengths and determining unknown measurements. The “Reflection,” “Journal,” and “Math Talk” prompts require students to explain how to determine perimeter, distinguish perimeter from area, describe strategies for finding missing dimensions, and justify their calculations of area. These activities support accurate, efficient, and flexible application of mathematical procedures while encouraging students to explain and apply appropriate solution strategies.

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.

The materials provide opportunities for students to practice applying efficient, flexible, and accurate mathematical procedures. For example, TEKS lesson 4.4C in the 4th Grade Math Practice Book Student Edition within the Practice Book pathway, the educator asks, “Would counting all the small squares be an efficient way of finding the product of 13 x 15? (no).” During the guided practice for the lesson, the educator’s guidance focuses on flexibility by having students “select a model to represent multiplication that they are comfortable with. If one model does not make sense to a student, encourage them to try another model.” Students then practice accuracy through a variety of problems included in the “Independent Practice” section.

In the 4th Grade Math TEKS-tivity Book within the TEKS-tivity pathway, students develop accurate, efficient, and flexible mathematical procedures by solving perimeter and area problems involving rectangles and squares, including determining missing side lengths and unknown measurements. “Reflection,” “Journal,” and “Math Talk” activities prompt students to explain how to determine perimeter; distinguish perimeter from area; and describe strategies for finding missing dimensions, supporting accurate application of procedures, efficient use of formulas, and flexible application of mathematical strategies across related problem types.

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.

The materials provide opportunities for students to evaluate the efficiency of mathematical procedures by comparing multiple solution strategies. In the 4th Grade Math Practice Book Teacher Edition, the “TEKS Lesson” section for 4.4C instructs educators to ask, “Would counting all the small squares be an efficient way of finding the product of 13 x 15?” Additional questions include, “How is the area model different from the array above it?” and “How is it like the array?” Educators use these questions to guide student reflection on the procedures and draw attention to variances among strategies. Students are also asked to share whether they prefer Student A’s method or Student B’s, and why. The “Why Do I Need to Know This?” section at the bottom of the page states, “Being able to multiply in different ways helps you understand the parts included in a multiplication problem and allows many calculations to be performed mentally.” These embedded opportunities encourage students to analyze multiple procedures, compare strategies, and evaluate the relative efficiency of different solution methods.

The materials provide tasks that provide opportunities for students to evaluate procedures, processes, and solutions for accuracy. For example, in the 4th Grade Math TEKS-tivity Book within the TEKS-tivity pathway, in the data analysis unit’s “Engaging Activity,” students are given the following problem and must explain who is correct and provide an explanation: “Lyn and Wendy worked on the following problem on their math test. In science class, the students measured the lengths of several worms in centimeters and recorded their data in a stem-and-leaf plot. How much longer is the longest worm compared to the shortest worm? Lyn said the answer is 2.8 cm. Wendy said the correct answer is 28 cm. Who solved the problem correctly? Explain the mistake that was made.” Students evaluate the accuracy of each solution, identify any mathematical errors, and justify their reasoning with evidence from the problem. These embedded opportunities require students to analyze solution processes, determine the correctness of mathematical work, and explain why one solution is accurate and the other is not.

Across the materials, students engage in tasks that require them to refine accurate and flexible mathematical procedures throughout units. For example, in the 4th Grade Math Practice Book Student Edition within the TEKS-tivity pathway, students progress from the “TEKS Lesson” to “Guided Practice,” “Partner Practice,” and “Independent Practice” while representing and interpreting data using frequency tables, dot plots, and stem-and-leaf plots. Students repeatedly create, analyze, and interpret data using multiple representations, providing opportunities to build procedural accuracy and to demonstrate flexibility in selecting and using different mathematical representations to solve problems.

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

The materials contain embedded supports to help educators guide students towards increasingly efficient approaches. For example, in the 4th Grade Math Practice Book Teacher Edition within the Practice Book pathway, the TEKS 4.4C lesson embeds educator guidance that supports increasingly efficient approaches to multiplication. Educators ask students whether counting every square is an efficient method, model how to decompose factors into smaller arrays, and facilitate a comparison of Student A’s and Student B’s solution methods. These prompts guide educators in helping students recognize and select more efficient approaches for solving multiplication problems.

During “Guided Practice” and “Independent Practice” for TEKS 4.4D, the educator guidance supports increasingly efficient approaches by prompting educators to connect multiple multiplication strategies to the standard algorithm. Educator notes identify the standard algorithm as the most efficient procedure, while misconception guidance directs educators to help students relate models and partial products to the algorithm and practice selecting strategies that best fit the problem. Since guidance appears in the “Independent Practice,” it is included for both instructional pathways.

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

The materials explicitly state how the conceptual and procedural emphasis of the TEKS is addressed for the Practice Book pathway at the beginning of each new TEKS lesson in the 4th Grade Math Practice Book Student Edition. For example, the “Conceptual Learning Goal” section for TEKS lesson 4.5C states, “Students understand how to derive formulas for perimeter and area of rectangles and squares by using models and repeated addition or multiplication.”

In the TEKS-tivity pathway, the 4th Grade Math TEKS-tivity Book Teacher Edition includes a “Unit Overview” at the beginning of unit 4 “Addition and Subtraction” that states, “The focus of this unit is on the concepts of addition and subtraction of fractions and decimals. Students will use objects, pictorial models and number lines to represent and solve addition and subtraction problems.” Additionally, it mentions that students will use the standard algorithm to add and subtract whole numbers and decimals. It ends by saying, “Throughout this unit, students need to explain their thinking of how they add and subtract fractions with the same denominator and decimals to the hundredths.” This connects conceptual understanding of addition and subtraction to the ability to use procedural strategies, such as algorithms, to solve problems.

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 materials include questions and tasks to use concrete models and manipulatives, pictorial representations, and abstract representations throughout the 4th Grade Math Practice Book Teacher Edition within the Practice Book pathway. For example, TEKS lesson 4.2E educator guidance states, “Provide base ten blocks for pairs of students. Explain that in order to model decimal place value, the one hundred square will now represent one unit. Ask, ‘How many of the tens rods make the one whole? If the large square is one whole, what is the value of the rod?’ Continue questioning regarding the small cubes. Make sure students understand that the place value blocks are named based on what they represent (the hundreds square has become one unit, the tens rods have become one-tenth, and the unit cubes have become one-hundredth.)” The lesson also includes a guided notes page with pictorial representations of ones, tenths, and hundredths using both base 10 blocks and money. Students continue to practice with both concrete and pictorial models throughout the “Independent Practice.” Students then build on their abstract knowledge of decimals by comparing and ordering decimals in the following TEKS lesson.

In the TEKS-tivity pathway, the 4th Grade Math TEKS-tivity Book Teacher Edition, unit 5, activity 2 provides a task in which students make connections between arrays, area models, and equations to determine which equation is being represented and match a set of three cards for each question. This provides students with the opportunity to pair the pictorial representations with abstract representations in the form of equations.

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.

The materials include supports for students to connect, create, define, and explain concrete and representational models of abstract concepts, as required by the TEKS. For example, in the 4th Grade Math Practice Book Student Edition, students create concrete models of angles using flexible straws, angle makers, and folded paper circles before transitioning to abstract geometric concepts. Educators guide students to explain that the measure of an angle represents the spread of its rays and that the vertex is the center of the circle, helping students connect their concrete models to abstract concepts of angle measure and central angles. This progression supports students in creating, connecting, defining, and explaining concrete models to develop conceptual understanding of geometric relationships.

Students transition from representational models to abstract geometric concepts by drawing rays to create right, acute, obtuse, and straight angles within circles, identifying and naming angles, and measuring central angles from diagrams. Students explain how the drawings represent angle relationships and write conclusions about circles and angles, supporting them in creating, connecting, defining, and explaining representational models of abstract geometric concepts.

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

The materials provide opportunities for students to develop academic mathematical language through the use of visuals, manipulatives, and structured language-development strategies. For example, in TEKS lesson 4.6A “Identifying Attributes” in the 4th Grade Math Practice Book Teacher Edition within the Practice Book pathway, students use visual representations of lines, line segments, rays, angles, and two-dimensional figures to identify, color code, and describe geometric attributes. During the “TEKS Lesson” section, the educator projects the display and asks students to identify and name segments, rays, angles, and lines in the figure using correct mathematical vocabulary. Students then work in small groups to outline and name these geometric elements before sharing their responses with the class. The educator is directed to circulate, ask guiding questions, and facilitate whole-class discussion as students explain how they identified specific attributes, including parallel and perpendicular lines. The lesson further extends students’ academic mathematical language by having them analyze a classroom object for geometric attributes and compare their observations with visual models. These routines combine visual representations, collaborative discussion, educator questioning, and opportunities to orally explain mathematical reasoning to support students’ development and use of precise academic mathematical language.

In the 4th Grade Math TEKS-tivity Book within the TEKS-tivity pathway, students respond to prompts such as, “Explain how to represent data using a dot plot” and “Explain how to represent data using a stem-and-leaf plot.” The prompts require them to explain mathematical concepts using academic language. Additionally, each unit includes a “Vocabulary” section where students interact with key mathematical terms. For example, in unit 11 “Data Analysis,” students work with the terms data, dot plot, fractions, decimals, key, whole numbers, and more and respond to prompts such as, “Pick two words and describe the relationship between them,” and “Pick two additional words and describe the relationship between them.” These activities provide opportunities for students to develop and use academic mathematical vocabulary through oral and written language.

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

The materials include embedded educator guidance to scaffold and support students’ development and use of academic mathematical vocabulary in context. For example, the TEKS 4.4G lesson in the 4th Grade Math Practice Book Student Edition, the students are provided visuals. The educator guidance states, “Ask for volunteers to read aloud the two example problems. Have students locate vocabulary in the problems that would indicate estimation.”

In the TEKS 4.10E lesson in the 4th Grade Math Practice Book Teacher Edition, the following guidance appears in the “Misconceptions” section: “Students may not understand all the vocabulary associated with banking. An anchor chart containing important vocabulary with illustrations and examples is helpful for understanding these ideas.” Since this guidance is listed during the “Independent Practice” section, it is present in both instructional pathways.

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 materials include educator guidance that supports the use of appropriate mathematical language through academic vocabulary and structured mathematical discussions within the “Math Talks” in the TEKS-tivity pathway. Educator guidance encourages students to share their thinking during “Math Talks” and other collaborative learning experiences, providing opportunities to hear and refine the mathematical language used by their peers and to engage in mathematical discourse.

The 4th Grade Math Implementation Guide provides “Emergent Bilingual Oral and Written Discourse Support” for each lesson. This chart provides guidance for vocabulary support, exemplar responses to tasks, and sentence stems for syntax support.

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

The materials integrate the TEKS process standards appropriately throughout. For example, in the 4th Grade Math Practice Book Student Edition, TEKS 4.9A, students represent and interpret data using frequency tables, dot plots, and stem-and-leaf plots while solving questions about the data. Throughout the lesson, students create and use multiple representations, analyze mathematical relationships among the representations, and communicate their reasoning, integrating the TEKS process standards into daily instruction.

In the 4th Grade Math TEKS-tivity Book, unit 11 “Data Analysis,” students represent and interpret data using frequency tables, dot plots, and stem-and-leaf plots while answering questions and communicating their mathematical reasoning. Students create and use multiple representations, analyze relationships among the representations, and justify their conclusions, integrating the TEKS process standards into the lesson.

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

The materials include a description of how the process standards are incorporated and connected throughout the course. The 4th Grade Math Practice Book Teacher Edition explicitly describes how the TEKS mathematical process standards are integrated throughout the program. The guide explains that “Practice Lessons,” “TEKS-tivities,” “Problem of the Day,” and “Power Review” intentionally embed problem-solving, reasoning, communication, representation, and strategic use of tools. The guide further states that the 4th Grade Math Practice Book Teacher Edition and 4th Grade Math TEKS-tivity Book Teacher Edition provide supports that guide educators in incorporating these process standards throughout daily instruction.

The 4th Grade Math Practice Book Teacher Edition includes a “Process Standards” alignment matrix that crosswalks each grade-level content TEKS with the applicable mathematical process standards (4.1A–4.1G). The matrix demonstrates that the process standards are intentionally embedded across the curriculum rather than addressed in isolated lessons, supporting their incorporation throughout the course.

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

The materials include a description within each unit of how the TEKS process standards are incorporated and connected throughout the unit. Each lesson includes the section “Incorporation and Connection Through the Learning Pathway” that outlines the process standards and connects them to the learning objectives throughout the unit.

For example, the unit 1 overview states, “Throughout the unit, students apply the mathematical process standards by analyzing relationships, representing problems with models and equations, and communicating mathematical reasoning.” This is then elaborated on in each lesson overview.

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

The materials include an overview of how the process standards are incorporated into each lesson within the 4th Grade Math Implementation Guide. Each lesson includes an “Incorporating and Connection Through the Learning Pathway” section that specifies how and where the process TEKS are incorporated throughout the lesson.

For example, unit 1, lesson 1 states, “The learning pathway begins in the ‘TEKS Lesson’ as students interpret the value of digits in place-value positions and describe ten-times and one-tenth relationships. Through place-value tables, multiplication and division by 10, decimals, and money, students build a shared conceptual model, communicate ideas in multiple forms, and analyze the relationships that define the content (4.1C, 4.1D, 4.1E, 4.1F, 4.1G). ‘Guided Practice’ maintains those representations while adding educator-supported problem analysis and strategy selection (4.1A, 4.1B, 4.1D, 4.1E, 4.1F). ‘Partner Practice’ then shifts the work to collaborative reasoning: students compare methods, question one another, and justify conclusions with models, symbols, measurements, or contextual evidence (4.1A, 4.1D, 4.1E, 4.1F, 4.1G). ‘Independent Practice’ removes the collaborative supports and asks students to transfer the same ideas to new formats and applications, complete the problem-solving process, and evaluate whether their answers are reasonable (4.1A, 4.18, 4.10, 4.1E, 4.1F, 4.1G).”

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

The materials provide opportunities for students to think mathematically and make sense of mathematics. In the 4th Grade Math TEKS-tivity Book, unit 11 “Data Analysis,” students engage in “Math Talks” by discussing prompts such as, “How do you represent data on a stem-and-leaf plot?” and “How do you represent data on a dot plot?” Students also respond to questions such as, “How do you solve problems from a dot plot representing whole numbers?” These prompts require students to analyze mathematical concepts, explain the purpose of mathematical representations, and connect the use of graphs to problem-solving, providing opportunities to think mathematically and develop conceptual understanding of mathematics.

In unit 5, “Engaging Activity 7” provides students with opportunities for persevering through problem-solving four open-ended, multistep problems. For example, the first question scenario asks, “Bridget purchased 25 boxes of plastic forks. Each box contained 12 forks. She gave each of the 5 customers the same number of forks. How many forks did she give each customer?” Because the directions only instruct students to show their work, students are free to explore mathematical strategies as they choose their own strategy for solving each problem.

In the “Problem of the Day Journal,” students engage with open-ended questions, multi-part tasks focused on the problem-solving process, and diverse visual models to connect math concepts. Built-in tools help students persevere through challenges by gradually increasing task difficulty and facilitating educator-led questioning.

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 materials support students in understanding and explaining that there are multiple ways to represent mathematical information. In unit 11 “Data Analysis” in the 4th Grade Math TEKS-tivity Book, students work with multiple representations of data, including frequency tables, dot plots, and bar graphs. “Reflection” activities and “Math Talk” prompts require students to explain their thinking using these representations through questions such as, “How do you solve problems from a dot plot representing whole numbers?” These opportunities support students in understanding that data can be represented using different mathematical models and in explaining how those representations are used to solve problems.

The materials support students in understanding and explaining that there can be multiple ways to solve mathematical problems. For example, in the 4th Grade Math Practice Book Teacher Edition, “TEKS Lesson: Multiplying Using Various Methods,” students are shown various multiplication strategies, including mental math, partial products, the use of mathematical properties, and the standard algorithm. Educator guidance directs students to discuss their strategies, share the reasoning behind each approach, and compare how they solved the same multiplication problem. “Extension Learning Opportunities” further instruct students to solve problems using two or more strategies and explain how each demonstrates the same mathematical reasoning.

Although the materials frequently ask students to explain their mathematical thinking, they do not support students in justifying that multiple representations or solution methods are valid. In unit 11 “Data Analysis” in the 4th Grade Math TEKS-tivity Book, “Reflection” activities ask students to respond to prompts such as “How do you solve problems from a dot plot representing whole numbers?” “Math Talk” prompts similarly ask students questions such as, “How do you solve a one-step problem using data?” These prompts require students to explain how they solved problems or describe the strategies they used. However, the materials do not require students to defend why one data representation should be selected over another, justify why one representation is more appropriate than another for a given data set, or compare and justify multiple solution strategies for solving the same problem.

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

The materials are designed to require students to make sense of mathematics through multiple opportunities to do, write about, and discuss mathematics with peers and educators. In the 4th Grade Math Practice Book within the Practice Book pathway, students engage in an educator-guided lesson, followed by “Guided Practice” and “Partner Practice,” in which they solve mathematical tasks and record their work. Educator guidance incorporates turn-and-talk prompts throughout the “TEKS Lesson,” providing opportunities for students to discuss their mathematical thinking with peers and educators. For example, in the 4th Grade Math Practice Book Teacher Edition, the “TEKS Lesson” section for 4.4H says, “Students may discuss the known information in small groups before solving parts A, B, and C. Have students work with a partner to read Paul’s problem and answer the questions.” The “Partner Practice” section provides three additional questions for students to work out. The 4th Grade Math Practice Book Teacher Edition mentions that “it is important for students to be able to explain the concept of remainders.” This emphasizes giving students opportunities to make sense of mathematics through math practice and peer discussion. The “Facilitating Questions” section provides opportunities for students to discuss math with their educator as questions are asked during “Guided Practice.”

The materials are designed to require students to make sense of mathematics through multiple opportunities to do, write about, and discuss mathematics with peers and educators. Within the 4th Grade Math TEKS-tivity Book in the TEKS-tivity pathway, students engage in collaborative mathematical activities with peers, participate in “Math Talks” to discuss mathematical ideas, and complete written “Reflection” and “Journal” prompts to explain and record their mathematical thinking. For example, in unit 11 “Data Analysis,” the “General Information” pages direct educators to place students in pairs, provide three to five minutes for discussion of the “Math Talk” prompts, and have multiple pairs share their responses with the class. Following these discussions, students complete written “Reflection” activities, “Journal” entries, and “Ticket Out the Door” tasks that require them to explain mathematical ideas, such as “What is a frequency table?”, “How do you solve problems from a dot plot representing decimal numbers?”, “Explain how to represent data using a dot plot,” and “How do you use data to solve problems?”. These instructional routines provide repeated opportunities for students to communicate mathematical thinking through both discussion and written responses with peers and educators.

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

In the 4th Grade Math Teacher Guide section titled “The Importance of Productive Struggle in Mathematics,” educators guide students to share and reflect on their problem-solving approaches by providing explicit guidance for facilitating reflection after solving mathematical problems. Educators are directed to ask reflective questions such as “What strategies worked well?” and “What would you do differently next time?” to encourage students to explain and evaluate their problem-solving approaches. The materials also encourage educators to have students use math journals to document challenges, strategies, and breakthroughs, providing opportunities for students to reflect on and justify their mathematical thinking.

In the 4th Grade Math Teacher Guide section titled “Using Facilitating Questions to Extend and Enrich Student Learning,” educators guide students to share and reflect on their problem-solving approaches. The educator guidance recommends using reflection questions to help students think about their learning processes and outcomes, questions that require explanation and justification to help students articulate their reasoning, and facilitating questions that drive group discussions in which students share ideas and learn from one another. These supports encourage educators to facilitate discussions that deepen students’ mathematical understanding through explanations, reflection, and justification.

The materials support educators in guiding students to share and reflect on their problem-solving approaches at the lesson level. For example, in the 4th Grade Math Practice Book Teacher Edition, the “TEKS Lesson” section for 4.3F directs educators to have students work in pairs or groups to agree or disagree with the statement, “I think 1/2 + 1/4 = 2/6.” Educators are instructed to ask “two or three volunteers to share their thinking with the whole group while asking questions to ensure that their explanations are understood.” This prompts students to share their thinking, justify the reasoning behind a solution, or argue for an alternative solution during a mathematical discussion about the reasonableness of adding and subtracting fractions using benchmark fractions.

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

Although the materials include a “Misconceptions” box in each lesson, they do not provide prompts or educator guidance for delivering explanatory feedback based on the anticipated misconceptions. For example, in unit 11 “Data Analysis,” lesson 2 “Solving Problems Using Data,” the 4th Grade Math Practice Book Teacher Edition states, “Students may be confused about how data are represented in each type of table. Provide practice with many different types of dot plots and stem-and-leaf plots.” While the misconception is identified and the mathematical concept is explained, the materials do not include educator prompts or instructional guidance describing how to respond to the misconception or provide principle-based explanatory feedback when students demonstrate this misunderstanding.

The materials do not provide prompts or guidance to support educators in providing explanatory feedback based on student responses. In unit 11 “Data Analysis,” students are tasked with making a table to organize the data on the tally sheet. The 4th Grade Math Practice Book Teacher Edition only includes the answer key, with no educator prompts or guidance on how to respond to students’ explanations or to provide principle-based feedback when a student’s response is correct or incorrect.