enVision+ Texas Mathematics, Adv 07

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

The Scope and Sequence tab, located under the “Browse” heading in the Navigation Guide, includes four files for school years of varying lengths (135, 165, 180, and 210 days). Each file includes topics (concepts) taught in the course, broken into individual lessons that indicate the Texas Essential Knowledge and Skills (TEKS) and the English Language Proficiency Standards (ELPS) addressed. For example, the 165-day scope and sequence describes topic 1, “Proportional and Nonproportional Relationships,” as a 12.5-day lesson that teaches TEKS 7AM.4A, 7AM.8A, 7AM.8B, 7AM.8C, and 7AM.9A and uses ELPS 1D, 1B, 2B, 2C, 2F, 3E, 3F, and 4B. This same topic spans 11 days, 13.5 days, and 16.5 days in the 135-day, 180-day, and 210-day scope and sequence files, respectively.

Additionally, the scope and sequence in the “End Matter” section of the enVision+ Texas Mathematics 2028 Advanced Grade 7 Teacher’s Edition provides a vertical scope and sequence, including advanced grades 6–8, geometry, and algebra II, detailing, “The statements in the Scope and Sequence are from the TEKS. The chart is organized to show progressions across similar strands.” For example, the scope and sequence chart includes 17 strands, such as Numbers and Operations and Circles, highlighting the strands taught in each course and showing that six of the 17 strands are taught in advanced grade 7.

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).

In the Pacing Guides tab under the “Browse” heading, four separate files include pacing guides for school years of varying lengths (135, 165, 180, and 210 days) and list the topics, the number of days each topic should take to teach, and the TEKS covered. The days allocated to each topic vary by instructional calendar length. Specifically, topic 10, “Financial Math,” requires 17 days under the 180-day instructional calendar and 16 days under the 165-day instructional calendar.

Likewise, under the “Browse” heading, four separate scope and sequence files for school years of varying lengths (135, 165, 180, and 210 days) include the suggested number of days allocated to each topic for each school-year length. For example, topic 1 “Proportional and Nonproportional Relationships” suggests 11 instructional days and two assessment days for the 135-day calendar and 16.5 instructional days and 3.5 assessment days for the 210-day calendar.

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 article “Advanced Grade 7 Content Organization Rationale” states that “Topics are sequenced to support mathematics progressions that connect new content to prior knowledge,” and explains that the TEKS recur in multiple lessons within and across topics to reinforce more connections.

Furthermore, in the “Program Overview” section of the Teacher’s Edition, a graphic organizer provides the rationale for the content grouping and how it builds mathematical connections. It states that topic 3 “Rational Number Operations” and topic 4 “Understand Real Numbers” are grouped because “Students apply mathematical process standards to extend what they know about operating with integers to fluently add, subtract, multiply, and divide positive and negative rational numbers. They expand their understanding of the number system to include irrational numbers. They apply their prior knowledge of rational numbers, exponents, and powers of 10 to compare and order real numbers, including numbers expressed in scientific notation.”

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

In Internalization Protocols and Observation Tools, a document titled “Teacher’s Topic Internalization Protocol” guides educators with the steps to internalize each unit and lesson by providing a four-part protocol with detailed sections for “Scope & Sequence and Pacing,” “Preparing to Teach the Topic,” “Assessing the Topic,” and “Gather and Prepare Materials.” For example, in the “Scope & Sequence and Pacing” section, step 1 guides educators to “Consult your scope and sequence to place this topic in the context of the year-long curriculum,” and step 3 of the “Preparing to Teach the Topic” section guides educators to “Identify relationships between lessons and how they build toward successful TEKS coverage.”

Additionally, the Teacher’s Edition provides a “Math Background” section for each topic. Specifically, topic 1, “Proportional and Nonproportional Relationships,” guides educators through key concepts, balance and coherence, process standards, and linguistic accommodations for the unit. Furthermore, the Teacher’s Edition provides side-by-side guidance for lesson internalization for each page of the lesson that corresponds to the Student Edition.

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

Internalization Protocols and Observational Tools provides several links as resources for instructional leaders to support educators in implementing the materials as designed, with step-by-step guidance on topic and lesson internalization. For example, the “Instructional Leaders’ Lesson Internalization Protocol” resource document contains a “Guidance” section that is broken down into three sections, one of which is “Implementation,” with guidance to “facilitate discussions about fundamental concepts and skills addressed in the lesson and how these are assessed through the lesson’s practice and the Exit Tickets.”

Furthermore, Internalization Protocols and Observational Tools provides the Instructional Leaders’ Student Work Analysis Protocol that has step-by-step guidance on analyzing student work. Specifically, guidance is provided for implementation to coach educators to “identify not just which TEKS are addressed, but which specific breakout of the TEKS” so that educators can “Sort and Categorize Student Work” to “create meaningful categories based on solution strategies, common misconceptions, levels of reasoning, [and] completeness of solution.”

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 Teacher’s Edition provides a “Math Background” section at the beginning of topic 2, “Analyze and Solve Percent Problems,” including guidance on key concepts, such as percent and proportion and representing the percent equation, and academic vocabulary, including linguistic accommodations for terms such as percent equation, markdown, and simple interest. For example, the “Vocabulary in Context” section includes commission, with a Math Meaning of “a portion of the price of an item that is paid directly to the salesperson” and other meanings, such as “a government group with a specific responsibility.”

Moreover, the “Math Background: Coherence” section provides how concepts connect to what students in grade A7 learned previously, such as ratio reasoning and rates in grade A6, and proportional relationships earlier in grade A7. It also explains how concepts such as scale drawings and the area of a triangle in topic 2 lead to concepts such as similarity in grade A8.

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 online platform includes a “Family Engagement” section for each topic that gives families access to the concepts in each lesson within the unit. For example, the “Family Engagement” section for lesson 1-1, “Understand Proportional Relationships,” includes two tutorial videos for the concept and hyperlinked glossary terms for proportion and proportional relationship. Families can change the language from English to Spanish by toggling the language selection at the top right of the window.

Additionally, each topic provides a “Home-School Connection” letter with detailed support and suggestions, in English and Spanish, that families can use to help their student understand and practice the topic’s concepts. For example, the “Home-School Connection Topic 1” letter includes an activity that challenges families to help their student identify the operation (multiplication or division) used with two fractions to find a solution. At the bottom of the letter, it suggests, “Have your child explain what the initial ratio means and describe how the unit rate expresses the same idea in a different way.”

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).

In the lesson plan, lesson 1-1, “Let’s Investigate: Understand Proportional Relationships” correlates with TEKS 7AM.4A and ELPS 4E for the Mathematics Objective “Determine whether quantities are proportional by testing for equivalent ratios” and the Language Objective “Describe how to test for equivalent ratios and explain, orally and in writing, whether quantities are in a proportional relationship.” The lesson includes questions such as “What operations might you use to enlarge measurements?” and uses a Quick Check from the Assessment Sourcebook as an instructional assessment that aligns with the objectives.

Additionally, lesson 8-3, “Describe Dilations,” provides “understanding dilations to enlarge or reduce a figure in a coordinate plane” as the objective. It correlates with TEKS 7AM.5B and ELPS 2D, provides students with an image of two T-shirts of different sizes but similar shape, indicates the width of the shirt, and then prompts the educator to ask, “If you wanted to print an image of the [smaller] shirt at the same size as the [larger] shirt, what would you do?” The lesson plan uses an Exit Ticket to assess student learning of dilations by providing four pairs of figures and asking students to identify which pair represents similar figures.

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 Texas Advanced Grade 7 Lesson Plans include lesson plans for every lesson in the course. The plans provide the number of days allocated for each lesson, then break them into detailed steps and indicate the number of minutes for each step. The document also includes the educator and student materials necessary for each lesson. For example, lesson 1-1, “Understand Proportional Relationships,” indicates the lesson should take two days, with four steps broken down into minutes for each step. The lesson lists necessary materials in the “Using Manipulatives: Understand Proportional Relationships” section: educators need centimeter grid paper and a centimeter ruler for students.

Similarly, each topic begins with a “Topic Overview” section that presents a chart of the lessons, citing the objectives, the materials educators and students need to deliver each lesson effectively, and the number of days allocated for each lesson within the topic. For example, the overview for topic 2, “Analyze and Solve Percent Problems,” includes lesson 2-1, “Let’s Investigate: Understand Percent as a Proportion,” which should take two days and lists play money as the necessary material.

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

Step 4 in most lessons in the Teacher’s Edition includes a lesson Quick Check formative assessment with guidance for educators on extended practice based on student performance, including suggested resources. For example, if a student scores zero to three points, the educator is guided to use a “Reteach to Build Understanding” activity or additional practice as an extension. If a student scores four to five points, the educator should use the “Enrichment” activity as an extension.

Moreover, the lesson plan document includes a blue plus sign symbol as educator guidance to indicate opportunities for extended practice in each step of the lesson. For example, in lesson 1-1 “Understand Proportional Relationships,” step 2 “Visual Learning,” a blue plus sign labeled “Extend Student Thinking” provides a challenge for students to look for patterns and generalize how to find perimeter on a coordinate plane and further challenges students to use the Pythagorean theorem to find the perimeter of a right triangle in a coordinate plane if they know the measure of the two sides.

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 grade A7 materials include a variety of instructional assessments at the unit and lesson level (including diagnostic, formative, and summative) that vary in task and question types in the Assessment Sourcebook. For example, each lesson has an Exit Ticket that serves as a formative assessment. The “Mid-Topic Performance Task” in each topic can be used as a summative assessment midway through the unit, which exhibits question types such as multiple-choice, open-ended, fill-in-the-blank, and graphing, and a “Readiness Assessment” as a diagnostic assessment at the beginning of each topic with varied question types including problem-solving, computational, and real-world problems.

Specifically, the Quick Check in lesson 7-3 informs differentiation needed for the lesson based on student performance, such as remediation, practice, or enrichment. The Try It! provided with each example can be used to gather data during and after instruction.

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

The Assessment Sourcebook includes the definitions and intended purposes for diagnostic, formative, and summative assessments in a chart that indicates the “why” and “when” for each type of assessment. For example, it states the following for diagnostic assessment: “Why: Diagnose students’ readiness for learning by assessing prerequisite content. When: Before instruction,” and goes on to provide “Instructional Outcomes Informed by Assessment Results” as “develop individual study plans, make grouping decisions, and prescribe specific activities to fill gaps in understanding of prerequisite content.”

Furthermore, the Teacher’s Edition provides detailed support for each lesson’s Exit Ticket, including its purpose and suggested instructional adjustments based on student answers, and ways to address common errors and misconceptions. For example, in lesson 6-3, the text guides educators in preventing misconceptions, including why students may mistakenly select answer choice A and how to respond.

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

The Assessment Sourcebook includes guidance to help educators administer instructional assessments consistently and accurately. For example, the section “How to Administer Assessments” guides educators to prepare for assessments by understanding and scheduling time for the assessment, ensuring a proper testing environment, and actively monitoring assessments, including making accommodations for emergent bilingual (EB) students.

Additionally, the Teacher’s Edition supports administering each Exit Ticket and Quick Check. For example, step 4 Quick Check includes guidance on addressing misconceptions, such as scripted prompt questions for educators, as well as a clock in the top corner of the page indicating the suggested time for the task.

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

In the Assessment Sourcebook, all assessment types throughout the course include answer keys that indicate the TEKS aligned to each question, as well as the objectives for each lesson and unit. For example, each Topic begins with a Readiness Assessment as a diagnostic tool for the specific TEKS and objectives students will learn during the unit. Throughout the topic, formative assessments such as the Quick Check and Exit Ticket gauge students’ achievement of the TEKS and objectives aligned with the individual lessons in the unit. Finally, the Topic Assessment and Topic Performance Task serve as summative assessments that align with all the unit’s TEKS and objectives.

Specifically, in the Teacher’s Edition, each Let’s Build lesson identifies the TEKS aligned to the lesson’s Exit Ticket. In addition, each lesson ends with an item analysis chart that aligns each Quick Check item to the assessed TEKS.

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

The grade A7 materials include instructional assessments with TEKS-aligned items at varying levels of complexity. In the Assessment Sourcebook, each assessment includes an answer key showing the Depth of Knowledge (DOK) level and the TEKS for each item-type question. For example, the topic 1 assessment includes eight questions (one DOK-1 and seven DOK-2), some of which are multiple-choice, while others are open-ended, two-part, or multi-select.

Moreover, in the Teacher’s Edition, each Let’s Build lesson includes Exit Ticket items aligned to the corresponding DOK level, and the end of each lesson includes an item analysis chart that identifies the appropriate DOK level for each Quick Check item. For example, lesson 12-3 has a Quick Check with an item analysis of the five questions, including the DOK and the TEKS for each question type, such as open-ended and multiple-choice.

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

In step 4 of each lesson, students answer five questions in an online Quick Check that is automatically scored; based on student performance, the system assigns a remediation, practice, or enrichment activity. The Teacher’s Edition gives a scoring interpretation for the Quick Check to guide educators to “use the Assessment Sourcebook version to prescribe targeted remediation or enrichment.” For example, the scoring interpretation guides educators to reteach to build understanding and use additional vocabulary support activities for students who score zero to three points.

Additionally, the Teacher’s Edition includes an Exit Ticket in each Let’s Build lesson overview and supports educators in interpreting and addressing student performance through TEKS-aligned assessment items. For example, at the end of lesson 3-3, an item analysis chart aligns the Quick Check item to the corresponding TEKS and identifies intervention lessons to support student skill development and understanding.

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

In the Assessment Sourcebook, each assessment includes an answer key with an Intervention Lesson tied to each question or task to support students with that concept. For example, if a student does not correctly answer the questions in the Quick Check for lesson 1-7, the educator is guided to use Intervention Lesson M34 for that student.

Specifically, the Quick Check support in step 4 of lesson 12-3 includes a rubric to determine whether remediation, practice, or enrichment is needed based on student performance and then directs the educator to the varied activities in the Differentiation Library.

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 grade A7 materials include charts for educators to track student progress and growth, and charts for students to track their own progress and growth. For example, the Student Progress and Growth Teacher Tool allows educators to mark student progress and growth according to the TEKS for each lesson, using symbols such as “x” for “working on it,” “–“ for “almost there,” and “+” for “got it.” Likewise, students can track their own progress and growth Before Topic, During Topic, and After Topic using the Student Progress and Growth Tracker for each lesson objective with selections such as “I Can,” “With Help,” and “Not Yet.”

Additionally, each lesson’s Exit Ticket in the Assessment Sourcebook includes a student Self-Assessment that allows students to track progress toward the lesson’s math and language objectives. For example, in lesson 6-3, one Exit Ticket question includes a self-assessment for students to complete at the bottom of the page for both the math and language goals. The students rate themselves as “Got it,” “Need help,” or “Working on it.”

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 Grades 6-8 Intervention System offers scaffolded lessons with educator guidance and student practice designed to support learners who need extra help mastering grade-level content and skills. For example, “Intervention System Booklet K: Expressions, Equations, and Functions, Grades 6–8” contains an intervention lesson, “K4,” for students struggling with expressions with addition and subtraction, which includes explicit educator steps in the “Guided Instruction” section, such as “Explain that students can use a variable, or letter, to represent the input. Then, using that variable, they can write an expression to represent the rule,” and a “Practice” section for students to complete some practice exercises that guides the educator with “Error Intervention” and “If You Have More Time” sections.

Additionally, the Teacher’s Edition provides differentiated support throughout each lesson, including strategies and activities to immediately meet student needs. The Exit Ticket in each Let’s Build lesson includes guidance for students who have not yet reached proficiency. In step 2, “Support Student Understanding,” strategies provide additional help during instruction, and the Quick Check in the fourth step helps educators identify appropriate remediation, guiding them to reteach to build understanding or provide additional vocabulary support activities to help students master the content and skills. For example, in lesson 6-3, “Let’s Build: Understand the Converse of the Pythagorean Theorem,” the Exit Ticket guides the educator in the “Prevent Misconceptions” callout: “Students who select answer choice A may be finding the sum of twice each smaller side and verifying that the sum equals twice the largest side. When working with identifying right triangles throughout the lesson, such as in Do You Know How Item 4, pause to remind students that squaring a number is not the same as doubling a number.”

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 grade A7 materials include pre-teaching and embedded supports for unfamiliar vocabulary and references within the text in the “Linguistic Accommodations” section at the beginning of each topic in the Teacher’s Edition. For example, in the “Context Setting Vocabulary” section of topic 4, pre-teaching supports state, “Students will encounter the following terms in this topic; be sure they understand their meaning to make sense of the problem situation.” It continues with terms that are referenced in each lesson, such as plot in Lesson 4-1, because the “Explore and Share” section asks students to “Plot and label as many different kinds of numbers you can think of on the number line from 0 to 4.” Likewise, the “Vocabulary in Context” section of the “Linguistic Accommodations” section provides meanings of the word power, including the Math Meaning as “The product obtained by multiplying a quantity by itself one or more times,” and Other Meanings as “Strength, ability to do something; energy.”

Moreover, every Let’s Build lesson contains an embedded Language Support description and activity that guides educators in connecting to prior knowledge and clarifying academic vocabulary. For example, the “Language Support” section in lesson 9-2, “Let’s Build: Connect Formulas for Lateral and Total Surface Area,” guides the educator in “Connecting to Students’ Experiences” to “ask if they have seen columns on a porch or other building,” and to “invite any students who have seen columns to describe their shape to the class, and encourage them to draw pictures on the board to show what they are describing.” The guidance continues to “direct students to the diagram of the cylinder in the solution,” and “Ask students to relate the figure to the discussion about porch columns…to write simple definitions for the height, base, and surface area of the cylinder in the context of the problem,” connecting prior knowledge of columns on buildings to the current lesson using the academic vocabulary of cylinders.

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 Teacher’s Edition provides differentiated instruction for each lesson with specific guidance on enrichment and extension activities, such as Early Finishers, which gives an additional question that challenges students to dive deeper into the concept. For example, in step 1, “Explore and Share,” of lesson 3-3, “Let’s Build: Fluently Multiply Rational Numbers,” students are multiplying rational numbers to find the length of blue fabric to use to make a replica of the United States flag if the blue region of the flag is seven-thirteenths the width and two-fifths the length of the flag, by choosing a length for the flag and solving the problem. The Teacher’s Edition guides educators to ask Early Finishers, “How would the problem change if Stella were creating a bedspread with a yellow section that was three-fourths the length of the entire bedspread?” Then, “Step 2: Visual Learning” includes guided examples with an “Extend Student Thinking” section that guides educators to “Challenge students to think about how they would determine Petra’s change in elevation if it were two and three-fourths times Ben’s change in elevation.” Finally, the “Quick Check” in “Step 4: Assess and Differentiate” includes guided differentiation for remediation, practice, or enrichment activities.

Furthermore, the materials introduce each topic with a Math Walk question and video to engage and excite students, connect to prior knowledge, and link to real-world experiences and scenarios. The “Pick A Project” follows, with differentiated extensions using varying DOK levels. For example, topic 3: Rational Number Operations” begins with a Math Walk that uses a video about scoring in different games, and asks students, “How are negative numbers used in scoring points?” The Teacher’s Edition provides a list of questions and guides the educator to “give students copies of these Math Walk questions or project them and have students turn and talk to a partner followed by a whole-class discussion.” Next, the “Pick A Project” activity of the “Differentiation Library Overview” section of the beginning topic pages guides the educator to “Use anytime,” offering four different project contexts, using “Varied Activity Modalities,” leading to “Varied Final Products,” such as 3B with an engaging context of crafting, the modality of design, and a “Budget and business proposal” as a final product.

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 Let’s Build lessons include explicit prompts and guidance the educator can use to explain the concepts. For example, lesson 3-2, “Let’s Build: Fluently Add and Subtract Rational Numbers” provides explicit guidance in the Teacher’s Edition to “Engage students in a discussion about the Essential Question [How are adding and subtracting integers related to adding and subtracting other rational numbers?]” in “Step 2: Visual Learning,” guiding the educator to “review some of the properties (Commutative, Associative) and procedures used for adding and subtracting signed integers,” if necessary. After introducing the example problem that uses a number line to find the distance between the summit of a volcano and sea level when the magma reservoir’s distance below sea level and the distance between the magma reservoir and the summit of the volcano is known, the Teacher’s Edition prompts the educator to ask, “Why are the numbers added?” and then to say, “The sum [negative two and three-fourths plus five and one-fourth] is rewritten as the difference [five and one-fourth minus two and three-fourths]. How can you use properties of numbers to show why these expressions are equivalent?”

Additionally, every Let’s Investigate lesson explicitly guides educators with prompts and guidance to model and explain the lesson’s concepts. For example, lesson 12-1, “Let’s Investigate: Understand Likelihood and Probability” introduces a probability situation using three spinners with three differently sized sections that a DJ will use to spin and choose which type of music to play (Classical, Rock, or Pop), and asks how the outcomes of the spins will be different for each of the three spinners. The Teacher’s Edition guides the educator to introduce the investigation with explicit prompts in the “Elevate Student Voice: Engage Students in the Context” section to ask questions such as, “Have you ever played games at a fair? Have you played board games with spinners?” Next, the materials guide the educator to “Use the Slow Reveal Slides” to “Reveal part of the information. Ask: What do you notice? What do you wonder?” Then, the class reviews and discusses four samples of student work in step 1, “Investigate,” that illustrate various approaches to the solution and possible errors. Each sample includes direct prompts for the educator to use when guiding students in analyzing the student samples, including “Does the size of the sections affect the probability?” to interpret a student’s work that incorrectly reasons that because there are three sections on each spinner, there is an equal chance of spinning each type of music.

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

The grade A7 materials include educator guidance and recommendations for effective lesson delivery and facilitation using a variety of instructional approaches across three lesson types: Let’s Build, Let’s Investigate, and Let’s Model. Each Let’s Build lesson includes problem-based learning and direct instruction, using four steps in which students move from problem-based investigations to direct instruction through guided examples leading to independent practice and problem solving, and ending with assessment. Let’s Investigate lessons include a problem-based learning task with time to investigate foundational understandings. For example, lesson 1-1, “Let’s Investigate: Understand Proportional Relationships,” guides the educator to “Anticipate students’ solution strategies. Think of various ways students will explore and use proportions and proportional relationships to enlarge a drawing of a puzzle,” in the Teacher’s Edition before introducing an investigation to create a larger puzzle from a smaller scale drawing. It continues with guidance to “Monitor Students at Work. Ask questions to assess and advance students’ thinking,” before guiding educators in the “Choose a Problem” section to “Assist students in selecting a problem to solve individually,” with recommendations for which students should select each problem (A, B, C, and D) according to their level of understanding of proportional relationships. Finally, Let’s Model lessons guide educators in leading students to investigate a real-world situation.

Furthermore, lesson 6-3, “Let’s Build: Understand the Converse of the Pythagorean Theorem,” guides educators through four steps with recommendations for effective lesson delivery and facilitation. For example, step 1, “Explore and Share,” in the Teacher’s Edition begins by guiding the educator to ask the class how they know if a triangle is a right triangle, then observe students as they try to identify what side lengths to select from a given set that will create a right triangle. It continues guiding the educator to “Have [students] discuss the methods they could use to check whether the triangles are in fact right triangles; they may suggest drawing the triangle and measuring the angles or using the Pythagorean Theorem.” Next, “Step 2: Visual Learning” guides educators to work through a structured sequence to build understanding of the converse of the Pythagorean Theorem before moving into practice. After the second example, the section “Support Student Understanding” recommends, “Review common errors that students make when using the Pythagorean equation,” posing sample student errors that struggling students can identify, and “Extend Student Thinking” recommends, “Have students investigate Pythagorean triples,” and provides several practice examples for students.

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.

The grade A7 materials include the Advanced Grade 7 Program Overview, which provides a chart that organizes a variety of practice types and opportunities by format (whole group, small group, or individual) and specifies whether each practice is guided, independent, or collaborative. For example, the recommended structures for Math Talks are whole group and small group, using guided or collaborative practice, and Topic Review is recommended for whole-group, small-group, or individual structures, using guided, collaborative, or independent practice.

Moreover, the materials explicitly guide educators on structuring practice across multiple formats throughout the lesson, such as in step 1, “Explore & Share,” of lesson 9-2, “Let’s Build: Connect Formulas for Lateral and Total Surface Area.” The Teacher’s Edition guides educators in facilitating a collaborative activity, recommended as a whole-group structure, where students discuss how to find the area of a rectangular prism net. Then, the materials recommend a small-group structure for students working to “Monitor, Select, and Sequence,” guiding that “Students might draw rectangles to represent a top and bottom of the box and then draw four rectangles to represent the sides of the box.” Next, “Step 2: Understand & Apply” guides educators through guided practice with “Try It!” problems embedded after each example, with answers provided, allowing educators to check for understanding before moving forward. Then, the materials provide “Support Student Understanding” and “Extend Student Thinking” sections tied to specific examples, offering additional guided and extension practice structures for individual students who need further support or challenge. Finally, the “Do You Understand?” and “Do You Know How?” sections provide a structured transition from guided to independent practice for individual students at the close of the lesson.

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 grade A7 materials include a “Linguistic Accommodations” section in the Teacher’s Edition that provides guidance and support for topic vocabulary. The ELPS chart at the bottom of the second page of the section identifies the specific ELPS targeted in each lesson, meeting the needs of all five language proficiency levels and aligning the ELPS modalities to the lesson content. For example, the ELPS chart in topic 5, “Solve Problems Using Equations and Inequalities,” indicates the targeted ELPS in each lesson, such as Writing 4C in lesson 1, Speaking 2D in lesson 2, and Reading 3F in lesson 3, which are designed to engage students in using increasingly more academic language. Specifically, lesson 5-2, “Let’s Investigate: Solve Equations with Variables on Both Sides,” guides the educator in the “Targeted ELPS Support” aligned to Speaking 2D that “[Pre-Production level] Students may be unfamiliar with some vocabulary,” providing questions such as “What type of operations are inverse operations?” and “What is the inverse operation of addition?” The section also guides educators to “Have students identify vocabulary words and define them based on the context of the problem,” and then ask varied questions for each level, such as “Why are the two sides of the scale equal to each other?” for Intermediate students and “What are your definitions based on the problem context?” for Advanced students.

Similarly, each lesson in the Teacher’s Edition includes directly embedded “Targeted ELPS Support” sections, with instruction at five differentiated language proficiency levels, guiding educators on how to scaffold language access and engage students in using increasingly academic language. In lesson 3-3, “Let’s Build: Fluently Multiply Rational Numbers,” the “Targeted ELPS Support” aligned to Listening 1D guides educators to read Example 1 to students, including the two solution methods, and support pre-production-level students by having students point to words they do know in the example and sketching an image of a mountain and “label words students may not know, such as descend and summit,” while beginning students respond to simple questions with one word. It also guides the educator in instructing intermediate students to use the idea of an elevator changing the height of people or objects in a building to frame their answer to the question.

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

The Linguistic Accommodations pages at the start of each topic in the Teacher’s Edition provide an extensive array of linguistic strategies and resources that may be integrated with any state-approved bilingual/ESL program. For example, the Linguistic Accommodations pages in topic 5, “Solve Problems Using Equations and Inequalities,” state, “Activities in this topic offer diverse and engaging experiences with math vocabulary to build confidence and support for all, but particularly for Emergent Bilingual (EB) students in developing both their academic and language skills.” The pages include sections such as “Topic Vocabulary Support,” “Metalinguistic Transfer to Spanish,” “Cognates,” and an ELPS chart to help educators use the materials effectively in state-approved bilingual/ESL programs.

Specifically, in topic 12 “Probability,” the “Linguistic Accommodations” pages offer educators explicit implementation guidance aligned to the ELPS, including the “Metalinguistic Transfer to Spanish” section that identifies transferable skills, non-transferable skills, cognates such as ramp/rampa and vacations/vacaciones, and false cognates such as carton and cartón, providing educators with specific cross-linguistic guidance for implementing instruction with Spanish-speaking EB students. Additionally, the materials include an ELPS alignment chart that maps specific listening, speaking, reading, and writing standards in each lesson across the topic, providing educators with a clear implementation roadmap for delivering 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 grade A7 materials include Linguistic Accommodations for each topic in the Teacher’s Edition, with embedded educator guidance to support emergent bilingual students in oral and written discourse and to build academic vocabulary by reinforcing previously learned terms, defining current concept vocabulary, and previewing upcoming vocabulary. These resources provide background knowledge, cross-linguistic connections, and guidance on Spanish transfer (including transferable terms, non-transferable terms, and cognates) to increase comprehension throughout the topic. For example, the Linguistic Accommodations section for topic 5, “Solve Problems Using Equations and Inequalities,” provides a “Topic Vocabulary Support” section that develops academic vocabulary to increase comprehension while building background knowledge, and guides the educator to “be sure [students] understand [context setting vocabulary] meaning to make sense of the problem situation,” highlighting the use of inequality for the topic, and terms for individual lessons, such as “infinitely many solutions” in lesson 2. It also includes guidance on cognates, such as panels/paneles, for cross-linguistic connections students will use in oral and written discourse, as well as false cognates, such as carton and cartón. Finally, each topic includes an ELPS chart, broken down by lesson, to guide educators in using the ELPS, particularly for oral and written discourse, such as in lesson 1 “Targeted ELPS Support: Writing 4C,” which guides the educator to “Read Example 1 to students. Then have [Pre-Production] students write the steps needed to solve it as you say them,” and to “Have [Advanced] students revise Example 1 to include only the needed information and process for solving. Have students edit each other’s work to shorten the summary.” Later, in lesson 4, the “Targeted ELPS Support: Speaking 2B” section guides the educator to “Have students review Example 1,” and continues with varied ways to engage the students in oral discourse for each level, such as “Have [High Intermediate] students use a complete sentence using the words the quantity of to state the equation being solved.”

Furthermore, the materials provide “Targeted ELPS Support” sections embedded directly within lesson instruction that guide educators in supporting emergent bilingual students across both oral and written discourse. In the Teacher’s Edition, lesson 4-1, “Let’s Build: Understand Rational Numbers” embeds guidance in the “Language Support” section for the educator to build background knowledge and increase comprehension of the word classify, and “Ask students to describe examples of things that people might classify,” and then to “have them use the examples to write a definition for the word,” to engage students in oral and written discourse to develop academic vocabulary. Later in the topic, lesson 4-3, “Let’s Build: Evaluate Square Roots and Cube Roots” increases comprehension by making cross-linguistic connections using the cognate cube/cubo in oral and written discourse to develop academic vocabulary. The “Language Support” section at the beginning of the lesson builds background knowledge through oral and written discourse by having students complete cloze sentences, “Addition and [subtraction] are [inverse operations] because they undo each other,” and “Multiplication and [division] are [inverse operations] because they undo each other,” to confirm that students understand and write similar sentences explaining that square roots and cube roots are inverse operations of squaring and cubing, respectively. Then, the Targeted ELPS Support in the lesson, aligned to Speaking 2F, guides educators to build background knowledge and increase comprehension through oral discourse by displaying a square and a cube with the same side and edge length and asking students to use the visual representations to compare squares and cubes.

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.

Each topic includes lessons that contain a “Practice and Problem Solving” section that challenges students’ depth of understanding in solving problems aligned to the TEKS of the lesson’s concept(s), and ends with a Topic Assessment that uses scaffolded DOK-leveled questions aligned to the topic’s TEKS to assess students’ learning. For example, lesson 2-2, “Let’s Build: Connect Percent and Proportion,” uses a variety of questions aligned to TEKS 7AM.4A in the “Practice and Problem Solving” section, such as questions requiring students to use proportions to calculate percents, real-world questions where students apply and analyze percent and proportion calculations, and questions that require students to demonstrate depth of understanding to communicate and evaluate reasonableness of percents and proportions. The Assessment Sourcebook provides a Topic Assessment for topic 2, with questions that have students demonstrate depth of understanding to use proportions to calculate percents and solve a real-world evaluation aligned to 7AM.4A, and real-world problems that require students to calculate and compare simple interest and compound interest earnings, demonstrating depth of understanding of TEKS 7AM.4B.

Additionally, lesson 2-1, “Let’s Investigate: Understand Percent as a Proportion,” requires students to demonstrate depth of understanding aligned to the TEKS. For example, the lesson opens with step 1 “Investigate,” in which students explore a real-world tipping scenario using play money and assessing and advancing questions that prompt students to identify the part, the whole, and the percent, and to reason if an answer should be greater or less than the whole, demonstrating conceptual thinking and proportional reasoning before formal instruction begins, aligning with TEKS 7AM.1C and 7AM.1F. During step 2, “Connect,” students engage with a Choose a Problem task that offers four differentiated real-world contexts at increasing complexity, including developing understanding of percents less than 100, percents greater than 100, percents less than 1, and evaluating fairness by comparing percent increases across different salary amounts, moving students from application of equivalent ratios toward analysis and reasoning about proportional relationships aligned with TEKS 7AM.4A. The embedded “Connect” items require students to justify their thinking, moving students beyond recall toward mathematical communication and reasoning aligned with TEKS 7AM.1D and 8AM.1F. The Key Concept and Talk About Math Ideas further consolidate understanding by requiring students to articulate how a percent over 100 equals a part over a whole and to discuss why percentages are useful when comparing small and large data sets. Next, step 3, “Practice and Problem Solving,” engages students with exercises across DOK levels 1–3, including higher-order thinking exercises, such as item 17, which requires students to compare two different commission structures and justify which worker earns more. Finally, the Quick Check assesses students at DOK levels 1 and 2 aligned with TEKS 7AM.4A, 7AM.1A, 7AM.1D, and 7AM.1F.

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

Lesson 12-2, “Let’s Build: Understand Theoretical Probability” uses scaffolded steps, including Explore and Share and Visual Learning, that guide educators in using a variety of strategies and visual models in the guided examples, such as spinners with different colors and letter and number grids, to use theoretical probability to make predictions. Next, the students use theoretical probability and proportional reasoning to make predictions. The “Practice and Problem Solving” questions begin with making predictions using theoretical probability in real-world situations, and progressively increase in rigor, requiring students to demonstrate higher order thinking for a theoretical probability real-world problem about a store giving customers scratch-off cards labeled with numbers from 1–10 that result in different discounts, including a 15 percent discount for an even number, a 30 percent discount for an odd number greater than 6, and a 20 percent discount for any other number. Students are asked to use this situation to determine the theoretical probability of each discount, then answer the question, “The store manager gives out 300 scratch-off cards. Which discount will the greatest number of customers likely receive? Explain,” leading to proficiency in TEKS 7AM.6D.

Additionally, lesson 2-1, “Let’s Investigate: Understand Percent as a Proportion” includes questions and tasks that progressively increase in rigor and complexity, leading to grade-level proficiency in the mathematics TEKS. In step 1, “Investigate,” students begin at a concrete, exploratory level by using play money to investigate a real-world tipping scenario, identifying the part, the whole, and the percent, and reasoning about whether their answer should be greater or less than the whole. Questions such as “Which number represents the part?” and “Which number represents the whole?” establish foundational understanding, while more challenging questions like “whether 18 to 20 percent of the bill is a good tip” and “when a tip becomes inappropriate” will help students move toward higher-order reasoning. In step 2, “Connect,” the Choose a Problem task offers four differentiated real-world contexts that systematically increase in complexity. For example, Problem A assesses how to use equivalent ratios to find percents less than 100. Problem B introduces percents greater than 100 and what they represent. Problem C increases the complexity by introducing percentages less than 1 and requiring students to convert between percent and decimal forms of rational numbers, and Problem D requires students to evaluate the fairness of a three percent raise across different salary levels and reason why the same percent increase does not produce the same dollar amount for different salaries. In step 3, “Practice and Problem Solving,” the item analysis confirms the progression across DOK levels. This scaffolding, from concrete proportional exploration to abstract multi-step percent reasoning, ensures that students develop grade-level proficiency aligned with TEKS 7AM.4A.

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

The grade 7 materials demonstrate coherence across units by explicitly connecting patterns, big ideas, and relationships between mathematical concepts in the Program Overview. The page “From the Authors: Advanced Grade 7 Content Organization Rationale” describes how the content is grouped and sequenced to build connections. For example, topics 6–8 focus on the big ideas that geometric shapes can be transformed through translations, reflections, and rotations to produce congruent figures; dilations produce similar figures; and the Pythagorean Theorem describes relationships among the side lengths of right triangles. The materials further explain that students apply prior mathematical process standards and knowledge of coordinate grids and rational numbers to connect the relationships between transformations of geometric figures with proportional thinking, and use algebraic expressions to describe transformations. The big idea of similarity, including scale factor, is used to analyze and find missing measures in similar figures, and students connect patterns of operations with real numbers to the Pythagorean Theorem, area, and volume in solving geometric problems.

Additionally, each topic in the Teacher’s Edition begins with guiding pages to prepare educators to teach its concepts, such as the “Math Background: Coherence” page, which connects the topic’s concepts to patterns, big ideas, and relationships that students previously learned in grade A7, as well as how they connect to concepts that students will learn later in grade A7. For example, the “Math Background: Coherence” page in topic 6, “Understand and Apply the Pythagorean Theorem,” explains in the “Earlier in Advanced Grade 7: Number System” section that “in Topic 4, students extended their knowledge of rational and irrational numbers,” which connects to the big idea of operations with rational numbers and relationships between the sides of a right triangle in topic 6. The “Look Ahead” section of the page includes “Apply the Pythagorean Theorem,” explaining that “in Topic 9, students will compute the surface area and volume of figures,” connecting the pattern of the Pythagorean Theorem, “to find the length of missing measurements such as the radius, height, or slant height of a cone.”

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 grade A7 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 at the beginning of each topic in the Teacher’s Edition. For example, topic 12, “Probability,” begins with several pages that prepare educators to teach the topic’s lessons, including “Math Background: Coherence” and “Linguistic Accommodations.” The “Math Background: Coherence” page is separated into three columns, titled “Look Back,” “Topic 12,” and “Look Ahead.” The “Look Back” section connects the content learned in grade A6 and earlier in grade A7 to the content students are learning in topic 12, demonstrating the mathematical language that connects the concepts, such as datasets: “In Advanced Grade 6, students examined data sets to determine statistical measures. Students analyzed statistical measures to make predictions,” and “Earlier in Advanced Grade A7: Students developed fluency solving percent problems in real-world applications in Topic 2 and drawing inferences in Topic 11.” The “Topic 12” section uses the mathematical language “Simple Probability” and “Compound Probability” as headings to describe the content students will learn throughout lessons in topic 12, such as how students will “explore the likelihood that an event will occur or not occur” and “determine possible outcomes of compound events.” Finally, the “Look Ahead” section explains how the content and language students will learn in topic 12 connect, including: “In high school, students will continue to find probabilities of simple and compound events.”

Additionally, the “Math Background: Coherence” page in topic 12, “Probability,” of the Teacher’s Edition connects the content from grade A6 in the “Look Back” section, explaining that students learned to examine and analyze measures from data sets to make predictions, and the “Linguistic Accommodations” connects the language of the topic to prior terms, including inference and valid inference. In the “Look Ahead” section of the “Math Background: Coherence” page, the materials reference high school, where students will extend knowledge from finding probabilities of single and compound events to making inferences and predictions using a two-way frequency table.

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 grade A7 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, as outlined in the “Coherence” section on the first page of each lesson in the Teacher’s Edition. For example, the first pages of lesson 8-6, “Let’s Build: Solve Problems Involving Area of a Circle,” include a Math Talk that connects students’ prior knowledge of concepts and procedures from prior grade level(s) by analyzing four geometric shapes with similar dimensions, such as the side lengths of polygons and the circumference or radius of a circle, posing the question, “Which one doesn’t belong?” The “Coherence” section on the first page highlights that students will “learn the equation for the area of a circle and apply the equation for the area of a circle to solve for radius, area, and circumference,” which connects to topic 9, where students will “solve real-world and mathematical problems involving cones, cylinders, and spheres.”

Additionally, the “Coherence” section on the first page of each lesson in the Teacher’s Edition demonstrates coherence across the lessons by connecting prior knowledge of concepts and procedures from current and previous levels to the new mathematical knowledge and skills. One example is the “Coherence” section at the beginning of each lesson in topic 2, “Analyze and Solve Percent Problems.” The “Coherence” section in lesson 2-2, “Let’s Build: Connect Percent and Proportion,” connects students’ prior knowledge of the concepts and procedures for expressing ratios as part-to-part or part-to-whole and using ratios to solve problems from grade A6 to the new mathematical knowledge and skills, including representing percent problems using proportions and writing and using percent equations. The “Math Talk” activity used to engage students shows four different representations of part-to-whole situations, including proportions and bar diagrams, and asks students to choose one representation and explain how it differs. Later, lesson 2-6, “Let’s Build: Solve Markup and Markdown,” builds on students’ prior knowledge of concepts and procedures in using the percent equation to understand percent change from the current topic to connect the new mathematical knowledge and skill in relating percent change to percent markup and markdown in real-world problems.

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

The grade A7 materials provide spaced retrieval opportunities with previously learned skills and concepts across lessons and units, as demonstrated in a Venn diagram on the Space and Interleaved Practice in enVision+ Texas Mathematics page in the Program Overview, which compares the sections within the materials that offer spaced and interleaved practice, identifying that Math Talks and Fluency Practice both provide spaced retrieval opportunities. For example, the Math Talk section in lesson 5-1, “Let’s Build: Combine Like Terms to Solve Equations,” of the Teacher’s Edition asks students to look for a pattern in a string of steps that uses the distributive property to simplify an expression with two variables, which are skills and concepts that were previously learned in grade A6. The Fluency Practice at the end of topic 5, “Solve Problems Using Equations and Inequalities,” provides spaced retrieval practice for fluently adding, subtracting, multiplying, and dividing rational numbers, which students use across lessons and concepts in grade A7.

Additionally, the Math Background pages of each topic in the Teacher’s Edition explain how the materials span skills across the units. Specifically, the “Math Background: Coherence” section shows how learning is distributed across units and provides opportunities for spaced retrieval practice. For example, in topic 1 “Proportional and Non-Proportional Relationships,” students learn about proportional relationships by using equivalent ratios, proportions, and the constant of proportionality. In topic 2, “Analyze and Solve Percent Problems,” students build on this learning by connecting percents and proportions and using percent proportions to solve problems. Then, in topic 5, “Solve Problems Using Equations and Inequalities,” students apply these understandings to create and analyze scale drawings.

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

The grade A7 materials provide interleaved practice opportunities with previously learned skills and concepts across lessons, in “Practice and Problem Solving,” and units in “Review What You Know.” For example, the “Practice and Problem Solving” section of lesson 10-8, “Let’s Build: Understand How to Save for the Future,” provides interleaved practice across lessons to calculate simple interest and compound interest, such as directly multiplying interest rates and whole dollar amounts, using a table to determine balance after earning interest, and subtracting, multiplying, and adding values to calculate interest and balance amounts. The “Review What You Know” section of topic 11, “Use Sampling to Draw Inferences About Populations” provides interleaved practice across topics, including the “Vocabulary” section with close sentences to use words including “center, data distribution, statistical question, and variability,” the “Statistical Measures” section that has students determine different statistical measures, including mean and median, from a set of data, the “Data Representations” section that has students create data displays from the given set of data, and the “Statistical Questions” section that has students identify statistical versus non-statistical questions that can be used to gather data.

Additionally, in topic 11, “Use Sampling to Draw Inferences About Populations,” students build on their understanding of populations and samples across multiple lessons. In lessons 11-2 and 11-3, students learn how to generate random samples and determine whether a sample represents a population. In lesson 11-4, students apply what they know about populations, random samples, and proportions to draw inferences about populations. In lesson 11-7, students apply their knowledge of data distributions, measures of center, and variability to make informal comparisons and inferences about populations. Students are not repeatedly completing the same type of problem. Instead, they apply concepts through different skills across the topic.

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

The Let’s Model in 3 Acts lessons in each topic of the Teacher’s Edition require students to create models to solve problems involving mathematical concepts and situations and to interpret, analyze, and evaluate their models to find efficient solutions. For example, lesson 2-4, “Let’s Model in 3 Acts: The Smart Shopper,” presents students with an 18-second video about students shopping at a video game store. After students watch the video, they are tasked to write a question they can solve using a model, guided by questions including, “After watching the video, what is the first question that comes to mind? Write the Main Question you will answer. Make a prediction to answer this Main Question. Explain your prediction,” followed by a number line model with boxes on the ends labeled, “Too small” and “Too large.” In the second part of the lesson, students receive the detailed information they need to solve the problem regarding the cost of three electronic items and three coupons with different offers, such as 20 percent off, $20 off any one item, and 15 percent off. Students then interpret how their model can be used, given the information, to determine the least total cost for the three items, and analyze which coupon should be used for each item. In the third part of the lesson, students evaluate their model once the answer has been revealed using questions 11 and 12 that ask, “Does your answer match the answer in the video? If not, what are some reasons that would explain the difference? Would you change your model now that you know the answer? Explain.”

Additionally, in lesson 9-4, “Let’s Build: Find Volumes of Prisms and Pyramids,” of the Student Edition, questions and tasks require students to work with visual models, formulas, diagrams, and mathematical representations to compare the volumes of prisms and pyramids. For example, in step 1, “Explore and Share,” and step 2, “Visual Learning,” students interpret models and representations when they examine the fish tank model, prism and pyramid diagrams, and volume formulas to determine what quantities are represented and how the dimensions relate to volume. Students analyze models and representations by comparing the visual and algebraic representations of triangular prisms and triangular pyramids, and investigate how changes in base area and height affect volume. Students evaluate models and representations in example 1 as they justify conclusions about the relationship between the volume of a prism and a pyramid with the same base and height, and they determine whether representations support the stated mathematical relationship in the “Try It!” task, which asks students to evaluate whether the relationship remains true when different triangular bases are used and justify their reasoning.

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

The grade A7 materials include questions and tasks that require students to create models to represent mathematical situations in the Let’s Model in 3 Acts lessons in each topic of the Teacher’s Edition. For example, lesson 6-1, “Let’s Model in 3 Acts: Go With the Flow” presents students with a 10-second video depicting someone rotating a three-dimensional model of a right triangle with a sand-filled square adjacent to each leg. As the person rotates the model, sand begins to fall into the square adjacent to the hypotenuse. After students watch the video, they are tasked with writing a question they can solve using a model, guided by questions including, “After watching the video, what is the first question that comes to mind? Write the Main Question you will answer. Make a prediction to answer this Main Question. ________% will fit into the third square,” followed by a question asking students to justify their prediction. The second part of the lesson gives students the triangle’s side lengths: a little more than five, a little less than seven, and about eight and a half. Students then create a model using the given information to determine what percent of the sand from the two smaller squares will fit into the larger square.

Additionally, in lesson 12-6, “Compound Events,” students create probability models to represent compound events and use them to determine possible outcomes and probabilities. In step 3, “Practice and Problem-Solving,” and step 4, “Assess and Differentiate,” of the Student Edition, students create models to solve compound probability situations using representations such as spinners, coins, number cubes, and probability diagrams. The “Practice and Problem-Solving” tasks require students to represent compound events and determine sample spaces and probabilities based on those representations. The Additional Practice items further require students to construct and use probability models involving multiple outcomes and compound events.

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

The grade A7 materials include questions and tasks that provide opportunities for students to apply conceptual understanding to new problem situations and contexts in the Let’s Investigate lessons throughout the topics. For example, lesson 6-2, “Let’s Investigate: Understand the Pythagorean Theorem” in the Student Edition begins with a guided activity, “Diagonal Discovery,” that uses squares with their areas to represent the length, width, and diagonal of a cell phone and a television. Students write the relationship between the cell phone’s sides and its screen size. Then, students determine the television’s screen size. The materials guide students in developing a conceptual understanding of how to use the Pythagorean Theorem to determine the hypotenuse of a right triangle. Next, students select a new problem from the “Choose a Problem” section that contains four similar contexts, including a word problem using the Pythagorean Theorem, a problem to solve for the length of the hypotenuse of a right triangle, a real-world situation to determine if a triangular shelf will fit into a corner of a room with a right angle, and researching Pythagorean Triples to create a chart and a scatter plot to analyze the relationship between the sum of the squares of the side lengths of a right triangle and the sum of its hypotenuse, to apply the conceptual understanding to new problem situations and contexts. A guiding question asks students, “How was the strategy you used in Choose a Problem the same as your strategy in Diagonal Discovery? How were your strategies different?”

Additionally, in step 2, “Visual Learning” of lesson 1-2, “Let’s Build: Describe Proportional Relationships: Constant of Proportionality” in the Student Edition, the Essential Question asks, “How can you represent a proportional relationship with an equation?” In example 1, students learn how to use the constant of proportionality to write an equation in the form of y = kx by answering the question, “What is an equation that represents the proportional relationship between the time and amount of water filtered?” Students apply this conceptual understanding to a new problem situation in the “Try It!” problem to write an equation relating the proportional amounts of grape juice and apple juice used to make batches of fruit punch. In example 2, students solve a problem involving inches and centimeters and respond to “Do you substitute 18 for x or for y?” In example 3, students determine whether situations can be represented by an equation in the form y = kx and answer the “Try It!” prompt, “How do you determine whether the quantities in each table can be represented by an equation in the form y = kx?”

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

The grade A7 materials provide tasks designed to build the automaticity and fluency students need to complete grade-level tasks, such as the Fluency Practice Activity at the end of each topic in the Student Edition. For example, topic 3, “Rational Number Operations” Fluency Practice Activity, is designed to build automaticity in multiplying and dividing rational numbers. Students use this fluency later in lessons that require them to multiply and divide rational numbers, such as the grade-level tasks in topic 10, “Financial Math.”

Additionally, in topic 12, “Probability,” of the Student Edition, the Fluency Practice Activity “Riddle Rearranging” requires students to fluently add, subtract, multiply, and divide rational numbers, including decimals, fractions, and mixed numbers with negative values, by simplifying nine expressions and then arranging the answers in order from least to greatest. Students build automaticity in operations with rational numbers, including negative rational numbers.

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 grade A7 materials provide opportunities for students to practice the application of efficient, flexible, and accurate mathematical procedures within lesson 1-8, “Let’s Build: Identify Proportional and Nonproportional Relationships.” For example, the Teacher’s Edition guides the educator in explaining to students in the Math Talk that it is more efficient to convert fractions to decimals or decimals to fractions when rational numbers are mixed, before determining whether they form a proportional or nonproportional relationship. Then, in the examples, students practice applying flexible and accurate mathematical procedures to identify proportional and nonproportional relationships, including writing an equation in the form y = kx, creating a table of x- and y-values, or graphing the situation. Students practice applying efficient mathematical procedures to identify proportional and nonproportional relationships by determining the most appropriate method based on how variables are represented in a graph, table, or real-world situation.

Additionally, in lesson 6-2, “Understand the Pythagorean Theorem,” students apply the Pythagorean Theorem to determine missing side lengths, verify whether triangles are right triangles, and analyze mathematical reasoning using multiple representations and solution methods throughout the lesson. In step 1 “Investigate,” step 2 “Connect,” and step 3 “Practice and Problem Solving” of the Student Edition, the lesson supports efficient mathematical procedures by teaching students to use the equation a² + b² = c² as a systematic method for finding missing side lengths and determining whether a triangle is a right triangle. For example, “Practice and Problem Solving” items 5–15 require the correct application of the theorem to find unknown side lengths and evaluate triangle relationships. The lesson also supports flexible mathematical procedures in “Connect Solution Strategies,” where students compare different approaches by representing and analyzing relationships using geometric models, the areas of squares, equations, diagrams, numerical calculations, and real-world contexts involving screen sizes and right triangles. Finally, the lesson supports accurate mathematical procedures by giving students opportunities to identify and correct errors in sample student work, justify reasoning during class discussions, apply the Pythagorean Theorem in multiple contexts, and complete “Practice and Problem Solving” items that require precise calculations and justification of solutions. For example, in “Sample Student Work,” “Student 3 Work” gives students an opportunity to analyze an incorrect solution and discuss accurate mathematical 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.

The grade A7 materials give students opportunities to evaluate procedures, processes, and solutions for efficacy, flexibility, and accuracy within the Let’s Model in 3 Acts lessons in each topic of the Teacher’s Edition. For example, lesson 5-6, “Let’s Model in 3 Acts: Powering Down” presents students with a 53-second video about a person whose phone has 20 percent battery remaining, looks unsuccessfully for a charger, yet continues to use the phone. After students watch the video, they are tasked with writing a question they can solve using a model, guided by questions including, “After watching the video, what is the first question that comes to mind? Write the Main Question you will answer. Make a prediction to answer this Main Question,” followed by a question asking students to justify their prediction. In the second part of the lesson, students receive detailed information about the battery’s remaining percentage at specific times. Students then use various procedures and processes to determine how long the phone’s battery will last. After some time, the educator reveals the solution, and students compare and evaluate their procedures, processes, and solutions for efficacy, flexibility, and accuracy, including possible errors, in small groups.

Additionally, in lesson 3-5, “Solve Problems with Rational Numbers,” of the Student Edition, students evaluate strategies, processes, and solutions. In step 1, “Explore and Share,” students evaluate two approaches to finding Stefan’s weekly profit from a phone accessory store: converting weekly profit to shares first and converting daily and monthly income and expenses to weekly values. Students then compare the strategies, noting that both require converting amounts to the same frequency and assessing why the methods do not yield the same profit, leading them to evaluate the accuracy and limitations of each approach. In step 2, “Visual Learning,” students evaluate processes and procedures to determine which operations to use across multiple problem types. In example 1, students need to evaluate how a visual model informs procedural decision-making. In example 2, students evaluate two different solution methods for flexibility, including multiplying first and applying the distributive property to find Kevin’s score in a trivia game. In step 3, “Practice and Problem Solving,” item 12 provides water data from a park and asks students to evaluate which operation best represents the change in water level; then they assess the accuracy of multiple possible approaches before selecting one. Item 13 asks students to write different expressions to find the total number of points Marcelo earned and to evaluate flexibility in how the same mathematical situation can be represented. Later in the unit, in lesson 3-6, “Let’s Model in 3 Acts: First to 100,” students evaluate the appropriateness, accuracy, and flexibility of mathematical models for representing a real-world situation involving the addition and subtraction of rational numbers. In act 2, “The Model,” students evaluate which tool or representation is better for modeling the problem, a number line or operations, and they must justify why, which requires them to assess the efficiency and accuracy of each approach.

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

The grade A7 materials contain embedded supports for educators to guide students toward increasingly efficient approaches in step 1, “Explore and Share,” and step 2, “Visual Learning,” of Let’s Build lessons. For example, the Teacher’s Edition embeds support for the educator in lesson 8-4, “Let’s Build: Solve Problems Involving Scale Drawings” to guide students through using scale models to find the dimensions of the actual objects in step 1 “Explore and Share,” including having small groups of students discuss the relationship between a small plane and the actual plane when given the length of each before moving to step 2 “Visual Learning” to use a double number line, measuring inches and feet, to compare the measurements of the scale and the actual size of a kitchen island. The embedded supports prompt the educator to ask, “How does the double number line help to find the scale of the drawing?” to help students efficiently determine the proportion to use for the scale. Next, students use the constant of proportionality to determine the area of an actual object from a scale model and to reproduce a different-scale version of the same model. Before students move on to individual practice, the Key Concept embedded question, “What does the equation y = 2x below the triangle represent? Explain,” helps the educator guide students toward the most efficient approach to solving problems involving scale drawings.

Additionally, in lesson 3-1, “Let’s Investigate: Write Rational Numbers as Decimals” of the Teacher’s Edition, step 2, “Connect,” includes the “Connect Solution Strategies” section, which provides embedded educator guidance for facilitating mathematical discussions using students’ work and mathematical vocabulary. The Teacher’s Edition directs educators to “Use your students’ work or the sample student work to facilitate responses phrased in students’ own words” and “Encourage students to use the terms rational numbers, repeating, terminating, and integer in their explanations.”

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

The grade A7 materials explicitly state how the conceptual and procedural emphasis of the TEKS are addressed in the Math Background pages at the beginning of each topic in the Teacher’s Edition. For example, the “Math Background: Balance” page in topic 3, “Rational Number Operations,” explicitly states the conceptual emphasis in the “Conceptual Understanding” section, “Rational Numbers and Decimals,” that “Students write rational numbers as fractions and decimals. Students learn about terminating and repeating decimals and understand how to recognize a decimal as its specific type. (7AM.3A).” In the “Procedural Skill and Fluency” section, “Adding Decimals” explicitly states, “students develop procedural skill in adding rational numbers. Students use their knowledge of working within place values to add decimals like they previously added whole numbers. In order to easily align place values, line up the decimal points. (7AM.3B).”

Additionally, in lesson 3-2 “Fluently Add and Subtract Rational Numbers” of the Teacher’s Edition, the “Key Concepts” section explains why students learn to add and subtract rational numbers by stating the “Essential Understanding: Adding and subtracting integers is related to adding and subtracting other rational numbers.” The “Balance” section further explains the “Conceptual Understanding: Students extend their knowledge and understanding of adding and subtracting integers to all rational numbers.” The materials then explain how students apply this understanding through the “Coherence” section, which states that students “extend their knowledge of positive and negative rational numbers to adding and subtracting with rational numbers” and “apply their knowledge of adding and subtracting rational numbers to solve real-world problems,” while in the “Balance” section, “Application” states that students “add and subtract rational numbers to solve real-world 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 Program Overview describes the progression of concrete to pictorial (representational) to abstract models in the article, “Concrete, Representational, Abstract (CRA) Instructional Model.” It details, “Explore and Share in Let’s Build lessons and Let’s Investigate lessons ask students to solve a problem that embeds new ideas and to solve it any way they choose. Students might use concrete materials (counters, geoboards, angles, algebra tiles) [or] pictorial representations (number lines, arrays, grids, strip diagrams).” Students have access to digital manipulatives through the Brainingcamp program embedded in the materials for use as concrete models, and the Brainingcamp Live feature allows educators to view each student’s work with the digital manipulatives in real time.

Additionally, in lesson 12-6, “Let’s Investigate: Recognize Compound Events” of the Student Edition, students conduct a compound probability experiment using concrete number cubes to determine which player is more likely to win in step 1, “Investigate,” by physically rolling the number cubes, recording the results, and comparing experimental outcomes. The lesson extends students’ thinking by asking, “How can you test to see if the probabilities you calculated are accurate?” and by guiding students in comparing experimental and theoretical probabilities. Then, in step 2, “Connect,” students represent compound probability situations using sample spaces and visual game cards to organize all possible outcomes. Educator guidance in the Teacher’s Edition directs students to “determine the sample spaces for all individual events that make up the compound event. Then match every outcome in the first sample space to every outcome of the second sample space to create the sample space of the compound event.” Students use these visual representations to analyze probability before determining theoretical probabilities. Finally, students use fractions to calculate theoretical probability after determining all possible outcomes in a sample space. “Student Work 3” models calculating the theoretical probabilities of Player A (16/36) and Player B (20/36) to determine which player is more likely to win. Students move from the visual representational sample space to abstract numerical representations to justify their conclusions.

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 grade A7 Program Overview describes the progression of concrete to pictorial (representational) to abstract in the article, “Concrete, Representational, Abstract (CRA) Instructional Model.” It details, “Explore and Share in Let’s Build lessons and Let’s Investigate lessons ask students to solve a problem that embeds new ideas and to solve it any way they choose. Students might use concrete materials (counters, geoboards, angles, algebra tiles) [or] pictorial representations (number lines, arrays, grids, strip diagrams)... When students share and discuss solutions, rich conversations deepen conceptual understanding of connections between concrete, pictorial, and abstract.” The article explains in the “Visual Learning” section that “The Visual Learning in a Let’s Build lesson provides explicit instruction that connects students’ work in the Explore and Share to new ideas taught and shows pictures of concrete materials, drawings of concrete materials, diagrams, or some combinations of those to represent math concepts. The Visual Learning connects these representations to abstract numbers, symbols, and procedures.” Students have access to digital manipulatives through the Brainingcamp program embedded in the materials, which serve as concrete models they can connect to abstract concepts. The Brainingcamp Live feature also allows educators to view each student’s work with the digital manipulatives in real time. Moreover, the Desmos digital program offers representational models that students can create to connect to abstract concepts. In each Let’s Build lesson, the progression from Explore and Share to Visual Examples supports students in connecting and creating concrete and representational models to connect with abstract concepts. Then, in the final guided examples, students discuss how to define and explain the abstract concepts they connect to the concrete and representational models.

Additionally, in lesson 7-2, “Let’s Build: Analyze Translations,” the materials explicitly support students in connecting and creating physical and pictorial models to abstract algebraic representations of translations. In step 1, “Explore and Share,” students use graph paper, rulers, and protractors to physically translate polygon ABCD along grid lines, building a concrete understanding of how a figure moves the same distance in the same direction. The “Connect Solution Strategies” discussion in the Teacher’s Edition then helps students connect the concrete experience to the representational level by asking whether polygon EFGH is a translation of polygon ABCD and using abstract reasoning to explain why, linking their physical movements to the visual properties of congruence. In step 2, “Visual Learning,” example 1 uses a real-world architectural floor plan as a pictorial representation of a translation, with educators prompted to ask students how every corner of the fire pit moves to form the new figure, connecting the visual diagram to the defining property that all points move the same distance and direction. Example 2 then connects the pictorial to the abstract by introducing algebraic notation such as (x, y), translating by (x + a, y + b) to describe the same translation students saw in the diagram, and the Key Concept shows the representational and abstract methods together. Example 3, “Describe a Translation,” supports students in explaining how the concrete graph and representational translation can be written using the abstract form (x, y) → (x + 1.5, y + 2), then students complete the Try It! problem to practice the concept.

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

The grade A7 materials give students opportunities to develop academic mathematical language through visuals and manipulatives in lessons, plus other language-development strategies in the “Advanced Grade 7: Additional Vocabulary Support” section in the “Resources” tab of Savvas Realize. For example, in lesson 1-7, “Let’s Build: Compare Proportional Relationships” of the Teacher’s Edition, students use visuals and digital manipulatives, including a picture of two buckets of apples with signs showing their quantities and prices, tables, and graphs, to write about and discuss how to compare proportional relationships. The “Advanced Grade 7: Additional Vocabulary Support” provides worksheets to accompany the lesson, helping students develop their academic mathematical language through other language development strategies, including cloze sentences and vocabulary charts with definitions and pictures of mathematical vocabulary terms.

Additionally, in lesson 3-3, “Fluently Multiply Rational Numbers,” the materials give students opportunities to develop and use mathematical vocabulary. The “Language Support” section of the Teacher’s Edition guides educators in having students create individual index cards summarizing the rules for multiplying rational numbers and complete sentence stems such as “When the signs are the same, the product is ______” and “When the signs are different, the product is _____.” In step 2, “Visual Learning,” the “Language Routine: Discussion Supports” has one student explain how to solve part a, using the terms “product, numerator, denominator, positive, and simplify,” and has the other partner explain how to solve part b using either fractions or decimals, and then has the partners collaborate to convert between these forms. The materials also provide scaffolding opportunities to develop academic mathematical language. For example, item 18 in step 3 “Practice and Problem Solving” encourages students who lack the vocabulary to describe a multiplication error to first use informal language or diagrams, then transition to reviewing and applying precise mathematical vocabulary.

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

The grade A7 materials include embedded educator guidance to scaffold and support students’ development and use of academic mathematical vocabulary in context within the “Vocabulary Review” section of the Topic Reviews at the end of each topic. For example, the Vocabulary Review in the Teacher’s Edition contains embedded educator guidance in topic 11, “Use Sampling to Draw Inferences About Populations: Topic Review,” that directs educators to have students use the academic mathematical vocabulary terms, including “population, inference, mean absolute deviation, valid inference, and representative sample,” in context orally and in writing to scaffold and support their development of the terms. The Oral Language embedded guidance directs educators to “Have students create a comic strip that illustrates a scene that incorporates all the vocabulary words.” Next, the Writing in Math embedded guidance adds another level of support after the students complete the page to “Have students write creative scenarios about a person collecting data. Have volunteers read aloud their scenarios and discuss the population and sample in each context.”

Additionally, the Vocabulary Review within the Topic Review of topic 3 “Rational Number Operations” directs educators in the Teacher’s Edition to have students “think of synonyms for the words positive and negative” and “work in groups to think of situations that involve positive and negative change in a real-life scenario,” providing structured opportunities for students to develop and apply academic mathematical vocabulary in meaningful contexts. The Writing in Math activity further extends vocabulary use by having students “work in groups to create a simple board game that involves positive and negative movements to reach the end of the game.”

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 grade A7 materials include embedded educator guidance within Let’s Build lessons to support the appropriate academic mathematical vocabulary, syntax, and discourse that support mathematical conversations, providing opportunities for students to hear, refine, and use math language with peers, developing their math language toolkit over time, and Sample Student Work that guides educators to support student responses using exemplar responses to questions and tasks. For example, in the Teacher’s Edition, lesson 12-2, “Let’s Build: Understand Experimental Probability” includes a “Language Support” section with educator guidance to “point out the term event. Explain to students that an event is a single outcome or group of outcomes from a sample space. Have students recall the term outcome from the previous lesson. Ask: How is an event related to an outcome? Give students time to turn and talk with a partner, then ask for oral responses. Help students describe the relationship between the two terms in complete sentences. Reiterate that an event is a possible outcome,” supporting student discourse using appropriate academic vocabulary and syntax, providing opportunities for students to hear, refine, and use math language with peers, and developing their math language toolkit over time. In the “Explore and Share” section of the lesson, students consider a soccer player’s chances of scoring on a penalty kick, since he will either score or not score the goal. The Teacher’s Edition provides Sample Student Work with exemplar responses, including “Kumar applies his prior knowledge of probability and his knowledge of soccer. Cara applies her prior knowledge of probability and analyzes the situation in a little more detail than Kumar does.”

Additionally, lesson 3-3, “Let’s Build: Fluently Multiply Rational Numbers” guides educators in using the “Language Support” activity before example 1, directing educators to have students “explain what a rational number is and brainstorm some examples,” then complete sentence frames such as “When the signs are the same, the product is _” to reinforce precise vocabulary and syntax. The “Language Routine: Discussion Supports” guides the educator to have students work as partners to explain how to solve parts (a) and (b) of example 1, using the terms product, numerator, denominator, negative, positive, and simplify to support discourse using appropriate mathematical language and to hear, refine, and use math language with their peers. Embedded exemplar responses throughout Try It! and Talk About Math Ideas model precise mathematical explanations. For example, in the Try It! for example 1, the sample response explains, “The Commutative Property says that numbers can be multiplied in any order. The product of two factors with different signs will always be negative.” Similarly, the “Talk About Math Ideas” exemplar for the Essential Question states, “If the rational numbers have different signs, the product is negative; if the rational numbers have the same sign, the product is positive.”

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

The grade A7 materials appropriately integrate the TEKS process standards, as discussed in the Mathematical Process Standards in Instruction in the Front Matter of the Teacher’s Edition. For example, the article explains how the TEKS process standards are integrated into the materials through lessons, problems, and assessments in four sections with specific information, including “Mathematical Process Standards are infused and explicitly highlighted in lesson instruction using teal colored type.” The Savvas Realize digital program also includes a Problem-Solving Model that integrates the TEKS process standards into the materials, which students can use at any time to support their problem-solving.

Additionally, the Teacher’s Edition explicitly identifies where the mathematical process standards are appropriately integrated within lesson instruction, guided and independent practice, problem-solving activities, and assessments. For example, in lesson 10-5, “Let’s Build: Understand Monetary Incentives,” the first page identifies the TEKS addressed in the lesson, including 1A, 1C, 1D, and 1F. These standards emphasize applying mathematics to solve problems, selecting appropriate tools and techniques, communicating mathematical ideas effectively, and analyzing mathematical relationships, and the materials embed these practices throughout daily instruction, ensuring students consistently engage in mathematical reasoning, problem solving, communication, representation, and analysis while developing grade-level mathematical content knowledge.

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

The grade A7 materials describe how the TEKS process standards are incorporated and connected throughout the course, as discussed in the Mathematical Process Standards in Instruction in the Front Matter of the Teacher’s Edition. For example, the article explains, “Special Emphasis on Two Process Standards per Topic: a ‘TEKS Mathematical Process Standards’ page in front of every topic provides suggestions you may choose to implement as a way of giving special emphasis to two Process Standards in the topic.” It continues to describe how the process standards are connected by stating, “All math tasks evoke the selection, use, and management of multiple Process Standards,” and “Items that assess content also engage students in using Process Standards. The topic performance tasks are especially good opportunities to assess students’ proficiency with Process Standards.”

Additionally, the materials include a description of how the TEKS process standards are connected throughout the course in the “165-Day Pacing Guide” in the Teacher’s Edition, which explicitly states that “TEKS Mathematical Process Standards are integrated throughout every Topic: 7AM.1A, 7AM.1B, 7AM.1C, 7AM.1D, 7AM.1E, 7AM.1F, 7AM.1G.” The pacing guide identifies these process standards across all 12 topics while listing the content TEKS and ELPS associated with each topic, demonstrating that the mathematical process standards are intentionally connected and integrated throughout the grade 7 course rather than taught as isolated skills. The Topic Content pages in the Front Matter of the Teacher’s Edition corroborate this by listing the process standards for each lesson across the topics in bold.

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

The grade A7 materials include a description for each unit showing how the TEKS process standards are incorporated and connected throughout the topic, on the Mathematical Process Standards page at the beginning of the topic in the Teacher’s Edition. For example, topic 3 “Rational Number Operations” uses the Mathematical Process Standards page to describe how 7AM.1B is incorporated and connected throughout the topic, including “Mathematically proficient students make sense of fractions and decimals and their relationships to each other, decide which operations to use when solving problems with rational numbers, and are flexible in the use of operations with rational numbers.” The page details that 7AM.1D is incorporated and connected throughout the topic because “Mathematically proficient students create a logical representation of problems with rational numbers, fluently convert rational numbers between fraction and decimal form, and use representations, such as number lines, to model rational numbers.”

Additionally, the topic 3 overview “Rational Number Operations” in the Teacher’s Edition outlines the sequence of lessons, essential understandings, mathematical objectives, language objectives, vocabulary, materials, the TEKS, and mathematical process standards for the entire topic. Across lessons 3-1 through 3-6, students progress from writing rational numbers as decimals to adding, subtracting, multiplying, and dividing rational numbers, then apply mathematical modeling in a real-world context. Throughout the unit, each lesson identifies the applicable mathematical process standards (7AM.1B, 7AM.1C, 7AM.1D, 7AM.1E, 7AM.1F, and 7AM.1G) and shows how the TEKS process standards consistently connect to the mathematical content and learning objectives across the topic.

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

The grade A7 materials include an overview of the TEKS process standards incorporated into each lesson in the Teacher’s Edition, in the “Item Analysis: Practice and Problem Solving” answer key in the “Practice and Problem Solving” section. For example, in lesson 2-7, “Let’s Build: Solve Simple Interest Problems,” the “Item Analysis: Practice and Problem Solving” answer key provides an overview showing that 7AM.1D is integrated into examples 1 and 2 and items 12 and 13, and 7AM.1B is integrated into example 3 and item 14. Furthermore, the Quick Check at the end of the lesson incorporates 7AM.1B and 7AM.1C into the five-question formative assessment.

Additionally, the first page of each lesson in the Teacher’s Edition lists the TEKS content standards and the mathematical process standards addressed in the lesson. For example, lesson 12-4, “Let’s Build: Use Probability Models” identifies mathematical process standards 7.1B, 7.1C, 7.1D, 7.1F, and 7.1G that support students in acquiring and demonstrating mathematical understanding as they engage with the lesson content, enabling educators to easily identify the TEKS mathematical process standards incorporated throughout each lesson.

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

The grade A7 materials provide opportunities for students to think mathematically, persevere through solving problems, and to make sense of mathematics in Let’s Build lessons, such as lesson 3-5, “Let’s Build: Solve Problems with Rational Numbers.” For example, the Teacher’s Edition shows in step 1, “Explore and Share,” that students think mathematically by using an “Estimated Income and Expenses” chart that depicts varying types, amounts, and frequencies of income and expenses, such as $950 in income from sales each week and a $7.50 expense for travel each day. Students persevere through problem-solving to reason about whether Stefan should rent the phone accessory store and to make sense of mathematics in a small-group setting before sharing their methods with the whole class, such as adding all income and then subtracting all expenses.

Additionally, each topic includes a “Build G.R.I.T.” section that provides educators with concrete talking points and a modeled classroom dialogue to cultivate a growth mindset, resilience, self-efficacy, and time management as students work through multistep, real-world math tasks. In topic 2, “Analyze and Solve Percent Problems,” the “Build G.R.I.T.” section of the Teacher’s Edition provides opportunities for students to think mathematically about percent problems, encouraging educators to have students use percentages to talk about their own personal experiences, and prompting students to start by estimating solutions and end by checking that their answers make sense in context. It offers ways for educators to help students build confidence, such as celebrating progress when students overcome challenges and having them relate absolute value concepts to the reason percent error is always positive to make sense of mathematics, building resilience to persevere through solving problems by encouraging students to break problems into smaller steps, developing self-efficacy by reminding students of previously mastered skills like multiplying and dividing rational numbers, and supporting time management through modeling strategies like bar diagrams to represent markup and markdown problems. This is modeled through a sample dialogue in which the educator helps a student, Ming-Na, find a percent decrease by guiding her to use a bar diagram to represent the problem rather than simply giving her the formula.

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 grade A7 materials use the Math Talk and Explore and Share activities in the Let’s Build lessons to help students understand, justify, and explain that there are multiple ways to represent and solve problems and complete tasks. For example, lesson 3-3, “Let’s Build: Fluently Multiply Rational Numbers” in the Teacher’s Edition uses the Math Talk opening task, which presents the expression “–0.75 x two-ninths x one-half,” and asks students to “Decide on a first step,” supporting students in understanding that there can be multiple ways to represent and solve problems and complete tasks. Next, step 1, “Explore and Share,” supports students in choosing a length for a flag, then determining the length of blue fabric needed, given an image showing that the blue section takes up two-fifths of the flag’s length, to work in small groups and explain and justify that there can be multiple ways to represent and solve problems. The “Connect Solution Strategies” section of the Teacher’s Edition instructs educators to have students discuss, as a whole class, the connections among strategies for multiplying by the rational number two-fifths and for dividing by five and then multiplying by two. The Sample Student Work that accompanies the activity shows how students can justify their solution using a bar diagram or the multiplication algorithm.

Additionally, lesson 6-2, “Let’s Investigate: Understand the Pythagorean Theorem” of the Teacher’s Edition supports students in understanding that there can be multiple ways to represent and solve problems and complete tasks by presenting the Pythagorean Theorem through multiple representations, including diagrams, geometric models, equations, authentic student work, and real-world contexts through the “Select and Sequence,” “Connect Solution Strategies,” and “Present and Analyze” sections, where educators sequence different student approaches and facilitate discussions comparing valid solution methods. Educator prompts such as “What is the Pythagorean Theorem?,” “What is the hypotenuse?,” and “Given any three numbers, how can it be determined whether they represent the sides of a right triangle?” support students in explaining that there can be multiple ways to represent and solve problems and complete tasks by requiring students to explain how different representations model the same mathematical relationship, and by having students compare sample and peer solutions, explain similarities and differences among strategies, and discuss how different approaches determine the missing side of a right triangle. The Teacher’s Edition directs educators to “Encourage students to justify their explanations” as students compare sample student work, evaluate different representations, and defend why each appropriately models the problem using the “Present and Analyze,” “Connect,” and “Talk About Math Ideas” sections, where students defend the validity of different solution methods using mathematical evidence. The lesson concludes with Practice and Problem Solving, Challenge, Quick Check, and Additional Practice, providing opportunities to apply, compare, and justify that multiple ways can represent and solve problems and complete tasks.

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 grade A7 materials include a Math Talk in every Let’s Build lesson, giving students multiple opportunities to make sense of mathematics and discuss it with peers and educators. For example, in the Teacher’s Edition, lesson 9-1, “Let’s Build: Solve Problems Involving Surface Areas of Prisms and Pyramids,” includes a Math Talk “Which one doesn’t belong” activity that shows four nets of three-dimensional figures, one of which is a pyramid, requiring students to make sense of the mathematics and discuss in a small group of peers and with the educator the core shapes that comprise the figure. Examples 2 and 3 model the steps for finding the lateral surface area, total surface area, and the surface area of isolated portions of prisms and pyramids, giving students opportunities to do and write about math with their peers and educator.

Additionally, in lesson 10-7, “Let’s Build: Understand Credit Cards and Loan Repayments,” students do math with peers and educators during the “Explore and Share” activity, using an online calculator to find the total cost of repaying a fence loan, and later applying the same process in the “Apply Math” extension to compare repayment costs across different lenders. Students write about their thinking on items with peers and educators throughout “Practice and Problem Solving,” such as explaining whether the total cost of credit will increase or decrease over time, and a “Higher Order Thinking” problem analyzing how minimum monthly payments affect a credit card balance, as well as on “Try It!” problems calculating and justifying the cost of a loan under different terms. Students discuss math with peers and educators through small-group work during “Monitor, Select, and Sequence” in the Teacher’s Edition, where they share and compare solution strategies for the fence-repair problem, through the “Language Routine: Co-Craft Questions and Problems,” in which students form groups using loan amount, interest rate, and term note cards to build their own real-world problem, and through “Talk About Math Ideas,” where partners discuss how interest rates affect the amount of money repaid on a loan. Educator prompts provide questions to ask during “Explore and Share” and “Visual Learning” sections, such as “Why does the cost of interest increase each month while the balance of the loan decreases?” and support a whole-class discussion connecting solution strategies to the Essential Question about comparing the cost of credit.

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

The grade A7 materials include a “Problem-Solving Model” on the Savvas Realize digital program that supports educators in guiding students to share and reflect on the explanations, arguments, and justifications within their problem-solving approaches, using guiding questions and a graphic organizer. For example, the model includes guiding questions that are broken into categories to support explanations, arguments, and justifications, such as “Analyze Given Information,” “Determine a Solution,” and “Justify the Solution and Evaluate its Reasonableness.” The “Problem-Solving Model Recording Sheet” is a graphic organizer that gives students space to share their problem-solving approaches, with sections that correspond to the guiding questions on the previous page. Students use the graphic organizer to write the problem, “Analyze Given Information” into “Need to Find” and “Given,” and then share their explanations and arguments in the “Formulate a Plan” section, which provides sample ways to represent problems and math tools to use to “Determine a Solution.” At the bottom of the page, students share the justification for their problem-solving approach in the “Justify the Solution and Evaluate its Reasonableness” section.

Additionally, the “Language Routine: Collect and Display” section of the Teacher’s Edition in lesson 3-1, “Let’s Investigate: Write Rational Numbers as Decimals,” step 1, “Investigate,” directs educators to have students “discuss their table with a group,” choose different numerators to expand the table collaboratively, and “review the results as a class” so students can share and reflect on the similarities and differences of their problem-solving approaches and explain any variations in their findings. The guidance further directs educators to “Monitor Students at Work” with prompts such as, “How do you think the different numerators will impact the decimal representation?,” “Why do some decimal representations change from repeating to terminating, depending on the numerator?,” and “How do you think the decimal representations would change if you included negative numerators as possible numerators?” to guide students in sharing and reflecting on arguments for their problem-solving approaches. During “Discuss Student Solutions,” educators prompt students to justify their problem-solving approaches as they share and reflect by asking, “Why is it important to multiply a repeating decimal by a power of 10 to convert it to a fraction?” and “Do we have enough information to write repeating decimals as fractions?” The guidance suggests that students will likely answer yes, and explains that if they do, prompt them further by asking: “How do you know you have enough information?” and “How can you check that your answer is correct?”

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

The grade A7 materials include a “Prevent Misconceptions” section for the Exit Ticket in every Let’s Build lesson, which supports educators with prompts and guidance for providing explanatory feedback based on student responses and anticipated misconceptions. For example, in lesson 6-4, “Let’s Build: Apply the Pythagorean Theorem to Solve Problems,” the Exit Ticket gives students four choices (10 in., 39 in., 51 in., and 102 in.) for the correct answer to finding the length of the diagonal of a rectangle with sides that measure 15 in. and 36 in., and the “Prevent Misconceptions” section of the Teacher’s Edition guides the educator that if students selected 51 in., they may be finding the sum of twice each smaller side and then dividing the sum by 2 to solve for the hypotenuse. In the “Explore and Share” activity at the beginning of the lesson, students work in small groups to determine which of the three boxes with different dimensions could ship a 37.5-inch umbrella. The “Monitor, Select, and Sequence” section of the Teacher’s Edition guides the educator to observe the students working and consider what strategies they use to identify how the umbrella could be placed in a box, giving potential student responses to the question, including “Students may reason that the umbrella cannot be laid down flat, but instead needs to be placed on a diagonal. Students will then identify, using the Pythagorean Theorem, if the umbrella could fit in any of the boxes.” The section includes a prompt with explanatory feedback, such as “Could the umbrella lay flat in any of the boxes?” to anticipate misconceptions.

Additionally, in lesson 10-8, “Let’s Build: Understand How to Save for the Future,” the section “Prevent Misconceptions” in the Teacher’s Edition addresses item 6 of the “Do You Understand/Do You Know How?” guided practice section of step 2, “Visual Learning,” guiding educators for anticipated misconceptions that “some students may not understand what amount of principal earns interest each year as new money is added into the account.” To help students work through this misconception, the materials prompt the educator to provide explanatory feedback and ask, “How much principal earns interest during the first year?” with the expected student response being “500,” followed by “When money is added at the end of the first year, when does it see its first interest?,” with the expected student response being “At the end of the second year.”