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The quality review is the result of extensive evidence gathering and analysis by Texas educators of how well instructional materials satisfy the criteria for quality in the subject-specific rubric. Follow the links below to view the scores and read the evidence used to determine quality.
Section 1. Texas Essential Knowledge and Skills (TEKS) and English Language Proficiency Standards (ELPS) Alignment
TEKS Student %
TEKS Teacher %
ELPS Student %
ELPS Teacher %
Section 2. Concept Development and Rigor
Section 3. Integration of Process Skills
Section 4. Progress Monitoring
Section 5. Supports for All Learners
Section 6. Implementation
Section 7. Additional Information
|Grade||TEKS Student %||TEKS Teacher %||ELPS Student %||ELPS Teacher %|
Throughout the lessons, the materials concentrate on the development of the primary focal areas for the grade-level as outlined in the TEKS. In addition, materials strategically and systematically develop this content knowledge through appropriate practice opportunities, ensuring students achieve proficiency.
Evidence includes but is not limited to:
The online materials contain resources that clearly state the focal areas of a unit, and those focal areas align with the grade-level TEKS. Chapters 1–3 cover Integers and Positive Rational Numbers, Chapters 4–5 cover Ratios and Rates, and Chapters 6–9 cover Expressions and Equations to Represent Relationships. Academic rigor increases over time to meet the full intent of the primary focal areas. Each chapter’s “Teacher Plan” includes a “Practice and Apply” section that summarizes how problems increase in complexity level from 1–4. These levels roughly correspond to the levels of Bloom’s Taxonomy. For example, in the lesson on multiplying integers, questions build from low-level items such as, “Do the integers have the same sign?” to “How does the number line illustrate this product?” and finally, “Generate a different multiplication expression in which the product is also -15.”
Each chapter begins with an “Are You Ready?” check to ensure each student has the necessary skill set to be successful. If students are unsuccessful, teachers have access to a quick review and four reteach options. Each chapter includes a TEKS trace, chapter overview, and pacing guide. TEKS trace focuses on the progression of knowledge and skills within the grade level. Chapter overviews highlight what students have already learned and what they will now develop. Pacing guides clearly state the focal areas of individual lessons. For example, a chapter on multiplying and dividing rational numbers includes background and TEKS information for multiplying and dividing decimals, multiplying fractions, dividing fractions, and multiplying and dividing mixed numbers. Additionally, each lesson plan lists how exercises, problems, and questions align with the TEKS. One example of this is in the lesson on Ratios where exercises require multiple steps and integrate TEKS from multiple grades and focal areas.
Lessons display the importance of introducing and reviewing key concepts by outlining how previous concepts relate to current concepts. In Chapter 4, the previous concept had students represent problems involving ratios and rates using scale factors and tables; the lesson plan describes how this concept aligns with the current concept of having students create graphs from a ratio or rate table. The “Teach the Concept” portion of each lesson summarizes how to introduce each concept, while also providing the teacher with guidance for students who are approaching, on, or beyond grade level. This section sometimes includes alternative strategies and opportunities for students to collaborate, including a round-robin activity and a “Gallery Walk.”
Each lesson includes real-world situations promoting the application of mathematics to everyday life. For example, in Chapter 6, a group of friends is going to the museum and each friend must pay an admission price of $9. Students complete the ordered pairs within a table given the x values of 1, 2, 3, and 4, and then they graph the resulting ordered pairs (1,9), (2,18), (3,27), and (4,36). Students write an explanation to describe the graph and write the equation t= 9(n) to find the cost of n tickets. Next students write a statement to identify the independent quantity as the number of students and dependent quantity as the total cost.
Lessons also contain “H.O.T Problems” or Higher Order Thinking problems at the end of independent practice. For example, in Chapter 9, question 14 asks students to analyze the conclusion about the two acute angles in a right triangle and justify their response. In question 15, students evaluate whether the following statement is true or false: “If the sum of two acute angles in a triangle is less than 90 degrees then the triangle is obtuse.” For question 17, students create an example of an acute scalene triangle and label their triangle with measurements to justify their response. These types of questions increase rigor and provide practice opportunities for students to master the content. Finally, diagnostic, formative, and summative assessments are interwoven between lessons; teachers can use these results to plan and provide students individualized intervention.
The materials sequence concepts from concrete to representational to abstract (CRA) as is appropriate for the grade-level and content. Throughout the lessons, the materials include a variety of types of concrete models and manipulatives, pictorial representations, and abstract representations, as appropriate for the content and grade level. They also support teachers in understanding and appropriately developing students’ progression along the CRA continuum.
Evidence includes but is not limited to:
The online virtual manipulatives resource included with each lesson provides students with a digital means to explore concepts and teachers with a way to create problem-based learning opportunities. The resource contains algebra tiles, base ten blocks, centimeter cubes, a clock, connecting cubes, currency, fraction circles and tiles, geoboard and bands, a hundreds chart, number cubes, number lines, a spinner, tangrams, a thermometer, and two color counters. Also included in this resource is a variety of hands-on manipulatives to be used within the classroom. The materials provide pictorial models within the lesson components so that students can transition from their concrete exploration to representational practice. To further increase the rigor toward the abstract, the materials include multi-step problem solving and higher-order thinking questions.
Throughout the materials, teachers are given suggestions on how to understand and appropriately develop students’ progression through the CRA continuum, whether they are approaching, on, or beyond grade-level proficiency. The “Are You Ready” section in the chapter overview of the teacher plan has quick checks for the teacher to gauge student understanding. If students have difficulty with any exercises, the materials provided an additional example to clarify misconceptions. This section also includes a diagnostic test.
In Chapter 1, the hands-on lab provides a 10 x 10 grid used to represent hundreds and percentages. Students use the grid to model the percent of tiles in a given mosaic that are green. In another example, students model 25% on a 10 x 10 grid. The activity shows bar diagrams and strip diagrams as other methods to model percentages. After the hands-on lab in lesson 1, students see how to express 50% as a fraction in simplest form using a grid model in the introduction. Following the introduction, the guided and independent practice contains a variety of questions asking students to express percents as fractions or fractions to percents with and without models.
In Chapter 3, students determine the sum of -3 + (-2) with a vertical number line using an activity. They start at 0 then move down 3 units to show -3. From there, students move down 2 units to show -2. After moving down 2 units the line stops at -5. So, -3 + (-2) is -5. The model shows how the sum of two negative integers is negative.
In Chapter 8, there are four hands-on labs and several resources, for example, “The Geometer’s Sketchpad,” with explicit guidance and training on how to use these resources. The materials provide pictorial models within the lesson component so that students can transition from their concrete exploration to representational practice. To further increase the rigor toward the abstract, multi-step problem solving and higher-order thinking questions are included. In one activity, students use cups and counters to model and solve one-step equations. Throughout the chapter, students referenced pictorial models of cups and counters while practicing. The chapter also used bar diagrams for students to better connect the concept of solving equations. Toward the end of Chapter 8, students solve real-world problems by setting up a one-step equation and then solving for the variable. Students also solve higher-order thinking questions labeled as create, analyze, and evaluate. The models, manipulatives, and representations are used for concept exploration and attainment for the primary focal area, requiring students to recreate the manipulatives used during the lesson by drawing the concept to show understanding.
In Chapter 9, the teacher reviews angles and introduces angle relationships. The unit progresses from review material to a hands-on lab lesson on angles and their relationships in triangles. This leads to the properties of triangles and modeling triangle inequalities. In the modeling activity, students cut plastic straws into various sizes and try to make triangles. After modeling side lengths that work to make a triangle, students finish a pre-made table, then create a “rule.” Teachers are provided with checkpoint guidance within the lab lesson, with the objective that students should be able to answer, “HOW can I select tools and techniques to determine when three lengths form a triangle?” The lesson connects directly to the lab from the prior lesson and includes common error guidance as students transition to more abstract concepts. Additionally, students practice and apply what they learned with multi-step problem solving. In the “Multi-Step Problem Solving” section, teachers find strategies that can be completed by the whole group, small group, or independently.
The materials provide strategic and integrated instruction in all components of mathematical rigor: conceptual understanding, procedural fluency, and application. Throughout the lessons, the materials include some support for students to build their vertical content knowledge by accessing prior knowledge and understanding of concept progression. The materials also include some tasks and problems that intentionally connect two or more concepts, as appropriate, for the grade-level and provide opportunities for students to explore relationships and patterns within and across concepts. The materials have support for teachers in understanding the horizontal and vertical alignment guiding the development of concepts.
Evidence includes but is not limited to:
The materials include supports for students to build their vertical content knowledge by accessing prior knowledge and understanding of concept progression. The materials contain tasks that use familiar models and strategies from previous units, but do not always connect to what will be used in future grade levels. The “Plan and Present” resource in each chapter contains tasks that help students connect concepts that are appropriate to their grade level. Even though the materials provide opportunities to understand how mathematical ideas might connect to one another, there is limited evidence the materials help teachers question students in order to make connections between concepts. The suggested questions for teachers are directly related to the concept being taught. For example, the launch of the lesson may provide students the opportunity to examine patterns within a concept to make connections, but there is less evidence of examining relationships across concepts.
There are opportunities for students to explore relationships and patterns within and across concepts. Multi-step problem solving opportunities contain spiral review, and some teacher examples mention a specific strategy. In the digital components, within the “Teach the Concept” tab, a section entitled “Mathematical Background” explains how to connect new learning to previously learned concepts, knowledge, and skills. For example, in Chapter 3, before addressing multiplication and division with negative numbers, the materials provide teachers with options to review multiplication as repeated addition, using counters to begin the development of the rules for multiplying integers. The teacher reference section contains tasks that use familiar models and strategies that students will use from previous chapters. For example, in the same chapter, there is a “Quick Review” that focuses on examples from Chapter 1. Students are required to determine the absolute value and place numbers on a number line.
The materials build learners’ vertical content knowledge in some instances by referencing or showing how concepts progress in rigor. In Chapter 9, teachers use the “Quick Review Math Handbook,” which contains grade-appropriate lessons and lessons from previous grade bands, such as lessons on perimeter polygons. The handbook also goes above grade-level standards, referencing surface area, and circles.
The materials provide support for teachers in understanding the horizontal and vertical alignment guiding the development of concepts. The materials provide the “TEKS Skill Trace” at the beginning of each lesson. TEKS Skill Traces are available for each lesson and map concepts students have already learned, what they will learn in this lesson, and what they will learn in future lessons. Also included is a mathematical background for each chapter and lesson. In Chapter 3, the TEKS Skill Trace shows the progression from models of integer addition to the fluent algorithm, and onto models for subtraction.
The “Plan and Present” resource in each chapter of the materials supports teachers in understanding the horizontal and vertical alignment guiding the development of concepts. Within the “Chapter Overview,” the section entitled “Mathematical Background” explains how the skills covered in each lesson progress vertically and horizontally, enhancing the teacher’s understanding of how students should progress in their knowledge and skills throughout the materials. The materials do not always include vertical alignment; however, they do contain the entirety of what is necessary for sixth-grade standards and horizontal alignment. Teachers are provided with a table of contents and brief pacing which provides the topic and a suggested number of days. Teachers are also given a correlation document that outlines which TEKS are covered in each lesson. There is some correlation provided to teachers between current TEKS and those covered in previous grade levels, but teachers are not provided with an explanation of the depth, breadth, and complexity of current concepts and their connections to the expectations of student understanding for the next year.
Teachers are provided mathematical background information for each lesson along with an in-depth “Professional Development Library.” “Problem-Based Learning Investigations,” “Hands-On Labs,” “Focus on Mathematical Processes Activities,” and “Chapter Projects” support concept progression, as well as give students the opportunity to connect multiple concepts.
Support for horizontal alignment is presented at the launch of each lesson, in the “Building on the Essential Question” section. This compilation of questions is again referenced in the “wrap-up” section of each chapter, along with Vocabulary and Key Concepts checks, to ensure students are making connections between concepts both within and across lessons and subsequent chapters.
The materials are built around quality tasks, designed to engage students, that address content at the appropriate level of rigor and complexity (conceptual understanding, procedural fluency, or application) as identified in the TEKS and as appropriate for the development of the content and skill. Throughout the lessons, the materials integrate contextualized problems, providing students with some opportunities to apply math knowledge and skills to new and varied situations. The materials also include some teacher guidance on anticipating student responses and strategies. The “Mathematical Processes Handbook” outlines for the teacher the mathematical concepts and goals behind each task.
Evidence includes but is not limited to:
Throughout the materials, students are guided through CRA with increasing depth and complexity. In Chapter 1, conceptual understanding is built by launching the lesson using fractions to compare the length of different insects. The teacher-led examples in the lesson progress through the procedure of comparing like types of rational numbers, such as decimal to decimal and fraction to fraction with both positive and negative values, and ends with a real-world problem. The guided practice continues to move through procedural to real-world problems and concludes with multi-step problem-solving. Each lesson throughout the materials follows this pattern to ensure students work through the CRA process. As the year progresses, the complexity of the units increases. The sixth-grade units progress from operational fluency, which is then used in later units on proportions, equations, and geometry. The year ends with providing students the opportunity to gain a deeper understanding of statistical displays, including box plots, and a unit covering financial literacy.
Students work through the CRA process and the materials outline for the teacher the mathematical concepts and goals behind each task. The materials provide a mid-chapter check and formative assessments in the guided practice section to assess students' understanding of the concepts being taught in each lesson. Chapter 1 has a formative assessment where the teacher places students in pairs. Student 1 interviews Student 2 using the interview questions provided. Student 2 then interviews Student 1 using the same questions, but for the next exercise. The teacher then calls on either student to explain the solution to the exercise. There is some evidence that explaining how following the progression of each task builds student efficacy toward mastery or conceptual understanding.
The materials integrate contextualized problems throughout, providing students some opportunity to apply math knowledge and skills to new and varied situations. In Chapter 2, students must multiply and divide fractions. At the end of the unit, students are required to write a problem involving multiplication of a fraction and a whole number with a product that is between 8 and 10. Students must then analyze the following question, “Jenny made five loaves of banana bread that had ¼ cup of oil in each loaf. After she was done baking, she had ⅝ cup of oil remaining. How much oil did she have before baking?”
The materials provide some teacher guidance on preparing for and facilitating strong student discourse grounded in the quality tasks and concepts. Throughout the materials, teachers are provided with questions and activities to facilitate and support discourse, but there are no rubrics to provide feedback during verbal discourse. In Chapter 4, teachers are provided with directions and instruction in facilitating students through the activities of “Think-Pair-Share” and “Find the Fib.” To engage in Find the Fib, teachers have students work with a partner to write two facts and one fib. Students then exchange facts and fibs with another pair of students. Each pair identifies the other pair's facts and fib. Teachers are not provided with how to direct student misunderstandings or misconceptions. In the materials, rubrics are provided for the performance-based tasks, but there is no evidence of rubrics provided for teachers to give students feedback based on discourse. The ELL guide does provide rubrics to assess the oral and writing skills of students who are English Learners, but not all students.
The materials provide some teacher guidance on anticipating student responses and strategies. For example, the “Plan and Present” section in the teacher reference section reviews essential questions and provides sample answers. The “Practice and Apply” tab includes a section entitled “Watch Out,” which provides teachers with common misconceptions on student responses and strategies, as well as how to combat those misconceptions. In a Chapter 7 lesson about prime factorization, the materials direct teachers to watch for students who include composite numbers in the prime factorization. Teachers are told to guide students to keep a list of the first several prime numbers as reference. The examples in the teacher plan may have teachers use a specific strategy, but they do not rationalize why the strategy is appropriate at that time. The materials are not sequenced based on the complexity of the strategy, but rather on the ability level of the students or the complexity of the questions which can be identified in the practice and apply section of the teacher plan.
The Mathematical Processes Handbook gives examples of goals and what to look for to indicate mastery. It describes the way students should be engaged with the math as they are learning. The Mathematical Process Standards are embedded throughout Texas Math, especially present in the hands-on labs, strong problem-solving emphasis in all lessons, and higher-order thinking exercises. In addition, the English Language Learners handbook found in the online materials contains strategies and teacher guidance for facilitating activities.
The materials provide teachers with guidance and support for conducting fluency practice appropriate for the concept development and grade. Materials integrate fluency at appropriate times and with purpose as students progress in conceptual understanding. Additionally, materials contain some scaffolds and supports for teachers to differentiate fluency development for all learners.
Evidence includes but is not limited to:
Materials include some teacher guidance and support for conducting fluency as appropriate for the concept development and grade. Each lesson progresses from basic practice to Higher Order Thinking questions. The mathematical backgrounds included in each chapter overview explain how students achieved conceptual understanding in prior grades. Then, in the lessons that follow, the materials contain reteach strategies as well as strategies and techniques on how students who have not yet shown fluency can hone or demonstrate their fluency with the “new” material. The materials provide fluency activities that encourage strategic and flexible use of strategies.
The “English Language Learner’s Guide: Book G” provides the teacher with a comprehensive reference supporting connections between concept development and fluency. The guide begins with “Building Math Concepts and Language Skills.” It includes sections like “Helping All Children Learn Mathematics” and “Integrating Language Development with Mathematics.” The Integrating Language Development with Mathematics section is broken down into seven key goals that allow teachers to meet the challenges of combining second language instruction with mathematics. However, there is no evidence that the materials describe the purpose behind the fluency practice within these programs.
The materials integrate fluency opportunities as appropriate for the concept development and grade, but it is not always explicitly stated. For example, Lesson 2-a targets students' understanding of how to use powers of 10 to move the decimal point while multiplying. Students use a table to complete several multiplication problems, but there is no reference to building fluency. In Lesson 2-4, the teacher asks an approaching grade-level student why they shade a certain number of rows when modeling the multiplication of fractions. Re-teach activities are only provided for the current lesson and not for a previous skill to help students who have not yet mastered the desired level of fluency make connections to previous concepts. Instead, fluency practice worksheets are found online.
The materials do include scaffolds and supports for teachers to differentiate fluency development for all learners. The “Plan and Present” resource included with each lesson provides scaffolding suggestions for students needing additional experiences and opportunities to meet grade-level fluency expectations. For example, within the “Launch the Lesson” tab of Lesson 8-4, the materials prompt teachers to provide students with a completed bar diagram for a given exercise regarding a student’s monthly allowance. Then students use repeated addition to determine the monthly allowance for a given student and explain why multiplication can also be used to determine her allowance. For students beyond grade level, BL, the instructions advise teachers to ask students to alter the scenario so that the $5 the student spends is one-third of her allowance and explain how the bar diagram and solution would change. The materials also provide guidance for determining if students need differentiated supports for fluency activities within each chapter. Each chapter includes diagnostic assessments to assess student fluency. In addition, within the “Are You Ready” section in the Chapter Overview, there is an online readiness quiz and a quick review. Based on the results of this diagnostic exam, students receive a table to address their individual needs before beginning the chapter. The same occurs for students who approach level, need intensive intervention, or perform beyond level.
While the materials provide numerous opportunities to support fluency, the textbook and accompanying resources do not provide a specific year-long plan for building fluency to the concept development and expectation of the grade level. Materials do provide a content brief, which can be found in the program overview. Also, each chapter provides a pacing guide for the expected amount of time each lesson or activity should take.
The materials provide support to students in the development and use of mathematical language. Throughout the lessons, the materials include embedded opportunities to develop and strengthen mathematical vocabulary. Online materials include guidance for teachers on how to scaffold and support students’ development and use of academic mathematical vocabulary in context.
Evidence includes but is not limited to:
The materials include embedded opportunities to develop and strengthen mathematical vocabulary. The “Plan and Present” resource included with each chapter demonstrates a strategic approach to developing the mathematical vocabulary of students. A “Vocabulary” tab is included within the “Chapter Overview” resource, which contains a list of the vocabulary words for the chapter. Additionally, materials contain vocabulary activities, “Visual Kinesthetic Vocabulary Cards,” and the “Student Built Glossary” that can be used as a vocabulary study guide. Finally, each Chapter Overview includes the “Texas Course Glossary” with definitions for vocabulary necessary for the lessons. The materials highlight the continued use of vocabulary; however, there are no learning goals that explicitly address the development of mathematical vocabulary.
The “Professional Development” section also provides an opportunity for teachers to strengthen the students' vocabulary. In this section, a teacher can find an article on developing academic vocabulary. This document outlines the need and strategies for teaching academic vocabulary to students. One such learning strategy for teaching academic vocabulary is using context to unlock the meaning of unknown words or using the Six-Step Strategy as outlined by Marzano.
The materials do support language development and the use of academic vocabulary for English Learners (ELs) by looking up cognates for the given mathematical vocabulary. The ELL handbook also provides language prompts for Beginner, Intermediate, and Advanced students that are oral and written discussion starters. Although the materials note the ELPS, the learning goals do not address the development of mathematical vocabulary. The materials use formal vocabulary throughout the lessons rather than using informal language to make connections. For example, Lesson 6-5 uses the mathematical language of additive, representations, input, and output. Furthermore, in lessons throughout Chapter 6, the materials use congruent instead of equal and decompose instead of separate.
The vocabulary is clearly outlined and intentionally introduced in the appropriate chapter of each lesson. The teacher plan also directs teachers to have students follow the routine choral reading of saying each term out loud and having students say each term out loud after the teacher. The materials provide cooperative learning strategies that allow students to listen, speak, read, and write using the mathematical vocabulary embedded in a set of problems or tasks. Chapter 1 lists the vocabulary words at the beginning of the chapter then prompts students to review vocabulary while using a graphic organizer to help remember important vocabulary terms.
As teachers move through each chapter, they introduce new vocabulary terms using the choral reading routine.
Materials provide opportunities for students to apply mathematical knowledge and skills to solve problems in new and varied contexts, including problems arising in everyday life, society, and the workplace. Throughout the lessons, the materials include opportunities for students to successfully integrate knowledge and skills together to problem solve and use mathematics efficiently in real-world problems. They also provide students opportunities to analyze data through real-world contexts.
Evidence includes but is not limited to:
The materials include opportunities for students to successfully integrate knowledge and skills together to problem solve and use mathematics efficiently in real-world problems. Within the “Launch the Lesson” activity at the start of most lessons, students solve a real-world problem. Lesson 1-6 opens with a real-world problem in which students order insects by length. The lesson continues to a guided practice in which students compare rational numbers with symbols, horizontal number lines, and vertical number lines. Other real-world situations include working with the melting points of elements, water levels, and rainfall.
The “Chapter Overview” of each chapter contains a graphic novel activity that allows students to solve real-world problems based on a variety of contexts. In Chapter 2, the graphic novel activity tells the story of three students buying bird seeds to raise money for their class trip. The students buy five bags that weigh 3¾ pounds and determine later in the chapter the number of bags they have if they divide the large bag into smaller 1½ pound bags.
The materials also provide students with opportunities to analyze data through real-world contexts. In Chapter 2, there is a chapter project in which students plan a party with a budget. The project requires students to analyze flyers from local stores, compare prices with unit cost, and post their party plan. In addition, each lesson opens with a “Math in the Real-World” activity, which requires students to analyze a set of data. For example, in Lesson 2-1, students analyze the weights of an object on various planets. Students use this data to convert the weights of various other objects.
All chapters end with a “Problem-Solving Project” section. In Chapter 3, students work on the project, It’s Out of this World, which requires students to choose three planets in the solar system, use the internet to research each planet, find its average orbital speed in miles per second or kilometers per second, and organize the information in a table. The students then find and record the orbital distance traveled in 1, 2, and 3 seconds for each planet they chose. Next, the students describe how the orbital distance of each planet changes with time. For the three planets, the students list the ordered pairs representing time and distance and graph each set of ordered pairs on a coordinate plane, connecting each set of points with the line. Students compare the graphs and then write equations to represent each relationship.
In Lesson 4-7, students analyze a table that shows the approximate weight in tons of several large animals. The materials instruct students to use a ratio table to convert each weight from tons to pounds and represent the ratios in a graph.
The materials require students to integrate knowledge and skills to make sense of a context and develop an efficient and successful solution strategy within each lesson. In Lesson 5-5, students solve problems in the context of determining the original price of a jersey when given a discount and the percent of students wearing tennis shoes versus not. All the contexts presented are developmentally appropriate for grade-level students as well. Later in Chapter 5, students use a table of data in an example problem. The table shows the percent of each movie type rented during a month. The students are asked, “What fraction of the rentals were action movies?” Lessons also contain data in other forms, such as circle graphs, tables, and real-world context.
The materials are partially supported by research on how students develop mathematical understandings. The materials include cited research that supports the design of teacher and student resources and research-based guidance for instruction that enriches educator understanding of mathematical concepts and the validity of the recommended approach. Cited research is academic, relevant to skill development in mathematics, and applicable to Texas-specific context and demographics. Cited research is not found throughout the curriculum, and no current research sources are cited (dates between 1956–2011). Additionally, no clear bibliography is present within the materials.
Evidence includes but is not limited to:
The materials include cited research that supports the design of teacher and student resources within the “White Pages” resource located in the “Professional Development” section of the resource. The White Pages cite research about the design of instructional materials and how students learn mathematics. The articles within the White Pages include “21st Century Skills: Preparing Kids for THEIR Future,” “Developing Academic Vocabulary,” “Understanding by Design,” “The Benefits of Write-In Textbooks,” “Does the Use of Technology Improve Learning?” “The Answer Lies in Design?,” “Women’s and Minorities in STEM Careers Advancing Our World,” “Differentiating Instruction in Responsive Middle and High School Classrooms,” “Science, Technology, Engineering and Mathematics (STEM) Education,” “Fostering Visual Literacy in the XBox Generation,” “Differentiating Mathematics Instruction So EVERYONE Learns,” “Strategies to Teach and Engage English Language Learners in Mathematics Classrooms,” and “Homework Research Gives Insight to Improving Teaching Practice.” Another resource, “Understanding by Design,” offers a planning framework to guide curriculum, assessment, and instruction. The two key ideas are to focus on teaching and assessing for understanding and transfer, as well as designing curriculum “backward.” The cited research is only in the teacher resources within the White Pages, not in the student materials.
Additionally, the cited research included in the White Pages is academic and relevant to skill development in mathematics. The article “Differentiating Mathematics Instruction So EVERYONE Learns” describes that, by using formative assessments, flexible grouping, targeted instruction, adjusted levels of cognitive demand, utilization of learning frameworks, and progress monitoring, the teacher can implement more effective instruction for students. Though the cited research is academic and relevant to skill development in mathematics, the references for this research are not current and dates between 1956–2011.
The materials provide guidance for instruction that enriches educator understanding of mathematical concepts and the validity of the recommended approach in parts of the curriculum; however, it is unclear if the guidance is research-based. The materials start each unit with a pacing guide that shows the recommended sequence of the concepts and the number of days. Materials also include a mathematical background for each lesson. In Lesson 1-4, the mathematical background provided notes the following: “any number that can be expressed as a fraction is a rational number. Place value can be used to express decimals as fractions and mixed numbers. Answers should usually be written in the simplest form. To simplify a fraction, divide the numerator and the denominator by the greatest common factor, GCF. To convert fractions with denominators that are factors of 10, 100, or 1,000 to decimals, multiply the numerator and denominator by the missing factor to find an equivalent fraction with a denominator of 10, 100, or 1,000. Every fraction can be expressed as a decimal by dividing the numerator by the denominator.” The mathematical background, although helpful guidance, is not research-based. In Chapter 4, the materials specify that students previously represented and used rational numbers in a variety of forms. In Lessons 1 and 2, students learn about ratios and rates and how to represent them. The materials include the definition of a ratio and the description of writing ratios in three ways. Although the materials provide guidance for instruction, the guidance does not cite research.
Additionally, the “eSolutions Manual” in the “Resources” section provides step-by-step solutions to problems along with answers to the problems. However, it does not provide research-based guidance that enriches the educator’s understanding of the concept. While the solutions and answers are provided, there is no rationale for why the solution is correct or how to explain the concept to the students. There are also several videos on implementing Dinah Zike Foldables, but there is no evidence showing this approach is research-based.
The materials provide some cited research that is academic and relevant to skill development in mathematics and applicable to Texas-specific context and demographics; however, it is not current or consistent. English Learners, for example, are provided with collaborative strategies, differentiation strategies, and an ELL handbook. Several lessons, for example, Lesson 3-3, recommend that teachers pair the lesson with one in the ELL handbook, Lesson 7, Multiplying Integers. The Mathematical Process Standards provide a correlation to the Texas Essential Knowledge and Skills. For example, the “TEKS Skill Trace” table in each chapter breaks down the TEKS for the grade, highlights the lessons in which they are used, and provides pages for reference. The materials also describe Texas-specific content and demographics within each chapter. For example, Chapter 3 opens with a problem related to the crude oil in the Edwards Plateau region of Texas. However, there is no evidence that the materials describe Texas student demographics in the research used to design the program.
The materials guide students in developing and practicing the use of a problem-solving model that is transferable across problem types and grounded in the TEKS. They also prompt students to apply a transferable problem-solving model and provide guidance to prompt students to reflect on their problem-solving approach. In addition, the materials provide guidance for teachers to support student reflection of approach to problem solving.
Evidence includes but is not limited to:
The materials guide students in developing and practicing the use of a problem-solving model that is transferable across problem types and grounded in the TEKS. An overview of the model is provided in the “Mathematical Processes Handbook.” The overview defines each component of the model: Analyze, Plan, Solve, Justify, and Evaluate. The problem-solving model is used at the beginning of the multi-step problem-solving section of each lesson and continuously throughout the materials. The problem-solving model is grounded in the mathematical process standards of the TEKS, where students are “analyzing given information, formulating a plan or strategy, determining a solution, justifying the solution, and evaluating the problem-solving process and the reasonableness of the solution.” The model provides clear opportunities for students to practice and apply each part of the process within the TEKS mathematical process standards. These opportunities are included in several areas, including the “Focus on Mathematical Processes” lessons located in the middle of most chapters, the “Multi-Step Problem Solving” sections at the end of each lesson, and the “Higher-Order Thinking (H.O.T)” problems at the close of the independent practice in each lesson.
Students are prompted to use the problem-solving model at the beginning of the multi-step problem-solving section of each lesson. The first problem of this section is an example that provides a step-by-step outline of the model and directions for completion. The outline designates Step 1 as Analyze, followed by the bolded phrase, “Read the problem.” Students are then prompted to circle the information they know. Next, the students will underline what the problem is asking them to find. After the example, the directions tell students to “Use the problem-solving model to solve each problem.” Each chapter also provides the opportunity to focus deeply on the mathematical process. In Chapter 3, students are provided with an “Analyze and Reflect” activity where they are required to work with a partner to complete a table. The students use counters if needed. The first exercise is already done for the students. Next, the students are prompted to connect models to rules. Students are asked to study the pattern in the table. They will then write a rule they can use to find the product of two integers without using counters. In Lesson 5-6, students apply the problem-solving model within the multi-step problem-solving section. At the end of Chapter 5, the chapter review contains another multi-step problem-solving model that uses the same steps as the lesson for continuity.
Teachers are also provided with guidance to prompt students to reflect on their approach to problem-solving. Chapter 1 provides students with the opportunity to analyze and reflect. For example, “Analyze Relationships: what negative number is the same distance from 0 as the number +4? Locate both numbers on the number line below.” The word “Analyze” in bold purple print is written as the first component of the problem-solving model included with the multi-step problems at the end of each lesson. The materials then prompt students to “Read the problem, circle the information you know, and underline what the problem is asking you to do.” This guidance continues as students complete the remaining parts of the problem-solving model. Students are asked the following questions: “What will you need to do to solve the problem? Write your plan in steps,” “Use your plan to solve the problem and show your steps,” and “How do you know your solution is accurate.” In Lesson 8-1, the plan component of the multi-step problem-solving activity includes the steps students use to choose the solution to a given equation from answer choices A-D. This step reads, “Test each answer choice to determine if a true number sentence is created.” The materials prompt students during the problem-solving process with questions such as, “How do you know your solution is accurate?” “Does the answer make sense?” and “Use the information in the problem to check your answer.” Each chapter also has a reflection section at the end.
The materials provide guidance for teachers to support student reflection of their approach to problem-solving. In a Chapter 3 lab, teachers are given specific instructions to push students to reflect and post student reflections around the classroom. In the lab, students explain how the models illustrate the actions of multiplying integers. The “Diagnose Student Errors” component in the Multi-step Problem-Solving section of the “Teacher Plan” also provides guidance for teachers. In Lesson 4-1, the teacher guides students through the model using the Rally Coach collaborative strategy. Students work in pairs to complete an exercise. Student 1 will talk through each step in the four-step problem-solving plan while Student 2 listens, coaches, and encourages. Next, students correct themselves, if needed. Finally, students alternate roles for each successive step.
The materials also suggest the “Circle the Sage” activity in which the teacher polls the class to see which students have a solid understanding of how to solve the problem in any given exercise or lesson. These students, the sages, spread around the room while the rest of the class divides into small groups. Each group member reports to a different sage, and the sages lead the discussion on how to solve the problem. Next, the materials prompt all students to return to their groups to compare what was discussed with each sage.
Throughout the lessons, the materials provide opportunities for students to select and use real objects, manipulatives, representations, and algorithms as appropriate for the stage of concept development, grade, and task. They also provide opportunities for students to select and use technology (e.g., calculator, graphing program, virtual tools) as appropriate for the concept development and grade. In addition, the materials provide teacher guidance on tools that are appropriate and efficient for the task.
Evidence includes but is not limited to:
Some lessons in the materials provide a section titled “Select Tools and Techniques” to solve a problem. In Chapter 2 Hands-On Lab 5a, students answer the question, "How can I select tools and techniques to help me understand what it means to divide fractions?" The lesson materials prompt students to use rulers, a measuring tape, fraction bars, and number lines to understand the concept better.
The “Hands-On Labs” included in most chapters provide students opportunities to select grade-appropriate tools for solving tasks. In Hands-On Lab 1a in Chapter 3, students are directed to either use concrete objects, such as counters, or the two-color counters in the virtual manipulatives to complete the lab. Before beginning the lab work, students are asked to reflect, “How can I select tools and techniques to determine when the sum of two integers is a negative number?”
The “Plan and Present” section provides teacher guidance about the tools introduced within the materials. Additionally, each chapter overview breaks down the entire chapter and provides support for teachers as well as which manipulatives will be used in the chapter. The Hands-On Labs included in most chapters provides professional development videos for teachers, sharing the tools that are appropriate and efficient for the task. The professional development video of Chapter 3 Hands-On Lab 1a emphasizes that students need to practice working with integers and recognizing the significance of absolute value. The materials use live videos from teachers and students to model the concept of zero pairs and the additive inverse property using colored counters and a number line and discuss the absolute value of a number.
The materials provide opportunities for students to select and use real objects, manipulatives, representations, and algorithms as appropriate for the stage of concept development, grade, and task. The “Launch the Lesson” activities at the start of most lessons allow students to use representations from the grade-level TEKS to solve tasks and enhance their understanding of concepts by exploring mathematical ideas and making and testing conjectures. In the Launch the Lesson activity in Lesson 5-1, the materials ask students how to display the results after choosing their favorite sport to play. Then, students shade a 10 x 10 grid for each sport to represent the number of students that chose the sport as their favorite. Next, the materials prompt students to write a fraction with a denominator of 100 for each sport. As the lesson progresses, students learn that a percent is a ratio that compares a number to 100 and how to generate equivalent forms of fractions and percents to show equal parts of the same whole through the use of 10 x 10 grids and bar models.
The “Graphing Technology Labs” included in some chapters throughout the materials provide students opportunities to select grade-appropriate technology for solving tasks. In Chapter 6, Graphing Technology Lab 6b, students answer the question, "How can I select tools to compare additive and multiplicative relationships?" The materials prompt students to use a graphing calculator to differentiate between additive and multiplicative relationships.
The materials provide opportunities for students to select and use technology as appropriate for concept development and grade. In the Hands-On Lab 6a, students have three sketchpad resources. The “Geometer’s Sketchpad” is a software program that gives students a tangible, visual way to learn mathematics. Students use this tool to manipulate a parallelogram whose vertices have integer coordinates. They discover that by keeping the parallelogram’s base and height measurements constant, they can create many parallelograms with the same area as a rectangle with the same base and height. This discovery leads to the area formula for all parallelograms.
In Chapter 9, students complete the Virtual Manipulative Technology Lab 2a, where they work with virtual manipulatives such as algebra tiles, base ten blocks, centimeter cubes, clock, connecting cubes, currency, fraction circles, fraction tiles, geoboards and bands, hundreds chart, number cubes, number line, spinner, tangrams, thermometer, and two-color counters. In the lab, students use the straight line tool to draw three different triangles. The virtual manipulatives shared in the online textbook also provide students with a “Help” section in the bottom taskbar. This section provides students with a step-by-step written tutorial of how to use the platform, the toolbar functions, and the various manipulatives.
The materials provide opportunities for students to select appropriate strategies for the work, concept development, and grade. Throughout the lessons, the materials prompt students to select a technique (mental math, estimation, number sense, generalization, or abstraction) as appropriate for the grade-level and the given task. They also support teachers in understanding the appropriate strategies that could be applied and how to guide students to more efficient strategies. In addition, the materials provide opportunities for students to solve problems using multiple appropriate strategies.
Evidence includes but is not limited to:
The “Plan and Present” resource included with each lesson within the materials support teachers in understanding which strategies are appropriate for solving a task and how to give students the most efficient strategies. The mathematical background in each lesson provides support for teachers in understanding strategies developed within the materials. In Chapter 3, the materials discuss the use of color counters and the rules for multiplying integers to solve multiplication problems with integers.
The materials prompt students to select a technique (mental math, estimation, number sense, generalization, or abstraction) appropriate for the grade level and the given task. In Lesson 5-5, a table shows the data from a student keeping track of her weekly quiz grades. Students select a technique as appropriate to complete a table and determine in which class the student has the highest score. Next, the materials prompt students to determine how many questions were correct if that student scored a particular score on a 50-question quiz. The materials in most chapters support students in selecting techniques appropriate for the grade level task. The “Focus on the Mathematical Process Lessons” included in most chapters support teachers in guiding students toward increasingly efficient strategies. Lesson 5-5 states that students should be able to determine when it is better to use a fraction, a decimal, or a percent. The teacher presentation for the lesson provides multiple methods for solving a specific problem.
The materials provide opportunities for students to solve problems using multiple, appropriate strategies. In Chapter 5, the text models the strategies of using a proportion, the 10% method, a bar diagram, estimation, converting a percent to a decimal, and multiplying in order to calculate the percent of a number. The materials ask students to justify their choice. In Lesson 5-4, the “Launch the Lesson” activity prompts students to draw and label a bar diagram representing how a benchmark percent and its multiples can be used to estimate. As the lesson progresses, students continue to use bar diagrams along with estimations, using the rate per 100 to estimate parts of a whole.
The materials support teachers in understanding which strategies are appropriate for solving a task with an additional resource labeled, “Real World Problem Solving Graphic Novels.” The teacher edition of this handbook explains which strategies to use for each problem within the handbook. For example, in the lesson Use Ratios to Make Predictions: Crunching Numbers, materials explain how to use equivalent ratios to solve a proportional problem.
The materials develop students’ self-efficacy and mathematical identity by providing opportunities to share strategies and approaches to tasks. Throughout the lessons, the materials support students to see themselves as mathematical thinkers who can learn from solving problems, make sense of mathematics, and productively struggle. They also support students in understanding that there can be multiple ways to solve problems and complete tasks. In addition, the materials support and guide teachers in facilitating the sharing of students’ approaches to problem solving.
Evidence includes but is not limited to:
The materials foster a mathematical community that ensures all students participate and engage as mathematical thinkers who can learn from solving problems and making sense of mathematics in each lesson. The “Program Overview” contains a “Cooperative Learning Strategies” resource that provides structures to support the development of a mathematical community where students are active learners of mathematics. For example, in the activity entitled “Find the Fib,” the materials direct teachers to have students work individually or in groups to write down facts and inaccuracies about a given problem or topic on index cards. Students then trade cards with other students, who must then discern the facts from the inaccuracies. Students participate in productive struggle while working through the problem-solving process lesson in each chapter, as well as in the chapter project, which allows students flexibility in creating their final product. The materials also provide some opportunities during independent practice to “Find the Error,” where students are presented with a student mistake and correct it.
Lesson 2-5 offers additional activities for differentiated instruction based on learner type. For example, for students who are verbal and linguistic learners, the lesson recommends writing a short story in which a character needs to divide whole numbers by a fraction to connect to the material. The materials include tasks designed to support students in productive struggle within each lesson. For example, in the self-checking assessment in the lesson, each problem provides a hint to help students who may struggle to solve the problem. In a question dividing a whole number by a fraction, the hint reminds students about the concept of a reciprocal.
Each chapter contains a project that allows students to step away from memorized algorithms into real-world applications. In Chapter 4, students produce a skit demonstrating how to increase or decrease a recipe. Students have to use strategies and formulas learned to manipulate recipes depending on the number of people served.
The materials provide an alternative teaching strategy for struggling students, a “Watch Out” section for noticing a common error, and a “Diagnosing Student Errors” section within the multi-step problem solving. Each lesson also provides a “Ticket Out the Door” to formatively assess student understanding. The materials provide support for monitoring students as they develop solution strategies within each lesson. In Lesson 4-4, the Watch Out section prompts teachers to remind students that the order in which the coordinates are listed is important. Students will still graph a straight line if the ordered-pair values are transposed, but that line will be incorrect. The materials prompt teachers to encourage students to "run" along the x-axis and then "rise" to the y-value.
The materials prompt students to effectively communicate mathematical ideas, reasoning, and their implications using multiple representations. Throughout the lessons, the materials provide students with an opportunity to communicate mathematical ideas and solve problems using multiple representations, as appropriate for the task. They also guide teachers in prompting students to communicate mathematical ideas and reasoning in multiple representations, including writing and the use of mathematical vocabulary, as appropriate for the task.
Evidence includes but is not limited to:
In Chapter 1, materials prompt teachers to introduce each vocabulary term using the choral response method of saying each term aloud after the teacher. An example provided by the materials is, “Absolute value is the distance between the number and zero on a number line. An example of this is the absolute value of −3 is 3.” Teachers are then instructed to ask, “What is | −8|?” The “Vocabulary” section in each chapter begins by providing all the vocabulary words for the chapter and indicating their corresponding lesson. Teachers are also provided with a vocabulary activity that helps to support EL students. The “Student-Built Glossary” is available for students to use as a vocabulary study guide. The materials provide teachers with a vocabulary “White Paper” that has a list of effective strategies.
In Chapter 2, Hands-On Lab 2a, students complete a table and fill in blanks, determine places by moving the decimal point, analyze relationships and justify arguments, and create rules and answer inquiry-based questions. Each chapter contains foldables to organize their thinking. Chapter projects and labs allow students to collaborate as they investigate, share their research results, and reflect on how they communicate mathematical ideas.
In Chapter 3, students work on a project to explore the orbital speed of different planets and satellites. Students create tables of their results, develop an equation to represent the relationship, and write a summary of their findings. Finally, students reflect on how to communicate mathematical ideas effectively.
The “Hands-On Labs” included in most chapters include tasks that provide students with opportunities to share and discuss mathematical ideas and representations using visual, physical, contextual, verbal, and symbolic representations. In Chapter 5 Hands-on Lab 1a, students answer the question, “How can I use diagrams to communicate mathematical ideas?” Throughout the lab, students work with a partner to identify and model percentages with 10 x 10 grids, bar diagrams, and strip diagrams. Students explain their reasoning for each solution. At the conclusion of the lab, students write a real-world problem that involves a percent, then create a model of the percent used in the problem.
Lesson 8-1 references “Teach with Tech,” where students use an interactive balance to communicate their thinking when solving one-step equations. Later, in Lesson 8-4, students engage in a “Pairs Discussion,” where they work in pairs to complete given exercises. For each equation, students draw a bar diagram and describe how it can be used to find the solution. Each student pair shares their bar diagrams with the class.
In Chapter 10, students write about what they have learned in previous lessons in the chapter. The prompts provided state, “In previous lessons, I learned…., and in this lesson...” and “What I learned in previous lessons helped me in this lesson because….”
Throughout the lessons, the materials provide opportunities for students to engage in mathematical discourse in a variety of settings (e.g., whole group, small group, peer-to-peer). They also integrate discussion to support students’ development of content knowledge and skills appropriate for the concept and grade-level. The materials guide teachers in structuring and facilitating discussions as appropriate for the concept and grade-level.
Evidence includes but is not limited to:
The “Program Overview” contains a “Cooperative Learning Strategies” resource that provides strategies and opportunities for all students to discuss mathematics during every lesson with partners, small groups, and the whole class. In the activity “Paired Heads Together,” teachers pose a question or problem to students in a whole group setting and allow adequate time for thinking. Students write their ideas for solving on a piece of paper and then pair with another student to compare ideas. Pairs then work together to solve the problem, using the best idea. Students may be paired with another partner for further communication and reasoning. Each lesson provides Cooperative Learning Strategies.
The materials integrate discussion to support students’ development of content knowledge and skills appropriate for the concept and grade-level. Within the “Plan and Present” resource, the materials describe the opportunities for discussion in all phases of concept and skill development for each lesson. The materials present these discussion opportunities as Cooperative Learning Strategies, which appear in multiple phases of the lesson plan. For example, in Lesson 2-1, the first Cooperative Learning Strategy is shown in the “Launch the Lesson” tab at the beginning of the lesson. In the “Pairs Discussion” activity, students work in pairs to discuss and complete exercises from the lesson. Next, the “Teach the Concept” tab mid-lesson includes the “Round Robin” activity in which students work in groups of four to complete a set of problems. Finally, the materials provide the “Three Stay, One Stray” activity to use within the Multi-step Problem at the end of the lesson. Within this activity, students work in a small group to find their solutions.
In Chapter 3, within the first two lessons, there are four unique discussion strategies: Round Robin, Pairs Discussion, “Teammates Consult,” and “Pair Consult.” During the practice section of a lesson, students are sometimes paired with a partner to share and demonstrate their thinking.
In Lesson 10-4, students develop their understanding of dot plots with a variety of sections through opportunities for discussion. In the Launch the Lesson activity, students do a Pairs Discussion, complete the first two steps of the exercise, and discuss how the frequency table and dot plot are similar. Next, students perform a “Pairs Project” where pairs of students use the Internet, or another source, to locate a dot plot that uses real-world data. Students determine the measures of center and spread of the data. Students then create a visual display that shows how to determine each measure. Finally, students are prompted to display their visual around the room as a reference to use throughout the chapter. In the “Multi-step Problem Solving” section, students do the “Talking Chips” activity where students work in small groups to complete an exercise. Each student is given five chips. As a group, students discuss each step of the four-step problem-solving plan. Students must place a chip in the center of the table each time they contribute to the discussion, offering their opinions and ideas. After they have used all of their chips, they may no longer contribute to the discussion. All students must use all of their chips. Each lesson is set up with the same structure but with different cooperative learning tasks. Some of the lessons also provide a formative exit ticket that requires students to write about a given concept.
The materials guide teachers in structuring and facilitating discussions as appropriate for the concept and grade-level. For example, teachers are required to watch a clip on the Meaning of Equations. From the clip, the teacher learns how to lead students in a discussion of the meaning of an equals sign, balancing equations, and solving for unknown quantities.
Teachers are also provided with a “White Paper” on 21st-century skills to strengthen math skills, which includes communication and collaboration. The “Professional Development” section provides a webinar on setting up your classroom for differentiated instruction and collaborative practice and how to teach mathematical communication.
The materials provide opportunities for students to justify mathematical ideas using multiple representations and precise mathematical language. Throughout the lessons, the materials provide opportunities for students to construct and present arguments that justify mathematical ideas using multiple representations. The materials assist teachers in facilitating students to construct arguments using grade-level appropriate mathematical ideas.
Evidence includes but is not limited to:
The materials provide opportunities for students to construct and present arguments that justify mathematical ideas using multiple representations. The materials introduce justifying arguments within the mathematical processes handbook. Students justify the conjectures of various hypothetical people. Within each multi-step problem solving section of the lesson, students justify their solutions. Hands-on labs contain justification opportunities using multiple representations. For example, in Lesson 6-6b, students use both a table and a grid of the first quadrant to justify when two equations intersect. Students are then asked to justify their solutions throughout each chapter, which can be found by looking for the MP (Mathematical Processes) symbol followed by Justify Arguments, such as on pg. 68, and in the multi-step problem solving when students have to justify and evaluate or explain their answer. On a question on page 89, students justify arguments based on the question, “If you interchange the coordinates of any point in Quadrant II, in which quadrant would the new point be located?”
Some exit tickets require students to write about a concept and construct arguments using grade-level appropriate mathematical ideas. For example, in Lesson 3-1, students write a comparison and contrast of the given expressions. In Lesson 3-3, the materials direct the teacher to have students write about how the lesson concepts helped them with the lesson materials. Also, in Lesson 4-2, the exit ticket provides teachers with three different sentence stems to share with students to help them write about how the lesson on ratios and rates helped prepare them for ratio tables. Teachers are provided prompts for student responses within the plan and present section. For example, Lesson 4-2 prompts the teacher to ask questions such as “How does the unit rate help you determine the answer?”, “What do you notice about this rate?”, “Why can't we just compare the number of beats 2,100 and 2,600?”, and “Describe another way you can solve this problem.” The lesson also prompts teachers when it suggests that students explain their answers or thinking. Each lesson throughout the material is structured in the same manner as listed above.
The “Mathematical Processes Handbook Focus” on Mathematical Process G, Justify Arguments, has several discussion strategies to facilitate discussion. The materials provide solutions and methods for diagnosing errors. The following resources are provided for teachers: an overview of the TEKS, a “Launch the Lesson” section with “TEKS Skills Trace,” “Ideas for Use,” a “Practice and Apply” section with Ideas for Use, “Alternate Strategies,” and an assessment that includes a “Ticket Out the Door” for students to explain how using the principles of math can help to solve problems.
The materials include developmentally appropriate diagnostic tools (e.g., formative and summative progress monitoring) and guidance for teachers and students to monitor progress. Throughout the lessons, the materials include a variety of diagnostic tools that are developmentally appropriate (e.g., observational, anecdotal, and formal). They also provide guidance to ensure consistent and accurate administration of diagnostic tools. In addition, materials include tools for students to track their own progress and growth and diagnostic tools to measure all content and process skills for the grade level, as outlined in the TEKS and Mathematical Process Standards.
Evidence includes but is not limited to:
The materials include a variety of diagnostic tools that are developmentally appropriate. The materials include formal assessment measures designed to support the teacher in determining a student’s understanding and fluency with critical content and skills. Each chapter contains a diagnostic test in Word and PDF format within the tools section of the “Chapter Overview” in the “Teacher’s Edition.” For example, in Chapter 3, the diagnostic test supports the teacher in determining the students’ understanding of absolute value and locating sets of numbers on a number line. The materials also include informal measures, such as a checklist for specific content and skills. Before beginning each chapter, the materials prompt teachers to instruct students to go to the “Track Your TEKS Progress” document to rate their current knowledge of the TEKS within the chapter. The document includes a list of the sixth-grade TEKS and student expectations with columns for students to rate their knowledge of each. In the chapter overview section of the teacher plan, there is an “Are You Ready” section. Within this section, the teacher will find a pre-test, diagnostic test, and an “Are You Ready” review to use with students for the upcoming chapter. These materials are on level and appropriate for the grade level and chapter. Also, when launching each chapter, the teacher can send home a family letter in English or Spanish that outlines what the student will learn in the chapter, key vocabulary, and at-home activities. The letter invites the parents to contact the teacher with any questions or concerns. Students can also demonstrate understanding by using the “Track your TEKS Progress” document along with the rate yourself tool, such as the one in Lesson 1-1 that has students rate how confident they are with integers and graphing. The materials contain tools to allow students to show understanding in a variety of methods within each chapter. This help includes, but is not limited to, an “Are You Ready” assignment, self-check quiz, e-assessment, ticket out the door, multi-step problem solving, chapter pre-tests, and “got it” checks. Other assignments include chapter projects and performance tasks. Also, students show their understanding with their peers in cooperative learning activities.
The materials also provide guidance to ensure consistent and accurate administration of diagnostic tools. The chapter overview in the “Plan and Present” section breaks down the Are You Ready portion of the text. The materials prompt teachers to use the student page to determine if students have the skills that are needed for the chapter. Students also have the option to take the “Online Readiness Quiz.” The “Quick Check” instructs teachers on helping students who have difficulty with the exercises by presenting an additional example to clarify any misconceptions they may have. The materials contain an assessment section that provides the various assessments for the chapter. For example, the vocabulary test and diagnostic assessments are located in the chapter overview. The mid-chapter check is a stand-alone link, and the chapter test is located in the “Wrap-Up” section. Teachers are provided with a description of the level of students for which each test was designed. The materials also have a help section that includes a component for assessing the students. This component guides teachers through creating, assigning, and viewing reports in the test generator. The reports section provides teachers with the option to view assignment results, compare classes, grade book, prescription report, proficiency report, proficiency chart, progress report, and item analysis report. Also, in the assessment generator provided in the resource, teachers can click on the starred section titled “See What’s New in eAssessment.” This section provides teachers with a walk-through on all the components of the assessment generator, along with a search feature to provide further support. In the implementation support, the materials provide videos on how to create a new test, how to assign these two classes, how to run reports, and how to customize pre-made assessments. The materials include recommendations to support the consistent administration of the diagnostic tools within the help section. In the help area, there is a section labeled “Assessing Your Students.” Within this area, there are several views. The videos have tips throughout, including how to make a study guide for a student, how to create additional question sets, and how to add limits. These limits include scrambling questions and answers and limiting the number of attempts.
The materials include tools for students to track their own progress and growth. The “Track Your TEKS Progress” document provides opportunities for students to rate their level of understanding of TEKS within each chapter. Before beginning a chapter, the materials prompt teachers to have students go to the document to rate their current knowledge of the TEKS. At the end of the chapter, the materials remind teachers to have students return to the Track Your TEKS Progress pages to rate their knowledge again to see that their knowledge and skills have increased. Students can use red, yellow, and green faces to rate their comfort level with each content standard before and after learning it. For example, Lesson 3-2 has students rate themselves on how well they understand subtracting integers. The materials also provide students with a self-check quiz and the answers to the odd-numbered questions, both of which allow students to monitor their understanding of a specific concept. Each chapter also provides a task for students to reflect on their learning. Chapter 11 has students use what they learned about financial literacy to complete a graphing organizer, and the problem-solving projects also have a reflection component.
The materials also include diagnostic tools to measure all content and process skills for the grade level, as outlined in the TEKS and Mathematical Process Standards. The assessment generator has a section titled “Mastering the TEKS,” which allows the teacher to select specific standards to be assessed. The summative tests will also note which content TEKS are being assessed on each question. The diagnostic tools included measure all the content provided in the book, but it does not specify the process and skills as outlined in the grade-level TEKS. For example, the diagnostic test is broken down by chapter and covers the content based on the TEKS. However, the test does not specify that this is how it was outlined. The materials include tools to measure all content and process skills, as outlined in the grade-level TEKS. This measurement includes, but is not limited to, “Are You Ready” assignments, self-check quizzes, e-assessments, tickets out the door, multi-step problem solving, chapter pre-tests, and “got it” checks. Other assignments include chapter projects and performance tasks. Also, students show their understanding with their peers in cooperative learning activities. The “Multi-Step Problem Solving” at the end of each lesson is an informal diagnostic tool designed to measure all content and process skills outlined in the grade-level TEKS. Each exercise is dual-coded with content and process TEKS and tagged with spiral review TEKS. In Lesson 3-4, the “Multi-Step Problem Solving” exercises 25–29 require students to use multiple steps and integrate TEKS from multiple grades/focal areas. These standards include 6.3D, 6.1A, and 6.1B.
The materials include some guidance for teachers and administrators to analyze and respond to data from diagnostic tools. Throughout the lessons, the materials support teachers with guidance and direction to respond to individual students’ needs in all areas of mathematics, based on measures of student progress appropriate to the developmental level. Diagnostic tools also yield meaningful information for teachers to use when planning instruction and differentiation. In addition, materials provide a variety of resources and teacher guidance on how to leverage different activities to respond to student data. The materials provide guidance for administrators to support teachers in analyzing and responding to data.
Evidence includes but is not limited to:
The materials support teachers with guidance and direction to respond to individual students’ needs in all areas of mathematics, based on measures of student progress appropriate to the developmental level. The materials use the designation AL (Approaching Level), OL (On Level), and BL (Beyond Level). Chapter 8, which covers solving equations, moves students through the concept using concrete models and pictorial representations, and solving algebraically. In the teacher plan for Lesson 8-4, the materials provide guidance to the teacher on how to scaffold for various learners. For example, the materials provide alternate strategies for AL and BL students when launching the lesson. In this case, the AL strategy states that the teacher should provide students with a completed bar diagram for Exercise 1. Teachers are prompted to have students use repeated addition to determine Leslie's monthly allowance and explain why multiplication can also be used to determine her allowance. Also, during the “teach the concept” portion of Lesson 8-4, teachers are given guiding questions for students at all three levels and another alternate strategy for students who are AL. In each lesson of the materials, differentiated activities for each level of learner are provided, as well as a guide to assign homework for each level of learner. The materials provide teachers with a guide to help them determine each student’s level based on their performance on the diagnostic test. This table can be found in the “Are You Ready” section of the chapter overview. Within this table, the teacher will also find recommended activities for each level of learner. This section of the chapter overview also recommends that teachers use the quick check and pre-test to assess students' level of understanding.
Throughout the materials, diagnostic tools yield meaningful information for teachers to use when planning instruction and differentiation. The materials provide a guide for understanding the results of diagnostic tools within the chapter overview. In the “Plan and Present” section, teachers find a chapter overview. The chapter overview has a section titled “Are You Ready.” The materials suggest to teachers that, based on students' quick check results, they may wish to further evaluate their readiness for this chapter by administering the diagnostic test from the assessment masters. The materials then prompt the teachers to use the information to address the individual needs of students before beginning the chapter. They are then provided a table that guides them through the process of determining which students are Approaching Level, On Level, and Beyond Level. The help section provides teachers with guidance to create reports from the assessment data. These reports give the teachers the option to view assignment results, class comparisons, grade books, prescription reports, proficiency reports, proficiency charts, progress reports, and item analysis reports. The reports are color-coded for easy interpretation by the teacher. A sample picture of a report can be found in the assessment by clicking on “See What’s New,” and searching reports. The materials also provide a scoring rubric for teachers to use when grading each performance task. The “Response to Intervention” section in the chapter overview tells teachers how to proceed based on the quick check results and breaks the students into tiers and levels that will help teachers improve the results. In Chapter 3, the “Response to Intervention” section under the Are you Ready tab provides teachers with guidance based on students' quick check results. The materials prompt teachers to further evaluate students' readiness for this chapter by administering the diagnostic test from the assessment masters.
The materials also provide a variety of resources and teacher guidance on leveraged different activities to respond to student data. They provide various activities to use based on the results of the chapter diagnostic exam. Teachers have access to the Are You Ready practice section, the “Quick Review Math Handbook,” and a “Self-Check Quiz” section. In addition, the Plan and Present section for each lesson provides the teacher with guiding questions to ask students based on their level. When teaching the concept, the materials provide teachers with questions to ask as a result of the students’ understanding of the example problems. For example, in Lesson 1-1, the teacher is provided with several questions after students have completed Example 1. At the Approaching level, students are asked, “In Example 1, does the word "loss" indicate moving forward or moving backward on a football field?” At the On Level, students are asked, “What is the meaning of zero in Example 1?” At the Beyond Level, students are asked, “How would you write an integer for a rainfall of 2 inches below normal?” Within the same lesson, there is an alternative teaching strategy provided for students who are approaching level. For example, if students are having trouble reading and writing integers, teachers can try one of several re-teach options provided in the resource. Beyond the plan and present, the materials also provide specific differentiated instruction resources for students depending on their level of understanding.
Administrators are given the opportunity to access content from and share content with instructors. For example, the test generator helps provide instruction to administrators that will allow them to share question sets with teachers and lock the shared content to prevent recipients from editing the content they receive. Administrators can also access multiple school districts and work from one profile. The materials do include data that can be analyzed across multiple spectrums. For example, the “Prescription Report” details class performance on a selected assignment, and based upon each student's proficiency, students may receive a prescription for the assignment. The “Compare Class Report” compares the standards covered by two classes for each standard. The “Proficiency Report” details class proficiency on all standards during a specific term or date range and for each standard covered. The materials do not include guidance for administrators to support teachers in designing instruction to respond to data.
The materials include frequent, integrated opportunities to monitor and respond to student progress toward the development of appropriate grade level and content skill development. Throughout the lessons, the materials include routine and systematic progress monitoring opportunities that accurately measure and track student progress, and the frequency of progress monitoring is appropriate for the age and content skill.
Evidence includes but is not limited to:
The materials include routine and systematic progress monitoring opportunities that accurately measure and track student progress. Each lesson begins with a quick check to review and assess the skills presented in the previous lesson. Each chapter is designed so that teachers can check student’s understanding as they progress through the concepts. In the “Plan and Present” section, the materials provide a chapter overview, in which teachers will find an “Are You Ready” section, a diagnostic test, and a pre-test. These are designed to check students' understanding at the beginning of the chapter and allow teachers to determine if students are Approaching Level, On Level, or Beyond level. Each chapter also contains a mid-chapter check for teachers to monitor students’ progress from where they started to where they are at by the midpoint and make adjustments accordingly. Finally, at the end of each chapter, the teacher has multiple versions of the chapter assessment, which are designed for teachers to give to students based on their level of understanding so that they can accurately assess their progress.
Each lesson also allows teachers to monitor student progress by using an exit ticket. For example, the exit ticket in Lesson 3-1 has students determine the sum of −3 + (−5) and −3 + 5. Then the lesson prompts students to write a few sentences comparing and contrasting the expressions. Along with the exit ticket, teachers are provided with suggestions for a quick check based on the students’ understanding of the concept. Also, the materials provide progress monitoring opportunities to measure and track student progress accurately. For example, students are prompted to track their TEKS based on the mathematical process standards. In the Plan and Present section, teachers are reminded to have each student rate their knowledge of each content standard covered in that chapter at the beginning of each chapter. Then, at the end of each chapter, teachers remind students to rate their knowledge again. Students use red, yellow, and green faces to rate their comfort level with each content standard.
The launch of the lesson has a “Building on the Essential Question” section that describes what students should be able to do at the end of the lesson. Lesson 3-5 states that students should be able to answer the prompt, "Explain how the four-step plan is used in solving multi-step problems with integers." When launching Lesson 3-5, students engage in some basic mixed practice for solving problems with integers before moving into a multi-step example problem. In return, the teacher plan provides suggested questions to ask students based on their understanding of the concept, which allows them to assess their level of understanding moving forward. As students continue the lesson, the materials provide formal practice in real-world problems, higher-order thinking problems, and multi-step problem solving, all of which are progress monitoring opportunities for the teacher. The materials also provide opportunities to track students independently and in small groups. In Lesson 3-5, the materials suggest students who are approaching level engage in a “Numbered Heads Together” activity, while students who are beyond level investigate and prepare a report of the use of negative numbers in the stock market. The e-assessment allows teachers to create and assign assessments. After students take these exams, teachers can create reports of each student’s progress through mastery.
The frequency of progress monitoring throughout the resources is appropriate for the age and content skill. Within the Plan and Present resource included with each lesson, the materials include suggestions to support more frequent monitoring of students demonstrating difficulty to support instructional interventions and response to intervention. For example, the materials suggest a variety of progress monitoring tools as informal and formal assessments. The tools within each lesson include the quick check, cooperative learning activities, “Ticket Out the Door,” and a self-check quiz. The additional tools within each chapter include a diagnostic test, an online readiness quiz, an “Are You Ready” activity, and a chapter pretest. Students are provided with a mid-chapter check in all chapters that allows students to conduct a vocabulary check, key concept check, and a multi-step problem.
The materials also remind teachers when launching the chapter to have students use the student tracker at the beginning of the chapter to rate their current knowledge and then do it again at the end of the chapter to see how their knowledge and skills have increased. In the professional development section under “TEKS/Texas Assessment,” the materials suggest using the student tracker to involve students in their own understanding of the TEKS. It also outlines for teachers to use independent practice, higher-order thinking problems, and multi-step problem solving to help prepare students for the Texas Assessment. Teachers can monitor student progress on these items in the teacher plan, within the practice and apply sections that suggest which exercises students should complete based on the level of complexity and understanding. Students are also guided to the self-check quiz, where they are given a chance to assess their progress based on content for that chapter. For example, in Chapter 7, Lesson 7-6 provides students with a self-check quiz that can be taken online. Students are also provided with hints throughout the quiz and receive immediate feedback at the end.
The instructional materials reviewed for grade 8 meet the expectations for materials providing targeted instruction and activities for all levels of learners, as well as students who struggle to master content and students who have already mastered the content.
Evidence includes but is not limited to:
Throughout the units, the students are provided with lessons that include scaffolded questioning examples for various types of learners. The materials provide guidance for differentiation to support struggling students. Teachers are provided with teacher guides for launching the lesson, an outline for teaching the concept, a designation of which practice problems students should do, and additional activities for differentiation based on level. Guidance for scaffolding the lessons is provided in the form of example questions that are broken apart by students’ level of understanding. The materials provide teachers with opportunities to develop precursor skills in the area titled “TEKS Skills Trace.” This section provides an introductory activity to develop the upcoming concept by focusing on what preceded the concept or skills. Examples of the provided materials included for scaffolding instructions and differentiating activities are mnemonic devices, foldables, videos, and quizzes.
Each lesson begins with an assessment that will allow students to gauge their understanding of prerequisite skills. Following the assessment at the beginning of each lesson, the students are provided level-appropriate material to meet their individualized needs. For example, in the function unit, Approaching Level students are asked to identify features based on vocabulary, On Level students are asked to elaborate based on the key features of the function with answers being provided by the graphic, and Beyond Level students are asked to identify functions and explain their rationale for their answer. The lesson materials include graphic organizers and criteria for success that will allow students to analyze each step of the problem properly. The materials provide students with the opportunity to appropriately access prior knowledge in order to have a conceptual understanding of the information.
The materials also provide additional items for English Learners (ELs), higher-order thinkers, as well as real-world applications to support those who have mastered the content. In addition, materials provide a response to intervention resources in each lesson with additional examples and practice for students who struggle to understand the concepts. “Personal Tutor” resources are included with each lesson as well to provide additional practice developing skills in a variety of ways. The Personal Tutor resources are available in both English and Spanish to provide additional support for ELs. While the materials provide some instructional strategies such as videos for the hearing impaired, they do not provide direct support for orthopedic or vision impairment. Materials provide activities for students who have mastered the content.
During the chapter readiness quiz for Chapter 1, students access their prerequisite knowledge of prime factorization by choosing the solution to the prime factorization of 72. There are four answer choices, along with a “Need a Hint?” hyperlink. The hint provides a reminder to use a factor tree. At the end of the ten-question quiz, students can choose the “Grade the quiz” button for immediate feedback on their performance. For example, in Chapter 1, students are provided with a graphic organizer equipped with sentence stems to answer the essential question: “Why is it helpful to express numbers in different ways?”
In the Personal Tutor video provided for Lesson 4-4, an online teacher explains the systematic process for graphing function y = x+3. The teacher creates a table to plug different values of x into the equation to solve for y. For example, by plugging 0 into the table for x and solving the equation y = 0+3, the value of y is 3. The resulting ordered pair (0,3) is plotted on the graph. The process continues using x values 1, 3, and -4. The respective ordered pairs (1,4), (-3,0), and (4,7) are plotted on the graph using different colors for the distinction of points. Next, a line is drawn to determine if all four points fall on a line. Students can make visual connections to linear functions, while the pause video feature allows students to work at their own pace.
In Unit 5, the chapter begins with a vocabulary preview, then continues with a section entitled “The Structure of Math.” This section uses flowchart symbols to classify triangles by their sides. The materials also include a Personal Tutor resource throughout each lesson to provide additional practice developing skills in a variety of ways. In addition, the Personal Tutor resources are available in both English and Spanish. The differentiated activity for Lesson 5-4 specifically targets On-Level naturalistic learners. Students are given rulers, and the classroom is set with stations of three boxes of varying sizes. Students work in groups of three to find the diagonals of the top, side, and front face and the diagonal from the upper corner of the back face to the lower corner of the front face. Student groups move from one station to the next until all groups have worked at all stations. The materials include a section called “Solving a Simpler Activity” that allows students to apply the skills that they have acquired in multiple ways. For example, in Chapter 5, students have a vocabulary preview that allows them to review the structure of math using flowcharts symbols. In this specific example, students must classify triangles by their sides. The resource itself also includes five problem-solving projects and two STEM projects (School Renovation and Sports Recreation), which can be found in the “Plan and Present” section.
The differentiated activity for Lesson 8-2 challenges auditory learners to plot the points for the vertices of a square as the teacher calls them out. The instructor tells students the coordinates of one of the new vertices. Students then find all the possible coordinates for the other vertices. The activity expects students to find the four possibilities. The materials also include real-world application activities that allow students to explore and investigate the skills they have learned in multiple ways.
The materials provide instructional methods that appeal to a variety of learning interests and needs. Throughout the lessons, the materials include instructional approaches to engage students in the mastery of the content. They also provide some support toward developmentally appropriate instructional strategies, flexible grouping, and multiple types of practices (e.g., guided, independent, and collaborative) and provide guidance and structures to achieve effective implementation.
Evidence includes but is not limited to:
The materials include instructional approaches to engage students in mastery of the content. The materials include virtual manipulatives, visual representations, symbolic algorithms, and graphic organizers. These are included in hands-on labs as well as lessons that are usually in the opening materials. Manipulatives include counters, algebra tiles, protractors, and more.
The materials include foldables and graphic organizers that provide support for visual and tactile learners. The first chapter of each unit begins with a foldable that provides students with an opportunity to grasp the concept properly. This chapter also contains other hands-on labs for students to engage in the mastery of the content. There are also graphic organizers included at the end of each chapter to further engage students and offer students a reflection to complete. In Chapter 6, the graphic organizer asks the essential question, “How can you express a relationship between two quantities in different ways?” Students are then expected to provide an example of a table, equation, and graph to complete the graphic organizer, but the students are not provided with guidance on creating these.
The materials support developmentally appropriate instructional strategies in some instances. Within the grade 6 materials, there are several resources available to support teachers in implementing instructional strategies. There is a guide included for English Learners (ELs), which provides key language strategies, group formats, and a three-part lesson. The language level prompts tasks both orally and in written form. Teacher professional development includes videos of teacher examples by lesson. For example, in the unit on equations and inequalities, there are two video types to support instruction. The “Personal Tutor” shows an interactive whiteboard with a teacher thinking aloud and modeling their thinking, and the professional development videos show actual teachers teaching the material with students.
The materials provide support for teachers to know how and when to use developmentally appropriate materials, but a specific outline for selecting strategies is not provided. Specifically, each lesson has examples that can be differentiated for students based on the level of understanding. The materials provide some support for flexible groupings such as small groups, whole groups, and individual learning. The materials provide guidance to teachers on when to use a specific grouping structure based on the needs of students within the plan and present resources included with each lesson. The materials note to have students complete the “Quick Check” provided to review and assess the skills presented in the previous lesson as they enter the classroom. Some of the structures provided are for small group or whole group instruction.
Lastly, the materials support multiple types of practices and provide some guidance and structures to achieve effective implementation. Within the sixth-grade lesson cycle, there are multiple opportunities for students to practice with teachers, peers, and self. The materials give clear guidance for activities to support guided learning, whole group learning, independent learning, and cooperative learning. In a lesson on multiplying fractions and whole numbers, the materials use cooperative activities in the “Engage and Explore” sections of the lesson cycle. The lesson embeds small group instruction based on the results of practice and ends with independent practice and assessment. The materials support teachers in facilitating guided, collaborative, and independent practice throughout. Each lesson has an outline that gives teacher strategies and guidance through each component of the lesson itself, as well as when a particular type of practice may be useful. The materials also define levels of independent practice to help determine which set of questions may be appropriate for a given group of students. They do provide RTI activities, but these activities are not necessarily designed for individual students and are more likely to be used with a group of students.
For example, in Lesson 1, students are expected to work with a partner to complete a table representing each location in relation to the sea level. They are then required to analyze their findings with their partners before creating a conclusion on their own. Students are required to complete a reflection document at the end of each chapter. These reflection graphic organizers begin with an essential question. Students have a variety of chances for independent practice, but the materials give limited guidance on how to facilitate practice opportunities. For example, in the guided practice “Trade a Problem” activity, teachers prompt students to write their own real-world multi-step problem involving multiplication of fractions by whole numbers, but the material provides no guidance on facilitating the process. The materials provide limited evidence on how to facilitate independent practice.
The materials include supports for English Learners (EL) to meet grade-level learning expectations. Throughout the lessons, the materials include accommodations for linguistics (communicated, sequenced, and scaffolded) commensurate with various levels of English language proficiency and provide scaffolds for ELs. In addition, materials encourage the strategic use of students’ first language as a means to develop linguistic, affective, cognitive, and academic skills in English (e.g., to enhance vocabulary development).
Evidence includes but is not limited to:
The materials include accommodations for linguistics that commensurate with various levels of English language proficiency. The English Language Learners (ELL) Guide Book G, included in the chapter overview of the tools section in the Teachers Edition of most chapters, includes various linguistic accommodations for students who are learning English, particularly regarding their level of English language proficiency within each chapter. For example, the “Language-Free Math Inventory” for sixth grade assesses the mathematical ability of incoming EL students at the previous grade level, and each student takes it independently. This assessment includes relating fractions, decimals and percents, prime factorization, fractions and decimals on a number line, adding, subtracting, multiplying and dividing decimals, etc. The results will reveal which students may need remediation.
The “English Language Learner’s Guide” provides a section titled “Facilitating Language Growth Across the Stages of Language Acquisition.” In this section, teachers are provided with a guide for identifying stages of language acquisition. It breaks it down into stages and student behaviors and then provides teachers’ behaviors and strategies. At the Beginning Level, stages and student's behaviors are broken down into preproduction and early production. In addition, within each lesson, the materials contain additional activities for ELs.
The materials also provide scaffolds for ELs. The materials contain research-based scaffolds within the “English Language Learner’s Guide.” Within this guide, professional development cites several research papers. Scaffolds include, but are not limited to, simplified language, activation of prior knowledge, multiple modalities instruction, sheltered vocabulary, various ways to show understanding, and graphic organizers. The “Vocabulary” tab in the chapter overview resource includes a vocabulary activity labeled with the EL. During this activity, the materials prompt teachers as they proceed through the chapter to introduce each vocabulary term using the following routine, “Ask the students to say each term aloud after you say it.” The materials also encourage the strategic use of students’ first language as a means to develop linguistic, affective, cognitive, and academic skills in English.
The materials include an English-Spanish glossary of important or difficult words used throughout the textbook. Terms and definitions are presented in English and Spanish. Teachers are encouraged to activate EL prior knowledge and cultural perspective. Teachers can ask students to demonstrate rhythms, kinesthetic actions, and techniques they were taught to use in their native culture to solve math problems. In the English Learners Guide, there are “Strategies for EL Success.” The guide lists six key strategies to employ during EL instruction that can make teaching easier and learning more efficient: activate EL prior knowledge and cultural perspective; use manipulatives, realia, and hands-on activities; create a risk-free environment; organize curriculum for ELs; utilize a variety of methods and representations; and anticipate common language problems.
For example, in the English Language Learners Guide, Lesson 1 begins by listing the “Key Language Strategy,” where teachers must use strategies found in the “Teacher Edition,” under differentiated instruction options, scaffolded questions, teaching modalities, and vocabulary links. Teachers are also provided with multilevel language oral and writing prompts that support beginning, intermediate and advanced students.
In Chapter 4, students define an equivalent ratio as two ratios that express the same relationship between two quantities. The examples include, 12:6 is equivalent to 20:10. The materials prompt teachers to ask, “What is an equivalent ratio to 9:81? Provide sample answers.” The materials include resources and support materials that make scaffolding intentional and natural in the lessons. Lessons begin with a lesson launch. This launch introduces essential questions and vocabulary. The lesson progresses to teaching the concept, which includes mathematical background. Examples include scaffolded questions by student level: Approaching Level, On Level, and Beyond Level. Guided practice includes opportunities for cooperative learning. Independent practice accumulates with multi-step problem-solving.
In Lesson 4-3, the strategy provided is called “Circle the Sage.” The teacher polls the class to see which students have a solid understanding of how to solve the problem presented in Exercise 11. These students (the sages) spread around the room. Next, they have the rest of the class divide into small groups. Then, each group member reports to a different sage, if possible. The sages lead the discussion on how to solve the problem. The teacher then has all students return to their groups to compare what was discussed with each sage.
The materials include a cohesive year-long plan that is vertically aligned to build students’ mathematical concept development. Throughout the curriculum, the materials provide review and practice opportunities for mathematical knowledge and skills.
Evidence includes but is not limited to:
The materials include a cohesive, year-long plan to build students’ mathematical concept development. The content plan is cohesively designed to build upon students’ current level of understanding with clear connections within and between lessons and grade levels. Each chapter of the materials includes a mathematical background section that shares a plan for instruction that spans the year. This plan includes a vertical alignment reference table and a TEKS correlation document that shows how activities align to the TEKS and, both directly and indirectly, to concepts and skills outlined for students in preceding and subsequent lessons. For example, in Chapter 8, the vertical alignment table specifies that students should have proficiency in TEKS 6.7 regarding concepts of expressions and equations before beginning the work of that chapter, which references TEKS 6.9 regarding the use of equations and inequalities to represent situations. The guide states that after achieving proficiency in both TEKS 6.7 and 6.9, students will later work with TEKS 6.8 regarding the use of geometry to represent relationships. The reference tables, however, do not always align with the relevant standard from the previous grade level or reference the following year. The year-long plan of content delivery includes a table with each chapter and the suggested number of days. The program is 146 days with an additional 20 days that includes five days of assessment review and 15 days of problem-solving projects.
The materials provide some review and practice of mathematical knowledge and skills throughout the curriculum. For example, all chapters are equipped with a “Mid-Chapter Check,” as well as a “Chapter Review” at the end of each chapter. The Chapter Review consists of a vocabulary check that reviews important vocabulary throughout the chapter, a key concept check that uses foldables to review pertinent information, a multi-step problem-solving opportunity, and a reflection. In Chapter 2, students begin with learning how to multiply decimals by decimals, moving on to fractions, and finally ending with mixed problem solving of rational numbers. Each lesson allows students to practice the concept and skills through different modalities such as teacher-led examples, guided practice, independent practice, and multi-step problem solving. The problems students practice align with the current TEKS or skills being covered. Additionally, embedded in each lesson are review tools such as the “Quick Check,” “Cooperative Learning Activities,” “Ticket Out the Door,” and “Self Check Quiz.” For example, within a Ticket Out the Door activity in Chapter 1, students demonstrate their understanding of integers by explaining how they would compare and order the amounts from a given scenario from least to greatest. Review and practice materials can also be found in the provided teacher resources. Teachers have the option of using a standardized test practice that aligns with the TEKS. Teachers can also access “Key Concept Checks” for students through the e-solutions application.
Throughout the lessons, the materials are accompanied by a TEKS-aligned scope and sequence outlining the essential knowledge and skills that are taught in the program, the order in which they are presented, and how knowledge and skills build and connect across grade levels. They also include supports to help teachers implement the materials and resources, and guidance to help administrators support teachers in implementing the materials as intended. In addition, they include a school year’s worth of math instruction, including realistic pacing guidance and routines.
Evidence includes but is not limited to:
The materials are accompanied by a TEKS-aligned scope and sequence outlining the essential knowledge and skills that are taught in the program, the order in which they are presented, and how knowledge and skills build and connect across grade levels. The materials include a scope and sequence for instruction within the program overview included in the “Plan and Present” resource of the materials. This scope and sequence shows clear alignment with the Texas Essential Knowledge and Skills for Math Grades 6–8 and outlines the sequence of instruction toward the end of year outcomes, and includes an organized chart that clearly delineates which knowledge and skills are introduced and which are reviewed within each lesson.
Furthermore, each chapter overview provides a condensed scope and sequence showing the order of topics for each component (lesson, hands-on lab) in the chapter and the length of time given toward their completion. At the beginning of the text, the students are provided with a breakdown of all the TEKS for the unit, and they can track their progress as they travel throughout the text. The scope and sequence detail the order in which content is presented. This is the same order of the chapter and lesson. The “Mathematical Background” section in the “Chapter Content” tab of the chapter overview included with each chapter of the materials include guidance for teachers on the scope and sequence and describe how the essential knowledge and skills build and connect across grade levels. The materials also include supports to help teachers implement the materials as intended.
The materials provide teachers with a professional development section to support their understanding of how the components of the materials were intended to be used. Specifically, in this section, teachers find implementation support, a professional learning community kit, sketchpad support, Dinah Zike/Foldable videos, STEM videos, on-demand webinars, and white papers. The implementation support guides teachers through in their understanding of how to use their online planning tools, how they can identify and locate the TEKS in the resource, use of the engagement tools (such as collaboration activities, differentiation activities, and activities for EL students), and how to use the online digital and print instruction. The professional development includes multiple videos on how to implement these materials. Other resources include videos, animations, personal tutors, and more. The materials contain planning tools such as recommended lesson plans, a planner, and a professional development section.
The materials include resources and guidance to help administrators support teachers in implementing the materials as intended. The materials include support for teachers to implement the materials as intended, including information in understanding appropriate learning environments, structures, and approaches that support the acquisition of mathematical knowledge. This support can also guide administrators in supporting teachers to implement the materials as intended. The materials contain a printed and digital TEKS-aligned scope and sequence outlining the essential knowledge and skills that are taught in the program, the order in which they are presented, and how knowledge and skills build and connect across grade levels. This plan includes pacing for 166 school days and includes a breakdown of pacing and days for each of the following: The Mathematical Processes Handbook, Chapters 1–11, Texas Assessment and Problem-Solving Projects. Through the access of the teacher plan, administrators can recognize the suggested best instructional practices and arrangements in a middle school classroom.
The materials also include a school year’s worth of math instruction, including realistic pacing guidance and routines. Beyond mapping out the number of days for each lesson and unit, leading up to the state assessment, they also provide projects for students to complete after the assessment has been completed. In the event that teachers have students complete the activities specifically outlined within the lesson, the materials include additional activities for differentiation, chapter projects, STEM projects, resources (such as extra practice), and enrichment. For example, in the “Plan and Present” section, the “Chapter Overview” provides “Chapter Contents” and “Suggested Pacing” for each chapter, which continues for a full year of classroom instructions. Hands-on lessons and reviews are half-day lessons, while traditional lessons have a pacing of one day. The materials also include a full day of review and testing for each chapter. The plan includes pacing for 166 school days and includes a breakdown of pacing and days for the Mathematical Processes Handbook, Chapters 1-11, and Texas Assessment and Problem-Solving Projects. The instructional pacing is realistic at the lesson and chapter level.
In Chapter 7, the mathematical background for Lesson 4 and 5 states that students have previously used variables to represent algebraic relationships. In this lesson, they use variables to evaluate and write algebraic expressions. The vertical alignment highlights what happens in previous grades, what the students are working on now, and what they will be expected to learn next.
In Lesson 9-5, administrators can recognize if teachers use the suggested strategy of “Teammates Consult.” Along with suggested strategies, administrators can determine if teachers are asking the guiding questions designed for each level of learners when they are teaching the concept. Administrators can also use the support provided by the white papers, such as the “Developing Academic Vocabulary” paper, which provides strategies for effectively teaching vocabulary to students. Administrators can then observe if these arrangements and practices are being used.
Throughout the lessons, the materials provide guidance for strategic implementation without disrupting the sequence of content that must be taught in a specific order following a developmental progression. In addition, they are designed in a way that allows LEAs the ability to incorporate the curriculum into district, campus, and teacher programmatic design and scheduling considerations.
Evidence includes but is not limited to:
The materials provide guidance for strategic implementation without disrupting the sequence of content that must be taught in a specific order following a developmental progression. The materials also provide a suggested sequence of lessons within the overview of each chapter that considers the interconnections between the development of conceptual understanding and procedural fluency.
The materials clearly delineate the order of units to ensure students learn about precursor concepts first. The materials also provide access to different tools at the chapter, lesson, and planner level to customize lessons. The materials provide a content brief and pacing that outlines the order of the units and the key focal concept. This outline allows teachers to see the suggested order of the chapters based on the TEKS and the “Mathematical Processes Handbook.” The units are arranged in an order that will teach skills that will be used in later units.
The sixth-grade units are ordered so that students multiply and divide rational numbers before they solve proportions, solve equations and inequalities, and represent geometry with algebra. The materials include guidance that supports areas aligned to the classroom to provide pathways for students with varying abilities. Each chapter has a diagnostic test that helps the teacher determine if a student is Approaching Level, On Level, or Beyond Level. Each component of the lesson guide has structures in place to support the teaching of each level of student proficiency. For example, when the teacher is teaching the concepts, the materials provide a different set of question stems. Teachers also have additional differentiated tasks for each level of learner, as well as a different summative assessment at the end of the chapter. The materials map content in a sequential order to ensure students have prerequisite knowledge prior to higher-level learning.
The materials are also designed in a way that allows LEAs the ability to incorporate the curriculum into district, campus, and teacher programmatic design and scheduling considerations. For example, the implementation support within the professional development resource of the materials supports teachers in understanding how to use the materials as intended. This information includes an “e-In-service” resource that contains guidance for teachers with online planning tools. This in-service provides teachers with answers to questions such as, “How do I pace print and digital instruction?” and “How can I differentiate instruction using print and digital resources?” Here, teachers can find videos and documents that will guide and support implementation. This tool provides advice on using the planning tools to change lessons and the teacher planner by editing content, adding or deleting resources, or creating brand new lessons. The online resource has everything that the textbook has and more. It allows teachers to set up online discussions, create and administer tests, set up classes, and track assignments. The teacher guide in the plan and present section does reference tasks that are best suited for full class or small group instruction.
In Lesson 10-5, students can participate in a “Pairs to Group” activity. The materials provide pacing calendars and customizable lesson plans that could be adapted to a variety of settings. There are various grouping options depending on student needs. This grouping includes differentiated options based on ability and language. The program supports digital instruction allowing for things to be exported to Google Classroom and in-person instruction with print materials.
The materials provide guidance on fostering connections between home and school. Throughout the lessons, the materials support the development of strong relationships between teachers and families. In addition, they specify activities for use at home to support students’ learning and development.
Evidence includes but is not limited to:
The materials support the development of strong relationships between teachers and families. Before beginning each chapter, the materials recommend that teachers send home the family letter and at-home activities for students to complete with their parents. The letter describes what students will learn in the chapter, with key vocabulary words and activities parents can do with their students. The materials include both English and Spanish versions with chapter vocabulary, hands-on activities, and online activities. The materials also specify activities for use at home to support students’ learning and development. The materials include online access to resources parents can use at home. Online materials include resources with each chapter that are easy to use on common devices and are related to current skills. There are printable versions of worksheets, the eBook, family letter and at-home activities, virtual manipulatives, and the “eToolkit.” The materials also provide electronic access to an “eglossary,” where students or parents could select to view the terms in English or Spanish. By searching Spanish in the “Plan and Present” section, teachers will find access to the entire textbook in Spanish. They could download specific sections to be sent home as support for Spanish speaking parents.
For example, the letter from chapter 2 states: “Today we began Chapter 2 Multiply and Divide Rational Numbers. In this chapter, your student will learn how to multiply and divide decimals, fractions, and mixed numbers. Included in this letter are key vocabulary words and activities you can do with your student. If you have any questions or comments, feel free to contact me at school.”
In Chapter 4, the real-world activity asks students to make a grocery list with their families, compare the prices for different sizes of times at the store, and find unit rates for the items to determine the better buy. The students discuss reasons when purchasing the more expensive items if appropriate for the situation. In Chapter 9, representing Geometry with Algebra, the online activity is to design a swimming pool that can be divided into smaller shapes. The real-world activity is to use beans or pasta to estimate the volume of various boxes.
There are also options for video tutorials to be viewed in Spanish, such as in Lesson 7-2. Students and parents have access to ALEKS, a student account home for K–12 students. Students and parents can access assignments for their current active class.
The visual design of student and teacher materials (whether in print or digital) is neither distracting nor chaotic. Throughout the lessons, the materials include appropriate use of white space and design that supports and does not distract from student learning. In addition, pictures and graphics are supportive of student learning and engagement without being visually distracting.
Evidence includes but is not limited to:
The materials include appropriate use of white space and design that supports and does not distract from student learning. For example, the pages of the math student book have large print, simple graphics, and plenty of white space. Tables, charts, and visuals included are clear and concise, without being distracting. The student edition provides an adequate workspace for students to solve problems. On pages 216 and 217, for example, there is a designated workspace in the margins. If there is no designated workspace in the margins, there is an adequate workspace on the page itself. The materials are consumable, thus allowing students to remove the page for ease of use. All graphics, artistic and mathematical, are easy to view and understand.
The text is filled with an abundance of visual aids that supports student learning. The beginning of each chapter is equipped with a graphic novel representation of a problem. Students read the problem and answer it later on in the chapter. The headings for each lesson are bolded, have a distinct color scheme, and are located at the top of the page. Students can distinguish between lessons and other activities throughout the chapter. The text comes equipped with lines for students to capture their answers and a “Work Zone” on the side of specific pages, where they can work out their problems.
The student e-book is set up in a logical sequence with scaffolds to increase ease of use. These include a table of contents, glossary, comics for engagement, tools, reading materials, and an index. Chapter overviews contain a “Mathematical Background” within the “Chapter Content” tab. The mathematical background makes clear references to other lessons and ancillary materials that can be used to support differentiated learning. In Chapter 3, the materials discuss the use of color counters or the rules for multiplying integers to solve multiplication problems with integers.
The materials provide a teacher's edition that is virtually identical to the students’ textbook. In addition, the materials provide teachers with a digital platform titled “Plan and Present.” There, each lesson will be broken down into components such as TEKS, “Lesson Launch,” “Teach the Concept,” “Practice and Apply,” “Multi-Step Problem Solving,” “Additional Activities for Differentiated Instruction,” and “Assessment.” In each section, teachers are provided with specific materials to support learning. These materials include videos, blackline masters of student worksheets, virtual manipulatives, and step-by-step tutorials.
The Plan and Present resource is broken down into sections that are then further broken down into subsections using a drop-down arrow. Teachers can navigate the subsections quickly due to the color-coding, reference tables, and graphics available within the content. Lesson guidance has designated areas for the TEKS, lesson launch, teaching the concept, practice, multi-step problem solving, additional differentiated activities, English Learner activities, assessment, and sketchpad resources. The implementation support within the “Professional Development” resource of the materials consistently includes a place for instructional support to aid teachers in planning and implementing lessons. This support includes an “e-Inservice” resource that includes guidance for teachers with online planning tools, TEKS/Texas assessments, “Engagement and Collaboration” sections, integrating print and digital instruction, and program assessment resources.
The pictures and graphics are also supportive of student learning and engagement without being visually distracting. Most often, the pictures are related to a real-world problem or task that students are currently engaged in. For example, there is a picture of a roller coaster next to an integer problem involving a roller coaster. All chapters start with a graphic novel illustration that students can use to solve a math problem. Lessons contain graphic organizers, usually in the form of foldables and guided notes.
The materials follow the guidelines of User Interface Design. The resource provides real-world problem solving graphic novels. The stories are written in a comic strip format, are easy to read and grade-level appropriate. The book of linked graphic novels is in black and white; however, the graphic novels included in the student textbook are vibrant and in color. Also, throughout the materials, any tables, number lines, or pictorial models are clear and easy to read. The font is clear and easy to read. Items with photographs and colorful pictures do not distract from the text on the page or interfere with learning. Display charts such as number charts and number lines are also clear and easy to read.
The materials include technology or online components that are appropriate for grade-level students and provide support for learning. Throughout the lessons, technology aligns with the curriculum’s scope and approach to mathematics skill progression. In addition, the technology supports and enhances student learning as appropriate, as opposed to distracting from it, and includes appropriate teacher guidance.
Evidence includes but is not limited to:
The technology in the resources aligns with the curriculum’s scope and approach to mathematics skill progression. Materials contain an eBook with a “Go Online” option for students. This option contains direct links to watch lesson animations and videos, worksheets, vocabulary, a personal tutor, tools, and checks for understanding. Each option includes a pictorial reference that appears in various places throughout the lessons to allow students to interact digitally with tasks. Lesson 4-1, for example, includes a pictorial reference for students to watch the lesson video “Dogs.”
The technology components align with the scope and sequence of the materials. The materials provide recommendations for when to use the technology components through the “Plan and Present” section. When teachers expand each section of the lesson, any suggested technology components are clearly labeled along the right-hand side. It has the suggested videos, tutorials, and whether or not virtual manipulatives may be appropriate. When appropriate, the lesson has an expandable section for “Geometers Sketchpad.” Also, the bottoms of the textbook pages have links to the technology components that support instruction at that specific time in the scope and sequence. If something does not apply, there is not a link.
Technology icons are placed strategically through the chapter and provide students with an additional reference as they matriculate throughout the resource. Students can watch videos and complete activities as needed. Virtual manipulatives are included to help students see the material in a hands-on way using technology. The materials provide recommendations for teachers on when to utilize technology with students and if there is a time during lessons that the technology would enhance student learning within most lessons. This suggestion is outlined in the “Teach with Tech” section under the “Teach the Concept” tab of the Plan and Present resource. In Lesson 8-3, the Teach with Tech prompts teachers to have students work in pairs, using emails to solve additions and subtraction equations.
The technology also supports and enhances student learning as appropriate, as opposed to distracting from it, and includes appropriate teacher guidance. The digital student edition, eBook, of the math book is age-appropriate for sixth- through eighth-grade students. Students’ pages have navigation buttons for digital copies of the student text, tutorial videos, and online skills practice. For example, the student edition contains a “Quick Check” at the beginning of each chapter, including a “Chapter Readiness Quiz” where students may go to practice and receive feedback. In Chapter 1, Rational Numbers and the Coordinate Plane, students practice solving inequalities.
The materials provide teachers with sufficient guidance on how to utilize the technology components provided. The “eImplementation” professional development platform provides teachers with a section on how to use the online planning tools, as well as a section on how to integrate print and digital instruction. There is also a section provided within the professional development section of the resource for teachers to seek help in implementing the “Geometer’s Sketchpad” tool. The help section also provides teachers with video tutorials on using the components of the online teaching platform. For example, they can watch videos on how to create and manage their classes. The “Professional Development” section provides multiple videos that educate teachers on how to use technology with students. The materials give teachers appropriate and sufficient guidance on how to use technology with students and how to support students with technology use. There are several professional development resources for students and teachers on the sketchpad and Texas Instruments Nspire and TI-84 tech labs.
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