STEMscopes Texas Math Grade 4

Evaluation for 2.1
Materials dedicate most attention to the development of the primary focal area for the grade-level.

Students’ content knowledge is strategically and systematically developed throughout the school year. Instruction is intentionally aligned to both the grade-level primary focal areas and the concepts outlined in the TEKS. Overall, students receive enough practice opportunities to master the content.

Evidence includes but is not limited to: 

Teachers have access to a “Scope and Sequence” planning guide for the academic year; this resource describes instructional progression over time and is organized by TEKS groups. Instructional materials are organized into “Scopes,” and these scopes directly align to the grade-level primary focal areas; Scope titles include “Multiplication and Division Problem Solving,” “Add and Subtract Decimals,” and “Angles,” among others. Each scope has an “Essentials” section that describes in detail the grade-level TEKS that are covered within the scope. The “Home” section includes information about how this individual scope fits into the vertical TEKS alignment. The “Content Support” tab includes explanations of the TEKS, background knowledge, misconceptions, and obstacles to student learning of the concepts. 

Most lessons include materials and tasks that reinforce the primary focal skills for fourth grade. For example, in the “Compare Fractions” scope, students use manipulatives and drawings before advancing to word problems. As the scope progresses, students build mastery through math stories, games, hands-on activities, interactive investigations, worksheets, “Career Connection,” and videos.

Throughout the year, questions and tasks build in rigor to meet the full intent of the primary focal areas. For example, in the “Represent Decimals” scope, students begin by reviewing previous content knowledge. They recall the different forms of numbers and practice determining the value of a digit given its place in a number. In the “Explore” lessons, students relate decimals to money amounts and place value. In a later scope, “Add and Subtract Decimals,” students apply their knowledge of place value to add and subtract decimals within story problems; instead of using concrete or pictorial representations, students use an algorithm. At the end of this scope, students complete a real-world problem-solving situation: they represent the amount of money they have left after purchasing a video game or a bubble gum machine. 

Practice opportunities are also varied, numerous, and aligned to the TEKS; tasks include stations, practice problems, digital games, virtual manipulatives, independent practice reading stories, making career connections, and problem-based tasks. For example, in the “Division Models” scope, students begin by independently reading and solving different division scenarios. Each task requires them to justify their thinking. Then they use manipulatives to practice equally sharing quantities, thus building a division model. Students draw and label their models and discuss them with a small group. Continuing through the scope lessons, students build up their knowledge and complete practice opportunities until they can respond to tasks independently. These include the “Math Story,” STAAR-aligned questions, a quiz, and the “Create Your Own” project-based learning assignment. 

Additionally, each scope includes “STAAR-Based Assessments,” “Skills Quizzes,” and “Decide and Defend” tasks to determine student mastery of the content. The STAAR-Based Assessments are multiple-choice, standards-based assessments. The Skills Quizzes assess a student’s ability to compute efficiently and accurately in a short, standards-based format. Decide and Defend tasks ask students to answer open-ended questions, reason mathematically, and support ideas with evidence.

Evaluation for 2.2
Materials strategically develop students’ conceptual understanding by following a progression of learning from concrete to representational to abstract (CRA) as is appropriate for the grade-level and content.

The materials include a variety of types of models: concrete models and manipulatives, pictorial representations, and abstract representations throughout the year. Teachers also receive the support necessary to understand the CRA continuum and assist students’ progression along the continuum.

Evidence includes but is not limited to: 

The “Communicate Math” section of the “Teacher Toolbox” guides teachers on how to help students move through the phases of the CRA continuum. For example, the “Representations” document explains math representations and the expectations for students at this grade level. It provides suggestions on how to provide concrete, representational, and abstract models for mathematical concepts. In each scope, the “Intervention” and “Acceleration” tabs provide teachers guidance when intervening with students who are not mastering content and when extending for students who have mastered content. 

All scopes include manipulatives, pictorial models, abstract models, and concrete models. Varied materials include open number lines, place value disks, fraction circles, grid paper, 3-D shapes, geoboards, and scales.

Each scope begins with the “Engage” portion, where students access prior knowledge. Next is the “Explore” section, where students use manipulatives to learn new concepts. For example, in the “Represent Decimals” scope, students read scenarios and model the situations with play money. This section includes direct instruction of manipulative usage. Teachers have access to questions and statements meant to help students understand the value of base-ten blocks. As students move through the scope, they replace these concrete models with pictorial models to represent decimal amounts. Scopes also include teacher supports meant to help them understand the continuum. The “Content Support” section describes the different stages of student development. It describes how students use concrete models like base-ten blocks, pictorial models like place value disks, and abstract models like place value charts to make connections to numbers. Discussion points for teachers are included.

In the “Add and Subtract Decimals” scope, students again use base-ten blocks to model numbers in an algorithm. The materials include a student handout titled “Problem-Based Task” that has visuals of which place value the base-ten blocks represent. This document can be used as an intervention method for any students struggling to master the content. Later in the “Compare and Order Decimals” scope, students use place value disks to model decimals on a place value mat. Students then use the concrete model to compare the value of two decimal numbers. Moving down the CRA continuum, students finish the scope by drawing their own model and using symbols to represent which is greater than or less than.

Evaluation for 2.3
Materials support coherence and connections between and within content at the grade-level and across grade levels.

The lessons and tasks intentionally connect two or more concepts as appropriate for the grade-level. Students explore relationships and patterns and are also given the opportunity to make connections across content. Teachers have adequate support in helping them understand the concept alignment that guides instructional development. 

Evidence includes but is not limited to: 

The materials follow the 5E-IA teaching model: Engage, Explore, Explain, Elaborate, Evaluate, Intervention, and Acceleration. Each scope begins with an “Engage” section; activities in this section review previously learned concepts and connect them to new learning. For example, in the “Multiplication Models” scope, students determine if a multiplication model is correct or incorrect and then justify their answer. This reviews the third grade standard of representing multiplication using a variety of approaches. In the “Compose and Decompose Fractions” scope, students compare two fractions and justify if a given statement is true or false. The activity reviews the third grade standard of comparing two fractions with the same numerator or denominator. 

In the “Explore” section of each scope, students discuss how mathematical ideas connect to one another. Usually, this happens during “Math Chat.” For example, in the “Problem-Solve Using the Four Operations” scope, students represent multistep problems using strip diagrams and equations. During Math Chat, students share their observations and learning by answering the question “What are different ways you represented the problem?” Then during the “Elaborate” section of each scope, students recognize math in other contexts through “Career Connections” and “Math Story” activities. For example, in the “Area and Perimeter” scope, students read a short passage titled Raising Animals for Show and answer math-related questions based on the passage. During the Career Connection activity, students watch a video about how a podiatrist uses area and perimeter as a tool for the job. When students get to the “Evaluate” section of each scope, they apply this understanding to tasks that integrate multiple math concepts. In the “Compose and Decompose Fractions and Mixed Numbers” scope, students first review how to name fractional parts and how to compose or decompose numbers. The teacher then explains how to compose and decompose fractions in the same way. For practice, students use fractional pieces to model fractional amounts; for instance, they model the following situations: 1/3+1/3=2/3 and 1/4+1/4+1/4=3/4. Students observe that fractions can be composed and decomposed in a variety of ways and still represent the same total amount. 

Many tasks integrate familiar models and strategies from previous units. Lessons connect what has been done in the past to what will be used in the future. For example, in the “Compare Fractions” scope, students compare fractional parts using fraction bars, tiles, and circles. In the “Student Journal” portion of the lesson, students locate the fractional parts on a number line and write a comparison statement using the correct symbol. This task requires them to build upon the concrete models to represent fractions abstractly. In the “Properties of Two-Dimensional Figures” scope, students use cut-out two-dimensional figures to describe attributes of shapes, parallel lines, and right angles. Later, students classify 2D shapes based on the presence of parallel and perpendicular lines. The “Scope Overview” explains that these same models and representations will be used in fifth grade. Both students and teachers are made aware of this content progression.

Within each scope, “Content Support” and “TEKS Unwrapped” sections help teachers understand horizontal and vertical alignment. They outline and describe the TEKS in the current scope, the matching TEKS from previous grade levels, and the TEKS that align in the following grade level. TEKS Unwrapped provides definitions of the nouns and verbs in the TEKS, instructional implications, student misconceptions, and vertical alignment. For example, in the “Compose and Decompose Fractions and Mixed Numbers” scope, defined words include represent, decompose, fraction, denominator, sum, and whole number. Students visualize multiple parts to form a whole and decompose fractions that are greater than one. The vertical alignment section references TEKS from third, fourth, and sixth grades. Outside of scopes, teachers have access to a “Teacher Toolbox” that includes numerous documents that describe how instruction is connected; these documents include a “Scope List,” “Scope and Sequence,” and different “Vertical Alignment Charts.”

Evaluation for 2.4
Materials are built around quality tasks that address content at the appropriate level of rigor and complexity.

Instruction is built around quality tasks that address content at the appropriate level of rigor and complexity, as identified in the TEKS. Students are given many opportunities to apply their math ability to new and varied situations. The goal behind each mathematical task is clearly outlined for teachers, and they receive guidance anticipating student responses and facilitating discourse. 

Evidence includes but is not limited to: 

The “STEMscopes Math New Teacher Navigation Guide” describes how each step of the 5E-IA model increases in rigor: there is a “gradual transition from teacher-led instruction to student-driven learning… [allowing] students to explore context before content, to develop a deep mathematical understanding of the standards.” Each scope begins with an activity to review prior knowledge in the “Engage” section; next, the “Explore” lessons introduce new concepts and summarize additional resources; the “Explain” section includes activities for students to practice and demonstrate understanding of the learning; the “Elaborate” section provides an opportunity for more rigorous tasks to extend learning; and the “Evaluate” section assesses student learning. Additional “Intervention” and “Acceleration” sections provide scaffold and extension activities based on student mastery. 

This progression can be seen in the “Compare and Order Decimals” scope. In the Engage activity, students order a set of whole numbers with the intention of accessing prior knowledge. In the Explore section, students relate this knowledge to decimal place values and explore how to create visual models of decimals. During Elaborate and Evaluate activities, students apply their knowledge by playing fluency games and solving problem-based tasks. The scope concludes with an “Acceleration” activity: “Create Your Own Task.” Here, students use their knowledge of comparing and ordering decimals to create a board game.

Scopes include many tasks that are relevant to students and set in real-world contexts. These activities include “Hooks,” “Problem-Based Tasks,” and “Math Today.” For example, in the “Compose and Decompose Fractions and Mixed Numbers” scope, the Hook activity requires students to discuss how to share a pizza equally with friends given various descriptors and parameters. In the Problem-Based Task, students determine how long an obstacle course is and how far each person has to run to get to the finish line. Then in the “Area and Perimeter” scope, students determine the amount of material needed to frame rectangular and square art pieces. This task requires rulers, ribbon, and drawing to help students determine the perimeter and area. Later in the scope, the Problem-Based Task is set on a rescue farm: students determine the area of the animal pen, measure how much fencing is needed around the perimeter, and calculate how many animals can be rescued based on a specific budget.

Each scope contains a “Home” section that explains math concepts addressed within the scope. Resources in this section outline the mathematical concepts for teachers and communicate the goals behind each task. The “Content Support” subsection includes a list of skills students should have mastered in previous grades, potential misconceptions or obstacles that could hinder student understanding, key vocabulary terms for the current scope, different ways to represent concepts visually, and what students will learn in future grade levels. Here is an example from the “Number Patterns” scope: “Students have solved real-world word problems since kindergarten and have used visual aids. Students have been exposed to unknowns and how to solve for them...” This section also lists current scope goals like “students will recognize number patterns” and “students will both construct and evaluate tables to solve problems.”

Teachers also have access to scope-specific sentence stems, discussion reminders, possible student responses, teaching strategies, and misconceptions. For example, in the “Perimeter and Area” scope, possible misconceptions include students confusing the meaning and formulas of area and perimeter, forgetting to add unlabeled sides, and not using the correct operation. Then in the “Represent Decimals” scope, students may misunderstand place value when there is a 0 in the number. In both instances, strategies to help prevent misconceptions are offered. Generally, the “Daily Numeracy” component includes sentence stems and hand signals meant to help the teacher facilitate discussion. “Math Chat” questions also increase discourse in the classroom. In the “Multiplication Models” scope, Math Chat questions include “How did you solve this?” and “Why is an area model helpful?” For these questions, teachers also have access to sample student responses. Outside of these two instructional tools, teachers can reference the “Communicate Math” section in their “Teacher Toolbox” for an overview of discourse facilitation. While there are no rubrics or assessments, there is guidance for student grouping.

Evaluation for 2.5
Materials include cohesive, year-long plan for students to develop fluency in an integrated way.

Math fluency instruction follows an intentional year-long plan, both in fluency-specific lessons and integrated throughout the units. Students’ conceptual understanding progresses purposefully and appropriately for the grade level. Teachers have access to guidance for conducting fluency practice and for offering scaffolds, supports, and differentiation to effectively reach all learners.

Direct guidance for teachers on how to implement differentiation in fluency instruction according to student needs, including extension, was not found. 

Evidence includes but is not limited to: 

The materials include two specific fluency scopes and fluency instruction cycled into all other scopes. The two specific fluency scores are “Fact Fluency: Addition and Subtraction” and “Fact Fluency: Multiplication and Division.” Both follow a four-step process: “(1) Introducing the strategy with discussion and hands-on manipulation, (2) Reinforcing the strategy with discussion and visual models, (3) Practicing the strategy with discussion and games, and (4) Applying the strategy with discussion, games, and everyday applications.”

The Fact Fluency: Addition and Subtraction scope is the same for grades K-5, and the Fact Fluency: Multiplication and Division scope is the same for grades 3-5. Both scopes are divided into sections, and each section includes two stations, two games, and an online assessment. These scopes include integrated discourse opportunities around math fluency concepts. For example, in a station during the Fact Fluency: Multiplication and Division scope, students discuss numbers that are multiples of both five and ten, the relationship between nickels and dimes, and how this relationship can help when finding total amounts. While there are online fluency assessments included in the curriculum, there is no guidance directing teachers on how to use this data to support students.

The adding and subtraction scope also includes mini-lessons for each section, while the multiplication and division scope does not. Lessons in the addition and subtraction scope focus on “doubles, making 10, sums within 20, and differences within 20.” These mini-lessons provide instructions for introducing and reinforcing each strategy. Students engage with the strategies through discussion, hands-on manipulation, and visual models. During the mini-lesson for making 10, students use a ten frame and two sets of color counters to make 10 in as many ways as possible. These manipulatives and visuals help scaffold the activity for all students. They then record their representations and write corresponding number sentences. Like all mini-lessons, this one includes teacher guiding questions and possible student answers. 

Outside of the two fluency-specific scopes, other scopes include “Fluency Builder” activities to help students develop their skills. These activities are included to “develop fluency of new concepts through independent and partner games.” For example, in the “Multiplication and Division Problem Solving” scope, students play Risky Wagers and Tic Tac Toe to practice solving one- and two-step multiplication and division problems. Later in the “Place Value of Whole Numbers” scope, students play Place Value Bingo and Place Value Match to practice recognizing place value of digits in a number. 

Teachers receive directions to conduct fluency activities, support to help them understand fluency concepts, and descriptions summarizing the expected progression of student learning. The “Lesson Planning Guide” found in the “Teacher Toolbox” provides two options to integrate fluency instruction into the daily schedule. First, teachers can begin class time with whole-group “Fact Fluency” or “Daily Numeracy” activities. Second, teachers can complete Daily Numeracy during whole-group instruction and Fact Fluency as part of a station. Teachers also receive summaries that describe the strategies students should use, and conceptual connections they should make, during each fluency scope station. Here is the summary for the Fact Fluency: Multiplication and Division scope, Station 1: “Students should use the doubling strategy to find the product of 2 and another number. Likewise, students should relate the multiplication facts to their corresponding division facts to record a multiplication and division equation for each model.” While many fluency activities include these scaffolding components, teachers do not have access to lesson-specific supports or explanations that respond to students’ various needs. When and Why to implement scaffolds for struggling students are not included. Additionally, teachers do not have the guidance necessary to extend fluency activities for those who master fluency concepts. However, there are still enough supports to provide adequate differentiation generally.

Evaluation for 2.6
Materials support students in the development and use of mathematical language.

The materials support students in the development of mathematical language. There is a strategic approach to building vocabulary, ensuring students have embedded opportunities to listen, read, write, and speak using mathematical language. To support students, teachers have access to scaffolds, facilitation guides, and lesson directives; these directives include vocabulary-specific discussion prompts, questions, and explanations. 

Evidence includes but is not limited to: 

The “Communicate Math” section of the “Teacher Toolbox” resource outlines vocabulary facilitation suggestions for teachers to use throughout the scopes. These suggestions include the use of adequate wait time, the use of different discussion structures, and the inclusion of a variety of approaches for students to convey their learning. Then, each scope includes a “Content Support” section that identifies, defines, and explains vocabulary that will be taught within the specific scope. However, most strategic mathematical vocabulary development occurs with the “Explore” section of each scope. 

As stated in the “STEMscopes Math Research and Philosophical Approach” document: “Explore activities include facilitation for the teacher on how to attach academic vocabulary to the student’s experiences during instruction. These activities also include discussion prompts for the teacher to guide students in communicating their thoughts using academic language. The embedded ELPS Strategies can help support English language learners as they acquire new vocabulary. The Picture Vocabulary presentation is a support tool for teachers to represent new vocabulary.”

Vocabulary introduction is embedded within the context of mathematical tasks. For example, in the “Points, Lines, and Angles” scope, students create a four-square court. Sequenced teacher prompts help students transfer concept vocabulary from informal to formal language. For instance, teachers ask students to “describe the lines” on the court. After students give their response, the teacher models an exemplar answer that utilizes content vocabulary: “Lines such as the ones in the middle of the court are called perpendicular lines.” Another example can be found in the “Angles” scope. Students fold a plate into four equal sections after finding the midpoint. The lesson outline includes a scripted teacher explanation that uses the scope vocabulary in context: “Explain that those lines that extend from the midpoint have created angles which are part of the 360 degrees that create a circle. The lines that create angles are called rays, and when the two rays intersect at the midpoint of the circle, that point is now called a vertex.”

Explore lesson activities are also experience-based and formatted so students can learn vocabulary as they relate to each concept. For example, in the “Profit, Budgets, and Banking” scope, students are presented with a scenario about opening a cookie business. Students work in groups to determine fixed and variable expenses, discuss with other groups, and find the sum of their expenses. Then, they read a scenario describing profits and participate in a teacher-led discussion. Through these experiences, students strengthen their understanding of the scope vocabulary. In other scopes, students use informal and formal mathematical language during activities like “Math Chat,” “Student Journal,” and “My Math Thoughts.” 

The materials provide scaffolding suggestions within the lessons to support language development. “Procedure and Facilitation Points” outline discussion points and questions that require vocabulary usage. Teachers can implement these points whenever students need additional practice. Also, each Explore section contains an “Instructional Supports” resource that includes ELPS scaffolding strategies. For example, in the “Multiplication and Division Problem-Solving” scope, the Instructional Supports reminder suggests having groups of students discuss problems together before they solve the problem. Then in the “Profits, Budgets, and Banking” scope, students justify a sales price based on profit and a savings account balance. The materials suggest creating a visual glossary of key terms for students to use during independent work. Teachers can also reference the “Picture Vocabulary” slideshow located within each scope; each slide has one math vocabulary word, a related picture, and the definition. Additional ELPS strategies include having the class count by multiples together, using different facilitation options like popcorn reading, individually reviewing vocabulary, previewing lesson scenarios ahead of time, and creating vocabulary review cards.

Evaluation for 2.7
Materials contain 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 materials, students integrate math knowledge and skills to solve problems in a variety of real-world contexts. These problems relate to students’ current lives, possible experiences in the future, and relatable scenarios. Problem-solving opportunities also often require real-world data analysis.

Evidence includes but is not limited to: 

Students solve real-world problems throughout the steps of the 5E-IA structure of learning experiences: Engage, Explore, Explain, Elaborate, Evaluate, Intervention, and Acceleration. For example, in the “Engage” section of the “Elapsed Time” scope, students solve a problem based on picking up their grandmother from the airport at the correct time. During the “Explore” activities of this scope, students practice calculating the elapsed time of different scenarios, such as watching a movie. In the “Explain” section, students solve more problems about elapsed time, but this time they explain their thought process. In the “Elaborate” section, students read about a family looking to be more efficient and answer related questions. Finally, in the “Evaluate” section, students complete the 10-question “STAAR-Based Assessment” before explaining why a family arrived late to a play as part of a “Decide and Defend” activity. 

These Decide and Defend activities are located in the Evaluate section of each scope. They require students to integrate knowledge and skills in order to develop an efficient solution strategy. In this open-ended assessment, students read a given scenario, analyze the information, draw a conclusion based on that information and the knowledge acquired in the scope, and justify their thinking. For example, in the “Unit Conversions” scope, students help a girl determine if a package meets weight restrictions before it can be shipped. 

Other Evaluate tasks require students to solve problems in various contexts. During the “Fluency Builder—Four in a Row” activity from the “Add and Subtract Decimals” scope, students solve problems involving addition and subtraction of decimals. After the game, students record real-life situations involving mathematical operations. Then during the “Show What You Know” activity from the “Compare and Order Numbers” scope, students compare the high scores of video game players, determine the highest-scoring player, and explain their answer. 

Often tasks require students to analyze data through a real-world context. In the “Number Patterns” scope, students read about food trucks and answer questions regarding input-output table relationships. During the “Career Connections” activity of the “Estimation and Compatible Numbers” scope, students use estimation to solve a problem related to elevator installation. Finally, the “Represent and Interpret Data” scope contains multiple real-world context data problems. For example, students analyze graphs and discuss the relationship between arm length and shoe size. Another problem in this scope has students analyze a frequency table with data from an African Safari, create a new graph based on the data, interpret the information, and construct word problems for their peers.

Evaluation for 2.8
Materials are supported by research on how student develop mathematical understandings.

The materials include cited research that supports the design of teacher and student resources. This research guides instruction, enriches educator understanding, and is current to the skill development of mathematics. All resources supporting the program’s philosophy and design are cited.

Evidence includes but is not limited to: 

The “STEMscopes Math Research and Philosophical Approach” document explains the research and philosophies behind the materials. The document provides summaries and excerpts of research that correspond with elements of instruction: “Learning with Real-World, Relevant Context, Conceptual Understanding and Number Sense, CRA Approach, Using Manipulatives, Collaborative Exploration, Computational Fluency, Promoting Equity, Content Knowledge of Teachers and Parents, and Building Academic Language.” The included bibliography of research is both current and relevant. Examples of cited research include “Teaching Students to Communicate Mathematically” from 2018, “Math in Practice: A Guide for Teachers” from 2016, and “Practical Guidelines for the Education of English Language Learners: Research-based Recommendations for Instruction and Academic Interventions” from 2006.

The document goes on to explain how the research influences instruction: “Curriculum tasks are accessible to students of all ability levels, while giving all students opportunities to explore more complex mathematics” and “Teachers can build equity within the classroom community by employing complex instruction” (Boaler and Staples, 2008). In the “Collaborative Exploration” section, the document includes short research quotes from the National Council of Teachers of Mathematics (NCTM) explaining the importance of communication and collaboration for math learning. These quotes explain that by allowing students to work together while learning new concepts, various solutions can be explored in depth, and communication skills are strengthened. The document then states, “Most of the elements in STEMscopes Math involve student collaboration and require a learning community within the classroom. In the Hook and Explore activities, students work together to gain an understanding of a new math concept. These activities include teacher guidance for facilitating math discussions. In the Problem-Based Task, students work together to use the new skills they just learned. Each of these elements prompts students to communicate their understanding and evaluate the reasoning of others.”

Teachers can find additional research-based commentary in the “Conceptual Understanding and Number Sense” section. This document quotes research from multiple sources, including Marilyn Burns, and summarizes its relevance: “[when] students understand why they are doing something, they are more likely to compute accurately and determine whether an answer is reasonable.” Students with this “deep conceptual understanding and strong number sense will have the tools they need to reason mathematically and solve problems in the real world.” The document then describes the components of the program that address this aspect of learning: Fact Fluency, Explore, Decide and Defend, and Small-Group Intervention. 

STEMscopes Math Research and Philosophical Approach includes a section titled “Content Knowledge of Teachers and Parents” that describes the program’s philosophy on parent and teacher support, and it provides the research to support it. The document states “The ability of teachers and parents to help students understand math is limited by their own basic understanding.” Content support is provided for parents and teachers who “need additional background knowledge to fully support their student’s understanding.” 

Teachers can find this content support in their “Teacher Toolbox” under “Process Standards.” Here, the process standards are grouped and explained. Research to support the process standard is quoted and summarized, and suggestions for instruction are listed. For example, in the “Process Standards—Analyze Relationships to Communicate Ideas” section, the materials cite NCTM 2000, provide an explanation of Process Standards (A) and (F), and give teacher guidance in the sections “What Teachers Should Do” and “Putting the Standards into Action: What Might It Look Like?” Teachers also have resources to aid their understanding within the scopes. For example, in the “Essentials” section of each scope, the materials explain the concept being taught, possible discussion prompts, and sample strategies to be used. This section also describes each standard covered in the scope, how it relates to the mathematical concepts of the scope, and cites the TEKS. In the “Content Support” section of each scope, there are examples of how to teach and explain mathematical concepts. The program states "This element will include why a concept is being taught a certain way by explaining what the students have already learned and giving insight to the concepts students will learn next."

Evaluation for 3.A.1
Materials develop student ability to use and apply a problem-solving model.

Students develop problem-solving ability that is transferable across problem types and grounded in the TEKS. Opportunities to practice are consistently found throughout the year, and students periodically reflect on their own approach. Teachers receive the necessary guidance to support student problem-solving reflection.

Evidence includes but is not limited to: 

The “Teacher Toolbox” includes the “Process Standards—Using a Problem Solving Model” that explains the problem-solving philosophy of the materials. Throughout instruction, students develop their problem-solving ability with intentional scaffolding, productive struggle, and real-world scenarios. Grounded in the Mathematical Process Standards, instruction is divided into six sections: “Analyze Relationships to Communicate Ideas, Communicate Mathematical Ideas and Their Implications, Create and Use Representations, Display, Explain and Justify Mathematical Ideas, Intentional Selection of Tools and Techniques to Solve Problems, and Using a Problem Solving Model.” Each section includes an explanation of the standard, cited research, corresponding TEKS, teacher guidance, and examples of what instruction looks like in each grade level (K-5). There is also a “CGI Story Problem Type Framework” chart that offers teachers examples of different types of math problems, according to Cognitively Guided Instruction (CGI).

For example, the “Process Standards—Analyze Relationships to Communicate Ideas” summary section references the following aligned Mathematical Process Standard: A) Apply mathematics to problems arising in everyday life, society, and the workplace and F) Analyze mathematical relationships to connect and communicate mathematical ideas. The “What Teachers Should Do” section offers suggestions like “Provide opportunity for students to analyze and create non-examples as well as to explain orally or in written form.” 

The “Content Support” section of each scope describes the types of problem-solving students will encounter and the methods they will use to solve those problems; example problems with visuals and solutions are included. For instance, in the “Add and Subtract Decimals” scope, students will add and subtract decimals using strategies like the addition algorithm and addition with partial sums. Students accomplish this goal by manipulating a number line or strip diagram, writing an equation, estimating, solving the problem, and offering a solution statement. In the “Multiplication and Division Problem Solving” scope, the problem-solving model includes a strip diagram, equation, and solution. 

Every scope follows the 5E-IA teaching model: Engage, Explore, Explain, Elaborate, Evaluate, Intervention, and Acceleration. In each step, students have opportunities to practice problem-solving. For example, in the “Explore” section of the “Add and Subtract Decimals” scope, students determine the amount of wood needed to build different items. They discuss the situation with a group and use place value disks to model the problem. The teacher asks questions like “What did you have to do if there were 10 or more in one place value?” 

Also in the Explore section, students complete “Student Journals” as part of problem-solving practice. For example, on a Student Journal page of the “Multiplication Models” scope, students solve a problem about pizza. They “draw an area model representing each pizza” and “find the Partial Products.” In the “Multiplication and Division Problem Solving” scope, students solve problems about school. They draw a strip diagram, write the equation, and solve the equation. 

Opportunities for problem-solving reflection are found in different components of the 5E-IA model. In “My Math Thoughts” activities, students reflect on problem-solving along three areas: “Content,” “Process,” and “Affective.” For example, in the “Addition and Subtraction Models” scope, students use a number line to solve a fraction word problem, explain their reasoning stating whether a fraction comparison is correct, and describe how adding and subtracting fractions makes them feel. “Problem-Based Tasks” also provide students an opportunity to apply a problem-solving model. In the “Angles” scope, students determine the measurement of missing angles when given the measure of one angle. Upon completion of the Problem-Based Task, students share their solutions and discuss their strategies.

Outside of direct instruction, teachers have access to a problem-solving rubric broken down into four areas: Understanding, Computation, Reasoning, and Product. Teachers facilitate problem-solving reflection throughout. For example, in the “Unit Conversions” scope, students complete a series of tasks to determine how many cups it takes to make a pint; then, the teacher facilitates a discussion to help students reflect on their problem-solving approach. One question used in this discussion asks, “What process do we use for converting a large unit into a smaller unit?”

Evaluation for 3.A.2
Materials require students to select appropriate tools for the task, concept development and grade.

Throughout the year, students have ample opportunities to select and use objects, manipulatives, algorithms, and technology. They apply these tools successfully as appropriate for the concept, grade, and task. Each scope includes teacher guidance, ensuring students know which tools are appropriate and efficient for the specific situation.

Evidence includes but is not limited to: 

The materials provide students opportunities to learn to use grade-appropriate tools for solving tasks and understanding concepts. The “Explore” step of each scope includes teacher-guided problem-solving questions based on concepts being taught. The teacher models the different steps of problem-solving, including appropriate tools to use for each problem. For example, in the Explore lesson of the “Elapsed Time” scope, students practice finding start times and end times using geared clocks, T-Charts, and number lines. Teachers review finding time on a clock, using the clock to show elapsed time, and transferring the information to a number line. Students practice using the tools to solve problems, then reflect on their strategies during “Math Chat,” in which they answer questions such as “What strategy did you use to find the missing information?” 

The materials provide students opportunities to select grade-appropriate tools for problem-solving tasks. In the “Problem-Based Task” of each scope, students use knowledge and tools from the current and previous scopes to solve real-world problems. For example, in the “Measurement Systems” scope, students work to determine the number of lights needed to decorate for a party. Students use their notes from previous activities to help them work through the problems and choose appropriate strategies.

The materials provide students opportunities to use a variety of grade-appropriate tools, including manipulatives, representations, and algorithms, during their exploration of content. For example, in the “Place Value of Whole Numbers” scope, students use place value cutouts, a place value chart, and place value circles to represent and understand the value of numbers to the billions place. These manipulatives are used throughout the scope for composing and decomposing numbers.

The materials provide opportunities to select grade-level appropriate technology to solve tasks and understand concepts. Every scope includes an “Interactive Practice” activity, a technology-based game that reviews different concepts. For example, in the “Area and Perimeter” scope, students play the game Armadillo Crossing, finding the area and perimeter of different shapes. Some scopes include a “PHeT” activity, a technology-based interactive investigation tied to the TEKS that the students are learning in the scope. For example, in the “Number Patterns” scope, students use the technology interactive “Function Builder” to create and practice different rules in data charts. 

The materials include virtual manipulatives in almost every scope, as well as prompts on when and how to use them. Virtual manipulatives include place value disks, base-ten blocks, area models, two-color counters, and coins. For example, in the “Add and Subtract Fractions” scope, students complete the “Decide and Defend” activity by choosing any method learned. In this activity, they use virtual manipulatives as needed to show a comparison of fractions. In the “Multiplication Strategies and Algorithm” scope, students choose from virtual manipulatives that consist of base-ten blocks or place value disks. 

The materials provide teachers guidance about the tools introduced and which tools are appropriate for each task. The “Content Support” section of each scope has pictures, explanations, and uses for tools referenced in the scope. In the “Compare Fractions” scope, the materials provide an explanation for students of how to compare using fraction tiles. For example, “Each of these shaded areas covers an equal part of the whole circle. The fractions are different but equivalent.” 

Within the Explore tab of each scope, the materials provide a video with a detailed explanation of the scope, materials, and how students can choose to model or solve given problems. In the “Home” section of every scope, teachers find a customizable list of materials needed for the activities and tasks in that scope. Also included are step-by-step “Procedure and Facilitation Points” that provide teachers with guidance for lesson delivery, including the use of the appropriate tools. For example, in the “Represent Decimals” scope, the needed materials listed include play money bills and coins. Teaching points about the proper use of tools are included. 

The materials include opportunities for teachers to explain the significance of certain tools related to a task. In the “Hook” activity of the “Represent and Interpret Data” scope, teachers introduce multiplying two-digit numbers using area models. Students are given dimensions of a stage to build. As students work through activities in the scope, students use base-ten blocks to practice two-digit multiplication. The materials list directions and guiding questions for teachers to ask students as they practice using the tools, such as “How are area models similar to arrays?”

Evaluation for 3.A.3
Materials require students to select appropriate strategies for the work, concept development, and grade.

The materials provide opportunities for students to select appropriate grade-level and content-appropriate techniques for the given task. There are supports for teachers to understand and teach strategies, including explanations and examples. Lessons include wording for student questioning and explanation of multiple strategies. Lessons and activities help students to learn, use, and choose between these various strategies. Strategy instruction progresses throughout and across the scopes. 

Evidence includes but is not limited to: 

Students select a technique within multiple components of each scope. For example, in the “Addition and Subtraction of Decimals” scope, students learn a variety of techniques to find a sum or difference, including using place value mats, disks, blocks, and the standard algorithm. In the “Problem-Based Task,” students select an appropriate technique for adding and subtracting money and justify their reasoning. In the “Compare and Order Decimals” scope, students learn techniques including using place value disks and place value charts. During the “Math Chat,” students discuss the various tools and methods they used to solve assigned problems. In the “Explore” activity of the “Multiplication Strategy and Algorithm” scope, teachers follow a script prompting students to select and use different techniques, including decomposing numbers and the distributive property. In the “Problem Solve Using Four Operations” scope, students discuss how they represented a problem during the Math Chat. During the “My Math Thoughts” activity, students explain how they would solve a given scenario and why they picked the strategy they did. 

The “Home” section of each scope provides teachers with valuable information: the standards being taught in the scope, misconceptions students may have, ways to address misconceptions, and example math problems with solutions. During the Explore activity at the beginning of each scope, students watch a short video that explains the lesson and what they are expected to do in the lesson. 

The “STEMscopes Math Philosophy” document explains the importance of a Concrete Representational Abstract (CRA) approach to teaching problem-solving strategies. The “Engage” step of every scope includes a “Hook” in which students watch a video, analyze the problem, and discuss their ideas and strategies for solving the problem using concrete objects like blocks and coins. During the Hook lesson, students are taught the skills needed to solve the problem using the CRA Approach. Students continue to practice those skills during lessons, choosing the tools and techniques they have learned. In the “Evaluate” step of the scope, students choose the most efficient strategy to solve problems, which is evaluated for the level of mastery by the teacher. For example, in the “Multiplication Models” scope, students select arrays and area models to solve a multiplication problem. The teacher facilitates a discussion comparing the strategies and questioning their efficiency. The materials provide a rubric to score students’ reasoning, understanding, and computation. The “Compare Fractions” scope includes three Explore activities that teach specific strategies: Generating Equivalent Fractions, Comparing Fractions Using Models, and Comparing Fractions Using Common Denominators. The Math Chat section of these activities includes a sample teacher-led class discussion script regarding strategies used to solve problems. During the “My Math Thoughts” activity at the end of the scope, students choose their favorite way to solve a problem and explain why.

The materials support students learning and using multiple appropriate strategies to solve problems. For example, in the “Add and Subtract Decimals” scope, students learn to solve problems using place value disks, place value charts, number lines, and the standard algorithm. In the “Compare and Order Decimals” scope, students are introduced to options for comparing and ordering decimals, including place value disks, base-ten blocks, hundreds and tens grids, and number lines. In the “Multiplication Models” scope, the students are introduced to concrete area models and pictorial area models, in conjunction with skip counting and repeated addition. Later in the scope, students are introduced to abstract area models, arrays, and, finally, the algorithm. In the following scope, multiplication strategies include multiplying by tens and hundreds with partial products, the distributive property, and the algorithm.

Evaluation for 3.A.4
Materials develop student’s self-efficacy and mathematical identity by providing opportunities to share strategies and approach to tasks.

The materials develop students’ self-efficacy by providing learning experiences where students share strategies, collaborate, and discuss their work; included teacher guidance helps facilitate this sharing. Students are presented with relevant problem scenarios that align with learning and facilitate productive struggle, supporting students to see themselves as capable mathematical thinkers. The materials support students in understanding that there can be multiple ways to solve problems by incorporating opportunities for teachers and students to share strategies and techniques. 

Evidence includes but is not limited to: 

The materials support students to see themselves as mathematical thinkers who can learn from solving problems, make sense of mathematics, and productively struggle. The materials are designed in the 5E-IA model: Engage, Explore, Explain, Elaborate, Evaluate, Intervention, and Acceleration. Progression through the components is sequential, with learning built on previous lessons, tasks, and experiences. This progression supports the productive struggle of students.

The “STEMscopes Math Research and Philosophical Approach” document explains principles on which the program is based, including “Collaborative Exploration” and “Promoting Equity.” The document states that every scope includes a “Hook,” “Explore” activities, and a “Problem-Based Task” in which students work together to solve real-world problems and “begin to reason mathematically as they discuss their ideas and debate about what will or will not work to solve a problem.” The document states that, based on the cited research, “Allowing groups of students to work together to solve real-world tasks creates a sense of community and sets a common goal for learning for all students.” Through experiences presented in the materials, students explore scenarios together, listen to different approaches, communicate their understanding, and respond to the reasoning of others. For example, in the Explore activity of the “Estimation and Compatible Numbers” scope, students work in groups to solve problems about miles traveled on trips. Students estimate solutions and share strategies within their groups. Students then participate in a “Math Chat,” sharing strategies used to solve the problems with the whole class. The lesson directions include prompts and questioning for the discussion. For example, “Why is it useful to be able to estimate the solution to a problem?

The materials challenge beliefs and biases that conflict with all students seeing themselves as mathematical thinkers. The “STEMscopes Math Philosophy” states “Curriculum tasks are accessible to students of all ability levels, while giving all students opportunities to explore more complex mathematics.” For example, the “Daily Numeracy” activities provide opportunities for students to “fortify and develop their understanding beyond the procedure.” In the “Blank Number Line” activity of Daily Numeracy, students place number cards, including fractions, decimals, and whole numbers, on a number line. The teacher presents scenarios and adjusts the activity to promote questioning and alignment with students’ prior knowledge. In the “What Do You See?” activity, students are shown a slideshow and determine number patterns. The teacher models critical thinking and strategies through think-aloud. 

Materials support students in understanding that there can be multiple ways to solve problems and complete tasks. For instance, in the “Problem-Based Task” found in each scope, students solve a real-world problem using multiple strategies. Regarding the Problem-Based Task, the STEMScope Math Philosophy document states “In each practice opportunity, students have the flexibility to use different processes and strategies to reach a solution. Students will develop fluency as they become more efficient and accurate in solving problems.” Each scope also contains a Hook activity in which a real-world problem is presented, along with a video to prompt discussion among students. Students apply previous knowledge to solve the problem. After working through the Explore activities in each scope, the problem in the Hook is revisited, and students discuss how they determined their solutions and revise them if needed. For example, in the Hook activity of the “Perimeter and Area” scope, students create a model of the fencing needed for a garden. Students use the model to determine the number of materials needed for the fence. The teacher introduces toothpicks and craft sticks as concrete models and facilitates discussion regarding students’ strategies and solutions.

The materials provide instructional supports for facilitating and sequencing the sharing of student approaches. For example, each scope includes Math Chats found in the Explore section. Math Chats are teacher-led discussions of strategies. A script is with questions, prompts, and possible answers is included in the materials. The contents of each Math Chat align with the “Explain” activities of the scope. Each scope also includes a “Decide and Defend” activity, found in the “Elaborate” section, in which students determine if a given solution is correct or incorrect and justify their mathematical thinking. For example, in an Explore activity of the “Angles” scope, students participate in a whole group lesson, creating a model of angle measurements. The materials list questions for teachers to ask while creating the model with students. For example, “What do you notice about the vertex of this angle?” In the next part of the lesson, students work in groups to create a dance that incorporates turns measured in degrees. The teacher then leads a Math Chat regarding the real-life use of angle measurements. In the Decide and Defend task of the scope, students analyze angle estimates made by hypothetical students.

Evaluation for 3.B.1
Materials prompt students to effectively communicate mathematical ideas, reasoning, and their implications using multiple representations.

Students have multiple opportunities to communicate mathematical ideas throughout the scopes and lessons. They are guided to use multiple representations when solving problems and to use representations appropriate for the task. The materials also provide guidance for teachers in prompting students to communicate mathematical ideas in a variety of representations, including writing and the use of mathematical vocabulary. 

Evidence includes but is not limited to: 

The materials provide opportunities for students to communicate mathematical ideas. Each scope or unit in the materials is structured in a 5E teaching model: Engage, Explore, Explain, Elaborate, and Evaluate. Within the components, students collaborate to analyze real-world problems, explain their thinking using manipulatives and visual representations, and respond orally and in writing. For example, in the “Decide and Defend” activity of the “Evaluate” step in the “Represent and Interpret Data” scope, students evaluate a set of data displayed in a stem-and-leaf plot. Students read four statements about the data, determine which statement is false, and explain their conclusion in writing. Students also explain why the other three statements are true and are encouraged to support their thinking with drawings or models. 

The materials contain tasks that can be solved using a variety of mathematical representations. For example, in the “Explore” lesson of the “Compare and Order Decimals” scope, students evaluate data about different amusement parks to determine which park would be the best for a city. Students use place value disks to build the numbers that represent the data in the chart, draw a pictorial representation of the place value disks in their journal, and discuss their thinking with their classmates. Students then compare two decimals they have represented with the disks and write the comparison using digits and symbols. 

The materials contain tasks that ask students to use representations to organize and show their thinking to communicate with others. The “Preparation” section of the “My Math Thoughts” activity of every scope directs teachers to “Allow students to have access to a variety of mathematical tools, such as place-value blocks, fraction circles, and mathematical models such as place-value charts, fraction walls, number lines, etc.” The “Procedure and Facilitation Points” states to “Encourage students to persevere through their thinking and to use mathematical tools and models as necessary.” For example, in the “Points, Lines, and Angles” scope, students determine the classification of a set of shapes, then describe how a shape was drawn with two obtuse angles. Next, they explore their surroundings for real-world objects that contain angles and describe their uses. The teacher script lists student prompts to use during the process: prompt students to discuss their thoughts with a partner, use mathematical tools or models to demonstrate their thinking, and write their thoughts using appropriate vocabulary.

The materials provide suggestions for teachers to support the communication of mathematical ideas, both in writing and orally. The “Teacher Toolbox” contains the section titled “Communicate Math—Writing” that provides facilitation points and ways to incorporate writing in the math classroom. The guide includes suggestions for “Expectations” and “Possible Types.” Expectations listed include “provide writing stems for students to use if necessary.” Possible Types listed include concept maps, Frayer models, and word problems. 

The “STEMscopes Math Philosophy” found in the “Essentials” section of the “Teacher Toolbox” explains that collaboration provides opportunities for students to begin reasoning mathematically “as they discuss their ideas and debate about what will or will not work to solve a problem.” Teachers facilitate “Math Chats,” found in the Explore lessons of each scope. Students share their thinking and listen to their classmates’ reasoning about solving math problems. The Math Chat directions include discussion questions and sample student responses. For example, a Math Chat in the “Add and Subtract Decimals” scope includes questions about the relationship between addition and subtraction. Students work in groups to solve problems that include adding and subtracting decimals before participating in the Math Chat. The questions ask students about their experiences as they solve the problems. For instance, “What is the relationship between adding and subtracting decimals and adding and subtracting whole numbers?”

Teachers guide students to reflect on learning by asking questions and instructing students to record reflections in their journals. For example, in the Explore lesson of the “Compose and Decompose Fractions and Mixed Numbers” scope, teachers direct students through a series of steps with the objective of decomposing fractions. Students record their thinking in their “Student Journal.” The materials provide teachers with prompts for discussion about the process, such as “How can we decompose an improper fraction?” 

The materials support teachers in developing students’ use of mathematical vocabulary. The STEMscopes Math Philosophy explains that “Students learn academic vocabulary by attaching new words to prior knowledge and experiences.” In every scope, “The Explore activities [provide] facilitation for the teacher on how to attach academic vocabulary to the student’s experiences during instruction.” Each scope includes picture vocabulary to be used during instruction with students. The “Terms to Know” section of the “Content Supports” lists vocabulary taught in the scope.

Evaluation for 3.B.2
Materials provide opportunities to discuss mathematical ideas to develop and strengthen content knowledge and skills.

The materials provide opportunities for students to engage in mathematical discourse throughout the scopes. Opportunities for discourse are outlined in varied formats, including small group, whole group, and peer-to-peer. Discussion is integrated throughout lessons and activities and supports students’ development of content knowledge. The discussion formats, questioning, prompts, and content are appropriate for the concepts being addressed and the grade-level. Teachers receive guidance for implementing and facilitating discussion.

Evidence includes but is not limited to: 

The materials intentionally provide opportunities for all students to engage in mathematical discussions in a variety of groupings. As instruction progresses through the steps of the 5E teaching model, students communicate and explain their ideas visually, orally, and in writing. For example, each scope begins with a “Hook,” in which students view a video and determine a solution to the given scenario. The Hook is a whole group lesson that includes discussion questions such as “What do you notice?” and “Where can you see math in this situation?” In the Hook activity of the “Compare Fractions” scope, students participate in a class discussion about the video they watched. Next, students are split into groups to solve problems comparing fractions. Students discuss their thoughts with questions such as, “If your group got two fractions that were equal, what did you notice?” In the “Explore” step, students work in groups to determine different fractional ways a bakery can serve pies. Students follow prompts from their “Student Journal” and record their work. In the following portions of the lesson, students work in groups to divide cakes. The materials include questions to support student learning, such as “Each third is a group of how many sixths?” Once the groups have completed the tasks, students complete an exit ticket.

Within the “Daily Numeracy” component of the scopes, teachers lead whole group discussion about mathematical strategies using mathematical language. The materials include participation hand signals to use during the discussion, such as a hand signal to show “I am thinking” or “I agree.” The materials provide question stems for the discussion, such as “How is this similar to/different from…?”

The materials include opportunities for discussion in all phases of concept and skill development. In the “Multiplication Models” scope, during the Hook activity, students work in groups to create a model of a stage that meets certain size requirements. Discussion questions in the activity include “Does this mean that a stage that is 10 feet by 15 feet would work?” During the Explore lesson of the “Division Models” scope, students use school supplies and base ten blocks to model division of larger numbers. Students work in groups and follow prompts on their “Student Journal” pages; for example, “Explain your process for splitting up large amounts evenly.” Students participate in a “Math Chat” with teacher-stated questions about their strategies. Students work through another set of division scenario problems, and then groups share how they solved different scenarios. The materials provide sentence stems and questions for students to use in discussion, including “I agree with…, because....”

The materials offer guidance for teachers on how to structure a discussion that is appropriate for the grade level. For example, the “STEMscope Mathematical Philosophy” explains how the materials are designed for collaborative exploration. The document states “Most of the elements in STEMscopes Math involve student collaboration and require a learning community within the classroom. In the Hook and Explore activities, students work together to gain an understanding of a new math concept. These activities include teacher guidance for facilitating math discussions. In the Problem-Based Task, students work together to use the new skills they just learned. Each of these elements prompts students to communicate their understanding and evaluate the reasoning of others.”

The “Process Standards—Communicate Mathematical Ideas and Their Implications” section of the “Teacher Toolbox” describes how classroom discussion should look and feel. It describes classroom characteristics, such as building a safe environment, modeling how to interact, ensuring academic language is in use, and promoting oral and written conversations with different formats. The section also shows what this might sound like in each grade level by providing a sampling of questions. The “Communicate Math—Discourse” section includes a description of discourse and expectations for different grade levels, such as “Include a variety of approaches to convey knowledge, strategies, justifications, and conclusions.”

Evaluation for 3.B.3
Materials require students to justify mathematical ideas using multiple representations and precise mathematical language.

The materials provide opportunities for students to construct and present arguments. Students are prompted to use multiple representations, use mathematical language, and justify their ideas. The materials assist teachers in facilitating students to construct arguments. The teacher facilitation points and contexts that elicit student arguments are grade-level appropriate.

Evidence includes but is not limited to: 

The materials provide students with opportunities to construct arguments to justify mathematical ideas using multiple representations. For example, in the “Represent Decimals” scope, the materials relate decimals to money amounts and weights. In the “Problem-Based Task,” students determine the solution to a problem regarding an ancient number code. After completing the problem, students participate in a discussion, sharing how they solved the problem and why they chose the method they used. In the “Compose and Decompose Fractions and Mixed Numbers” scope, students decompose fractions, determining whether a given solution statement is correct. Students then participate in a “Math Chat,” justifying their ideas while answering questions like “How do you know which number is greater or less?”

Every scope includes a “Decide and Defend” activity in which students make a mathematical conclusion, explain their conclusion, and justify it. The format of the activity varies, including writing to respond, showing models to respond, and having group discussions to respond. For example, in the Decide and Defend activity of the “Number Patterns” scope, students analyze three statements regarding the relationship in a table. Students construct an argument to justify their ideas. In the “Represent and Interpret Data” scope, students analyze a stem-and-leaf plot, determine which statements about the data set are true, and justify their reasoning. In the “Rational Numbers on a Number Line” scope, students decide and explain which set of numbers is correctly placed on a number line. Students use number lines, concrete models, or pictorial models to share their thinking.

Every scope includes Math Chat discussions within lessons. The discussions include opportunities for students to construct and present arguments. For example, in a Math Chat in the “Rational Numbers on a Number Line” scope, students explain why it is important to locate fractions and decimals on a number line. Students use number lines, concrete models, or pictorials models to share their thinking. In a Math Chat in the “Represent and Interpret Data” scope, students determine which representation of data is the most efficient and how different representations, such as dot plots and frequency tables, are useful for data. In the “Add and Subtract Fractions” scope, students participate in a Math Chat after solving word problems. The Math Chat includes the question “If you added these fractions in a different order, would the sum be different?”

The materials provide routines and structures for teachers to facilitate students’ construction of arguments. The “Communicate Math—Discourse” section of the “Teacher Toolbox” includes an “Expectations” list for student discussion. The list includes guidance such as “Include a variety of approaches to convey knowledge, strategies, justifications, and conclusions,” and “Ensure each student contributes to the discussion with clear and organized thoughts and ideas.”

The “Process Standards—Display, Explain and Justify Mathematical Ideas” section of the Teacher Toolbox includes an explanation of Process Standards (A) and (G). The materials explain “This standard focuses on students validating their conjectures and conclusions with displays, explanations, and justifications. Emphasis is given to mathematical ideas and arguments. Problems provide a context in which students may draw conclusions and support mathematical ideas or arguments with their evidence.” This section includes a “What Teachers Should Do” list, including “Expect mathematical idea arguments and promote a productive discussion environment.” Also included are descriptions of what the standard may look like at different grade levels. For example, the materials state that in the study of partial products in fourth grade, students should use tools to solve problems using the area model. The guidance also states that “As they work, encourage precise mathematical language to include factor and product. They will display their work with a partner, followed by a small group. Conclusions and justifications are made.”

Evaluation for 4.1
Materials include developmentally appropriate diagnostic tools (e.g. formative and summative progress monitoring) and guidance for teachers and administrators to monitor progress.

The materials include a variety of diagnostic tools and guidance for teachers to monitor student progress. These tools assess all content and process skills for the grade level. Formal and informal diagnostic tools are found within every scope, with guidance for administration and analysis. Diagnostic tools measure content taught within the scopes, within the lessons, across the grade level, and from previous grade levels. However, the materials do not include tools for students to track their own progress and growth.

Evidence includes but is not limited to: 

The materials include formal and informal diagnostic tools that are developmentally appropriate. The materials include the formal” Benchmark Assessment” for grade levels 3, 4, and 5. The assessment “provides meaningful data that can be used to inform instruction in the classroom.” Teachers assign assessments online and use online analytic tools in the areas of student performance, standards analysis, and item analysis. The “Pre-Assessment” portion of the benchmark assesses previous grade-level standards. The “Mid-Assessment” combines an assessment of grade-level and previous grade-level standards. The “Post-Assessment” assesses student mastery of standards in the current grade level. Student data from the benchmarks is analyzed by the “Quantile Framework” and assigned a Quantile measure or score. Online tools provide information about Quantile measures, including student performance levels, what content the student is ready for, student growth tracking, and predictions of student performance on STAAR.

Each scope contains three different formal assessments that can also be used to determine understanding of concepts. The “STAAR-Based Assessment” is a STAAR-aligned assessment in which students answer multiple-choice questions. “Decide and Defend” is an assessment where students evaluate a given solution and explain why the solution is correct or incorrect. A provided rubric for Decide and Defend includes three sections: analyzing student reasoning, computation, and understanding. The “Skills Quiz” is a number skills and computation assessment of concepts taught in the scope. 

The materials also include informal assessments. For example, each scope contains a “Show What You Know” assessment in which students demonstrate an understanding of concepts taught in the scope’s previous lessons. In the “Place Value of Whole Numbers” scope, students complete place value relationship analogies and determine a number when given place value clues. The Show What You Know provides sample student answers and explanations for the teacher to determine student accuracy. Informal “Exit Ticket” assessments are provided for lessons in the “Explore” section of each scope to assess student learning of concepts within the lesson.

The materials include a “Quantile Parent Guide,” explaining the Quantile Framework, the meaning of students’ scores, and how to use scores to help student learning. Quantile scoring is used for the “Benchmark Assessments.” Each scope contains a parent letter explaining what students will be learning in the scope and ways to provide support at home. The materials do not contain guidance for parents on understanding assessment within each scope.

The materials include recommendations to support consistent and accurate administration of the tools throughout the school year. The Benchmark Assessment section provides guidance on when and how to administer this formal assessment three times a year. The “Standards Progress Tracker,” found in the “Teacher Toolbox,” is a form for teachers to track individual student mastery of standards for the entire grade level. The Show What You Know and formal assessments, including benchmarks, provide sample student answers and explanations for the teacher to determine student accuracy. The “Quantile Educator Guide” explains how to use the Benchmark assessments’ data, as well as what they measure. The materials include a “Scope and Sequence” in the Teacher Toolbox that states when diagnostic assessments should be administered. While there are numerous resources for the teacher to track student progress, there are no opportunities for students to track their own progress and growth. 

The materials contain diagnostic tools to measure all content and process skills, as outlined in the grade-level TEKS. Each scope contains the Show What You Know section in which students are informally assessed and demonstrate their understanding of grade-level content. Each scope includes an Evaluate section with three types of assessment: STAAR-Based Assessment, Decide and Defend, and Skills Quiz. The Quantile Measures, which reports student performance on math skills on the material’s three benchmark tests, gives information on how students are progressing through increasingly difficult mathematical concepts and provides recommendations for intervention skills.

Evaluation for 4.2
Materials include guidance for teachers to analyze and respond to data from diagnostic tools.

The materials include guidance for teachers to analyze and respond to data. Protocols are included for formal and informal assessment, with guidance for teachers on how to use the data to drive instruction. Assessment and response routines are present within the scopes to address student learning needs. The materials include guidance for administrators to support teachers in analyzing and responding to data.

Evidence includes but is not limited to: 

The materials include recommendations to support teachers in adjusting instruction to meet student needs, based on formal and informal assessments throughout the units or scopes. The “Lesson Planning Guides” describe how the components of the materials can be presented, based on the number of “Explore” sections in the scope. The guide includes “Assessment and Closure,” daily recommendations to assess student learning. The document includes footnotes with suggestions for teachers of what to do after completing the “Evaluation” part of each scope. For instance, a footnote states “Use intervention if APK [Assessing Prior Knowledge] shows foundational gaps,” and “Use Exit Tickets as well as Show What You Knows for each Explore completed.” 

The materials include guidance for scaffolding instruction based on students’ needs. The “Intervention” section of each scope contains differentiated lessons to teach prerequisite skills and guidance for teachers on how to group students and administer intervention lessons. For example, the “Represent Decimals” scope Intervention section contains a “Teacher Checklist” for teachers to collect notes on students’ progress. The materials include a scripted intervention lesson and a “Checkup” to administer after the lesson to determine mastery or progress.

The materials include guidance to support teachers in understanding the results of diagnostic tools. For example, the materials include a “Benchmark Assessments” section explaining the three assessments to be used at the beginning, middle, and end of the year. The “Teacher Toolbox” contains the “Quantile Measures” section, providing an explanation of scores and how it drives instruction. The “Quantile Educator Guide” includes an explanation of the framework, how to analyze the results, and a link to a website that houses free tools for teacher use. The tools include options to collect, record, and analyze student data. For example, the “Quantile Growth Planner” is used to determine if students are “on the path to college and career readiness or if they need additional support.” The “Math Skills Database” provides activities and resources aligned to state standards and Quantile scores. 

The results of the assessment tools support teachers in identifying areas of need, as well as providing guidance on selecting from a variety of activities in a way that responds to data. Each scope contains an “Accessing Prior Knowledge” activity in the “Engage” section, the opening portion of the unit. If students show difficulty with the skill, the materials provide the “Foundation Builder” intervention lesson. For example, in the Accessing Prior Knowledge activity of the “Division Models” scope, students choose a picture model that correctly represents a given scenario. If students have difficulty, the Foundation Builder lesson reviews grouping objects equally.

The materials include resources to differentiate instruction based on student progress. Each scope contains “Show What You Know” activities, found in the “Explain” section. Students answer questions to show their mastery level of skills taught in the Explore section of the scope. The materials suggest using data collected from the Show What You Know to determine if students would benefit from intervention lessons or options found in the “Elaborate” and “Acceleration” sections of the scope. For example, in the “Represent Decimals” scope, the intervention lesson reviews place value using concrete models. In an Acceleration activity, students create a game board that incorporates decimals.

The materials provide guidance for the administrators in supporting data analysis in STEMcoach In Action, an embedded professional development tool that administrators can use to support specific teacher needs as they implement the curriculum.

Evaluation for 4.3
Materials include frequent, integrated formative assessment opportunities.

The materials include routine and systematic progress monitoring throughout the lessons and scopes. These progress monitoring components accurately measure student progress, and tools are included to track student progress. The frequency of progress monitoring is appropriate for the grade level and content.

Evidence includes but is not limited to: 

The materials include routine and systematic progress monitoring opportunities. The curriculum is constructed using the 5E-IA teaching model: Engage, Explore, Explain, Elaborate, Evaluate, Intervention, and Acceleration. Within the components of the materials are progress monitoring routines, including both formal and informal assessments. 

“Benchmark Assessments” are indicated to be administered at the beginning, middle, and end of the school year. The materials state “The intent of each assessment is to evaluate students on standards they have already learned. This means the Pre-Assessment will assess the standards from the previous grade level.”

The materials include progress monitoring throughout the scopes. For example, the materials include “Exit Tickets” at the closure of “Explore” lessons. “My Math Thoughts” written assignments and “Show What You Know” checkpoints are found within the “Explain” portion of each scope. “Checkups” are included after each “Intervention” lesson.

There are three different types of assessment at the end of each scope: “STAAR-Based Assessment,” “Decide and Defend,” and “Skills Quiz.” The materials guide teachers to collect data in a color-coded format to assess student progress and determine if the next steps should include intervention, acceleration, or practice grade-level skills within stations. 

For example, in the “Number Patterns” scope, the materials include an Exit Ticket where students determine missing information in a table and an equation to determine the “output.” In the My Math Thoughts assignment, students complete a table and describe their process in writing. In the STAAR-Based Assessment, students answer multiple-choice questions regarding numerical relationships. In the Decide and Defend assessment, students explain their thinking regarding a numerical relationship in a table. In the Skills Quiz, students answer a variety of question types about numerical relationships.

The program includes the “Quantile” progress monitoring tool, which measures and tracks student progress. The Quantile system includes resources aligned with the state standards (TEKS) and options for differentiated instruction based on students’ needs, as determined by the assessment tools. The “New Teacher Navigation Guide” explains that “STEMscopes Math includes unique pre-, post-, and progress monitoring assessments that correlate to a Quantile measurement for each student. Similar to Lexile reading levels but for math, this measurement can be used to determine a student’s current level of proficiency and readiness for new content, and to help parents understand their child’s learning progression.”

The materials include an appropriate frequency of progress monitoring, appropriate for the age and content. The “Teacher Toolbox” includes the “Scope and Sequence” outlining the week, scope, and standards to be taught for that grade level. The “Lesson Planning Guide” also gives suggested timelines for each scope. The timelines include the various assessments found within the materials. The “TEKS Checklist and Standards Progress Tracker” are provided to track student learning. For example, according to the Scope and Sequence, the “Represent Decimals” scope addresses TEKS 4.2B, 4.2E, and 4.2G and should be taught in weeks 5 and 6. This scope includes Exit Tickets at the closing of every “Explore” activity. The materials direct teachers to use Exit Tickets to determine which students need additional support to master the content skill and which students require support to extend their learning. The materials provide Intervention and “Acceleration” activities and lessons to address both needs.

Evaluation for 5.1
Materials include guidance, scaffolds, supports, and extensions that maximizes student learning potential.

The materials include targeted instruction and activities for both students who struggle to master content and students who have already mastered content. There are corresponding enrichment activities for all levels of learners. Targeted instruction and activities are found consistently throughout the scopes, and each scope includes recommendations to address different student needs. 

Evidence includes but is not limited to: 

The materials provide recommended targeted instruction and activities for students who struggle to master content. The “Intervention” tab of each scope includes teacher guidance, recommendations for scaffolds to support students, and additional practice resources. For example, in the “Small Group Intervention” lesson of the “Represent Decimals” scope, students review place value vocabulary, a place value chart, and the relationship between each place on the chart. The teacher guides students through a series of tasks using base-ten blocks to represent decimals. Students roll dice, write the digits in a place value chart, use the base-ten blocks to represent a decimal, and write the decimal. Students discuss how the decimal is written as a fraction. The Interventions are separated into three categories: “Adaptive Development,” “Cognitive Development,” and “Social and Emotional Development.” Within each category, possible areas of student need are listed with corresponding ways to support the student. For example, the materials provide options to help a student who is struggling with content due to cognitive difficulties. The strategies listed include modifying instructions, chunking work, modeling tasks, or using tangible objects to express abstract ideas. Each strategy includes a descriptor.

Each scope also includes an “Engage” section to teach prerequisite skills students may be lacking. For example, in the “Estimation and Compatible Numbers” scope, students participate in a partner discussion about using number lines with compatible numbers as a tool for rounding. The teacher helps students create an open number line, place numbers between multiples of ten, and round a given number. Students progress to using compatible numbers to solve expressions. If students cannot do this successfully, the “Foundation Builder” lesson addresses this knowledge gap. Foundation Builders teach prerequisite skills students may be lacking. For example, in the “Represent Decimals” scope, the students practice expanded notation during whole group instruction. If a student struggles with this skill, the Foundation Builder lesson incorporates the use of base-ten blocks to reteach the concept. 

The materials provide a “Teacher Toolbox” that includes an “Interventions” tab. This tab is not part of a specific scope but is a resource for the entire set of materials. The Interventions are separated into categories such as Adaptive Development, Cognitive Development, and Social and Emotional Development. Within each category, possible areas of student need are listed with corresponding ways to support the student. For example, the materials provide options to help a student who is struggling with content due to adaptive difficulties. The strategies listed include providing illustrated vocabulary (which is included in the materials), engaging in classroom conversation by repeating student statements, answering student questions while replacing common terms with key vocabulary, or providing students with a word bank. Each strategy includes a descriptor.

The materials provide recommended targeted instruction and activities for students who have mastered content. The “Acceleration” portion of each scope provides various activities for exploration, application, and extension of learning. In the “Area and Perimeter” scope, students explore a real-world situation with science connections. Students view a video on South African worms, then use the formulas to complete word problems on the “Student Handout.” In the “Compare and Order Decimals” scope, students evaluate the career of Melvil Dewey, the inventor of the Dewey Decimal System. Students learn about mathematical careers and what skills are needed to succeed in this field. Within the Acceleration portion of each scope is a “Create Your Own” activity, where students create their own inventions, plays, songs, technology apps, etc. For example, in the “Rational Numbers on a Number Line” scope, students create a song and dance to teach others how to find decimals on a number line. In the “Problem Solving Using the Four Operations” scope, students create a board game to help their classmates review the four operations. 

The materials provide additional enrichment activities for all levels of learners. The “Elaborate” section of each scope provides differentiated activities such as a spiral review, journal prompts, problem-based tasks, career connections, and interactive practice through games. For example, In the Elaborate section of the “Profits, Budget, and Banking” scope, students solve a real-world problem regarding earning money walking dogs. Students work in groups to determine a reasonable rate to charge for dog walking and calculate income, profit, and expenses.

Evaluation for 5.2
Materials provide a variety of instructional methods that appeal to a variety of learning interests and needs.

The materials include a variety of developmentally appropriate instructional strategies to engage students in mastery of the content. Lessons include flexible grouping, such as whole group, partners, and small groups. The materials support multiple types of practices and provide guidance and structures to achieve effective implementation.

Evidence includes but is not limited to: 

The materials incorporate the 5E-IA model in every scope. These components include a hook for student engagement, concrete models, virtual manipulatives, visual vocabulary, and media content. Lesson routines often include whole group and small group components. Student work routines include independent practice, partner work, and group work. The materials use multiple teaching strategies to meet students’ learning needs. For example, each scope includes hands-on practice with manipulatives, student handouts to support learning, and a variety of visual representations. 

The materials offer guidance to support teacher understanding of developmentally appropriate strategies to support learning. Each scope contains a “Content Support” section presenting the teacher with information about the content to be covered. For instance, in the Content Support section of the “Problem Solve Using the Four Operations” scope, the materials describe background knowledge for the TEKS in the scope. This includes a description of what students learned in previous grades. It also states misconceptions and obstacles that their students might encounter. For example, a student could be unsure of which operation to use when solving parts of a multi-step problem. The materials then share terms to know, measures to address the issues in the scope, phrases to avoid using, and coming attractions for the next grade level.

The materials provide an opportunity for students to work collaboratively, independently, or with teacher support. Students work independently on “My Math Thoughts” and “Show What You Know” and in partners during the “Fluency Builder” and “Problem-Based Task.” The materials provide teachers with support in facilitating whole group and small group instruction in the “Teacher Toolbox.” The plan for whole group instruction includes guidance for students on the mastery level, meets level, and approaching level. The materials outline a daily time split of 20 minutes for small group instruction with 70 minutes for small groups, stations, and closure.

Each scope contains an “Engage” section and an “Explore” section in which students use manipulatives and partner discourse to connect content to prior learning. In the “Compose and Decompose Fractions and Mixed Numbers” scope, students use fraction towers and tiles to model composing and decomposing fractions. Students work in small groups in a station rotation to model the assembly of different types of cakes. In the “Division Strategies and Algorithm” scope, students access prior knowledge by determining if a statement regarding division is true or false. Students must justify their thinking. In the “Explore” section, students are placed in small groups and given a math scenario. Students use a work mat to create a division model and an algorithm to match the scenario. Students use the “Math Chat” routine at the end to share their observations and learning. 

The materials guide teachers on when to use specific grouping structures. This information is found under the “Procedure and Facilitation” tab. For example, in the “Number Patterns” scope, students work individually in the “Engage” section and work with a partner or small group when they explore patterns within tables. Students who understand this concept complete the “PhET-Function Builder,” either with a partner or in a small group. For students needing additional support, the teacher pulls a small intervention group based on needs to reteach the concept. Teachers can find grouping instructions, lesson outlines, and scripted directions for both activities in the Procedure and Facilitation tab. In the “Represent Decimals” scope, students match standard notations with expanded notations to access and review prior knowledge. For students who cannot complete this task, the materials provide a “Foundation Builder” under the Procedure and Facilitation tab to address knowledge gaps.

Evaluation for 5.3
Materials include supports for English Learners (EL) to meet grade-level learning expectations.

The materials include accommodations for linguistics. Accommodations for English Learners are directly communicated in one component of the student learning experiences. The accommodations are not clearly scaffolded for various levels of English language proficiency. Guidance for teachers to support students at different English proficiency levels are not included. Although the materials include student materials in Spanish, they do not encourage the use of students’ first language to enhance vocabulary development.

Evidence includes but is not limited to: 

The materials are designed using the 5E-IA model: Engage, Explore, Explain, Elaborate, Evaluate, Intervention, and Acceleration. The “New Teacher Navigation Guide” states “By providing context before introducing new content, STEMscopes Math’s time-tested instructional model helps ELLs to better absorb new material when language is an obstacle. Research shows that the 5E instructional model and SIOP best practices (building background through Engage, improving comprehension with Intervention materials, etc.) are indispensable for teaching new material to ELLs. STEMscopes Math uses both.” 

The materials include linguistic accommodations for students who are learning English. Within the “Content Support” section of each scope, the materials include a “Terms to Know” list consisting of terms essential for student understanding and mastery of the current skill. For example, in the “Division Models” scope, the terms include array, area model, and quotient. A definition is proved for each term.

Each “Foundation Builder” lesson, found in the “Engage” section of every scope, contains a table listing multiple-meaning words or words that could be misunderstood by students. For example, in the “Compare and Order Decimals” scope, the materials list one word, order, and explain how students could interpret this to mean “to order an entree at a restaurant.” Definition and examples are provided for the teacher to explain the word in a mathematical context.

Included in all “Explore” lessons is an “ELPS Strategies” section. This is a box found at the bottom of the lesson that lists strategies for use within the lesson and the corresponding ELPS standard. For example, in the Explore 1 lesson of the “Add and Subtract Decimals” scope, the materials cite ELPS standard “(4.D) Use pre-reading supports such as graphic organizers, illustrations, and pre-taught topic-related vocabulary and other pre-reading activities to enhance comprehension of written text.” The ELPS Strategies box includes three strategies including, “Before beginning the lesson, preread the work mat and word problem with students and discuss what each is asking. Determine key information in each word problem,” and “Students might benefit from the addition of pictures (such as that of a patio, treehouse, etc.) for each word problem.” In the Explore 1 lesson of the “Compare Fractions” scope, the ELPS strategies include “During the math chats, provide students with sentence frames to answer. This can be done by flipping the question, using examples such as the following: Question: What did you notice about your cake each time you made a cut? Answer: Every time I made a cut, I noticed...about the cake.”

Lessons and activities within the other components of the materials do not contain ELPS Strategies sections or guidance specifically noted for English Learners. The supports provided for English Learners are not separated by English language proficiency level, nor do the materials provide supports for specific proficiency levels.

An “Instructional Supports” section is also included in Explore lessons. This section provides suggestions for teachers to help students who need help understanding the mathematical content that is introduced in the lesson. This section is not labeled as specifically for English Learners. For example, in the Explore 1 lesson of the “Rational Numbers on a Number Line” scope, the Instructional Supports listed include “Some students may benefit from having key benchmarks marked with masking tape on the meterstick to help them measure,” and “It might be challenging for some students to draw the points in the proper locations on the number lines in their Student Journal. Encourage them to draw benchmark locations, such as 0.25, 0.50, and 0.75, on each number line in their Student Journal.”

“Picture Vocabulary” is included in the “Explain” section of each scope. The vocabulary is presented in a slide show and a student handout. Each term has a written definition and visual representation of the word. One set of scope-specific, grade-level words is included in each scope. For example, the Picture Vocabulary in the “Multiplication Models” scope has 12 words that include equal, multiplication, array, and area model.

The STEMscopes Math Philosophy cites research that states “Academic language is believed to be one of the most important factors in the academic success of ELLs” (Francis, Rivera, Lesaux, Kieffer, & Rivera, 2006). In connection to this, the document states that the materials include opportunities for informal student communication, opportunities for students to respond in writing, and Explore activities that include teacher guidance to “attach academic vocabulary to the student’s experiences.”

Student materials are provided in Spanish, including “Student Journal” pages, “Exit Tickets,” “STAAR-Based Assessments,” and “Station Cards.” The resources do not encourage strategic use of students’ first language to develop linguistic, affective cognitive, and academic skills in English. There is no evidence that the Spanish content provides examples of how to use students’ first language as the foundation for developing skills in English.

Evaluation for 6.1
Materials include year-long plans with practice and review opportunities that support instruction.

The materials include a year-long plan to build students’ concept development. The instruction shows vertical alignment that builds year to year. The materials consistently provide review and practice of skills throughout the curriculum.

Evidence includes but is not limited to: 

The materials include a cohesive, year-long plan that considers vertical alignment and builds students’ concept development. The materials include a grade level “Scope List,” which states the name of each scope, the corresponding TEKS of the scope, the number of “Explore” lessons in each scope, and the suggested number of weeks to allot for each scope. The materials also include a “Scope and Sequence” for each grade level. The Scope and Sequence lists a tentative instruction schedule for 36 weeks, listing the Week, Scope(s), and Standards (TEKS.) The materials include “Vertical Alignment Charts” that explain the standards above and below the current grade level. The Vertical Alignment Charts are divided into six strands that include Process Skills, Number and Operations, Algebraic Reasoning, Geometry and Measurement, Data Analysis, and Personal Financial Literacy.

The content plan is cohesively designed to build upon students’ current level of understanding with clear connections between lessons and grade levels. Every scope follows the 5E-IA (Engage, Explore, Explain, Elaborate, Evaluate, Intervention, and Acceleration) model of teaching. The “Assessing Prior Knowledge” lesson is part of the “Engage” step. Teachers guide students to recall previously learned content as a way to assess the level of readiness for the current scope. If the students perform well in this section, the materials direct teachers to proceed to the new content in the scope. If prior knowledge is missing, teachers use the student’s current understanding and build upon the understanding with the “Foundation Builder” lesson. 

During the “Explore” step of the scope, the materials provide activities for students to learn new concepts. During the “Explain” step, the materials outline skill practice for students to solidify their understanding. Within the “Elaborate” section, the materials provide TEKS aligned games and other activities for students to deepen their understanding of the scopes’ concepts. The materials include activities for students who show mastery in the “Accelerate” section and “Intervention” lessons for students who have difficulty. 

For example, in the Foundation Builder of the “Compare and Order Numbers” scope, the lesson is cited to address third-grade TEKS 3.2D. The lesson directs students to compare numbers as part of a partner game. Within the lesson, the materials list “Possible Preconceptions” students may have about the concept and “Suggested Solutions” to address them. For example, the materials state “Students may confuse the terms digit and number. Suggested Solution: Digit refers to any of the 10 digits in our base-10 number system, 0–9, and number is all the digits together, such as 345.”

In the Explore lesson of the scope, students order whole numbers through the hundred-millions place. In the “Show What You Know—Part 2” activity of the Explain section, students practice this skill, looking at groups of numbers. Students who have mastered this skill continue to the Acceleration activities, including “Math Today—Fish Trouble,” in which students analyze a real-world scenario. Students who have not mastered the content participate in small group lessons found in the Intervention section.

The “Content Support” section of each scope outlines current grade levels TEKS and “Coming Attractions” of the next grade level. In the “TEKS Unwrapped” section of each scope, the materials describe how the TEKS in the scope were taught in previous grade levels and how it will look in future grade levels. The “Vertical Alignment” section within this same document shows the TEKS of other grade levels that connect with the TEKS in this scope. For example, in the “Rational Numbers on a Number Line” scope, the materials list the TEKS of the scope, including “4.2H Determine the corresponding decimal to the tenths or hundredths place of a specified point on a number line.” The document includes a description of previous grade-level learning (“In third grade, students learned to compare and order whole numbers to 100,000”) and a description of learning in fifth grade (“students will...extend their knowledge and use equivalent fractions, decimals, and percentages to show equal parts of the same whole while solving problems”).

The materials provide review and practice throughout the curriculum. “Spiraled Review” is included in the Elaborate section of every scope. The description of the section states “Students review previous or current grade-level content based on the focal points set for each grade.” For example, in the Spiraled Review of the “Add and Subtract Decimals” scope, the activity reviews comparing numbers, converting decimals to fractions, and locating rational numbers on a number line. In the Spiraled Review of the “Represent and Interpret Data” scope, the activity reviews angles, measurements, and unit conversions.

The materials also include “Fluency Builder” activities in the Elaborate section of each scope. The Fluency Builder activities review currently taught content and previously taught grade-level content. The Elaborate section also includes “Interactive Practice” for students to practice skills taught in the scope. For example, in the Fluency Builder of the “Represent Decimals” scope, students match decimal models with decimal numbers while playing a game. In the Interactive Practice, students play a computer-based game reviewing decimal place value.

Evaluation for 6.2
Materials include implementation support for teachers and administrators.

The materials include a TEKS-aligned scope and sequence that outlines the skills taught in the program. Vertical alignment components of the materials show how the knowledge and skills build and connect across grade levels. The materials include supports to help teachers implement the materials as a cohesive program. The materials include a school year’s worth of math instruction, including pacing guidance. The materials include resources and guidance to help administrators support teachers in implementing the materials.

Evidence includes but is not limited to: 

The materials include a Scope List that outlines the name of each scope, the TEKS referenced in the scope, the number of lessons in the scope, and suggested pacing by the number of weeks. The materials also include a Scope and Sequence, which lists the order of the scopes to be covered and TEKS covered in each scope.

The materials include documents titled 2019 Texas Math TEKS Kindergarten-3rd Grade Vertical Alignment Chart and 2019 Texas Math TEKS 4th-6th Grade Vertical Alignment Chart. The documents outline how the TEKS are presented and connected within and across grade levels. Within the TEKS Unwrapped section of each scope, the materials explain the vertically-aligned TEKS that correspond with that scope. The Content Support section of each scope provides detailed information about the TEKS in the scope including, Background, Misconceptions and Obstacles, Concrete Models, and Pictorial Models.

The materials include supports to help teachers implement the materials. The New Teacher Navigation Guide outlines the STEMscopes program, including information about how each scope was designed, the digital features of the materials, the components of every scope, assessments, embedded literacy, and ELL supports. 

The Home section of every scope includes components with information for teachers. The Scope Overview describes the parts and flow of the unit. Content Support explains the learning objectives and common misconceptions. TEKS Unwrapped breaks down and describes the current standards being taught and shares previous and future TEKS alignment. The Materials List outlines items needed to deliver the lessons as intended. The Parent Letter explains to parents the skills that will be taught in the scope and what students need to be successful. 

At the beginning of the Explore lesson of every scope, the materials include a video demonstrating the delivery of the lesson, followed by the materials and preparation steps needed for that lesson. Each Explore lesson also includes Procedure and Facilitation Points, a step-by-step guide for instruction, including possible student answers.

The materials include resources and guidance to help administrators support teachers in implementing the materials as intended. The available tools include STEMcoach In Action, an embedded professional development tool that administrators can use to support specific teacher needs as they implement the curriculum.

The materials include a school years’ worth of math instruction, including realistic pacing guidance and routines. The Scope and Sequence Document outlines a full year’s worth of instruction. This includes 36 weeks of total instruction, 34 weeks of new instruction, and two weeks of review and test prep for the STAAR test. The Scope and Sequence indicates a majority of the lessons support the development of the TEKS, with focus on the primary focal areas of the grade level.

Evaluation for 6.3
Materials provide implementation guidance to meet variability in programmatic design and scheduling considerations.

The materials provide guidance for strategic implementation without disrupting the sequence of content that must be taught in a specific order. Guidance from the materials allows for variability in programmatic design and scheduling considerations. The materials are designed in a way that allow LEAs the ability to incorporate the curriculum into the district.

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 order to follow a developmental progression. The materials include a “Scope List” and “Scope and Sequence.” The Scope and Sequence provides a suggested sequence of the scopes, or units, but states “STEMscopes Math program is flexible, and there are variations in implementation within the guidelines provided here. This Scope and Sequence is meant to serve as a tool for you to lean on as you find how STEMscopes Math best meets the needs of the students in your classroom.”

The suggested sequence of units includes concepts that build on each other. For example, it is suggested that fourth-grade students learn about place value of whole numbers before learning to represent decimals. Grade-level scopes first introduce place value, then addition and subtraction, then multiplication and division, and finally area and perimeter. This order accounts for the progression of skills.

The materials include “Vertical Alignment Charts.” These documents outline how the TEKS are presented and connected within and across grade levels. Within each scope, vertical alignment of standards is listed in the “TEKS Unwrapped” section.

The materials are designed in a way that allows LEAs the ability to incorporate the curriculum into district, campus, and teacher programmatic design and scheduling considerations. The “Lesson Planning Guide” provides suggestions for how to implement the materials within a school year. Suggestions include whole group, small group, and virtual learning options. The Lesson Planning Guide outlines two options: a five-day whole group and small group plan for scopes with one to three “Explore” lessons, and a five-day whole group and small group plan for scopes with three to five Explore lessons.

Evaluation for 6.4
Materials provide guidance on fostering connections between home and school.

The materials support the development of relationships between teachers and families with the inclusion of parent letters that include content information and suggestions for supporting learning at home. The materials include explanations of and resources for families to support students’ learning and development.

Evidence includes but is not limited to: 

The materials support the development of relationships between teachers and families. The STEMScopes Math Philosophy states “STEMscopes Math provides Content Support for teachers or parents who need additional background knowledge in order to fully support their student’s understanding. This element will include why a concept is being taught a certain way by explaining what the students have already learned and giving insight to the concepts students will learn next.”

The materials provide a “Parent Letter” to be sent home at the beginning of the school year. The letter includes an overview of the STEMscopes Math program, including its philosophies and components. The letter is provided in English and Spanish. The topics described in the letter include the 5E lesson format, parts of each scope, alignment with the standards, hands-on exploration, making connections, inquiry, and analysis.

Each scope, or unit, includes a Parent Letter explaining the knowledge and skills students will learn in the unit. The letter is provided in English and Spanish. The letter includes a description of requirements needed to master a skill, examples of what a skill looks like, key vocabulary related to the concept, and encouragement for parents to ask students about their learning and have them identify real-life examples of the skill. For example, the Parent Letter of the “Add and Subtract Fractions” scope explains that students will build on their knowledge of decomposing fractions from third grade and learn how to “find solutions to problems with addition and subtraction of fractions, improper fractions, and mixed numbers.” The letter gives definitions of key vocabulary such as numerator, denominator, benchmark fractions, and improper fraction estimation. The letter suggests that parents use the words during discussions with their student about what they are learning. The letter also explains that students will use the key vocabulary in class during activities such as “Math Chats” and class discussions.

The materials specify activities for use at home to support students’ learning and development. The materials include online access to resources for parents to work with their children on specific skills. The “Teacher Toolbox” contains a “Quantile Information” section, which includes a “Parent Guide.” The guide provides parents with an explanation of the “Quantile Framework” and how to use the “Quantile Measures.” One of the sections, entitled “Practice Math That Supports Your Child,” provides parents an example of activities they can use at home based on “matching the student’s math ability to the difficulty of the math material.”

Each Parent Letter includes information about how learning at school can be supported at home with specific discussions and activities. For example, in the “Compare and Order Decimals” scope, the Parent Letter communicates how students learn values of decimal numbers, shows example comparisons, and lists concept vocabulary. The letter describes how ordering and comparing decimals can be connected to experiences at home when observing decimal labels of items at a store and making buying decisions based on price. The Parent Letter from the “Compare and Order Numbers” scope states “Encourage your child to share these experiences with you and to teach you what he or she has learned. Ask your child to identify examples of what he or she is learning in everyday life, such as comparing the cost of two items or ordering items from smallest price to greatest price.”

Home support materials are available in English and Spanish. There is no evidence of the home support materials in other languages.

Evaluation for 6.5
The visual design of student and teacher materials (whether in print or digital) is neither distracting nor chaotic.

The visual design of the materials supports student learning. The materials include the appropriate use of white space, and pictures and graphics are supportive of student learning without being visually distracting. Pictures and graphics are relevant to concepts being taught and relatable and recognizable to students. The design of the teacher materials includes instructional supports that are clearly stated and easily identifiable within the materials. Instructional supports have consistent locations within the materials.

Evidence includes but is not limited to: 

The materials are designed in a manner that supports student learning. Student materials are available both online and in printable versions. Both versions of student pages include enough white space to perform calculations. The student pages have clean, bright graphics to support learning.

The teacher guides are designed with clear, designated places for important information. The materials are organized in sections, with tabs that can be clicked. The tabs contain a lesson planner, student data, benchmark testing data, and the lessons themselves. Within the units or scopes, the tabs contain scope information and the scope lessons. The tabs are arranged chronologically through the scope, starting with introductory teacher information in the “Home” tab. This tab includes “Content Supports,” “TEKS Unwrapped,” “Materials Lists,” and “Parent Letters.” The next tab is titled “Engage” and includes the first lessons of the scope. The materials include an instructional video in every “Explore” lesson demonstrating the “procedures and facilitation points.” 

The materials consistently include a place for instructional support to aid teachers in planning and implementing lessons. For example, the “Teacher Toolbox” contains the “Lesson Planning” guide, which explains how to implement the various scopes and their components. Every scope piece has an “Add to Planner and Bookmark Element” option for teachers to compile material components during lesson planning.

The materials include pictures that are easily identifiable by students and support student learning. All graphics support the concept being covered in the scope. The “Math Story” found in each “Elaborate” tab contains a picture directly related to the story being told. All charts and graphs are clear and concise.

Each scope includes “Picture Vocabulary” cards. The cards include the word, its definition, and pictures that are clear and identifiable to students. 

The materials adhere to the User Interface Design by including “Visibility of System Status.” For example, the cursor changes from an arrow to a hand when an aspect can be clicked. Users can easily navigate forward and backward. Consistency standards are present as the components of every scope look the same.

Evaluation for 6.6
If present, technology or online components included are appropriate for grade level students and provide support for learning.

The technology-based and online components of the materials are appropriate for the grade level and support student learning. The technology included in the materials aligns with the curriculum’s scope and approach to mathematics skill progression. The technology components are consistent throughout the materials. The technology supports and enhances student learning through the use of tools such as games, manipulatives, and online assessments.

Evidence includes but is not limited to: 

The materials contain technology that is aligned with the curriculum’s scope and supports the progression of teaching math skills. Each component contains “Virtual Manipulatives” for students to model math scenarios, solve problems, and justify their thinking. Each component also contains an “Interactive Practice” game that reviews concepts taught in that section. The game can be played as a class or by individual students. For example, in the “Represent Decimals” scope, the materials include virtual place value disks and an interactive game where players match fractions and decimals in order to assemble a robot.

The materials include assignments and assessments that can be completed digitally including, “Show What You Know,” “Math Story,” “Problem-Based Task,” “Decide and Defend,” “STAAR-Based Assessment,” and “Skills Quiz.” Some components of the materials have editable Google files for differentiation of the resource. The materials have a right sidebar with links to available files, digital assignments, and handouts.

The online component includes embedded tools such as note-taking, decrease and increase of font size, text-to-speech, dictionary, annotations, highlighting, and editable forms.

The materials contain a section titled “Virtual Learning: Fourth Grade.” This section includes a video lesson that teaches math concepts aligned with the scope. The video lesson includes the use of manipulatives. 

The Virtual Learning: Fourth Grade component is divided into categories that align with the TEKS, including “Numbers & Operations,” “Algebraic Reasoning,” and “Geometry & Measurement.” The virtual lessons correspond with lessons in the original scopes. For example, the lessons in the Numbers & Operations section correspond with the “Explore” lessons in the “Place Value of Whole Numbers” scope. 

The Virtual Learning materials provide guidance for teachers on how to use technology with students and how to support students with technology use, including suggestions if students are learning at home and manipulatives are not available, comprehension questions to review student learning, and resources that can be printed to use while watching the lesson. The materials also provide teachers with guidance on how to help students make connections between their digital components and the resources within the scopes.