STEMscopes Texas Math Grade 3

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 “Place Value Relationships,” “Multiplication Models,” and “Modeling Fractions,” among others. Each scope has an “Essentials” section that describes in detail the grade-level TEKS 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 of the lessons within these scopes reinforce a primary focal area. Students are introduced to these concepts through stories, games, hands-on activities, interactive investigations, worksheets, and videos. For example, in the “Place Value Relationships” scope, students practice using manipulatives to show place value relationships, discuss place value relationships during “Math Chat,” and analyze a math-based story. 

Throughout the year, questions and tasks build in rigor to meet the full intent of the primary focal areas. For example, in the “Multiplication Models” scope, students access prior knowledge from second grade by matching multiplication sentences to pictures. As the scope progresses, students build arrays, show multiplication on a number line, use skip counting, and finally describe multiplication as a comparison. When multiplication instruction continues in the following scope, “Multiplication Strategies and Algorithms,” students learn new strategies for multiplying larger numbers. 

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 use various models to make equal groups and solve word problems with their own representations or drawings. In the “Equivalent Fractions” scope, students use concrete manipulatives and pictorial representations to learn about equivalent fractions. They complete the scope by solving different types of word problems. 

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 the content and when extending for students who have mastered the content. 

All scopes include manipulatives, pictorial models, abstract models, and concrete models. Varied materials include open number lines, place value disks, fraction circles, paper plates, 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 “Place Value Relationships” scope, students solve problems using dried beans to show groups of ten. This section includes direct instruction of manipulative usage. Teachers have access to questions and statements meant to help students understand how to use base-ten blocks. For example, “How many rods are equal to a flat? Ten rods are equal to a flat.” Students continue their exploration using place value disks to show a concrete example of their number. Finally, students work with the numbers on paper when they complete the “Place Value Match” game. For the Place Value Relationships scope, teachers can also implement an “Intervention” lesson; in this case, students first use base-ten blocks and then progress to writing numbers on a place value mat. Students complete the task by writing numbers in expanded form. Later in the scope, students can “Checkup,” where they answer questions on a handout without manipulatives. This structure ensures that all students move along the CRA continuum. 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.

During the “Multiplication Models” scope, students use colored tiles, draw arrays, and finally connect arrays to the multiplication algorithm. Later in the “Area” scope, students review the array concept by determining the area of arrays. As lessons continue, students draw and label arrays and discuss how the area formula relates to the multiplication algorithm. In the “Multiplication and Division Problem Solving” scope, a gummy bear array is used in a question to activate students’ prior knowledge. This consistent usage of array representations is both grade-level appropriate and appropriate for the content.

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 “Area” scope, students demonstrate their knowledge of a corresponding second-grade standard. They match a pictorial model with its correct area and discuss with classmates their reasoning for the match. Additionally, students view a set of models and discuss with a partner the area of the figure. In the “Place Value Relationships” scope, students determine if a place value statement is correct or incorrect. The statements are a review of the previous grade level’s content, in which students represented numbers up to 1,200. They explain their thinking as a whole group or in a small group. 

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 “Multiplication Models” scope, students discuss the connection between arrays, area models, repeated addition, and multiplication equations. 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 “Representing Numerical Relationships” scope, students learn about the career of a teacher and use numerical relationships to solve a problem about classroom supplies. In the “Modeling Fractions” scope, students read about people working to beautify a city, using area and perimeter math skills in the process. When students get to the “Evaluate” section of each scope, they apply this understanding to tasks that integrate multiple math concepts. In the “Place Value Relationships” scope, teacher questioning and prompts outline how counting by ones, tens, and hundreds interrelates with number place values. The teacher demonstrates this concept using groups of items such as seeds, a place value chart, and base-ten blocks. Students then have to answer questions that combine these math concepts. 

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 “Multiplication Models” scope, students review repeated addition and use pictorial models to determine equal groups. Then, taking the knowledge and skills from this practice, they progress to using an array or area model. Lessons remind teachers that in the next grade level, students will solve two by two-digit multiplication problems using a variety of strategies: mental math, partial products, the commutative property, the associative property, the distributive property, and the algorithm. In the “Compose and Decompose Fractions” scope, students review fraction vocabulary and remember the following concept: fractional parts are equal parts of a whole. Then they use fraction bars, towers, and circles to create various fraction models. In the “Student Journal” portion of the lesson, students write a numerical equation for each model created. The “Scope Overview” explains that these same models and representations will be used in fourth grade when students explore fractions larger than one and mixed numbers. Both teachers and students are made aware of the vertical alignment and 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 “Modeling Fractions” scope, defined words include represent, solve, fraction, numerator, and pictorial model. The vertical alignment section references TEKS from second, third, 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 some guidance 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 “Addition and Subtraction Fluency” scope. In the Engage activity, students determine if a solution to a presented problem is correct or incorrect and then justify their answer. In the Explore section, students work through addition and subtraction regrouping activities until they are able to complete mixed practice with and without regrouping. The Evaluate section contains different activities, including STAAR-aligned multiple-choice questions and a “Decide and Defend” activity. The scope concludes with an Acceleration activity: “Create Your Own Task.” Here, students create their own technology application, song, or dance to showcase their learning.

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 “Fractions on a Number Line” scope, the Hook is set in a scenario where students ride a bike to a friend’s house one mile away. Students determine the distance to the house if it is eight blocks away. During the Math Today activity, students watch a video titled Concerns About Baby Food. Students answer math questions related to the video and plot discussed fractions on a number line. 

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 “Compare and Order Numbers” scope: “Students have been introduced to the idea of comparing and ordering numbers beginning in kindergarten. Students have a foundational understanding of comparative language and symbols. They also possess an understanding of how to use place value to compare numbers. In second grade, students mastered comparing and ordering numbers to 1,200.” 

Teachers also have access to scope-specific sentence stems, discussion reminders, possible student responses, teaching strategies, and misconceptions. For example, in the “Perimeter” scope, possible misconceptions include students mixing up area and perimeter, forgetting to add unlabeled sides, and not having prior knowledge of 2D geometric shapes. The “Modeling Fractions” scope provides a possible student response during a lesson on fractions and number lines: “To place a fraction on a number line, we count the hops, not the tick marks, to find the numerator. The total number of hops was the denominator.” 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 “Place Value Relationships” scope, a Math Chat question asks “What do you notice about most of the sets?” 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 is aligned to the grade level. Teacher guidance clearly describes how to conduct fluency practice as appropriate for concept development. While there are limited lesson-specific supports and limited extensions, there are still enough effective general scaffolds to differentiate for all learners. 

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 scopes 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 addition 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 Four in a Row and Risky Wagers to practice solving one- and two-step problems that include multiplication and division. 

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 Explore section of the “Division Models” scope, students divide groups of cupcakes. Sequenced teacher prompts help students transfer concept vocabulary from informal to formal language. For instance, one question reads “How many groups did we have, and what did each group represent from the scenario?” After students attempt to answer the question, the teacher models an exemplar response that utilizes content vocabulary: “We had eight groups, and they represented the number of students. This number...is called the divisor.” 

Explore lesson activities are also experience-based and formatted so students can learn vocabulary as they relate to each concept. For example, in the “Multiplication Models” scope, students explore finding equal groups of items in the classroom. Students draw a model, share their drawing, and write a multiplication sentence to match. Practice continues, requiring students to determine the total of a larger group of items and requiring students to use a meter stick as a number line. Through these experiences, students strengthen their understanding of the terms skip counting and multiples. In other scopes, students use informal and formal mathematical language during discussions and 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 “Estimation and Compatible Numbers” scope, the Instructional Supports suggest to “Provide support of vocabulary (such as middle, between, closer, near, almost, and farther) by using examples or picture support.” To accomplish this suggestion, teachers 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, creating a glossary of key terms, 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” step of the “Represent and Interpret Data” scope, students solve a problem based on a teacher-created frequency table based on a class survey. During the “Explore” activities of this scope, students practice gathering and recording data on age-appropriate topics, such as what students like to do on rainy days. In the “Elaborate” section, students read a story about a boy who collects badges and answer related questions. In the “Evaluate” step, students complete the 10-question “STAAR-Based Assessment” before addressing a situation about zoo penguins as part of the “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 “Compare and Order Numbers” scope, students read about a group of students who have individual sticker collections and determine who has the most stickers. 

Other Evaluate tasks require students to solve problems in various contexts. For example, in the “Addition and Subtraction Fluency” scope, students read about the Chesapeake Bay and answer math questions regarding its wildlife. Then in the “Problem-Based Task” of this scope, students analyze a teacher’s work with base-ten blocks before using base-ten blocks, subtraction models, and algorithms to justify their response to a real-world question. During Fluency-Builder Bingo from the “Weight and Capacity” scope, students determine if the information read represents a unit of weight or a unit of capacity. After the game, students answer questions about capacity and provide examples of objects that can be measured by capacity. In the “Show What You Know” activity of the “Representing Numerical Relationships” scope, students complete five tables showing the relationship between two sets of numbers and then justify their answers by describing the relationships.

Often tasks require students to analyze data through a real-world context. In the “Acceleration” activity of the “Compare and Order Numbers” scope, students analyze data about the number of gallons of drinking water made at a desalination plant. The “Math Story” of the scope tells about the number of steps individual students take in a week and includes a corresponding data chart. Finally, the “Represent and Interpret Data” scope contains multiple real-world context data problems. For example, students measure their classmates’ height, collect their data, and use a graph to represent the information. Another problem in this scope has students analyze a bar graph based on reading goals, create a new graph-based on actual data, interpret the information, and explain their process.

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 include 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 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 an 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 “Multiplication and Division Problem Solving” scope, students will solve one- and two-step multiplication and division problems. To achieve this goal, students will use strategies and tools, including concrete models, pictorial models, equations, and algorithms. 

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 “Addition and Subtraction Models” scope, students explore part-whole relationships in the real-world scenario of filling candy bins. The lesson includes two “Math Chat” sections where students solve world problems, answer questions in writing, and share their reflections through teacher-led discourse. For this specific lesson, students respond to questions like “What process did you use to find a missing total?” In the Explore activity of the “Perimeter” scope, the materials include reflection prompts like “Ask students to share how they solved for the perimeter of each polygon.” 

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 “draw the display” and “write the addition equation.” In the “Compare Fractions” scope, students answer questions like “How do you determine which fraction is greater if they both have the same denominator?”

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 with three areas: “Content,” “Process,” and “Affective.” For example, in the “Addition and Subtraction Models” scope, students pick their favorite way to solve two given equations, one addition and one subtraction, and then describe which method they prefer and why. “Problem-Based Tasks” also provide students an opportunity to apply a problem-solving model. In the “Modeling Fractions” scope, students solve problems about the fractions of crops on a farm. Students shade models of the fractions and answer questions. At the end, they reflect on their approach, answering questions like “Which part of the fraction did you look at to determine how many pieces to partition each shape into?” 

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 “Multiplication Models” scope, students complete a series of tasks to model multiplication in different ways; then, the teacher facilitates a discussion to help students reflect on their problem-solving approach. One question used in this discussion asks, “What are some strategies you used to discover what fact you were working with?”

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 “Content Support” section of each scope has pictures, explanations, and descriptions for each tool referenced in the scope. For example, in the “Place Value Relationships” scope, students use place value blocks to show the number 1,156. In this section, there is a pictorial representation of how to build the number with place value blocks. 

Within the “Explore” tab of each scope, the materials provide a video explaining the scope, materials, and models. In the “Home” section of every scope, teachers find a customizable list of materials needed for all the activities and tasks. Also included are step-by-step “Procedure and Facilitation Points” that provide teachers with guidance for lesson delivery, including using the appropriate tools. For example, in the “Represent and Interpret Data” scope, the needed materials listed include centimeter rulers and yardsticks. In the “Hook” activity of the “Addition and Subtraction Models” scope, teachers introduce modeling addition and subtraction using drawings. Students listen to a scenario, draw a picture of the information given, and then write an equation that corresponds with their picture. The teacher asks probing questions like “What information is given in this problem?” Throughout the activities in the scope, students work through the Explore activities that ask students to use tools including base-ten blocks, strip diagrams, and number lines. The materials include directions and guiding questions for teachers to ask students as they practice using the tools, such as “How did you know where your jumps were landing on the number line?” 

The materials provide students opportunities 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 “Estimate and Problem-Solve” scope, students practice identifying odd and even numbers using manipulatives to divide the numbers into two equal groups. Students record their findings on a chart and reflect on their strategies during the teacher-led “Math Chat.” The teacher makes connections between their experiences with the manipulatives and numbers on a place value chart, such as multiples of ten.

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 “Weight and Capacity” scope, students sort measurements of food as a measurement of weight or volume. Students make a plan for food delivery based on the given information. The activity lists teacher-guidance questions about tool selection: “If there is not a container big enough or the food weighs too much for the drone, how can you make sure that the amount needed is still delivered?” Students are encouraged to use their notes from previous activities to help them work through the problems.

The materials provide students opportunities to use a variety of tools, including manipulatives, representations, and algorithms, during their exploration of grade-level content. For example, in the “Place Value Relationships” scope, students use dried beans, base-ten blocks, and place value disks to make connections in the base-ten system. Students use these manipulatives again to compose and decompose various numbers up to the hundred-thousands place. In the “Represent and Interpret Data” scope, students gather data using tally marks. Students decide whether to use a dot plot, T-chart, bar graph, or pictograph representation and justify their choice.

The materials provide students opportunities to select grade-appropriate tools for solving tasks. For example, in the “Equivalent Fractions” scope, students use fraction circles, fraction bars, and number lines to complete the “Show What You Know” activities. The student directions state “Create an equivalent fraction for each of the given fractions. Prove it by drawing fraction circles or fraction bars. You may use your fraction bars and fraction circle manipulatives if needed.” 

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 concepts from the scope. For example, in the “Perimeter” scope, students play the game “Raptor Park,” finding the perimeter of different fenced areas. Every scope includes a “PHeT” activity, a technology-based interactive investigation tied to the TEKS taught in the scope. For example, in the “Area” scope, students use the technology interactive “Area Builder” to create different shapes with different areas. 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, the materials include virtual color counters and color tiles in the “Multiplication Models” scope. The materials include virtual geoboards in the “Two and Three Dimensional Figures” scope.

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 are prompted to select a technique within multiple components of each scope. For example, in the “Addition and Subtraction Model” scope, students learn methods to find a sum or difference, such as using part-whole relationships, strip diagrams, and number lines. In the “Problem-Based Task” of the scope, students select a technique and justify their reasoning as they work on developing a new business. In the “Multiplication and Division Problem Solving” scope, students use the properties of operations, recall facts, strip diagrams, and arrays to solve problems. During the Problem-Based Task of this scope, students choose a technique that will help determine the number of families they can feed at a food bank based on the given information. In the “My Math Thoughts” activity of the “Division Models” scope, students solve a word problem, choosing one of the strategies taught in the “Explore” section of the scope; the strategies include equal groups and fact families. In the Explore activity of the “Addition and Subtraction Fluency” scope, students select the grade-level appropriate techniques for each problem. The students “decide how they want to visually represent the problem. Students could use a number line, strip diagram, etc. Students should estimate the solution and then choose any strategy they want to solve the problem. Encourage students to use the standard algorithm, but allow them to use other strategies as needed.” 

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 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 “Math Chat” of the “Problem Solving with Multiplication and Division,” students share strategies they chose during a teacher-led discussion. The materials explain for teachers how to find the product or quotient using appropriate strategies. In the “Skills Quiz” of the Evaluate section, students solve multiplication and division word problems, choosing a strategy. The “Addition and Subtraction” scope includes three Explore activities that teach specific strategies: Part and Whole Relationships, Modeling with StriphDiagrams, and Modeling with a Number Line. During the Math Chat section of these activities, students share strategies they used to solve a problem. During the “My Math Thoughts” activity at the end of the scope, students choose their favorite way to solve the problem and explain why. 

The materials support students learning multiple appropriate strategies to solve problems. For example, in the “Area” scope, students determine the area of a figure by counting the square units in the figure and using the formula for area. The “Addition and Subtraction Models” scope introduces concrete models, pictorial models, then abstract models. As the size of the numbers in problems increases, students learn how to use the number line. In the following scope, students are introduced to the algorithm with regrouping. In the “Estimation and Compatible Numbers” scope, students use number lines, mental math, rounding, and compatible numbers. In the “Modeling Fractions” scope students use drawing pictures, strip diagrams, and number lines. In the “Add and Subtract Time” scope, students use geared clocks, paper clocks, and number lines.

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 “Representing Numerical Relationships” scope, students work in a group to solve problems about a store’s inventory. Students then participate in a “Math Chat,” sharing strategies used to solve the problems. The lesson directions include prompts and questions for the discussion. For example, “As students share their strategies to the previous question, encourage other groups to listen and respond to other groups’ ideas. Encourage students to look for similarities and differences between their strategy and the strategies of others.”

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 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-alouds.

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, as well as revise them if needed. For example, in the Hook activity of the “Area” scope, students create a model of a patio and use it to determine the area and a formula for area. The teacher facilitates discussion and extends their learning by introducing composite figures by combining two or more patios.

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. The materials include a script with questions, prompts, and possible answers. 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 must determine if a given solution is correct or incorrect and justify their mathematical thinking. For example, in an Explore activity of the “Estimation and Compatible Numbers” scope, students work in groups to estimate the total costs of camping supplies. Students share their estimation strategies within their group. After completing the estimations, the teacher leads the Math Chat portion of the lesson. The materials list questions to ask students about their estimation strategies. In the Decide and Defend task, students analyze estimations made by a concessions manager.

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 of the “Build a Budget” scope, students evaluate a purchasing scenario and determine which of three options would be the best buy. Students answer questions like “Which should he buy in order to spend the least amount of money?” Students represent their thinking visually and write an explanation of their decision. 

The materials contain tasks that can be solved using a variety of mathematical representations. For example, in the “Explore” lesson of the “Area” scope, students explore ways to plant crops in equal rows, determining the area. Students use tiles to create a model, draw models in their journal, discuss their thinking with the class, and write a corresponding equation. 

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 “Weight and Capacity” scope, students help determine the weight of a traveler's three pieces of luggage. Students respond in writing to questions like “What unit of measurement should he use and why?” Students discuss their thinking 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, in a Math Chat for the “Multiplication Strategies and Algorithm” scope, the teacher asks, “What is the relationship between the equation and the area model?” 

Teachers guide students to reflect on their own knowledge by asking probing questions and instructing students to record reflections in their journals. For example, in the Explore lesson of the “Multiplication Strategies and Algorithm” scope, students build a model representing the distributive property of multiplication. The materials include a list of prompts and directions for teachers to guide students through experience. The teacher script includes statements like “As students are ready, encourage them to try to draw the area model without using the Base Ten Blocks by imagining what they would build.”

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. Next, the teacher “[Splits] students into groups of up to five students each.” Groups solve a fractional quantity comparison question involving sizes of pieces of cake. Students discuss their thoughts with questions such as “If a cake is divided into eight equal slices, what fraction of the cake is each slice?” In the “Explore” step, student partners compare two fractions with equal denominators and record their observations and conclusions in their “Student Journal.” In the following activity, students work in groups of two or four to make decisions in four “court cases” involving fractions. The materials include questions to support struggling students, such as “Why would the greater-number denominator give you smaller pieces?” Once groups have made their decisions, the class discusses the process by answering questions like “What does the denominator do to the whole?” Students communicate their mathematical ideas in writing by completing 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 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. For example, during the Hook activity of the “Multiplication Models” scope, students work in groups to determine supplies needed for a party and answer discussion questions. In the Explore lesson, students use counters to group objects and make connections with repeated addition and multiplication. Students talk with partners as they work, and the lesson conclusion is a whole group “Math Chat.” In the “Career Connections” activity in the “Elaborate” section, students learn about and discuss the career of James Gosling, a computer scientist. 

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 “Addition and Subtraction Models” scope in the “Explore” activities, students learn about part-part-whole relationships. Students construct a strip diagram, explain what helped them make their strip diagram, and explain how making a strip diagram helped them solve a problem. Next, students use number lines and justify the decisions they made when constructing their number line. In the “Compare and Order Numbers” scope, students use place value disks and place value charts to compare numbers. Students participate in a “Math Chat” justifying their ideas, 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 “Multiplication Models” scope, students analyze two different opinions of a profit scenario. Students construct an argument to justify their conclusions.

Every scope includes Math Chat discussions within lessons. The discussions include opportunities for students to construct and present arguments. For example, during a Math Chat in the “Perimeter” scope, students determine and discuss which perimeters were easiest to measure, what tool was appropriate to use, and what strategy was the most efficient. Students use measurement tools, the perimeter formula, and pictorial models to explain their solutions. During a Math Chat in the “Fractions on a Number Line” scope, students explain why it is better to measure using fractions than whole numbers and what increment is most precise. Students use number lines, concrete models, or pictorials models to share their thinking. In the “Addition and Subtraction” scope, students participate in a Math Chat after solving word problems. The Math Chat includes the prompts “How did you know where your jumps were landing on the number lines?” and “How did you know what your final solution was?”

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 even and odd numbers in third grade, students should use the divisibility rule, and “As they display their ideas, listen for place value language to be part of the justification.”

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. Decide and Defend’s provided rubric 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 Relationships” scope, students learn about groups of ten and the value of digits. During the “Show What You Know” assessment, students determine the value of 10 groups of 7, 10 groups of 70, and complete a place value chart for the number 31,845. 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 materials’ components 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 “Addition and Subtraction Models” 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 “Compare and Order Numbers” scope, students analyze number comparison statements. If students have difficulty, the Foundation Builder lesson reviews comparing and ordering numbers up to 1,200.

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 “Multiplication Strategies and Algorithm” scope, the intervention lesson reviews multiplication properties using concrete models. In an Acceleration activity, students create a play about multiplication strategies.

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 practicing grade-level skills within stations. 

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

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 “Addition and Subtraction Models” scope addresses TEKS 3.5A 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” section of the “Count Money” scope, students complete a series of activities beginning with a verbal review of skip counting, a matching activity in which they identify a given coin by name and value, and a count and comparison of a collection of coins. 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 state options to help students 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 “Multiplication Models” scope, students determine and explain whether a multiplication model and a multiplication sentence match. If students cannot do this successfully, the “Foundation Builder” lesson addresses this knowledge gap. During the Foundation Builder, students look at slides that show multiplication models and use play-doh to create their own models, as the teacher asks guiding questions. Once students can describe the models effectively, they move to Part 2. In Part 2, students roll dice, create an array showing what they rolled, and explain the array. In the Foundation Builder lesson of the “Place Value Relationships” scope, students use supplemental aids, including a place value mat and base-ten blocks, to compose and decompose numbers. Students begin with composing three-digit numbers and progress to numbers in the hundred-thousands place, reinforcing content from previous grades.

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. For example, in the “Place Value Relationships” scope, students explore connections and applications of math with other content areas in the activity “Math Today-Invasive Species.” During this activity, students learn about an invasive species of animal through a provided video and use the information to answer multi-step word problems. In the “Two and Three Dimensional Figures” scope, students investigate the career of a painter and how math is used in this career. Students identify ways in which a painter uses 2-dimensional and 3-dimensional shapes, as well as explain why it is important for painters to know and understand the attributes of these shapes. Also found within the Acceleration portion of each scope is a “Create Your Own” activity, during which students create their own inventions, plays, songs, technology apps, etc. For example, in the “Addition and Subtraction Models” scope, students are given the task of creating a technology app to help classmates add and subtract. 

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 “Addition and Subtraction Models” scope, students who have mastered the content interact with the real-world concepts of supply and demand. This includes playing a partner game to determine if a business is successful. In the “Representing Numerical Relationships” scope, differentiation for different levels of learners is provided with three different games in the “Fluency Builder” tab: Missing Values, Who Will Rule, and Multiplication Model Match. This section also provides Math Story—Drought!, Problem-Based Task—Betty’s Bow-tique, Career Connections—Teacher, and an Interactive Practice—Alien Analysis.

In the “Perimeter” scope, students use a “Physics Education Technology” (PhET) computer simulation to create various shapes, label the shapes’ measurements, and calculate the perimeter of the shapes. Students also play a game in which the objective is to build different shapes using digital blocks that meet a given perimeter and area. Six different variations of the game are provided in order to support learners of different levels.

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. The materials support the teacher's understanding of instructional strategies in the “Explore” and “Explain” sections by including guiding questions, instructional supports, ESL strategies, and a “Picture Vocabulary.”

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.

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 “Engage” lessons of “Place Value Relationships” scope, students work individually and in groups. At the end of the scope, students who have mastered the place-value concepts taught complete the “Math Today-Invasive Species” enrichment activity found in the Procedure and Facilitation tab. This small-group intervention lesson includes a detailed outline and is geared towards students who need additional support or a reteach of the concept.

The materials include “Procedures and Facilitation Points” in each scope for each activity. These points guide the teacher in how to group students, how students should speak and respond to each other, and the materials needed. For example, in the “Add and Subtract Time” scope, as students find the start and stop times in real-world scenarios, they are split into two groups. As they complete the activity, they use the “Math Chat” routine to discuss their solutions and justify their mathematical thinking. In the “Count Money” scope, students look at money picture cards and determine the amount shown. Next, the teacher reads a scenario involving money and questions students regarding their thinking. In the “Explain” section, students show what they know by skip-counting like coins and calculating the total. Students are given the opportunity to write about their mathematical thinking and processes. Think time and partner sharing is used before writing time. 

Instructional routines are included to engage students with the concepts of the lessons. For example, in the “Estimation and Compatible Numbers” scope, students use number lines and number cards to access and review knowledge of number placement on number lines. For students who cannot complete this task, the materials provide a “Foundation Builder” to address knowledge gaps. As students move through the scope, students work in a small group to determine which two multiples a number falls between and which number it is closest to. Students complete an “Exit Ticket” to show mastery. For those unable to complete the exit ticket correctly, the “Small-Group Intervention” lesson is provided. In the “Addition and Subtraction Models” scope, students are engaged in the lessons through various components, including a basketball video with a word problem, base-ten blocks, virtual manipulatives, and a journal prompt including a number line. Later in the scope, to demonstrate skill mastery, students choose a model for a problem-based task, check it with the algorithm, and create a word problem that can be represented by the model.

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 “Representing Numerical Relationships” scope, the terms include table, represent, and verbal descriptions. A definition is provided 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 “Place Value Relationships” scope, the list includes the words one and ten/tens and explains how students could interpret these words as “won” and “tin/tins.” Definitions 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 “Multiplication Strategies and Algorithms” scope, the materials cite ELPS standard “(4.G) Demonstrate comprehension of increasingly complex English by participating in shared reading, retelling, or summarizing material, responding to questions, and taking notes commensurate with content area and grade-level needs.” The ELPS Strategies box includes one strategy: “Invite students to take turns reading aloud to their group. After they are done, have the student to the right of each reader summarize and retell in his or her own words. The student to the right of each summarizer will underline or highlight important information in the question or scenario.” In the Explore 2 lesson of the “Estimation and Compatible Numbers” scope, the materials list three ELPS strategies, including “Write a checklist of key vocabulary for the lesson on the board. Have students use the list to self-monitor their use of the vocabulary words. Students should aim to use each word (written or oral) at least once during the lesson,” and “When students are in groups, prompt them to notice and encourage each other's use of the target vocabulary words (those on the checklist).”

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 “Fractions on a Number Line” scope, the Instructional Supports listed include “Remind students that a fraction represents equal parts of a whole,” and “If students are struggling to create a number line, it might be worth revisiting the concept of number lines with whole numbers.”

“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, 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 the 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 skills 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 “Area” scope, the lesson addresses second-grade TEKS 2.9F. Students look at images to determine how many square units are in different rectangular figures. 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 concept of area with perimeter. Suggested Solution: ask the students to trace their fingers around the perimeter and place their palm on the area. This will help them make a sensory connection with the concept.” 

In the Explore lesson of the scope, students determine the area of rectangles using multiplication. In the “Show What You Know—Part 1” activity of the Explain section, students practice this skill, looking at images of rectangles and finding their area. Students who have mastered this skill continue to the Acceleration activities in which they 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 level 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 “Multiplication Models” scope, the materials list the TEKS of the scope, including “3.4D Determine the total number of objects when equally-sized groups of objects are combined or arranged in arrays up to 10 by 10.” The document includes a brief description of previous grade-level learning (“Second graders were introduced to the concept of multiplication using concrete sets of equivalent objects that were joined together using repeated addition”) and a description of learning that will take place in fourth grade (“students will multiply larger numbers”).

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 “Addition and Subtraction Fluency” scope, the activity reviews place value, estimation, and locating numbers on a number line. In the Spiraled Review of the “Representing Numerical Relationships” scope, the activity reviews multiplication and division equations and pictorial models.

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 Representing Numerical Relationships scope, students determine the rule of given number patterns while playing a game. In the Interactive Practice, students play a computer-based game determining missing numbers in tables.

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 do not include resources and guidance to help administrators support teachers in implementing the materials as intended. The tools that are available 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 a 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 allows 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 third-grade students learn multiplication and division models and strategies before learning how to find the area. Grade-level scopes first introduce place value, then addition and subtraction, then multiplication and division, and finally area and perimeter. This order builds from one skill to the next. 

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 “Estimation and Compatible Numbers” scope explains that students will build on their knowledge of number lines from second grade, stating that students will learn “how to represent various numbers up to 100,000 on a number line by estimating its location.” The letter gives definitions of key vocabulary such as estimation, consecutive, round, and compatible numbers. The letter suggests that parents use the words during discussions with their students 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 Numbers” scope, the Parent Letter communicates how students learn values of numbers up to 100,000, shows example comparisons, and lists concept vocabulary. The letter describes how ordering and comparing numbers can be connected to experiences at home with height, elevation, and money. The Parent Letter from the “Area” 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 the space needed to make a garden or the amount of flooring for a room.” 

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 include 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 “Addition and Subtraction Models” scope, the materials include virtual base-ten blocks and an interactive addition game that incorporates strip diagrams and other models.

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: Third Grade.” This section includes a video lesson that teaches math concepts aligned with the scope of the given lesson. The video lesson includes the use of manipulatives. 

The Virtual Learning: Third 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 Relationships” 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.