6th to 8th Grade - Gateway 3
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Teacher and Student Supports
| Score | |
|---|---|
| Gateway 3 - Meets Expectations | 100% |
| Criterion 3.1: Teacher Supports | 10 / 10 |
| Criterion 3.2: Student Supports | 6 / 6 |
| Criterion 3.3: Intentional Design |
The materials reviewed for Eureka Math2 Grade 6 through Grade 8 meet expectations for Teacher & Student Supports. The materials meet expectations for Criterion 1, Teacher Supports, Criterion 2, Student Supports and Criterion 3, Intentional Design.
Criterion 3.1: Teacher Supports
Information on Multilingual Learner (MLL) Supports in This Criterion
For some indicators in this criterion, we also display evidence and scores for pair MLL indicators.
While MLL indicators are scored, these scores are reported separately from core content scores. MLL scores do not currently impact core content scores at any level—whether indicator, criterion, gateway, or series.
To view all MLL evidence and scores for this grade band or grade level, select the "Multilingual Learner Supports" view from the left navigation panel.
Materials include opportunities for teachers to effectively plan and utilize with integrity to further develop their own understanding of the content.
The materials reviewed for Eureka Math2 Grade 6 through Grade 8 meet expectations for Teacher Supports. The materials provide clear guidance through useful annotations and suggestions for enacting both student and ancillary materials. They include explanations and examples of grade-level concepts and standards, along with how these connect to prior and future grade levels, supporting teacher content knowledge. A year-long scope and sequence is provided, along with standards correlation information. The materials offer strategies for communicating with stakeholders and suggestions to support student progress. Additionally, they explain the program’s instructional approaches, identify research-based strategies, and clarify the role of the standards. A comprehensive list of required supplies is included. The materials meet expectations for providing consistent opportunities to determine student learning throughout the school year. The assessment system provides sufficient teacher guidance for evaluating student performance but provides limited guidance for interpreting student performance and determining instructional next steps.
Indicator 3a
Materials provide teacher guidance with useful annotations and suggestions for how to enact the student materials and ancillary materials, with specific attention to engaging students in engaging students to guide their mathematical development.
The materials reviewed for Eureka Math² Grade 6 through Grade 8 meet expectations for providing teacher guidance with useful annotations and suggestions for how to enact the student materials and ancillary materials, with specific attention to engaging students in order to guide their mathematical development.
Materials provide comprehensive guidance to assist teachers in presenting the student and ancillary materials. The Implementation Guide provides guidance for understanding the organization and purpose of the materials, lesson structure and pacing, assessment, differentiation, lesson facilitation, and student resources.
Examples include:
Grade 6-9 Implementation Guide, Inside Teach, Module-Level Components, Overview states, “Your Teach book begins with the Overview, a topic-by-topic summary that shows the development of learning throughout the module. It also provides connections to work done before and after the module, helping you understand the module’s place in the overall development of learning in and across the grade levels.”
Grade 6-9 Implementation Guide, Inside Teach, Module-Level Components, Why states, “The Why Behind the Lesson Design section gives insight into the decisions made during the writing of the module. This insight helps you understand the underlying structure of the module, flow of the content, and coherence of the different parts of the curriculum.”
Grade 6-9 Implementation Guide, Inside Teach, Module-Level Components, Achievement Descriptors state, “The Achievement Descriptors (ADs) section is a helpful guide that identifies specific ADs for the module. The Achievement Descriptors resource provides more guidance and is found at the end of each Teach book.”
Grade 6-9 Implementation Guide, Inside Teach, Module-Level Components, Lesson Structure states, “Each lesson is structured in four sections: Fluency, Launch, Learn, and Land. Lessons are designed for one 45-minute instructional period. Fluency provides distributed practice with previously learned material. Launch creates an accessible entry point to the day’s learning through activities that build context and often create productive struggle that leads to a need for the learning that follows. Learn presents new learning related to the lesson objective, usually through a series of instructional segments. This lesson component takes most of the instructional time. Land helps you facilitate a brief discussion to close the lesson and provides students with an opportunity to complete the Exit Ticket.”
Materials include sufficient and useful annotations and suggestions that are presented within the context of specific lessons. Teacher Notes, Universal Design for Learning (UDL) suggestions, and Differentiation supports provide point-of-use guidance for lesson implementation, student engagement, and learner needs. The Implementation Guide states, “Throughout your Teach book, you will find different types of instructional guidance that appear in the margins. These notes provide information about facilitation, differentiation, and coherence. Teacher Notes communicate information that helps with implementing the lesson. Teacher Notes may enhance mathematical understanding, explain pedagogical choices, give background information, or help you identify common
misconceptions. Universal Design for Learning (UDL) suggestions offer strategies and scaffolds that address learner variance. These suggestions promote flexibility with engagement, representation, and action and expression, the three UDL principles described by CAST. These strategies and scaffolds are additional suggestions to complement the curriculum’s overall alignment with the UDL Guidelines.”
Examples include:
Grade 6, Module 1, Topic E, Lesson 25, Teach Book, Launch, Teacher Note states, “Problem 1 promotes critical thinking about percents and wholes through the pictorial representation of a circle graph. If students are unfamiliar with this way of displaying data, support them by asking the following questions. Why are the colored regions of the circle graphs different sizes? What is the total percent shown for each circle graph? Which color balloon do Sana and Tara have the least number of? How do you know? Which color balloon do Sana and Tara have the greatest number of? How do you know? If the circle graphs impede student understanding of and engagement with this task, consider eliminating them and referencing only the tape diagrams.”
Grade 7, Module 6, Topic D, Lesson 18, Teach Book, Learn, UDL: Action and Expression states, “To support students in monitoring their own progress, consider providing questions that guide self-monitoring and reflection. For example, post the following for students to refer to as they work independently: How is this problem like the jigsaw puzzle problem? How have we used mean absolute deviation in previous problems similar to this?”
Grade 8, Module 3, Topic C, Lesson 11, Teach Book, Launch, Differentiation: Support states, “Some students may have difficulty recognizing the difference between a rotation and a reflection. Encourage students to trace a figure and label its vertices on a transparency and to use the transparency to review how the orientation of a figure changes under a reflection but remains the same under a rotation.”
Indicator 3b
Materials contain explanations and examples of grade-level/course-level concepts and/or standards and how the concepts and/or standards align to other grade/course levels so that teachers can improve their own knowledge of the subject.
The materials reviewed for Eureka Math² Grade 6 through Grade 8 meet expectations for containing explanations and examples of grade-level/course-level concepts and/or standards and how the concepts and/or standards align to other grade/course levels so that teachers can improve their own knowledge of the subject.
The materials contain adult-level explanations and examples of complex grade-level concepts so that teachers can improve their own knowledge of the subject.
Examples include:
The materials provide video resources at the modular level, “How to Use Tabular Models to Represent Equivalent Expressions”, “How to Use Tape Diagrams to Solve Single-Variable Equations,” that explain the math of the module to the teacher and provide teachers’ strategies and support within the module.
The materials include a section called Math Past and Math Past Slides that gives the teacher historical background of the mathematics.
The Implementation section contains Program Overview Videos, Model and Domain Coherence Videos, How-to Videos, and Routine Videos, so that a teacher can gain knowledge on all aspects of the grade-level concepts.
The Knowledge Hub Resources tab includes: Webinars, Aha! Blogs, Research and Whitepapers, as well as Case Studies and Implementation Stories that all can be used by the teacher to improve their own knowledge.
The materials contain adult-level explanations and examples of concepts beyond the current course so that teachers can improve their own knowledge of the subject. The Grade 6–9 Implementation Guide explains that the Teach Book Overview “provides connections to work done before and after the module, helping you understand the module’s place in the overall development of learning in and across the grade levels.”
Examples include:
Grade 6, Module 1, Topic Resources, Topic A Overview, Topic A Ratios states, “Topic A introduces students to ratios. In the elementary grades, students learn to recognize number patterns, make equal groups, write multiplicative comparisons, and work with fractions. Students apply these skills in grade 6 as they recognize part-to-part and part-to-whole relationships, write ratios, and explain the meaning of ratios.”
Grade 7, Module 3, Module Resources, Module 3 Overview, Topic A Equivalent Expressions states, “Topic A centers on writing expressions in equivalent forms. Students move from doing familiar work with numerical expressions to determining when algebraic expressions are equivalent. Through the application of properties of operations—namely the distributive property—as well as the use of the tabular model, students multiply and factor expressions with rational and negative numbers.”
Grade 8, Module 5, Module Resources, Module 5 Overview, Systems of Linear Equations, Coherence: After this Module states, “Algebra I Module 2 Students continue their study of systems of equations and learn a new method for finding a solution: the elimination method. Students broaden their understanding of systems to include systems composed of linear inequalities as well as systems composed of one linear equation and one quadratic equation.”
Indicator 3c
Materials include a year-long scope and sequence with standards correlation information.
The materials reviewed for Eureka Math² Grade 6 through Grade 8 meet expectations for including a year-long scope and sequence with standards correlation information.
The materials include multiple ways of viewing a year-long scope and sequence for each grade level. Each grade includes:
A Curriculum Guide that provides a Year-Long Curriculum Overview of grades 6-Algebra 1, allowing teachers to see the progression of modules being taught across the grade levels.
A Pacing Guide that provides a detailed description of each component of the program and a recommended number of days for lessons and assessments. The guide outlines suggested pacing for teaching the entire course and includes Topic and Lesson Objectives.
A Scope and Sequence that provides the Module, how many Topics in each module, and the number of Lessons in each topic.
Standards correlation information is provided by the state in the State Standard Alignment Study. This is found digitally under Implementation and State Standard Alignment Study. It includes each state's standards and where those standards are located in the lessons.
The Module Resources include Mathematical Practice by Lesson correlation guides that identify the Mathematical Practice emphasized in each topic and lesson.
Indicator 3d
Materials provide strategies for informing all stakeholders, including students, parents, or caregivers about the program and suggestions for how they can help support student progress and achievement.
The materials reviewed for Eureka Math² Grade 6 through Grade 8 provide strategies for informing all stakeholders, including students, parents, or caregivers, about the program and suggestions for how they can help support student progress and achievement.
Family Resources are available through greatminds.org and provide families with a curriculum overview, information about the program and student materials, articles, and videos that provide information and offer guidance for supporting students' mathematical learning.
The student Learn book includes a Recap (Levels 6–Algebra I) that “outlines key learning from the lesson and provides examples with supporting notes. The Recap summarizes the main learning in the lesson. Definitions of any terms introduced in the lesson are included. Each Recap also shows problems like those completed in class and examples of the thinking that helps students solve the problems. For middle and high school students, Recaps are the activities designed to be completed at home with families. Whether your student is missing class or could use additional support at home, Recaps can help students preview or review lesson concepts.” The Implementation Guide states, “You may use the Recaps as a guide to support practice outside of class. Recaps are also useful for anyone supporting the student’s learning, including family members, tutors, and special educators.” However, these Recaps are only available in English.
Indicator 3e
Materials explain the program’s instructional approaches, identify research-based strategies, and explain the role of the standards.
The materials reviewed for Eureka Math² Grade 6 through Grade 8 meet expectations for explaining the program’s instructional approaches, including reference to research-based strategies, and explaining the role of the standards.
Across lessons, the instructional approach follows a consistent sequence of Fluency, Launch, Learn, and Land. Lessons begin with distributed practice with previously learned material to develop fluency. Next, the Launch section creates an accessible entry point to the day’s learning through activities that build context and can create productive struggle leading to a need for the information supplied in the lesson. Every Launch ends with a transition statement that sets the goal for the day’s learning. Then, new learning related to the lesson objective is found in the Learn section. This section is the largest part of the instructional time. Finally, Land allows for discussion to close the lesson and provide students an opportunity to complete the Exit Ticket.
Materials explain the instructional approaches of the program. According to the Grades 6-9 Implementation Guide, Mathematical Language Routines, Eureka Math2 uses mathematical language routines, or predictable patterns of classroom interaction, to allow students and teachers to focus on mathematical content. Routines intentionally support engagement, discussion, and building content knowledge. Directions for a routine are included in a lesson every time the routine is used. That way, the specific facilitation guidance is immediately available to you as you work through the lesson. Many of the same routines appear across grade levels from
Prekindergarten to Algebra I using age-appropriate variation
Examples include:
Instructional Routine: Always Sometimes Never, students make justifications and support their claims with examples and nonexamples. Implementation Guides, Mathematical Language Routines, Procedures, states, “Present a mathematical statement to students. This statement may hold true in some, all, or no contexts, but the goal of the discussion is to invite students to explore mathematical conditions that affect the truth of the statement. Give students an appropriate amount of silent think time to evaluate whether the statement is always, sometimes, or never true. Have students discuss their thinking with a partner. Circulate and listen as they talk. Identify a few students to share their thinking. Then facilitate a class discussion. Invite students to share their thinking with the whole group. Encourage them to provide examples and nonexamples to support their claim. Encourage use of the Talking Tool. Conclude by bringing the class to consensus that the statement is [always/sometimes/never] true [because …].”
Instructional Routine: Critique a Flawed Response, students communicate with one another to critique others’ work, correct errors, and clarify meanings. Implementation Guide, Mathematical Language Routines, Procedures, states, “Present a prompt that has a partial or broken argument, incomplete or incorrect explanation, common calculation error, or flawed strategy. The work presented may either be authentic student work or fabricated work. Give students an appropriate amount of time to identify the error or ambiguity. Invite students to share their thinking with the class. Then provide an appropriate amount of time for students to solve the problem based on their own understanding. Circulate and identify a few students to share their thinking. Purposefully choose work that allows for rich discussion about the prompt given. Then facilitate a class discussion by inviting students to share their solutions with the whole group. Encourage use of the Talking Tool. Lead the class to a consensus about how best to correct the flawed response.”
Instructional Routine: Stronger, Clearer Each Time, students revise and refine their written responses. Implementation Guide, Mathematical Language Routines, Procedures, states, “Present a problem, a claim, or a solution path and prompt students to write an explanation or justification for their solution path, response to the claim, or argument for or against the solution path. Give students an appropriate amount of time to work independently. Then pair students and have them exchange their written explanations. Provide time for students to read silently. Invite pairs to ask clarifying questions and to critique one another’s response. Circulate and listen as students discuss. Ask targeted questions to advance their thinking. Direct students to give specific verbal feedback about what is or is not convincing about their partner’s argument. Finally, invite students to revise their work based on their partner’s feedback. Encourage them to use evidence to improve the justification for their argument.”
Instructional Routine: Five Framing Questions supports students in analyzing a work sample, mathematical argument, or solution strategy by guiding them through progressive stages of discovery. Implementation Guide, Mathematical Language Routines, Procedures, states, “Present work to be analyzed. Invite students to analyze the work or solution strategy presented by using a sequence of framing questions. To begin, ask the following: Notice and Wonder: What do you notice about this work? From your observations, what do you wonder? Organize: What steps did this student take? How do you know? Advance the discussion to focus on a specific strategy or feature and encourage student thinking that makes connections to a particular lesson objective or concept. Reveal: Let’s focus on [strategy/feature]. Where do you see that in this work? Distill: What difference does [strategy/feature] make in this work? Know: How is [strategy/feature] helpful to [lesson objective/concept]?
Throughout the Teach book, different types of instructional guidance appear in the margins. Notes provide information about facilitation, differentiation, and coherence. Sample Solutions are examples of solutions to problems students engage with during the lesson, including those in the Practice section. These are only sample solutions; teachers are encouraged to accept accurate responses, reasonable explanations, and equivalent answers.
Materials include and reference the role of the standards in the program. Achievement Descriptors (ADs) are descriptions that detail what students should know and be able to do based on the instruction. ADs are written by using portions of mathematical content standards to form a clear, concise description of the work covered in each module. The Achievement Descriptors, found underneath the module resources, identify which standards are being measured in each lesson/topic. The module overview provides a description and explanation of skills covered in each topic. The lesson overview includes content standards addressed in the lesson. Additionally, each module has its own set of ADs, and the number of ADs varies by module. Taken together, the sets of module-level ADs describe what students should accomplish by the end of the year. ADs and their proficiency indicators support teachers with interpreting student work. Correlation information and explanations are present for the mathematics standards addressed throughout the grade level in the context of the series.
Each module has its own set of ADs, and the number of ADs varies by module. Taken together, the sets of module-level ADs describe what students should accomplish by the end of the year. Each lesson identifies the ADs aligned with that lesson in the Achievement Descriptors Overview section. The Achievement Descriptors align with grade-level expectations and support conceptual development and progression across standards.
Materials include and reference research-based strategies. The Grades 6-9 Implementation Guide, Works Cited, states, “A robust knowledge base underpins the structure and content framework of Eureka Math2. A listing of the key research appears in the Works Cited for each module.” Implementation, Knowledge Hub Resources, Education Research From Great Minds, states, “Learn about the Great Minds® approach to curricula, instructional design, supports for student learning, and building educator and student knowledge. Here you will find our foundational and efficacy research, white papers, and research briefs. If you are looking for district and school implementation and data stories, you can find those on our Case Studies page.” Also in the Implementation Guides, Mathematical Language Routines, “Eureka Math² features a set of instructional routines that optimize equity by increasing access, engagement, confidence, and students’ sense of belonging. Each routine aligns to the Stanford Language Design Principles to support sense‑making, optimize output, cultivate conversation, and maximize linguistic and cognitive meta-awareness.”
Indicator 3f
Materials provide a comprehensive list of supplies needed to support instructional activities.
The materials reviewed for Eureka Math² Grade 6 through Grade 8 meet expectations for providing a comprehensive list of supplies needed to support instructional activities.
Each module and individual lesson identify materials needed by teachers and students. Lesson Preparation identifies materials teachers need to create or assemble in advance. Each module also includes an overview of materials recommended for a class of 24 students. A numerical identifier in parentheses indicates the suggested quantity of each material.
Examples include:
Grade 6, Module 3, Topic D, Lesson 16, Teach Book, Materials states, “Teacher: None, Student: Coordinate Plane removable.” Lesson Preparation states, “Have students tear out the Coordinate Plane removable and place it into their personal whiteboards.”
Grade 7, Module 6, Topic A, Lesson 3, Teach Book, Materials states, “Teacher: Small paper cup. Students: Colored pencils (1 each of blue, red, purple, green, and yellow per student pair), Small paper cup (1 per student pair). Lesson Preparation: None.”
Grade 8, Module 2, Topic A, Lesson 3, Teach Book, Materials states, “Teacher: Translation or Reflection Cards (1 set), Transparency film. Students: Translation or Reflection Cards (1 set per student pair), Transparency film, Sticky notes (2 per student pair), Straightedge.” Lesson Preparation states, “Copy and cut out the Translation or Reflection Cards (in the teacher edition). Prepare enough sets for 1 per student pair and 1 for display during discussion.”
Indicator 3g
The assessment system provides consistent opportunities to determine student learning throughout the school year. The assessment system provides sufficient teacher guidance for evaluating student performance and determining instructional next steps.
The materials reviewed for Eureka Math² Grades 6 through Grade 8 meet expectations for providing consistent opportunities to determine student learning throughout the school year. The assessment system provides sufficient teacher guidance for evaluating student performance but provides limited guidance for interpreting student performance and determining instructional next steps.
The assessment system provides multiple opportunities to determine student learning throughout the school year and provides guidance for teachers to evaluate and interpret student performance. The materials provide teachers with an observational assessment recording sheet to document assessment proficiency. Implementation Guide, Resources, Achievement Descriptors: Proficiency Indicators, “Achievement Descriptors (ADs) are standards-aligned descriptions that detail what students should know and be able to do based on instruction they receive. The number of ADs addressed in each lesson varies depending on the content. This resource includes proficiency indicators for each AD. Proficiency indicators are descriptions of work that is partially proficient, proficient, or highly proficient. Proficiency indicators help you assess your students’ level of proficiency.” The Implementation Guide, Assessment at a Glance, Eureka Math² Assessment System at a Glance, identifies the assessment components, provides details about each component, and identifies where each component appears in the materials. The assessment system provides guidance for evaluating and interpreting student performance through Scoring Guides for Module Assessments and Topic Quizzes.
Examples include:
Grade 6, Module 6, Module Assessment, Version 2, Problem 2, Part D states, “Which is the more appropriate measure of variability: the mean absolute deviation or the interquartile range? Explain.” Student response includes the following components: Reasoning: 1 point. The student correctly identifies that the interquartile range is the better descriptor. Reasoning: 1 point. The student correctly justifies their response.10. The interquartile range is the more appropriate measure of variability. The data distribution is skewed to the right. This tells me that the median is a more appropriate measure of center than the mean and the interquartile range is a more appropriate measure of variability than the mean absolute deviation.
Grade 7, Module 1, Topic C, Topic Assessments, Version 1, Problem 5 states, “A scale drawing of a parking lot is shown. In the drawing, 1 inch represents 4 feet of the actual parking lot. What is the area of the actual parking lot? A. 16 square feet B. 180 square feet C. 720 square feet D. 1,024 square feet.” Sample solution states, “Distractor rationale: A. Incorrect. The student may have calculated the actual area represented by 1 square inch in the drawing but did not attend to the area within the entire figure. B. Incorrect. The student may have multiplied the area of the scale drawing in square inches by 4, rather than by the square of 4, before changing the units from square inches to square feet. C. Correct. D. Incorrect. The student may have composed the region into a rectangle and used the overall length (8 inches) and overall width (8 inches) to calculate the area.”
Grade 8, Module 2, Module Assessment, Version 2, Problem 2 states, “Figure ABCD, PQ, and line 𝓂 are shown in the diagram. Figure A″B″C″D″ is the image of figure ABCD under the following sequence of rigid motions. Translation along PQ⟶Reflection across the line. Which diagram shows figure ABCD and its correct image, figure A″B″C″D″ ?” Sample Solution states, “A. Incorrect. The student may have applied only the reflection. B. Correct. C. Incorrect. The student may have applied the reflection first and then translated along a ⟶vector other than PQ.”
The assessment system provides limited guidance for interpreting student performance and determining instructional next steps. The materials provide a general process for responding to assessment results by directing teachers to Proficiency Indicators and lessons associated with Achievement Descriptors. In the Implementation Guide, Assessment, Respond to Student Assessment Performance, “Proficiency indicators increase in cognitive complexity from partially proficient (PP) to proficient (P) to highly proficient (HP). If a student has difficulty with content of the P indicator of a given AD, follow up with the student by revisiting the content at the PP indicator of the same AD as shown in the AD proficiency indicator charts. Select the class standards report from the digital platform. Filter by proficiency indicator and any individual or group of assessments. When the report indicates proficiency of an AD has not been met, refer to the module’s Achievement Descriptors: Proficiency Indicator resource and use the lower‑complexity task to build toward full understanding. Use the examples provided with the Proficiency Indicator(s) as the basis for responsive teaching. Example: For students who do not meet the Proficient indicator (6.Mod1.AD1.P), consider focusing on the Partially Proficient indicator (6.Mod1.AD1.PP). In this case, strengthen students' foundational understanding of identifying ratios that describe relationships between two quantities to build toward proficient understanding with writing and explaining ratios that describe relationships between two quantities.”
While the materials identify resources teachers can revisit based on assessment results, they do not consistently provide specific instructional responses based on students’ demonstrated errors, misconceptions, or levels of understanding. Teachers must determine which lesson guidance or practice problems to use to address identified student needs. Therefore, the materials provide guidance for determining instructional next steps, but the guidance is not consistently sufficient across the assessment system.
Indicator 3h
This is not an assessed indicator in Mathematics.
Indicator 3i
This is not an assessed indicator in Mathematics.
Criterion 3.2: Student Supports
Information on Multilingual Learner (MLL) Supports in This Criterion
For some indicators in this criterion, we also display evidence and scores for pair MLL indicators.
While MLL indicators are scored, these scores are reported separately from core content scores. MLL scores do not currently impact core content scores at any level—whether indicator, criterion, gateway, or series.
To view all MLL evidence and scores for this grade band or grade level, select the "Multilingual Learner Supports" view from the left navigation panel.
Materials are designed for each child’s regular and active participation in grade-level/grade-band/series content.
The materials reviewed for Eureka Math2 Grade 6 through Grade 8 meet expectations for Student Supports. The materials provide strategies to ensure that students in special populations can access grade-level content and meet or exceed grade-level standards. They offer regular extensions and opportunities for advanced students to engage with mathematics at greater depth. Across the series, the materials include varied approaches to learning tasks and offer multiple ways for students to demonstrate their understanding, along with opportunities for self-monitoring. Teachers are supported with strategies for using varied grouping methods. The materials provide a range of representations of people and include guidance and support for educators to incorporate and build upon students’ cultural, social, and community backgrounds to enrich learning experiences. Manipulatives, both virtual and physical, accurately represent mathematical concepts and, when appropriate, are connected to written methods. The materials partially provide assessments that include accommodations that allow students to demonstrate their knowledge without altering the content and some supports are included for varying reading levels to ensure accessibility.
Indicator 3j
Materials provide strategies and support for students in special populations to work with grade-level content and meet or exceed grade-level standards, which support their regular and active participation in learning.
The materials reviewed for Eureka Math² Grades 6 through Grade 8 meet expectations for providing strategies and support for students in special populations to work with grade-level content and meet or exceed grade-level standards, which support their regular and active participation in learning.
The materials provide differentiation strategies and scaffolds throughout the program to support students in accessing grade-level mathematics. The Implementation Guide, Instructional Supports, explains that the Teach books include instructional guidance in the margins that provides information about facilitation, differentiation, and coherence. Instructional Supports, Differentiation, states, “Differentiation suggestions provide targeted ways to help meet the needs of specific learners based on your observations or other assessments. There are two types of suggestions: support and challenge. Use these to support students in the moment or to advance learning for students who are ready for more of a challenge.”
The materials also incorporate Universal Design for Learning (UDL) principles to address learner variability through multiple means of engagement, representation, and action and expression. The Implementation Guide explains, “Universal Design for Learning (UDL) is a framework based on current research from cognitive neuroscience that recognizes learner variance as the norm rather than the exception.... Although the concept of UDL has roots in special education, UDL is for all students. When instruction is designed to meet the needs of the widest range of learners, all students benefit. Eureka Math² lessons are designed with these principles in mind.”
Examples include:
Grade 6, Module 1, Topic E, Lesson 25, Teach Book, Learn, Differentiation: Support states, “For extra practice or to solidify understanding of finding a different percent before finding the whole, have students complete the following problem before they work problem 3. Kayla has 12 red balloons. If this is 75% of the total number of balloons she has, what is the total number of balloons Kayla has?”
Grade 7, Module 4, Topic D, Lesson 20, Teach Book, Learn, Differentiation: Support states, “If students find it difficult to calculate the surface area by looking at the pyramid, move them forward by having them create a net for the pyramid.”
Grade 8, Module 4, Topic F, Lesson 26, Teach Book, Learn, Differentiation: Support states, “Consider supporting students in understanding the context by first creating a table that represents the money Mr. Adams spends for each visit to the park.”
Indicator 3k
Materials regularly provide extensions and/or opportunities for advanced students to engage with grade-level/course-level mathematics at greater depth.
The materials reviewed for Eureka Math² Grades 6 through Grade 8 meet expectations for regularly providing extensions and/or opportunities for advanced students to engage with grade-level/course-level mathematics at greater depth.
The materials regularly provide differentiation opportunities that challenge students to engage more deeply with grade-level mathematics through alternative problems and extended applications. According to the Implementation Guide, Instructional Supports, “Throughout your Teach book, you will find different types of instructional guidance that appear in the margins. These notes provide information about facilitation, differentiation, and coherence.” The Implementation Guide, Differentiation, suggestions provide targeted ways to help meet the needs of specific learners based on your observations or other assessments. There are two types of suggestions: support and challenge. Use these to support students in the moment or to advance learning for students who are ready for more of a challenge.
Examples include:
Grade 6, Module 3, Topic B, Lesson 6, Teach Book, Learn, Differentiation: Challenge states, “For students who need an additional challenge, consider providing the following problem instead of problems 2 and 3. Alternatively, provide a list of numbers that does not include any integers, similar to the following list.”
Grade 7, Module 5, Topic C, Lesson 10, Teach Book, Learn, Differentiation: Challenge states, “Challenge students who finish early to solve a problem such as the following in which they must determine the original amount from the percent increase and the new amount: This Saturday, Maya sets up her taco truck at a concert. She has 189 customers, which is an 80% increase from the number of customers she had last Saturday. How many customers did Maya have last Saturday?”
Grade 8, Module 4, Topic F, Lesson 26, Teach Book, Learn, Differentiation: Challenge states, “Have students find the number of weeks it takes for Lily to have $10,000 in savings. Some students might think that doubling the time will double the savings, but at 48 weeks Lily has saved only $9740. It takes two more weeks for her to save $10,140.”
Indicator 3l
Materials provide varied approaches to learning tasks over time and variety in how students are expected to demonstrate their learning with opportunities for students to monitor their learning.
The materials reviewed for Eureka Math2 Grades 6 through Grade 8 provide varied approaches to learning tasks over time and variety in how students are expected to demonstrate their learning with opportunities for students to monitor their learning.
Students engage with problem-solving in a variety of ways within a consistent lesson structure: Fluency, Launch, Learn, Land. According to the Implementation Guide, Lesson Structure, “Each lesson is structured in four sections: Fluency, Launch, Learn, and Land. Lessons are designed for one 45-minute instructional period. Fluency provides distributed practice with previously learned material. It is designed to prepare students for new learning by activating prior knowledge and bridging small learning gaps. Launch creates an accessible entry point to the day’s learning through activities that build context and often create productive struggle that leads to a need for the learning that follows. Every Launch ends with a transition statement that sets the goal for the day’s learning. Learn presents new learning related to the lesson objective, usually through a series of instructional segments. This lesson component takes most of the instructional time. Suggested facilitation styles vary and may include direct instruction, guided instruction, group work, partner activities, interactive video, and digital elements. Land helps you facilitate a brief discussion to close the lesson and provides students with an opportunity to complete the Exit Ticket. In the Debrief portion of Land, suggested questions, including key questions related to the objective, help students synthesize the day’s learning. The Exit Ticket provides a window into what students understand so that you can make instructional decisions.”
Examples include:
Grade 6, Module 2, Topic D, Lesson 15, Teach Book, Learn, students work together to complete problems and perform error analysis. “...have students remain in their groups of 3 and direct them to problems 4–7. Assign one problem to each group, and assign part (a), (b), or (c) to each student in the group. Instruct group members to find the product for their assigned part. Once all three group members find the product for their assigned parts, have them add their products. If the sum does not match the target sum shown for that problem, instruct group members to work together to find and correct any mistakes in each other’s work. If groups finish early, direct them to complete as many problems as they can, as time permits.”
Grade 7, Module 3, Topic D, Lesson 21, Teach Book, Launch, students participate in a whole-class activity to sort values of x based on whether they produce a larger perimeter. Teacher Notes state, “In case most students post 7 as a value of x that produces a larger perimeter and 5 as a value of x that does not produce a larger perimeter, consider having a variety of values written on sticky notes to be added to the Larger and Not Larger portions of the chart. Before placing each value in a portion of the chart, ask students where that value belongs.”
Grade 8, Module 4, Topic B, Lesson 8, Teach Book, Learn, students work in pairs on a card sort activity. “Students solve and compare the structure of linear equations with only one solution, infinitely many solutions, and no solution. Have students work in pairs on the card sort activity. Distribute one set of Linear Equations cards to each pair. Have students review the cards, identify relationships among them, and then sort them into three groups. Encourage students to use the space in their book for work. Tell students they should be prepared to describe their groups to the class.”
Students have opportunities to share their thinking, to demonstrate changes in their thinking over time, and to apply their understanding in new contexts. For example:
Grade 6, Module 4, Topic E, Lesson 24, Teach Book, students represent real-world relationships with graphs and equations in the form y=x-b. “When most students are finished, bring the class together. Ask the following questions to discuss Riley’s lemonade stand. What are the independent and dependent variables in the lemonade stand situation? Explain. Why is the relationship between the number of cups of lemonade sold and the profit a non–ratio relationship? Why do you think Riley does not have a profit until she sells 9 cups of lemonade? What kinds of costs might Riley have when operating a lemonade stand? Should the points on the graph representing Riley’s profit be connected? Explain. The equation y=x−8 represents the relationship between the profit y in dollars and the number of cups of lemonade sold x. What is the coefficient of x? What is its
meaning in this situation? In the equation, what does it mean to subtract 8 from the number of cups of lemonade sold? Invite students to share how they determined which equation represents the table in problem 5. Highlight the strategy of substituting every pair of values from the table into each equation for d and c and evaluating to determine whether the values make a true number sentence.”
Grade 7, Module 3, Topic B, Lesson 10, Teach Book, Learn, students work in pairs to solve angle relationship problems, check their answers using an answer key, identify and correct errors, and reflect on the challenges they encountered and the strategies they used to correct their mistakes. “Have students work in pairs on problems 3-7. Place an answer key in an easily accessible location. Tell students to use the answer key to check their answer to each problem in the set. If students answer correctly, have them move on to the next problem. If they answer incorrectly, have them return to the problem and attempt to find and correct their errors. Facilitate a class discussion by using the following prompts. Are these problems more challenging than some of the other angle relationship problems we have encountered in this topic? If so, how? When you checked your answers and reviewed your work, did you find that you had made errors? If so, how did you correct your mistakes?”
Grade 8, Module 1, Topic B, Lesson 7, Teach Book, Problems 1-6, students use the properties of exponents for positive whole-number exponents and exponents of 0. The teacher directions state, “Reinforce this new definition with a Whiteboard Exchange. Present the following problems and ask students to rewrite each expression by using the exponent properties and definition of the exponent of 0. Students independently solve on the white side of their whiteboards. Students turn their whiteboards over, red side up, when finished (“Red when Ready”). Students show their work, and the teacher gives quick, individual feedback.” The Universal Design for Learning: Engagement side note states, “Offer feedback that emphasizes the importance of finding and understanding errors. For example, discuss specific actionable steps that students might take the next time they encounter a similar problem to help avoid making errors. Consider sharing questions that students may ask themselves as they prepare to solve a similar problem. How have I solved problems like this before when I needed to apply the properties of exponents? How have I solved problems like this before when there is an exponent of 0?”
Indicator 3m
Materials provide opportunities for teachers to use a variety of grouping strategies.
The materials reviewed for Eureka Math2 Grades 6 through Grade 8 provide opportunities for teachers to use a variety of grouping strategies.
The teaching support within each chapter and lesson features whole-class, small-group, and paired collaborations, as well as independent work time that includes reflection. The Fluency segments are usually a balance of whole-class and independent activities. The Launch segment often includes a whole-class discovery, while Learn segments include explicit instruction for both the whole class and small groups. The Land segment gives students the opportunity to analyze and synthesize their individual learning through whole-class discussion. Problem Sets and Practice can be completed independently or in structured groupings based on student needs.
Mathematical Language Routines offer multiple grouping strategies that provide a structure for facilitating different types of student interactions, including paired, small-group, and whole-class. Margin notes embed support and scaffolding suggestions that engage students in collaboration. They also include specific recommendations to align grouping strategies to different needs.
For example:
Grade 6, Module 4, Topic E, Lesson 24, Teach Book, Launch states, “Divide students into groups of 4 and then divide each group of 4 into pair A and pair B. Use the Co–construction routine to have pairs create a situation that could be represented by the graph. Have pair A use graph A and pair B use graph B. Tell students to be prepared to verbally describe the situation and the labels and numbers on each axis to another group. Give pairs 2 minutes to compare the contexts they created with the other pair in their group.”
Grade 7, Module 3, Topic C, Lesson 14, Teach Book, Problem 1 states, “During a scavenger hunt activity, students work with a partner to solve equations in order to find letters that they unscramble to solve a riddle. The structure of the activity allows students to develop self-checking strategies and routinely reflect on their solution pathways with classmates.” In the Learn section, students can work individually or with partners to solve linear equations on posters around the classroom. Students use the solutions to the equations to find the next poster. “Consider having students complete this activity with a partner.”
Grade 8, Module 6, Topic C, Lesson 14, Teach Book, Launch states, “Have students think–pair–share about the following question. What do you notice about the association between fuel efficiency and the independent variable?” After a whole-class discussion, students complete Problem 1 independently. “Have students complete problem 1 independently. Then have them compare their predictions with a partner.”
Indicator 3n
Assessments offer accommodations that allow students to demonstrate their knowledge and skills without changing the content of the assessment.
The materials reviewed for Eureka Math2 Grade 6 through Grade 8 partially offer accommodations that allow students to demonstrate their knowledge and skills without changing the content of the assessment.
Materials provide three analogous versions of each Topic Quiz and two analogous versions of each Module Assessment. According to the Implementation Guide, “Analogous versions target the same material at the same level of cognitive complexity. However, typical items on analogous versions are not clones of the original version. Use the analogous versions to give retakes, with reteaching or additional practice between takes, until students score proficient or above.” The materials provide the analogous versions for retakes rather than as accommodations for accessing assessments.
Implementation Guide, Assessment, Exit Tickets, provides teachers with guidance for determining when to extend the allotted time for students to complete Exit Tickets. “Exit Tickets are short, paper-based assessments that close lessons. These assessments use at least one problem, question, or writing prompt to assess whether a student has learned the basic skills and concepts needed for success in upcoming lessons. Items reflect the minimum that students must demonstrate to meet the lesson objectives. You may look for evidence of the mathematical practice identified as the focus practice for the lesson in student work on the Exit Ticket. In a typical classroom, most students with basic understanding can finish within 3-5 minutes. In some settings, honoring the timeframe is more important than requiring students to finish. For example, a student’s inability to finish within 5 minutes may be valuable information. In other settings, you may extend the time to allow all students to finish as appropriate. Exit Tickets are not graded. They are paper-based so that you can quickly review and sort them. Occasionally, an alternative assessment activity may substitute for an Exit Ticket at the end of a lesson.”
Indicator 3o
Materials provide a range of representation of people and include detailed instructions and support for educators to effectively incorporate and draw upon students’ different cultural, social, and community backgrounds to enrich learning experiences.
The materials reviewed for Eureka Math2 Grade 6 through Grade 8 provide a range of representations of people and include detailed instructions and support for educators to effectively incorporate and draw upon students’ different cultural, social, and community backgrounds to enrich learning experiences.
For example:
Grade 6, Module 3, Topic A, Lesson 4, Teach Book, Launch states, “Students explore why the ancient Chinese and Indians needed negative numbers. Around 200 BCE, Chinese merchants bought and sold animals. The merchants subtracted the money they spent buying animals from the money they received selling animals. They called the amount of money that was left over a surplus. Around 620 CE, merchants in India called the amount of leftover money a fortune. The merchants kept a record of the fortunes after buying and selling animals.” The Teacher Note states, “This lesson provides an ideal time to incorporate the material in the Math Past resource. The Math Past resource includes more information about the history of negative numbers as they were developed in different cultures, including a more detailed explanation of Chinese counting rods. If students are interested in further study of the history of negative numbers, consider incorporating other activities provided in the Math Past resource.”
Grade 7, Module 3, Topic C, Lesson 11, Teach Book, Launch states, “The following text, which has been translated into English, first appeared in an Egyptian mathematical papyrus that is now housed in a museum in Moscow, Russia. After students have analyzed the two problems, take a poll of which method they prefer. Ask volunteers to elaborate on why they chose that method. Which method do you prefer? The Egyptian rhetorical style or the modern symbolic style? Why do you prefer that method? Provide students with some more information about these styles of writing and solving problems and frame the learning of the lesson. For thousands of years, rhetorical style remained the only style for writing mathematics, not just in Egypt but in every civilization. Symbolic style first appeared in print in 1526 with the symbols for the plus sign, subtraction sign, and equal sign. From there, the symbolic style evolved to avoid tedious repetition of words. Today, we will solve a problem from real life. These problems are usually described in words, not in mathematical symbols. Your group must decide how to solve the problem.”
Grade 8, Module 1, Topic A, Lesson 3, Teach Book, Launch, states, “Archimedes was a prominent Greek mathematician. He lived in Sicily during the third century BCE and was credited with the development of several concepts in geometry, calculus, and physics. Fascinated by very large numbers and living on the coast of the Ionian Sea, Archimedes set out to determine how many grains of sand are needed to fill the known universe. Consider engaging students in a discussion by using the following questions: Would finding the number of grains of sand needed to fill the known universe be an interesting quest in Archimedes’s day? How many grains of sand do you think are needed to fill the universe? What is a number that is too high? Too low?”
Throughout the program, illustrations of hands used for counting include different skin shades, and illustrations of students and adults represent people with different appearances and abilities. The materials provide teachers with instructions and resources for incorporating and drawing upon students’ cultural, linguistic, family, and community knowledge and experiences during instruction. Math Past resources situate mathematics within historical and cultural contexts and provide examples of how people from different cultures and communities developed and used mathematics. The Additional Resources include a Culturally Responsive Teaching Resource with resources for teachers and leaders, including Valuing Students’ Assets and Knowledge, Creating a Culture of High Expectations for All Students, Communicating and Collaborating with Students and Families, Empowering Students as Agents of Change, and Supporting Culturally Responsive Teachers.
Examples include:
Introduction to the Culturally Responsive Teaching Resource Video: this video states, “A culturally responsive approach is not a checklist, a set of strategies, or found only in the pages of a curriculum. It's a combination of many important elements –anchored first and foremost in our beliefs and mindsets. It's about the relationships we build with students and families . . . the community we create within the classroom, the high expectations we hold for all students, and the instructional practices we embrace. When we take a culturally responsive approach, we invest in getting to know ourselves and our students, so that we can honor and sustain the ways of knowing and being that our students bring to the classroom. The videos in this resource explore four tenets that include these important elements: Valuing students' assets and knowledge; Creating a culture of high expectations for all students; Communicating and collaborating with students and families; and Empowering students as agents of change. Collectively, these tenets can provide a framework for implementing a culturally responsive approach to teaching. The videos can be accessed in any order and used flexibly. You may choose to collaborate with other teachers or explore these videos independently.”
Video Companion for Leaders: This PDF shares information with leaders on the different video series. It states, “Valuing Students’ Assets and Knowledge Video, What Teachers Will Learn, Why it’s important to uncover their own potential biases. How they can identify and leverage students’ knowledge, experience, and interests to make lessons relevant. How to Support Teachers’ Learning. Regularly reflect to develop self-awareness and actively uncover your own biases. Build the staff’s capacity to engage in conversations about equity by collaboratively setting expectations and agreeing on community norms. Highlight what’s working by asking teachers how they’ve been able to make learning more relevant. During professional learning time, prioritize colleagues sharing their success.
Video Companion for Teachers: This PDF shares information with teachers on the different video series. It states, “QUESTIONS FOR CONSIDERATION, Why should we reflect on our own experiences and biases? How can we better understand and use the funds of knowledge that our students bring to the classroom? Key Takeaways: Culturally responsive teaching is an asset-based pedagogy. Identifying and reframing bias or deficit thinking helps uncover student assets. Student strengths can include funds of knowledge from home and prior math knowledge. Surveys, family nights, and simply making notes when students share about their experiences are great ways to learn about their funds of knowledge. Connecting new content to prior knowledge and experiences supports learning and engagement. Eureka Math2 supports valuing students’ assets by making real-world connections, promoting engagement through the mathematical language routines, and leveraging students’ interests and experiences using engagement strategies in Universal Design for Learning margin notes.
Valuing Students’ Assets and Knowledge Video: This video states, “Culturally Responsive Teaching is one example of an asset-based pedagogy where students' experiences are seen as valuable resources that support connections to new knowledge. Culturally responsive teachers consider their own mindsets and reflect on their identities as a way to understand and identify potential biases. This type of self-reflection prepares us to welcome multiple aspects of student identities into classrooms. You can consider your layers of identity with a tool such as an Identity Wheel. This tool helps you think about the different aspects of your own identity and which aspects have the strongest effect on how you see yourself as a person, and how you perceive others. Engaging in this type of reflection helps you build awareness and reframe biased thinking. Creating a Culture of High Expectations for All Students Video: This video states, “Let's summarize how to create a culturally responsive math classroom where expectations are high, and the conditions are provided for students to experience success. Set high expectations and believe that all students can succeed. Ensure that all students are included in grade-level, cognitively demanding, rigorous instruction. Leverage the available scaffolds to ensure all students experience academic success. Now for some action steps, choose an upcoming lesson and study the sequence of learning. Consider each of your students and identify potential barriers to their success. Use suggestions in the lesson's margin notes and other recommended supports and scaffolds to minimize barriers to learning. If you haven't done so already, please download the video Companion.”
Communicating and Collaborating with Students and Families Video: This video states, “How do you build relationships with your students' families? In this video, let's consider two questions: why should we communicate in linguistically and culturally responsive ways, and how can we better involve families in the learning partnership? Then we'll explore a few ways to apply these ideas using Eureka Math Squared. Communication is an integral part of the learning process. Teachers who communicate in culturally and linguistically responsive ways honor and respect the cultures and home languages of students and their families. In a culturally responsive classroom, teachers encourage students to use their home language and view this as an asset. Using students’ home language can contribute to their academic success and emotional safety. When students feel comfortable, they can engage more fully in math instruction and discourse. Culturally responsive teachers understand that culture impacts communication styles. Students may demonstrate differences in verbal communication, such as in the way they participate in class discussions, and non-verbal communication, such as the use of eye contact and facial expressions. Appreciating and honoring diversity of communication styles ensures that all students and their families feel welcome and valued.
Empowering Students as Agents of Change Video: This video states, “When establishing a classroom culture, be curious and affirming of students' diverse identities. As teachers, it's important we take time to learn about students in and out of school, including their cultural, linguistic, and academic assets. This builds a foundation for bringing real-world issues that matter to them into discussions. Culturally responsive teachers welcome diversity of thought. They support students in listening, questioning to understand, and respectfully critiquing each other’s strategies and solutions. Practicing these skills with math content, such as when engaging in the construction of viable arguments and critiquing the reasoning of others, prepares students to engage in discussions of real-world contexts. This practice can build the foundation for discussions that might center around sensitive ideas involving injustice and the differences in opinion that may arise. Addressing students’ real-world concerns through Math will be a natural next step.
Indicator 3p
Materials provide supports for different reading levels to ensure accessibility for students.
The materials reviewed for Eureka Math2 Grade 6 through Grade 8 partially provide supports for different reading levels to ensure accessibility for students.
The Grades 6–9 Implementation Guide provides guidance for addressing readability and reducing reading barriers while maintaining grade-level mathematics. The Readability section states, “A student’s relationship with reading should not affect their relationship with math. All students should see themselves as mathematicians and have opportunities to independently engage with math text. Readability and accessibility tools empower students to embrace the mathematics in every problem. Lessons are designed to remove reading barriers for students while maintaining content rigor.” Improving Readability in Math Without Compromising Rigor states, “Some ways that Eureka Math² clears these barriers are by including wordless context videos, providing picture support for specific words, and limiting the use of new, non-content-related vocabulary, multisyllabic words, and unfamiliar phonetic patterns.”
Examples include:
Grade 6, Module 4, Topic A, Lesson 3, Teach Book, Learn, Teacher Note states, “In prior grades, students used the term expanded form to describe a number sentence that expresses the value of each digit in a number. For example, they wrote 432 as 4\times100+3×\times10+2\times1. In later grades, students use the term expanded form in other ways. As needed, clarify that, in this lesson, the expanded form of a number represents repeated multiplication by interpreting the exponent as repeated multiplication of the base.”
Grade 7, Module 3, Topic C, Lesson 11, Teach Book, Learn, Universal Design for Learning: Engagement states, “The domino tower video provides an interesting context for students to apply to writing and solving equations. After watching the video, students naturally generate questions about the context.”
Grade 8, Module 4, Topic F, Lesson 26, Tech Book, Learn, UDL: Representation states, “Presenting the water park problem in a video format supports students in understanding the problem context by removing barriers associated with written and spoken language.”
Materials do not identify multiple entry points to help struggling readers access and engage in grade-level mathematics.
Indicator 3q
Manipulatives, both virtual and physical, are accurate representations of the mathematical objects they represent and, when appropriate, are connected to written methods.
The materials reviewed for Eureka Math2 Grade 6 through Grade 8 meet expectations for providing manipulatives, both virtual and physical, that are accurate representations of the mathematical objects they represent and, when appropriate, are connected to written methods.
On the Implementation tab, Manipulatives & Instructional Tools, teachers can access multiple resources, including Manipulatives in Math, Interactive Virtual Manipulatives, and the Non-Didax Materials List.
Manipulatives are embedded across lessons and provide students with opportunities to use concrete representations of mathematical concepts and connect these representations to written methods.
Examples include:
Grade 6, Module 4, Topic A, Lesson 1, Teach Book, Learn, students use interlocking cubes to model expressions involving addition and subtraction. The lesson states, “Provide each student with 20 cubes. Have each student complete the following steps: Build a stack of 8 cubes. Add 7 more cubes to the stack. Write an expression on your whiteboard to represent how the number of cubes in the stack changed. Have students display their whiteboards and verify that they wrote 8+7. Then, ask students to add 2 cubes to the stack and revise the expression on their whiteboards to represent this change. Have students display their whiteboards and verify that they wrote 8+7+2.”
Grade 7, Module 6, Topic A, Lesson 2, Teach Book, Learn, Problem 2, students use a bag containing 20 cubes of various colors to investigate empirical probability. The lesson states, “You and your partner have 20 cubes that were randomly selected from a large bucket of cubes. These 20 cubes represent the outcomes of 20 trials in which a cube was randomly selected from the large bucket and then replaced.” Students use a data table to record the number of cubes of each color. After conducting multiple trials of the chance experiment and collecting data, students calculate the empirical probability of an event.
Grade 8, Module 3, Topic A, Lesson 2, Teach Book, Learn, students use transparencies and dry-erase markers to model dilations. The lesson states, “Ensure each student has a transparency and a dry-erase marker. Then direct students to problem 2. Model the use of the transparency as a tool to apply a dilation as students recreate your actions with their own transparency.”
Complete manipulative kits are available and include a set of math manipulatives for a class of 24 students, with supplemental kits available for purchase for an additional six students.
Criterion 3.3: Intentional Design
Materials include a visual design that is engaging and references or integrates digital technology, when applicable, with guidance for teachers.
The materials reviewed for Eureka Math2 Grade 6 through Grade 8 include or reference digital technology that provides opportunities for teachers and/or students to collaborate with each other, when applicable. The visual design supports student engagement with the content and is clear and organized without being distracting. The materials include or reference digital tools that facilitate collaboration among teachers or students. The materials partially integrate technology, including interactive tools, virtual manipulatives, and dynamic mathematics software, to engage students with grade-level standards.
Indicator 3r
Materials integrate technology such as interactive tools, virtual manipulatives/objects, and/or dynamic software in ways that engage students in the grade-level/series standards, when applicable.
The materials reviewed for Eureka Math² Grade 6 through Grade 8 partially integrate technology such as interactive tools, virtual manipulatives/objects, and/or dynamic software in ways that engage students in the grade-level/series standards, when applicable.
Digital technology and interactive tools are available through the Digital Platform. Digital interactives are primarily designed for teacher-facilitated use; however, teachers can send interactive slides to student devices for individual student interaction. The Digital Platform states, “Lessons that include digital interactives are authored so that while you demonstrate the digital interactive, students engage with the demonstrations as a class. Eureka Math² digital interactives help students see and experience mathematical concepts interactively. You can send slides to student devices in classroom settings where it feels appropriate to do so.” Teachers can also use Teacher View to send slides, monitor student progress, facilitate discussion, and view students’ activity individually or collectively. The materials do not provide student-facing data collection or modeling tools.
Digital tools support student engagement in mathematics. Materials incorporate digital interactives and context videos throughout the curriculum. Module Resources, Instructional Design & Curriculum Components, Digital Resources, state, “The digital platform provides seamless digital access to items in Teach and Learn. It also includes lesson slides, videos, digital interactives, assignments and assessments, implementation videos, asset-based teaching supports, and data science projects and activities.” Digital resources include fluency activities, videos, teacher-led interactives and demonstrations, images and text from Teach or Learn, and pages from Learn, including Classwork, removables, Problem Sets, and Exit Tickets.
The digital materials are fixed in format and cannot be customized for local use, including student or community interests.
Indicator 3s
Materials include or reference digital technology that provides opportunities for teachers and/or students to collaborate with each other, when applicable.
The materials reviewed for Eureka Math² Grade 6 through Grade 8 include or reference digital technology that provides opportunities for teachers and students to collaborate, when applicable.
The Implementation Guide recommends providing one device for each student pair when a lesson is designed to promote discussion and collaboration. Across the grade levels, digital lessons engage students in interactive mathematical investigations involving concepts such as rational numbers, expressions, geometry, probability, the Pythagorean theorem, similarity, and linear equations. Students use the technology to model situations, make predictions, test ideas, examine feedback, and develop mathematical conclusions.
Digital lessons provide opportunities for student-to-student collaboration as students work with partners, compare strategies, and discuss their reasoning. For example, students collaborate to model operations on a number line, construct geometric figures, investigate areas of polygons, describe outcomes of chance experiments, and compare mathematical representations. Students communicate their observations and explain their mathematical approaches while working with partners.
The Digital Lesson Teacher View provides opportunities for teacher-to-student interaction and facilitates mathematical discussion. Teachers can present lesson content, monitor all students’ screens or view individual student work, and move among Guidance, Monitoring, and Gallery modes. Teachers can also use pacing gates to prevent students from advancing, pause the class when needed, and create discussion points around a concept, strategy, or discovery.
The digital technology supports student-to-student and teacher-to-student collaboration.
Indicator 3t
The visual design (whether in print or digital) supports students in engaging thoughtfully with the subject, and is neither distracting nor chaotic.
The materials reviewed for Eureka Math² Grades 6 through 8 have a visual design, in both print and digital formats, that supports students in engaging thoughtfully with the subject and is neither distracting nor chaotic.
Eureka Math² incorporates a consistent visual design across student materials. A consistent organization across modules, topics, and lessons provides students and teachers with predictable locations for information. Learn Book pages follow the instructional sequence of Launch, Learn, and Land, while clearly labeled Exit Tickets, Recaps, and Practice pages communicate the purpose of each lesson component. Lesson Structure, “Each lesson is structured in four sections: Fluency, Launch, Learn, and Land. Lessons are designed for one 45-minute instructional period.” Lessons consistently present Fluency, Launch, Learn, and Land in the same sequence.
Module-level components include an Overview. Your Teach book begins with the Overview, a topic-by-topic summary that shows the development of learning throughout the module. It also provides connections to work done before and after the module, helping you understand the module’s place in the overall development of learning in and across the grade levels.” For example, Grade 8, Module 2, Overview states, “Coherence: Before This Module. Grade 6 Module 5, In grade 6, students learn to find the distance between two points with the same x- or y-coordinate. In grade 8, students find the distance between any two points in the coordinate plane. Grade 7 Modules 2, 3, and 5: Students expand on their grade 7 knowledge of supplementary, complementary, vertical, and adjacent angles by applying these angle relationships to angles formed by parallel lines cut by a transversal. Students explore the conditions that determine a unique triangle in grade 7 and apply these conditions to prove the converse of the Pythagorean theorem in grade 8. Coherence: After This Module Algebra I Module 3, In Algebra I, students apply rigid motions to describe transformations of functions and to graph functions in the coordinate plane. Geometry: In Geometry, students combine their knowledge of rigid motions and functions to recognize a rigid motion as a function of the plane. They also use the properties of translations, reflections, and rotations to justify triangle congruence theorems.” Modules also include lesson titles and objectives, as well as the why behind the lesson design.
Topic-level components include a Topic Overview. “Each topic begins with a Topic Overview that is a summary of the development of learning in that topic. It typically includes information about how learning connects to previous or upcoming content.” Topics also include a progression of lessons and an observational assessment recording sheet. For example, Grade 7, Module 3, Topic D, Lesson 20, Teach Book, “In this lesson, students find a more efficient way to solve inequalities. They explore whether the if–then moves used with equations also work with inequalities. Through examining different cases, students determine that adding or subtracting the same number on both sides of an inequality preserves a true inequality statement. However, students also determine that this does not always work for multiplication and division. Multiplying or dividing both sides of an inequality by a negative number does not preserve a true inequality statement. Students explore why this happens and determine that, in these cases, the inequality statements will remain true when the inequality symbol is reversed.”
Visual design is also consistent throughout the materials. “In the Teach book, color coding and other types of text formatting are used to highlight facilitation recommendations and possible statements, questions, and student responses. These are always suggestions and not a script. Each section includes a bold line of text that gives the purpose of that section. These purpose statements, taken together, support the overall objective of the lesson. Dark blue text shows suggested language for questions and statements that are essential to the lesson. Light blue text shows sample student responses. Bulleted lists provide suggested advancing and assessing questions to guide learning as needed. Text in magenta shows possible student responses. These responses appear only in the Teach book.” For example, in Grade 8, Module 1, Lesson 1, Teach Book, the bolded line of text states, “Write very large and very small numbers in a form that uses exponents to prepare students for scientific notation. Approximate very large and very small quantities.” The dark blue text states, “The Eiffel Tower is one of the objects from the demonstration and is approximately 300 meters high. First, we write 300 in unit form. What kind of units do we use to write a number in unit form?” The light blue text states, “We use place value units to write a number in unit form.”
Each Module includes a consistent layout of definitions found in the module that tells students and families that these terms are introduced in the module and to use the blank space to make notes and drawings. For example, Grade 6, Module 4, Module Resources, Student Terminology For Families, states, “additive identity, Because n+0=n for any number n, the number 0 is called the additive identity. (Lesson 19)”
Indicator 3u
Materials provide teacher guidance for the use of embedded technology to support and enhance student learning, when applicable.
The materials reviewed for Eureka Math2 Grade 6 through Grade 8 provide teacher guidance for the use of embedded technology to support and enhance student learning, when applicable.
Eureka Math² integrates digital resources with lesson materials and provides point-of-use guidance for their implementation. Notes in the Teach Books explain the purpose of lesson-specific interactives and provide guidance for how teachers can use them to support students’ understanding of mathematical concepts. Lesson-specific interactives include opportunities for students to use visual models, explore mathematical relationships, identify patterns, and solve problems, including interactives for dividing fractions with tape diagrams, determining unknown angle measures, and investigating relationships within polygons.
The Grades 6-9 Implementation Guide provides additional guidance for using the digital experience to facilitate mathematical discourse, provide opportunities for students to share their thinking, and give teachers information about student understanding. Additional implementation resources include virtual manipulatives, how-to videos, downloadable activities, and assessment and reporting guidance.