8th Grade - Gateway 3
Back to 8th Grade Overview
Note on review tool versions
See the series overview page to confirm the review tool version used to create this report.
- Our current review tool version is 2.0. Learn more
- Reports conducted using earlier review tools (v1.0 and v1.5) contain valuable insights but may not fully align with our current instructional priorities. Read our guide to using earlier reports and review tools
Loading navigation...
Usability
Gateway 3 - Meets Expectations | 88% |
|---|---|
Criterion 3.1: Teacher Supports | 9 / 9 |
Criterion 3.2: Assessment | 7 / 10 |
Criterion 3.3: Student Supports | 8 / 8 |
Criterion 3.4: Intentional Design |
The materials reviewed for Eureka Math² Grade 8 meet expectations for Usability. The materials meet expectations for Criterion 1, Teacher Supports; partially meet expectations for Criterion 2, Assessment; and meet expectations for Criterion 3, Student Supports.
Criterion 3.1: Teacher Supports
The program includes opportunities for teachers to effectively plan and utilize materials with integrity and to further develop their own understanding of the content.
The materials reviewed for Eureka Math² Grade 8 meet expectations for Teacher Supports. The materials: provide teacher guidance with useful annotations and suggestions for enacting the student and ancillary materials; contain adult-level explanations and examples of the more complex grade-level concepts and concepts beyond the current grade so that teachers can improve their own knowledge of the subject; include standards correlation information that explains the role of the standards in the context of the overall series; provide explanations of the instructional approaches of the program and identification of the research-based strategies; and provide a comprehensive list of supplies needed to support instructional activities.
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 order to guide their mathematical development.
The materials reviewed for Eureka Math2 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 that will assist teachers in presenting the student and ancillary materials. These are found in a variety of sections within the Implementation Guide, including the Overview, Why, Achievement Descriptors Overview, and Lesson Structure. Examples include:
Grade 6-9 Implementation Guide, Inside Teach, Module-Level Components, 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.”
Grade 6-9 Implementation Guide, Inside Teach, Module-Level Components, Why, “The Why 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, “The Achievement Descriptors: Overview section is a helpful guide that describes what Achievement Descriptors (ADs) are and briefly explains how to use them. It identifies specific ADs for the module, with more guidance provided in the Achievement Descriptors: Proficiency Indicators resource at the end of each Teach book.”
Grade 6-9 Implementation Guide, Inside Teach, Module-Level Components, 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. 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. This guidance can be found for teachers within boxes called Differentiation, UDL, and Teacher Notes. The Implementation Guide states, “There are six 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, five background information, or help 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:
Module 1, Topic A, Lesson 2: Comparing Large Numbers, Learn, Teacher Note, “Writing the factors of 10 helps make the division simpler by allowing students to pair factors of 10 in the numerator and denominator to create quotients of 1.”
Module 3, Topic C, Lesson 11: Similar Figures, Launch, Differentiation: Support, “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.”
Module 5, Topic B, Lesson 7: The Substitution Method, UDL: Action and Expression, “Consider providing access to the Equation Assistant interactive during this lesson. This interactive is meant to support students with efficiently and accurately rewriting equations in preparation for solving systems of equations with substitution.”
Indicator 3b
Materials contain adult-level explanations and examples of the more complex grade-level/course-level concepts and concepts beyond the current course so that teachers can improve their own knowledge of the subject.
The materials reviewed for Eureka Math2 Grade 8 meet expectations for containing adult-level explanations and examples of the more complex grade-level concepts and concepts beyond the current grade so that teachers can improve their own knowledge of the subject.
Materials consistently contain adult-level explanations, examples of the more complex grade/ course-level concepts, and concepts beyond the course within Topic Overviews and/or Module Overviews. According to page 7 of the Grade 6-9 Implementation Guide, “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.” Page 9 outlines the purpose of the 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.” Examples include:
Module 1: Scientific Notation, Exponents, and Irrational Numbers, Module Overview, Why, “Why are operations with numbers written in scientific notation in topics A and C? Topic A sparks students’ interest through engaging contexts that utilize their exponent and place value understanding. Having students write the many factors of 10 foreshadows and drives the need for the properties and definitions of exponents. In topic C, students become fluent in applying the properties and definitions of exponents by operating with numbers written in scientific notation. Why are exponential expressions written as 10^{5+2} and 3^{5\cdot4}? In lesson 5, the expression 10^5\cdot10^2 is intentionally shown as the equivalent expression 10^{5+2} to emphasize the use of the product of powers with like bases property. Writing 10^{5+2} has more instructional value than writing 10^7. When students are ready, ask them to express the sum of the exponents as an integer.”
Module 4: Linear Equations in One and Two Variables, Module Overview, Why, “Why do we say the value of the ratio? In rade 6, students learn that a ratio is an ordered pair of numbers that are not both zero. For a ratio A : B, the value of the ratio is the quotient \frac{A}{B} as long as B is not zero. Therefore, when students determine the slope of a line, they find the value of the height-to-base ratio of a slope triangle for the line.”
Module 6: Functions and Bivariate Statistics, Module Overview, Why, “The goal of introducing functions to students is to carefully connect prior knowledge so that students build new understanding as an extension of previous learning. In this module, students explore the connection of functions to average speed and linear relationships. Functions represent real-world situations, whether they be numeric or nonnumeric. Choosing to present functions in real-life contexts grounds students’ work with functions as a tool to understand the world around them.”
Indicator 3c
Materials include standards correlation information that explains the role of the standards in the context of the overall series.
The materials reviewed for Eureka Math2 Grade 8 meet expectations for including standards correlation information that explains the role of the standards in the context of the overall series.
The Achievement Descriptors, found in the Overview section, identify, describe, and explain how to use the standards. The lesson overview includes content standards addressed in the lesson. Additionally, a Proficiency Indicators resource at the end of each Teach book, helps assess student proficiency. Correlation information and explanations are present for the mathematics standards addressed throughout the grade level in the context of the series. Examples include:
Module 1: Scientific Notation, Exponents, and Irrational Numbers, Achievement Descriptors and Standards, “8.Mod1.AD1 Determine whether numbers are rational or irrational. (8.NS.A.1, 8.EE.A.2)”
Module 2, Topic D, Lesson 19: Using the Pythagorean Theorem and Its Converse, Achievement Descriptors and Standards, “8.Mod2.AD7 Explain a proof of the Pythagorean theorem and its converse geometrically. (8.G.B.6)”
Module 5: Percents and Application of Percent, “Students graph systems of linear equations in two variables, estimate the coordinates of the intersection point on the graph, and verify that the ordered pair is a solution to the system. They also analyze systems of linear equations to determine the number of solutions. Students find that estimating solutions from a graph is difficult for solutions composed of one or more fractional values. So they use the substitution method to write a system of linear equations in two variables as one linear equation in one variable. Now equipped with various solution methods, students are challenged to write and solve systems resulting from numerical, geometrical, historical, and real-world contexts.”
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.
Indicator 3e
Materials provide explanations of the instructional approaches of the program and identification of the research-based strategies.
The materials reviewed for Eureka Math2 Grade 8 meet expectations for providing explanations of the instructional approaches of the program and identification of the research-based strategies.
Materials explain the instructional approaches of the program. According to the Grades 6-9 Implementation Guide, “Eureka Math2 features a set of instructional routines that optimize equity by increasing access, engagement, confidence, and students’ sense of belonging. The following is true about Eureka Math2 instructional routines: Each routine presents a set of teachable steps so students can develop as much ownership over the routine as the teacher. The routines are flexible and may be used in additional math lessons or in other subject areas. Each routine aligns to the Stanford Language Design Principles (see Works Cited): support sense-making, optimize output, cultivate conversation, maximize linguistic and cognitive meta-awareness.” Examples of instructional routines include:
Instructional Routine: Always Sometimes Never, students make justifications and support their claims with examples and nonexamples. Implementation Guide 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 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 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.”
Materials include and reference research-based strategies. The Grades 6-9 Implementation Guide states, “In Eureka Math2 we’ve put into practice the latest research on supporting multilanguage learners, leveraging Universal Design for Learning principles, and promoting social-emotional learning. The instructional design, instructional routines, and lesson-specific strategies support teachers as they address learner variance and support students with understanding, speaking, and writing English in mathematical contexts. 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.”
Indicator 3f
Materials provide a comprehensive list of supplies needed to support instructional activities.
The materials reviewed for Eureka Math2 Grade 8 meet expectations for providing a comprehensive list of supplies needed to support instructional activities.
Each module and individual lesson contains a materials list for the teacher and student. The lesson preparation identifies materials teachers need to create or assemble in advance. Examples include:
Module 2, Topic A, Lesson 3: Reflections, Materials, “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: 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.”
Module 5: Systems of Linear Equations, Module Overview, Materials, “The following materials are needed to implement this module. The suggested quantities are based on a class of 24 students and one teacher. (1) Chart paper, tablet, (6) Construction paper, 12″ x 18″ sheets, (25) Dry-erase markers, (24) Grid paper, sheets, (24) Learn books, (1) Marker, (25) Pencils, (25) Personal whiteboards, (25) Personal whiteboard erasers, (1) Projection device, (96) Sticky notes, (25) Straightedges, (12) Student computers or devices, (1) Tape, transparent roll, (1) Teach book, (1) Teacher computer or device.”
Module 6, Topic B, Lesson 8: Comparing Functions, Materials, “Teacher: None. Students: Function Representations Match card. Lesson Preparation: Copy and cut out the Function Representations Match cards (in the teacher edition). Prepare enough cards so each student has one card.”
Indicator 3g
This is not an assessed indicator in Mathematics.
Indicator 3h
This is not an assessed indicator in Mathematics.
Criterion 3.2: Assessment
The program includes a system of assessments identifying how materials provide tools, guidance, and support for teachers to collect, interpret, and act on data about student progress towards the standards.
The materials reviewed for Eureka Math² Grade 8 partially meet expectations for Assessment. The materials identify the content standards assessed in formal assessments, but do not identify the mathematical practices for some of the formal assessments. The materials provide multiple opportunities to determine students' learning and sufficient guidance to teachers for interpreting student performance, but do not provide specific suggestions for following-up with students. The materials include opportunities for students to demonstrate the full intent of grade-level standards and mathematical practices across the series.
Indicator 3i
Assessment information is included in the materials to indicate which standards are assessed.
The materials reviewed for Eureka Math2 Grade 8 partially meet expectations for having assessment information included in the materials to indicate which standards are assessed. The materials identify the standards assessed for all of the formal assessments, but the materials do not identify the practices assessed for some of the formal assessments.
According to the Grade 6-9 Implementation Guide, Core Assessment Components, Exit Tickets (p. 47), “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 objective. You may look for evidence of the Standard for Mathematical Practice (MP) identified as the focus MP for the lesson in student work on the Exit Ticket.” Topic Quizzes (p. 48), “Typical Topic Quizzes consist of 4–6 items that assess proficiency with the major concepts from the topic. Many items allow students to show evidence of one or more of the Standards for Mathematical Practice (MPs). You may use the Standards and Achievement Descriptors at a Glance charts to find which MPs you may be more likely to see from your students on a given assessment item in relation to the content that is assessed. For example, you may be likely to see evidence of MP2 and MP8 on the Level 7 Module 1 Topic A Quiz as those are the MPs explicitly identified in the lessons of that topic.” Module Assessments (p.48), “Typical Module Assessments consist of 6–10 items that assess proficiency with the major concepts, skills, and applications taught in the module. Many items allow students to show evidence of one or more of the Standards for Mathematical Practice (MPs). You may use the Standards and Achievement Descriptors at a Glance charts to find which MPs you may be more likely to see from your students on a given assessment item in relation to the content that is assessed. Module Assessments represent the most important content, but they may not assess all the strategies and standards taught in the module.”
Additionally, within the Grade 6-9 Implementation Guide (pp. 52), Achievement Descriptors, Standards and Achievement Descriptors at a Glance, “Every module in grade 6 through Algebra 1 has a Standards and Achievement Descriptors at a Glance chart. These charts identify the location and show the frequency of the content standards, Standards for Mathematical Practice, and Achievement Descriptors (ADs) in each module.” Within the Proficiency Indicators section (p. 52), “Each AD has its own set of proficiency indicators. Proficiency indicators are more detailed than ADs and help you analyze and evaluate what you see or hear in the classroom as well as what you see in students’ written work. Each AD has up to three indicators that align with a category of proficiency: Partially Proficient, Proficient, or Highly Proficient. Proficiency Indicators use language that offers insights about which MPs may be observed as students engage with assessment items. For example, Proficiency Indicators that begin with justify, explain, or analyze likely invite students to show evidence of MP3: Construct viable arguments and critique the reasoning of others. Proficiency Indicators that begin with create or represent likely invite students to show evidence of MP2: Reason abstractly and quantitatively.”
The Standards and Achievement Descriptors at a Glance chart is provided within each grade level’s Implementation Resources, within the Maps section. “How to use the Standards and Achievement Descriptors at a Glance; Identity Where Content is Taught before Teaching” states, “The Standards and Achievement Descriptors at a Glance charts identify the location and show the frequency of the content standards, Standards for Mathematical Practice, and Achievement Descriptors (ADs) in each module.” While these documents align the MPs to specific lessons and corresponding Exit Tickets, the MPs are not identified within Topic Quizzes or Module Assessments. Examples include but are not limited to:
Module 1: Scientific Notation, Exponents, and Irrational Numbers, Topic C, Quiz 1, Item 4, “A technology company designs a phone that weighs about 0.068125 pounds. What is the weight of the phone rounded to the nearest hundredth pound? Enter your answer in scientific notation. (8.EE.A.3)”
Module 3: Dilations and Similar Figures, Module Assessment 1, Item 6, “A volleyball player hits the ball when it is h feet above the ground. The volleyball net is 8 feet tall. The ball lands 15 feet away from the base of the net, as shown. What is the height of the ball when the player hits it? (8.G.A.5)” The ball is shown landing 15 feet from the net with a hypotenuse of 20.825 feet.
Module 5: Systems of Linear Equations, Module Assessment 1, Item 6, “A bike rental company rents out scooters for $8.50 per day and bikes for $15.20 per day. On Tuesday, they rent out a combined total of 8 scooters and bikes. They make $101.50 for the rentals. How many scooters and bikes does the bike rental company rent on Tuesday? (8.EE.C.8.c)”
Module 6: Functions and Bivariate Statistics, Module Assessment 2, Item 2, “Sara goes for a two-day hike. She hikes for the first day and then camps for the night. The next morning she hikes at a constant speed. The table shows the number of hours Sara hiked on the second day and the total distance that she hiked in two days. Part A Enter an equation for a function that represents the total distance hiked y in miles when Sara has hikedx hours on the second day. Part B What do the initial value and the rate of change in your function represent? (8.F.B.4)”
Indicator 3j
Assessment system provides multiple opportunities throughout the grade, course, and/or series to determine students' learning and sufficient guidance to teachers for interpreting student performance and suggestions for follow-up.
The materials reviewed for Eureka Math2 Grade 8 partially meet expectations for including an assessment system that provides multiple opportunities throughout the grade, course, and/or series to determine students’ learning and sufficient guidance to teachers for interpreting student performance and suggestions for follow-up.
The assessment system provides multiple opportunities to determine students' learning, and sufficient guidance for teachers to interpret student performance is reinforced by the Proficiency Indicators. However, suggestions to teachers for following up with students are general and minimal, for example, “Look back at those lessons to select guidance and practice problems that best meet your students’ needs.” While teachers can refer back to specific lessons, it is incumbent on the teacher to determine which guidance and practice problems meet the needs of their individual students. Examples include:
Grade 6-A1 Implementation Guide, Resources, Achievement Descriptors: Proficiency Indicators (p. 15), “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.”
Grade 6-A1 Implementation Guide, Assessment, Standards and Achievement Descriptors at a Glance (pp. 52), “Every module in grade 6 through Algebra 1 has a Standards and Achievement Descriptors at a Glance chart. These charts identify the location and show the frequency of the content standards, Standards for Mathematical Practice, and Achievement Descriptors (ADs) in each module. Use these charts to quickly determine where and when standards and ADs are taught within and across modules to help you target observations. You may also use these charts in conjunction with assessment data to identify targeted ways to help meet the needs of specific learners. Use assessment data to determine which ADs and Proficiency Indicators to revisit with students. Use the examples provided with the Proficiency Indicator(s) as the basis for responsive teaching or use the modules’ Standards and Achievement Descriptors at a Glance chart to identify lessons that contain guidance and practice problems to support student follow up.”
Grade 6-A1 Implementation Guide, Assessment, Respond to Student Assessment Performance (p. 60), “After administering an assessment, use the assessment reports in the Analyze space of the Great Minds Digital Platform to view student performance by Achievement Descriptor (AD). Analyze the student-performance data and select one or both of the following methods to address learning needs.” Proficiency Indicators: “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 Student Performance report in the Analyze space of the Great Minds 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 (4.Mod1.AD1.P), consider focusing on the Partially Proficient indicator (4.Mod1.AD1.PP). In this case, strengthen student foundational understanding of creating one comparison statement to build towards proficient understanding with two comparison statements.”
Grades 6-A1 Implementation Guide, Assessment, The Standards and Achievement Descriptors at a Glance Charts (p. 61), “Select the Student Performance report in the Analyze space of the Great Minds 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 Standards and Achievement Descriptors at a Glance charts to identify lessons that teach the concepts of that AD. Navigate to those lessons to find guidance and practice problems to follow up with students. Example: If students struggle with 4.Mod1.AD1, use the Standards and Achievement Descriptors at a Glance chart to find that lessons 1, 2, 3, 4, and 6 address the AD. Look back at those lessons to select guidance and practice problems that best meet your students’ needs.”
The assessment system provides guidance to teachers for interpreting student performance within Scoring Guides for Module Assessments and Topic Quizzes. Examples include:
Module 2, Assessment 2, Item 1, “Consider the diagram. Which point is the image of point I under a dilation with center O and scale factor 3? A. F, B. G, C. H, D. J” Sample Solution states, “A. Incorrect. The student may have selected the point that is the image of point G under a dilation centered at O with scale factor 3. B. Incorrect. The student may have selected the point that is the same distance from O as I is from O. C. Incorrect. The student may have selected the point that is the image of point I under a dilation centered at O with scale factor \frac{1}{3}. D. Correct.”
Module 4, Topic D, Quiz 1, Item 3, “A line passes through the points (5, 4) and (2, -3). What is the slope of the line? A. \frac{7}{1} B. \frac{1}{7} C. \frac{3}{7} D. \frac{7}{3}” Sample Solution states, “A. Incorrect. The student may have added the y-values and the x-values instead of subtracting them and calculated the slope by using the formula m=\frac{x_2+x_1}{y_2+y_1}. B. Incorrect. The student may have added the y-values and the x-values instead of subtracting them. C. Incorrect. The student may have calculated the slope by using the formula m=\frac{x_2-x_1}{y_2}. D. Correct.”
Module 6, Topic B, Lesson 10: Graphs of Nonlinear Functions, Exit Ticket, “A car travels at a constant speed for a while and then comes to a stop at a red light. The light stays red for a few minutes. When the light changes to green, the car speeds up and then maintains a slightly faster constant speed. a. Sketch a graph of a function to match the description b. Identify whether the function is linear or nonlinear. How do you know?” Sample solution shows a graph of the function and states, “b. The function is nonlinear because the graph is not a line, so it cannot be the graph of a linear function.”
Indicator 3k
Assessments include opportunities for students to demonstrate the full intent of grade-level/course-level standards and practices across the series.
The materials reviewed for Eureka Math2 Grade 8 meet expectations for providing assessments that include opportunities for students to demonstrate the full intent of grade-level/ course-level standards and practices across the series.
Assessments identify standards and include opportunities for students to demonstrate the full intent of grade-level/course-level standards. Examples include:
Module 2, Module Assessment 1, Item 5, students use a digital applet to prove the Pythagorean theorem and explain their reasoning. “Part A: Rearrange the triangles to help prove the Pythagorean theorem. Drag the four triangles onto the blank square on the right. Part B: Explain how your rearrangement helps prove the Pythagorean theorem. (8.G.B.6)”
Module 4, Topic B, Quiz 1, Item 3, students solve linear equations. “Consider the equation 3(1.5x-0.75)-1=ax+b. The equation has infinitely many solutions. What are the values of a and b? The value of a is ____. The value of b is _____. (8.EE.C.7.a)”
Module 6, Topic C, Quiz 1, Item 1, students model real world data using a scatter plot. “Mrs. Banks coaches a softball team. She records the number of home runs batted in for each player. Create a scatter plot of the number of home runs and the number of runs batted in. (8.SP.A.1)”
Assessments do not identify mathematical practices in either teacher or student editions. Although assessment items do not clearly label the MPs, students are provided opportunities to engage with the mathematical practices to demonstrate full intent. Examples include:
Module 1, Module Assessment 2, Item 7, “Yu Yan knows that the value of \pi rounded to the nearest tenth is 3.1. She says the value of \sqrt{\pi}\approx1.76 because \sqrt{3.1}\approx1.76. Yu Yan enters \sqrt{\pi} into a computer program to check her answer. The program displays this number line. Part A: Based on the number line, what is the value of \sqrt{\pi} rounded to the nearest hundredth? Part B: Why is Yu Yan's value of \sqrt{\pi} different from the computer's value of \sqrt{\pi}? Justify your answer.” This item addresses MP3, construct viable arguments and critique the reasoning of others.
Module 3, Module Assessment 2, Item 6, “A table tennis player hits the ball when it is h inches above the table. The table tennis net is 6 inches tall. The ball lands 8 inches away from the base of the net, as shown. What is the height of the ball when the player hits it?” This item addresses MP2, reason abstractly and quantitatively.
Module 5, Topic C, Quiz 1, Item 1, “Eve's aunt is 7 years older than twice Eve's age. The sum of Eve's age and her aunt's age is 52. How old is Eve? How old is Eve's aunt?” This item addresses MP1, make sense of problems and persevere in solving them.
Indicator 3l
Assessments offer accommodations that allow students to demonstrate their knowledge and skills without changing the content of the assessment.
Criterion 3.3: Student Supports
The program includes materials designed for each student’s regular and active participation in grade-level/grade-band/series content.
The materials reviewed for Eureka Math² Grade 8 meet expectations for Student Supports. The materials provide: strategies and supports for students in special populations and for students who read, write, and/or speak in a language other than English to support their regular and active participation in learning grade-level mathematics; multiple extensions and/or opportunities for students to engage with grade-level mathematics at higher levels of complexity; and manipulatives, both virtual and physical, that are accurate representations of the mathematical objects they represent and, when appropriate, are connected to written methods.
Indicator 3m
Materials provide strategies and supports for students in special populations to support their regular and active participation in learning grade-level/series mathematics.
The materials reviewed for Eureka Math2 Grade 8 meet expectations for providing strategies and supports for students in special populations to support their regular and active participation in learning grade-level/series mathematics.
Materials provide strategies, supports, and resources for students in special populations to support their regular and active participation in grade-level mathematics. According to the Implementation Guide, “There are six types of instructional guidance that appear in the margins. These notes provide information about facilitation, differentiation, and coherence.” Additionally, “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. The guiding principles of the UDL framework are based on the three primary networks of the brain. 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:
Module 2, Topic B, Lesson 9: Ordering Sequences of Rigid Motions, Learn, Language Support, “Consider using the Talking Tool throughout this lesson to support student discussion by using the following examples. Ask students to use prompts from the Share Your Thinking section when discussing whether order matters in their given sequence of rigid motions. As students circulate for the gallery walk, consider directing students to use the Say It Again section to rephrase how other students describe whether the order matters in each sequence of rigid motions.”
Module 3, Topic A, Lesson 2: Enlargements, Learn, UDL: Representation, “Consider gesturing to the points when asking about the distance between O and P′ and the distance between O and P. This will connect the auditory cue to a visual cue for students.”
Module 4, Topic F, Lesson 26: Linear Equations from Word Problems, Learn, Differentiation: Support, “If the y-intercept’s meaning in this context is difficult for students to interpret, consider having them write the y-intercept point (0,140). Then have them interpret the x-value and y-value in this context.”
Indicator 3n
Materials provide extensions and/or opportunities for students to engage with grade-level/course-level mathematics at higher levels of complexity.
The materials reviewed for Eureka Math2 Grade 8 meet expectations for providing extensions and/or opportunities for students to engage with grade-level/course-level mathematics at higher levels of complexity.
Materials do not require advanced students to do more assignments than their classmates. Instead, students have opportunities to think differently about learning with alternative questioning, or extension activities. Specific recommendations are routinely highlighted as Teacher Notes within parts of each lesson, as noted in the following examples:
Module 2, Topic B, Lesson 7: Working Backward, Differentiation: Challenge, “For students who finish early, ask if they can find another rigid motion that maps a figure onto its image for problems 3 and 4.”
Module 6, Topic B, Lesson 8: Comparing Functions, Learn, Differentiation: Challenge, “Challenge students who finish early to create other representations for problems 1–4. Have them compare the written description, equation, graph, and table.”
Module 5, Topic A, Lesson 4: More Than One Solution, Learn, Differentiation: Challenge, “If pairs finish early, challenge them to write three of their own systems: one with only one solution, one with no solution, and one with infinitely many solutions.”
Indicator 3o
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.
Indicator 3p
Materials provide opportunities for teachers to use a variety of grouping strategies.
Indicator 3q
Materials provide strategies and supports for students who read, write, and/or speak in a language other than English to regularly participate in learning grade-level mathematics.
The materials reviewed for Eureka Math2 Grade 8 meet expectations for providing strategies and supports for students who read, write, and/or speak in a language other than English to regularly participate in learning grade-level mathematics.
Support for active participation in grade-level mathematics is consistently included within a Language Support Box embedded within parts of lessons. The Implementation Guide explains supports for language learners, “Multilingual learners, or learners who speak a language other than English at home, require specific learning supports for gaining proficiency with the English needed to access the mathematics. Research suggests that best practices for these learners include opportunities and supports for student discourse and for using precise terminology. In addition to precise domain-specific terminology, high-impact academic terminology that supports learners across learning domains is explicitly introduced and used repeatedly in various contexts to build familiarity and fluency across the grade levels. Eureka Math2 is designed to promote student discourse through classroom discussions, partner or group talk, and rich questions in every lesson.”
Examples include:
Module 2, Topic D, Lesson 22: On the Right Path, Learn, Language Support, “In addition to playing the video, consider supporting the context further by drawing on student experience. For example, show picture examples of each ride to facilitate a discussion about which ride might take up the greatest amount of total time based on the wait and ride times. Discuss and clarify possible assumptions needed to solve the problem, such as wait times remaining constant over the 1.5 hours or deciding whether to account for the time taken to get on and off a ride.”
Module 3, Topic B, Lesson 6: The Shadowy Hand, Learn, Language Support, “As groups discuss solution strategies, some students may benefit from additional support in the form of sample questions to drive group discourse. Consider providing the following examples for students to ask one another during group work time: What are we trying to find? What information do we need? What can we measure? What do we need to calculate?”
Module 4, Topic D, Lesson 15: Comparing Proportional Relationships, Learn, Language Support, “Students may benefit from support with the term steeper line. Consider displaying the graphs of two linear equations and discussing which line is steeper.”
Indicator 3r
Materials provide a balance of images or information about people, representing various demographic and physical characteristics.
Indicator 3s
Materials provide guidance to encourage teachers to draw upon student home language to facilitate learning.
Indicator 3t
Materials provide guidance to encourage teachers to draw upon student cultural and social backgrounds to facilitate learning.
Indicator 3u
Materials provide supports for different reading levels to ensure accessibility for students.
Indicator 3v
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 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.
Manipulatives provide accurate representations of mathematical objects. Examples Include:
Module 3, Topic A, Lesson 2: Enlargements, Learn, “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.”
Module 5, Topic B, Lesson 7: The Substitution Method, Learn, UDL: Action & Expression, “Consider providing access to the Equation Assistant interactive during this lesson. This interactive is meant to support students with efficiently and accurately rewriting equations in preparation for solving systems of equations with substitution.”
Module 6, Topic C, Lesson 13: Informally Fitting a Line to Data, Learn, “Students informally fit a line to data in a scatter plot. Direct students to work in pairs to complete problems 1(b)–(d). Allow for student choice in their approach to fitting a line to the data by providing access to a variety of tools, such as a ruler, a transparency, and uncooked spaghetti. 1. The scatter plot shows the sizes and prices of 16 houses for sale in a midwestern city. a. How much do you think the price of a 3000-square-foot house might be? Explain your reasoning. b. Draw a line in the scatter plot that you think fits the pattern of the data. c. Use your line to predict the price of a 3000-square-foot house. d. Use your line to predict the price of a 1500-square-foot house.”
Criterion 3.4: Intentional Design
The program includes 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 8 integrate technology such as interactive tools, virtual manipulatives/objects, and/or dynamic mathematics software in ways that engage students in the grade-level standards; include or reference digital technology that provides opportunities for teachers and/or students to collaborate with each other; have a visual design that supports students in engaging thoughtfully with the subject that is neither distracting nor chaotic; and provide teacher guidance for the use of embedded technology to support and enhance student learning.
Indicator 3w
Materials integrate technology such as interactive tools, virtual manipulatives/objects, and/or dynamic mathematics software in ways that engage students in the grade-level/series standards, when applicable.
Indicator 3x
Materials include or reference digital technology that provides opportunities for teachers and/or students to collaborate with each other, when applicable.
Indicator 3y
The visual design (whether in print or digital) supports students in engaging thoughtfully with the subject, and is neither distracting nor chaotic.
Indicator 3z
Materials provide teacher guidance for the use of embedded technology to support and enhance student learning, when applicable.