Eureka Math

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Overall Summary

The instructional materials for Eureka Grade 8 meet the expectation for alignment to the CCSS. In Gateway 1, the instructional materials meet the expectations for focus by assessing grade-level content and spending at least 65% of class time on the major clusters of the grade, and they are coherent and consistent with the Standards. In Gateway 2, the instructional materials reflect the balances in the Standards and help students meet the Standards’ rigorous expectations, and they partially connect the Standards for Mathematical Content and the Standards for Mathematical Practice.

Alignment
Meets Expectations
Usability
Partially Meets Expectations

Focus & Coherence

The instructional materials for Eureka Grade 8 meet the expectation for focusing on the major work of the grade and having a sequence of topics that is consistent with the logical structure of mathematics. The materials do not assess topics before the grade level indicated, spend at least 65% of class time on the major clusters of the grade, and are coherent and consistent with the Standards.

Gateway 1
Meets Expectations

Criterion 1.1: Focus

Materials do not assess topics before the grade level in which the topic should be introduced.

The instructional materials for Eureka Grade 8 meet the expectations for not assessing topics before the grade level in which the topic should be introduced. Overall, the materials assess grade-level content.

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The instructional material assesses the grade-level content and, if applicable, content from earlier grades. Content from future grades may be introduced but students should not be held accountable on assessments for future expectations.

The instructional materials reviewed for Eureka Grade 8 meet expectations that they assess grade-level content. Each Eureka Module includes one or more assessments that hold students accountable for Grade 8 content. These assessments are the Mid-Module and End-of-Module assessments. Examples of the assessments include:

• In Module 1, Mid-Module Assessment: Students use their knowledge of prime numbers and apply the properties of integer exponents to generate an expression equivalent to a given expression (8.EE.1). Question 2 states, “Let m be a whole number. Use the properties of exponents to write an equivalent expression that is a product of unique primes, each raised to an integer power. 6 to the 21st power multiplied by 10 to the 7th power divided by 30 to the 7th power.”
• In Module 4, End-of-Module Assessment: Students solve a system of equations (8.EE.8). Question 5 states, “Students sold 275 tickets for a fundraiser at school. Some tickets are for children and cost $3, while the rest are adult tickets that cost$5. If the total value of all tickets sold was 1,025, how many of each type of ticket was sold?” • In Module 7, Mid-Module Assessment: Students evaluate square roots and cube roots of perfect squares (8.EE.2). In Questions 6c and 6d, students use their knowledge of solving linear equations to write equations of the form $$x^2=p$$, equivalent to the given equations. While solving quadratic equations, in general, aligns to standards beyond Grade 8, these problems are aligned to grade-level standards (8.EE.2, 8.EE.8). Question 6d states, “Determine the positive solution for each of the following equations. $$x^3+3x-9=x-1+2x$$” • In Module 7, End-of-Module Assessment: Students find the length of the hypotenuse of a right triangle when the area and the length of one side are known (8.G.7). Question 1c states, “The area of the right triangle shown below is 30 feet squared. The segment XY has a length of 5 ft. Find the length of the hypotenuse.” Criterion 1.2: Coherence Students and teachers using the materials as designed devote the large majority of class time in each grade K-8 to the major work of the grade. The instructional materials for Eureka Grade 8 meet the expectation for students and teachers using the materials as designed devoting the majority of class time to the major work of the grade. Overall, the instructional materials spend at least 65% of class time on the major clusters of the grade. Indicator {{'1b' | indicatorName}} Instructional material spends the majority of class time on the major cluster of each grade. The instructional materials reviewed for Eureka Grade 8 meet expectations for spending a majority of instructional time on major work of the grade. This includes all clusters within the domains 8.EE and 8.F as well as clusters A and B in 8.G. • More than 65 percent of the lessons are explicitly focused on major work, with major work often included within supporting-work lessons as well. • Of the seven modules, Modules 1-4 focus on major work. Modules 5, 6, and 7 contain lessons related to the major work of the grade. • Of the 180 days, 146 days (81 percent) are spent on major work of the grade. The remaining lessons also make specific connections to the major work. Criterion 1.3: Coherence Coherence: Each grade's instructional materials are coherent and consistent with the Standards. The instructional materials for Eureka Grade 8 meet the expectation for being coherent and consistent with the Standards. Overall, the instructional materials have supporting content that enhances focus and coherence, are consistent with the progressions in the Standards, and foster coherence through connections at a single grade, where appropriate and required by the Standards. Indicator {{'1c' | indicatorName}} Supporting content enhances focus and coherence simultaneously by engaging students in the major work of the grade. The instructional materials reviewed for Eureka Grade 8 meet expectations that supporting work enhances focus and coherence simultaneously by engaging students in the major work of the grade. Supporting standards/clusters are connected to the major standards/clusters of the grade. For example: • In Module 5, Lesson 9: 8.G.9 supports the major work of 8.F. Students write a function to calculate an area of a partial space. Classwork Question 4 states, “Write a function that would allow you to calculate the area of a 1-inch white border for any sized square picture measured in inches.” • In Module 6, Lesson 11: 8.SP.2-3 supports the major work of 8.F.4. Students create a linear prediction model from a scatter plot. Classwork Exercise 1 Question 1c states, “Suppose that Chang believes the variables to be linearly related. Use the first and last data points in the table to create a linear prediction model.” • In Module 7, Lesson 1: 8.G.C supports the major work of 8.G.B. In Exercise 3, students use the Pythagorean theorem to find the slant height of a cone. • In Module 7, Lesson 1: 8.NS.A supports the major work of 8.G.B. In Problem Set Question 1, students use the Pythagorean theorem to estimate the length of the unknown side of a right triangle. Indicator {{'1d' | indicatorName}} The amount of content designated for one grade level is viable for one school year in order to foster coherence between grades. Instructional materials for Eureka Grade 8 meet expectations that the amount of content designated for one grade-level is viable for one year. As designed, the instructional materials can be completed in 180 days. The suggested amount of time and expectations of the materials for teachers and students are viable for one school year as written and would not require significant modifications. The instructional materials consist of seven modules. Instruction and assessment days are included in the following count: • Module 1: 20 days • Module 2: 25 days • Module 3: 25 days • Module 4: 40 days • Module 5: 15 days • Module 6: 20 days • Module 7: 35 days All lessons are paced to be 45 minutes in length. Information on how to customize lessons is included in the Preparing To Teach A Lesson section. Indicator {{'1e' | indicatorName}} Materials are consistent with the progressions in the Standards i. Materials develop according to the grade-by-grade progressions in the Standards. If there is content from prior or future grades, that content is clearly identified and related to grade-level work ii. Materials give all students extensive work with grade-level problems iii. Materials relate grade level concepts explicitly to prior knowledge from earlier grades. The instructional materials for Eureka Grade 8 meet expectations for the materials being consistent with the progressions in the standards. The instructional materials give all students extensive work with grade-level problems and identify as well as explicitly connect grade-level work to prior or future grades. Each module starts with a summary of what concepts will be taught within that module. This summary explains how the lessons support the progression of Grade 8 standards by explicitly stating connections to prior or future grades. For example: • Module 4, Linear Equations: “In Module 4, students extend what they already know about unit rates and proportional relationships (6.RP.A.2, 7.RP.A.2) to linear equations and their graphs. Students understand the connections between proportional relationships, lines and linear equations in this module (8.EE.B.5, 8.EE.B.6). Also, students learn to apply the skills they acquired in Grades 6 and 7 with respect to symbolic notation and properties of equality (6.EE.A.2, 7.EE.A.1, 7.EE.B.4) to transcribe and solve equations in one variable and then in two variables.” Each module has a “Module Standards” section that contains tabs named “Focus Grade-Level Standards” and “Foundational Standards.” The Focus Grade-Level Standards tab contains Grade 8 standards that are covered within the module. The Foundational Standards tab contains prior grade-level standards as well as grade-level standards that are the foundational skills needed for the lessons within the module. Foundational standards from Grade 7 or from previous Grade 8 work are included for each module. An example from Module 1 is: • Apply and extend previous understandings of arithmetic to algebraic expressions 6.EE.1 • Expressions and Equations 6.EE.1 • Geometry 7.G.6 | 7.G.4 • Number and Operations in Base Ten 5.NBT.2 • Solve real-life and mathematical problems involving angle measure, area, surface area, and volume 7.G.6 | 7.G.4 • Understand the place value system 5.NBT.2 The instructional materials for Eureka Grade 8 contain content from future grade levels that is identified and explanations are provided. Module 6, Lesson 12 begins with a note explaining why the optional lesson has been included in the Grade 8 materials. A similar explanation appears at the beginning of Lesson 4 in Module 7. Lesson 5 in Module 7 contains two problems that address content from future grades and are labeled as Challenge Problems 9-10. The instructional materials attend to the full intent of the grade-level standards by giving all students extensive work with grade-level problems. Most lessons contain a “Problem Set” which include questions and word problems that focus on the standards of the lesson. In Module 5, Lesson 7, Problem Set Question 1 states, “The graph below represents the distance in miles, y, Car A travels in x minutes. The table represents the distance in miles, y, Car B travels in x minutes. It is moving at a constant rate. Which car is traveling at a greater speed? How do you know?” Students compare the properties of two functions (8.F.2). Most lessons contain an “Exit Ticket” with grade-level problems that focus on the standards taught in the lesson. In Module 1, Lesson 10, Exit Ticket Question 1 states, “The speed of light is 3 x 10 to the 8th power meters per second. The sun is approximately 230,000,000,000 meters from Mars. How many seconds does it take for sunlight to reach Mars?” Students use operations with numbers in Scientific Notation to solve problems (8.EE.4). Indicator {{'1f' | indicatorName}} Materials foster coherence through connections at a single grade, where appropriate and required by the Standards i. Materials include learning objectives that are visibly shaped by CCSSM cluster headings. ii. Materials include problems and activities that serve to connect two or more clusters in a domain, or two or more domains in a grade, in cases where these connections are natural and important. The instructional materials for Eureka Grade 8 meet expectations that materials foster coherence through connections at a single grade, where appropriate and required by the standards. Materials include learning objectives that are visibly shaped by CCSSM cluster headings. For example: • In Module 1, Topic A: “Exponential Notation and Properties of Integer Exponents” is visibly shaped by 8.EE.A, “Expressions and equations work with radicals and integer exponents.” • In Module 5, Topic A: “Functions” is visibly shaped by 8.F.A, “Define, evaluate and compare functions.” Materials include problems and activities that connect two or more clusters in a domain, or two or more domains in a grade, in cases where these connections are natural and important. For example: • In Module 4, Lesson 15: 8.G.A connects to 8.EE.A when students use similar triangles to explain why slope is the same between any two distinct points on a non-vertical line in the coordinate plane. • In Module 4, Lesson 31: 8.EE.C connects to 8.G.B when students use a system of equations to find Pythagorean triples. • In Module 4, Optional Topic E: 8.EE.C connects to 8.G.B when students learn about the Babylonian method for finding Pythagorean triples which requires an understanding and use of a system of linear equations. • In Module 5, Lesson 9: 8.F.A connects to 8.G.A when students write rules to express functions related to geometry. “Write a function that would allow you to calculate the area of an 11-inch white border for any-sized square pictures measured in inches.” • In Module 5, Lesson 9, Exercise 4: 8.F.A connects to 8.G.C as students write rules to express functions related to geometry. • In Module 5, Lesson 10: 8.G.C connects to 8EE.B as students use proportional reasoning to develop the formula for the volume of a cone. Overview of Gateway 2 Rigor & Mathematical Practices The instructional materials for Eureka Grade 8 meet the expectation for rigor and mathematical practices. The instructional materials attend to each of the three aspects of rigor individually, and they also attend to the balance among the three aspects. The instructional materials identify the mathematical practices and use them to enrich mathematics content within and throughout the grade level, emphasize mathematical reasoning by prompting students to construct viable arguments and analyze the arguments of others, and attend to the specialized language of mathematics. Gateway 2 Meets Expectations Criterion 2.1: Rigor Rigor and Balance: Each grade's instructional materials reflect the balances in the Standards and help students meet the Standards' rigorous expectations, by helping students develop conceptual understanding, procedural skill and fluency, and application. The instructional materials for Eureka Grade 8 meet the expectation for reflecting the balances in the Standards and helping students meet the Standards’ rigorous expectations, by helping students develop conceptual understanding, procedural skill and fluency, and application. The instructional materials develop conceptual understanding of key mathematical concepts, give attention throughout the year to procedural skill and fluency, spend sufficient time working with engaging applications, and do not always treat the three aspects of rigor together or separately. Indicator {{'2a' | indicatorName}} Attention to conceptual understanding: Materials develop conceptual understanding of key mathematical concepts, especially where called for in specific content standards or cluster headings. The instructional materials for Eureka Grade 8 meet expectations for developing conceptual understanding of key mathematical concepts, especially where called for in specific standards or cluster headings. The materials include problems and questions that develop conceptual understanding throughout the grade level. For example: • In Module 2, Lesson 1, students develop conceptual understanding of coherence through a series of hands-on activities with shapes and transparencies. Students move shapes around (transformations) to check congruence. (8.G.1) • In Module 4, Topic D, students develop conceptual understanding of systems of equations simultaneously through contexts, tables, graphs and equations. (8.EE.8b) • In Module 5, Topic A, students develop conceptual understanding when using non-linear data to make predictions. The predictions develop an understanding that a function is a rule that for every input there is only one output. (8.F.1) The materials provide opportunities for students to demonstrate conceptual understanding independently throughout the grade level. For example: • In Module 2, Lesson 2, students independently demonstrate understanding of translations. Students name a pictured vector, choose and name the vector along which a translation of a plane would map a point to its image, draw a vector that would translate one segment onto another segment, and explain why the lengths of the segments must be the same. (8.G.1a) • In Module 2, Lesson 12, students independently demonstrate understanding when creating a table of solutions to a two-variable equation and plotting the solutions on a graph in order to see that the solution to that equation will be an ordered pair. (8.EE.5) • In Module 5, Lesson 1, students independently demonstrate understanding when they make predictions of whether the given situation is linear or nonlinear. Students make predictions then analyze real-life data to determine if it is correct and identify what makes a situation non-linear. (8.F.A) Indicator {{'2b' | indicatorName}} Attention to Procedural Skill and Fluency: Materials give attention throughout the year to individual standards that set an expectation of procedural skill and fluency. The instructional materials for Eureka Grade 8 meet expectations that they attend to those standards that set an expectation of procedural skill. The instructional materials develop procedural skill throughout the grade level. For example: • In Module 4, Lesson 4, students develop procedural skill of using properties of equality to solve linear equations void of any context. Classwork Exercise 1, Problem 1 states, “Solve the linear equation x + x + 2 + x + 4 + x + 6 = -28. State the property that justifies your first step and why you chose it.” (8.EE.7b) • In Module 4, Lesson 6, students develop procedural skill of transforming mathematical equations into simpler forms using the distributive property in order to find a solution or solutions. (8.EE.7b) • In Module 4, Lesson 28, students develop procedural skill when solving systems of equations void of any context by examining the equations, by sketching the graphs of the system, and by algebraic means. The teacher is prompted to ask the following questions in Classwork Example 1, “Use what you noticed about adding equivalent expressions to solve the following system by elimination: 6x - 5y = 21, 2x + 5y = -5. Notice that terms -5y and 5y are opposites; that is, they have a sum of zero when added. If we were to add the equations in the system, the y would be eliminated. Just as before, now that we know what x is, we can substitute it into either equation to determine the value of y. The solution to the system is (2, -9/5). (8.EE.8b) The instructional materials provide opportunities to demonstrate procedural skill independentlythroughout the grade level. For example: • In Module 4, Lesson 1, students independently demonstrate procedural skill of linear equations when writing statements using symbols to represent numbers. Problem Set Question 4 states, “One number is six more than another number. The sum of the squares is 90.”(8.EE.7) • In Module 4, Lesson 25, students independently demonstrate procedural skill of solving systems of linear equations when completing the Exit Ticket activity. Lesson 25 Exit Ticket states, “Sketch the graphs of the linear system on a coordinate plane: 2x - y = -1, y = 5x -5” (8.EE.8b) • In Module 5, Lesson 10, students independently demonstrate procedural skill using formulas to find the volume of cones and cylinders. (8.G.9) Indicator {{'2c' | indicatorName}} Attention to Applications: Materials are designed so that teachers and students spend sufficient time working with engaging applications of the mathematics, without losing focus on the major work of each grade The instructional materials for Eureka Grade 8 meet expectations that the materials are designed so that teachers and students spend sufficient time working with engaging applications of the mathematics. Engaging applications include single and multi-step problems, routine and non-routine, presented in a context in which the mathematics is applied. The instructional materials include multiple opportunities for students to engage in routine and non-routine application of mathematical skills and knowledge of the grade level. For example: • In Module 4, Lesson 5, students engage in grade-level mathematics when applying knowledge of angle relationships, congruence, and the triangle sum theorem to write and solve linear equations. These problems are non-routine because they rely on a broad range of mathematical knowledge, and can be solved in a variety of ways. Classwork Example 2 states, “Given a right triangle, find the degree measure of the angles if one angle is ten degrees more than four times the degree measure of the other angle and the third angle is the right angle.” (8.G.A, 8.EE.7b) • In Module 5, Lesson 3, students engage in grade-level mathematics when writing a linear function that describes the volume of water in a bathtub as a function of time, and solve the equation to find how long it will take to fill the bathtub. Classwork Example 4 states, “Water flows from a faucet into a bathtub at the constant rate of 7 gallons of water pouring out every 2 minutes. The bathtub is initially empty, and its plug is in. Determine the rule that describes the volume of water in the tub as a function of time. If the tub can hold 50 gallons of water, how long will it take to fill the tub?” (8.F.B, 8.EE.7b) • In Module 6, Lesson 1, students engage in grade-level mathematics when using knowledge of linear relationships to solve problems involving rate plans. Problem Set Question 2 states, “A shipping company charges a4.45 handling fee in addition to \$0.27 per pound to ship a package. Using x for the weight in pounds and y for the cost of shipping in dollars, write a linear function that determines the cost of shipping based on weight. Which line (solid, dotted, or dashed) on the following graph represents the shipping company’s pricing method? Explain.” (8.EE.8)
• In Module 7, Lesson 22, students engage in grade-level mathematics when solving for the average rate of change in various situations involving the rate of water filling a cone at a constant rate. Classwork Discussion Exercise states, “The height of a container in the shape of a circular cone is 7.5 ft., and the radius of its base is 3 ft., as shown. What is the total volume of the cone? Water flows into the container (in its inverted position) at a constant rate of 6 ft. cubed per minute. Approximately when will the container be filled?” (8.G.9)

The instructional materials provide opportunities for students to demonstrate independently the use of mathematics flexibly in a variety of contexts. For example:

• In Module 5, Lesson 11, students independently demonstrate the use of mathematics by calculating the volume of various choices of ice cream (1-, 2-, 3-scoops in a cup or cone) and determining which choice is the best value. Problem Set Question 6 states, “Bridget wants to determine which ice cream option is the best choice. The chart below gives the description and prices for her options. Use the space below each item to record your findings. A scoop of ice cream is considered a perfect sphere and has a 2-inch diameter. A cone has a 2-inch diameter and a height of 4.5 inches. A cup, considered a right circular cylinder, has a 3-inch diameter and a height of 2 inches. Determine the volume of each choice. Use 3.14 to approximate pi. Determine which choice is the best value for her money. Explain your reasoning.”(8.G.9)
• In Module 6, Lesson 8, students independently demonstrate the use of mathematics by informally fitting a straight line to data displayed in a scatter plot and making predictions based on the graph of a line that has been fit to data. Problem Set Question 2 states, “The scatter plot below shows the results of a survey of eighth-grade students who were asked to report the number of hours per week they spend playing video games and the typical number of hours they sleep each night. What trend do you observe in the data? What was the fewest number of hours per week that students who were surveyed spent playing video games? The most? What was the fewest number of hours per night that students who were surveyed typically slept? The most? Draw a line that seems to fit the trend in the data, and find its equation. Use the line to predict the number of hours of sleep for a student who spends about 15 hours per week playing video games.” (8.SP.2-3)
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Balance: The three aspects of rigor are not always treated together and are not always treated separately. There is a balance of the 3 aspects of rigor within the grade.

The instructional materials for Eureka Grade 8 meet expectations that the three aspects of rigor are not always treated together and are not always treated separately.

Conceptual understanding is addressed in Classwork. During this time, the teacher guides students through a new concept or an extension of the previous day’s learning. Students practice solving procedural problems in problem sets. The materials provide engaging applications of grade-level concepts throughout each lesson. The program balances all three aspects of rigor in every lesson.

All three aspects of rigor are present independently throughout the program materials. For example:

• In Module 7, Lesson 6, students develop conceptual understanding of irrational numbers as they examine the decimal expansion of numbers. Classwork Example 1 states, “Consider the fraction 5/8. Write an equivalent form of this fraction with a denominator that is the power of 10, and write the decimal expansion of this fraction.” (8.NS.1-2)
• In Module 4, Lesson 12, students develop procedural skill when finding solutions for linear equations. The Exit Ticket states, “Is the point (1,3) a solution to the linear equation 5x - 9y = 32? Explain. Find three solutions for the linear equation 4x - 3y = 1, and plot the solutions as points on a coordinate plane.” (8.F.4).
• In Module 7, Lesson 18, students engage in the application of mathematics when using the Pythagorean Theorem to solve real-world problems. Problem Set Question 1 states, “A 70 inch TV is advertised on sale at a local store. What are the length and width of the television?” (8.G.7).

Multiple aspects of rigor are engaged simultaneously to develop students’ mathematical understanding of a single topic/unit of study throughout the materials. For example:

• In Module 3, Lesson 12, students develop conceptual understanding of the properties of similar triangles when solving problems in real-world contexts. Problem Set Question 1 states, “The world’s tallest living tree is a redwood in California. It’s about 370 feet tall. In a local park, there is a very tall tree. You want to find out if the tree in the local park is anywhere near the height of the famous redwood. Describe the triangles in the diagram, and explain how you know they are similar or not. Assume Triangle ESO is similar to Triangle DRO. A friend stands in the shadow of the tree. He is exactly 5.5 feet tall and casts a shadow of 12 feet. Is there enough information to determine the height of the tree? If so, determine the height. If not, state what additional information is needed. Your friend stands exactly 477 feet from the base of the tree. Given this new information, determine about how many feet taller the world’s tallest tree is compared to the one in the local park.” (8.G.4)
• In Module 1, Lesson 8, students practice procedural skill when computing scientific notation to solve real-life situations. Classwork Example 1 states, “In 1723, the population of New York City was approximately 7,248. By 1870, almost 150 years later, the population had grown to 942,292. We want to determine approximately how many times greater the population was in 1870 compared to 1723. ” (8.EE.4)

Criterion 2.2: Math Practices

Practice-Content Connections: Materials meaningfully connect the Standards for Mathematical Content and the Standards for Mathematical Practice

The instructional materials for Eureka Grade 8 partially meet the expectation for meaningfully connecting the Standards for Mathematical Content and the Standards for Mathematical Practice. Overall, the materials identify the mathematical practices and use them to enrich mathematics content within and throughout the grade level, emphasize mathematical reasoning by prompting students to construct viable arguments and analyze the arguments of others, and attend to the specialized language of mathematics.

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The Standards for Mathematical Practice are identified and used to enrich mathematics content within and throughout each applicable grade.

The instructional materials reviewed for Eureka Grade 8 meet expectations that the Standards for Mathematical Practice are identified and used to enrich mathematics content within and throughout the grade level.

All of the eight MPs are identified within the grade-level materials. The Standards for Mathematical Practice are identified at the beginning of each module under the Module Standards. The tab named “Highlighted Standards for Mathematical Practice” lists all of the MPs that are focused on in the module. Each MP is linked to the definition of the practice as in which lessons throughout the series that practice can be found.

Each Module Overview contains a section titled, “Focus Standard for Mathematical Practice.” Every practice that is identified in the module has a written explanation with specific examples of how each practice is being used to enrich the content of the module. For example:

• In Module 4, the explanation for MP 1 states, “Make sense of problems and persevere in solving them. Students analyze given constraints to make conjectures about the form and meaning of a solution to a given situation in one-variable and two-variable linear equations, as well as in simultaneous linear equations. Students are systematically guided to understand the meaning of a linear equation in one variable, the natural occurrence of linear equations in two variables with respect to proportional relationships, and the natural emergence of a system of two linear equations when looking at related, continuous, proportional relationships.”

Each lesson specifically identifies where MPs are located, usually within the margins of the teacher edition.

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Materials carefully attend to the full meaning of each practice standard

The instructional materials reviewed for Eureka Grade 8 partially meet expectations that the instructional materials carefully attend to the full meaning of each practice standard. Examples of where the instructional materials attend to each of the MPs include:

• In Module 3, Lesson 3, MP 6 is identified in the teacher edition and attends to the full meaning of the practice where students use precision to dilate points of a triangle.
• In Module 4, Lesson 1, MP 2 is identified in the teacher edition and attends to the full meaning of the practice where students compare a mathematical statement with a given equation. “Show students the text of a mathematical statement compared to the equation. Ask students to write or share aloud (a) how these two are related, (b) which representation they prefer, and (c) why. Then, continue with the discussion that follows.”
• In Module 5, Lesson 7, MP 1 is identified in the teacher edition and attends to the full meaning of the practice where students make sense of problems involving linear functions as a group and discuss various methods in which to solve the problems. “Students work in small groups to complete Exercises 1–4. Groups can select a method of their choice to answer the questions and their methods will be a topic of discussion once the Exploratory Challenge is completed. Encourage students to discuss the various methods (e.g., graphing, comparing rates of change, using algebra) as a group before they begin solving.”

There are a few instances where the materials do not attend to the full meaning of one or two MPs. For example:

• In Module 2, MP 5 is identified as a Focus Standard for Mathematical Practice. While students do use a variety of tools, none of the lessons are marked as an opportunity for student engagement in MP 5.
• In Module 3, Lesson 2, MP 5 is identified in the teacher edition where students perform dilations. “In this lesson, students become familiar with using a straightedge and a compass to perform dilations. Students can follow along on their own papers as the teacher works through Examples 1–3 so that students can begin to develop independence with these tools.” This is an example of not attending to the full practice as students are given a straightedge and a compass to use to perform the dilations. Students do not choose the appropriate tool to solve the problem.
• In Module 6, Lesson 10, MP 4 is identified in the teacher edition where students write linear functions. “Let x represent the independent variable and y represent the dependent variable. Use the variables x and y to write the function representing the relationship you indicated in Exercise 4.” This is an example of not attending to the full practice as students are given parameters to create a model to represent the mathematics.
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Emphasis on Mathematical Reasoning: Materials support the Standards' emphasis on mathematical reasoning by:
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Materials prompt students to construct viable arguments and analyze the arguments of others concerning key grade-level mathematics detailed in the content standards.

The instructional materials reviewed for Eureka Grade 8 meet expectations for prompting students to construct viable arguments and analyze the arguments of others concerning key grade-level mathematics.

Student materials consistently prompt students to construct viable arguments and analyze the arguments of others.

• In Module 3, Lesson 2, students construct a viable argument when working with dilations. Problem Set Question 5 states, “Angle GHI measures 78 degrees. After a dilation, what is the measure of angle G’H’I’? How do you know?”
• In Module 3, Lesson 8, students work with similarity. Exercise 3 states, “Are the two triangles shown below similar? If so, describe a sequence that would prove triangle ABC is similar to triangle A’B’C’. If not, state how you know they are not similar.”
• In Module 4, Lesson 13, students construct viable arguments and analyze the arguments of others when graphing linear equations with two variables. Exercise 5 states, “Joey predicts that the graph of -x + y = 3 will look like the graph shown below. Do you agree? Explain why or why not.”
• In Module 5, Lesson 9, students construct viable arguments and analyze the arguments of others when determining the equation of a line. Exercise 4 states, “Several students decided to draw lines to represent the trend in the data. Consider the lines drawn by Sol, Patti, Marrisa, and Taylor, which are shown below. For each student, indicate whether or not you think the line would be a good line to use to make predictions. Explain your thinking.”
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Materials assist teachers in engaging students in constructing viable arguments and analyzing the arguments of others concerning key grade-level mathematics detailed in the content standards.

The instructional materials reviewed for Eureka Grade 8 partially meet expectations for assisting teachers in engaging students to construct viable arguments and analyze the arguments of others concerning key grade-level mathematics.

There are some missed opportunities where the materials could assist teachers in engaging students in both constructing viable arguments and analyzing the arguments of others. The teacher material frequently provides quality questions the teacher can pose to students to elicit their reasoning, however, guidance for the teachers to assist students in critiquing the reasoning of others is significantly less.

Teacher materials sometimes assist teachers in engaging students in both constructing viable arguments and analyzing the arguments of others.

• The Module 2 Overview states for teachers, “Throughout this module, students construct arguments around the properties of rigid motions. Students make assumptions about parallel and perpendicular lines and use properties of rigid motions to directly or indirectly prove their assumptions. Students use definitions to describe a sequence of rigid motions to prove or disprove congruence. Students build a logical progression of statements to show relationships between angles of parallel lines cut by a transversal, the angle sum of triangles, and properties of polygons like rectangles and parallelograms.”
• In Module 3, Lesson 6, teachers are prompted to have students write claims about the effect of dilations on coordinates and verifying the claims. “Show the diagram below, and ask students to look at and write or share a claim about the effect that dilation has on the coordinates of dilated points. Show students the second diagram below so they can check if their claims were correct. Give students time to verify the claims that they made about the above graph with the one below. Then, have them share their claims with the class. Use the discussion that follows to crystallize what students observed.”

However, there are some missed opportunities where the materials could assist teachers in engaging students in both constructing viable arguments and analyzing the arguments of others.

• In Module 1, Lesson 4, teachers are prompted to engage students in constructing viable arguments as they analyze conjectures about the meaning of the 0th exponent of a number. There are no directives or suggestions for facilitating a viable student argument or for analyzing the arguments of others. The prompt reads more as the directions to the exercise and does not ask students to construct or analyze an argument. “Have students independently complete Exercise 1; provide correct values for and before proceeding to the development of cases (A)–(C).”
• In Module 4, Lesson 2, teachers are prompted to have students sort linear and nonlinear expressions. The Discussion states, “The following chart contains both linear and nonlinear expressions in x. Sort them into two groups, and be prepared to explain what is different about the two groups. Identify which equations you placed in each group. Explain your reasoning for grouping the equations.” An opportunity for students to analyze the arguments of others is not suggested.
• In Module 4, Lesson 6, teachers are prompted to lead a discussion with students involving linear questions. There are no directives or suggestions for facilitating student thinking and the prompt reads more as the directions to the exercise. “Lead a discussion with the conclusion that since 2 is not equal to -3, then the equation has no solution. Allow students time to try to find the value of x that would make it true by guessing and checking. After they realize that there is no such number x, make it clear to students that some equations have no solution. Ask the following question. Why do you think this happened? What value of x would make the following linear equation true?” An opportunity for students to analyze the arguments of others is not suggested.
Indicator {{'2g.iii' | indicatorName}}
Materials explicitly attend to the specialized language of mathematics.

The instructional materials reviewed for Eureka Grade 8 meet expectations for explicitly attending to the specialized language of mathematics.

In each module, the instructional materials provide new or recently introduced mathematical terms that will be used throughout the module. The mathematical terms that are the focus of the module are highlighted for students throughout the lessons and are reiterated at the end of most lessons.

Each mathematical term that is introduced has an explanation, and some terms are supported with an example. The terminology that is used in the modules is consistent with the terms in the standards.

The materials provide explicit instruction in how to communicate mathematical thinking using words, diagrams and symbols. For example:

• In Module 3, Lesson 9, the materials guide teachers through the teaching process of properties of similarity. The Concept Development states, “Expect students to respond in a similar manner to the response for part (d). If they do not, ask questions about what similarity means, what a dilation does, and how figures are mapped onto one another. For any two figures $$S$$ and $$S'$$, if $$S\backsim S'$$, then $$S'\backsim S$$. This is what the statement that similarity is a symmetric relation means.”
• In Module 5, Lesson 2, the materials guide teachers through a class discussion on functions. The Discussion notes state, “Let’s examine the definition of function more closely: For every input, there is one and only one output. Can you think of why the phrase one and only one (or exactly one) must be included in the definition? Most of the time in Grade 8, the correspondence is given by a rule, which can also be considered a set of instructions used to determine the output for any given input. For example, a common rule is to substitute a number into the variable of a one-variable expression and evaluating. When a function is given by such a rule or formula, we often say that function is a rule that assigns to each input exactly one output.”

The materials use precise and accurate terminology and definitions when describing mathematics and support students in using them. For example:

• In Module 2, Lesson 1, the materials precisely define transformation in the Lesson Summary, and students use new vocabulary as they describe transformations. Problem Set Question 2 states, “Describe, intuitively, what kind of transformation is required to move Figure A on the left to its image on the right.”
• In Module 5, Lesson 3, students use words to describe a function in terms of area mowed and time. Exercise Question 1b states, “Hana claims she mows lawns at a constant rate. The table below shows the area of lawn she can mow over different time periods. Describe in words the function in terms of area mowed and time.”

Usability

Gateway 3
Partially Meets Expectations

Criterion 3.1: Use & Design

Use and design facilitate student learning: Materials are well designed and take into account effective lesson structure and pacing.

The instructional materials for Eureka Grade 8 meet the expectations for being well designed and taking into account effective lesson structure and pacing. The instructional materials distinguish between problems and exercises, have exercises that are given in intentional sequences, have a variety in what students are asked to produce, and include manipulatives that are faithful representations of the mathematical objects they represent.

Indicator {{'3a' | indicatorName}}
The underlying design of the materials distinguishes between problems and exercises. In essence, the difference is that in solving problems, students learn new mathematics, whereas in working exercises, students apply what they have already learned to build mastery. Each problem or exercise has a purpose.

The instructional materials reviewed for Eureka Grade 8 meet the expectation that the underlying design of the materials distinguishes between lesson problems and student exercises for each lesson. It is clear when the students are solving problems to learn and when they are applying their skills to build mastery.

Each lesson follows a sequence that is facilitated by the teacher and may include components such as Opening Exercise, Examples, Challenges, Discussion and Closing.

Exercises are included in each lesson to be completed by students within the class period either individually or with a partner. These Exercises generally reinforce and/or extend the new mathematical concepts explored in a lesson.

Students build mastery when they apply what they have learned to solve problems in the Problem Set component of a lesson. The Problem Set problems typically mirror the types of problems introduced in the Exercises.

Most lessons include an Exit Ticket at the end of a lesson. The Exit Ticket is aligned to problems in the Exercises and Problem Sets a majority of the time.

Indicator {{'3b' | indicatorName}}
Design of assignments is not haphazard: exercises are given in intentional sequences.

The instructional materials reviewed for Eureka Grade 8 meet the expectation for not being haphazard; exercises are given in intentional sequences.

Module sequences follow the progressions outlined in the CCSSM Standards to support students’ conceptual and skill development.

Lessons within modules are intentionally sequenced so students develop understanding leading to content mastery. The overall structure of a lesson provides students with problems and activities that are sequenced from concrete to abstract thinking.

Indicator {{'3c' | indicatorName}}
There is variety in what students are asked to produce. For example, students are asked to produce answers and solutions, but also, in a grade-appropriate way, arguments and explanations, diagrams, mathematical models, etc.

The instructional materials reviewed for Eureka Grade 8 meet the expectation for having variety in what students are asked to produce.

The instructional materials prompt students to produce mathematical models and explanations of their reasoning when finding solutions to various problems. Students produce solutions, construct viable arguments, and critique the reasoning of others within all components of the instructional materials including group and partner discussions. For example, in Module 4, Lesson 5, students solve a problem using any method they choose and share their solution with classmates. The students construct an argument and justify their steps when sharing their solution.

Students use mathematical models such as number lines, double number lines, tape diagrams, graphs and tables. The materials consistently call for students to use the language and intent of the standards when producing solutions.

Indicator {{'3d' | indicatorName}}
Manipulatives are faithful representations of the mathematical objects they represent and when appropriate are connected to written methods.

The instructional materials reviewed for Eureka Grade 8 meet the expectation for having manipulatives that are faithful representations of the mathematical objects they represent and, when appropriate, are connected to written methods.

The series includes a variety of manipulatives and integrates hands-on activities that allow the use of physical manipulatives. For example:

• Manipulatives are consistently aligned to the expectations and concepts in the standards. The majority of manipulatives used are geometry tools. In Module 2 Lesson 4, students use protractors and rulers when measuring angles and length of line segments when exploring the properties of reflection.

Examples of manipulatives for Grade 8 include:

• Geometric Volume Set
• Compasses
• Protractors
• Rulers
Indicator {{'3e' | indicatorName}}
The visual design (whether in print or online) is not distracting or chaotic, but supports students in engaging thoughtfully with the subject.

The visual design in Eureka Grade 8 is not distracting or chaotic and supports students in engaging thoughtfully with the subject.

The instructional materials follow a consistent visual format. The teacher materials coincide with the student materials when both consistently label the modules, topics and lessons. Within each module, lessons with similar or related content are grouped into topics.

The print and visuals on the materials are clear without any distracting visuals or an overabundance of text features. Lesson materials for students have distinct consistent headings such as Classwork or Problem Set to distinguish group work from individual work. A framed Lesson Summary is often included at the end of the lesson to emphasize important concepts to students.

Student practice problem pages frequently include enough space for students to write their answers and demonstrate their thinking. Exit Tickets provide clearly labeled models as well as space to solve the given problem. There are no distracting or extraneous pictures, captions or "facts" within lessons.

Criterion 3.2: Teacher Planning

Teacher Planning and Learning for Success with CCSS: Materials support teacher learning and understanding of the Standards.

The instructional materials for Eureka Grade 8 partially meet the expectations for supporting teacher learning and understanding of the Standards. The instructional materials contain full, adult-level explanations and examples of the more advanced mathematics concepts in the lessons so that teachers can improve their own knowledge and explain the role of the specific grade-level mathematics in the context of the overall mathematics curriculum.

Indicator {{'3f' | indicatorName}}
Materials support teachers in planning and providing effective learning experiences by providing quality questions to help guide students' mathematical development.

The instructional materials reviewed for Eureka Grade 8 partially meet the expectation for supporting teachers in planning and providing effective learning experiences by providing quality questions to help guide students’ mathematical development.

Each lesson contains an opening narrative for the teacher. Included in this narrative is a section labeled Student Outcomes, and often included is a section labeled Lesson Notes. The Student Outcomes section lists the objectives of the lesson, and the Lesson Notes section gives teachers a mathematical summary of the concept being presented, examples of the concept, as well as suggestions to help students make connections between concepts. The Classwork section provides questions for discussion and guiding questions designed to increase classroom discourse and ensure understanding of the concepts. For example:

• In Module 6, Lesson 10, a Closing question states, “How are these examples different from the data we have been studying before this lesson?”

However, the materials do not include instructions or guidance for how to adjust a lesson or the questions that a teacher asks to guide instruction based on the needs of students.

There is not sufficient guidance on how to group students or structure questions that can support all students in accessing the material.

Indicator {{'3g' | indicatorName}}
Materials contain a teacher's edition with ample and useful annotations and suggestions on how to present the content in the student edition and in the ancillary materials. Where applicable, materials include teacher guidance for the use of embedded technology to support and enhance student learning.

The instructional materials reviewed for Eureka Grade 8 partially meet the expectations for containing a teacher edition with ample and useful annotations and suggestions on how to present the content in the student edition and in the ancillary materials. Where applicable, materials also include teacher guidance on the use of embedded technology to support and enhance student learning.

Some lessons include a Lesson Notes section which provides useful suggestions on how to present content and/or explanations as to why a particular model is used. Most lessons have pictures or other graphics with annotations, demonstrating the concepts for the teacher.

Often, the scaffolding provided is to "remind students." There are limited suggestions for how to modify lessons, questions and/or problem sets for students who already understand or struggle with the content of the given lesson.

Beyond an occasional link to a video, there are no suggestions for teachers on the use of technology, including a calculator, and therefore no guidance on how to use such technology.

Answer keys are included for all of the Problem Sets, Exit Tickets, Homework, and Tests, including written annotations to show how student work should look.

Indicator {{'3h' | indicatorName}}
Materials contain a teacher's edition (in print or clearly distinguished/accessible as a teacher's edition in digital materials) that contains full, adult-level explanations and examples of the more advanced mathematics concepts in the lessons so that teachers can improve their own knowledge of the subject, as necessary.

The instructional materials reviewed for Eureka Grade 8 meet expectations for the teacher edition containing full, adult-level explanations and examples of the more advanced mathematics concepts in the lessons so that teachers can improve their own knowledge.

The module Overview provides information about the mathematical connections of concepts being taught. Previous and future grade levels are also referenced to show the progression of the mathematics over time. Important vocabulary is included along with definitions and examples of the terms.

Lesson narratives provide specific information as well as examples about the mathematical content within the lesson and are presented in adult language. These narratives contextualize the mathematics of the lesson to build teacher understanding, as well as guidance on what to expect from students and important vocabulary.

The teacher edition provides each step of the solution to the problems posed to students.

Indicator {{'3i' | indicatorName}}
Materials contain a teacher's edition (in print or clearly distinguished/accessible as a teacher's edition in digital materials) that explains the role of the specific grade-level mathematics in the context of the overall mathematics curriculum for kindergarten through grade twelve.

The materials do contain a teacher edition (in print or clearly distinguished and accessible as such in digital materials) that explains the role of the specific grade-level mathematics in the context of the overall mathematics curriculum for Kindergarten through Grade 12.

• Each module has an overview section that gives teachers an understanding of the mathematical content in the lessons as well as where it fits in the scope of mathematics from Kindergarten through Grade 12.
• Knowledge required from prior modules and/or grades is explicitly called out in this section.
Indicator {{'3j' | indicatorName}}
Materials provide a list of lessons in the teacher's edition (in print or clearly distinguished/accessible as a teacher's edition in digital materials), cross-referencing the standards covered and providing an estimated instructional time for each lesson, chapter and unit (i.e., pacing guide).

The instructional materials reviewed for Eureka Grade 8 provide a list of concepts in the teacher edition that cross-references the standards addressed and provides an estimated instructional time for each unit and lesson.

The materials provide a module overview that specifies the grade-level standards addressed in each module. The standards are listed in the Focus Standards section of the overview. An estimated number of instructional days is given for each module to be completed.

Each section within a lesson is labeled with an estimated number of minutes that it should take to complete.

Indicator {{'3k' | indicatorName}}
Materials contain strategies for informing parents or caregivers about the mathematics program and suggestions for how they can help support student progress and achievement.

The instructional materials reviewed for Eureka Grade 8 contain strategies for informing parents or caregivers about the mathematics program and suggestions for how they can help support student progress and achievement.

There are resources online that inform parents about the mathematics of the program as well as give suggestions for how they can help support their child.

The online parent resources are divided into several categories. The Parent Support section allows parents to create an account to gain access to resources. Parent Tip Sheets are free to parents and include suggested strategies, vocabulary, and tips to support learning at home. Parents can learn more about the spiral bound books that can be purchased that provide step-by-step explanations of homework problems in the Homework Helpers section. The Grade Roadmaps section explains grade-level math concepts and gives suggestions on facilitating learning outside of the classroom.

There is also a section where parents can download card games to help build fluency in math.

Indicator {{'3l' | indicatorName}}
Materials contain explanations of the instructional approaches of the program and identification of the research-based strategies.

The instructional materials reviewed for Eureka Grade 8 contain some explanations of the instructional approaches of the program. Some modules contain Methods of Instructional Delivery. When this section is available, it provides teachers with information on how to prepare to teach the lesson, strategies utilized throughout the lesson, and the benefits of the strategies. There is additional information about the instructional approaches in A Story of Ratios Curriculum Overview. Lastly, the opening letter from Executive Director Lynne Munson addresses some of the research and philosophy behind the instructional materials.

Criterion 3.3: Assessment

Assessment: Materials offer teachers resources and tools to collect ongoing data about student progress on the Standards.

The instructional materials for Eureka Grade 8 do not meet the expectations for offering teachers resources and tools to collect ongoing data about student progress on the Standards. The instructional materials provide ongoing review and practice with feedback. The instructional materials do not provide strategies for gathering information about students’ prior knowledge, partially provide strategies for identifying and addressing common student errors and misconceptions, partially have assessments with standards clearly denoted, and do not include aligned rubrics and scoring guidelines that provide sufficient guidance to teachers.

Indicator {{'3m' | indicatorName}}
Materials provide strategies for gathering information about students' prior knowledge within and across grade levels.

The instructional materials reviewed for Eureka Grade 8 do not meet the expectations for providing strategies for gathering information about students' prior knowledge within and across grade levels.

There are no strategies or assessments that are specifically for the purpose of assessing prior knowledge.

Indicator {{'3n' | indicatorName}}
Materials provide strategies for teachers to identify and address common student errors and misconceptions.

The instructional materials reviewed for Eureka Grade 8 partially meet the expectation for providing strategies for teachers to identify and address common student errors and misconceptions.

The teacher edition often identifies common student errors and/or misconceptions within the lesson, although strategies to address the errors and/or misconceptions are not provided.

Teachers can address errors and misconceptions by facilitating mathematical conversations between students. Teachers are provided with a list of possible discussion questions for most lessons.

Indicator {{'3o' | indicatorName}}
Materials provide opportunities for ongoing review and practice, with feedback, for students in learning both concepts and skills.

The instructional materials reviewed for Eureka Grade 8 meet the expectation for providing opportunities for ongoing review and practice, with feedback, for students in learning both concepts and skills.

The lesson structure consisting of an opening exercise, discussion, exercises, closing, exit ticket, and problem sets provides students with opportunities to connect prior knowledge to new learning, engage with content, and synthesize their learning. Throughout the lesson, students have opportunities to work independently with partners and in groups where review, practice, and feedback are embedded into the instructional routine.

The Opening Exercise section of a lesson provides ongoing review and practice of previously taught concepts. The Problem Set problems for each lesson activity reinforce skills and enable students to engage with the content and receive timely feedback. In addition, discussion questions in the Discussion section provide opportunities for students to engage in timely discussion on the mathematics of the lesson.

The summative assessments contain rubrics to provide feedback to the teacher and student on a student’s progress towards mastery.

Indicator {{'3p' | indicatorName}}
Materials offer ongoing formative and summative assessments:
Indicator {{'3p.i' | indicatorName}}
Assessments clearly denote which standards are being emphasized.

The instructional materials reviewed for Eureka Grade 8 partially meet the expectation for assessments clearly denoting which standards are being emphasized.

The summative assessments which include the Mid-Module and End-of-Module Assessment meet the expectations by clearly denoting the standards being emphasized; however, the formative assessments such as Exit Tickets do not.

The Mid-Module and End-of-Module Assessments align each item to specific standard(s). Each of these assessments include a Progression Toward Mastery rubric that lists specific standards being assessed and describes how mastery is determined.

Indicator {{'3p.ii' | indicatorName}}
Assessments include aligned rubrics and scoring guidelines that provide sufficient guidance to teachers for interpreting student performance and suggestions for follow-up.

Formative assessments include aligned rubrics and scoring guidelines that provide sufficient guidance to teachers for interpreting student performance but do not include suggestions for follow-up.

• Each Mid-Module and End-of-Module assessment includes a rubric as well as worked-out solutions for correct responses.
• There are no strategies or suggestions for follow-up provided.
• There are no rubrics or scoring guidelines for any formative assessment tasks (nor are any items or tasks identified as formative assessment opportunities).
Indicator {{'3q' | indicatorName}}
Materials encourage students to monitor their own progress.

The instructional materials for Eureka Grade 8 do not include opportunities for students to monitor their own progress.

There are no evident strategies or opportunities for students to monitor their own progress. Objectives or outcomes for each lesson and/or assignment are not provided to students in any of the student material.

Criterion 3.4: Differentiation

Differentiated instruction: Materials support teachers in differentiating instruction for diverse learners within and across grades.

The instructional materials for Eureka Grade 8 do not meet the expectations for supporting teachers in differentiating instruction for diverse learners within and across grades. The instructional materials provide a balanced portrayal of various demographic and personal characteristics, but the instructional materials partially provide: strategies to help teachers sequence or scaffold lessons; strategies for meeting the needs of a range of learners; tasks with multiple entry points; support, accommodations, and modifications for English Language Learners and other special populations; and opportunities for advanced students to investigate mathematics content at greater depth.

Indicator {{'3r' | indicatorName}}
Materials provide strategies to help teachers sequence or scaffold lessons so that the content is accessible to all learners.

The instructional materials reviewed for Eureka Grade 8 partially meet the expectation for providing strategies to help teachers sequence or scaffold lessons so that the content is accessible to all learners.

The modules and topics within each module are sequenced according to the CCSSM "Progressions of Learning." A description of the module sequence and layout is provided.

In the module and topic overviews, the structure of how the lessons build and develop a concept is discussed in narrative form. Lessons are sequenced to build from conceptual understanding, using representations ranging from concrete and pictorial to the more abstract.

There is little guidance to support teachers if a lesson does not work as written or if students need additional support to master the content.

Indicator {{'3s' | indicatorName}}
Materials provide teachers with strategies for meeting the needs of a range of learners.

The instructional materials reviewed for Eureka Grade 8 partially meet the expectation for providing teachers with strategies for meeting the needs of a range of learners.

The lesson structure: Opening Exercise, Examples, Challenges, Discussion, and Closing all include guidance for the teacher on the mathematics of the lesson, possible misconceptions, and specific strategies to address the needs of a range of learners.

There are limited marginal notes that provide strategies in the teacher materials. The suggested strategies are vague such as "use questioning strategies" or "remind students of a definition" and do not offer strategies that will impact the outcome of a lesson/problem.

The differentiation list online mirrors the strategies in the teacher materials; however, it does not offer additional clarification or suggestions.

Indicator {{'3t' | indicatorName}}
Materials embed tasks with multiple entry-points that can be solved using a variety of solution strategies or representations.

The instructional materials reviewed for Eureka Grade 8 partially meet the expectation that materials embed tasks with multiple entry­ points that can be solved using a variety of solution strategies or representations.

Although most of the tasks allow students to utilize multiple entry points and to solve problems using a variety of strategies, paths and/or models, the materials sometimes undermine this concept by using tasks that explicitly state how to solve the problem or which representation to use.

At times, teachers are prompted to lead students through a particular task rather than provide students with an opportunity to create a solution path on their own. Students are not always encouraged to produce a variety of solution strategies. For example:

• In Module 4, Lesson 16, students learn to find the slope of a nonvertical line. In this lesson, teachers guide students through finding the slope of a line where the horizontal distance is not 1. However, instead of having students explore that no matter which points on the line they choose they will get the same slope, they structure the process, thus eliminating the opportunity for students to apply their own reasoning to arrive at this conclusion.
Indicator {{'3u' | indicatorName}}
Materials suggest support, accommodations, and modifications for English Language Learners and other special populations that will support their regular and active participation in learning mathematics (e.g., modifying vocabulary words within word problems).

The instructional materials reviewed for Eureka Grade 8 partially meet the expectation that the materials include support, accommodations, and modifications for English Language Learners and other special populations that will support their regular and active participation in learning mathematics.

There are limited marginal notes that provide strategies in the teacher materials. The suggested strategies are vague, such as "use questioning strategies" or "remind students of a definition," and do not offer strategies that will impact the outcome of a lesson/problem.

The differentiation list online mirrors the strategies in the teacher materials; however, it does not offer additional clarifications or suggestions for English Language Learners and other special populations.

Indicator {{'3v' | indicatorName}}
Materials provide opportunities for advanced students to investigate mathematics content at greater depth.

The instructional materials reviewed for Eureka Grade 8 partially meet the expectation that the materials provide opportunities for advanced students to investigate mathematics content at greater depth.

There are limited marginal notes in the teachers edition that provide strategies for advanced students. The Notes on Multiple Means of Engagement give teachers suggestions about meeting the needs of advanced students.

“Challenge” problems are occasionally included; however, it is difficult to determine if those problems were optional for the entire class, to be scaffolded for the class, or explicitly for students who needed advanced mathematics.

The curriculum specifies that not all pieces within a section of a lesson must be used, so advanced students could be asked to tackle problems or sections a teacher does not use for all students. Overall, the materials provide minimal opportunities for advanced students to go beyond the mathematics provided in the classroom lessons.

Indicator {{'3w' | indicatorName}}
Materials provide a balanced portrayal of various demographic and personal characteristics.

The instructional materials reviewed for Eureka Grade 8 meet the expectation for providing a balanced portrayal of various demographic and personal characteristics.

The lessons contain a variety of tasks and situations in the story problems that interest students of various demographic and personal characteristics. The names chosen in the lessons represent a variety of cultural groups.

The application problems include real-world situations that would appeal to a variety of cultural and gender groups.

There is a balanced approach to the use of gender identification.

Indicator {{'3x' | indicatorName}}
Materials provide opportunities for teachers to use a variety of grouping strategies.

The instructional materials reviewed for Eureka Grade 8 provide limited opportunities for teachers to use a variety of grouping strategies.

Notes within the lessons provide teachers a variety of options for whole group, small group, partner, or individual work. Although suggestions are made, there is often no mention of the reason that a student should work within a specific group size. The groups do not have explicitly-stated assigned roles or expectations to help teachers enhance the involvement of every student.

There are opportunities for different groupings, however the fundamental models are Modeling with Interactive Questioning, Guided Practice, and Independent Practice.

Indicator {{'3y' | indicatorName}}
Materials encourage teachers to draw upon home language and culture to facilitate learning.

The instructional materials reviewed for Eureka Grade 8 do not encourage teachers to draw upon home language and culture to facilitate learning.

There is no evidence of teachers needing to draw upon home language and culture to facilitate learning.

Criterion 3.5: Technology

Effective technology use: Materials support effective use of technology to enhance student learning. Digital materials are accessible and available in multiple platforms.

Reviews for this series were conducted using print materials, which do not include an instructional technology component. Materials were not reviewed for this criterion.

Indicator {{'3aa' | indicatorName}}
Digital materials (either included as supplementary to a textbook or as part of a digital curriculum) are web-based and compatible with multiple internet browsers (e.g., Internet Explorer, Firefox, Google Chrome, etc.). In addition, materials are "platform neutral" (i.e., are compatible with multiple operating systems such as Windows and Apple and are not proprietary to any single platform) and allow the use of tablets and mobile devices.

Reviews for this series were conducted using print materials, which do not include an instructional technology component. Materials were not reviewed for this indicator.

Indicator {{'3ab' | indicatorName}}
Materials include opportunities to assess student mathematical understandings and knowledge of procedural skills using technology.

Reviews for this series were conducted using print materials, which do not include an instructional technology component. Materials were not reviewed for this indicator.

Indicator {{'3ac' | indicatorName}}
Materials can be easily customized for individual learners. i. Digital materials include opportunities for teachers to personalize learning for all students, using adaptive or other technological innovations. ii. Materials can be easily customized for local use. For example, materials may provide a range of lessons to draw from on a topic.

Reviews for this series were conducted using print materials, which do not include an instructional technology component. Materials were not reviewed for this indicator.

Materials include or reference technology that provides opportunities for teachers and/or students to collaborate with each other (e.g. websites, discussion groups, webinars, etc.).

Reviews for this series were conducted using print materials, which do not include an instructional technology component. Materials were not reviewed for this indicator.

Indicator {{'3z' | indicatorName}}
Materials integrate technology such as interactive tools, virtual manipulatives/objects, and/or dynamic mathematics software in ways that engage students in the Mathematical Practices.

Reviews for this series were conducted using print materials, which do not include an instructional technology component. Materials were not reviewed for this indicator.

Report Overview

Summary of Alignment & Usability for Eureka Math | Math

Product Notes

Eureka Math K-8 (2015) was previously reviewed by EdReports. This is a re-review of the 2015 program due to added digital/online components.

Math K-2

The instructional materials for Eureka Grades K-2 meet the expectations for focus and coherence in Gateway 1. All grades meet the expectations for focus as they assess grade-level topics and spend the majority of class time on major work of the grade, and all grades meet the expectations for coherence as they have a sequence of topics that is consistent with the logical structure of mathematics. In Gateway 2, all grades meet the expectations for rigor and balance, and all grades partially meet the expectations for practice-content connections. In Gateway 3, all grades meet the expectations for instructional supports and usability. The instructional materials show strengths by being well designed and taking into account effective lesson structure and pacing, supporting teacher learning and understanding of the Standards, and supporting teachers in differentiating instruction for diverse learners within and across grades.

Kindergarten
Alignment
Meets Expectations
Usability
Meets Expectations
Alignment
Meets Expectations
Usability
Meets Expectations
Alignment
Meets Expectations
Usability
Meets Expectations

Math 3-5

The instructional materials for Eureka Grades 3-5 meet the expectations for focus and coherence in Gateway 1. All grades meet the expectations for focus as they assess grade-level topics and spend the majority of class time on major work of the grade, and all grades meet the expectations for coherence as they have a sequence of topics that is consistent with the logical structure of mathematics. In Gateway 2, all grades meet the expectations for rigor and balance, and all grades partially meet the expectations for practice-content connections. In Gateway 3, all grades meet the expectations for instructional supports and usability. The instructional materials show strengths by being well designed and taking into account effective lesson structure and pacing, supporting teacher learning and understanding of the Standards, and supporting teachers in differentiating instruction for diverse learners within and across grades.

Alignment
Meets Expectations
Usability
Meets Expectations
Alignment
Meets Expectations
Usability
Meets Expectations
Alignment
Meets Expectations
Usability
Meets Expectations

Math 6-8

The instructional materials for Eureka Grades 6-8 meet the expectations for focus and coherence in Gateway 1. All grades meet the expectations for focus as they assess grade-level topics and spend the majority of class time on major work of the grade, and all grades meet the expectations for coherence as they have a sequence of topics that is consistent with the logical structure of mathematics. In Gateway 2, all grades meet the expectations for rigor and balance, and all grades partially meet the expectations for practice-content connections. In Gateway 3, all grades partially meet the expectations for instructional supports and usability. The instructional materials show strength in being well designed and taking into account effective lesson structure and pacing.

Alignment
Meets Expectations
Usability
Partially Meets Expectations
Alignment
Meets Expectations
Usability
Partially Meets Expectations
Alignment
Meets Expectations
Usability
Partially Meets Expectations

Overall Summary

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Usability
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