## Eureka Math

##### v1
###### Usability
Our Review Process

Showing:

### Overall Summary

The instructional materials for Eureka Grade 6 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 6 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 6 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.

##### Indicator {{'1a' | indicatorName}}
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 6 meet expectations that they assess grade-level content. Each Eureka Module includes one or more assessments that hold students accountable for Grade 6 content. These assessments are the Mid-Module and End-of-Module assessments. Examples of the assessments include:

• In Module 1, Mid-Module Assessment: Students identify the ratio and choose an appropriate model to explain (6.RP.3). Question 2 states, “Wells College in Aurora, New York was previously an all-girls college. In 2005, the college began to allow boys to enroll. By 2012, the ratio of boys to girls was 3 to 7. If there were 200 more girls than boys in 2012, how many boys were enrolled that year? Use a table, graph, or tape diagram to justify your answer.”
• In Module 1, End-of-Module Assessment: Students solve unit rate problems involving unit pricing and constant speed. Unit rates are limited to non-complex fractions (6.RP.3b). Question 4 states, “Your mother takes you to your grandparents’ house for dinner. She drives 60 minutes at a constant speed of 40 miles per hour. She reaches the highway, quickly speeds up, and drives for another 30 minutes at constant speed of 70 miles per hour. How far did you and your mother travel altogether? How long did the trip take?”
• In Module 2, Mid-Module Assessment: Students solve a word problem involving division of a fraction by a fraction to determine the number of people that can be served 19½ pints of ice cream if each person is served ¾ of a pint (6.NS.1).
• In Module 3, End-of-Module Assessment: Students name positive and negative integers (6.NS.5,6a). Question 1 states, “Mr. Kindle invested some money in the stock market. He tracks his gains and losses using a computer program. Mr. Kindle receives a daily email that updates him on all his transactions from the previous day. This morning, his email read as follows: Good morning, Mr. Kindle, Yesterday’s investment activity included a loss of $800, a gain of$960, and another gain of $230. Log in now to see your current balance. a. Write an integer to represent each gain and loss.” • In Module 4, Mid-Module Assessment: Students express the perimeter of a patio in terms of ????, first using addition and then using multiplication, and use substitution to determine if the two expressions are equivalent (6.EE.2a-c,4). #### 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 6 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 6 meet expectations for spending a majority of instructional time on major work of the grade. This includes all clusters within the domains 6.RP and 6.EE as well as clusters A and C in 6.NS. • 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 six modules, Modules 1, 3 and 4 focus on major work. Modules 2 and 5 contain lessons related to the major work. • Of the 180 days, 120 days (67 percent) are spent on major clusters of the grade. #### Criterion 1.3: Coherence Coherence: Each grade's instructional materials are coherent and consistent with the Standards. The instructional materials for Eureka Grade 6 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 6 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 2, Topic B: 6.NS.3 supports the major work of 6.EE.3. Students build fluency in using the distributive property as they solve multiplication problems involving decimals. This supports their work in applying the distributive property to generate equivalent expressions. • In Module 5, Topic B: 6.NS.8 supports the major work of 6.G.3. Students build fluency in finding the distance between points on a coordinate plane while applying this knowledge to determine distance, perimeter and area on the coordinate plane. • In Module 5, Topic D: 6.G.4 supports the major work of 6.EE.1. Students determine the surface area of a right rectangular prism while writing expressions • In Module 6, Lessons 9-11: 6.SP.5c supports the major work of 6.RP.5-6. Students determine Mean Absolute Value while using signed numbers. ##### 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 reviewed for Eureka Grade 6 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 six modules. Instruction and assessment days are included in the following count: • Module 1: 35 days • Module 2: 25 days • Module 3: 25 days • Module 4: 45 days • Module 5: 25 days • Module 6: 25 days All lessons are paced to be 45 minutes in length. Information on how to customize lessons is included at the beginning of each module 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 6 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, and how the lessons support the progression of Grade 6 standards by explicitly stating connections to prior or future grades. For example: • Module 1, Ratios and Unit Rates: “In this module, students are introduced to the concepts of ratio and rate. Their previous experience solving problems involving multiplicative comparisons, such as Max has three times as many toy cars as Jack, (4.OA.A.2) serves as the conceptual foundation for understanding ratios as a multiplicative comparison of two or more numbers used in quantities or measurements (6.RP.A.1).” 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 6 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 5 or from previous Grade 6 work are included for each module. An example from Module 1 is: • Apply and extend previous understandings of multiplication and division to multiply and divide fractions | 5.NF.3 • Convert like measurement units within a given measurement system 5.MD.1 • Geometry 5.G.1 | 5.G.2 • Graph points on the coordinate plane to solve real-world and mathematical problems 5.G.1 | 5.G.2 • Measurement and Data | 5.MD.1 • Number anand Operations - Fractions | 5.NF.3 • Operations and Algebraic Thinking | 4.OA.2 • Use the four operations with whole numbers to solve problems | 4.OA.2 The instructional materials for Eureka Grade 6 materials do not contain content from future grade levels. In places where the content might be confused with that of a future grade, explanations are provided, such as the one found in the Lesson Notes for Lesson 7 in Module 6 (page 77): “Notice that deviations are actually signed distances, but calculations involving signed numbers are not covered until Grade 7. Here students can rely on knowledge from Grade 6, Modules 3, 4 and 5, as they work with the unsigned distances above and below the mean. In Grade 6, Module 3, students identified zero as a balance point between opposites on a number line. In this module, students understand that the mean balances total distances to the left of the mean and to the right of the mean on the number line.” 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 are questions and word problems that focus on the standards of the lesson. In Module 5, Lesson 13, Problem Set Question 4 states, “Determine the volume of a cube with a side length of 5 ⅓ inches.” Students find the volume of a right rectangular prism with fractional edge lengths (6.G.2). Most lessons contain an “Exit Ticket” with grade-level problems that focus on the standards taught in the lesson. In Module 3, Lesson 1, Exit Ticket Question 2 states, “Below is a list of numbers in order from least to greatest. Use what you know about the number line to complete the list of numbers by filling in the blanks with the missing integers. -6, -5, __, -3, -2, -1, __, 1, 2, __, 4, __, 6.” Students develop the concept of positive and negative numbers on a number line and real-life applications (6.NS.5). ##### 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 6 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, Lesson 1: “Ratios” is visibly shaped by 6.RP.A, “Understand ratio concepts and use ratio reasoning to solve problems.” • In Module 1, Lesson 16: “From Ratios to Rates” is visibly shaped by 6.RP.A, “Understand ratio concepts and use ratio reasoning to solve problems.” • In Module 4, Topic G: “Solving Equations” is shaped by 6.EE.B, “Reason about and solve one-variable equations and inequalities.” • In Module 4, Lesson 33: “From Equations to Inequalities” is shaped by 6.EE.B, “Reason about and solve one-variable equations and inequalities.” 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 2, Lesson 14: 6.NS.A connects to 6.NS.B as students use their understanding of division of fractions to develop an algorithm for dividing decimals. • In Module 3, Lesson 19: 6.G.A connects to 6.NS.C as students determine that the length of a line segment drawn on a coordinate plane is the distance between its endpoints. They use this information to solve problems involving side lengths and areas of rectangles and triangles. • In Module 4, Lesson 18: 6.EE.A connects to 6.EE.B when students understand mathematical language (sum, difference, etc.) to write expressions for real situations. • In Module 6, Lesson 10: 6.NS.B connects to 6.SP.B as students describe a distribution involving decimals using the mean and mean absolute value. • In Module 6, Lesson 16: 6.EE connects to 6.SP when students use variables and expressions to solve for quartiles. “A formula for the IQR could be written as Q3 - Q1 = IQR. Suppose you knew the IQR and and the Q1. How could you find the Q3?” ###### Overview of Gateway 2 ### Rigor & Mathematical Practices The instructional materials for Eureka Grade 6 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 6 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 6 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 1, Lesson 1, students develop conceptual understanding when introduced to ratios through the use of various visual models (tape diagrams, bar models and tables). Students develop their understanding of a ratio and how to write it in notation form. (6.RP.A) • In Module 1, Lesson 13, students develop their understanding of proportional relationships when using ratio tables to write equations that represent the relationship. (6.RP.A) • In Module 4, Lessons 1-4, students develop conceptual understanding by using tape diagrams to represent and understand the relationships of operations. Students use the tape diagrams to generate equivalent expressions, first using numbers, and then using both numbers and letters. (6.EE.2a-b, 6.EE.3, 6.EE.6) • In Module 4, Lesson 25, students develop an understanding of inequalities and equations by using bar diagrams, number lines and algebra. (6.EE.B) The materials provide opportunities for students to demonstrate conceptual understanding independently throughout the grade level. For example: • In Module 3, Lesson 2, students independently demonstrate an understanding of positive and negative numbers. Students use the number line to represent real-life situations. (6.NS.5) • In Module 4, Lesson 9, students independently demonstrate an understanding of writing expressions by using tables and visual diagrams. Classwork Exercise 2 states, “Write two expressions to show w increased by 4. Then, draw models to prove that both expressions represent the same thing.” (6.EE.A) • In Module 4, Lesson 24, Exit Ticket, students independently demonstrate an understanding of solving an equation or inequality. Students state when the given equations and inequalities will be true and when they will be false. (6.EE.6) ##### 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 6 meet expectations that they attend to those standards that set an expectation of procedural skill and fluency. The instructional materials develop procedural skill and fluency throughout the grade level. For example: • In Module 2, Lesson 13, students develop procedural skill and fluency by explaining how the standard algorithm works when dividing multi-digit numbers. The Closing section of the Teacher Materials state, “Explain in your own words how the division algorithm works.” (6.NS.2) • In Module 2, Lesson 14, students develop procedural skill and fluency by converting decimal division into whole-number division using fractions. The teacher is prompted to ask the following questions in Classwork Example 2, “We determined that when we multiply a divisor by a power of ten, the decimal point is moved to the right the number of times we multiply by a power of ten. How many places does the decimal point move to the right when we multiply the divisor by ten? Explain why the decimal point moves twice to the right when we multiply the divisor by one hundred? We can use decomposition to explain.” (6.NS.3) The instructional materials provide opportunities to demonstrate procedural skill and fluency independently throughout the grade level. For example: • In Module 5, Lesson 1, students independently demonstrate procedural skill and fluency with decimal operations. Problem Set Question 9 states, “A parallelogram has an area of 20.3 cm squared and a base of 2.5 cm. Write an equation that relates the area to the base and height, h. Solve the equation to determine the height of the parallelogram.” (6.NS.3) • In Module 5, Lesson 18, students independently demonstrate procedural skill and fluency of decimal operations when calculating the surface area of a rectangular prism. Problem Set Question 2 states, “Calculate the surface area of each figure below. Figures are not drawn to scale. 2.3 cm, 8.4 cm, 18.7 cm.” (6.NS.3) • In Module 6, Lesson 8, students independently demonstrate procedural skill and fluency of multi-digit division with the standard division algorithm when calculating mean and mean absolute deviation. Classwork Exercise 1, Problem 1 states, “Use the data in the table provided in Example 1 to answer the following: Calculate the mean of the monthly average temperature for each city.” (6.NS.2) ##### 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 6 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 1, Lesson 19, students engage in grade-level mathematics when solving various problems involving unit rates. Classwork Exercise 1 states, “Bryan and ShaNiece are both training for a bike race and want to compare who rides his or her bike at a faster rate. Both bikers use apps on their phones to record the time and distance of their bike rides. Bryan’s app keeps track of his route on a table, and ShaNiece’s app present the information on a graph. The information is shown below. At what rate does each biker travel? Explain how you arrived at your answer. ShaNiece wants to win the bike race. Make a new graph to show the speed ShaNiece would have to ride her bike in order to beat Bryan.” (6.RP.3b) • In Module 4, Lesson 32, students engage in grade-level mathematics when writing equations with two-variables representing the total amount of money saved. Classroom Exercise 1 states, “Each week Quentin earns$30. If he saves this money, create a graph that shows the total amount of money Quentin has saved from week 1 through week 8. Write an equation that represents the relationship between the number of weeks that Quentin has saved his money, w, and the total amount of money in dollars he has saved, s. Then, name the independent and dependent variables. Write a sentence that shows this relationship.” (6.EE.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 2, Lesson 5, students independently demonstrate the use of mathematics by creating their own story problems by applying their understanding of division. The Exit Ticket states, “Write a story problem using the measurement interpretation of division for the following: 3/4 divided by 1/8 = 6.” (6.NS.1)
• In Module 4, Lesson 29, students independently demonstrate the use of mathematics by by writing equations and creating tables to determine the amount of dog food to purchase. The Exit Ticket states, “A pet store owner, Byron, needs to determine how much food he needs to feed the animals. Byron knows that he needs to order the same amount of bird food as hamster food. He needs four times as much dog food as bird food and needs half the amount of cat food as dog food. If Byron orders 600 packages of animal food, how much dog food does he buy? Let ???????? represent the number of packages of bird food Byron purchased for the pet store.” (6.EE.7)
• In Module 5, Lesson 11, students independently demonstrate the use of mathematics by calculating the volume of a rectangular prism with fractional sides to solve a real-world problem. Classwork Exercise 3 states, “A toy company is packaging its toys to be shipped. Each small toy is placed inside a cube-shaped box with side lengths of ½ in. These smaller boxes are then placed into a larger box with dimensions of 12 in. x 4 1/2 in. x 3 1/2 in. What is the greatest number of small toy boxes that can be packed into the larger box for shipping? Use the number of small toy boxes that can be shipped in the larger box to help determine the volume of the shipping box.” (6.G.2).
##### Indicator {{'2d' | indicatorName}}
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 6 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. Fluency is also addressed as an independent component in selected lessons. 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 4, Lesson 8, students develop conceptual understanding of expressions in which letters stand for numbers. Classwork Example 2 states, “g x 1 = g, Remember a letter in a mathematical expression represents a number. Can we replace g with any number? Choose a value for g, and replace g with that number in the equation. What do you observe? Will all values of g result in a true number sentence? Experiment with different values before making your claim. Write the mathematical language for this property below:” (6.EE.2a).
• In Module 5, Lesson 17, students practice fluency of solving one-step equations using addition or subtraction with some equations requiring decimal calculations. Fluency-Addition and Subtraction Equations-Round 1 Question 28 states, “23.6 = m - 7.1” (6.EE.7)
• In Module 5, Lesson 19, students engage in the application of mathematics when solving real-world problems involving surface area. Problem Set Question 5 states, “A swimming pool is 8 meters long, 6 meters wide, and 2 meters deep. The water-resistant paint needed for the pool costs \$6 per square meter. How much will it cost to paint the pool? How many faces of the pool do you have to paint? How much paint (in square meters) do you need to paint the pool? How much will it cost to paint the pool?” (6.G.4)

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 1, Lesson 5, students develop conceptual understanding of equivalent ratios by drawing tape diagrams to solve real-world problems. Classwork Example 1 states, “A County Superintendent of Highways is interested in the numbers of different types of vehicles that regularly travel within his county. In the month of August, a total of 192 registrations were purchased for passenger cars and pickup trucks at the local Department of Motor Vehicles (DMV). The DMV reported that in the month of August, for every 5 passenger cars registered, there were 7 pickup trucks registered. How many of each type of vehicle were registered in the county in the month of August? Using the information in the problem, write four different ratios and describe the meaning of each. Make a tape diagram that represents the quantities in the part-to-part ratios that you wrote. How many equal-sized part does the tape diagram consist of? What total quantity does the tape diagram represent?” (6.RP.3)
• In Module 2, Lesson 4, students practice procedural skill and fluency of dividing a fraction by a fraction as they solve real-world problems. Classwork Example 1 states, “Molly has 1 3/8 cups of strawberries. She needs 3/8 cup of strawberries to make one batch of muffins. How many batches can Molly make? Use a model to support your answer.” (6.NS.1)

#### 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 6 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.

##### Indicator {{'2e' | indicatorName}}
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 6 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 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 3, the explanation for MP 7 states, “Look for and make use of structure. Students understand the placement of negative numbers on a number line by observing the patterns that exist between negative and positive numbers with respect to zero. They recognize that two numbers are opposites if they are the same distance from zero and that zero is its own opposite. Students extend their understanding of the number line's structure to the coordinate plane to determine a point’s location. They recognize the relationship between the signs of a point’s coordinates and the quadrant in which the point lies.”

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

##### Indicator {{'2f' | indicatorName}}
Materials carefully attend to the full meaning of each practice standard

The instructional materials reviewed for Eureka Grade 6 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 4, MP 6 is identified in the teacher edition and attends to the full meaning of the practice when students clarify any misconceptions about how to represent situations as integers. “Seven blocks to the left” would not be written as “-7 blocks from the bookstore” or “-7 units from 0. Positive numbers are counting numbers and do not have a sign.”
• In Module 4, Lesson 4, MP 8 is identified in the teacher edition and attends to the full meaning of the practice when students determine if the relationship between division and subtraction is always true. “Determine the relationship between 20/5 = 4 and 20 - 5-5-5-5 = 0. Is this relationship always true? Let’s try to prove that it is.”
• In Module 5, Lesson 14, MP 7 is identified in the teacher edition and attends to the full meaning of the practice where students discuss how to find the volume of a sandbox. However, MP 7 is not listed at the beginning of the module.

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

• In Module 1, Lesson 5, MP 5 is identified in the teacher edition where students demonstrate how to calculate the number of different types of vehicles. “Find the values of the partial quantities in Example 2. Since every section of the tape diagram represents 12 vehicles, demonstrate how to calculate the number of each type of vehicle. 168 non-commercial vehicles and 60 commercial vehicles.” This is an example of not attending to the full practice as students are given a tape diagram to use to solve the problem. Students do not choose the appropriate tool to solve the problem.
• In Module 5, Lesson 6, MP 5 is identified in the teacher edition where students take measurements of a real-world object. The Discussion states: “All students should understand which measurement units to use and to what precision they are expected to measure.“ Students are provided the measurement instrument and thus do not choose the appropriate tool.
##### Indicator {{'2g' | indicatorName}}
Emphasis on Mathematical Reasoning: Materials support the Standards' emphasis on mathematical reasoning by:
##### Indicator {{'2g.i' | indicatorName}}
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 6 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 5, Lesson 3, students analyze the arguments of others when finding the area of the triangle. Classwork Exercise 4 states, “Joe found the area of a triangle by writing A = 1/2 (11in.)(4 in.), while Kaitlyn found the area by writing A = 1/2 (3 in.)(4 in.) + 1/2 (8 in.)(4 in.). Explain how each student approached the problem.
• In Module 6, Lesson 12, students analyze the arguments of others when determining the median of a data set. Students determine if the strategy of a fictional student has resulted in a correct value for the median, and explain their decision. Exercise 4d states, “Betse argued that the median was halfway between 60 and 85, or 72.5. Do you think she is right? Why or why not?”
##### Indicator {{'2g.ii' | indicatorName}}
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 6 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.

• In Module 5, Lesson 9, teachers are prompted to allow time for students to share their thinking to their solution to an area problem. There are guiding questions to ask students that support critiquing the work that they did in class. “There appear to be multiple ways to determine the area of a polygon. What do all these methods have in common?”
• In Module 5, Lesson 15, teachers are prompted to facilitate a discussion between students. “Encourage a short discussion, inviting all views.” “As students make claims, ask for supporting evidence of their position.”

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 the students in a debate. “Allow students to indicate their answers orally for each problem and debate with classmates when there are disagreements.” However, there are no suggestions or directives for ways to teach students debate skills when there are disagreements.
• In Module 3, Lesson 9, teachers are prompted to allow time for students to share their solutions and explain their reasoning. There are no directives or suggestions for facilitating any student to student discourse and the prompt reads more as the directions to the exercises. “Students read each of the following scenarios and decide whether they agree or disagree. They must defend and explain their stance in writing. Allow time for students to share their answers with the class and explain their reasoning. The class should come to a consensus for each one.”
##### Indicator {{'2g.iii' | indicatorName}}
Materials explicitly attend to the specialized language of mathematics.

The instructional materials reviewed for Eureka Grade 6 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 1, Lesson 1, teachers are prompted to “Encourage students to be precise about the order in which the quantities are stated (emphasizing that order matters) and about the quantities being compared.” An example is provided for the teacher stating, “That is, instead of saying the ratio of boys to girls, encourage them to say the ratio of the number of boys to the number of girls.”
• In Module 4, Topic D Overview, the instructional material provides explicit instruction in the use of a bar diagram to differentiate between the mathematical terms subtract and subtract from. The Topic D Overview states, “Students also use bar diagrams to differentiate between the mathematical terms subtract and subtract from. For instance, when subtracting b from a, they know they must first represent a in order to take away b, leading to an understanding that the expression must be written a - b.”

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

• In Module 1, Lesson 1, the student materials use precise language when stating ratios between quantities. Problem Set Question 2b states, “What is the ratio of the number of milk cartons remaining to the number of milk cartons taken?”
• In Module 2, Lesson 2, students draw upon previously learned vocabulary in order to represent new vocabulary (multiplicative inverse.) Example 1 Question 1 states, “As you travel to each model, be sure to answer the following questions: How many ½ miles are in 12 miles? Corresponding division expression. Corresponding Multiplication Expression. Write an equation showing the equivalence of the two expressions.”
• In Module 4, Lesson 22, students use the precise language of using formulas in geometry. Example 3 states, “This box has a width, w. The height of the box, h, is twice the width. The length of the box, l, is three times the width. That is, the width, height, and length of a rectangular prism are in the ratio of 1:2:3. For rectangular solids like this, the volume is calculated by multiplying length times width times height. Follow the above example to calculate the volume of these rectangular solids, given the width, w.”

### 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 6 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 6 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 6 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 6 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 use mathematical models such as number lines, double number lines, tape diagrams, graphs and tables. For example, in Module 1, Lesson 3, students create and share one-sentence story problems about a ratio and represent this ratio with a table and a tape diagram. The students conjecture what the ratio would be if each bar of the tape diagram represents twice what it did before and justify their answer in writing.

Students produce solutions, construct viable arguments, and critique the reasoning of others within all components of the instructional materials including group and partner discussions. 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 6 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 measurement and geometry tools. In Module 5 Lesson 11, students use centimeter cubes when finding the volume of a rectangular prism with fractional dimensions.

Examples of manipulatives for Grade 6 include:

• Compasses
• Centimeter Cubes
• Set Squares
• Scientific Calculators
• Rulers
• Meter Sticks
##### 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 6 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 6 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 6 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 3, Lesson 11, a Closing question states, “How can we use absolute value to determine magnitude? For instance, how far below zero is -8 degrees?”

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 6 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 6 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 or accessible 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 at the beginning that gives teachers an understanding of the mathematical content in the lessons as well as where it fits in the scope of math 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 6 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 6 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 6 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 6 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 6 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 6 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 6 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 6 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 6 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 6 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 6 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 6 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 6 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.

##### 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 6 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 edition. 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 edition; 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 6 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 6 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 6 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 6 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

## Report for {{ report.grade.shortname }}

### Overall Summary

###### Alignment
{{ report.alignment.label }}
###### Usability
{{ report.usability.label }}

### {{ gateway.title }}

##### Gateway {{ gateway.number }}
{{ gateway.status.label }}