## Eureka Math

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### Overall Summary

The instructional materials for Eureka Grade 2 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
Meets Expectations

### Focus & Coherence

The instructional materials for Eureka Grade 2 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 2 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 Grade 2 meet the expectations for focus within assessment. Overall, the instructional material does not assess any content from future grades within the summative assessment sections of each module. These assessments are the Mid-Module and End-of-Module assessments. Examples of the assessments include:

• In Module 3, End-of-Module Assessment Task: Students engage with place value (2.NBT.1-4). Students compare numbers and write numbers in standard, expanded and word form.
• In Module 4, Mid-Module Assessment Task: Students build fluency with addition/subtraction and use them in 1-step or 2-step word problems (2.OA.1). Students are assessed on strategies/algorithms for addition/subtraction. The materials state, “1. Solve. Show your mental math strategy. 35 + 25 = ___. 2.) Solve and show your work with a model. 116 + 74 = ____. 4. Sarah solved the word problem below. 4a. Explain why Sarah’s addition strategy worked. 4b. There are 18 fewer cats than birds. How many birds are in Cuddle’s Pet Shop? Use another place-value strategy to find the answer. Show your work.”
• In Module 6, Mid-Module Assessment Task: Students work with arrays and repeated addition to build a foundation for multiplication in Grade 3 (2.OA.4). Question 4 states, “Sarah won a prize at school! Her teacher said that she would have two choices for the prize: Choice 1: Get $3 a day for the next 3 days. Choice 2: Get$2 a day for the next 5 days. Draw an array for each choice. Which way would Sarah get more money? Explain how you know.”

#### 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 2 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 2 meet expectations for spending a majority of instructional time on major work of the grade. This includes clusters A and B in 2.OA, all clusters in 2.NBT and clusters A and B in 2.MD.

• 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 152 lesson days, approximately 100 days (66 percent) are spent on the major clusters of the grade.
• Of the eight modules, Modules 1, 2, 4 and 5 focus on major work. Modules 3 and 7 devote a few lessons to supporting work.
• Of the 28 assessment days, 20 assess 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 2 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 2 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 3, Lesson 8: 2.MD.8 supports the major work of 2.NBT.8. Using monetary amounts, students mentally add 10 and use place value. Problem Set Questions 1-12 state, “Show each amount of money using 10 bills: $100,$10 and $1 bills. Whisper and write each amount of money in expanded form. Write the total value of each set of bills as a number bond.” • In Module 7, Lesson 3: 2.MD.D supports the major work of 2.MD.B. Students create bar graphs of data for four different categories and then with teacher guidance turn the graph sideways and compare to a number line with equal spacing of numbers. • In Module 7, Lesson 7: 2.MD.8 supports the major work of 2.NBT.2, 2.NBT.5 and 2.NBT.6. Students solve word problems using the value of coins and addition and subtraction. Problem Set Questions 1 and 2 state, “Grace has 3 dimes, 2 nickels and 12 pennies. How much money does she have?” and “Lisa has 2 dimes and 4 pennies in one pocket and 4 nickels and 1 quarter in the other pocket. How much money does she have in all?” • In Module 8, Lesson 14: 2.MD.7 supports the major work of 2.NBT.2 and 2.OA.2. While working with time, students mentally count by 5’s. “Fill in the missing numbers. 0, 5, 10, _____, _____, _____, _____, 35, _____, _____, _____, _____, ____ ____, _____, _____, 45, 40, _____, _____, _____, 20, 15, _____, ____, ____. Fill in the missing minutes on the face of the clock.” • In Module 8, Lesson 4: 2.G.A supports the major work of 2.MD.A. Students identify shapes by the number of sides they have. Students construct shapes by measuring to specific lengths in centimeters using a ruler. ##### 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 2 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 eight modules. Instruction and assessment days are included in the following count: • Module 1: 10 days • Module 2: 12 days • Module 3: 25 days • Module 4: 35 days • Module 5: 24 days • Module 6: 24 days • Module 7: 30 days • Module 8: 20 days All lessons are paced to be 60 minutes in length. Lessons include fluency practice, application problems, concept development and a student debrief. Lessons vary in amount of time spent on various sections, but time estimates are reasonable and appropriate for the activities described. ##### 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 2 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. The lessons support the progression of Grade 2 standards by explicitly stating connections to prior or future grades. The following examples are from Module 8: • “In the final module students extend their understanding of part–whole relationships through the lens of geometry. As students compose and decompose shapes, they begin to develop an understanding of unit fractions as equal parts of a whole.” • “Students build on their prior knowledge of a shape’s defining attributes.” • “Students apply their understanding of partitioning the whole into halves and fourths to tell time to the nearest five minutes.” • “If pacing is a challenge, consider consolidating Lessons 9 and 10.” Foundational standards from Kindergarten and Grade 1 are included. An example from Module 1 is: • Add and subtract within 20 1.OA.5 | 1.OA.6 • Number and Operations in Base Ten K.NBT.1 | 1.NBT.2.a | 1.NBT.2.b |1.NBT.2.c | 1.NBT.4 | 1.NBT.5 | 1.NBT.6 • Operations and Algebraic Thinking K.OA.3 | K.OA.4 | 1.OA.5 | 1.OA.6 • Understand addition and understand subtraction K.OA.3 | K.OA.4 • Understand place value 1.NBT.2.a | 1.NBT.2.b | 1.NBT.2.c • Use place-value understanding and properties of operations to add and subtract 1.NBT.4 | 1.NBT.5 | 1.NBT.6 • Work with numbers 11-19 to gain foundations for place value K.NBT.1 The instructional materials attend to the full intent of the grade-level standards by giving all students extensive work with grade-level problems. The following examples are from Module 4: • Module 4 builds on place-value understanding, allowing students to compose and decompose place- value units to add and subtract within 200. Students apply fluency to one and two-step word problems within 100. • In Lesson 3, students work on mental addition and subtraction. Problem Set Question 2 states, “Solve using the arrow way, number bonds, or mental math. Use scrap paper if needed.” • In Lesson 8, students build fluency in two-digit addition and subtraction within 100. Problem Set Question 1 states, “Solve vertically. Draw and bundle place-value disks on the place-value chart.” • In Lesson 15, students build fluency in two-digit addition and subtraction within 100. Exit Ticket Question 1 states, “Solve using vertical form. Show the subtraction on a place-value chart with chips. Exchange 1 ten for 10 ones, when necessary. 164 - 49” • In Lesson 23, students are encouraged to be flexible in their thinking and to use multiple strategies in solving problems, including the use of drawings such as tape diagrams, which they relate to equations. Problem Set Question 2 states, “Use a number bond to show how you would take 8 tens from 126.” ##### 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 2 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 4, Lesson 6: “Use manipulatives to represent the composition of 10 ones as 1 ten with two-digit addends.” is shaped by 2.NBT.B, “Use Place Value Understanding and Properties of Operations to Add and Subtract.” • In Module 7, Topic A: “Problem Solving with Categorical Data” is shaped by 2.MD.D, “Represent and Interpret Data.” 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 7, Lesson 23: Measurement and Data (2.MD) connects to Operations and Algebraic Thinking (2.OA). Students record data using tally marks and problem solve with addition/subtraction. Exit Ticket Question 2 states, “If 8 more lines were measured to be longer than 5 inches and 12 more lines were measured to be shorter than 5 inches, how many tallies would be in the chart?” • Module 8, Lesson 16: Measurement and Data (2.MD) connects to Number and Operations in Base Ten. Students apply subtraction skills to solve problems involving time intervals. Problem Set Questions 2a and 2b state, “Tracy arrives at school at 7:30 a.m. She leaves school at 3:30 p.m. How long is Tracy at school?” and “Anna spent 3 hours at dance practice. She finished at 6:15 p.m. What time did she start?” ###### Overview of Gateway 2 ### Rigor & Mathematical Practices The instructional materials for Eureka Grade 2 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 emphasize mathematical reasoning, partially identify the Mathematical Practices (MPs), and partially attend to the full meaning of each practice standard. ##### 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 2 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 2 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 3, Lesson 1, students develop conceptual understanding of place value. Students work with teacher guidance to count 1000 straws. The teacher leads students in creating bundles using place value (ten ones to make a ten, ten tens to make a hundred) and discusses with students how each place value contains the collection of the preceding place, i.e., the number of tens contained in 100. (2.NBT.A) • In Module 6, Lesson 6, students develop conceptual understanding of the foundation for multiplication. Students practice using addition to find the total number of objects arranged in an array. Problem Set Question 1a states, “Complete each missing part describing each array. Circle rows. 5 rows of ___ = ___ + ___ + ___ + ___ + ___ = ___.” (2.OA.4) The materials provide opportunities for students to demonstrate conceptual understanding independentlythroughout the grade level. For example: • In Module 3, Lesson 20, students independently demonstrate conceptual understanding of place value. Students model 10 more and 10 less when solving word problems involving changing the hundreds place. Problem Set Question 4 states, “Jenny loves jumping rope. Each time she jumps, she skip-counts by 10s. She starts her first jump at 77, her favorite number. How many times does Jenny have to jump to get to 147? Explain your thinking below.” (2.OA) • In Module 5, Lesson 19, students independently demonstrate conceptual understanding of place value. Students choose which strategies to apply to a variety of addition and subtraction problems and explain their choices/listen to the reasoning of their peers. In the Concept Development part of the lesson, the teacher is prompted to ask the following questions, “Problem 1: 180 + 440. Give students three minutes to solve the problem using the strategy of their choice. T: Turn and talk: Explain your strategy and why you chose it to your small group. S1: I used a chip model to represent the hundreds and tens for each number because there were no ones. Then, I added the tens together and the hundreds together. Since there were 12 tens, I renamed 10 tens as 1 hundred, and that leaves 2 tens. 5 hundreds and 1 hundred more makes 6 hundreds. So, my answer is 620. S2: I used the arrow way. I started with 180, added 400 to get 580, added 20 to make 600, and added 20 more is 620. S3: I used a number bond to take apart 440. I took 20 from the 440 and added it to 180 to make 200. 200 plus 420 is 620.” (2.NBT.B) ##### 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 2 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 4, Lesson 14, students develop procedural skill and fluency of adding and subtracting within 100 using strategies based on place value. The teacher is prompted to ask the following questions, “T: (Write 184.) Say the number in standard form. S: 184. T: What digit is in the tens place? S: 8. T: (Underline 8.) What’s the value of the 8? S: 80. T: State the value of the digit 1. S: 100. T: 4? S: 4. Repeat using the following possible sequence: 173, 256, and 398.” • In Module 6, Lesson 12, students develop procedural skill and fluency of adding and subtracting within 100 using strategies based on place value. Students complete the activity, Compensation. This activity reviews the mental math strategy of compensation, which is, by making a multiple of 10, students solve a much simpler addition problem. “Using number bonds for visualization: T: (Write 42 + 19 = ____.) Let’s use a mental math strategy to add. How much more does 19 need to make the next ten? S: 1 more. T: Where can 19 get 1 more from? S: From the 42. T: Take 1 from 42, and give it to 19. Say the new simplified number sentence with the answer. S: 41 + 20 = 61. T: So, 42 + 19 is…? S: 61. T: 37 + 19? S: 36 + 20 = 56.” The instructional materials provide opportunities to demonstrate procedural skill and fluency independently throughout the grade level. For example: • In Module 4, Lesson 20, students independently demonstrate procedural skill and fluency of adding within 100 by using a place-value chart to solve a problem. Problem Set Question 1 states, “Solve vertically. Draw chips on the place-value chart and bundle, when needed. a. 23 + 57 = ____.” • In Module 4, Lesson 27, students independently demonstrate procedural skill and fluency of subtracting within 100 by using a place-value chart to solve a problem. Problem Set Question 2a states, “Solve vertically. Draw chips on the place-value chart. Unbundle when needed. A. 100 - 61 = ____.” Students build fluency for adding and subtracting to 20 using mental strategies in 5-10 minute fluency practice activities before lessons. These fluency practices are provided in all eight modules. For example: • In Module 3, Lesson 12, students complete timed “sprints” to practice a variety of addition facts within 20. • In Module 3, Lesson 14, students complete timed “sprints” to practice a variety of subtraction facts within 20. • In Module 5, students practice subtracting from a number which has tens (primarily teens numbers) by a single-digit number. Students begin using pennies and dimes to count and add different totals. • In Module 6, students utilize “sprints,” coins, flashcards and differentiated problems selected by the teacher to build fluency for addition and subtraction up to 20, primarily working with addition and subtraction of teen numbers. Students build fluency for adding and subtracting within a 100 in 5-10 minute fluency practice activities before lessons. These fluency practices are provided in all eight modules. For example: • In Module 1, students subtract a single-digit number from a multiple of ten. • In Module 3, students use meter sticks to both add and subtract different numbers from multiples of ten within 100. • In Module 4, students practice addition and subtraction to 100, primarily by adding and subtracting by tens (making a ten to add or to subtract, counting numbers of tens). • In Module 5, students subtract tens within 100, use compensation to subtract, practice subtraction that crosses multiples of tens, and use linking cubes to model subtraction facts. • In Module 8, students practice using addition to solve subtraction facts quickly. ##### 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 2 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 solving two-step story problems using tape diagrams and number bonds. The Concept Development Problem 3 states, “Solve a two-step problem by drawing a tape diagram and using a number bond to solve. There are 31 students on the red bus. There are 29 more students on the yellow bus than the red bus. How many student are on the yellow bus? How many students are on both buses combined?” (2.OA.1) • In Module 5, Lesson 14, students engage in grade-level mathematics when solving one and two-step word problems within 100. The Application Problem states, “Brienne has 23 fewer pennies than Alonzo. Alonzo has 45 pennies. How many pennies does Brienne have? How many pennies do Alonzo and Brienne have altogether?” (2.OA.1) • In Module 6, Lesson 9, students engage in grade-level mathematics when solving word problems involving addition of equal groups. Concept Development Problem 2 states, “Miss Tam arranges desks into 4 rows of 5. How many desks are in her classroom? Draw a picture to solve, and write a repeated addition equation. Then, write a statement of your answer.” (2.OA.4) 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 13, students independently demonstrate the use of mathematics by solving two-step story problems using tape diagrams and number bonds. The Application Problem states, “A fruit seller buys a carton of 90 apples. Finding that 18 of them are rotten, he throws them away. He sells 22 of the ones that are left on Monday. Now, how many apples does he have left to sell? Note: This problem is designed for independent practice. Possibly encourage students to use the RDW process without dictating what to draw. Two-step problems challenge students to think through the first step before moving on to the second. The number sentences can help them to see and articulate the steps as well.” (2.OA.1) • In Module 4, Lesson 16, students independently demonstrate the use of mathematics by using place-value strategies to solve one and two-step word problems within 100. Problem Set Question 5 states, “Thirty-six books are in the blue bin. The blue bin has 18 more books than the red bin. The yellow bin has 7 more books than the red bin. How many books are in the red bin? How many books are in the yellow bin?” (2.OA.1) • In Module 7, Lesson 20, students independently demonstrate the use of mathematics by solving two-digit addition and subtraction problems involving length. Problem Set Question 5 states, “Solve using tape diagrams. Use a symbol for the unknown. The total length of all three sides of a triangle is 96 feet. The triangle has two sides that are the same length. One of the equal sides measures 40 feet. What is the length of the side that is not equal?” (2.MD.5) ##### 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 2 meet expectations that the three aspects of rigor are not always treated together and are not always treated separately. The lessons include components such as: Fluency Practice, Concept Development, and Application Problems. Conceptual understanding is addressed in Concept Development. During this time, the teacher guides students through a new concept or an extension of the previous day’s learning. Students engage in practicing procedures and fact fluency while modeling and solving these concepts. Fluency is also addressed as an independent component within most lessons. Lessons may contain an Application Problem which connects previous learning to what students are learning for the day. 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 5, Lesson 18, students engage in the application of mathematics by solving a real-world problem involving subtraction and addition within 100. The Application Problem states, “Joseph collected 49 golf balls from the course. He still had 38 fewer than his friend Ethan. How many golf balls did Ethan have? If Ethan gave Joseph 24 golf balls, who had more golf balls? How many more?” (2.OA.1) • In Module 7, Lesson 2, students develop conceptual understanding of representing a data set with up to four categories by creating a picture graph. Problem Set Question 1 states, “Use grid paper to create a picture graph below using data provided in the table. Then, answer the questions.” (2.MD.10) • In Module 2, Lesson 8, students practice addition fluency within 100 by filling in the missing number of the given addition equation. Sprint Question 11 states, “23 cm + ___ = 100 cm” (2.NBT.5) 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 8, students develop conceptual understanding of place value and practice fluency of addition within 1000 when when writing the amount of money in expanded form. Problem Set Question 1 states, “Show each amount of money using 10 bills:$100, $10, and$1 bills. Whisper and write each amount of money in expanded form. Write the total value of each set of bills as a number bond. \$136” (2.NBT.1)
• In Module 4, Lesson 25, students develop conceptual understanding of place value and practice fluency of subtraction within 100 when using place-value chips and place-value disks to solve problems. Problem Set Question 1a states, “Solve the following problem(s) using the vertical form, your place-value chart, and place-value disks. Unbundle a ten or hundred when necessary. Show your work for each problem. 72 - 49” (2.NBT.5)

#### 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 2 partially meet the expectation for meaningfully connecting the Standards for Mathematical Content and the Standards for Mathematical Practice. Overall, the materials emphasize mathematical reasoning by prompting students to construct viable arguments and analyze the arguments of others, assist teachers in engaging students in constructing viable arguments and analyzing 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 2 partially meet expectations that the Standards for Mathematical Practice are identified and used to enrich mathematics content within and throughout the grade level.

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 well 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 1, the explanation for MP 2 states, “Reason abstractly and quantitatively. Students reason abstractly when they decontextualize a word problem, representing a situation with a number sentence (e.g., Mark had a stick of 9 green linking cubes. His friend gave him 4 yellow linking cubes. How many linking cubes does Mark have now?). In their solutions, students write 9 + 4 = 13. In so doing, they have decontextualized the quantity from the situation. They then contextualize the solution when they write a statement of the answer (e.g., “Mark has 13 linking cubes now.”). They reason that the 13 refers to the quantity, or number, of linking cubes.”

Each lesson specifically identifies where MPs are located, usually within the margins of the teacher edition. However, there is no additional teacher guidance or explanation as to how the practice enriches the content specifically within that lesson. This is evident in all modules within the series.

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

The instructional materials reviewed for Eureka Grade 2 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 6, Lesson 10, MP 4 is identified in the teacher edition and attends to the full meaning of the practice when the students use tiles to make arrays that relate to repeated addition. “T: Now, keep 16 tiles on your desk, and put the rest in your bag. T: Create an array with equal rows and columns. S: (Create equal rows and columns.) T: What strategies did you use to figure out how many rows and how many columns? S: I started by creating groups of 2. Then, I realized that if I made groups of 4, I would have 4 groups. I know that 4 + 4 + 4 + 4 = 16, so I made 4 rows of 4. I made two rows of eight and then saw it was a double of 2 rows of 4, so I just moved half the tiles down.”
• In Module 5, Lesson 15, MP 7 is identified in the teacher edition and attends to the full meaning of the practice when the students look for and make use of structure when justifying why a statement is true. “T: Read the complete number sentence. S: 941 – 587 = 354. T: How can you prove that this statement is true? If 941 – 587 = 354, then 354 + 587 = 941. Discuss this with your partner. S: You can draw a number bond. You could do the addition and see if it equals the whole. If 354 is the missing part, when you add it to the other part, 587, it will equal the whole, 941. T: Please check the answer by drawing a chip model to add 354 + 587. Check your model and addition with your partner. If you are correct, write the number bond for this problem.”
• In Module 3, Lesson 19, MP 8 is identified in the teacher edition and attends to the full meaning of the practice when students discuss how 1 more and 10 more changes numbers in a place value. “T: Talk to your partner about how our 1 more and 10 more lists are the same and different. S: The hundreds are all the same. In both lists, only 1 number changes. When we count by tens, the tens place changes, same for the ones. The numbers in both lists grow by 1 each time. They look like they’re growing by 1 in the tens list, but they’re really growing by 10. T: (Label a 100 more list to the left of 10 more.) Let’s count by hundreds. What place will change? S: The hundreds place!”

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

• In Module 7, Lesson 23, MP 5 is identified in the teacher edition where students use a ruler to measure their handspan. “T: Now, stretch your fingers all the way out. (Demonstrate.) T: Talk to a partner. How many inches do you think it is from the tip of your pinky to the tip of your thumb? S: (Various guesses.) T: This measurement from the tip of our pinky to the tip of our thumb is called our handspan. We will be measuring that today. T: (Hold the ruler with the right hand, and show the ruler against the handspan, as in the picture to the right, mirroring what students will do.) Look at how I measure my handspan. What are some important things I need to remember when I measure this? S: Start measuring at zero on the ruler. Remember what unit you are using. Notice where your handspan starts and ends. T: Very good! I just measured my handspan, and it is ___ inches. Even though it was not exactly that many inches, I said it was about ___ inches because it was closer to the next whole inch. (Write the measurement on the board.)” This is an example of not attending to the full practice as students are told to use a ruler to measure the length of their hand.
##### 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 2 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. For example:

• In Module 2, Lesson 7, the materials prompt students to analyze a measurement solution and explain why the solution was incorrect. Problem Set Question 4 states, “Christina measured Line F with quarters and Line G with pennies. Line F is about 6 quarters long. Line G is about 8 pennies long. Christina said Line G is longer because 8 is a bigger number than 6. Explain why Christina is incorrect.”
• In Module 4, Lesson 10, the materials prompt students to analyze a place-value model of an addition problem and fill in the missing addends of the equation. Homework Question 4 states, “Jamie started to solve this problem when she accidentally dropped paint on her sheet. Can you figure out what problem she was given and her answer by looking at her work?”
• In Module 5, Lesson 7, the materials prompt students to analyze a subtraction equation and the strategy used to solve it. Problem Set Question 2 states, “Circle the student work that correctly shows a strategy to solve 721 - 490. Fix the work that is incorrect by making a new drawing in the space below with a matching number sentence.”
• In Module 5, Lesson 18, the materials prompt students to analyze two subtraction equations and explain why the strategy used provided a correct solution. Problem Set Question 4 states, “Prove the students' strategy by solving both problems to check that their solutions are the same. Explain to your partner why this way works. 800 - 543 = ___, 799 - 542 = ___.”
##### 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 2 meet expectations for assisting teachers in engaging students to construct viable arguments and analyze the arguments of others concerning key grade-level mathematics.

Teacher materials assist teachers in engaging students in both constructing viable arguments and analyzing the arguments of others, frequently throughout the program. The teacher materials consistently provide teachers with question prompts for student discussion and possible student responses to support that discussion. For example:

• In Module 2, Lesson 7, teachers are prompted to engage students in constructing an argument by having students measure the lengths of different objects in paperclips and discussing with a partner the reason that some of the lengths may be different. “T: Measure your straw with your paper clips. T: How long is the straw? T: Why do you think the measurements are different? Turn and talk.”
• In Module 4, Lesson 10, teachers are prompted to engage students in constructing an argument and analyze the arguments of others by having students discuss the differences and similarities between two addition models. “When students have finished, invite two volunteers to the board. One draws a model of 35 + 106 before bundling a ten. The other draws the model after bundling the ten. Encourage the remaining students to be active observers and to notice the similarities and differences between the models. T: Talk with your partner. Describe how the models are similar and different before and after bundling a ten.”
• In Module 5, Lesson 7, teachers are prompted to engage students in constructing an argument and analyzing the arguments of others by having students discuss the different strategies used to solve addition problems. “T: (Write 697 + 223) The problem is 697 + 223. Turn and talk to your partner about how you would solve this problem. T: How did Student A solve this problem? Explain to your partner what this student was thinking. What strategy did Student A use? T: Let’s look at a different way to solve this. T: What did Student B choose to do? Turn and talk. T: Which way would you do it? Discuss with your partner.”
• In Module 8, Lesson 3, teachers are prompted to engage students in constructing an argument and analyzing the arguments of others by asking students a combination of questions to facilitate a discussion about the attributes of two-dimensional shapes. “Any combination of the questions below may be used to lead the discussion. T: Look at Problems 1(b) and 2(b). How are these problems similar? How are they different? T: Look at Problems 1(d) and 2(d). Do all of your six-sided polygons look alike? What can we call a six-sided polygon? Can hexagons have five sides? Why not? T: Look closely at our polygon chart. Do you agree with the way that we sorted and named all of the polygons? If not, which do you disagree with and why?”
##### Indicator {{'2g.iii' | indicatorName}}
Materials explicitly attend to the specialized language of mathematics.

The instructional materials reviewed for Eureka Grade 2 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. A compiled list of the terms along with their definitions is found in the Terminology tab at the beginning of each module. Each mathematical term that is introduced has an explanation, and some terms are supported with an example.

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. 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.

• In Module 2, Lesson 6, the Notes on Multiple Means of Action and Expression states, “Couple comparative vocabulary with illustrative gestures and questions such as the following: Who is taller? Shorter? (Ask with students standing back to back.) How wide is this shoe? How long? Which shoe is longer? Which shoe is shorter? Point to visuals while speaking to highlight the corresponding vocabulary.”
• In Module 3, Lesson 20, the Notes on Multiple Means of Action and Expression states, “The complexity of moving 10 less and changing the hundreds place together can be a big jump for some students. Therefore, use the language of tens for the following problem: What is 10 less than 508? T: How many tens are in 508? S: 50 tens.”
• In Module 6, Lesson 20, the Notes on Multiple Means of Representation states, “At other times in the school day, consider relating the mathematical term even to the everyday term even by asking questions such as the following: What does it mean for kickball teams to be even? When you are playing cards with two people, why do we deal an even number? When we share our grapes with a friend, do we try to make our shares even? What does even mean then?”

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

• In Module 2, Lesson 4, the mathematical term meter is in bold writing within a question listed in the Student Debrief section. These questions guide teachers in leading a class discussion. “What new (or significant) math vocabulary did we learn today? (Chart student responses. Prompt students to list vocabulary from the lesson such as measure, measurement, length, height, length unit, measuring tool, meter tape, meter, and meter stick.)”
• In Module 3, Lesson 5, the materials use precise terminology of unit form and word form while using the terms when showing an example of each. The Concept Development states, “T: (Write on the board ___ hundreds ___ tens ___ ones.) Tell me the number of each unit. (Point to the number modeled in the place-value box.) S: 2 hundreds 3 tens 4 ones. T: That is called unit form. T: We can also write this number as (write on board) two hundred thirty-four. This is the word form. T. Work with your partner with your Hide Zero cards showing 234. Pull the cards apart and push them together. Read the number in unit form and in word form.”
• In Module 6, Lesson 5, the materials use accurate terminology when students create equal rows. Problem Set Question 1 states, “Circle groups of four. Then, draw the triangles into 2 equal rows.”

### Usability

##### Gateway 3
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 2 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 2 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 typical sequence that is facilitated by the teacher and may include components such as Fluency Practice, Application Problem, Concept Development and Student Debrief.

The Fluency Practice component is found in a majority of lessons and builds mastery of grade-level math facts.

Students apply previously learned mathematical knowledge to solve a problem in the Application Problem component of a lesson.

Within the Concept Development component of a lesson, Problems are included in each lesson to be completed by students within the class period either individually or with a partner. These Problems 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 during the Concept Development portion of a lesson.

Most lessons include an Exit Ticket at the end of a lesson. The Exit Ticket is aligned to the Problems 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 Kindergarten 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 2 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. The Read, Draw, Write procedure provides students with an opportunity to represent their solution in a drawing and make connections between the drawing and the equations.

Students use mathematical models such as number lines, number bonds, tape diagrams, tens frames and place-value charts. For example, in Module 4, Lesson 8, students represent their solution to an addition problem on a place-value chart. Problem Set Question 1a states, “Solve vertically. Draw and bundle place value disks on the place-value chart. 27 + 15 = ___”

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 2 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 place-value and measurement tools. In Module 5 Lesson 13, students use place value disks when subtracting 3-digit numbers.

Examples of manipulatives for Grade 2 include:

• Rekenreks
• Dice
• 2-D and 3-D Shapes
• Centimeter Cubes
• Meter Sticks
• Place-Value Disks
• Base Ten Blocks
##### 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 2 is not distracting or chaotic and supports students in engaging thoughtfully with the subject.

The instructional materials follow a consistent visual format. The instructional materials 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 overabundance of text features. Lesson materials for teachers are divided into sections with consistent bold headings such as Concept Development and Student Debrief. Lesson materials for students are labeled as Problem Set to signify individual practice problems. The Homework section of each lesson is visually formatted to match the Problem Set.

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 2 meet the expectations for supporting teacher learning and understanding of the Standards. The instructional materials support: planning and providing learning experiences with quality questions; contain ample and useful notations and suggestions on how to present the content; and contain full, adult-level explanations and examples of the more advanced mathematics concepts in the lessons so that teachers can improve their own knowledge.

##### 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 2 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 narratives for the teacher to help guide student development and provide quality questions. Lessons contain various narratives that are labeled, “Notes on Multiple Means of Representation,” “Notes on Multiple Means of Engagement,” “A Note on Standards Alignment,” “Note on Materials” to name a few. These narratives provide teachers with mathematical summaries of the concept being presented, examples of the concept, suggestions to help students make connections between concepts, and correct vocabulary use within the lesson.

Quality questions are provided for the teacher to guide students through the concepts being taught in the Concept Development section of the lesson. The Student Debrief section provides questions for discussion and guiding questions designed to increase classroom discourse and ensure understanding of the concepts. For example:

• In Module 4, Lesson 3, a Student Debrief question states, “How does mentally adding and subtracting tens help us with numbers that are close to tens, like 19 and 41?”
##### 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 2 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.

The Overview of each module provides several suggestions for delivering instruction such as alignment to standards, important vocabulary, assessment, and foundational skills for future grades.

Each lesson provides teachers with various side narratives and examples on how to present the content. Most lessons have pictures or other graphics with annotations, demonstrating the concepts for the teacher.

The Concept Development section includes a sample script to prepare the teacher for what might happen when presenting the material.

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.

There is a repeated process for solving word problems called the Read, Draw, Write approach, which the manual explains in the module overview.

##### 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 2 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 instructional materials reviewed for Eureka Grade 2 partially meet expectations for explaining the role of the specific grade-level mathematics in the context of the overall mathematics curriculum.

In the Module Overview, there are a few specific descriptions of the coherence of the mathematics; however, it is usually focused on the previous grade level. The previous grade-level standards are listed in the Foundational Standards section. There is no explanation of the role the grade-level mathematics plays to future grades, and the standards for future grades are not listed.

There is no discussion of the grade-level content's role in Kindergarten through Grade 12.

In the document called "A Story of Units: A Curriculum Overview for Grades P-5," there is a description of the module sequence which includes the connection to the previous grade and the next future grade. No connection is made to other grade levels.

##### 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 2 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 2 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 2 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 Units 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 2 partially meet the expectations for offering teachers resources and tools to collect ongoing data about student progress on the Standards. The instructional materials provide opportunities for identifying and addressing common student errors and misconceptions and ongoing review and practice with feedback. The instructional materials do not provide strategies for gathering information about students’ prior knowledge, partially have assessments with standards clearly denoted, and partially 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 2 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 2 meet the expectation for providing strategies for teachers to identify and address common student errors and misconceptions.

Each End of Module Assessment includes a chart titled Progression toward Mastery to help teachers with assessing progress toward mastery.

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

Exit tickets completed during the Student Debrief can be used as informal assessments to identify and address errors and misconceptions. The teacher materials suggest “A review of their work will help with assessing students’ understanding of the concepts that were presented in today’s lesson and planning more effectively for future lessons.”

The marginal notes often suggest ways to support students as a whole and subgroups of students who might need support. In particular, the "Multiple Means of..." notes tend to focus on student misconceptions.

##### 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 2 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 fluency activities, an application problem, concept development practice, 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 Fluency 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 Student Debrief 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 2 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.

The materials reviewed for Grade 2 partially meet the expectations for this indicator. The summative assessments meet the expectations, but the formative assessments do not.

• For the Mid-Module and End-of-Module assessments, there are rubrics for scoring the items, as well as an answer key with sample answers.
• Rubrics and scoring guides are clear and helpful. Examples of student work receiving top grades on the rubric are included.
• In the Progression toward Mastery section of the summative assessments there is a detailed rubric for grading student mastery from 1 to 4. If the student does not achieve total mastery (step 4), then the teacher can look at the next steps to see what or how to follow up with the student. For example, when a student's mastery is step 2, teachers can look at steps 3 and 4 to guide follow-up instruction.
##### Indicator {{'3q' | indicatorName}}
Materials encourage students to monitor their own progress.

The instructional materials for Eureka Grade 2 do not include opportunities for students to monitor their own progress. There is one exception within the Fluency Sprints. Students complete the sprint twice with a goal of increasing their score on the second round.

#### 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 2 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. The instructional materials also consistently 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 2 meet the expectation for providing strategies to help teachers sequence or scaffold lessons so that the content is accessible to all learners.

Lessons are sequenced to build from conceptual understanding, using representations ranging from concrete and pictorial to the more abstract.

Marginal notes in most lessons often suggest ways for teachers to support students as a whole as well as subgroups of students who might need extra support. This includes support for vocabulary, representations, engagement options and materials.

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.

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

The instructional materials reviewed for Eureka Grade 2 meet the expectation for providing teachers with strategies for meeting the needs of a range of learners.

The lesson structure: Fluency, Application Problem, Concept Development, and Student Debrief 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.

The marginal notes often suggest ways to support students as a whole and subgroups of students who might need extra support. This includes support for vocabulary, representations, engagement options, and materials.

##### 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 2 meet the expectation that materials embed tasks with multiple entry­ points that can be solved using a variety of solution strategies or representations.

Most lessons include problems within the components of Application Problem, Problem Sets, and Homework that students can choose their own solution strategy and/or representation as well as solve the problems in a variety of ways.

The embedded tasks include multiple representations such as drawings, charts, graphs, or numbers or words.

##### 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 2 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 marginal notes that provide strategies for English Language Learners and other special populations in the teacher materials. The “Notes on Multiple Means of Engagement” give teachers suggestions about meeting the needs of ELL students. These margin notes include sentence starters, physical responses, and vocabulary support.

On pages 14-20 of "How to Implement A Story of Units," there are suggestions for working with ELL students and students with disabilities. Page 14 states, "It is important to note that the scaffolds/accommodations integrated into A Story of Units might change how a learner accesses information and demonstrates learning; they do not substantially alter the instructional level, content, or performance criteria. Rather, they provide students with choices in how they access content and demonstrate their knowledge and ability."

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

The instructional materials reviewed for Eureka Grade 2 meet the expectation that the materials provide opportunities for advanced students to investigate mathematics content at greater depth.

There are 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.

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.

Teachers are given suggestions for working with above-grade-level students on page 20 of "How to Implement A Story of Units."

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

The instructional materials reviewed for Eureka Grade 2 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 2 provide 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.

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

There are also suggestions for small-group work within the differentiation pages of the "How to Implement" document.

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

The instructional materials reviewed for Eureka Grade 2 occasionally encourage teachers to draw upon home language and culture to facilitate learning.

There is limited evidence of teachers needing to draw upon home language and culture to facilitate learning.

There are occasions (mostly with Spanish) where students are encouraged to make connections to words in their home languages.

"How to Implement A Story of Units" offers teachers this guidance: "Know, use, and make the most of student cultural and home experiences. Build on the student's background knowledge.”

#### 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

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### Overall Summary

###### Alignment
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###### Usability
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##### Gateway {{ gateway.number }}
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