## Alignment: Overall Summary

The instructional materials for Eureka Grade 5 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.

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## Gateway 1:

### Focus & Coherence

0
7
12
14
14
12-14
Meets Expectations
8-11
Partially Meets Expectations
0-7
Does Not Meet Expectations

## Gateway 2:

### Rigor & Mathematical Practices

0
10
16
18
16
16-18
Meets Expectations
11-15
Partially Meets Expectations
0-10
Does Not Meet Expectations

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## Gateway 3:

### Usability

0
22
31
38
33
31-38
Meets Expectations
23-30
Partially Meets Expectations
0-22
Does Not Meet Expectations

## The Report

- Collapsed Version + Full Length Version

## Focus & Coherence

#### Meets Expectations

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Gateway One Details

The instructional materials for Eureka Grade 5 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.

### Criterion 1a

Materials do not assess topics before the grade level in which the topic should be introduced.
2/2
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Criterion Rating Details

The instructional materials for Eureka Grade 5 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

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.
2/2
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Indicator Rating Details

The instructional materials reviewed for Eureka Grade 5 meet expectations that they assess grade-level content. Each Eureka Module includes one or more assessments that hold students accountable for Grade 5 content. These assessments are the Mid-Module and End-of-Module assessments. Examples of the assessments include:

• In Module 2, Mid Module Assessment Task: Students practice addition, subtraction, multiplication and division of decimals to the hundredths place (5.NBT.7). Question 5 states, “For a field trip, the school bought 47 sandwiches for $4.60 each and 39 bags of chips for$1.25 each. How much did the school spend in all?”
• In Module 3, Mid-Module Assessment Task: Students add and subtract fractions with unlike denominators by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators (5.NF.1) and solve word problems involving addition and subtraction of fractions referring to the same whole (5.NF.2). Question 1a states, “Lila collected the honey from 3 of the beehives. From the first hive she collected 2/3 gallon of honey. The last two hives yielded 1/4 gallon each. How many gallons of honey did Lila collect in all? Draw a diagram to support your answer.”
• In Module 5, End-of-Module Assessment Task: Students practice finding the area of a rectangle with fractional side lengths (5.NF.4b). Question 2a states, “Heather has a rectangular yard. She measures it and finds out it is 24 1/2 feet long by 12 4/5 feet wide. She wants to know how many square feet of sod she will need to completely cover the yard. Draw the yard, and label the measurements.”
• In Module 6, End-of-Module Assessment Task: Students use the coordinate plane to solve real-world problems (5.G.2). Question 4b states, “An airplane is descending into an airport. When its altitude is 5 miles, it is 275 miles from the airport. When its altitude is 4 miles, it is 200 miles from the airport. At 3 miles, it is 125 miles from the airport. For the plane to land at the airport, the altitude will need to be 0, and the distance from the airport will need to be 0. Should the pilot continue this pattern? Why or why not?”

The instructional materials for Grade 5 have two questions that assess future grade-level standards. In Module 1, End-of-Module Assessment Task, Questions 4b and 4c: Students solve a word problem to the thousandths place. 5.NBT.7 indicates performing operations with decimals to the hundredths place. The problem reads: “Dr. Mann mixed 10.357 g of chemical A, 12.062 g of chemical B, and 7.506 g of chemical C to make 5 doses of medicine. 4b. Find the actual amount of medicine mixed by Dr. Mann. What is the difference between your estimate and the actual amount? 4c. How many grams are in one dose of medicine? Explain your strategy for solving this problem.” The off-grade level items could be removed without affecting the sequence of learning for the students or the mathematical integrity of the materials.

### Criterion 1b

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.
4/4
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Criterion Rating Details

The instructional materials for Eureka Grade 5 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

Instructional material spends the majority of class time on the major cluster of each grade.
4/4
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Indicator Rating Details

The instructional materials reviewed for Eureka Grade 5 meet expectations for spending a majority of instructional time on major work of the grade. This includes all clusters within the domains 5.NBT and 5.NF as well as cluster C in 5.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 140 lesson days, approximately 110 days (79 percent) are spent on major clusters of the grade.
• Of six modules, Modules 1, 2, 3, 4 and 5 focus on major work with only a few lessons devoted to additional and supporting work.
• Module 6 consists of additional and supporting work with a few major work lessons included.
• Of the 31 assessment days, 22 are devoted to major work.

### Criterion 1c - 1f

Coherence: Each grade's instructional materials are coherent and consistent with the Standards.
8/8
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Criterion Rating Details

The instructional materials for Eureka Grade 5 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

Supporting content enhances focus and coherence simultaneously by engaging students in the major work of the grade.
2/2
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Indicator Rating Details

The instructional materials reviewed for Eureka Grade 5 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 1, Lesson 4: 5.MD.1 supports the major work standard 5.NBT.2. Students convert a unit of measurement and write an equation with an exponent. Problem Set Question 1 states, “Convert and write an equation with an exponent. Use your meter strip when it helps you. b. 105 centimeters to meters.”
• In Module 2, Lesson 3: 5.OA.2 supports the major work standard 5.NBT.5. Students write simple expressions to multiply multi-digit whole numbers. Problem Set Question 6a states, “A box contains 24 oranges. Mr. Lee ordered 8 boxes for his store and 12 boxes for his restaurant. Write an expression to show how to find the total number of oranges ordered.”
• In Module 2, Lesson 14: 5.MD.1 supports the major work standard 5.NBT.7. Students solve conversion problems with decimals. Problem Set Question 2f states, “An alligator is 2.3 yards long. What is the length of the alligator in inches?”
• In Module 4, Lesson 1: 5.MD.B supports the major work cluster 5.NF.A. Students create line plots using measurements to the nearest ½, ¼, and ⅛ of an inch. Students answer questions based off of the created line plots. Problem Set Question 5 states, “Use all three of your line plots to complete the following. b. What is the difference between the measurements of the longest and the shortest pencils on each of the three line plots?”

### Indicator 1d

The amount of content designated for one grade level is viable for one school year in order to foster coherence between grades.
2/2
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Indicator Rating Details

Instructional materials for Eureka Grade 5 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: 20 days
• Module 2: 35 days
• Module 3: 22 days
• Module 4: 38 days
• Module 5: 45 days
• Module 6: 25 days

All lessons are paced to be 60 minutes in length. Lessons generally 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. Module 6 includes 14 days for Multi-Step Word Problems and The Year in Review that include culminating activities and preparation for summer practice.

### Indicator 1e

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.
2/2
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Indicator Rating Details

The instructional materials for Eureka Grade 5 meet expectations for the materials being consistent with the progressions in the standards. The instructional materials give all students extensive work with grade-level problems and identify as well as explicitly connect grade-level work to prior or future grades.

Each module starts with a summary of what concepts will be taught within that module. This summary explains how the lessons support the progression of Grade 5 standards by explicitly stating connections to prior or future grades. For example:

• Module 3, Addition and Subtraction of Fractions: “In Module 3, students’ understanding of addition and subtraction of fractions extends from earlier work with fraction equivalence and decimals. This module marks a significant shift away from the elementary grades’ centrality of base ten units to the study and use of the full set of fractional units from Grade 5 forward, especially as applied to algebra. In Topic A, students revisit the foundational Grade 4 standards addressing equivalence. When equivalent, fractions represent the same amount of area of a rectangle and the same point on the number line. These equivalencies can also be represented symbolically.”

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 5 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 3 or 4 as well as from previous Grade 5 work are included for each module. An example from Module 5 is:

• Apply and extend previous understandings of multiplication and division to multiply and divide fractions. 5.NF.4 | 5.NF.4.a
• Draw and identify lines and angles, and classify shapes by properties of their lines and angles. 4.G.1 | 4.G.2
• Geometric measurement: understand concepts of angle and measure angles. 4.MD.5 | 4.MD.5.a | 4.MD.5.b | 4.MD.6 | 4.MD.7
• Geometric measurement: understand concepts of area and relate area to multiplication and to addition. 3.MD.5.b | 3.MD.5.a | 3.MD.5
• Geometry 3.G.1 | 4.G.1 | 4.G.2
• Measurement and Data 4.MD.3 | 4.MD.5 | 4.MD.5.a | 4.MD.5.b | 4.MD.6 | 4.MD.7
• Number and Operations – Fractions 5.NF.4 | 5.NF.4.a
• Reason with shapes and their attributes 3.G.1
• Solve problems involving measurement and conversion of measurements 4.MD.3

The instructional materials attend to the full intent of the grade-level standards by giving all students extensive work with grade-level problems. Lessons begin with a fluency practice that is also labeled with a grade-level standard. For example:

• In Module 1, Lesson 12, the Fluency Practice focuses on standard 5.NBT.7. Adding Decimals and Finding the Product is the focus of the 12-minute fluency practice.
• In Module 2, Lesson 7, the Fluency Practice focuses on standards 5.NBT.2 and 5.NBT.6. Multiply by Multiples of 10 and 100 and Multiply Using the Area Model is the focus of the 12-minute fluency practice.

Most lessons contain a “Problem Set” which are questions and word problems that focus on the standards of the lesson. In Module 3, Lesson 6, Problem Set Problem 2 states, “Jean-Luc jogged around the lake in 1 ¼ hour. William jogged the same distance in ⅚ hour. How much longer did Jean-Luc take than William in hours?” Students solve word problems involving fractions with unlike denominators (5.NF.2).

Most lessons contain an “Exit Ticket” with grade-level problems that focus on the standards taught in the lesson. In Module 5, Lesson 5, the Exit Ticket states, “Find the volume of the prism.” Students use the volume formula to find the volume of a right rectangular prism (5.MD.5b).

### Indicator 1f

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.
2/2
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Indicator Rating Details

The instructional materials for Eureka Grade 5 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 2, Topic C: “Decimal Multi-Digit Multiplication” is visibly shaped by 5.NBT.B, “Perform operations with multi-digit whole numbers and with decimals to hundredths.”
• In Module 3, Lesson 3: "Add fractions with unlike units using the strategy of creating equivalent fractions," is visibly shaped by 5.NF.A, "Use equivalent fractions as a strategy to add and subtract fractions."
• In Module 4, Lesson 14: “Multiply unit fractions by non-unit fractions” is visibly shaped by 5.NF.B, "Apply and extend previous understandings of multiplication and division to multiply and divide fractions."
• In Module 5, Topic A: “Concepts of Volume” is visibly shaped by 5.MD.C, “Geometric measurement: understand concepts of volume and relate volume to multiplication and to addition.”

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 15: 5.NBT.B connects to 5.MD.A when students solve a multi-step problem by multiplying multi-digit whole numbers and converting a unit of measurement. Problem Set Question 3 states, “Each costume needs 46 centimeters of red ribbon and 3 times as much yellow ribbon. What is the total length of ribbon needed for 64 costumes? Express your answer in meters.”
• In Module 4, Lesson 10: 5.OA.A connects to 5.NF.B when students write and solve an expression involving fractions. Exit Ticket Question 2 states, “Write an expression, and then solve. Three less than one-fourth of the product of eight thirds and nine.”
• In Module 5, Lesson 6: 5.NBT.B connects to 5.MD.C when students use multiplication of multi-digit whole numbers to find the volume of 3-D figures made up of non-overlapping right rectangular prisms. Problem Set Question 2 states, “A sculpture (pictured below) is made of two sizes of rectangular prisms. One size measures 13 in by 8 in by 2 in. The other size measures 9 in by 8 in by 18 in. What is the total volume of the sculpture?”

## Rigor & Mathematical Practices

#### Meets Expectations

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Gateway Two Details

The instructional materials for Eureka Grade 5 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.

### Criterion 2a - 2d

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.
8/8
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Criterion Rating Details

The instructional materials for Eureka Grade 5 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

Attention to conceptual understanding: Materials develop conceptual understanding of key mathematical concepts, especially where called for in specific content standards or cluster headings.
2/2
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Indicator Rating Details

The instructional materials for Eureka Grade 5 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 7, students develop conceptual understanding of rounding a decimal number to a place value. A vertical number line is used to model rounding to a place value. Problem Set Question 1 states, “Fill in the table, and then round to the given place. Label the number lines to show your work. Circle the rounded number.” (5.NBT.4)
• In Module 2, Lesson 6, students develop conceptual understanding of the distributive property using area models to understand the distributive property of multiplication and the connection to partial products. Problem Set Question 1 states, “Draw an area model. Then, solve using the standard algorithm. Use arrows to match the partial products from your area model to the partial products in the algorithm.” (5.NBT.7)

The materials provide opportunities for students to demonstrate conceptual understanding independentlythroughout the grade level. For example:

• In Module 4, Lesson 7, students independently demonstrate conceptual understanding of multiplication of fractions. Tape diagrams are used to represent multiplication involving fractions. Problem Set Question 2 states, “Solve using tape diagrams. 2a. There are 48 students going on a field trip. One-fourth are girls. How many boys are going on the trip?” (5.NF.4)
• In Module 5, Lesson 4, students independently demonstrate conceptual understanding of division of fractions. Tape diagrams are used to represent division involving fractions. Problem Set Question 1 states, “Draw a tape diagram to solve. Express your answer as a fraction. Show the multiplication sentence to check your answer.” (5.NF.7)
• In Module 6, Lesson 5, students independently demonstrate conceptual understanding of a coordinate plane. Students demonstrate understanding by using words and pictures to justify their solution. Problem Set Question 7 states, “Adam and Janice are playing Battleship. Presented in the table is a record of Adam’s guesses so far. He has hit Janice’s battleship using these coordinate pairs. What should he guess next? How do you know? Explain using words and pictures.” (5.G.2)

### Indicator 2b

Attention to Procedural Skill and Fluency: Materials give attention throughout the year to individual standards that set an expectation of procedural skill and fluency.
2/2
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Indicator Rating Details

The instructional materials for Eureka Grade 5 meet expectations that they attend to those standards that set an expectation of procedural skill and fluency.

In A Story of Units Curriculum Overview, 5.NBT.5 is identified as the fluency standard for Grade 5. The standard 5.NBT.5, fluently multiply multi-digit whole numbers using the standard algorithm, is addressed explicitly in Module 2.

The instructional materials develop procedural skill and fluency throughout the grade level. For example:

• In Module 2, Lesson 8, students develop procedural skill and fluency of multiplying multi-digit whole numbers by using the standard algorithm. Students use the standard algorithm to solve problems like “314 × 236.”
• In Module 4, Lesson 25, Problem 3, students develop procedural skill and fluency of dividing a whole number by a unit fraction. The teacher guides students through solving: “Tien wants to cut 1/4 foot lengths from a board that is 5 feet long. How many boards can he cut?”

The instructional materials provide opportunities to demonstrate procedural skill and fluency independently throughout the grade level. For example:

• In Module 1, Lesson 4, students independently demonstrate procedural skill and fluency of converting units and writing equations with exponents. Problem Set Question 1b states, “Convert and write an equation with an exponent. 105 centimeters to meters, 105 cm = ____ m.”
• In Module 2, Lesson 1, students independently demonstrate procedural skill and fluency of multiplying multi-digit whole numbers using the standard algorithm. Problem Set Question 1b states, “Fill in the blanks using your knowledge of place-value units and basic facts. 230 x 20, Think: 23 tens x 2 tens = ____, 230 x 20 = ____.”
• In Module 5, Lesson 9, students independently demonstrate procedural skill and fluency of multiplying multi-digit numbers when using a visual model to calculate the volume of a figure consisting of two non-overlapping rectangular prisms. The Exit Ticket states, “A student designed this sculpture. Using the dimensions on the sculpture, find the dimensions of each rectangular prism. Then, calculate the volume of each prism.”

### Indicator 2c

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
2/2
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Indicator Rating Details

The instructional materials for Eureka Grade 5 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 2, Lesson 7, students engage in grade-level mathematics when applying knowledge of multiplication of decimals. The Application Problem states, “The length of a school bus is 12.6 meters. If 9 school buses park end-to-end with 2 meters between each one, what’s the total length from the front of the first bus to the end of the last bus?” (5.NBT.7)
• In Module 4, Lesson 23, students engage in grade-level mathematics when applying knowledge of conversion of measurement units and division to solve word problems. The Application Problem states, “Jasmine took 2/3 as much time to take a math test as Paula. If Paula took 2 hours to take the test, how long did it take Jasmine to take the test? Express your answer in minutes.” (5.NF.7)
• In Module 5, Lesson 11, students engage in grade-level mathematics when applying knowledge of area and multiplication of decimals to solve real-world problems. The Application Problem states, “Mrs. Golden wants to cover her 6.5 foot by 4 foot bulletin board with silver paper that comes in 1 foot squares. How many squares does Mrs. Golden need to cover her bulletin board? Will there be any fractional pieces of silver paper left over? Explain why or why not. Draw a sketch to show your thinking.” (5.NBT.7)

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

• In Module 1, Lesson 16, students independently demonstrate the use of mathematics by applying knowledge of decimal operations to solve word problems. Problem Set Question 3 states, “Mr. Hower can buy a computer with a down payment of $510 and 8 monthly payments of$35.75. If he pays cash for the computer, the cost is \$699.99. How much money will he save if he pays cash for the computer instead of paying for it in monthly payments?” (5.NBT.7)
• In Module 4, Lesson 11, students independently demonstrate the use of mathematics by applying understanding of multiplication of fractions to solve word problems. Problem Set Question 5 states, “Create a story problem about a fish tank for the tape diagram below. Your story must include a fraction.” (5.NF.6)
• In Module 4, Lesson 24, students independently demonstrate the use of mathematics by applying understanding of multiplication of fractions and mixed numbers to solve various word problems. Problem Set Question 3 states, “Andres completed a 5-km race in 13.5 minutes. His sister’s time was 1 1/2 times longer than his time. How long, in minutes, did it take his sister to run the race?” (5.NF.6)
• In Module 5, Lesson 15, students independently demonstrate the use of mathematics by applying knowledge of area and fractions to solve word problems. Problem Set Question 3 states, “Janet bought 5 yards of fabric 2 1/4 feet wide to make curtains. She used 1/3 of the fabric to make a long set of curtains and the rest to make 4 short sets. Find the area of the fabric she used for the long set of curtains. Find the area of the fabric she used for each of the short sets.” (5.NF.6)

### Indicator 2d

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.
2/2
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Indicator Rating Details

The instructional materials for Eureka Grade 5 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 serves as an anticipatory set for the concept or standard that is the focus of the lesson. This Application Problem 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 7, students engage in the application of mathematics when finding the volume of a rectangular prism. Problem Set Question 1 states, “Geoffrey builds rectangular planters. Geoffrey’s first planter is 8 feet long and 2 feet wide. The container is filled with soil to a height of 3 feet in the planter. What is the volume of soil in the planter? Explain your work using a diagram.”
• In Module 6, Lesson 14, student practice fluency of multiplying multi-digit whole numbers using the standard algorithm. The Fluency Practice - Multiply Multi-Digit Whole Numbers states, “This drill reviews year-long fluency standards. T: Solve 45 × 25 using the standard algorithm. S: (Solve 45 × 25 = 1,125 using the standard algorithm.) Continue the process for 345 × 25, 59 × 23, 149 × 23 and 756 × 43.”
• In Module 3, Lesson 3, students develop conceptual understanding of adding fractions with unlike denominators by drawing models of equivalent fractions. Problem Set Question 1a states, “Draw a rectangular fraction model to find the sum. Simplify your answer, if possible. 1/2 + 1/3 = ___”

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 4, Lesson 9, students develop conceptual understanding of multiplication of fractions by using tape diagrams to solve real-life problems. Problem Set Question 4 states, “A jewelry maker purchased 20 inches of gold chain. She used 3/8 of the chain for a bracelet. How many inches of gold chain did she have left?”
• In Module 2, Lesson 8, students practice fluency of multi-digit multiplication of whole numbers to solve measurement of real-world measurement problems. Problem Set Question 2 states, “Each container holds 1 L 275 mL of water. How much water is in 609 identical containers? Find the difference between your estimated product and precise product.”
• In Module 3, Lesson 4, students develop conceptual understanding of adding fractions with sums between 1 and 2 and practice fluency of adding fractions with unlike denominators. Problem Set Question 1b states, “For the following problems, draw a picture using the rectangular fraction model and write the answer. When possible, write your answer as a mixed number. 3/4 + 2/3 = ___”

### Criterion 2e - 2g.iii

Practice-Content Connections: Materials meaningfully connect the Standards for Mathematical Content and the Standards for Mathematical Practice
8/10
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Criterion Rating Details

The instructional materials for Eureka Grade 5 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

The Standards for Mathematical Practice are identified and used to enrich mathematics content within and throughout each applicable grade.
1/2
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Indicator Rating Details

The instructional materials reviewed for Eureka Grade 5 partially 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 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 5, the explanation for MP 2 states, “Reason abstractly and quantitatively. Students make sense of quantities and their relationships when they analyze a geometric shape or real-life scenario and identify, represent, and manipulate the relevant measurements. Students decontextualize when they represent geometric figures symbolically and apply formulas.”

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

Materials carefully attend to the full meaning of each practice standard
1/2
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Indicator Rating Details

The instructional materials reviewed for Eureka Grade 5 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 2, Lesson 5, MP 7 is identified in the teacher edition and attends to the full meaning of the practice where students look for and make use of structure when comparing the area model for multiplication with the standard algorithm. Students discuss and explain the connections between the area model and the standard algorithm. “Take a look at the area model and the standard algorithm. Compare them. What do you notice? S: We added 1 unit of 23 to 30 units of 23. In the area model we added two parts just like in the algorithm. First, we wrote the value of 1 twenty-three. Then, we wrote the value of 30 twenty-threes. T: Explain the connections between (30 × 23) + (1 × 23), the area model, and the algorithm. S: (Explain the connections.)”
• In Module 4, Lesson 14, MP 2 is identified in the teacher edition and attends to the full meaning of the practice where students reason abstractly about fraction multiplication. “T: Does our rectangular fraction model support our thinking from before?”
• In Module 5, Lesson 3, MP 4 is identified in the teacher edition and attends to the full meaning of the practice where students practice finding the volume of a rectangular prism by using cubes to model the problem while writing equations.

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

• In Module 4, Lesson 1, MP 5 is identified in the teacher edition where students measure the lengths of pencils and create a line plot. “T: Are all of the pencils used for these measurements exactly the same length? (Point to the X’s above the most frequent data point: 4 1/2 inches on the exemplar line plot.) Are they exactly 4 1/2 inches long? S: No. These measurements are to the nearest half inch. The pencils are different sizes. We had to round the measurement of some of them. My partner and I had pencils that were different lengths, but they were close to the same mark. We had to put our marks on the same place on the sheet even though they weren’t really the same length. T: Now, let’s measure our strips to the nearest quarter inch. How is measuring to the quarter inch different from measuring to the half inch? Turn and talk. S: The whole is divided into 4 equal parts instead of just 2 equal parts. Quarter inches are smaller than half inches. Measuring to the nearest quarter inch gives us more choices about where to put our X’s on the ruler.” This is an example of not attending to the full practice as students are told what tool and strategy to use rather than selecting a tool and/or strategy to create the line plot using their measurements.
• In Module 6 Lesson 33, MP 1 is identified in the teacher edition where students measure materials and decide how to store them. “T: Use a ruler to measure your summer practice materials and decide how you will store them. Will they be rolled, folded, or flat? Then, decide on the reasonable whole number dimensions for Box 2. T: In order to make the lid fit snugly, you will need to make it only slightly larger than Box 1. Record the dimensions of each box and the lid on your Problem Set along with your reasoning about why those dimensions make sense. Work with a partner if you choose.” This is an example of not attending to the full practice as students do not persevere in calculating numbers as they are limited to reasoning about why the dimensions make sense.

### Indicator 2g

Emphasis on Mathematical Reasoning: Materials support the Standards' emphasis on mathematical reasoning by:
0/0

### Indicator 2g.i

Materials prompt students to construct viable arguments and analyze the arguments of others concerning key grade-level mathematics detailed in the content standards.
2/2
+
-
Indicator Rating Details

The instructional materials reviewed for Eureka Grade 5 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 1, Lesson 2, the materials prompt students to analyze a statement involving place-value equivalence and explain the error that was made. Problem Set Question 4 states, “Janice thinks that 20 hundredths is equivalent to 2 thousandths because 20 hundreds is equal to 2 thousands. Use words and a place-value chart to correct Janice’s error.”
• In Module 3, Lesson 10, the materials prompt students to analyze an addition word problem involving mixed numbers with a given solution and prove whether they agree or disagree with the given solution. Problem Set Question 4 states, “Clayton says that 2 1/2 + 3 3/5 will be more than 5 but less than 6 since 2 + 3 is 5. Is Clayton’s reasoning correct? Prove him right or wrong.”
• In Module 4, Lesson 21, the materials prompt students to construct an argument and critique the reasoning of others when multiplying fractions. Problem Set Question 3 states, “Jack said that if you take a number and multiply it by a fraction, the product will always be smaller than what you started with. Is he correct? Why or why not? Explain your answer, and give at least two examples to support your thinking.”
• In Module 5, Lesson 21, the materials prompt students to construct an argument and critique the reasoning of others when working with attributes of two-dimensional figures. Problem Set Question 2 states, “John says that because rhombuses do not have perpendicular sides, they cannot be rectangles. Explain his error in thinking.”

### Indicator 2g.ii

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.
2/2
+
-
Indicator Rating Details

The instructional materials reviewed for Eureka Grade 5 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.

• In Module 1, Lesson 2, teachers are prompted to engage students in constructing an argument by asking students to explain what patterns they noticed when working with place value. “Work with your partner to solve these problems. Write two complete number sentences on your board. Explain how you got your answers. What are the similarities and differences between the two answers?”
• In Module 3, Lesson 7, teachers are prompted to engage students in constructing an argument and analyze the arguments of others by having students discuss with a partner what is different and the same about each strategy used to solve a problem. “T: Turn and share with your partner, and follow each solution strategy step by step. Share what is the same and different about them. S: (Share.) T: If you have to solve a similar problem again, what kind of drawing and solution strategy would you use? Turn and share. S: (Share.)”
• In Module 3, Lesson 13, teachers are prompted to engage students in analyze an expression involving fractions and explain their thoughts to a partner. “Think about this expression without solving it using paper and pencil. Share your analysis with a partner. What do you know about the total value of this expression without solving?”

### Indicator 2g.iii

Materials explicitly attend to the specialized language of mathematics.
2/2
+
-
Indicator Rating Details

The instructional materials reviewed for Eureka Grade 5 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. For example:

• In Module 1, Lesson 1, the Note on Multiple Means of Action and Expression states, “Throughout A Story of Units, place-value language is key. In earlier grades, teachers use units to refer to a number such as 245, as two hundred forty-five. Likewise, in Grades 4 and 5, decimals should be read emphasizing their unit form. For example, 0.2 would be read 2 tenths rather than zero point two. This emphasis on unit language not only strengthens student place value understanding, but it also builds important parallels between whole number and decimal fraction understanding.”
• In Module 2, Lesson 3, the Notes on Multiple Means of Engagement states, “A review of relevant vocabulary may be in order for some students. Words such as sum, product, difference and quotient might be reviewed, or a scaffold such as a word wall in the classroom might be appropriate.”
• In Module 5, Lesson 4, the Notes on Vocabulary states, “While it is true that any face of a rectangular prism may serve as the base, it is not true for other prisms or cylinders. For example, a right triangular prism has two triangular bases, but the remaining rectangular faces are not bases.”

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

• In Module 1, Lesson 3, the materials use precise terminology when teaching about exponents. The Concept Development Problem 1 states, “T: (Write the term exponent on the board.) We can use an exponent to represent how many times we use 10 as a factor. We can write 10 × 10 as $$10^2$$. (Add to the chart.) We say, “Ten to the second power.” The 2 (point to exponent) is the exponent, and it tells us how many times to use 10 as a factor. T: How do you express 1,000 using exponents? Turn and share with your partner.”
• In Module 5, Lesson 1, the materials use precise terminology of volume and support students in using the term when calculating the volume of several figures. Problem Set Question 1 states, “Use your centimeter cubes to build the figures pictured below on centimeter grid paper. Find the total volume of each figure you built, and explain how you counted the cubic units. Be sure to include units.”
• In Module 5, Lesson 17, the materials use precise terminology of symmetrical and support students in using the term. Exit Ticket Problem 2 states, “Use your set square and ruler to draw symmetrical points about your line that correspond to T and U, and label them V and W.”

## Usability

### Criterion 3a - 3e

Use and design facilitate student learning: Materials are well designed and take into account effective lesson structure and pacing.
8/8
+
-
Criterion Rating Details

The instructional materials for Eureka Grade 5 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

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.
2/2
+
-
Indicator Rating Details

The instructional materials reviewed for Eureka Grade 5 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

Design of assignments is not haphazard: exercises are given in intentional sequences.
2/2
+
-
Indicator Rating Details

The instructional materials reviewed for Eureka Grade 5 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

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.
2/2
+
-
Indicator Rating Details

The instructional materials reviewed for Eureka Grade 5 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, tape diagrams, graphs and place-value charts. For example, in Module 1, Lesson 7, students round a given decimal to a given place using vertical number line. Problem Set Question 1 states, “Fill in the table, and then round to the given place. Label the number lines to show your work. Circle the rounded number. 3.1”

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

Manipulatives are faithful representations of the mathematical objects they represent and when appropriate are connected to written methods.
2/2
+
-
Indicator Rating Details

The instructional materials reviewed for Eureka Grade 5 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 place-value tools. In Module 5 Lesson 2, students use centimeter cubes when finding the volume of a rectangular prism.

Examples of manipulatives for Grade 5 include:

• Two-Color Counters
• Rulers
• Decimal Place Value Disks
• Whole Number Place-Value Disks
• Number Lines
• Tape Diagrams
• Place-Value Charts

### Indicator 3e

The visual design (whether in print or online) is not distracting or chaotic, but supports students in engaging thoughtfully with the subject.
0/0
+
-
Indicator Rating Details

The visual design in Eureka Grade 5 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 3f - 3l

Teacher Planning and Learning for Success with CCSS: Materials support teacher learning and understanding of the Standards.
7/8
+
-
Criterion Rating Details

The instructional materials for Eureka Grade 5 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

Materials support teachers in planning and providing effective learning experiences by providing quality questions to help guide students' mathematical development.
2/2
+
-
Indicator Rating Details

The instructional materials reviewed for Eureka Grade 5 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 6, Lesson 2, a Student Debrief question states, “Why would it be important for us to all follow the same order when we write down the x- and y- coordinates? Talk to your partner.”

### Indicator 3g

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.
2/2
+
-
Indicator Rating Details

The instructional materials reviewed for Eureka Grade 5 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.

### Indicator 3h

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.
2/2
+
-
Indicator Rating Details

The instructional materials reviewed for Eureka Grade 5 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

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.
1/2
+
-
Indicator Rating Details

The instructional materials reviewed for Eureka Grade 5 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

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).
0/0
+
-
Indicator Rating Details

The instructional materials reviewed for Eureka Grade 5 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

Materials contain strategies for informing parents or caregivers about the mathematics program and suggestions for how they can help support student progress and achievement.
0/0
+
-
Indicator Rating Details

The instructional materials reviewed for Eureka Grade 5 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

Materials contain explanations of the instructional approaches of the program and identification of the research-based strategies.
0/0
+
-
Indicator Rating Details

The instructional materials reviewed for Eureka Grade 5 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 3m - 3q

Assessment: Materials offer teachers resources and tools to collect ongoing data about student progress on the Standards.
6/10
+
-
Criterion Rating Details

The instructional materials for Eureka Grade 5 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

Materials provide strategies for gathering information about students' prior knowledge within and across grade levels.
0/2
+
-
Indicator Rating Details

The instructional materials reviewed for Eureka Grade 5 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

Materials provide strategies for teachers to identify and address common student errors and misconceptions.
2/2
+
-
Indicator Rating Details

The instructional materials reviewed for Eureka Grade 5 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

Materials provide opportunities for ongoing review and practice, with feedback, for students in learning both concepts and skills.
2/2
+
-
Indicator Rating Details

The instructional materials reviewed for Eureka Grade 5 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

Materials offer ongoing formative and summative assessments:
0/0

### Indicator 3p.i

Assessments clearly denote which standards are being emphasized.
1/2
+
-
Indicator Rating Details

The instructional materials reviewed for Eureka Grade 5 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

Assessments include aligned rubrics and scoring guidelines that provide sufficient guidance to teachers for interpreting student performance and suggestions for follow-up.
1/2
+
-
Indicator Rating Details

The materials reviewed for Grade 5 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

Materials encourage students to monitor their own progress.
0/0
+
-
Indicator Rating Details

The instructional materials for Eureka Grade 5 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 3r - 3y

Differentiated instruction: Materials support teachers in differentiating instruction for diverse learners within and across grades.
12/12
+
-
Criterion Rating Details

The instructional materials for Eureka Grade 5 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

Materials provide strategies to help teachers sequence or scaffold lessons so that the content is accessible to all learners.
2/2
+
-
Indicator Rating Details

The instructional materials reviewed for Eureka Grade 5 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

Materials provide teachers with strategies for meeting the needs of a range of learners.
2/2
+
-
Indicator Rating Details

The instructional materials reviewed for Eureka Grade 5 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

Materials embed tasks with multiple entry-points that can be solved using a variety of solution strategies or representations.
2/2
+
-
Indicator Rating Details

The instructional materials reviewed for Eureka Grade 5 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

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).
2/2
+
-
Indicator Rating Details

The instructional materials reviewed for Eureka Grade 5 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 in the teacher edition that provide strategies for English Language Learners and other special populations. 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

Materials provide opportunities for advanced students to investigate mathematics content at greater depth.
2/2
+
-
Indicator Rating Details

The instructional materials reviewed for Eureka Grade 5 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

Materials provide a balanced portrayal of various demographic and personal characteristics.
2/2
+
-
Indicator Rating Details

The instructional materials reviewed for Eureka Grade 5 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

Materials provide opportunities for teachers to use a variety of grouping strategies.
0/0
+
-
Indicator Rating Details

The instructional materials reviewed for Eureka Grade 5 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

Materials encourage teachers to draw upon home language and culture to facilitate learning.
0/0
+
-
Indicator Rating Details

The instructional materials reviewed for Eureka Grade 5 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.

Effective technology use: Materials support effective use of technology to enhance student learning. Digital materials are accessible and available in multiple platforms.
0/0
+
-
Criterion Rating Details

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 3z

Materials integrate technology such as interactive tools, virtual manipulatives/objects, and/or dynamic mathematics software in ways that engage students in the Mathematical Practices.
0/0
+
-
Indicator Rating Details

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 3aa

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.
0/0
+
-
Indicator Rating Details

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

Materials include opportunities to assess student mathematical understandings and knowledge of procedural skills using technology.
0/0
+
-
Indicator Rating Details

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

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.
0/0
+
-
Indicator Rating Details

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.).
0/0
+
-
Indicator Rating Details

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 Published Date: 08/27/2018

Report Edition: 2015

All publishers are invited to provide an orientation to the educator-led team that will be reviewing their materials. The review teams also can ask publishers clarifying questions about their programs throughout the review process.

Once a review is complete, publishers have the opportunity to post a 1,500-word response to the educator report and a 1,500-word document that includes any background information or research on the instructional materials.

## Educator-Led Review Teams

Each report found on EdReports.org represents hundreds of hours of work by educator reviewers. Working in teams of 4-5, reviewers use educator-developed review tools, evidence guides, and key documents to thoroughly examine their sets of materials.

After receiving over 25 hours of training on the EdReports.org review tool and process, teams meet weekly over the course of several months to share evidence, come to consensus on scoring, and write the evidence that ultimately is shared on the website.

All team members look at every grade and indicator, ensuring that the entire team considers the program in full. The team lead and calibrator also meet in cross-team PLCs to ensure that the tool is being applied consistently among review teams. Final reports are the result of multiple educators analyzing every page, calibrating all findings, and reaching a unified conclusion.

## Rubric Design

The EdReports.org’s rubric supports a sequential review process through three gateways. These gateways reflect the importance of standards alignment to the fundamental design elements of the materials and considers other attributes of high-quality curriculum as recommended by educators.

• Materials must meet or partially meet expectations for the first set of indicators to move along the process. Gateways 1 and 2 focus on questions of alignment. Are the instructional materials aligned to the standards? Are all standards present and treated with appropriate depth and quality required to support student learning?
• Gateway 3 focuses on the question of usability. Are the instructional materials user-friendly for students and educators? Materials must be well designed to facilitate student learning and enhance a teacher’s ability to differentiate and build knowledge within the classroom. In order to be reviewed and attain a rating for usability (Gateway 3), the instructional materials must first meet expectations for alignment (Gateways 1 and 2).

## Key Terms Used throughout Review Rubric and Reports

• Indicator Specific item that reviewers look for in materials.
• Criterion Combination of all of the individual indicators for a single focus area.
• Gateway Organizing feature of the evaluation rubric that combines criteria and prioritizes order for sequential review.
• Alignment Rating Degree to which materials meet expectations for alignment, including that all standards are present and treated with the appropriate depth to support students in learning the skills and knowledge that they need to be ready for college and career.
• Usability Degree to which materials are consistent with effective practices for use and design, teacher planning and learning, assessment, and differentiated instruction.

## Math K-8 Rubric and Evidence Guides

The K-8 review rubric identifies the criteria and indicators for high quality instructional materials. The rubric supports a sequential review process that reflect the importance of alignment to the standards then consider other high-quality attributes of curriculum as recommended by educators.

For math, our rubrics evaluate materials based on:

• Focus and Coherence

• Rigor and Mathematical Practices

• Instructional Supports and Usability

The K-8 Evidence Guides complement the rubric by elaborating details for each indicator including the purpose of the indicator, information on how to collect evidence, guiding questions and discussion prompts, and scoring criteria.

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